Tarek ahmed phd PE reservoir engineering handbook, fourth edition 2010

Gulf Professional Publishing is an imprint of Elsevier 30 Corporate Drive, Suite 400, Burlington, MA 01803, USA The Boulevard, Langford Lane, Kidlington, Oxford, OX5 1GB, UK © 2010 ELSEVIER Inc All rights reserved No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher Details on how to seek permission, further information about the Publisher’s permissions policies and our arrangements with organizations such as the Copyright Clearance Center and the Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions This book and the individual contributions contained in it are protected under copyright by the Publisher (other than as may be noted herein) Notices Knowledge and best practice in this field are constantly changing As new research and experience broaden our understanding, changes in research methods, professional practices, or medical treatment may become necessary Practitioners and researchers must always rely on their own experience and knowledge in evaluating and using any information, methods, compounds, or experiments described herein In using such information or methods they should be mindful of their own safety and the safety of others, including parties for whom they have a professional responsibility To the fullest extent of the law, neither the Publisher nor the authors, contributors, or editors, assume any liability for any injury and/or damage to persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions, or ideas contained in the material herein Library of Congress Cataloging-in-Publication Data Ahmed, Tarek H., 1946– Reservoir engineering handbook / Tarek Ahmed.—4th ed p cm Includes bibliographical references and index ISBN 978-1-85617-803-7 (alk paper) Oil reservoir engineering Oil fields Gas reservoirs I Title TN871.A337 2010 622′.3382—dc22 2009039148 British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library For information on all Gulf Professional Publishing publications visit our Web site at www.elsevierdirect.com 10 11 12 13 Printed in the United States of America Working together to grow libraries in developing countries www.elsevier.com | www.bookaid.org | www.sabre.org This book is dedicated to my children, Jennifer, Justin, Brittany, and Carsen Ahmed The book is also dedicated to a very special person, “Wendy.” ACKNOWLEDGMENTS Much of the material on which this book is based was drawn from the publications of the Society of Petroleum Engineers (SPE) Tribute is due to the SPE and the petroleum engineers, scientists, and authors who have made numerous and significant contributions to the field of reservoir engineering This book reflects my style of teaching during my tenure at Montana Tech of the University of Montana and my understanding of the subject of reservoir engineering I would like to thank all my former students at Montana Tech for putting up with me and my Egyptian temper I hope that my friends and colleagues in academia will enjoy this edition of the book Special thanks to Dr Bob Chase, Dr Tom Blasingame, Dr J Tiab, Dr F Civan, and Dr Nathan Meehan for their constructive (I think) criticisms and discussions I would like also to thank the Petroleum faculty and their students at Cairo University and Suez Canal University for their suggestions for updating and improving the book It was my pleasure to spend the past years with Anadarko Petroleum and work with an outstanding group of professionals Special thanks to Kevin Corrigan, Brian Roux, Diana McCranie, and Aydin Centilmen I would like to thank the editorial and production staff of Elsevier for their work and professionalism, particularly Ken McCombs and Sarah Binns xi PREFACE TO THE FOURTH EDITION To make the fourth edition of this textbook as complete as possible, I have added Chapter 17 that deals