PVT and phase behaviour of petroleum reservoir fluids danesh

PVT AND PHASE BEHAVIOUR OF PETROLEUM RESERVOIR FLUIDS Volumes 1-5, 7, 10, 11, 13, 14, 16, 17, 21, 22, 23-27, 29, 31 are out of print 12 15a 15b 18a 18b 19a 19b 20 28 30 32 33 34 3,5 36 37 38 39 Fundamentals of Numerical Reservoir Simulation Fundamentals of Reservoir Engineering Compaction and Fluid Migration Fundamentals of Fractured Reservoir Engineering Fundamentals of Well-log Interpretation, The acquisition of logging data Fundamentals of Well-log Interpretation, The interpretation of logging data Production and Transport o f Oil and Gas, A Flow mechanics and production Production and Transport o f Oil and Gas, B Gathering and Transport Surface Operations in Petroleum Production, I Surface Operations in Petroleum Production, II Geology in Petroleum Production Well Cementing Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part I Fluid Mechanics for Petroleum Engineers Petroleum Related Rock Mechanics A Practical Companion to Reservoir Stimulation Hydrocarbon Migration Systems Analysis The Practice of Reservoir Engineering Thermal Properties and Temperature related Behavior of Rock/fluid Systems Studies in Abnormal Pressures Microbial Enhancement of Oil Recovery- Recent Advances - Proceedings of the 1992 International Conference on Microbial Enhanced Oil Recovery 40a Asphaltenes and Asphalts, I 41 Subsidence due to Fluid Withdrawal 42 Casing Design - Theory and Practice 43 Tracers in the Oil Field 44 Carbonate Reservoir Characterization: A Geologic-Engineering Analysis, Part II 45 Thermal Modeling of Petroleum Generation: Theory and Applications 46 Hydrocarbon Exploration and Production 47 PVT and Phase Behaviour o f Petroleum Reservoir Fluids PVTAND PHASEBEHAVIOUROF PETROLEUMRESERVOIRFLUIDS ALl DANESH Department of Petroleum Engineering Heriot Watt University Edinburgh, Scotland ~ ELSEVIER Amsterdam - Boston - London - New Y o r k - Oxford - Paris San Diego - San Francisco - Singapore - S y d n e y - Tokyo -~ 1998 Elsevier Science B.V All 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The Netherlands CONTENTS PREFACE NOMENCLATURE PHASE BEHAVIOUR FUNDAMENTALS 1.1 RESERVOIR FLUID COMPOSITION 1.2 PHASE BEHAVIOUR Pure Compound Corresponding States Multicomponent Mixture CLASSIFICATION OF RESERVOIR FLUIDS Dry Gas Wet Gas Gas Condensate Volatile Oil Black Oil REFERENCES EXERCISES 10 15 22 24 25 25 27 28 29 30 PVT TESTS AND CORRELATIONS 33 34 34 36 1.3 1.4 1.5 o 2.1 2.2 2.3 FLUID SAMPLING Well Preparation Sample Collection PVT TESTS 38 2.2.1 Dry Gas 2.2.2 Wet Gas 2.2.3 Black Oil 2.2.4 Gas Condensate 2.2.5 Volatile Oil EMPIRICAL CORRELATIONS 2.3.1 Black Oil Bubble Point Pressure Gas in Solution Oil Formation Volume Factor Total Formation Volume Factor Oil Density Oil Viscosity 2.3.2 Natural Gas Volumetric Data Gas Viscosity 2.3.3 Formation Water Water Content of Hydrocarbon Phase Hydrocarbon solubility in Water Water Formation Volume Factor Compressibility of Water Water Density Water Viscosity 2.4 2.5 REFERENCES EXERCISES 40 41 42 52 65 66 67 68 70 70 71 73 77 79 80 83 86 87 90 92 92 93 93 95 99 o 3.1 3.2 3.3 3.4 o 4.1 4.2 PHASE EQUILIBRIA CRITERIA FOR EQUILIBRIUM Chemical Potential Fugacity Activity EQUILIBRIUM RATIO Raoult's Law Henry's Law Empirical Correlations REFERENCES EXERCISES EQUATIONS OF STATE VIRIAL EOS AND ITS MODIFICATIONS Starling-Benedict-Webb-Rubin EOS CUBIC EQUATIONS OF STATE 4.2.1 Two-Parameter EOS Soave-Redlich-Kwong EOS Peng-Robinson EOS Volume Shift 4.2.2 Three-Parameter EOS Schmidt- Wenzel EOS Patel-Teja EOS 4.4 4.5 4.2.3 Attraction Term Temperature Dependency MIXING RULES 4.3.1 Random Mixing Rules 4.3.2 Non-Random Mixing Rules REFERENCES EXERCISES So PHASE BEHAVIOUR CALCULATIONS 4.3 5.1 5.2 5.3 5.4 5.5 5.6 o 6.1 6.2 6.3 VAPOUR-LIQUID EQUILIBRIUM CALCULATIONS Root Selection Rapid Flash Calculations STABILITY ANALYSIS Stability Limit CRITICAL POINT CALCULATIONS COMPOSITIONAL GRADING Equilibrium Assumption Non-Equilibrium Fluids Heat of Transport Significance REFERENCES EXERCISES FLUID CHARACTERISATION EXPERIMENTAL METHODS Distillation Gas Chromatography CRITICAL PROPERTIES Lee-Kesler Correlations Riazi-Daubert Correlations Perturbation