Reservoir Simulation: Mathematical Techniques in Oil Recovery (CBMS-NSF Regional Conference Series in Applied Mathematics, 77)

248 Pages·2007·13.36 MB·English

by  Zhangxin Chen

CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 1
Reservoir Simulation
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 2
CBMS-NSF REGIONAL CONFERENCE SERIES
IN APPLIED MATHEMATICS
A series of lectures on topics of current research interest in applied mathematics under the
direction of the Conference Board of the Mathematical Sciences,supported by the National
Science Foundation and published by SIAM.
GARRETTBIRKHOFF,The Numerical Solution of Elliptic Equations
D. V. LINDLEY,Bayesian Statistics,A Review
R. S. VARGA,Functional Analysis and Approximation Theory in Numerical Analysis
R. R. BAHADUR,Some Limit Theorems in Statistics
PATRICKBILLINGSLEY,Weak Convergence of Measures:Applications in Probability
J. L. LIONS,Some Aspects of the Optimal Control of Distributed Parameter Systems
ROGERPENROSE,Techniques of Differential Topology in Relativity
HERMANCHERNOFF,Sequential Analysis and Optimal Design
J. DURBIN,Distribution Theory for Tests Based on the Sample Distribution Function
SOLI. RUBINOW,Mathematical Problems in the Biological Sciences
P. D. LAX,Hyperbolic Systems of Conservation Laws and the Mathematical Theory
of Shock Waves
I. J. SCHOENBERG,Cardinal Spline Interpolation
IVANSINGER,The Theory of Best Approximation and Functional Analysis
WERNERC. RHEINBOLDT,Methods of Solving Systems of Nonlinear Equations
HANSF. WEINBERGER,Variational Methods for Eigenvalue Approximation
R. TYRRELLROCKAFELLAR,Conjugate Duality and Optimization
SIRJAMESLIGHTHILL,Mathematical Biofluiddynamics
GERARDSALTON,Theory of Indexing
CATHLEENS. MORAWETZ,Notes on Time Decay and Scattering for Some Hyperbolic Problems
F. HOPPENSTEADT,Mathematical Theories of Populations:Demographics,Genetics
and Epidemics
RICHARDASKEY,Orthogonal Polynomials and Special Functions
L. E. PAYNE,Improperly Posed Problems in Partial Differential Equations
S. ROSEN,Lectures on the Measurement and Evaluation of the Performance
of Computing Systems
HERBERTB. KELLER,Numerical Solution of Two Point Boundary Value Problems
J. P. LASALLE,The Stability of Dynamical Systems - Z. Artstein,Appendix A:Limiting
Equations and Stability of Nonautonomous Ordinary Differential Equations
D. GOTTLIEBANDS. A. ORSZAG,Numerical Analysis of Spectral Methods:Theory
and Applications
PETERJ. HUBER,Robust Statistical Procedures
HERBERTSOLOMON,Geometric Probability
FREDS. ROBERTS,Graph Theory and Its Applications to Problems of Society
JURISHARTMANIS,Feasible Computations and Provable Complexity Properties
ZOHARMANNA,Lectures on the Logic of Computer Programming
ELLISL. JOHNSON,Integer Programming:Facets,Subadditivity,and Duality for Group
and Semi-Group Problems
SHMUELWINOGRAD,Arithmetic Complexity of Computations
J. F. C. KINGMAN,Mathematics of Genetic Diversity
MORTONE. GURTIN,Topics in Finite Elasticity
THOMASG. KURTZ,Approximation of Population Processes
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 3
JERROLDE. MARSDEN,Lectures on Geometric Methods in Mathematical Physics
BRADLEYEFRON,The Jackknife,the Bootstrap,and Other Resampling Plans
M. WOODROOFE,Nonlinear Renewal Theory in Sequential Analysis
D. H. SATTINGER,Branching in the Presence of Symmetry
R. TEMAM,Navier-Stokes Equations and Nonlinear Functional Analysis
MIKLÓSCSÖRGO,Quantile Processes with Statistical Applications
J. D. BUCKMASTERANDG. S. S. LUDFORD,Lectures on Mathematical Combustion
R. E. TARJAN,Data Structures and Network Algorithms
PAULWALTMAN,Competition Models in Population Biology
S. R. S. VARADHAN,Large Deviations and Applications
KIYOSIITÔ,Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces
ALANC. NEWELL,Solitons in Mathematics and Physics
PRANABKUMARSEN,Theory and Applications of Sequential Nonparametrics
LÁSZLÓLOVÁSZ,An Algorithmic Theory of Numbers,Graphs and Convexity
E. W. CHENEY,Multivariate Approximation Theory:Selected Topics
JOELSPENCER,Ten Lectures on the Probabilistic Method
PAULC. FIFE,Dynamics of Internal Layers and Diffusive Interfaces
CHARLESK. CHUI,Multivariate Splines
HERBERTS. WILF,Combinatorial Algorithms:An Update
HENRYC. TUCKWELL,Stochastic Processes in the Neurosciences
FRANKH. CLARKE,Methods of Dynamic and Nonsmooth Optimization
ROBERTB. GARDNER,The Method of Equivalence and Its Applications
GRACEWAHBA,Spline Models for Observational Data
RICHARDS. VARGA,Scientific Computation on Mathematical Problems and Conjectures
INGRIDDAUBECHIES,Ten Lectures on Wavelets
