T H E U N I V E R S I T Y O F T U L S A

THE GRADUATE SCHOOL

MECHANISTIC MODELING OF SOLID-LIQUID SEPARATION

IN SMALL DIAMETER HYDROCYCLONES

by Jose G. Severino

A thesis submitted in partial fulfillment of

the requirements for the degree of Master of Science

in the Discipline of Petroleum Engineering

The Graduate School

The University of Tulsa

2007

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ABSTRACT

Jose G. Severino (Master of Science in Petroleum Engineering) Mechanistic Modeling of Solid-Liquid Separation in Small Diameter Hydrocyclones Directed by Prof. Ovadia Shoham and Prof. Ram S. Mohan 192 pp. Chapter 7: Summary, Conclusions, Recommendations

(247 words)

Efficient and reliable solids removal systems are critical for different industrial

applications. Hydrocyclones have been used for more than a century for separating solid

particles, as well as, denser liquid droplets from continuum liquid and gas media. The

main objective of this work is the development of a mechanistic model to predict the

solids separation efficiency of small diameter solid-liquid hydrocyclones (SLHC) and

validate it against available oilfield data.

The developed model is a modification of the Caldentey et al. (2002) model for

liquid-liquid hydrocyclones (LLHC). The SLHC model enables the prediction of the

continuous-phase swirl intensity and velocity profile which are used to determine particle

trajectories, and hence the grade separation efficiency curves. An existing hydrocyclone

design code has also been upgraded to incorporate the developed SLHC model.

The experimental data used to validate the model were acquired by Culwell et al.

(1994). A total of 155 experiments are available under a wide range of flow conditions

and equipment configurations. Some of the inlet conditions include: liquid velocities

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ranging from 14 to 24 m/s, pressures ranging from 100 to 130 psig, solids concentrations

ranging from 40 to 370 mg/L with an average density of 2.0 gr/cc. Particle size

distributions range from 2 to 60 µm with Sauter mean diameter (d32) ranging from 12 to

32 µm.

Very good agreement is observed between model predictions and experimental

data. Agreement of the proposed model with the global and average grade separation

efficiency data is 94.7% and 88.2% respectively.

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ACKNOWLEDGEMENTS

First and foremost thanks to God for this wonderful opportunity. Special thanks

are given to co-advisors Dr. Ovadia Shoham, Dr. Ram Mohan, and Dr. Luis Gomez for

constant guidance and assistance throughout this study. Thanks are also due to Dr. Leslie

Thompson and to Dr. Gene Kouba (Chevron) for their valuable input and for serving on

the thesis committee.

The financial support from the Tulsa University Separation Technology Projects

(TUSTP) and its member companies, the Industry/University Cooperative Research

Center (I/UCRC) on Multiphase Transport Phenomena (MTP), and the Oklahoma Center

for the Advancement of Science and Technology (OCAST) made possible this research.

The author is also indebted to Chevron for providing the experimental data used in this

study, especially to Ms. Kristin Machen for her guidance on the experimental program.

Thanks also to Kevin Juniel from NATCO for providing the specifications of the tested

equipment.

Appreciation is extended to the Faculty of the University of Tulsa, especially to

Dr. Shoubo Wang for many productive discussions during the Compact Separators

course. Special thanks are given to Mrs. Judy Teal for her kind support, help and

friendship; to Eduardo and Carolina Pereyra for helping with the code for the validation

of the model; and to my nephew Jesus Brito-Severino and to Valeria Lazcano for drawing

many of the figures and helping with the manuscript.

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Finally, thanks to my wife Abiguey and to my kids, Adrian and Sophia for being

my source of inspiration and for enduring the many hours of study and writing.

Continuous motivation and support from my sisters: Angela, Mariela, and Maria; from

my spiritual mother Nadeska; and from my close friends: Yesenia Gomez, Lissett and

Maurizio Gazzini, Fernando and Rosa Bermudez, Mauricio and Edivia Papa, and Antonio

Bruno are acknowledged with thanks.

With love to my father, El Capitan, who passed away during the course of this

study; and to my mother, who has been watching from above all this time.

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TABLE OF CONTENTS Page ABSTRACT............................................................................................................... iii ACKNOWLEDGEMENTS....................................................................................... v TABLE OF CONTENTS........................................................................................... vii LIST OF TABLES..................................................................................................... xii LIST OF FIGURES ................................................................................................... xiv CHAPTER 1: INTRODUCTION 19

1.1 Motivation and Scope ................................................................................ 20 1.2 Objectives..................................................................................................... 21 1.3 Contribution of this Work to the Oil Industry......................................... 21 1.4 Thesis Structure .......................................................................................... 22

CHAPTER 2: REVIEW OF HYDROCYCLONE TECHNOLOGY 24 2.1 Introduction ............................................................................................... 24 2.2 Description of SLHC Separators ............................................................... 24 2.3 Geometry of SLHC Separators.................................................................. 25

2.3.1 Feed Inlet ........................................................................................... 27 2.3.2 Overflow Outlet.................................................................................. 28 2.3.3 Vortex Finder ..................................................................................... 28

2.3.4 Underflow Outlet ............................................................................... 29 2.4 SLHC Operating Principle ....................................................................... 29

2.4.1 Hydrodynamic Flow Behavior ........................................................... 30 2.4.2 Pressure Drop and Flow Rate ........................................................... 30 2.4.3 Flow Reversal .................................................................................... 32 2.4.4 Formation of Gas or Air Core ........................................................... 32 2.4.5 Effect of Solid Properties on Separation ........................................... 33

2.4.5.1 Effect of Particle Size........................................................... 33 2.4.5.2 Effect of Particle Density ..................................................... 33 2.4.5.3 Effect of Particle Shape........................................................ 33

2.5 Definition of Separation Efficiency .......................................................... 34 2.5.1 Global Solids Separation Efficiency .................................................. 34 2.5.2 Split Ratio........................................................................................... 35 2.5.3 Cut Point or Cut Size ......................................................................... 35

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2.5.4 Grade Separation Efficiency, G(x) .................................................... 36 2.5.5 Reduced Grade Separation Efficiency, G’(x) .................................... 37 2.5.6 Separation Efficiency Based on Particle Tracking ............................ 38

2.6 Theories of Hydrocyclone Separation ....................................................... 39 2.7 Hydrocyclone Modeling ............................................................................. 39

2.7.1 Experimental (Empirical) Models...................................................... 39 2.7.2 Theoretical (Exact-Solution) Approach............................................. 40 2.7.3 Numerical and CFD Approach ......................................................... 41 2.7.4 Mechanistic Modeling........................................................................ 41

CHAPTER 3: LITERATURE REVIEW 42

3.1 Experimental Studies ................................................................................. 42 3.1.1 Global Separation Performance Studies ........................................... 43 3.1.2 Internal Flow Pattern Studies ............................................................ 46

3.1.2.1 Early Visualization Methods ................................................ 49 3.1.2.2 Photographic and Videographic Techniques........................ 49 3.1.2.3 Laser Induced Fluorescence (LIF) ...................................... 51 3.1.2.4 Laser Doppler Velocimetry (LDV) ...................................... 51 3.1.2.5 Electrical Impedance Tomography (EIT)............................. 54 3.1.2.6 Particle Dynamics Analyzer (PDA) ..................................... 55 3.1.2.7 Particle Size Determination.................................................. 56

3.2 CFD and Numerical Studies ..................................................................... 56 3.3 Mechanistic Modeling and Theoretical Studies ...................................... 65 3.4 Factors Influencing Solid-Liquid Separation .......................................... 78

3.4.1 Effect of Geometry ............................................................................ 78 3.4.1.1 Influence of Feed Pipe Diameter.......................................... 79 3.4.1.2 Influence of Vortex Finder Length and Orifice Diameter ... 79 3.4.1.3 Influence of Spigot Diameter .............................................. 79 3.4.1.4 Effect of Apex Cone Height ................................................. 80 3.4.1.5 Effect of Inclination Angle on Cut Size ............................... 80

3.4.2 Effect of Particle Properties ............................................................. 80 3.4.2.1 Effect of Feed Solids Concentration .................................... 81 3.4.2.2 Particle-Fluid and Fluid-Particle Interactions .................... 82

3.4.3 Effect of Temperature and Pressure ................................................. 82 3.4.4 Effect of the Air Core ....................................................................... 83 3.4.5 The Fish-Hook Effect in Classifiers ................................................... 83

3.5 Instrumentation and Online Control ....................................................... 84 CHAPTER 4: EXPERIMENTAL PROGRAM 86

4.1 Introduction ................................................................................................ 86 4.2 Test Objectives and Scope ......................................................................... 86 4.3 Applications of SLHC ................................................................................ 87 4.4 Experimental Setup .................................................................................... 87

4.4.1 Test Site Description ......................................................................... 88 4.4.2 Experimental Procedure .................................................................... 88 4.4.3 Description of Tested Equipment....................................................... 90

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4.4.3.1 Mozley 10-mm x 40 Hydrocyclone Assembly..................... 90 4.4.3.2 Mozley 1-inch x 20 Hydrocyclone Assembly...................... 92

4.4.4 Fluid Properties ................................................................................. 92 4.4.5 Properties of Solid Particles .............................................................. 93 4.4.6 Test Configurations............................................................................ 94 4.4.7 Data Acquisition ................................................................................ 94

4.4.7.1 Measurement of the Oil Concentration ................................ 94 4.4.7.2 Measurement of Particle Size and Solids Concentration ..... 95

4.5 Data Preparation and Handling................................................................ 95 4.5.1 Data Compilation............................................................................... 95 4.5.2 Data Integrity Evaluation ................................................................. 96

4.5.2.1 Review of Data Files and Test Procedures........................... 96 4.5.2.2 Data Auditing ...................................................................... 96

4.6 Data Processing and Evaluation .............................................................. 97 4.6.1 Discrete Particle Size Distributions................................................... 97

4.6.1.1 Number Frequency Distribution of Particle Size ................. 98 4.6.1.2 Volume Frequency Distribution of Particle Size ................. 99 4.6.1.3 Cumulative Volume Frequency Distribution of Particle...... Size ....................................................................................... 100 4.6.1.4 Weighted Volume Frequency Distribution of Particle Size . 102 4.6.1.5 Calculated U/F Volume Frequency Distribution of ............ Particle Size.......................................................................... 105

4.6.2 Statistical Parameters ........................................................................ 106 4.6.2.1 Sauter Mean Diameter (d32) ................................................. 106 4.6.2.2 Volume-Average Mean Particle Diameter ........................... 107 4.6.2.3 Volume Variance.................................................................. 107 4.6.2.4 Standard Deviation ............................................................... 107

4.7 Data Culling and Verification .................................................................. 107 4.7.1 Repeatability of Test Results .............................................................. 110 4.7.2 Reported Sources of Systematic Uncertainties ................................. 114

4.7.2.1 Flow Rates and Mass Measurement ..................................... 114 4.7.2.2 Removal of Oil Contained in Samples ................................. 114 4.7.2.3 Shape and Density of Solids................................................. 115

4.7.3 Mass Balance Verification ................................................................. 115 4.7.4 Differences in Separation Efficiency Results ................................... 117 4.7.5 Stochastic Forecast of Global Separation Efficiency ........................ 122

4.8 Experimental Results ................................................................................. 125 4.8.1 Summary of Results............................................................................ 125 4.8.2 Grade Separation Efficiency.............................................................. 127 4.8.3 Global Separation Efficiency ............................................................. 134

4.8.3.1 Effect of Inlet Liquid Flow Rate and Velocity..................... 134 4.8.3.2 Effect of Overflow to Inlet Feed Split Ratio ........................ 135 4.8.3.3 Effect of Inlet Solids Mass Flow Rate and Solids Concentration ....................................................................... 136 4.8.3.4 Effect of the Feed Oil to Solids Concentration Ratio........... 137 4.8.3.5 Effect of Inlet Temperature .................................................. 137

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4.8.3.6 Effect of Inlet Pressures and Outlet Backpressures.............. 139 4.8.3.7 Effect of the Feed Solids Mean Particle Size ....................... 140

4.9 Database Management System.................................................................. 142 CHAPTER 5: MECHANISTIC MODEL DEVELOPMENT 143

5.1 Modeling Assumptions .............................................................................. 144 5.2 Continuous Phase Modeling ...................................................................... 148

5.2.1 Swirl Intensity .................................................................................... 148 5.2.2 Velocity Field ..................................................................................... 152

5.2.2.1 Tangential Velocity .............................................................. 152 5.2.2.2 Axial Velocity....................................................................... 154 5.2.2.3 Radial Velocity..................................................................... 156

5.2.3 Pressure Drop .................................................................................... 156 5.3 Dispersed Phase Modeling ......................................................................... 159

5.3.1 Particle Trajectories .......................................................................... 159 5.3.2 Separation Efficiency ......................................................................... 162

5.4 Design Code................................................................................................. 165 CHAPTER 6: MODEL COMPARISONS AND DISCUSSION 166

6.1 Definition of Model Discrepancy ............................................................. 166 6.2 Verification of Mechanistic Model Predictions ...................................... 168

6.2.1 Global Separation Efficiency Comparison ........................................ 168 6.2.2 Average Grade Separation Efficiency Comparison........................... 170 6.2.3 Grade Separation Efficiency Predictions .......................................... 172

6.3 Analysis of Model Sensitivity to Different Experimental Parameters .. 178 6.3.1 Inlet Liquid Flow Rate and Feed Velocity ......................................... 178 6.3.2 Overflow Split Ratio........................................................................... 179 6.3.3 Feed Solids Mass Flow Rate and Feed Solids Concentration ........... 180 6.3.4 Feed Oil to Solids Concentration Ratio............................................. 181 6.3.5 Inlet Temperature............................................................................... 181 6.3.6 Underflow (U/F) to Overflow (O/F) Backpressure Ratio.................. 183 6.3.7 Effect of the Feed Solids Mean Particle Size ..................................... 183

CHAPTER 7: SUMMARY, CONCLUSIONS AND RECOMMENDATIONS 185

7.1 Summary and Conclusions ........................................................................ 185 7.1.1 Experimental Results ......................................................................... 185 7.1.2 Mechanistic Modeling........................................................................ 188

7.2 Main Contributions .................................................................................... 190 7.3 Recommendations ...................................................................................... 191

NOMENCLATURE ................................................................................................. 193 REFERENCES ......................................................................................................... 199

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APPENDIX A: Experimental Data and Modeling Results .................................. 217 APPENDIX B: CycloneMaster Database Management System.......................... 226

B.1 Database Architecture ............................................................................... 226 B.1.1 Test Conditions Table ........................................................................ 229 B.1.2 Particle Size Data Table .................................................................... 231 B.1.3 Equipment Specifications Table......................................................... 231 B.1.4 Instrumentation Specifications Table ................................................ 234 B.1.5 Test Objectives and Field Notes Table .............................................. 234 B.1.6 Particle Size Distribution Calculations ............................................. 234

B.2 CycloneMaster DB Management System Description ............................ 238

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LIST OF TABLES

Page 3.1 Design Equations Used in Kraipech et al. (2006) Comparative Study............. 47 3.2 Example of Grading System for Hydrocyclone Performance: Prediction of Lime/Water – Run TD3 (Kraipech et al., 2006) ............................................... 48 3.3 Summary of Milestones in Numerical Solutions of Flow in Hydrocyclones

(Nowakoswky et al., 2004) ............................................................................... 62 3.4 Forces Caused by Particle-Fluid Interactions in Turbulent Flow (Kraipech et al., 2005) ...................................................................................... 75 3.5 Effect of Neighboring Particles on Particle Motion (Kraipech et al., 2005) .... 76 4.1 Geometrical Configurations of Tested Hydrocyclones.................................... 94 4.2 Sample of Experimental Data for Several Datasets ........................................ 109 4.3 Experimental Data for 38 Datasets with Higher Uncertainty ......................... 121 4.4 Summary of Statistical Parameters and Forecast Results ................................. 124 4.5 Classification and Definition of Dataset Groups .............................................. 125 5.1 Drag Coefficient Constants............................................................................... 162 6.1 Summary of Model Predictions and Experimental Results .............................. 167 6.2 Global Model Discrepancy Results per Dataset Group .................................... 168 6.3 Average Grade Model Discrepancy Results per Dataset Group....................... 171 A.1 Experimental Data and Model Prediction Results for All Datasets.................. 218 A.2 Experimental Conditions and Equipment Specifications for All Datasets ....... 218 B.1 Hydrocyclones Data Files and Inventory of Floppy Disks............................... 227

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B.2 Summary of Data Review and Audit Results (Data Log)................................. 228 B.3 Design of the “Test Conditions” Data ............................................................. 230 B.4 Design of the “Particle Size” Data ................................................................... 232 B.5 Design of the “Equipment Specifications” Data .............................................. 233 B.6 Design of the “Instrument Specifications” Data .............................................. 235 B.7 Design of the “Objectives and Field Notes” Data ........................................... 236 B.8 Design of the “Particle Size Distribution Calculations” Data ......................... 237

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LIST OF FIGURES Page 2.1 Typical Design of a SLHC Separator (Courtesy of NATCO Group) .............. 26 2.2 Most Common Cyclone Inlet Designs.............................................................. 28 2.3 SLHC Inner and Outer Recirculation Zones..................................................... 31 2.4 Schematic of SLHC Flow Structure (Cullivan et al., 2004) ............................. 31 2.5 Colman and Thew (1983) Hydrocyclone Geometry......................................... 32 2.6 Idealized Particle Size Distribution Curves (Rushton et al., 2000) .................. 36 2.7 Idealized Grade Efficiency Curve (Rushton et al., 2000)................................. 37 2.8 Grade and Reduced Grade Efficiency Curves (Svarovsky, 1984).................... 38 3.1 Computational Diagram for Cylindrical-conical Hydrocyclone

(Lagutkin et al., 2004)....................................................................................... 68 4.1 Schematic of Test Site and Experimental Setup ............................................... 89 4.2 SLHC Solids Dosing / Injection System and Test Setup.................................. 91 4.3 Discrete Number Frequency Distribution of Particle Size (Crowe, 2005) ....... 99 4.4 Inlet Volume Frequency Distribution of Particle Size (Dataset 1) ................... 101 4.5 U/F Volume Frequency Distribution of Particle Size (Dataset 1) .................... 101 4.6 O/F Volume Frequency Distribution of Particle Size (Dataset 1) .................... 102 4.7 U/F Weighted Volume Frequency Distribution of Particle Size (Dataset 1).... 104 4.8 O/F Weighted Volume Frequency Distribution of Particle Size (Dataset 1).... 104

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4.9 U/F Calculated Weighted Volume Frequency Distribution of Particle Size Including Inlet / Outlet Cumulative Distributions (Dataset 1).................. 106 4.10 Effect of Feed Liquid Flow Rate on Global Separation Efficiency.................. 111 4.11 Effect of Inlet Flow Velocity on Global Separation Efficiency ....................... 111 4.12 Effect of Overflow Split Ratio on Global Separation Efficiency ..................... 112 4.13 Effect of Solids Mass Flow Rate on Global Separation Efficiency.................. 112 4.14 Effect of Solids Concentration on Global Separation Efficiency ..................... 113 4.15 Effect of U/F to O/F Backpressure on Global Separation Efficiency............... 113 4.16 Grade Separation Efficiency Curve (Dataset 4). G = 44%, E= 82% ............... 116 4.17 Grade Separation Efficiency Curve (Dataset 12).G = 79%, E= 83% .............. 117 4.18 Comparison of Global and Average Grade Separation Efficiency Data .......... 119 4.19 Difference Between Global and Average Grade Separation Efficiency .......... 120 4.20 Grade vs. Global Efficiency Difference per Dataset (in Chronological .......... Order)................................................................................................................ 122 4.21 Probabilistic Frequency Distribution of Global Efficiency (1-inch unit) ......... 123 4.22 Probabilistic Frequency Distribution of Global Efficiency (10-mm unit)........ 123 4.23 Global Separation Efficiency by Dataset (Group A) ........................................ 126 4.24 Feed Sauter Mean Diameter (d32) per Dataset (Group A) ................................ 126 4.25 Standard Deviation of Feed Particle Size Distribution per Dataset ................. (Group A).......................................................................................................... 127 4.26 Grade Separation Efficiency Curve – 1” Unit (Dataset 1)................................ 128 4.27 Grade Separation Efficiency Curve – 1” Unit (Dataset 22).............................. 128 4.28 Grade Separation Efficiency Curve – 1” Unit (Dataset 110)............................ 129 4.29 Grade Separation Efficiency Curve – 1” Unit (Dataset 120)............................ 129 4.30 Grade Separation Efficiency Curve – 10mm Unit (Dataset 126) ..................... 130

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4.31 Grade Separation Efficiency Curve – 10mm Unit (Dataset 128) ..................... 130 4.32 Grade Separation Efficiency Curve – 10mm Unit (Dataset 135) ..................... 131 4.33 Grade Separation Efficiency Curve – 10mm Unit (Dataset 148) ..................... 131 4.34 Grade Separation Efficiency Curve – 10 mm Unit (Dataset 149) .................... 132 4.35 Grade Separation Efficiency Curve – 10 mm Unit (Dataset 151) .................... 132 4.36 O/F–U/F Weighted Volume Frequency Distribution of Particle Size (Dataset 5)......................................................................................................... 133 4.37 O/F–U/F Weighted Volume Frequency Distribution of Particle Size (Dataset 129)..................................................................................................... 133 4.38 Effect of Feed Liquid Flow Rate on Global Separation Efficiency.................. 134 4.39 Effect of Inlet Velocity on Global Separation Efficiency................................. 135 4.40 Effect of O/F Split Ratio on Global Separation Efficiency .............................. 135 4.41 Effect of Solids Mass Flow Rate on Global Separation Efficiency.................. 136 4.42 Effect of Solids Concentration on Global Separation Efficiency ..................... 137 4.43 Effect of Oil/Solids Concentration Ratio on Global Efficiency ....................... 138 4.44 Effect of Temperature on Global Separation Efficiency .................................. 138 4.45 Effect of Inlet Pressure on Global Separation Efficiency................................. 139 4.46 Effect of U/F to O/F Backpressure Ratio on Global Separation Efficiency ..... 140 4.47 Effect of Sauter Mean Diameter (d32) on Global Efficiency ........................... 141 4.48 Effect of Feed Particle Volume-Averaged Mean Size on Global Efficiency ... 141 4.49 Main Screen of the CycloneMaster DB System ............................................... 142 5.1 Schematic of the SLHC and Model Nomenclature........................................... 147 5.2 Rankine Vortex Tangential Velocity Profile .................................................... 153 5.3 Typical Axial Velocity Profile along the Radial Position of the Cyclone........ 155

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5.4 Schematic of the Particle Trajectory Model ..................................................... 160 5.5 Schematic of Particle Trajectory and Separation Efficiency ............................ 163 5.6 Grade Separation Efficiency Probability Curve ............................................... 164 6.1 Experimental Global Efficiency Results vs. Model Predictions....................... 169 6.2 Discrepancy of Model Predictions vs. Global Efficiency for each Dataset ..... 170 6.3 Experimental Average Grade Efficiency Results vs. Model Predictions ......... 171 6.4 Discrepancy of Model Predictions vs. Average Grade Efficiency per Dataset............................................................................................................... 172 6.5 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 1) ........... 173 6.6 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 22) ......... 173 6.7 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 110) ....... 174 6.8 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 120) ....... 174 6.9 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 126) ....... 175 6.10 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 128) ....... 175 6.11 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 135) ....... 176 6.12 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 148) ....... 176 6.13 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 149) ....... 177 6.14 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 151) ....... 177 6.15 Global Efficiency Discrepancy as a Function of Feed Liquid Flow Rate ...... 178 6.16 Global Efficiency Discrepancy as a Function of Inlet Velocity ...................... 179 6.17 Global Efficiency Discrepancy as a Function of Overflow Split Ratio .......... 179 6.18 Global Efficiency Discrepancy as a Function of Solids Mass Flow Rate ...... 180 6.19 Global Efficiency Discrepancy as a Function of Solids Concentration .......... 181

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6.20 Global Efficiency Discrepancy as a Function of Oil/Solids Concentration Ratio ................................................................................................................. 182 6.21 Global Efficiency Discrepancy as a Function of Inlet Temperature ............... 182 6.22 Global Efficiency Discrepancy as a Function of U/F to O/F Backpressure Ratio.................................................................................................................. 183 6.23 Global Efficiency Discrepancy as a Function of Feed Particle Volume-Averaged Mean Size .......................................................................... 184 6.24 Global Efficiency Discrepancy as a Function of Sauter Mean Diameter ......... 184 B.1 Main Menu: Dataset Reference Info Panel....................................................... 239 B.2 Main Menu: Dataset Detailed Info Panel and Performance Plots Tab Page .... 239

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CHAPTER 1

INTRODUCTION

Hydrocyclones have been widely used for more than a century (Bretney, 1891)

for various applications and by different industries, including the Mineral (Fahlstorm,

1963; Neesse et al., 2004), Chemical (Dhamo, 1994; Dickey et al., 1997), Petrochemical

(Seyda and Petty, 1991), Petroleum (Kelsall, 1952; Colman et al., 1980; Caldentey et al.,

2002), Food and Drug (Adupeasah et al., 1993; Dickey et al., 1997), Pulp and Paper

(Kure et al., 1999), Environmental (Syed, 1994; Klima and Kim, 1997), and Biology

(Bendixen and Rickwood, 1994), among others.

Common hydrocyclone applications include classification of solids or removal of

particulates from a liquid or a gas stream. The use of the solid-liquid hydrocyclone

(SLHC) has emerged as a sound alternative to conventional filtration and other separation

systems, which are bulky, require backwashing, frequent replacement of filters, chemical

additives, and have greater pressure drop, resulting in higher operating costs. The

Petroleum industry, for example, has utilized the SLHC to remove oilfield solids from

produced water in order to make it suitable for downhole re-injection, either for reservoir

waterflooding or for disposal. Hydrocyclones are also an attractive solution for offshore

applications where space, efficiency, and reliability are important.

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Different types of hydrocyclones have been used by the Petroleum industry in the

past to separate solid-solid (classifiers) liquid-liquid (both dewatering and deoiling), gas-

liquid, gas-solid, and solid-liquid mixtures. This study focuses on the latter application.

1.1 Motivation and Scope

With rising needs for efficient and reliable solids removal systems in the mineral

and energy industries, the SLHC has emerged as a sound and proven technological

alternative. Proper hydrocyclone design is therefore crucial for achieving maximum

performance and ensuring the highest and most reliable solids separation efficiency.

However, there is still a lack of detailed understanding of the hydrodynamic flow

behavior and separation mechanism that occur in the hydrocyclone; thus, more research

is needed in order to achieve these goals.

Up to date, the design of the SLHC has relied on empirical experience (Kelsall,

1952; and Rietema, 1961), and more recently on CFD and numerical modeling

(Narasimha et al., 2005, 2006, 2007; Delgadillo and Rajamani, 2005; Brennan et al.,

2007), which has had some success owing to the improvement of computing power. Still,

CFD models require a large amount of computing power, and simulations are time-

consuming and costly. Mechanistic models are a sound intermediate solution to describe

the physical behavior of the fluid flow within the hydrocyclone. However, very limited, if

any, mechanistic modeling work has been performed to date for solid-liquid separation in

hydrocyclones.

The present work is aimed at developing a mechanistic model capable of

predicting the hydrodynamic flow behavior and separation efficiency of the SLHC over a

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wide range of geometrical configurations and operating conditions. The proposed model

is verified against SLHC oilfield experimental data collected by Culwell et al. (1994).

The description of the experimental program, the data handling and verification

processes, as well as, the analysis of experimental results, are an integral part of this

thesis work. An automated database system to standardize and store the data and a SLHC

design code has also been developed. Both these tools facilitate the analysis of the data,

the verification of the proposed mechanistic model, and the performance prediction of the

small diameter SLHC.

1.2 Objectives

The main objective of this study is to develop a mechanistic model for the solid-

liquid hydrocyclone (SLHC). The developed model is a modification of the Caldentey et

al. (2002) liquid-liquid hydrocyclones (LLHC) model. The SLHC model will enable the

prediction of the continuous-phase swirl intensity and velocity profile, and the pressure

drop; which are used to determine particle trajectories, and hence the grade separation

efficiency curves. Oilfield experimental data acquired by Culwell et al. (1994) is used to

validate and refine the proposed model.

Finally, an existing hydrocyclone design code is upgraded to incorporate the

developed SLHC mechanistic model.

1.3 Contribution of this Work to the Oil Industry

The main contribution of this study is the development of a mechanistic model

and a computer code for the design and optimization of the SLHC. The model will also

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serve as a tool for the prediction of the separation performance of small diameter SLHC

under a wide range of flow conditions.

Inadvertent sand production in many oilfields has become a significant and costly

issue for the Petroleum industry. Most visible is the disposal of thousands of pounds of

sand every day from gathering plants and oilfield facilities. Separators at production pads

and at processing plants are back flushed multiple times every day to clear out the solids,

with associated inefficiency and loss of production. Sand in power fluid to jet-pump wells

causes premature failure due to erosion that requires early replacement with

corresponding high operating costs. Completions may be washed out requiring expensive

rig workovers. Sand entrained in injection water damages the reservoir, reduces the

injection capacity and contributes to water breakthrough to producers. Sand in pipelines,

wellbores and process equipment may also lead to erosion and premature failures with

possible health, safety and environmental consequences.

The industry relies on the use of different filtering and separation devices, among

which the SLHC offers important advantages. The SLHC is one of the most attractive

technologies available owing to its low cost, simplicity of operation, acceptable reliability

and good performance. However, hydrocyclone technology needs to be improved in

order to achieve higher performance levels for different applications and flow conditions.

The industry needs better and more practical design tools in order to make this happen.

1.4 Thesis Structure

Current chapter is a brief preface to the study. It begins with the motivation, scope

and main objectives of this study. The second chapter presents an overview of

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hydrocyclone technology, covering SLHC phenomena and basic definitions. Chapter 3

follows with a comprehensive literature, pertinent mainly to modeling efforts for the

SLHC. The first section starts with a review of experimental studies, covering some

empirical models. Next, a description of the most relevant studies using different

visualization and measuring techniques of the flow field inside the hydrocyclone is

presented. The third section covers some of the numerical studies, including CFD

modeling and simulation. The theoretical and few of the available mechanistic modeling

work involving hydrocyclones are covered next. The last part of this chapter presents

some of the research investigating the factors influencing solid-liquid separation in

hydrocyclones, including instrumentation and online control work.

Chapter 4 introduces the experimental study conducted by Culwell et al. (1994) to

investigate the performance of small diameter SLHC for solids removal. The test facility,

experimental procedure, and data acquisition process are described. Following, the data

gathering, auditing, and data analysis and verification process are described. The last

section presents the experimental results, including a discussion of the effects of some

flow variables on separation efficiency.

Chapter 5 is the core of this thesis work. It presents the development of the

proposed SLHC mechanistic model and describes the developed design code. In Chapter

6, the proposed model is validated against the oilfield experimental data and refined

accordingly. Detailed discussions and model prediction comparisons with the data are

presented in this chapter. Finally, conclusions, contributions and recommendations for

future work are described in Chapter 7.

24

CHAPTER 2

REVIEW OF HYDROCYCLONE TECHNOLOGY

2.1 Introduction

The first U.S. Patent on a hydrocyclone design was granted to Bretney in 1891

(No. 453, 105). However, it was until after World War II when the hydrocyclone

technology gained popularity in different industrial applications. Recently, there has been

a revival of interest in hydrocyclones, especially in the oil and chemical industries, due to

several reasons. One of them is the need of the oil industry for compact, reliable and

simple separators, such as the SLHC, to deploy offshore in deep and ultra deep waters,

and in sub sea operations. Also, the hydrocyclone plays an important role in different

other industrial applications, such as, fluids clarification, thickening, classification,

sorting, washing, solids removal, liquid-liquid separation, liquid degassing, and particle

size distribution measurement.

2.2 Description of SLHC Separators

The SLHC separator is a type of cyclone that facilitates the centrifugal separation

of solid particulates from a liquid stream. Different from the slow gravity vessel

separator (1 g force), the hydrocyclone utilizes the energy obtained from fluid pressure to

create rotational fluid motion, yielding much larger values of the g-force that can vary

from 800 g to about 50,000 g in a 10-mm diameter cyclone. This high swirling motion

25

is applied over a shorter residence time causing the particles suspended in the liquid to

separate fast and effectively from the liquid itself (Rushton et al., 2000).

The SLHC units from Mozley Engineering (NATCO Group) analyzed in this study

(see Figure 2.1) are typically used to remove oilfield particles from produced water. The

produced water may have a low content or traces of oil in the form of small droplets. The

equipment tested is described in detail in Chapter 4.

2.3 Geometry of SLHC Separators

Hydrocyclones are simple, compact, and highly efficient separators when

properly designed and operated. Figure 2.1 is a general representation of a typical SLHC

separator. The SLHC generally consists of a vertical cylinder with a conical or tapered

section attached to it. The cylindrical part is closed at the top by a cover where the vortex

finder extends to a certain length into the body of the cyclone. Near the top cover is the

feed inlet orifice, either of circular or rectangular shape, through which the fluid mixture

enters tangentially into the cylindrical chamber. An orifice in the apex of the conical

section, also known as spigot or underflow outlet, serves as the exit of the separated-

phase stream. This underflow stream consists of a mixture of some liquid and solid

particles coarser than the cut size (d50). Most of the liquid stream along with some

particles finer than the cut size exit through the overflow outlet via the vortex finder. The

SLHC utilizes the centrifugal forces promoted by the tangential entry to separate the

dispersed-phase (solid particles) from the continuous-phase (liquid mixture).