with the topics of Fracture Reservoirs and Hydraulically Fracture Wells The book documents the technical materials that have published and addressed this subject over the last 20 years, particularly the research work that has been authored by Dr H Kazemi and Dr Steve Holditch xii PREFACE TO THE THIRD EDITION To make the third edition of this textbook as complete as possible, I have included the following: a new chapter on decline curve and type curve analysis, a section on tight and shallow gas reservoirs, and waterflood surveillance techniques Many of my colleagues have provided me with valuable recommendations and suggestions that I have included through the textbook to make it more comprehensive in treating the subject of reservoir engineering xiii PREFACE TO THE SECOND EDITION I have attempted to construct the chapters following a sequence that I have used for several years in teaching three undergraduate courses in reservoir engineering Two new chapters have been included in this second edition; Chapters 14 and 15 Chapter 14 reviews principles of waterflooding with emphasis on the design of a waterflooding project Chapter 15 is intended to introduce and document the practical applications of equations of state in the area of vapor-liquid phase equilibria A comprehensive review of different equations of state is presented with an emphasis on the Peng-Robinson equation of state xiv PREFACE TO THE FIRST EDITION This book explains the fundamentals of reservoir engineering and their practical application in conducting a comprehensive field study Chapter reviews fundamentals of reservoir fluid behavior with an emphasis on the classification of reservoir and reservoir fluids Chapter documents reservoir-fluid properties, while Chapter presents a comprehensive treatment and description of the routine and specialized PVT laboratory tests The fundamentals of rock properties are discussed in Chapter and numerous methodologies for generating those properties are reviewed Chapter focuses on presenting the concept of relative permeability and its applications in fluid flow calculations The fundamental mathematical expressions that are used to describe the reservoir fluid flow behavior in porous media are discussed in Chapter 6, while Chapters and describe the principle of oil and gas well performance calculations, respectively Chapter provides the theoretical analysis of coning and outlines many of the practical solutions for calculating water and gas coning behavior Various water influx calculation models are shown in Chapter 10, along with detailed descriptions of the computational steps involved in applying these models The objective of Chapter 11 is to introduce the basic principle of oil recovery mechanisms and to present the generalized form of the material balance equation Chapters 12 and 13 focus on illustrating the practical applications of the material balance equation in oil and gas reservoirs xv ABOUT THE AUTHOR Tarek Ahmed, Ph.D., P.E is a Senior Reservoir Engineering Advisor with Baker Hughes International at the Reservoir Engineering Technology Center Before joining BHI, Dr Ahmed was a professor and the head of the Petroleum Engineering Department at Montana Tech of University of Montana Until recently he was a Reservoir Engineering Advisor with Anadarko Petroleum He holds a Ph.D from Oklahoma University, 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 Equations of State and PVT Analysis (Gulf Publishing, 2007) xvi C H A P T E R FUNDAMENTALS OF RESERVOIR FLUID BEHAVIOR Naturally occurring hydrocarbon systems found in petroleum reservoirs are mixtures of organic compounds that exhibit multiphase behavior over wide ranges of pressures and temperatures These hydrocarbon accumulations may occur in the gaseous state, the liquid state, the solid state, or in various