Manual JKSimMet V5.1

steady state mineral

processing simulator

Ve

rsion 5.1 November 2001

Revised February 2003

Isles Road Indooroopilly Qld

AUSTRALIA 4068 Telephone 07 3365 5842

Email [email protected] www.jktech.com.au

Facsimile 07 3365 5900

JKSimMet is a powerful tool for analysis and simulation of mineral processing plant data. As the program developers do not control data collection, analysis or interpretation, it is the sole responsibility of the JKSimMet user to verify that input data are accurate, and that both process unit operation conditions and stream outputs are reasonable. In no event will JKTech Pty Ltd be liable for direct, indirect, special, incidental or consequential damages arising out of the use or inability to use the software or documentation.

Note: The detailed descriptions of the mathematical models in this manual are provided for the information of the software licensees. These models are not public domain and they may not be used in other software without written permission from or a licensing agreement with JKTech Pty Ltd.

Copyright © 1987 - 2003 JKTech Pty Ltd All rights reserved. Both the software and documentation of JKSimMet are copyright.

JKTech Pty Ltd Isles Road Indooroopilly Queensland Australia 4068

Telephone - (07) 3365 5842 International: +61 7 365 5842 Fax - (07) 3365 5900 International: +61 7 365 5900 Email - [email protected] JKSimMet Internet URL- www.jksimmet.com JKTech Internet URL - www.jktech.com.au

Preface Contents

Version 5.1 February 2003 Contents Page i

CONTENTS Page No

ACKNOWLEDGMENTS iv

ABOUT THIS MANUAL vi

1. OVERVIEW

1.1 About JKSimMet 1-2 1.2 Equipment Requirements 1-4 1.3 Cautionary Tales 1-5 1.4 Program Structure 1-6 1.5 JKSimMet Support 1-7

2. INSTALLING JKSimMet

2.1 Contents of the Package 2-2 2.2 Computer Hardware/Software 2-3 2.3 JKSimMet V5 Installation 2-4 2.4 Compatability Between V4 and V5 2-5 2.5 What Is New in Version 5.0 2-6 2.6 What Is New in Version 5.1 2-8

3. LEARNING JKSimMet

3.1 How JKSimMet Works 3-2 3.2 The Mouse 3-6 3.3 The JKSimMet Display 3-7 3.4 JKSimMet Startup 3-8 3.5 Working with an Existing Project 3-9 3.5.1 Selection of a Flowsheet 3-10 3.5.2 Simulation 3-11 3.5.3 Displaying the Simulation Results 3-16 3.5.4 Printing the Simulation Results 3-20 3.5.5 Summarising the Results - Overview 3-22 3.5.6 Summarising the Results - Report 3-23 3.5.7 Exporting Data from JKSimMet 3-25 3.58 Finishing a JKSimMet Session 3.25 3.6 Making Changes to an Existing Flowsheet 3-27 3.6.1 Selecting the Flowsheet to Use 3-27 3.6.2 Altering Operating Conditions 3-29 3.6.3 Saving the Session 3-33 3.6.4 Graphing Your Results 3-35 3.7 Creating a New Project 3-38 3.7.1 Starting a New Project 3-38 3.7.2 Define Flowsheet Name 3-40 3.7.3 Drawing a New Flowsheet 3-41 3.7.4 Create Connecting Streams 3-44 3.7.5 Adding a Circuit Feed Stream 3-47

Contents Preface

Page ii Contents Version 5.1 February 2003

3.7.6 Adding Water to the Circuit 3-47 3.7.7 Adding Information Blocks and Labels to the Flowsheet 3-50

3.7.8 Entering Data 3-54 3.7.9 Define Data for Rod Mill 3-55 3.7.10 Examining Data 3-57 3.7.11 Rod Mill Circuit Exercises 3-58 3.8 Learning Simulation 3-60 3.9 Learning Graphing 3-63 3.9.1 Drawing a Graph 3-65 3.9.2 Defining the Graph Format 3-65 3.9.3 Definition of the Data to be Graphed 3-67 3.9.4 Easy Manipulation of the Graphing Features 3-70 3.9.5 Saving the Session 3-71 3.9.6 Graphing Limitations 3-72 3.9.7 Graphing Related Problems 3-72 3.10 Learning Overview 3-73 3.11 Learning to use Report 3-78 3.12 Summary 3-84

4 USING JKSimMet

4.1 JKSimMet Description 4-2 4.1.1 JKSimMet Simulation Technique 4-3 4.1.2 JKSimMet Capabilities 4-3 4.1.3 JKSimMet Constraints 4-4

4.1.4 JKSimMet Expandability 4-5 4.2 Definition of Terms used in JKSimMet 4-6 4.3 The JKSimMet Cursor 4-7 4.4 The JKSimMet Menus and Toolbars 4-8 4.4.1 The Main JKSimMet Menu 4-9 4.4.2 The Functions Toolbar 4-9 4.4.3 The JKSimMet Tools Toolbar 4-11 4.5 JKSimMet Windows 4-12 4.5.1 The Session Window 4-12 4.5.2 The Project View Window 4-14 4.5.3 Equipment Data Windows 4-15

4.5.4 Port Data Windows 4-16 4.6 Building and Manipulating a Flowsheet 4-17 4.6.1 Loading a Project 4-17 4.6.2 Defining the Project Name 4-18 4.6.3 Defining the Flowsheet Name 4-19

4.6.4 Building the Flowsheet–Equipment Units 4-20 4.6.5 Building the Flowsheet–Connecting Ports 4-23

4.6.6 Flowsheet Related Problems 4-25 4.7 Editing the Flowsheet Data 4-26 4.7.1 The Equipment Data Window 4-26 4.7.2 Editing the Equipment Data 4-29 4.7.3 The Port Data Window 4-32

Preface Contents

Version 5.1 February 2003 Contents Page iii

4.7.4 Editing the Port Data 4-34 4.7.5 The Feed Data Window 4-40 4.7.6 Editing the Feeder Data 4-41 4.7.7 The Water Feeder Data Window 4-41 4.7.8 Editing the Water Feeder Data 4-43 4.8 Annotating the Flowsheet 4-46 4.8.1 Adding Port Information Blocks 4-47 4.8.2 Adding Equipment Information Blocks 4-51 4.8.3 Adding Labels to the Flowsheet 4-53 4.9 User-Configured Graphing – The Graph Definition

Window 4-55 4.9.1 Define the Graph Format 4-55 4.9.2 Defining Data for Graphing 4-57 4.9.3 Viewing the Graph 4-62 4.10 Using Quick Graph 4-63 4.10.1 Opening the Quick Graph Window 4-63 4.10.2 The Quick Graph Toolbar 4-64 4.10.3 Features of Quick Graph 4-65 4.11 Using Overview 4-66 4.11.1 The Overview Window 4-66 4.11.2 Configuring an Overview Table 4-67 4.11.3 Recovery Mode 4-70 4.12 Printing in JKSimMet 4-72 4.13 Using Report 4-75 5 MODEL FITTING

5.1 Introduction to Model Fitting 5-2 5.2 Data Collection 5-3 5.3 Background 5-7 5.4 How the Model Fitting Program Works 5-8 5.5 A Simple Example 5-10 5.6 Learning Fitting 5-13 5.6.1 Preparation for Model Fitting 5-13 5.6.2 Start Model Fitting 5-14 5.6.3 Selecting Data 5-15

5.6.4 Setting up the Parameters 5-19 5.6.5 Master/Slave Fitting 5-21

5.6.6 Fit the Model Parameters 5-22 5.7 Checking the Fit 5-24 5.8 Presentation of Model Fitting Results 5-25 5.9 Problems Related to Model Fitting and Possible Solutions 5-27 5.10 References 5-30 6 MASS BALANCING

6.1 Introduction to Mass Balancing 6-2 6.2 Data Collection 6-3 6.3 Background 6-4 6.4 How the Mass Balancing Program Works 6-7 6.5 A Simple Example 6-9

Contents Preface

Page iv Contents Version 5.1 February 2003

6.6 Learning Mass Balancing 6-14 6.6.1 Preparation for Mass Balancing 6-14 6.6.2 Model Types for Mass Balancing 6-15 6.6.3 Selecting Data 6-15 6.6.4 Component 6-17 6.6.5 Water 6-20 6.6.6 Solution Controls 6-21 6.6.7 Carrying out the Mass Balance 6-22 6.7 Checking the Balance 6-24 6.8 Presentation of Mass Balancing Results 6-26 6.8.1 Overview 6-26 6.8.2 Printing the Mass Balance Results 6-28 6.8.3 Plotting Graphs 6-29 6.9 Problems Related to Mass Balancing and Possible Solutions 6-32 6.9.1 The Middlings Problem 6-33 6.9.2 The Infinite Division Problem 6-34 6.10 Metallurgical Accounting 6-35 6.11 References 6-36

APPENDICES

A1 Introduction A-2 A2 Hydrocyclone (Model 200, 201) A-7 A3 Single Deck Screen (Model 230) A-21 A4 Efficiency Curve Models (210, 610, 211, 611, 203) (General Classifier Models) A-31 A5 Efficiency Curve Variable d50c (Model 251) A-37 A6 Crusher (Model 400) A-41 A7 Rod Mill (Model 410) A-59 A8 Perfect Mixing Ball Mill (Model 420) A-69 A9 Autogenous Mill Model (Model 430) and Semi –Autogenous Mill Model (Model 431) A-81 A10 Size Converter Model (Model 490) A-101 A11 Variable Rates SAG Model (Model 435) A-103 A12 High Pressure Grinding Rolls (Model 402) A-123 A13 Simple Degradation (Model 480) A-141 A14 Splitters (Models 810, 811, 812, 870) A-145 B ERROR MESSAGES C JK BREAKAGE TESTING All Trade Marks acknowledged

Preface Acknowledgements

Version 5.1 November 2001 Acknowledgements Page v

ACKNOWLEDGEMENTSMore than twenty-five years of development has gone into thesimulation models used in JKSimMet. This represents a hugecontribution by the students and staff of the Julius KruttschnittMineral Research Centre (JKMRC). There is not sufficient spaceavailable to acknowledge all the contributors separately, and only afew outstanding contributions are mentioned.

The founding Director of the JKMRC, Professor Alban Lynch, andhis co-worker, Dr T C Rao, developed the first practical models ofgrinding and classification, and successfully applied them at MountIsa Mines. Professor Lynch and his successors Dr Don McKee andDr Tim Napier-Munn have presided over subsequentdevelopments.

Dr Bill Whiten is responsible for the generalized model structure,many of the models, and the general purpose data-fitting routines.

The simulator structure has gone through several softwaregenerations and hardware implementations. The original enginewas programmed by Dr Alex Kavetsky, who has also contributed agreat number of the models. The major contributors to the DOSsimulator are principally Mr David Wiseman, and also Dr FredHess and Dr Thomas Kleine.

The original documentation was developed by the Centre forInformation Technology Research at the University of Queensland.

The testing and debugging of JKSimMet has mostly been done byJKTech, headed by Dr Rob Morrison and assisted by Mr ChrisBailey, Mr Dennis Noreen and Mr Philip Baguley.

Major thanks are due to the many sponsors who have contributed tothe AMIRA projects which have resulted in the development ofJKSimMet.

Special thanks are also due to the organizations listed below whichpurchased pre-release copies and have helped by testing thesoftware in an industrial environment:

• ZC Mines Limited • Renison Limited• Bougainville Copper Limited • Billiton Research B.V.• Western Australian School of Mines (Kalgoorlie)

Version 4

Six years of JKSimMet marketing have lead to the licensing of morethan 150 sites world wide. Meanwhile, application and modeldevelopment continue at the JKMRC. The development ofVersion 4 and revision of the manual has been the result ofcontributions from the all the JKTech team, in particular MichalAndrusiewicz and Phil Baguley.

Acknowledgements Preface

Page vi Acknowledgements Version 5.1 November 2001

Version 5.0

Version 5 is a complete rebuilding “from the ground up” of theJKSimMet interface to bring it into Windows 95/98.

The major conceptual changes to the interface are due to StephenTreloar-Bradford. Detailed implementation has been by PhillipBaguley and Phil Beak. The DLL engines were programmed byPhillip Baguley and Michal Andrusiewicz.

The Help files were developed by Andrew Schroder.

Cathy Evans has developed the V5 documentation.

Ricardo Pascual developed the V4 to V5 conversion program.

Rob Morrison provided overall project leadership.

Version 5 provides a platform for future mineral process modellingat the JKMRC.

Overall, the development of JKSimMet V5 represents a majorachievement for the development team and a major investment inthe future for JKTech

Special thanks are also due to the V5 beta testers in industry.

Version 5.1

Version 5.1 is an upgrade of Version 5.0 which operates in theWindows 2000 environment.

Several extra models have been added to the extensive model libraryand many operability improvements have been made. A series ofbug fixes is also included.

The evolution of V5.1 has been accomplished as a joint projectbetween the JKTech software group and the JKTech consultinggroup.

Most of the changes have come from suggestions by many of thecurrent users, assembled and tested by the JKTech consultants andcoded by the JKTech software group.

Preface About this Manual

Version 5.0 December 1999 About this Manual Page vii

ABOUT THIS MANUALThis manual is intended for users at all levels of experience with thesystem. It has been designed for novice users at both computing andthe use of mineral processing plant simulation. It provides areference section for more experienced users, and it offers advancedinformation for those users who wish to fine tune their simulationsin order to maximize the benefit of their tests.

Depending on your experience you will wish to refer to differentsections of the manual.

If you have just bought the package and it is not yet installed onyour system:

• read Chapter 2 first, and then install JKSimMet on yourcomputer.

If you are new to computing or JKSimMet:

• work through the tutorial section in Chapter 3.

If you are familiar with JKSimMet simulation techniques:

• read Chapters 4, 5 and 6.

If you wish to fine tune JKSimMet to your own requirements:

• read Chapter 5.

About this Manual Preface

Page viii Version 5.0 December 1999

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Overview Overview

Version 5.1 November 2001 Chapter 1 Page 1-1

CHAPTER 1

OVERVIEW

About JKSimMet Overview

Page 1-2 Section 1.1 Version 5. 1 November 2001

1. OVERVIEW

1.1 About JKSimMet

JKSimMet is a mineral processing plant simulator which runs onthe Intel Pentium family of computers under Windows 95, 98, ME,NT4 or 2000. It gives engineers the ability to design and optimizeany crushing or grinding circuit including stages of classification.It allows engineers to:

• design a circuit on the graphics monitor• enter model and plant data• simulate the circuit• graph and print the results.

JKSimMet performs steady state simulation of a range ofcomminution and classification operations. Process models of thefollowing units are available:

• secondary and tertiary cone crushers• jaw crushers• gyratory crushers• rolls crushers• autogenous and semi-autogenous mills• rod mill, ball mill• HPGR crusher• simple degradation• vibrating screen• DSM screen• hydrocyclone classifier• several general classifier efficiency curves• several splitters.

New process models can readily be incorporated into JKSimMet byJKTech. This is done by defining their characteristics assteady-state models and creating an icon for each to represent themon the screen.

JKSimMet is intended for use by plant engineers not necessarilyskilled in either modelling or computing. For that reason, it hasbeen written to operate in a user-friendly manner. Users selectoptions from menus or lists and build flowsheets on the screen.This removes the need for specialized computer skills whilemaintaining flexibility.

Overview About JKSimMet

Version 5. 1 November 2001 Section 1.1 Page 1-3

The main features of JKSimMet are:

• graphical user interface• flowsheet specified interactively on the graphics screen• models selected from a built-in library• model parameters specified by the user• range of data output displays and printed reports• simple data transfer.

JKSimMet has been designed primarily as a powerful aid to anengineer. The principal application of JKSimMet for many userswill be to carry out process analysis and optimisation of existingcircuits.

JKSimMet is also extremely useful for conducting conceptualdesign studies, where the purpose is to assess the suitability ofdifferent flowsheets to achieve a desired performance objective.

Limitations Provided that the data used in the process models are relevant tothe ore being studied, JKSimMet can be used to generate detaileddesign information. Until experience is gained in detailed designstudies using JKSimMet, it is recommended that design tasks becarried out in consultation with JKTech.

It is important at the outset to understand what JKSimMet will andwill not do. JKSimMet will predict the performance of a circuitwithin the limitations of the data and the models selected.JKSimMet will not determine of its own accord the best circuit, thebest operating conditions or the changes that are required to ensurethat a circuit operates efficiently. JKSimMet does not allowprocess constraints to be specified.

Constraints The operator has an essential role in deciding the conditions to besimulated and in critically assessing the simulation predictions.This is a deliberate result of the design philosophy of JKSimMet,which places considerable emphasis on the process experience andknowledge of the operator.

This point is amplified at the beginning of Chapter 4, and thereader is strongly advised to keep these points in mind when usingthe system for simulation analysis.

Equipment Requirements Overview


1.2 Equipment Requirements

For successful operation of JKSimMet you must have:

ComputerSystem

Intel Pentium PC (or other fully compatible computer) with all ofthe following:

• Processor speed 400MHz minimum• 128Mb memory minimum – 256Mb recommended• CD-ROM Drive• 1.4 Mbyte (3.5 inch) diskette drive• 2 Gbyte or larger fixed disk drive (with 100Mbytes free space)• A SVGA or fully compatible equivalent graphics controller

(minimum) – Recommended an XGA graphics controllerr• a suitable monitor – 15 inch minimum

17 inch recommended.

Printer An MS Windows 95,98, ME, NT or 2000 compatible printer:

OperatingSystem

MS Windows 95,98, ME, NT(4 sp5 or later) or 2000

Pointing Device Microsoft Mouse or functional equivalent.

EquipmentTested

A wide range of equipment combinations has been successfullytested but if you are in doubt JKTech will be pleased to commenton a particular combination.

Overview Cautionary Tales


1.3 Cautionary Tales

BackupJKSimMetDiskette

JKSimMet V5 is supplied on CD-ROM with an additionalinstallation program on a 3.5 floppy disk.

A hardware key (Hard Lock) is required for operation.

It is recommended that you make a backup copy of the files on theDiskette. If you do damage your one and only copy of a JKSimMetdiskette, you can acquire a new diskette from JKTech by notifyingthem and quoting the version number of your copy of JKSimMet.

Read.MePrint.Me

Any modifications to procedures since the production of thismanual are in a file called READ.ME. Print this file and read itbefore going further.

Learn byExample

JKSimMet is a program which is rich in capabilities and easy tooperate. The simplest way to become familiar with the techniquesof using JKSimMet and the capabilities it has to offer, is to followthrough a structured example. Such an example is provided withthe package. This example assumes no experience with JKSimMetand leads you through a session exploring the use of the variousmodelling and simulation features of the program. We recommendthat you spend some time working through the example inChapter 3 until you are confident that you can apply JKSimMet toyour own problems. The data analysis capabilities of JKSimMetare supported by examples in Chapters 5 and 6.

Backup Work As you input each section of data (say a flowsheet or a data set) youshould save your work to the hard disk. Usually you will want tooverwrite your earlier version. If you do this regularly, then when,not if, there is a power failure or other mishap, your work up to thelast save will be waiting for you on the hard disk; it will not havebeen lost forever.

Once you are a proficient user of JKSimMet, you will be creatingand using mathematical models of your plant. These models arestored on your fixed disk between sessions. It is possible, usuallythrough carelessness but occasionally through computermalfunction, to lose information from the fixed disk. Therefore,we recommend that you make a backup copy of the informationstored on your fixed disk frequently.

Backup WorkFiles

You should use the backup facilities within JKSimMet to backupsimulator work sessions to a server or other archival storage suchas a Zip Disk.

Windows Backup Alternatively, Project Data Files(*.JKSM5) only need be backedup.

Program Structure Overview


1.4 Program Structure

ProgramStructure

JKSimMet consists of the following software modules:

• Main Program

• Supporting DLL’s

• Program Database

• Project Databases

ProcessModels

Models of the following units are supplied:

• rod mill• ball mill• autogenous mill• semi-autogenous mill• cone crusher• HPGR crusher• two rolls crusher• jaw crusher• single deck screen• DSM screen• hydrocyclone• rake classifier• spiral classifier• splitter• combiner (sump, stockpile, bin)• size converter• degradation model

CustomModels

Contact JKTech if you are interested in adding other models tothose listed above.A developer’s kit is also available for model development.

Overview JKSimMet Support


1.5 JKSimMet Support

Documentation Three levels of documentation are supplied:

• user manual• model documentation• context sensitive Help files.

Installation andTraining

JKTech can provide assistance to install the system and can alsoprovide on-site training to match particular user needs.

Courses JKTech offers regular courses in simulation technology at variouslocations around the world and on-line.

ExtendedBackup

Continuing backup support is provided by JKTech either through aMaintenance Agreement, telephone or facsimile contact, or throughvisits by JKTech to site.

Email Help JKSimMet project files can be sent electronically to JKTech via theInternet for assistance. Send files to [email protected]

Updates Updates and bug fixes will be supplied for one year from date ofinstallation/supply and are available under a maintenance contractthereafter.

Restrictions A standard licence for the use of JKSimMet permits operation ofthe software on a single workstation only. Extension of the licencefor additional workstations at a single site is available for a smallfee.

Distribution of copies of JKSimMet to other company sites is notpermitted. Additional copies for other sites are available at reducedcost.

Hardware Key JKSimMet will not operate without a hardware key. The standardkey is suitable for a parallel port. Keys are also available to suitPCMCIA or USB ports.

JKSimMet Support Overview


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Installing JKSimMet Installing JKSimMet


CHAPTER 2

INSTALLING JKSimMet

Contents of the Package Installing JKSimMet

Page 2-2 Section 2.1 Version 5.1 November 2001

2. INSTALLING JKSimMet

2.1 Contents of the Package

PackageContents

The JKSimMet system comes as a package containing this manual,a CD, a floppy disk and two “Hardlock” keys

The manual contains information on the installation andmaintenance of the JKSimMet software, a tutorial guide for first-time users and a comprehensive reference chapter.

Installing JKSimMet Computer Hardware/Software

Version 5.1 November 2001 Section 2.4 Page 2-3

2.2 Computer Hardware/Software

For successful operation of JKSimMet you must have:

ComputerSystem

Intel Pentium PC or other fully compatible computer with all of thefollowing:

• Processor speed 400MHz minimum• 128Mb memory minimum (256Mb recommended)• CD-ROM Drive• 1.4 Mbyte (3.5 inch) diskette drive• 2 Gbyte or larger fixed disk drive (with 100 Mbytes free space)• A SVGA or fully compatible equivalent graphics controller

(minimum) – Recommended XGA• a suitable monitor – 15 inch minimum

17 inch recommended.

Printer Any MS Windows 95, 98, ME, NT or 2000 compatible printer.

OperatingSystem

MS Windows 95, 98, ME, NT(V4 sp5 or later) or 2000

Pointing Device Microsoft Mouse or functional equivalent.

EquipmentTested

A wide range of equipment combinations has been successfullytested but if you are in doubt JKTech will be pleased to commenton a particular combination.

JKSimMet V5 Installation Installing JKSimMet


2.3 JKSimMet V5 Installation

JKSimMet V5Installation

JKSimMet V5 is a standard Windows Program.

Step 1 Make a backup copy of any existing projects

Step 2 If you have JKSimMet V5 installed already on yourcomputer, go to:

Control PanelSelect Add/Remove, andSelect JKSimMet V5Uninstall

Step 3 Insert CD-ROM in drive

Step 4 From the Windows Start Menu, select RUN and then Browse to find Setup.exe on your CD Drive

Eg. D:\Setup.exe

Step 5 Press OK and follow the instructions on screen

Step 6 The installation procedure will prompt you for thesupplied floppy diskette and will copy your companyspecific copy of JKSimMet to enable the software.

If you do not have an A: drive floppy disk, you can double click onthe self exploding zip file to install JKSimMet.exe in yourJKSimMet V5.1 directory.

If an update is provided by email, you can copy it to a floppy diskor unzip as in the previous paragraph

Note: The install program will also ask to update your HTML helpfile viewer. This will allow full use of JKSimMet V5 help.

Notes forWindows NT or2000 installation

Note 1: Your computer must be using NT4 with service pack 5 orlater or 2000.Note 2: As JKSimMet V5 requires several device drivers, you musthave full administrator privileges to install or uninstall JKSimMet.

Installing JKSimMet Making a Backup Copy


If you choose notto use the defaultpath forinstallation

If you choose not to use the default path (/Program Files/JKSimMetV5.1) for installation, you will need to modify the UnZip path forthe JKSimMet V5.1.exe file.

Modify this line to your install path

Non-Englishversions ofWindows

If you are installing in a non-English version of windows, thespelling of the install path may be different. If this is the case youmust modify the UnZip path to the correct spelling as discussedabove.

2.4 Compatibility and Conversion BetweenV4 and V5

A conversion utility is included to transfer User directories fromVersion 4 into a series of flowsheets within one or more projects asspecified by the user.

These projects are then accessible to Version 5.

Note that Versions 2 to 4 used Ryan McFarland (IBM) ProFortwhich is a 16-bit FORTRAN compiler.

Version 5 uses MS Power Station FORTRAN which is a 32-bitcompiler. (Now supported by COMPAQ/DEC).

There may be minor differences in calculated parameters as a resultof this change.

The converted project will also be slightly ambiguous regardingdata type in some cases because V2 to V4 used calculated data tostore the results of simulation, mass balancing or model fitting.

Version 5 has sufficient space to store several data types. Hence, itwould be prudent to re-run a simulation, balance or fit to guaranteethe integrity of the calculated data.

What Is New in Version 5 Installing JKSimMet


2.5 What Is New in Version 5.0

The short answer is just about everything.

The interface has been redesigned to take advantage of the featuresof MS Windows 95.

Interaction within each of the modules (i.e. simulation, fit andbalance) has been standardised and has access to all of the datapresentation and transfer tools.

• Flowsheets now provide for automatic drawing of equipmentconnections.

• Flowsheets are expandable to 4 “pages”

• Many flowsheets are accessible within a project

• A generalised Select function is provided to allow sub-sections of any flow sheets to be simulated, fitted orbalanced. This supersedes the multi-circuit feature of V4.

• Data and flowsheets from other projects may be copied intothe current project

• Use of the Windows 95 operating system and a FORTRAN90 compiler potentially removes the V4 limits on numbers ofmodels etc.

• The flowsheet can be annotated with Data Information blockswhich provide stream information as well as access toequipment data. The previous annotation capability has beenreplaced by labels.

• Project and flowsheet notes may be included as properties.

• A Quick Graph Facility is now available for each piece ofprocess equipment

• The Overview Tool has been generalised to present manykinds of data

• A configurable Report tool allows a selection of data to beprinted, copied to clipboard and to a range of file types.

• Comprehensive copy and paste capabilities are provided toassist transfer of data and results to other Windowsapplications.

• Program configuration has been completely implementedwithin a relational database.

• This will allow other JKSim** simulators to be incorporatedas JKSimMet modules.

Installing JKSimMet What Is New in Version 5


• There is also scope to include a series of “supplementary”examples within the defined model types. However, caveatsabout inappropriate use are still applicable.

• The database structure and DLL engines will allow forseamless integration of models developed by others via adevelopers kit and a compatible compiler.

• A number of Version 5 objects are also designed to be sharedwith new JKTech products such as JKMetAccount and theMLA Data Presentation program

• Last and by no means least, the V5 structure provides foreventual expansion to a fully integrated dynamic simulator, atsome time in the future.

What Is New in Version 5 Installing JKSimMet


2.6 What Is New in Version 5.1

The major change in V5.1 is compatibility with Windows 2000.

Several new models including the HPGR, simple degradation andan improved range of splitters have been added and several moreclassifier icons included.

In addition, the file structure has changed so that .JKSM5 files areconsiderably smaller and no longer grow with use. Compaction isno longer required. This change in file structure has resulted inmuch faster loading and saving.

Many of the user settings which were “forgotten” on file save andload are now “remembered”. For example, the graph colours, thelock status and % passing size are now stored with the file, as arethe default settings for data and error displays in port windows.

Almost all of the reported bugs have been fixed and as many aspossible of the feature improvements requested by users have beenimplemented.

Learning JKSimMet Learning JKSimMet


CHAPTER 3

LEARNING JKSimMet

How JKSimMet Works Learning JKSimMet


3. LEARNING JKSimMetLearningJKSimMet

Learning JKSimMet is designed primarily as a tutorial exercise. Itis anticipated that the first time user of JKSimMet might spend twoto three hours working through this chapter step by step. In thisway the user will gain sufficient confidence and knowledge tobegin using the system in earnest.

Given the nature and design of JKSimMet, the user will veryquickly be able to learn the basic operating techniques. It isassumed that the user already understands the techniques of mineralprocessing simulation and also has some appreciation of thestandard features of the MS Windows 95/98/ME/NT/2000interface.

3.1 How JKSimMet Works

AboutJKSimMet

JKSimMet is a general-purpose computer software package for theanalysis and simulation of mineral processing operations. Thepackage is designed to service the diverse needs of plant anddevelopment metallurgists, who need to apply modern processanalysis techniques to characterise plant behaviour and designengineers, who require accurate process simulation models tofacilitate the evaluation of various plant designs.

JKSimMet integrates all tasks associated with optimisation, designand simulation, including the storage and manipulation of models,data and results, within one package. It is fully interactive andoperates with high-resolution colour graphics capabilities. Thesegraphics facilitate the display of detailed plant flowsheets andaccompanying information.

The engineer using JKSimMet proceeds through a series of tasks:

• building a flowsheet diagram of the processing plant on thecomputer screen

• assigning characteristics to the various process units andmaterial flows of the simulation model

• simulating the flow of materials through the simulated plant( Or a subsection of the plant).• reviewing and presenting the results.

Once a model has been built the engineer can alter the design andchange the parameters as he sees fit until he arrives at a satisfactorydesign or an optimum operating condition for an existing plant.

Learning JKSimMet How JKSimMet Works


The results may be graphed, printed in summary form and stored onhard disk or archived to diskette. The results can also betransferred to other suitable programs via the clipboard.

Building aSimulationModel

Simulation is based on the ability to build a model that isrepresentative of a real system. The behaviour or characteristics ofthe model must be similar to the characteristics of the real system.In order to build the model the engineer must analyse the overallplant and break it down into a number of sections (circuits), in sucha way that the circuits are easily understandable and identifiable.The circuits are interconnected to form the total system.

The data structure within JKSimMet V5 consists of the following:

Project A project is the container in which the userstores all of the data related to a particularbody of work. The project contains one ormore flowsheets and the associated equipmentunit and stream data.

Flowsheet A flowsheet is a graphical representation of acomplete processing plant or a componentsection of that plant. The flowsheet can haveinternal recirculating streams.A flowsheet may be increased in size torepresent a large, complex circuit. Either thecomplete flowsheet or selected sections of itmay be simulated, mass balanced or modelfitted.Note that this capability to select items forinclusion in simulation, modelling or mass-balancing replaces the circuit-orientedflowsheets required by the DOS versions ofJKSimMet.

Equipmentand Ports

Version 5 introduces a new concept. Eachflowsheet item is now a piece of equipmentwhich can have any number of ports. Theseports represent the connections to each pieceof equipment. The reason for this change is toallow for future development of a dynamicsimulator. This approach also will allow forpipes and conveyors to be modelled as piecesof equipment.Units and Streams still provide a convenientway of thinking about flowsheets and forpractical purposes, the terms equipment andports mean the same things as units andstreams.

How JKSimMet Works Learning JKSimMet


Units A unit is any type of unit process such as a ballmill or a hydrocyclone classifier. JKSimMetallows you to select the appropriate unit froman exhaustive list of processing unit types andto display their pictorial representations(icons) on the screen. These units areidentified within the system by a name whichthe user specifies. You can specify theorientation of the units (direction of flowthrough the unit left to right or vice-versa) andalso the position of units on the flowsheetdiagram.

Streams A stream is a description of any flow ofmaterial. The description is usually in termsof solids flowrate, water flowrate and particlesize distributions (plus assays for massbalancing if required). The stream connectionsbetween units are made by drawing linesconnecting the appropriate feed and productports on the units. JKSimMet automaticallychecks to ensure that the stream connectionsare valid. Each stream or port is named byJKSimMet as a combination of its equipmentname and port name. The user can edit theequipment names as required but the portnames for each piece of equipment are fixed.

The unit models currently available for simulation include:

• Feeder • Autogenous mill• Stockpile • Semi-autogenous mill• Bin • Rod mill• Pump sump • Ball mill• Sump • Single deck screen• Splitter • DSM Screen• Gyratory crusher • Hydrocyclone• Two rolls crusher • Spiral classifier• Jaw crusher • Rake classifier• HPGR crusher • Degradation model

Learning JKSimMet How JKSimMet Works


SpecifyingFlowsheet Data

Once the flowsheet has been drawn the engineer must provide datafor each process unit and also provide raw data in the form of flowsand size distributions for the streams in the circuit. This is done bystepping through the process units and the streams one-by-one,adding circuit data and building up an annotated description of themodelled processing circuit on the screen. The unit data for theprocess equipment may come from previous experience, from adesign database or they may be derived from plant data. Thestream data can be entered in one of three size distribution formats,depending on the preferences of the user. The engineer can reviewor correct the data at any time after entering the data.

FlowsheetSimulation

Once the flowsheet has been specified and the required unit andstream data have been entered, the simulation can be run. Theresults of the simulation are stored and can be displayed on thescreen or printed as required. The following options are availablefor examining the results:

• view the detailed data in the equipment and port datawindows,

• view summary data for equipment and ports via datainformation blocks,

• view summary data in overview tables,• view the size distribution data plotted as graphs on the

screen or in printed form,• generate configurable reports at summary or detailed level,• copy-and-paste the data into other programs (eg.

MS Excel) via the clipboard• print the results to a Windows compatible printer or to a

file.

Recorded data include:

• flowrates of solids and water• percentage solids• pulp densities• full particle size distributions.

After analysis of the results, you can alter the flowsheet, adjust theequipment parameters or port data and repeat the simulationprocess until you obtain a satisfactory result.

FlowsheetSelection

A new capability in V5 is that a subset of the flowsheet may beselected for simulation, mass balancing or model fitting.

The Mouse Learning JKSimMet


3.2 The Mouse

The Mouse The standard two-button mouse is used as the pointing device inJKSimMet. In this manual we refer to "left-click" and "right-click"which simply means to press the left- or right-hand button on themouse.The manual assumes that you are familiar with common mousetechniques such as double-clicking and click-and-drag.

The Cursor In JKSimMet V5 the cursor (your position on the screen) isindicated by an arrowhead. When the cursor is over an equipmentunit in the flowsheet window the cursor will change to indicate thatthe drop-down menu can be accessed by right-clicking on this zone.

In data windows, the position of the active data cell (i.e. the cellwhere anything that you type will appear) is indicated by a thickgrey border

CursorMovement

The mouse can be used to move the cursor when working withJKSimMet. In the equipment and stream data windows the cursorcontrol keys (also known as the arrow keys) may also be used tomove the cursor from one data cell to the next.

Appearance As with all MS Windows programs, the preferences which the usersets for the Windows desktop will provide colours and fonts formany of the tools and menus within JKSimMet.

Keyboard Access Most of the functionality of JKSimMet can also be accessed fromthe keyboard using standard MS Windows conventions.

Learning JKSimMet The JKSimMet Display


3.3 The JKSimMet Display

The JKSimMet V5 display uses windows to present the varioustypes of data on the JKSimMet desktop. These windows includethe following:

• flowsheet window,• equipment and port data windows• graph windows• data overview window.• the report window

Users may have as many windows open on the screen as they wishat any one time. An XGA video card and a large monitor arerecommended for this strategy.

Many of the windows are divided into several distinct areas whichare accessed by selectable tabs. Each area is used to conveyspecific types of information.

Note that most windows may be minimised for convenience.However, some non-critical changes (eg. an equipment namechange) may require that a window be closed before other windowsare updated.

JKSimMet Startup Learning JKSimMet


3.4 JKSimMet Startup

JKSimMetStartup

The instructions for starting JKSimMet V5 are as follows:

Step 1 Right-click on the Windows Start button at the bottomleft-hand corner of the screen to bring up the Start menu.

Step 2 Move the cursor to select the Programs sub-menu.

Step 3 Move the cursor to highlight the JKSimMet V5.1 programfrom the list displayed in this sub-menu and left-click tolaunch the program. The JKSimMet logo is displayedwhile the program is launching.

Having successfully launched the program you enter JKSimMet atthe main JKSimMet desktop window as shown below. From here,the next step is typically to open a previously saved data set (notethat each data set is known as a project in V5) or to enter the datafor a new project. Section 3.5 describes the steps involved inworking with an existing project.

Alternatively, JKSimMet can be launched by selecting an existingproject file (extension .JKSM5) and double clicking it. Thislaunches JKSimMet with the chosen file as the active project.

The JKSimMet desktop window

Learning JKSimMet Working with an Existing Project�


3.5 Working with an Existing Project

About thisExercise

As a first exercise in the use of JKSimMet follow the instructionsin this section. They will show you how to:

• Load an existing demonstration project for a simple ball milland hydrocyclone circuit. This project was created by JKTechand was installed with JKSimMet.

• Use the simulation tools in JKSimMet to simulate the action ofthe circuit under predefined feed conditions.

• View the results of the simulation on the computer screen andprint selected results on the printer.

The files which define the flowsheet, process units and streams thatmake up the demonstration circuit are already on your computer.They were installed onto the hard drive during the JKSimMetinstallation procedures. They can be recalled by following a fewsimple steps outlined below.

Loading anexisting project

Step 1 Left-click on the Open Project icon on the JKSimMettoolbar at the top left-hand corner of the JKSimMetwindow. This will open the Project View window asshown in the screen image below.

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OpenProject

Working with an Existing Project Learning JKSimMet


Step 2 Left-click on the tab marked Saved in the Project Viewwindow. This displays a list of all the existing projectfiles (along with a description of each project in theObject Description box)

Step 3 Move the cursor to the red book of the project whichyou want to load, in this case the Learner Flowsheetsproject, and left-click, hold and drag it across to theJKSimMet desktop to load the project. Note that whenyou click on a project name, its file name, completewith directory location appears in a strip at the bottomof the Project View window.

Step 4 Left-click on the main window to make it the activewindow.

3.5.1 Selection of a Flowsheet

Within each project the user can define one or more flowsheets torepresent the circuit(s) which he wants to investigate. Eachflowsheet can be expanded in size to make room for complexflowsheets. We will work with a flowsheet called Example BallMill – Cyclone simulation in the project Learner Flowsheets.Follow the steps outlined below to select this flowsheet as theactive flowsheet.

Loading anexistingFlowsheet

Step 1 Left-click on the text box at the bottom right of theJKSimMet flowsheet window to view a drop-down listof the flowsheets which have been created in theLearner project.



Step 2 Move the cursor down the list to highlight the name ofthe flowsheet which you want to use (in this caseExample Ball Mill – Cyclone simulation) and left-clickon this to bring the chosen flowsheet into view on themain screen.

Changing thesize of theflowsheetwindow

Step 3 If the flowsheet you want to work with is notcompletely visible in the window you can change theheight and width of the window by placing the cursoron the bottom, right corner of the flowsheet windowand left-clicking and dragging the window edge until itis the required size.

3.5.2 SimulationThe Example Ball Mill – Cyclone simulation flowsheet alreadycontains all the stream data and parameters required to simulate thiscircuit. We will use the JKSimMet simulation capabilities topredict the product stream size distributions and capacity of thesimulated circuit, but first we will find out how to look at theequipment unit data and port data.

Drop-down listof flowsheetsin this project



Key to theDemonstrationCircuit

The demonstration circuit consists of a ball mill and a nest of fourhydrocyclones. These equipment units are connected by streams.The streams enter and leave the equipment units through feed andproduct ports.

Note that there are also two specialised units in this circuit, thesebeing the Feed and the Water Feeder. The Feed unit allows newfeed material to be introduced to a circuit as dry solids or a slurry.The Water Feeder allows the addition of water to the circuit.

Examiningequipment andport data

The data windows for each equipment unit and its associatedstreams can be accessed by placing the cursor over the unit andright-clicking the mouse button to view the pop-up menu.

Left-clicking on the word Equipment on the pop-up menu bringsthe equipment data window into view.

Left clicking on the name of a stream port in the pop-up menu (inthe cyclone example these choices are combiner, underflow oroverflow) brings the data window of that stream port into view.

Selectable tabs Note that the port and equipment data windows use selectable tabsto provide access to the several types of data which are availablewithin each window. To view the available data left-click on eachtab in turn.

Nest of fourcyclones Water

FeederFeedunit



Arrangingwindows on thedesktop

If there are several windows open on the JKSimMet desktop theuser has several options to organise the windows to suit theirneeds.

The options available can be seen by left-clicking on the icon atthe top, left-hand corner of the window which you want to move,close etc. Clicking on this icon brings into view a drop-downmenu which allows the user to move, minimise or close the datawindow by selecting the appropriate command.

Move a window Select the word Move on the drop-down menu and then move themouse or use the keyboard arrow keys to move the window asrequired. To stop moving the window left-click with the mouse orpress the Enter key on the keyboard.

Alternatively a window can be moved by simply left-clicking anddragging on the window title bar to move the window to whereyou want it.

Minimise/Restorea window

To minimise a window select the word Minimise on the drop-down menu or left-click on the minimise button at the top, right-hand side of the title bar. This shrinks the window to a small titlebar at the bottom of the JKSimMet desktop area. To return thewindow to its previous size and position left-click on the Restorebutton at the top, right-hand side of the title bar.

Close a window Select the word Close on the drop-down menu or left-click theClose button at the top, right-hand corner of the window or holdthe Ctrl key down and press the F4 key.

Closewindowbutton

Minimise window buttonon open window.

Left-click this icon toview drop-down menuto move, minimise orclose this window.



Resize a window

(Flowsheetwindow only)

The width and height of the flowsheet window can be adjusted byselecting the word Size on the drop-down menu. The size of thewindow can then be adjusted by using the arrow keys or by left-clicking and dragging a corner of the window

Another alternative for arranging windows on the desktop is to usethe options available under the Window menu on the JKSimMetmenu bar. These options allow the user to arrange all of thewindows in one operation, the choices for arranging the openwindows being cascade, tile horizontal, tile vertical.. There is alsoan option Arrange Icons, which organises the icons of anyminimised windows into rows at the bottom of the screen.

Concept:Convergence

To simulate a closed circuit, JKSimMet uses an iterative procedure.In the first iteration, an estimate (perhaps zero) of the circulatingload is used. This allows the calculation of a better estimate of thecirculating load to be used for the second iteration and so on. Theprocedure is repeated until the difference between succeedingestimates of the circulating load are less than a specified amount(the convergence limit). The circuit is then said to haveconverged.

The convergence value is shown by JKSimMet during simulation.The tolerance limits can be changed by the user.

Closewindowbutton

Minimise window buttonon open window.

Left-click this icon toview drop-down menuto move, minimise orclose this window.

Restore window buttonon minimised window



General Approach JKSimMet V5 uses a standardised approach for all of theanalysis tools – simulation, mass balancing and modelfitting. As shown in the Simulate window example below,the tabbed window for each tool offers a Control tab todefine parameters and set the limits for the operation. Italso has a Select tab which allows the user to choose asubset of the flowsheet components for simulation orbalancing etc. Each selection list can be named and saved,allowing the user to analyse as many subsets as required.This capability was only available within the massbalancing module of earlier versions of JKSimMet. Itshould remove the need for multiple circuits in all but thelargest multi-survey data sets. Once the Select list isdefined, a simulation can be run.

Running aSimulation

Step 1 To simulate the example left-click on the Simulation icon.This brings the Simulate window into view.

Step 2 A glance at the flowsheet shows which parts of theflowsheet have been selected to be included in thissimulation as all of these items are outlined in blue on theflowsheet. In this example every item on the flowsheet isselected to be used in the simulation.

Step 3 Run the simulation by left-clicking on the Start button atthe bottom left of the Run Simulation tab area of theSimulate window.

The simulation will now run iteratively through the circuit.As each iteration in the simulation is completed the valuesin the simulation window will be updated. Once theexecution of the simulation has finished it is possible toassess the simulation results by looking at the values in thesimulation window. More detailed information can beviewed via the port and equipment unit data windows. Weshall first look at techniques for examining the data on thecomputer screen and then at printing the data.

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3.5.3 Displaying the Simulation Results

The simulation has calculated the flows of through each of thevarious equipment units of the circuit and their ports. The RunSimulation tab has a section where the results of the simulation aresummarised. The detailed data for each piece of equipment andport on the flowsheet can be examined individually by displayingthe appropriate data window on your screen, as described insection 3.5.2.

Data Display The data windows contain all of the information that JKSimMetuses to perform the simulation and also show the results of thesimulation. The port data windows list the raw and calculatedvalues for mass flows of water and solid and the size distributionvalues while the equipment data windows show the modelparameters used for simulation together with any data that resultfrom the simulation (e.g. cyclone operating pressure).

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Step 1 To examine all of the data for any equipment unit orport in the circuit, move the cursor over the unit whosedata you wish to examine. Right-click on theequipment unit to bring the pop-up menu into view (asshown below) and then move the cursor to highlight therequired information (equipment or port name) on thislist and click the left mouse button. This will bring theselected data window into view. In this example theCyclone equipment data window is shown. Note thatwhen a data window is the active window, theequipment unit to which the data relate is highlighted inred on the flowsheet.



Step 2 There are several alternative methods to look at the portdata associated with each equipment unit. One methodmentioned previously is to return to the flowsheet,right-click on the equipment icon of the unit which thestream feeds into or flows out of and then left-click onthe name of the port whose data you want to examine.

The alternative method, which is useful if theequipment data window is already open, is to left-clickon the Port Detail drop-down list at the top, centre ofthe equipment data window and then to select the nameof the port whose data you want to view. Both of theseactions bring up the port data window. The cycloneunderflow data window is shown below as an example.

Another way to access the equipment data window onlyworks if the flowsheet is “locked”. If you have finishedediting the flowsheet, you may click on the Lock theFlowsheet icon on the tool bar. The lock button willstay depressed indicating that the flowsheet icons canno longer be moved. This prevents “accidental”editing.In this locked mode a double click on an equipmenticon will open its data window immediately.

Step 3 The port data window has three areas for the user toexamine. The major part of the window is the areawhere the data are listed. Two selectable tabs allow theuser to view the mass flow data for water and solids

Data window forhydrocyclone



and their associated data and the size distribution data,simply by left-clicking on the appropriate tab. Note thata third tab is present here when component (e.g. assay)data have been included in the flowsheet data. Theother areas of this window are the drop-down menusfor Format (sizing format), Data type and Error whichallow the user to choose how the data are presented.The Set SDs button which, as its name implies, allowsthe user to set the SD values for the data, will bediscussed in a later section.

Concept:Data Formats

The JKSimMet user can view a variety of data in the stream datawindow by selecting the required format from the Format, DataType and Error drop-down sub-menus. The size distribution datacan be displayed in one of three formats - % retained at size,cumulative % retained at size or cumulative % passing size. TheData menu gives the user the option of displaying GSIM datatypes (experimental and calculated data only) or SDs data types(experimental data, calculated data, SDs and errors) or all data,which as the name implies, displays all of the data types includingbalanced and fitted data as separate columns.

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Left click on the drop-downlists to select the data formatyou wish to view.

Left click on a tab toview the associated data.



Concept:Data Types

Exp(ExperimentalStream Data)

Data which the user has entered which arethe results from sampling, sizing and assay.

Bal(Mass-balanced data)

Calculated data which are the output of themass-balancing procedure.

Fit(Model-fitted data)

Calculated data which are the output of themodel-fitting procedure.

Sim(Simulated Data)

Calculated data which are the output of asimulation model.

SD An estimate (standard deviation) of theaccuracy of an experimental measurement(see chapters 5 and 6 for details).

Errors The error is the difference between themeasured or experimental data and thecalculated data. Chapters 5 and 6 discusserrors in detail.

Changingcolumn width

The user can change the width of the columns in which the dataare presented in both the port data and equipment data windows.To change the width of a column move the cursor to the right-hand edge of the cell at the top of the column whose width youwish to change. When it is positioned over the border line, thecursor will change from the usual arrowhead to a vertical linewith arrows on each side of it; left-click and drag with this cursorto change the column width as required and release the mousebutton when the column width is to your satisfaction.



3.5.4 Printing the Simulation Results

When you are satisfied with your simulation, you can print theresults out on the printer. The printing facilities contain functionsthat:

• print the raw and calculated data for a selected port, includingSDs and errors if selected on the window display

• print all details for a selected equipment unit• print the flowsheet• print an overview table• print a graph of selected data• print a user-configured report.

The user can print quick or generic graphs, an overview table ofdata and a report once these have been created by the user. Theoverview, report and graph plotting functions are comprehensiveand they are discussed separately from printing later in the manual.The printing functions are invoked via the main JKSimMet menu atthe top of the JKSimMet desktop or from the Print button on theactive window. A Print Preview functionis available in most cases.

Reports The simulator can print reports in several formats, these are:

• equipment (a selection or individual)• ports (a selection or individual)• equipment feed streams (a selection or individual)• overviews• configured reports

Quick TextPrinting

To print the contents of a port or equipment data window simplyopen the required data window and click on the Print Preview iconon the JKSimMet toolbar. A Print Preview window will display thedata as they will be printed; clicking on the Print icon in this previewwindow prints the page(s) immediately. Alternatively, the datawindow contents can be printed immediately by clicking on the Printicon in the data window.

Flowsheet Print The current flowsheet can be printed by selecting File on theJKSimMet main menu, selecting the Print Flowsheet option and thenselecting the required option for colour or monochrome printingfrom the sub-menu. Selecting Print to Clipboard sends a copy of thescreen image to the Windows clipboard from which it can be pastedinto other suitable applications such as MS Word or MS Paint.



Graph Print Quick or generic graphs can be printed via the Print icon on theirwindow or copied to the clipboard.

�PrintingSimulation Data

Step 1 To print the simulation data, select each piece ofequipment and port in turn, open its data window andclick on the Print Preview icon. This will preview thepages to be printed. Click the Print icon on the PrintPreview window toolbar to send the pages to the defaultWindows printer. If you do not want to print a page,close the Print Preview window by clicking its closebutton.

Data TypeSelection

Step 1 Select the data to be displayed from either GSIM(grinding simulation which shows measured andcalculated data), or SDs which also displays standarddeviations and errors or All Data which shows all of theavailable data types.

You may also wish to keep a printed copy of the circuitflowsheet. It is possible to print the flowsheet window asfollows:

Print CircuitFlowsheet

Step 1 With the desired flowsheet as the active window, selectthe Print Flowsheet option on the File menu of theJKSimMet main menu. Then select the required option toprint to file or clipboard in colour or monochrome fromthe four shown on the sub-menu.

There will be a short pause while JKSimMet translatesthe screen data into a format suitable for the printer.

Report Printing Step 1 Click on the report icon on the tool bar.

Step 2 Click on the Print icon on the Report window to print thedefault report.

For details on the Report feature refer to section 3.5.6.



3.5.5 Summarising the Results - Overview

The Overview feature gives you a powerful means of summarisingyour data and checking it for adjustment problems. The overviewwindow displays a configurable list for presentation of data fromall selected streams. The overview window can display eitheractual experimental or calculated data. Alternatively the overviewwindow can show calculated recovery data in cases wherecomponent data (e.g. assays) have been entered.

Step 1 Left-click on the Overview Config icon on the mainJKSimMet toolbar to bring the overview window intoview.An overview list named Simulation results overviewhas already been prepared for this example.

Step 2 Resize the overview window by clicking and draggingthe bottom right-hand corner of the window. Thisallows you to see all of the data summarised in theoverview window. Alternatively you can use the scrollbar at the bottom of the overview window to view all ofthe data. You may also need to make the columnswider to see the data clearly.

A typical use of the overview window would be tocheck that the % solids of all the simulated streams arewithin acceptable operating range. Is this the case inour example?

Note: The % passing and passing size are set as a FlowsheetProperty. These provide a very useful summary via theoverview table.



3.5.6 Summarising the Results - Report

The Report feature gives you a powerful means of summarising andprinting both the port and equipment data. The Report windowdisplays a list of all of the equipment units and ports on the currentflowsheet and the user can select from this list the items which areto be included in the report printout. The report feature allows theuser to select experimental or calculated data with or without SDvalues and/or error values. A typical use of the report feature wouldbe to print a standard set of data for inclusion in a technicalmemorandum.

Step 1 Left-click on the Report icon on the main JKSimMettoolbar to bring the Report window into view.Ensure that the prepared example report named ReportConfig Example is selected in the Report drop-downlist.

Step 2 Click on the Print Preview icon in the Report windowto see what the selected data will be look like whenprinted. Experiment with the various options in theReport window and use the Print Preview window tosee how each option changes the printed report format.



The Report Print Preview window



3.5.7 Exporting Data from JKSimMet

While JKSimMet provides a range of options for examining yourdata, there may be occasions when it would be useful to be able touse JKSimMet data in a report or a presentation. Version 5provides a copying facility which allows the user to copy data fromthe equipment and port windows to the Clipboard. These data canthen be pasted into any clipboard compatible application such as aspreadsheet (e.g. MS Excel) or a word processor (e.g. MS Word).

Note that there are two types of Copy buttons on the equipment andport data windows. These are:

Copy Selected Cells toClipboard

Copies only the data cells which arecurrently selected to the Clipboard.

Copy Grid to Clipboard Copies all visible cells on the currenttab to the Clipboard, including rowand column labels.

Hint: If you wish to copy all of the tabs at once, use the printpreview button and then the Copy to clipboard button on the PrintPreview window.

(Also see information on exporting data via tab-delimited andcomma-delimited text files in Exporting data using Report insection 3.10)

3.5.8 Finishing a JKSimMet Session

You have completed your simulation of the ball mill and cyclonecircuit and examined and printed both the flowsheet and thesimulation data. In the next exercise we will attempt to improvethe operation of the circuit by varying the parameters of some ofthe components, and then running simulations to observe thepredicted effect.

Before doing this, end the JKSimMet session as explained below.

Note that JKSimMet will ask you if you wish to save the flowsheetover the original copy of Example Ball Mill - Cyclone on the harddrive. Normally you would save changes, but in this case wesuggest that you do not do so because it will change the nature ofthe example for the next person who uses these exercises to learnJKSimMet.



Ending theJKSimMetSession

Step 1 To quit from JKSimMet move the cursor to the Filemenu on the menu bar at the top of the screen and left-click to view the drop-down File menu.

Step 2 Move the cursor down the File menu to select Exit.

Step 3 A pop-up window will ask you whether you want toleave the session. Left-click on the Yes button.

Step 4 Another pop-up window will ask you whether you wantto save the last changes to the file. In this case left-clickon the No button so that the Learner project file on thehard drive remains unchanged for the next user.

In future if you want to save changes you have made toyour own project file before exiting from JKSimMet,left-click on the Yes button to save the file.

Save As If you do not want to overwrite the Learner project,select Save As from the File drop-down menu. ASave As window will appear as shown below. Thisallows the user to save the file under any chosen nameand in any chosen directory. The JKSimMet files areidentified by the five-letter filename extension jksm5.

Learning JKSimMet Making Changes to an Existing Flowsheet


3.6 Making Changes to an ExistingFlowsheet

About thisSection

Now that you have successfully simulated the ball mill and cyclonedemonstration circuit supplied with JKSimMet, this exercise willextend your knowledge by showing you how to:

• change the standard data provided with a test, in an attempt toimprove the performance of the circuit under changingconditions

• re-simulate the circuit• view the results of the altered simulation and plot selected

results as a graph on the screen or using overview or on theprinter.

The objective is to optimise the performance of the circuit bychanging key parameters of the units and streams. The selection ofthese parameters is the engineer's job and you may well have yourown ideas and wish to experiment. However, we have decided forthis exercise to vary:

• cyclone conditions to achieve a finer product• throughput to compensate for a change in ore hardness.

This should have the effect of changing the performance of thegrinding circuit that you are going to simulate.

Note that there are two ways of changing the test circuitperformance; you can change the parameters for the existing circuitcomponents, as we are doing in this exercise, or you can replace oradd components. We will see how to do the latter in section 3.7.

3.6.1 Selecting the Flowsheet to Use

In this and the following sections you will perform many of thesame steps as in section 3.5 using a demonstration test. We willassume that you are starting a fresh session with JKSimMet andneed to start the program and load the Learner Flowsheets projectand the flowsheet named Example Ball Mill – Cyclone.

We begin by starting JKSimMet, loading the Learner Flowsheetsand flowsheet named Example Ball Mill – Cyclone.

Step 1 Start the JKSimMet program and load thedemonstration project Learner Flowsheets, followingthe same procedure as you did in section 3.5.

Making Changes to an Existing Flowsheet Learning JKSimMet


Step 2 Select the flowsheet Example Ball Mill – Cyclone inthe drop-down list in the JKSimMet main window,following the same procedure as you did in section3.5.1.

Step 3 Open the equipment data window for the Feed usingthe procedure outlined in section 3.3.6. Alternatively,lock the flowsheet using the Lock icon on the toolbarand double click on each piece of equipment when youwish to view the data window for it or its ports.

