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CONTEMPORARY MATHEMATICS
295
Fluid Flow and Transport in Porous Media:
Mathematical and Numerical Treatment
Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference
on Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment
June 17-211 2001 Mount Holyoke College I South Hadley I Massachusetts
Zhangxin Chen Richard E. Ewing
Editors
Fluid Flow and Transport in Porous Media:
Mathematical and Numerical Treatment
http://dx.doi.org/10.1090/conm/295
CoNTEMPORARY MATHEMATICS
295
Fluid Flow and Transport in Porous Media:
Mathematical and Numerical Treatment
Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference
on Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment
June 17-21 I 2001 Mount Holyoke College I South Hadley I Massachusetts
Zhangxin Chen Richard E. Ewing
Editors
American Mathematical Society Providence, Rhode Island
Editorial Board Dennis DeThrck, managing editor
Andreas Blass Andy R. Magid Michael Vogelius
The 2001 AMS-IMS-SIAM Joint Summer Research Conference on "Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment" was held at Mount Holyoke College, South Hadley, Massachusetts, June 17-21, 2001, with support from the National Science Foundation, grant DMS-9973450-
2000 Mathematics Subject Classification. Primary 76S05, 76M25, 65M60, 65M25, 65N55, 35R60, 35K05, 92D25, 49L20, 68W10.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.
Library of Congress Cataloging-in-Publication Data AMS-IMS-SIAM Joint Summer Research Conference on Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment (2001 : Mount Holyoke College)
Fluid flow and transport in porous media, mathematical and numerical treatment : proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Fluid Flow and T.-ansport in Porous Media: Mathematical and Numerical Treatment, June 17-21, 2001, Mount Holyoke College, South Hadley, Massachusetts / Zhangxin Chen, Richard E. Ewing, editors.
p. em. -- (Contemporary mathematics, ISSN 0271-4132 ; 295) Includes bibliographical references. ISBN 0-8218-2807-X (alk. paper) 1. Porous materials---Permeability---Mathematical models-Congresses. 2. Transport theory-
Mathematical models-Congresses. 3. Fluid dynamics--Congresses. I. Chen, Zhangxin, 1962-11. Ewing, Richard E. III. Title. IV. Contemporary mathematics (American Mathematical Society) ; v. 295.
QC173.4.P67 A57 2001 620.1'16-dc21 2002018626
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10987654321 07 06 05 04 03 02
Contents
Preface 1x
A new approach to upscaling for two-phase flow in heterogeneous porous media J0RG AARNES AND MAGNE S. ESPEDAL 1
Modeling fractures as interfaces for flow and transport in porous media CLARISSE ALBOIN, JEROME JAFFRE, JEAN E. ROBERTS, AND CHRISTOPHE SERRES 13
A family of higher-order Eulerian-Lagrangian localized adjoint methods for advection-diffusion equations MOHAMED AL-LAWATIA AND HONG WANG 25
Algorithmic aspects of a locally conservative Eulerian-Lagrangian method for transport-dominated diffusive systems CESAR ALMEIDA, JIM DOUGLAS, JR., FELIPE PEREIRA, LUIS c. ROMAN, AND LI-MING YEH 37
A streamline front tracking method for two- and three-phase flow including capillary forces INGA BERRE, HELGE K. DAHLE, KENNETH H. KARLSEN, AND HANS F. N ORDHAUG 49
Adaptive and formfree identification of nonlinearities in fluid flow from column experiments SANDRO BITTERLICH AND PETER KNABNER 63
Overall behaviour of fractured porous media versus fractures' size and permeability ratio ALAIN BOURGEAT 75
Hysteresis and upscaling in two-phase flow through porous media MICHAEL A. CELIA AND ANDREW J. GuswA 93
Simulation of biobarrier-protozoa interaction in porous media BENITO M. CHEN-CHARPENTIER AND HRISTO v. KOJOUHAROV 105
Mixed discontinuous FE methods and their applications to two-phase flow in porous media HONGSEN CHEN, ZHANGXIN CHEN, GUANREN HUAN, AND ZHONGXIAO WANG 113
v
vi CONTENTS
Two-phase immiscible flow with the viscous drag in naturally fractured reservmrs ZHANGXIN CHEN, YANLI Cui, AND QIAOYUAN JIANG 127
Mixed finite element methods for multiphase flow in petroleum reservoirs with multiple wellsMixed finite element methods for multiphase flow in petroleum reservoirs with multiple wells ZHANGXIN CHEN, GUANREN HUAN, AND BAOYAN LI 141
An acceleration procedure for the spectral element ocean model formulation of the shallow water equations CRAIG C. DOUGLAS, GUNDOLF HAASE, AND MOHAMED ISKANDARANI 153