26

Figure 2.1 Typical Design of a SLHC Separator (Courtesy of NATCO Group)

27

2.3.1 Feed Inlet

The inlet orifice has the important role of providing a smooth flow pattern at the

point of entry into the cyclone. The main goal is to inject the feed in a way so as to

achieve the highest tangential acceleration possible, reducing turbulence effect, pressure

drop and shear stress to an acceptable level. This is especially critical in oil-water

separation in order to avoid the rupture of the oil droplets that may lead to a reduction in

the separation efficiency. Rectangular or circular shaped, single or twin inlets have been

most frequently used by different researchers. Two commonly used feed inlet

configurations are the tangential and the involuted entry, as shown in Figure 2.2. The

involuted feed entry aims at maximizing the efficient conversion of kinetic energy to

centrifugal force, while minimizing turbulence effects that could be detrimental to fine

particle separation and causing excessive wear. This is achieved by minimizing the

intersecting angle between the incoming feed and the already rotating fluid inside the

hydrocyclone (Svarovski, 1984). Some manufacturers have tried to reduce entry

turbulence by using a helical top cover inlet. Besides avoiding the impingement effect on

the flow occurring inside the cyclone, it also promotes an additional downward

momentum on the feed (Svarovski, 1984). On the other hand, the twin inlets have been

considered to maintain better symmetry, resulting in a more stable reverse core (Colman

et al., 1983 and Thew et al., 1984).

28

Figure 2.2 Most Common Cyclone Inlet Designs

2.3.2 Overflow Outlet

This is a small diameter orifice that plays a major role in the split ratio, defined as

the relationship between the overflow rate to the inlet flow rate. Most commercial

hydrocyclones allow for changing the diameter of this orifice to suit a wide range of

operating conditions.

2.3.3 Vortex Finder

The vortex finder is the overflow pipe located at the center top of the cylindrical

section extending some length into the cyclone body. It is necessary that the length of the

vortex finder extends below the feed entry in order to increase separation efficiency by

avoiding short-circuiting, that is, the early exit of the feed stream to the overflow. The

diameter of the vortex finder is generally that of the overflow orifice. Similarly, some

manufactures provide interchangeable vortex finders for increased efficiency and a more

flexible operation over a wide range of feed conditions.

29

2.3.4 Underflow Outlet

Also called spigot, the underflow is a small diameter orifice located at the apex of

the cone. The spigot plays an important role in the control of the volumetric flow split

and underflow density, as it has a direct effect on the underflow-to-throughput ratio, the

underflow concentration and the cut size (Svarovski, 1984). Most commercial units are

also supplied with a variable, changing, or adjustable orifice size to accommodate for a

wide range of operating conditions and optimize the separation process. Maximum

particle size at the feed entry should be considered in order to avoid spigot clogging or

malfunctioning and, thus, operation interruption.

2.4 SLHC Operating Principle

The SLHC utilizes the principle of centrifugal sedimentation to separate

particulate matters based on size, shape, and density. A liquid stream (or slurry)

containing a concentration of fine particles is fed tangentially into the body of the

hydrocyclone. The tangential inlet flow induces centrifugal forces causing solids coarser

than the cut point size to be pushed radially toward the wall, move downward, and be

rejected from the underflow via the spigot, along with some liquid. Most of the liquid-

phase with some solids finer than the cut point size move upward (reverse flow) and exit

through the overflow via the vortex finder. The term ‘d50 cut point' stands for the particle

size at which the cyclone is 50% efficient (refer to Figures 2.1 and 2.4)

30

2.4.1 Hydrodynamic Flow Behavior

The swirling motion is produced by the tangential injection of the pressurized

fluid mixture into the hydrocyclone. The flow pattern consists of a spiral within another

spiral moving in the same circular direction (Seyda and Petty, 1991). These are the most

conspicuous flows in the hydrocyclone and are sometimes called primary and secondary

vortices (see Figures 2.3 and 2.4). The primary or outer (free-like) vortex moves

downward carrying suspended particles or material along the axis of the cyclone to the

underflow outlet. The secondary or inner (forced) vortex is located inside the primary

vortex (in the region close to the cyclone axis) moving upward (reverse direction)

carrying mainly a clean liquid stream to the overflow outlet (Rushton et al., 2000).

Recirculation zones associated with the high swirl intensity at the inlet region, and

with long residence times and very low axial velocity, have been found to be diminished

as the flow enters the low angle tapered section (see Figure 2.5).

2.4.2 Pressure Drop and Flow Rate

The pressure drop is the differential pressure between the locations right before the

feed entry and right after the overflow outlet. The hydrocyclone develops its swirling

motion (separation power) utilizing the fluid pressure energy. A hydrocyclone of fixed

dimensions, operating with a given flow mixture and flow conditions, gives a fixed

relationship between the volumetric throughput and the pressure drop. The two variables

are therefore interdependent, namely, increasing flow rate results in increasing pressure

drop.

31

Figure 2.3 SLHC Inner and Outer Recirculation Zones

Figure 2.4 Schematic of SLHC Flow Structure (Cullivan et al., 2004)

32

Figure 2.5 Colman and Thew (1983) Hydrocyclone Geometry

2.4.3 Flow Reversal

With a high swirl at the inlet region, the pressure is high near the wall region and

very low toward the centerline, in the core region. As a result of the pressure gradient

profile across the cyclone diameter, which decreases with downstream position, the

pressure at the downstream end of the core is greater than at the upstream, causing flow

reversal (Hargreaves, 1990) in the region along the cyclone axis.

2.4.4 Formation of Gas or Air Core

Gas dissolved in the liquid-phase can come out of solution due to pressure

reduction in the core region, which can easily migrate to the cyclone axis and leave

abruptly through the overflow outlet (Thew, 1986). This phenomenon is known as

formation of gas or air core, which can be detrimental to the cyclone’s performance if it

33

becomes unstable due to turbulence. A significant amount of gas can be tolerated but

excessive amounts will disturb the vortex. An experimental study on this topic is found in

Smyth and Thew (1996).

2.4.5 Effect of Solid Properties on Separation

2.4.5.1 Effect of Particle Size

Some finer particles can become entrained in the liquid-phase, not separated, and

leave together with the liquid through the overflow. In classifier units, coarser particles

tend to migrate to the wall of the cyclone and move downward, while finer particles tend

to exit with the overflow. Classification is not totally accurate and some coarse particles

may exit together with the finer solid stream.

2.4.5.2 Effect of Particle Density

Heavier (denser) particles tend to sink toward the underflow, while the lighter

particles tend to float and be dragged to the overflow. When the feed mixture contains

solids of two different average densities, the classification is more effective if one type of

solids is denser and the other type is lighter than the feed liquid. In the solid-liquid

separation case, the removal of solids from the liquid is more pronounced if both types of

solids are heavier than the continuous liquid-phase.

2.4.5.3 Effect of Particle Shape

The shape of a particle has a direct impact in its settling velocity, and therefore,

on its trajectory inside the cyclone.

34

2.5 Definition of Separation Efficiency

The main application of the SLHC subject to this study is to efficiently remove

solids from liquid slurries. Separation efficiency is then a measure of the SLHC ability to

recover solids through the underflow outlet, while allowing most of the clean liquid to

continue through the overflow, and thus, through the rest of the process. Following are

the definitions of some important parameters used to define SLHC separation efficiency.

2.5.1 Global Solids Separation Efficiency

A practical interpretation of separation data considers the purity of individual

discharge streams, namely, overflow (o) and underflow (u). Many authors have made

attempts to quantify the relative phase composition of the separated streams in the form

of a percentage by volume measurement. Bradley (1965) defined global separation

efficiency, also known as total solids recovery, as the total mass (or volume) fraction of

feed solids separated through the underflow, irrespective of particle size. Thus, a

generalized and widely used definition for the solids separation efficiency, E, is given by:

%100×=si

suqqE (2.1)

where qsi is the flow rate of solids at the feed entry, and qsu is the flow rate of solids

through the underflow. Utilizing continuity equation yields:

suusoosiisi cqcqcqq ×+×=×= (2.2)

where cs is the solids concentration in volume at the inlet (i), overflow (o), and underflow

(u) respectively. Then, Eq. (2.1) can be rewritten as:

35

%cqcq

Esii

soo 1001 ×⎟⎟⎠

⎞⎜⎜⎝

⎛××

−= (2.3)

Note that when cso tends to zero, the separation efficiency is maximum. Also note

that an efficiency, E, of 100% can be obtained by simply blocking off the overflow outlet,

achieving no separation at all. Thus, the definition of E should be more rigorous by

incorporating a mass balance verification term to account for the effective solid-liquid

separation. Mass or volumetric flow rates of the liquid-phase reported to both the

overflow and the underflow outlets should be balanced by the feed entry rates.

2.5.2 Split Ratio

The split ratio is the ratio of the overflow rate to the inlet flow rate, as given by

the following expression:

%qq

Fi

o 100×= (2.4)

where F is the split ratio, qo is the total flow rate at the overflow outlet of the SLHC, and

qi is the total inlet flow rate.

2.5.3 Cut Point or Cut Size

A common approach to define SLHC efficiency is based on the cut size, d50, the

size at which particle separation or classification is 50% efficient. That is, the size having

50% probability of going to the overflow or the underflow (Rushton et al., 2000). Figure

2.6 represents an idealized size distribution of feed split into overflow and underflow.

36

2.5.4 Grade Separation Efficiency, G(x)

The grade efficiency or is defined as the fraction of solid particles, usually by

mass or volume, of a particular size range reporting to the underflow (Rushton et al.,

2000), and is defined as:

%100)(

)()( ×=feedinxgradesizeinmass

underflowinxgradesizeinmassxG (2.5)

where x represents the grade or particle size range under consideration. Figure 2.7 shows

the grade efficiency curve for the idealized particle size distribution of the separation case

described in Figure 2.6. The actual grade efficiency curve can be determined

experimentally using series of batches of same-sized solids.

Figure 2.6 Idealized Particle Size Distribution Curves (Rushton et al., 2000)

37

Figure 2.7 Idealized Grade Efficiency Curve (Rushton et al., 2000)

2.5.5 Reduced Grade Separation Efficiency, G’(x)

This concept was introduced to incorporate the flow splitting or dead flux effect.

This effect is known to modify the shape of the grade efficiency curve and make it look

more optimistic. It is caused by the very fine particles that simply follow the flow and are

split in the same ratio as the fluid (Svarovsky, 1984). As shown in Figure 2.8, a typical

SLHC grade efficiency curve does not start from the origin of the coordinates, as it

should be expected for inertial separation. The intercept is usually the underflow-to-

throughput ratio, Rf. This effect needs to be corrected, as suggested by Svarovsky (1984),

in order to make a normalized comparison of equipment performance, as follows:

f

f

RRxG

xG−

−=

1)(

)(' (2.6)

38

Figure 2.8 Grade and Reduced Grade Efficiency Curves (Svarovsky, 1984)

2.5.6 Separation Efficiency Based on Particle Tracking

In this study, the SLHC solids separation efficiency is predicted based on particle

trajectory analysis. Particle trajectories are traced in the continuous liquid-phase using a

Lagrangian approach. This is accomplished by performing a force balance on each

characteristic particle size present in the feed in order to predict its velocity. Thus, it is

possible to predict if a characteristic particle is either able to reach the underflow outlet

and be separated, or if it reaches the reverse flow region, dragged by the continuous-

phase and carried to the overflow. Details of this analysis and the overall modeling

approach are provided in Chapter 5.

39

2.6 Theories of Hydrocyclone Separation

These are theories or physical models proposed by several authors that are derived

from fundamental principles. They seek to describe the separation process in a

hydrocyclone based on the physics of the fluid flow and not merely on empirical

experience. These models can be classified into four different categories, namely,

Equilibrium Orbit Theory, Residence Time Theory, Crowding Theory, and Turbulent

Two-Phase Flow closure models. An overview of these theories is presented by

Svarovsky (1984) and Rushton et al. (2000).

2.7 Hydrocyclone Modeling

2.7.1 Experimental (Empirical) Models

The phase separation process in hydrocyclones is a complex phenomenon.

Hence, the early approach was based on experimental experience and developing

empirical correlations by relating key operating variables to the separation and

classification efficiency. As a result, a large number of empirical coefficients are

derived from fitting the data, which must be recalculated for each new data set. Early

empirical models have been able to meet the practical needs of the industry but still

have major limitations. The correlations are generally capable of predicting well their

original data, but correlations obtained from one system are not necessarily valid for

other systems. This approach should be based on dimensional analysis in order to be

able to yield a universal solution; otherwise, the correlations cannot be applied with

confidence over a range of conditions and configurations different from the conditions

40

under which they were developed. However, the turbulent nature of the flow field in

the hydrocyclone and the large number of variables involved limit the applicability of

dimensional analysis to develop solutions for hydrocyclone systems.

2.7.2 Theoretical (Exact-Solution) Approach

This approach is based on the hydrodynamic flow behavior and requires the

rigorous solution of the fundamental conservation equations, namely, the mass

balance, momentum balance and turbulence effect, using the proper boundary

conditions. The mass balance is described using the continuity equation, the momentum

balance using the Navier-Stokes equations, and the turbulence effect utilizing a

turbulence-closure model.

Undoubtedly, this is the most accurate approach when applicable. However,

very few systems can be solved rigorously because of the complex nature of turbulent

flow. Thus, the exact solution approach is limited to laminar, well behaved flow

regimes, which is not the case for the hydrocyclone. The swirl nature of the flow field

within the cyclone generates turbulence that is highly anisotropic (Delgadillo, 2006).

On the other hand, the continuity and the Navier-Stokes equations are three-

dimensional nonlinear partial differential equations, and therefore, need to be solved

numerically utilizing CFD simulations.

2.7.3 Numerical and CFD Modeling

In recent years, the advancement of computer technology has promoted the use of

Computational Fluid Dynamics (CFD) to study complex fluid flow systems, such as the

41

hydrocyclone. Fundamental equations, as well as, turbulent closure models are solved

numerically over a grid system domain. The exact geometry and flow conditions can be

reproduced, reducing the need for complex and costly experiments. However, CFD

models come with a high price in the form of required computer power and lengthy

simulations. The most sophisticated computers and CFD software available today can

take several weeks to run a single hydrocyclone case. Besides, closure relationships still

have some unresolved issues that can affect the results, which need to be addressed in

further studies. As a result, the use of CFD simulation has a limited application in

hydrocyclone design and performance optimization. Thus, simpler, yet realistic models

have been sought, such as mechanistic models.

2.7.4 Mechanistic Modeling

Mechanistic modeling is an intermediate approach between the empirical and the

exact-solution approaches. In this approach, simplified physical models are built in an

attempt to describe the fluid flow phenomena in the hydrocyclone and the related

separation efficiency. The physical model is then described mathematically providing a

flexible and simple analytical tool for design and performance prediction. The developed

models can be validated and refined using limited experimental data, and can be

extrapolated to different flow conditions with more confidence. The closer the physical

model is to the real phenomena, the higher is the confidence in the mathematical model to

be used for hydrocyclone design and separation performance predictions over a wider

range of conditions.

42

CHAPTER 3

LITERATURE REVIEW

Many studies have been published on hydrocyclones in the past four decades. A

representative sample is summarized in this chapter with emphasis on solid-liquid

separation and modeling work. Some studies performed on gas-liquid, gas-solid, liquid-

liquid, and solid-solid separation are also discussed and referenced, as many of them have

set the grounds for understanding the hydrodynamic flow behavior in hydrocyclones.

Two textbooks that condense pioneering work on hydrocyclones are Bradley

(1965) and Svarovsky (1984). A more recent textbook by Rushton et al. (2000) compiles

a broad range of solid-liquid filtration and separation technologies, with one chapter

dedicated to centrifugal separation. All three textbooks cover in detail fundamental

theories, experimental work, design, and performance aspects of hydrocyclones.

3.1 Experimental Studies

The early experimental studies have focused on the performance and global

separation efficiency of hydrocyclones. Empirical correlations were developed relating

classification efficiency or cut size separation to hydrocyclone geometry and in many

cases to the slurry feed flow rate and solids concentration. Later experimental studies

were more rigorous, focusing on the understanding of the flow field in the hydrocyclone

43

by means of sophisticated visualization techniques. Some of these works are described in

the following two sections.

3.1.1 Global Separation Performance

One of the earliest experimental studies was that of Dahlstron (1949). He studied

the flow of liquid suspensions of quartz in a 225-mm hydrocyclone having a 20° cone

angle, and developed an expression for the cut size parameter (d50). However, the

validity of this correlation is limited to feed pulps up to 20% of solids by weight and

underflow volume splits of up to 15% of the total flow. Yoshioka and Hotta (1955) later

proposed a new expression for the d50 based on their experimental work using dilute

slurries in hydrocyclones of different sizes, ranging from 75-mm to 150-mm.

Fahlstrom (1963) was the first to propose the "crowding theory" suggesting that

the cut size is a function of inlet particle size distribution and the capacity of the

underflow orifice. However, flaws in the original theory were later revised by Bloor et al.

(1980) providing a more scientific proof of the crowding theory based on mathematical

modeling work.

The effect of fluid viscosity on the classification of solids in a 30-mm

hydrocyclone was examined by Agar and Herbst (1966). They suggested that cut size is

proportional to viscosity, μc, where c is an empirical constant found to be c = -0.58.

Many years later, Kanungo and Rao (1973) studied the performance of a 3-inch

hydrocyclone observing linear relationships between: the flow-rate of water in the feed

and the overflow product from the cyclone; the flow-rate of solids in the feed and the

44

underflow product from the cyclone. The authors compared the performance of the 3-

inch hydrocyclone to available results from a 20-inch cyclone.

Sheng et al. (1974) investigated the performance of a conventional hydrocyclone

and the effect of the construction material on the separation efficiency. Lynch and Rao

(1975) conducted extensive experimental work with slurries ranging from 15% to 70%

solids in hydrocyclones of different sizes ranging from 100-mm to 375-mm. Plitt (1976)

used aqueous pulps of flour silica in smaller hydrocyclones of sizes, 32-mm to 150-mm

diameter, conducting 174 experimental tests. He supplemented the data sets with other

data gathered earlier by Lynch and Rao (1975) utilizing larger diameter hydrocyclones.

In the same year, Johnson et al. (1976) conducted experiments using two small cyclones

to separate Freon droplets from water. They also developed a correlation derived from

solid-solid separation theory and a particle size distribution approach to predict liquid-

liquid separation efficiencies.

A general revision of the hydrocyclone developed at Southampton University was

conducted by Thew (1986). The author also discussed issues previously presented by

Moir (1985).

Bednarski and Listewnik (1988) presented a hydrocyclone design for

simultaneous separation of less dense liquid dispersion (droplets) and solids from a

denser liquid mixture, for oil concentrations between 2% and 5%. The authors suggested

that smaller feed inlets cause break-up of droplets, while the larger ones do not produce a

swirl of sufficient intensity required for efficient separation.

45

Choi (1990) tested a system of six hydrocyclones (35-mm) operating in parallel

for produced water treatment. Plitt et al. (1990) developed an equation to calculate water

recovery from a coarse feed product stream, for solid separation in a cyclone.

Seyda and Petty (1991) examined the separation performance of the cylindrical

tail pipe section in a hydrocyclone. The authors developed a semi-empirical model to

predict the velocity field in a cylindrical chamber used to predict particle trajectories and,

thus, the grade efficiency. The proposed model assumed that the axial velocity was

independent of axial location and considered a constant eddy viscosity. Theoretical

results showed that an optimum split ratio exists and that the efficiency increases

proportionally with increased feed flow rate.

A small hydrocyclone for sludge thickening of domestic waste-water was utilized

by Ortega and Medina (1996) to study the effect of pressure drop and underflow diameter

on the separation efficiency. Shah et al. (2006) developed an improved correlation based

on regression analysis to predict water split in a hydrocyclone, and verified it using

experimental data. They used spigot and vortex finder diameters as individual variables

instead of using the ratio of spigot and vortex finder diameter as one variable. The

authors claim that using this ratio could be misleading. They also used feed pressure as

another model parameter.

Kraipech et al. (2006) performed a comprehensive comparative study on the

performance of several empirical models for industrial hydrocyclone design. The study

included the design methods presented by Moder and Dahlstrom (1952), Yoshioka and

Hotta (1955), Tarjan (1961), Abbott (1968), Lynch and Rao (1968), Flintoff et al. (1987),

Svarovsky (1994), Nageswararao (1995) and Besendorfer (1996). The different sets of

46

design equations were fine-tuned with a selected set of experimental data for added

reliability before utilizing them to predict the performance of the same hydrocyclones but

under different flow conditions. The authors observed that the predictions were

acceptable if the pressure drop and feed concentration remained the same, but when

pressure drop and/or feed concentration varied, the design equations were unreliable.

The design equations used by Kraipech et al. (2006) are grouped by performance

parameter for each set of equations and summarized in Table 3.1. An example of the

evaluation system used to compare the performance prediction of each set of equations is

shown on Table 3.2. The actual design equations proposed by each of the researchers, as

well as, the detailed performance results are described in Kraipech et al. (2006).

3.1.2 Internal Flow Pattern Studies

The understanding of the hydrocyclone internal flow field is necessary to assess

its performance, and for modeling and design optimization purposes. Many researchers

have used different visualization techniques to examine and measure the 3D flow field,

namely, the tangential, radial, and axial velocities of the dispersed and continuous phases.

Most studies include both qualitative examination of the flow pattern features and

quantitative measurements of fluid velocity profiles. Efforts have been made to

distinguish and track particle or droplet trajectories, as well as to characterize the nature

of the primary and secondary flows, flow mixing and flow reversal zones occurring in the

hydrocyclone. Though sometimes questionable, most of these data have set the basis of

the modeling work that is currently used in hydrocyclone design practice. Details of the

most commonly used experimental methods are provided by Cullivan et al. (2001).

47

Tabl

e 3.

1 D

esig

n E

quat

ions

Use

d in

Kra

ipec

het

al.

(200

6) C

ompa

rativ

e S

tudy

.

48

Tabl

e 3.

2 E

xam

ple

of G

radi

ng S

yste

m fo

r Hyd

rocy

clon

e P

erfo

rman

ce: P

redi

ctio

n of

Lim

e/W

ater

–R

un T

D3

(Kra

ipec

het

al.,

200

6)

49

3.1.2.1 Early Visualization Methods

The earliest visualization methods included the use of probes, spheres, aluminum

flakes, paddles or vanes. These were mounted on free rotating spindles placed inside the

air core and observed with the help of a stroboscope or a rotating microscope (Siato and

Ito, 1951; Kelsall, 1952; Fontein and Dijksman, 1952; and Lilge et al., 1957).

Kelsall (1952) was probably the first to study experimentally in detail the flow

phenomena in the cyclone. The author studied small cyclones with dilute feeds by

illuminating fine aluminum flakes and observing the motion with a microscope having

rotating objectives. Tangential and axial velocity components were measured at chosen

locations, and radial velocities were calculated using the continuity equation. Kelsall’s

experimental results are still considered the most widely used data among

contemporaneous hydrocyclone researchers.

Turbulence in decaying swirling flow through a pipe was studied experimentally

by Algifri et al. (1988) using a single rotating inclined hot-wire probe. The results were

presented in the form of the three mean components of the velocity profiles. They

observed that for high intensity swirl, the Reynolds number had a strong effect on the

velocity distribution. With the advancement of technology and the limitations set off by

the early methods, new techniques have been sought, as presented next.

3.1.2.2 Photographic and Videographic Techniques

Photographic and filming techniques have been used successfully to examine the

flow pattern inside the hydrocyclone. However, they fail to provide detailed information

on local velocities. Also, the reliability of the data obtained by the photography method is

50

sometimes questionable. The major constraint of such techniques is its inability to allow a

rigorous analysis of flow reversals and short-circuiting flows. Some of the studies that

have made use of these techniques are discussed in this section.

Ohashi and Maeda (1958) tracked the velocity field of polystyrene particles in a

75-mm hydrocyclone by illuminating the particles with stroboscopic flashes at controlled

time intervals. Obtained results were consistent with Kelsall's (1952) measurements of

axial, reversal and re-circulating flows, while the radial velocity was found to be smaller

and asymmetrical with respect to the cyclone axis. Bradley and Pulling (1959) also used

photographic techniques to examine the movement of a dye injected into transparent

hydrocyclones.

The three-dimensional flow pattern in a 75-mm hydrocyclone was measured by

Knowles et al. (1973) utilizing high-speed movies of Anisole droplets. They also studied

the effects of the air core on the velocity profiles and found similarities in the tangential

and axial components, with and without an air core. The radial velocities, when no air

core was formed, were relatively smaller in magnitude and in agreement with Ohashi and

Maeda (1958).

Bhattacharyya (1984) examined the flow pattern of dye injection through the side

and end walls of a 105-mm hydrocyclone, utilizing photography. They observed that the

locus of zero axial velocity was unaffected by the length of the vortex-finder up to 0.6Dc

and also that it was not sensitive to cone angle or underflow orifice size.

Ketcham et al. (1984) employed high-speed video to track solid particles in a 100-

mm hydrocyclone. The authors noticed that particles released near the vortex-finder wall

ended up being trapped in the boundary layer. Coarser particles formed a thin film along

51

the vortex-finder wall and eventually reported to the overflow, while particles in the

range between d50 to 3d50 experienced 20 to 40% less “short-circuiting" when introduced

at the bottom of the inlet pipe, as compared to those introduced at the top.

3.1.2.3 Laser Induced Fluorescence (LIF)

Weispfennig and Petty (1991) studied the flow structure in a LLHC using the LIF

visualization technique. Different types of inlets were studied including an annular entry.

They observed that vortex instability and recirculation zones were strongly dependent on

the swirl intensity of the flow and a characteristic Reynolds Number.

3.1.2.4 Laser Doppler Velocimetry (LDV)

Understanding of the fluid flow phenomena within the hydrocyclone has

advanced to a great extent with the increased sophistication of LDV optical and signal

processing systems. The LDV technique has become a common non-intrusive flow

measurement and diagnostic tool for transparent cyclone prototypes. The LDV is not as

complicated and time-consuming as the photographic and filming technique and does not

cause flow distortion like the Pitot tubes (Chakraborti and Miller, 1992). Following is a

discussion of some of the studies that have made use of this technique.

Dabir and Petty (1984, 1986) used LDV to measure the axial and tangential

components of the mean velocity in a 3-inch (76-mm) hydrocyclone operating without

either a solid phase or a gas core. Flow visualization using dye injection revealed

multiple flow reversals in the vortex, which were consistent over a considerable length of

the hydrocyclone. They also observed a little radial mixing between the secondary flows

52

and the outer helical flow. Their study showed that for some designs and operating

conditions, a jet-like flow occurred from the apex region to the vortex finder, while the

multiple flow reversals in the core region disappeared when the vortex-finder size was

larger than the apex diameter. According to the authors, a 2:1 contraction ratio in the

vortex finder caused four distinct simultaneous countercurrent flows in the conical

section of the hydrocyclone.

The LDV technique was used by Gu and Li (1987) to measure tangential and

axial velocities of heavy-medium and water-only in cyclones. The authors observed that

the vortex finder wall thickness had an influence on the velocity profiles, especially on

the loci of zero axial velocity. They also observed that reducing the air core diameter

resulted in a more stable flow pattern and higher central flow velocity.

Luo et al. (1989) measured the three-dimensional velocities in a conventional 82-

mm hydrocyclone using LDV, and compared them with those obtained with a water-

sealed hydrocyclone (with no air core). They noted that the water-sealed cyclone

experienced a significant increase in tangential velocity and a wider zone of zero axial

velocity. The radial velocity in both cyclones had a distribution similar to that of the

tangential velocity, in disagreement with Kelsall (1952) and other observations.

Tangential and axial velocity measurements were carried out by Hsieh (1988) in a

75-mm hydrocyclone utilizing LDV. Tangential velocities were measured at 0° and 180°

to examine the axi-symmetry of the flow, while axial velocities were measured at four

different angles 90° apart. The author used water and water-glycerol mixtures to simulate

the variation of slurry viscosity due to the concentration of solid particles in the liquid

stream. The results revealed multiple flow reversals in the region between the vortex

53

finder wall and the cylindrical wall. Short-circuiting flows were predominant at the back

side of the tangential inlet, especially with the increase in fluid viscosity and flow rate.

Monredon (1990) continued Hsieh’s (1988) work measuring the velocity profiles

in a 75-mm and 150-mm hydrocyclones utilizing LDV. The study revealed new

information on the effect of several design variables, namely, vortex finder diameter,

spigot diameter and cone angle, on the velocity profiles. The author observed that with

increased vortex finder and spigot diameters the locus of zero axial velocity remained the

same in the cylindrical section, while shifting inwards in the conical section.

Later, Devulapalli (1997) scaled-up the model proposed by Hsieh (1988) to

account for larger hydrocyclone geometries. The author validated the accuracy of the

model by comparing the predicted velocity profiles with new LDV experimental data.

The predicted classification curves had good agreement with the LDV experimental

curves for concentrated suspensions obtained in a 250-mm hydrocyclone.

Peng et al. (2001) utilized Laser Doppler Anemometry (LDA) to study the flow

patterns in a tangential inlet gas-solid cyclone separator. Results showed that a

recirculatory flow pattern in the axial/radial directions exists in the upper part of the inlet

region. According to the authors, this phenomenon is associated with secondary flows

induced by the swirling motion in the boundary layer by the cyclone lid.

The internal 3D flow patterns in a hydrocyclone were studied by Fisher (1998),

and Fisher and Flack (2002) using LDV. Data collected are comprehensive and of high

quality, and can be used as benchmark data for the development of computational

models. The integrated velocities yielded mass flows within 3% of the measured mass

flows, suggesting high accuracy of the velocity measurements. A total of seven axial

54

planes were examined, and the inlet flow rate and rejects rate were independently varied

to identify the effects each had on the flow field. Observations confirmed that velocity

profiles behave like a forced vortex at the region near the air core, and like a free vortex

in the outer region of the flow near the cyclone wall. The tangential velocity was found to

be the most dominant velocity component. Its magnitude increased in the inner forced

vortex region as the reject rate was increased. However, the radial velocity was found to

be most crucial for the separation process. They also noticed reverse flows in the axial

velocity profile in the near inlet region, but they disappeared in the outlet region.

Many other researchers (Fanglu and Wenzhen, 1987; Jirun et al., 1990; Fraser and

Abdullah, 1995; Hsieh and Rajamani, 1991; He et al., 1997 and Erdal, 2001) have used

this technique to measure the velocity field and turbulence intensities. Most of them have

then used the collected data to validate their CFD and modeling work.

3.1.2.5 Electrical Impedance Tomography (EIT)

The EIT technique can be used to measure internal flows non-intrusively, fast and

with a high degree of accuracy, as the measurements are not affected by the opacity of

the feed slurry. Since measurements are taken at 2 milliseconds per frame, fast

fluctuations in the internal flow can be measured.

Gutierrez et al. (2000) used EIT for controlling the hydrocyclone underflow

discharge. The authors conducted a series of experiments to investigate the distribution of

solids in a 44-mm hydrocyclone. They examined the particle distribution inside the

separator, the formation of an air core as a function of the feed rate and solids

55

concentration, and the relationship between the air core behavior and the type of

underflow discharge, namely, spray or rope.

Cullivan et al. (2001, 2003, 2004) used EIT and ultrasound tomography (UST)

among other methods to examine the flow field structure within the hydrocyclone.

3.1.2.6 Particle Dynamics Analyzer (PDA)

PDA is a new type of laser surveying instrument based on laser doppler theory

and is a non-intrusive measurement technology. It does not disturb the flow field and can

simultaneously provide accurate results on the velocity, diameter and concentration of

both the dispersed particle and the liquid-phase.

Chu and Chen (1993) used PDA to directly measure the radial and axial velocity

components and the size and concentration of solid particles at selected positions within a

transparent hydrocyclone. They were able to obtain profiles of the solid particle flow

field, and observed that the maximum concentration was at the loci of zero axial velocity,

and that separation of some particles took place in the inner helical flow. Su and Mao

(2006) employed a three-dimensional Particle Dynamic Analyzer (3D-PDA) to measure

the two-phase flow pattern of a gas-solid stream in a square cyclone separator with a

downward gas-exit. The authors observed that the center of the flow field deviated from

the geometrical center of the cyclone, having a strong swirling region in the central part

and pseudo-free eddy region and a weak swirling intensity near the cyclone wall

(Rankine eddy). They also noticed a local vortex forming at the corners of the cyclone.

56

3.1.2.7 Particle Size Determination

Particle size analyzers based on laser diffraction (e.g., Malvern laser particle size

analyzer) are widely used in the lab for both online and offline measurements. Many of

the techniques available for offline determination of particle size were described by Allen

(1983). Commercially available online slurry particle size analyzers have been based on

laser diffraction, ultrasound, distance measurement, and laser scattering (Sparks and

Dobbs, 1993). The latter technique is based on a constant speed scanning laser beam-

microscope system. The particle size distribution experimental data used to validate the

mechanistic model developed in this study was acquired using the Coulter Counter (CC)

Multisizer equipment similar to the Malvern.

3.2 CFD and Numerical Studies

Rigorous phenomenological models based on fluid dynamics have three main

components: the mass balance described by the continuity equation, the momentum

balance described by the Navier-Stokes equations, and the turbulence effect closure

model. Solving the continuity and the Navier Stokes equations for non-turbulent flow can

be achieved with the computational resources available today for simple or complex

geometries. However, at large Reynolds numbers current resources struggle to attain the

instantaneous velocity and the pressure fields, even for simple geometries (Hubred et al.,

2000). Slack et al. (2003) proposed an automated CFD modeling interface for

hydrocyclone design, providing the non-CFD analyst or design engineer with a flexible

hydrocyclone simulation tool.