combinations of gas, liquid, and solid These differences in phase behavior, coupled with the physical properties of reservoir rock that determine the relative ease with which gas and liquid are transmitted or retained, result in many diverse types of hydrocarbon reservoirs with complex behaviors Frequently, petroleum engineers have the task to study the behavior and characteristics of a petroleum reservoir and to determine the course of future development and production that would maximize the profit The objective of this chapter is to review the basic principles of reservoir fluid phase behavior and illustrate the use of phase diagrams in classifying types of reservoirs and the native hydrocarbon systems CLASSIFICATION OF RESERVOIRS AND RESERVOIR FLUIDS Petroleum reservoirs are broadly classified as oil or gas reservoirs These broad classifications are further subdivided depending on: © 2010 Elsevier Inc All rights reserved Doi: 10.1016/C2009-0-30429-8 1440 Reservoir Engineering Handbook Figure Hexane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 Appendix 1441 Figure Heptane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 1442 Reservoir Engineering Handbook Figure 10 Octane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 Appendix 1443 Figure 11 Nonane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 1444 Reservoir Engineering Handbook Figure 12 Decane Conv press 5,000 psia Courtesy of the Gas Processors Suppliers Association Published in the GPSA Engineering Data Book, Tenth Edition, 1987 INDEX A Absolute open flow, 488 permeability correlations, 250 porosity, 190 Absolute open flow, 488 Acentric factor, 25 correlations, 26 After-breakthrough production, 976 Ahmed’s splitting scheme, 1215 Alani-Kennedy equation, 1149 API gravity, 76 Apparent molecular weight, 32 Aquifer, 651 boundary conditions, 653 classification, 651 flow geometry, 653 flow regimes, 653 prediction models, 655 Areal sweep efficiency (EA), 985 Asymmetric mixture, 1179 Average reservoir pressure, 419, 770, 866 Averaging permeability, 241 porosity, 184 relative permeability, 313 saturation, 197 B Back pressure equation, 556 plot, 557 Baurdet and Gringarten model, 1355 Behavior of real gases, 36 Bilinear flow, 1386 Binary interaction coefficient, 1172 Bottom-water drive, 669, 692 Breakthrough, 965 Bubble-point pressure, 86, 871 curve, definition of, 86 methods of determining, 86, 1125, 1198, 1201 phase equilibrium, 1179 Buildup testing, 467 1445 1446 Index Bulk compressibility coefficient, 255 C Campbell’s equilibrium ratio method, 1121 Capillary pressure, 203 curve, 208 definition, 203 hysteresis, 209, 211 Carter-Tracy water influx model, 718 Carter type curve, 1291 Characterizing petroleum fractions, 25 Combination drive, 801 Component, 1096 Compressibility coefficient bulk, 255 definition, 59 formation, 256 gas, 59 matrix, 255 oil, 98, 148 pore, 255 Compressibility factor calculation, 38, 1159 definition, 37 Compressibility of natural gases, 59 Concept of permeability jail, 1339 Condensate liquid dropout, 182 retrograde, 171 Conductance ratio, 1016 Cone, 585 stable, 585 unstable, 585 Coning, 583 gas, 588 in horizontal wells, 629 in vertical wells, 587 water, 589 Constant composition tests, 137, 174 terminal pressure , 384 terminal rate, 384 volume depletion tests, 176 Convergence pressure, 1113 Hadden’s method, 1115 Rzasa’s method, 1118 Standing’s method, 1117 Correcting constant-composition data, 164 differential liberation date, 166 separator data, 169 viscosity data, 167 Counterflow, 945 Cox chart, 1097 Craig-Geffen-Morse oil recovery prediction method, 1065 Cricondenbar, Cricondentherm, Critical compressibility factor, 26 flow rate, 586 point, pressure, temperature, Crude oil density, 97, 141, 1142 gravity, 75 properties, 74 Cubic equation of state, 1158 D Dalton’s Law, 1099, 1107 Darcy’s