Expansion Correlations DESCRIPTION OF FLUID HEAVY END Single Carbon Number Function Continuous Description vi 105 105 107 108 111 111 112 114 116 125 127 129 130 131 132 138 140 141 141 145 146 147 149 153 154 158 162 165 167 168 175 179 183 189 192 195 197 198 200 201 203 206 209 210 210 215 221 221 222 223 227 228 234 6.4 6.5 o 7.1 7.2 7.3 7.4 7.5 So 8.1 8.2 8.3 8.4 8.5 o 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Direct Application REFERENCES EXERCISES 241 247 249 GAS INJECTION MISCIBILITY CONCEPTS Miscibility in Real Reservoir Fluids 253 254 258 EXPERIMENTAL STUDIES Slim Tube Rising Bubble Apparatus Contact Experiments PREDICTION OF MISCIBILITY CONDITIONS First Contact Miscibility Vaporising Gas Drive Condensing-Vaporising Gas Drive REFERENCES EXERCISES 260 260 265 266 270 270 270 273 277 279 INTERFACIAL TENSION MEASUREMENT METHODS PREDICTION OF INTERFACIAL TENSION Parachor Method Corresponding States Correlation Comparison of Predictive Methods WATER-HYDROCARBON INTERFACIAL TENSION REFERENCES EXERCISES 281 282 285 285 288 289 292 295 297 APPLICATION IN RESERVOIR SIMULATION GROUPING Group Selection Group Properties Composition Retrieval COMPARISON OF EOS Phase Composition Saturation Pressure Density Gas and Liquid Volumes Robustness TUNING OF EOS Fluid Characterisation Selection of EOS Experimental Data Selection of Regression Variables Limits of Tuned Parameters Methodology DYNAMIC VALIDATION OF MODEL Relative Permeability Function Viscosity Prediction Implementation EVALUATION OF RESERVOIR FLUID SAMPLES REFERENCES EXERCISES 301 302 302 308 310 314 316 318 319 320 322 323 324 325 325 327 330 330 331 333 334 338 340 345 349 APPENDICES 353 INDEX 385 vii PREFACE Reliable measurement and prediction of phase behaviour and properties of petroleum reservoir fluids are essential in designing optimum recovery processes and enhancing hydrocarbon production This book explains relevant fundamentals and presents practical methods of determining required properties for engineering applications by judicious review of established practices and recent advances Although the emphasis is on the application of PVT and phase behaviour data to engineering problems, experimental methods are reviewed and their limitations are identified This should provide the reader with a more thorough understanding of the subject and a realistic evaluation of measured and predicted results The book is based on the material developed over many years as lecture notes in courses presented to staff in gas and oil industry, and postgraduate students of petroleum engineering It covers various aspects of the subject, hence can be tailored for different audience The first two chapters along with selected sections from chapters and can serve as the subject matter of an introductory course, whereas the rest would be of more interest to practising engineers and postgraduate students Ample examples are included to illustrate the subject, and further exercises are given in each chapter Graphical methods and simple correlations amenable to hand calculations are still used in the industry, hence they are included in this book The emphasis, however, is on the more advanced compositional approaches which are attaining wider application in industry as high computational capabilities are becoming readily available I would like to thank Professor DH Tehrani for reviewing the manuscript and valuable suggestions stemming from his vast industrial experience Also, I am grateful to Professors M Michelsen and C Whitson for their helpful comments on sections of the book Much of the material in this book is based on the author's experience gained through conducting research sponsored by the petroleum industry, at Heriot-Watt University I am indebted to the sponsors, my students and colleagues for their contributions that made this book possible In particular, I would acknowledge valuable contributions of Professor AC Todd, Mr F Goozalpour, Dr DH Xu, Mr K Movaghar Nezhad and Dr D Avolonitis My son Amir cheerfully helped me in preparing the book graphics viii NOMENCLATURE a A b B Bg Bo Bt Cg Co f G h h H Hi hi k k~j K Kw m M n N Pa Pb Pk Po ps R R~ S T Tb U V V V