57

CFD has been used in the past to numerically solve the governing equations and

to study hydrocyclone turbulent flow phenomena. Choosing an appropriate turbulence

model and the numerical solution scheme is paramount for achieving good results.

Traditional turbulence models, such as the standard form of the Prandtl mixing-length or

the k-є model, are not suitable for the highly complex turbulent flow in the hydrocyclone.

However, the use of more elaborated turbulence models may increase computational

times and requirements to inconvenient or uneconomical limits.

To deal with these limitations and requirements, some researchers have used a

modified Prandtl mixing-length model along with some simplifications and the use of

flow symmetry (Rajamani and Hsieh, 1988; Hsieh and Rajamani, 1991; and Rajamani

and Devulapalli, 1994). Hsieh and Rajamani (1991) used a stream function-vorticity

version of the equation of motion and the symmetry assumption to solve the Navier-

Stokes equations in two dimensions. The authors observed good agreement between the

CFD simulations and the experimental data they collected using LDV. Dai et al. (1999)

extended the work of Hsieh and Rajamani (1991) to account for the air core effect,

occurring in the inner region, also using a modified k-ε turbulence model. The authors

presented good agreement between the numerically simulated three-dimensional velocity

profiles and the data measured using LDA. The study showed that improving the flow

pattern in the cylindrical section reduced significantly the energy dissipation in a

hydrocyclone. However, according to Delgadillo (2006), the modified Prandtl mixing-

length model for the axial and tangential velocity components is not an accepted standard

in CFD, nor has this hypothesis been conclusively proven.

58

The standard k-є model has also been modified by other authors to account for the

anisotropic characteristic of the turbulent viscosity in the hydrocyclone (Malhotra et al.,

1994; Dyakowsky and Williams, 1995, 1996; and He et al., 1997, 1999). This modified

k-є model is sometimes referred as Renormalization Group (RNG). Results published by

Malhotra et al. (1994) show that the modified k-є model considerably improved the

velocity profile predictions, but only in the absence of an air core. He et al. (1997, 1999)

also reported good results in the prediction of the flow field. They utilized a three-

dimensional model in a cylindrical coordinate system and curvilinear grid. However,

according to Delgadillo (2006) there is no conclusive evidence that such modifications to

the closure model adequately predict the turbulence in hydrocyclones and therefore, other

alternatives were sought.

In a series of studies, Shubert and Neesse (1980a, 1980b) investigated the

turbulence phenomenon inside the hydrocyclone, using electrodes to measure it. The

authors concluded that the turbulence dispersion coefficient was a function of tangential

velocity and the diameter of cyclone’s body. They generated a classification curve based

on the turbulent dispersion of solid particles.

Morandi and Salasnich (1998) studied turbulence and bifurcation of the flow

motion in the hydrocyclone by using a Finite Element Method (FEM) based on the

Navier–Stokes equations. They obtained numerical results that were in good agreement

with the experimental data. Nowakowski et al. (2000) presented a multi-continuum

numerical simulation approach for calculating solid-liquid hydrocyclone performance.

They considered particle-particle and particle-fluid interactions derived from lubrication

59

and collision theories, and discretized the governing equations by applying an

unstructured grid consisting of tetrahedral elements.

The Large Eddy Simulation (LES) turbulence closure model was used by De

Souza and Silveira-Neto (2002), capturing the main features of the flow pattern in a 76-

mm diameter water-fed hydrocyclone operating without an air core. The turbulent

viscosity was computed with the Smagorinsky (1990) subgrid scale model. The authors

compared the LES predictions with published experimental data from different

researchers (Dabir, 1983; Hsieh and Rajamani, 1991; and Svarovsky, 1994). The

agreement between simulated and experimental values of pressure drop and axial

velocities was found to be reasonable. However, predicted results for the velocities in the

near wall region were not satisfactory. Therefore, the model requires the tuning of a scale

energy transfer constant with experimental information for each Reynolds number and

the refinement of the mesh.

Cullivan et al. (2003, 2004) incorporated a second-order pressure-strain

Reynolds-Stress turbulence model (RSM) in transient three-dimensional CFD

simulations. They demonstrated that air-core development is transport-driven as opposed

to pressure-driven. The study also showed that the air core is a highly asymmetric helical

structure of alternating radial velocity. This results in a stochastic turbulent transport of

particles between the wall and core flows, mainly in regions of favorable radial velocity.

They later included a full three-dimensional CFD modeling and a high-order differential

stress turbulence model (DSM), including a significant stochastic component, which led

to a new understanding of particle-separation classification within the hydrocyclone. The

authors performed a detailed and comprehensive experimental verification of the

60

predicted flow field structure within the hydrocyclone. Different measurement techniques

were used, including high-speed video, radiography, ultrasound tomography (UST) and

electrical impedance tomography (EIT). Modeling results were confirmed by the

experimental data, indicating that the observed asymmetry throughout the hydrocyclone

results from the single tangential inlet and wall bounded streamline curvature. According

to the researchers, such asymmetry throughout the hydrocyclone plays a key role in

determining the particle separation mechanism.

A comparative study of the four most important turbulence-closure models,

namely, the RNG, the κ–ε, the RSM, and the LES models, was conducted by Delgadillo

and Rajamani (2005). The models were compared for the predictions of air-core

dimension, mass split, and axial and tangential velocities. The researchers concluded that

the LES model better matched the experimental data, mainly due to its ability to capture

detailed turbulence features. However, they also observed that LES predictions were not

very accurate in the near wall region where molecular viscosity has a significant effect.

This is in agreement with observations made by De Souza and Silveira-Neto (2002).

Yablonskii (2003) solved numerically a system of equations describing the flow

of a non-Newtonian fluid with a free surface in a cylindrical-conical hydrocyclone. The

authors studied the influence exerted by the rheological properties of the fluid and by the

defining similarity criteria on the flow hydrodynamics. They calculated the velocity and

pressure fields, as well as the dependence of the thickness of the fluid film on the axial

coordinate. They reported that the tangential velocity component at the film surface first

decays in the axial direction of the cylindrical part and then increases in the conical part

as it becomes narrower. The steepest increase was observed near the film surface. For

61

pseudo plastic fluids, the rate of tangential velocity component decay decreases as the

anomaly of the non-Newtonian properties becomes more prominent.

A review of recent CFD work and new developments in the application of 3D

finite element code to hydrocyclone modeling was presented by Nowakowski et al.

(2004). They examined and summarized some of the most relevant studies and

contributions from many researchers. The authors discussed important factors in the

numerical solution of the model equations, namely, proper representation of geometry,

imposition of boundary conditions and the choice of the turbulence model. They also

outlined the key challenges that still need to be addressed in order to produce a complete

and validated model of the hydrocyclone flow-field, including 1) 3D unstructured grid

tool for geometrical flexibility; 2) Full coupling of the fluid and particle phases using the

approach of Patankar and Joseph (2001); and, 3) Air-core modeling capturing the liquid–

gas interface using the level set method proposed by Osher and Sethian (1988) and

further developed by Caiden et al. (2001). Table 3.3 summarizes the most important CFD

solution developments for the cyclone problem published before 2004.

62

Tabl

e 3.

3 S

umm

ary

of M

ilest

ones

in N

umer

ical

Sol

utio

ns o

f Flo

w in

Hyd

rocy

clon

es (N

owak

osw

kyet

al.,

200

4)

63

Tabl

e 3.

3 (c

ont’d

)

64

Later studies include the work of Doby et al. (2005), who developed a Finite

Element Method (FEM) based on mixed approximation of the velocity and pressure

space. With this numerical technique, the authors performed 3D simulations of

incompressible fluid flow within a SLHC to predict the outlet velocity patterns. This

technique incorporates the boundary conditions and also deals with the complex

geometry of the top entry section. The authors investigated the interaction between the

swirling flow and velocity profile at the outlet, claiming that such formulation offers

significant advantages in the solution of convection dominated internal flows, which have

one inlet and two or more outlets.

Narasimha et al. (2006) developed a CFD model capable of predicting the flow

pattern in the hydrocyclone, including accurate prediction of the flow split, as well as the

size and shape of the air-core. They used the Differential Reynolds Stress Model (DRSM)

and the LES model for the prediction of flow velocities and air-core diameter, along with

the Volume of Fluid (VOF) model for the air-phase. Simulation results were compared

with experimental data, showing that the LES model resulted in an improved turbulence

field prediction leading to a more accurate prediction of the pressure and velocity fields.

The axial pressure profile results suggest that air-core development is mainly a transport

effect rather than a pressure effect, which is in agreement with earlier observations by

Cullivan et al. (2003).

Other recent studies have attempted to compare the different turbulence closure

models and their variations (Matvienko, 2004; Ko et al., 2006; and Kang and Choi,

2006).

65

3.3 Mechanistic Modeling and Theoretical Studies

Theoretical and mathematical models based on the physical principles of motion

of solid particles in a fluid medium have been proposed in the past (Bloor and Ingham,

1973, 1984, 1987; Schubert and Neesse, 1980b; Bloor, 1987; Kang, 1984; Braun and

Bohnet, 1990; Barrientos and Concha, 1992; Monredon et al., 1992; Svarovsky, 1994;

and Mueller and Bohnet, 1998). However, according to Svarovsky (1996) they have not

made a significant impact on the prediction of hydrocyclone performance for industrial

applications, and have been somewhat abandoned in favor of numerical simulations due

to the complexity of highly turbulent multiphase flow. Mass and momentum conservation

equations have been solved mathematically, mainly for incompressible and inviscid

fluids, using the stream function concept in an axis-symmetric configuration.

A comparative study of seven theoretical and semi-empirical hydrocyclone

models, including some of the ones mentioned above, was performed by Chen et al.

(2000). The authors evaluated the validity of these models for practical applications and

found that most of them work well for certain conditions but none of the models could

predict all applications. Therefore, they recommended that more than one model be used

and that some data be obtained to select the most appropriate model for each case.

Kraipech et al. (2006) arrived at similar conclusions when examining empirical models as

discussed earlier. Some theoretical studies are discussed next.

The separation model proposed by Schubert and Neesse (1980b) was based on

turbulent two-phase flow, assuming a homogenous, stationary turbulent field, with the

particles moving under Stokes' Law.

66

A mathematical model of the hydrocyclone based on the hydrodynamic flow

behavior was developed by Hsieh (1988). However, this model was a large CFD

computer code capable of solving numerically the governing Navier-Stokes equations,

employing a modified Prandtl mixing-length model as the turbulence closure, and an

algebraic slip approach to model the particle trajectories in the hydrocyclone. The model

was validated against experimental data collected in a 75-mm glass hydrocyclone. One

limitation of the model is its inability to account for the non-Newtonian behavior of

concentrated slurries and transport of particles by turbulent eddies. Therefore, caution is

advised when applying the model for high feed slurry concentrations.

Braun and Bohnet (1990) developed a theoretical model to describe the separation

efficiency of hydrocyclones in terms of the reduced grade efficiency, G’(x), instead of

using the usual definition that uses the grade efficiency. The so called, true performance

of the hydrocyclone was then described as follows:

(3.1)

The authors described the pressure drop, ϕpΔ , occurring inside the hydrocyclone

using energy dissipation balance, which included the frictional, accelerational, and static

radial pressure gradient components, as follows:

(3.2)

i

u

i

u

pi

pu

VV

VV

MM

xG

&

&

&

&

&

&

−

−

=1

)('

⎥⎦

⎤⎢⎣

⎡−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−⎥

⎦

⎤⎢⎣

⎡

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

⎥⎥⎦

⎤

⎢⎢⎣

⎡+=Δ

i

ouu

i

ooo

ii V

VwpVVwpwpp

&

&

&

&1*

2*

22

2'

2'

2' ρρρ

ϕ

67

The model considered the effects of both feed solids concentration and flow split

ratio and showed a good agreement with the experimental data. The variables used in the

previous equations are:

pM& = mass flow rate of solids [kg/s]

V& = volumetric flow rate [m3/h]

p’ = static pressure [N/m2]

w = radial velocity [m/s]

ρ = flow density [kg/m3]

where the subscripts i, o, and u correspond to inlet, overflow and underflow respectively.

A cylindrical co-current hydrocyclone was used by Lagutkin et al. (2004) for

examining the separation of solid-liquid suspensions. They developed a set of equations

to determine solids removal efficiency and residence time as a function of tangential

velocity, turbulent viscosity, densities and dimensions of the cyclone. Figure 3.1 shows

the model nomenclature. The authors used a relationship for a particle radial motion in

the cylindrical-conical hydrocyclone proposed by Ternovskii and Kutepov (1994), as

follows:

(3.3)

where m is the mass and d is the diameter of a particle of the fineness class under

consideration, vϕr is the particle tangential velocity component, ρm is the density of the

dispersion medium, ρp is the density of the dispersed-phase (solids), r is the radius of the

particle under consideration, ξ is the coefficient of hydraulic resistance (ξ = 24/Re), dr/dt

421

2

22

2

2 ddtdr

rm

dtrdm

rm

p

mr πνρ

ξρρν

ϕ⎟⎠⎞

⎜⎝⎛ ±

⎟⎟⎠

⎞⎜⎜⎝

⎛−±= m

68

is the particle radial velocity component, and vr is the radial velocity component of the

dispersion medium. The upper signs (+ and -) before the terms in Eq. (3.3) apply to the

case when the direction of motion of the particle and flow are opposing, while the lower

signs (- and +) apply to the case when the particle and flow are moving in the same

direction.

Figure 3.1 Computational Diagram for Cylindrical-Conical Hydrocyclone:

1) Cylindrical-Conical Housing; 2) Feed (intake) Pipe; 3) Upper Drain Pipe;

4) Sand Packing (Lagutkin et al., 2004)

69

An equation for solving the particle radial velocity component in Eq. (3.3) was

proposed by Baranov et al. (1996). The authors considered the particle acceleration in the

radial direction (a term that was generally neglected by previous researchers), showing

that radial acceleration exerted a significant influence on separation of particles coarser

than 150 μm. Assuming that the tangential velocity component of the particles

(dispersed-phase) and that of the dispersion medium are equal, that is, neglecting the

slippage of particles in the circumferential direction with respect to the flow, the particle

velocity in the radial direction can be obtained from the following relationship:

(3.3.1)

where B = Qc / 2πh, Qc is the output of the hydrocyclone through the overflow, and A is a

constant defined for the cylindrical-conical hydrocyclone structural and operating

conditions, as the one shown in Figure 3.1, given by:

(3.3.2)

It is also assumed that the resisting force acting on the particle can be determined

from Stoke’s Law, namely,

Re24

=ξ (3.3.3)

⎟⎠⎞

⎜⎝⎛ −+

−=

42

3

31rA

rBm

rB

rA

dtdr

β

β

ρρ

νϕ

⎟⎟⎠

⎞⎜⎜⎝

⎛−

⎥⎦⎤

⎢⎣⎡ +

=p

m

tee

DRmA

1

4)2( 2

70

and the Stoke’s resistance coefficient, β, is defined as:

dmυπρβ 3= (3.3.4)

where υ is the kinematic viscosity of the dispersion medium. In most cases, ξ, should be

computed from the relationship for the transitional region of particle motion, as follows:

(3.3.5) In such cases, β, is defined as:

4.16.0* 26.7 dmυρβ = (3.3.6)

and Eq. (3.3) takes the form:

(3.4)

The constant tangential flow velocity of the dispersion medium, νϕe, from the wall

of the cyclone to the radius, Rte, is defined as follows:

(3.4.1)

where νin is the inlet flow velocity. Ternovskii and Kutepov (1994) defined the radius,

Rte, using the following relationship:

(3.4.2)

32.01.3

−

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛=

DL

Dd cyin

ine ννϕ

2.058.0

)(tan)(25.1 α⎟⎠⎞

⎜⎝⎛−=

DddDR in

inte

6.0Re5.18

=ξ

4.1*

2

2

21 ⎟

⎠⎞

⎜⎝⎛ ±⎟

⎟⎠

⎞⎜⎜⎝

⎛−±=

dtdr

rm

dtrdm r

p

mrνβ

ρρν

ϕm

71

Lagutkin et al. (2004) also demonstrated the influence of the Coriolis force

(acting in the circumferential direction of the hydrocyclone) on the separation of coarser

particles (> 150 μm). According to their findings, the Coriolis effect is more significant

in the core zone of the cyclone due to the sharp increase of the flow tangential velocity

component, which results in a rapid increase of the drift velocity of the system within this

region. In a later study, Lagutkin and Baranov (2004) further examined this phenomenon

also concluding that the influence of the particle radial acceleration is pronounced with

particle sizes coarser than 100 μm.

The Coriolis force acts in the direction opposite to the Coriolis acceleration

displacing a particle in the circumferential direction with respect to the flow. The Coriolis

force is approximated from Stoke’s Law, as:

(3.5)

where rrel ϕϕ ννν −= and the Coriolis acceleration is determined from the relationship:

(3.6) where ωdr = νϕ/r, and the tangential, νϕ, and radial velocity, νϕr, components of the

continuous flow (dispersion medium) are defined by Eq. (3.7) and (3.8), given by:

(3.7)

relcorF βν=

rDRtee

4)2( +

= ϕϕ

νν

dtdra drcor ω2=

72

(3.8)

Rewriting Eq. (3.8) in terms of the flow tangential velocity and the particle radial

velocity component, dr/dt, yields:

(3.9)

A relationship for the acceleration of a particle in the radial direction can be

derived from Eq. (3.3.1) as proposed by Baranov et al. (1996), yielding:

(3.10)

Following, Lagutkin et al. (2004) suggested that Eq. (3.9) be substituted into Eq.

(3.3) for calculating the radial velocity component of the flow, to account for the effect of

Coriolis force. They observed that particles in the zone of ascending flow were slowed by

the Coriolis force, and that their tangential velocity component was much smaller than

the circumferential velocity of the flow. Furthermore, the authors proposed a new

relationship for calculating the radial motion of a particle that accounted for both the

Coriolis force and the effects of particle radial acceleration. The proposed equation was

obtained by substituting Eqs. (3.9) and (3.10) into Eq. (3.3), resulting in:

⎟⎠⎞

⎜⎝⎛ −=

dtdr

rm

r2β

βν

ν ϕϕ

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ +−

−−

+=

β

νν ϕ

ϕ

42

3

321

4)2(

rAm

rmB

rB

rA

rm

rDRtee

r

⎟⎟⎠

⎞⎜⎜⎝

⎛−= 422

2 3rA

rB

dtdr

dtrd

73

(3.11)

When a particle stops moving in the radial direction (dr/dt =0), then the cut size

diameter, d50, can be determined. Particles smaller than the d50 are carried over with the

clarified flow, while the coarser ones are separated and run off with the underflow.

The maximum radius of the hydrocyclone body at which the radial velocity

component of the dispersion medium is equal to zero can be determined with the

following equation proposed by Povarov (1978):

(3.12)

where du and dl are the diameters of the overflow and the underflow outlets respectively.

Thus, when a particle stops moving in the radial direction at r = rz0 (dr/dt = 0 and

d2r/dt2 = 0), it will have 50% (d50) chance of being separated and exit with the underflow.

The cut size, d50, can be calculated by substituting r by rz0 in Eq. (3.11) and using the

proper boundary conditions (dr/dt = 0 and d2r/dt2 = 0), yielding:

(3.13)

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74

Akbar et al. (2001) proposed an equation for the motion of a spherical particle in a

fluid flow, neglecting the interactions with other particles, given by:

(3.14)

The term on the left-hand side of Eq. (3.14) describes the particle inertia, and the

terms on the right-hand side are the forces caused by the particle–fluid interactions as

explained by Kraipech et al. (2005) in Table 3.4. The term mp is the mass of the particle,

up is the particle instantaneous velocity and g is the body acceleration. The densities of

fluid and solid particles are represented by ρ and ρp respectively. When a particle’s

motion is affected by a neighboring particle, the other forces have to be altered, as shown

in Table 3.5.

The effect of the particle–fluid and particle–particle interactions of the flow

within a hydrocyclone was investigated by Kraipech et al. (2005). The authors applied

time scale analysis and showed that particle–particle interactions play a key role only in

the near wall region and close to the air core, owing to lubrication and collision

mechanisms. In the remaining region, particle–fluid interactions were observed to be

dominating.

PGLMLSBasAppDp

pp

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Tabl

e 3.

4 Fo

rces

Cau

sed

by P

artic

le–F

luid

Inte

ract

ions

in T

urbu

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raip

ech

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005)

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76

Tabl

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5).

77

Dwari et al. (2004) developed a mathematical model for predicting particle

separation efficiency and cut size particle diameter. The author also developed a

correlation for predicting percentage removal of particles and retention of particles for a

new type of hydrocyclone, suitable for sand and sand-ash systems.

The proposed relationship for the d50 cut size is given by:

(3.15)

The particle separation efficiency is given by:

(3.16)

By applying dimensional and multiple linear regression analyses to evaluate the

constants and coefficients of the equation, the authors obtained a semi-empirical

relationship for the separation efficiency of particles, as described by:

(3.17)

where a, b, and c are empirical constants obtained by regression analysis to be -0.82,

0.63, 0.82, respectively. The rest of the variables are described in the Nomenclature

section.

Recently, Yablonskii and Ryabchuk (2006) developed a mathematical model for

predicting the separation of suspensions for a non-Newtonian dispersion medium in a

s

f

PR

LVRC

RLQd

ΔΔ−⎟

⎠⎞

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5018

inletatparticleofWtoverflowatparticleofWtinletatparticleofWt

%%% −

=η

c

s

b

i

a

is Dd

VDS ⎟⎟

⎠

⎞⎜⎜⎝

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⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛=

ρρ

ρμη

78

hydrocyclone. The model accounts for the effect of the Coriolis force on the solid-phase

particles, the effect of the Froude number, the Reynolds number, the dimensionless flow

rate parameter, and the rheological properties of the dispersion medium. The set of partial

differential equations describing the separation process was reduced to a set of ordinary

differential equations that were solved numerically. They proposed an equation for the

motion of the solid-phase particle that is affected by the centrifugal buoyancy force, the

drag force, and the Coriolis force, along the r and ϕ axes. The authors described the

effect of the determining similarity parameters and the dispersion medium rheology on

the concentration distribution.

The mechanistic modeling approach followed in the present study is described in

Chapter 5.

3.4 Factors Affecting Solid-Liquid Separation in Hydrocyclones

3.4.1 Effect of Geometry

The geometrical configuration and the different dimensions of each component of

the hydrocyclone, such as the cone angle, length and diameter of the cylindrical chamber,

length and diameter of the vortex finder, outlet orifice diameter and feed pipe diameter, have

been found by several researchers to have a significant influence on particle

separation/classification performance. Hence, the understanding of the impact of each

component size and geometry on performance could lead to significant improvements to

hydrocyclone design.

79

3.4.1.1 Effect of Feed Pipe Diameter

Salcudean et al. (2003) studied the effects of changing the different components of

the cyclone. They found out that the most critical variable was the diameter of the feed pipe.

A decrease in feed pipe diameter promotes higher feed velocities while the mass flow input

is kept constant, thus, decreasing the number of particles carried over by up to 80%.

However, an increase of particle residence time was also observed as a result of smaller feed

diameters, which can lead to flocculation of particles. The optimum size of the feed diameter

was found to be half of the width of the annular chamber.

3.4.1.2 Effect of Vortex Finder Length and Orifice Diameter

The diameter of the vortex finder outlet has a significant effect on cut size, flow

split, and hence, on separation and fractionation. Salcudean et al. (2003) observed that an

increase in the vortex-finder diameter led to an increase in the number of particles carried

upward, thus, decreasing separation efficiency.

3.4.1.3 Effect of Spigot Diameter

Ahmed et al. (1985) studied the effect of apex diameter on the pattern of

solid/liquid ratio distribution within a hydrocyclone using a 100-mm hydrocyclone.

Measurements were taken along orbit radii at several horizontal level positions along the

cyclone body length. The results provided a complete pattern of pulp-solid content

distribution for different spigot sizes. Also, an empirical equation relating the pulp

solid/liquid ratio to apex diameter was proposed.

80

3.4.1.4 Effect of Apex Cone Height

Experimental and simulation studies were conducted by Yoshida et al. (2003) to

examine the effect of the apex cone height on particle separation performance. They

found that the main effect of the apex cone was to decrease the cut size and to increase

the collection efficiency. In general, the inlet velocity determines the optimum apex cone

height. As feed velocities increased, the optimum height changed to a lower position.

3.4.1.5 Effect of Inclination Angle on Cut Size

Banisi and Deghan-Nayeri (2005) examined the influence of the hydrocyclone

inclination angle on cut size using a 75-mm Krebs cyclone. They found out that an

increase in inclination angle resulted in a cut size increase, in particular for angles above

45 degrees from horizontal and feed solid concentrations above 10%.

3.4.2 Effect of Particle Properties

The effect of the properties of the solid-phase on hydrocyclone performance was

examined by Salcudean et al. (2003). They observed a decrease in particle carry-over as

particle density increased. They also found out that the magnitude of this effect was

affected by the particle diameter and length. The carry-over sharply decreased with larger

particle diameters, as would have been expected. This is in agreement with Dwari et al.

(2004) observations. They reported that larger particles are removed easily, thus, with an

increase in particle size, at a particular inlet pressure, separation efficiency increases.

The effect of particle length on separation was found by Salcudean et al. (2003) to

be closely related to the values of particle diameter and density. The particle diameter at

81

which the trend reverses depends on the particle density due to the variation of the drag

coefficient.

3.4.2.1 Effect of Feed Solids Concentration

The influence of feed solids concentration on the separation efficiency of the

cyclone has been recognized in the past by several authors. Braun and Bohnet (1990)

developed and tested a theoretical model that considers the effects of both feed solids

concentration and flow split ratio on separation efficiency and pressure drop. The results

suggest that an increase in feed solids concentration, while keeping all other operating

parameters constant, leads to a coarser cut size, reduced separation sharpness and higher

pressure drop across the cyclone. According to the authors, at higher flow rates the

pressure drop increases significantly with both feed concentration and flow split ratio.

They concluded that this is partly caused by hindered settling, an effect produced when a

large number of particles moving radially outwards increase the velocity of the fluid

flowing towards the axis of the cyclone to satisfy continuity. High particle concentration

promotes particles hampering the radial motion of one another and limiting the capacity

of the apex valve, and this in turn produces changes in the flow field within the

hydrocyclone and causes additional particles to be entrained by the overflow promoting

the formation of a rotating bed of solid particles near the exit (Braun and Bohnet, 1990).

3.4.2.2 Particle-Fluid and Fluid-Particle Interactions

Kraipech et al., (2005) investigated the effect of the particle–fluid and particle–

particle interactions with the application of a time scale concept. They observed that the

82

liquid–particle interaction (drag) play a crucial role in the main body of a hydrocyclone.

However, for particle–particle interactions both the lubrication and collision mechanisms are

predominant within the regions near the wall and the air core. They concluded that these

interactions play a key role on separation efficiency and that the results of solid mechanics

should also be incorporated in modeling particle–particle collisions in the vicinity of the

hydrocyclone walls, especially when solids concentrations are significant.

3.4.3 Effect of Temperature and Pressure

A CFD model was used by Shi et al. (2006) to predict the pressure drop and

velocity profiles in cyclones at high temperatures and high pressures. The results showed

that density had a considerable effect on the pressure distribution, while the effect of

viscosity was insignificant. Temperature increase led to decrease in tangential velocity,

while the reverse flow in the center of the cyclone became weaker, resulting in a decrease

in the cyclone’s collection efficiency. On the other hand, an increase in pressure led to an

increase in the collection efficiency for the same inlet velocity. Fluid density increases

with pressure, and this in turn increases the tangential velocity in the outer vortex region.

Su and Mao (2006) studied experimentally the effect of cyclone wall temperature

on the flow field. They observed that the flow field became more uniform with increased

suspension temperature. They also noticed that local vortices at the corners were

weakened and the swirling intensity lowered, which led to decreased total mean

separation efficiency from about 81 % to 76.5 %. These results are in agreement with

observations by Shi et al. (2006).

83

3.4.4 Effect of the Air Core

The air-core formed in the cyclone is a very important internal structure of the

cyclone. Stability of the flow field is necessary for effective performance. The effect of the

air core on the main flow field was investigated by Luo and Xu (1992) concluding that it is

detrimental to particle classification. They observed that the air core enhanced instability

and asymmetry of the flow field and disturbed the regular distribution of classified particles.

Many researchers have neglected the effect of the air core in their modeling and simulation

work for simplicity. However, this simplification can lead to inaccuracies in the prediction

of the flow field and overall hydrocyclone separation efficiency.

Some of the investigators that have addressed the effects of the air core are

Barrientos et al. (1993), Dyakowsky and Williams (1995), Concha et al. (1996), and

Narasimha et al. (2006), among others.

3.4.5 The Fish-Hook Effect in Classifiers

The Fish-Hook effect consists in an increase in the recovery of fine particles in

the underflow with decreasing particle size. Patil and Rao (2001) experimentally

examined the factors affecting the recovery of very fine particles. They found that

particle sizes at which this effect occurs is mainly a function of feed size distribution and

solids concentration, and is less dependent on the design variables. This effect has also

been studied by Nageswararao (2000), Kraipech et al. (2002), and Schubert (2003).

3.5 Instrumentation and Online Control of Hydrocyclones

Monitoring and controlling the operation of hydrocyclones is important as

downstream processes could be seriously affected by particle size variations in the

84

cyclone outlet streams. The classifying efficiency parameter of the hydrocyclone, d50,

cannot be measured directly. Thus, it is estimated from indirect or empirical methods

based on the relationship between the weight fraction of each particle size in the overflow

and underflow streams. In practical applications, the corrected cut size, d50c, is obtained

by assuming a fraction of the heavier particles that can report to the overflow stream.

This is equivalent to the fraction of liquid in the underflow. A good estimation of d50c is

important for obtaining the overall efficiency. Any deviation from a desired d50c value

can only be re-established by altering the operating conditions and/or geometry of the

hydrocyclone. Monitoring changes in d50c is achieved by sampling both outlet streams.

Eren and Gupta (1988) developed a computerized control system and various

control algorithms for the automatic control and optimization of hydrocyclones. The

automatic control is achieved by manipulation of the operational parameters, such as the

spigot diameter, vortex finder height, inlet flowrate, and the density of the slurries, for a

desired value of d50c. The output signal d50c cannot be sensed directly and thus, needs to

be calculated from the operational parameters. The accurate prediction of d50c is essential

to generate the control signals for the actuators.

The application of Artificial Neural Networks (ANN) was proposed by Eren et al.

(1997) to substantially improve the accuracy in the estimation of d50c, incorporating

various non-conventional operational variables, such as water and solid split ratios,

overflow and underflow densities, apex and spigot flowrates, as the input parameters.

Despite the accurate predictions of d50c obtained by applying the ANN technique,

the main drawback is its inability to transfer the acquired knowledge to the user, as the

trained network is represented by a collection of inaccessible weights. Fuzzy logic

85

systems, which make use of human understandable rules, seem to be more appropriate.

Fuzzy set theory is capable of handling vagueness and uncertainty in most engineering

applications, allowing the incorporation of intelligent and human knowledge to deal with

each considered case. This enables modeling of human observations, expressions and

expertise. The approach seems to be suitable for d50c determination.

In that sense, Wong et al. (2003) suggested the practical use of fuzzy interpolation

rule for multidimensional input spaces for determining d50c. They used the improved

multidimensional fuzzy interpolation technique to generate the d50c of the hydrocyclone.

They showed that the sparse fuzzy rule base, extracted from the observed d50c can

improve in-line hydrocyclone control. Karr and Weck (1998) also investigated fuzzy

systems for modeling hydrocyclones, among other fine particle separation equipment.

86

CHAPTER 4

EXPERIMENTAL PROGRAM

4.1 Introduction

This chapter describes the experimental work by Culwell et al., (1994), a group of

oilfield researchers. These data are made public for the first time in the present study. The

experimental program was aimed at understanding the solids removal performance of

small diameter SLHC. Details of the experimental program, tested SLHC equipment,

definitions of pertinent separation parameters, and a summary of obtained results are

described in this chapter. Also described in detail are the data handling and compilation

process that were performed as part of this thesis. This includes the development of a

hydrocyclone database management system to facilitate the analysis of the experimental

results and the mechanistic modeling verification process.

4.2 Test Objectives and Scope

The main goal of the experimental work was to establish whether small diameter

hydrocyclones, such as the Mozley 1-inch and 10-mm SLHC, could be used to efficiently

remove oilfield solids from produced water and make it suitable for reinjection, as an

alternative to the use of filtering media. The quality of water suitable for reinjection must

meet certain criteria to comply with special regulations in order to prevent injectivity

decline in the reservoir.

87

4.3 Applications of SLHC

Produced water is treated for disposal at the surface or injection back into the

reservoir to enhance production, or in some cases for downhole disposal. Efficient

removal of solids and fine particulates is critical for water injection treatment systems in

order to prevent plugging of the zone of reinjection, which can cause injection decline.

Water cleaning is usually achieved utilizing different types of filters. The use of small

diameter SLHC, also called mini-hydrocyclones, is an attractive alternative to the use of

filters offering continuous operation at lower costs. Most available filters are bulky and

require back-washing, and / or chemical additives to achieve maximum performance. In

most cases, filter performance is reduced by excessive oil contamination.