Law, 228 Dead-oil viscosity, 115 Index Decline curve analysis, 1235 Exponential decline, 1237, 1241 Harmonic decline, 1238, 1249 Hyperbolic decline, 1238, 1250 Deliverability equation, 556 Density calculations, 1142 Depletion-drive mechanism, 735, 761 Desaturating process, 210 Dew-point, 11, 1179 curve, Dew-point pressure, 3, 1179 definition of, 1123, 1195 methods of determining, 1195, 1201 Differential liberation, 149 Differential separation, 1130 Diffusivity equation, 381 Dimensionless diffusivity equation, 395 gravity number, 1039 pressure, 393 radius, 394 time, 394 Displacement efficiency (ED), 934 Downdip flow, 943 Drainage process, 293 Drawdown test, 454 Driving mechanisms, 761 combination, 752 depletion, 735 gas-cap, 787 gravity-drainage, 746 solution gas, 735, 761 water-drive, 792 Dry-gas reservoirs, 15 Dykstra-Parsons Modified, 1062 oil recovery prediction method, 1059 1447 permeability variation method, 1042 sequencing technique, 1046 E Ei-function, 385 Edge-water drive, 669 Edmister correlation, 1178 Effective permeability, 289 porosity, 191 wellbore radius, 437 End-point mobility ratio, 1050 Energy plots, 866 Equation(s) of state, 1134 applications, 1194 cubic, 1158 Peng-Robinson, 1182, 1203, 1295 Redlich-Kwong, 1160 Soave-Redlich-Kwong (SRK), 1169, 1205 Van der Waals, 1150 vapor pressure, 1205 Equilibrium ratio, 1099 applications, 1122 Campbell’s method, 1121 determination of, 1194 Katz’s method, 1122 phase equilibrium, 1179 for plus fractions, 1120 for real solutions, 1107 three-phase, 1199 Winn’s method, 1121 Equilibrium separation, 1130 Equivalent time, 1364 Exponential integral, 385 Extrapolation of reservoir fluid data, 164 1448 F Felsenthal, Cobb, and Heuer oil recovery prediction method, 1062 Fetkovich’s IPR equation, 509 method, 509 Type curve, 1275 Water influx, 722 Fill-up, 1027 Finite-radial reservoir, 398 Flash calculations, 1103, 1202 Flash separation, 1130 Flood patterns, 927 Confiment, 1080 Conformance, 1082 Flow equations, 340 periods fractured wells, 1384 regimes, 334 Flowing material balance, 1308 Fluids classification of, injectivity, 1012 properties, 29 Formation compressibility, 254 Correlations, 259 Formation linear flow, 1394 Formation volume factor gas, 65 oil, 92 Fractional flow equation, 936 Fracture linear flow, 1385 Fratures Finite-condutivity, 1322 infinite-condutivity, 1322 Uniform-flux, 1323 Index Fractured Carbonates, 1341 Reservoirs, 1338 Sandstones, 1346 Shales, 1344 Wells, 1321 Free water level, 213 Frontal advance equation, 952 Frontal displacement theory, 936 Fugacity, 1175 coefficient, 1176 Fundamentals of reservoir fluid behavior, reservoir fluid flow, 331 rock properties, 189 G Gas coning, 583 dry gas, 10, 15 fugacity, 1175 material balance equation, 859 in place, 856 properties, 29 reservoirs, 10, 855 saturation, 873 solubility, 78 viscosity, 68 well performance, 546 wet gas, 10 Gas-cap drive reservoirs, 787 Gas-condensate reservoirs, 10 Gas-oil ratio, 372 Gas solubility correlations, 78 Gas well performance, 546 Geometric average permeability, 249 shape factor, 1350 Index Gravity crude oil, 75 solution gas, 76 Gravity-drainage reservoirs, 746 H Hadden’s convergence pressure method, 1115 Hall Plot, 1071 Harmonic average permeability, 245 Havlena and Odeh, 772 Heptanes-plus fraction, 1191, 1207 Heterogeneity, 261 vertical, 261 High shrinkage oil, Hong’s mixing rules, 1222 Horizontal heterogeneity, 261, 274 well breakthrough, 624 gas, 577 oil, 528 Horner’s plot, 470 Hurst and van Everdingen, 668 Hurst’s steady-state method, 663 Hydraulically fractured wells, 1375 I Image wells, 450 Imbibition process, 296 Incompressible fluids, 332 Infinite acting, 374, 396 acting psendoradial flow, 1397 Infinite-conductivity fractures, 1381 vertical fractures, 1380 1449 Inflow performance relationships gas, 547 oil, 488 Injection rate, 