Equations of State and PVT Analysis Applications for Improved Reservoir Modeling Tarek Ahmed, Ph.D., P.E Gulf Publishing Company Houston, Texas Equations of State and PVT Analysis: Applications for Improved Reservoir Modeling Copyright © 2007 by Gulf Publishing Company, Houston, Texas All rights reserved No part of this publication may be reproduced or transmitted in any form without the prior written permission of the publisher HOUSTON, TX: Gulf Publishing Company Greenway Plaza, Suite 1020 Houston, TX 77046 AUSTIN, TX: 427 Sterzing Street, Suite 104 Austin, TX 78704 10 Library of Congress Cataloging-in-Publication Data Ahmed, Tarek H Equations of state and PVT analysis : applications for improved reservoir modeling / Tarek Ahmed p cm Includes bibliographical references and index ISBN 1-933762-03-9 (alk paper) Reservoir oil pressure—Mathematical models Phase rule and equilibrium—Mathematical models Petroleum—Underground storage I Title TN871.18.A34 2007 622'.3382—dc22 2006033818 Printed in the United States of America Printed on acid-free paper Text design and composition by Ruth Maassen This book is dedicated to my children Carsen, Justin, Jennifer, and Brittany Ahmed Acknowledgments It is my hope that the information presented in this textbook will improve the understanding of the subject of equations of state and phase behavior Much of the material on which this book is based was drawn from the publications of the Society of Petroleum Engineers Tribute is paid to the educators, engineers, and authors who have made numerous and significant contributions to the field of phase equilibria I would like to specially acknowledge the significant contributions that have been made to this fascinating field of phase behavior and equations of state by Dr Curtis Whitson, Dr Abbas Firoozabadi, and Dr Bill McCain I would like to express appreciation to Anadarko Petroleum Corporation for granting me the permission to publish this book Special thanks to Mark Pease, Bob Daniels, and Jim Ashton I would like express my sincere appreciation to a group of engineers with Anadarko Petroleum Corporation for working with me and also for sharing their knowledge with me; in particular, Brian Roux, Eulalia Munoz-Cortijo, Jason Gaines, Aydin Centilmen, Kevin Corrigan, Dan Victor, John Allison, P K Pande, Scott Albertson, Chad McAllaster, Craig Walters, Dane Cantwell, and Julie Struble This book could not have been completed without the editorial staff of Gulf Publishing Company; in particular, Jodie Allen and Ruth Maassen Special thanks to my friend Wendy for typing the manuscript; I very much appreciate it, Wendy xi Preface The primary focus of this book is to present the basic fundamentals of equations of state and PVT laboratory analysis and their practical applications in solving reservoir engineering problems The book is arranged so it can be used as a textbook for senior and graduate students or as a reference book for practicing petroleum engineers Chapter reviews the principles of hydrocarbon phase behavior and illustrates the use of phase diagrams in characterizing reservoirs and hydrocarbon systems Chapter presents numerous mathematical expressions and graphical relationships that are suitable for characterizing the undefined hydrocarbon-plus fractions Chapter provides a comprehensive and updated review of natural gas properties and the associated well-established correlations that can be used to describe the volumetric behavior of gas reservoirs Chapter discusses the PVT properties of crude oil systems and illustrates the use of laboratory data to generate the properties of crude oil for suitable use or conducting reservoir engineering studies Chapter reviews developments and advances in the field of empirical cubic equations of state and demonstrates their practical applications in solving phase equilibria problems Chapter discusses issues related to flow assurance that include asphaltenes deposition, wax precipitation, and formation of hydrates About the Author Tarek Ahmed, Ph.D., P.E., is a Reservoir Enginering Advisor with Anadarko Petroleum Corporation Before joining the corporation, Dr Ahmed was a professor and the head of the Petroleum Engineering Department at Montana Tech of the University of Montana He has a Ph.D from the University