MULTIPHASE FLOW OF OIL, WATER AND GAS IN HORIZONTAL PIPES by Andrew Robert William Hall A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Imperial College of Science, Technology and Medicine, University of London October 1992 1 A.R.W.HALL 1992 THIS IS A BLANK PAGE ABSTRACT This thesis describes an experimental and theoretical study of the multiphase flow of two immiscible liquid phases (oil and water) and a gas phase. The experimental study has been carried out using a new high pressure multiphase flow facility. Known as WASP (Water, Air, Sand, Petroleum), this facility has a main test section of length 42 m and diameter 78 mm and can operate at pressures up to 50 bar. Experimental studies concentrated on the measurement of pressure gradient and holdup and the observation of flow patterns for flows of water, air and a light lubricating oil. These experiments have provided new data in an area for which there is little published work in the scientific literature. The theoretical studies have been based on the concept of a three-fluid model of horizontal stratified three-phase flow, based on similar models for two-phase (gas-liquid) flow. This basic model was tested against a numerical solution of the steady-state momentum equations, making use of bipolar coordinate grids to match the geometry of a circular pipe with planar interfaces, for both laminar flows and turbulent flows (using a Prandtl-mixing length approach to give an effective turbulent viscosity). The stratified flow model has been tested against published experimental data for stratified three-phase flows and has been used as a basis for modelling the transition from stratified to intermittent flows. Combination with empirical correlations from the literature has allowed modelling of the separation of oil and water in three-phase slug flows. A simple model for three-phase slug flow has been developed from similar work for gas-liquid flows, taking into account the effect of the second liquid phase. Calculations of pressure gradient and holdup from this model were compared with experimental data. Empirical correlations for pressure gradient in two-phase flows have been adapted for use in three-phase flows, by particularly considering the correct effective viscosity which should be used. Equations for the calculation of the viscosity of oil-water dispersions have been used and the results compared both with previously-published data and with new data from the experimental studies. 3 CONTENTS ABSTRACT 3 LIST OF FIGURES 9 LIST OF TABLES 14 ACKNOWLEDGMENTS 15 CHAPTER 1 INTRODUCTION 17 CHAPTER 2 LITERATURE REVIEW 21 2.1 INTRODUCTION 21 22 EXPERIMENTAL STUDIES OF THREE-PHASE FLOWS IN PIPES 22 2.3 EXPERIMENTAL STUDIES OF OIL-WATER FLOWS IN PIPES 25 2.4 EMPIRICAL TOOLS FOR TWO-PHASE FLOW 27 2.4.1 Correlations for frictional pressure gradient 27 2.4.2 Flow pattern maps 29 2.43 Correlations for slug frequency 31 2.4.4 Rheology of liquid-liquid mixtures 32 2.5 ANALYTICAL STUDIES OF TWO-PHASE FLOWS 34 2.5.1 Pressure gradient and holdup 34 232 Stratified to slug flow transition 37 2.6 PRACTICAL EXAMPLES FROM THE OIL INDUSTRY 39 2.7 SUMMARY 40 CHAPTER 3 EMPIRICAL PRESSURE GRADIENT