1012 Interfacial tension, 200 Interference, 1012 Interporosity flow coefficient, 1351 IPR, 484, 488 Fetkovich’s, 509 Standing’s, 505 Vogel’s, 493 Inverse distance method, 276 Inverse distance squared method, 277 Isothermal compressibility coefficient gas, 59 oil, 98 rock, 254 J J-function, 224 K Katz’s equilibrium ratio method, 1122 splitting scheme, 1210 Kay’s mixing rules, 1223 Klinkenberg effect, 234 L Laboratory PVT tests, 136 routine, 136 special, 136 Laminar flow, 342 Laminar-Inertial-Turbulent, 558 1450 Index Layers, minimum number of, 1043 Lee and Kessler correlation, 1178 Lee’s mixing rules, 1223 Leverett J-function, 224 Linear flow, 338 Liquid dropout, 12 LIT approach, 558 Lohrenz’s splitting scheme, 1212 Lorenz coefficient, 268 Lost oil saturation, 824 Low-shrinkage oil, Lumping schemes, 1218 Whitson’s, 1219 M m(p)-solution method, 405 Material balance equation (MBE), 733, 958 gas, 958 oil, 733 straight-line, 772 Material balance pseudo-time, 1301 Matrix compressibility coefficient, 254 Maximum liquid dropout, 13 Method of images, 450 Mixing rules, 1161, 1222, 1223 Mobility ratio, 987 Muskat’s material balance method, 838 N Natural gases, compressibility of, 59 Naturally fractured reservoirs, 1340 Near-critical crude oil, Near-critical gas condensate, 10 Non-Darcy flow, 438 Nonstabilized zone, 957 Normalized material balance pseudo-time, 1301 Normalizing relative permeability, 313 O Odeh and Havlena, 772 Oil formation volume factor, 92 for undersaturated oils, 103 Oil material balance equation, 773 Oil properties, 74 Oil recovery predicting, 81 Oil reservoirs, Oil saturation, 824 Oil saturation adjustment for combination drive, 822 for gas-cap expansion, 820 for water influx, 819 Oil viscosity, 115 Oil-water contact, 213 Oil well performance, 484 Optimum gas saturation, 922 Optimum separator pressure, 1131 Ordinary black oil, P p/z gas equation, 861 pattern balancing, 1079 Pedersen’s splitting scheme, 1214 Peng-Robinson equation of state, 1182, 1203, 1205 Permeability, 227 absolute, 227 Index averaging, 242 effective, 289 relative, 288 variation, 262 Permeability jail, 1339 ordering, 1046 Phase diagram, Phase equilibrium, 1179 Plant products, 173 Plus fractions, 1191, 1207 lumping, 1218 splitting, 1208 Poisson’s ration, 1377 Polygon method, 276 Pore compressibility coefficient, 255 volume, 192 Porosity, 190 absolute, 190 effective, 191 Porosity averaging methods, 194 Positional permeability variation, 1046 Pot aquifer, 655 Predicting oil reservoir performance Craig-Geffen-Morse method, 1065 Dykstra-Parsons method, 1069, 1062 Felsenthal, Cobb, and Heuer method, 1062 Muskat’s method, 838 Tarner’s method, 843 Tracy’s method, 831 Pressure bubble-point, 3, 86, 1125, 1198, 1201 buildup, 467 1451 drawdown, 454 drop due to skin, 472 capillary, 203 dew-point, 3, 1123, 1179, 1195, 1201 pseudo-critical, 38 pseudo reduced, 37 separator, 1128 -squared approximation, 408 vapor, 1205 Pressure-approximate method, 404 Pressure-squared method, 404 Pressure-temperature diagram, Primary porosity, 1367 recovery mechanisms, 761 Probability-log scale, 264 Productivity index, 473 Properties of crude oil systems, 74 natural gases, 29 rocks, 189 water, 124 Pseudocritical pressure, 42 temperature, 42 Pseudoization, 1218 Pseudosteady-state flow, 413 R Radial diffusivity equation, 382 flow of gases, 429 Raoult’s Law, 1099, 1107 Real solutions, 1107 Redlich-Kwong equation of state, 1162 Reduced gas density, 56 1452 Reduced pressure, 37 Reduced temperature, 37 Relative oil volume, 141 Relative permeability, 288 averaging, 313 concepts, 288 correlations, 296 three-phase, 320 two-phase, 289 Relative total volume, 141 Reservoir apparent molecular weight, 32 composition of, 137 density, 33 fluid properties, 29 geometry, 336 heterogeneity, 261 ideal gases, 30 specific gravity, 34 specific volume, 33 