The Feed is a special equipment unit which representsthe flow of new material into a circuit. The Feedequipment data window allows us to examine the feedstream data, both mass flow and size distribution data.It layout is the same as that found in the port datawindows which contain stream data.

The Feed equipment data window



Step 4 Click on the Overview Config icon on the mainJKSimMet toolbar to view the overview window.Make sure that the pre-defined Simulation ResultOverview is selected on the drop-down list.

Step 5 Use the Print icon on the toolbar to print the overviewwindow. This provides a printed record of the baseresults for the flowrates, % solids and other data fromthe original simulation.

Step 6 Click on the flowsheet window to make this the activewindow.

3.6.2 Altering Operating Conditions

One of the powerful tools which JKSimMet provides for the user isthe ability to adjust the data for the components of the test circuit.While it is difficult and costly to experiment with real equipment,the JKSimMet simulator allows the engineer to experiment with awide range of changes and to view the predicted results of thesechanges.

Understanding the power of this adjustment method is importantand this section proceeds by:

• showing you how to make changes and re-simulate• providing exercises for you to practise• familiarising you with some short-cuts and additional useful

techniques.

The general technique is to decide the changes you want to make,select the component whose parameters you want to change, makechanges to the parameters, re-simulate and observe the results.You then have the choice of making further changes, undoing thechanges and trying some other ideas or accepting the changes andsaving the file on disk as a permanent record.

The parameters are characteristics of the equipment models andtheir ports which can be altered. In a real plant we can alter mostequipment parameters (with varying degrees of difficulty and withvarying degrees of expense!). A few stream parameters, such as themass flowrate and feed size distribution can also be varied.Simulation allows us to vary any of the parameters which affect theprocess performance such as ball mill size and ore hardness withgreat ease.



The exercises in this section will investigate what happens whenyou change the following parameters:

• the number of parallel hydrocyclones, and their keyvariables such as vortex finder and spigot sizes

• ore work index• feed size distribution• cyclone feed density.

You are welcome to experiment with changing other parameters ofother components but we suggest that you follow the exercise untilyou are confident that you understand JKSimMet.

Concept:Changing DataFields

Note that in the data windows some of the data values aredisplayed in blue characters and some in black.

Blue Blue text on a white background indicates thatthe user can change the displayed data. Tochange the data, highlight the old value bydouble-clicking on it, type in the new valueand press Enter to register the change.

Black Black text on a grey background indicates thatthe data cannot be changed by the user. Theseare result fields which are controlled by theJKSimMet system.

Step 1 Open the hydrocyclone equipment data window (byplacing the cursor over the cyclone icon on theflowsheet, right-clicking to view the drop-down menuand selecting the word Equipment).

The hydrocyclone equipment data window



Step 2 Using the mouse or cursor control keys, move thehighlight to the data entry box whose data you wish tochange (in this example the Parallel data entry box).

Step 3 Double-click the left mouse button to highlight thenumber you wish to change (in this case the number ofcyclones) and then type in the new value of 3.

Step 4 Left-click on the Simulation icon at the top of thescreen. This brings the Simulate window into view.

Step 5 Left-click on the Start button in the Simulate window tostart the simulation.

Step 6 The simulation will begin and you will see the iterationcounter increase until the simulation converges.

Step 7 Click on the overview window to bring it into view andexamine the results of this simulation with threecyclones. Now compare the circuit performance againstyour previous printout. Is it better or worse? (withrespect to, say, cyclone overflow P80 or water split tounderflow)

Steps 2 and 3 can be repeated before simulating to change otherparameters of the hydrocyclone. Steps 1 to 4 can be repeated tochange parameters for several components.

Concept: WaterAddition toEquipmentUnits

JKSimMet allows for water addition to the feed port of anequipment unit by connecting a Water Feeder unit. The wateraddition can be specified in tonnes per hour or as the amountrequired to achieve a given feed density or simply as thatdetermined from the densities of the combined feed streams (i.e. nowater added). The water addition control method is specified inthe Water Feeder equipment window using the drop-down listlabelled Model.

CycloneVariationExercises

Step 1 Bring the cyclone equipment window into view andchange the number of parallel cyclones back to 4.

Step 2 Change the vortex finder diameter from 0.365m to0.390m and run the simulation. Note the cyclonepressure drop (by looking in the Performance Datatable of the cyclone equipment window).

Step 3 Reset the vortex finder diameter to 0.365m.



Step 4 Change the spigot (Apex) diameter from 0.203m to0.190m. Run the simulation again and observe thecyclone pressure drop.

Step 5 Reset the spigot diameter to 0.203m.

Ball MillVariationExercises

Step 1 Bring the ball mill product port data window into viewand note the product 80% passing size.

Step 2 Bring the ball mill equipment data window into viewand then select the work index for the simulated mill andincrease the value of the index by 2.0.

Step 3 Run the simulation again and observe the increase inball mill product size (which is displayed in the ball millproduct port data window).

Step 4 Left click on the Simulate window to make it the activewindow. Left-click on the Control tab and then left-click on the Start Condition drop-down list and selectExperimental Data.

Step 5 Now view the circuit feed stream data by right-clickingon the Feed unit and selecting the Equipment option.Change the value of TPH solids for the feed, run thecircuit simulation and observe the mill product stream80% passing size. Repeat these steps until the originalproduct size is achieved.

�Cyclone FeedDensityExercise

One of the easiest operating parameters to change in an actualplant is the pulp density of the cyclone feed. This exerciseexamines the effect on the grinding product of changing thecyclone feed density.

Step 1 Place the cursor on the Water Feeder icon which isconnected to the cyclone feed port on the flowsheet andright-click to view the drop-down menu. Move thecursor to highlight the Equipment option and left-click.The data window for the Water Feeder unit will appear.

Step 2 Move the cursor to the Model drop-down list and left-click. Move the cursor to highlight the Water Feeder –Required % solids option and left-click to select thisoption.



Step 3 Left click on the Required % Solids data cell to make itthe active cell, type in the value 60.0 and press Enter.

Step 4 Run a simulation and observe the effect of this change incyclone feed density on the streams in the circuit.

FeedCharacteristicVariationExercises

Ore type variations or changes to a crushing plant often causealterations in the mill feed size distribution. This exerciseexamines the effect of a feed size change on the grinding product.�

Step 1 Bring the circuit feed stream data window into view byright-clicking on the Feed icon and selecting theEquipment option on the drop-down list.�

Step 2 Left-click on the Sizing format drop-down list, movethe cursor to highlight % Retained and left-click onthis to make this the active sizing format.

Step 3 Left-click on the tab labelled Size Distribution to viewthe sizing data. Use the cursor or mouse to input thefollowing new size distribution. Start at Size 1 16mmand input in the Exp column the following values; 0.5,3, 8.5, 19, 17, 11, 8, 7, 5, 3.5, 2, 1.8, 1.5, 1.4, 1.3, 1.2,1.1 and 1.0. JKSimMet will supply the last value of6.2 at size 19.

Step 4 Run a simulation of the circuit and examine thecyclone operating conditions and product size.

3.6.3 Saving the Session�

Once you have made changes to the test circuit data, you shouldremember that the changes have only been made to the copy held inthe computer's memory. To record the changes for posterity, youmust also make sure that the files on the hard drive have beenupdated. This is done by saving the test to the hard drive.

It is good practice to save your work at regular intervals while youare making changes. This will protect your work against powerfailure, computer malfunction or mistakes that you will inevitablymake from time to time.



Saving theSession

To save the session as it is now, perform the following steps:

Step 1 Left-click on the File menu on the main JKSimMetmenu bar.

Step 2 Move the cursor to highlight the Save As option andleft-click to open the Save As window.

Step 3 Type the new filename in the File name box and selectthe directory in which you want to save the file. Ifrequired, you can create a new folder for storingJKSimMet files by clicking on the Create New Folderbutton.

Step 4 Once the filename and its directory have been entered,click on the Save button to save the file.

�


Version 5.0 December 1999 Section 3.6 Page 3-35

3.6.4 Graphing Your Results

JKSimMet has a graphing facility which you can use to creategraphs of your results on the display screen and to print thesegraphs.

The facility has been designed so that users can produce graphsvery simply using a selection of standard layouts in the Quick graphfeature, while the Generic Graph Configuration window providesthe flexibility for the user to develop customised layouts.

The Generic Graph Configuration window allows the user to drawgraphs of:

• size distributions of all raw and calculated data for the streamsin a circuit,

• equipment parameters such as efficiency curves for the rawand calculated data for classifying units in a circuit orappearance functions for ball mills,

Up to 15 curves can be drawn on a single graph and the user canhave open on the screen as many graph windows as required. Theflexibility which the Generic Graph Configuration provides alsobrings a certain amount of complexity and we shall avoid this hereby first describing Quick graphing with the standard layouts. Atutorial on the full graphing features is given in section 3.8(Learning Graphing). As an introduction to graphing we will lookinitially at the basic graphs which the user can create with a fewclicks of the mouse.

About thisExercise

From the Example Ball Mill – Cyclone flowsheet, you will create agraph of size distribution data by:

• selecting the circuit data to be graphed• using the Quick graph facility.

The graph will be displayed on the screen.

The sizing format for this graph will be selected from the availabledefault graph formats. A drop-down list allows the user to changethe sizing format to % retained, cumulative % retained, orcumulative % passing. Another drop-down list in the windowallows the user to select either the experimental data, calculateddata or the absolute error to be plotted on the graph. By using thebuttons on the graph window you can add or remove gridlines asrequired.

Drawing aGraph

Step 1 Place the cursor over the cyclone unit on the flowsheetand right-click to view the drop-down menu..


Page 3-36 Section 3.6 Version 5.0 December 1999

Step 2 Move the cursor to select the word Graph from thedrop-down menu. JKSimMet will open a windowwhich graphs the stream data for the feed and productsstreams of the selected unit, as shown below.

Step 3 The graph which is displayed in the window is thedefault format of cumulative % passing size for thecalculated data.

Step 4 Add gridlines to the graph by left-clicking on both thex-axis and y-axis gridline buttons. Your graph shouldnow look like this.

Step 5 The final feature of this basic graph is that the user canselect any port attached to the unit for its data to beplotted individually. Left-click on the Show SinglePort button at the top left corner of the graph window toview only one data set on the graph and then select therequired port from the drop-down list of port names(Single Port Selection list). Note that this drop-downlist of port names is inactive until the single data setoption has been selected.

Drop-down list toselect Experimentaldata, Calculated dataor absolute error.

Buttons toadd gridlinesto graph

Drop-downlist to selectformat of sizeplot

Plot single dataset button



Concept:Printing aGraph

Once you have set up the graph to your satisfaction you can printthe graph window. Whether the graph is printed in colour dependson whether or not the printer connected to your computer can printin colour.

Printing aGraph

Step 1 Use the Printer Setup option in the File menu to set theorientation of the paper to landscape or portrait asrequired.

Step 2 To print the graph click on the Print icon on the QuickGraph window. This will print the graph immediately.

Step 3 Quit from JKSimMet by selecting Exit from the Filemenu on the main JKSimMet menu. When askedwhether you want to save any changes to your filerespond with no in order to keep the original examplefor future users.

Creating a New Project Learning JKSimMet


3.7 Creating a New Project

About thisSection

In this section you will build a JKSimMet project from scratch, justas you would do with a real project. The techniques covered in thisChapter are the initial steps in setting up a project and flowsheetwhich are common to all of the JKSimMet mass-balance, model-fitting and simulation tools.

The first step in every new project is to build the flowsheet. Thensome of the data required for the equipment and streams of the newcircuit will be entered by you, the user, and some will be copiedfrom an existing project. The techniques available to you forexamining the data such as graphing and printing, will also bedescribed in this section.

This section will show you how to:

• create a new project and define new project and flowsheetnames,

• build a flowsheet,• re-use component data (such as for the ball mill unit) from

previously created projects,• define data for equipment units and streams,• run a simulation and view the results for the new test you have

created.

3.7.1 Starting a New Project

This exercise begins with the creation of a new project followingthe steps outlined below.

Concept:Projects

A project consists of one or more flowsheets. It is only possible towork on one project at a time (although each project may containseveral flowsheets). If you already have a project open and youcreate a new project, the new project will overwrite in memory thecurrently open project.

All of the projects that you create will be saved on the hard driveand will be quite separate from the Learner Flowsheets project.

Step 1 Start JKSimMet and left-click on the Open Project icon inthe toolbar. This will bring the Project View window onto the screen with the Saved tab active.

Step 2 Left-click on the New tab to make this the active tab.

Learning JKSimMet Creating a New Project

Version 5.1 February 2003 Section 3.7 Page 3-39

Step 3 Click on the red Default Project icon and drag it across on to the JKSimMet flowsheet window. This will load the Default Project which is a blank project, for you to work on.


Page 3-40 Section 3.7 Version 5.1 February 2003

3.7.2 Define Flowsheet Name

The flowsheet window in this version of JKSimMet can accommodate much larger circuits than was the case in previous versions. Users can now draw a flowsheet which is larger than the screen. Scroll bars are used to move around the flowsheet window. In mass balance, model fit and simulation modes the user can select a subset of any of the units and streams for analysis.

Each flowsheet must be given a name so that the user can select the required flowsheet for display. In this case we are only creating a simple flowsheet with a single circuit, but it is still advisable to name the flowsheet.

Define Flowsheet Name

Step 1 Left-click on the JKSimMet flowsheet window to make this the active window and then right-click on any blank area of this window.

Step 2 On the pop-up menu which appears, move the cursor to highlight the word Flowsheet and then move the cursor to highlight Properties on the sub-menu which appears and left-click to select this option. This will bring into view the Flowsheet Definition window.

Step 3 In the box labelled Title in the Flowsheet Definition window type in your own title for the flowsheet. The user can also type other details such as any comments on the flowsheet in the appropriate spaces in the Flowsheet Definition window.

.Step 4 While the Flowsheet Definition window is open you should also take the opportunity to set the % passing size values which are used in the port data displays.

Step 5 Close the Flowsheet Definition window by left-clicking on the Close icon in the window title bar. Note that the name of the flowsheet now appears in the drop-down list box at the bottom, right-hand corner of the flowsheet window



3.7.3 Drawing a New Flowsheet

To draw a new circuit directly on to a blank flowsheet window you will need to follow these steps:

• select the units that make up your circuit and place their icons (pictures that represent the units) on the flowsheet (make sure that they are positioned so that it will be easy to connect the streams between them),

• connect the appropriate feed and product ports of the units with streams that represent the flow of material between the units,

• add feeders to carry the input material into the circuit, • connect water addition points to the circuit. Each piece of equipment on the flowsheet has a default name which can be edited by the user. Naming the components of the flowsheet is recommended as this makes it easier to identify the data later, for example when you want to define the operating parameters of an equipment unit or identify it in a report.

Concept: Unit Naming Conventions

JKSimMet identifies all components of a circuit by the names that you give to them. The program does not enforce any conventions in naming and you may select any name you wish. You may call the ball mill Bert if you wish, but you will no doubt find that naming a ball mill, Ball Mill or some abbreviation thereof, while somewhat less interesting, is in practice easier to remember. JKSimMet will not forget what Bert is, but you probably will!

You now have a blank flowsheet window on the screen in front of you and you can begin to draw in a new circuit. You must position the process equipment before connecting the ports of the new circuit.

Create New Equipment Units on the Flowsheet

Step 1 To create a new equipment unit on the flowsheet firstleft-click on the Project View window to make it theactive window and then left-click on the tab labelled New to make it the active tab. Note that once a project has been loaded there is only one item in the New list in the Project view window – Default Equipment .

Step 2 Double-click with the left mouse button on the Default

Equipment book icon to “open” the book and display the list of equipment categories which are available to you.

Step 3 To view a list of the units which are available in each equipment category simply left-click on the plus-sign which is next to the category name. In this case, left-



click on the Mill category to show the list of mills available.

Step 4 Left-click on the icon of the equipment unit which you

want to add to the flowsheet and drag it on to the flowsheet. In this case, click and drag the Rod Mill icon to the flowsheet, placing it in the position you want it to appear and releasing the mouse button to leave the unit in the required position.

Positioning A Unit

Equipment units may be moved around the flowsheet window whenever you want to move them, providing that the flowsheet is not locked. Simply place the cursor over the icon of the unit you wish to move, left-click and drag the equipment icon to its new position and release the mouse button to leave the icon in place. If there are streams attached to the unit they will remain attached after moving it.

Changing Feed Direction

In order to make flowsheet layout uncluttered, the orientation of equipment units can be changed so that the feed end is facing left or right as required. To change the feed direction move the cursor to the unit you wish to change and right-click to view the drop-down menu. Move the cursor to highlight the word Flip and left-click to make the unit change from left-hand feed to right-hand feed or vice-versa. While it is possible to Flip units which have streams attached, it is better to plan the orientation of the units before you connect them together with streams or you may end up with some very convoluted pipework.

Deleting a Unit An equipment unit can be deleted by placing the cursor over the unit on the flowsheet and right-clicking to view the drop-down menu. Select the Delete option from the menu and the unit (and any attached streams) will be deleted from the flowsheet.

Default Equipment bookhas been “opened” toshow the list of equipmentcategories.

Default Equipment bookhas been “opened” toshow the list of equipmentcategories.



Concept:Re-using data

Re-using equipment data that have been created for a previousproject is a convenient short-cut. It allows the engineer to quicklyconstruct similar flowsheets based on the same components.

Use ExistingEquipment Unitson the Flowsheet

Step 1 To use equipment units which have been used in aprevious project first left-click on the Project Viewwindow to make it the active window and then left-click on the tab labelled Saved to make it the active tab.This brings into view a list of the projects which havebeen saved in the current directory on the hard disk. Ifthe project which you want to access is in anotherdirectory, click on the Browse Directories button andselect the required directory in the Select Directorywindow.

Step 2 Double-click with the left mouse button on the bookicon of the project whose data you wish to re-use. Thiswill display the list of flowsheets which are thecomponents of the project. In this case we will look atthe project called Learner Flowsheets.

Step 3 Left-click on the plus sign to the left of the flowsheetwhere the data you wish to re-use are located. This willreveal a list of the equipment units which are part of theflowsheet. In this case left-click on the plus sign for theExample Ball Mill Cyclone simulation flowsheet.

Step 4 Move the cursor to the icon of the equipment unitwhose data you wish to re-use and left-click and dragthe unit icon onto your current flowsheet. For theexample you are working on, click and drag thePrimary Mill and then the Cyclones units to theflowsheet you are building.

The first stage of building the flowsheet is complete and yourflowsheet should look similar to the one shown below.



The Learner Flowsheets Example Ball Mill Cyclone circuit is alarge, single-stage ball mill treating a coarse feed and producing arelatively coarse product. Another common circuit configuration isto use a rod mill followed by a ball mill to produce a finer product.The first part of this exercise will investigate the use of thisarrangement. Because the ball mill is very large, it is necessary toconfigure the circuit with three rod mills in parallel.

In reality, this is not a practical configuration without the use of afeed sump. However, for simplicity we will not draw a feed sumpon the flowsheet at this stage.

3.7.4 Create Connecting Streams

The next step is to create streams to join the equipment units youhave placed on the flowsheet.

The combiner and product ports of each unit are represented on theequipment icons by a short grey line which resembles a short lengthof pipe with a flange at the end. Up to three streams can connect toa combiner port. Only one stream can connect to each product port.If an equipment unit has more than one product (for example, acyclone has two products) there will be a separate product port foreach product stream on the unit icon. The hydrocyclone icon isshown below as an example.

Cyclone product(underflow) port withno stream connected.

Cyclone combiner portwith one stream connected.

Cyclone product(overflow) port withno stream connected.



ConnectingPorts

Step 1 To begin to draw in a stream to connect a combiner anda product port, first position the cursor over thecombiner port of a unit.

Step 2 When the cursor has changed into a hand grasping aspanner with the word JOIN in black text above it, left-click the mouse button. The word above the cursor willchange to PROD to tell the user that the firstconnection has been made and to make the secondconnection by joining the stream to a product port.

Step 3 Move the cursor to the product port of the unit youwish to join.

Step 4 When the cursor is in the correct position to join thestreams the cursor will change to a mirror image ofitself, with the word PROD now in white text. At thisposition left-click the mouse button to make thesecond connection. The simulator will draw in theconnecting stream on the flowsheet.

In the example flowsheet that you are building the units should beconnected as shown in the picture below. Repeat steps 1 to 4 aboveto connect all of the units as shown. Note that your streams mayfollow slightly different paths, depending on the order in which youmake the connections and the relative positions of the units on theflowsheet.



Errors inConnectingStreams

JKSimMet will not allow you to draw connecting streams whichcould not exist in a real plant. For example, JKSimMet does notallow you to draw connecting streams from one combiner port toanother combiner port or from one product port to another whenyou draw in the circuit diagram.

DeletingConnectingStreams

If the user makes a mistake when drawing connecting streams thestream can be deleted as follows:

Step 1 To delete a stream place the cursor over the equipmentunit from which the stream emanates as a product andright-click to view the pop-up menu.

Step 2 Move the cursor to highlight the Delete option and toview its sub-menu which lists all of the items which canbe deleted

Step 3 Move the cursor along the list in the Delete sub-menu toselect the port name whose stream you wish to delete.Note that if you choose the combiner port from theDelete sub-menu all streams connected to that port willbe deleted.

Concept:Unit FeedPorts

Each equipment unit has a three-stream combiner at its feed port(hence the name combiner used to denote the feed port). If there ismore than one stream entering the unit, the combiner port datawindow displays the data for the combined feed streams.

Concept:Unit ProductStreams

Each equipment unit has one, two or three product streams,depending on what type of unit it is. On the flowsheet, eachproduct stream which leaves a unit is denoted by a product port(shown as a short grey line which resembles a short length of pipewith a flange at the end). Only one product stream flows from eachproduct port.



3.7.5 Adding a Circuit Feed Stream

The next step in building the flowsheet is to define a feed stream to the circuit. In JKSimMet V5 the source of new material to feed into a flowsheet is a special unit called the Feed. The Feed allows the user to enter the stream data which define the feed material, such as mass flows and size distribution.

Adding a New Feed to a Flowsheet

Step 1 Left-click on the Saved tab in the Project View window to view the Saved Equipment list. Double left click on the Learner Flowsheets Template.

Step 2 Left-click on the plus sign of the Example Ball Mill-Cyclone Simulation circuit.

Step 3 Left-click and drag the Feed icon on to the flowsheet and place it near to the feed end of the Rod Mill.

Step 4 Left-click on the flowsheet to make this the active window.

Step 5 Draw in a connecting stream between the Feed unit product port and the Rod Mill unit combiner port.

3.7.6 Adding Water to the Circuit

The flowsheet diagram is now almost complete. The final task in drawing our circuit flowsheet is to make provision for water to be added to the rod mill and the cyclone feed.

Concept: Water Addition

In JKSimMet V5 all water additions are made by means of a special type of unit called a Water Feeder. Water may only be added to the feed port of an equipment unit. The water addition can be specified as either tonnes per hour of new water or controlled by the required percent solids of the unit feed stream. The choice of options is controlled by selecting the appropriate model in the Water Feeder equipment data window.

Adding Water to a Flowsheet

Step 1 Left-click on the New tab in the Project View window to view the Default Equipment list. If only the Default Equipment icon is visible, double-click on the closed book icon to view the list.

Step 2 Left-click on the plus sign of the Feed category icon to

view the list of feed of feed options available.



Step 3 Left-click and drag the Water Feeder icon on to the flowsheet and place it near to the feed end of the Rod Mill.

Step 4 Left-click on the flowsheet to make this the active

window. Step 5 Right click on the Water Feeder icon and select

Equipment from the Drop Down list. Step 6 Enter an appropriate % solids value in the Water

Feeder equipment window Step 7 Draw in a connecting stream between the Water Feeder

product port and the Rod Mill unit feed port. Step 8 Repeat Steps 3 to 7, placing the second Water Feeder

icon near the cyclone and connecting it to the cyclone feed port.

Step 9 It would be wise to record your work at this stage.

Right-click on a blank area of the flowsheet, move the cursor to select Project and then select Save from the sub-menu.- or select File and then Save from the menu.

The circuit flowsheet is now complete and should now look like the flowsheet shown below. At this stage it is advisable to Lock the flowsheet by clicking on the Lock button on the JKSimMet toolbar. If required, the user can add various information such as stream name labels or equipment unit information blocks to the flowsheet. The techniques for annotating the flowsheet in this way will be discussed in the next section.



Concept: Locking the Flowsheet

Locking a flowsheet prevents the equipment units on the flowsheet from being moved accidentally. It is advisable to lock a flowsheet once you have finished drawing it, particularly large complex flowsheets, because if a unit is moved accidentally whilst trying to access data the flowsheet is redrawn and this may take several seconds for complex diagrams. Locking a flowsheet also allows users to access the equipment data window by double-clicking on the equipment icon on the flowsheet.

Concept: Port Naming Conventions

JKSimMet V5 automatically creates names for all of the ports on the flowsheet. Each port name is created by identifying which unit it is attached to and describing whether it is a feed or product port for that unit. For example, if the user has a nest of cyclones named Deslime Cyclones, their feed port will automatically be named Deslime Cyclone Combiner. The product ports are given the descriptors which are appropriate for the particular item of equipment. For example, cyclone product ports are overflow and underflow and flotation product ports are concentrate and tails.



3.7.7 Adding Information Blocks and Labels to the Flowsheet

Displaying Data on the Flowsheet

You can easily put information about the ports and equipment units on your new flowsheet. This is done by adding Information Blocks to the flowsheet. This is a very useful feature as it allows the user to examine the circuit performance in terms of port data and equipment data in pictorial form on the flowsheet.

Concept: Information Blocks

Each of the units and ports on the flowsheet can be annotated with an Information Block which can display data for that that item on the flowsheet. For equipment units the information block displays two items of data while for ports up to four items of data can be displayed. The user can select which data items are displayed in the information block. The information block can be placed in any position the user chooses on the flowsheet screen.

Firstly you will place information blocks on the flowsheet for some key ports.

Adding a Port Information Block To the Flowsheet

Step 1 Make the flowsheet window the active window.

Step 2 Left-click on the Information Block Configuration button on the main JKSimMet toolbar. This opens the Configure/Assign Information Blocks and Labels window as shown below.

The Ports tab for configuring Port Information Blocks

Step 3 Left-click on the selectable tab labelled Ports to configure the information blocks for the port data.

Step 4 Check that the box marked Allow Dual Data Types is empty. This will allow you to place four different data items in the information block. If this box has a tick in it you can place two data items in the information block and view two types of data (e.g. experimental and simulated data) for them both.



and view two types of data (e.g. experimental andsimulated data) for them both.

Step 5 Decide which four data items from the Configurationlist you want displayed in the port information blockand then left-click on each in turn to place them in theblock. For this example select Solids (t/h), % Solids,Vol.Flowrate and % Passing X. If you make a mistakeor want to change any of the selected data items simplyclick on the Clear button below the list and repeat theselection process. Note that % - X mm and Y PassingSize are set from the Flowsheet properties windowaccessed via the tool bar icon or a left click on theflowsheet.

Step 6 From the data type drop-down list select the type ofdata which you want to display in the informationblock. In this case select Sim to display simulated data.

Step 7 Once you have the required configuration for theinformation block left-click on the Apply button toapply your selection to the information block. Notethat this action places an information block legend onthe flowsheet.

Step 8 From the list of ports at the left of the window selectthe port for which you want to add an informationblock. For this example, select the Ball Mill Combiner.

Step 9 Left-click on the Add New Block button to place theinformation block on the flowsheet. The new blockappears behind and slightly to the side of the PortLegend block. Note that the information block has thename of the port across the top of it. This will help toidentify which port the data relate to if the informationblock is not placed directly next to the port on theflowsheet.

Step 10 Repeat steps 3 to 8 for any other ports for which youwant to display an information block.

The user can also add an information block for each equipment uniton the flowsheet. This allows the user to observe the effect of anychanges to the circuit on unit parameters such as cyclone operatingpressure. For the example which you are working on here, aninformation block for the cyclones would be useful.



Adding anEquipment UnitInformation Block

Step 1 With the Configure/Assign Information Blocks andLabels window as the active window, left-click on theselectable tab labelled Equipment to configure theinformation blocks for the equipment unit data.

Step 2 From the list of units at the left of the window selectthe equipment unit for which you want to add aninformation block. For this example, select the PrimaryCyclones unit. The list of unit parameters in theConfiguration section of the window will change toreflect the type of unit which has been selected, asshown below.

The Equipment tab for adding Equipment Information Blocks

Step 3 Decide which two data items from the Configurationlist you want displayed in the unit information blockand then left-click on each in turn to place them in theblock. For this example scroll down the list and selectCal Operating Pressure and D50c Cal. If you make amistake or want to change any of the selected dataitems simply click on the Clear button below the listand repeat the selection process.

Step 4 Once you have the required configuration for theinformation block left-click on the Apply button toapply your selection to the information block for theselected unit.

Step 5 Left-click on the Add New Block button to place theinformation block on the flowsheet. Click and drag onthe information block to place it where you want it onthe flowsheet. Note that the information block has thename of the unit across the top of it. This will help toidentify which unit the data relate to if the information



block is not placed directly next to the unit on theflowsheet.

Step 6 Repeat steps 2 to 5 for any other units for which youwant to display an information block.

The final option for annotating the flowsheet is to add one or moreLabels. This allows the user to type in their own text in a text boxwhich can be formatted in a range of colours and styles.

Adding a Labelto the Flowsheet

Step 1 With the Configure/Assign Information Blocks andLabels window as the active window, left-click on theselectable tab titled Labels to set up a label on theflowsheet.

Step 2 In the box marked Text type the text you want todisplay on the flowsheet. Note that as you type thePreview box shows how the label will look on theflowsheet.

Step 3 Select the required text justification by clicking on theradio button in the Text Alignment box. View theresults of your selection in the Preview box.

Step 4 Select whether word wrap and/or borders are requiredfor the text box.

Step 5 If you want to use a different background colour for thelabel click on the Background Colour box to view thepalette of colours from which you can select a newcolour.

Step 6 If the height and width of the label set by the Autosizefunction are not suitable for your label click on theAutosize On box to switch the Autosize function off.Then enter the required size (in millimetres) of the labelin the boxes marked Height and Width.



Step 7 When you are happy with the format of your text box asshown in the Preview, click on the Add Label button toplace the label on the flowsheet. Click and drag thelabel to the required position. Note that once a labelhas been placed on the flowsheet its text and formatcannot be edited.

Step 8 If you want to delete a label simply double-click on it toremove it permanently from the flowsheet.

The Labels tab for adding Text Labels to the Flowsheet

3.7.8 Entering Data

Having completed your circuit diagram the next step is to supplydata for each component of the circuit. This can be done in twoways:

Enteringnew data

The user can enter new data using thekeyboard or by copying and pasting data froma spreadsheet.

Re-usingthe data fromexisting projects

The user can re-use the data for a unit createdin a previous project by dragging onto thecurrent flowsheet the icon of the unit from theexisting project that is stored on thecomputer's hard disk.

Once imported the data can be modified asrequired.

We have already seen how to re-use equipment unit data by usingthe icons for an existing ball mill and cyclones when drawing the



circuit flowsheet for My RM-BM-Cyc Circuit. In the next sectionyou will learn how to enter new data into the default equipmentunit used on the flowsheet.

3.7.9 Define Data for Rod Mill

The only equipment unit in the new circuit without data is the rodmill. You will use the keyboard to enter a new set of data for therod mill. The data to be entered are listed below and are alsoshown in the Rod Mill unit data windows opposite.

UNIT DATA FOR FLOWSHEET My RM-BM.CYC

ROD MILL

Data which canbe entered

ROD MILLModel Lynch/KavetskyNumber of Rod Mills 3Data for Simulated MillInternal Mill Diameter (m) 3.40Internal Mill Length (m) 4.90Fraction Critical Speed .650Load Fraction .350Ore Work Index 15.0

Data from Original MillRod Mill Constant 2079Internal Mill Diameter (m) 3.40Internal Mill Length (m) 4.90Fraction Critical Speed 0.650Load Fraction 0.350Ore Work Index 14.1Feed 90% passing size (mm) 11.5

Selection Function DataFunction is constant below XC (mm) 7.43Intercept of function at Size 0 IN -3.6Slope of function with Size SL 0.500

CalculatedDuringSimulation

Calculated DataChange in breakage stages 1.53Number of breakage stages 7.30



EquipmentUnit DataEntry

Step 1 Place the cursor over the Rod Mill icon on theflowsheet and right-click to view the drop-down menu.

Step 2 Move the cursor down the drop-down menu to selectthe Equipment option.

Step 3 The unit data window for the Rod Mill appears on thescreen, ready for you to enter the data listed above.Note that there are already data in the window. Thesedata are typical values for a rod mill which have beenselected as default data for this unit. You will replacethese data with the values listed previously.

Note: Notice that there are more data elements thanwill fit in the unit data window. As discussedpreviously you can view the various groups of data byleft-clicking on the appropriate selectable tab.

Step 4 First change the name of the Rod Mill to Rod MillsNo. 21,22,23 by clicking and dragging across theexisting name to highlight it, typing in the new nameand then pressing Enter. Note that the new nameappears in the title bar of the rod mill data window assoon as you press Enter.

Step 5 Now change the number of parallel units to three bydouble-clicking on the number in the cell labelledParallel and typing the number 3.

Step 6 Enter the data for the simulated and original mill in thedata cells with blue text which are visible under the tabnamed Scaling. Left-click on a data cell to make it theactive cell and then use the arrow keys to move theactive cell as required.

Note: It is possible to overwrite any of the values thatappear in blue.

Select tab to viewthis data group



Step 7 Left-click on the tab named Selection function andCalculated Data and type in the appropriate data fromthe list.

Step 8 Click on the Simulation icon on the main JKSimMettoolbar to bring the simulation window into view.

Step 9 Click on the Start button on the Run Simulation tab tosimulate the circuit.

Step 10 Check the results and save the file if you are happy withthe results.

Step 11 Print out equipment and port data as a base case for theexercises in the next section.

3.7.10 Examining Data

Before we move on to the rod mill circuit exercises it is worthwhileto summarise the techniques which are available to the user forexamining the large amount of data which exist in the flowsheet.

Equipment UnitAnd PortData Windows

The equipment and port data windows are the source of the mostdetailed data about these items. The user can have as many of thesewindows open on the JKSimMet desktop as he wishes. To makethe desktop less cluttered, use the Minimise button to close thewindows while allowing easy access to them. The windows willreturn to their original size and position when the Maximise buttonis clicked.

In port data windows, the user can choose which data types todisplay (experimental, simulated etc.) by selecting the appropriateitem from the Data drop-down list. Similarly the user can choose toview the size distribution data in one of three formats and canchoose the error format by selecting the required type from theFormat or Error drop-down lists respectively.

Quick Graph The Quick Graph feature provides a quick and easy method tocheck for errors or discontinuities in sizing data by plotting a graphof cumulative percent passing or cumulative percent retained vs.size.

Tool window The JKSimMet tool window (Mass Balance, Model Fit or Simulatewindow as appropriate) provides a summary of stream data showingthe results which have been calculated by running the balance, fit orsimulate tool.



Flowsheet print The flowsheet (streams and units) can be printed via the print icon.Selecting Print Flowsheet from the file menu allows the flowsheetto be printed or sent to the clipboard from where it can be pastedinto MSPaint for editing or to any clipboard aware application.

3.7.11 Rod Mill Circuit Exercises

It is apparent that a more realistic circuit can be made with somefurther changes to the circuit data. These are:

• reduce the number of rod mills to one• alter the % solids in two places to allow for an addition of water.

Single Rod MillExercise

Reduce the number of rod mills from three to one. Add the finerfeed cyclone parameters and scale the new feed rate, ball mill sizeand cyclones to suit one rod mill.

Step 1 Make the Rod Mill equipment data window the activewindow.

Change Numberof Rod Mills

Step 2 Change the number of rod mills to 1 and press Enter toregister your change

Step 3 Position the cursor over the Water Feeder icon which isconnected to the rod mill feed port and right-click toactivate the drop-down menu.

Step 4 Move the cursor to select the Equipment option to bringthe Water Feeder unit data window into view.

Set Rod MillFeed Density

Step 5 Left-click on the Model drop-down list and move thecursor to select the Water Feeder – Required % Solidsoption

Step 6 In the Operating Conditions area of the data windowovertype the 'Required % solids' field with the newvalue of 75.

Step 7 Press Enter to register your changes.

Step 8 Left-click on the flowsheet window to make it theactive window.

Step 9 Position the cursor over the Water Feeder icon which isconnected to the cyclone feed port and right-click toactivate the drop-down menu.

Set CycloneFeed Density

Step 10 Repeat Steps 4 to 7 for the cyclone feed water addition,setting the required % solids to a new value (try 60).

Step 11 Simulate and examine the results.



Cyclone FeedSize Exercise

Note that the cyclone feed and product are now MUCH finer thanbefore. This causes a problem with the simulation of the existingcircuit because the cyclone model is NOT valid for large variationsin feed size. A second set of cyclone model parameters is givenbelow for you to try out. As an exercise, enter the data into thecorrect windows and run the simulation again. Examine the circuitdata to see how the different cyclone parameters affect the circuitperformance.

CYCLONE DATA FOR FLOWSHEET My RM-BM CYC

Data which canbe entered

HYDROCYCLONEModel NageswararaoOperating VariablesNumber of Cyclones 3Cyclone Diameter (m) .660Inlet Diameter (m) .280Vortex Finder Diameter (m) .300Spigot (Apex) Diameter (m) .175Cylinder Length (m) .487Cone Angle (degrees) 15.0

Model ConstantsKD0 (D50) .000104KQ0 (Capacity) 595.5KV1 (Volume Split) (m) 7.25KW1 (Water Split) 9.57alpha (Efficiency Curve) 2.01beta (Efficiency Curve) 0.00

CalculatedDuringSimulation

Calculated DataWater split to O/F (%) 80.93Corrected D50 (mm) .2019Operating Press. (kPa) 161.4

AdditionalExercises

Follow the same general sequence to:

• scale the new feed rate to produce the same product size,• adjust the size of the ball mill instead,• check the effects of a new set of cyclone parameters,• add a sump to the flowsheet,

and anything else that may be of interest to you.

For a quick summary of each, copy the Simulate tab to theclipboard and paste each result summary in sequence into a suitablespreadsheet for comparison of results.

Learning Simulation Learning JKSimMet


3.8 Learning Simulation

Simulation within JKSimMet V5.0 is controlled via its ownwindow (or tabbed dialogue). Which is accessed by clicking on theSimulate icon on the JKSimMet tools toolbar

The Simulate window has three selectable tabs which provideaccess to the three data areas in the window. These are:

• Control• Select, and• Run Simulation

The Control tab in the Simulate window

Control tab The Control tab allows the user to set the parameters for thesimulation. For the most part, the default values for theparameters should be appropriate. However, for flowsheets withvery large flows, the convergence limit can be reduced toincrease the “accuracy” of what goes in equalling what comesout.

A choice of spline or linear size interpolation is available. Thespline interpolation is well suited to grinding data while forsharply classified size distributions (which sometimes occur incrushing circuits), linear interpolation may be useful.

Learning JKSimMet Learning Simulation


Select tab This tool is a more general version of the select list used in theMbal module of Version 4. The standard operating conditionwill be to select all equipment and streams. However, it is oftenuseful to work with a subset of the flowsheet. To do this, the userdefines a new select list as follows:

Step 1 Click on the New button to create a new select list. Ifyou wish, you may give the list a name by typing aname into the Name text box. This name helps todifferentiate this list from the other lists.

Step 2 Select only the equipment and streams which are partof the circuit of interest by placing a tick in the boxnext to the name of each in the select list. Ensure thatall other select boxes are empty.

The Select tab in the Simulate window

For example, if you are working with a rod mill - ball mill circuitand wish to simulate and fit the rod mill only, do the following:

• create a new list by clicking on the New button,• select the feed, water addition and rod mill,• select the connecting streams.

Now run the simulation or fit as required.

Using Subsetsof a Flowsheet

When working with a subset of a flowsheet which does notcontain a Feed unit, you must select the stream (or streams)which is (or are) are the feed to your chosen sub-circuit.

RenamingStreams in theSelect list

In the Select list the stream names appear as Stream 1, Stream 2etc. rather than the descriptive names which are visible in theport data windows. If you wish to give a stream a moremeaningful name in the Select list, right click on its name andselect Rename from the pop-up menu which appears. Type thenew stream name into the text box and click on OK to confirmthe change. Note that these names are only used in the Select list.

Learning Simulation Learning JKSimMet


The Select tab in the Simulate window

Run Simulation This is the working tab which allows the user to start and stop asimulation. It also provides a summary of port data for thoseequipment ports which have been selected for inclusion in thesimulation.

The Run Simulation tab also displays the Convergence value andthe number of iterations which the simulation algorithm has gonethrough. These values are updated while the simulation isproceeding.

Configure theRun Simulationdata summary

To configure the summary table on the Run Simulation tab, clickon each data column header in turn and select the required datafrom the drop-down list of port data which appears. If you want tochange the % Passing Size X or the X% Passing Size values, openthe Flowsheet Properties window (using the View option on theJKSimMet main menu) and type in the desired value. You willneed to close and then reopen the Simulate tab to apply the new% Passing Size values.

If you want to view the updated summary data values after eachiteration as the simulation is proceeding, ensure that the SimulationUpdates box on the Control tab has a tick in it. This feature allowsthe user to check the data for unrealistic values (e.g. cycloneunderflow percent solids of 90%) and to stop the simulation ifnecessary. If the Simulation Updates box is not ticked, thesummary data are not displayed until the simulation is complete

Exporting thesimulation datasummary

The Copy to Clipboard button which is between the Start and Stopbuttons, copies the simulation data summary to the clipboard. Thisfeature can be used to easily compare several alternativesimulations by copying the data summary and then pasting it into aclipboard compatible spreadsheet such as MS Excel forcomparison.

Learning JKSimMet Learning Graphing


3.9 Learning Graphing

About thisSection

The JKSimMet graphing module can plot graphs of simulation dataor other types of data, including some equipment related data, onthe computer screen or on the printer.

The data can either be plotted simply using the JKSimMet QuickGraph feature to choose the appearance of the graph as insection 3.6.4 or the full graphing facilities can be used to configurethe plot to the user’s requirements. This gives you the ability toprepare sophisticated graphs suitable for publication andpresentation.

In this section you will follow a prepared example that will guideyou through the creation of a graph. The example is set up forsimulated sizing curves for all streams in the Example Ball MillCyclone flowsheet.

The steps you will follow are:

• definition of the overall format of the graph including labellingof axes, tick marks and so on,

• definition of the data sets to be plotted and of the method fordrawing curves,

• assembly of a graph from the definitions of data and format,• note that while annotation of the graph is not available, an

automated legend facility has been added.• production of the final graphs on the screen and printer.

GraphDefinition

The Graph Definition window allows the user to define the formatof the graph and to select which data sets are plotted on the graph,using three selectable tabs to access the data fields.

Format tab Define the overall features of the whole graph,including the titles to be used for the graph andits axes, the ranges of the axes, scaling andmodification and the format of the numberlabels on the graph axes.

Data tabs Define the sets of data values to be graphed,their range, and the shape and colour ofsymbols to be drawn at the data points.JKSimMet can plot up to 15 data sets on asingle graph.

Learning Graphing Learning JKSimMet


It is a time consuming procedure to produce a final graph that looksexactly right. You will discover that you may refine your originaldefinitions several times before you are satisfied. Reproducingoriginal definitions from scratch also takes time. The Format tab ofthe Graph Definition window allows the user to set up a suite offormats which can then be recalled and applied to any data set.

Types of Datathat can beGraphed

Up to fifteen curves can be drawn on a single graph. The typesof data that can be used to produce curves are:

• Graphs of sizings of all raw and calculated data for the streamson a flowsheet.

• Efficiency curves for the raw and calculated data for all theclassification devices on a flowsheet.

• Selected functions used in the mathematical models for all ofthe equipment units in a project.

The Port Data and Equipment Data sections of the GraphDefinition window both contain fifteen columns, each of whichdescribes one curve. Thus the user can configure a named GraphData Set which plots up to fifteen items, either all port data, allequipment data or a mixture of the two where this is appropriate.



3.9.1 Drawing a Graph

About thisExample

The aim of this tutorial example is to create a single graph ofcalculated sizing data for the Example Ball Mill - Cycloneflowsheet, and in the process, to learn a stepwise procedure forusing JKSimMet's graphing facilities.

The example proceeds through the following steps:

• identifying the data sets to be graphed, and defining therepresentation of the data on the screen (Port Data tab)

• defining the appearance of the overall graph (Format tab)• viewing the graph and progressively refining the layout• display of the final graph.• optionally, add a legend to the graph.

Before starting the graphing example, we suggest that you save theLearner project under a new name, for example Graph Demo. Thiswill avoid corrupting the Learner Flowsheets file for futureJKSimMet learners.

Step 1 Open the project Learner flowsheets and load ExampleBall Mill - Cyclone flowsheet.

Step 2 Save the Learner project under a new name using theSave As option under the File menu.

Step 3 Left-click the Generic Graph Config button on theJKSimMet toolbar to bring into view the GraphDefinition window.

3.9.2 Defining the Graph Format

The Format tab on the Graph Definition window provides variousoptions for the user to define the overall appearance of the graph.These include:

• labels for the graph and for the X and Y axes• ranges, scaling and modification for the axes• format of the numbers at the tick marks along the axes.

By creating named Format definitions users can save time whencreating graphs in the future by re-using these previously definedgraph formats.



Defining thegraph format

For the tutorial example you will set up the graph format byfollowing the instructions below:

Step 1 Left-click on the New Format button at the top, rightcorner of the Graph Definition window, type the nameof your graph format into the Name box and press enterto place the name into the Graph Format drop-downlist. We will use Cum % Passing as the name in ourexample.

Labels Step 2 In the Labels section of the Format tab enter anappropriate label for the Y-axis and press Enter.Leaving this field blank means that no axis label isrequired.

Step 3 Double-click on the Font button to set the format forthe text of the axis label. Repeat this step for the FontSize.

Font and Font Size not available in version 5.1.

Step 4 Repeat Steps 2 and 3 of this section for the X-axis labeland for the graph title.

Axes and DataInterpretation

Within the Axes and Data Interpretation area of the Format tab dothe following:

Range Step 5 In the columns marked Min and Max type in theminimum and maximum data values required for thegraph axes (i.e. the range) for both the X-axis andY-axis. The values are .01 and 100 for the X-axis and 0and 100 for the Y-axis.

Scale Factor Step 6 Set the scale factor as required; 1 is the usual value andthis is used for our example.

Plotting Scale Step 7 Double-click in the Plot Style cell to view the drop-down list and select the required axis format from thelist. In this case select Logarithmic for the X-axis andLinear for the Y-axis.

Grid On Step 8 If gridlines are required for the X-axis or Y-axis place atick in the appropriate box in the Grid On column.

NumberFormats

Step 9 Move the highlight to the number format column anddouble-click to view the available options on thedrop-down list. Select the required format from the list.In the tutorial example use Decimal for both the X-axisand Y-axis.



The Format tab should now look like the example below.

Having defined the graph format you are now ready to define whichdata are plotted on the graph.

3.9.3 Definition of the Data to be Graphed

About thisSection

The next step in creating a graph is to identify the data which are tobe plotted and to define how the line and points which represent thedata are to appear. This is done through the Port Data andEquipment Data tab sections of the Graph Definition window.

This section requires you to specify:

• the data set to be graphed (this is done by choosing the item typeand then selecting one item from a list of those available),

• the range of data to be graphed, that is the minimum andmaximum values that are to appear,



• the curve characteristics in terms of- interpolation method between points- solid line or no line between points- character used to represent each point.

Each definition of a data set to be plotted on a graph is named bythe user and can be recalled and re-used within JKSimMet.

Note that the items which can be plotted on a graph includeequipment unit data such as classifier efficiency curves, ball millappearance functions, as well as the size distribution of the streams.In our tutorial example, we will plot size distribution data for theports.

Invoking DataDefinition

Step 1 Select the Port Data tab at the top of the GraphDefinition window.

Step 2 To define a new data set, left-click on the buttonmarked New, then type the name of your data set intothe Name box and press Enter.

Item Selection Step 3 Position the cursor in column 1 of the row labelled Portand double-click (or left-click and then press Enter) toview the drop-down list of port names. Move thehighlight to the port data which you want to plot anddouble-click to select it.

Step 4 Once a port name is selected for plotting JKSimMetwill enter a range of default values for the plottingformat. The user can edit these as required.

Step 5 Move the highlight to the Format row and double-click.This brings into view the drop-down list of availablegraph plotting formats. Select the Format option fromthe drop-down list.

For the tutorial example select the Cum % Passingoption.



Data Type Step 6 Move the highlight to the Data row and double-click toview the drop-down list of data options.

Select simulated data (Sim) for this plot.

GraphicalRepresentation

Note that you can have either a point or a line to represent a dataset. It is not necessary to have both. When a single data type hasbeen chosen for plotting (e.g. Exp or Fit) both the line and pointmarker represent this data. However, when the paired data typeshave been chosen for plotting (e.g. Exp & Sim, Exp & Fit or Exp &Bal) the point markers represent the experimental data and the linerepresents the second item of the data pair (Fit, Sim or Bal asappropriate). This feature is useful for comparing the calculateddata with the experimental data.

Line Type Step 7 Position the highlight over the appropriate cell in theLine row, and double-click to view the list of availableline types.

Select the required option from the Line drop-down listdisplayed, and press ENTER.

Symbol at Points Step 8 Move to the Point row and double click to view the listof symbols which can be used to represent the datapoints. This defines the symbol that is displayed tomark the coordinate points on each curve within thegraph.



Select the required symbol from the list.Colour Step 9 Move to the Colour row and double click to view the

list of colours which can be used to represent the datapoints and lines. Select the required colour from thelist.

SplineInterpolation

Step 10 The user can choose to use spline interpolation for thecurve which is drawn for each data set. To use splineinterpolation left click on the spline box to place a tickin it.

Graph OverRange

Step 11 Move the highlight to Min and Max rows and set theminimum and maximum plotting range values (on thex-axis) for each curve as required.

Steps 3 to 11 can be repeated to select up to 14additional data sets to be drawn on the same graph.

3.9.4 Easy Manipulation of the Graphing Features

Now that you have a general understanding of the function andoperation of the data and format definitions, it is easier tounderstand that the production of a quality graph may requireseveral iterations to refine the appearance of the graph by adjustingsettings through the format and data definitions.

The typical procedure for fine-tuning graphs is:

• set up a format definition,• display the graph defined by the data and format definitions

already completed in section 3.8.2 (Defining the Graph Format)and section 3.8.3 (Definition of the Data to be Graphed),

• change the format definition items which are not to yoursatisfaction,

• display the graph again,• repeat this define and display sequence until you are satisfied

with the appearance of the graph.

Step 1 Click on the Generic Graph Config icon on the mainJKSimMet toolbar to bring the Graph Definitionwindow into view.



Step 2 Click on the View/Refresh Graph button. JKSimMetwill display the graph defined by the data and formatdefinitions built earlier. Note that you can change thesize of the graph window to make it easier to see thegraph. Your graph should look similar to the one shownbelow.

Step 3 Use the Display X Axis Grid and Display X Axis Gridbuttons on the graph window to add or removegridlines. Similarly the legend can be added or removedby clicking on the Display Legend button on the graphwindow. Note that the position of the legend cannot bechanged.

Step 3 Return to the Graph Definition window by clicking onthe Edit Graph Definition button on the graph window.Select the Format tab and change the label settings.

Step 4 Click on the View/Refresh Graph button to view theadjusted graph.

This procedure can be repeated until you are satisfied with theresulting graph.

3.9.5 Saving the Session

Saving the data It is often a good idea to save the project during graphing, in casesomething untoward happens to all that information you have justentered.



3.9.6 Graphing Limitations

One Data SourceLimitation

A graph can contain data from only one flowsheet (the currentflowsheet). However, you can set up a dummy circuit on aflowsheet and import key results (such as a product sizedistributions) from several other flowsheets. The dummy circuitcan just consist of the equipment units to whose ports the requiredstreams are attached.

Note also that a single flowsheet may contain many independentsimulation circuits.

3.9.7 Graphing Related Problems

If there are any problems an error message will appear on thescreen. There are three levels of problems - refer to section 4.18(Errors) if you are not familiar with them.

Learning JKSimMet Learning Overview


3.10 Learning Overview

AboutOverview

The JKSimMet overview module provides a flexible and powerfultool for users to summarise, review and report results of massbalancing, model fitting and simulation work.

The overview screen is fully configurable by the user, and candetail data attributes (e.g. volumetric flowrate) for any or all of thestreams on a flowsheet. There is no limit on the number ofoverviews which can be created by the user for a particularflowsheet. One useful aspect of the overview facility is the abilityto create any number of overview displays and to have more thanone overview window open on the JKSimMet desktop at any time.

These overviews can be readily printed, and so provide the idealmeans to produce results in a format suitable for reports orpresentations.

In this section, you are guided through the procedure to set up anew overview display. The example is for display of simulationdata in the Example Ball Mill-Cyclone simulation. The steps youwill follow are:

• creation of a new overview display• selection of streams• selection of data to be displayed• selection of type of data to be displayed• display recovery and stream data values• printing the new overview.

Create a NewOverview

Step 1 Left-click on the Overview Config button on the mainJKSimMet toolbar to bring an overview window intoview. As you can see, the overview window opens withthe default setting which displays four columns of datafor all of the streams in the current flowsheet.

New OverviewSelect List button

Delete OverviewSelect List button

Learning Overview Learning JKSimMet


Step 2 Left-click on the New Overview Select List icon at thetop of the overview window to create a new overviewlist.

Step 3 Highlight the default name in the Name text box, typein a new name for your overview (Summary No.2 isused in the example) and press Enter. Your chosenoverview name will now appear in the drop-down list atthe top, left corner of the overview window. Also notethat the name of the current overview selection appearsin the title bar of the overview window.

DeletingStreams fromthe Overview

Step 4 The user can remove streams from the overview list bysimply placing the cursor anywhere in the appropriaterow and then clicking on the Delete Row icon todelete the row. In this example, remove the last streamfrom the list (Cyc Feed Water Add).

Change columnand window size

Step 5 If a column is too narrow for you to read the text in it,place the cursor over the right border line in the titlecell at the top of the column and click and drag thecolumn border to the required width. If the Overviewwindow is too small to view all of the data, click anddrag the bottom, right corner of the window to changethe window size as required.

Adding Streamsto the Overview

Step 6 If you want to add a stream to the list (for example ifyou delete a stream by mistake) click on the Insert Rowicon to add a new row to the bottom of the overviewlist.

Step 7 In this new row, place the cursor on the cell in theEquipment column and press Enter to view a drop-down list of the equipment units in the flowsheet.Select the equipment unit to which the required streamis connected and press Enter to place your selection inthe cell.

Step 8 Move the cursor to the Port column and press Enter toview a list of ports associated with the equipment unit.Select the name of the port by which the requiredstream enters or leaves the equipment unit.

Selecting StreamData for Display

You will now select the stream data to be displayed in theoverview.



Step 9 Place the highlight in the title cell at the top of thecolumn whose data you wish to change. Press Enter toview a drop-down list of the types of stream data whichare available for display. Select the type of data youwant to include in the overview and press Enter toplace this choice in the table. In this example, selectTPH Solids for the first column.

Note that if you are using Mass Balance and have enteredcomponent data you may select Components from the list of data tobe displayed in the overview. If you choose Components as thetype of data to be displayed, you must then select the componentyou want displayed from your list of components. This is done byselecting the required component from a drop-down list whichbecomes available in the cell below the title cell in the Componentscolumn. This second row of the data selection cells is blank if anyother type of data is selected for display.

Select Data Type Step 10 To select the data type place the highlight in the titlecell in the third cell down from the top of the columnwhose data you wish to change. Press Enter to view adrop-down list of the types of data which can bedisplayed, including Experimental data, the variousforms of calculated data and data SDs. Select the typeof data you want to include in the overview and pressEnter to place this choice in the table. In this example,select Sim (simulated data) for the first column.

The other options - Experimental, Standard Deviation, and Error,are very useful for model fitting and mass balancing.

Learning Overview Learning JKSimMet


As an exercise, set up the overview as shown below. Note that thiswindow and some of the columns have been resized (as describedpreviously) to make it easier to see all of the data.

Clearing aColumn

To clear display data from a column, place the highlight on the topcell in the column to be cleared, press ENTER to view the drop-down list and select None.

DisplayingRecoveryInformation

A useful feature of the overview facility is the ability to switchbetween actual data and recovery information.

To view the recovery data, place a tick in the box labelledRecovery by left-clicking on the box. The overview window willnow display stream data as a percentage of the stream chosen forthe recovery basis, in this case, MILL FEED.

The stream used for the recovery basis can be selected by placingthe cursor over the name of the stream in the overview list andright-clicking. A pop-up window will ask you whether you want tomake the selected stream the reference for the recovery



calculations. Click on Yes to make the stream the basis for therecovery calculations. Note that this stream is now listed in boldtext in the overview table to denote that all recoveries arecalculated with respect to this stream.