4.4 Experimental Setup

Culwell et al. (1994) presented the range of conditions, equipment setup, and

experimental facility for the field tests that they conducted. The experimental work was

completed in two different phases. Phase I was carried out in the United Kindom and

corresponded to laboratory evaluation of the cyclones under simulated oilfield conditions.

Phase II of the program focused on the field examination of the SLHC for the removal of

solids from produced water. More than 400 field tests were completed between 1992 and

1993 in La Habra, California. The efficiency of 1-inch and 10-mm diameter

hydrocyclones for solids removal was investigated over a wide range of conditions and

cyclone configurations. These included different sizes of vortex finders and spigots.

Bundles of cyclones in parallel and two in series (dual configuration) were tested to

88

determine the most efficient configuration. The effects of different pressures and different

pressure drops between the overflow (O/F) and the underflow (U/F) were also examined.

4.4.1 Test Site Description

The test site was located at the Murphy-Coyote Field in California, approximately

one mile south of the former La Habra laboratory facilities property of Chevron and close

to the lease water treatment facility. The site was chosen owing to the availability of a

suitable feed stream of produced water. Figure 4.1 shows a schematic of the test site and

its main components.

4.4.2 Experimental Procedure

The source water for the tests came from a 5,000 bbl residence time settling tank

that was fed from a set of horizontal free water knockouts (FWKO’s). The water had an

oil content of 60-300 mg/L (Black Death oil). A six-stage Moyno progressing cavity

pump with an operating range of 24-50 gpm at 90-350 psig fed the test loop. The main

components of the loop were a Hydropack Liquid-Liquid Hydrocyclone (LLHC), a set of

two SLHCs subject to the evaluation, and a solids injection / dosing system, as shown in

Figure 4.2. The upstream LLHC was configured to reduce the oil concentration to about

40 ppm. The solids concentration was controlled by the injection of solids slurry with a

small Moyno pump. For most of the experiments, the slurry was made of produced water

and an oilfield solids concentrate (tank bottoms) in a 55-gallon drum. Solids

concentration was controlled by varying pumping flow rates.

89

Figure 4.1 Schematic of Test Site and Experimental Setup

90

A maximum particle size of about 60 μm was controlled by means of a strainer

screen upstream of the SLHC to avoid clogging of the cyclones. The underflow pressure

for each of the cyclones was either atmospheric or set up with a maximum backpressure

of 25 psig. For atmospheric conditions, the underflow stream was drained into a 30-

gallon drum, and was then recycled or sent to a pit. In the case of back-pressured

configuration, the underflow streams were hard piped into the loop and recycled back to

the 55-gallon drum.

4.4.3 Description of Tested Equipment

The research focused on small 1-inch and 10-mm diameter SLHCs. Tested

equipment included a Mozley 10-mm x 40 cyclones assembly and a 1-inch x 20 cyclones

assembly. The operating principle of both cyclones is similar and is described in Chapter

2.

4.4.3.1 Mozley 10-mm x 40 Hydrocyclone Assembly

This unit consists of forty 10-mm hydrocyclones housed in a vessel designed

according to BS:5500:1991:CAT 2 pressure code, manufactured from Stainless Steel

Grade 316 S12. The cyclones are manufactured in 96% Alumina Ceramic or in L167

Polyurethane with 96% Alumina Ceramic inserts. Operating temperature ranges from

95oC to 130oC when the all-ceramic units are fitted. Three different vortex finder caps are

available in sizes of 3.2 mm, 2.6 mm, and 2.0 mm, enabling the cyclone to yield d50 cut

points of about 2 to 5 microns (SG 2.6). Body inserts with spigots having diameters of

2.0 mm, 1.5 mm and 1.0 mm allow for the control of volume split and underflow density.

91

Figure 4.2 SLHC Solids Dosing / Injection System and Test Setup

Flow rates in the range of 4 to 15 m3/h are attained by adjusting the vortex finder

size and pressure drop. Blank vortex finder and dummy cyclones can be used to reduce

the capacity of the assembly by taking some hydrocyclones out of operation. To control

the volume split to the underflow, a restrictor plate can be fitted to the outlet of the

underflow conical section. This allows the use of larger hydrocyclone spigots reducing

the incidence of spigot blockage. Restrictor plates are available in outlet diameters

ranging from 9.4 to 3.2 mm and are fitted with a single ceramic lined outlet inserts. The

assembly feed, overflow, and underflow pipes diameter is 50 mm (nominal).

92

4.4.3.2 Mozley 1-inch x 20 Hydrocyclone Assembly

This unit consists of twenty one-inch diameter hydrocyclones housed in a vessel

designed according to BS:5500:1991:CAT 2 pressure vessel code, manufactured using

Stainless Steel Grade 316 S12. The cyclones are manufactured from either L167

Polyurethane or from 96% Alumina Ceramic with L167 Polyurethane sleeves. Operating

temperature is up to 95oC. Two different vortex finder caps are available in the sizes of

7.0 mm and 5.5 mm, enabling the cyclone to yield d50 cut points of 4 to 6 microns (SG

2.6). Spigot caps with diameters of 3.2 mm and 1.5 mm allow for the control of volume

split and underflow density. Flow rates in the range of 10 to 24 m3/h (for the assembly

unit) are attained by adjusting the vortex finder size and pressure drop. Blank vortex

finder and dummy cyclones can be used to reduce the capacity of the assembly by taking

some hydrocyclones out of operation.

To control the volume split to the underflow, a restrictor plate can be fitted to the

outlet of the underflow conical section. This allows the use of larger hydrocyclone

spigots reducing the incidence of spigot blockage. Restrictor plates are available in outlet

diameters ranging from 9.4 to 3.2 mm and are fitted with a single ceramic lined outlet

inserts. The assembly feed, overflow, and underflow pipes diameter is 50 mm (nominal).

4.4.4 Fluid Properties

The continuous-phase consisted of produced oilfield water with traces of oil

having the following properties:

93

Temperature: 100-160 oF (37.8 – 71.1 oC)

Oil API gravity: 29o

Water specific gravity (SG), avg: 0.989

Differential oil-water specific gravity: 0.133

Mean inlet oil droplet size: 5-15 μm

Inlet oil concentration: 20-100 ppm

4.4.5 Properties of Solid Particles

The oilfield solids used in most of the experiments were sediments taken from the

bottoms of oilfield tanks. In some cases, silica flour was used instead of the oilfield

solids. Solids were stored in a 55-gallon drum provided with a slurry-mixer to

homogenize the slurry concentration. The drum was shoveled, stirred, and then small

samples were shoveled to the Solids Slurry Injection Drum where they were pumped by a

small Moyno Solids Pump at varying rates to provide a wide range of solids

concentrations. However, there was no complete control of the solids concentration since

produced water used for the experiments contained a small amount of organic

particulates. The feed and underflow solids were characterized by means of X-Ray

fluorescence and electron microscopes (scanning and elemental resolution). The main

bulk mineral composition included: Calcite, clay and Mica. Also present were: Quartz,

Potassium, Feldspar, Plagioclase, Pyrite and Dolomite. The average density of the solids

was about 2.0 gr/cc. The mean particle size was 14.4 μm with a maximum size of about

60 μm. In some tests, silica flour with an average particle density of 2.2 gr/cc was used.

The range of solids concentrations was from 40 to 370 mg/L.

94

4.4.6 Test Configurations

The experimental program included a variety of equipment configurations and

geometries. Tests were performed by setting a single cyclone (solo) or bundles of

cyclones in parallel and two in series (dual) to determine the most efficient setup. Both

cyclones were tested with different vortex finders and spigot sizes, and varying the

number of blanked cyclones. The effect of different flowrates, inlet pressures, and

overflow/underflow counter-pressure was also examined by the researchers. Table 4.1

presents a summary of geometries and configurations of the tested hydrocyclones.

Table 4.1 Geometrical Configurations of Tested Hydrocyclones

Hydrocyclone Unit

Vortex Finders (mm)

Spigots (mm)

1-inch 2.0 / 5.5 3.2 / 2.2

10-mm 2.0 / 2.2 / 2.6 1.0 / 1.5

4.4.7 Data Acquisition

Flow rates, pressure, and temperature were measured at different points in the

loop, as shown in Figure 4.1. The data were collected through a real time telemetry

system located in a trailer adjacent to the test facility where all data were processed.

4.4.7.1 Measurement of the Oil Concentration

Oil concentration in the feed stream was determined by solvent extraction of the

oil from water that contained 1,1,1-trichloroethane (TCE) and using a spectrophotometer.

95

4.4.7.2 Measurement of Particle Size and Solids Concentration

Particle size and total solids concentration were determined by direct sampling of

water at the different sampling points located at the inlet, overflow and underflow; then

filtering the sample to extract the solids; and finally measuring and counting the particles

by means of a Coulter Counter (CC) Multisizer electronic device.

The CC was calibrated using latex spheres, which produced accurate reproducible

results, as long as oil and solvent were not present. The presence of oil in the feed stream

represented a main challenge and a source of data processing errors. The measurement

procedure was carefully formulated to avoid counting oil droplets as solids. Other

difficulties experienced included: different characteristics of oily solids from plain solids;

solids alteration and disintegration of organic solids by TCE; and coalescence,

agglomeration and attrition of solids. According to the researchers, the most successful

technique was to filter each sample, wash the filter paper with solvent, dry the paper, and

finally loosen the solids by suspending them in isoton and using sonic vibration.

4.5 Data Preparation and Handling

4.5.1 Data Compilation

Data from different experimental studies and different cyclones were recovered

from a set of 27 different 3.5” floppy disks, most of them in MAC format. The data

consisted of different spreadsheets, Coulter Counter files, plots, figures, macros,

documents, and text delimited files. These data files corresponded to different oilfield

testing of LLHC and SLHC performed between 1991 and 1993. Tested equipment

included Vortoil, Hydroswirl, Mozley SLHC, and other cyclone separators.

96

The data compilation process included the inventory of available electronic and

hardcopy records, data file conversion from MAC to PC files and disk recovery process,

and data files organization. Table B.1 in Appendix B contains an inventory of the

available floppy disks and a summary of their information content.

4.5.2 Data Integrity Evaluation

4.5.2.1 Review of Data Files and Test Procedures

This process involved the review of files content, data filtering and sorting, and

the understanding of testing and data acquisition procedures. This was accomplished

through the examination of electronic data files, test reports and documentation (Culwell

et al., 1994), field memos, equipment manuals, and data printouts. After completing this

phase, a set of surveys or questionnaires were prepared for interviewing key personnel

involved in the research to pursue missing data, clarify unknown information and become

familiar with the experimental work.

The review process shed some light about the origin of the data, data integrity,

field-testing practices, fluid properties and test conditions, main sources of uncertainty,

unreported data, used instrumentation and specifications of the tested cyclones and other

test facility equipment.

4.5.2.2 Data Auditing

A rigorous process was carried out that made possible the amendment and

compilation of all available data sets. The process involved thoroughly examining

97

hardcopies to pursue unreported data, missing or damaged records, scan for typos, data

inconsistencies and/or mishandling. This was done to improve data quality and integrity

and estimate the uncertainty and confidence level of the available information.

The auditing process revealed the occurrence of partially or completely missing

electronic records of some test runs, unreported values such as the head temperature, data

swap between different test runs, mistyped values of oil and solids concentrations, inlet to

outlet pressures contradictions, and overlapped records of some data sets from dual

cyclone experiments ran in series. Other less relevant discrepancies were observed in the

determination of cut size diameters. A summary of the most common problems and

discrepancies encountered is presented in Table B.2 in Appendix B.

4.6 Data Processing and Evaluation

This section presents the data processing approach, including a detailed

description of the methods and techniques used to plot and present the experimental data

results to facilitate the analysis and modeling processes. These include discrete volume

frequency and cumulative volume particle size distribution plots, as well as separation

efficiency plots and statistical parameters used to establish equipment performance

confidence under a given set of operating conditions.

4.6.1 Discrete Particle Size Distributions

Representative size intervals, ∆d, were chosen based on a characteristic particle

diameter corresponding to the midpoint of the interval. These size intervals were

considered to be large enough to contain a representative number of particles, but yet

98

small enough to obtain sufficient detail for each characteristic diameter. The particle

diameter of the samples taken varied from 2 to 60 microns. Size distributions can be

described by using the number of particles per interval as the dependent variable. This

approach is referred to as Number Frequency Distribution of Particle Size or Probability

Density Function. Another approach uses the mass or the volume of the particles instead,

as the dependent variable. Both methods are described next.

4.6.1.1 Number Frequency Distribution of Particle Size

The number of particles in each size interval is counted, recorded, and divided by

the total number of particles in the sample. This process is repeated for the feed inlet and

the overflow and underflow outlets. The results are plotted in the form of a frequency

histogram, as the one shown in Figure 4.3. As described by Crowe (2005), the ordinate

corresponding to each characteristic size interval is defined as the number

frequency, )(~jn df . The sum of the number frequency of all the size intervals should be

equal to one (normalized distribution), as given by:

(4.1)

where N is the total number of size intervals, ∆d.

1)(~

1=∑

=

N

jjn df

99

Figure 4.3 Discrete Number Frequency Distribution of Particle Size (Crowe, 2005)

4.6.1.2 Volume Frequency Distribution of Particle Size

Volume frequency distributions were used to represent the particle size

distributions data. Volume or mass frequency distributions are considered to be more

representative than Number frequency distributions when dealing with very large number

of particles and a large spread in particle sizes. Thus, the number of particles in each size

interval is counted and recorded and the volume of each particle, Vp, is computed

assuming a spherical shape, as follows:

(4.2)

where Rp is the radius of the characteristic particle size. Next, the volume fraction

associated with each size interval (that is, the total volume for each size interval divided

by the total sample volume) is used to construct the distribution. This process is repeated

34 3

pp

RV

π=

100

for the feed inlet, the overflow (O/F) and underflow (U/F) outlets. The results are plotted

in the form of a frequency histogram, as the ones shown in Figures 4.4 to 4.6. The

ordinate corresponding to each characteristic size interval is given as the volume

frequency, )(~jv df , and the sum of the volume frequency over of all the size intervals

should be equal to one, for a normalized distribution (Crowe, 2005), and is given by:

(4.3)

where N is the total number of size intervals, ∆d, which in all cases of the present

experimental data was N = 31, corresponding to the maximum number of channels in the

Coulter Counter (CC) Multisizer.

4.6.1.3 Cumulative Volume Frequency Distribution of Particle Size

The cumulative volume frequency distribution of particle size, vF~ , is the sum of

the volume frequency distribution, )(~jv df , associated with size dk, and is given by

(Crowe, 2005):

(4.4)

The value of )(~ dkFv is the fraction of particles with sizes less than dk. The value

of )(~ dkFv for the largest particle is equal to unity (100%) for normalized distributions.

Figures 4.4 to 4.6 show both the volume and cumulative volume frequency distribution of

particle size for the feed inlet, the overflow and the underflow streams.

1)(~

1=∑

=

N

jjv df

∑=

=kd

jjvkv dfdF

1)(~)(~

101

0

2

4

6

8

10

12

14

16

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Volu

me

Freq

uenc

y (%

)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

Volu

me

Fr

eque

ncy

(%)

Inlet_Vol_pct Inlet_Cum_Vol_pct

Figure 4.4 Inlet Volume Frequency Distribution of Particle Size (Dataset 1)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Volu

me

Freq

uenc

y (%

)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

Vol

ume

Fr

eque

ncy

(%)

UF_Vol_pct UF_Cum_Vol_pct

Figure 4.5 U/F Volume Frequency Distribution of Particle Size (Dataset 1)

102

0

2

4

6

8

10

12

14

16

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Volu

me

Freq

uenc

y (%

)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

Volu

me

Fr

eque

ncy

(%)

OF_Vol_pct OF_Cum_Vol_pct

Figure 4.6 O/F Volume Frequency Distribution of Particle Size (Dataset 1)

4.6.1.4 Weighted Volume Frequency Distribution of Particle Size

To analyze the SLHC separation performance, individual outlet stream’s

distributions were normalized considering the split ratio between the outlet and the feed

entry. In this case, both the volume and cumulative volume frequency distribution of

particle size for the overflow and the underflow streams were normalized with respect to

the feed inlet. The result is a weighted or normalized volume distribution that takes into

consideration the individual outlet solids mass flow rates weighted against the feed.

The weighted volume frequency distributions, )(~jv dwf , for the underflow and the

overflow are computed, respectively, as follows:

- Underflow: sii

suujvujvu cq

cqdfdwf )(~)(~

= (4.5.1)

103

- Overflow: sii

soojvojvo cq

cqdfdwf )(~)(~

= (4.5.2)

where )(~

jv df is the volume frequency distribution of particle size, q is the flowrate, and

cs is the solids concentration. The subscripts u, o, and i, correspond to the underflow, the

overflow and the inlet respectively.

Similarly, the weighted cumulative volume frequency distributions, )(~kv dwF , for

the overflow and underflow are computed as follows:

Underflow: sii

suukvukvu cq

cqdFdwF )(~)(~ = (4.6.1)

Overflow: sii

sookvokvo cq

cqdFdwF )(~)(~ = (4.6.2)

Figures 4.7 and 4.8 show both the discrete weighted volume frequency

(histogram) and the cumulative volume frequency (curve) distribution of particle size for

the underflow and the overflow streams, respectively.

104

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Wt.

Volu

me

Freq

uenc

y (%

)

0

10

20

30

40

50

60

70

Wt.

Cum

. Vol

ume

Fr

eque

ncy

(%)

UF_Weighted_Vol_pct UF_Weighted_CumVol_pct

Figure 4.7 U/F Weighted Volume Frequency Distribution of Particle (Dataset 1)

0.0

0.5

1.0

1.5

2.0

2.5

3.0

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Wt.

Volu

me

Freq

uenc

y (%

)

0

2

4

6

8

10

12

14

16

18

Wt.

Cum

. Vol

ume

Fr

eque

ncy

(%)

OF_Weighted_Vol_pct OF_Weighted_CumVol_pct

Figure 4.8 O/F Weighted Volume Frequency Distribution of Particle Size (Dataset 1)

105

4.6.1.5 Calculated U/F Volume Frequency Distribution of Particle Size

Particle size distribution and solids concentration for the inlet and outlet streams

were not measured in real time during the experimental program. Instead, batch samples

were collected at different times and at each of the sampling points. Solids were

continuously fed into the hydrocyclone at a certain rate and concentration. Nevertheless,

solids tend to accumulate or reside inside the hydrocyclone for a certain period of time.

This suggests that the total amount of solids measured at the feed entry is not equal to the

sum of the amount of solids measured at the outlet streams. Therefore, to correct for this

effect and satisfy mass balance, that is, uooutin mmmm &&&& +== , the underflow calculated

weighted volume frequency distribution, )(~jvu dcf , was obtained from the difference

between the inlet and the overflow frequency distributions, as follows:

)(~)(~)(~

jvojvijvu dwfdfdcf −= (4.7)

Similarly, the underflow calculated cumulative volume frequency distribution,

)(~kvu dcF , was obtained from the following relationship:

)(~)(~)(~

kvokvikvu dwFdFdcF −= (4.8)

The U/F calculated cumulative volume frequency distribution of particle size is

also a measure of SLHC grade separation efficiency, and hence it is relevant for the

present study. Figure 4.9 shows the discrete calculated volume frequency at the

underflow stream, and the cumulative volume frequency distributions.

106

0

2

4

6

8

10

12

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Cal

c. W

t. Vo

lum

e Fr

eque

ncy

(%)

0

10

20

30

40

50

60

70

80

90

100

Calc

. Wt.

Cum

. V

olum

e Fr

eq. (

%)

UF_Calc_Wt_Vol_pct UF_Calc_Wt_CumVol_pctInlet_Cum_Vol_pct OF_Weighted_CumVol_pct

Figure 4.9 U/F Calculated Weighted Volume Frequency Distribution of Particle Size

Including Inlet / Outlet Cumulative Distributions (Dataset 1)

4.6.2 Statistical Parameters

4.6.2.1 Sauter Mean Diameter (d32)

The Sauter Mean Diameter (SMD) is the ratio of the particle volume to surface

area in a distribution and is defined as:

(4.9)

∑

∑

=

==N

jjvj

N

jjvj

dfd

dfd

d

1

2

1

3

32

)(~

)(~

107

4.6.2.2 Volume-Average Mean Particle Diameter

The volume-average mean particle diameter of the distribution, vd , is obtained

from the following relationship:

(4.10)

4.6.2.3 Volume Variance

The volume variance, 2vσ , a measure of the spread of the distribution, is defined

by:

(4.11)

4.6.2.4 Standard Deviation

The standard deviation is defined as the square root of the variance, as follows:

(4.12)

4.7 Data Culling and Verification

After compiling more than 180 datasets from the experimental work of Culwell et

al. (1994), the data were analyzed in an attempt to establish the uncertainty and

confidence level of the available datasets. Some of the datasets had incomplete records or

corresponded to experiments that examined the performance of dual cyclone

arrangements, whereby no individual cyclone overflow outlet data were available. As a

2

1

2

1

22 )(~)(~)( vN

jjvj

N

jjvvjv ddfddfdd −=−= ∑∑

==σ

2vv σσ =

∑=

=N

jjvjv dfdd

1)(~

108

result, only 155 datasets were complete and of value for the present study. A sample of

the experimental data including test results for one every four datasets is shown in Table

4.2. The experimental data results and conditions for all datasets are shown in Tables A.1

and A.2, respectively in Appendix A.

In general, the data acquisition process was affected by flow transients that were

neither measured nor reported. Evidence of inaccuracies in the sampling methods and the

solids content determination were reported but their magnitudes were not quantified.

Besides, the lack of information about the instruments and calibration data impedes a

thorough assessment of systematic uncertainties. On the other hand, the large number of

datasets provides good confidence in the data and can be used to establish the uncertainty

trend.

The 155 available datasets underwent a thorough verification process to determine

their overall uncertainty and confidence level. The first step consisted of analyzing the

repeatability of the test results as a function of different flow and operating conditions

and geometrical parameters. Next, the quality of the datasets was assessed by determining

mass balance inconsistencies, and presence of significant differences between global and

grade separation efficiency results. Finally, a stochastic simulation was performed to

establish a probabilistic distribution of the separation efficiency.

109

Table 4.2 Sample of Experimental Data for Several Datasets

Feed Conditions Feed Particle Size Geometric Specs Experimental ResultsD

atas

et #

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Mea

n Pa

rt.

Dia

m ( μ

m)

Feed

Dis

t. St

d.

Dev

. (μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effic

.

Gra

de-G

loba

l Ef

fic. D

iff.

1 1.19 0.253 213 105 26.1 12.7 18.6 20.6 5.5 3.2 83.2% 81.1% 2.1%4 1.21 0.187 155 107 14.5 15.0 16.8 20.6 5.5 3.2 81.9% 44.0% 37.9%8 1.25 0.303 242 116 20.8 16.5 20.0 20.6 5.5 3.2 84.3% 69.6% 14.7%12 1.24 0.315 254 114 17.3 13.2 16.3 20.6 5.5 3.2 83.3% 79.3% 4.0%16 1.25 0.180 144 116 13.1 10.2 12.5 20.6 5.5 3.2 80.9% 79.4% 1.5%20 1.29 0.449 349 124 22.1 18.7 22.0 20.6 5.5 3.2 90.0% 74.6% 11.6%24 1.30 0.216 166 125 20.7 15.2 18.9 20.6 5.5 3.2 85.4% 80.9% 4.5%28 1.29 0.453 351 126 22.4 17.0 21.1 20.6 5.5 3.2 88.1% 82.2% 5.9%32 1.29 0.306 238 124 25.2 16.7 21.9 20.6 5.5 3.2 85.8% 78.5% 7.3%36 1.29 0.445 346 125 22.6 16.0 20.5 20.6 5.5 3.2 86.4% 79.0% 7.4%40 1.28 0.253 197 126 20.6 11.5 15.8 20.6 5.5 3.2 86.4% 86.5% 0.1%44 1.23 0.164 134 116 19.2 10.0 14.0 20.6 5.5 3.2 79.2% 75.5% 3.7%48 1.22 0.111 91 115 27.7 15.1 21.5 20.6 5.5 3.2 72.5% 56.9% 15.6%52 1.23 0.128 104 115 27.8 16.4 23.0 20.6 5.5 3.2 84.9% 73.8% 11.1%56 1.26 0.112 89 125 30.7 14.9 22.5 20.6 5.5 3.2 44.9% 19.6% 25.3%60 1.27 0.110 86 124 15.6 8.7 11.6 20.6 5.5 3.2 59.5% 42.4% 17.1%64 1.21 0.242 200 110 25.0 17.0 22.6 20.6 5.5 3.2 79.2% 77.3% 1.9%68 1.21 0.182 150 110 27.0 17.7 23.5 20.6 5.5 3.2 78.8% 71.8% 7.0%72 1.21 0.226 187 110 25.1 17.6 22.8 20.6 5.5 3.2 79.0% 74.3% 4.7%76 1.21 0.113 93 111 20.3 17.2 21.0 20.6 5.5 3.2 82.8% 72.2% 10.6%80 1.21 0.238 197 110 25.0 16.9 22.1 20.6 5.5 3.2 84.3% 77.3% 7.1%84 1.29 0.151 117 126 33.4 17.0 25.6 20.6 5.5 3.2 67.2% 47.2% 20.1%88 1.28 0.342 267 126 24.9 7.0 12.5 20.6 5.5 3.2 51.7% 34.5% 17.2%92 1.27 0.137 107 126 21.9 12.6 16.6 20.6 5.5 3.2 81.6% 76.7% 4.9%96 1.28 0.213 166 126 14.4 9.8 12.2 20.6 5.5 3.2 84.4% 82.5% 1.9%100 1.27 0.282 221 126 17.7 10.6 13.7 20.6 5.5 3.2 82.1% 80.2% 1.8%104 1.26 0.062 50 106 30.3 17.2 25.0 20.6 5.5 2.2 77.0% 67.2% 9.8%108 1.26 0.153 122 106 29.6 15.9 22.5 20.6 5.5 2.2 79.7% 70.6% 9.1%112 1.24 0.167 134 106 17.8 13.9 17.0 20.6 5.5 2.2 80.3% 70.3% 10.0%116 1.29 0.176 137 113 20.7 14.0 18.1 20.6 5.5 2.2 85.7% 74.8% 10.9%120 1.35 0.245 182 105 17.7 13.6 16.6 20.6 5.5 2.2 83.6% 71.2% 12.5%124 1.26 0.187 148 126 19.3 14.8 18.5 20.6 5.5 3.2 80.1% 72.0% 8.1%128 0.27 0.050 183 125 28.9 16.5 23.2 3.2 2.0 1.5 76.5% 65.5% 10.9%132 0.29 0.035 122 125 22.7 14.2 18.6 4.5 2.6 1.5 82.8% 71.4% 11.4%136 0.28 0.043 153 126 30.0 18.9 24.9 4.5 2.6 1.5 89.9% 75.8% 14.2%140 0.27 0.082 302 116 19.5 12.9 16.3 4.5 2.6 1.5 89.0% 80.1% 8.9%144 0.27 0.018 67 116 21.6 14.4 18.8 4.5 2.6 1.5 75.3% 51.1% 24.2%148 0.28 0.019 69 116 17.3 11.6 15.1 4.5 2.6 1.5 79.5% 68.7% 10.8%152 0.16 0.032 203 104 17.2 14.3 16.9 3.2 2.0 1.0 77.5% 50.5% 27.0%155 0.17 0.037 218 125 23.8 20.4 24.3 3.2 2.0 1.0 81.0% 45.7% 35.3%

110

Following this verification process, a total of 117 datasets (or 76%) were

considered to have the lowest uncertainty and to be most representative (95% confidence

level) for the analysis of the data and for the verification of the proposed SLHC

mechanistic model. The data verification process is explained in more detail in the

following sections.

4.7.1 Repeatability of Test Results

The repeatability of results from a large number of experiments, which are

performed under similar conditions and for the same geometrical parameters, can shed

light on possible existence of systematic errors or measurement bias. Thus, in this study

the relationship between the global separation efficiency data and different test variables

was examined for all available datasets, as presented in Figures 4.10 to 4.15. The legend

on the figures is as follows: VF is the vortex finder, IN is the inlet slot, UF is the

underflow outlet and OF is the overflow outlet.

The results show a small group of datasets with equipment efficiencies that

departs from the general trend of the majority of the data (large spread). This dataset

group generally shows equipment under-performance for the same flow conditions, as

compared to the vast majority of the experiments. This can be considered just as an

indication of possible systematic bias or higher uncertainty, and thus, further analysis is

necessary to establish the uncertainty level of these dataset groups.

111

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Feed Liquid Flow Rate (m3/hr)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.10 Effect of Feed Liquid Flow Rate on Global Separation Efficiency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

12 13 14 15 16 17 18 19 20 21 22 23 24

Inlet Velocity (m/s)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.11 Effect of Inlet Flow Velocity on Global Separation Efficiency

112

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Overflow Split Ratio

Glo

bal E

ffic

ienc

y (%

)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.12 Effect of Overflow Split Ratio on Global Separation Efficiency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Mass Flow Rate of Feed Solids (kg/hr)

Glo

bal E

ffic

ienc

y (%

)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.13 Effect of Solids Mass Flow Rate on Global Separation Efficiency

113

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0 50 100 150 200 250 300 350 400

Feed Solids Concentration (mg/L)

Glo

bal E

ffic

ienc

y (%

)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.14 Effect of Solids Concentration on Global Separation Efficiency

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

U/F to O/F Backpressure Ratio

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.15 Effect of U/F to O/F Backpressure on Global Separation Efficiency

114

4.7.2 Reported Sources of Systematic Uncertainties

4.7.2.1 Flow Rates and Mass Measurement

As stated before, the water for the experiments was taken directly from the

oilfield as it was produced, with these properties: Temperatures from 100 to 160 oF, oil

content of up to about 100 ppm, and inlet solids concentrations up to 370 ppm. The Cahn

microbalance that was utilized is sensitive to static electricity in the field environment. As

inlet solids concentration had a significant effect on SLHC performance, the combined

effects of particle size, solids concentration, and oil concentration makes it more difficult

to examine the experimental results. At times, the underflow piping and flowmeter had to

be removed in order to get good results and subsequently, the underflow was measured

with a bucket and stopwatch, representing another source of measurement uncertainty.

Also, many of the channel/channel mass balances showed a loss of volume through the

system for the small particles and a gain in volume for the large particles. This suggests

that particle agglomeration did occur in the SLHC, likely promoted by the oil droplets.

4.7.2.2 Removal of Oil Contained in Samples

To accurately determine the solids concentration and the size distribution, it was

needed to first remove the oil contained in the samples because the CC apparatus does

not discriminate between oil droplets and solid particles. A double solvent extraction was

initially used with Trichloroethane (TCE) at a solvent to TCE ratio of 1:1. However, this

process became another source of error since each extraction required a phase separation,

as solids could have settled into the heavier than water organic-phase or trapped at the

115

interface. Also, solvents have the potential of interacting with the dissolved oil to

precipitate Asphaltenes or to dissolve organic solids. Thus, the phase separation is never

100% efficient as solids tend to stick at the interface and get discarded with it.

4.7.2.3 Shape and Density of Solids

The solids were assumed to be all spheres with a measured average density of 2.0

g/cc. The error in the CC total particle volume measurement varied with sample dilution.

Overflow and underflow samples required different dilutions in the CC, thus, increasing

sampling discrepancy. As the experiments were involved with very fine particles the

shape assumption may be a good approximation, but the average density assumption may

be a source of error because of the wide variety of solids present in the sample. Coarser

particles were filtered upstream of the SLHC to avoid clogging.

4.7.3 Mass Balance Verification

The sum of the particle volumes from the CC in most cases was not equal to the

solids content measured by the filter cake. The main reason for this discrepancy was that

the sample dilution was different for each sample. Additionally, an error of only one

particle in a large channel size could have a significant effect in the calculated total

sample volume. Therefore, the filter weight was used as the most accurate estimate of the

total sample weight and volume, and the particle volume was estimated in each channel

by distributing that total weight in accordance with the measured CC distribution. Even

then, the channel/channel mass balance, which compared the inlet / outlet characteristic

particle distributions in each CC channel, sometimes varied up to 200%.

116

These mass balance (MB) inconsistencies are an indication of higher uncertainty

due to measurement error, unrecorded flow transients, or instrument calibration or

operational problems. As mentioned previously, particle size distribution and solids

concentration were sampled at different times, as continuous or real time measurement

was not available. An example of such discrepancies in the feed-to-outlet stream mass

balance, even after measurements were normalized, is shown in Figure 4.16.

-20-10

0102030405060708090

100

2.1

2.6

3.2

4.1

5.1

6.3

7.9

9.8

12.3

15.3

19.2

23.9

29.8

37.3

46.5

58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.16 Grade Separation Efficiency Curve (Dataset 4). G = 44%, E = 82%

As can be seen in Figure 4.16, the global separation efficiency is about 82% while

the average grade efficiency is only 44%. Also note that the weighted O/F cumulative

particle volume percent for particle sizes smaller than 5.4 microns is greater than the feed

cumulative particle volume (mas out > mass in). In contrast, Figure 4.17 shows an

example of a dataset having overall mass balance consistency.

Channel Mass Balance inconsistency

(O/F > Feed)

117

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.17 Grade Separation Efficiency Curve (Dataset 12). G = 79%, E= 83%

4.7.4 Differences in Separation Efficiency Results

The SLHC global separation efficiency is obtained considering the relationship of

the outlet to inlet solids mass concentration ratio. On the other hand, the cyclone’s grade

separation efficiency, a more rigorous approach, is a measure of the efficiency obtained

for each characteristic particle size in the feed solids. The average grade separation

efficiency should yield close results as those obtained using the global efficiency

definition, provided that flowrates, solids concentrations, and mass or volume frequency

distributions of particle size are representative and measured accurately. Significant

differences between the global and the average grade efficiency could point to systematic

bias or measurement error. Thus, major differences between both results can be used to

qualify the uncertainty level of a particular dataset.