standard volume, 33 water properties, 122 Reservoir drive mechanisms, combination, 752 gas-cap, 787 solution gas-drive, 735 water-drive, 792 Reservoirs, classification of, Residual oil saturation, 196 Retrograde gas reservoirs, 10 Riazi and Daubert correlation, 1191 Rock compressibility, 254 properties, 189 Routine laboratory PVT tests, 136 Rzasa’s convergence pressure method, 1118 Index S Saturated oil reservoirs, viscosity, 117 Saturation, 189 averaging, 195 critical oil, 196 movable oil, 196 pressure, 137 residual oil, 196 trapped gas, 873 water, 197 Schilthuis’s steady-state method, 655, 659 Secondary Porosity, 1367 Semisteady-state, 336, 414 Separator tests, 146, 152 Shallow gas reservoirs, 900 Shape factor, 423, 466 Shock front, 967 Shrinking gas cap, 822 Skin factor, 431 Soave-Redlich-Kwong (SRK) equation of state, 1168 modifications of, 1178 Splitting schemes, 1108 Ahmed’s, 1215 Lohrenz’s, 1212 Pedersen’s, 1214 Stabilized zone, 957 Stage separation, 1128 Standing-Katz density calculation method, 1142 Standing’s convergence pressure method, 1117 correlation, 1108, 1166 IPR equation, 505 Steady-state flow, 334, 342 Index Stiles’ permeability variation method, 1050 Stone’s I model, 324 Stone’s II model, 326 Storativity ratio, 1351 Superposition, 442 Surface tension, 121, 200 T Tarner’s method, 843 Three-phase equilibrium, 1199 Three-phase relative permeability, 320 correlations, 322 Tight gas reservoirs, 866 Time end of infinite-acting, 465 Total formation volume factor, 159 Tounquing, 1038 Tracy’s form of the MBE, 803 method, 831 Transition zone, 213 Trapped gas saturation, 873 Turbulent flow factor, 437 Two-phase Formation volume factor, 108, 159 relative correlations, 296 relative permeability, 289 z-factor, 178 Type-curve Anash, 1311 Carter, 1292 Fetkovich, 1275 Fractured wells, 1321, 1326 Palacio-Blasingame, 1299 Type-curve analysis, 1264 1453 U Undefined petroleum fractions, 24 Undersaturated oil reservoirs, 4, 825 viscosity, 117 Uniform-flux fractures, 1381 Unsteady-state flow, 373 V Van der Waals equation of state, 1149 Van Everdingen-Hurst’s unsteadystate model, 668 Vapor pressure, 1096, 1205 Vertical gas well performance, 546 heterogeneity, 262 oil well performance, 484 sweep efficiency (EV), 1061 Viscosity dead oil, 115 gas, 67 oil, 114 saturated oil, 117 undersaturated oil, 119 water, 125 Vogel’s IPR equation, 493 Volatile crude oil, Volume translation method, 1180 Volumetric sweep efficiency, 934 W Warren and Roots model, 1349 Water properties, 124 viscosity, 125 1454 Water coning, 589 Water-drive reservoirs, 792 gas, 870 oil, 792 Water fingering, 1038 Waterflooding Factors to consider, 910 optimum time, 915 patterns, 927 recovery factor (RF), 932 surveillance, 1069 trapped gas, 865 Water influx, 650 Carter-Tracy model, 718 Fetkovich’s model, 722 Water isothermal compressibility, 126 Water-oil ratio, 372, 946 Waterflood surveillance, 1069 Wellbore storage, 460 Wet-gas reservoirs, 14 Index Wettability, 199 Whitson and Torp correlation, 1119 Whitson’s lumping scheme, 1219 Wilson’s correlation, 1108, 1118 Winn’s equilibrium ratio method, 1121 X X-plot, 1075 Y Y-function, 143 Young’s modulus, 1377 Z Zonation problem, 1046 Z-factor, 37, 151 ... Cataloging-in-Publication Data Ahmed, Tarek H., 1946– Reservoir engineering handbook / Tarek Ahmed. —4th ed p cm Includes bibliographical references and index ISBN 978-1-85617-803-7 (alk paper) Oil reservoir engineering. .. reservoir fluid Accordingly, reservoirs can be classified into basically two types These are: • Oil reservoirs—If the reservoir temperature T is less than the critical temperature Tc of the reservoir. .. reservoir fluid, the reservoir is classified as an oil reservoir 4 Reservoir Engineering Handbook • Gas reservoirs—If the reservoir temperature is greater than the critical temperature of the hydrocarbon