Process Simulations Using Computer Technology

Steve Frankland Dargo Associates Ltd

What is a Process Simulations?

•  Mathematical prediction of the outcome of a physical or chemical process

•  Linking of several unit processes together

•  Presentation of the results in an understandable form

What can be simulated?

•  Any unit process that can be described mathematically – Separations – Phase Changes

Subjects for today

•  Simulations/Models – Density – Size – Others – Crushers

•  Flowsheeting – Link the processes together – Control of calculations

Density Separations

•  Tromp Curves •  Float/sink data

Tromp Curve

0

20

40

60

80

100

1.20 1.30 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.10 2.20

Density

Rec

ove

ry t

o S

inks

%

How do you use it?

Lower Density

Upper Density

Average Mass % Partition Coeff

Floats Mass

Sinks Mass

1.25 1.55 1.40 59.7 98.5 58.8 0.91.55 1.65 1.60 2.2 50.0 1.1 1.11.65 1.75 1.70 2.0 5.0 0.1 1.91.75 1.85 1.80 0.8 2.0 0.0 0.81.85 1.95 1.90 0.8 1.0 0.0 0.81.95 2.5 2.23 0.4 0.0 0.0 0.4

How do you generate the Tromp Curve

•  Normalised Curve –  Independent of Epm and Density

EpmPCDensityPartitionPC normalised *_ −=

•  Equation

⎟⎟⎠

⎞⎜⎜⎝

⎛+

−=−

Epme

PC DensityDensityPartition ))_(*098.1(

1

11

Assumptions

•  There is one assumption – That the quality for each density

fraction is the same for floats and sinks – True enough if the density fractions are

closely spaced

UK Applications

•  Largest UK mining activity is quarrying

•  Most quarries classify rock •  Large number have breakers/

crushers •  Going to look more deeply at these

activities

Sizing

•  Tromp Curve –  Basically the same separation as density but

using size. •  Equation

( )⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−+⎟⎠

⎞⎜⎝

⎛

−−

2_*

1*1α

α

α eSeparationSizeSizee

eRf

Rf = Amount of fines bypassing to O/Size α = efficiency factor

Crushing

•  Crushing is a complex process •  Depends on difficult to measure

parameters – Type of Comminution machine – Settings of machine – Throughput – Hardness of material

Types of Crusher Model

•  Use known data of crusher product size distribution –  This are often provided by manufacturers –  Difficult to match for all rock types –  Not always accurate

•  Whiten method –  Based on fundamental understanding of

crushing –  Can be applied to any crusher and rock

combination

Schematic of a Breaker

Classification

Breakage

As described by Whiten and Anderson

Functions •  Classification

–  All particles less than a certain size (K1) pass directly to the undersize

–  All particles above a certain size (K2) report to breakage

–  All particles between K1 and K2 are partitioned (like sizing and density separations) between being broken and passing directly through

•  Breakage –  Broken particles are classified again

Maths again

If x < K1 then C(x) = 0.0

If x > K2 then C(x) = 1.0

If K1 < x < K2 then 3

1220.1)(

K

KKxKxC ⎥⎦

⎤⎢⎣

⎡−−

−=

Where x = size of particle C(x) = proportion reporting to breakage K1, K2 are as before K3 describes the shape of the classification function

THE CLASSIFICATION FUNCTION

Determining K1, K2 and K3

•  K1 = A0 + A2*TPH + A3*F80 •  K2 = B0 ± B1*CSS + B3*F80 – B4*LHR

+B5*ET •  K3 = 2.3

Where CSS = Closed side Setting (mm) TPH = Feed Rate F80 = 80% passing size LHR = Liner age (hr) ET = Eccentric Throw (mm)

Meaning?

•  K1 is very dependent on closed-side setting and throughput and a little on feed size

•  K2 is very dependent on closed-side setting and throughput and a little on liner age and the crusher movement

•  K3 is a constant

Use in practice

•  For most applications, there are estimates of the constants Ax and Bx.

•  For more accurate simulations, they can be determined by regression analysis.

The Breakage Function •  For unusual rocks a detailed

examination may be required but for most rocks:

Where T10 = % passing 1/10th of original size 5-10 for primary crushing 10-15 for secondary crushing and 15-20 for tertiary crushing CSS = closed side setting TPH = dry throughput rate F80 = 80% passing size (mm)

80FDTPHDCSSDDT 321010 ×−×+×−=

Other simulations

•  Froth Flotation –  For coal use laboratory tests –  Where good models exist they can be

incorporated •  Magnetic Separations

–  Simple mass balance based on recovery and RD of overdense

•  Thickeners –  Simple mass balance based on solids in O/flow

and underflow.

Linking the processes together

•  Going to use LIMN as an example – Generalised flowsheeting package – Based on Microsoft’s Excel®

spreadsheet – Models are placed in Worksheets – Drawing on screen

•  Other packages – JKSimMet – USBM

Dense Medium Bath

Case Study

•  Consider a stone quarry •  Flow diagram shown on next slide •  Each crusher has a specific power

consumption •  Plus 100mm has no value •  100mm x 40mm = £5.00/t •  Minus 40mm = £3.00/t •  What is the optimum setting to give

maximum revenue

Comminution Circuit

Scenarios

Proc ess  Simula tions  Using  C omputer  Tec hnolog y

Steve  Frankla ndDa rg o  Assoc ia tes  Ltd

Optimisation Net Revenue

725.0

730.0

735.0

740.0

745.0

750.0

70.00 75.00 80.00

Secondary Crusher CSS

£

250.00150.00100.0050.00

Prim Scr Ap

Optimisation 2 Net Revenue

738.0739.0740.0741.0742.0743.0744.0745.0746.0

70.00 75.00 80.00

Secondary Crusher CSS

£

95.00100.00105.00110.00

Sec Scr Ap

Product Check Variables Results

Cell Address 77.50 110.00 125.415 870.0 744.5 20.7 5.15

Cell Description Sec CSS Sec Scr Cost Revenue Diff Prod <40 >10070.00 95.00 136.002 874.8 738.8 23.215 3.56872.50 95.00 137.150 881.6 744.5 21.439 3.56875.00 95.00 137.146 881.6 744.4 21.45 3.56877.50 95.00 137.141 881.5 744.4 21.46 3.56870.00 100.00 131.740 871.5 739.7 22.827 4.09772.50 100.00 132.698 877.8 745.1 21.181 4.09775.00 100.00 132.694 877.7 745.0 21.191 4.09777.50 100.00 132.690 877.7 745.0 21.202 4.09770.00 105.00 128.014 868.0 740.0 22.463 4.62772.50 105.00 128.825 873.9 745.1 20.928 4.62775.00 105.00 128.822 873.9 745.0 20.938 4.62777.50 105.00 128.818 873.8 745.0 20.948 4.62770.00 110.00 124.726 864.6 739.8 22.121 5.15172.50 110.00 125.422 870.0 744.6 20.682 5.15175.00 110.00 125.418 870.0 744.6 20.692 5.15177.50 110.00 125.415 870.0 744.5 20.701 5.151

Control

Summary Features

•  Ease of use •  Calculation of many different

configurations •  Correctly balanced flowsheets •  Optimisation •  Training aid