STEPHENF. MCCORMICK,Multilevel Projection Methods for Partial Differential Equations
HARALDNIEDERREITER,Random Number Generation and Quasi-Monte Carlo Methods
JOELSPENCER,Ten Lectures on the Probabilistic Method,Second Edition
CHARLESA. MICCHELLI,Mathematical Aspects of Geometric Modeling
ROGERTEMAM,Navier–Stokes Equations and Nonlinear Functional Analysis,Second Edition
GLENNSHAFER,Probabilistic Expert Systems
PETERJ. HUBER,Robust Statistical Procedures,Second Edition
J. MICHAELSTEELE,Probability Theory and Combinatorial Optimization
WERNERC. RHEINBOLDT,Methods for Solving Systems of Nonlinear Equations,Second Edition
J. M. CUSHING,An Introduction to Structured Population Dynamics
TAI-PINGLIU,Hyperbolic and Viscous Conservation Laws
MICHAELRENARDY,Mathematical Analysis of Viscoelastic Flows
GÉRARDCORNUÉJOLS,Combinatorial Optimization:Packing and Covering
IRENALASIECKA,Mathematical Control Theory of Coupled PDEs
J. K. SHAW,Mathematical Principles of Optical Fiber Communications
ZHANGXINCHEN,Reservoir Simulation:Mathematical Techniques in Oil Recovery
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 4
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 5
ZHANGXIN CHEN
University of Calgary
Calgary, Alberta, Canada
Reservoir Simulation
Mathematical Techniques
in Oil Recovery
SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS
PHILADELPHIA
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 6
Copyright © 2007 by the Society for Industrial and Applied Mathematics.
10 9 8 7 6 5 4 3 2 1
All rights reserved. Printed in the United States of America. No part of this book may be
reproduced,stored,or transmitted in any manner without the written permission of the
publisher. For information,write to the Society for Industrial and Applied Mathematics,
3600 Market Street,6th floor,Philadelphia,PA 19104-2688.
Trademarked names may be used in this book without the inclusion of a trademark symbol.
These names are used in an editorial context only; no infringement of trademark is intended.
Library of Congress Cataloging-in-Publication
Chen,Zhangxin,1962–
Reservoir simulation :mathematical techniques in oil recovery / Zhangxin Chen.
p. cm. – (CBMS-NSF regional conference series in applied mathematics ; 77)
Includes bibliographical references and index.
ISBN 978-0-898716-40-5 (alk. paper)
1. Oil reservoir engineering–Mathematical models. 2. Oil reservoir
engineering–Simulation methods. 3. Porous materials–Permeability–Mathematical
models. 4. Transport theory–Mathematical models. I. Title II. Series.
TN871.C465 2007
622’.3382015118–dc22
2007061749
is a registered trademark.
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 7
This book is dedicated
to my parents, wife, and children.
(cid:2)
CB77_Chenfm_A.qxp 9/7/2007 12:29 PM Page 8
chenb
(cid:1) (cid:1)
2007/9
pageix
(cid:1) (cid:1)
Contents
ListofFigures xiii
ListofTables xv
ListofNotation xvii
Preface xxvii
1 Introduction 1
1.1 PetroleumReservoirSimulation . . . . . . . . . . . . . . . . . . . . . 1
1.2 ClassicalReservoirEngineeringMethods . . . . . . . . . . . . . . . . 1
1.2.1 MaterialBalanceMethods . . . . . . . . . . . . . . . . . 1
1.2.2 DeclineCurveMethods . . . . . . . . . . . . . . . . . . 2
1.2.3 StatisticalMethods . . . . . . . . . . . . . . . . . . . . . 2
1.2.4 AnalyticalMethods . . . . . . . . . . . . . . . . . . . . 2
1.3 ReservoirSimulationMethods . . . . . . . . . . . . . . . . . . . . . 3
1.3.1 ReservoirSimulationStages . . . . . . . . . . . . . . . . 3
1.3.2 ReservoirSimulatorClassifications . . . . . . . . . . . . 4
1.3.3 ReservoirSimulationApplications . . . . . . . . . . . . 4
1.4 SIMetricConversionFactors . . . . . . . . . . . . . . . . . . . . . . 6
2 AGlossaryofPetroleumTerms 7
2.1 ReservoirRockProperties . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 ReservoirFluidProperties . . . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Wettability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 FluidDisplacementProcesses . . . . . . . . . . . . . . . . . . . . . . 13
2.5 ReservoirRock/FluidProperties. . . . . . . . . . . . . . . . . . . . . 13
2.5.1 Two-PhaseRelativePermeability . . . . . . . . . . . . . 15
2.5.2 Three-PhaseRelativePermeability . . . . . . . . . . . . 17
2.6 TermsUsedinNumericalSimulation . . . . . . . . . . . . . . . . . . 20
3 Single-PhaseFlowandNumericalSolution 23
3.1 BasicDifferentialEquations . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 MassConservation . . . . . . . . . . . . . . . . . . . . . 23
3.1.2 Darcy’sLaw . . . . . . . . . . . . . . . . . . . . . . . . 25
ix
(cid:1) (cid:1)
(cid:1) (cid:1)