Relations between phase mobilities and capillary pressures for two-phase flows in fractured media JIM DOUGLAS, JR., FELIPE PEREIRA, AND LI-MING YEH 159
Parameter estimates for high-level nuclear transport in fractured porous media JIM DOUGLAS, JR. AND ANNA M. SPAGNUOLO 173
Overlapping grids for welltest analysis DUGALD B. DUNCAN AND YIQI QIU 185
Upscaling of biological processes and multiphase flow in porous media RICHARD E. EWING 195
A numerical simulation of multicomponent gas flow in porous media by projection methods RICHARD E. EWING, JUNPING WANG, SUZANNE L. WEEKES, AND YONGJUN YANG 217
Recent developments on modeling and analysis of flow of miscible fluids in porous media XIAOBING FENG 229
A simple model for scale up error JAMES GLIMM, YOON-HA LEE, AND KENNY YE 241
Conservative front tracking in one space dimension JAMES GLIMM, XIAO LIN LI, AND YINGJIE LIU 253
BEM with collocation for the heat equation with Neumann and mixed boundary values NORBERT HERRMANN 265
Applications of the control volume function approximation method to reservoir simulations GUANREN HUAN, ZHANGXIN CHEN, AND BAOYAN LI 279
Analysis of 1-D moment equations for immiscible flow KENNETH D. JARMAN AND THOMAS F. RUSSELL 293
Locally optimal pumping and treatment rates in uncertain environments DANIELL. KERN, JOHN J. WESTMAN, AND FLOYD B. HANSON 305
CONTENTS vii
A general multigrid framework for a class of perturbed problems Do Y. KWAK 317
Modeling horizontal wells using hybrid grids in reservoir simulations BAOYAN LI, ZHANGXIN CHEN, AND GUANREN HUAN 327
A multiblock mixed finite element method for 2D and 3D elliptic problems on mixed unstructured grids and its parallelization JICHUN LI 343
Network flow model studies and 3D pore structure W. BRENT LINDQUIST 355
Pore scale network modelling of gas slippage in tight porous media QINGJIE LIU, PINGPING SHEN, AND PUHUA YANG 367
The calculation of relative permeability by history matching and Beth network model QINGJIE LIU, JINXUN WANG, PUHUA YANG, AND PINGPING SHEN 377
Comparison between pore-level and porous medium models for natural convection in a non-homogeneous enclosure ALI A. MERRIKH, JOSE L. LAGE, AND ABDULMAJEED A. MOHAMAD 387
New models for predicting temperature-dependent viscous effects on flow through porous media ARUNN NARASIMHAN AND JOSE L. LAGE 397
Balancing domain decomposition for porous media flow in multiblock domains GERGINA PENCHEVA AND IVAN YOTOV 409
Non conforming methods for transport with nonlinear reaction BEATRICE RIVIERE AND MARY F. WHEELER 421
A high order Lagrangian scheme for flow through unsaturated porous media LOUIS F. Rossi 433
Partition of unity coarse spaces MARCUS SARKIS 445
Uncertainty reduction in reservoir modeling SAM SUBBEY, MIKE CHRISTIE, AND MALCOLM SAMBRIDGE 457
A Eulerian-Lagrangian substructuring domain decomposition method for multidimensional, unsteady-state advection-diffusion equations HONG WANG, JIANGGUO LIU, MAGNE S. ESPEDAL, AND RICHARD E. EWING 469
An ELLAM simulator for highly compressible flow in porous media with multiple wells H. WANG, W. ZHAO, R. E. EWING, S. L. LYONS, AND G. QIN 481
Single-degree freedom collocation method using Hermite polynomials LI Wu AND G. F. PINDER 489
viii CONTENTS
A Taylor-Galerkin finite element method for one-dimensional hyperbolic conservation laws XIJUN Yu AND YONGHONG Wu 501
Morphological evolution of a 3D array of particles under surface diffusion WEN ZHANG AND IAN GLADWELL 519
Preface
The interest in the mathematical and numerical treatment of fluid flow and transport in porous media has been increasingly rising. For example, the emer-gence of complex enhanced recovery procedures in the field of hydrocarbon extrac-tion techniques has emphasized the need for sophisticated mathematical models and numerical tools capable of predicting, understanding, and optimizing intri-cate physical phenomena occurring in this field. A joint American Mathematical Society (AMS), Institute of Mathematical Sciences (IMS), and Society for Indus-trial and Applied Mathematics (SIAM) summer research conference, entitled "Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment", was successfully held at Mount Holyoke College in South Hadley, Massachusetts, USA, June 17-21, 2001. The goal of this conference was to bring together applied mathematicians, computational scientists, and engineers working actively in the mathematical and numerical treatment of fluid flow and transport in porous me-dia. A broad range of researchers presented papers and discussed both problems and current, state-of-the-art techniques.