118

In an attempt to establish the quality of the data, differences between the global

and the grade efficiencies were analyzed. As described in Chapter 2, the generalized

definition for the global solids separation efficiency, E, is given by Eq. (2.3), as follows:

%cqcq

Esii

soo 1001 ×⎟⎟⎠

⎞⎜⎜⎝

⎛××

−= (2.3)

Similarly, the solids grade or channel separation efficiency, G(x), is defined as the

fraction of solid particles (by mass or volume) of a particular size range or grade, x, under

consideration reporting to the underflow as compared to the feed, which is given by Eq.

(2.5), as follows:

%100)(

)()( ×=feedinxgradesizeinmass

underflowinxgradesizeinmassxG (2.5)

As stated before, the global efficiency deals with the overall SLHC efficiency

regardless of mass or volume fraction for each particle size in the feed; whereas the grade

efficiency considers the particle size distribution for each characteristic particle diameter

(by mass or volume) and normalizes the outlet distributions with respect to the feed solids

using fraction concentrations. Thus, the volume grade efficiency for a characteristic

diameter size, dj, is given by:

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−=

)(~)(~

1)(jvi

jvoj df

dwfdG (4.13)

The average grade separation efficiency is computed using the following expression:

119

N

df

dwf

G

N

j jvi

jvo∑=

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

=1 )(~

)(~1

(4.14)

and the global-grade efficiency difference, Ed, is obtained as follows:

GEEd −= (4.15)

Global and average grade efficiency results are compared in Figures 4.18 and

4.19. Good agreement is observed with about 117 of the datasets (or 76%) having

differences lower than 15%. Also, 23 of the 38 datasets (or 61%) having efficiency

differences greater than 15% also have mass balance inconsistencies.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Avg. Grade Efficiency

Glo

bal E

ffic

ienc

y

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)](*) Dataset w / Mass Balance Inconsistency: OF >IN

38 datasets (or 24%)

117 Datasets (or 76%)

(*) 23 / 38 datasets (61%)

Figure 4.18 Comparison of Global and Average Grade Separation Efficiency Data

120

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Global Efficiency (%)

Avg

. Gra

de v

s. G

loba

lEf

ficie

ncy

Diff

eren

ce

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)](*) Dataset w / Mass Balance Inconsistency: OF >IN

38 datasets (or 24%)

117 Datasets (or 76%)

(*) 23 / 38 datasets (or 61%)

Figure 4.19 Difference Between Global and Average Grade Separation Efficiency

Not surprisingly, almost half of the 38 experiments with higher efficiency

difference and mass balance inconsistency correspond to tests performed on a single day

or during few contiguous days. Figure 4.20 shows that at least 19 of the 38 tests were

performed in three different days (10/5/92, 10/8/92, and 11/25/92) with 7, 9, and 3 tests,

respectively. This may be another indication that systematic errors likely occurred during

few particular days, which could have been caused by instrument failure, non-recorded

significant flow transients, or any other measurement problems. Table 4.3 presents a

summary of the experimental results for the 38 datasets with higher uncertainty (included

in Groups B and C). The 23 datasets with MB inconsistencies (included in Group C) are

highlighted and shown in bold blue font.

121

Table 4.3 Experimental Data for 38 Datasets with Higher Uncertainty (Groups B & C)

Feed Conditions Feed Particle Size Geometric Specs Experimental ResultsD

atas

et #

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Mea

n Pa

rt.

Dia

m ( μ

m)

Feed

Dis

t. St

d.

Dev

. (μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effic

.

Gra

de-G

loba

l Ef

fic. D

iff.

2 1.19 0.392 330 105 30.3 24.4 30.6 20.6 5.5 3.2 82.6% 64.5% 18.1%3 1.21 0.153 127 106 30.9 35.6 38.7 20.6 5.5 3.2 84.0% 52.7% 31.4%4 1.21 0.187 155 107 14.5 15.0 16.8 20.6 5.5 3.2 81.9% 44.0% 37.9%5 1.20 0.252 210 106 16.7 14.7 17.1 20.6 5.5 3.2 83.2% 51.8% 31.3%46 1.22 0.111 91 115 24.2 14.7 20.0 20.6 5.5 3.2 72.5% 56.8% 15.7%48 1.22 0.111 91 115 27.7 15.1 21.5 20.6 5.5 3.2 72.5% 56.9% 15.6%55 1.26 0.112 89 125 14.9 8.7 11.5 20.6 5.5 3.2 44.9% 29.2% 15.7%56 1.26 0.112 89 125 30.7 14.9 22.5 20.6 5.5 3.2 44.9% 19.6% 25.3%57 1.26 0.112 89 125 22.8 12.7 18.1 20.6 5.5 3.2 44.9% 22.3% 22.6%58 1.27 0.110 86 124 14.9 8.8 11.7 20.6 5.5 3.2 59.5% 44.1% 15.4%59 1.27 0.110 86 124 10.3 7.4 9.2 20.6 5.5 3.2 59.5% 41.4% 18.1%60 1.27 0.110 86 124 15.6 8.7 11.6 20.6 5.5 3.2 59.5% 42.4% 17.1%63 1.26 0.199 157 126 27.2 11.5 17.8 20.6 5.5 3.2 69.0% 52.6% 16.4%82 1.29 0.151 117 126 29.1 15.5 22.8 20.6 5.5 3.2 67.2% 48.6% 18.6%83 1.29 0.151 117 126 30.3 12.9 20.4 20.6 5.5 3.2 67.2% 51.0% 16.2%84 1.29 0.151 117 126 33.4 17.0 25.6 20.6 5.5 3.2 67.2% 47.2% 20.1%85 1.28 0.208 163 124 24.4 12.6 18.3 20.6 5.5 3.2 57.8% 39.9% 17.9%86 1.28 0.208 163 124 20.8 11.3 16.0 20.6 5.5 3.2 57.8% 39.2% 18.6%87 1.28 0.208 163 124 20.8 11.7 16.3 20.6 5.5 3.2 57.8% 37.6% 20.2%88 1.28 0.342 267 126 24.9 7.0 12.5 20.6 5.5 3.2 51.7% 34.5% 17.2%89 1.28 0.342 267 126 25.5 7.1 12.8 20.6 5.5 3.2 51.7% 35.6% 16.1%90 1.28 0.342 267 126 25.0 6.6 11.9 20.6 5.5 3.2 51.7% 35.6% 16.1%98 1.28 0.213 166 126 22.3 15.7 19.6 20.6 5.5 3.2 84.4% 61.4% 23.1%101 1.27 0.282 221 126 23.9 16.0 20.4 20.6 5.5 3.2 82.1% 59.7% 22.3%105 1.26 0.062 50 106 30.8 18.8 26.5 20.6 5.5 2.2 77.0% 60.4% 16.6%118 1.34 0.059 44 124 19.6 13.9 17.7 20.6 5.5 2.2 68.4% 47.9% 20.5%123 1.26 0.236 187 126 29.2 19.4 25.5 20.6 5.5 3.2 80.7% 62.0% 18.6%127 0.27 0.024 87 125 25.5 17.3 22.7 3.2 2.0 1.5 76.0% 56.1% 19.9%133 0.29 0.028 98 126 29.4 19.3 25.6 4.5 2.6 1.5 83.4% 64.8% 18.6%143 0.27 0.021 77 117 20.8 12.9 17.0 4.5 2.6 1.5 75.5% 53.8% 21.6%144 0.27 0.018 67 116 21.6 14.4 18.8 4.5 2.6 1.5 75.3% 51.1% 24.2%145 0.28 0.015 52 126 16.9 13.1 16.0 4.5 2.6 1.5 72.4% 43.9% 28.5%147 0.28 0.010 36 116 17.1 12.1 15.4 4.5 2.6 1.5 62.2% 31.6% 30.7%150 0.16 0.009 54 116 18.3 12.9 16.3 3.2 2.0 1.0 62.3% 30.4% 31.9%152 0.16 0.032 203 104 17.2 14.3 16.9 3.2 2.0 1.0 77.5% 50.5% 27.0%153 0.16 0.026 167 104 24.1 16.1 20.7 3.2 2.0 1.0 84.8% 63.0% 21.8%154 0.16 0.010 64 104 14.1 10.9 13.1 3.2 2.0 1.0 75.0% 52.3% 22.7%155 0.17 0.037 218 125 23.8 20.4 24.3 3.2 2.0 1.0 81.0% 45.7% 35.3%

122

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151

Dataset # (in Chronological Order)

Avg

. Gra

de v

s. G

loba

lEf

ficie

ncy

Diff

eren

ce

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)](*) Dataset w / Mass Balance Inconsistency: OF >IN

(*) 23 / 38 datasets (or 61%)

Figure 4.20 Grade vs. Global Efficiency Difference per Dataset (in Chronological Order)

4.7.5 Stochastic Forecast of Global Separation Efficiency

It is accepted that the true value of the efficiency (the target) is unknown and

systematic uncertainty or bias is not observable within the data. However, a probabilistic

forecast of the separation efficiency may shed some light on the likelihood of obtaining a

certain range of results. It helps to have a large number of experiments performed under

a wide range of conditions with good repeatability. Thus, a probabilistic frequency

distribution of the global separation efficiency was forecasted by means of Montecarlo

simulation and using a commercial application. The forecast was performed for each

SLHC unit, namely, the 1-inch unit and the 10-mm unit.

Figures 4.21 and 4.22 show the forecasted probabilistic distribution with a 90%

certainty range for each of the equipment. Table 4.4 provides a summary of the statistical

predictions for both forecasts.

123

Mean = 76.7%.000

.008

.016

.023

.031

0

77.75

155.5

233.2

311

0.0% 25.0% 50.0% 75.0% 100.0%

Figure 4.21 Probabilistic Frequency Distribution of Global Efficiency (1-inch SLHC)

Figure 4.22 Probabilistic Frequency Distribution of Global Efficiency (10-mm SLHC)

124

Table 4.4 Summary of Statistical Parameters and Forecast Results

Statistical Parameter 1-inch SLHC 10-mm SLHC

Mean 76.7% 79.2%

Median 81.7% 83.1%

Standard Deviation 18.1% 15.1%

Variance 3.3% 2.3%

Skewness -3.2 -2.2

Range of Results (90% Certainty)

56.9 to 96% 58.5 to 96.1%

According to forecasted results, the global separation efficiency should likely be

between 56.9 to 96% for the 1-inch unit, and from 58.5 to 96.1% for the 10-mm unit with

a 90% certainty. Note in Figure 4.18 that the measured separation efficiency is lower than

that predicted by the Montecarlo simulation, for many of the questionable 38 datasets.

After the complete data verification process, the datasets have been grouped and

their confidence level has been assessed, as presented in Table 4.5. The 117 datasets

(Group A) that exhibit better repeatability of results, mass balance consistency, and lower

global-grade efficiency discrepancies (<15%) are believed to have a 95% confidence

level. A second dataset group (Group B) with a total of 132 datasets is formed by adding

to the first group the 15 datasets having efficiency differences in excess of 15% but with

no mass balance inconsistencies. This group is said to have a 90% confidence level.

Finally, a third dataset group (Group C) includes all 155 available datasets, which have

been assigned 68% confidence level. Notice that this group does include the 23 datasets

having mass balance inconsistencies.

125

Table 4.5 Classification and Definition of Dataset Groups

Culled Datasets 95% Global-Grade Efficiency Difference, Ed < 15% 117

MB Consistent Datasets 90%All datasets excluding those with MB

Inconsistency and Ed > 15% 132

ALL Datasets 68% All available datasets 155

Dataset Groups # DatasetsPremiseConfidence

Level

4.8 Experimental Results

Table A.1 in Appendix A presents a summary of the experimental data including

test conditions for all datasets. Analysis of the results follows in the next sections.

4.8.1 Summary of Results

Figure 4.23 shows a summary of global separation efficiency for the 117 culled

datasets (Group A) in chronological order. Figure 4.24 shows the feed Sauter mean

diameter (d32) for each dataset. The standard deviation of the feed particle size

distribution per dataset is given in Figure 4.25. Results show that both SLHC units tested

were able to remove about 75% to 92% of up to 370 ppm feed solids from a water

mixture having a 14.8 μm mean diameter (d32 of 23.1 μm) with a standard deviation of

19.4 μm. The U/F recovered an average 13.5 μm mean particle diameter (18.8 μm Std.

Dev.). Also, both SLHC’s recovered about 85% of the feed water through the O/F. This

stream consisted of a 35 ppm of 7.8 μm mean solids diameter (3.1 μm Std. Dev.). A

detailed discussion follows regarding results for each SLHC configuration.

A)

B)

C)

Conditions

126

40%

50%

60%

70%

80%

90%

100%

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160

Dataset # (in Chronological Order)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.23 Global Separation Efficiency by Dataset (Group A)

0

5

10

15

20

25

30

35

0 20 40 60 80 100 120 140 160Dataset # (in Chronological Order)

Feed

d32

Par

ticle

Dia

met

er

(mic

rons

)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.24 Feed Sauter Mean Diameter (d32) per Dataset (Group A)

127

0

5

10

15

20

25

30

0 20 40 60 80 100 120 140 160Dataset # (in Chronological Order)

STD

. Dev

iatio

n of

Fee

d Pa

rtic

le S

ize

Dis

trib

utio

n (m

icro

ns)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.25 Standard Deviation of Feed Particle Size Distribution per Dataset (Group A)

4.8.2 Grade Separation Efficiency

In general, of the 1-inch configurations, the cyclone with a 5.5 mm vortex finder

(VF) and a 3.2 mm spigot (U/F) shows better capacity to remove larger sized particles

(Datasets 1 and 22). On the other hand, of the 10-mm configurations, the cyclone with a

2.6 mm vortex finder and the 1.5 mm spigot exhibited the highest efficiency (Datasets

135 and 148). Overall, the least efficient setup was the 10-mm unit with the 2.0 mm

vortex finder and 1.5 mm spigot. Detailed test conditions are shown in Table A.1 in

Appendix A. Two examples of grade efficiency results for the 1-inch and 10-mm SLHC

configurations are shown in Figures 4.26 to 4.29 and 4.30 to 4.35, respectively. Typical

Volume Particle Size Distributions are shown in Figures 4.36 and 4.37.

128

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.26 Grade Separation Efficiency Curve – 1” Unit (Dataset 1)

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.27 Grade Separation Efficiency Curve – 1” Unit (Dataset 22)

Qin: 1.19 m3/hr; Pin: 114 psig Cs,in: 213 ppm; inm& = 0.253 kg/hr VF: 5.5 mm; U/F: 3.2 mm

Qin: 1.30 m3/hr; Pin: 126 psig Cs,in: 166 ppm; inm& = 0.216 kg/hr VF: 5.5 mm; U/F: 3.2 mm

129

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.28 Grade Separation Efficiency Curve – 1” Unit (Dataset 110)

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.29 Grade Separation Efficiency Curve – 1” Unit (Dataset 120)

Qin: 1.25 m3/hr; Pin: 106 psig Cs,in: 220 ppm; inm& = 0.275 kg/hr VF: 5.5 mm; U/F: 2.2 mm

Qin: 1.35 m3/hr; Pin: 105 psig Cs,in: 182 ppm; inm& = 0.245 kg/hr VF: 5.5 mm; U/F: 2.2 mm

130

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.30 Grade Separation Efficiency Curve – 10mm Unit (Dataset 126)

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.31 Grade Separation Efficiency Curve – 10mm Unit (Dataset 128)

Qin: 0.26 m3/hr; Pin: 124 psig Cs,in: 63 ppm; inm& = 0.016 kg/hr VF: 2.0 mm; U/F: 1.5 mm

Qin: 0.27 m3/hr; Pin: 125 psig Cs,in: 183 ppm; inm& = 0.050 kg/hr VF: 2.0 mm; U/F: 1.5 mm

131

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.32 Grade Separation Efficiency Curve – 10mm Unit (Dataset 135)

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.33 Grade Separation Efficiency Curve – 10mm Unit (Dataset 148)

Qin: 0.28 m3/hr; Pin: 126 psig Cs,in: 17 1 ppm; inm& = 0.048 kg/hr VF: 2.6 mm; U/F: 1.5 mm

Qin: 0.28 m3/hr; Pin: 116 psig Cs,in: 69 ppm; inm& = 0.019 kg/hr VF: 2.6 mm; U/F: 1.5 mm

132

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.34 Grade Separation Efficiency Curve – 10 mm Unit (Dataset 149)

0102030405060708090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Sepa

ratio

n Ef

ficie

ncy

(%)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pct OF_Weighted_CumVol_pct

Figure 4.35 Grade Separation Efficiency Curve – 10 mm Unit (Dataset 151)

Qin: 0.16 m3/hr; Pin: 116 psig Cs,in: 196 ppm; inm& = 0.031 kg/hr VF: 2.0 mm; U/F: 1.0 mm

Qin: 0.17 m3/hr; Pin: 116 psig Cs,in: 136 ppm; inm& = 0.022 kg/hr VF: 2.0 mm; U/F: 1.0 mm

133

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Volu

me

Freq

uenc

y (%

)

Figure 4.36 O/F–U/F Weighted Volume Frequency Distribution of Particle Size (Dataset 5)

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1

Particle Diameter (microns)

Volu

me

Freq

uenc

y (%

)

UF_Weighted_Vol_pct OF_Weighted_Vol_pct

Figure 4.37 O/F–U/F Weighted Volume Frequency Distribution of Particle Size (Dataset 129)

134

4.8.3 Global Separation Efficiency

Analysis of the effects that the most relevant flow variables have on SLHC global

separation efficiency is presented in this section.

4.8.3.1 Effect of Inlet Liquid Flow Rate and Velocity

The effect of inlet flowrate on the efficiency is not very evident from the data for

any of the SLHC configurations (Figure 4.38). Instead, analysis of the inlet velocities

seems more important, as it accounts for the effect of the inlet slot area. Figure 4.39

reveals that optimum feed velocities are between 16 to 17.5 m/s for both units. High

enough inlet velocities are necessary to create sufficient swirl to promote efficient

particle separation. However, this effect seems to be reversed at higher velocities as they

may promote greater turbulence that can destabilize the inner vortex.

40%

50%

60%

70%

80%

90%

100%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Feed Liquid Flow Rate (m3/hr)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.38 Effect of Feed Liquid Flow Rate on Global Separation Efficiency

135

40%

50%

60%

70%

80%

90%

100%

12 13 14 15 16 17 18 19 20 21 22 23 24

Inlet Velocity (m/s)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.39 Effect of Inlet Velocity on Global Separation Efficiency

4.8.3.2 Effect of Overflow to Inlet Feed Split Ratio

Optimum O/F to inlet split ratio for the 10-mm SLHC appears to be from 0.83 to

0.87, and from 0.87 and 0.93 for the 1-inch unit. Split ratios outside of these ranges

appear to be detrimental to cyclone’s separation efficiency, as shown in Figure 4.40.

40%

50%

60%

70%

80%

90%

100%

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Overflow Split Ratio

Glo

bal E

ffic

ienc

y (%

)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.40 Effect of O/F Split Ratio on Global Separation Efficiency

136

4.8.3.3 Effect of Inlet Solids Mass Flow Rate and Solids Concentration

The experimental results suggest that solids removal efficiency increases as the

feed mass flow rates and solids concentrations increase. As evidenced in Figures 4.41 and

4.42, particle carry-over is sharply reduced at higher mass flow rates and feed solids

concentrations, regardless of equipment configuration. However, this effect might be

reversed if the solids concentration continues to increase.

This phenomenon cannot be observed from the available data due to the narrow

range of solids concentrations used for the experiments. Nevertheless, literature data

suggest that an increase in solids mass flow rates and in feed solids concentration, while

keeping all other operating parameters constant, leads to a coarser cut size, reduced

separation sharpness, and results in a higher pressure drop across the cyclone (Braun and

Bohnet, 1990).

40%

50%

60%

70%

80%

90%

100%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Mass Flow Rate of Feed Solids (kg/hr)

Glo

bal E

ffic

ienc

y (%

)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]Li (1 i h [VF 5 5 UF 3 2 (0 60 UF/VF 0 85 IN/VF)])

Figure 4.41 Effect of Solids Mass Flow Rate on Global Separation Efficiency

137

40%

50%

60%

70%

80%

90%

100%

0 50 100 150 200 250 300 350 400 Feed Solids Concentration (mg/L)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]Li (10 [VF 2 6 UF 1 5 (0 60 UF/VF 0 85 IN/VF)])

Figure 4.42 Effect of Solids Concentration on Global Separation Efficiency

4.8.3.4 Effect of the Feed Oil to Solids Concentration Ratio

Separation efficiency decreases when the feed oil to solids concentration ratio

increases, regardless of geometry. As shown in Figure 4.43, high feed oil to solids

concentration ratios are detrimental to separation efficiency as oil tends to agglomerate

solids and carry (buoy) them into the overflow.

4.8.3.5 Effect of Inlet Temperature

Efficiency seems to slightly improve with higher flow temperatures due to

viscosity reduction. However, inlet temperatures maintained during the experiments were

not broad enough to confirm this assessment, and thus, further investigation is

recommended under a wider range of temperatures (see Figure 4.44)

138

40%

50%

60%

70%

80%

90%

100%

0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40

Oil / Solids Concentration Ratio

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

(1 3 2 (0 60 / 0 8 / ) )

Figure 4.43 Effect of Oil/Solids Concentration Ratio on Global Efficiency

40%

50%

60%

70%

80%

90%

100%

90 100 110 120 130 140 150 160 170

Inlet Temperature (oF)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.44 Effect of Temperature on Global Separation Efficiency

139

4.8.3.6 Effect of Inlet Pressures and Outlet Backpressures

The effect of inlet pressure on separation efficiency cannot be established clearly

from the data, as shown in Figure 4.45. Instead, an analysis of the effect of imposed O/F

and U/F backpressures was performed but neither showed a clear trend. In general, the

O/F backpressure seems to improve the efficiency of the 1-inch unit but has an opposite

effect on the 10-mm geometry. Similarly, the efficiency seems to be unaffected by the

U/F backpressure in the 1-inch geometry, but the 10-mm unit is negatively affected by an

increase in U/F backpressure. It seems though, that the ratio of U/F to O/F backpressure

is important for optimal operation (see Figure 4.46). Caution is advised as to maintaining

U/F to O/F backpressure ratios greater than 50% as this may promote the formation of a

gas core that could disturb the vortex.

40%

50%

60%

70%

80%

90%

100%

100 105 110 115 120 125 130

Inlet Pressure (psig)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.45 Effect of Inlet Pressure on Global Separation Efficiency

140

40%

50%

60%

70%

80%

90%

100%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

U/F to O/F Backpressure Ratio

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 4.46 Effect of U/F to O/F Backpressure Ratio on Global Separation Efficiency

Further investigation is recommended to establish the optimum limits of outlet

backpressure to inlet pressure ratios that would maximize efficiency.

4.8.3.7 Effect of the Feed Solids Mean Particle Size

In general, solids carry-over decreases with larger particle diameters regardless of

geometrical configuration of the SLHC, as shown in Figures 4.47 and 4.48. This is in

agreement with Dwari et al. (2004) observations who reported that the larger particles are

more easily removed. Thus, with an increase in particle size, and keeping the rest of the

variables constant, the separation efficiency increases.

141

40%

50%

60%

70%

80%

90%

100%

12 14 16 18 20 22 24 26 28 30 32 34

Feed d32 Particle Diameter (microns)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5mm; UF: 3.2mm (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5mm; UF: 2.2mm (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0mm; UF: 1.0mm (0.50 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.0mm; UF: 1.5mm (0.75 UF/VF; 1.0 IN/VF)]10-mm [VF: 2.6mm; UF: 1.5mm (0.60 UF/VF; 0.85 IN/VF)]Li (1 i h [VF 5 5 UF 3 2 (0 60 UF/VF 0 85 IN/VF)])

Figure 4.47 Effect of Sauter Mean Diameter (d32) on Global Efficiency

40%

50%

60%

70%

80%

90%

100%

10 12 14 16 18 20 22

Feed Particle Volume-Averaged MEAN Size (microns)

Glo

bal E

ffici

ency

(%)

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]Li (10 [VF 2 6 UF 1 5 (0 60 UF/VF 0 85 IN/VF)])

Figure 4.48 Effect of Feed Particle Volume-Averaged Mean Size on Global Efficiency

142

4.9 Database Management System

A database (DB) management system, named CycloneMaster, was created to

store, organize and consolidate all the available SLHC data. The amount of information

and other requirements suggested the use of relational database management software

like Microsoft Access. This reduces data redundancy, boosts storage capacity, improves

accessibility and facilitates benchmarking of mechanistic models and available

simulators. The DB consists of a set of different data tables that are related by a Unique

or Primary key, and has the flexibility to accommodate a variety of data from other types

of cyclones. Figure 4.49 shows the main screen menu of the CycloneMaster. Detailed

description of the DB system is included in Appendix B.

Figure 4.49 Main Screen of the CycloneMaster DB System

143

CHAPTER 5

MECHANISTIC MODEL DEVELOPMENT

A mechanistic model for liquid-liquid hydrocyclones (LLHC) was proposed by

Caldentey (2000). Later, Gomez (2001) carried out an experimental program aimed at

validating and refining the original model. The final model was presented by Caldentey et

al. (2002). The SLHC mechanistic model developed in this study is a modification of the

model proposed by Caldentey et al. (2002) LLHC model.

The SLHC model takes into account the fundamental differences between solid-

liquid and liquid-liquid systems and the hydrodynamic implications of such differences.

Detailed fundamental differences between solid-liquid and liquid-liquid separation in

hydrocyclones can be found in Thew (1986). Some of these differences include:

• The density difference between the dispersed and the continuous phases is

generally higher for solid-liquid systems, but still requires operating at high

centrifugal forces, especially for the efficient separation of fine particles.

• Unlike liquid droplets, solid particles can be considered rigid spheres that do

not deform, break up or coalesce due to interaction with external forces.

Instead, agglomeration of solids could occur, especially if the particles are oil-

coated or the liquid phase contains a significant amount of oil.

• The operational parameters for the continuous phase in the SLHC differ from

that of the LLHC. For solid-liquid separation, about 90% of the flow exits

144

from the top of the hydrocyclone (overflow outlet). In the LLHC about 10%

of the flow exits from the overflow.

• In the LLHC more attention is given to the reverse core region (away from the

wall) where separation occurs. Instead, the wall region and boundary layer are

relatively more important for the SLHC case (Bloor et al., 1980). Solid

particles tend to move outward until they reach the wall and fall to the

underflow outlet due to the centrifugal force.

The proposed model enables the prediction of the hydrodynamic flow behavior in

the SLHC, as well as the characteristic particle size grade separation efficiency. Due to its

simplicity and general formulation, the model also allows detailed and timely analysis

and performance prediction for any given SLHC geometry and operating conditions,

including separation efficiency and flow capacity (pressure drop – flow rate relationship).

The model has been verified experimentally using oilfield data gathered by Culwell et al.

(1994) in facilities of Chevron in California, as presented in Chapter 4.

5.1 Modeling Assumptions

In order to obtain a sufficiently simple model, yet accurate, the physical

phenomena is simplified by neglecting some of the effects occurring inside the

hydrocyclone. These assumptions reduce the numerical effort without compromising the

model prediction capability. Following is a summary of the main modeling assumptions:

1. The model is limited to mixtures of two immiscible liquids, namely, a

continuous-phase formed by a mixture of water with trace amounts of oil and

a dispersed-phase composed of very fine solid particulates.

145

2. The feed slurry is a highly diluted water solution (very low solids

concentration, < 5 g/L or 5000 ppm) of very small particles (< 150 μm).

3. The rheological properties of the slurry are assumed to be Newtonian. The

mixture density is expressed as a linear combination of component densities.

4. The flow in the main body of the hydrocyclone is regarded as inviscid and

highly rotational, and thus, all flows are subjected to the centrifugal field.

5. The feed slurry is considered to have a homogeneous or uniform distribution

of solid particles throughout the carrier liquid and across the inlet entry.

6. The solid particles of the dispersed phase are considered rigid spheres and are

assumed to have a known feed particle size distribution.

7. Steady-state flow and separation process occurs inside the hydrocyclone, with

no accumulation of material (or agglomeration) and break-up or grinding of

dispersed-phase particles.

8. No turbulence effects are considered on the particle trajectory.

9. Collision effects among particles and with the wall or the center core region

interface are also neglected. This is considered as a sound assumption for

highly dilute systems (low solid concentrations). According to Kraipech et al.

(2005) particle–particle interactions play a key role only in the near wall

region and close to the air core, owing to lubrication and collision

mechanisms. In the remaining region, particle–fluid interactions were

observed to be dominating.

10. The separation is isothermal or has negligible temperature changes.

146

11. Oil properties and concentrations are only considered in the calculation of the

continuous-phase density and viscosity. Oil droplet trajectories and their

direct effect on separation efficiency are not modeled.

12. No gas core occurring in the hydrocyclone. This is considered a valid

assumption as long as the gas dissolved in the oil droplets contained in the

continuous-phase is not sufficient enough to migrate to the core region and

disturb the vortex (Smyth and Thew, 1996).

13. Inlet slot cross sectional area, regardless of shape, is considered by the model.

Thus, rectangular and circular inlets are therefore treated in the same manner.

14. Both involuted single inlet and the twin inlets, the two most commonly used

inlet configurations, are modeled.

15. The angle of the tapered section is an important geometrical parameter

considered in the model.

16. Axis-symmetric flow is considered where there is no variation in the

tangential velocity component.

Schematic of the SLHC and nomenclature is presented in Figure 5.1. The model

is divided into a continuous-phase and a dispersed-phase sub-models. The continuous-

phase sub-model includes the swirl intensity, velocity field and the pressure drop

equations. The dispersed-phase sub-model is composed by the particle trajectory and the

separation efficiency relationships. These are described in the following sections.

147

Figure 5.1 Schematic of the SLHC and Model Nomenclature

LVF

do, dvf, ṁo, qo

di

Lb = Barrel (Cylindrical Section) Length

Lc = Length of Conical Section

Feed Inlet

Underflow (U/F) Outlet

Overflow (O/F) Outlet

Rev

erse

Flo

w C

ore

ṁi, qi

du, ṁu, qu

DCSLHC

Characteristic Diameter

148

5.2 Continuous Phase Modeling

5.2.1 Swirl Intensity

The swirl intensity is produced by the feed tangential inlet of the hydrocyclone.

The definition of the swirl intensity relates the ratio between the axial fluxes of the

angular and axial momentums. The swirl intensity number, Ω, is thus defined as the ratio

of the local tangential momentum flux to the total momentum flux (Chang and Dhir,

1994 and Mantilla, 1998) and is presented by the following expression:

FluxMomentumAxialFluxMomentumTangential

UR

uwrdr

avzzc

Rc

z

==Ω∫

220

2

πρ

πρ (5.1)

The axial velocity of the continuous phase is u, w is its tangential velocity, r is the

radial position, ρc is the density of the continuous phase, Rz is the SLHC radius at given

axial position, z, and Uavz is the average axial velocity.

Since these velocities are not known in advanced, a swirl number correlation was

utilized by Caldentey et al. (2002) to predict the swirl intensity and its decay along the

axis of the hydrocyclone. The swirl number equation utilized by Caldentey et al. (2002) is

a modification of the Mantilla (1998) correlation, based on Erdal (2001) CFD

simulations, which takes into account the effect of the semi-angle of the tapered section.

The modified correlation is given by:

149

*))tan(2.11(Re49.0 15.093.0

2118.0 β+⎟⎟⎠

⎞⎜⎜⎝

⎛=Ω I

MM

T

t

( )( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡+⎟

⎠⎞

⎜⎝⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎠⎞

⎜⎝⎛− 12.0

7.016.035.04 tan21

Re1

21 β

DczI

MMEXP

zT

t (5.2)

where β is the semi-angle of the conical sections; Dc is the characteristic diameter of the

SLHC; Mt/MT is the ratio of inlet to the axial momentum fluxes at Dc; Re is the Reynolds

number at the inlet section, and Rez is the Reynolds number at any given axial position.

The Reynolds number is calculated using the average flow velocity in the

cylindrical section, UDc. It is computed again for each given axial location, z, to account

for the swirl decay in the conical or tapered section starting from Dc and using the

average axial velocity at z, Uavz,.

The Reynolds Number at the inlet cylindrical section is given by:

c

Dcc DcUμ

ρ=Re (5.3)

Similarly, the Reynolds Number at a given axial location, z, of the conical section

is given by:

c

zavzcz

DUμ

ρ=Re (5.4)

where μc is the viscosity of the continuous fluid.

150

In this study, the average inlet flow velocity, UDc, in the cylindrical section is

calculated using the annular area, ADc, existing between the barrel or cylinder section wall

and the vortex finder outside diameter, as follows:

Dc

iDc A

FqU

)1( −= (5.5)

where qi is the inlet feed flow rate, F is the split ratio, and ADc is calculated by:

4)( 22

vfDc

ODDcA

−=

π (5.6)

In Eq. (5.6), ODvf is the external diameter of the vortex finder that runs from the

SLHC cap to some length into the cylindrical barrel.