CALCULATION METHODS 43 3.1 INTRODUCTION 43 31 PRESSURE GRADIENT CALCULATION 44 3.2.1 Introduction 44 311 Calculation of frictional pressure gradient from homogeneous model 45 323 Calculation of frictional pressure gradient from the separated flow mode145 33 LIQUID MIXTURE VISCOSITY 46 33.1 Liquid mixture viscosity equations 46 33.2 Comparison of experimental data with Brinkman's equation 47 3.33 Inversion point 48 3.4 ANALYSIS OF EXPERIMENTAL DATA 50 3.4.1 Malinowsky 50 3.4.2 Latin & Oglesby 52 3.43 Sobocinski 54 3.4.4 Stapelberg 56 33 ANALYSIS OF FIELD DATA 56 33.1 Fayed & Otten 56 332 UK National Multiphase Flow Database 57 3.6 SUMMARY 58 4 CHAPTER 4 SIMPLE MODELS FOR STRAilkiED THREE-PHASE FLOW 61 4.1 INTRODUCTION 61 4.2 SOLUTIONS FOR LAMINAR FLOWS BETWEEN FLAT PLATES 63 4.2.1 Single phase flow 63 4.2.2 Two-phase flow 66 4.2.3 Three-phase flow 69 4.2.4 Solution of systems of non-linear equations (Newton's method) 73 43 TAITEL & DUICLER TWO-FLUID MODEL FOR STRATIFIED GAS-LIQUID FLOW IN PIPES 74 4.4 TWO-FLUID MODEL FOR STRATIFIED OIL-WATER FLOW 75 43 THREE-FLUID MODEL OF STRATIFIED OIL-WATER-GAS FLOW IN PIPES 77 4.5.1 Model derivation 77 4.5.2 Model solution 80 4.6 COMPARISON WITH EXPERIMENTAL DATA FOR THREE-PHASE STRATIFIED FLOW 81 4.7 SUMMARY 83 CHAPTER 5 NUMERICAL MODELLING OF STRATIFIED THREE-PHASE FLOW 85 5.1 INTRODUCTION 85 5.2 MODELLING OF STRATIFIED TWO-PHASE FLOW 86 5.2.1 Bipolar coordinate system 86 5.2.2 Navier-Stokes equations 87 5.23 Finite difference scheme 88 5.2.4 Turbulence modelling 89 5.23 Solution 91 53 CALCULATIONS FOR OIL-WATER FLOWS 91 53.1 Comparison of models 91 532 Experimental results from the WASP Facility 93 533 Experimental results from Russell. Hodgson & Govier 94 53.4 Experimental results from Stapelberg & Mewes 95 535 Experimental results from Charles 97 5.4 MODELLING OF STRATIFIED THREE-PHASE FLOW 98 53 CALCULATIONS FOR OIL-WATER-GAS FLOWS 100 53.1 Stapelbeig & Mewes 100 53.2 Sobocinski 101 533 Nuland 102 5.6 SUMMARY 103 5 CHAPTER 6 FLOW PATTERN TRANSITIONS IN THREE-PHASE FLOW 105 6.1 INTRODUCTION 105 6.2 TRANSITION FROM STRATIFIED TO INTERMITTENT FLOW USING STEADY-STATE (KELVIN-HELMHOLTZ) THEORY 106 6.2.1 Kelvin-Helmholtz instability in a two-dimensional channel 106 6.2.2 Taitel & Dukler transition model for flow in a pipe 107 6.23 Taitel & Dukler transition model applied to oil-water-gas flow: separate oil and water layers 107 6.2.4 Taitel & Dukler transition model applied to oil-water-gas flow: dispersed oil and water layers 109 63 TRANSITION FROM STRATIFIED TO INTERMITTENT FLOW USING LINEAR STABILITY THEORY: TWO-DIMENSIONAL CHANNELS! 10 63.1 Conditions for neutral stability for a turbulent-turbulent gas-liquid flow in a two-dimensional channel 110 63.2 Conditions for neutral stability for turbulent-gas laminar-liquid flow in a two-dimensional channel 113 633 Reduction to the Kelvin-Helmholtz instability 115 63.4 Application of two-phase linear stability analysis to three-phase flow in a two-dimensional channel 115 6.33 Comparison of two-dimensional models 118 6.4 T'RANSMON FROM STRATIFIED TO INTERMITTENT FLOW USING LINEAR STABILITY THEORY: FLOWS IN PIPES 120 6.4.1 Conditions for neutral