Over seventy people from many countries attended this conference and more than fifty papers were presented on a variety of subjects in multiphase fluid flow and transport in porous media. This book contains forty-three papers selected from this conference. They cover recent advances and developments in mathemat-ical modeling, network flow modeling, contemporary numerical methods, parallel computation, optimization, chemically reactive phenomena, multiscale phenomena, upscaling, uncertainty reduction, well treatment, and media characterization. This book serves as an excellent research reference for all graduate students, geoscientists, mathematicians, physicists, and engineers who work in the field of mathematical modeling and numerical simulation of fluid flow and transport in porous media.
This conference would not have been possible without the help and support of a number of people in the American Mathematical Society. In particular, we would like to thank Mr. Wayne Drady for his hard work at the conference site. We would also like to thank Mrs. Christine M. Thivierge for her technical assistance in preparing this volume. Finally, we would like to acknowledge the financial support of the National Science Foundation for funding this summer research conference.
ix
Zhangxin Chen Richard E. Ewing
Texas
Selected Titles in This Series
295 Zhangxin Chen and Richard E. Ewing, Editors, Fluid flow and transport in porous media: Mathematical and numerical treatment, 2002
294 Robert Coquereaux, Ariel Garda, and Roberto Trinchera, Editors, Quantum symmetries in theoretical physics and mathematics, 2002
293 Donald M. Davis, Jack Morava, Goro Nishida, W. Stephen Wilson, and Nobuaki Yagita, Editors, Recent progress in homotopy theory, 2002
292 A. Chenciner, R. Cushman, C. Robinson, and Z. Xia, Editors, Celestial Mechanics, 2002
291 Bruce C. Berndt and Ken Ono, Editors, q-series with applications to combinatorics, number theory, and physics, 2001
290 Michel L. Lapidus and Machiel van Frankenhuysen, Editors, Dynamical, spectral, and arithmetic zeta functions, 2001
289 Salvador Perez-Esteva and Carlos Villegas-Blas, Editors, Second summer school in analysis and mathematical physics: Topics in analysis: Harmonic, complex, nonlinear and quantization, 2001
288 Marisa Fernandez and Joseph A. Wolf, Editors, Global differential geometry: The mathematical legacy of Alfred Gray, 2001
287 Marlos A. G. Viana and Donald St. P. Richards, Editors, Algebraic methods in statistics and probability, 2001
286 Edward L. Green, Serkan Ho§ten, Reinhard C. Laubenbacher, and Victoria Ann Powers, Editors, Symbolic computation: Solving equations in algebra, geometry, and engineering, 2001
285 Joshua A. Leslie and Thierry P. Robart, Editors, The geometrical study of differential equations, 2001
284 Gaston M. N'Guerekata and Asamoah Nkwanta, Editors, Council for African American researchers in the mathematical sciences: Volume IV, 2001
283 Paul A. Milewski, Leslie M. Smith, Fabian Waleffe, and Esteban G. Tabak, Editors, Advances in wave interaction and turbulence, 2001
282 Arlan Ramsay and Jean Renault, Editors, Groupoids in analysis, geometry, and physics, 2001
281 Vadim Olshevsky, Editor, Structured matrices in mathematics, computer science, and engineering II, 2001
280 Vadim Olshevsky, Editor, Structured matrices in mathematics, computer science, and engineering I, 2001
279 Alejandro Adem, Gunnar Carlsson, and Ralph Cohen, Editors, Topology, geometry, and algebra: Interactions and new directions, 2001
278 Eric Todd Quinto, Leon Ehrenpreis, Adel Faridani, Fulton Gonzalez, and Eric Grinberg, Editors, Radon transforms and tomography, 2001
277 Luca Capogna and Loredana Lanzani, Editors, Harmonic analysis and boundary value problems, 2001
276 Emma Previato, Editor, Advances in algebraic geometry motivated by physics, 2001 275 Alfred G. NoiH, Earl Barnes, and Sonya A. F. Stephens, Editors, Council for
African American researchers in the mathematical sciences: Volume III, 2001 274 Ken-ichi Maruyama and John W. Rutter, Editors, Groups of homotopy