PrintingOverview

To print the overview display follow these steps:

Step 1 With the Overview window as the active window, clickon the Print Preview button on the overview window.This brings into view the Print Preview window.

Step 2 If necessary, change the orientation of the page to fitthe overview data table by selecting the appropriatechoice from the Orientation drop-down list.

Step 3 When the preview is to your satisfaction, click on thePrint button at the top, right-hand corner of the PrintPreview window to print it.

Exportingoverview data

You may transfer an overview to the clipboard using the Copy toClipboard and Copy Grid to Clipboard icons on the overviewwindow. The Copy to Clipboard icon copies only the data cellsselected by the user to the clipboard while the Copy Grid toClipboard copies the title cells and all of the data cells to theclipboard.

Alternatively, the overview data can be exported to the clipboard inits printed format (as shown in the Print Preview window) via theCopy to Clipboard button in the Print Preview window. Otherbuttons in the Print Preview window allow the user to save theprinted form of the overview table as a tab-delimited, comma-delimited or text file.

Learning to use Report Learning JKSimMet


3.11 Learning to use Report

AboutReport

The JKSimMet Report feature provides a flexible tool for users toprint the results of mass-balancing, model fitting and simulationwork.

The printed report is fully configurable by the user, and can presentselected data for any or all of the ports or equipment on a flowsheet.There is no limit on the number of reports which can be created bythe user for each flowsheet. One useful aspect of the report tool isthe ability to create any number of report configurations which canbe used to generate printed outputs as required.

Each report can be readily viewed in a print preview window andthen printed and thus provides the ideal mechanism for producingresults in a format suitable for reports or presentations. The data inthe reports can also be exported from JKSimMet in a range offormats (e.g. tab-delimited or comma-delimited text files) using theoptions available in the report Print Preview window.

In this section, you are guided through the procedure to set up anew report configuration. The example is for printing a selectionof simulation data in the Example Ball Mill-Cyclone simulation.The steps you will follow are:

• selection of port and equipment data for the report• selection of data types to be printed• viewing the report via the print preview feature• printing the report.

Create a NewReport

Step 1 Left-click on the Report button on the main JKSimMettoolbar to bring the Report window into view. As youcan see there is a default set of selections made for thereport.

Create NewReport button

Name ofcurrent report

Learning JKSimMet Learning to use Report


Step 2 To create a new report configuration click on the CreateNew Report button in the Report window. This bringsinto view a grid which lists all of the ports andequipment items on the current flowsheet. Note thatnone of the items in the grid are currently selected.

Step 3 To name the new report format double-click in theName box to highlight the default name of the reportconfiguration and then type in a new name for thereport (the name Cyclone Data will be used here). PressEnter to confirm the name change.

Selecting Datafor the Report

Step 4 Select whether the report will print port data only orequipment data only or both port and equipment databy selecting the appropriate choice on the Print Whatdrop-down list. In this case choose the option Both.

Step 5 Select the equipment and port items whose data youwant to be printed in this report by clicking on the boxnext to the name of each to place a tick in the box. Ifyou place a tick in the wrong box simply click on itagain to delete the tick. Note that each equipment itemand each port can be selected individually. For ourexample, select the Cyclone and Cyclone Feed WaterAdd equipment data and the Primary Mill product andCyclone combiner, overflow and underflow port datafor inclusion in the report.

Note that a Select All Items and an Unselect All Itemsbuttons have been provided on the Report windowtoolbar to help users in selecting data for the report.

Unselect AllItems button

Select All Itemsbutton



Selecting DataTypes for theReport

Step 6 Next select the type of data to be listed in the report byplacing a tick in the box next to the name of therequired data types in the Data types to print area of theReport window. In this case only tick the simulateddata (Sim) box.

Selecting Errordata for inclusionin a report

Step 7 When working on fitting or mass-balancing data, theuser can choose to include the data error in a report byplacing a tick in the Error box in the Error Type area ofthe Report window. The user can then select from theadjacent drop-down list the particular error that is to beincluded in the report. In this case the error is notrelevant so leave the Error box clear.

Selecting Portdata

Step 8 If you have included port data in your selected items, asis the case here, you can choose to print the Totals dataand/or the size distribution data for the ports by placinga tick in the appropriate boxes in the Port data to printarea of the Report window. Note that if Componentdata have been entered, these can also be selected forinclusion in the report here.

The Report window should now look like the picture shown below.

Previewing areport printout

Step 9 Once you have configured the report to yoursatisfaction, click on the Print Preview button to viewthe report as it will be printed.

Step 10 The Print Preview window opens at Page 1 of theprintout with the Zoom setting at 25% of normal size.Change the Zoom setting to 100% by selecting thisvalue from the Zoom drop-down list and also resize thePrint Preview window to view the entire page width.



Step 11 Use the Next Page and Previous Page buttons on thePrint Preview window toolbar to view all of the pagesin the report and check that they show the requireddata.

Printing thereport

Step 12 To print the report simply click on the Print button onthe Print Preview window toolbar. Alternatively thereport can be printed directly from the Report windowby clicking on the Print button on that window’stoolbar.

Preparing aSummary report

The Report window has a box marked Summary.When this box is ticked, the Report feature uses asummary mode to present the port and equipment datain the printed report in a different format. The user canchoose to use whichever mode suits their requirements.

In the case of the port data, Summary mode prints all ofthe data of a given type (e.g. Experimental) for all portsin one table. Each data type selected is printed as aseparate table, with all ports listed in each table. Thiscompares with the normal report mode which prints thedata for each stream on a separate page, with all datatypes for each stream being listed on this one page foreach stream.

This difference between the Summary and normalmode is illustrated in the Print Preview windows shownbelow.



Print Preview Window showing Summary report data format

Print Preview Window showing normal report data format



Exporting datausing Report

A useful feature of the Report Print Preview window is the abilityto export data in report form from the simulator in a variety offormats. Four buttons on the Print Preview window toolbarprovide the following data export features:

Copy data to Clipboard for pasting into other applications.

Save the data as a tab-delimited file (suitable for importing into aspreadsheet such as MS Excel).

Saves the data as a comma-delimited file (suitable for importinginto a spreadsheet such as MS Excel or a word processingapplication such as MS Word).

Saves the data as a text file.

These data export options allow the user to transfer data to otherapplications for preparation of presentations and reports.

Summary Learning JKSimMet


3.12 Summary

By working through this section on Learning JKSimMet, you havelearned to:

• run a supplied demonstration simulation• display and/or print the results of simulations• change some of the simulation data• re-simulate• build your own flowsheet, import some of its data from a

previous circuit and input new data.

You have also learnt how to plot graphs from the simulationresults.

In this way, you have learnt all the basic techniques necessary touse JKSimMet. Additional advanced techniques for model-fittingand for the maintenance of your system are covered in subsequentsections.

JKSimMet Reference Using JKSimMet


CHAPTER 4

JKSimMet----REFERENCE

Using JKSimMet JKSimMet Reference


4. USING JKSimMet

Contents ofthis Section

This chapter covers all the basic operational features of JKSimMet.While Chapter 3 is a tutorial, Chapter 4 is structured as a referencesection. Section 4.1 (JKSimMet Description) contains an overviewof JKSimMet. Section 4.2 contains some important definitions ofkey terms. Section 4.4 (Menus and Toolbars) describes theoperating structure and its conventions while Section 4.5 describesthe various types of windows used to display information inJKSimMet.

Sections 4.6 to 4.8 contain the information on building andannotating a circuit flowsheet. Sections 4.8 to 4.11 discuss theoptions available for presenting data by graphing and summarytables.

4.1 JKSimMet Description

About thePackage

JKSimMet is a computer software package designed to facilitatethe simulation of mineral processing plant operations. Itsdevelopment follows 30 years experience in the modelling andsimulation of minerals processing at the Julius Kruttschnitt MineralResearch Centre.

JKSimMet is designed for use by mineral processing engineers whomay not be skilled in either computing or modelling. It enhancesan engineer's capability to design and simulate all aspects ofcrushing and grinding circuits, including classification stages.

JKSimMet allows engineers to:

• design a circuit on the computer screen• enter model and plant data• fit model parameters to that data• run a simulation of the circuit• present the data and results as flowsheets, text or graphs to print

or export to file or to the clipboard..

Version 5 of JKSimMet is a user-friendly system which uses theMS Windows interface, with features such as switching betweenapplications, import and export of data and figures via copy andpaste functions and drop-down menus for quick editing and datamanipulation now available to the user. In this version there is acommon structure for all of the analysis tools (simulate, model fitand mass balance) and the engineer uses the same flowsheet andfollows the same data entry procedures for all of the analysismodes.



4.1.1 JKSimMet Simulation Technique

Process Models JKSimMet performs steady state simulation of a range ofcomminution and classification operations. Units for whichprocess models are available in JKSimMet include:

• Stockpile • Rod mill• Bin • Ball mill• Pump sump • Ball mill (air swept)• Sump • Screen, one deck• Splitter • DSM screen• Gyratory crusher • Hydrocyclone• Two rolls crusher • Spiral classifier• Jaw crusher • Rake classifier• Autogenous mill • O-Sepa classifier• SAG mill • General air classifier• HPGR • Simple Degradation

ModelDescriptions

These units may be combined in both simple and complexflowsheet circuits to enable the engineer to simulate the operationsof plants or subsections of plants. Simulations may be controlledthrough the specification of model parameters, the selection ofnecessary process mathematical models, and the specification ofoperating data such as sizings and equipment sizes.

The algorithms for each model are outlined in Appendix A.

4.1.2 JKSimMet Capabilities

SimulationCapabilities

In addition to the simulation capabilities discussed above,JKSimMet encompasses all the functions necessary for theengineer to use and maintain a number of data sets.

JKSimMet provides process engineers and metallurgists with apowerful tool for conceptual design, tuning and monitoring processplants and their elemental circuits and units. It enables an almostinfinite number and variety of circuit designs to be simulated sothat the optimal design for the task and expected range of variationof input and flow conditions may be arrived at, or at leastapproximated, before expensive experiments with real plant areundertaken. Once operating, a plant can be modelled withJKSimMet to allow monitoring and fine tuning functions to beundertaken on an ongoing basis without interruption of theproduction.

With the model-fitting tool the JKSimMet models can also betuned to more specific user operating conditions; such that thesimulation can more nearly approximate real plant conditions.Having said all this, however, JKSimMet does not and cannot

Using JKSimMet JKSimMet Reference


replace the process engineer. It facilitates the simulation of circuitand plant designs; it does not design. Like any tool, the standard ofthe work that it does is, in the final analysis, directly related to theskill of the craftsman that uses it.

4.1.3 JKSimMet Constraints

SystemConstraints

While JKSimMet is a powerful and flexible system there are,necessarily, some constraints. These are:

Size distribution There is a maximum of 30 size fractions inthe size distribution for any one stream.

Number ofFlowsheets

There is no defined limit to the number offlowsheets which may be included in aproject. However, the database will becomevery large and may cause slower systems toslow down perceptibly.

Model FittingConstraints

In Version 5• only one flowsheet can be simulated or

fitted at a time.• up to 10 primary parameters (masters)

may be selected• a further 10 can be “slaved” to each

primary parameter.• up to 10 ports and 10 pieces of

equipment can be selected to provide anobjective function for model fitting.

Note: The database structure introduced inVersion 5 will allow for a substantialincrease in these capabilities in futurereleases.

Number andType of Models

For a list of the available models refer tosection 4.1.1 (JKSimMet SimulationTechnique). The user can add new modelswith the optional software developers kit(see section 4.1.4). However, JKTechwelcomes suggested new models which willbe considered for subsequent releases ofJKSimMet. JKTech can also developcustom models for an individual client.

Mass Balancing The JKMBal algorithm can process up to 50ports with data and 30 pieces of equipment.



4.1.4 JKSimMet Expandability

PackageExpandability

JKSimMet is a self-contained package providing within itself allthe features required to build, execute and maintain a library of datasets.

JKSimMet is supplied with process models for those units listed insection 4.1.1 (JKSimMet Simulation Technique). While thesemodels cover many of the typical processes encountered incomminution processing, JKSimMet has been designed to facilitatethe incorporation of new models. While the user cannot add newmodels to the system, recommendations to JKTech will beconsidered for inclusion in later releases. The user can, however,through the use of model-fitting, modify the models currently in thesystem by, for example, setting new regression equation constants.

For sophisticated users a software developers kit (SDK) is availableas an option. Use of the SDK requires knowledge of a suitablecomputer language such as MS C, or PowerStation FORTRAN.The SDK includes an editor which allows user-designed modeltabbed dialogs to be added to JKSimMet.

Additional multi-component modules are planned. These will beadd ons at additional cost.

Definition of Terms JKSimMet Reference


4.2 Definition of Terms used in JKSimMet

JKSimMetComponents

A number of the terms and names used within the JKSimMetsystem have a specific meaning which it is important to understand.These terms are defined here to avoid ambiguity.

Project JKSimMet is organised and based upon theconcept of a project. A project can beconsidered as a portfolio in which the userstores one or more flowsheets and theirrelated data.

Flowsheet A flowsheet consists of one or many processcircuit diagrams and related data. Theflowsheet may contain one item of processequipment or many. Complex multi-stagecircuits or many circuits in parallel areacceptable. The generalised select toolallows these to be considered one at a timeor together.

Equipment The process equipment is a component ofthe circuit. Each equipment item consistsof:• an icon on the flowsheet diagram• a data window which details the process

model and its model parameters.

Ports A port is a model of a flow of solids and/orwater into or out of an item of equipment.Each equipment unit has one input port towhich up to three input connectors can beattached and one, two or three output ports,depending on the particular type ofequipment. Only one connector can beattached to each output port. For the modelsin JKSimMet, the stream characteristics ofinterest are density, size distribution andsolids and water flow rates. A port consistsof:

• an input or output port attached to anequipment unit on the flowsheet

• a data window which contains the portdata (solids and water flows, sizedistribution and assays (as appropriate).

JKSimMet Reference JKSimMet Cursor


4.3 The JKSimMet Cursor

The cursor which indicates your position on the screen takes several forms in JKSimMet, depending on what operation the user is performing.

The arrowhead cursor

This shape is the usual form of the cursor for pointing in all JKSimMet data windows, graph windows etc.

The Arrowhead with crosshair cursor

The arrowhead cursor with crosshairs appears when the cursor ispositioned over an equipment unit on the flowsheet. The change in shape of the cursor indicates that the user can either move the equipment unit by left-clicking and dragging it on the flowsheet or can access the drop-down menu for that unit by clicking the right-hand mouse button. Note that equipment cannot be moved if the flowsheet is locked (see 4.4)

The spanner cursor

The arrowhead cursor changes to the spanner in hand cursor when it is positioned over a feed or product port to which a stream can be connected. The orientation of the spanner and the word next to it changes to guide the user during the stream connection process. Note that if a port already has its maximum number of streams connected, the cursor will not change to the spanner when it is positioned over the port connection point.

If you decide not to continue with a stream connection, press escape to return to the arrow cursor.

The JKSimMet Interface JKSimMet Reference


4.4 The JKSimMet Menus and Toolbars

JKSimMet V5 has been developed to run under the MS Windows 95/98/ME/NT/2000/XP operating systems and makes use of the windows interface to provide easy and flexible access to the large amount of data stored in the JKSimMet software. A typical JKSimMet screen is shown below with various components of the screen labelled.

The various components of the JKSimMet menus and toolbars are described in detail in the following section and also in the comprehensive JKSimMet online help system.

Main Menu

Balance-ModelFit-Simulate toolbar

Functions toolbar

Status bar Session window

JKSimMet Reference The JKSimMet Interface


4.4.1 The Main JKSimMet Menu

The Main Menu of the JKSimMet interface follows the standard Windows menu layout, with a selection of drop-down submenus which allow the user to access a range of commands. Each submenu is accessed by clicking on the appropriate word on the Main menu bar.

The File submenu

New opens the Project View window so that the user can load a new project. Open opens the Project View window so that the user can load a project. Close shuts the current Project. Opening a second (or a new) project also closes the current project after offering an option to Save the current project. Save saves the flowsheet and all the data associated with the units and streams as a data file. These data files are managed automatically by JKSimMet. Save As allow the user to save a copy of the current project under a new name and/or in a new directory. The default file name extension is .jksm5. Print displays a Print Preview window of the active window, allowing the user to print the active window if required. Printer Setup allows the user to select a printer and specify the number of copies printed etc. in the standard way. Print Preview allows the selected window to be displayed on screen as it would appear in the printed version. An option to copy the printed format to the clipboard is also offered by most print preview screens. Print Flowsheet provides options for the user to print the flowsheet to file or the clipboard in colour or monochrome. Exit closes JKSimMet. The user is prompted to save the current project if the project has not been saved recently.

4.4.2 The Functions Toolbar

Many of the functions which are available in the drop-down menus of the main JKSimMet menu can be accessed via the icon buttons on the Functions Toolbar.

Note that, if required, this toolbar can be moved to a more convenient place on the screen by simply clicking and dragging it. Similarly, the shape of the toolbar can be adjusted to your personal preference by dragging its edge.

The buttons on the menu perform the following tasks:

The JKSimMet Interface JKSimMet Reference


The first five buttons on the Functions toolbar provide shortcuts to the standard New, File Open, Project Open, Save and Print options which also appear in the File menu of the main JKSimMet menu.

These buttons open the Project Definition window and Flowsheet Definition window respectively. These windows allow users to enter names and descriptions of the active project and active flowsheet.

The Information Block Configuration button brings into view the Configure/Assign Information Blocks and Labels window. This provides several options for displaying data and information on the flowsheet and is discussed in more detail in section 4.8.

The Generic Graph Config button is a shortcut to bring the Graph Definition window into view. This window, which allows the user to configure a graph to their own requirements, is discussed in detail in section 4.9.

Clicking on the Overview Config button opens a new Overview window which the user can configure to display a range of port data from the current flowsheet. More than one overview window can be open at a time. The configuration procedure is described later.

The Report button is a shortcut to bring into view the Report window. This window provides the facility to select any of the port and equipment data for printing (see section 4.12)

As its name suggests, the Toggle Tool Bar button toggles the JKSimMet Tool toolbar on and off (i.e. makes it visible or not).

The Run button allows the user to run Simulate or Model Fit or Mass Balance – whichever is currently active. If none is active, the button has no effect.

The Lock the Flowsheet button does just that, locking the flowsheet and preventing items on the flowsheet from being accidentally moved while trying to access data on the flowsheet. This is particularly useful when large, detailed flowsheets are being used as it minimises the time spent waiting for the screen to be redrawn if the user accidentally moves one item of equipment. Users can still change data while the flowsheet is locked. While the flowsheet is locked, double clicking on a piece of equipment will open its window.

The Flowsheet Size drop-down list allows the user to set the size of the flowsheet at 1x1 or 2x2 panels, depending on the users requirements.

JKSimMet Reference The JKSimMet Interface


4.4.3 The JKSimMet Tools Toolbar

The JKSimMet tools toolbar allows the user to select which of thethree available JKSimMet tools is to be used for analysis of thedata.

To select mass balance, model fit or simulate mode, simply clickon the appropriate button. Note that these buttons toggle from onto off. Pressing another button (or the same one twice) will closethe current tool.

The Run Mass Balance button brings the Mass Balance windowinto view. This window allows the user to select equipment andports to be included in the mass balancing procedure. (Massbalancing is discussed in detail in Chapter 6).

The Run Model Fit button brings the Model Fit window into view.This window allows the user to select equipment and ports fromthe flowsheet to be included in the model fitting procedure. Fordetailed information about the model fitting tool see Chapter 5.

The Run Simulation button brings the Simulate window into view.This window allows the user to select equipment and ports to beincluded in the simulation procedure. The simulation tool isdiscussed in more detail in section 3.8.

JKSimMet Windows JKSimMet Reference


4.5 JKSimMet Windows

Version 5 of JKSimMet makes full use of the windows interface toallow users to view whichever data they choose on the screen atany one time by simply opening the required windows. Thissection describes briefly each of the main window types whichmake up the JKSimMet interface.

4.5.1 The Session Window

The session window is the driving seat of JKSimMet. In thiswindow the user creates the flowsheets for analysis with the massbalance, model fit or simulate tools.

After starting the JKSimMet program a blank session window isvisible on the JKSimMet desktop, as shown below.

The Session Window at JKSimMet Startup

The user has two options at this point – to create a new project or toload an existing (i.e. previously saved) project. To do either, theuser must first bring the Project View window into view byclicking on the Open Project icon on the toolbar.

To create a new project the user drags the Default Project on theNew tab of the Project View window onto the session window.This loads a blank project in which the user can create one or moreflowsheets, using the equipment from the Default Equipment fileon the New tab of the Project View window or existing equipmentfrom project listed on the Saved tab. The procedure for creating aflowsheet will be discussed in more detail in the following sections.

JKSimMet Reference JKSimMet Windows


Alternatively, the user can load a previously saved project from thelist which is visible on the Saved tab of the Project View window.This will also be covered in more detail in the following sections.

Once a blank project or an existing project has been loaded in thesession window the JKSimMet Toolbar is available, giving accessto the mass balancing, model fit and simulate tools. Note that thetoolbars can be moved and resized as required by the user.

The Session Window after a Project has been Loaded



4.5.2 The Project View Window

The Project View window gives the user access to previously savedprojects, to the Default Project (a blank project) and also to the listof all of the equipment units which are available for use whenadding equipment to a flowsheet.

The default equipment list is shown in the picture of the ProjectView window below. Individual equipment units are accessed bydouble clicking on the Default Equipment book on the New tab andthen on the appropriate book which contains the unit you areseeking. Once the required equipment unit icon is visible, the usercan drag the icon onto the flowsheet in the session window in orderto add it to the circuit. (Note that the Default Equipment is notavailable until a project has been loaded into the session window.)

Previously saved projects can be accessed by clicking on the Savedtab to view a list of all of these projects. If the required project hasbeen saved in another directory (other than the default directoryC:\Program Files\JKSimMet V5.1\User) the Browse Directoriesbutton allows the user to make this directory the active one and toview its list of files in the Saved tab. Note that when the Saved tabis selected, the current directory name appears at the bottom of theProject View window. Also, only files whose name includes the.jksm5 extension will appear in lists in the Project View window.

To make a saved project the active project, simply drag the requiredproject from the Project View window to the session window. If aproject is already loaded in the session window, JKSimMet willwarn you that loading this project will overwrite the current project.

JKSimMet Reference JKSimMet Windows


4.5.3 Equipment Data Windows

The data for each equipment unit can be viewed in the Equipment datawindow. The equipment data window for each unit is accessed byplacing the cursor over the equipment unit on the flowsheet and right-clicking to view the drop-down menu. Selecting the word Equipmenton the drop-down menu brings the equipment data window into view.

Alternatively, when the flowsheet is locked, double-clicking on theequipment icon brings the equipment data window into view. Oncethe window is open the user can view or edit the equipment data asrequired.

Note that while the contents and format of the data area of the windowvaries between equipment types and also the model chosen, thegeneral layout of the window (Name text box, Model list etc.) iscommon to all equipment units. The data layouts for all of theequipment and model types are detailed in Appendix A.

Click on a port name to open its data window.

Hint: If you wish to see the information on all tabs in the data windowat once, click on the printer icon on the tool bar to activate PrintPreview.

User-defined namefor unit (also usedin window title bar)

Names of portsattached to thisequipment unit

Model typeselected fromdrop-down list

Buttons tocopy andpaste data

Number ofparallel units

Data area of the window (the actualcontents and format varies according toequipment type and model selected).

Selectable tabs giveaccess to the variousdata types for the unit

Buttons toprint data



4.5.4 Port Data Windows

The data for each port can be accessed in the port data window.The port data windows can be opened by two methods; the firstoption, if the relevant equipment data window is open, is to clickon the port name at the top, right-hand corner of this window. Thesecond route is to select the port name from the drop-down menuwhich appears when the user right-clicks on the flowsheet icon ofthe unit to which the port is attached.

The layout of the port data window is the same for all ports. Notethat the name of the port shown in the window title bar is definedby JKSimMet, based on the name of the unit to which the port isattached and the appropriate name for the port according to itslocation on the equipment unit (eg. feed, underflow or overflow forcyclones or feed and product for ball mills). In the example above,the data window belongs to the Underflow port of the PrimaryCyclones, so its name is Primary Cyclones Underflow.

The data contained in the port data window are discussed in detailin Section 4.7.4 on entering data.

Drop-down listfor selecting sizedistribution dataformat.

Drop-down list toselect type of datato be displayed.

Drop-down list toselect type of errorto be displayed.

Button to open SetSDs pop-up windowfor defining datastandard deviations.

Buttons tocopy andpaste data.Selectable tabs to

access the mass flow,sizing and assay dataassociated with theport.

JKSimMet Reference Building and Manipulating a Flowsheet


4.6 Building and Manipulating a Flowsheet

In JKSimMet V5 each flowsheet is stored as a sub-unit of a project. Therefore, to work with an existing flowsheet the user must first load the appropriate project into the session window or alternatively, to set up a new flowsheet the user must first load the blank Default Project into the session window.

4.6.1 Loading a Project

The first step in working with a flowsheet is to load the project in which the flowsheet is stored. This is done by opening the Project View window and dragging the project onto the session window, as described in section 4.5.1.

In the example used here, the Default Project is being loaded so that the user can create a new project and set up a new flowsheet.

If a project is dragged from the Project View window on to a session window where a project is already open, the user will be reminded that the project being loaded will overwrite the current project (in RAM-not the copy on disk) and be given the opportunity to save the open project before continuing.

An alternative method is to select File Open from the menu bar.

Building and Manipulating a Flowsheet JKSimMet Reference


4.6.2 Defining the Project Name

Whenever a file is saved, the file name is also the Project Name which is used to distinguish it from all the other projects in the Saved tab list of the Project View window.

If you wish to save a copy of the project under a different name, use the Save As option on the File menu of the main JKSimMet menu. Selecting Save As opens the Save As window which allows the user to type in the chosen name for the file and to save it in any chosen directory. The filename will be given the extension .jksm5 which identifies it as a JKSimMet V5 file.

You may also rename these files from Windows but it is a good idea to keep the .jksm5 file extension.

The user can also enter more detailed information about the project in the Project Definition window which is accessed by clicking on the Project Properties button. The default port selection may also be set from this window.



The Project Definition window lists the name of the project and has text boxes for details such as the who set up the project, when the project was last saved and the number of flowsheets in the project.

The user can edit the Done By, Done For and Comments text for the project. The text entered in the comments box appears in the Object Description section of the Project View window and can be useful in identifying a project in the list. Once all the required changes have been made in the Project Definition window, it is closed by clicking on the close button in its title bar.

Note that it is not possible to edit the title of the project in the Project Definition window. The Project Name or Title is locked to the File Name.

There are two other methods to bring the Project Definition window into view. One is to select the Properties option in the View menu on the main JKSimMet menu. The final method is to right-click on a blank area of the flowsheet and to select Project and then Properties from the pop-up menus which appear.

4.6.3 Defining the Flowsheet Name

Since a project can contain more than one flowsheet it is useful to give each flowsheet a name to make finding it easier. Once a flowsheet has been named, its name appears in the drop-down list at the bottom, right-hand side of the session window. To define the flowsheet name, click on the Flowsheet Properties button on the toolbar to open the Flowsheet Definition window. Alternatively, right-click on a blank area of the flowsheet and select Flowsheet then Properties from the pop-up menus which appear.

To change the name of the flowsheet simply highlight the text in the Title box, type in the new name and press Enter to register the name. The flowsheet name will appear in the drop-down list at the bottom, right-hand corner of the session window.

The user can also edit the Comments text for the flowsheet. These comments appear in the Object Description section of the Project



View window and can be helpful in identifying flowsheets when there is a large number of projects in the Saved file list.

The final items which the user can edit in the Flowsheet Definition window are the values for the percentage passing size data for the stream size distributions. Changing the values here changes the values in all port data windows. These values appear in the port Information Blocks when these are used to annotate the flowsheet.

When all the required changes have been made, the Flowsheet Definition window is closed by clicking on the close button in its title bar.

4.6.4 Building the Flowsheet - Equipment Units

When the Default Project has been loaded, the user is presented with a blank flowsheet. The first step in entering the data for the project is to build the flowsheet. This procedure is the same for all of the analysis modes which JKSimMet provides (mass balance, model fit and simulate).

JKSimMet uses an equipment unit to represent each unit process on a flowsheet. For the purposes of flowsheet construction, the equipment unit is made up of:

• a name (defined by the user) • an equipment unit type, including an icon • a data window containing equipment dimensions and model

parameters. The first step in building the flowsheet is to place the appropriate equipment icons on the flowsheet . The user has two options when adding an equipment unit to a flowsheet. These are to select a new item of equipment from the Default Equipment list in the New tab of the Project View window or to copy an existing equipment unit by selecting it from the list of Saved items in the Project View window. The list of equipment which is available in JKSimMet is shown below in the same form as it appears in the Project View window.



List of Equipment available in JKSimMet

The default equipment has typical values for the equipmentdimensions, model parameters etc. as its default data. Re-using anexisting equipment unit can save time entering the data for an itemof equipment if a previously saved unit has suitable data associatedwith it.

Adding a pieceof equipment tothe flowsheet

To add an item of equipment to the flowsheet open the ProjectView window and select an equipment unit from the list in the Newor Saved tab as required. (Equipment in the New tab containsdefault parameter values and that in the Saved tab contains thevalues entered by the user for that particular item.) Click on theicon of the equipment unit and drag it onto the flowsheet.



Adding equipmentor flowsheets fromanother project

You may double click on an existing project to reveal itsflowsheets and then double click on each flowsheet to reveal itsequipment. The equipment can be dragged and dropped into a newflowsheet. You may also drag a complete flowsheet from a savedproject into the current project.

Editing anequipment uniton the flowsheet

Once an equipment unit icon has been placed on the flowsheet theuser can edit or manipulate it in several ways.

Move To move a unit to a different position on the flowsheet place thecursor over the unit and hold the left mouse button down while youdrag the equipment unit to its new position. When the unit is in therequired position release the mouse button to place the unit. Anystreams which are attached to the ports on the equipment willremain attached after moving it.

Lock To lock a unit in place on the flowsheet click on the Lock button onthe main JKSimMet Functions toolbar. This prevents accidentalmovement of the equipment unit when the user is working on otheritems on the flowsheet. Locking the flowsheet is particularly usefulwhen working with large, complex flowsheets since accidentallymoving a unit requires the flowsheet to be redrawn, a processwhich can take several seconds.

EquipmentProperties

Most of the options for editing an equipment unit which areavailable to the user are presented in a pop-up menu which appearswhen the cursor is placed over the equipment unit and the rightmouse button is clicked. Note that the options listed in the menuact on the equipment unit to which the pop-up menu is attached(and on its associated ports). The format of the pop-up menu is thesame for all equipment units, except that the names of the portschange according to the type of unit (e.g. a ball mill would haveonly Combiner and Product ports listed, while the cyclone in theexample below has Combiner, Underflow and Overflow).



The pop-up menu gives the user access to the followingactions:

Add Opens the Project View window to allow the user toadd another equipment unit to the flowsheet.

Delete Select the Delete option from the pop-up menu. Thiswill open up a pop up sub-menu which offers a choiceof deleting the equipment or its ports. Deleting theequipment also deletes its connected streams.

Equipment Opens the equipment unit data window. The user canexamine and edit the equipment unit data as necessary.

Combiner Opens the Combiner port data window. This allows theuser to view or edit the stream data for that port.

Underflow Opens the Underflow port data window.

Overflow Opens the Overflow port data window.

Graph Opens the Quick Graph window which allows the userto view a standard suite of size distribution data plotsfor the ports which are associated with the equipmentunit.

Flip Changes the orientation of the equipment unit. Thisoption flips the equipment unit so that the feed end ofthe unit changes from right to left or vice-versa.

Help Opens the JKSimMet Online Help files. The helpsystem is context sensitive and will open at theappropriate section of the help files.

4.6.5 Building the Flowsheet -Connecting Ports

The flow of material (solids and/or water) between the equipmentunits on the flowsheet is represented by streams which connect thefeed and product ports on the equipment units. Material enters andleaves each equipment unit via these ports.

A port is a model of a flow of particles and/or water into or out ofan equipment unit. For the purposes of flowsheet construction aport is made up of:

• an input or output point on an equipment unit.• a data window with size distribution, solids SG and solids and

water flowrates data



Feed andProduct Ports

A unit can have only one feed port to which up to three input slurrystreams and one water addition can be connected. This feed port iscalled a combiner to highlight the fact that its data represent thecombined streams if two or three streams are connected to this port.

The number of product ports on an equipment unit depends onwhat type of unit it is; for example a ball mill has one product port,a hydrocyclone has two product ports. Each product portrepresents one stream discharging from the equipment unit andtherefore only one stream can connect to a product port.

Note that there are some specialised equipment units which do nothave a feed port. These are the Feed unit which is a source of newfeed (dry solids or solids and water) to a circuit and the WaterFeeder which is a source of water additions to a circuit.

The flow of material between the equipment units is created on the flowsheet byconnecting the feed and product ports of the appropriate equipment units.

Connecting Ports To connect a product port to a feed port the user places the cursorover the product port of the equipment unit first. When the cursorchanges to a hand grasping a spanner with the word JOIN next to it,left click to start the connection process. The word next to thecursor will change to FEED (or PRODUCT if you are connecting feedto product) in black text to tell you to what type of port you needto connect. Position the cursor over the port to which you want toconnect the stream and when the cursor changes so that the spannerchanges orientation and the word FEED (or PRODUCT) is now inwhite text, left click to make the connection. A connecting streamwill be drawn on the flowsheet as soon as both ends are connectedto the correct ports.

Note that JKSimMet will not allow the user to connect a feed port to another feed port.Similarly, it will not allow a product port to be connected to another product port.

Three streamsattached to thefeed port

One stream attached tothe Underflow productport .

One stream attached tothe Overflow productport .



4.6.6 Flowsheet Related Problems

As we have already mentioned in passing, JKSimMet detects manyof the possible errors during the building of flowsheets andprovides an on-screen error message. If you require a fullerexplanation of the error the error number provides the key to theerror messages section of the documentation. Refer to Appendix B.

Having gained an appreciation of what error has been made andhow it has occurred it is usually a simple matter to return to theoffending stage in the setting up of the circuit or project and redo it.Getting the circuit design right depends on the skill of the designengineer.

Note that the auto stream drawing is computationally intensive.Allowing reasonable space between pieces of equipment will letthe streams draw more quickly.

Lock StreamRedraw

Due to the large amount of computation required for automaticstream drawing, editing a complex flowsheet can become quitetime consuming. To minimuse this problem, the Lock StreamRedraw option available on the View drop down menu should beset. When this option is active, stream redrawing is disabled sothat as many equipment item moves as required can be made.When all the equipment items are in place, the Lock StreamsRedraw must be switched off to allow the streams to be drawn.

Editing the Flowsheet Data JKSimMet Reference


4.7 Editing the Flowsheet Data Overview Once the flowsheet has been configured with equipment units and

their ports have been connected to form a circuit, the next step is toedit the equipment unit and port data. The data for these items areaccessed by opening the equipment unit or port data window asrequired and typing the data into the appropriate places in thewindow.

Data EntryConventions

There is a convention that the fields in the data window which areavailable for data entry have a white background. This helps theuser to see at a glance which fields can be edited. The text fieldsand those which have a drop-down list for selection of a field entryhave black text on a white background. Those fields which requirea number to be entered are displayed as blue text on a whitebackground. These conventions apply to both the equipment andport data windows.Note that the exact appearance and colours of each window willalso depend on how your MS Windows desktop is set up.

4.7.1 The Equipment Data Window

Each equipment unit on the flowsheet has a data window associatedwith it. This data window contains all of the information about theequipment which JKSimMet requires to perform model-fitting andsimulation tasks.

Opening anequipment datawindow

An equipment unit data window can be opened in two ways. Thefirst method is to place the cursor over the icon of the equipmentunit on the flowsheet and right-click to bring the drop-down menuinto view. Then move the cursor to select the Equipment optionfrom the menu and left-click. The second method can be used toopen an equipment unit data window when the flowsheet is locked.In this case, double-clicking on the icon of the equipment unitopens its data window.

Equipment datawindow layout

The basic layout of the equipment unit data window is the same forall types of equipment; the common interface features and thosewhich vary between equipment types are discussed below.

JKSimMet Reference Editing the Flowsheet Data


The features which are common to all equipment unit datawindows are shown in the picture of a typical data window below.

A Typical Equipment Data Window

The common features found in all equipment data windows are asfollows:

Title bar The title bar displays the name of the equipmentunit.

Name box The user can enter a name for the equipment unit inthis box. Note that this name will be used to identifythe equipment in various other tables in JKSimMetand will also be used to create names for the portswhich are attached to the unit. For example, if youcall your ball mill Bert its ports will be called BertCombiner and Bert Discharge. It is advisable to usenames which you can recognise easily.

Port buttons The names of the ports which are attached to theequipment unit are listed here. Clicking on the nameof a port opens its data window.

Model box Clicking on the model name in the box brings intoview a drop-down list of the JKSimMet modelswhich are available for the equipment type. Theuser can select the required model by highlighting itsname on the drop-down menu and left-clicking. Themodels listed here vary from one equipment type toanother.

Title bar

Name box

Port buttons

Model drop-down list

Number ofparallel units

Copy andpaste buttons

SelectabletabsEquipment

data area

Print buttons



Parallel Units The number of parallel units represented by theequipment unit icon is entered in this box.

Data transfer The four buttons in this area of the equipment unitdata window allow the user to transfer data to andfrom JKSimMet and other programs by copying andpasting data to and from the clipboard. The buttonsperform slightly different functions as follows:

Copy Selected Cellsto Clipboard

Copies only the data cellswhich are currently selectedto the Clipboard.

Paste Clipboard toSelected Cells

Pastes data from theClipboard to the currentlyselected cells

Copy Grid toClipboard

Copies all visible cells onthe current tab to theClipboard, including rowand column labels.

Paste Clipboard to Grid

Pastes data from theClipboard to the data cells.Data on Clipboard mustcorrespond exactly to thedata cells.

Print buttons The Print Preview button displays the print previewwindow which shows the data as they will appearwhen printed. This print preview window is often auseful means of viewing the data from several tabsat one time. The print preview window also providesseveral options to export the data to text file in arange of formats. The Print button immediatelyprints the equipment data.

Data area The lower section of the equipment data windowcontains the area where data such as equipmentdimensions and model parameters are entered. Thecontents of this section of the data window varyfrom one equipment unit type to the next. Thecyclone data window will be examined to illustratethe features of this data area.

Selectabletabs

These tabs provide access to the groups of datawhich describe the equipment unit. The number oftabs varies from one to seven, depending on theequipment unit and model type. In the cyclone datawindow there are three tabs which give access to theOperating Conditions, Model Parameters andPerformance Data.



4.7.2 Editing the Equipment Data

When a piece of equipment has been added to the flowsheet fromthe Default Equipment list, its data will be set to the JKSimMetdefault values for that particular type of equipment. The user canedit these values as required, replacing them with values whichrepresent the actual equipment they want to model or simulate.Once they are familiar with JKSimMet each user will develop theirown data entry routine. This section describes a step by stepprocedure for data entry as a guide for users.

The equipment window for a cyclone will be used to illustrate thedata entry procedures. The cyclone data window shown below isthe default equipment hydrocyclone.

Changing theEquipment name

Each piece of equipment can be given a name chosen by the user.To rename an equipment unit left-click on the text in the Name boxto highlight it. Then type in the required name for the equipmentand press Enter to register the change.

The equipment name serves several purposes; it appears in the titlebar of the equipment data window and is used to identify theequipment in other tables such as the Overview window and theModel Fit and Simulate dialogue windows. The equipment name isalso used to create the names of the ports which are associated withthe unit. For example, if you name a cyclone Primary Cyclone theports will be called Primary Cyclone Combiner, Primary CycloneOverflow and Primary Cyclone Product.

Defining theNumber ofParallel Units

The equipment icon on the flowsheet can represent one unit ofequipment or several units operating in parallel. The user definesthe number of units operating in parallel by left-clicking on thenumber in the Parallel Units box to highlight it, typing the requirednumber in the box and pressing Enter.



Selecting theEquipment Model

Each equipment type has one or more process models associatedwith it which JKSimMet uses in the Model Fit and Simulationprocedures. The user can select which model is used to representthe equipment in the process by left-clicking on the drop-down listlabelled Model and highlighting the required model to select it.Note that the contents of the data area of the equipment datawindow will change according to which model is selected.

Accessing theEquipment data

When a model type has been selected, the contents of the data areaof the equipment data window will change to display theappropriate data for that type of model. There is often too muchinformation to be displayed in the available space so JKSimMetuses selectable tabs in the data area to provide access to groups ofdata. To view each group of data the user clicks on the selectabletab to bring it into view.

If you want to view all of the equipment data at the same time auseful technique is to use the Print Preview window to display theentire contents of the equipment unit data window. To view thePrint Preview window simply click on the Print Preview button atthe top, right corner of the equipment data window. The windowcan be resized and the Zoom set to 100% to make the text easier toread. When you have finished looking at the data close the PrintPreview window.

Editing theEquipment databy typing data

There are two methods to enter numerical data for an equipmentunit. One option is to type the data into the appropriate data fieldsin the data area of the window. To do this, use the cursor to selectthe cell (denoted by the grey border around the cell), type the newvalue and press Enter to accept this value. If you make a mistake indata entry you can revert to the previous value by pressing the Esckey but this will only work if the Enter key has not been pressed.

Note that if you enter a value which is outside the normal range forany data item a warning message will be displayed to tell you thatthe value is outside the normal range and asking whether the userwants to use this value or have it clipped to the maximum value ofthe normal range.

If you want to know what maximum and minimum values definethe normal range for a data item double click on the cell for thatitem and the Parameter Detail information window will bedisplayed. This details the maximum and minimum acceptable



values for the item and lists other information about the item whichis not relevant here.

A typical Parameter Detail window

EnteringEquipment datausing copy andpaste

The second method available for entering data in an equipment datawindow is to copy and paste the data. The values can be copiedfrom the data window of another unit of the same type or from anExcel spreadsheet. The data are pasted into the appropriate cells inthe data window by selecting those cells and then clicking on thePaste Clipboard to Selected Cells button.

Out of range data Note that, as before, if you paste a value which is outside thenormal range for any data item a warning message will bedisplayed. If in your view, the value is reasonable, answer Yes tothe warning message and your value will be used.However, when you use an out of range parameter, you shouldcheck your simulation results for reasonableness even morecarefully than usual.



4.7.3 The Port Data Window

Each port on the flowsheet has a data window associated with it.This data window contains all of the information about the materialflowing through the port which JKSimMet requires to performmass balancing, model-fitting and simulation tasks.

Opening a portdata window

A port data window can be opened in two ways. The first methodis to place the cursor over the icon of the equipment unit on theflowsheet and right-click to bring the drop-down menu into view.Then move the cursor to select the name of the port whose data youwant to view from the menu and left-click. The second method canbe used to open a port data window when the equipment datawindow is the active window. In this case, clicking on the name ofthe appropriate port from the list on the equipment data windowopens the port data window.

Port datawindow layout

The layout of the port data window is the same for all ports. Theonly feature which varies is the number of columns in the data areaof the window.

A Typical Port Data Window

The common features found in all port data windows are asfollows:

Title bar The title bar displays the name of the port. Thename is created by JKSimMet using the name of theequipment unit to which the port is attached and aname that identifies which port on that unit is beingexamined. In the example above the data window isthe underflow port of the Primary Cyclones so thename of the port is Primary Cyclones Underflow.

Title bar

Formatdrop-down

Data type drop-down list

Set SDsbutton

Error drop-down list

Copy andpaste buttons

Selectabletabs

Port dataarea

Printingbuttons



Format list Clicking on the format box brings into view a drop-down list of the sizing data formats which areavailable. These are % Retained, Cumulative %Retained and Cumulative % Passing. The user canselect the required format by highlighting its nameon the drop-down menu and left-clicking.

Data list The Data drop-down list allows the user to selectwhich data types are displayed in the data area of theport data window. The number of columns in thedata area varies depending on the data typesselected.

Data transfer The four buttons in this area of the equipment unitdata window allow the user to transfer data to andfrom JKSimMet and other programs by copying andpasting data to and from the clipboard. The buttonsperform slightly different functions as follows:









Data area The lower section of the port data window containsthe area where data such as mass flows and sizedistribution data are displayed.

Selectabletabs

These three tabs provide access to the groups of datawhich describe the flow of material through the port.The tabs are labelled Totals, Size Distribution andComponents.



4.7.4 Editing the Port Data

When a piece of equipment has been added to the flowsheet fromthe Default Equipment list, its port data will be set to zero. Theuser can edit these values, replacing them with values whichrepresent the material flows they want to analyse. Once they arefamiliar with JKSimMet each user will develop their own dataentry routine. This section describes a step by step procedure fordata entry as a guide for users.

The port data window for a cyclone underflow of a DefaultEquipment cyclone which has just been added to the flowsheet isshown below. The data cells are blank except for the solids SGvalue which is set to the default value of 2.70. Note that if a DefaultEquipment unit is added to an existing flowsheet the solids SGvalue for the port data is automatically set to the same value as theflowsheet feed.

Default PortFormat

You may set the default size format, data format and error formatfrom the Project Properties window.

Selecting theFormat forsizing data

If the data which describe the material flowing through the portincludes sizing data you can select the format for this data to bedisplayed on the Size Distribution tab using the Format drop-downlist. Click on the Format box to view the list of options, move thecursor to highlight the required format and click on it to select it.The available options are % Retained, Cumulative % Retained andCumulative % Passing size



Selecting theData typesfor display

The user can select the types of data which are displayed in the dataarea of the port data window. To do this click on the Data box,move the cursor to highlight the required data group and click on itto select it. The available choices are:GSIM Displays two columns of data – Exp (experimental) and

one other which is either Sim (simulated) or Fit (modelfitted) or Bal (mass balanced), depending on whichJKSimMet analysis mode is currently active.

SD’s Displays the two columns as for GSIM, together with acolumn for experimental data standard deviations (SDs)and another for calculated Error.

All Data Displays all of the data types which are available inJKSimMet – Exp, SD, Sim, Fit, Bal, and Error.

Selecting theError type

The Error column in the data area of the port data window candisplay the absolute (Abs), percentage (Pct) or weighted (Wtd)error for the simulated (Sim), fitted (Fit) or Balanced (Bal) data asrequired. The user selects the required error type from the Errordrop-down list.

Accessing thePort data

With mass flow, sizing and component data there is too muchinformation to be displayed in the available space in the data areaso JKSimMet uses selectable tabs to provide access to groups ofdata. In the case of port data windows the data is grouped asTotals, Size Distribution and Components. To view each group ofdata the user clicks on the selectable tab to bring its data into view.

If you want to view all of the port data at one time a usefultechnique is to use the Print Preview window to display the entirecontents of the port data window. To view the Print Previewwindow simply click on the Print Preview at the top, right area ofthe port data window. The window can be resized and the Zoomset to 100% to make the text easier to read. When you havefinished examining the data close the Print Preview window.

Editing thePort data bytyping data

There are two methods to enter numerical data for a port. Oneoption is to type the data into the appropriate data fields in the dataarea of the window. To do this, use the cursor to select the cell(denoted by the grey border around the cell), type the new valueand press Enter to accept this value. If you make a mistake in dataentry you can revert to the previous value by pressing the Esc keybut this will only work if the Enter key has not been pressed.

EnteringPort data usingcopy and paste

The second method available for entering data in a port datawindow is to copy and paste the data. The values can be copiedfrom the data window of another port or from an Excelspreadsheet. The data are pasted into the appropriate cells in thedata window by selecting those cells and then clicking on the PasteClipboard to Selected Cells button.



The Totalsdata tab

The Totals tab contains the mass flow data for solids and waterthrough the port. If experimental values are available for these datathey are entered in the appropriate data cells. Note that if a solidsmass flow and solids SG have been entered, only one of the otherdata items is required and the remainder will be calculated byJKSimMet. For example if you enter the TPH solids and the% Solids, JKSimMet will calculate the TPH Water, Pulp Densityand Vol. Flow. The user must ensure that the Solids SG is correct.

A Port Data Window with the Totals tab displayed

The size for the % Passing x mm and the percentage for the x %passes size data items can be set in one of two ways. If you wantthe values to be applied only to this port, double-click on the labelof the item you want to change. This brings into view an Enter NewValue window in which the required value is entered.

If you want to change the size for the % Passing x mm and/or thepercentage for the x % passes size data items values for all ports,right click on a blank area of the flowsheet to view the pop-upmenu and select Flowsheet and then Properties to bring theFlowsheet Definition window into view. The size for the % Passingx mm and the percentage for the x % passes size data items can beentered in the appropriate boxes in this window. (See section 4.6.3for more information on the Flowsheet Definition window).



The SizeDistributiondata tab

The Size Distribution tab contains the sizing data for the solidsflowing through the port. If experimental data are available forthese data they are entered in the appropriate data cells. The firststep is to enter the sizes to which the data relate. The size valuesare in millimetres. Note that if the required size distribution isdefined for the first equipment unit placed on a flowsheet, anyfurther unit placed on the flowsheet will automatically use thesesize data in the port data windows.

There are several options for entering the size data. The first optionis to use the √2 button on the port data window to place a √2 sizeseries in the Size column. The first step is to zero the size data bytyping a zero in the Top Size box and pressing Enter. As thewarning message will tell you, doing this will delete all size andsizing data. Then type the new top size in the Top Size box andclick on the √2 button. JKSimMet places a √2 size series of 30values from the user-defined top size down to zero. To truncate thesize list simply type a zero where required in the column. The usercan also edit individual values in the list as required.

Alternatively, any or all of the size values can be entered by typingthe values or copying and pasting them from another port datawindow. A useful shortcut is to store the most commonly usedsizing series in an Excel spreadsheet so that these data can becopied and pasted whenever required.

A Port Data Window with the Size Distribution tab displayed

The Top Size must be chosen so that no material is retained at thissize. Note that the sizes must be entered in descending order ofsize. If you try to enter a size which is larger than the size in thedata cell above it, JKSimMet will not accept the value.

The experimental sizing data should be entered next. Note that thesize distribution data are constrained such that their total is 100%.If you try to enter a value which causes the total to be greater than



100% one of two things will happen; either the incorrect value isnot accepted and the value in that data cell is unchanged or thevalue is accepted but the amount of material in the finest sizefraction with material in is reduced to maintain the total at 100%.

If any problems occur with entering the sizing data check that thedata already entered are correct. JKSimMet will calculate theamount of material in the pan or sub-mesh fraction to make thetotal 100%. If the value calculated by JKSimMet is not the same asthe value in your data, check the data which has been entered forkeying errors.

The Componentstab

If the user has defined a list of components to be used in massbalancing in the Mass Balance window then the Components tab ineach port data window will be configured to accept data. In thiscase the user can enter component data such as assay data for solidsflowing through the port. If experimental values are available forthese data they are entered in the appropriate data cells. Note thatthe component data are only used in mass balancing in JKSimMet.

A Port Data Window with the Components tab displayed

If no component list has been defined by the user the Componentstab will not contain any data cells.



The Set SD’sbutton

Estimates of the accuracy of the experimental data can be providedby entering data standard deviations (SDs) for the data. To do this,make the appropriate selectable tab active and selects SD’s in theData drop-down list so that the SD values can be seen in the dataarea. . There are two methods for the user to enter SD values forthe data. The first method is simply to type in the required SDvalues in each data cell in turn. The second method uses the SetSD’s button to apply a selected SD model to all of the data on thattab. In most cases users will use the two methods to enter SDs byapplying an SD model to all of the data and then fine tuning someSDs by typing new values in.

To apply an SD model click on the Set SD’s button to bring theSelect SD Values window into view.

The Select SD Values window lists a wide range of options forsetting SD models. Select an option by clicking on it and then clickon OK to close this window and return to the port data window.

The Whiten error model is useful for sizings in grinding circuits(other than SAG feed) and acceptable for assays (at percent levels)in mass balancing. The SD model is a generalised two term errormodel ie it uses a fixed and a proportional term to estimate assayerrors. These issues are also discussed in Chapters 5 and 6.



4.7.5 The Feed Data Window

The Feed unit is a specialised equipment item which is the sourceof feed additions to a flowsheet. The feed material can be dry solidsor solids plus water. As can be seen below, the Feed data windowis very similar to the standard port data windows.

Opening theFeeder datawindow

A Feed data window can be opened in two ways. The first methodis to place the cursor over the Feed icon on the flowsheet and right-click to bring the drop-down menu into view. Then move thecursor to select the word Equipment from the menu and left-click.The second method can be used to open the Feed data windowwhen the flowsheet is locked. In this case, double-clicking on thefeeder icon opens its data window.

The Feed data window has one feature in common with a standardequipment data window – the Name box where the user can definea name for the feeder. The remaining parts of the Feed data windoware the same as a standard port data window with Totals, SizeDistribution and Components tabs to access various groups of data.

Note that the Feed has only one port, a product port. As it is thesource of new material to be added to the circuit it does not have afeed port.



4.7.6 Editing the Feeder Data

The data entry procedure for the Feed follows the same pattern asfor the port data windows. The user should enter a name for theFeed in the name box and then enter the mass flow and sizing datawhich describe the feed material on the appropriate tabs. (Seesections 4.7.3 and 4.7.4 for more detailed information on enteringdata in port data windows).

4.7.7 The Water Feeder Data Window

The Water Feeder is a specialised equipment item which is thesource of water additions to a flowsheet. Note that the WaterFeeder has only one port, a product port. As it is the source of newwater to be added to the circuit it does not have a feed port. Waterfeeders can only be connected to the feed port of an equipmentunit.

Opening WaterFeeder window

A water feeder data window can be opened in two ways. The firstmethod is to place the cursor over the water feeder icon on theflowsheet and right-click to bring the drop-down menu into view.Then move the cursor to select the word Equipment from the menuand left-click. The second method can be used to open the waterfeeder data window when the flowsheet is locked. In this case,double-clicking on the water feeder icon opens its data window.

Water Feederwindow layout

The layout of the water feeder data window is shown in the pictureof the window below. As can be seen, some of the elements foundon the equipment unit data windows appear here, such as the Namebox and Model drop-down list. However, the layouts of theOperating Conditions tabs are unique to the water feeder datawindow.

Data tab for WaterAddition model



The features found in the water feeder data window are as follows:

Title bar The title bar displays the name of the water feeder.

Name box The user can enter a name for the water feeder inthis box. Note that this name will be used to identifythe equipment in various other tables in JKSimMetso it is advisable to use names which you canrecognise easily.

Model box Clicking on the model name in the box brings intoview a drop-down list of the three JKSimMetmodels which are available for the water additions toa circuit. The user can select the required model byhighlighting its name on the drop-down menu andleft-clicking.

Parallel Units The number of parallel units represented by thewater feeder icon is entered in this box. For mostpurposes this value can be left as 1.

Data transfer The four buttons in this area of the water feeder datawindow allow the user to transfer data to and fromJKSimMet and other programs by copying andpasting data to and from the clipboard. The buttonsperform slightly different functions as follows:









Data area The lower section of the water feeder data windowcontains the area where data about the wateraddition are entered. The contents of the sectionvaries between the three water addition modelswhich are available.



4.7.8 Editing the Water Feeder Data

Data entry for the water feeder is a simple procedure. As a first stepthe water feeder can be named by the user by typing the requiredname in the Name box and pressing Enter. The chosen name isused to identify the water feeder in various tables in JKSimMet andit makes sense to choose a name which describes the water additionpoint e.g. Cyclone feed water addition. The next step in the dataentry procedure is to select the required water addition model.

Selecting theWater FeederModel

The water feeder has three water addition models associated with itwhich JKSimMet uses in the Mass Balance, Model Fit andSimulation procedures. The user can select which model is used torepresent the water addition to the circuit by left-clicking on thedrop-down list labelled Model and highlighting the required modelto select it. Note that the contents of the data area of the equipmentdata window will change according to which model is selected.The water addition models are described below.

Feed Streamsmodel

When this model is selected the water feeder does not add anywater to the equipment unit to which it is attached. The watercontent of the feed to the equipment to which the water feeder isconnected, is controlled by the water contents of its feed streamsonly. There are no data to be entered by the user on the OperatingConditions tab for this model.

Water Feeder data window with Feed Streams model selected



Required % Solidsmodel

When this model is selected JKSimMet adjusts the water additionto obtain the required percent solids in the equipment feed. Theuser must enter the value of the required percent solids on theOperating Conditions tab.

This model is useful in simulations, where the user can select therequired percent solids for a feed port, e.g. a cyclone feed, andJKSimMet adjusts the cyclone feed water to cope with any changesin cyclone feed mass flows which are caused by other changes tothe flowsheet.

Water feeder data window with Required % solids model selected



Water Additionmodel

In this model the water addition is fixed at the value set by the user.The user must enter the value of the required water addition in theNew Water Addition box on the Operating Conditions tab.