xi Yi Zi Z ZRA attractive term parameter of equation of state dimensionless attractive term parameter of equation of state repulsive term(co-volume) parameter of equation of state dimensionless repulsive term parameter of equation of state gas formation volume factor oil formation volume factor total formation volume factor gas isothermal compressibility coefficient oil isothermal compressibility coefficient fugacity Gibbs energy height molar enthalpy total enthalpy Henry's constant partial molar enthalpy permeability binary interaction parameter gas relative permeability oil relative permeability equilibrium ratio Watson characterisation factor slope in (x correlation with temperature molecular weight (molar mass) mole or carbon number number of components number of pseudo-components pressure atmospheric pressure bubble point pressure convergence pressure parachor vapour pressure universal gas constant gas in solution specific gravity, relative density at 288 K (60 ~ temperature normal boiling point temperature molar internal energy molar volume velocity volume mole fraction mole fraction in vapour phase mole fraction compressibility factor Rackett compressibility factor ix 374 PRESSURE, PSIA Equilibrium Ratio ,00o ooo K=Y/ K-Y/x Pressure, kPa Figure D.3 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure ETHANE Equilibrium Ratio PRESSURE, PSIA Q K =Y/x K =Y/x Pressure, k P a Figure D.4 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure PROPANE 376 Equilibrium Ratio PRESSURE, PSIA K=Yh ( {H~!~['.~!]I ~ LJ I | ! !! !l[!l[l]tl!lJ!!il![I]ltll!lll!!,l!'!*l'_!l!lIlflllllll I 1, I I I I 11 ;J!llllllllllllLLHllllll.}.Jt~!lltl!illllilllHlllIHI Pressure, kPa Figure D.5 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure L :2 I ! !l !ll~Li.liLJl~l!i,~lllit]]]|ll:tLLt'J "i BUTANE Equilibrium Ratio | 377 PRESSURE, PSIA K ,=Y/x K =Y/x ( II1!II!,I ~11"00 I!'.' ! l : ' l ! I _':1: !!:1!:!!11: ~ 31~0 : ' ~1".!:1l!'!11!I:1' P ~~ ~; I ~z '~:! t f,000'I: _' t ! ' I _,!lltill!'.'.:l:'!IIl ' l l ! l ! l3l ,l0[ l~l l l ! ! l l ~l l l l l l '"! l l l ~l l l l ~ II [I fO,OOO , i l Pressure, kPa Figure D.6 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure '_ 1:2 t: i.,~,l:_'r_i3 L:~ S n BUTANE 378 PRESSURE, PSIA Equilibrium Ratio K-Y/x ,w ,.,w , Pressure, kPa F i g u r e D.7 E q u i l i b r i u m r a t i o at M P a ( 0 p s i a ) c o n v e r g e n c e p r e s s u r e ~T PENTANE Equilibrium Ratio LO 379 PRESSURE, PSIA '1 100"" 7~ S, 4, 9, 8, 7, 6, S; | | '=Ylx K=Y/x , 0.1 01 9' 8' 7' 6' 4' ool I:I:Z:~ I111'.1~:,~{I111:18 1"00~ l ~ ~ I ~ :!~l:llllll~lll::2 1: ' 31~ 411: ~ll,~ll:llltl!:lll!'l!ll~lslx) ~ ) ~ I i,0[:)olt I l i 11 !I!t i1lltllll~ll!llll!~ll 1 ! 3~,101~1 ~ t 1 1~ 1i 1i 1" 1 1~1 1~.1 l l~1l t f0,O00[ [ ' ! ["I Pressure, kPa Figure D.8 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure ;~ll ,tlr::~l'3 ,~i :,.1~ ~l,_l[:.ll_,~:t4 S n- PENTANE 380 PRESSURE, PSIA Equilibrium Ratio K =Y/x K =Y/x ,IX), Pressure, kPa Figure D.9 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure ItEXANE Equilibrium Ratio 381 PRESSURE, PSIA (~ 300 s 500 Plotted from 1947 tabulations of G G Brown, University of Michigan Extrapolated and drawn by The Fluor Corp Ltd in 1957 1.0 ,0.1 K =Y/x K =Y/x 01 {301 (}01 "O(X)|IIwh.l: I : ! iil'o0- 0001 ]9 I' :':l-!~:l'.!i!ll! i!!:3]!!:-l!!!!h-lllil~l!!!:l!llll i I ! I ll!Iilil!Jl!:i~ll!:!111!!l'.!-l!:]dl-!JI|lllllll!lllllrl ! I !'_'I ~!ll'.~(:l, ~,i~:l,:l:l'-:::l:~ - i 3(X) i 500 I I iix'o00 z 3,0()0 i " i ) iil'o, o00 Pressure, kPa Figure D 10 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure i i ~ HEPTANE i 382 Equilibrium Ratio PRESSURE, PSIA 100 t 300 Plotted from 1947 tabulations of G G Brown, University of Mich- JHI igon Extrapolated a n d d r o w n by t The Fluor Corp Ltd in 1957 K =Y/x K =Y/x 001 I~t}!tii]ilL]!i ! t ,.~|i:].l~!!l!ll')ilL!t/!~!:i[zlilli[!l]!ll[l];!illl]lfi~| i I i ilL:l)f]lilli)illltitiiii!l'llii"ll]]!i~q,]l Pressure, kPa Figure D 11 Equilibrium ratio at 34.47 MPa (5000 psia) convergence pressure i iHI ! , :1 )]|-~ /~,h~L,A,~L~L~|,,~iL~ OCTANE Equilibrium Ratio 383 PRESSURE, PSIA I1o K=Y/x IrI!'l I,.! ! It ! I ! ! !~l]!!!ll!llll!'lll!!'.l!'.!|,.l_,!l!!l:l!~!!l!