self-equivalences and related topics, 2001 273 A. V. Kelarev, R. Gobel, K. M. Rangaswamy, P. Schultz, and C. Vinsonhaler,
Editors, Abelian groups, rings and modules, 2001 272 Eva Bayer-Fluckiger, David Lewis, and Andrew Ranicki, Editors, Quadratic
forms and their applications, 2000 (Continued in the back of this publication)
Selected Titles in This Series (Continued from the front of this publication)
271 J. P. C. Greenlees, Robert R. Bruner, and Nicholas Kuhn, Editors, Homotopy methods in algebraic topology, 2001
270 Jan Denef, Leonard Lipschitz, Thanases Pheidas, and Jan Van Gee!, Editors, Hilbert's tenth problem: Relations with arithmetic and algebraic geometry, 2000
269 Mikh~il Lyubich, John W. Milnor, and Yair N. Minsky, Editors, Laminations and foliations in dynamics, geometry and topology, 2001
268 Robert Gulliver, Walter Littman, and Roberto Triggiani, Editors, Differential geometric methods in the control of partial differential equations, 2000
267 Nicolas Andruskiewitsch, Walter Ricardo Ferrer Santos, and Hans-Jiirgen Schneider, Editors, New trends in Hopf algebra theory, 2000
266 Caroline Grant Melles and Ruth I. Michler, Editors, Singularities in algebraic and analytic geometry, 2000
265 Dominique Arlettaz and Kathryn Hess, Editors, Une degustation topologique: Homotopy theory in the Swiss Alps, 2000
264 Kai Yuen Chan, Alexander A. Mikhalev, Man-Keung Siu, Jie-Tai Yu, and Efim I. Zelmanov, Editors, Combinatorial and computational algebra, 2000
263 Yan Guo, Editor, Nonlinear wave equations, 2000 262 Paul Igodt, Herbert Abels, Yves Felix, and Fritz Grunewald, Editors,
Crystallographic groups and their generalizations, 2000 261 Gregory Budzban, Philip Feinsilver, and Arun Mukherjea, Editors, Probability
on algebraic structures, 2000 260 Salvador Perez-Esteva and Carlos Villegas-Blas, Editors, First summer school in
analysis and mathematical physics: Quantization, the Segal-Bargmann transform and semiclassical analysis, 2000
259 D. V. Huynh, S. K. Jain, and S. R. Lopez-Permouth, Editors, Algebra and its applications, 2000
258 Karsten Grove, Ib Henning Madsen, and Erik Kjaer Pedersen, Editors, Geometry and topology: Aarhus, 2000
257 Peter A. Cholak, Steffen Lempp, Manuel Lerman, and Richard A. Shore, Editors, Computability theory and its applications: Current trends and open problems, 2000
256 Irwin Kra and Bernard Maskit, Editors, In the tradition of Ahlfors and Bers: Proceedings of the first Ahlfors-Bers colloquium, 2000
255 Jerry Bona, Katarzyna Saxton, and Ralph Saxton, Editors, Nonlinear PDE's, dynamics and continuum physics, 2000
254 Mourad E. H. Ismail and Dennis W. Stanton, Editors, q-series from a contemporary perspective, 2000
253 Charles N. Delzell and James J. Madden, Editors, Real algebraic geometry and ordered structures, 2000
252 Nathaniel Dean, Cassandra M. McZeal, and Pamela J. Williams, Editors, African Americans in Mathematics II, 1999
251 Eric L. Grinberg, Shiferaw Berhanu, Marvin I. Knopp, Gerardo A. Mendoza, and Eric Todd Quinto, Editors, Analysis, geometry, number theory: The Mathematics of Leon Ehrenpreis, 2000
250 Robert H. Gilman, Editor, Groups, languages and geometry, 1999 249 Myung-Hwan Kim, JohnS. Hsia, Yoshiyuki Kitaoka, and Rainer
Schulze-Pillot, Editors, Integral quadratic forms and lattices, 1999
For a complete list of titles in this series, visit the AMS Bookstore at www.ams.org/bookstorej.
This volume contains research papers written and edited by prominent researchers work-ing with the mathematical and numerical treatment of fluid flow and transport in porous media. Papers are based on a 2001 joint AMS-IMS-SIAM summer research conference held at Mount Holyoke College (South Hadley, MA). Topics cover a variety of subjects, such as network flow modeling, contemporary numerical methods, parallel computation, opti-mization, multiscale phenomena, upscaling, uncertainty reduction, well treatment, and media characterization.
The book serves as an excellent reference work for all geoscientists, mathematicians, physicists, and engineers working in the mathematical modeling and numerical simulation of fluid flow and transport in porous media.
ISBN 0-8218-2807-X
9 780821 828076