This model is useful in mass balancing and model fitting where theuser often has measured water addition data to be incorporated inthe flowsheet. If the flowsheet data are being mass balanced theuser can also enter standard deviation (SD) values for the wateraddition.After a mass balance, the “calc” result needs to be copied manuallyto “Exp” for use in simulation and model fitting.

Annotating the Flowsheet JKSimMet Reference


4.8 Annotating the Flowsheet Overview JKSimMet allows you to annotate the flowsheet with three types of

information – equipment unit data or port data in InformationBlocks and user-defined text in Labels. These features areillustrated in the flowsheet shown below.

Access All of the annotation features are accessed through theConfigure/Assign Information Blocks and Labels window. Thiswindow is brought into view by clicking on the Configure/AssignInformation Blocks and Labels button on the JKSimMet toolbar.

The Ports tab of the Configure/Assign Information Blocksand Labels window

Each type of annotation is accessed by clicking on the appropriateselectable tab in the Configure/Assign Information Blocks andLabels window to bring its configuration table into view.

Port datainformation block

Equipment datainformation block

Label with textentered by user

JKSimMet Reference Annotating the Flowsheet


4.8.1 Adding Port Information Blocks

Each feed and product port can be annotated with its owninformation block. This block shows the name of the port to whichthe data apply and displays up to four items of data for that port.The user can select from a standard list the data items which appearin the information block. Note that the four items selected appear inall of the port information blocks on the flowsheet. In other words,the user cannot vary the types of port data displayed from one portinformation block to the next.

A Typical Port Information Block

Access the PortsInformation BlockConfiguration tab

Left click on the Configure/Assign Information Blocks and Labelsbutton on the JKSimMet toolbar to bring the Configure/AssignInformation Blocks and Labels window into view. Click on the tablabelled Port to make this the active tab.

Selecting the portdata for display

The first step in adding a port information block is to decidewhether to display one type of data (e.g. Experimental data only orSimulated data only) or to view two data types (e.g. Experimentaland Simulated) together.

Note that ore feeder and water feed data can be accessed via theequipment table – (Section 4.8.2)

List of port dataitems, up to four ofwhich can beselected for displayin the informationblocks.

List of ports forwhich informationblocks can bedisplayed

Drop-down list ofdata types to bedisplayed.



One data type The default setting is for one type of data to be displayed. Thismeans that the user can view the chosen data (e.g. experimental)for up to four different data items (e.g. TPH solids, % solids, Vol.Flowrate and % Passing size). The user can select the data type tobe displayed from the drop-down list that appears in the lower partof the Configuration area. The available choices are Exp, SD, Sim,Fit, Bal, Calc Bal SD and Error.

The next step in the configuration is to select up to four items fordisplay from the list of port data items. To select an item in the listsimply click on it. As an item is selected it will be placed in theinformation block and at the same time it is removed from theconfiguration list. If you make a mistake when selecting the dataitems simply click on the Clear button at the bottom right corner ofthe information block window. This will clear the entire contentsof the information block so that you can reconfigure its contents.

Add aninformationblock legend

Once you have configured the contents of the information block toyour satisfaction, click on the Apply button. This creates aninformation block legend which shows the data type selected in theinformation block title bar and lists the names of the data items inthe appropriate boxes.

A Typical Port Information Block Legend (One data type)

Select requireddata type fromdrop-down list

Name of data typeto be displayed.

Names of data item to bedisplayed in each box.



Placing aninformation blockon the flowsheet

To place the information block for a port on the flowsheet selectthe name of the port from the list at the left side of the window andthen click on the Add New Block button. The information blockwill appear on the flowsheet behind the legend information blockand may be dragged to the required position. Note that the name ofthe port to which the data apply is displayed in the title bar at thetop of the information block.

A Typical Port Information Block (One data type)

Adding Port information blocks to the flowsheet

Deleting aninformationblock

To delete the information block from the flowsheet simply click onthe Close button at the top, right corner of the information block.Note that when an information block is deleted it does not reappearimmediately in the list in the Configure/Assign Information Blockand Labels window. To make the deleted port appear in the listclose and then reopen the Configure/Assign Information Block andLabels window.

Name of port Data values (legendinformation blockshows which dataitems are displayed

Primary BM Combiner information blockhas just been added to the flowsheet andneeds to be dragged to its correct position



The alternative to viewing one data type for four data items in an information block is toview two data types for two data items. In other words the user can choose to display,for example, experimental and fitted data for two items such as TPH solids and %solids.

Displaying DualData Types ininformationblocks

To view two data types for two data items in the information blockthe user must click on the box labelled Allow Dual Data Types toplace a tick in the box. The Configuration area of theConfigure/Assign Information Block and Labels window willchange to display two drop-down lists from which to choose thedata type, as shown below.

The data type and data item selection procedures are the same asdiscussed previously but in the dual data type case the user mustchoose two data types (one from each drop-down list) and can onlyselect two data items to display.

When dual data type information blocks are being used, the title barof the legend information block shows the names of the two datatypes selected for display as shown below.

Typical Port Information Block Legendand Information Block for Dual Data Types

With the Allow DualData Types boxticked, two drop-down lists appear forselecting data types



4.8.2 Adding Equipment Information Blocks

Each equipment unit can be annotated with its own informationblocks. Each information block can display one or two items ofdata for that equipment unit. The user selects the data items whichappear in the information block from a standard list. Since the datato be displayed varies from one equipment type to the next, the usermust configure the information block for each unit individually.Note that more than one information block can be configured foreach equipment unit.

Access theEquipmentInformation BlockConfiguration tab

Left click on the Configure/Assign Information Blocks and Labelsbutton on the JKSimMet toolbar to bring the Configure/AssignInformation Blocks and Labels window into view. Click on the tablabelled Equipment to make this the active tab. Note that theinterfaces of the Port and Equipment tabs are similar; both have alist of the things for which an information block can be displayedon the left of the window and an information block configurationarea at the right side of the window.

The Equipment tab of the Configure/Assign Information Blocksand Labels window

Selecting theequipment unitfor display

The first step in adding an equipment unit information block is toselect the required equipment unit from the list at the left of theConfigure/Assign Information Blocks and Labels window. Left-click on the name of the unit to select it.

Selecting theequipment datafor display

Once a unit has been selected, a list of the data items for thatequipment unit type is displayed in the Configuration area of thewindow. The user can select one to two items from this list fordisplay in the information block. To select a data item simply clickon its name and the data item will appear in the information blockabove the list. To change the selected data items the user must usethe Clear button to remove all selected items from the informationblock and to select the required ones from the list again.

List of equipmentunits on flowsheet

When an equipmentunit is selected, thedata items availablefor display are listedhere

Equipment unitinformation blockwill display one ortwo data items



Add an equipmentunit informationblock

Once you have configured the contents of the information block toyour satisfaction, click on the Apply button to confirm theselection. Click on the Add New Block button to place theequipment unit information block on the flowsheet. This creates aninformation block which shows the names of the data items andtheir values and also shows the name of the equipment unit in theinformation block title bar.

A Typical Equipment Information Block

The information block can be dragged to the required position onthe flowsheet. If you want to display more data for an equipmentunit on the flowsheet a second (or third or more) information blockcan be configured for the unit and added to the flowsheet byrepeating the standard procedure described above.

Deleting aninformationblock

To delete the information block from the flowsheet simply click onthe Close button at the top, right corner of the information block.

Water Feederequipment unitinformationblocks

The Water Feeder equipment unit is a specialised form of theequipment unit. The data items which can be displayed in itsinformation block include information about the experimental andcalculated water additions and the SD and weighted error of thewater addition.

Two information blocksconfigured for ball mill.

List of cyclone data items displayed, readyto configure a second information block.

Name of equipment unit

Names of equipment dataitems displayed

Data values



4.8.3 Adding Labels to the Flowsheet

The flowsheet can be annotated with labels in which the user cantype text. The user can add as many labels as required to theflowsheet and the format of each label can be configured from arange of formatting options (e.g. background colour, with/withoutborder). Note that once a label has been placed on the flowsheet itcannot be edited.

Access the LabelConfiguration tab

Left click on the Configure/Assign Information Blocks and Labelsbutton on the JKSimMet toolbar to bring the Configure/AssignInformation Blocks and Labels window into view. Click on theLabels tab to make this the active tab.

The Labels tab of the Configure/Assign Information Blocksand Labels window

Enter the labeltext

To enter the text which you want to display in the flowsheet labeldouble click the default text in the Label Text box to highlight itand then type in the required text. As you type, the text appears inthe Preview area of the window. The position of the text in the boxcan be adjusted by using the Enter key to add blank lines and thespace bar to add extra spaces as required.

Format the label The user can select the alignment of the text from the choices in theText Alignment area of the window.

The Label Properties area allows the user to wrap text in the labelby clicking in the Word Wrap On box to place a tick in the box.Similarly the user can place a border around the label by ticking theLabel Border On box.

The user can use the Autosize function to set the height and widthof the label box automatically. Alternatively, if the Autosize box isnot selected the user can type the required dimensions of the textbox into the Height and Width boxes which are situated above thePreview area of the tab.

Preview of labelis displayed here

Change the labelbackground colourby double clickinghere

Type labeltext here

Select formatfrom theseoptions



Select the labelbackground colour

The user can change the default background colour of the label bydouble clicking on the Label Background Colour panel of thewindow. This brings up the colour palette from which the user canselect an existing colour or create a custom colour for the label.

Add the label tothe flowsheet

Once you have configured the label to your satisfaction, click onthe Add Label button to place the label on the flowsheet. The labelcan be dragged to the required position on the flowsheet. Note thatonce the label has been placed on the flowsheet its format andcontents cannot be edited or changed in any way

Delete a labelfrom theflowsheet

A label can be deleted from the flowsheet by double-clickinganywhere on the label.

Click on this button to add thelabel to the flowsheet once youhave finished formatting it.

The Preview area showshow the label will appearon the flowsheet.

JKSimMet Reference Graphing in JKSimMet


4.9 User-Configured Graphing – the GraphDefinition Window

Overview JKSimMet allows you to graph a wide range of data. The user has achoice of graphing tools – the Generic Graph Config tool whichallows each user to configure graphs to their requirements and theQuick Graph tool which uses a JKSimMet-defined format toquickly produce a size distribution graph. The features of the userconfigured graphing are discussed in detail below, while QuickGraph is detailed in section 4.10

The user-configured graphing system is accessed by left-clicking onthe Generic Graph Config button on the main JKSimMet toolbar.This opens the Graph Definition window. Note that when theGraph Definition window is opened for the first time in a project, aGraph window displaying the default data is also opened. Thisdefault graph window can be closed while the user configures therequired format and data definitions.

4.9.1 Define the Graph Format

Creating aGraph Format

By creating named Format definitions users can save time whencreating graphs in the future by re-using these previously definedgraph formats.

To create a new format, left click on the New Format button at thetop of the Graph Definition window. The format is then configuredin the Labels and Axes and Data Interpretation section of theFormat tab.

The Graph Definition window with the Format tab selected

Graphing in JKSimMet JKSimMet Reference


Labels Labels for the graph as a whole and for the X and Y axes arespecified by typing in the text for the labels and using the Font andFont Size drop-down lists to format them as required. To type textinto a label, double-click on the existing text to highlight it andthen type the replacement text. The text can then be set to therequired typeface and size by selecting the required items from theFont and Font Size drop-down lists.

Axes and DataInterpretation

The axes and data interpretation section of the Format tab definesthe ranges and scales of the axes.

The components of the data interpretation section are:

Min and Max Defines the value at the origin (Min) and themaximum value (Max) for each axis. Tochange the value, highlight the existingnumber and then type the new value in itsplace.

Caution: Watch out for zero points whichcannot exist with logarithmic scales.

Scale Factor Can be used to scale the axes, for examplefrom millimetres to metres or from metric toimperial. The usual value is 1.0. To changethe value, highlight the existing number andthen type the new value.

Plot Style Allows the user to choose the axis format aseither linear or logarithmic. The plot style ischanged by double clicking on the Plot Stylebox to bring a drop-down list into view.

The required option is selected from the list byhighlighting it and then left-clicking.

Grid On JKSimMet will add grid lines to the X or Yaxes if a tick is placed in the appropriate boxby clicking on it. Gridlines can be removed byclicking on the box again to remove the tick.

Number Format The format of the numbers at the tick markscan be changed by selecting the requiredformat from the drop-down list in this column.The choices are Decimal, Scientific (Nx10n) orEngineering.



Re-using anexisting GraphFormat

Re-using previously defined graph formats saves time re-enteringlabels etc. when configuring graphs.

To use an existing format, left click on the Graph Format box at topof the Graph Definition window. This brings into view a drop-down list of all the graph formats which have been defined in thecurrent project. Move the cursor to highlight the required formatand left-click to make this the current format.

The Graph Definition window with the drop-down listof user-defined Graph Formats visible.

4.9.2 Defining Data for Graphing

The user must define which data are to be plotted on the graph.This is done by defining named Graph Data Sets using the PortData and Equipment Data tab sections of the Graph Definitionwindow. A Data Set can contain port data only, equipment dataonly or a mixture of port and equipment data as appropriate. Amaximum of 15 items can be plotted on each graph.

Select otherexisting user-defined formatsfrom this list.



The Graph Definition window with the Port Data tab selected.

Creating aGraph Data Set

Each definition of a data set to be plotted on a graph is named bythe user and can be recalled and re-used within the JKSimMetproject. By creating named Graph Data Sets users can save timewhen creating graphs by re-using these previously defined datasets.

To create a new data set, left click on the New Data button at topof the Graph Definition window. The data set is then configured inthe Data Selection sections of the Port Data and Equipment Datatabs.

Note that the items which can be plotted on a graph includeequipment unit data such as classifier efficiency curves, ball millappearance functions, as well as the size distribution of the streams.For the sake of simplicity, the Port and Equipment Data tabs arediscussed separately here.

Port Data

The various data cells in the Data Selection area of the Port Datatab are discussed below. Each column in the Data Selection area isused to configure the data presentation for one port. Note that theuser can select an individual port more than once in the DataSelection area. For example, if the user wanted to present theexperimental data for a port with green dots and the simulated datawith a blue line, it would be necessary to configure this format intwo separate columns.

The defaultgraph data set isdisplayed here



Port Selection The first row of the Data Selection area is labelled Port and it is inthis row that the user defines the name of the port whose data are tobe plotted on the graph. Double click on the Port cell to view a listof the port names on the current flowsheet. Move the highlight toselect the required port and press Enter to make the selection.

Note that once a port name has been selected, JKSimMet places astandard set of choices in the formatting cells in that column. Theuser can edit these if required.

To remove a port from the selection to be graphed and clear all theother selections in its column, double-click on the Port cell andselect None from the drop-down list of port names.

Format The Format defines which type of plot is presented for the port.Double-clicking on the Format cell brings into view the drop-downlist of available graph plotting formats.

Move the highlight to the required format and left-click to selectthat format.

Data Move the highlight to the Data row and double-click to view thedrop-down list of data types which can be selected for graphing.

If the single data type options are selected (Exp, Sim, Fit or Bal),both the line and point markers for these data represent the chosendata type. However, when the paired data types are selected forplotting (e.g. Exp & Sim), the data point markers represent theexperimental data and the line represents the second item of thedata pair (Fit, Sim or Bal as appropriate). This feature is useful forcomparing the calculated data with the experimental data.

Line The Line option allows the user to choose the style of line whichwill be used to represent the data. The choices are accessed bydouble-clicking on the Line row cell and selecting the required linestyle from the drop-down list. Note that the user can choose tohave no line plotted by selecting the option None on the list.



Point JKSimMet places a marker at every data point on the graph. Theuser can select the style of marker to be used for the port from a listof point marker styles. The choices are accessed by double-clickingon the Point row cell and selecting the required marker style fromthe drop-down list. Note that the user can choose to have no pointmarker plotted by selecting the option None on the list.

Colour The user can choose what colour is used to display the line andpoint markers on the graph. To view the list of available colours,double-click on the Colour cell. Move the highlight the requiredcolour and left-click to select it.

Spline The user can choose to use spline interpolation for the curve whichis drawn between the data markers for each port. To use splineinterpolation left-click on the spline box to place a tick in it.

X Min and X Max The user must define the minimum and maximum plotting rangevalues (along the X axis) for the data. These values are typed intothe appropriate cells

Equipment Data

Many of the formatting cells on the Equipment Data tab performthe same function as in the Port Data tab. Only those cells whichperform different functions are discussed below.



Each column in the Data Selection area is used to configure thedata presentation for one item of equipment. Note that the user canselect an individual item of equipment more than once in the DataSelection area. For example, if the user wanted to present thecorrected efficiency of a cyclone with red dots and the reducedefficiency with a blue line, it would be necessary to configure thisformat in two separate columns.

The Graph Definition window with the Equipment Data tab selected.

Equipment The first row of the Data Selection area on the Equipment Data tabis labelled Equipment and it is in this row that the user selects theitem of equipment whose data are to be plotted on the graph.Double click on the Equipment cell to view a list of the equipmentnames on the current flowsheet. Move the highlight to select therequired item and left-click to make the selection.

Note that once an item of equipment has been selected, JKSimMetplaces a standard set of choices for that particular equipment typein the formatting cells in that column. The user can edit these ifrequired.

To remove an equipment item from the selection to be graphed andclear all the other selections in its column, double-click on theEquipment cell and select None from the drop-down list ofequipment names.

Function The Function cell defines which type of data function is presentedfor the equipment. Double-clicking on the Function cell brings intoview the drop-down list of available functions. The list of functionswill change according to the type of equipment which has beenselected.

Move the highlight to the required function and left-click to selectthat function.

The remaining formatting cells perform the same function as thoseon the Port Data tab and have been discussed in the previous pages.



4.9.3 Viewing the Graph

Once the user has defined a graph format and a data set, the graphcan be viewed by clicking on the View/Refresh Graph buttonat the top, right corner of the Graph Definition window. This opensthe Graph window with the selected data plotted.

The Graph window

The Graph window has several features which allow the user tomake changes to the appearance of the graph without returning tothe Graph Definition window and to print or copy the graph. Theseare accessed via the buttons on the Graph window toolbar.

The Display X Axis Grid and the Display Y Axis Grid buttonsallow the user to add and remove gridlines from the graph.

The Display Legend button adds or removes the legend. Note thatif the legend overlaps the plot area of the graph this can beovercome by making the Graph window wider.

The Edit button makes the Graph Definition window the activewindow, allowing the user to edit the format or data definitions.

The Refresh button redraws the graph. This allows the user toupdate the graph after changing data or formats.

The Copy to Clipboard button copies the graph to the clipboardfrom where it can be pasted into word processing documents,presentations etc.

The Print Graph button immediately prints the graph to thecurrently selected printer. The printed graph will have the sameappearance (overall size, relative dimensions etc.) as it does in thegraph window. The size of the graph can be changed by adjustingthe Graph window as required. Note that a message window mayappear while JKSimMet spools the graph to the printer.

The name of thedata set is shownin the Graphwindow title bar

JKSimMet Reference Using Quick Graph


4.10 Using Quick Graph

Overview JKSimMet allows you to quickly view size distribution data in astandard form via the Quick Graph window. The user can change alimited range of features of the Quick Graph such as adding orremoving gridlines, plotting data as percent retained or cumulativepercent passing etc. If more choices are required in defining thegraph format the Graph Definition window should be used.

4.10.1 Opening the Quick Graph Window

To view a Quick Graph for a stream the user must first place thecursor over the equipment unit to which the stream’s port isattached and right-click to view the drop-down menu.

Selecting the Graph option from the menu brings the Quick Graphwindow into view. The name of the equipment unit to which thedata relate is shown in the title bar of the Quick Graph window.Note that, by default, the graph plots the size distribution data forall of the ports connected to the equipment unit as a cumulativeweight percent passing size format. These settings can be changedusing the buttons on the Quick Graph window toolbar.

Select the Graphoption to viewthe Quick Graphwindow

Using Quick Graph JKSimMet Reference


4.10.2 The Quick Graph Toolbar

The Quick Graph feature is designed as a means for users toquickly view on the screen a standard graph of size distributiondata. This helps users to compare size distributions and to checkthe sizing data for discontinuities. The type of data which areplotted and a limited range of the Quick Graph features can bechanged via the buttons on the Quick Graph window toolbar.

The functions of these buttons are described below.

The Show Single Port button displays the size distribution data forone port only on the graph. The user can select which port’s sizedistribution is displayed using the Single Port Selection list whichis described below.

The Show All Ports button displays on the graph the sizedistribution data for all of the ports connected to the equipmentunit.

The Display X Axis Grid and Display Y Axis Grid buttons allowthe user to add and remove gridlines on the graph. If the gridlinesare switched on, clicking on the button again removes the gridlinesfrom the graph.

The Sizing Format drop-down list allows the user to select theformat for plotting the size distribution data. The options are% Passing (cumulative weight % passing), % Weight (weight %retained) and % Retained (cumulative weight % retained).

The Single Port Selection drop-down list allows the user to selectwhich of the ports attached to the equipment unit has its sizing datadisplayed on the graph when the Show Single Port button isselected. The list of port names changes to reflect the type ofequipment unit selected. Note that this list is only accessible whenthe Single Port button is selected; when the Show All Ports optionis selected this drop-down list is inactive (greyed out).

The Data Type drop-down list allows the user to select the type ofdata to be plotted on the Quick Graph. The choices areExperimental, Calculated, Absolute Error and Exp and Cal (bothexperimental and calculated data plotted on the graph). Note thatthe type of data plotted as Calculated (mass balanced, fitted orsimulated) depends on which JKSimMet tool is selected at thetime.

JKSimMet Reference Using Quick Graph


The Print Graph button immediately prints the graph on thecurrently selected printer. The graph bitmap image is enlarged to fitthe page and as a result the printed graph can appear jagged. If asmoother printed graph is required, copy it to the clipboard andpaste it into a suitable file for printing (e.g. a word-processingprogram).

The Copy to Clipboard button places a copy of the graph on theClipboard. This can then be pasted into other programs such as aword processing document or a presentation file.

4.10.3 Features of Quick Graph

The Quick Graph window has some features which help to user toanalyse the data which are presented on the graph. These aredescribed below.

Viewing the portdata window

Quick Graph provides a shortcut for users to quickly access thedata window for any of the ports whose data are plotted on theQuick Graph. To do this the user simply clicks on the line whosedata window he wishes to examine. This brings that port datawindow into view.

Identifying lineson the graph

While Quick Graph does not provide a legend, the user can find outwhich port a line represents on the Show All Ports graph bypointing at the line with the cursor. When this is done a pop-uplabel displays the name of the port to which the data relate.

Identifying datapoints on thegraph

On the Show Single Port graph the user can find out what the Xand Y values are at any data point by pointing at the data markerwith the cursor. When this is done, a pop-up label displays the Xand Y values at that data marker.

Using Overview JKSimMet Reference


4.11 Using Overview

Overview JKSimMet allows you to collate a wide range of data using theOverview feature. An Overview table provides a summary of thestream data for any or all of the ports on the flowsheet. Chapter 3provides a tutorial on the use of Overview.

Access The Overview feature is accessed by clicking on the OverviewConfig button on the main JKSimMet toolbar. This brings theOverview window into view. Note that the user can have as manyoverview windows open as required, with each displaying adifferent overview configuration.

A typical overview window with default settings displayed

When first opened, the overview window displays a default set ofdata. The user can define one or more overviews to display therequired port information.

4.11.1 The Overview Window

The overview window consists of two main areas, the Overviewtoolbar and the data display area. The overview toolbar contains anumber of buttons which perform the functions described below.

The Select List is a drop-down list of all of the overviewconfigurations which have been set up for the current flowsheet.

The Name box is a text box where the user can type a name for thecurrent overview.

The New Overview button adds a new overview to the select list.

JKSimMet Reference Using Overview


The Delete Overview button deletes the currently selectedoverview. A dialogue window requires the user to confirm that theoverview is to be deleted.

As the name implies the Insert column and Delete Column buttonsadd and delete a data column in the overview table.

As their names imply, the Insert Row and Delete Row buttons addand delete port data rows in the Overview table.

The Recovery box allows the user to set the overview table inRecovery Mode where recovery data are presented in place of theactual mass flow data.

The Copy to Clipboard and Copy Grid to Clipboard buttons copythe overview table to the clipboard. This allows the data to bepasted into other software packages.

The Print Preview button opens the print preview window,allowing the user to see the overview table as it will be printed.

The Print button prints the overview table on the currently selectedprinter.

4.11.2 Configuring an Overview Table

The first step in configuring an Overview table is to create a newoverview and to name it.

Create a newOverview

To create a new Overview click on the New Overview button onthe overview window. This displays a default data set which showsfour data columns for all of the ports on the flowsheet.

Name anOverview

JKSimMet allows the user to create as many overviews as requiredand therefore it is useful to name each one so that it may berecalled from the Select List for display. To name an overviewclick on the text in the Name box to highlight it and then type in thenew name. Press Enter to register the change. Note that the namenow appears in the Select list box and also in the title bar of theoverview window.

The next step in configuring the overview is to decide which data are to be displayed inthe table and in which order. Before doing this it may be necessary to make theEquipment and Port columns wider in order to read the names of these items. If thewindow is too small to view all of the data the user can adjust the window to therequired size.



Make a datacolumn wider

The width of each column in the overview table can be adjusted byplacing the cursor over the right border of the title cell for thecolumn and clicking and dragging the border until the column isthe required width.

Resize theOverview window

The Overview window can be resized by clicking and dragging anyside or corner of the window.

The user can arrange the order in which the port names appear in the table by selectingthe required port name in each row. Firstly the user must select the equipment unit towhich the port is attached and then the name of the port itself.

Select anequipment unitfor display

To select an equipment unit for display in the list double click onthe appropriate cell in the column labelled Equipment. This bringsinto view a drop-down list of all the equipment units on theflowsheet. Move the cursor to highlight the required equipmentunit name and press Enter to register the change. If a row of blankcells is required to help make the table easier to read the user canselect None from the list of equipment names. All other cells in thisrow will remain blank.

Select a port namefor display

Once an equipment unit has been selected in the Equipmentcolumn the user can select the required port. To do this, double-click on the appropriate cell in the column labelled Port to bringinto view the drop-down list of ports associated with the equipmentunit. Move the cursor to highlight the required port name and pressEnter to register the change.

The default overview table may contain more or less data rows than are required. Rowscan be deleted or added as required using the Delete Row or Insert Row buttons.

Delete a row fromthe overview table

To remove a row of port data from the list in the overview simplyclick anywhere in the row and click on the Delete Row button. AJKSimMet dialogue window will ask you to confirm that you wishto delete this row. Click on Yes to remove the row from theoverview table. More than one row can be deleted by highlightingtwo or more adjacent rows and using the Delete Row button asdescribed above.

Add a row to theoverview table

To add a row to overview table click anywhere in a row in the tableand then click on the Insert Row button. Note that the new row isalways added immediately above the cursor position and by defaultthis row contains data from the first port of the first unit in theequipment unit list. You can select the information to be displayedin the new row by clicking on the relevant cells and selecting fromthe drop down lists.



Once the list of port names has been defined the next stage in configuring the overviewis to define which data are displayed in the data columns. All of the data which appearon the Totals tab of the port data window (e.g. TPH solids, % solids) are available fordisplay in the overview table. If component data have been entered for a port these canalso be selected for display. As well as defining what data items are displayed the usermust also define what data type (e.g. experimental, fitted etc.) is displayed in eachcolumn. The user can configure as many data columns as required to display the portdata.

Select a data itemfor display

Each column displays the values of a selected data item. To definethe data item place the cursor in the title cell at the top of the datacolumn and double click. This brings into view the drop-down listof all available data items.

Move the highlight to select the required item and press Enter toconfirm the selection. Note that an item can be selected in morethan one column. This allows the overview to display, for example,one column with experimental data, one with data SDs and onewith fitted data. Selecting the option None from the drop-down listresults in all other cells in the column being blank (a feature whichcan help to make large tables easier to read).Note that the available size markers are set from the FlowsheetProperties window.

Select acomponent namefor display

If the Component data item has been selected at the head of acolumn the user must select the name of the component in thesecond row of the title section for the column. To select thecomponent name double click on the second row cell in the columnto view a list of components available for display. (The list ofnames will vary according to the component names which the userhas defined). Move the highlight to select the required componentand press Enter to make the selection.

Note that the second row cell remains blank if Component has notbeen selected as the data item.



Select a data typefor display

Each data item has several data types associated with it and the usercan choose which of these is displayed in each column. Doubleclicking on the third row cell in the column brings into view thedrop-down list of data types.

Move the highlight to select the required component and pressEnter to make the selection.

Add a datacolumn to theoverview

Clicking on the Insert Column button adds a new data column tothe overview table. Each new column is added to the left of thecursor position. The newly added column is configured withexperimental data for TPH solids and so must be configured to theusers requirements.

Remove a datacolumn fromthe overview

A column can be deleted from the overview table by placing thecursor anywhere in the column and then clicking on the DeleteColumn button. A JKSimMet dialogue window will you to confirmthat you want to delete this column. Click on Yes to delete thecolumn. More than one column can be deleted by selecting two ormore adjacent columns and using the Delete Column button asdescribed above.

4.11.3 Recovery Mode

The overview window can also display recovery data for theappropriate data items. Clicking on the Recovery box to place atick in it changes the overview window to recovery mode, (asdenoted by the words Recovery Mode in the title bar). Conversely,removing the tick from the Recovery box returns the overview toits normal display mode.

Note that recovery values are only presented for TPH solids, TPHwater, volumetric flowrate data and for component data. Any otherdata columns in the overview table remain blank in recovery mode.



A Typical Overview Window in Recovery Mode

The stream port with respect to which all of the recovery values arecalculated is indicated by its name being shown in bold text in thetable. This port is known as the recovery basis port. The defaultrecovery basis port is the circuit feed.

Change therecoveryreference stream

The user can change the recovery basis port by placing the cursorover the name of the new recovery basis port in the overview tableand right clicking. A JKSimMet dialogue window will ask you toconfirm that the chosen port is to be the basis for the recoverycalculations. Click on Yes to confirm the change. The recoveryvalue sin the overview table will change to reflect the change inrecovery basis.

Printing in JKSimMet JKSimMet Reference


4.12 Printing in JKSimMet

Overview JKSimMet provides the facility to print data, graphs and theflowsheet. The basic procedure is the same, regardless of whichitem you want to print.

Printing theFlowsheet

The flowsheet can be printed in colour or black and white to theprinter or copied to the clipboard. Select File from the main menufollowed by Print Flowsheet and select the desired option.

PrintingEquipment andPort Data

To print individual equipment or port data, the window containingthe required data must be the active window. Once the requiredwindow is active, click on the Print button on the JKSimMettoolbar. This will bring the print preview window into view toallow the user to check that the appearance of the printed documentis satisfactory.

Print Preview forCyclones equipmentdata window

JKSimMet Reference Printing in JKSimMet


Note that the printed format allows the user to see all of the datathat are contained on all selectable tabs in the data window. Thedata which are displayed on separate tabs in the window are printedin consecutive areas of the printed data.

It is worth checking that the columns in the printed tables are wideenough for the data values to fit. If the columns are too narrow,close the print preview window, make the column in the datawindow wider and then open the print preview window again.

Print Previewwindow

The Print Preview window which opens when the Print button isclicked shows how the printed form of the data will appear.

By default, the print preview window shows the printed page at25% of full size. The user can view the print preview at othermagnifications by selecting the required view from the Zoom drop-down list.

Similarly, the user can change the orientation of the paper byselecting the required orientation (portrait or landscape) from theOrientation drop-down list.

The print preview window can be resized by dragging its lowerright corner. The example below shows the Cyclones print previewwindow from the previous figure which has been zoomed to 100%and resized to show all of the data.

Print Preview window at 100% zoom factor with window resized to view all data

To print the data asshown click on thisPrint button

Printing in JKSimMet JKSimMet Reference


If the printout comprises more than one page the user can movebetween pages by clicking on the Next Page or Previous Pagebuttons.

Once the print preview is satisfactory, click on the Print icon in thePrint Preview window to print the data. To remove the PrintPreview window from the screen close its window.

Printing Overviewtables

The user can configure one or more Overview tables to summarisedata selected by the user (see section 4.11 for details of theOverview features). Printing the overview table follows thestandard procedure of making the overview window the activewindow and then clicking on the Print button on the JKSimMettoolbar. This brings the Print Preview window into view andallows the user to check that the appearance of the printeddocument is satisfactory. Make any adjustments required and thenclick on the Print icon on the Print Preview window to print thedata.

PrintingQuick Graphs

The Quick Graph feature allows user to create size distributiongraphs for the feed and products of each equipment unit. Thesegraphs are printed by clicking on the print button on the toolbar ofthe Fast Graph window. Note that the graph prints as a bitmap andtherefore text and graphics can appear with jagged edges. A lessjagged printout can be obtained by using the Copy to Clipboardbutton, pasting the graph image into a word processing program(e.g. MS Word) and then printing

Quick Graph window showing Print button

To print thegraph as shownclick on thisPrint button

JKSimMet Reference Using Report


4.13 Using Report

Overview JKSimMet provides a Report feature to generate printed reports ofthe results of mass-balancing, model fitting and simulation work.The Report window is accessed by clicking on the Report button onthe main JKSimMet toolbar.

Each printed report is fully configurable by the user who mustselect the data to be printed for any or all of the ports or equipmenton a flowsheet. There is no limit on the number of reports whichcan be created by the user for each flowsheet. A useful aspect of thereport tool is the ability to create any number of reportconfigurations which can be used to generate printed outputs asrequired. Note that unlike the overview tables which present portdata only, the Report outputs can include equipment data ifrequired.

Each report can be readily viewed in a print preview window andthen printed and thus provides the ideal mechanism for producingresults in a format suitable for reports or presentations. The data inthe reports can also be exported from JKSimMet in a range offormats (e.g. tab-delimited or comma-delimited text files) using theoptions available in the report Print Preview window.

The first stage in preparing a report configuration is to create a newreport.

Create a NewReport

To create a new report configuration click on the Create NewReport button in the Report window. This brings into view atable which lists all of the ports and equipment items on the currentflowsheet. Note that in the default configuration none of the itemsin the grid are currently selected.

Using Report JKSimMet Reference


Name a report To name the new report format double-click in the Name box tohighlight the default name of the report configuration and then typein a new name for the report. Press Enter to confirm the namechange. The new name will now appear in the Report list and alsoin the title bar of the report window.

Setting the sizingdata format

The user can choose the format which is used to present any sizedistribution data in the report. To do this click on the Format drop-down list and select the required sizing format from the list.

Selecting Datafor the Report

The user must select the equipment and port items whose data areto be printed in the report. To do this the user can click on the boxnext to the name of each item to place a tick in the box.Alternatively, if all items listed in the window are to be included inthe report, click on the Select All Items button at the top of thereport window. To remove an item from the report simply click onthe items box again to delete the tick.

Using a CircuitSelect list

A shortcut for selecting ports and equipment for inclusion in thereport is to use the circuit select list option. If this is ticked the usercan choose from the drop-down list one of the Select lists whichwere defined as part of the simulation, model-fitting or massbalancing procedure. The items from the flowsheet which wereincluded in the select list are automatically ticked for inclusion inthe report. This feature is useful when working with large, complexflowsheets.

The Print Whatlist

The report window has a Print What drop-down list which allowsusers to print port data only, equipment data only or to print both.This list allows users to (temporarily) not print port or equipmentdata items without having to remove the ticks from all those itemsin the list.

Selecting DataTypes for theReport

To select the type of data to be listed in the report (e.g. Exp, Simetc.) place a tick in the box next to the name of the required datatypes in the Data types to print area of the Report window. Theuser can select as many data types as required for inclusion in thereport.

Selecting Errordata for inclusionin a report

The user can choose to include the data error in a report by placinga tick in the Error box in the Error Type area of the Report window.The user must then select from the adjacent drop-down list theparticular error that is to be included in the report. The error data isuseful when working on fitting or mass-balancing data.



Selecting Portdata

If port data have been selected for inclusion in the report the usercan choose to print the Totals data and/or the size distribution datafor the ports by placing a tick in the appropriate boxes in the Portdata to print area of the Report window. Note that if Componentdata have been entered, these can also be selected for inclusion inthe report here. If component data have not been entered, thisoption is inactive (as shown here).

Previewing areport printout

Once you have configured the report to your satisfaction, click onthe Print Preview button to view the report as it will be printed.By default, the Print Preview window opens at Page 1 of theprintout with the Zoom setting at 25% of normal size. The user canchange the Zoom setting using Zoom drop-down list and if requiredcan resize the Print Preview window by dragging any edge orcorner.

The Next Page and Previous Page buttons on the Print Previewwindow toolbar allow the user to view all of the pages in the report.

Printing thereport

To print the report simply click on the Print button on the PrintPreview window toolbar. Alternatively the report can be printeddirectly from the Report window by clicking on the Print button onthat window’s toolbar.

Preparing aSummary report

The Report window has a box marked Summary. When this box isticked, the Report feature uses a summary mode to present the portand equipment data in the printed report in a different format to thestandard format. The user can choose to use whichever mode suitstheir requirements.

In the case of the port data, the Summary mode prints all of the dataof a given type (e.g. Experimental) for all ports in one table. Eachdata type selected is printed as a separate table, with all ports listedin each table. This compares with the normal report mode whichprints the data for each stream on a separate page, with all datatypes for each stream being listed on this one page for each stream.

This difference between the Summary and normal mode isillustrated in the examples of Print Preview windows shown belowEquipment summary formats provide a more compact output of keyequipment data..



Print Preview Window showing Summary report data format

Print Preview Window showing normal report data format



Exporting datausing Report

A useful feature of the Report Print Preview window is the abilityto export data in report form from the simulator in a variety offormats. Four buttons on the Print Preview window toolbarprovide the following data export features:

Copy data to Clipboard for pasting into other applications.

Save the data as a tab-delimited file* (suitable for importing into aspreadsheet such as MS Excel).

Saves the data as a comma-delimited file* (suitable for importinginto a spreadsheet such as MS Excel or a word processingapplication such as MS Word).

Saves the data as a text file*.

These data export options allow the user to transfer data to otherapplications for preparation of presentations and reports.Note that once any of these file types has been opened, furthersaves will append data to it. That is, records of several simulationsin sequence can be accumulated for comparison.



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Model Fitting Model Fitting


CHAPTER 5

MODEL FITTING

Introduction to Model Fitting Model Fitting


5. MODEL FITTING

5.1 Introduction to Model Fitting

Purpose Chapter 5 describes how to use the JKSimMet model-fitting mode.Model fitting allows JKSimMet to be fine-tuned to each specificplant and operating condition, or even to particular ore types. Itdoes so by adjusting selected model parameters on the basis ofsystematic differences between measured product data andsimulation predicted product data.

The model fitting procedure can take into account any measuredflowrates and estimates of their accuracies.

Overview For both plant designer and plant operator, model fitting isprimarily concerned with the collection of accurate experimentaldata, at either pilot or full plant scale. The model fitting processprovides a powerful means of data examination or assessment aswell as the compression of thousands of data points into a fewparameters.

The parameters characterise how a particular ore behaves in aparticular plant. This characterisation can be used to find theoptimum plant settings with respect to various criteria, or even tofind an optimal plant configuration to achieve stated objectives.

As with all data analysis or prediction processes, however, thequality of the output is strongly dependent on the quality of theinput. The computer jargon for this phenomenon is GIGO orGARBAGE IN - GARBAGE OUT. A serious difficulty with allrealistic simulation systems like JKSimMet is that they willproduce very plausible looking nonsense from rubbishy data.

Hence, just as the spreadsheet is not a replacement for theaccountant, JKSimMet is not a replacement for a metallurgist orprocess engineer. There is no substitute for professional expertiseor experience, especially in the collection and analysis of largequantities of data. JKSimMet provides such a professional with atool of enormous power.

The general procedure is for model fitting is:

• collect data• analyse data• optimise plant using models• adjust plant• collect data to confirm

and start the cycle again.

Model Fitting Data Collection


5.2 Data Collection

This section is not essential for learning how to drive the model-fitting program. However, it is highly relevant to using the modelfitting system, and should be studied in detail before gathering datafor model fitting.

The data entry menus provide a guide to the unit dimensions andoperating variables which should be recorded during each test. Thestream data or feed stream data menus provide a guide to whatshould be measured wherever possible.

Flowrates Flowrate measurements are very useful indeed. Hence, calibrationof all flow measurement devices (weightometers, flow meters, etc.)is important. Whenever possible, try for an independent flowratecheck. In small or pilot plants, time and weigh a known volume ofmaterial.

Sample Analysis Stream size distributions are crucial characteristics for many of theJKSimMet models. Therefore:• use a set of sieves that you can trust,• use the same set of sieves for sizing all of the samples in each

test (sieves can have variations and holes!).• use a 2 sieve series (size fractions can always be combined

later for convenience)• sieve to the top of coarse sizes, ie. less than 5% on top screen

and as close to the bottom as possible.

Percent Solids The percent solids of a slurry as measured with a Marcy scale aresubject to error, due to solids density variations in the circuit. Suchvariations are common in cyclone underflow streams. Therefore,percent solids determined from wet and dry sample weights arepreferred.

Steady State JKSimMet is a steady state simulator. Hence, models can mostusefully be fitted to data which were taken at steady state. Thereare two practical approaches to this problem:

• Take a series of regular samples (every 15 minutes say) andcombine them to make composite samples which cover a periodwhich is long (several hours) compared with circuit fluctuations.

• Alternatively, watch the trends and, when you are convinced thecircuit is stable, take simultaneous samples of each point.Recheck the trends. If not stable, discard the samples and tryagain.

Data Collection Model Fitting


If circuit variations are a serious problem, sample and fit oneprocess unit at a time. JKSimMet can be used to combine the unitsand predict circuit steady state behaviour.

Sampling Sampling is a topic in itself. Some useful references are those ofGy (1982) and Lyman (1986).

For a detailed ‘How to Do It Guide’ see the Help Files and Chapter5 of the Monograph Reference.

For a simple estimating technique for sampling requirements referto the paper by Lyman (1986).

Ore TypeCharacterisation

Ore type characterisation is also a substantial topic. Thecomminution models in JKSimMet come with a breakage functionbased on the Rosin-Rammler distribution. This behaviour istypical of a hard, uniform ore. Over the past decade, the JKMRChas researched in some detail how different ores break. The modelparameters also list breakage functions for some other ore types.For a really accurate description of breakage behaviour, a breakagetest is recommended. JKTech will carry out such tests for astandard feed. The tests require 1000kg of –100 +12mm size oreand can even be carried out on complete (i.e. not split!!) drill coresamples. These breakage characteristics can be used to estimatefull-scale performance of crushers and mills, and also of SAG orautogenous mills when the JK abrasion test is added.

Hence, the results can be very useful either for existing plants or forproposed designs.

ReplicateSampling

For serious plant testing, where small differences may be worthlarge sums of money, it is often worth carrying out at least onemultiple sample test. That is, instead of taking just one sample set,take 5 to 10 replicate samples. Then process and analyse eachreplicate separately. These 5 to 10 replicates will provide a meanand standard deviation for every data point. This will provideinvaluable information about the accuracy (or lack thereof) of everydata point.

Model Fitting Data Collection


Concept:Weighted Sumof Squares

If the precision of each data point is measured (or can be estimatedfrom experience), then each difference between experimental dataand simulation prediction can be normalized by dividing by itsprecision. That is, a small difference between an accurate datapoint and its simulation prediction will make the same contributionto the weighted sum of squares as a large difference from aninaccurate data point.

Concept:StandardDeviation

The usual measure of precision is the standard deviation. If wemake repeated measurements of any data point, experimentalvariations will cause variations in the measured value xi.

Then with many repeats, the mean x- of the values will provide anestimate of the true value of x.

Subject to a number of assumptions, the expected variations fromtrue x can be characterized by one number - the standard deviation -which is defined as:

Standard Deviation =

(xi - x-)2

i=1,n

n

(n -1)

∑

If the measurements are normally distributed then, out of 100measurements, 67 could be expected to lie within plus or minus onestandard deviation of the true value (as estimated by the mean), 95within plus or minus two standard deviations and 97 within plus orminus three standard deviations.

Concept:EstimatingStandardDeviation

Experimentally, 5 to 10 complete observations will provide a goodestimate of standard deviation. The mean of such a set ofmeasurements should provide a good test of sampling precision - ifthe test circuit was at steady state.

Concept:Whiten StandardDeviation

For accuracies of size analyses on a weight % retained basis, theWhiten errors often provide a realistic estimate. These arecalculated as relative errors:• A standard deviation of 0.1% plus one tenth of the fraction is

assumed, up to a maximum weight of 1%.

The Select SD Values window lists a wide range of options forsetting SD models. Select an option by clicking on it and then clickon OK to close this window and return to the port data window.

Data Collection Model Fitting


The Whiten error model is useful for sizings in grinding circuits(other than SAG feed) and acceptable for assays (at percent levels)in mass balancing. The SD model is a generalised two term errormodel ie it uses a fixed and a proportional term to estimate assayerrors. These issues are also discussed in Chapter 6.

Concept:Least SquaresFitting

The simulator takes all of the feed streams as input and uses themodels and parameters to predict all of the circuit streams.

If some (or all) of these streams are measured (sampled and sized,etc), the experimental measurements can be compared with thesimulator predictions. The sum of squares of the differencesbetween measured data and simulated results is taken as a measureof goodness of the model fit. The best estimates of the parametersare expected to be those which MINIMISE the sum of squares.

Hence, the model fitting program adjusts user selected modelparameters to find a best set of parameter estimates which makethe simulator output match the experimental measurements asclosely as possible.

Model Fitting Background


5.3 Background

The JKSimMet models are provided with a set of defaultparameters and, in most cases, a range of parameter values. (Seethe Supplementary Parameters Manual supplied by JKTech).

For any real mineral processing operation, the best-fit parameterswill almost certainly be different from the default values providedwith the system.

There are several classes of parameters used as model inputs:

• Machine dependentparameters

Typically dimensions and keyoperating adjustments.

• Ore dependent parameters For example, the work index orspecific gravity or breakagefunction for a particular ore ata particular energy.

• Calculated or measuredoperating parameters

These usually depend on acombination of machine andore dependent parameters andore feedrates, etc. Examplesare cyclone feed pressure andcrusher power draw.

• Circuit flowrates of solidsand water

Process instrumentation oftenprovides an estimate of, say,solids mass flowrate to acyclone classifier. In somecases, such a flow can betreated as data. If it isunmeasured, it may be varieduntil a best fit to other data isachieved. In this case, theflowrate effectively becomes aparameter.

• Model parameters which canbe fitted.

Each model has a list ofparameters which can be fitted.Each parameter to be fitted isselected from a menu for thatmodel. These menus are listedwith each model description inAppendix A.

.

How the Model Fitting Program Works Model Fitting


5.4 How the Model Fitting Program Works

The model fitting program works by calculating the differencesbetween the predicted and the experimental data, and deriving fromthese a weighted sum of squares value (WSSQ). On its firstiteration (step), the program adjusts each parameter in theparameter list in turn by a small amount, and notes the effect of thisadjustment on the weighted sum of squares value after an internallyexecuted simulation. This step is used to estimate the magnitudeand direction of the adjustments to the parameters required tominimise the WSSQ. On subsequent iterations, the program variesall the fitted parameters simultaneously, noting the effect of theadjustments. This process is repeated until the program is stoppedfor one of the following reasons:

• a minimum WSSQ has been reached,• the maximum number of steps set by the user has been reached,• the adjustments made to the parameters are having no significant

effect on the weighted sum of squares value or• operator intervention.

Whereas simulation uses given feed data and given modelparameters to predict the product data, the model fitting programuses the sum of the squares of the differences between the predictedand the actual product data to adjust the model parameters.

Model Fitting How the Model Fitting Program Works


Schematically:

MODEL FITTING

Simulator

Model Fit

Sum ofSquares

Best FitParameters

Simulator

SIMULATION

MODELPARAMETERS

Feed Description

Circuit Configuration

Predicted Productsand Streams

Feed Description

Circuit Configuration

Predicted Productsand Streams

Adjusted ModelParameters

Iterate toMinimum Sumof Squares

Measured Productsand Stream Data

MODEL PARAMETERESTIMATES

A Simple Example Model Fitting


5.5 A Simple Example

A very simple example has been included in the LearnerFlowsheets project of JKSimMet. This example provides a quickguided tour of the fitting menus to get the flavour of the fitting sub-system. You will, however, still need to work through section 5.6(Learning Fitting) in detail with several real cases in order tobecome confident with the model-fitting mode.The example is a single Ball Mill in open circuit. There is only onestream predicted – the product. Therefore, there is only one streamthat can be fitted.Step 1 Load the Learner Flowsheets project and select the

flowsheet called Ball Mill Model Fit.

Step 2 Examine the mill feed and product port data. You willfind the raw data in the Ball Mill Feed Feederequipment unit data and in the Ball Mill Product streamdata. Run a simulation by clicking on the Simulate iconand compare the raw and calculated values for the BallMill Product. (Use a graph for easier comparison of thesize distributions).

Step 3 Now select Model-Fit mode by left-clicking on theModel Fit icon. This will bring up the Model-Fittabbed dialogue window shown below.

Model Fit Dialogue Window

Step 4 Left-click on the Select tab of the Model Fit window toview the list of equipment and streams which the usercan select to be used for model fitting. Note that theequipment and streams which have been selected forfitting are highlighted in blue on the flowsheet. Thisfeature is useful for checking that you have selected allof the items on the flowsheet which you want to use inthe model-fitting and is particularly useful for complexflowsheets.



Step 5 Left-click on each item in the list on the Select tab andobserve whether or not it has been selected for fitting.If the item is selected for fitting the box labelledSelected will contain a tick. Note also that as you clickon each item in the list it is highlighted in red on theflowsheet. This feature is useful for identifying whichitems you are selecting when the flowsheet is a complexone.

Step 6 Left-click on the Parameters tab to examine the list ofunit parameters to be fitted. You will find the listnamed Ball Mill Parameter List which shows the threespline knots for the ball mill as the parameters to befitted. The initial values of the knots for the fitting are1.0, 3.0 and 4.0.

Step 7 Select the tab Data to view a list of the port andequipment data which can be selected for use in thefitting. The list is named Ball Mill Data List. Note thatthe Data list defines which data (and SDs) the modelsuse in the weighted sum of squares which is minimisedin fitting.

Step 8 The final step before running the model fitting is to setthe standard deviations (SDs) of the stream data whichwill be used in the fitting (in this case, the Ball MillProduct). Bring the Ball Mill Product port data windowinto view and, from the drop-down list under DataType, select the SDs option. This allows you to viewthe data SDs and the Error data along with themeasured and calculated data values. The SD values arethe estimates of the accuracy of the data while Err(Error) data are differences between experimentalvalues and those calculated by the model-fitting.

Hint: Experimental, Calculated, SD and Error data canalso be examined on the same screen using theoverview facility which is available from Overview oron the Data Tab of the Model Fit Window.

Step 9 Make the Model Fit window the active window andclick on the Run Fit tab. Click on the Start button tostart the model-fitting process. The model fittingprogram will take these initial estimates provided by theuser and search for better ones, given the experimentaland calculated streams values. It searches until it findsa minimum residual error (weighted sum of squares ofdifferences).

If the program finds what looks like a genuineminimum, it will terminate by providing parametererror estimates (SDs). In this example, the fit is quitegood. The Errors SDs value is less than 1. This means



that the data are slightly more accurate than the enterederror estimates suggest.

Hint: set the scroll bar slider on the Run Fit window toallow you to see the fitted parameters being updatedafter each iteration.

Step 10 The best fit values for the R/D* knot parameters arelisted in the Selected Model Parameters section, alongwith the SDs of these values. (You may need to scrollacross to view these data).

Step 11 Look at the Ball Mill Product port data. Examine thedifferences between experimental and fitted data byselecting the Abs-Fit option from the Error Type drop-down list and observing these values in the errorcolumn. The differences are relatively small.

Step 12 As an exercise, try graphing the experimental and fitteddata.

This concludes the short guided tour of the model fitting sub-system. The next step is to work through the tutorial and referencesection with a set of real data.



5.6 Learning Fitting

The real power of JKSimMet lies in its ability, through the modelfitting sub-system, to tune the JKSimMet simulation models tospecific real world operating conditions. To do this, the usercollects experimental (stream) data and periodically engages inmodel fitting to update parameters.

Model fitting consists of the adjustment of model parameters on thebasis of collected experimental data. The data are collected fromthe real plant or circuit, and primarily concerns the circuit product.

Basically, the situation is as follows. Initially, the one set of datathat the engineer has is the plant or circuit feed data. TheJKSimMet simulation provides the engineer with a set of predictedor expected product data on the basis of this known feed. Theengineer monitors the real circuit or plant product, building up a setof experimental data which can then be compared with the expectedor predicted data. The essence of model fitting is to analyse anysystematic difference between the predicted and experimental data,and to use it to adjust the selected model parameters.

5.6.1 Preparation for Model Fitting

The subsequent sections of chapter 5 lead the user through the stepsnecessary in order to execute the model fitting, but there are twoessential preliminaries.

Simulation The user must ensure that the circuit or test for which the fitting isto be done has plausible simulation feed and model parameter data.That is to say that it must have run through simulation toconvergence. Thus, it is necessary to select an appropriate test andcircuit, and to run a simulation before continuing. The simpler thecircuit used in model fitting, the better. Indeed, a circuit with asingle unit (model) is the ideal for a first fitting with a new oretype.

If you enter new data, or in any way alter the flowsheet which youselect, you should run a new simulation, even if one has been runbefore.

Learning Fitting Model Fitting


5.6.2 Start Model Fitting

Select the Model-Fit mode by clicking on the Model Fit icon at thetop of the screen. This brings the Model Fit window into view.

Model Fit dialogue with Run Fit tab active

The tasks involved in preparation for the execution of model fittingare:

• Selection of the appropriate section of the flowsheet ie the selectlist (which is a feature common to all of the JKSimMet analysismode dialogues – Model-Fit, Simulate and Mass Balance).

• Selection of the model data. This involves both the selection ofthe data which the models must match, and entering the streamand feed stream data.

• Setting up the parameters. This involves both the editing(displaying and recording) of the unit parameters and theselection of the unit parameters to be adjusted.



5.6.3 Selecting Data

Fitting involves the adjustment of parameters and the comparisonof data. As has been outlined, there are two data sources for thiscomparison. They are the data output from the simulation, and thedata collected by the plant engineer and entered into the modelfitting sub-system.

Select itemsfor inclusion inModel-Fitting

In contrast with earlier versions, in JKSimMet V5 the user canchoose any items on the flowsheet to be included in the model-fitting process. This is useful if the user wants to model asubsection of a large flowsheet or even one piece of equipmentfrom a flowsheet. So the first task in preparing to model fit data isto select the equipment and ports that will be available for use inthe fitting procedure. If an item is selected here, it will be availablefor selection in the Parameter and Data lists.

Step 1 Click on the Select tab in the Model-Fit window.

Step 2 Click on the button marked New to create a new datalist. Firstly, you should give a name to the Select list bytyping the chosen name into the text box labelled Nameand pressing Enter. Any name will do, but we haveused Taconite Mill.

Step 3 Click on each of the equipment and port names in theEquipment list in turn and select the items whose datayou wish to use in the model fitting. To select an itemsimply click in the appropriate box to place a tick in it.A glance at the flowsheet shows which parts of theflowsheet have been selected to be included in themodel fitting as all selected items are outlined in blueon the flowsheet.

Select thePortsfor Fitting

The next task is to define which port data the models must match.This means selecting the ports to be used during the fitting usingthe Data tab in the Model Fit window.

Step 1 Click on the Data tab in the Model-Fit dialogue.

Step 2 Click on the button marked New to create a new datalist. Firstly, you should give a name to the port data listby typing the chosen name into the text box labelledName and pressing Enter. Any name will do, but wehave used 'Ball Mill Data Fit List'.

Step 3 Click on each of the port names in the Equipment PortData list in turn and select the items whose data youwish to use in the model fitting. To select an itemsimply click in the appropriate box in the columnlabelled Fit? to place a tick in the box.



The maximum number of ports which can be fitted in one fit list isten .

Entering andEditing PortData

Essentially, this involves entering your data and declaring yourconfidence about each item in the data set.

Step 1 Bring into view the port data window of the streamwhose data you wish to edit. Note that you may find itconvenient to minimise these windows on screens otherthan a very large computer display. A minimisedwindow will reopen at the tab and position at which youclosed it.

Step 2 Left-click on the Data section and select the SDs optionfrom the drop-down menu. This brings the SD andError columns into view in the port data window, alongwith the experimental and calculated data.

STREAM DATA ENTRY (SDs type)

Port Data The Totals area of the port data window contains data pertaining tothe total stream: solids, water and volumetric flowrates, percentsolids, pulp SG and solids SG values. Note that numeric charactersdisplayed in blue on a white background can be entered by the user.Numeric fields with a grey background are calculated byJKSimMet and cannot be edited by the user.