of Oklahoma, an M.S from the University of Missouri–Rolla, and a B.S from the Faculty of Petroleum (Egypt)—all degrees in petroleum engineering Dr Ahmed is also the author of other textbooks, including Hydrocarbon Phase Behavior (Gulf Publishing Company, 1989), Advanced Reservoir Engineering (Elsevier, 2005), and Reservoir Engineeering Handbook (Elsevier, 2000; 2nd edition, 2002; 3rd edition, 2006) ix Contents Preface ix Acknowledgments xi Fundamentals of Hydrocarbon Phase Behavior Single-Component Systems Two-Component Systems 19 Three-Component Systems 28 Multicomponent Systems 29 Classification of Reservoirs and Reservoir Fluids Phase Rule 54 Problems 55 References 57 Characterizing Hydrocarbon-Plus Fractions Generalized Correlations 62 PNA Determination 82 Graphical Correlations 92 Splitting and Lumping Schemes 99 Problems 130 References 132 Natural Gas Properties 135 Behavior of Ideal Gases 136 Behavior of Real Gases 141 Problems 176 References 178 PVT Properties of Crude Oils 181 Crude Oil Gravity 182 Specific Gravity of the Solution Gas 183 Crude Oil Density 184 Gas Solubility 200 vii 59 32 contents viii Bubble-Point Pressure 207 Oil Formation Volume Factor 213 Isothermal Compressibility Coefficient of Crude Oil Undersaturated Oil Properties 228 Total-Formation Volume Factor 231 Crude Oil Viscosity 237 Surface/Interfacial Tension 246 PVT Correlations for Gulf of Mexico Oil 249 Properties of Reservoir Water 253 Laboratory Analysis of Reservoir Fluids 256 Problems 321 References 327 218 Equations of State and Phase Equilibria 331 Equilibrium Ratios 331 Flash Calculations 335 Equilibrium Ratios for Real Solutions 339 Equilibrium Ratios for the Plus Fractions 349 Vapor-Liquid Equilibrium Calculations 352 Equations of State 365 Equation-of-State Applications 398 Simulation of Laboratory PVT Data by Equations of State Tuning EOS Parameters 440 Original Fluid Composition from a Sample Contaminated with Oil-Based Mud 448 Problems 450 References 453 Flow Assurance 457 Hydrocarbon Solids: Assessment of Risk 458 Phase Behavior of Asphaltenes 470 Asphaltene Deposit Envelope 480 Modeling the Asphaltene Deposit 482 Phase Behavior of Waxes 495 Modeling Wax Deposit 502 Prediction of Wax Appearance Temperature 505 Gas Hydrates 506 Problems 530 References 531 Appendix Index 535 551 409 Fundamentals of Hydrocarbon Phase Behavior A PHASE IS DEFINED AS ANY homogeneous part of a system that is physically distinct and separated from other parts of the system by definite boundaries For example, ice, liquid water, and water vapor constitute three separate phases of the pure substance H2O, because each is homogeneous and physically distinct from the others; moreover, each is clearly defined by the boundaries existing between them Whether a substance exists in a solid, liquid, or gas phase is determined by the temperature and pressure acting on the substance It is known that ice (solid phase) can be changed to water (liquid phase) by increasing its temperature and, by further increasing the temperature, water changes to steam (vapor phase) This change in phases is termed phase behavior Hydrocarbon systems found in petroleum reservoirs are known to display multiphase behavior over wide ranges of pressures and temperatures The most important phases that occur in petroleum reservoirs are a liquid phase, such as crude oils or condensates, and a gas phase, such as natural gases The conditions under which these phases exist are a matter of considerable practical importance The experimental or the mathematical determinations of these conditions are conveniently expressed in different types of diagrams, commonly called phase diagrams The objective of this chapter is to review the basic principles of hydrocarbon phase behavior and illustrate the use of phase diagrams in describing and characterizing the volumetric behavior of single-component, two-component, and multicomponent systems Single-Component Systems The simplest type of hydrocarbon system to consider is that containing one component The word component refers to the number of molecular or atomic species present in the substance equations of state and pvt analysis A single-component system is composed entirely of one kind of atom or molecule We often use the word pure to describe a single-component