On the other hand, the average axial velocity, avzU , is the average velocity

changing with axial diameter, Dz, from the beginning to the end of the tapered section,

and is defined as follows:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −= 2)(

)1(4Dz

FqU iavz

π (5.7)

The split ratio, F, is defined as the ratio of the overflow rate to the inlet flow rate,

and is expressed as follows:

%qq

Fi

o 100×= (5.8)

151

The ratio of the inlet momentum flux to the axial momentum flux, Mt/MT, at the

characteristic diameter position, is obtained using the following relationship:

i

c

cci

ici

avci

ii

T

tAA

AmAm

UmVm

MM

===ρρ

//

&

&

&

& (5.9)

where ρc is the density of the continuous-phase; Vi is the flow velocity at the inlet slot;

Uavc is the average axial velocity at Dc; im& is the total inlet mass flow rate; Ai and Ac are

the cross sectional area of the feed inlet slot and the cross sectional area of the SLHC

characteristic diameter respectively.

The total feed mass flowrate is equal to the sum of the O/F and U/F mass

flowrates, assuming no accumulation of material in the hydrocyclone. The material

balance equation for the feed mass flowrates, im& , can be expressed as:

(5.10)

Similarly, the total volumetric flow rate is given by:

(5.11)

where qi, qo, qu are the total volumetric flow rates at the inlet, O/F, and U/F respectively.

The inlet factor, I, as suggested by Erdal (2001) is defined as:

(5.12)

where n = 1 for involuted single inlet and n = 1.5 for twin inlets.

uoi mmm &&& +=

uoi qqq +=

⎟⎠⎞

⎜⎝⎛−−=

21 nEXPI

152

5.2.2 Velocity Field

The tangential and axial velocities are calculated following a similar procedure to

the one proposed by Mantilla (1998). The first step is to predict the swirl intensity at a

specific axial location and then use it to predict the local axial and tangential velocities,

as these are related by definition, to the swirl intensity (Mantilla, 1998). The radial

velocity is the smallest in magnitude and can be obtained using the continuity equation,

accounting for the wall effect. Following is a detailed description of the calculation

procedure.

5.2.2.1 Tangential Velocity

The tangential injection of the pressurized fluid mixture into the hydrocyclone

produces a swirling motion of the flow having a pattern consisting of a spiral within

another spiral moving in the same circular direction (Seyda and Petty, 1991). This

behavior is known as Rankine Vortex and has been confirmed by Weispfennig and Petty

(1991) using LDA measurements.

The tangential velocity profile within the hydrocyclone is then a combination of a

forced vortex near the hydrocyclone axis, and a free vortex in the outer wall region,

neglecting the effect of the wall boundary layer. The outer (free-like) vortex moves

downward carrying suspended particles or material along the axis of the cyclone to the

underflow outlet. It can be represented by a linearly increasing velocity with decreasing

radius. The inner (forced) vortex is located in the region close to the cyclone axis and

moves upward (reverse direction) carrying mainly a clean liquid stream to the overflow

outlet and it is represented by an increasing velocity with increasing radius, reaches a

153

maximum and then decreases until it reaches zero at the cyclone’s centerline (Rushton et

al., 2000). This velocity profile can be seen in Figure 5.2.

Figure 5.2. Rankine Vortex Tangential Velocity Profile

The proposed model utilizes an equation proposed by Algifri et al. (1988), also

used by Caldentey et al. (2002), to predict the flow tangential velocity profile, given by

the following relationship:

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2

1c

c

m

avc RrBEXP

Rr

TU

w (5.13)

where w is the local tangential velocity normalized using the average axial velocity, Uavc,

at the characteristic diameter; Rc is the radius at the characteristic location and r is the

radial location; Tm is the maximum momentum of the tangential velocity at the section;

and B represents the radial location at which the maximum tangential velocity is attained.

The following expressions, which are functions of the swirl intensity, were obtained by

Algifri et al. (1988) by curve-fitting several sets of experimental data.

154

Ω=mT (5.14)

Involuted single inlet: 7.17.55 −Ω=B (5.15)

Twin inlets: 35.28.245 −Ω=B (5.16)

5.2.2.2 Axial Velocity

The high swirling tangential motion at the inlet region promotes the rise of

centrifugal forces pushing the fluid toward the outer region (Algifri 1988). The pressure

is high near the wall region and very low towards the centerline, in the core region. Such

a radial shift of the fluid also results in a reduction of the axial velocity near the axis.

Also, the pressure gradient profile across the cyclone diameter decreases with

downstream position and therefore the pressure at the downstream end of the core is

greater than at the upstream, causing flow reversal in the region along the cyclone axis

when the swirl intensity is sufficiently high (Hargreaves, 1990). This characteristic

reverse flow phenomenon around the SLHC axis allows the separation of fluids and

materials of different densities. A typical axial velocity profile is shown in Figure 5.3.

The positive values of the axial velocity represent downward flow near the wall,

which is the main flow direction. Negative values represent upward reverse flow near the

SLHC axis. The flow reversal radius, rrev, is the radial position where the axial velocity is

equal to zero.

155

Figure 5.3 Typical Axial Velocity Profile along the Radial Position of the Cyclone

Caldentey et al. (2002) assumed an axis-symmetric geometry and neglecting the

effects of turbulence near the wall region (boundary layer). This resulted in an axial

velocity profile that is only function of the swirl intensity, Ω, and is given by:

17.02

33

2++⎟⎟

⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

CRr

CRr

CUu

zzavz (5.17)

where the constant C, is defined as:

7.0232

−⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=

z

rev

z

revRr

Rr

C (5.18)

and,

156

3.021.0 Ω=zR

rrev (5.19)

5.2.2.3 Radial Velocity

The radial velocity of the continuous-phase, v, is very small as compared to the

tangential and axial velocities. The continuity equation and wall conditions suggested by

Kelsall (1952) and Wolbert (1995) can be used to predict the radial velocity profile in the

SLHC, as follows:

)tan(βuRrvz

−= (5.20)

The radial velocity is a function of the axial velocity and the geometrical

parameters, as can be observed in Eq. (5.20). In the particular case of cylindrical

sections, where tan(β) = 0, the radial velocity, v, is equal to zero.

5.2.3 Pressure Drop

Caldentey et al. (2002) presented a modification of the Bernoulli’s equation for

the prediction of the pressure drop from the inlet to the underflow outlet of the LLHC. A

centrifugal force correction factor, n, in the centrifugal losses term was used to

compensate for the use of Bernoulli’s Equation under a high swirling flow condition. The

modified pressure drop equation was described as follows:

LghhUPVP cfcfcucuici θρρρρ sin)(21

21 22 ++++=+ (5.21)

157

In a similar manner, this modified pressure drop equation can be used to predict

the pressure drop in the SLHC. In such case, ρc is the density of the continuous phase; Pi

and Pu are the inlet and underflow outlet pressures respectively; Vi is the average inlet

velocity and Uu is the underflow average axial velocity; L is the SLHC total length, that is

L = Lb + Lc; where Lb and Lc are the length of the barrel and conical sections,

respectively. The Greek letter θ is the angle of the SLHC axis with the horizontal. The

variable hcf corresponds to the centrifugal force losses, which are the most relevant as

they account for most of the total pressure drop in the SLHC. Frictional losses are

described by the variable hf.

Following is a procedure proposed by Caldentey et al. (2002) to calculate the

pressure drop that can also be adopted for the SLHC:

1. Calculate the frictional losses. These are calculated in a similar manner as in

pipe flow as follows:

2)(

)()()(

2 zVzDzzfzh r

fΔ

= (5.22)

where f is the friction factor and Vr is the resultant velocity. In the conical sections, all

parameters in Eq. (5.22) are dependent of the axial position, z. The calculation procedure

divides the conical section into “m” segments and assumes a cylindrical geometry in each

segment. Then, the total frictional losses are the sum of the losses in each of the “m”

segments, and are given by:

158

( )2

Δz/2

2DD

Δz, ))12((2

1 n1n)(

−∑= − +

=natr

m

nzf

Vzfconicalh (5.23)

where Vr, is the resultant velocity and is calculated as the vector sum of the average axial

and tangential velocities. In this case, only the annular downward flow region is

considered, as given in the following equations:

222 )( zzr WUzV += (5.24)

∫ ∫

∫ ∫= π

π

φ

φ

20

20

z

rev

z

revRr

Rr

zrdrd

WrdrdW (5.25)

To simplify the calculations, the average axial velocity in Eq. (5.24), Uz, is

calculated assuming plug flow, that is, Uz is equal to the total flow rate over the annular

area from the wall to the reverse radius, rrev. The Moody friction factor is calculated using

Hall’s Correlation (Hall, 1957).

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

3/164

)Re(10

)(10210055.0)(

zzDxzf ε

(5.26)

where ε is the pipe roughness factor and Re is the Reynolds Number at a given z location,

calculated based on the resultant velocity computed in Eq. (5.24).

159

2. Calculate the centrifugal losses using the following expression:

∫= u

rev

R

ru

cf drr

rnWh

)()( 2 (5.27)

where Wu is calculated from Eq. 5.25 at the underflow outlet. In this case, the centrifugal

force correction factor, n, is equal to 2 for twin inlets, and to 3.2 for involuted single inlet.

5.3 Dispersed Phase Modeling

5.3.1 Particle Trajectories

The trajectory of a given size particle is mainly a function of the SLHC velocity

field and the physical properties of the dispersed and continuous phases. In this study, the

same Lagrangian approach utilized by Caldentey et al. (2002) is adapted to track particle

trajectories in the continuous liquid phase.

The physical model is described in Figure 5.4 that shows a solid particle at times t

and t + dt respectively. During the differential time dt, the particle moves radially with a

velocity Vr = dr/dt and axially with a velocity Vz = dz/dt. The particle velocity in the

tangential direction is assumed to be the same as that of the continuous fluid (no slip

condition). This is considered a valid assumption for the small particles that are in the

size range of the proposed SLHC model (< 150 μm).

160

Figure 5.4 Schematic of Particle Trajectory Model

The governing equation for the particle trajectory displacement is obtained by

combining the axial and radial velocity equations, and solving for the axial distance as

follows:

∫=⇒== drVVz

VV

dtdrdtdz

drdz

r

z

r

z (5.28)

Again, assuming no-slip conditions in the axial direction, in other words,

neglecting the axial buoyancy force, the particle axial velocity, Vz is equal to the fluid

axial velocity; u. Caldentey et al. (2002) considered this a reasonable simplification since

centrifugal acceleration in the radial direction is thousand times larger than the

acceleration due to gravity. On the other hand, the particle velocity in the radial direction

is equal to the fluid radial velocity, v, plus the slip velocity, Vsr. Thus, the total trajectory

displacement of the particle, z, can be obtained by rearranging Eq. (5.28) as follows:

161

rVvuz rr

rrsr

Δ⎟⎟⎠

⎞⎜⎜⎝

⎛+

= ∑ ==

2

1 (5.29)

The radial slip velocity, Vsr, is solved by balancing the forces acting on the

particle in the radial direction, as shown in Figure 5.4, and assuming a local equilibrium

momentum, as described by the following relationship:

421

6)(

22

32 dVCdr

wsrcDcd

πρπρρ =− (5.30)

The left side of Eq. (5.30) is the centripetal force, and the right side is the drag

force. Solving for the radial slip velocity, results in:

21

2

34

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

Dc

cdsr C

dr

wVρ

ρρ (5.31)

where d is the particle diameter, ρd is the density of the dispersed phase, ρc is the density

of the continuous phase and CD is the drag coefficient.

The drag coefficient is calculated using a relationship presented by Morsi and

Alexander, (1971) and Hargreaves, (1990), as follows:

232

1ReRe dd

DbbbC ++= (5.32)

The “b” coefficients are dependent on the Reynolds Number of the particles (dispersed-

phase), which is defined as:

162

c

srcd

Vdμ

ρ=Re (5.33)

Table 5.1 shows values for the “b” coefficients, as functions of the range of Red.

Table 5.1. Drag Coefficient Constants

Range b1 b2 b3

Red < 0.1 0 24 0

0.1 < Red < 1 3.69 22.73 0.0903

1 < Red < 10 1.222 29.1667 -3.8889

10 < Red < 100 0.6167 46.5 -116.67

Finally, the axial location of the given particle is determined by numerically

integrating Eq. (5.29), as a function of the radial position.

5.3.2 Separation Efficiency

The SLHC separation efficiency is determined based on the particle trajectory

approach discussed in the previous section. The particle separation probability is a

function of its radial position, r, along the hydrocyclone axial length, Lc. As illustrated in

Figure 5.5, the approach used in this study consists of launching a particle of a given size

at the SLHC centerline (r = 0) right above the underflow outlet (Lcrit = 0). The trajectory

of the particle is then tracked as it moves upward with axial and radial velocities to

determine whether it is able to reach the downward flow region (Rc > r > rrev). If the

particle reaches the downward flow region before reaching the top end of the conical

section, (Lcrit < Lc), it has a higher probability to be separated through the U/F outlet.

163

Conversely, particles that remain longer in the reverse core region are more likely

to be carried upward by the clean liquid phase and be discharged through the O/F outlet.

If a particle is within the reverse core region (r < rrev) and its axial position is greater than

the length of the conical section (Lcrit > Lc), the particle is not separated, and therefore

has a separation efficiency equal to zero (ε(d) = 0). Also, if a particle moving down (in

the downward flow region) reaches again the reversed core region at any given length

before the U/F exit (Lcrit > 0), the tracking process is repeated until the particle exits

either through the underflow [ε(d) = 1)] or the overflow outlet [ε(d) = 0].

Figure 5.5 Schematic of Particle Trajectory and Separation Efficiency

164

Assuming a homogeneous distribution of particles inside the SLHC, the

separation efficiency of a given particle diameter, ε(d), can be expressed as the ratio of

the length within which the particle reaches the downward flow region and is separated

(Lcrit), over the total trajectory length, Lc. Thus, the particle separation efficiency

prediction proposed in this study is given by:

⎪⎪

⎩

⎪⎪

⎨

⎧

≤

<<−

≥

=

0,1

0,

,0

)(

crit

ccritc

critc

ccrit

Lif

LLifL

LL

LLif

dε (5.34)

Repeating this tracking procedure for the different feed particle sizes, yields the

grade separation efficiency curve, as given in Figure 5.6. This curve normally has an “S”

shape and represents the grade separation efficiency, ε(d), as a function of particle

diameter, d. As can be observed, smaller particles have efficiencies close to zero while

increasing particle size sharply increases ε(d) until d100 is reached. The parameter d100

represents the smallest particle size with a 100% separation probability.

Figure 5.6 Grade Separation Efficiency Probability Curve

165

The grade separation efficiency curve is known as the characteristic separation

curve for a given SLHC configuration, set of conditions and properties of the continuous

and dispersed phases. This curve is independent of the feed particle size distribution and

is used in many cases to evaluate the separation sharpness of a given SLHC geometry.

Using the grade separation efficiency curve, ε(d) and the feed particle size

distribution, another separation efficiency parameter known as the O/F purity, εo, can be

determined as follows:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−=∑

∑

jj

jjj

o iV

iVd

~

~)(

1

ε

ε (5.35)

where jiV~ is the cumulative feed percent volume distribution of particle size, dj. The

O/F purity also measures the ability of the SLHC to separate the dispersed phase from the

continuous phase.

5.4 Design Code

A design code for the SLHC was developed based on the proposed SLHC

mechanistic model. The Caldentey et al. (2002) design code for the LLHC was coupled

with the new SLHC design code; resulting in a comprehensive hydrocyclone design tool

for either LLHC or SLHC equipment. The program provides the industry with a more

flexible and efficient design and performance analysis tool, as compared to costly and

lengthy CFD simulations.

166

CHAPTER 6

MODEL COMPARISONS AND DISCUSSION

This chapter presents comparisons between the proposed SLHC mechanistic

model predictions and the experimental data acquired by Culwell et al. (1994).

Comparisons are made for each of the different SLHC configurations, and against global

and average grade separation efficiencies for all available datasets.

A detailed analysis of model discrepancies with Dataset Group A (117 datasets)

as a function of different operational and flow conditions is also presented in an attempt

to establish the sensitivity of the model to these parameters. Table 6.1 shows results of

model predictions versus experimental data for one every four datasets. Datasets with

mass balance (MB) inconsistencies are highlighted and shown in bold font. Table A.1 in

Appendix A shows results for all datasets.

6.1 Definition of Model Discrepancy

The global efficiency discrepancy, ED, between model predictions and

experimental data is calculated as follows:

m

mpD E

EEE

−= (6.1)

where Ep is the efficiency predicted by the model and Em is the measured global

efficiency. Model agreement with global efficiency data is defined as 1-ED.

167

Table 6.1 Summary of Model Predictions and Experimental Results

Feed Conditions Geometric Specs Experimental Results Model Predictions

Dat

aset

#

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Inle

t Pre

ssur

e (p

sig)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effic

.

Gra

de-G

loba

l Ef

fic. D

iff.

Mod

el E

ffic.

Glo

bal E

ffic.

D

iscr

ep.

Gra

de E

ffic.

D

iscr

ep.

1 1.19 0.253 213 105 20.6 5.5 3.2 83.2% 81.1% 2.1% 82.6% -0.7% 1.8%4 1.21 0.187 155 107 20.6 5.5 3.2 81.9% 44.0% 37.9% 82.0% 0.1% 86.3%8 1.25 0.303 242 116 20.6 5.5 3.2 84.3% 69.6% 14.7% 82.0% -2.8% 17.7%

12 1.24 0.315 254 114 20.6 5.5 3.2 83.3% 79.3% 4.0% 82.2% -1.4% 3.7%16 1.25 0.180 144 116 20.6 5.5 3.2 80.9% 79.4% 1.5% 80.2% -0.9% 0.9%20 1.29 0.449 349 124 20.6 5.5 3.2 90.0% 74.6% 11.6% 81.0% -10.0% 8.5%24 1.30 0.216 166 125 20.6 5.5 3.2 85.4% 80.9% 4.5% 81.3% -4.8% 0.5%28 1.29 0.453 351 126 20.6 5.5 3.2 88.1% 82.2% 5.9% 81.5% -7.5% -0.9%32 1.29 0.306 238 124 20.6 5.5 3.2 85.8% 78.5% 7.3% 81.0% -5.6% 3.2%36 1.29 0.445 346 125 20.6 5.5 3.2 86.4% 79.0% 7.4% 81.6% -5.5% 3.4%40 1.28 0.253 197 126 20.6 5.5 3.2 86.4% 86.5% 0.1% 85.8% -0.6% -0.8%44 1.23 0.164 134 116 20.6 5.5 3.2 79.2% 75.5% 3.7% 89.2% 12.7% 18.2%48 1.22 0.111 91 115 20.6 5.5 3.2 72.5% 56.9% 15.6% 88.5% 22.1% 55.5%52 1.23 0.128 104 115 20.6 5.5 3.2 84.9% 73.8% 11.1% 84.6% -0.3% 14.6%56 1.26 0.112 89 125 20.6 5.5 3.2 44.9% 19.6% 25.3% 87.0% 93.9% 344.4%60 1.27 0.110 86 124 20.6 5.5 3.2 59.5% 42.4% 17.1% 86.5% 45.4% 104.0%64 1.21 0.242 200 110 20.6 5.5 3.2 79.2% 77.3% 1.9% 82.8% 4.5% 7.1%68 1.21 0.182 150 110 20.6 5.5 3.2 78.8% 71.8% 7.0% 82.8% 5.0% 15.4%72 1.21 0.226 187 110 20.6 5.5 3.2 79.0% 74.3% 4.7% 83.6% 5.9% 12.5%76 1.21 0.113 93 111 20.6 5.5 3.2 82.8% 72.2% 10.6% 84.6% 2.1% 17.2%80 1.21 0.238 197 110 20.6 5.5 3.2 84.3% 77.3% 7.1% 85.4% 1.3% 10.5%84 1.29 0.151 117 126 20.6 5.5 3.2 67.2% 47.2% 20.1% 81.5% 21.3% 72.9%88 1.28 0.342 267 126 20.6 5.5 3.2 51.7% 34.5% 17.2% 82.2% 59.0% 138.3%92 1.27 0.137 107 126 20.6 5.5 3.2 81.6% 76.7% 4.9% 86.8% 6.4% 13.2%96 1.28 0.213 166 126 20.6 5.5 3.2 84.4% 82.5% 1.9% 86.4% 2.3% 4.7%100 1.27 0.282 221 126 20.6 5.5 3.2 82.1% 80.2% 1.8% 86.8% 5.8% 8.2%104 1.26 0.062 50 106 20.6 5.5 2.2 77.0% 67.2% 9.8% 83.0% 7.7% 23.5%108 1.26 0.153 122 106 20.6 5.5 2.2 79.7% 70.6% 9.1% 83.4% 4.6% 18.1%112 1.24 0.167 134 106 20.6 5.5 2.2 80.3% 70.3% 10.0% 83.4% 3.8% 18.6%116 1.29 0.176 137 113 20.6 5.5 2.2 85.7% 74.8% 10.9% 83.6% -2.4% 11.8%120 1.35 0.245 182 105 20.6 5.5 2.2 83.6% 71.2% 12.5% 78.5% -6.2% 10.3%124 1.26 0.187 148 126 20.6 5.5 3.2 80.1% 72.0% 8.1% 80.7% 0.8% 12.1%128 0.27 0.050 183 125 3.2 2.0 1.5 76.5% 65.5% 10.9% 75.5% -1.2% 15.3%132 0.29 0.035 122 125 4.5 2.6 1.5 82.8% 71.4% 11.4% 78.2% -5.6% 9.5%136 0.28 0.043 153 126 4.5 2.6 1.5 89.9% 75.8% 14.2% 78.6% -12.5% 3.8%140 0.27 0.082 302 116 4.5 2.6 1.5 89.0% 80.1% 8.9% 77.2% -13.3% -3.7%144 0.27 0.018 67 116 4.5 2.6 1.5 75.3% 51.1% 24.2% 77.5% 2.8% 51.6%148 0.28 0.019 69 116 4.5 2.6 1.5 79.5% 68.7% 10.8% 80.3% 1.1% 17.0%152 0.16 0.032 203 104 3.2 2.0 1.0 77.5% 50.5% 27.0% 84.2% 8.7% 66.7%155 0.17 0.037 218 125 3.2 2.0 1.0 81.0% 45.7% 35.3% 82.5% 1.9% 80.7%

168

Similarly, the grade efficiency discrepancy, εD, between model predictions and

experimental data is calculated as follows:

m

mpD

Eε

εε

−= (6.2)

where mε is the measured average grade efficiency. Model agreement with average grade

efficiency data is defined as 1-εD.

6.2 Verification of Mechanistic Model Predictions

6.2.1 Global Separation Efficiency Comparison

A summary of model predictions agreement with global efficiency data for the

three different dataset groups is given in Table 6.2. As can be seen in this table, model

predictions are in very good agreement with experimental global separation efficiency

data.

Table 6.2 Global Model Discrepancy Results per Dataset Group

Average

Agreement

Culled Datasets 95% 117 94.7%

MB Consistent Datasets 90% 132 92.9%

ALL Datasets 68% 155 89.5%

Dataset Groups#

DatasetsConfidence

Level

A)

B)

C)

169

As can be observed, the average agreement of Dataset Group A is about 94.7%

(or 5.3% discrepancy). Also, about 91% of this group has data-model differences lower

than 10%, as can be observed in Figure 6.1.

As can also be seen in Figure 6.2, about 88% of the culled datasets (Group A)

have discrepancies lower than 10% and about 95% of them have discrepancies below

15%. For instance, only 2.6% of the culled datasets have discrepancies above 25%, with

a maximum global discrepancy of +28.7%.

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Model Efficiency Predictions

Expe

rimen

tal

Glo

bal E

ffici

ency

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)](*) Dataset w / Mass Balance Inconsistency: OF >IN

91% of Datasets < 10% difference

Figure 6.1 Experimental Global Efficiency Results vs. Model Predictions

170

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30%

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50%

1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151

Dataset # (in Chronological Order)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.2 Discrepancy of Model Predictions vs. Global Efficiency for each Dataset

Model predictions appear to be in good agreement with the data regardless of

SLHC geometry. However, very few data are available for some of the geometrical

configurations (e.g. 10-mm SLHC with 2.0 mm VF and 1.5 mm spigot), and therefore,

further investigation is recommended for these geometrical setups.

6.2.2 Average Grade Separation Efficiency Comparison

A summary of results showing model discrepancy with the three different

dataset groups is shown in Table 6.3. As can be seen, model predictions are in very good

agreement with the average experimental grade separation efficiency results. The overall

average agreement with the culled datasets (having 95% confidence level) is about 88.2%

(or 11.8% discrepancy). Figure 6.3 shows that more than 70% of the culled datasets have

differences lower than 10%.

171

Table 6.3: Average Grade Model Discrepancy Results per Dataset Group

Average

Agreement

Culled Datasets 95% 117 88.2%

MB Consistent Datasets 90% 132 81.5%

ALL Datasets 68% 155 68.5%

Dataset Groups # Datasets

Confidence Level

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Model Efficiency Predictions

Expe

rimen

tal

Avg

. Gra

de E

ffici

ency

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)](*) Dataset w / Mass Balance Inconsistency: OF >IN

70% of Datasets < 10% difference

Figure 6.3 Experimental Average Grade Efficiency Results vs. Model Predictions

As shown in Figure 6.4, more than 70% of the culled datasets have discrepancies

lower than 15%, and about 86% have discrepancies lower than 20%. For instance, only

5.1% of the culled datasets have discrepancies in excess of 25% and only 2.6% of the

datasets have discrepancies greater than 30%, with a maximum discrepancy observed of

+44.7%.

A)

B)

C)

172

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0%

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1 11 21 31 41 51 61 71 81 91 101 111 121 131 141 151

Dataset # (in Chronological Order)

Mod

el v

s. A

vg. G

rade

Effi

cien

cy

Disc

repa

ncy

- [(E

p - ε

m) /

εm

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.4 Discrepancy of Model Predictions vs. Average Grade Efficiency per Dataset 6.2.3 Grade Separation Efficiency Predictions

Experimental grade efficiency curves presented in Chapter 4 are now compared

against the mechanistic model predictions, as shown in Figures 6.5 to 6.14. These include

two sample datasets for each of the five different geometrical configurations tested. As

can be observed, in most cases the model grade efficiency curves show very good

agreement with the experimental curves for a wide range of conditions for all geometrical

arrangements. The 10-mm SLHC with 2.0 mm VF and 1.5 mm spigot (U/F) shows the

highest disagreement. However, very few experiments are available for this unit

configuration, and therefore further investigation is recommended for this and other

geometrical setups.

173

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.5 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 1)

010

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6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.6 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 22)

Qin: 1.30 m3/hr; Pin: 126 psig Cs,in: 166 ppm; inm& = 0.216 kg/hr VF: 5.5 mm; U/F: 3.2 mm

Qin: 1.19 m3/hr; Pin: 114 psig Cs,in: 213 ppm; inm& = 0.253 kg/hr VF: 5.5 mm; U/F: 3.2 mm

174

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.7 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 110)

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.8 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 120)

Qin: 1.25 m3/hr; Pin: 106 psig Cs,in: 220 ppm; inm& = 0.275 kg/hr VF: 5.5 mm; U/F: 2.2 mm

Qin: 1.35 m3/hr; Pin: 105 psig Cs,in: 182 ppm; inm& = 0.245 kg/hr VF: 5.5 mm; U/F: 2.2 mm

175

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.9 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 126)

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n Ef

ficie

ncy

(Dat

a vs

. Mod

el)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.10 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 128)

Qin: 0.26 m3/hr; Pin: 124 psig Cs,in: 63 ppm; inm& = 0.016 kg/hr VF: 2.0 mm; U/F: 1.5 mm

Qin: 0.27 m3/hr; Pin: 125 psig Cs,in: 183 ppm; inm& = 0.050 kg/hr VF: 2.0 mm; U/F: 1.5 mm

176

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n Ef

ficie

ncy

(Dat

a vs

. Mod

el)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.11 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 135)

y

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.12 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 148)

Qin: 0.28 m3/hr; Pin: 126 psig Cs,in: 17 1 ppm; inm& = 0.048 kg/hr VF: 2.6 mm; U/F: 1.5 mm

Qin: 0.28 m3/hr; Pin: 116 psig Cs,in: 69 ppm; inm& = 0.019 kg/hr VF: 2.6 mm; U/F: 1.5 mm

177

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.13 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 149)

010

2030

4050

6070

8090

100

2.1 2.6 3.2 4.1 5.1 6.3 7.9 9.8 12.3 15.3 19.2 23.9 29.8 37.3 46.5 58.1Particle Diameter (microns)

Gra

de S

epar

atio

n E

ffici

ency

(D

ata

vs. M

odel

)

Inlet_Cum_Vol_pct UF_Calc_Wt_CumVol_pctOF_Weighted_CumVol_pct Model_OF_CUMVol_pctModel_UF_CUMVol_pct

Figure 6.14 Grade Separation Efficiency - Data vs. Model Predictions (Dataset 151)

Qin: 0.17 m3/hr; Pin: 116 psig Cs,in: 136 ppm; inm& = 0.022 kg/hr VF: 2.0 mm; U/F: 1.0 mm

Qin: 0.16 m3/hr; Pin: 116 psig Cs,in: 196 ppm; inm& = 0.031 kg/hr VF: 2.0 mm; U/F: 1.0 mm

178

6.3 Analysis of Model Sensitivity to Different Experimental Parameters

This section presents the analysis of model discrepancy with global and grade

separation efficiency data, as a function of several experimental conditions. This analysis

seeks to evaluate trends of model disagreement with the data and the sensitivity of the

model to different flow and geometrical parameters.

6.3.1 Inlet Liquid Flow Rate and Feed Velocity

The model closely predicts the global efficiency for the entire range of

experimental inlet flowrates and feed velocities as shown in Figures 6.15 and 6.16. Good

agreement is observed for low as well as high range of inlet flow velocities. The more

significant discrepancies are observed for the mid range of feed velocities; however, this

could be due to the effect of a different variable, and thus, further analysis follows.

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-10%

0%

10%

20%

30%

40%

50%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

Feed Liquid Flow Rate (m3/hr)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.15 Global Efficiency Discrepancy as a Function of Feed Liquid Flow Rate

179

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-10%

0%

10%

20%

30%

40%

50%

10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Inlet Velocity (m/s)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(

Ep -

Em

) / E

m]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.16 Global Efficiency Discrepancy as a Function of Inlet Velocity

6.3.2 Overflow Split Ratio

Good agreement of model predictions is observed for split ratios lower than 0.95

(Figure 6.17). Above this value, the discrepancy increases as efficiency is over-estimated.

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0%

10%

20%

30%

40%

50%

0.70 0.75 0.80 0.85 0.90 0.95 1.00

Overflow Split Ratio

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.17 Global Efficiency Discrepancy as a Function of Overflow Split Ratio

180

6.3.3 Feed Solids Mass Flow Rate and Feed Solids Concentration

In general, model agreement with the data deteriorates at low feed solids mass

flow rates and concentrations, regardless of geometry (Figures 6.18 and 6.19).

Nevertheless, this effect might be reversed if solids concentration continues to increase,

and therefore further verification of model predictions at higher solids concentrations is

necessary. Particle interactions become more significant at high solids concentrations and

the assumptions in the model regarding particle-particle interactions might not be

realistic.

As discussed earlier, Braun and Bohnet (1990) suggested that an increase in solids

mass flow rates or in feed solids concentration, while keeping all other operating

parameters constant, leads to a coarser cut size, reduced separation sharpness, and higher

pressure drop across the cyclone. They also suggested that at higher mass flow rates, the

pressure drop increases due in part to the hindered settling effect.

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0%

10%

20%

30%

40%

50%

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50

Mass Flow Rate of Feed Solids (kg/hr)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.18 Global Efficiency Discrepancy as a Function of Solids Mass Flow Rate

181

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0%

10%

20%

30%

40%

50%

0 50 100 150 200 250 300 350 400

Feed Solids Concentration (mg/L)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.19 Global Efficiency Discrepancy as a Function of Solids Concentration

6.3.4 Feed Oil to Solids Concentration Ratio

Model predictions do not seem to be affected by the feed oil to solids

concentration ratio increases, as shown in Figure 6.20. There is only a slight increase in

model discrepancy as the concentration ratio increases, but further investigation under

higher concentration ratios is recommended to better establish this connection.

6.3.5 Inlet Temperature

Model predictions do not seem to be sensitive to inlet temperature under the given

experimental conditions, and therefore, to its effect on fluid viscosity (Figure 6.21).

However, further investigation at higher temperatures is also recommended to establish

the sensitivity of the model to a wider range of fluid viscosity changes.

182

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0%

10%

20%

30%

40%

50%

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Oil / Solids Concentration Ratio

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.20 Global Efficiency Discrepancy as a Function of Oil/Solids Concentration Ratio

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0%

10%

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30%

40%

50%

90 100 110 120 130 140 150 160 170

Inlet Temperature (oF)

Mod

el v

s. G

loba

l Effi

cien

cy

Disc

repa

ncy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.21 Global Efficiency Discrepancy as a Function of Inlet Temperature

183

6.3.6 Underflow (U/F) to Overflow (O/F) Backpressure Ratio

As explained in Chapter 4, it is critical that constant outlet backpressures be

applied to avoid disturbing the vortex and creating instabilities. The ratio of U/F to O/F

backpressure is also very important for optimal operation and to avoid the formation of a

gas core. The model does not consider the effect of the imposed outlet backpressures,

resulting in greater discrepancies at higher backpressure ratios, as shown in Figure 6.22.