The Size Distribution tab area contains the list of the sizings fromTop Size to Size 30 with the value (%) for each size. Whether the% experimental value refers to % Retained, Cumulative % Retainedor Cumulative % Passing depends upon the setting of the streamformat field shown at the top left of the screen. This setting can bechanged as required by selecting the required sizing format fromthe drop-down list in the Format box.



Notice that there are often more size distribution data than will fitin the port data window. If this is the case, scroll bars at the edgeof the window will allow you to view all of the data. The Page-Up,Page-Down, Home or End keys or the cursor arrow keys can beused to move around.

The user must set the SD values, so we shall deal with these datafields now.

DataAccuracyEntry

The SD (Standard Deviation) column is next to the Experimentaldata. The SD field must contain a value in each data cell. Thereare three ways to enter values into these SD fields.

• Leave most or all of the entries at the default value of 1.0,simply overtyping the ones you wish to change individually.

• Globally change all the SDs to one of the six other availableoptions by:

Step 1 Left-click on the button labelled Set SDs which is to befound at the top right-hand corner of the port datawindow.

Step 2 Select the required option from the Select SD valuespop-up window which is displayed.

• The user can change any individual field by overtyping an SDvalue. The number you enter is an expression of yourconfidence in the experimental value.

Concept:IgnoringData

Note that a zero SD means the error, i.e. the difference betweenthis experimental and calculated value, will be ignored in themodel fitting process. NB This is different from mass balancewhere a zero FIXES the result at the measured value!



Concept:High AccuracyData

If you have high confidence in an experimental value, set the SD toa small value.

Error Display Error values can be expressed in one of several ways: AbsoluteError, Percentage Error, or Weighted Error. The user can furtherchoose whether the error displayed is related to the mass-balancing,model-fitting or simulation mode of JKSimMet. The user candetermine which of these forms is displayed by the followingprocedure:

Step 3 Position the cursor over the Error cell at the top of thedata window and left-click on the black invertedtriangle to make the drop-down list appear.

Step 4 Select the error type required from the drop-down listwhich is displayed.

AbsoluteError

Tells you the actual difference between the calculated and theexperimental values.

PercentageError

Tells you the percentage difference between the calculated and theexperimental values.

WeightedError

Tells you the number that the parameter-fitting program will use inits weighted error sum of squares. You will probably find this themost useful setting.

Error typedrop-downlist



5.6.4 Setting Up the Parameters

The second task in preparing for model fitting is to define whichequipment parameters are to be fitted

Unit SpecificComments

Appendix A contains model descriptions and default parametervalues. It also contains a section of specific comments on fitting ofeach type of model and the parameters which can be selected forfitting for each model.

EquipmentParameterSelection

The Parameter tab data in the Model-Fit window is used to definewhich equipment parameters are adjusted in the model fitting.Initial estimates of the values of these parameters are entered in theGuessed Value column. These initial estimates of the parametervalues are necessary for the first iteration of the model fittingprocess. In subsequent runs of model fitting for the same model,the user can use the values output from the previous model fittingrun.The task is to select the equipment (ie model) parameters you wantto adjust in the fitting process.

Step 1 With the Model-Fit window as the active window,select the Parameters tab. Firstly you should create anew parameter list by clicking on the New button. Typea name for your list in the Name box and press Enter.Using the same name that you gave the data list is agood option, but anything will do. The example shownhere is called Ball Mill Parameter List.

ParameterSelection

Step 2 Place the cursor in the first data cell of the equipmentcolumn and press Enter to bring into view the drop-down list of equipment on the flowsheet



Step 3 Select the item of equipment which you want to model-fit and press Enter to make the selection appear in thecell. In this example, Ball Mill is the only item in thelist.

Step 4 Left-click on the Parameter cell and select the requiredparameter from the drop-down list which appears. Thelist of parameters changes with each equipment type,only showing those parameters which can be fitted forthat particular equipment. In this case select parameterLnR/D1.

Step 5 Note that JKSimMet automatically inserts your initialestimate of the parameter value from the equipmentdata window in the Guessed Value column. The ScaleFactor is also automatically set at 10% of the initialestimate. If you wish, these values can be changed byhighlighting the existing value and over-typing with anew value.

Step 6 By default, JKSimMet places a tick in the Fit? columnfor each parameter as it is entered to indicate that theparameter will be adjusted in the fitting procedure. Ifyou do not want a parameter to be fitted, click on theitem’s check box to remove the tick. Note that theguessed value will be copied into the model whether itis checked for fit or not.

This entry completes the parameter tab data entry.

Cancel Entry To delete a row of data from the parameter list, select theequipment name in the row you wish to delete and press Enter tobring the drop-down list into view. Select the option None fromthe list to clear the data from the row.

Note: Being able to decide whether a parameter is adjusted in thefitting is useful because it allows you to try a fit without certain ofthe parameters by not selecting them for fitting and then to fit usingthose parameters by simply changing the flag selecting them again.This saves deleting and re-typing all the details. Slaved units willuse the same scale factors, guessed values and fit modes. (Seesection 5.6.5 for a description of Master/Slave fitting).

Repeat the above steps for each of the parameters you wish toinclude in the model fitting. The maximum number of parametersis 10. You may, however, define as many parameter lists as youwish.



5.6.5 Master/Slave Fitting

Master/Slave Fitting

Master/slave model fitting allows the same parameters to be fitted to two or more (up to a maximum of ten) units in a single flowsheet. The parameters fitted will have the same values for all the slave units. Master/Slave fitting can be used when fitting survey data collected simultaneously from parallel units with the same operating conditions. Alternatively, it can be used for survey data collected sequentially from a single process unit, where it is expected that model parameters will not be affected by any change in operating conditions. The circumstances that indicate whether master/slave model fitting can be used are therefore dictated by the type of data and the type of model to be fitted. Note that not all models are suitable for Master/Slave Fitting.

Slave units are entered on the right-hand side of the Parameters tab.

Place the cursor in the slave column, and press ENTER to view the pop-up list of available units. Up to 10 master units are available, with up to 10 slave units per master.

If slave fitting is used, ensure that the appropriate slave stream SD's are set. It is necessary to select the streams to be model fitted for the slave units in the Select tab.

Note that the fitting statistics displayed (eg. Data SD, Residual Error) will include the slave units.



5.6.6 Fit the Model Parameters

Before running the model fitting procedure you may wish to change the maximum number of steps to be executed in fitting. To do so:

Step 1 Left-click on the Control tab in the Model Fit window and check that the required parameter list is selected in the Parameter Fit List drop-down list. Use the cursor to highlight the number in the Maximum Iterations box. Overtype with the value required, and press Enter to register the change.

The default number of steps is 100. You may well feel that this is too few, particularly if there is more than one item of equipment. A value of 200 to 300 is probably better.

Having collected together the circuit simulation data and your experimental data, and nominated which model parameters you wish to fit, you are now ready to execute the model-fitting program.

Step 2 Left-click on the Run Fit tab and then click on the button marked Start to begin the model fitting.

The model-fitting program updates the unit (model) parameters, effectively running a simulation. During execution, the program fills in the result values, but it will update the SDs if it reaches a satisfactory fit. For interpretation of the model fitting results, refer to section 5.7 (Checking the Fit).



StoppingExecution of theProgram

The maximum number of steps field can be set to stop theiterations of the fitting program when required. Alternatively, thefitting program can be stopped at any time, simply by clicking onthe button marked Stop on the Run Fit tab.

Concept:Data StandardDeviations

At the best-fit point, an estimate of the goodness of fit is calculatedby dividing the weighted sum of squares (Residual Error) by thenumber of points less the number of parameters, and taking thesquare root. If the data and the error estimates are in agreement,and if the model is appropriate, this number will tend towards one.

Concept:Stream DataSDs

The same approach can be used for each stream point. Thesevalues are reported for each fitted stream in the Data tab of theModel Fit window. A small stream data SD, i.e. where SDapproaches a value of one, indicates a good match betweenexperimental and calculated data for that stream.

Concept:ParameterStandardDeviations

The solution of the minimisation also provides estimates ofparameter accuracy. The mathematical proof of this estimate ofaccuracy is complex. Intuitively, if the parameter is well defined,the sum of squares will vary more rapidly as the parameter isadjusted. For a more detailed explanation, see Lynch (1977),chapter 7.

If the program finds small variations in a parameter make NOapparent difference to the sum of squares at the minimum, it setsthe parameter SD to 1E20. Such parameter fits should be treatedwith CAUTION and the data examined for problems.

Checking the Fit Model Fitting

Page 5-24 Section 5.7 Version 5.0 June 1999

5.7 Checking the Fit

During the execution of the fitting program, the Model-Fit windowis displayed. As the fitting program goes through each iteration thevalues in the results section of the window are updated. Assumingthat the fitting reached a satisfactory conclusion, the standarddeviations (SDs) of the parameters are updated when the fittingprogram stops.

There are various ways in which the user can judge whether theresults are good or bad:

• Compare the size or order of magnitude of the SDs with that ofthe associated value. When the SD is small compared with thevalue as a ratio, it is a good fit, when large, it is a poor fit.

• The summary values in the lower half of the Model Fit windowalso indicate the success of the fit. Low values in the Residual,Error Sum, and Errors SD fields indicate a good fit; large values,a poor fit. Moreover, in the case of these fields, crosscomparisons between fittings can be made. If these values aresmaller in the most recent run of the fitting than they were in theprevious run, the fit is getting better. If they are getting larger,you are going in the wrong direction.

• The engineer can also judge the relative success of the fitting bylooking at the stream data windows. Examine the Error column.Weighted Error and Percentage Error versions of the differencebetween calculated and experimental data are most useful.These are displayed by selecting the appropriate item from theError drop-down list.

• The graph plotting facility of JKSimMet allows the engineer toplot raw and fitted data on the same graph, as detailed in section5.8 (Presentation of Model Fitting Results).

• The overview facility of JKSimMet allows key experimental andcalculated data for multiple streams to viewed in a summarytable. These overviews are configurable by the user (see section3.10 for details).

Model Fitting Presentation of Model Fitting & Results


5.8 Presentation of Model Fitting Results

There are two main ways to present the results of model fitting:

• printing data• plotting graphs

.We shall deal with these in turn.

Printing ModelFit Results

Given that model fitting concerns the experimental (raw) data andthe predicted (fitted) data for streams, our task is to print these twotypes of data for the streams concerned.

To easiest method to print the data for individual ports is simply toprint the data in the relevant port data window as follows.

Step 1 Bring into view the data window for the port whosedata you want to print.

Step 2 Left-click on the Print icon on the main JKSimMettoolbar to view the Print Preview window for this item.

Step 3 If the Print Preview shows that the layout is to yoursatisfaction, click on the Print icon at the top, right-hand corner of the Print Preview window (you mayneed to resize this window to see the Print icon)

Step 4 Repeat Steps 1 to 3 for all the other ports whose datayou want to print.

These steps also apply to any other window which has data that youwant to print, such as equipment data.

The best way to produce a printed copy of the error and SDinformation on the Parameters and Data tabs in the Model Fitwindow is simply to print this window.

Hint: The Overview window provides a convenient means oflooking at experimental and model fitted data on the screen. Thisoverview can also be printed, using the Print icon.

The Report feature provides a means of printing both port andequipment data. The user can configure the report to showexperimental and fitted data, SDs and errors for any ports. (Seesection 3.11 for more information on the Report feature).

Problems & Solutions Related to Model Fitting Model Fitting


Plotting Graphsof the ModelFitting Results

The graphs presenting model fitting results are, once again, ofstream data. They involve experimental (raw) data, and predicted(fitted) data. The simplest way to begin is to configure a graph andsimply nominate the data to be plotted. You can then edit the graphformat and annotation as required.

Step 1 Left-click on the Generic Graph Config button on themain JKSimMet toolbar to bring the Graph Definitionwindow into view.

Step 2 For this exercise, you will create a new graph so clickon the Port Data tab.

Note that the default setting for the graphing facility already hassome data pre-selected so you must now define which data youwant to plot on the graph.

Step 3 Specify a new Port Data list by left-clicking the Newbutton and typing a name for your data set into theName box and then pressing Enter.

Step 4 Move the highlight to the row labelled Port in the firstcolumn and press Enter.

Step 5 Select the name of the required port from the drop-down list which appears.

Step 6 Position the highlight on the first cell in the Format rowand press Enter.

Step 7 Select the required graph format from the Format drop-down list. Cum % Passing is a good choice.

Step 8 Select the option Exp & Fit from the drop-down list inthe row labelled Data. Note that the list allows the userto plot single data types (e.g. Experimental data only)for the port or pairs of data types (Exp and Fit or Expand Sim). Where a pair of data types is the selectedoption, JKSimMet represents the experimental datawith data markers and the calculated data with a line.

Step 9 Move to the Line row and select the required style ofline from the drop-down list.

Step 10 Move to the Point row and select the required symbolfor the data marker from the drop-down list.

Step 11 Move to the Colour row and choose the colour withwhich the line and data markers will be drawn on thegraph.

Step 12 If a spline interpolation is required between the datapoints on the graph click on the box in the Spline rowto place a tick in the box.

Model Fitting Presentation of Model Fitting & Results


Step 13 Set the minimum value of x to be plotted for this dataset by typing the value in the X Min cell. Place thehighlight in the cell, double-click and then type the newvalue.

Step 14 Repeat step 13 for the maximum value of x in theX Max cell.

Step 15 Repeat Steps 4 - 14 for each of the streams you want toplot on the graph.

Step 16 Left-click on the Display Graph button at the top of theGraph Definition window. Your new graph will nowbe displayed.

You can now refine the format of the plot and print the plot, etc, asoutlined in the section 3.9 (Learning Graphing). Repeat the abovesteps for each of the streams for which you wish to compare theraw and fitted data. The quality of fit is represented by thecloseness of the points to the line, (the closer the better).

Overview This facility provides an excellent summary. Set the % passingsize properties from the Flowsheet Icon on the tool bar, e.g. P80and % -75 µm.

Overview can summarise flows and these key sizes forexperimental and fitted data.

5.9 Problems Related to Model Fitting andPossible Solutions

There are, of course, many problems that may be encounteredduring model fitting. It is possible, however, to point out some ofthe more common mistakes, so that you are aware of them.

Errors, Warnings,Faults

Some problems detected by JKSimMet produce error messages.ERRORS 140-163 are relevant to the Model Fitting module.Please refer to the expanded descriptions of these errors inAppendix B.

Skillversus Practice

Model fitting is not a cut and dried procedure. The only way toacquire a useful skill level is to practice on a wide range of realdata. JKSimMet offers a user-friendly environment for what arereally very complex and powerful mathematical techniques.

Problems & Solutions Related to Model Fitting Model Fitting


Initial ParameterEstimates

As with all non-linear least squares programs, Model Fitting issensitive to initial parameter estimates. The default values and thesupplementary information provide a useful guide. However, trialand error may be necessary to find the best estimates to use with anew circuit or new data.

GraphicalAnalysis

The graph capability of JKSimMet is the most powerful way toexamine your data fit. Discontinuities in size distributionshighlight poor data or a change in measurement technique.Graphical analysis also highlights any bias in the data fit.

Different SizeMeasurementTechniques

Be very careful of changes in size measurement technique, such asfrom sieves to Cyclosizer.

No ApparentProgress

When nothing much seems to be happening in model fitting, asimple first check is to ensure that you have a reasonableMaximum Number of Steps setting, and that the streams andparameters that you intend to include in the fitting are selected witha tick in the Parameters section of the Model Fit window.

Data Note that it is necessary to have as much feed and product data aspossible for each of the unit Models to be tuned. Simulationrequires only feed data, but fitting must have some product data aswell.

Not EnoughData

Even when you have the necessary data to perform model fitting, itis essential to ensure that there are enough readings to be useful forfitting; in general terms, the more data the better.

SDs andEmphasis

The SD settings in the stream data window may be set so that theycan cause such an over-emphasis on one parameter that thepotential of the fitting is compromised. Always try to make theSDs as good an estimate as possible.

Model Fitting Problems & Solutions Related to Model Fitting


Scale Factors The Scale Factor in the Parameters section of the Model-Fitwindow can also be a source of problems. If the scale factor is toobig the fitting may stop, because any adjustment in the parameterproduces such a large change that it steps over the minimum of thesum of squares. On the other hand, however, if the scale factor istoo small, the fitting may stop because any adjustment produces achange of so small a scale as to be judged insignificant, eventhough you may not be close to a minimum point. So, be verycareful with scale factors. As a guide, perhaps a scale factor one-tenth of the magnitude of the parameter estimate would be areasonable place to start.

ParameterProblems

Appendix A contains model descriptions, default values and asection on fitting for each specific model. These comments mayhelp to overcome problems with parameters.

Large WeightedErrors

Examine the weighted errors carefully. These often indicatesuspicious data points. A typical example is a screen top sizewhich contains several times the predicted weight, because thelaboratory screen stack did not extend to a large enough top size.Set the error to zero for this fraction to fix the problem.

Knot Positions Where spline functions are used, the knot values can usually befitted, but not the knot positions.

These models provide a fairly smooth response because of the useof spline functions. A simple guide to knot positioning is thatknots should be selected wherever a bend is needed. After all, thespline function is a mathematical model of a draftsman’s splinecurve - a thin strip of steel with screw positions which areequivalent to spline knots.

Slave/MasterModel Fitting

If problems are encountered when model fitting slave units, tryfitting them individually. Despite all good intentions, all data setsin a survey may not have the same operating conditions andtherefore may require different model fitting parameter values.Examine raw and calculated data for each unit to identify poor fits.One set of poor data, or data with inappropriate operatingconditions, can prevent a good model fit solution being reached.

References Model Fitting

Page 5-30 Section 5.10 Version 5.0 June 1999

5.10 References

GY, P.M., 1982. Sampling of Particulate Materials: Theory andPractice, 2nd Ed. Elsevier, Amsterdam.

LYMAN, G.J., 1986. Application of Gy's Sampling Theory toCoal, International Journal of Mineral Processing, 17,pp 1-22.

LYNCH, A.J., 1977. Mineral Crushing and Grinding Circuits,(Elsevier, Amsterdam).

NAPIER-MUNN, T.J., MORRELL, S., MORRISON, R.D., &KOJOVIC, T. 1996. Mineral Comminution Circuits – TheirOperation and Optimisation. JKMRC Monograph Series inMining and Mineral Processing 2. Series Editor T.J. Napier-Munn, Julius Kruttschnitt Mineral Research Centre, University ofQueensland.

Mass Balancing Mass Balancing

Version 5.0 December 1999 Section 6 Page 6-1

CHAPTER 6

MASS BALANCING

Introduction to Mass Balancing Mass Balancing


6. MASS BALANCING

6.1 Introduction to Mass Balancing

Purpose Chapter 6 describes how to use the JKSimMet mass balancingsub-system.

Overview Even the most carefully collected plant survey data are subject tomany sources of variation. Some of these errors are due to:

• statistical effects• sampling procedures or design• assaying procedures• sizing procedures• fluctuations in plant flowrates.

As with all data improvement processes, the usefulness of themassaged data will be strongly dependent on the quality of the inputdata. The mass balancing module can help you to assess dataefficiently and to refine your experimental technique whenproblems are detected. Mass Balancing will make good qualitydata better. It will not fix poor quality data or do anything morethan highlight inadequate experimental technique.

The module is used to mass balance sizing data, assay data andflowrate data collected at steady state. The balancing processproduces best fit estimates of flowrates and a set of adjusted sizeand assay data which is consistent with those flowrates.

As with model fitting, the overall process is:

• collect data,• analyse data,• check accuracy of data fit and• refine experimental technique and instrumentation until desired

level of accuracy is obtained.

Mass Balancing Data Collection


6.2 Data Collection

The comments in section 5.2 are just as relevant for mass balancingas for model fitting.

Some additional comments about assay measurements andtechniques are appropriate here.

There are well established rules for calculating the accuracy of asampling and assay process (Gy, 1982). These can be used toestablish an error model which can then be used to provideestimates of standard deviation for each point. Alternatively, 5 to10 replicate samples can be taken and processed. If these inputaccuracies are established, then the program estimates of accuracyfor flowrates will be real estimates and not relative estimates.

If replicate sampling is carried out for assays on a number ofstreams (ie. a range of assay values), a simple two term error modelcan be generated by plotting relative standard deviation againstaverage assay values from each stream.

The intercept and slope of this plot will provide fixed (minimum)and relative (%) error components which can be used in thegeneralised version of the Whiten model.

You also need to s pecify a sensible maximum (absolute) error.

Background Mass Balancing


6.3 Background

Mass Balancing can be thought of as a type of model fitting. Themodels in this case are quite fundamental. Hence, they do notimpose the experience knowledge (which is built into othermathematical process models) onto the data.

These mass balancing models are:

• a mixer (for example, a pump sump),

• a general classifier (for example, a hydrocyclone),

• a unit which conserves some properties but not others(for example, a grinding mill will preserve total assaysand flowrates but not size fractions.

The basis of the mass balancing algorithms is the differences incomposition of various streams, that is, the differences generated bythe process equipment.

Consider a process with these streams having assays a, b, c:

a b

c

If the flowrate in stream of assay a is 100 tph, then:

100 a = x*b + (100-x)*c

where x is the flowrate in stream of assay b and then:

x = 100 (a-c)/(b-c)

This is the basis of the traditional three-product solution, where a, band c may be assays for size, Cu or any other conserved property.

It does not matter what kind of assays a, b and c are, as long as thereis some difference in their values.

If the process is just a splitter and the assays are all the same:

a = b = c

and therefore x = 0/0 which is undefined.

Mass Balancing Background


Expressed another way, the flowrates can be estimated only if aprocess imposes a difference on its products, that is, the informationis imparted by the process. If no information is imposed, as with asplitter, then the information cannot be used to make estimates, as itis not there to begin with. If this program produces a good balancearound a splitter, then the splitter is behaving as a classifier andshould probably be re-engineered.

It follows that the most useful properties to use for mass balancingaround a process unit will be those which have the largestdifference in the product streams.

This means that size assays will work well around a size classifiersuch as a screen or a hydrocyclone, and copper assays will workwell around a copper flotation circuit. The reverse will generallynot be true, with some notable exceptions. For example, goldand/or lead assays are often very useful around a hydrocycloneclassifier because its density-separating characteristic will usuallyproduce a large difference in these assays.

The power of this program lies in its ability to use a wide range ofassays across a large flowsheet. The program algorithm is drivenby the assays with large differences but still takes account of thosewith small differences.

Concept:Mass Balancing

The mass balancing module takes all selected streams andcalculates the smallest set of data adjustments which will make thedata consistent.

If some (or all) of these streams are measured (sampled and sized,etc), the experimental measurements can be compared with thedata. The sum of squares of the differences between measured dataand adjusted data is taken as a measure of goodness of fit of themodel.

Hence, the mass balancing program adjusts user selected flowratesto find a best set of flowrates which make the balance output matchthe experimental measurements as closely as possible.

Concept:Weighted Sumof Squares

If the precision of each data point is measured (or can be estimatedfrom experience), then each difference between experimental dataand simulation prediction can be normalized by dividing by itsprecision. That is, a small difference (or adjustment) between anaccurate data point and its simulation prediction will make thesame contribution to the weighted sum of squares as a largedifference from an inaccurate data point.

Background Mass Balancing


Concept:StandardDeviation

The usual measure of precision is the standard deviation. If wemake repeated measurements of any data point, experimentalvariations will cause variations in the measured value xi.

Then with many repeats, the mean x- of the values will provide anestimate of the true value of x.

Subject to a number of assumptions, the expected variations fromtrue x can be characterized by one number - the standard deviationdefined as:

Standard Deviation =

∑(i=1,n)

n(xi - x-)2

(n-1)

If the measurements are normally distributed then, out of 100measurements, 67 could be expected to lie within plus or minus onestandard deviation of the true value (as estimated by the mean), 95within plus or minus two standard deviations and 97 within plus orminus three standard deviations.

Concept:EstimatingStandardDeviation

Experimentally, 5 to 10 complete observations, that is, samplingplus analysis, will provide a good estimate of standard deviation.The mean of such a set of measurements should provide a good testof sampling precision - if the test circuit was at steady state.

Concept:Whiten StandardDeviation

For accuracies of retained size analyses, the Whiten errors oftenprovide a realistic estimate. These are calculated as relativeerrors:

• For fractions greater than 10%, a standard deviation of 1.0% isassumed.

• For fractions less than 1%, a standard deviation of 0.1% isassumed.

• For fractions between 1% and 10%, a standard deviation of0.1% plus one tenth of the fraction is assumed.

Mass Balancing How the Mass Balancing Program Works


6.4 How the Mass Balancing Program Works

As noted earlier, the mass balancing problem is a special case ofthe non-linear least squares fitting problem.

The mass balancing program used by JKSimMet is a programcalled MBal written by Dr Bill Whiten and based on an algorithmdeveloped by Dr Rob Morrison. The balancing algorithm usesspecial assumptions about data accuracy to linearise the problem.This allows for an initial flowrate solution which is analogous tothe multiple linear regression solution, that is, a solution which iscomputationally rapid and does not require initial estimates offlowrates other than one flowrate to use as a basis for all others.

The mass balancing program refers to this algorithm as theMorrison solution. If the data are accurate, these flowrates will beindistinguishable from those produced by the correctly weightedsolution.

The Morrison solution provides the initial flowrate estimates forwhat becomes essentially a constrained non-linear least squaresfitting.

A minimum set of flowrates is adjusted to minimise a trueweighted sum of squares of data adjustments. However, the keydifference between mass balancing and model fitting is that all datastreams are adjusted, that is, the imbalances in the mass balance aredistributed over both feed and product streams.

For the model fitting minimisation, all of the errors are allocatedover the product streams. That is, the feed streams are assumed tobe accurate.

This difference is important where aspects of the feed stream aremore difficult to measure than those of the products. This isespecially true with streams of coarse particles encountered incrushing and screening plants. For these plants, sampling errorbecomes critical and the mass balanced feed stream will usually bemore useful than the experimental data as a basis for assessment ofoperation and for simulation.

How the Mass Balancing Program Works Mass Balancing


Schematically:

Mass Balancing

Feed

Product 1

Product 2

Mass Balance Adjusted Data

Model Fitting

Feed

Feed

Parameter Adjustments

Product 1

Product 1

Product 2

Product 2

FeedProduct 1

Product 2

(Observed - Calculated)

(Observed - Calculated)

Minimize the differencebetween observed and calculated

(minimize adjustments)

SIMULATION

(minimize adjustment)

(+ δ)

(+ δ)

(+ δ)

Mass Balancing A Simple Example


6.5 A Simple Example

The simplest, non-trivial case for mass balancing is a separator ofsome type which receives one feed stream and separates the feedstream into two products. Interestingly, this is also the mostcommon application of mass balancing.

This example provides a quick guided tour of the mass balancingmodule to get the feel of the system. To use it effectively, you willneed to work through Learning Mass Balancing (Section 6.6).

The example which is included in the Learner Flowsheets projectis called Example Cyclone Mass Balance.

This example is a single hydrocyclone in open circuit.

Step 1 Load the Learner Flowsheets project. Select theflowsheet named Example Cyclone Mass Balance

Step 2 Left-click on the Mass Balance icon on the toolbar toactivate the mass balancing mode and to bring the MassBalance window into view.

Step 3 Click on the Select tab to view the list of units andstreams. Note that the current list is called Select-1 andthat the user can set up more than one list of selecteditems.

Click on each stream or unit name in turn to see whichexperimental data have been selected for use in themass balance. The presence of a tick in the boxesmarked Selected, Water, Feed etc. indicates that theitem will be included in the mass balance. You willfind the unit named Cyclone has three ports selected.

A Simple Example Mass Balancing


You will find that all the units and water additions andstreams are selected initially. You may turn these onand off with by left-clicking on the box to make thetick appear or disappear as required.

Step 4 Click on the Run Balance tab and then select the GSIMoption on the check box on the top right hand corner ofthe Run Balance tab window. Also ensure that Select-1is the option chosen in the drop-down list for the Selectlist.

Data Entry Step 5 Bring the Cyclone Overflow data window into view.

Step 6 From the Data drop-down list select the SDs option andfrom the Error drop-down list select the Abs-Baloption. You will see the stream data in a format whichis almost exactly like that in Model Fitting.

The experimental stream data and the related SDs aredisplayed as well as the balanced data and its relatederrors.



Stream Data The Totals tab section of the window contains the experimentalsolids and water mass flow values and related data for the stream.The Size Distribution tab contains the list of the sizings from TopSize to Size 30 with the value (%) for each size fraction. Whetherthe % experimental value refers to % Retained, % Passing, orCumulative % Passing depends upon the choice of stream formatselected in the Format drop-down list at the top left of the screen.The Components tab section of the window contains any assay datafor the stream.

Scrolling Notice that the Size Distribution tab section contains too much datato display all of it in the window at one time. You can scrollthrough the data by using the Page-Up, Page-Down, Home or Endkeys, or the cursor up and down control keys. You may also clickon the Print icon on the JKSimMet tool bar for a printout of thewindow you are working on.

DataAccuracyEntry

The user must set the data standard deviation (SD) values in thecolumn labelled SD. This column must contain a value in each cellwhere corresponding experimental data are entered. Note that thisstandard deviation is your estimate of data accuracy obtained fromrepeat samples or from experience.

There are three ways to enter values into these SD fields.

• Leave most or all of the entries at the default value of 1.0 andsimply over-typing the ones you wish to change individually.

• Globally change all the SDs to one of the three other availableoptions by:

Step 1 Click on the Set SDs button at the top,right-hand corner of the stream datawindow to bring the Select SD Valueswindow into view.

A Simple Example Mass Balancing


Step 2 Select the required option from the SelectSD Values window which is displayedand click on the OK button to change theSDs for the stream to the option whichyou have chosen.

• The third option is that you can change the individual fields byover-typing an SD value. The number which you enter is anexpression of your confidence in the experimental value.

Concept:IgnoringData in MassBalancing

Note that in mass balancing mode a large SD means the error willbe largely ignored. This is different from Model Fitting where azero SD switches an error off completely. In mass balancing modea zero value for the SD will make the mass balancer hold theexperimental value constant, ie. it will not be adjusted.

Concepts:High AccuracyData

If you have high confidence in an experimental value to be used inmass balancing, set the SD to a small value.

Concepts:CalculatingMissing Data

If both the experimental value and SD are set to zero, the massbalancer will treat this datum as unknown, and estimate a value, ifthere are sufficient other data provided. This is useful when flowdata cannot be obtained in the stream sample survey.

Now that we know about setting SDs, we can continue our tour.

Step 7 Look at the data window for each port. For thisexample you should examine the Feeder called CycloneFeed and the Cyclone Underflow and CycloneOverflow port data windows.

Step 8 Bring the Mass Balance window into view and selectthe Run Balance tab. Left-click on the button markedStart to run the mass balance algorithm. The programwill execute and when it is completed the results willbe displayed.

Step 9 Bring into view the port data windows and examine theraw and adjusted data in each stream.

Step 10 Compare the raw and adjusted data graphically byselecting Graph from the Cyclone properties list (Right-click on Cyclone Icon). Select experimental thencalculated for a quick comparison.



For a numerical comparison of the experimental and calculateddata select the absolute difference option on the Error drop-downlist.

This completes our brief tour through Mass Balancing.

Learning Mass Balancing Mass Balancing


6.6 Learning Mass Balancing

The mass balancing module of JKSimMet is useful in two areas.Firstly, it provides a check on data accuracy which is not modeldependent. The mass balancing models are correct (that is, theycontain no built in experience). Hence, if the data balance well butthe model fitting does not fit well, it indicates that the model is notappropriate.

Where coarsely sized samples are used, as in crushing andscreening circuits, the mass balanced data may be more useful formodel fitting than the raw data.

Secondly, mass balancing is useful for determining flowrates andrecoveries around complex circuits. The example which we willuse in this section, Learning Mass Balancing, is concerned withflowrates and recoveries in a copper flotation circuit.

6.6.1 Preparation for Mass Balancing

For our tutorial, mass balancing is performed on a circuit flowsheetthat has already been established. Ensure that you have eitherselected an existing project, or you have input a new flowsheet (seesection 3.7 on Creating a New Project if you are unfamiliar with thesteps necessary to establish a project).

A tutorial example called Copper Flotation has been provided forthis section.

Step 1 Load the Learner Flowsheets project and select theflowsheet named Copper Flotation from the drop-downlist. If necessary, resize the flowsheet window to viewthe entire flowsheet. Ensure that the flowsheet islocked.

Step 2 Click on the Mass Balance icon on the toolbar to bringthe Mass Balance window into view.

Mass Balancing Learning Mass Balancing


Notice that the Mass Balance window has a four selectable tabs forthe user to enter the information required for mass balancing. Theitems in the Select and Component sections need to be definedbefore running the mass balancing. If you have not defined theseitems, JKSimMet will provide error messages to indicate whatinformation is missing.

6.6.2 Model Types for Mass Balancing

In Version 5 of JKSimMet the flowsheet drawing for massbalancing is the same one used for simulation and model-fitting,with the full range of equipment icons available to draw a circuitdiagram. However, no matter what equipment icon is visible, thereare only two model types in mass balancing. These are:

• classifier or mixer unit

This unit either selects particles to go to different product portsof the unit (classifier) or adds particles from different feeds(mixer). That is, particles are sorted or mixed in this type of unit,not broken down or altered.

• transform unit

In this unit assays are preserved but size structures aredestroyed. In mass balancing all comminution devices aretransform units.

The mass balance algorithm decides which type of mass balanceunit is required according to the flowsheet icon selected by theuser.

6.6.3 Selecting Data

As is the case in the Simulation and Model-Fitting modules youmay select a single unit or a cluster of units on your flowsheet tomass balance. This allows you to check small parts of a circuit fordata consistency.

Step 1 Bring the Mass Balance window into view.

Step 2 Left-click on the Select tab to bring the Select sectioninto view.



For the Copper Flotation example the selection list iscalled Mass Balance Select List 1. The defaultselection for a new select list is for none of the unitsand streams to be selected. Therefore the first stage indefining a select list is to examine the list of equipmentand streams and to select the required items by clickingon the box next to the item name to enter a tick. ASelect All and a Select None button have been providedto help users to configure select lists quickly.

Note that as you click on each item on the list itsflowsheet icon is highlighted in red. Also note thatitems which have been selected for inclusion in themass balancing are highlighted in blue on theflowsheet. These visual cues help users to identify theequipment and streams on complex flowsheets.

Step 3 Work through the Select list and ensure that:

• all equipment units are selected• all streams are selected• all water additions are not selected

Note that for GSIM, percent solids and internal water flows arealways enabled.

Because each Select list has a name, you may set up severaldifferent lists to examine different sections of a circuit. You canselect every stream and flow to balance or any single unit orselection of streams.

Note: in V5.0 stream data are stored in equipment ports. Tobalance a subset of the data, you need to choose both equipmentand ports.

The “water” check box, applies to Water Feeders. These shouldonly be used with GSIM or when “% solids as a component” ischecked on the component tab.



6.6.4 Component

The mass balancing module can analyse two types of data, namelycomponents or size distributions. The model-fitting and simulationmodes in JKSimMet only use size distributions. The size format iscalled GSIM for Grinding Simulation. JKSimMet uses GSIM asthe default component type. If GSIM is selected via the GSIMMode check box on the Run Balance tab or the Components tab, nofurther data entry is required.

However, it is possible to define your own labels for othermeasurements of stream characteristics, such as assays, which canbe used to mass-balance the flows around a circuit. The user mustspecify the component list names before running mass balancing.Note that while the mass balance module can handle streamcomponents other than size e.g. assays, these cannot be combinedwith balancing by size distribution. Therefore a circuit can bebalanced based on size distributions only or assays only.

To perform a mass balance using data other than size the user mustselect a Component list and give it a name. The next step is todefine each of the components.

Step 1 Left-click on the Component tab to view thecomponent list. For the Copper Flotation example, thelist is called CuFe and the components are copper andiron assays, %Cu and %Fe.

To use GSIM modeclick in this box toselect it. No furthercomponent data entryis required.



Step 2 Ensure that both the %Cu and %Fe assays are selectedfor use (i.e. each has a tick in the box in the Usecolumn which is beside the Component Name column).

Step 3 Relative SDs may be specified as automaticallycalculated from here. However, their use is notrecommended as a balance using relative SDs takesmost note of the smallest assay values which are oftenthe least well defined.

Step 4 The Control area of the Component section has a boxmarked %Solids as a component. If this box does nothave a tick in it, all %Solids, water flows etc. areignored i.e. adjustment differences are absorbed in theunspecified components and will not be shown on thescreen or printouts. For the Copper Flotation examplewe will leave the box empty.

Typically you would use % solids as a component whenbalancing a set of specific gravity fractions. If you use% solids as a component you must specify appropriatewater additions. For what happens when % solids areincluded as a component see section 6.6.5 on Water.

EnteringComponentData

Once a Component list has been defined in the Component tab ofthe Mass Balance window, JKSimMet sets up the correct numberof data cells for the component data to be entered in each of theport data windows. The component data can be accessed byclicking on the Component tab of the port data window.

The flowsheet is now set up to mass balance the data usingcomponent data, in this case assay data. All that remains to be doneis to enter the assay data into the port data windows.

Step 1 To enter (or examine) stream assay data, open a portdata window and click on the Component tab. Thiswindow will now contain as many rows of componentsas the user has defined in the Mass Balance windowComponent tab. The user enters new assay data (oredits existing data) by typing over the values in bluetext in the column marked Exp. In the Copper Flotationexample the %Cu and %Fe assay data have alreadybeen entered as shown in the example below.

Step 2 Select the SD’s error display type from the Data drop-down list.



Step 3 Select the data standard deviation value by clicking onthe Set SDs button and selecting the required SD fromthe choices presented in the Select SD Values pop-upwindow. Alternatively the user can type in their ownvalues for the SDs. In the Copper Flotation examplethe assay SDs are set to 10%. However, for less welldefined data, the Whiten Error provides a more realisticerror model.

Step 4 Repeat steps 2 and 3 above for each port in turn.

Step 5 Finally, open the Feed unit equipment window toexamine the feed stream data. Ensure that the measuredfeed flowrate has been entered (and the % solids byweight if available).

Error Display The right-most column under the Components tab in the streamdata window is the Error column, and the values in it can beexpressed in one of three ways; Absolute Error, Percentage Error orWeighted Error. The user can select which of these forms isdisplayed by the following procedure:

Step 1 Click on the Error box to view the drop-down list.

Step 2 Select the required mass balance error type from the list(either Abs-Bal for absolute error, Pct-Bal forpercentage error or Wtd-Bal for weighted error).

Absolute Error Tells you the actual difference between the calculated and theexperimental values.

PercentageError

Tells you the percentage difference between the calculated and theexperimental values.



WeightedError

Tells you the number that the program will use in its sum ofsquares. You will probably find it the most useful setting. Thevalue of this weighted error is

(exp - adj)

S.D.2

6.6.5 Water

If you have selected %Solids as a component on the current MassBalance window Component tab you can also mass balance anywater additions to the circuit.

In Version 5, mass balance water additions are made by selectingthe appropriate water feeder and including it on the Select list. Forthis example, you will need to add two water feeders to theflowsheet. Measured data and estimated SDs are entered in thewater addition data window. This removes the need for the wateraddition list used in Version 4.

See Appendix A1.2 for a detailed description of the Water Feeder.

Some typical water addition and % solids data are tabled below.Select % Solids as a component on the Component tab (see section6.6.2 on Components) and also select water additions on the Selecttab (see section 6.6.4 on Selecting Data) to use this facility

Stream % Solids % Solids Exp SD

FEED 30.0 1.00COMB SCAV CONC 28.0 3.00RGH 1 CONC 45.0 2.00RGH 1 TAIL 29.0 2.00RGH 2 CONC 40.0 2.00RGH 2 TAIL 28.0 2.00SCAV CONC 35.0 2.00FINAL TAIL 27.0 2.00CLNR SCAV CONC 40.0 4.00CLNR FEED 28.0 3.00CLNR SCAV TAIL 28.0 3.00CLNR 2 TAIL 40.0 4.00CLNR 1 CONC 45.0 3.00CLNR 1 TAIL 30.0 5.00FINAL CONC 50.0 5.00



Water Feeders:

Clnr Feed Sump 20 SD 1.0Scav Conc Sump 15 SD 1.0

Remember:

Select the Water Feeders and tick % solids as a component in theMass Balance dialogue window.

6.6.6 Solution Controls

With the Mass Balance window as the active window, click on theControl tab to bring the control section into view.

Note that it is not necessary to understand this section to use themass balance module. The following comments are for users witha mathematical background.

The mass balancing algorithm runs in several stages.

The first is the simple solution which is analogous to multiplelinear regression. Unless the data has serious problems it willconverge in one step; that is, the second solution will be the sameas the first.

If small negative values occur, increase the number of steps toeliminate these values. However, recheck your data carefully.Negative values indicate measurement bias.

For higher numerical accuracy you may increase the iterationlimits. However, there will be no gain in the balance accuracybecause data accuracy will be the usual limit.



Hint: Read section 6.9 on Problems relating to Mass balancingbefore adjusting these settings.

The values shown above are the default values.

If the adjusted data show unacceptable inconsistencies (forexample, Au assays in ppm or 1.0 E-06 will not work too well witha convergence criterion of 1.0 E-05) then you must either reducethe limit or, more sensibly, re-scale the assay. For example,express your gold assays as Au ppm and do not constrain the assaytotal to 100%.

6.6.7 Carrying out the Mass Balance

This is the simplest step. Once the components have beenspecified, the desired equipment and streams selected and the datahave been input, the mass balancing can begin.

Step 1 Click on the Run Balance tab of the Mass Balancewindow.

Step 2 Ensure that the correct Select and Component lists areselected in the cells above the main data area. For theCopper Flotation example we will use the existingSelect list Mass Balance Select List 1 and theComponent list CuFe.

Step 3 Left-click on the Start button to start the massbalancing program.



The mass balancing program will run and when it is complete theresults will be summarised in the Mass Balance window as shownbelow. The user can also examine the detailed data in the port datawindows or using the Overview or graphing features.

Checking the Balance Mass Balancing


6.7 Checking the Balance

During the execution of the balance program, the Mass Balancewindow is displayed. Once execution has stopped, the values inthe results section of the window are updated. Assuming that thebalance has reached a satisfactory conclusion, the calculatedstandard deviations of the solid flowrates are also updated.

The standard deviations calculated by the mass balancing programfor each solids flowrate are analogous to the Model Fittingestimates of parameter accuracy, that is, solids stream flowrates arethe parameters of Mass Balancing.

There are various ways in which the user can assess the results:

• The overview window is probably the most useful way to checkdata and results. It also allows recovery of any component to bedisplayed for all streams. See Section 6.8.1 for details of theoverview facility.

• Compare the size or order of magnitude of the SDs with that ofthe associated value. When the SD is small compared with thevalue as a ratio, it is a good fit; and when large, a poor fit.

• The summary values in the Sum of Squares section at the foot ofthe Run Balance tab also indicate the overall success of the fit.Low values indicate a good balance while large values of theseitems indicate a poor balance. Moreover, in the case of thesefields, cross comparisons between mass balances can be made.If these values are smaller in the most recent run of the balancethan they were in the previous run, the balance is getting better.If they are getting larger, your mass balancing is going in thewrong direction.

• The engineer can also judge the relative success of the massbalancing by looking at the port data windows. Examine thevalues in the Error column. The Weighted Error and PercentageError versions of the difference between balanced andexperimental data for sizings are most useful.

• The graph plotting facility of JKSimMet allows the user to plotraw and balanced size distribution data (GSIM) on the samescreen, as detailed in section 6.8 (Presentation of MassBalancing Results).

• Mass Balancing can be carried out one unit (or a small set ofunits) at a time. This allows you to put the test data under amicroscope. If circuit conditions were changing as you did yourtest work, unstable sections will give unusable results andvarying conditions will usually produce nonsense.

Mass Balancing Checking the Balance


Concept:Data StandardDeviations

At the best-fit point, an estimate of the goodness of fit is calculatedby dividing the weighted sum of squares (Residual Error) by thenumber of points less the number of parameters, and taking thesquare root. If the data and the error estimates are in agreement,and if the model is appropriate, this number will tend towards one.With Whiten SDs, good data achieve values in the range 1 - 4.

Concept:Stream DataSDs

The same approach can be used for each stream point. Thesevalues are reported for each fitted stream in the Mass Balancewindow and the stream data windows.

The solution of the mass balancing minimisation also providesestimates of parameter accuracy. The parameters in this case arethe stream flowrates. The mathematical proof of this estimate ofaccuracy is complex. Intuitively, if the parameter is well defined,the sum of squares will vary more rapidly as the parameter isadjusted. For a more detailed explanation, see LYNCH (1977),chapter 7.

If the program finds that small variations in a parameter make NOapparent difference to the sum of squares at the minimum, it setsthe parameter SD to 1E18 Such mass balance results should beTREATED WITH CAUTION.

Note also that such a result may mean you are trying to balancearound a splitter or a classifier which is not classifying.

Presentation of Mass Balancing Results Mass Balancing


6.8 Presentation of Mass Balancing Results

There are two main ways to present the results of mass balancing:

• the overview window and• printing

We shall deal with these in turn. For mass balanced data, graphplotting is limited to GSIM format.

6.8.1 Overview

The overview window gives you a powerful means of summarisingyour data and checking it for adjustment problems. Each overviewdata set defined by the user displays a list of data from all selectedstreams. The user can select the types of data which are displayedin the overview window.

The best way to use the overview feature is to compareexperimental and calculated values for each assay (or size fraction)across the complete circuit. This will give a very useful picture ofthe accuracy of the data and the mass balance. Note that theoverview window can be configured to show either data orcalculated Recovery information.

Step 1 Left-click on the Overview Config button on the mainJKSimMet toolbar. This brings the Overview windowinto view.

Step 2 Select the existing overview.

Mass Balancing Presentation of Mass Balancing Results


Step 3 In order to make it easier to view the data in theoverview window, resize the window by clicking anddragging the bottom, right-hand corner of the window.Also widen the Equipment and Port columns byclicking and dragging the right-hand border of the titlecell in each column.

Step 4 You can now add a column to view the Fe assay SDdata by clicking on the Insert Column icon at the top ofthe overview window.

Step 5 Place the cursor in the top title cell of the new columnand press Enter to bring a drop-down list of optionsinto view. Select Components from the list.

Step 6 Place the cursor in the middle title cell of the newcolumn and press Enter to bring a drop-down list ofcomponent options into view. Select %Fe from the list.

Step 7 Place the cursor in the lowermost title cell of the newcolumn and press Enter to bring a drop-down list ofoptions into view. Select Calc Bal SD from the list ofoptions. The overview window should now look likethe picture below.

RecoverySelection

To examine recovery data for the components in the streams selectRecovery by placing a tick in the Recovery box.

Note: The balanced recovery selection will calculate recoveriesbased on mass balanced assays and flowrates.

By default, the recovery is calculated with respect to the circuit feedstream. This reference stream is labelled in bold text in theOverview table. To change the stream which is the reference for



recovery calculations, move the cursor to the row in the overviewwindow which has the named stream in and right-click in theequipment column. This brings up a dialogue window as shownbelow which allows you to define the selected stream as thereference for the recovery calculations.

6.8.2 Printing the Mass Balance Results

PrintingMass BalanceResults

Printing can be selected from any window by clicking on the Printicon on the JKSimMet toolbar. When this is done, the currentwindow will be printed.

Given that mass balancing concerns the experimental (raw) dataand the adjusted (mass balanced) data for streams, our task is toprint these two types of data for the streams concerned. One way todo this is to print individual port data windows. In this case ensurethat the port data window Data type is set to SD’s.

An alternative method for printing the experimental and adjusteddata is to configure a Report. This allows the user to select any ofthe port data types for printing and includes a Summary formatwhich is useful for comparing data.

To print recovery data, use the overview table with the Recoveryoption selected. Remember to select a stream to use as the recoverybasis. (If this stream is the feed stream, this will produce anelement distribution which is often the objective of massbalancing).



6.8.3 Plotting Graphs

Plotting Graphsof the MassBalancing Results

The graphs presenting mass balance results are, once again, ofstream data. They involve experimental (raw) data and adjusteddata. The simplest way to begin is to select the default formatoptions available in the graphing sub-system and simply nominatethe data to be plotted. You can then edit the format and axes asrequired.

At present, graphing is available only for GSIM format. Therefore,to examine graphing for mass balancing, leave the Copper Flotationflowsheet and select the flowsheet named Example Cyclone MassBalance. For this exercise, you will create a new graph.

Step 1 Left-click on the Generic Graph Config button on themain toolbar to open the Graph Definition window

Step 2 Left-click on the Format tab to make this the active tab.

Step 3 Left-click on the New button at the top, right corner ofthe Graph Definition window to create a new graphformat.

Step 4 Place the cursor in the Name text box and double-clickto highlight the default graph format name. Now typein a new format name and press Enter. Any new namewill do.

Step 5 Change the labels and the information in the Axes andData Interpretation area of the Format tab, using thepicture below as a guide.



The next step in configuring the graph is to tell JKSimMet where tofind the data to be plotted.

Step 6 Left-click on the Port Data tab to make this the activetab and click on the New Data icon to create a newgraph data set.

Step 7 Name your data set, following the procedure describedin Step 4.

Step 8 Move the cursor across to column 1 of the row labelledPort in the Data Selection - Ports area of the windowand press Enter to view the drop-down list of portswhose data can be graphed. Select the CycloneUnderflow by highlighting its name and pressing Enter.

Step 9 Move the cursor to the Format cell and press Enter toview the drop-down list of format options. For this plotselect the Cum. % Passing option.

Step 10 Move the cursor to the Data cell and press Enter toview the drop-down list of data which can be plotted.Note that individual data types (e.g. Simulated) or pairsof data types (Experimental and Simulated) can beselected. In the latter case the Experimental data are



represented by the data marker and the calculated dataare represented by the line. For this graph select theExp & Bal option.

Step 11 If you would like to change the style of line or datamarker or the colour used to display the data on thegraph select the required items in the Line Point andColour cells respectively.

Step 12 Ensure that the box in the Spline cell is not ticked.

Step 13 Move the cursor to the X Min cell and enterappropriate values in the minimum graph range for thelines you want to plot. This is a type-over field. In thiscase enter the value 0.01 for the minimum value of Xto be plotted.

Step 14 Repeat Step 13 for the X Max cell, in this case enteringthe value 10 for the maximum value of X to be plotted.

Step 15 Repeat Steps 8 - 14 for all streams required, placingeach in a new column.

Step 18 Left-click on the Display Graph icon at the top right-hand corner of the Graph Definition window to viewyour graph. The plot for the Cyclone Mass BalanceExample looks like the picture below.

You can now refine the format of the graph and print it etc., asoutlined in the section 3.8 (Learning Graphing). Repeat the abovesteps for each of the streams for which you wish to compare theraw and calculated data. The goodness of fit is represented by thecloseness of the points to the line; the closer the lines and points,the better the fit.

Problems and Possible Solutions Mass Balancing


6.9 Problems Related to Mass Balancingand Possible Solutions

There are, of course, many problems that may be encounteredduring mass balancing. It is possible, however, to point out some ofthe more common mistakes, in order to alert you to some of themajor pitfalls.

Errors, Warnings,Faults

Some problems detected by JKSimMet produce error messages.See Appendix B for such problems.

ERRORS 120-139 are relevant to the Mass Balancing module.Please refer to the expanded descriptions in Appendix B.

Skillversus Practice

Mass Balancing is not a cut and dried procedure. The only way toacquire a useful skill level is to practise on a wide range of realdata. JKSimMet offers a user-friendly environment for what arereally very complex and powerful mathematical techniques.

GraphicalAnalysis

The graph capability of JKSimMet is the most powerful way toexamine your data fit (in GSIM stream format only).Discontinuities in size data highlight poor data or a change in sizemeasurement technique. Graphical analysis also highlights anybias in the data fit.

Different SizingTechniques

Be very wary of changes in size measurement technique e.g. fromscreens to Cyclosizer.

Different AssayTechniques

Where assay techniques change between stream samples, as theysometimes do for different assay ranges, there may be inherentbiases within the assay techniques. These will lead to biases withinthe mass balance.

Data Note that it is necessary to have enough feed and product data toachieve a useful mass balance.

Some CommonMass BalancingPitfalls

There are a couple of simple traps which can appear in manyguises. If you become aware of these now you may recognize themmore easily when you encounter them.

Mass Balancing Problems and Possible Solutions


6.9.1 The Middlings Problem

If we return to our one unit flow diagram and add on a middlingstream of assay m:

a

b

m

c

It is easy to see that there are not enough assays to go around.However, if we have two assays in each stream, we would writethem out as simple equations and solve for two unknowns.However, as m really is a middlings stream, it will be close to a incomposition and very often recycled back to it.

In this case, no matter how accurately we can sample and assay thestreams, we can only find out:

• the ratio between flows b & c (if m goes elsewhere)or

• the flows in b and c if a is recycled.

However, the actual flowrate in m can be either zero or infinity.There is a straightforward solution. Measure (or estimate) theflowrate in stream m and input this flowrate as data.

The mass balancing module allows you to do this.

Problems and Possible Solutions Mass Balancing


6.9.2 The Infinite Division Problem

The InfiniteDivision Problem

If one wishes to extract maximum information from a survey, it isnot unusual to assay on a two (or even three) dimensional matrix,for example, assay by size or assay by size by specific gravity.

This subdivides the stream into even smaller sub-groups. Eachsub-group has an extra step of processing and an increased relativeerror. Hence, we tend towards trying to solve for (0 - 0) / (0 - 0).This is not a useful numerical exercise.

Once again, the solution is straightforward. Use the total assayswith large differences to calculate the Mass Balancing flowratesolutions. Once you have these flowrates, fix them by enteringthem as experimental flowrates with low standard error estimatesand add all of the small assays into the problems.

Now that the flowrates are defined, the Mass Balancing module canallocate the minimum adjustments required to make all of thefractional assays consistent.

(Note this balancing module does not balance across the matrix formore than one component at a time - this component is usuallysize.)

Mass Balancing Metallurgical Accounting


6.10 Metallurgical Accounting

The day to day data collected from a mineral processing plant arerarely consistent and will almost always contain redundantinformation. In general, any two methods of calculation will yielddifferent results. The challenge for metallurgical accounting is toproduce adjusted data which are both self-consistent and asaccurate a representation of plant performance as possible.

Consider a typical base metal concentrator with several productsfrom several circuits,

FeedCopper Au Circuit

Lead Circuit

ZincCircuit

Tailings

Cu AuConc

PbConc

ZnConc

x x x x

x x x

At each point marked ⊗, we have Au, Cu, Fe, Pb and Zn Assays.For the feed, we have weightometer readings and for theconcentrates we have load out weights with stockpile surveys.

If we select an accounting period which is large compared with thecircuit residence time, we can carry out a mass balance over thiscomplete data set. If large adjustments are required, these may bemeasurement problems in sampling or assay techniques. Selectsmaller circuits to mass balance to isolate these problems.

Once a consistent set of adjusted data is produced for eachaccounting period, the sums of these sets will also be consistent.

If assays and flowrates are available on a short time scale, eg.several times per shift, these data can be balanced for each timeperiod, printed to file or exported to most Windows spreadsheetand word processing packages by copying and pasting.

JKMetAccount For users with a serious interest in metallurgical accounting, theJKMetAccount program was created to enable the Metallurgist orPlant Manager to track the performance of a mineral processingplant over time. It's major strength comes from harnessing thepower of the JKMBal mass balancing engine within a rigorous datamanagement environment. Changes to your plant flowsheet, whichcan cause major problems for a spreadsheet based accountingsystem, are handled with ease by JKMetAccount. Combine thesefeatures with a graphical flowsheet drawer and the ability to use thefull formatting power of Excel in your reports and you have a toolthat we believe you will soon come to regard as indispensable.Further details are available from JKTech or atwww.metaccount.com

References Mass Balancing


6.11 References

LYNCH, A.J., 1977. Mineral Crushing and Grinding Circuits,(Elsevier, Amsterdam), Chapter 7.

LYMAN, G.J., 1986. Application of Gy's sampling theory to coal,International Journal of Mineral Processing, Vol 17:1-22.

GY, P.M., 1982. Sampling of particulate materials: theory andpractice, 2nd Ed, (Elsevier, Amsterdam).

MORRISON, R.D., 1976. A two stage least squares technique forthe general material balance problem, JKMRC InternalReport No 61 (unpublished).

Appendix A Model Descriptions

Version 5.1 November 2001 Appendix A Page A-1

APPENDIX A

Model Descriptions

Introduction Appendix A

Page A-2 Appendix A1 Version 5.1 November 2001

A1 IntroductionThis appendix of model descriptions contains:

• a description of each model available in JKSimMet• key equations which are the mathematical basis of the models• known limitations and restrictions• some guidance and restrictions for parameter fitting• typical model parameter values, where appropriate

There are a number of generic models included in JKSimMet,which can be used to describe the behaviour of a wide range ofprocesses. For example, the simple efficiency curve model can beused to describe any sort of classification device, such as a cyclone,or a spiral classifier. Selection or fitting of parameters for thesemodels will depend entirely on the type of process being modelled.