stability for a turbulent-turbulent gas-liquid flow in a pipe (Lin & Hanratty) 120 6.4.2 Application of Lin & Hanratty two-phase analysis to three-phase flow in a PiPe 124 6.43 Reduction of three-phase flow equations to two-phase flow equations for zero water flow 129 6.4.4 Comparison of models 129 6.4.5 Comparisons with experimental data 130 63 SEPARATION OF WATER PHASE IN THREE-PHASE PIPE FLOWS 131 6.6 OIL-WATER INTERFACE MIXING (TRANSITION FROM STRATIFIED TO WAVY FLOW) 134 6.7 SUMMARY 136 CHAPTER 7 SIMPLE MODELS FOR THREE-PHASE SLUG FLOWS 137 7.1 INTRODUCTION 137 7.2 DIUKLER & HUBBARD MODEL FOR TWO-PHASE SLUG FLOWS137 73 MODIFICATIONS FOR THREE-PHASE FLOWS 140 73.1 Acceleration zone 140 73.2 Slug body 142 7.33 Film region 143 7.4 SUMMARY 144 CHAPTER 8 HIGH PRESSURE MULTIPHASE FLOW FACILITY 145 8.1 DESCRIPTION OF WASP FACILITY 145 8.1.1 History 145 8.1.2 Layout and design 146 6 8.2 CONTROL & INSTRUMENTATION 147 8.2.1 Control system 147 8.2.2 Flow metering 148 8.23 Pressure drop measurement 149 8.2.4 Liquid tank levels 149 8.2.5 Flow visualisation 150 8.2.6 Holdup measurement 150 83 OIL SELECTION 151 83.1 Flammability properties 152 83.2 Health and environment 153 833 Physical properties 153 83.4 Practical features 153 83.5 Summary 154 8.4 OIL PROPERTIES 154 8.4.1 Separation from water 154 8.4.2 Viscosity 154 8.4.3 Density 155 8.4.4 Growth of micro-organisms 155 CHAPTER 9 EXPERIMENTAL INVESTIGATION OF THREE-PHASE OIL-WATER-GAS FLOWS 157 9.1 EXPERIMENTAL PROGRAMME 157 9.2 RESULTS 158 9.2.1 Pressure gradient 158 9.2.2 Holdup 161 9.23 Flow visualisation 164 93 SUMMARY 167 CHAPTER 10 CONCLUSIONS 169 10.1 CONCLUSIONS 169 10.1.1 Pressure gradient correlations 169 10.1.2 Multi-fluid stratified flow models 169 10.13 Numerical stratified flow models 170 10.1.4 Flow pattern transitions in three-phase flows 170 10.13 Simple models for three-phase slug flows 171 10.1.6 Experimental studies of three-phase flows 171 10.2 RECOMMENDATIONS FOR FURTHER WORK 171 10.2.1 Further analysis 171 10.2.2 Further experimental data 171 REFERENCES 173 7 NOMENCLATURE 179 FIGURES 183 APPENDIX A SUMMARY OF PRESSURE GRADIENT CORRELATION EQUATIONS 245 A.1 Common Calculations 245 A.2 McAdams-Homogeneous 245 A.3 Schlichting 246 A.4 Friedel 247 A.5 Lockhart & Martinelli 248 A.6 Beggs & Brill 249 A.7 Dukler 252 A.8 Theissing 253 APPENDIX B FINITE DIFFERENCE SOLUTION FOR STRATIFIED TWO-PHASE FLOW USING BIPOLAR COORDINATES 255 B.1 Finite difference equations for the upper phase 255 B.2 Listing of the source code for the bipolar solution 256 APPENDIX C TABLES OF EXPERIMENTAL DATA POINTS 269 APPENDIX D WASP EXPERIMENTAL DATA POINTS (THREE-PHASE FLOW) 273 8 LIST OF FIGURES Figure 2.1 Guzhov oil-water flow pattern map 185 Figure 2.2 Guzhov pressure gradient in oil-water flow 185 Figure 2.3 Flow pattern map for oil-water equal density flow 186 Figure 2.4 Charles & Lilleleht pressure gradient correlation for oil-water flow 186 Figure 2.5 Schneider gas-liquid flow pattern map 187 Figure 2.6 Baker gas-liquid flow pattern map 187 Figure 2.7 Mandhane gas-liquid flow pan= map 188 Figure 2.8 Taitel & Dukler gas-liquid flow pattern map 188 Figure 2.9 Arirachakaran oil-water flow