Macroscale Models of Flow Through Highly Heterogeneous Porous Media

By: Mikhail Panfilov, M. B. Panfilov

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Hardcover | 29 February 2000

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392 Pages

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24.77 x 17.15 x 3.18

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The The book book was was planned planned in in such such a a manner manner that that two two basic basic goals goals would would be be reached. reached. On On the the one one hand, hand, the the goal goal was was to to show show some some new new results results in in the the field field of of modeling modeling transport transport through through highly highly heterogeneous heterogeneous media, media, based based on on the the homogenization homogenization theory. theory. Multiple Multiple new new mathematical mathematical models models of of transport transport are are presented presented herein, herein, studying studying their their properties, properties, developing developing methods methods to to compute compute effective effective parameters parameters of of the the averaged averaged media, media, simulation simulation of of cell cell problems, problems, using using new new models models to to simulate simulate some some practical practical problems. problems. High High heterogeneity heterogeneity being being subjected subjected to to the the homogenization homogenization procedure, procedure, generates generates non-local non-local phenomena phenomena and and then then gives gives a a possibility possibility to to develop develop a a new, new, non-local non-local (or (or "dynamic"), "dynamic"), theory theory of of transport transport in in porous porous media. media.

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Published: 6th December 2010

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Introduction
One Phase Darcy's Flow in Double Porosity Media	p. 1
Actual State of the Problem	p. 1
Setting of the Problem, Classification of Media	p. 11
Upscaling Flow in Highly Heterogeneous Media	p. 23
Derivation of the Macroscale Equations	p. 34
Macroscale Models for Source Media	p. 44
Macroscale Model for Media of Translation Type	p. 49
Macroscale Model for Translation-Source Media	p. 53
Generalized Macroscale Model	p. 62
Calculation of the Macroscale Mass-Exchanges Parameters	p. 70
Effective Permeability of Highly Heterogeneous Media	p. 77
Depletion of Highly Heterogeneous Reservoirs. Solution of Model Problems	p. 92
Homogenization of Two-Scale Disordered Media	p. 101
Chemical or Heat Convection-Diffusion Transport Through Highly Heterogeneous Porous Media	p. 125
Introductory Notes	p. 125
Setting of the Problem	p. 133
Classification of Flows	p. 141
C-S System: Deduction of Homogenized Equations	p. 148
C-S System: Particular Solutions of Cell Problems	p. 158
C-S System: General Solutions of Cell Problems. General Closure Relations	p. 171
C-S System: Macroscale Model	p. 177
D-S System	p. 180
DC-S System (With Convective Boundary Layer)	p. 184
C-T System	p. 187
Memory Effects in Delay Model of Tracer Transport	p. 197
Dispersion Tensor in Anisotropic Network Media. Stream Configuration Method	p. 211
Description of the Lattice Model of Porous Medium	p. 211
Cell Problem of Chemical Transport Through the Lattice Medium	p. 219
Method of Stream Configurations	p. 224
Solution of the Cell Problem	p. 234
Effective Dispersion Tensor in Anisotropic Lattices	p. 239
Two-Phase Flow in Double Porosity Media	p. 245
Introductory Notes	p. 245
Basic Problems	p. 256
Definition of the Problem	p. 261
Classification of Two-Phase Flows	p. 270
Equilibrium Modes of Capillary Dominated Flow	p. 277
Deduction of the Macroscale Model for D-S Flow	p. 283
Macroscale Models of Two-Phase Flow with Capillary Forces. Capillary Relaxation	p. 291
Effective Phase and Relative Permeabilities	p. 298
Numerical Simulation of Effective Relative Permeability	p. 305
Macroscale Models for Particular Structures of Two-Phase Flow	p. 312
Numerical Simulation of Two-Phase Flow in Highly Heterogeneous Medium	p. 315
Two-Phase Flow in Pseudo-Cavity Media	p. 329
Introducing Notes	p. 329
Definition of the Problem	p. 331
Deduction of the Macroscale Model	p. 336
Macroscale Equations for Quasi-Linear Mode of Flow	p. 346
Partially Frozen Mode. Pore-Network Modeling	p. 354
Comparison with Experimental Results	p. 359
Table of Contents provided by Blackwell. All Rights Reserved.

Macroscale Models of Flow Through Highly Heterogeneous Porous Media

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