Most of the process units available to the user when drawing theflowsheet can be described by a number of models. Typically, aprocess unit will have a specific model, developed for thatparticular device, and a number of generic models. Selection of theappropriate model is at the user's discretion and will often dependon available test data.

A1.1 Parameter Defaults and Range Limits

Model parameters in V5 have default values and a permitted range.The default value and range can be viewed by double clicking onthe parameter value.

These values are not currently editable by the User.

A1.2 Model Differences in JKSimMet V5.0and 5.1

To provide a more ‘obvious’ structure for Version 5, a class offeeder models has been added.

These provide:• A source for ore• A source for water

Later modules will provide access to configuration data. For thelong term option of a full dynamic simulator, the feeder modelswill provide a way of inputting variation with time.

Appendix A Introduction

Version 5.0 December 1999 Appendix A1 Page A-3

A1.2.1 Ore Feeder

Ore Feeder The ore feeder (called Feed) is a specialised piece of equipmentwhich has a single ‘product’. The Feed unit allows you to set upthe flowsheet ore SG and the default size distribution.

The size markers, i.e. Percent passing a particular size and size ata particular percent passing can be set by double clicking on thosefields on the Totals tab. Note that while the flowsheet propertiesdialogue allows you to set global properties for Data Informationblocks and tools such as simulation and model fit, theseproperties for the feeder and ports may be set at different valuesfor each.

A1.2.2 Water Feeder

Water Feeder The water feeder replaces the ‘Unit Feed Density’ section of eachmodel in JKSimMet Version 4. The three models provided withthe Water Feeder are functionally identical to the three options for‘Unit Feed Density’.

Option 1 - FeedStreams

No water is added.

The model reports on flow rates of solids and water added to thepiece of equipment to which it is connected. This information isredundant as it is also contained in the feed port of that piece ofequipment. This model is provided for compatibility withVersion 4.



Option 2 –Required %Solids

This option allows the user to set a maximum percent solids forthe total feed to the connected equipment.

If the feed percent solids is higher than ‘Required % Solids’ thewater feeder adds additional water to achieve the required percentsolids.

If the percent solids value is already lower than required, thewater feeder adds no water. It does NOT remove water toachieve the required value.

Appendix A Introduction


Option 3 – WaterAddition

Water Addition is the recommended mode for common use. Theuser specifies the required water addition in cubic metres perhour.

This option has two more uses. The experimental water additionmay be used as a parameter in Model Fitting. That is, a model fitmay use water addition as a parameter when water flows wereunmeasured or the measurement is dubious.

The ‘exp Water Addition’ is subject to optional update after amodel fit as are all other parameters.

Note that percent solids or water flow from the circuit should beconstrained by a small SD value to provide a constraint on totalwater addition.

The third use of this option is for mass balancing of wateradditions.

The User provides the ‘exp New Water Addition’ and an ‘sd’estimate on this model. The other requirement is that the WaterFeeder and Water are selected on the Select Tab of the MassBalance tool.

The balanced water addition is returned to the calc* field of theWater Feeder. If you wish to use this value for fitting orsimulation, copy it into the Exp value.



A1.2.3 Variable Rates SAG Mill Model

Variable RatesSAG Model

The Variable Rates SAG model also has some differences –detailed in Appendix 11.

A1.2.4 Splitters

Splitters The range of splitter models has been increased. These arediscussed in Appendix 14.

Appendix A Hydrocyclone (Model 200, 201)

Version 5.1 November 2001 Appendix A2 Page A-7

A2 Hydrocyclone (Model 200, 201)

A2.1 Model Description

The model is based on the concept of a reduced efficiency curve,which in turn is developed from the actual efficiency curve and thecorrected efficiency curve for the classifier treating a particular ore.The important concept is that the reduced efficiency curve is acharacteristic function of an ore and is independent of thedimension or operating conditions of the cyclone. A typical set ofefficiency curves for a cyclone is shown in Figure A2.1.

The model consists of a series of equations which are describedbelow. At least one cyclone test on a particular ore is required toprovide data for the calculation of constants in the equations.

A2.2 Model Equations

The model consists of a series of equations which are describedbelow.

Pressure-ThroughputRelationship

The pressure-throughput relationship can be expressed as:

Q = KQ2 Dc2 (P/ρp)0.5 (Do/Dc)0.68 (A2.1)

where

KQ2=KQ1 (Di/Dc)0.45 (θ)-0.1 (Lc/Dc)0.2 (A2.2)

The proportionality constant, KQ1, is a function of the feed materialand the diameter of the cyclone. For cyclones of Krebs design,treating identical feed solids, the dependence on cyclone diametermay be empirically represented by the equation

KQ1=KQ0 Dc-0.1 (A2.3)

where KQ0 depends on feed solids characteristics (eg. specificgravity) only.

Hydrocyclone (Model 200, 201) Appendix A


ClassificationSize Relationship

For normal industrial operation, the classification size can berelated to the variables according to the equation

d50c/Dc=KD2(Do/Dc)0.52 (Du/Dc)-0.47 λ0.93(P/{ρp g Dc})-0.22

. . . (A2.4)

where KD2 is related to the minor design variables Di, Lc and θ by

KD2=KD1 (Di/Dc)-0.5(Lc/Dc)0.2 (θ)0.15 (A2.5)

and KD1 may be written as

KD1=KD0 (Dc)-0.65 (A2.6)

KD0 depends on feed solids characteristics only (such as sizedistribution and specific gravity).

(Note that the classification sizes for specific minerals within thefeed stream can be estimated using the following formula:

d50c = FeedSG -1MineralSG -1

* d50c( )m

where FeedSG is the mean feed solids density, d50c is the overallcorrected d50, MineralSG is the density of the specific mineral ofinterest, and d50c(m) is the corrected d50 of the mineral ofinterest.)

Recovery toUnderflowRelationships

Water recovery (Rf) and volume pulp recovery (Rv) to underfloware related to the major variables by:

Rf=Kw2(Do/Dc)-1.19 (Du/Dc)2.40 (P/{ρp g Dc})-0.53 (λ)0.27

. . .(A2.7)

and

Rv=Kv2 (Do/Dc)-0.94 (Du/Dc)1.83 (P/{ρp g Dc})-0.31 (A2.8)

Further, the effects of inlet diameter, cone angle and cylinder lengthhave been evaluated as

Kw2=Kw1 (Di /Dc)-0.50 (θ)-0.24 (Lc/Dc)0.22 (A2.9)

and

Kv2=Kv1 (Di/Dc)-0.25 (θ)-0.24 (Lc/Dc)0.22 (A2.10)



Here Kw1 and Kv1 are constants also depending on feed solidscharacteristics. The current data indicate that Kw1 and Kv1 areindependent of cyclone diameter for geometrically similar cyclonestreating identical feed solids. Small quantities of viscositymodifiers such as clay, can have a marked effect on these variables.

Efficiency CurveRelationship

The efficiency curve used in this model is given below:

Eo(d/d50c)=C⋅(1+β⋅β*⋅d/d50c) (exp(α) - 1)/(exp(α⋅β*⋅d/d50c)

+ exp(α) - 2) (2.11)

When β is 0, β* is 1 the above equation reduces to

Eo(d/d50c)=C⋅(exp(α) - 1)/(exp(α⋅d/d50c) + exp(α) - 2) (A2.12)

The shape parameter β determines the initial rise, while αdetermines the slope at larger values of d (d≈d50c). Both α and βare normally constant for given feed solids, while C and d50c varywith cyclone dimensions and operating conditions. Theparameter β* is determined, for given values of α and β, by thecondition that

Eo(1) = C/2 (A2.13)

β* is calculated iteratively in the model.

Figures A2.1 and A2.2 show the effects of α and β on the shape ofthe efficiency curve.

ModifiedEfficiency Curve

An alternative to the standard efficiency curve is available with theNageswararao Fines hydrocyclone model.

With this model the user can specify the value of the reducedefficiency curve (ie. fraction reporting to overflow) at 33% and66% of the d50c size.

The curve is fixed (by definition) at the 100% point for zero sizeand at the d50c. A cubic spline curve is used to describe theefficiency curve for sizes below the d50c point. For sizes largerthan the d50, a log-normal distribution curve is used. The log-normal curve is determined so that there is no discontinuity in slopeat the d50c point.

Figure A2.3 below shows how the modified efficiency curveworks. The user needs to specify (or model fit) the values of thecurve at 33% and 66% of the curve only.



The other parameters used by the model are used in the same wayas the standard Nageswararao model.

The Nageswararao-Fines model is useful for describing asymmetricefficiency curves where a long 'tail' exists for either coarse or finematerial.

Interactions The interactions of variables within a cyclone are complex. Referto section A2.7 (Summary Table) for a summary of interactiondependencies.

Scaling Facilities for scaling the operation of the hydrocyclone are builtinto the model.

d/d50 (corrected)

% o

f Fee

d to

Ove

rflow

(cor

rect

ed)

0

20

40

60

80

100

0.00 0.50 1.00 1.50 2.00 2.50

Increasing Alpha

Figure A2.1: Effect of αααα on Reduced Efficiency Curve



d/d50 (corrected)

% o

f Fee

d to

Ove

rflow

(cor

rect

ed)

0

20

40

60

80

100

120

140

160

180

0.00 0.50 1.00 1.50 2.00 2.50

Increasing Beta

Figure A2.2: Effect of ββββ on Reduced Efficiency Curve

d/d50(corrected)

% o

f Fee

d to

Ove

rflow

(cor

rect

ed)

0

20

40

60

80

100

120

140

160

180

0.00 0.50 1.00 1.50 2.00 2.50

Efficy. curve at 0.33xd50c

Efficy. curve at d50c

Efficy. curve at 0.66xd50c

Figure A2.3: Efficiency curve used in the Nageswararao-FinesModel



A2.3 Hydrocyclone Model Printout(Nageswararao) (Model 200)

Hydrocyclone Model Printout(Nageswararao - Fines) (Model 201)



A2.4 Symbols

Symbol Meaning

α reduced efficiency curve sharpness parameter

β reduced efficiency curve hook parameter

β* reduced efficiency curve calculated parameter

C 100 - Rf or recovery of water to overflow, %

Dc cyclone diameter, m

Di diameter of circle with the same area as cyclone inlet, m

Do diameter of circle with the same area as vortex finder, m

Du diameter of circle with the same area as spigot, m

Eo(d) percentage of feed material of size d reporting to overflow

g gravitational acceleration

KD constant in the classification size relationship

KQ constant in the volume pulp recovery relationship

Kv constant in the volume pulp recovery relationship

Kw constant in the water recovery relationship

Lc length of cylindrical section, m

P feed pressure at inlet, kPa

Q cyclone throughput, m3/hr

Rf recovery of water to underflow, %

Rv volumetric recovery of feed pulp to underflow, %

d mean size of particle, mm

d50c size of a particle in feed which has equal probability ofgoing to underflow or overflow, due to centrifugal action,mm

Cv volumetric fraction of solids in feed slurry

λ 101.82Cv/ (8.05 ∗ (1.0 − Cv)2)

ρp density of feed pulp, tonnes/m3

θ cone full angle, degrees



A2.5 Known Restrictions

• As the feed becomes coarser, d50c tends to decrease evenwhen all the other variables are kept constant. The effect ofsize distribution of the feed material becomes insignificantwhen the feed consists of mainly –53 µm particles, and alsowhen the proportion of –53 µm particles is less than 25% ofthe feed solids.

• The analytic form used does not provide a perfectrepresentation for the reduced efficiency curve. As a resultthe model often tends to predict fewer coarse particles in theoverflow than occur in real operation, however, the magnitudeof the error is considered to be small.

• Viscosity variations due to changes in pulp density are largelyaccounted for by the model. Viscosity variations caused byvariable quantities of slimes affect the parameters in quite asystematic way.

• As viscosity (or slimes fraction) increases, the cut sizebecomes coarser, the water split to overflow is reduced, andthe cyclone pressure drop becomes larger. However, thereduced efficiency curve remains relatively constant until theonset of roping.

• The model may be used to estimate operation during roping:

– the cut size will become 5 to 10 times larger (ie. multiplyKD0 by 5 to 10 times

– the efficiency curve will become an “inefficiency” curvewith an α value typically of 0.1 - 0.2.

– water split and pressure drop are relatively unaffectedalthough a small drop in pressure is often claimed. Thismay result from a reduced volume of solids to overflow.

• The onset of cyclone roping is difficult to predict. In general50% solids by volume is a practical underflow limit.However, very coarse underflow may achieve higher densityand finer ones somewhat lower density as detailed below.

JKSimMet will warn you that roping is likely if either of thedensity limits (detailed below) are exceeded.



Cyclone RopingConstraint

If the cyclone feed density is less than 35% solids by volume, theSPOC constraint (Laguitton 1985) is claimed to predict onset ofroping.

Vol % solids in U/F = Limiting Vol % solids (~56)+ 0.2 (Vol % Solids in Feed -20)

The limiting % solids is defined as the onset of roping at avolumetric feed density of 20%.

In tabular form:

at sg 2.7 at sg 4.0Feed

DensityUnderflow

DensityFeed

DensityUnderflow

DensityFeed

DensityUnderflow

Density% by Volume % by Weight % by Weight

5 53 12.4 75.3 17.4 81.810 54 23.1 76.0 30.8 82.415 55 32.3 76.7 41.4 83.020 56 40.3 77.5 50.0 83.625 57 47.4 78.2 57.1 84.130 58 53.6 78.8 63.1 84.735 59 59.2 79.5 68.3 85.2

EmpiricalConstraint

Industrial experience demonstrates that a coarse underflow willremain in spray discharge at a higher density than a fine underflow.This is intuitively reasonable in terms of slurry viscosity butdifficult to predict.

Plitt et al (1987) have developed an empirical relationship based onLynch (1965) data and others.

Vol % Solids in U/F = 62.3

)

60m size U/Fpassing 50%-( exp-1 µ

This approach puts a 50% solids by volume limit on an underflowwith 50% passing 100 µm and 60% at a P50 of around 200 µm.This function decreases sharply with size dropping to 45% solidsby volume at a P50 of 80 µm and 40% at a P50 of 60 µm.



In tabular form:

Roping onset% Solids by Vol.

Underflow50% passing (µm)

% Solidsat sg 2.7

% Solidsat sg 4.0

35.2 50 59.4 68.539.0 60 63.3 71.945.9 80 69.6 77.250.5 100 73.4 80.353.9 120 75.9 82.458.6 170 79.3 85.060.0 200 80.2 85.761.3 250 81.0 86.4

The two effects are probably competitive to some degree. Further,each operation has a 'comfort limit' on cyclone underflow densitywhich may be a good deal lower than the above limits.

A2.6 Summary Table

SUMMARY OF THE EFFECTS OF VARIABLES ONCYCLONE OPERATION

Variable Resultant effect on parameter

Increased Q d50c Rf Rv

Dc increase (.57) increase (.82) decrease (-.4) decrease (-.55)

Di increase (.45) decrease (0.5) decrease (-.5) decrease (.25)

Do increase (.68) increase (.52) decrease (-1/19) decrease (-.94)

Du -- decrease (-.47) increase (2.4) increase (1.83)

Lc increase (.2) increase (.2) increase (.22) increase (.22)

p increase (.5) decrease (-.22) decrease (-.53) decrease (-.31)

λ -- increase (.93) increase (.27) --

ρp decrease (-.5) increase (.22) increase (.53) increase (.31)

θ decrease (-.1) increase (.15) decrease (-.24) decrease (-.24)

Note: The numbers listed in brackets are exponents for dependenceof the parameter on the variable.

Examples of the effects of α and β on reduced efficiency curves aregiven in the attached Figures A2.1 and A2.2. The β* parametersused in the model are calculated.



A2.7.1 Fitting the Cyclone Model (200)PARAMETER MENU

Pressure Data If you wish to predict cyclone pressure accurately at otherconditions you will need at least one accurate pressuremeasurement and a set of at least two out of three of the feed,underflow and overflow samples.

If pressure data are not available, an approximate pressure can beestimated from the manufacturers published data.

The calculated pressure is used in the equations for classificationsize and recovery to underflow. Hence, the cyclone pressure is animportant measurement.

The measured or assumed pressure data must be entered on thePerformance Data tab of the cyclone equipment data window. If anaccuracy estimate is available, use it to calculate the standarddeviation. If not, use 10% of the pressure value.

The capacity constant KQO can be calculated from the cycloneflowrate and the cyclone dimensions. (Refer to equations A2.1-A2.3).

Typical values of KQO are in the range 300-600. The scale factorfor fitting should be 100.

To make the pressure observation available to the fittingcalculation, it must be selected with a tick on the Equipment Datatab of the Model Fit dialogue window.

ClassificationSize (KDO)

Equations A2.4 to A2.6 define the cut size. KDO is typically asmall number - say 0.001 to .00001. Therefore, a scale factor of0.0001 is usually suitable.

Water Split % toO/F (Cal WS)

The actual water split to overflow (Cal WS) is fitted rather than thetwo parameters, KV1 and KW1, which are defined by a singlewater split.

When model fitting a single set of cyclone data, ALWAYS fitCal WS. A good starting point is 50% with a scale factor of 5.

After fitting, the calculated values of KV1 and KW1 are displayedon the cyclone equipment data window (Model Parameters tab).



Efficiency Curve(αααα and ββββ)

The reduced efficiency curve is an "S" shaped function as shown inFigure A2.1.

Typical values of a α range from 0.5 to 4. Beyond 5, the efficiencycurves become very sharp and larger numbers are not significant. Agood initial estimate is 2.0.

The β factor modifies the "S" curve to add an additional "hook" - ora negative portion to the actual efficiency curve. A typical value iszero. However, a poor fit at fine sizes can be tested by tryingvalues of β of 0.01 to 0.5. Fitting of β is available but notrecommended. A scale factor of 0.1 is suitable once a good initialestimate has been found by trial.

If the efficiency curve is a poor fit at coarse sizes, try the alternativefines modified or spline efficiency curve models.

Master/SlaveFitting

Multiple sets of cyclone data can be model-fitted using theMaster/Slave facility, with one important provision. The watersplit (Cal WS) cannot be fitted using Master/Slave fitting.

Fit KD0, KQ0, α and Cal WS for each data set independently, anddetermine the average values of KV1 and KW1 for each cyclonedata set from the fit. Use the average values of KV1 and KW1 ineach cyclone data set. Use Master/Slave to fit KD0, KQ0, α and (ifrequired) β, over all data sets.

A2.7.1 Fitting the Nageswararao Fines Model(201)PARAMETER MENU

The comments in A2.7.1 above apply equally to Model 201 exceptfor the Efficiency Curve parameters α and β which are replaced byEff @ 0.33 (of d50c) and Eff @ 0.66 (of d50c).

Typical values are 0.85 and 0.65 respectively.



A2.8 References

DE KOOK, S.K., 1956, Symposium on recent developments in theuse of hydrocyclones - a review J. Chem. Metal. Min. Soc.S.Afr., Vol. 56:281-294.

KAVETSKY, A., 1979. Hydrocyclone modelling and scaling.JKMRC report to AMIRA, November.

KELSALL, D.F., 1953. A further study of the hydraulic cyclone.Chem. Eng., Sci., Vol. 2:254-273.

LAGUITTON, D. (Ed), 1985. The SPOC Manual SimulatedProcessing of Ore and Coal, CANMET EMR Canada, Ch.5.1 (Part B).

LYNCH, A.J. 1965. The characteristics of hydrocyclones and theirapplication as control units in comminution circuits, AMIRAProgress Report No. 6, University of Queensland(unpublished).

LYNCH, A.J. and RAO, T.C., 1965. Digital computer simulationof comminution systems. Proc. 8th Comm. Min. Metall.Congr., Aust., N.Z., Vol. 6:597-606.

NAGESWARARAO, K., 1978. Further developments in themodelling and scale-up of industrial hydrocyclones. Ph.D.Thesis (unpublished). University of Queensland.

PLITT, L.R., FLINTOFF, B.C. and STUFFCO T.J., 1987. Ropingin hydrocyclones. 3rd International Conference onHydrocyclones, Oxford England, Elseveir, pp21-23.

YOSHIOKA, N. and HOTTA, Y., 1955. Liquid cyclone as ahydraulic classifier. Chem. Eng. Jpn., Vol. 19:632-640.



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Appendix A Single Deck Screen (Model 230)


A3 Single Deck Screen (Model 230)


Mechanistically a screening process can be regarded as a series oftrials, as a result of which particles of a particular size have aprobability of entering the fine product. This concept of definingthe screening efficiency in terms of a number of trials (or bounces)is the basis for a screen model.

A typical efficiency curve for a vibrating screen is shown inFigure A3.1. There are three regions on the curve:

Particle Size

A

B

C

Figure A3.1 :A Typical Efficiency Curve for a Vibrating Screen

• the region describing the above-aperture size material (regionA),

• the region describing the below but near aperture size material inwhich the probability of passing through the aperture is directlydependent on particle size (region B),

• the region describing the ultra-fines that adhere to the coarseparticles (region C).

Region B of the efficiency curve is the important region formodelling purposes, and it can be described by the equation(Whiten and White 1977).

E(x) = exp[-TRN.fo.(1-x/d)k] (A3.1)

where E(x) is the fraction of particles in the feed of size x whichenter the coarse product, d is the screen aperture; fo the fractionopen area, TRN is the efficiency parameter and k is a minorparameter used for precise fitting purposes. Typically, the value ofk is about 2. The performance of the screen in region C can only bedetermined experimentally since it will be dependent on local

Single Deck Screen (Model 230) Appendix A

Page A-22 Appendix A3 Version 5.0 December 1999

conditions such as the moisture content of the ore which causessmall particles to adhere to large particles. For design purposes it isnecessary to make a reasonable assumption about the shape of thecurve in region C and this assumption is made by the designengineer based on knowledge of local conditions.

The typical dependence of the efficiency parameter, TRN, which isanalogous to the number of trials, on the feed rate is shown inFigure A3.2 for different materials used for the screen deck.

Steel

Rubber

100

10

1.00 F W1 FW2 High

Feed Rate/Unit Width

Figure A3.2: The dependence of the screen efficiency parameters on thefeed rate for rubber and steel decks.

The explanation of Figure A3.2 is that when the feed rate to screenswith rubber decks is low the particles move independently,accumulate energy, take large bounces and have little opportunityto pass through the screen aperture.

An increase in feed rate causes an increase in inter-particlecollisions, reduction in particle energy and bounce lengths, and anincrease in number of trials. Hence, the screen efficiency increases.A further increase in feed rate causes more particle interference, adecrease in the number of trials due to particles not reaching thescreen surface, and a decrease in screening efficiency.

With steel screens, however, the coefficient of restitution is lowand particles do not accumulate energy. Particle bounces are smalland high efficiencies occur at low feed rates. As the feed rateincreases the inter-particle interference increases and this reducesthe number of trials and the screening efficiency.



ModelLimitations

A better understanding is required of the relationship betweenparticle shape, aperture shape and screen efficiency, and also ofscreening performance in the difficult area between dry and wetscreening. The first is a problem of optimization of existingscreens, the second is a problem of plant operation.


Region B (Figure A.3.1) is described by equation 1.

E(x) = exp (- TRN * P/T) (A3.2)

where

P = fo*((1-fs) (1 - x/d)2 + fS*(1 - x/d))T (A3.3)

and

fS = 1 - (W/L) (A3.4)

In region A

E(x) = 1.0 (A3.5)

In region C an adjustment is made using the submesh factor (SF).This adjustment transfers some of the submesh material in theundersize stream to the submesh fraction of the oversize stream,that is to account for the small particles that adhere to the largerones.

The important operating parameter is feed rate per unit screenwidth (FW) and this function is approximated by several straightlines as shown in Figure A3.2.

The number of trials TRN is related to operating parameters by aset of regression equations of the following form.

Ln(TRN) = A + B * FW + U * P1 + V * P2 FW<FW1 (A3.6)

Ln(TRN) = C + D * FW + U * P1 + V * P2 FW1<FW< FW2(A3.7)

where

C = A + (B-D) * FW1 by continuity (A3.8)

and

Ln(TRN) = C + D * FW2 + U * P1 + V * P2 FW>FW2 (A3.9)

SF is also related to operating parameters by a regression equation

SF = E + F * PSF + G * TSF (A3.10)



Fines Factor The fines factor is used to describe the "piggyback" effect of fineson coarse material.

The material coarser than the "fines critical size" is considered interms of its notional surface area.

Area of particles Voli(xi + xi+1) / 2

αi

n∑

and SF* Area is the t/h of fines which are carried into the oversizeproduct.

MoistureBehaviour

For damp ores, the behaviour of moisture can be very important.There are sometimes several kinds of moisture. The only one ofinterest to this model is in the fines, that is, fractions finer than the"Moisture Split Critical Size XM".

All of the feed moisture is assumed to be carried in material finerthan this size. It is then allocated across the coarse and fineproducts in proportion with how the material finer than XM isallocated.

Scaling The model allows scaling of screen length by linear scaling of thenumber of trials parameter, TRN.

Scaling of screen width is accomplished within the normal modelstructure as FW is feed rate per unit width.

Aperture, fraction open area and slot shape are also included asnormal model parameters.



A3.3 Single Deck Model Printout showing Default Parameter Values



A3.4 Symbols

Symbol Meaning

xi size of particles in the ith size fractionE(x) fraction of particles in the feed of size

x which enter the coarse product

X1,X2 lower and upper screen sizes at fraction being considered

X3 a critical size - if required - close toscreen aperture. However V is usually zero

X4 sub-mesh screen size, i.e., the smallest sieve in the series

TRN efficiency parameter (number of bounces or trials)

fo fraction open areaT total area of screenW width of aperturesL length of aperturesfs fraction slot = 1-(W/L)d maximum size of particle than can pass

through the screen, ie. aperture sizeFW solids feed rate/unit width of screenP1 % of feed of size x such that X1<x<X2P2 % of feed < size X3SF submesh factorPSF % of feed < size X4TSF tonnes/hour feed of size , X4XF fines factor critical sizeXM moisture split critical sizeA Regression constantB "C "D "E Regression constantF "G "U "V "




Accurate application of the screen model requires data from thescreen to be simulated for parameter fitting. For simulation ofscreens for which data are not available, data for a similar screentype with similar feed may be used. Using data from operationswith markedly different screens or feeds will not provide usefulresults.

The same square root of two series of screen sizes should be usedfor both fitting and simulation.

The regression equations of the screen model make it quitecomplex and more difficult to handle than most JKSimMet models.

For most processing plants only the tonnage dependence isrequired. That is the values of U and V can be left at zero. Forwire mesh screens often equation A3.5 is adequate on its own.

Where there are large variations in the fitted submesh factor (SF)try the dependencies of equation A3.9 as detailed in Sub MeshFactor Modelling. However, a constant SF is often adequate.

In a situation where you really want to tune a screen and areprepared to collect a lot of accurate data, contact JKTech forassistance with the parameter and regression fitting.



A3.6 Parameter Fitting the Screen Model

PARAMETER MENU

Ap LengthAp WidthOA %A int (TRN)B*FW (TRN)D*FW (TRN)U*P1 (TRN)U*P2 (TRN)E int (FF)F*PSF (FF)G*PSF (FF)XFXM

The basic concept of a number of trials is quite simple. However,the extensive correction factors and sectionalised curves make thisquite a difficult model to fit.

The Model Fitting program can process only one set of flowsheetdata at a time. However, one flowsheet may contain manymeasured sets of screen data. Clearly, the flowrate and near sizedependencies require several sets of data to define the curvesshown in Figure 2.

To describe any particular set of screen data, only a number of trialsTRN (parameter 22) and a submesh factor SF (parameter 23) needto be found. Good initial estimates for these parameters are 5 and0.1 respectively. However, both TRN and SF are calculatedvariables in this model. Therefore, we need to fit them asregression parameter A (Ln TRN) and regression parameter E withFW1 set to a larger value than any anticipated screen feed rates perunit of width and with B, V, U, D, F and G all set to zero.

Master/SlaveFitting

Master/Slave model fitting allows the secondary dependencies onthe parameter menu to be established when multiple sets of data areavailable. Setting up Master /Slave fitting is detailed in section5.6.5. Parameter dependencies are discussed in A3.7.However, fitting of multiple data sets is complex and assistancefrom JKTech consultants is strongly recommended if you intend totackle this aspect of the fitting process.

Aperture Lengthand Width

Where screen data do not provide precise aperture and wiredimensions, the screen aperture can be fitted to the data.Note that for slotted screens, effective aperture length depends onthe shape of the particle because the size data are measured usingsquare mesh screens.



Selection of feedsize parametersX1 to X4

Screen performance can be affected by the feed size distribution.This is usually a secondary dependence compared with feed rate.However the model does allow it to be incorporated. X1 and X2are the upper and lower sizes of a critical size fraction (orfractions). If a particular range of sizes in your feed data is highlyvariable use X1 and X2 to bracket it.

Set X3 to the screen aperture; or the average screen aperture, if youare going to fit several screen mesh sizes.

Set X4 to say - 2 or 3 times the submesh top size. The finer part ofa size distribution has most of the surface area and will tend todominate surface carryover.

Traditional screen design techniques relate a different “fines factor”to half of the screen aperture. You can use X3 set to half the screenaperture to approximate this dependence if there are largevariations in fines in the feed.

Similarly, a traditional approach would use a “near size”dependence of aperture size to half aperture size and X1-X2 can beset to estimate this dependence.

A3.7 Regression Model Parameters

Trials versusFeedrate

This is the important dependence.

Fit each of the data sets available. This will give you a set of TRNvalues at each fitted feed rate. You may also have a set of fractionsbetween P1 and P2 at each TRN value.

The next step is to plot up (TRN) versus feedrate. Any graphingpackage eg MS Excel, can be used. Select FW1 and FW2 to letyou describe the curve accurately in three sections. An alternativemethod is to print out your graph (with a full grid) and rule onseveral line sections to suit. Their slopes and intercepts willprovide B and A and D and C respectively.

A multiple linear regression program can also be used - if you areadept with such programs. Most spreadsheet programs (eg. Lotus,MS Excel) have built-in multiple linear regression functions).

Critical SizeDependencies

If your Trials (TRN) versus feedrate data are erratic and your dataare a good fit (less than 2 stream SD with Whiten weights), then itis worth trying P1 and P2 dependencies.

Use a multiple linear regression program to fit ln (TRN) againstfeedrate, P1 and P2 and divide into separate data sets using yourestimates of FW1 and FW2.



You can impose the continuity constraint by correcting equations 6and 8 Ln(TRN) values by equation 7.

If you have a constrained non-linear fitting program which canhandle multiple equations, you can fit FW1 and FW2 as well.However, you will need lots of good data.

Submesh FactorModelling

This is the other important dependence. For many operations, SF issmall and more or less constant. However, for operations withdamp ore, it can be crucial to a good model.

Once again, plot your best fit SF values against the calculated PSFand TSF values from the parameter screens and draw a linearregression line against any one variable. Print out the graph with afine grid for this slope (for G) and the intercept E. points.

Running theScreen Model

Input your estimated values back into the screen menu and importto each of your data sets. Try a simulation and check agreementon product streams. Expect to make errors in this procedure thefirst few times.

Master/SlaveFitting

For up to 10 data sets, Master/Slave fitting provides an excellentway of estimating these dependencies for good data. You can addsecondary dependencies one at a time to test for a significantreduction in the sum of squares.Hint : Only the undersize and a flowrate is needed for a full screenfit.

A3.8 References

WHITEN, W.J. and WHITE, M.E., 1977. Modelling andsimulation of high tonnage crushing plants, XIIInternational Mineral Processing Congress, Brazil, VolumeII, 148-158.

WHITEN, W.J., 1984. Models and control techniques for crushingplants, Control 84, Mineral/Metallurgical Processing,(Editor, J A Herbst), Publishers - AIME, New York, 217-225.

Appendix A Efficiency Curves (210, 610, 211, 611, 203)


A4 Efficiency Curves (Models 210, 610,211, 611, 203)(General Classifier Models)

A4.1 General Model Description

These models (210, 211, 203) use simple efficiency curves todescribe the operation of any classification device. They are alsoprovided as some of the optional models for the flotation cell andflotation column (610, 611). For these two flotation devices, theconcentrate is the coarse stream.

A4.2 Simple Efficiency Curve (210, 610)

A4.2.1 Model Description

The model is simply an efficiency curve with a fixed d50c and afixed water split to fine product. Refer to Figures A2.1 and A2.2 ofthe Hydrocyclone model for efficiency curve shapes. A typicalDSM screen has an α value of 4 and a β value of 0.

The model can be used to approximate many classifiers. Thereforethe default parameter values should be used with caution.

A4.2.2 Model Equations



Eo(d/d50c) = C⋅(1+(β⋅β*⋅d/d50c)) (exp(α) - 1) / (exp(α⋅β*⋅d/d50c)

+ exp(α) - 2)

When β is 0, β* is 1 and the above equation reduces to:

Eo(d/d50c) = C⋅(exp(α) - 1) / (exp(α⋅d/d50c) + exp(α) - 2)

The shape parameter β determines the initial rise, while αdetermines the slope at larger values of d (d ≈ d50c). Both α and βare normally constant for given feed solids. The parameter β* isdetermined, for given values of α and β, by the condition that:

Eo(1) = C/2

β* is calculated iteratively in the model. C is the fractional watersplit to the fine product.

Scaling This form of the model does not permit scaling.

Efficiency Curves (210, 610, 211, 611, 203) Appendix A


A4.2.3 Efficiency Curve Model (210) Printout(with default values)

A4.3 Simple Efficiency Curve - Water andFine (Model 211, 611)


The model is also a simply an efficiency curve with a fixed d50c asdescribed above for Model 210 with the added feature of allowingthe fines and water splits to be different.



The efficiency curve used in this model is the same as thatdescribed in A4.2.2 above except that C (fractional water split tofine product) is replaced in the equations with a separate parameterF (fractional split of fines to fine product):

Eo(d/d50c) = F⋅(1+(β⋅β*⋅d/d50c)) (exp(α) - 1) / (exp(α⋅β*⋅d/d50c)

+ exp(α) - 2)


Eo(d/d50c) = F⋅(exp(α) - 1) / (exp(α⋅d/d50c) + exp(α) - 2)

The shape parameter β determines the initial rise, while αdetermines the slope at larger values of d (d ≈ d50c). Both α and βare normally constant for given feed solids. The parameter β* isdetermined, for given values of α and β, by the condition that:

Eo(1) = F/2

β* is calculated iteratively in the model. F is the fractional finessplit to the fine product.

The water split is calculated directly from C, the fractional watersplit to fines product.





A4.4 Splined Efficiency Curve (Model 203)


The model is also a simply an efficiency curve but the analytic formof the curve used in Models 210 and 211 is replaced by a four knotspline curve.



The efficiency curve in this model is provided by specifying fourpairs of coordinates through which a smooth curve (piecewisecubic spline function) is constructed. Fine end of the curve isspecified by the water split as in Model 210.





A4.5 Symbols

Symbol Meaning

EquivalentJKSimMetparameter

α Reduced efficiency curve sharpnessparameter. Alpha

β Reduced efficiency curve dipparameter. Beta

β* Parameter for describing thereduced efficiency curve. Beta*

C Water split to fines product. WS%Fines

F Fines split to fines product FI%Fines

d50cSize of particle in the feed whichhas equal probability of going tofine or coarse product.

D50c


Range of Validity The highly simplified form of these models means thatextrapolation away from the conditions at which the parameterswere determined will significantly decrease the accuracy. If a widerange of data is available, it may be possible to use Model 251 (seeAppendix A5) which has a variable cut point.



A4.7 Fitting the Efficiency Curve Models

A4.7.1 Fitting the Simple Efficiency CurveModel (210, 610)

PARAMETER MENU

This is a simple model to fit as it has no scaling capabilities. Fitthe water split, alpha and d50c. See the comments regarding fittingBeta in the cyclone model description (Appendix A2).

For DSM Screens, initial estimates of 4 for alpha and 50% for thewater split should be adequate for most data sets. An initial d50cestimate of half of the actual screen aperture is appropriate.

A4.7.2 Fitting the Simple Efficiency CurveModel – Water and Fine (211, 611)

PARAMETER MENU

This also is a simple model to fit as it has no scaling capabilities.Fit the water split, the fines split, alpha and d50c. See thecomments regarding fitting Beta in the cyclone model description(Appendix A2).

A4.7.3 Fitting the Splined Efficiency CurveModel (203)

PARAMETER MENU

This also is a simple model to fit as it has no scaling capabilities.Fit the water split and the four efficiency values at the knots on the



spline curve. It is important to remember to set the size values forthe knots before attempting model fitting.

Even though it seems incorrect, it is possible for the fittedefficiency values to be greater than 1 or less than 0. Sometimes,model fitting arrives at values at the ends of the curve which areoutside the 0 – 1 range in order to achieve the best shape for thecurve inside the 0 – 1 range. This is due to the properties of thespline curve for which the values at the ends of the curve have aneffect on the shape of the curve in the centre region.

The simulation model code truncates the efficiency values to beless than 1 and greaster than 0.

The combination of these two features, control of the shape of thecentre of the curve and truncation at 0 and 1 ensures that the modelpredictions are sensible.

A4.8 References

LYNCH, A.J., 1977, Mineral Crushing and Grinding Circuits.(Elsevier, Amsterdam) pp. 124-126.

Appendix A Efficiency Curve Variable D50c (Model 251)

Version 5.1 February 2003 Appendix A5 Page A-37

A5 Efficiency Curve Variable D50c (Model 251)


This model is an extension of the Efficiency curve (Fixed D50c) model to include a regression relationship for d50c. The water split to the fine product remains fixed.


d50c Relationship

For normal operation the classification size d50c can be related to the operating variables according to the equation:

Log10 (d50c) = W * log10 (SW) + X * FW * C / 100 + Y * FPS + Z . . .(A5.1)

Efficiency Curve Relationship


Eo(d / d50c) = 100.C.(1+(β.β*.d / d50c)) (exp(α) - 1) / (exp(α.β*.d/ d50c) + exp(α) - 2) (A5.2)


Eo(d/d50c) = 100.C.(exp(α) - 1) / (exp(α.d / d50c) + exp(α) - 2) . . . (A5.3)

The shape parameter β determines the initial rise, while α determines the slope at larger values of d (d close to d50c). Both α and β are normally constant for given feed solids. The parameter β* is determined, for given values of α and β, by the condition that:

Eo(1) = 100⋅C / 2

β* is calculated iteratively in the model.


Efficiency Curve Variable D50c (Model 251) Appendix A

Page A-38 Appendix A5 Version 5.1 February 2003

A5.3 Efficiency Curve Variable D50c Model Showing Default Values

A5.4 Symbols

Symbol Meaning

α reduced efficiency curve sharpness parameter

β reduced efficiency curve dip parameter

β* reduced efficiency curve calculated parameter

W,X,Y,Z regression constants in the d50c equation

d50c size of particle in the feed which has equal probability of going to fine or coarse product

C % water split to fine product

SW slot width (mm)

FW volume flow rate of water in the feed (m3)

FPS % solids in the feed

Appendix A Efficiency Curve Variable D50c (Model 251)



As Model 251 is based on a regression equation, extrapolation beyond the scope of the data used in the regression will decrease accuracy significantly.

Effect of the log relationship

The relationship between D50c and Slot Width is defined in Log space. This means that the multiplier coefficient W will have a different effect for slot widths less than and greater than 1.0 mm. For slot widths less than 1.0 mm a multiplier greater than 1 will make the calculated D50c value smaller than the slot width. However, for slot widths greater than 1.0 mm, the effect is reversed.This can cause unexpected results when changing slot width.

Screen Wear DSM screens are sensitive to wire wear condition. The screens are usually reversed on a regular basis. If possible, test data shouldrecord the wear condition. If this is not possible, test at both new and worn to obtain a range of likely operation.

A5.6 Fitting PARAMETER MENU

W * Slot X * FPS Y * FdWater Z (int) Sharpness α Dip β C

This is a simple model to fit as it has no scaling capabilities. Fit the water split, α and d50c. See the comments regarding fitting β in the cyclone model description (Appendix A2).

Initial estimates of 4 for α and 50% for the water split should be adequate for most data sets.

An initial d50c estimate of half of the actual screen aperture is appropriate.

Multiple Data Sets

If the data cover a range of feed rates, feed percent solids, slot widths and screen widths, proceed as follows: • Fit each data set for α, C and d50.

• Refit with average α and C set constant. That is, force all the variation into the cut size.

• Use Master/Slave fitting to fit the separation size equation (A5.1) for W, X, Y and Z.

Efficiency Curve Variable D50c (Model 251) Appendix A


Note: If the slot width does not have a strong effect on d50c, then the data are very questionable.

A5.7 References

LYNCH, A. J., 1977, Mineral crushing and grinding circuits, (Elsevier, Amsterdam), pp 124-126.

Appendix A Crusher (Model 400/405)


A6 Crusher (Models 400 and 405)

A6.1 Model Description (Andersen/Awachie/Whiten)

The crusher model considers the crushing process as two components:

• the selection of particles for breakage, and • the breakage of the particles so selected.

Selection Clearly, whether or not a particle is selected will depend principally upon its size relative to the closed-side setting (CSS) of the crusher and the extent of choke feeding. The size distribution of the daughter products of breakage will depend principally upon the initial size of the particle and upon its physical properties.

New feed entering the crusher is classified (or selected). Some material, predominantly the finer fraction, bypasses the breakage process entirely and reports directly to the product. The remainder is broken, and the daughter fragments are then recycled to the classification step. The new fine fraction exits via the product, and the coarser material is rebroken.

Perfect Mixing Model

If we think of a crusher as a stagewise breakage process, then we can model it in terms of a steady state balance.

ClassificationFunction

FunctionAppearance

f xp

C*xA*C*x

Figure A6.1: Schematic representation of the crusher model

A schematic representation of the crusher model is given in the above figure. Mass balance equations may be written about each node as:

x = f + ACx (A6.1)

x = p + Cx (A6.2)

Crusher (Model 400/405) Appendix A


where x is a vector representing the amount in each size fraction in the crusher

f is the feed size distribution vector

p is the product size distribution vector

C is the classification function, a diagonal matrix describing the proportion of particles in each size interval entering the crushing zone

A is the appearance function, a lower triangular matrix giving the relative distribution of each size fraction after breakage.

Combining (A6.1) and (A6.2) results in the Whiten crusher model equation:

p = ( I - C ) * ( I - AC ) -1 * f (A6.3)

where I is the unit matrix.

Since the feed and product are expressed as size distributions, and the properties of the internal classification and breakage mechanisms are expressed with respect to particle size intervals or mean sizes, it is convenient to represent these quantities as vectors and matrices respectively.

Since f is known and p is the desired output, the problem resolves itself into obtaining estimates of C and A for a particular machine and feed material. These values can then be manipulated by simulation to explore the effects of changing machine parameters, material characteristics or operating conditions upon the product size distribution.

An important limiting factor in crusher operation is the power drawn by the machine. This model permits estimates of power draw to be made for a given condition, so that the simulations can be constrained by power requirements (by the user). The power draw can be normalised to experimental data or estimated from data for similar crushers in the Supplementary Parameters Manual. Note: a single particle breakage test of the ore is required for either type of power estimate.




p = (I - C) * (I - A * C)-1 * f

Selection Where C is the classification function (a diagonal matrix) and where C(x) is the probability of selection for breakage of a particle of size x and is defined as:

C(x) = 1 (A6.4)

for x > K2 i.e. all particles are broken

C (x) = 1 -

K2 - x

K2 - K1

K3 (A6.5)

for K1 < x < K2

C(x) = 0 (A6.6)

for x < K1 i.e. no particles are broken (x = mean particle size)

An example of the classification functions is given in Figure A6.2.

K3

K1 K2

1.0

0.0

Particle Size x Figure A6.2 - Classification function, C

The model equations are developed by non-linear regression analysis of survey data collected over a wide range of operating conditions, followed by multiple linear regression of the fitted parameters against the operating conditions. The general form of these relationships is:

K1 = A0* Crusher gap - A1 * Throughput + A2* Feed coarseness

K2 = B0* Crusher gap - B1 * Throughput + B2* Feed coarseness

K3 = C0 (generally held constant at a value of 2.3)



First Approximation

For many crusher types performance can be estimated by setting K1 to the closed side setting, K2 to the open side setting (or K1 plus eccentric throw). Both K1 and K2 will decrease with particle interference as the crusher throughput increases to choke feeding.

The breakage severity (t10) will also increase (see A6.6 and equation A6.11).

The model allows for inclusion of minor variables where more detailed data are available The equations in the model are of the form:

K1 = A0* CSS + A1 *TPH + A2 * F80 + A3 LLen + A4 (A6.7)

K2 = B0* CSS - B1 * TPH + B2 * F80 + B3 * LHr + B4 * ET + B5 (A6.8)

K3 = C0 (usually 2.3) (A6.9)

Where Closed side setting CSS Liner Length LLen Eccentric Throw ET Liner Hours LHr Crusher Feed Rate TPH Crusher Feed 80% passing size F80 Crusher Product 80% passing size P80

Note that only closed side setting and crusher throw will normally be used. The other relationships require a very detailed experimental database.



A6.3 Ore Breakage Characterisation

Andersen Breakage Model

The Andersen model uses the results of JK breakage testing of coarse particles to predict both breakage and crusher power consumption. This model has been extensively tested on cone crushers (mostly operating as secondary crushers) over a broad range of ore types. When the model was developed, only the pendulum device was available for single particle breakage tests. However, the JK Drop Weight test is now used as it provides for a wider range of energies and particle sizes. The first step is to use the JK breakage test to characterise ore breakage over a range of input and absorbed energies. The absorbed energy (per unit mass of particle) is referred to as the specific comminution energy.

For details of the testing procedure, see Appendix 13.

A6.4 Breakage Distribution Parameter t10

A typical size distribution of product from the JK breakage tester is given in the figure below. This product size distribution may be adequately described by a one parameter (t) family of curves (Awachie (1983); Narayanan and Whiten (1983)). The parameter t10 is defined as the cumulative percent passing one tenth of the geometric mean size, Y, of the test particle. The parameter is shown in the figure below, together with other tn values - t2 and t4,- which are defined in a similar manner to t10. Using the tn values (n= 10, 2, 4, 25, 50 and 75), the whole of the size distribution may be fully described.

t2

t4

t10

Y/10 Y/4 Y/2 YParticle size mm

Y = Test Particle Size

Figure A6.3 - Typical pendulum product size distribution



The tn values (n = 10, 2, 4, 25, 50 and 75) for the product size distributions for nine pendulum tests on hard rock ores from four major crushing operations at different sites were determined and a 'best-fit' spline curve was drawn through all of the tn data using a JKMRC multiple spline regression package, MSR. This breakage distribution information may be conveniently stored as a three dimensional spline relationship between the breakage distribution parameter, t10 ( a measure of the amount of breakage or reduction), the cumulative percent passing a particular relative size, and the relative size, tn, of the particle being broken. Using the t10 spline knots 10.0, 20.0 and 30.0, Table A.6.1 gives the cumulative percent passing the relative sizes t75, t50, t25, t4, and t2 i.e. the cumulative percent passing the Y/75 size (etc), where Y is the size of the original particle being broken as shown in Figure A6.4. The distribution for any intermediate value of t10 is determined by spline interpolation.

Table A6.1: Appearance Function Data

SIZE RELATIVE TO INITIAL SIZE

T75 T50 T25 T4 T2

Breakage Parameter t10

CUMULATIVE PERCENT PASSING

10.0 2.8 4.0 5.5 22.2 51.4

20.0 5.6 7.2 10.7 43.4 80.8

30.0 8.9 11.3 16.4 60.7 93.0



Figure A6.4: The relationship between t10 and the remainder of the product size distribution

A6.5 Breakage Parameters

Breakage parameters can be established from regression analysis of the same data as the classification equations.

t10 = D0*Crusher gap + D1*Throughput – D2* Feed coarseness (F80) + D3 (A6.10)

This equation shows the intuitively expected dependence on the crusher gap, throughput and feed size distribution.

The "feed coarseness" factor is somewhat application dependent. That is, it will be influenced by crusher liner profile and effective slope as well as closed side setting and gap.

First Approximation

Typical cone crusher operation for secondary and tertiary crushers will be at a t10 of 15 to 20. For a lightly loaded crusher (size control on a primary jaw crusher) will operate at a t10 of 5-10. A high reduction crusher (toothed roll or choke fed tertiary) may achieve a t10 up to 25.



A6.6 Crusher Power Predictions

Energy - Size Reduction Relationship

The JK breakage test also provides important information on the specific comminution energy (kWh/t) required for a fixed size reduction, quantified by the breakage distribution parameter t10, for each particle size broken. The specific comminution energy, Ecs, defined as the amount of energy available for breakage, is derived as the energy absorbed from the drop weight on impact. This energy has been found to have a linear relationship with the breakage distribution parameter, t10, but is also dependent on the test particle size. This relationship is ore-specific and is used to characterise ores and compare the crushing energy requirements of different ores.

Figure A6.5 shows the energy - size - size reduction relationship derived from a JK breakage test for a fine-grained, siliceous copper ore.

1.5

1.2

0.9

0.6

0.3

0.010 14 18 22 26 30

Size mm

t10 = 30.0t10 = 20.0t10 = 10.0

Figure A6.5 - Energy size reduction relationship

This information as used in the crusher model program in the spline form is tabulated below. The energy required for a given reduction increases with a decrease in particle size.

In Model 400, provision is made for data for three particle sizes. In Model 405, the matrix is extended to accept data for five particle sizes to match the data available from the JKTech Drop Weight Test.



Table A6.2 - Energy-Size Reduction Relationship (Spline Form) – Model 400

Reduction parameter Particle size mm

t10 14.50 20.63 28.89

% Specific comminution energy kWh/t

10.0 0.35 0.30 0.25

20.0 0.80 0.70 0.50

30.0 1.2 1.0 0.80

Table A6.2 - Energy-Size Reduction Relationship (Spline Form) – Model 405

Reduction parameter

Particle size mm

t10 14.50 20.63 28.89 41.10 57.80

% Specific comminution energy kWh/t

10.0 0.35 0.30 0.25 0.20 0.15

20.0 0.80 0.70 0.50 0.40 0.30

30.0 1.2 1.0 0.80 0.60 0.40

Power Prediction Method

A power prediction method has been developed using energy –size-reduction information from the pendulum test (Andersen & Napier-Munn, 1988) and is also applicable to the Drop Weight test.

Using the ore-specific energy-size-reduction relationship from the pendulum test, the breakage function, B the classification values Ci (from the parameter fitting or model regression equations, the model calculates the total energy required to reduce the feed size distribution to the product size distribution as if all the feed was broken in the pendulum or drop weight testing device, i.e. it defines the energy which would have been used by the breakage device to achieve the same degree of breakage observed in the crusher. The sum of the products of the amount of material selected for breakage in each size fraction, Ci*xi (tonnes) (from equation (A6.3)), and the Ecs (kWh/t) for each size at the breakage parameter value t10 (determined from the parameter fitting or model regression equation (A6.11)), is the total comminution energy calculated by the model, Pcalc (kWh).



This total model-calculated energy is then regressed against the actual power draw observed during the plant surveys on a particular crusher using multiple linear regression analysis, resulting in a simple equation of the form given below.

Pobs = E1 * Pcalc + E2 (A6.11)

where Pobs is the observed crusher power draw (kW)

Pcalc is the model calculated comminution energy(kWh)

E1 is a constant dependent on the efficiency of the crusher

E2 is a constant of similar value to the 'no-load' power draw

The constant included in the regression equation adequately accounts for the crusher machine power draw (the power required to overcome machine frictional losses), or 'no-load' power draw as it is commonly termed. This 'no-load' power appears to vary slightly with throughput and is a function of both plant power factor and drive motor efficiency.

Feed rate (t/h) and feed coarseness are usually less significant variables and a satisfactory model can be obtained by absorbing these effects into the constant term. These variables are implicitly included in the pendulum power calculation.

The power regressions developed may be used to predict the power requirements of crushers operating on different ores after determining the relationship between the breakage parameter, t10, test particle size, and the specific comminution energy, Ecs, for the ore under investigation. The pendulum test should be conducted on representative ore particles over the range of the crusher feed size. Where a specific mathematical performance model of the form of equations A6.7 to A6.10 has been developed from extensive plant surveys, the power draw may then be predicted for different operating conditions.

In a design situation, given the feed and the desired product size distributions, the t10-size-Ecs relationship for the ore to be processed must be obtained from the pendulum test and this information used in the model to calculate the total comminution energy required. The crushing power requirements can then be determined for a similar crusher from a power regression of the form of equation A6.11 obtained from another site.



Model 400

Model 405

A6.7 Crusher Model (400/405) Printout Showing Default Values



A6.8 Symbols

Symbol Meaning

f feed size distribution (vector)

p product size distribution (vector)

A appearance function (matrix)

C classification function (diagonal matrix)

I unit matrix

K1 size below which C = O

K2 size above which C = 1

K3 exponent in the equation for C

CSS closed side setting (mm)

TPH tonnes/hour feed

F80 coarseness of feed, e.g. 80% - 25.4mm

t10 breakage distribution factor total power consumed in size reduction using the pendulum (from laboratory tests results) Ai regression constants

Bi "

Ci "

Di "

Ei "




This is the most general of the crusher models developed at the JKMRC. It has been extensively tested for large (7ft) cone crushers. The model provides an excellent description for individual results for many types of crusher, e.g., jaw, roll, toothed roll, hammer mill etc., but has not been extensively tested on these other crusher types.

The feed coarseness relationships are usually based on scalped feed oversize variations. They could well be different from variations in scalping screen aperture. This interaction is a subject for continuing investigation.

For power calculations large particles are apparently softer (see Table A6.2). The drop weight test is not suitable for particles of diameter larger than 63mm. Hence, using specific comminution energies derived on smaller particles will tend to overestimate required pendulum power.

There is also a physical flow limit for most types of crushers. For crushers which cause a considerable increase in volume, this limit is important. Hence for cone or 'Gyra disk' types, check the simulated flowrates against the design tables for that type of crusher and the corresponding bowl and mantle. Typical flowrates are available from standard references such as Mular and Bhappu (1978), Chapter 11.



A6.10 Fitting the Crusher Model

The model fitting subsystem only analyses one data set at a time. Hence the actual parameters adjusted are the constant terms in each of the equations A6.7, A6.8, A6.9 and A6.10.

That is, A4 for K1

B5 for K2

and D3 for t10

PARAMETER MENU

There are two distinct levels of use of the crusher model. The different uses require different fitting strategies.

Limited Data One data set allows a (somewhat approximate) estimate of product size for small variations in closed side setting.

For one data set:

fit A4 and B5

with A0 = 1.0, and B0 = 2.0 and (for cone crushers) K3 = 2.3.

Set other A and B values to zero.

Similarly for the breakage function:

fit D3

D0, D1 and D2 are set to zero.

Note that one data set does not provide useful information about power dependencies.



Extensive Data The model is much more useful with a range of data. This means 5 to 10 data sets covering a range of crusher settings, feed rates and (if possible) feed sizes.

JKTech can undertake breakage tests to characterize an ore as shown in Figure A6.3 and Table A6.1 and to determine the size single particle breakage/power as shown in Figure A6.5 and Table A6.2.

HP Grinding Rolls (and others)

Note that the value of K3 is generally 2.3 for cone, jaw and gyratory crushers only. For other types of crushers, such as grinding rolls and hammer mills, it is advisable to fit K3 also, with 2.3 as a good initial estimate

Master/Slave Fitting

Master/Slave model fitting is available for the crusher model in the general release version of JKSimMet. Model fitting of multiple data sets is complex; assistance from JKTech consultants is strongly recommended if you intend to tackle this aspect of the fitting process. Setting up Master/Slave fitting is detailed in Section 5.6.5



A6.11 Regression Modelling

The procedure is very similar to that for the screen model. Hence, an efficient test program can be designed to gather screen and crusher data together.

Fit each test using only constant terms, A1, with all of the other regression terms set to zero.

Use the ore Specific Appearance and Power Data measured by JKTech, or use the defaults (average of 4 ore types). Measured oretype data should give more accurate results for breakage and are essential for realistic power estimates.

Each data set produces estimates of K1, K2, K3 and A and B.

Set K3 = 2.3

Use a multiple linear regression package to fit each estimate to the measured variables. If any coefficients plus or minus their estimated errors bracket zero, try a refit without that variable included. If the error of prediction improves (i.e., gets smaller), omit the variable by setting its model coefficient to zero.

A6.12 Model Testing

Import each feed and product into the model and simulate to check each set. This is quite a complex model and it is not difficult to make errors.

If any data sets are seriously in error, try to track down the reason. Check the calculated K1, K2, and t10 against your fitted estimates. When all else fails (or much earlier, if you prefer), ask JKTech, who will be happy to assist.

As soon as you have reasonable parameter estimates, you may use Master/Slave fitting on up to ten data sets at a time to test secondary crusher model dependencies.



A6.13 References

ANDERSEN, J. A., 1989. M.Sc. Thesis, University of Queensland, (unpublished).

ANDERSEN, J.A. and NAPIER-MUNN, T.J., 1988. Power prediction for cone crushers, Mill Operators' Conference, Cobar.