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0%

10%

20%

30%

40%

50%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

U/F to O/F Backpressure Ratio

Mod

el v

s. G

loba

l Effi

cien

cy

Disc

repa

ncy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.22 Global Efficiency Discrepancy as a Function of U/F to O/F Backpressure Ratio

6.3.7 Effect of the Feed Solids Mean Particle Size

The model shows good agreement for the range of experimental particle size

(Figures 6.23 and 6.24). However, model sensitivity is observed for finer particles (< 10

μm). This could be explained as finer particles become more easily entrained by the

continuous liquid phase and carried-over, and therefore, modeling their trajectories

requires a more rigorous approach.

184

-50%

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

8 10 12 14 16 18 20 22

Feed Particle Volume-Averaged MEAN Size (microns)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.23 Global Efficiency Discrepancy as a Function of Feed Particle Volume-

Averaged Mean Size

-50%

-40%

-30%

-20%

-10%

0%

10%

20%

30%

40%

50%

10 12 14 16 18 20 22 24 26 28 30 32 34

Feed Mean Sauter d32 Diameter (microns)

Mod

el v

s. G

loba

l Effi

cien

cy

Dis

crep

ancy

- [(E

p - E

m) /

Em

]

1-inch [VF: 5.5; UF: 3.2 (0.60 UF/VF; 0.85 IN/VF)]1-inch [VF: 5.5; UF: 2.2 (0.40 UF/VF; 0.85 IN/VF)]10-mm [VF: 2.0; UF: 1.0 (0.50 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.0; UF: 1.5 (0.75 UF/VF; 1.00 IN/VF)]10-mm [VF: 2.6; UF: 1.5 (0.60 UF/VF; 0.85 IN/VF)]

Figure 6.24 Global Efficiency Discrepancy as a Function of Sauter Mean Diameter

185

CHAPTER 7

SUMMARY, CONCLUSIONS AND RECOMMENDATIONS

This chapter presents a summary of results, conclusions, and contributions of the

present study, as well recommendations for future research.

7.1 Summary and Conclusions 7.1.1 Experimental Results

• The experimental data used in the present study to validate the proposed

mechanistic model were acquired by Culwell et al. (1994). The data include

155 experimental datasets performed utilizing two small diameter SLHCs,

namely, 10-mm and 1-inch units, for a wide range of flow conditions and

configurations, including: inlet velocities between 14 to 24 m/s, inlet pressures

from 100 to 130 psig, feed solids concentrations from 50 to 370 mg/L, feed

solids particle size distribution ranging from 2 to 60 µm, Sauter mean

diameter (d32) from 12 to 32 µm, oil concentrations from 30 to 400 ppm,

specific gravity of the continuous-phase of 0.989, and average oilfield solids

density of 2.0 gr/cc.

• The experimental data underwent a rigorous evaluation process to determine

their consistency and certainty level. Subsequently, the datasets were

186

classified according to their confidence level, namely 95% confidence (Group

A), 90% confidence (Group B), and 68% confidence (Group C or all datasets).

• Group A with the highest confidence level (95%) contains a total of 117

“culled datasets” representing 76% of the total available datasets. This group

exhibits better repeatability of results, mass balance consistency, and smaller

differences between global and grade separation efficiencies (< 15%).

• Results from the culled datasets show that both SLHC units tested were able

to remove about 75% to 92% of up to 60 ppm feed solids from produced

water having a 14.8 μm mean diameter (d32 of 23.1 μm) with a 19.4 μm

standard deviation. Also, the SLHCs recovered 85% of the feed water through

the O/F outlet, with a 35 ppm of 7.8 μm mean diameter (3.1 μm std. dev.).

The U/F recovered an average 13.5 μm mean particle diameter with 18.8 μm

standard deviation.

• Regarding equipment dimensions and configurations, the best 1-inch unit

efficiency was attained with the 5.5 mm vortex finder (VF) and a 3.2 mm

spigot, also showing better capacity to remove larger sized particles.

• The best 10-mm unit was attained with a 2.6 mm vortex finder and a 1.5 mm

spigot. Of the two units tested, the 10-mm SLHC showed slightly higher

solids removal efficiency, with a smaller particle size cut point. However, the

number of tests on the 10-mm unit was fewer, and therefore further

investigation of such assessment is recommended.

187

• Overall, the less efficient setup seems to be the 10-mm unit having a 2.0 mm

vortex finder and a 1.5 mm spigot, but very few data are available for this

configuration, and therefore the observations are not conclusive.

• The optimum feed velocities are between 16 to 17.5 m/s for both SLHC units.

• The optimum O/F to inlet split ratio for the 10-mm SLHC is in the range of

0.83 to 0.87, and from 0.87 to 0.93 for the 1-inch unit. Split ratios outside

these ranges appear to be detrimental to separation efficiency.

• Solids removal efficiency increases as the feed mass flow rates and solids

concentrations increase, regardless of equipment geometry. However, this

effect might be reversed if solids concentrations continue to increase beyond a

certain limit, according to Braun and Bohnet (1990).

• Separation efficiency is affected by high feed oil to solids concentration ratio,

regardless of equipment configuration. This is likely to be caused by the oil

tendency to agglomerate solids and carry (buoy) them into the O/F.

• Efficiency seems to slightly improve with higher flow temperatures due to

viscosity reduction. However, the experimental temperature range was not

broad enough to confirm this statement, and thus, further investigation is

recommended.

• The effect of inlet pressure on separation efficiency could not be clearly

established from the data, and therefore an analysis of the imposed

backpressures in the O/F and U/F outlets was performed. Results reveal that

188

imposing outlet backpressures may help stabilize fluctuations due to flow

transients and reduce or avoid the formation of a gas core.

• According to the results, the optimum U/F to O/F backpressure ratio is below

0.5. However, further investigation is recommended to establish the optimum

limits of outlet to inlet pressure ratios that would maximize efficiency.

• In general, solids carry-over deteriorates with larger particle diameters

regardless of SLHC geometrical configuration. This is in agreement with

Dwari et al. (2004) and several other observations reported in the literature.

7.1.2 Mechanistic Modeling

• The proposed SLHC mechanistic model is a modification of the model

proposed by Caldentey et al. (2002) for liquid-liquid hydrocyclones (LLHC).

The model enables the prediction of the hydrodynamic flow behavior in the

SLHC, as well as the solids global and grade separation efficiency curves.

These efficiency curves are determined based on swirl intensity prediction and

particle trajectory analysis. The inlet-to-U/F pressure drop is estimated

utilizing an energy balance equation, as proposed by Caldentey et al. (2002).

• The required input for the model includes the hydrocyclone geometry,

properties of the dispersed and continuous phases, inlet particle size

distribution, feed solids concentration, and operational conditions.

• Very good agreement is observed between model predictions and the

experimental data. The model is able to predict the global separation

189

efficiency with a 94.7% agreement and the average grade separation

efficiency with an 88.2% agreement for Group A datasets.

• Model predictions appear to be in good agreement with the data regardless of

unit geometry. However, further investigation is recommended for the 10-mm

SLHC with 2.0 mm VF and 1.5 mm spigot.

• A detailed analysis of model discrepancies with the culled datasets as a

function of different operational and flow conditions was performed in an

attempt to establish the sensitivity of the model to these parameters.

• The model is capable of closely predicting global efficiency for the entire

range of experimental inlet flow rates and feed velocities. Also, good and

consistent agreement is observed for split ratios lower than 0.95. Above this

value, model discrepancy increases generally overestimating equipment

separation efficiency.

• In general, model agreement deteriorates at low feed solids mass flow rates

and concentrations, regardless of SLHC geometry. Further verification of the

model at higher solids concentrations is necessary, as particle interactions

become more significant at higher concentrations. It is likely that the

assumptions of the model regarding particle-particle interactions might not

capture these effects and their impact on separation efficiency.

• Model predictions do not seem to be affected by variations in the feed oil to

solids concentration ratio and in inlet temperatures. This might be due to

190

simplifications in the model regarding continuous phase densities and slurry

viscosities. Further verification is also recommended regarding this issue.

• The model considers neither the effect of the gas core nor of the imposed

outlet backpressures, resulting in greater model discrepancies at higher

backpressures ratios.

• The model shows good agreement for the range of particle size used in the

experiments. However, some sensitivity is observed for the smaller particle

sizes (< 10 μm) as compared to the coarser particles. This is probably due to

the fact that smaller particles become more easily entrained by the continuous

liquid phase and carried-over, and therefore, it is more challenging to model

their trajectories.

7.2 Main Contributions

• A new mechanistic model for the efficient design and performance analysis of

small diameter Solid-Liquid Hydrocyclones (SLHC) has been developed and

validated against available experimental data from the industry.

• A design code for the SLHC was developed based on the proposed SLHC

mechanistic model. The Caldentey et al. (2002) design code for the LLHC

was coupled with the new SLHC design code; resulting in a comprehensive

hydrocyclone design tool for either LLHC or SLHC equipment. The program

provides the industry with a more flexible and efficient design and

performance analysis tool, as compared to costly and lengthy CFD

simulations.

191

• A database (DB) management system, known as CycloneMaster, was

developed to store, organize and consolidate all the available SLHC data. The

DB system is also a powerful tool to benchmark this and other simulators and

mechanistic models, as model predictions versus experimental data can be

easily plotted side-by-side, compared and analyzed. The DB interface

provides users with the most relevant information of the experimental

program, including equipment documentation, test objectives, test

configurations, and the description of the experimental procedures.

• The DB management system enables addition of future data sets.

7.3 Recommendations

General recommendations for future work have been included and discussed

throughout this manuscript. Other more specific recommendations include:

• The effect of variations in solids density needs to be addressed. The available

experimental data utilized oilfield produced solids having an average density

of 2.0 gr/cc. Very few experiments were conducted using silica flour with a

2.2 gr/cc density. However, most of these datasets had mass balance

inconsistencies or high global-grade efficiency differences, and therefore,

results are inconclusive. As a result, it is recommended that additional data be

gathered under a wider range of solid particles densities to further validate the

proposed model.

• The proposed model has been verified for very fine particles (2 to 60 μm) and

small diameter hydrocyclones. Caution is advised in using the model for

192

larger geometries and coarser particles, and therefore, further investigation

needs to be conducted to establish the validity of the model, or to adapt it to

such conditions.

• The effect of the vortex finder length is not considered in the proposed model.

Thus, it would be a good contribution to model and validate the influence of

this geometrical parameter on the equipment efficiency.

• Investigate the effect of other types of continuous fluid medium on solids

separation, in particular, fluids of different viscosities and densities.

• Future research should consider comparing the proposed SLHC model to the

model proposed by Lagutkin et al. (2004) and Lagutkin and Baranov (2004)

using the available oilfield data, new acquired data, and other published data.

This will be particularly useful to study the effect of the Coriolis force on

solids separation efficiency.

• In future experimental investigations, it is recommended to continuously

monitor and record flow transients. In-line (real time) particle size distribution

measurement is also recommended.

• Finally, it is recommended that in further experimental investigations, tests

under same or similar range of conditions as those with the higher uncertainty

level of the experimental work of Culwell et al. (1994) be conducted.

193

NOMENCLATURE

A = cross sectional area / constant cylindrical-conical hydrocyclone structural and

operating conditions (Baranov et al., 1996)

a = diameter of air core in cyclone, m

acor = Coriolis acceleration

B = peak tangential velocity radius factor / overflow output of the hydrocyclone

c = concentration

cs = concentration of solids, mg/L

C1 = concentration of solids in suspension, kg/m3

CD = drag coefficient

D = diameter

d = diameter of a particle, mm

dr/dt = flow tangential velocity / particle radial velocity component, m/s

d50 = cut size diameter of particle, mm

Dc = characteristic diameter of the hydrocyclone, m

Dvf = inside diameter of vortex finder, m

E = global separation efficiency, %

F = split ratio

Fcor = Coriolis force

FD = steady-state drag force

194

FApp = added mass force

FBas = Basset force

FLS = Saffman lift force

FLM = Magnus lift force

FPG = pressure gradient force

)(~kv dF = cumulative volume frequency distribution of particle size

)(~jv df = volume frequency distribution of particle size

f = friction factor

G(x) = grade separation efficiency, %

G’(x) = reduced grade separation efficiency, %

g = acceleration due to gravity, m/s2

h = losses

I = inlet factor

L = total length of cyclone from top plate to apex, m

m = Nº of segments / mass (Ternovskii and Kutepov, 1994; Baranov et al., 1996)

= mass flow rate

pM& = mass flow rate of solids, kg/s

MT = axial momentum flux at the characteristic diameter position

Mt = momentum flux at the inlet slot

n = centrifugal force correction factor / inlet factor / number

N = total number of size intervals of characteristic particle size (CC channels)

P = pressure

p’ = static pressure, N/m2

m&

195

Q = volumetric flow rate, m3/s

q = volumetric flow rate, m3/s

R = radius, m

R1= R − 1/2a – 1/2Di

Re = Reynolds number

Rf = underflow-to-throughput ratio

Rte = cyclone radius (Ternovskii and Kutepov, 1994)

r = any radius, m / radial position, m

rZ0 = maximum radius of the hydrocyclone body at νϕr = 0 (Povarov, 1978)

S = regression constant

t = time

Tm = maximum tangential velocity momentum

U = bulk axial velocity / radial velocity of liquid, m/s

u = continuous phase local axial velocity, m/s

up = particle instantaneous velocity, m/s

Up = radial velocity of particle relative to the liquid, m/s

v = continuous phase local radial velocity, m/s

νϕe = tangential flow velocity of the dispersion medium, m/s

νin = inlet flow velocity, m/s (Ternovskii and Kutepov, 1994)

νϕr, = radial velocity, m/s

V = volumetric fraction / fluid velocity, m/s

jiV~ = cumulative feed percent volume distribution of particle size, dj.

V& = volumetric flow rate, m3/h

196

V1 = tangential velocity in cyclone, m/s

Vr = particle radial velocity, m/s

Vsr = particle slip velocity in the radial direction

Vz = particle axial velocity

W = axial velocity in cyclone, m/s

w = continuous phase tangential velocity / radial velocity (Braun and Bohnet, 1990)

z = axial position

Greek Letters:

α = angle

Ω = swirl intensity

β = taper section semi-angle / Stoke’s resistance coefficient (Baranov et al., 1996)

∆d = size of the intervals of characteristic particle diameter

pΔ = pressure drop

ε = grade efficiency / purity / pipe roughness

ξ = coefficient of hydraulic resistance (Ternovskii and Kutepov, 1994)

η = particle separation efficiency

θ = axis inclination angle to horizontal

μ = viscosity

υ = kinematic viscosity of the dispersion medium

ρ = density / flow density, kg/m3

Φ = horizontal plane angle

197

Subscripts:

av = average

b = barrel or cylindrical section

c = characteristic diameter location / continuous phase / corrected / conical section

cf = centrifugal

cy = cyclone

crit = critical

d = dispersed phase / particle

f = frictional / fluid

g = gravity acceleration / body acceleration (Akbar et al. 2001)

i = inlet

in = inlet

j = No. of iterations for frequency distributions of particle size

k = index of maximum particle size in a cumulative volume frequency distribution

m = dispersion medium

n = number

o = overflow

p = particle

r = resultant

rev = reverse

sr = slip radial velocity

s = solids

u = underflow

198

v = volume

z = axial position

Abbreviations:

ANN = Artificial Neural Networks

CFD = Computational Fluid Dynamics

CC = Coulter Counter Multisizer

EIT = Electrical Impedance Tomography

DRSM = Differential Reynolds Stress Model

DSM = Differential Stress Turbulence Model

FEM = Finite Element Method

LDA = Laser Doppler Anemometry

LDV = Laser Doppler Velocimetry

LES = Large Eddy Simulation

LIF = Laser Induced Fluorescence

LLHC = Liquid-Liquid Hydrocyclones

MB = Mass Balance

O/F = overflow outlet

PDA = Particle Dynamics Analyzer

RSM = Reynolds-Stress turbulence model

RNG = Renormalization Group (k-є)

UST = Ultrasound Tomography

U/F = underflow outlet

VOF = Volume of Fluid

199

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217

APPENDIX A

EXPERIMENTAL DATA AND MODELING RESULTS

Detailed experimental data and model prediction results are presented in this

section. Datasets shown in boldface blue font identify those having MB inconsistency.

Table A.1 Experimental Data and Model Prediction Results for All Datasets

Feed Conditions SLHC Specs Efficiency Data Model Predictions

Dat

aset

#

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Split

Rat

io (%

)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effii

ency

Gra

de-G

loba

l Ef

fic. D

iffer

.

Mod

el E

ffic.

Glo

bal E

ffic.

D

iscr

ep.

Gra

de E

ffic.

D

iscr

ep.

1 1.19 0.253 213 89% 105 26.1 20.6 5.5 3.2 83.2% 81.1% 2.1% 82.6% -0.7% 1.8%

2 1.19 0.392 330 89% 105 30.3 20.6 5.5 3.2 82.6% 64.5% 18.1% 82.5% -0.1% 28.0%

3 1.21 0.153 127 89% 106 30.9 20.6 5.5 3.2 84.0% 52.7% 31.4% 82.2% -2.2% 56.0%

4 1.21 0.187 155 88% 107 14.5 20.6 5.5 3.2 81.9% 44.0% 37.9% 82.0% 0.1% 86.3%

5 1.20 0.252 210 89% 106 16.7 20.6 5.5 3.2 83.2% 51.8% 31.3% 82.3% -1.1% 58.7%

6 1.20 0.247 207 90% 105 17.2 20.6 5.5 3.2 82.7% 81.5% 1.2% 83.4% 0.8% 2.3%

7 1.26 0.404 322 88% 119 23.9 20.6 5.5 3.2 84.6% 71.8% 12.7% 81.9% -3.2% 14.0%

8 1.25 0.303 242 89% 116 20.8 20.6 5.5 3.2 84.3% 69.6% 14.7% 82.0% -2.8% 17.7%

9 1.25 0.258 207 89% 117 20.3 20.6 5.5 3.2 84.9% 76.0% 8.9% 82.7% -2.6% 8.8%

10 1.25 0.255 204 89% 117 18.3 20.6 5.5 3.2 85.1% 78.1% 6.9% 82.7% -2.8% 5.9%

11 1.25 0.238 190 89% 117 20.4 20.6 5.5 3.2 84.1% 70.1% 14.1% 82.3% -2.1% 17.5%

12 1.24 0.315 254 89% 114 17.3 20.6 5.5 3.2 83.3% 79.3% 4.0% 82.2% -1.4% 3.7%

13 1.24 0.236 189 89% 116 24.1 20.6 5.5 3.2 84.9% 70.3% 14.6% 82.2% -3.1% 17.0%

14 1.25 0.180 144 88% 116 21.9 20.6 5.5 3.2 80.5% 71.8% 8.7% 81.6% 1.4% 13.6%

15 1.25 0.180 144 86% 116 14.2 20.6 5.5 3.2 80.9% 80.4% 0.5% 80.2% -0.9% -0.3%

16 1.25 0.180 144 86% 116 13.1 20.6 5.5 3.2 80.9% 79.4% 1.5% 80.2% -0.9% 0.9%

17 1.29 0.449 349 87% 124 19.6 20.6 5.5 3.2 90.0% 88.5% 1.4% 81.0% -9.9% -8.5%

18 1.29 0.449 349 87% 124 25.7 20.6 5.5 3.2 90.0% 87.8% 2.2% 81.0% -10.0% -7.8%

19 1.29 0.449 349 87% 124 25.9 20.6 5.5 3.2 90.0% 84.2% 5.7% 81.0% -10.0% -3.8%

20 1.29 0.449 349 87% 124 22.1 20.6 5.5 3.2 90.0% 74.6% 11.6% 81.0% -10.0% 8.5%

21 1.30 0.216 166 88% 125 22.5 20.6 5.5 3.2 85.4% 80.3% 5.1% 81.3% -4.8% 1.2%

22 1.30 0.216 166 88% 125 18.2 20.6 5.5 3.2 85.4% 82.1% 3.3% 81.3% -4.7% -0.9%

23 1.30 0.216 166 88% 125 26.9 20.6 5.5 3.2 85.4% 79.2% 6.2% 81.3% -4.8% 2.6%

24 1.30 0.216 166 88% 125 20.7 20.6 5.5 3.2 85.4% 80.9% 4.5% 81.3% -4.8% 0.5%

25 1.30 0.216 166 88% 125 23.1 20.6 5.5 3.2 85.4% 80.9% 4.5% 81.3% -4.8% 0.6%

26 1.30 0.216 166 88% 125 21.7 20.6 5.5 3.2 85.4% 79.6% 5.8% 81.3% -4.8% 2.2%

27 1.29 0.247 191 88% 126 22.8 20.6 5.5 3.2 86.0% 78.0% 7.9% 81.5% -5.2% 4.5%

28 1.29 0.453 351 88% 126 22.4 20.6 5.5 3.2 88.1% 82.2% 5.9% 81.5% -7.5% -0.9%

29 1.29 0.453 351 88% 126 17.8 20.6 5.5 3.2 88.1% 86.2% 1.9% 81.5% -7.4% -5.4%

218

Table A.1 Experimental Data and Model Prediction Results for All Datasets (Cont’d)

Feed Conditions SLHC Specs Efficiency Data Model PredictionsD

atas

et #

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Split

Rat

io (%

)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effii

ency

Gra

de-G

loba

l Ef

fic. D

iffer

.

Mod

el E

ffic.

Glo

bal E

ffic.

D

iscr

ep.

Gra

de E

ffic.

D

iscr

ep.

30 1.29 0.453 351 88% 126 24.9 20.6 5.5 3.2 88.1% 85.1% 3.0% 81.5% -7.5% -4.2%

31 1.29 0.306 238 88% 124 25.4 20.6 5.5 3.2 85.8% 76.3% 9.5% 81.0% -5.6% 6.2%

32 1.29 0.306 238 88% 124 25.2 20.6 5.5 3.2 85.8% 78.5% 7.3% 81.0% -5.6% 3.2%

33 1.29 0.306 238 88% 124 25.1 20.6 5.5 3.2 85.8% 77.6% 8.2% 81.0% -5.6% 4.5%

34 1.29 0.445 346 88% 125 23.7 20.6 5.5 3.2 86.4% 80.9% 5.5% 81.6% -5.5% 0.9%

35 1.29 0.445 346 88% 125 25.5 20.6 5.5 3.2 86.4% 78.8% 7.6% 81.6% -5.5% 3.6%

36 1.29 0.445 346 88% 125 22.6 20.6 5.5 3.2 86.4% 79.0% 7.4% 81.6% -5.5% 3.4%

37 1.28 0.472 368 93% 126 20.7 20.6 5.5 3.2 89.2% 85.4% 3.9% 86.3% -3.3% 1.1%

38 1.28 0.472 368 93% 126 24.5 20.6 5.5 3.2 89.2% 85.4% 3.9% 86.3% -3.3% 1.0%

39 1.28 0.472 368 93% 126 21.8 20.6 5.5 3.2 89.2% 86.4% 2.9% 86.3% -3.3% -0.1%

40 1.28 0.253 197 93% 126 20.6 20.6 5.5 3.2 86.4% 86.5% 0.1% 85.8% -0.6% -0.8%

41 1.28 0.253 197 93% 126 26.9 20.6 5.5 3.2 86.4% 76.3% 10.0% 85.8% -0.6% 12.4%

42 1.28 0.253 197 93% 126 23.0 20.6 5.5 3.2 86.4% 83.3% 3.1% 85.8% -0.6% 3.1%

43 1.23 0.164 134 96% 116 16.8 20.6 5.5 3.2 79.2% 75.8% 3.4% 89.2% 12.7% 17.7%

44 1.23 0.164 134 96% 116 19.2 20.6 5.5 3.2 79.2% 75.5% 3.7% 89.2% 12.7% 18.2%

45 1.23 0.164 134 96% 116 20.4 20.6 5.5 3.2 79.2% 73.5% 5.7% 89.2% 12.7% 21.4%

46 1.22 0.111 91 96% 115 24.2 20.6 5.5 3.2 72.5% 56.8% 15.7% 88.5% 22.1% 55.8%

47 1.22 0.111 91 96% 115 30.4 20.6 5.5 3.2 72.5% 60.9% 11.6% 88.4% 22.1% 45.3%

48 1.22 0.111 91 96% 115 27.7 20.6 5.5 3.2 72.5% 56.9% 15.6% 88.5% 22.1% 55.5%

49 1.22 0.217 178 93% 116 17.8 20.6 5.5 3.2 84.1% 70.6% 13.5% 85.9% 2.1% 21.7%

50 1.22 0.217 178 93% 116 25.8 20.6 5.5 3.2 84.1% 73.5% 10.7% 85.8% 2.0% 16.8%

51 1.22 0.217 178 93% 116 21.7 20.6 5.5 3.2 84.1% 77.7% 6.4% 85.9% 2.1% 10.5%

52 1.23 0.128 104 92% 115 27.8 20.6 5.5 3.2 84.9% 73.8% 11.1% 84.6% -0.3% 14.6%

53 1.23 0.128 104 92% 115 30.4 20.6 5.5 3.2 84.9% 75.2% 9.7% 84.6% -0.4% 12.5%

54 1.23 0.128 104 92% 115 32.4 20.6 5.5 3.2 84.9% 76.5% 8.4% 84.6% -0.4% 10.6%

55 1.26 0.112 89 94% 125 14.9 20.6 5.5 3.2 44.9% 29.2% 15.7% 87.1% 94.0% 198.1%

56 1.26 0.112 89 94% 125 30.7 20.6 5.5 3.2 44.9% 19.6% 25.3% 87.0% 93.9% 344.4%

57 1.26 0.112 89 94% 125 22.8 20.6 5.5 3.2 44.9% 22.3% 22.6% 87.1% 94.0% 290.5%

58 1.27 0.110 86 94% 124 14.9 20.6 5.5 3.2 59.5% 44.1% 15.4% 86.5% 45.4% 96.4%

59 1.27 0.110 86 94% 124 10.3 20.6 5.5 3.2 59.5% 41.4% 18.1% 86.5% 45.4% 109.0%

60 1.27 0.110 86 94% 124 15.6 20.6 5.5 3.2 59.5% 42.4% 17.1% 86.5% 45.4% 104.0%

61 1.26 0.199 157 96% 126 16.6 20.6 5.5 3.2 69.0% 61.5% 7.5% 88.8% 28.7% 44.5%

62 1.26 0.199 157 96% 126 16.5 20.6 5.5 3.2 69.0% 61.4% 7.6% 88.8% 28.7% 44.7%

63 1.26 0.199 157 96% 126 27.2 20.6 5.5 3.2 69.0% 52.6% 16.4% 88.8% 28.7% 68.9%

64 1.21 0.242 200 89% 110 25.0 20.6 5.5 3.2 79.2% 77.3% 1.9% 82.8% 4.5% 7.1%

65 1.21 0.242 200 89% 110 28.7 20.6 5.5 3.2 79.2% 71.9% 7.3% 82.8% 4.5% 15.1%

66 1.21 0.242 200 89% 110 26.9 20.6 5.5 3.2 79.2% 73.3% 6.0% 82.8% 4.5% 13.0%

67 1.21 0.182 150 89% 110 25.4 20.6 5.5 3.2 78.8% 74.2% 4.6% 82.8% 5.0% 11.6%

68 1.21 0.182 150 89% 110 27.0 20.6 5.5 3.2 78.8% 71.8% 7.0% 82.8% 5.0% 15.4%

69 1.21 0.182 150 89% 110 27.9 20.6 5.5 3.2 78.8% 72.2% 6.6% 82.8% 5.0% 14.7%

70 1.21 0.226 187 90% 110 25.5 20.6 5.5 3.2 79.0% 74.1% 4.9% 83.6% 5.9% 12.8%

71 1.21 0.226 187 90% 110 28.3 20.6 5.5 3.2 79.0% 73.9% 5.0% 83.6% 5.8% 13.0%

219

Table A.1 Experimental Data and Model Prediction Results for All Datasets (Cont’d)

Feed Conditions SLHC Specs Efficiency Data Model Predictions

Dat

aset

#

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Split

Rat

io (%

)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effii

ency

Gra

de-G

loba

l Ef

fic. D

iffer

.

Mod

el E

ffic.

Glo

bal E

ffic.

D

iscr

ep.

Gra

de E

ffic.

D

iscr

ep.

72 1.21 0.226 187 90% 110 25.1 20.6 5.5 3.2 79.0% 74.3% 4.7% 83.6% 5.9% 12.5%

73 1.21 0.160 132 92% 111 28.5 20.6 5.5 3.2 84.9% 77.1% 7.8% 85.4% 0.7% 10.9%

74 1.21 0.160 132 92% 111 27.6 20.6 5.5 3.2 84.9% 77.4% 7.4% 85.4% 0.7% 10.3%

75 1.21 0.160 132 92% 111 23.8 20.6 5.5 3.2 84.9% 80.1% 4.8% 85.4% 0.7% 6.7%

76 1.21 0.113 93 91% 111 20.3 20.6 5.5 3.2 82.8% 72.2% 10.6% 84.6% 2.1% 17.2%

77 1.21 0.113 93 91% 111 28.1 20.6 5.5 3.2 82.8% 71.7% 11.1% 84.5% 2.1% 18.0%

78 1.21 0.113 93 91% 111 26.6 20.6 5.5 3.2 82.8% 74.6% 8.2% 84.5% 2.1% 13.3%

79 1.21 0.238 197 92% 110 25.3 20.6 5.5 3.2 84.3% 78.9% 5.4% 85.4% 1.3% 8.2%

80 1.21 0.238 197 92% 110 25.0 20.6 5.5 3.2 84.3% 77.3% 7.1% 85.4% 1.3% 10.5%

81 1.21 0.238 197 92% 110 26.8 20.6 5.5 3.2 84.3% 75.6% 8.8% 85.4% 1.2% 13.0%

82 1.29 0.151 117 88% 126 29.1 20.6 5.5 3.2 67.2% 48.6% 18.6% 81.5% 21.3% 67.8%

83 1.29 0.151 117 88% 126 30.3 20.6 5.5 3.2 67.2% 51.0% 16.2% 81.5% 21.3% 59.8%

84 1.29 0.151 117 88% 126 33.4 20.6 5.5 3.2 67.2% 47.2% 20.1% 81.5% 21.3% 72.9%

85 1.28 0.208 163 89% 124 24.4 20.6 5.5 3.2 57.8% 39.9% 17.9% 82.2% 42.3% 106.1%

86 1.28 0.208 163 89% 124 20.8 20.6 5.5 3.2 57.8% 39.2% 18.6% 82.2% 42.3% 110.0%

87 1.28 0.208 163 89% 124 20.8 20.6 5.5 3.2 57.8% 37.6% 20.2% 82.2% 42.3% 118.6%

88 1.28 0.342 267 89% 126 24.9 20.6 5.5 3.2 51.7% 34.5% 17.2% 82.2% 59.0% 138.3%

89 1.28 0.342 267 89% 126 25.5 20.6 5.5 3.2 51.7% 35.6% 16.1% 82.2% 59.0% 131.0%

90 1.28 0.342 267 89% 126 25.0 20.6 5.5 3.2 51.7% 35.6% 16.1% 82.2% 59.0% 131.0%

91 1.27 0.137 107 94% 126 18.9 20.6 5.5 3.2 81.6% 77.2% 4.4% 86.8% 6.4% 12.4%

92 1.27 0.137 107 94% 126 21.9 20.6 5.5 3.2 81.6% 76.7% 4.9% 86.8% 6.4% 13.2%

93 1.27 0.137 107 94% 126 16.0 20.6 5.5 3.2 81.6% 67.3% 14.3% 86.8% 6.4% 29.0%

94 1.27 0.137 107 94% 126 20.2 20.6 5.5 3.2 81.6% 70.6% 11.1% 86.8% 6.4% 23.1%

95 1.28 0.213 166 93% 126 17.1 20.6 5.5 3.2 84.4% 82.0% 2.5% 86.4% 2.3% 5.4%

96 1.28 0.213 166 93% 126 14.4 20.6 5.5 3.2 84.4% 82.5% 1.9% 86.4% 2.3% 4.7%

97 1.28 0.213 166 93% 126 22.7 20.6 5.5 3.2 84.4% 70.5% 13.9% 86.4% 2.3% 22.4%

98 1.28 0.213 166 93% 126 22.3 20.6 5.5 3.2 84.4% 61.4% 23.1% 86.4% 2.3% 40.7%

99 1.27 0.282 221 94% 126 23.5 20.6 5.5 3.2 82.1% 76.6% 5.5% 86.8% 5.8% 13.4%

100 1.27 0.282 221 94% 126 17.7 20.6 5.5 3.2 82.1% 80.2% 1.8% 86.8% 5.8% 8.2%

101 1.27 0.282 221 94% 126 23.9 20.6 5.5 3.2 82.1% 59.7% 22.3% 86.8% 5.8% 45.3%

102 1.27 0.282 221 94% 126 20.0 20.6 5.5 3.2 82.1% 67.5% 14.6% 86.8% 5.8% 28.6%

103 1.26 0.062 50 90% 106 30.9 20.6 5.5 2.2 77.0% 67.4% 9.6% 83.0% 7.7% 23.0%

104 1.26 0.062 50 90% 106 30.3 20.6 5.5 2.2 77.0% 67.2% 9.8% 83.0% 7.7% 23.5%

105 1.26 0.062 50 90% 106 30.8 20.6 5.5 2.2 77.0% 60.4% 16.6% 83.0% 7.7% 37.3%

106 1.26 0.153 122 90% 106 22.7 20.6 5.5 2.2 79.7% 69.6% 10.1% 83.4% 4.6% 19.8%

107 1.26 0.153 122 90% 106 30.7 20.6 5.5 2.2 79.7% 69.7% 10.0% 83.4% 4.6% 19.6%

108 1.26 0.153 122 90% 106 29.6 20.6 5.5 2.2 79.7% 70.6% 9.1% 83.4% 4.6% 18.1%

109 1.25 0.275 220 91% 106 24.2 20.6 5.5 2.2 84.5% 78.0% 6.5% 83.8% -0.9% 7.3%

110 1.25 0.275 220 91% 106 15.2 20.6 5.5 2.2 84.5% 79.5% 5.1% 83.8% -0.9% 5.4%

111 1.25 0.275 220 91% 106 15.7 20.6 5.5 2.2 84.5% 79.1% 5.5% 83.8% -0.9% 5.9%

112 1.24 0.167 134 90% 106 17.8 20.6 5.5 2.2 80.3% 70.3% 10.0% 83.4% 3.8% 18.6%

113 1.24 0.167 134 90% 106 20.5 20.6 5.5 2.2 80.3% 70.2% 10.1% 83.4% 3.8% 18.8%

220

Table A.1 Experimental Data and Model Prediction Results for All Datasets (Cont’d)

Feed Conditions SLHC Specs Efficiency Data Model PredictionsD

atas

et #

Flow

Rat

e (m

3 /hr)

Solid

s M

ass

Flow

rate

(k

g/hr

)

Solid

s C

onc.