system The qualitative understanding of the relationship between temperature T, pressure p, and volume V of pure components can provide an excellent basis for understanding the phase behavior of complex petroleum mixtures This relationship is conveniently introduced in terms of experimental measurements conducted on a pure component as the component is subjected to changes in pressure and volume at a constant temperature The effects of making these changes on the behavior of pure components are discussed next Suppose a fixed quantity of a pure component is placed in a cylinder fitted with a frictionless piston at a fixed temperature T1 Furthermore, consider the initial pressure exerted on the system to be low enough that the entire system is in the vapor state This initial condition is represented by point E on the pressure/volume phase diagram (p-V diagram) as shown in Figure 1–1 Consider the following sequential experimental steps taking place on the pure component: The pressure is increased isothermally by forcing the piston into the cylinder Consequently, the gas volume decreases until it reaches point F on the diagram, where the liquid begins to condense The corresponding pressure is known as the dew-point pressure, pd , and defined as the pressure at which the first droplet of liquid is formed The piston is moved further into the cylinder as more liquid condenses This condensation process is characterized by a constant pressure and represented by the horizontal line FG At point G, traces of gas remain and the corresponding pressure is called the bubble-point pressure, pb, and defined as the pressure at which the first sign of FIGURE 1–1 Typical pressure/volume diagram for a pure component APPENDIX 543 FIGURE A-8 1%-Pentnne conversion presswe, 5000 psi% Courtesy of the Gas Processors Suppliers Association Published in the GPSA EngineeringData BOA, 10th edition, 1987 544 FIGURE A-9 Hexane conversion pr-esswe, EQUATIOh'S O F S T A T E AND P V T ANALYSIS YO00 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA EngineaingDara B& t h edition, 1987 54s APPENDIX FIGURE A-I0 Heptnne conversion pyesswe, fiooopsia Courtesy of the Gas Processors Suppliers Association Published in the GPSA EqneaingData BaA, loth edition, 1987 46 E Q U A T I O N S O F S T A T E AND P V T ANALYSIS FIGURE A-11 Octane conversion presswe, 5000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA figkeriiigData B d , 10th edition, 1987 APPENDIX 547 FIGURE A-12 ,!!oizane co?azvel-s%oia p?*essure,YO00psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA fiiginasingData B d , 10th edition, 1987 548 E Q U A T I O N S O F STATE A N D PVT A N A L Y S I S FIGURE A-1 Decane conversion pyesmye, 5000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engjnming Dt Bmk, 10th edition, 1987 aa 549 APPENDIX FIGURE A-14 Ethane conversion presswe, 10,000 psin Courtesy of the Gas Processors Suppliers Assoclanon Published in the GPSA EngnwmgDaca Bo& 10th edinon, 198; INDEX Index Terms Links A Acentric factor API gravity 182 Apparent molecular weight 10 137 Asphaltene onset pressure 472 phase behavior 470 phase envelope 482 Average boiling point 85 B Bubble-point pressure Bubble-point pressure correlations 19 207 354 207 C CCE 260 Characterization of multiple samples 126 Characterizing plus-fraction Chemical potential Classification of reservoirs and fluids 59 384 32 Colloidal instability index 466 Compositional gradient 431 Compressibility factor 141 155 Constant composition expansion 260 415 Constant volume depletion 289 409 Contaminated oil sample 448 Convergence pressure 344 Correlations 346 Bergman 90 Cavett 66 This page has been reformatted by Knovel to provide easier navigation 402 Index Terms Links Correlations (Cont.) Edmister 69 Hall-Yarborough 72 Kesler-Lee 67 Magoulas-Tessios 72 Riazi-Daubert 65 Standing 71 TWU 72 Watansiri 69 Willman-Teja 71 Winn-Sim 68 Cox chart 10 Cricondenbar 30 Cricondentherm 30 Critical compressibility density 12 mixture 433 point 13 pressure 98 temperature 95 volume 14 high-shrinkage 33 35 low-shrinkage 33 near critical 33 ordinary 33 volatile oil 30 35 72 Crude oils Cubic EOS Curve boiling-point 37 331 92 bubble-point 32 dew-point 32 fusion melting point sublimation pressure vapor pressure This page has been reformatted by Knovel to