AWACHIE, S.F.A., 1983, Development of crusher models using laboratory breakage data, PhD Thesis, University of Queensland.

MULAR A. L. & BHAPPU, R. B. 1978, Mineral Processing Plant Design.

WHITEN, W.J., 1984, Models and control techniques for crushing plants, Control 84, Minl./ Metall.Process (Am.Inst.Min.Engrs. Annual Meet., Los Angeles, USA, February), 217-225.



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Appendix A Rod Mill (Model 410)


A7 Rod Mill (Model 410)


The rod mill model is based on the concept of stages of breakage.A stage of breakage has three components:

• selection• appearance• classification.

That is, each stage is equivalent to breakage, screening andrecirculation.

The mill is considered as a number of segments in order. Eachsegment is a stage of breakage.


Diagrammatically a stage of breakage may be considered as:

ONESTAGE OFBREAKAGE

Selection

Appearance

Contents

Classification

fj feed vector to stage j

m=C.q+f

S

A

q

C

pj

Segment contents Vector q

Diagonal Matrix C

Diagonal Matrix S(I-S).m

C.q

product vector from stage j

Lower Triangular Matrix A

Figure A7.1 A representation of the breakage process in a rod mill

Rod Mill (Model 410) Appendix A


Eliminating m and q by matrix algebra yields

pj = (I-C) . (A.S +I-S) . [I-C⋅(AS+I-S)]-1 . fj

or

pj = X . fj

since AS and C are assumed constant for all stages.

Stages ofBreakage

If there are v stages of breakage in the mill then:

p = (X)v ⋅ f (A7.1)

or

p = X⋅X⋅X ... ⋅ f for v times

Non-integer numbers of stages can only be calculated byinterpolation.

Once A, S and C are known, any particular operating condition canbe represented by a value of v.

Feed Rate The key dependence is the variation of stages of breakage v withmill feed rate F.

Experimentally:

F (v)1.5 = MC

where MC is the mill constant.

The mill constant can also be scaled as detailed later.

AppearanceFunction

The default Appearance Function is the modified Rosin-Rammlerequation:

A(x,y) = (1-e-x/y)/(1-e-1)

Where A(x,y) is the proportion after breakage of particles of initialsize y which are smaller than size x. The appearance A is made upof vectors of the differences in x for the specified screen interval.For specific ores, JKTech can measure the appearance function. Arange of appearance functions for various ores is given with theball mill model description in Appendix A8.




The classification function C is a diagonal matrix which provides asimple classifier. Each diagonal element gives the proportion ofthat size fraction returned to the breakage stage for rebreakage.

The usual values are (for a √2 size distribution)

1.0, 0.5, 0.25, 0.125, 0.063 and so on.

Hence, each stage of breakage in a rod mill will eliminate the topsize fraction from the product.

SelectionFunction

The selection function, S is a diagonal matrix. It gives theproportions of each size fractions which are selected forbreakage.

S is represented by three parameters XC, SL and IN as shown inthe figure below, and is calculated by:

Si = SL ⋅ Size + IN for Size i > XC

Si = SL ⋅ XC + IN for Size i < XC

and limited if Si > 1.0 then Si = 1.0

and if Si < 0.0 then Si = 0.0

An example of a selection function is given in the figure below.

1.0

0.0XC

Size

SelectionFunction

SL

IN

Figure A7.2 Graph of a rod mill selection function



Scaling The rod mill model is scaled by modifying the mill constantaccording to dimensions and operating conditions described below:

Mill SizeFACTA =

DSIM

DFIT

2.5 ⋅

LSIMLFIT

These scale factors only apply for rod mills with normal length todiameter ratios, that is, 1.2 < simulated L/D < 1.6 and L ≤ 7m.

Media Load Load Fraction (i.e. volume of mill occupied by charge and media atrest after grinding out)

FACTB = (1 - LF ) LF(1 - LF ) LF

SIM SIM

FIT FIT

⋅⋅

Note 30% < LF < 45%

Critical Speed Fraction Critical Speed

FACTC = CSSIMCSFIT

Note 50% < CS < 80%

These factors are applied to the Mill Constant MC of the originalmill to estimate the mill constant of the simulated mill.

MCSIM = MC ⋅ FACTA ⋅ FACTB ⋅ FACTC

The required number of stages of breakage is

vSIM =

MCSIM

FSIM

2/3

Feed Size Coarseness of feed (90% passing size)

FACTD = ln

F90FIT

F90SIM / ln 2

vSIM =

MCSIM

FRSIM

2/3 + FACTD



Ore Hardness Work Index

FACTE = - 0.8 ln

WISIM

WIFIT

FACTF = ln

S(I)FIT

1-S(I)FIT

+ FACTE

FACTG = exp (FACTF)

S(I)SIM =

FACTG

1+FACTG



A7.3 Rod Mill Model Printout ShowingDefault Values



A7.4 Symbols

Symbol Meaning

f feed size distribution (vector)

p product size distribution (vector)

A appearance function (step matrix)

C classification function (diagonal matrix)

S selection function (diagonal matrix)

Si element of selection function S from size i

v number of stages of breakage of original mill

vSIM v for simulated mill

F90FIT 90% passing size for fitted mill feed

F90SIM 90% passing size for simulated mill feed

MCSIM mill constant for simulated mill

MC mill constant for original or fitted mill

SL slope of selection function

IN intercept of selection function

XC Size below which selection function is constant

DSIM diameter of simulated mill

DFIT diameter of fitted mill

LSIM length of simulated mill

LFIT length of fitted mill

LFSIM load fraction of simulated mill

LFFIT load fraction of fitted mill

CSSIM fraction critical speed of simulated mill

CSFIT fraction critical speed of fitted mill

WISIM work index of ore for simulated mill

WIFIT Work index of ore for fitted mill

Note: The fitted mill is the rod mill which provided theexperimental data.




Scaling Note the restrictions for scaling in the section on Model Equations.

Change in FeedPulp Density

The number of stages of breakage is calculated from the feed solidsmass flow. No account is taken of water in the feed. It is assumedthat rod mills operate at 75 to 85 percent solids in the feed.

Effect of FeedSize

There is some doubt about the adjustment of number of stages ofbreakage according to feed coarseness. Data from some operationsexhibit an effect while data from others do not. If the particles arelarge enough and strong enough to resist a rod impact, thedependence is reasonable.

The scaling effect can be eliminated from open circuit operation bysetting F90FIT (parameter 16) equal to F90SIM (parameter 80).

Mill Speed This dependence is reasonable from 50-80% of critical speed atindustrial mill feed rates.

A7.6 Fitting the Rod Mill ModelPARAMETER MENU

Because the rod mill model is dependent on feed conditions, it isdifficult to fit in closed circuit until the parameters are very goodestimates. Therefore, mass balance a closed circuit rod mill first.Then fit the discharge using the mass balanced feed rate and sizing.(Use Whiten SDs for the product size distribution). If an orespecific breakage function is available, it should be used. The millconstant (MC) and the three selection function parameters can befitted.

For fitting, set the simulated and original mill dimensions etc. tothe same values.



Check the experimental feed 90% passing size and input it. Use a measured work index if available - an approximate one if not.

This model is fussy about initial estimates and some trial and error may be needed. These guidelines will help for many cases.

If you are new to the rod mill model use the rod mill example in Chapter 3 and graph the output to get a feel for how XC, SL and IN interact and change the shape of the product curve.

Set XC to about half of the top size of the mill feed and MC to 2000. Assume a selection value of 0.1 at XC and 1.0 at the feed top size. Calculate slope and intercept to suit. Try a simulation with these values. If the product distribution is approximately the right shape, (plot as cumulative percent passing both simulated and experimental products) fit the rod mill constant.

If the shape is very different, increase the assumed selection value for a steeper product slope and proceed when the slope is similar.

If the fitting program finds a reasonable minimum, - that is, the mill constant error is less than 20% - change the MC estimate to the new value and fit the slope. If the sum of squares decreases, update the SL guess to the fitted value and fit XC and IN also.

A7.7 Reference

LYNCH, A.J., 1977. Mineral crushing and grinding circuits, (Elsevier, Amsterdam), 51-60.



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Appendix A Perfect Mixing Ball Mill (Model 420)


A8 Perfect Mixing Ball Mill (Model 420)


This model considers a ball mill as a perfectly mixed tank withcontents described by a vector size distribution s.

The product vector p is produced by a discharge rate di for each sizefraction, where D is a diagonal matrix of rates, that is:

p = D•s (A8.1)

Within the mill, two factors control breakage. The first is the rateof selection of each size for breakage. The second is the way inwhich the selected particles are broken (or appear) in the millcontents.

Selected = R•s

where R is a diagonal matrix of rates.

Appearance = A•s

where A is a triangular matrix of breakage (appearance) functions (distributions).

At steady state, the mill feed minus the material selected forbreakage plus the material from breakage minus the materialdischarged must equal zero. This can be written as:

f - R•s + A •R•s - D•s = 0 (A8.2)

Discharge Rates For overflow mills and most of the operational range of gratedischarge mills, the discharge elements can be approximated by:

Di = Di* 4 v / (d2 l) (A8.3)

where Di* is close to unity v is the total volumetric mill feed rate d and l are mill diameter and length

A typical discharge function is given in Figure A8.1.



i

0.Discharge Screen SizeLog (size)

1

D*

Figure A8.1 - Typical graph of mill discharge function

Breakage Rates Breakage rates tend to increase rapidly with particle size, with theincrease tapering off at the feed top size.

Log (size)

iLog (R )

Figure A8.2 - Typical graph of breakage rate factor

AppearanceFunction

The appearance function A is ore dependent, and can be measuredusing the drop-weight testing technique developed at the JKMRC.A table of appearance functions for a variety of ore types and theassociated operating work indices is given in section A8.7. Thestandard Broadbent-Calcott appearance function is also included.




Considering equation 8.1 as the elements of each vector and matrix yields:

fi - Risi + A R s - D = 0ijj=1

ij j i∑ si (A8.4)

and: pi = Disi (A8.5) Substituting for si yields:

fi - RiDi

pi + Aijj=1

i∑

RD

j

j

pj- pi = 0 (A8.6)

where feed and product are related by R/D for a particular breakage function. Equation A8.3 can be used to scale for feed rate and mill dimensions. In general, the mill contents s is not known and it is not possible to separate the R/D* ratio into its components. The R/D* function is represented internally by a cubic spline function (that is, by a smooth curve). A number of spline knots (generally between 2 and 4) on the 1n(R/D*) function are fitted.

Scaling Scaling of the ball mill model is achieved by modifying the fitted R/D* function according to dimensions and operating conditions as described below.

Mill Diameter The mill diameter d is scaled.

FACTA =

dSIM

dFIT

Note: This factor is in addition to a direct volume effect which is built into the model.

Load Fraction The load fraction LF is the volume of mill occupied by charge and media at rest when the load is ground out.

FACTB =

FITFIT

SIMSIM

LF . )LF - (1LF . )LF - (1



Fraction Critical Speed

Fraction critical speed is scaled by:

FACTC =

FIT

SIM

CSCS

55% <CS < 78%

Work Index The Work Index is scaled by:

FACTD =

WISIM

WIFIT

0.8

Ball Size Scaling By assuming that the reduction mechanisms of impact and attrition occur in a ball mill, the following relationships can be derived from theoretical considerations. Impact breakage ∝ Db

3

Attrition breakage ∝ 1/Db where Db = ball top size diameter.

Impact breakage is assumed to predominate above a certain size xm whilst attrition is the main reduction mechanism at sizes below xm. The size xm is assumed to be equivalent to that at which maximum breakage occurs. Size xm can be related to ball diameter as follows:

xm = K . Db2

where K is the maximum breakage rate factor.

The value of K has been found to be of the order of 4.4 E-04. K can be calculated from the formula above if the value of xm is known. The graphing facility within JKSimMet allows easy graphing of the breakage rates to determine this value.

xm (fit) and xm (sim) are both calculated. The smaller of the two is denoted xm (small) and the larger as xm (large) .

The above relationships are used to scale R/D* values at each spline knot to account for ball size effects.

The scaling factor for ball size effects depends on the knot position size.

for knot position size < xm (small)

( )( ) SIM

FIT

FIT

SIM

Db Db

Db1

Db1

FACTE ==



for knot position size≥ xm (large) 2

FIT

SIM

Db Db FACTE

=

For knot positions between xm (small) and xm (large) linear interpolation is used.

The effect of ball size is shown in the diagram below.

Ball size decreasing

Knot 1 Knot 2 Knot 3 Knot 4

Old xmNew xm

Particle Sizex m

Figure A8.3: R/D* Relationship with Ball and Particle Size

Scaling Calculation

These factors are applied to each fitted 1n (R/D*) knot as follows:

R/D*SIM=R/D*FIT•FACTA•FACTB•FACTC/FACTD•FACTE

Scaling Using Breakage Functions

Where characteristic breakage functions have been measured (i.e. pendulum tested) for both ores, these breakage functions may be used to predict performance. Note that it is not valid to scale this way from the default breakage function.



A8.3 Ball Mill Model Printout Showing Default Values



A8.4 Symbols

Symbol Meaning

f feed size distribution vector

p product size distribution vector

s mill contents size distribution vector

A appearance function lower matrix

R breakage rate function diagonal matrix

D breakage discharge function diagonal matrix

D* normalised discharge function

R/D*SIM normalised R/D ratio for simulated mill

R/D*FIT normalised R/D ratio for fitted mill

dSIM diameter of simulated mill

dFIT diameter of fitted mill

LSIM length of simulated mill

v volume flow rate of feed

LFSIM load fraction of simulated mill

LFFIT load fraction of fitted mill

CSSIM fraction critical speed of simulated mill

CSFIT fraction critical speed of fitted mill

WISIM work index of ore for simulated mill

WIFIT work index of ore for fitted mill

Db ball diameter (top size)

DbSIM ball diameter for simulated mill (top size)

DbFIT ball diameter for fitted mill (top size)

K maximum breakage rate factor

xm maximum breakage size.




Change in Coarseness of Feed

It is known that the coarse end of the R/D* function does vary with gross changes in the amount of coarse material in the feed stream. As the amount of coarse material in the feed is decreased, the relevant R/D* values increase. This limitation is not considered significant for changes of less than plus or minus 50% in the amount of coarse material in the feed.

Critical Speed Range

The critical speed dependence is approximately valid for 55-78% of critical speed and incorrect outside of that range.

Predicting Rates at 'Missing Sizes'

If the ball mill model does not produce any of a coarse fraction (i.e. none in the mill discharge) then the effective rate of grinding is 'infinite'. One way to overcome this problem is to size the mill contents and expand to the perfect mixing model used for the SAG mill model.

This is usually not experimentally convenient. Some more practical approaches are to:

• test the mill at maximum tonnage with coarse feed. If there is any coarse material in the discharge, the actual rates can be estimated.

• use a set of rates and knot values from the supplementary information for a similar mill feed sizing and fit with Work Index alone the first time. Transfer the coarse rate values from calc to exp, return the Work Index to its original value and refit the two smaller rates. This procedure should give reasonable answers with a coarser feed. Work is proceeding on improving the ball mill model in this area.

High Mill Viscosity or Pulp Density

The perfect mixing mill model only takes account of pulp density variations as variations in mill volume. Therefore, higher pulp density will always predict higher grinding rates. In practice, the rates do improve until pulp viscosity begins to interfere with ball action and rates decrease rapidly. This onset is difficult to predict as it is highly ore type dependent. However, effective mill operation of greater than 50% solids by volume is unlikely and improbable at greater than 60% solids by volume.

Ball Size Scaling The ball size scaling relies on the R/D* function exhibiting a maximum. If there is no maximum in the fitted R/D* function,increasing the ball size will give optimistic results.



Wide Range SizeData

The mill model assumes a constant breakage function for all sizefractions. This assumption simplifies the model but experimentalevidence suggest strongly that partial breakage increases in severitywith decreasing size - down to some limiting size. Therefore, ifmore than (say) twenty size fractions are considered, an apparentminimum rate may be produced in the finer ranges. Thisphenomenon is more likely to be an artefact of an incorrectassumption than to have any physical significance. Research workcontinues in this area.

A8.6 Fitting the Perfect Mixing Ball Mill Model

PARAMETER MENU

The ball mill model is well-behaved for model fitting. It can befitted in closed circuit with the cyclone model with generally betterresults than by fitting each model to mass balanced data. Hence agood closed circuit fit will also provide a good mass balanceestimate of circulating load.

R/D* SplineKnots

Use three knots for normal grinding conditions and four knots for awider than usual size range (such as SAG mill discharge or a veryfine product).

KnotPositions

To determine an appropriate set of knot positions divide thenumber of size fractions covering the feed size distribution by thenumber of knots plus one. This will give about equal log sizespaces from both ends and between knots.

Knot Estimates Estimates for the function values at the knot positions are providedas ln(R/D*) values. A simple ascending series provides a goodfirst estimate, for example:

0.5 1.5 2.5



Work Index,Load Fraction

If you have several sets of data, use an operating Work Index foreach (calculated from mill feed rate, mill power, feed and product80% passing sizes). If the major variation is hardness only, thenthe average knots can be used.

The calculated R/D* values are displayed on the unit data entryscreen. There should be a smooth increase with size. Sometimesthe curve will have a maximum at the coarse end. If there are anysudden changes or ups and downs, try adjusting the knot positions.

There will often be a bump at a change in size measurementtechnique, such as the transition from screen sizing to Cyclosizersizing.

Systematic deviations can sometimes be removed by adjusting aknot towards the largest deviation.

Graph CumulativeSimulated andExperimentalProduct

When nothing else works, plot the experimental feed and producton a coarse scale (say 0-30%) percent retained against log size. Ifthere are any large discontinuities, check your data very carefully,and repeat your sampling if possible.

Master/SlaveFitting

The perfect mixing ball mill model is well suited to fitting ofmultiple data sets. The ln(R/D*) knot values can be fittedsimultaneously for a number of surveys. Ensure that you use thesame knot positions, and number of knots, for each mill in yourmaster/slave fitting test.



A8.7 Table of Appearance Functions

This table shows ore-specific appearance function valuesdetermined from single particle breakage tests using JK breakagetesters –pendulum or drop-weight.

Size Interval Ball milling circuits from which the samples were collected:Massive Massive Porphyry Porphyry MassiveSulphide Sulphide Hard Soft Sulphide

(Ni) Coarse (Cu) (Cu) Fine(Pb-Zn) (Pb-Zn)

1 0.000 0.000 0.000 0.000 0.0002 0.0591 0.0505 0.08586 0.05220 0.11283 0.1052 0.0974 0.1248 0.09919 0.14904 0.1318 0.1276 0.1387 0.1288 0.14975 0.1295 0.1278 0.1278 0.1284 0.12506 0.1127 0.1128 0.1076 0.1129 0.098857 0.0927 0.09469 0.08722 0.09423 0.078668 0.07486 0.07810 0.06960 0.07727 0.062899 0.06082 0.06428 0.05540 0.06339 0.04943

10 0.05005 0.05316 0.04428 0.05239 0.0384211 0.04166 0.04424 0.03574 0.04364 0.0300312 0.03462 0.03666 0.02899 0.03623 0.0237613 0.02723 0.02880 0.02278 0.02847 0.0186514 0.02054 0.02171 0.01743 0.02146 0.0144815 0.01537 0.01623 0.01325 0.01604 0.0112016 0.01144 0.01207 0.01004 0.01192 0.0086417 0.00849 0.00894 0.007581 0.00883 0.00664

Operating Work Index12.8 9.0 13.6 12.2 15.9

Size Interval Ball milling circuits from which the samples were collected:Quartzite Porphyry Massive Massive StandardSulphide Soft Sulphide Sulphide Function

Low Grade USA (Cu,Pb,Zn) (Pb, Zn, Cu)(Cu) (Cu)

1 0.000 0.000 0.000 0.000 0.0002 0.09514 0.05013 0.1171 0.1081 0.1933 0.1322 0.0970 0.1537 0.1442 0.1574 0.1417 0.1273 0.1522 0.1472 0.1265 0.1267 0.1276 0.1247 0.1253 0.1016 0.1049 0.1128 0.09723 0.1006 0.0827 0.08477 0.09481 0.07685 0.08050 0.0668 0.06778 0.07832 0.06131 0.06444 0.0539 0.05371 0.06451 0.04810 0.05076 0.043

10 0.04244 0.05336 0.03729 0.03958 0.03511 0.03379 0.04438 0.02911 0.03103 0.02812 0.02709 0.03677 0.02303 0.02459 0.02213 0.02127 0.02888 0.01810 0.01929 0.01814 0.01637 0.02177 0.01407 0.01496 0.01515 0.01254 0.01628 0.01089 0.01155 0.01216 0.009565 0.01211 0.008413 0.008888 0.01017 0.007279 0.008968 0.006483 0.006825 0.008

Operating Work Index:14.1 10.2 14.1 13.5



A8.8 References

LYNCH, A.J., 1977. Mineral crushing and grinding circuits,(Elsevier, Amsterdam), 309-312.

WHITEN, W.J., 1976. Ball mill simulation using smallcalculators, Proc. Australas. Inst. Min. Metall., 258, 47-53.

MORRELL, S. 1992. Ball size effects in ball mills. Chapter 2,End of project report, AMIRA/JKMRC Project P9J."Simulation and Automatic Control of Mineral TreatmentProcesses".

Appendix A Autogenous & SAG Mill Model (Model 430-431)


A9 Autogenous Mill Model (Model 430) and Semi-Autogenous Mill Model (Model 431)


The JKMRC has been involved in the development of a model ofautogenous and semi-autogenous grinding for many years. The firstmodel to provide useful predictions was the Leung model (Leung,1987). It used ore-specific breakage functions obtained off-lineusing a laboratory test procedure. It has largely been superseded bythe Variable Rates model( see Appendix 11). However, because ofits relative simplicity, the Leung model provides a goodintroduction to SAG mill modelling.

Caution: The Leung model scales on volume. This is irrelevant foroptimisation but is important for scale up from pilot to full scalemills of more than 8 to 9m in diameter.

The power model (Morrell, 1991) was added in 1992.

The Leung model has the general structure shown in Figure A9.1.The appearance function has two components:

• high energy corresponding to impact breakage, determinedfrom the twin pendulum single particle breakage apparatus, and

• low energy corresponding to an abrasion mechanism,determined from laboratory tumbling tests.

In both cases the functions are obtained off-line on representativesamples of ore and do not rely on being simultaneously back-fittedto operating data. The energy levels at which the high energyappearance function is determined are based on the mean energy inthe mill, which is related to mill diameter.

Discharge rates are determined as the product of the rate at whichthe load is presented to the grate, dmax, and the classification at thegrate (which is represented by a simple classification function).The model iterates to select a value of dmax equal to the fraction ofmill occupied by material of a size less than the grate size, which inturn is assumed to be a simple power function of feed rateexpressed as a proportion of mill volume.

The model predicts product size distributions and mill loads from aknown feed size and tonnage for a given mill and feed ore. Ballcharge is incorporated through the assumption that balls areequivalent to mill load particles of equal mass.

Average breakage rates are provided as defaults for both theautogenous and SAG mill models. Note that these rates aredifferent and are based on a limited data set.

Usually, breakage rates will be model fitted to plant data.

Autogenous & SAG Mill (Model 430-431) Appendix A

Page A-82 Appendix 9 Version 5.1 November 2001

Limitations/Caution

This model is a significant development of earlier models, and hasbeen shown to be successful in describing operating data on fullscale autogenous and SAG mills. Its scale-up capability is limitedto mills up to 8 to 9m in diameter from pilot mills of up to 2m.The dependency of the model parameters on operating conditionssuch as mill speed, percent solids, grate open area, linercharacteristics and pulp rheology was not well established whenthis model was developed. Most of these issues are addressed in theVariable Rates model(A13)

The Leung model is based on data from mills operating atapproximately 70% of critical speed and 60-70% solids by weightin the feed.

Breakage Mass Transferand Discharge

Load

Feed Product

Breakage Rate

Appearance Function

MassTransferFunction


HighEnergy(impact)

LowEnergy(abrasion)

Figure A9.1: Autogenous Mill Model Structure



A9.2 Model Equations- Particle Breakage

Particle Breakage This description follows the structure shown in Figure A9.1.

The model assumes that each size fraction experiences only oneenergy level of breakage. (The reality will certainly be adistribution of energy levels).

High EnergyBreakage

The relationship between the amount of breakage and the inputenergy is described by

t10= A (l - e - b Ecs ) (A9.1)

where t10 is the percentage of the broken particle which will passthrough a screen of one tenth the size of the original particle, andEcs is the energy absorbed per unit mass during breakage measuredin kWh/t.

A and b are the parameters which characterize this equation for aparticular ore. A is usually taken as 50. Parameter b is derivedfrom a drop-weight breakage test of closely sized ore particles.Required sample size varies according to ore variability. However,as a guide, about 50 kg of 50 mm material is needed.

Low EnergyBreakage

One or more 3 kg samples of 50 mm natural ore are tumbled for 10minutes in a small dry mill at 70% of critical speed. The productsof each run are sized and t10 is measured for each run.

Where 50mm material is not available, other sizes are used andadjusted using a simple linear model.

The t10 data are fitted to

t10 = a0 + a1 * mean size + a2 * sample mass + a3 * time. (A9.2)

The actual value of the abrasion parameter ta is one tenth (scalefactor only) of t10:

based on top size of 55*38 mm, mass 3 kg and time 10 minutes.



Low EnergyAppearanceFunction -Abrasion

The size distributions produced by ores tested to date have a similarshape. This shape can be scaled to the ta factor that is thepercentage passing one tenth of the original particle size.

A cubic spline function is used for smooth interpolation.

A 100mm particle is chosen as an example as particles of this sizewill typically undergo abrasion rather than crushing breakage.Parameter ta is taken as 1.0 to make the scaling obvious.

size (mm) % passing

t value scale* 100 100

t1.25 2.687*ta 80 2.687 t1.5 1.631*ta 67 1.631 t10 1.0*ta 10 1.0 t100 0.9372*ta 1 0.9372 t250 0.8070*ta 0.4 0.8070 t500 0.6365*ta 0.2 0.6365

The example shows that most of a 100 mm particle remainsunbroken.

This value of t is assumed to be equal for all size fractions.

Breakage Energy As the charge provides the grinding media, the level of availableenergy is related to the coarse fraction of the mill charge.

The average size of the top 20% of the charge is used as the highestenergy reference level.

S20 = (p100 * p98 * p96 ... p80) 1/11 (A9.3)

and the potential energy at the full height of the mill

E1 = 43 π (S20)3 ρ g D (A9.4)

where D is mill diameter in metres. An assumption due to Austinet al (1984) is used to relate other energy levels to E1. Austin et alprovided a rationale for energy levels in mills to be related by

E particle α 1/(x)1.5 (A9.5)

where x is particle diameter.

Hence, the energies experienced by smaller sizes are scaled usingthis relationship. This allows an Ecs to be calculated for each sizeand t calculated from equation (A9.1).



High EnergyAppearanceFunction(CrushingBreakage)

Once the energy of breakage is known, the distribution the particlebreaks into can be described by a cubic spline surface.

spline knots t = 0.0 10.0 30.0 50.0

function values for t2 0.0 50.53 92.49 96.47 t4 0.0 23.33 61.58 82.86 t10 0.0 10.00 30.00 50.00 t25 0.0 4.975 15.62 25.88 t50 0.0 3.064 9.412 14.71 t75 0.0 2.325 6.893 10.32

For example, for a 50 mm particle, a t of 30 would produce thisdistribution.

Size (mm) % passing

50 100t2 25 92.49t4 12.5 61.58t10 5 30.00t25 2 15.62t50 1 9.412t75 0.67 6.893

CombinedAppearanceFunction

As noted earlier, the abrasion distribution does not vary withparticle size while the crushing breakage is highly dependent onparticle size.

Hence, abrasion will tend to dominate for coarse particles andimpact for fine particles (from equation (A9.5)).

To generate an appearance function for each size fraction, the highand low energy appearance functions are combined proportionally.

a = tLE * a LE + t HE * a HE

tLE + t HE (A9.6)

where, aLE' aHE = low and high energy appearance functions

tLE' tHE = low and high energy t values



Equations (A9.1) to (A9.6) combined with the two tables of splineknots yield a complete appearance function (that is how eachcomponent will break) for each size in the mill load.

BreakageRates

To predict a product from the mill contents and the appearancefunction requires only a rate of selection for breakage for each sizefraction of the mill load.

These rates will be inherently scaled because the mill load will beconstrained by mill dimensions and the mill diameter (if the energyversus breakage assumptions are correct). These rates willcertainly vary if mill speed is changed but this dependence is notincluded in the Leung model.

To describe these rates, a five knot spline function is used.

Best fit values to data are tabulated.

Spline knots ln (Rate ln (Rate(mm) of Breakage) of Breakage)

Autogenous SAG

0.250 2.63 2.1764.00 4.04 4.44416.0 3.32 3.57744.8 1.98 2.753128 3.37 4.082

These are the default values in each model.

These rates are fitted to customize the model to any particularoperating mill.

SAG MillModification

The ball charge is approximated by a distribution of equivalentweight particles added to the mill load for the high energy breakagecalculation (equation (A9.3)). That is, only the appearancefunction will be varied by the addition of balls.

This completes the description of the Breakage area of the model.



A9.3 Model Equations (Mass Transfer and Discharge)

Classification The mill grate is modelled as a very simple classifier. When thismodel was developed the relationship between the classification,discharge and the operating conditions was not well defined.Hence, the classifier/discharge is assumed to be constant- for otherthan minus grate size hold up. A simple form is used.

D = 1 x < xm (A9.7)

D = 1n(x) - 1n(xg)

1n(xm) - 1n(xg) xg > x > xm

where xm is the particle size below which it will always passthrough the grate if presented to it - that is, behave like water. xg isthe size of the grate through which the largest particles will passthrough.

Pebble PortModification

Pebble port allows a small discharge rate of substantially coarserparticles. This modification affects the classification curve asshown below.

1.0

xm g

xxSize

fp

p

xp is the notional size of the pebble port

fp is the notional fraction open area of the pebble ports comparedwith the fraction of grate open area.

Typical values for fp are 2 to 5% ie. 0.02-0.05. While thismodification gives a good description of pebble product, the areasare notional only and in fact reflect relative discharge rates.

Discharge Rate The quantity of pulp discharged will depend on the quantity perunit time presented to the grate multiplied by the classificationfunction.

d = dmax * D (A9.8)



where dmax is the fraction of the load presented to the grate per unittime and D is the classification function.

The water is assumed to follow the sub mesh particles.

The actual value of D is found iteratively.

The required value satisfies the following empirical mass transferlaw (Austin, 1976).

Mass Transfer"Law"

The value of dmax is adjusted until the model prediction matchesthe required one. That is, until it lies on the operating line of

L = m1 Fm2 where

m1 = 0.37 (A9.9)

m2 = 0.37

L is the fraction of the active volume of the mill occupied by minusgrate size material and F is the total volumetric feed rate per minutedivided by the active volume of the mill.

Perfect MixingMill Model

The perfect mixing model at steady state provides the structure tocombine the various components of the model. It relates thedifferent parts in the following manner.

fi - ri si + rj s j aijj=1

i∑ - disi = 0 (A9.10)

pi = di * si (A9.11)

where fi, si, ri, di and pi are feed rate, contents, breakage rates,discharge rates and product rate vectors and aij is the combinedappearance function.

The form of equations (A9.10) and (A9.11) allows both the millload and the product to be calculated for any mill load anddischarge rate adjusted until equation (A9.9) is satisfied.



Calculation sequence

↓Calculate breakage rates

↓Calculate volume of below grate

size material in the mill, L

↓Calculate discharge rate

↓If error is acceptable exit else

make correction to Dmax

Mill Load This model is unusual because it uses an internal port to describethe mill contents. This port is accessible from the model propertiesdrop down or from the model window. It does not appear as streamequipment.

Scaling This model is inherently scaled for mill diameter and volume. Thisscaling optimistic in capacity as mill diameter is increased. It isreasonable for mills of up to 8 to 9m diameter.

A9.4 Prediction of AG/SAG Mill Power Draw

The GrindingMill Power

The gross power draw of the mill is that drawn by the millmotor(s), ie metered power. It is assumed that this has twocomponents, viz

• net power, ie. the power delivered to the charge

• no-load power, ie. the power to overcome drive train andbearing losses.

The gross power can, therefore, be represented by the followingequation

Gross Power Draw = No-Load Power + Net Power (A9.12)



The gross power draw is calculated from the fraction critical speed,ball SG and ball and rock porosity. These data are provided by theuser. The calculations use pulp load data generated by the modelcalculations.

The model data entry screen section for the power calculationsinclude the 'net power adjustment factor'. This is a calibrationconstant which varies slightly from mill to mill depending on millliner configuration and other factors.

Users are strongly recommended to leave this value set at 1.21.Other values should not be used unless a comprehensive range ofload vs power data are available.

Net Power Draw From photographic evidence, the charge shapes shown in FigureA9.2 were assumed to occur in grate discharge mills.

θ T

θ S

Grate Discharge

r m

r i

θ 0

90

270

180 o

o

o

o

Figure A9.2: Simplified AG/SAG Mill Charge Shape

By considering an element in the charge of cross sectional area r dsdθ and Len, the torque inertia of the element can be represented bythe following equation.

Torque Inertia of Element = gLenρr2 cosθ dθ dr (A9.13)

Power can be defined in terms of torque (τ) and rotational rate (N)as follows:

Power = 2π Nτ (A9.14)



For grate discharge mills, by integrating between the limits θs andθT and between ri and rm the net power (Pnet) is given by:

.drd cos r gLen 2 = P 2r

rnet

m

i

θθρπθ

θ∫ ∫

S

T

rN (A9.15)

No-Load Power The no-load power draw (i.e. that drawn by the mill whencompletely empty), is associated with various electrical andmechanical energy losses. The main ones are motor, gearing andbearing losses. None of these are fixed over the full mill operatingrange. Some, however, may have a fixed component. Forexample, bearing losses due to friction will be dictated by the mill'sdead weight (though even this will vary as liners and lifters wear),and the mill charge weight which will clearly vary with grindingcondition.

To determine the relationship between no-load power and milldesign parameters, data from pilot and industrial mills ranging from1.7 to 7.2 m in diameter were analysed. However, these no-loadpowers are difficult to measure precisely. The problems are powerfactor effects at low loads and achieving a completely empty mill.The parameter Diam3Len N was regressed against no load powerand found to provide a good fit (Figure A9.3). The relationshipdeveloped was as follows with N converted to the fraction ofcontrol speed:

No Load Power (kW) = 2.62 (Diam2.5 Len φ)0.804

Hence, this equation estimates the likely indicated no-load powerfor an installed mill.

Indicated (kW)

Pred

icte

d (k

W)

0

200

400

600

800

1000

0 200 400 600 800 1000

Figure A9.3: Indicated vs Fitted No-Load Power



Power CalculationAccuracy

The most recent JKMRC database currently includes power datafrom 63 different mills. Details are shown in Table A9.1.

Table A9.1: Data Base Details

Ball Mills SAG Mills AG MillsDiameter (m) 0.85-5.34 1.80-9.59 1.8-9.50Belly Length Inside Liners (m) 1.52-8.84 0.59-7.95 0.59-5.18Length/Diameter Ratio 1.00-1.83 0.33-1.50 0.33-1.0Percent of Critical Speed (%) 60-83 48-89 72-75Ball Filling (Vol %) 20-48 3-25 0Total Filling (Vol %) 20-48 7-38 10-31Specific Gravity of Ore 2.6-4.6 2.6-4.1 2.7-4.6Number of Mills 38 20 5Number of Data Sets 41 28 7Power Draw (kW) 6.8-4100 14.8-7900 12.5-5500

The power model has been applied to this database and was foundto give excellent results. The standard deviation of the relativeerror of the model was calculated to be 6.5% for gross power..

The model therefore requires a knowledge only of mill dimensionsand speed, ball charge, volume occupied by balls and pulp, and theore specific gravity. Full details of the model are given in Morrell(1991).

Because of the industrial database, the prediction of gross power isthe most reliable.

Restrictions This power model assumes the SAG mill grate and pulp lifters donot limit pulp throughput. For a large diameter mill (say > 7m) inclosed circuit with hydrocyclones or fine screens, this assumptionmay not be justified. A build up of fine slurry in the mill willremove some of the charge imbalance and reduce the actual powerdraw.



A9.5 SAG Mill Printout



A9.6 Symbols

Symbol Meaning

aij fraction of size j which breaks into size i

A Ecs model parameter

b Ecs model parameter

dmax discharge rate at xm

di discharge rate of size i

fi feed rate of size i

Ecs Energy absorbed per unit mass during breakagein each size fraction

E1, particle potential energy at full height of mill

F volumetric feed rate/mill volume

HE High Energy

LE Low Energy

L mill volume fraction of minus grate size

m1, m2 mass transfer parameters

si mill contents of size i

rj rate of breakage out of size jS20 average size of top 20% of mill load

t10 percentage which passes through a screenaperture of 10% of the original size.

tp percentage which will pass through a screen ofaperture original size /p

ta abrasion parameter

xi particle size

xg grate size (mm)

xm size below which all will pass through the grate (mm)

g gravitational constant

ρ charge density

r radial position of element



θ angular position of the element

Nr rotational rate at a radial distance r

rm mill radius

ri charge surface radius (see Figure A9.2)

θs angular position of the shoulder

θr angular position of the toe

Diam mill diameter (m)

Len mill length (m)

φ fraction of critical speed.


The model is not valid outside a range of 55% to 75% solids byweight in the feed.

Mill speed is assumed to be 70% of critical or close to it. Howeverfor small changes in speed (~ ± 5%) a good approximation can bemade by multiplying the rate at each knot by the relative change.That is, for +5% (ie. 70% increased to 73.5% critical) multiply by1.05 or add ln (1.05) to the logarithm of the knot value. Thisassumes the number of impacts per mill revolution will not change.In reality more speed will give more lift and a slightly higherbreakage energy.

The classification model is very simple and only dependent ongrate size. The xm parameter is driven by slurry viscosity. Forviscous ores, xm may be up to 1mm. For clean ores (hard rock,clay free) 0.1-0.2mm is typical.

This model has been tested against a large number of full-scaleoperations and a very wide range of pilot plant test data. Themodel has provided good predictions for design (Morrison, Kojovicand Morrell 1989) over a wide range of ore types.

Detailed comparison with pilot plant data has highlighted areaswhere the model assumptions are not a sufficiently goodapproximation. Known areas to treat with caution are as follows.

The assumption that grinding rates are constant at a given ball loadis not true when

• there are large variations in mill feed sizing

• the mill is taken from open circuit to closed circuit.



OperatingLimits

The model is numerically stable at any mill load (equation (A9.9)).Real world mills typically operate with maximum loads of 30 to35% by volume of charge.

However, they may be limited by motor power at much lowerloads. There is usually a limit on ball load of 5 to 10% because ofmechanical or power constraints.

It is the engineer's responsibility to check these parameters againstthe limits for a particular mill.

Feed Sizing The auto/SAG model 'forms its load' from the mill feed. If the millfeed size distribution is smooth (ie. a reasonably straight line on aRosin-Rammler plot), simulated variations in feed sizing givesensible results. If the coarse end of the feed distribution isartificially adjusted for the feed is preclassified in some way, thenthe S20 assumption that the load can be treated as a single numberbecomes unjustified. Hence artificially adjusted top sizes willcause the model to predict wide variations in performance.

(While these variations are excessive, it should be noted that realauto mills are also sensitive to feed top size).

Similarly, if those fractions that limit throughput (notional criticalsize) are prescreened from mill feed, the model will be optimisticabout increased throughput.

(Once again, real SAG mills will also achieve much higherthroughputs). However, predictions for recycle crusher are quiterealistic.

If mill operation is closed with a fine classifier (DSM screen orhydrocyclones) there is usually an increase in the observed grindingrates at 4mm. This means a typical SAG mill may have some 'free'grinding capacity for particles a few millimetres in diameter.Where the simulated mill is operating in closed circuit with ascreen, the circulating load will tend to vary more (and the millload less) with changes in hardness and feed sizing than the realmill. However trends will be correct and overall product sizingshould be close.

Mill Power Accurate measurements or estimates of mill dimensions, speed andball and pulp load are required for the power calculation. Ensurethat all data used are accurate.



Ball Size Effects Ball effect is estimated by generating an equivalent load of oreparticles. As the top 20% of this load is used to find S20, only thetop one or two ball sizes can have any 'impact' on this calculation.Manipulating the finer ball sizes (ie. < half top size) have very littleeffect. In practice, it does change the fine grinding rates.

Ball Load Effects These have been investigated in some detail at pilot scale. Ingeneral, the harder the ore (low b and low ta) the less the grindingrates are affected. A soft ore however follows the accepted wisdomthat increasing ball load will produce a coarser product. This maywell be because the increased number of balls are now breaking theore particles in the load which were doing the fine grinding.

Discharge Rates Considerable work has been carried out by Morrell (1990) onfactors affecting discharge rates. These effects are alsosummarised in Morrell and Morrison (1989). See A11 for details.

Overall, discharge rates will only become a limiting effect in veryhigh viscosity ores. In this case, operation at a lower pulp densityis recommended. The SAG mill is an effective pump and thecharge will remain relatively 'dry'.

Mill Liner Effects The SAG mill model is valid for correctly designed traditional'high/low' lifter type action. Wave liners or short lifters do notprovide enough lift to achieve the default rates. If poor lift iscombined with poor discharge, the mill only produces abrasionwith a very fine product at a correspondingly low throughput.

FurtherDevelopments

The JKMRC now has a substantial database of SAG/auto millsurveys and breakage characteristics. This data base has been usedto develop the wider range variable rates AG/SAG model describedin Appendix 11

Mill LoadLimits

The autogenous and SAG mill model does not include an explicitmaximum for the mill load. However, a warning will be flagged ifthe total load (ie. balls and pulp) exceeds 35% by volume. An errorwill be flagged if the total load exceeds 40%.



A9.8 Fitting the Autogenous and SAG Mill Models

PARAMETER MENU

XGXMRate 1Rate 2Rate 3Rate 4Rate 5

These models are complex and calculation intensive. However, anycomputer which is suitable for MS Windows 95/98/NT should beadequate for AG/SAG model fitting.

In the unlikely event that the fit is slow, the Select list may be usedto restrict the scope of calculation or to fix recycle streams as“feed” streams.

.

Initial Values Use the grate width and 100 µm as initial estimates for xg and xm.

The default breakage rates for auto and SAG will provide a goodguess for each knot value.

Ore TypeParameters

For accurate results, these are best derived from tests carried out onrepresentative samples at JKTech.

For an existing operation, the values provided in the volume ofsupplementary information provide some guide to possible values.

Mill Load If a reasonable estimate of load mass and sizing is available, thenfitting with a range of A and b values may provide a way ofestimating these values - that is - use the values which give the bestfit for ratio work.



Mill Load is fitted by inputting it as raw data into the dummyproduct stream. If you only have a total mill load estimate (eg.from bearing pressure), set the size fraction SDs to zero and theload SDs appropriately. Subtract the weight of balls from this loadfor a SAG mill and input it on the model screen.

Closed CircuitOperation

If the mill is being operated in closed circuit with hydrocyclones, itis better to reduce m1 from 0.37 to 0.25. This seems to provide abetter approximation of the mass transfer response for a largerecirculation of material finer than grate size.

Knot Positions The spline knot positions are better left where they are for the'normal' range of SAG mill feed sizings, 80mm < F80 < 250mm.However for very fine auto mill feeds, the limiting size fractionwill also be finer and it may help to scale down all the knots. Thatis, reduce them by the same ratio. An alternative is to simply fix thelarger knots at their default values.

Hint: If the closed circuit simulation gives a very differentcirculating load, check carefully for size biases in the fit or in thedata itself.

Master/SlaveFitting

The Master/Slave fitting can be used with multiple sets ofSAG/auto data. Ensure that you are using the same knots positionsfor each mill in the test. Similarly, each survey data set to be fittedsimultaneously should have been collected with the same grate andpebble port size, and ball load.

A9.9 References

AUSTIN, L.G., LUCKIE, P.T. and KLIMPEL, R.R., 1984. Theprocess engineering of size reduction: Ball Milling,S.M.E/A.I.M.E., NEW YORK: 561pp.

AUSTIN, L.G., WEYMONT, N.P., PRISBREY, K.A. &HOOVER, M., 1976. Preliminary results on themodelling of autogenous grinding. 14th Int. A.P.C.O.M.Conf. The Penn. State Uni.: 207-226pp.

LEUNG, K., 1987. An energy based ore specific model forautogenous and semi-autogenous grinding. Ph.D. Thesis,unpublished, University of Queensland.

LEUNG, K., MORRISON, R.D. and WHITEN, W.J., 1987. Anenergy based ore specific model for autogenous and semi-



autogenous grinding. Copper 87. Chilean Institute ofMining Engineers, Santiago, Chile.

MORRELL, S. 1990. Simulation of bauxite grinding in a semi-autogenous mill and DSM screen circuit. MEng Thesis,University of Queensland (unpublished).

MORRELL, S. and MORRISON R.D. 1989. Ore charge, ball loadand material flow effects on an energy based SAG millmodel. SAG Conference, University of British Columbia,Vancouver.

MORRELL, S., NAPIER-MUNN, T.J. and ANDERSEN, J. 1992. Theprediction of power draw in comminution machines.Comminution-Theory and Practice, K. Kawatra (ed), SME, Chapter17, pp. 235-247, 1992.

Appendix A Size Converter Model (490)

Version 5.1 November 2001 Appendix 10 Page A-101

A10 Size Converter Model (Model 490)

A10.1 Introduction

The model provides a product size distribution with a user

specified P80. This is achieved by adjusting the feed sizedistribution finer or coarser as required. The model is useful when there is no process knowledge of upstream comminution devices, or when a size distribution of aparticular size is required for sensitivity analysis.

A10.2 Model Details

The feed to the model is adjusted by moving it sideways on a

Cum % Passing v size plot until the product P80 matches the specified P80 as closely as possible.

A10.3 Fitting the Size Converter

There are no fittable parameters in this model.


The model is limited in its ability to generate a product which is

coarser than the feed by the coarsest screen available in the feedcombiner and product ports. It is always wise to plot and inspectthe graph of the feed and product to ensure that the shape of thedistribution is reasonable.

Appendix A Size Converter Model


(Blank Page)

Appendix A Variable Rates SAG Model (435)


A11 VARIABLE RATES SAG MODEL

A11.1 Introduction

The Leung AG/SAG model (A9) typically requires a full scale plant orpilot mill survey combined with ore breakage testing to generate a set ofgrinding rates. However research in the mid 1990’s using a largedatabase of pilot and full scale milling tests has lead to the developmentof a correlation between model grinding rates and mill operatingconditions. A further correlation between mill feed sizing and orebreakage characteristics has also been developed. These two correlationsnow allow mill performance to be predicted for a wide range of mill sizesand operating conditions. Hence the model can be used to evaluateoptimisation strategies in existing plants and to investigate (andcompare) grinding circuit configurations at the pre-feasibility stage thusreducing the cost of pilot testing.

The underlying model is still identical with that developed by Leung et al(1987) except that• grinding rates have been related to mill diameter and operating

conditions, and• A model which includes grate geometry (but does not

incorporate pulp lifter capacity) now describes slurry holdup.

This approach was reported by Morrell and Morrison, 1996.If you are new to SAG mill modelling, it is strongly recommendedthat you work through Appendix 9 (the Leung model) beforeattempting to use the Variable Rates model.The VR model interface has been slightly revised for Version 5mostly to make recycle effects easier to specify.

A11.2 Scaling Approach

A large proportion of AG/SAG model users either carry out pilotscale tests and wish to predict full scale operation or carry out full-scale tests and wish to predict performance at different operatingconditions. The variable rates model has been implemented tofacilitate this scaling process as in the rod and ball mill models.The variations in rates also depend on recycle and feed sizing.Hence, this model allows the user to select appropriate streams forrecycle data.

For model fitting, the original and simulated cases will usually beidentical. This is considered in detail in section A11.6.

A 11.3 Slurry Holdup Model

The transport of slurry through the mill is described by a function whichrelates the hold-up of slurry, grate design, grate open area and mill speed

Variable Rates SAG Model (435) Appendix A


to the volumetric discharge rate through the grate (Morrell andStephenson, 1996):

Jp = k Q0.5 γ-1.25 A-0.5 φ0.67 D-0.25 (A11.1)

whereJp = fractional slurry hold-upD = mill diameter (m)A = total area of the grate apertures (m2)φ = fraction of critical speedQ = volumetric flowrate out of the mill (m3/hr)γ = mean relative radial position of the grate apertures

γ = ri ai

rm ai

∑∑

ai = open area of all holes at a radial position rirm = radius of mill inside the liners.

Classification by the grate is related to the effective grate aperture by asimplified classification function. For illustrative purposes a conceptualview of the weighted radius model is shown in Figure A11.1.

0.75 - 0.8 0.85 - 0.95

Figure A11.1: Weighted Radius For Two Grate Designs



A11.4 Variable Rates Model

Relationships between the operating conditions and changes in thebreakage rate distributions within the JKMRC’s pilot mill database(Mutambo, 1993) were developed. These results were augmented withresults from full-scale mill data in cases where the pilot mill databasecontained little or no variation in the parameter of interest e.g. millspeed. To indicate the extent of the pilot mill database, Table A11.1summarises its details.

Table A11.1: Pilot Mill Database Details

RangeNew Feed F80 (mm) 35-140Ball load (%) 0-12Recycle load (%) 0-500No. different ores 16No. tests 52

The breakage rate distribution is described within the model using cubicsplines (Ahlberg, 1967). This gives rise to five breakage rate values eachof which relate to a particular particle size and which togethercharacterise the entire breakage rate distribution. The five standardparticle sizes chosen are 0.25, 4, 16, 44 and 128mm which haveassociated with them breakage rates which are labelled R1, R2, R3, R4and R5 respectively.

R5

R4

R3R2R1

1

10

100

1000

Breakage rate (hr^-1)

0 0 1 10 100 1000

Size (mm)

Figure A11.2: Characterisation of the Breakage Rate Distribution

These rate curves exhibit a characteristic shape. The coarser (R5 andR4) rates relate to abrasive breakage while the finer rates R1 and R2exhibit similar characteristics to those of coarse ball milling, ie.predominantly impact breakage. The pronounced dip in the rates at R3 isassociated with the critical size which may limit mill throughput bybuilding up to excessive levels. Typically it is in the 25-75mm range and



varies with particular combinations of feed sizing, breakagecharacteristics and the magnitude of the breakage energy developed inthe mill.

To determine the relationship between operating conditions and thebreakage rate distribution, the breakage rates R1-R5 were regressedagainst operating conditions. The resultant equations were of thefollowing form:

Ln (R1) = (k11 + k12Ln(R2) - k13Ln(R3) + JB (k14 - k15F80) - DB)/Sb……(A11.2)

Ln (R2) = k21 + k22Ln(R3) - k23Ln(R4) - k24F80 (A11.3)

Ln (R3) = Sa + (k31 + k32 Ln(R4) -k33 Rr) /Sb (A11.4)

Ln (R4) = Sb(k41 + k42 Ln(R5) + JB(k43 - k44F80 (A11.5)

Ln (R5) = Sa +Sb(k51 +k52F80 + JB (k53 -k54F80) - 3DB) (A11.6)

whereSa = rpm scaling factor

= Ln (simulated mill rpm/23.6)Sb = fraction of critical speed scaling factor

= simulated mill fraction of critical speed/0.75DB = ball diameter scaling factor

= Ln (simulated ball diameter/90)JB = % of total mill volume occupied by balls and

associated voidsRr = recycle ratio

= (tph recycled material_-20+4mm)(tph new feed) + (tph recycled material -20+4mm)

F80 = 80% passing size of new feed (mm)kij = regression coefficients

The regression coefficients for equations (A11.2)-(A11.6) are givenbelow and are based on the JKMRC current database at mid 1996. Asmore data are collected and our understanding of the various factorsincreases, these coefficients are likely to be modified.

Table A11.2: Regression Coefficients

j k1j k2j k3j k4j k5j12345

2.5040.3970.5970.1920.002

4.6820.4680.327

0.0085--

3.1410.4024.632

----

1.0570.3330.171

0.0014--

1.8940.0140.4730.002

--



It can be seen from the equations that the finer size rates are functions ofthe rates of the coarser sizes. Hence R1 is a function of R2 and R3 etc.The rates can be considered as falling into 2 groups which represent thegrinding media and product size fractions. Hence the grinding mediagroup contains the rates R4 and R5 (related to particles >30mm) themagnitude of which affect the throughput. The product groupincorporates rates R1, R2 and R3 (related to particles < 30mm) and themagnitude of these affects the final product size. It is of particular notethat the rates are interrelated in a complex manner and are bestunderstood by graphing the entire breakage rate distribution.

A11.5 Effect of Key Parameters

The variable rate model allows the effects of a number of key parametersto be considered independently.

It is worth mentioning that ‘original’ does not provide a basis forscaling in this model as it does in rod and ball mill models. Itprovides a marker to allow the user to see how much the rates havevaried from the original case.

Ball Load The effect of changing ball load on the breakage rate distribution isillustrated in Figure A11.3.

1

10

100

1000

10000

Breakage rate (1/hr)

0 1 10 100 1000

Size (mm)

8% balls

4% balls

0% balls

Figure A11.3: Effect of Ball Load on Breakage Rate Distribution

The resulting relationship is as expected in that by increasing the ballload the breakage rates increase at coarser sizes but reduce at finer sizes.This has the effect of predicting higher throughputs at coarser grinds asthe ball load is increased. However, it is commonplace to operate at toohigh a ball charge often because of historical experience with softer,



oxidised, surface ore. As the ore becomes harder it may well be possibleto replace balls with ore as grinding media for more power effectiveoperation.

Makeup BallSize

No significant dependence of the breakage rates on ball size was found inthe pilot mill database. The SAG model does account for ball sizechanges in terms of the energy provided during impact. It does this bychanging the mean grinding media-size, which in turn changes the‘energy level‘ of the mill. This ‘energy-level‘ term is used to determinethe specific energy of impact. As the ball size is increased, therefore, thespecific energy increases and hence for a given impact event a finerproduct size distribution occurs. However, as the ball size is increasedthe number of grinding media per tonne of charge will decrease. As thebreakage rate is related to the number of impacts provided by the grindingmedia then a reduction in the breakage rate may be expected to occur. Toaccount for this a ball scaling factor is used. Figure A11.4 illustrates theeffect of the ball size correction factor on the breakage rate distribution.

It should be emphasised that it is usually argued that a coarser ball sizewill give a higher throughput but with a coarser grind. In practice,experiments with full-scale mills are sometimes inconclusive and milloperators see little or no effect when experimenting with ball size. Thismay be due to the counter-effect of reduced numbers of balls providinghigher breakage energies when increasing ball size. The model predictssuch a response by increasing the breakage energy and reducing thebreakage rate. In some instances the one effect may outweigh the other,in which case a response will be noted. Over some ranges of ball sizes,however, little or no effect will be seen.

1

10

100

1000

Bre

akag

e ra

te (1

/hr)

0.01 0.1 1 10

100

1000

Size (mm)

125mm balls

94mm balls

Figure A11.4: Predicted Effect of Changing Ball Size



Feed Size F80

Effects for SAGMilling

The effect of F80 was found to be the most difficult one to evaluate as itinteracted with the ball charge level. At relatively high ball charges (10%or more) high F80 values were detrimental as evidenced by the reductionin the breakage rates illustrated in Figure A11.5.

1

10

100

1000

10000

Breakage Rate (1/hr)

0 1 10 100 1000

Size (mm)

f80=125;Jb=10%

f80=75;Jb=10%

Figure A11.5: Effect of F80 on Breakage Rate Distribution - (SAGmill)

Feed Size F80Effects forAutogenousMilling

However in the case of autogenous grinding the pattern is different. Inthis case a higher F80 promotes breakage in the coarser size fractions(Figure A11.6). This is to be expected when it is considered that inautogenous milling large rocks are required to break ore in the R5 sizerange (128mm). As the F80 increases, this will typically result in morecoarse rocks in the charge able to break R5-size ore and hence R5 willincrease. In SAG mills running with higher ball charges, the rockcomponent of the grinding media plays a lesser role in dictating thebreakage rate and contributes more to the rock ‘burden’ which has to beground down. Feeds with F80 values and hence more coarse feed rocks,can thus be expected to reduce the breakage rate.

Caution needs to be exercised, however, as it has been found that the F80is not always a good indication of the feed size distribution. This isparticularly noticeable with autogenous mills whose performance mayfluctuate considerably yet maintain a reasonably constant F80. In suchcases the distribution changes systematically with performance and thattypically higher proportions of 25-50mm material in the feed result inlower feedrates, ie. less sub-grate size material is present in the feed andmore near size material has to be broken.