(m

g/L)

Split

Rat

io (%

)

Inle

t Pre

ssur

e (p

sig)

Feed

d32

( μm

)

Inle

t Slo

t Are

a (m

m2 )

Vort

ex F

inde

r D

iam

. (m

m)

Spig

ot D

iam

. (m

m)

Glo

bal E

ffic.

Avg

. Gra

de

Effii

ency

Gra

de-G

loba

l Ef

fic. D

iffer

.

Mod

el E

ffic.

Glo

bal E

ffic.

D

iscr

ep.

Gra

de E

ffic.

D

iscr

ep.

114 1.24 0.167 134 90% 106 19.2 20.6 5.5 2.2 80.3% 71.7% 8.7% 83.4% 3.8% 16.3%

115 1.30 0.139 107 91% 115 20.0 20.6 5.5 2.2 84.5% 74.2% 10.3% 83.4% -1.3% 12.5%

116 1.29 0.176 137 91% 113 20.7 20.6 5.5 2.2 85.7% 74.8% 10.9% 83.6% -2.4% 11.8%

117 1.34 0.218 163 89% 125 17.2 20.6 5.5 2.2 80.2% 66.5% 13.6% 82.6% 3.0% 24.1%

118 1.34 0.059 44 89% 124 19.6 20.6 5.5 2.2 68.4% 47.9% 20.5% 82.6% 20.8% 72.4%

119 1.34 0.116 87 90% 125 20.4 20.6 5.5 2.2 79.7% 67.9% 11.8% 83.0% 4.1% 22.2%

120 1.35 0.245 182 84% 105 17.7 20.6 5.5 2.2 83.6% 71.2% 12.5% 78.5% -6.2% 10.3%

121 1.34 0.176 131 85% 106 20.3 20.6 5.5 2.2 80.8% 66.5% 14.3% 78.7% -2.6% 18.3%

122 1.26 0.164 130 88% 126 18.8 20.6 5.5 3.2 80.0% 65.8% 14.2% 81.5% 1.9% 23.9%

123 1.26 0.236 187 87% 126 29.2 20.6 5.5 3.2 80.7% 62.0% 18.6% 80.7% 0.1% 30.1%

124 1.26 0.187 148 87% 126 19.3 20.6 5.5 3.2 80.1% 72.0% 8.1% 80.7% 0.8% 12.1%

125 1.27 0.153 121 90% 126 15.7 20.6 5.5 3.2 76.5% 75.0% 1.4% 83.5% 9.2% 11.2%

126 0.26 0.016 63 74% 124 29.8 3.2 2.0 1.5 75.8% 60.8% 15.0% 76.3% 0.6% 25.5%

127 0.27 0.024 87 74% 125 25.5 3.2 2.0 1.5 76.0% 56.1% 19.9% 75.8% -0.2% 35.1%

128 0.27 0.050 183 73% 125 28.9 3.2 2.0 1.5 76.5% 65.5% 10.9% 75.5% -1.2% 15.3%

129 0.30 0.031 103 85% 125 21.5 4.5 2.6 1.5 83.7% 72.3% 11.4% 77.5% -7.4% 7.2%

130 0.30 0.020 67 86% 124 21.7 4.5 2.6 1.5 82.5% 68.0% 14.5% 78.0% -5.5% 14.7%

131 0.30 0.050 164 85% 125 21.3 4.5 2.6 1.5 83.4% 70.3% 13.1% 77.4% -7.2% 10.1%

132 0.29 0.035 122 86% 125 22.7 4.5 2.6 1.5 82.8% 71.4% 11.4% 78.2% -5.6% 9.5%

133 0.29 0.028 98 84% 126 29.4 4.5 2.6 1.5 83.4% 64.8% 18.6% 76.7% -8.1% 18.3%

134 0.28 0.034 119 86% 126 28.6 4.5 2.6 1.5 88.5% 81.4% 7.1% 78.1% -11.8% -4.1%

135 0.28 0.048 171 87% 126 23.2 4.5 2.6 1.5 89.3% 79.2% 10.2% 78.7% -11.9% -0.6%

136 0.28 0.043 153 87% 126 30.0 4.5 2.6 1.5 89.9% 75.8% 14.2% 78.6% -12.5% 3.8%

137 0.26 0.047 179 85% 116 28.2 4.5 2.6 1.5 91.5% 79.6% 11.8% 77.7% -15.0% -2.4%

138 0.26 0.023 88 86% 115 23.6 4.5 2.6 1.5 84.8% 70.4% 14.4% 78.5% -7.5% 11.5%

139 0.26 0.063 242 87% 116 25.8 4.5 2.6 1.5 92.2% 85.0% 7.1% 79.4% -13.8% -6.6%

140 0.27 0.082 302 84% 116 19.5 4.5 2.6 1.5 89.0% 80.1% 8.9% 77.2% -13.3% -3.7%

141 0.27 0.051 188 84% 116 17.4 4.5 2.6 1.5 92.3% 83.1% 9.1% 76.7% -16.8% -7.7%

142 0.27 0.056 207 84% 116 25.0 4.5 2.6 1.5 92.4% 86.6% 5.7% 77.1% -16.6% -11.1%

143 0.27 0.021 77 85% 117 20.8 4.5 2.6 1.5 75.5% 53.8% 21.6% 77.4% 2.5% 43.7%

144 0.27 0.018 67 85% 116 21.6 4.5 2.6 1.5 75.3% 51.1% 24.2% 77.5% 2.8% 51.6%

145 0.28 0.015 52 84% 126 16.9 4.5 2.6 1.5 72.4% 43.9% 28.5% 77.4% 6.9% 76.1%

146 0.28 0.019 69 84% 126 25.5 4.5 2.6 1.5 79.4% 69.0% 10.4% 77.1% -2.8% 11.8%

147 0.28 0.010 36 90% 116 17.1 4.5 2.6 1.5 62.2% 31.6% 30.7% 81.3% 30.6% 157.5%

148 0.28 0.019 69 88% 116 17.3 4.5 2.6 1.5 79.5% 68.7% 10.8% 80.3% 1.1% 17.0%

149 0.16 0.022 136 89% 117 11.8 3.2 2.0 1.0 83.0% 68.4% 14.6% 84.1% 1.3% 22.9%

150 0.16 0.009 54 89% 116 18.3 3.2 2.0 1.0 62.3% 30.4% 31.9% 84.2% 35.1% 176.8%

151 0.16 0.031 196 91% 116 24.9 3.2 2.0 1.0 84.1% 75.6% 8.5% 85.2% 1.3% 12.7%

152 0.16 0.032 203 89% 104 17.2 3.2 2.0 1.0 77.5% 50.5% 27.0% 84.2% 8.7% 66.7%

153 0.16 0.026 167 88% 104 24.1 3.2 2.0 1.0 84.8% 63.0% 21.8% 83.7% -1.3% 32.8%

154 0.16 0.010 64 88% 104 14.1 3.2 2.0 1.0 75.0% 52.3% 22.7% 83.2% 10.9% 59.1%

155 0.17 0.037 218 87% 125 23.8 3.2 2.0 1.0 81.0% 45.7% 35.3% 82.5% 1.9% 80.7%

221

Tabl

e A.

2 E

xper

imen

tal C

ondi

tions

and

Equ

ipm

ent S

peci

ficat

ions

for A

ll D

atas

ets

Feed

Con

ditio

ns

O

/F C

ondi

tions

U/F

Con

ditio

ns

S

LHC

Geo

met

ric S

pecs

Dataset #

Flow Rate (m

3/hr)

Solids Mass Flowrate (kg/hr)

Solids Conc. (mg/L)

Split Ratio (%)

Oil Concent. (mg/L)

Inlet Pressure (psig)

Head Temp. (oF)

Feed d32 (μm)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

O/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

O/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

U/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

U/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

Barrel Diam. (mm)

Barrel Length (mm)

Cone Length (mm)

Cone Angle (deg)

Inlet Slot Area (mm

2)

Vortex Finder Diam. (mm)

Spigot Diam. (mm)

11.

190.

253

213

89%

4010

513

926

.112

.718

.61.

0640

57.

21.

30.

1113

631

19.3

22.2

2215

135

7.0

20.6

5.5

3.2

21.

190.

392

330

89%

4010

513

930

.324

.430

.61.

0664

57.

61.

40.

1126

491

18.4

21.6

2215

135

7.0

20.6

5.5

3.2

31.

210.

153

127

89%

8810

613

430

.935

.638

.71.

0723

513

.92.

50.

1182

61

19.7

23.6

2215

135

7.0

20.6

5.5

3.2

41.

210.

187

155

88%

8810

713

514

.515

.016

.81.

0732

53.

20.

60.

1196

91

25.8

28.1

2215

135

7.0

20.6

5.5

3.2

51.

200.

252

210

89%

7910

613

816

.714

.717

.11.

0740

57.

71.

40.

1115

631

20.3

23.3

2215

135

7.0

20.6

5.5

3.2

61.

200.

247

207

90%

4410

513

317

.211

.014

.41.

0840

518

.244

.30.

1119

361

16.8

19.2

2215

135

7.0

20.6

5.5

3.2

71.

260.

404

322

88%

414

119

130

23.9

16.2

20.4

1.11

5616

8.0

1.4

0.14

2924

116

.519

.222

1513

57.

020

.65.

53.

28

1.25

0.30

324

289

%62

116

114

20.8

16.5

20.0

1.11

4316

9.1

1.6

0.14

2123

118

.021

.122

1513

57.

020

.65.

53.

29

1.25

0.25

820

789

%62

117

141

20.3

13.3

17.3

1.12

3517

6.3

1.1

0.14

1635

115

.818

.722

1513

57.

020

.65.

53.

210

1.25

0.25

520

489

%62

117

141

18.3

12.9

16.3

1.12

3417

6.2

1.1

0.14

1578

115

.018

.022

1513

57.

020

.65.

53.

211

1.25

0.23

819

089

%62

117

141

20.4

13.7

17.8

1.11

3416

5.8

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53.

213

1.24

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116

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115

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1513

57.

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151.

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180

144

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101

116

111

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10.9

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116

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57.

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53.

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111

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113

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619

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622

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20.

1618

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216

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622

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618

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216

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135

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241.

300.

216

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511

620

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201

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135

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251.

300.

216

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511

623

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21.

50.

1611

201

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135

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511

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40.

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191

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613

622

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255.

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90.

1611

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613

622

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50.

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291.

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624

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1624

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135

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306

238

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5312

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425

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246.

91.

20.

1619

101

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26.6

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222

Tabl

e A

.2

Exp

erim

enta

l Con

ditio

ns a

nd E

quip

men

t Spe

cific

atio

ns fo

r All

Dat

aset

s (C

ont'd

)

Feed

Con

ditio

ns

O

/F C

ondi

tions

U/F

Con

ditio

ns

S

LHC

Geo

met

ric S

pecs

Dataset #

Flow Rate (m

3/hr)

Solids Mass Flowrate (kg/hr)

Solids Conc. (mg/L)

Split Ratio (%)

Oil Concent. (mg/L)

Inlet Pressure (psig)

Head Temp. (oF)

Feed d32 (μm)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

O/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

O/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

U/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

U/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

Barrel Diam. (mm)

Barrel Length (mm)

Cone Length (mm)

Cone Angle (deg)

Inlet Slot Area (mm

2)

Vortex Finder Diam. (mm)

Spigot Diam. (mm)

321.

290.

306

238

88%

5312

410

425

.216

.721

.91.

1339

247.

21.

30.

1619

101

24.2

26.6

2215

135

7.0

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5.5

3.2

331.

290.

306

238

88%

5312

410

425

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1339

247.

61.

40.

1619

101

24.2

26.6

2215

135

7.0

20.6

5.5

3.2

341.

290.

445

346

88%

5312

512

123

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1353

268.

11.

50.

1625

121

19.1

22.2

2215

135

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5.5

3.2

351.

290.

445

346

88%

5312

512

125

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1353

268.

01.

40.

1625

121

19.1

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2215

135

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361.

290.

445

346

88%

5312

512

122

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1353

266.

91.

20.

1625

121

19.1

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135

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371.

280.

472

368

93%

8812

613

720

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2042

258.

11.

50.

0853

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381.

280.

472

368

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724

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257.

71.

40.

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391.

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368

93%

8812

613

721

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258.

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50.

0853

4011

28.2

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401.

280.

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93%

8812

613

820

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1929

259.

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60.

0829

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26.5

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411.

280.

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197

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613

826

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1929

257.

61.

40.

0829

3910

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7.0

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421.

280.

253

197

93%

8812

613

823

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1929

256.

71.

20.

0829

3910

24.1

26.5

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135

7.0

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5.5

3.2

431.

230.

164

134

96%

8811

613

316

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1829

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90.

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2111

26.6

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441.

230.

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8811

613

319

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1829

166.

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10.

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2111

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135

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451.

230.

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613

320

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1829

167.

91.

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461.

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111

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115

119

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2616

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1.0

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1196

1021

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57.

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53.

247

1.22

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8811

511

930

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1726

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111

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115

119

27.7

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57.

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53.

249

1.22

0.21

717

893

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116

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17.8

12.3

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1.13

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5.5

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527

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1513

57.

020

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53.

250

1.22

0.21

717

893

%29

116

134

25.8

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1.13

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4.9

0.9

0.10

1921

527

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1513

57.

020

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53.

251

1.22

0.21

717

893

%29

116

134

21.7

12.9

17.8

1.13

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4.9

0.9

0.10

1921

527

.931

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1513

57.

020

.65.

53.

252

1.23

0.12

810

492

%29

115

104

27.8

16.4

23.0

1.13

1714

4.6

0.8

0.10

1139

424

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1513

57.

020

.65.

53.

253

1.23

0.12

810

492

%29

115

104

30.4

18.3

26.1

1.13

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4.8

0.9

0.10

1139

424

.628

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1513

57.

020

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53.

254

1.23

0.12

810

492

%29

115

104

32.4

15.6

23.7

1.13

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4.6

0.8

0.10

1139

424

.628

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1513

57.

020

.65.

53.

255

1.26

0.11

289

94%

4312

512

814

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711

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1952

255.

81.

00.

0765

610

22.4

27.5

2215

135

7.0

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5.5

3.2

561.

260.

112

8994

%43

125

128

30.7

14.9

22.5

1.19

5225

5.0

0.9

0.07

656

1022

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1513

57.

020

.65.

53.

257

1.26

0.11

289

94%

4312

512

822

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.11.

1952

255.

10.

90.

0765

610

22.4

27.5

2215

135

7.0

20.6

5.5

3.2

581.

270.

110

8694

%43

124

116

14.9

8.8

11.7

1.19

3724

5.1

0.9

0.07

822

1023

.727

.422

1513

57.

020

.65.

53.

259

1.27

0.11

086

94%

4312

411

610

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49.

21.

1937

244.

50.

80.

0782

210

23.7

27.4

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135

7.0

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601.

270.

110

8694

%43

124

116

15.6

8.7

11.6

1.19

3724

5.9

1.1

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1513

57.

020

.65.

53.

261

1.26

0.19

915

796

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126

136

16.6

8.9

12.5

1.21

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4.8

0.9

0.07

1897

1124

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1513

57.

020

.65.

53.

262

1.26

0.19

915

796

%43

126

136

16.5

9.2

12.8

1.21

5125

4.9

0.9

0.07

1897

1124

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1513

57.

020

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53.

2

223

Tabl

e A

.2

Exp

erim

enta

l Con

ditio

ns a

nd E

quip

men

t Spe

cific

atio

ns fo

r All

Dat

aset

s (C

ont'd

)

Feed

Con

ditio

ns

O

/F C

ondi

tions

U/F

Con

ditio

ns

S

LHC

Geo

met

ric S

pecs

Dataset #

Flow Rate (m

3/hr)

Solids Mass Flowrate (kg/hr)

Solids Conc. (mg/L)

Split Ratio (%)

Oil Concent. (mg/L)

Inlet Pressure (psig)

Head Temp. (oF)

Feed d32 (μm)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

O/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

O/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

U/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

U/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

Barrel Diam. (mm)

Barrel Length (mm)

Cone Length (mm)

Cone Angle (deg)

Inlet Slot Area (mm

2)

Vortex Finder Diam. (mm)

Spigot Diam. (mm)

631.

260.

199

157

96%

4312

613

627

.211

.517

.81.

2151

255.

41.

00.

0718

9711

24.2

28.5

2215

135

7.0

20.6

5.5

3.2

641.

210.

242

200

89%

6611

014

525

.017

.022

.61.

0846

1010

.41.

90.

1215

620

25.6

29.3

2215

135

7.0

20.6

5.5

3.2

651.

210.

242

200

89%

6611

014

528

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0846

109.

01.

60.

1215

620

25.6

29.3

2215

135

7.0

20.6

5.5

3.2

661.

210.

242

200

89%

6611

014

526

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0846

109.

11.

60.

1215

620

25.6

29.3

2215

135

7.0

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5.5

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671.

210.

182

150

89%

6611

014

525

.417

.422

.81.

0936

1011

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10.

1211

180

27.0

30.2

2215

135

7.0

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5.5

3.2

681.

210.

182

150

89%

6611

014

527

.017

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0936

109.

51.

70.

1211

180

27.0

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2215

135

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5.5

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691.

210.

182

150

89%

6611

014

527

.918

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0936

1010

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90.

1211

180

27.0

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135

7.0

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701.

210.

226

187

90%

6611

014

525

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0944

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90.

1214

740

26.6

29.9

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135

7.0

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711.

210.

226

187

90%

6611

014

528

.319

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0944

1010

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80.

1214

740

26.6

29.9

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135

7.0

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5.5

3.2

721.

210.

226

187

90%

6611

014

525

.117

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.81.

0944

109.

61.

70.

1214

740

26.6

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731.

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160

132

92%

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114

728

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117.

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741.

210.

160

132

92%

4111

114

727

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118.

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751.

210.

160

132

92%

4111

114

723

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118.

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135

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761.

210.

113

9391

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111

147

20.3

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8.4

1.5

0.09

1181

527

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1513

57.

020

.65.

53.

277

1.21

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393

91%

4111

114

728

.120

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118.

21.

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27.5

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135

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781.

210.

113

9391

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111

147

26.6

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527

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1513

57.

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53.

279

1.21

0.23

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792

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110

146

25.3

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526

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53.

280

1.21

0.23

819

792

%41

110

146

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10.5

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526

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1513

57.

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53.

281

1.21

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792

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110

146

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9.0

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2377

526

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57.

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53.

282

1.29

0.15

111

788

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126

142

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15.5

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4425

4.9

0.9

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286

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389

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53.

287

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389

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142

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53.

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142

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256.

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280.

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267

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614

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112

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625

3.1

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711

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142

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270.

137

107

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614

718

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614

721

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137

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614

716

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2021

257.

61.

40.

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9710

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135

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224

Tabl

e A

.2

Exp

erim

enta

l Con

ditio

ns a

nd E

quip

men

t Spe

cific

atio

ns fo

r All

Dat

aset

s (C

ont'd

)

Feed

Con

ditio

ns

O

/F C

ondi

tions

U/F

Con

ditio

ns

S

LHC

Geo

met

ric S

pecs

Dataset #

Flow Rate (m

3/hr)

Solids Mass Flowrate (kg/hr)

Solids Conc. (mg/L)

Split Ratio (%)

Oil Concent. (mg/L)

Inlet Pressure (psig)

Head Temp. (oF)

Feed d32 (μm)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

O/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

O/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

U/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

U/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

Barrel Diam. (mm)

Barrel Length (mm)

Cone Length (mm)

Cone Angle (deg)

Inlet Slot Area (mm

2)

Vortex Finder Diam. (mm)

Spigot Diam. (mm)

941.

270.

137

107

94%

7312

614

720

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2021

255.

81.

00.

0613

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280.

213

166

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213

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723

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15.6

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1.25

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135

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160

21.4

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141

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109

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176

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313

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135

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816

389

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125

144

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124

144

19.6

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116

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125

144

20.4

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7.0

1.3

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801

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57.

020

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245

182

84%

4010

599

17.7

13.6

16.6

1.13

355

6.7

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017

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1513

57.

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52.

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176

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610

020

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61.

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390

22.6

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125

18.8

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529

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257.

11.

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17.1

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135

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126

125

19.3

14.8

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10.1

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57.

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53.

2

225

Tabl

e A

.2

Exp

erim

enta

l Con

ditio

ns a

nd E

quip

men

t Spe

cific

atio

ns fo

r All

Dat

aset

s (C

ont'd

)

Feed

Con

ditio

ns

O

/F C

ondi

tions

U/F

Con

ditio

ns

S

LHC

Geo

met

ric S

pecs

Dataset #

Flow Rate (m

3/hr)

Solids Mass Flowrate (kg/hr)

Solids Conc. (mg/L)

Split Ratio (%)

Oil Concent. (mg/L)

Inlet Pressure (psig)

Head Temp. (oF)

Feed d32 (μm)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

O/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

O/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

U/F Flow Rate (m

3/hr)

Solids Conc. (mg/L)

U/F Pressure (psig)

Mean Part. Diam (μm)

Dist. Std. Dev. (μm)

Barrel Diam. (mm)

Barrel Length (mm)

Cone Length (mm)

Cone Angle (deg)

Inlet Slot Area (mm

2)

Vortex Finder Diam. (mm)

Spigot Diam. (mm)

125

1.27

0.15

312

190

%58

126

125

15.7

10.9

13.8

1.15

3126

11.7

2.1

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018

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57.

020

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53.

212

60.

260.

016

6374

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124

135

29.8

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7.4

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0.06

175

118

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450

10.0

3.2

2.0

1.5

127

0.27

0.02

487

74%

3312

510

825

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2029

257.

11.

30.

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01

25.6

30.8

104

5010

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80.

270.

050

183

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3312

510

828

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256.

31.

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11

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5010

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3212

512

721

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2620

255.

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513

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127

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119

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450

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0.30

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485

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120

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450

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125

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450

10.0

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611

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104

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258.

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513

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823

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784

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116

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120

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2.6

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614

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280.

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120

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450

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613

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11.8

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112

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450

10.0

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614

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10.

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196

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614

124

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51.

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861

14.9

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226

APPENDIX B

CYCLONEMASTER DATABASE SYSTEM DESCRIPTION

B.1 Database Architecture

The structure of the database (DB) system consists of six different data tables

related by a Unique Primary Key which has been assigned to each dataset as a sequence

number based on the date the experiment was performed. Each of these tables has been

designed to store specific information of a single record, a group of them, or a complete

data set. Mainly, the data are organized as follows: test conditions and summary of

results, particle or droplet size distribution, cyclones specifications, instrumentation

specifications and test objectives and field notes. Table B.1 contains an inventory of the

available floppy disks and a summary of their content information. Also, a summary of

the most common problems and discrepancies encountered is presented in Table B.2.

The fields in each table have been documented to facilitate future DB expansion

and user maintenance. The following sections present the description of each of the data

tables forming the DB system.

227

Table B.1 Hydrocyclones Data Files and Inventory of Floppy Disks

Disk Label Disk # Main Content Type of Cyclone Test Dates Type of

Data Status

Hydrocyclone 1/15 SLHC data SLHC 09/01 - 09/10/92 Original OKHydrocyclone 2/15 SLHC data SLHC 09/11 - 09/14/92 Original OKHydrocyclone 3/15 SLHC data SLHC 09/15 - 09/23/92 Original OKHydrocyclone 4/15 SLHC data SLHC 09/24/92 Original RecoveredHydrocyclone 5/15 SLHC data SLHC 09/25 - 09/30/92 Original OKHydrocyclone 6/15 SLHC data SLHC 10/01 - 10/05/92 Original OKHydrocyclone 7/15 SLHC data SLHC 10/06/92 Original OKHydrocyclone 8/15 SLHC data SLHC 10/07/92 Original OKHydrocyclone 9/15 SLHC data SLHC 10/08/92 Original OKHydrocyclone 10/15 SLHC data SLHC 10/09/92 Original RecoveredHydrocyclone 11/15 SLHC data SLHC 10/14 - 10/19 Original OKHydrocyclone 12/15 SLHC data SLHC 10/20 - 10/28/92 Original OKHydrocyclone 13/15 SLHC data SLHC 11/02 - 11/05/92 Original OKHydrocyclone 14/15 SLHC data SLHC 11/06 - 11/12/92 Original OKHydrocyclone 15/15 SLHC data SLHC 11/18 - 11/25/92 Original OKONFIN4.XLS 1/1 LL / SL data LLHC/SLHC 09/01 - 12/09/92 Original OKLLHC/ MEMBREX / COULTER/ RANGLEY 1/1 LL / Well data LLHC 07/23 - 09/30/91 Original OK3M Field Trial Data / Vortoil K-liner Test 1/1

Alba Report Figures01/13/94 Original OK

Vortoil 1/1Overall Data .xls / multisizer Data,

Backwash Files, figs

Vortoil / SLHC

01/03/93 - 01/11/03 Original OK

HC Transport Disk 1/1

.xls, . Xlc files (DECO, ONFIN, NOR, CAL, POU, CWF, OCT,

NOV)

Misc Misc Original / Copy Recovered

Backup Word Files 1/1 .doc, .xls, LLHC Coulter data LLHC Original /

Backup OK

Preseparator HC Data 1/1

Vortoil.xls, K4MM*.xlc, K$MM*.xls, vortnote.doc

Vortoil 4/95 - 5/95 Original Ok

LLHC Main-0426 1/2 LL data LLHC 07/22/91 Original Unreadable LLHC Main-0426 2/2 LL data LLHC 07/22/91 Original UnreadableCoulter Data (Excel) 1/1 02/13/91 Original Unreadable

Hydroswirl Data Disc 1/1 Hydroswirl / Vortoil Data

Hydroswirl / Vortoil 07/30 - 07/31/91 Original Unreadable

LLHC System Disc "AUTOST" 1/1 LLHC data LLHC Original Unreadable

228

Table B.2 Summary of Data Review and Audit Results (Data Log)

Test_Date Comments / Observations on Data Review09/01/92 RUN II: Cut size diameter corrected from 9.0 to 3.509/03/92 OK09/08/92 Test conditions data was included into database.09/09/92 OK09/10/92 OK09/11/92 OK09/14/92 RUN I: Cut size diameter corrected from 9.0 to 6.509/15/92 OK09/17/92 No Hardcopy09/23/92 Data Swap. Data from 0.3 and 1.0 um (coulter filter size) were swapped 09/24/92 OK09/25/92 RUN IA, C: Cut size diameter corrected from 10 to 2.509/28/92 Data Not included. Bad solid/liquid mass balance09/29/92 Data Not included. Bad solid/liquid mass balance09/30/92 RUN IB: Cut size diameter corrected from 17 to 10.75 and RUN II from 15 to 10.7510/01/92 RUN IA, C: Cut size diameter corrected from 12 to 10.2510/05/92 OK10/06/92 OK10/07/92 Data Swap. Data from O/F of Run I and II were swapped 10/07/92 RUN I, II: Cut size diameter corrected. Data were not reported properly10/08/92 OK10/09/92 OK10/14/92 OK10/15/92 OK10/19/92 OK10/20/92 OK10/20/92 OK10/21/92 OK10/23/92 OK10/27/92 No Hardcopy. Temp. was estimated to be 126 F. Pinlet cyclone#2 was corrected10/28/92 No Hardcopy. Temp. was estimated to be 126 F. Pinlet cyclone#2 was corrected11/02/92 Pinlet cyclone#2 was corrected.11/03/92 Pinlet cyclone#2 was corrected.11/05/92 OK11/06/92 OK11/09/92 OK11/10/92 OK11/11/92 OK11/12/92 OK11/18/92 OK11/19/92 OK11/23/92 OK11/24/92 RUN 3: Cut size diameter corrected from 1.8 to 3.7511/25/92 OK11/25/92 OK12/01/92 No Electronic records. Data will be digitized and included in DB.12/02/92 OK12/03/92 No Electronic records. Data will be digitized and included in DB.12/09/92 No Electronic records. Data will be digitized and included in DB.

229

B.1.1 Test Conditions Table

This table contains all the general information regarding test and flow conditions,

test setup, test general objective, tested equipment and configuration, and instruments

used. This table also stores a summary of statistical results, including solids/droplets

concentrations at inlet/outlet conditions, and cyclone efficiencies of each single test run.

One important featured included in this table is the data source filename, which allows for

auditing data records and tracking original data source files.

A unique ID or Primary Key relates this table with the rest of the tables in the DB

so that specific information of a record of group of records can be accessed. In this case,

the key is the Test_ID, which consists of a nine-digit field, based on the Excel sequential

serial number of the test date, the test run number, and the run group number, which

represents a different set of conditions for the same test run. In summary, the Test_ID

field is formed as follows:

999999-9X

Table B.3 shows the list of each of the fields in the table with their corresponding

caption or description.

Excel built-in sequential serial number of the test date (PC-Format)

Test Run or Trial number Test Run Group letter

230

Table B.3 Design of the “Test Conditions” Data Table

231

B.1.2 Particle Size Data Table

The table, “Particle_Size_Data” contains all particle size distributions for each of

the datasets. Specifically, all particle size distributions are discriminated for inlet,

overflow and underflow conditions. The size distributions show the number of particles

measured by the Coulter Counter Multisizer (CC) for each of the 32 characteristic

diameters or channels. This information for all datasets is consolidated in a single table

where it can be easily accessed and uploaded for model and/or cyclone simulation

benchmarking. The Primary Key is also the Test_ID. Table B.4 shows the list of each of

the fields in the table and their respective caption or general description.

B.1.3 Equipment Specifications Table

This table, “Equipment_Specs” stores general cyclones’ description and specs,

namely, body, inlet, and outlet dimensions; manufacturers name; serial, model or

reference numbers; manufacturer rated efficiency, etc. This information helps to keep

record of relevant information of the tested cyclones, and to establish systematic data

uncertainties. The storage of this information also provides added flexibility and

convenience at the time of benchmarking. The Primary Key of this table is the Equip_ID

field. Table B.5 shows the list of each of the fields in the table and their respective

caption or general description.

232

Table B.4 Design of the “Particle Size” Data Table

233

Table B.5 Design of the “Equipment Specifications” Data Table

234

B.1.4 Instrumentation Specifications Table

A table called “Instruments_Specs” is available to store all relevant information

regarding the instruments used to measured flow rates, pressures, temperatures, and

droplet/particle size distributions. General and specific properties including specifications

and general description can be stored in this table. This is particularly useful to establish

systematic uncertainties and/or to determine the confidence level of the data. Table B.6

shows a list of each of the fields in the table and their general description for future use.

B.1.5 Test Objectives and Field Notes Table

The table “Test_Objectives&Notes” stores a set of test objectives and

experimental goals. In some cases, detailed field notes, findings, data analysis,

experimental setup description and other relevant information is also available. This

information has been stored in a separate table to avoid redundancy and increase database

capacity. A list showing each of the fields that form the DB table and their general

description is given in Table B.7

B.1.6 Particle Size Distribution Calculations

This table stores all hydrocyclone performance calculations results including test

conditions and geometrical configuration data. Mechanistic modeling results have been

added to this table by using a VBA program that performs all computations, and outputs

the results into an Excel spreadsheet that is linked to CycloneMaster. Table B.8 shows

the list of each of the fields in the table.

235

Table B.6 Design of the “Instrument Specifications” Data Table

236

Table B.7 Design of the “Objectives and Field Notes” Data Table

237

Table B.8 Design of the “Particle Size Distribution Calculations” Data Table

238

B.2 CycloneMaster DB Management System Description

The CycloneMaster DB management system was created using Microsoft Access

and Visual Basic (VBA). It can be used to store, handle and analyze experimental data.

The code is composed of a Main Menu Form that provides easy access to the stored

datasets. Also, a series of “Sub forms”, “Queries”, and “Reports” are linked to the Main

Form to make possible the plotting, listing, and visualizing the data. Some forms show

performance computations and can be used to generate Look-Up tables that are

particularly useful for benchmarking simulators and models. The interface also provides

the user with the most relevant information of the experimental program, including

equipment documentation, test objectives, test configurations, and the description of the

experimental procedures. The system has a Help Menu to guide users through the main

features of the program and provide a general description of the Experimental Procedure.

Sample screens are shown in Figures B.1 and B.2.

239

Figure B.1 Main Menu: Dataset Reference Info Panel

Figure B.2 Main Menu: Dataset Detailed Info Panel and Performance Plots Tab Page