provide easier navigation Index Terms CVD Links 289 D DE 269 De Boer plot 465 Dew-point pressure Differential expansion 417 19 269 400 417 E Effect of nonhydrocarbon components on the Z-factor 147 EOS 331 Equations of state 331 Peng-Robinson 388 Redlich-Kwong 371 Soave-Redlich-Kwong 376 van der Waals 365 Equilibrium ratios 332 correlations Equivalent gas volume 339 339 173 F Flash calculations 335 Flow assurance 457 Fugacity 382 Fugacity coefficient 382 Fusion temperature G Gibbs free energy 384 Gas density 139 Gas deviation factor 141 Gas expansion factor 164 Gas formation volume factor 163 Gas gravity 139 155 This page has been reformatted by Knovel to provide easier navigation Index Terms Links Gas isothermal compressibility 159 Gas properties 135 Gas reservoirs dry 38 43 near critical 38 41 retrograde 38 39 wet 38 41 Gas solubility 200 correlations 201 Gas density 139 Gas hydrates 509 Gas specific gravity 139 Gas viscosity 166 Gas/oil contact Gibbs energy GOC 46 144 53 432 53 432 384 46 H Hall-Yarborough correlation 72 High molecular weight gases 151 Hydrates 509 I Ideal gases 136 Interfacial tension 246 Inverse lever rule 27 Isothermal compressibility coefficient of crude oil 218 K K-value 332 L Laboratory analysis of reservoir fluids 256 Liquid blockage 304 This page has been reformatted by Knovel to provide easier navigation Index Terms Liquid dropout Lumping schemes Links 40 290 112 M Melting-point temperature Minimum miscibility pressure 309 MMP correlations 312 Multicomponent systems 29 N Near-critical gas-condensate reservoirs Nonhydrocarbon components 41 147 O Oil-based mud 448 Oil compressibility 218 Oil density 184 correlations Oil-formation volume factor correlations 195 213 214 Oil API gravity 182 Oil properties 181 undersaturated 228 Oil reservoirs gas-cap 33 saturated 32 undersaturated 32 Oil viscosity 237 P P-X diagram 23 P-T diagram 30 PNA 62 Phase rule 54 Plait point 30 82 This page has been reformatted by Knovel to provide easier navigation Index Terms Pour point Links 498 Pressure bubble-point 19 dew-point 20 vapor Pressure-composition diagram Properties of gases 207 354 10 23 135 Pseudo-critical pressure 146 temperature 146 PVT properties of crude oils 181 Q Quality lines 32 R Racket’s compressibility factor 17 Real gases 141 Refractive index 478 Resins 461 Riazi-Daubert correlation Routine laboratory PVT tests 65 260 S SARA analysis 460 Separator calculations 356 422 tests 271 422 Shift parameter 394 Simulation of laboratory data by EOS 409 Single-component systems Slim-tube test 308 Solution gas specific gravity 183 This page has been reformatted by Knovel to provide easier navigation 402 Index Terms Links Specific gravity of oil 182 of solution gas 183 of wet gases 171 Specific volume 139 Spencer-Danner 17 Splitting 99 Splitting and lumping 99 Surface tension 246 Swelling test 307 427 T TBP 61 Ternary diagram 29 Three-component systems 28 Three-phase flash calculations Tie line Total formation volume factor 403 491 29 231 True boiling point 61 Two-component systems 19 Two-phase formation volume factor 231 Tuning EOS parameters 440 Types of crude oil 33 U Undefined heavy fraction Undersaturated oil properties 59 228 Universal oil products 62 UOP 62 V Vapor pressure 10 407 Viscosity gas 166 oil 237 This page has been reformatted by Knovel to provide easier navigation Index Terms Volume shift parameter Links 394 W WAT 495 Water properties 253 Water-oil contact 52 Watson characterization factor 62 Wax appearance temperature 495 Wax phase envelope 498 53 495 WOC 52 498 53 Y Y-function 264 Z Z-factor 141 Z-factor direct calculations 155 155 This page has been reformatted by Knovel to provide easier navigation .. .Equations of State and PVT Analysis Applications for Improved Reservoir Modeling Tarek Ahmed, Ph.D., P.E Gulf Publishing Company Houston, Texas Equations of State and PVT Analysis: ... Components, Physical Constants equations of state and pvt analysis fundamentals of hydrocarbon phase behavior continued TABLE 1–1 equations of state and pvt analysis fundamentals of hydrocarbon phase behavior... Austin, TX 78704 10 Library of Congress Cataloging-in-Publication Data Ahmed, Tarek H Equations of state and PVT analysis : applications for improved reservoir modeling / Tarek Ahmed p cm Includes bibliographical