1

10

100

1000

Breakage Rate (1/hr)

0 1 10 100 1000

Size (mm)

f80=125;Jb=0%

f80=75;Jb=0%

Figure A11.6: Effect of F80 on Breakage Rate Distribution - (AGmill)

Effect of RecycleLoad

Recycle loads broadly fall into 2 categories viz.:

1. Coarse recycles from trommels, vibrating screens and recyclecrushers which typically comprise only -20 + 4 mm materialand have P80 values of the order of 8 - 12mm,

2. Fine recycles from hydrocyclones and DSM screens which are

predominantly –4 mm material and have P80 values of the orderof 0.2 - 0.5 mm.

It has been found that the amount of recycled material in the -20 + 4 mmsize range is inversely related to the amount of breakage that thismaterial is subjected to. This can be explained if one considers that theserocks are broken by coarser rocks and balls whose frequency does notappreciably change with changes in recycle load. However as theamount of recycled -20 + 4 mm rock increases, the amount of this sizematerial in the load will increase. As the breakage rate in a given sizeclass is related to the ratio of the number of coarser rocks and balls to thenumber of rocks in the given size class, then increasing the -20 + 4 mmrecycle will result in a drop in the breakage rate in this size range (R3size = 16 mm). The changes in the breakage rate distribution as thecoarser recycle increases is illustrated in Figure A11.7. Interestingly,recycle of fine material ie. –4 mm did not correlate with any of thebreakage rates. This may be related to the breakage mode of thismaterial which is believed to be dominated by attrition.

Where the material has been recycle crushed, it is considered to havesimilar properties to new feed and is not included as -20 +4 mm recycle.



1

10

100

1000

Bre

akag

e ra

te (1

/hr)

0.1 1 10

100

1000

Size (mm)

Rec=.1

Rec=.05

Rec=0

Figure A11.7: Effect of Recycle Load on Breakage Rate Distribution



Recycle Control inV5

For the most part, the Version 5 model is identical with theVariable Rates SAG model in Version 4. There are, however, acouple of important differences which relate to control of recycleof –20 +4mm material on the grinding rates.

As for V4, the User inputs new feed rate tonnes per hour and 80%passing size for Simulated and “Original” mills.

Recycle Options – In Version 4, there are two implied switches.The first is “Fixed Recycle”. If the User inputs a Fixed Recycletonnage, all simulations will use this value to calculate the recycleratio.

Version 5 uses this implied switch as well i.e. the fixed recycletonnage value is set to zero to allow for simulated recycle.

The second implied switch in Version 4 is to select one (or more)recycle streams from the flowsheet. In version 5, this switch isnow explicit as “Use Recycle in Calculations”. If this switch isset to one, the actual recycle is now calculated by the model as thedifference between –20 +4mm in new feed (specified by the user) and in the total feed to the SAG mill.

Hence the User uses the Ore Feeder size marker to estimate % -20mm and % -4mm and enters the difference into the appropriatefield on the SAG model.

Comment. The effect of recycle has always been difficult tomodel and it also the subject of current research. It providessome compensation for recycle material ‘survivors’ being likelyto be somewhat ‘harder’ than new feed particles in the same sizefraction.

However, if the recycle stream is crushed, new flaws will begenerated and the original feed properties retained. Therefore it isrecommended that ‘Use Recycle …. ‘ be turned off when arecycle crusher is used, with the following note of caution. If K1is larger than 4mm, a proportion of recycle crusher feed will notbe crushed. The bypassed –20 +4mm can be compensated for byiteratively adding the ‘new’ –20 +4mm in the crusher product tothe new feed % of –20 +4mm.

Excessive fine recycle may make this model unstable. However,excessive fine recycle will often make real AG/SAG millsunstable and it a consequence of a realistic model.



Mill Speed/MillDiameter

The breakage rate is related to the number of size reduction eventsper particle, per unit time and is hence a frequency. This in turnmust be related to the frequency with which the mill rotates (rpm).A scaling factor is therefore applied to account for changes in therotational rate. For a given fraction of critical speed the rpmdecreases with mill diameter0.5 and hence this scaling factor willalso change with mill diameter. All else being equal, therefore, alarger diameter mill will have a lower breakage rate than a smallerunit. However it is pointed out that the JKMRC model inherentlyscales on the basis of breakage energy which it relates to milldiameter. Therefore, whereas a larger diameter mill will have alower breakage rate it will have a higher breakage energy.

In a given mill as the rpm changes, apart from the rotational rate,the shape of the grinding charge will also change in line with thefraction of critical speed (Morrell, 1996). Typically as the fractionof critical speed increases the charge is subjected to increased liftand hence impact breakage is enhanced. It is at the expense ofattrition breakage which is normally associated with cascadingmotion and which is prevalent at lower speeds. To account forthese effects a further scaling factor is applied which is based onthe fraction of critical speed. Figure A11.8 illustrates the predictedchanges in the breakage rate distribution as speed is changed.

1

10

100

1000

10000

Size (mm)

65% Cs

75% Cs

85% Cs

Figure A11.8: Predicted Effect of Changing Speed on the BreakageRate Distribution

Mill Power The variable rates model allows the user to specify the conical slopeinside the liners of each mill end. The mill power estimate includesthe conical ends (Morrell, 1996).



A11.6 Parameter Fitting the Variable Rates Model

Fitting SingleData Sets

Model fitting the variable rates model is quite similar to fitting theLeung model (A9). The defaults for the original mill grinding ratesare all set to zero, ie. the intercepts of the rate equations (TableA11.2) are included in the model.

Hence the fitted rates indicate how far the measured mill isoperating from “typical” conditions. The recommend strategy is tofirst fit xg and xm with the grinding rate intercepts set to zero. Ifthe mill has pebble ports, set the initial pebble port size to thelargest measured particle in the mill discharge. If the xg and xm fitis plausible, add the pebble port size (PPSize). Use the measuredopen areas for pebble ports and grates and the measured weightedradius/mean relative radial position for the grates. Note that thegrate open area includes grates and pebble ports. The recyclestreams are selected from the unit menu.

The measured recycle rate (-20 +4 mm) should also be entered asdata. (When this field is zero, the calculated recycle is used. This isappropriate for simulation).

The new feed size (F80) should be noted and entered for bothSim(ulated) and Org(inal) mills as should all of the other measuredmill data.

If the xg, xm and PP (pebble port) size fit is plausible, adjust thescale factors on Breakage Rate “Constants” to 0.1 and include themin the next fit.

The open area fractions (Grate OA) can be selected to fit. They areonly suited to matching wear conditions and should not be fittedtogether with grate or pebble port sizes as the parameters are likelyto interact quite severely.

Given good data and ore characterisation this model will oftenpredict the measured results quite well and model fitting is verysimple.



Remember – xg, xm and PP size are all square mesh equivalentsizes. Therefore, aperture shape and particle shape will interact. Aslabby particle will appear much larger to a square mesh screenthan to a slotted grate aperture!

Fitting MultipleData Sets

A comprehensive pilot test program will produce data over a rangeof operational conditions. For sophisticated users, the variable ratesmodel allows several sets of pilot data to be analysedsimultaneously.

The first step is to analyse each set by using its own select list. Thisshould identify any data problems. Then add each data set onto acombined select list for master slave fitting.

One of the pilot data sets is selected as a base case. For this set,simulated and original inputs are the same. For the other sets,change the simulated mill conditions as required (eg. Ball load)and use the base case original mill conditions in all tests. Add allof the measured load and product streams to the model fit data list.Use the master/slave capability to simultaneously fit, xg, xm, PPortsize and grinding rate intercepts to all data sets at once.

Notes:• a fast computer (Pentium 166 or better) is required for three or

more SAG data sets• Multi-fit capability is not available in Version 5. However, the

number of fittable sets of port data will be expanded in laterreleases.

This approach can also be used to simultaneously analyse severalsets of operating plant data, even between different sizes of millstreating similar ores.

In either case, a good overall fit indicates a model which can beused for prediction over a wide range of operating conditions.

A poor overall fit, particularly if the grinding rates are lower thantypical (negative intercepts) may indicate shortcomings in datacollection. More seriously, it may also indicate more significantproblems such as poor liner design or inadequate pulp transportcapacity (i.e. pulp lifters).

Larger rates may indicate particularly good practice or at the coarseknots, decreasing ore competence at coarser sizes.



A11.7 Using the Variable Rates Model for Simulation and Design

This model is quite complex and a good appreciation of both themodel and SAG mill operations are recommended before use fordesign.

Comprehensive industrial research work over the last decade hasbuilt up the database for this model and exposed some conceptualweaknesses which are being addressed with two new models.However, the variable rates model is now a powerful tool for dataanalysis, circuit evaluation and AG/SAG mill design.

The following points should be noted.

Recycle Streams Up to three recycle streams can be selected from the model menu.These should be recycles which actually go into the mill, eg.Recycle crusher product, not feed. The “Fixed Recycle” inputshould be set to zero for simulation to allow the calculated flow of-20 +4mm to be used. (Input the measured flow for model fitting).

Where the material has been recycle crushed, it is considered tohave similar properties to new feed and is not included as -20 +4mm recycle.

NB: V5 handles recycle loads differently from V4. See pages 108-109 for details of the differences.

Load Limits The feed trunnion diameter indicates the maximum volumetric loadlimit. If the simulated mill limits at a lower level than the actualmill, reduce this diameter.

Beyond a certain load, the power model is unlikely to be reliableand the power estimates are set to zero.

Grate FlowLimits (MassTransfer“Law”)

The flow correlation detailed in A11.3 provides a maximum flowestimate at the simulated mill load. The user may enter a designmaximum load level for which a maximum flowrate estimate is alsocalculated. These estimates relate to flow through the grate. Theyassume that the pulp lifters can remove all of the grate discharge.This is not always true for mills operating in closed circuit withcyclone or fine screens.

If the simulated flow exceeds the maximum, the mill will likely fillup with fines and go into overload as the slurry pool reduces impactbreakage. This effect is not simulated by the model.

Feed SizeConsiderations

The F80 values for new feed for both simulated and original mills areentered by the user.



For design, a reasonable estimate of F80 is often difficult. Powerbased equations typically divide by the feed size so the assumptionbecomes unimportant but real mills are sensitive to feed sizing asare accurate models.

The JK database shows reasonably systematic dependence ofAG/SAG F80 (crusher P80) with all hardness measures. The harderan ore, the coarser the resulting crusher product at the same crusherclosed side setting. The best correlation is with the JK abrasionparameter ta.

For a design case, the F80 of the feed can be estimated from themeasured ta with a standard deviation of about 10% of the primarycrusher closed side setting.

F80 (mm) = {css - 78.7 - 28.4 ln (ta)} (A11.7)s.d. = 0.1 css.

This is not a perfect answer, as the size distribution slope alsovaries as shown below.

1000100101.1.01

1

10

100

Coarse/hard ore

Fine/soft ore

Size (mm)

Figure A11.9: Typical AG/SAG mill feed sizings

The size converter model (see Appendix A10) can be used to adjustfrom a similar ore to the target range for simulation.

(Note that it is also possible to conduct a test in a pilot adit toestimate the likely run of mine size distribution. This distributioncan be fed to the crusher model to predict the mill feed distribution.Contact JKTech for assistance with test blast design.)




This model does not take account of the variation in breakageenergy at different mill loads. Therefore pilot and industrialoperation should be measured at realistic operating loads (ie.>20%).

As noted earlier, pulp lifter capacity may limit before maximumgrate capacity is reached.

The single number grate characterisation (Mean relative radialposition) is a useful approximation. However, it should be usedwith actual grate designs, not hypothetical variations which maynot be able to be manufactured. As the database of very large millsexpands, it is becoming apparent that the charge in a large coarsefeed mill restricts the maximum circulating load. Hence for mills11m in diameter (or larger) treating coarse feed, the simulatedcirculating load should be restricted to 25% of new feed rate. Thiscan be done by reducing the grate open area parameter. This is anarea of continuing research at JKMRC.

With the large database of SAG mill test work, it is clear thatmaximum throughput does not always correspond to maximummill power draw or maximum mill load.For hard ores, maximum throughput requires sufficient impactenergy at the toe of the charge. Hence the maximum throughput (atmaximum discharge coarseness) will often occur between 20 and30% volume mill load.

Research at JKMRC is developing models which will account forthis effect and others such as the difficulty of removing pebbles forcrushing from very large mills. For mills of larger diameter than10m, a maximum recycle crusher flow of less than 25% of newfeed rate is recommended as a constraint on simulations. (Millswith very fine feed and large grates may exceed this estimate)

Manipulating the SAG mill feed size distribution by pre-crushing isanother way of shifting the throughput/product relationship for hardores.

A limitation has been found on the accuracy of the response of therate equations to changes in F80, particularly if the new feed F80 isoutside the range of the data base. The recommended F80 for usein the model is calculated from the equation:

F80 = 71.3 – 28.4 * ln (ta)

This F80 value should be used as the Reference F80 value on theRecycles tab in the Variable Rates SAG Model equipment window.



A11.9 Variable Rates SAG Model Printout





A11.10 References

Ahlberg J H, Nilson, E N & Walsh, J L, 1967. The Theory of Splinesand Their Applications. Mathematics in Science and Engineering,38, Academic Press, New York and London

Andersen J S, 1989. Development of a Cone Crusher Model. M.Eng.ScThesis, University of Queensland.

Leung. K, Morrison R D & Whiten W J, 1987. 1987. An Energy BasedOre Specific Model for Autogenous and Semi-autogenous GrindingMills. Copper 87, Santiago Chile.

Morrell, S. 1996. Power Draw of Wet Tumbling Mills and itsRelationship to Charge Dynamics. Part I: A Continuum Approach toMathematical Modelling of Mill Power Draw. Trans. Instn.Min.Metall, 105, C43-53.

Morrell S & Stephenson I, 1996. Slurry Discharge Capacity ofAutogenous and Semi-autogenous Mills and the Effect of GrateDesign. Int. J. Miner. Process. (In press).

Morrell S & Morrison R D, 1989. Ore Charge, Ball Load and MaterialFlow Effects on an Energy Based SAG Mill Model. Presented SAG1989, University of British Columbia. Editors. Mular & Agar.

Morrell S & Morrison R D, 1996. AG and SAG Mill Circuit Selectionand Design by Simulation. SAG 96, edited Mular, Barrett andKnight, Vancouver 769-790.

Mutambo. J, 1993. Further Development of an Autogenous and Semi-autogenous Mill Model. M. Eng Sci. Thesis. University ofQueensland (unpublished).

Needham T M & Folland G.V. 1994. Grinding Circuit Expansionat Kidston Gold Mine. Presented at SME Annual Meeting,Albuquerque, New Mexico. February 14 -17.



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Appendix A High Pressure Grinding Rolls (Model 402)


A12 High Pressure Grinding Rolls (402)

A12.1 Introduction The high pressure grinding rolls crusher(HPGR) - also known as the roller press or roller mill - was invented by Klaus Schönert in Germany as an outcome of his fundamental research on rock fracture (Schönert 1988). The device has been most widely used in cement clinker grinding in Europe, but is beginning to find application also in mineral processing. One of the first such applications was in diamond ore processing in Southern Africa and latterly in Australia, where it was shown that the device offered some degree of selective liberation of the diamond from the host rock. However the claimed advantage for most mineral processing operations is the very high reduction ratio achieved, and the favourable specific energy consumption, compared to conventional technologies. Some evidence has also been reported for downstream benefits such as reduced grinding strength and improved leachability due to microcracking (Knecht 1994). Potential applications therefore include preparation of material for fine grinding, replacement of tertiary crushing, rod milling and primary ball milling in primary grinding, and the attainment of enhanced leaching performance. The general principle is illustrated in Figure A12.1.

Figure A12.1: The high pressure grinding rolls (roller mill)

Schönert’s research has shown that the most efficient way to fracture a rock mechanically is to load it between two opposing platens until it fails. One way to do this at a high throughput is to compress a bed of such particles between two contra-rotating driven rolls. In industrial practice these rolls can be very large, up to 2.8 m in diameter. One roll is mounted on fixed bearings, and the other can move linearly against a hydraulic ram or (in small machines) a spring.

High Pressure Grinding Rolls (Model 402) Appendix A


The hydraulics are set to deliver a particular pressure to the bed of particles passing through the machine, compressing it to a density greater than 70% by volume. This pressure, which usually exceeds 50 MPa, controls the size reduction in the machine. The material leaves as a compressed cake (flake), which may have to be disagglomerated prior to further processing. Particular care must be taken to do this correctly when determining a product size distribution. The preferred method is to break-up the cake using a 2 or 3mm screen, take representative samples and then to use an ultrasonic bath to deagglomerate the particles. Deagglomeration can be completed in either water or acetone but preferably the latter. The objective is to produce a repeatable size distribution without additional comminution.

A12.2 Model Structure

Underlying the structure of the size reduction model are three assumptions about the inherent breakage mechanisms that occur in HPGRs. As shown in Figure 12.2.

Pre-crusher If particles are bigger than a certain critical size they will be broken directly by the roll faces as would occur in a conventional rolls crusher. The breakage in this zone can be considered as analogous to a ‘pre-crusher’, the products from which may subsequently pass to a region where a bed under compression has formed. The boundary between the pre-crusher and bed compression regions is defined by a critical gap (xc).

Edge Effect Crusher

Breakage at the edge of the rolls is different to that at the centre and conforms more to that experienced in a conventional rolls crusher. This is the so-called ‘edge effect’ which defines the proportion of relatively coarse particles usually seen in HPGR products. Its existence has been explained by the pressure gradient across the width of the roll and the static confinement of the ore at the edges of the rolls which the cheek-plates provide.

Compressive Bed Crusher

At some point away from the edges of the rolls, and extending upwards from the area of minimum gap (xg) to an area bounded by the critical gap (xc), is a compression zone where breakage conditions are similar to those experienced in a compressed packed bed. From a modelling viewpoint these assumptions can be accommodated in the conceptual structure shown in Figure A12.2. Feed firstly passes to the ‘pre-crusher’. Particles greater in diameter than the critical gap (xc) are crushed below this size in a single particle breakage mode. The products from this breakage



then combine with feed particles which are smaller than xc. A proportion is then diverted to another single particle crusher stage where all particles greater than the minimum gap (xg) are crushed to below this size. The remainder are diverted to a compression stage where all particles greater than xg are crushed below this size but in a compressed bed mode. All products then combine to produce the final HPGR product.

Precrusher: conventional rolls crusher; gap = x

Edge effect crusher: conventional rolls crusher; gap = x

Compressive bed breakage crusher; gap = x

Splitter: determines the fraction affected by the "edge" phenomenon

Product from the HPGR

Feed to the HPGR

c

g

Combiner

g

Figure A12.2: Schematic Structure of the HPGR Model

A12.3 Breakage Processes

HPGR Model The model contains three breakage processes and one splitting

process between the edge and compressed bed zones. For the breakage processes the JKSimMet crusher model is used to describe the size reduction. Four model parameters are required for each breakage process: K1, K2 and K3 and t10. The first three are used to describe the probability that a particle will be broken whilst the t10 is used to describe the product size distribution that results. For a detailed model description, refer to Appendix 6.3.

t10 Definition The t10 is defined as the percentage passing one tenth of the

original particle size in the product after breakage. Other tn parameters can be similarly obtained from a product size distribution, eg. t2 is the percentage passing one half of the original particle size. From breakage tests the t10 and a number of other tn values are determined from the breakage products. These values are stored in tabular form in the model which, given a value of t10, uses spline interpolation to determine the associated tn values and hence reconstructs the entire product size distribution.



Pre-crushing For the pre-crushing process, breakage of particles is assumed to be in single particle mode in which rocks are nipped directly by the faces of the rolls, similar to a conventional rolls crusher. The parameters used to describe crushing in this zone are determined from tests conducted in a conventional (non-HPGR) laboratory rolls crusher and single particle breakage tests, and remain constant in the model fitting and scale-up. The parameter K2 is set as the critical gap, xc, which is expressed by Morrell et al (1997)

{ }5.0

c

gg2c

Dx 4 - ) x+ D() x+ (D 5.0x

=

ρρ

gg (A12.1)

where xg is the working gap, D is roll diameter, ρc is bulk density of feed and ρg is flake density.

αc

cx

gxD

Figure A12.3: HPGR Schematic Showing Compression or Nip Angle

In the edge zones rock breakage is also assumed to take place in single particle mode. The parameters used to describe crushing in this zone are the same as that in the pre-crushing, except K2 which now takes the value of the working gap (xg).

Compressed Bed Breakage

In the compressed bed crushing zone, on the other hand, size reduction is assumed to be similar to that experienced by a bed of particles in a piston press. The parameters used to describe size reduction are determined from tests in a laboratory or pilot scale HPGR machine combined with breakage tests in a piston press. The piston press tests provide information on the relationship between size reduction and energy input in a compressed bed. They also provide a description of the characteristic shape of the product size distribution. If the piston press tests are not available, then the results from the single particle Drop Weight test may be used to determine the Compressed Bed Breakage Function (Section A12.4)

The parameter K2 for the compressed bed crushing is the working gap xg, whilst K1 is set as zero.



The parameters K3 and t10 are fitted to the laboratory scale HPGR test data. These are the only two breakage parameters required to be fitted to laboratory data.

Edge Crushing Bypass

The last sub-process in the model is the split to the edge and compressed bed zones. The edge zones are associated with the drop in pressure that is experienced towards the edge of the rolls. Their extent is assumed to be a function of the working gap. The fraction of feed which is crushed in the edge zones (f) can therefore be expressed as:

f = g xg L (A12.2)

where g is split factor and L is the roll width. Using pilot scale HPGR test results where sizing data of both pure flake and total product were available, the split factor g was found to be approximately constant with a value of 3.4. In physical terms this means that the edge effect zone extended from the edge of the roll a distance equivalent to 1.7 times that of the working gap. By sizing the pure flake and total products from lab/pilot test results f can be determined experimentally. Recent work suggests that the fraction of material being subjected to edge crushing is usually about 10%. Thus, the model may be simplified by manipulating g (split factor) to ensure that 10% of the feed reports to the edge crushing zone. A12.4 Compressed Bed Breakage Function

The product size distributions produced at different energy inputs (or reduction ratios) can be characterised by a family of “t” curves. Measurement and analysis for impact breakage are detailed in Appendices 6.3 and 6.4. This approach can be extended to predict required breakage power and scaled to net crushing power using an efficiency factor., typically - 1.25 (Appendices 6.5 and 6.6).

Single particle impact breakage data.

t10 t75 t50 t25 t4 t2 10.0 6.05 7.94 12.60 46.70 74.60 20.0 8.33 10.90 17.30 62.60 90.30 30.0 10.0 13.10 20.70 74.50 99.20

This approach can be extended to compressive breakage by using a piston press to compress closely size fractions ( ( )24 in a controlled manner. The resulting products are sized and fitted to a spline surface. This surface can be regenerated by the model from a matrix of spline function values. These values are input to the model as



Compressed Bed Breakage Test.

t10 t75 t50 t25 t4 t2 10.0 4.04 6.48 7.51 17.65 35.44 30.0 13.53 19.71 22.24 41.35 58.36 50.0 23.02 31.91 38.00 52.37 69.01

It can be clearly seen that these breakage models are different. The power requirements can also be characterised with particle size dependence if required and also related to motor power (Section A12.6).

A12.5 Throughput Throughput is controlled principally by roll dimensions, speed and profile, and material characteristics such as size hardness and particle-roll friction (and thus nip-angle). The profile and material of the roll surface is important in controlling both wear and machine performance, and various options are offered by the different manufacturers. The rolls throughput can be theoretically expressed as

Q = 3600 U L xgf ρg (A12.3)

where

Q = mass throughput (tph) U = circumferential velocity of the rolls (m/s) L = length of rolls (m) xgf = working gap (m) – from the flake thickness

measurements ρg = flake density (t/m3)

It is realised that A12.3 does not take into account the slip between feed material and the rolls surface, nor does the feed characteristics (particle size and size distribution, moisture, etc). Figure A12.3 shows the deviation between the measured throughput and the calculated one using Equation A12.1 for Primary diamondiferous ore treated through a 100 mm Polysius laboratory scale HPGR. It is obvious that Equation A12.3 over-predicts the HPGR throughput at high rolls speed, which may indicate that slip exists in the HPGR operation at these speeds.



0

2

4

6

8

10

12

0

tph

(mea

sure

d)

2 4 6 8 10 12

0.38 m/s

tph (calculated)

1.50 m/s2.50 m/s3.10 m/s

Figure A12.4: Deviation of the Throughput Calculated from Equation

A12.4 for Diamondiferous Ore Treated through a Laboratory HPGR at Various Speeds

To correct for the slip effect it is considered that for a specific feed the slip is a function of the rolls speed and the dimensionless working gap which is defined as xg /D, where D is the rolls diameter.

Figure A12.4 plots the correction factor c (c = Qm Qc , where Qm is

the measured throughput and Qc is the calculated by Equation A12.3) versus the product of the speed and the dimensionless gap

(U* xg D ) for the Diamondiferous ore using the laboratory HPGR

data. A linear regression on the plot was obtained and Equation A12.3 was accordingly modified as: Q = 3600 U L xg ρg c (A12.4)

where c is the correction factor determined from Figure A12.2.

Recent work by Schonert (2000) suggests that under normal operating conditions, slip does not occur in the compression zone. If normal operating conditions are assured, then the correction factor should be set to 1.0.



0.5

1.0

1.5

2.0

0 0.01

c =

Qm

/ Q

c

0.02 0.03 0.04 0.05 0.06

U * (Xg / D)

Figure A12.5: Throughput Correction Factor for Diamondiferous Ore Treated through a Laboratory Scale HPGR

0

5

10

15

0 5 10 15

Q (p

redi

cted

tph)

Q (measured tph)

LAB (D = 0.25 m)KHD (D = 0.80 m)POLYSIUS (D = 0.71 m)

Figure A12.6: Prediction of Throughput for Two Pilot Scale HPGRs from

Equation A12.4 with Model Parameter c Calibrated Using Laboratory Scale HPGR data

Using Equation A12.4 with c determined from Figure A12.5 the throughput of a laboratory scale HPGR (D = 0.25 m) and two pilot scale HPGRs (KHD, D = 0.8 m; Krupp Polysius, D = 0.71 m) was predicted. A comparison between the calculated and the measured throughputs is given in Figure A12.6. The rolls speeds varied from 0.29 m/s to 3.1 m/s, rolls length from 0.1 m to 0.21 m, rolls diameters from 0.25 m to 0.80 m, and working gaps from 3 mm to 23 mm. The throughput model prediction is seen to be good.



A12.6 Power Draw

Conventional Crusher Power

The impact size reduction model contains an energy balance equation (Andersen and Napier-Munn, 1988) which ensures that the energy for size reduction is compatible with that provided by the motor. The t10 parameter is related to the specific energy used by the machine and will follow a curve described by the equation: t10 = A (1 - e-bEcs) (A12.5) where A and b are parameters and Ecs is the specific energy.

HPGR Crusher Power

In the size reduction model the two parameters K3 and t10 were fitted to the laboratory scale HPGR power data. It was found that the fitted t10s for 24 sets of Diamondiferous ore tests under various rolls speeds and feed size conditions fell on a t10 - Ecs master curve, as shown in Figure A12.7 Equation A12.5 was hence fitted to these data to generate the A, b parameters, which are used for the scale-up as will be demonstrated in the next section. In JKSimMet, the points for t10 = 10, 30 and 50 are placed in the Compressive Breakage Specific Community Energy Matrix.

0

20

40

60

80

100

0 2 4

Fitte

d T1

0 (%

)

6 8 10

A = 100, b = 0.2084

Ecs of motors (kWh/t)

9.5 mm feed, 0.38 m/s speed9.5 mm feed, 1.50 m/s speed9.5 mm feed, 2.50 m/s speed9.5 mm feed, 3.10 m/s speed6.7 mm feed, 0.38 m/s speed6.7 mm feed, 3.10 m/s speedA,b fitted to Lab

Figure A12.7: The Fitted t10 vs Specific Energy Ecs for Diamondiferous Ore Treated through a Laboratory HPGR

A power coefficient kp is required which relates the measured power to that predicted by the model for size reduction. This model uses the specific energy (kWh/t) and associated t10 values from the piston press breakage experiments. From these it calculates the overall specific energy in a piston press. The



difference between this value and that observed from the motor is accommodated by kp, ie. kp is the ratio of the observed to the theoretical piston press specific energy. This coefficient has been found to be reasonably constant over a range of specific energies but increases rapidly beyond a certain limiting value. This is shown in Figure A12.8 for the 24 sets of data.

2.0

2.5

3.0

3.5

4.0

Pow

er c

oeffi

cien

t of H

PGR

0 2 4 6 8 10

Ecs of motors (kWh/t)

Figure A12.8: Relationship between Power Coefficient (kp) and Specific Energy for Diamondiferous Ore Treated Through a Laboratory Machine .

Where kp = Observed power/Piston Power

Power Draw vs Working Gap

The prediction of the working gap xg is also required for simulation. The working gap depends on pressure and power draw.

Working Gap/Specific Energy Relationship

This relationship is developed from the laboratory/pilot scale test. The specific motor energy is plotted against the working gap. The parameters ρc and ρg in Equation A12.2 are functions of feed type, operating conditions (eg working pressure) and the roll surface (eg smooth, chevroned, studded). Therefore, provided the pilot scale or the full scale machines are operating under similar conditions to the laboratory unit, then xg will be proportional to the diameter of the rolls. The principal dependence of the working gap will be on the working pressure, with the gap reducing as the pressure increases. As working pressure is directly related to specific energy, then it will be found that as the specific energy increases the gap will decrease. An example of this is shown in Figure A12.9 for Diamondiferous ore treated through a laboratory machine.



2

3

4

5

6

7

Wor

king

gap

(mm

)

0 2 4 6 8 10

Specific energy of motors (kWh/t)

Figure A12.9: Relationship between Working Gap and Specific Energy for Diamondiferous Ore Treated Through a Laboratory Machine



A12.7 HPGR Model Printout



A12.8 Fitting the HPGR Model SpFact K1H T10H Power Coeff. H

Split Factor (g) (SpFact)

This factor determines the proportion of material which is crushed in bypass mode. This is usually 1.7 times the effective gap width on each side for a default value of 3.4. (Section A12.3) Setting the split factor to zero and running a simulation generates the size distribution expected from pure compression crushing, ie. “pure flake” and may be compared with (or fitted to) an actual sample taken from the centre of the roll discharge.

Pre and Edge Crusher Model Parameters (K1H & T10H)

Using the same feed material as for the pilot/lab HPGR test, laboratory roll crusher is operated at close to the nipping gap and the working gap of the HPGR. The Whiten/Awachie/Anderson crusher model (Appendix 6) is used to derive K1 and t10 where K2 is the crusher gap and K3 is set at 2.3. The ratio K1/K2 is the input to the pre crush and edge effect model along with the fitted t10 values. It is unlikely that power can be measured with sufficient accuracy in this test to justify using other than the default power factor of 1.25.

Throughput Relationship

As noted in Section 12.5, throughput is strongly controlled by geometry at low throughputs and by slippage at high throughputs. Pilot or laboratory scale tests can be used to derive the slope and intercept for the slip correction factor Cp. The model defaults are for smooth rolls. It is highly likely that different roll surfaces will generate different correction factors.

Compressed Bed Breakage (t10 HPGR)

Breakage within the compressed bed is assumed to be uniform and able to be described by a single parameter t10 . The t10 parameter will increase as the reduction ratio increases. In compression, all particles are assumed to be able to be selected for breakage ie. K1 = 0 and every particle larger than the working gap will always be broken, ie. K2=cacluated Working Gap.

Power Model Fitting

The HPGR model takes a somewhat circuitous approach to power modelling. As noted in Section 12.6, the combination of piston press tests and laboratory/pilot scale HPGR produces a relationship between the compressive bed t10 and net motor power (Figure A12.7).



Developing this relationship requires some modelling using the Andersen/Whiten model (A6). The objective is to find a t10 for each data set with K2 set to the working gap and K3 a constant value over all sets. To do this, enter all sets of data into one test, master slave K3, set K2 to working gap and fit each of the t10 values. This provides a set of t10 values which can be plotted against the motor power per tonne (Ecs) corrected for no load and the power drawn by pre-crush and edge crushing (as in Figure A12.7). Equation A12.5 is fitted to this data with A=100 and Ecs values calculated at t10 =10, 30 and 50 for input into the Compressed Bed Breakage Matrix. This relationship allows compressive power draw to be calculated (as in Section 6.6) for any set of K1, K2, K3 and t10 values. Figure A12.7 shows the power coefficient (observed motor power divided by calculated “piston” power) for a range of energy inputs expressed as power per tonne. If this model was ideal, the coefficient would be constant. Between zero and 5 kWh/t it is approximately constant at, say, 2.5 and increases rapidly at high powers (ie. the crusher becomes less energy efficient). More energy is converted into heat and does not result in further comminution.

A12.9 Scaling the HPGR Model To predict the performance of pilot scale and full scale HPGRs the model is firstly calibrated using the results from the laboratory, conventional rolls, single particle breakage and piston bed breakage test. Figure A12.10 illustrates the scale-up procedures. Also shown in Figure A12.10 are the values of the parameters obtained from the calibration, which have been used to predict the two pilot scale units and one full size machines treating a Diamondiferous ore (Morrell, Shi and Tondo, 1997).



Figure A12.10: Schematic of the Model Algorithm and Scale-up Procedure The full scale-up procedure is implemented in JKSimMet. When running the simulations of pilot scale or of full scale machines, the parameter K3 for the compressed bed crushing zone is automatically adjusted until the model predicts the same power draw as was originally chosen for the simulation. As a result, the calculated power draw is identical to that observed, and the product size distribution is predicted based on this power consumption. In the simulation the maximum throughput of a scale-up HPGR is calculated using the throughput model (Equation A12.4) with the correction factor c determined in the laboratory unit with similar rolls surface on the same type of ore. The required power is then calculated from the maximum throughput and the specific energy

Input dataRolls dimension: diameter, length Select rolls speed, required specific energy Ecs Feed size distribution Bulk density of feed, flake density Working gap: chose the lab working gap by Ecs from Figure 12.9, multiplying the gap by the ratio of full scale to lab rolls diameters Nipping gap calculated from Equation 12.1 Throughput calculated from Equation 12.4 Power draw = Ecs required x throughput

Single particle breakage test (using a drop weight device)

Pre-crusher (parameters from the conventional rolls

test) K1p=0.64 K2p K2p = nipping gap K3p = 1.0 K3p = 1.0 t10p = 12.04

Mass Splitter Fraction split to the edge effect crusher is calculated by Equation 12.2 in which γ = 3.4 as determined from the KHD tests

Edge Effect Crusher (parameters from the conventional rolls test) K1e = 0.64 K2e K2e = working gap K3e = 1.0 t10e = 12.04

Bed breakage test(using a piston press device)

Power coefficient determined from Figure 12.8

HPGR k1h = 0 K2h = working gap t10h calculated from Equation 12.5 in which A = 100, b = 0.2084 determined from lab tests

Calculated power = observed power ? Adjust K3

Combined Product

N

Y



selected. The model is iterated until the breakage power, which is the sum of the power used in the three sub-processes of pre-crushing, compressed bed crushing and edge effect crushing, matches the required power. The overall product size is then predicted based on the breakage power. A12.10 Known Restrictions

Roll Surface Tests using a Krupp Polysius pilot roll (rolls diameter 0.71 m), with 4 mm profiles (on the rolls) resulted in a considerably larger working gap than was observed for the KHD pilot tests using smooth rolls. Therefore, laboratory tests must be conducted with a rolls surface similar to that proposed on the full scale machine.

Limited Data Base

As only limited production scale data were available, the models need to be further tested and validated against more real data in the future, and their capabilities explored in case studies.

Power Coefficient (kp)

Ideally, this coefficient should be constant. A better understanding and (possibly) a better representation need to be developed.

A12.11 Nomenclature

αc - nip angle (degree) γ - split factor ρc - bulk density of feed (t/m3) ρg - flake density (t/m3) c - correction factor for rolls throughput D - rolls diameter (m) Ecs - specific energy (kWh/t) f - fraction of feed which is crushed in the edge zones g - split factor K1,K2,K3 - size reduction model parameters kp - power coefficient L - rolls length (m) Qm - measured mass throughput (tph) Qc - calculated mass throughput without correction tph) t10 - size distribution parameter U - rolls circumferential speed (m/s) xc - critical gap (m) xgf - working gap (m).



A12.12 Acknowledgments

This model was developed with the financial support of the sponsors of the AMIRA P428 project (Application of High Pressure Grinding Rolls in Mineral processing) including the Centre for Mining Technology and Equipment (CMTE). Considerable assistance was also provided by the staff at KHD and Krupp Polysius, as well as the staff and students at the JKMRC and CSIRO, Division of Mineral products.

A12.13 References

Andersen J S and. Napier-Munn T J, 1988. Power prediction for cone crushers. Proc. 3rd Mill Ops Conf, Cobar, Aus. Inst. Min. Met. Andersen J S, 1988. Development of a cone crusher model. M. Eng. Sc. Thesis, University of Queensland (JKMRC). Fuerstenau D W, Shukla A and. Kapur P C. 1991. Energy consumption and product size distributions in choke-fed, high compression roll mills. Int. J. Miner. Process., 32: 59-79. Kapur P C, 1972. Self - preserving size spectra of comminuted particles. Chem. Engng. Science, 27: 425-431. Knecht, J, 1994. High pressure grinding rolls, a tool to optimise treatment of refractory and oxide gold ores. Fifth Mill Operators Conf. Roxby Downs, Oct, 51-59 (AusIMM, Melbourne) Morrell, S, Shi F & Tondo, L. 1997. Modelling and scale-up of High Pressure grinding rolls. IMPC Aachen. Morrell S, Lim, W, Shi F and Tondo L. 1997. Modelling of the HPGR crusher. SME Annual Conference, Denver, Colorado. Comminution Practices Symposium, Ed Kawatra, 117-126. SchÖnert K. 1988. A first survey of grinding with high compression roller mills. Int J of Min Proc, 22, 401-412. SchÖnert K.and Sander, U., 2000. Pressure and shear on the roller surfaces of high pressure roller mills, Proc. XXI IMPC, Rome, Italy, Sect A4, 97 - 103. Tondo L, 1996. Modelling of HPGR crushers. M. Eng Science Thesis, University of Queensland (unpublished). Whiten W J, 1972. The simulation of crushing plants with models developed using multiple spline regression. J. South Afr. Inst. Min. Metall. 72: 257-264.



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Appendix A Simple Degradation (Model 480)


A13 Simple Degradation (Model 480)

A13.1 Introduction

The concept of a degradation model has its origins in iron ore andcoal operations where particles may undergo significant sizereduction during mechanical handling such as dropping on to astock pile from a conveyor or perhaps at a conveyor transferpoint.

A13.2 Model Structure

The model structure is a simple representation of a single dropwhich results in the particles being broken to a specified t10 value.The breakage distribution parameter, t10, characterises the sizedistribution of the broken product. More details of this parameterand the concepts behind it are given in Appendix 6.4.

The appearance function data which are discussed in Appendix6.4 are required for the degradation model and are derived fromthe JKMRC Drop Weight test. This test is described in Appendix15.

BreakageDistributionParameter (t10)

The breakage distribution parameter, t10, is entered as a modelparameter. It must be calculated by the user and is generallybased on the Energy – Size Reduction relationship for theparticular ore derived from the JKMRC Drop Weight test.

SpecificComminutionEnergy

The Specific Comminution Energy in a drop is a function of theheight of the drop and can be calculated using the followingequation:

Ecs = 0.00272 * h (A13.1)

Where:Ecs = specific comminution energy (kWh/t)h = height of the drop (m)

Simple Degradation (Model 480) Appendix A


Energy –Size ReductionRelationship

The relationship between Specific Comminution Energy and sizereduction represented by t10 is also one of the results of theJKMRC Drop Weight test. The relationship is of the form:

t10 = A * ( 1 – exp( - b * Ecs )) (A13.2)

Where:t10 = Breakage Distribution ParameterEcs = specific comminution energy (kWh/t)A & b are ore characteristic parameters

Conditioning In most cases, the damage inflicted by a second drop is less thanthat inflicted by the first drop. This effect is known asconditioning. Of course, the height of each drop is important aswell as the number of drops.

Effectively, the particles become a little more resistant to impactafter each successive drop. The amount of this effective increasein resistance depends on the ore type and on the drop heights.

This effect can be included in the simulation by an appropriatereduction in the b value used in equation A13.2. For an ore whichis only a little affected by conditioning, a reduction of b to 75% ofits starting value is typical. For an ore which is significantlyaffected by conditioning b is typically reduced to 40% of itsstarting value.

Appendix A Simple Degradation (Model 480)


Example The A and b values from the JKMRC Drop Weight test for theexample ore are 50 and 0.5 respectively.

For a drop height of 20 m, from equation A13.1:

Ecs = 0.00272 * h= 0.00272 * 20= 0.054 kWh/t

and from equation A13.2

t10 = A * ( 1 – exp( - b * Ecs ))= 50 * ( 1 – exp( - 0.5* 0.054))= 1.33

this value of t10 is then entered into the model.

For a second 20 m drop of an ore which is strongly affected byconditioning, b is reduced to 0.2 (40% of 0.5) and

from equation A13.2

t10 = A * ( 1 – exp( - b * Ecs ))= 50 * ( 1 – exp( - 0.2* 0.054))= 0.54

this value of t10 is then entered into the model for the second drop.

Use for theVertical ShaftImpactor

The degradation model can be used to represent a lightly loadedVertical Shaft Impactor. In this case, the energy of an impact iscalculated from the velocity of the particle imparted by the rotor.This energy must be converted to units of kWh/t before equationA13.2 can be applied.

For example, for a VSI with a rotor diameter of 0.6 m spinning at2000 rpm, the energy imparted to a particle leaving the rotor at itsperipheral speed is:

Ecs = 0.5 * m * v2 / ( 3600 * m )= 0.5 * v2/ 3600= 0.5 * ( π * 0.6 * 2000 / 60 )2/ 3600= 0.55 kWh/t

Where:m = Particle mass (which cancels out)Ecs = specific comminution energy (kWh/t)v = peripheral velocity of rotor (m/s)3600 is the conversion factor for kWh/t

The Ecs value is substituted into equation A13.2 to calculate t10for use in the model.

Simple Degradation (Model 480) Appendix A


A13.3 Degradation Model Printout

A13.4 Fitting the Degradation Model

This is a very simple model to fit, the only fittable parameter beingt10.

A typical range of starting estimates for degradation by drop is 0.2 to 0.8 depending on amenability to degradation and drop height.

A typical range of starting estimates for the VSI is 5 to 20depending on rotor diameter and speed and ore type.


It is recommended that the ore specific appearance function ismeasured by a Drop Weight test rather than using the defaultvalues. Although the variation of the crusher appearance functiondata in the JKTech data base (of ores subjected to Drop Weighttesting) is not particularly large, ore specific values will providebetter results.

If several drops actually occur, it may be better to simulate these asseparate drops than as a single drop of the total accumulated dropheight, particularly if conditioning is likely.

It should also be noted that ores which are particularly susceptibleto degradation are also likely to be degraded during the process ofscreening to determine the size distrbution, thus making the sizedistributions somewhat doubtful.

Appendix A Splitters (Models 810, 811, 812, 870)


A14 Splitters (Models 810, 811, 812, 870)

A14.1 Introduction

These models provide splitters of varying complexity, from asimple mass split to two (810) or three products (870),independent mass splits of solids and water (811) and a splitgenerating a specific volume flow rate to one product (812).

A14.2 Model Details

A14.2.1 Simple Mass Split – Two Products (810)

The feed to this model is split into two streams with sizedistributions and pulp densities identical to the feed. Thecontrolling parameter is the Fraction Split to Top Product. Thetop product is the upper product on the equipment icon and ismarked with a T. The parameter range is 0.0 – 1.0.

A14.2.2 Simple Mass Split – Three Products(870)

The feed to this model is split into three streams with sizedistributions and pulp densities identical to the feed. Thecontrolling parameters are the Fraction Split to Top Product andthe Fraction Split to Bottom Product. The top product is theupper product on the equipment icon and is marked with a T. Theparameter range is 0.0 – 1.0.

Splitters (Models 810, 811, 812, 870) Appendix A


A14.2.3 Simple Mass Split – Two Products –Water and Solids (811)

The feed to this model is split into two streams with sizedistributions identical to the feed. The controlling parameters arethe Fraction Split to Top Product (Water) and Fraction Split toTop Product (Solids). The top product is the upper product on theequipment icon and is marked with a T. The parameter range is0.0 – 1.0.

A14.2.4 Fixed Volume Split – Two Products(812)

The feed to this model is split into two streams with sizedistributions and pulp densities identical to the feed. Thecontrolling parameter is the Volumetric Flow Rate to Top Product(m3/h). The top product is the upper product on the equipmenticon and is marked with a T. Should the volumetric flow rate ofthe feed stream be less than the required flow to the top product,the entire feed stream is directed to the top product.

Appendix B Error Messages

Version 5.1 February 2003 Appendix B Page B-1

APPENDIX B

Error Messages

JKSimMet Error Messages Error Messages

Page B-2 Appendix B.1 Version 5.1 February 2003

B. ERROR MESSAGES

These messages occur during operation of JKSimMet. The display warns that an error has occurred and provides the error number. The descriptions provided here give more information about the possible cause of the error message.

ERROR 58 Not enough size distribution data in the feed to an equipment item for spline interpolation to work. Check combiner ports with Exp TPH Solids values > 0.0 with limited or no Exp Size Distribution data.

One of the combiner ports of one of the equipment items on the select list has Exp TPH Solids greater than zero but limited or no size distribution data. Thus JKSimMet is not able to perform the required Spline Interpolation. Either add some size distribution information or zero the Exp TPH Solids.

ERROR 110 Hydrocyclone - SPOC predicts roping.

The results of the simulation violate the SPOC roping constraint indicating that under the simulated conditions, the hydrocyclone is likely to be roping. See Section A2.5 for more details. The simulation results may be unreliable.

ERROR 111 Plitt et al constraint predicts roping.

The results of the simulation violate the Plitt et al roping constraint indicating that under the simulated conditions, the hydrocyclone is likely to be roping. See Section A2.5 for more details. The simulation results may be unreliable.

ERROR 120 No data in a stream or streams. Please correct.

One of the streams you have selected in the Balance List contains no data.

ERROR 121 Two or more streams have different sieve series. Please correct.

For Mass Balancing with GSIM format data, all selected streams must have the same screen series.

ERROR 122 Sum of % component does not equal control value. Please correct.

If you have specified a component sum (on the active COMPONENT LIST) your assays must total this sum or less. A component sum of zero turns off this constraint. Normally a REMAINDER TERM is added to achieve the sum in the experimental data. To force a constraint, omit one of your categories and it will be the remainder term.

Error Messages JKSimMet Error Messages

Version 5.1 February 2003 Appendix B.2 Page B-3

ERROR 123 No COMPONENT LIST is currently selected. Please select or enter one.

You must have a current Component List before attempting to mass balance data. Either select one you have already created or create one.

ERROR 124 No BALANCE LIST is currently selected. Please select or enter one.

You must have a current Balance List before attempting to mass balance data. Either select one you have already created or create one.

ERROR 125 Modifications to flowsheet detected. Please check your current data.

Modifications have been made to the flowsheet since the last mass balance. You should check that your selected streams are still correct.

ERROR 126 No stream input to unit. Please check current SELECT list.

One of the units selected for inclusion in the balance has no input stream. You should check that input streams are selected for all of the selected units.

ERROR 127 No stream output from unit. Please check current SELECT list.

One of the units selected for inclusion in the balance has no output stream. You should check that output streams are selected for all of the selected units.

ERROR 128 Stream is not connected to unit. Please check current SELECT list.

One of the selected streams is not connected to any selected unit. You should check that all selected streams are connected to selected units.

ERROR 129 No unit/node is currently selected. Please check current SELECT list.

There are no units selected on the SELECT list. At least one unit and its associated streams must be selected to run a mass balance.

ERROR 130 Morrison solution error. See Morrison solution error Section 6.10.

The simple solution has not worked correctly. Check your data carefully and then read section 6.10. If you can find no data problems, try increasing the number of steps. Note that only one flow rate should be tightly constrained - not all of them.

ERROR 131 Morrison solution convergence error. Please increase step number



See also Error 130.

ERROR 132 Consistent assays convergence error. Please increase step number.

Check the SELECT screen to see that the step count has reached its nominated maximum. If so you may increase that count by a few steps. Caution: such long searches indicate poorly defined flows or some variation of the middlings problem. Refer to section 6.10.

ERROR 133 Adjusting sum convergence error. Please increase step number.

See also Error 132.

ERROR 134 Main loop convergence error. Please increase step number.

See also Error 132.

ERROR 135 Negative balance flow rates.

See also Error 132.

ERROR 136 Balance size distributions cal. err. Increase adj. sum step number.

See also Error 132.

ERRORS 137-139 are reserved for later versions.

ERROR 140 No Model-Fit data are selected. Fitting requires data.

No data have been selected on which to do the Model-Fit. Select some and try again.

ERROR 141 No Model-Fit parameters are selected. Fitting requires parameters.

No parameters have been selected on which to do the Model-Fit. Select some and try again.

WARNING 142 Model-Fit data include a stream with no experimental data.

One or more of the streams selected for the Model-Fit has no experimental data entered for it. It is ignored. Enter the necessary data before attempting the Model-Fit again or remove the stream from the data list.

WARNING 143 Model-Fit data do not include this stream. Normal editing only.

The Stream selected is not included for Model-Fit. Therefore, the extra information cannot be edited.

ERROR 144 Model-Fit data do not contain any streams. Fitting requires data.

No streams are selected for Model-Fit. The list of streams, whose data must be fitted, is empty.

WARNING 145 Poor convergence of fit. Check SDs / data.



The Model-Fit has not been able to make effective use of the data given. Try different SDs or reject some of your data.

Check your circuit and unit details also. Rerun the survey.

ERROR 146 No streams in the circuit have data. Please add some.

None of the Streams selected for the Model-Fit have data entered for them. At least one stream must have data. See ERROR 51.

ERROR 147 No parameters are selected for fitting. Please select some.

Model fitting works by adjusting parameters of models until simulated results match experimental data. You must specify at least one parameter to adjust.

ERROR 148 There are too many streams on the circuit. Please simplify!

Please simplify the circuit or break it into two circuits, The Model-Fit function has strict limits on the number of units and streams allowed. Please reduce the number you have selected, then try again. Refer to the manual for the current limits (there is a limit of 10 units, 20 streams).

ERROR 149 There are too many units on the circuit for fitting. Please simplify.

The Model-Fit function has strict limits on the number of units and streams allowed. Please reduce the number you have selected, then try again. Refer to the manual for the current limits (there is a limit of 10 units, 20 streams).

FAULT 150 An illegal parameter is selected. It won't be fitted.

This error should never occur. Please make a note of the error number and what you were doing, and contact JKTech.

ERROR 151 Constant residual error during fitting. Check SDs/parameters/scales.

See ERROR 154. The model fit gauges its success by a diminishing error between experimental and simulated data. The error was not changing with different parameter values. SDs, scales or the initial parameter estimates may be responsible.

ERROR 152 Fitting is not getting anywhere. Try again with better guesses.

The Model-Fit has not been able to make effective use of the data given. Please enter new parameter guesses and try again.

FAULT 153 Model fit array sizes were in error.

This error should never occur. Make a note of the error number and what you were doing, and contact JKTech.

ERROR 154 No errors were calculated. Only non zero SDs contribute an error.



The errors between experimental and simulated data are combined with each values SD. A zero SD implies the value should be ignored. If all SDs are zero, fitting has no data.

WARNING 155 No SDs have been entered on a stream. Unit SDs are assumed.

See ERROR 154.

ERROR 156 You have duplicate data entries. Please remove duplicate.

If you want one stream to have a greater significance reduce its SDs.

ERROR 157 You have duplicate parameter entries. Please remove duplicate.

Each parameter entry is independently adjusted. This becomes nonsense if one parameter is repeated.

ERROR 158 Only two parameters may be fitted per stream. Please correct.

There are only two independent parameters for a stream. See ERROR 157.

ERROR 159 Only one water parameter may be fitted per stream. Please correct.

Once stream's water parameters are independent. See ERROR 157.

All water parameters control the water content of a stream. There is only one way this may be selected. See Error 157.

WARNING 160 A new stream was selected.

Model-fitting is complex. It thus tries to select streams automatically when it starts. Occasionally this changes the selections you have made. The warning is then issued.

WARNING 161 A new unit feed stream was selected.

Refer to WARNING 160 above.

WARNING 162 New Model Fit data were selected.


WARNING 163 New Model Fit parameters were selected.


ERROR 164 That unit doesn't have experimental data suitable for model-fitting.

The unit selected has no parameters and can not be fitted.

ERROR 165 No units in the circuit have data. Please add some.

None of the units in the circuit have data. You must supply some.

WARNING 166 A new unit was selected.



The currently selected unit does not appear in the Parameter List

WARNING 167 The coarsest particles in the feed to the AG/SAG mill are in a size range either finer than 200 mm or coarser than 300 mm. This affects the calculation of energy values and the results of simulations using this feed are likely to be unreliable. Please modify your feed size distribution.

The energy calculations in the Variable Rates SAG model were based on data from mills with the top size of the feed in the region 200 – 300 mm. Simulating with feeds outside this region using the default rates will be unreliable.



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Appendix C JK Breakage Testing

APPENDIX C

JK BREAKAGE TESTING

Version 5.1 February 2003 Appendix B Page C-1

JK Breakage Testing Appendix C

C JK Breakage Testing

C.1 Drop Weight Test Procedure

This section provides a brief description of the drop weight test

procedure.

To characterise ore breakage at different energy levels, theJKTech method uses two complementary techniques:

1. To characterise breakage at moderate to high energy levels (i.e. impact breakage), a drop weight device is used.

2. To characterise breakage at low energy inputs (i.e. theabrasion component of breakage), a tumbling test is used.

C.2 Impact Breakage Testing

The JK drop weight device comprises a steel drop-weight which is raised by a winch to a known height. A pneumatic switchreleases the drop weight which falls under gravity and impactsthe rock particle which is placed on a steel anvil. The device isenclosed in perspex and incorporates a variety of features to ensure operator safety. By varying the height from which thedrop weight is released and the mass of the drop weight, a verywide range of energy power inputs can be generated. Aschematic drawing of the device is given in Figure C.1.

Perspexenclosure

5kg leadweights

Guide rail

Rock

Steel anvil

Adjustableheight (energy)

Large concrete base

Figure C.1: Schematic of the Drop Weight Device

Page C-2 Appendix C Version 5.1 February 2003

Appendix C JK Breakage Testing

After release of the drop weight, it descends under the influenceof gravity and impacts the target particle. The particle is brokenby the impact. The drop-weight is brought to rest at a distance above the anvil approximately equal to the largest productparticle. The difference in distance between the initial startingpoint and the final resting place of the drop-weight is used to calculate the energy that is expended in breaking the particle. The following equation is used: Ei = Mg(h - xM) (C.1) Where: Ei = energy used for breakage M = drop-weight mass g = gravitational constant h = initial height of the drop-weight above the anvil xM = final height of the drop-weight above the anvil.

Providing the drop-weight does not rebound after impact, the application of equation (C.1) is valid. Where rebound occurs anadditional term is required to account for the energy re-transmitted to the drop-weight. Rebound has been seen to occur only at elevated input energies. This energy will be measuredduring the testwork programme. It is likely, however, that itsmagnitude will be relatively small and can be ignored with only aminimal loss in accuracy. The assumption is made that all the energy provided is utilised inthe breakage of the particle. Thus Ecs = Eis = Ei / m (C.2) where: Eis = specific input energy Ecs = specific comminution energy m = mean particle mass To test an ore type, the original 100 kg sample is sized intoselected fourth-root-of-two size fractions. Ten to thirty particles are required in each size fraction for each energy level, dependingon particle mass. Typically fifteen size/energy combinations areselected. The input energy levels for a particular test aredesigned to suit ore hardness.

Version 5.1 February 2003 Appendix C Page C-3

JK Breakage Testing Appendix C

The breakage products of all particles for each size/energycombination are collected and sized. The size distributionproduced is normalised with respect to original particle size. For a wide range of energy input, particle sizes and ore types, therelative size distributions remain similar in shape and can bedescribed by a single point on the distribution. The JKTechconvention is to use the percentage passing one-tenth of the original particle size. This is referred to as the “t10”. In the manner described above, a set of t10 and Ecs values are produced for the 15 energy/size combinations.

C.3 Abrasion Breakage Testing

It is possible to characterise low energy (abrasion) breakage with a miniature drop weight and repeated impacts. However, Leung (1987) demonstrated that a tumbling test of selected single size fractions could produce a similar result with less experimental effort.

The standard abrasion test tumbles 3 kg of -55 +38 mm particles for 10 minutes at 70% critical speed in a 305 mm by 305 mm lab mill fitted with four 6 mm lifter bars. The resulting product is then sized and the t10 value for the product is determined.

The mean particle size of the original size fraction 55 x 38 mm is 45.7 mm. The t10 size is:

1/10 x 45.7 = 4.57 mm.

Page C-4 Appendix C Version 5.1 February 2003

Documents

Manual JKSimMet V5.1