Homogenization and Porous Media (Interdisciplinary Applied Mathematics, 6, Band 6) - Hardcover

Hardcover

ISBN 10: 0387947868 ISBN 13: 9780387947860

Verlag: Springer, 1996

Inhaltsangabe

1 Introduction.- 1.1 Basic Idea.- 1.2 First Examples.- 1.3 Diffusion in Periodic Media.- 1.4 Formal Derivation of Darcy's Law.- 1.5 Formal Derivation of a Distributed Microstructure Model.- 1.6 Remarks on Networks of Resistors, Capillary Tubes, and Cracks.- 2 Percolation Models for Porous Media.- 2.1 Fundamentals of Percolation Theory.- 2.2 Exponent Inequalities for Random Flow and Resistor Networks.- 2.3 Critical Path Analysis in Highly Disordered Porous and Conducting Media.- 3 One-Phase Newtonian Flow.- 3.1 Derivation of Darcy's Law.- 3.2 Inertia Effects.- 3.3 Derivation of Brinkman's Law.- 3.4 Double Permeability.- 3.5 On the Transmission Conditions at the Contact Interface between a Porous Medium and a Free Fluid.- 4 Non-Newtonian Flow.- 4.1 Introduction.- 4.2 Equations Governing Creeping Flow of a Quasi-Newtonian Fluid.- 4.3 Description of a Periodic s-Geometry, Construction of the Restriction Operator, and Review of the Results of Two-Scale Convergence in Lq-Spaces.- 4.4 Statement of the Principal Results.- 4.5 Inertia Effects for Non-Newtonian Flows through Porous Media.- 4.6 Proof of the Uniqueness Theorems.- 4.7 Uniform A Priori Estimates.- 4.8 Proof of Theorem A.- 4.9 Proof of Theorem B.- 4.10 Conclusion.- 5 Two-Phase Flow.- 5.1 Derivation of the Generalized Nonlinear Darcy Law.- 5.2 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Reservoir with Capillary Forces (Finite Peclet Number).- 5.3 Upscaling Two-Phase Flow Characteristics in a Heterogeneous Core, Neglecting Capillary Effects (Infinite Peclet Number).- 5.4 The Double-Porosity Model of Immiscible Two-Phase Flow.- 6 Miscible Displacement.- 6.1 Introduction.- 6.2 Upscaling from the Micro-to the Mesoscale.- 6.3 Upscaling from the Meso-to the Macroscale.- 6.4 Discussion.- 7 Thermal Flow.-7.1 Introduction.- 7.2 Basic Equations.- 7.3 Natural Convection in a Bounded Domain.- 7.4 Natural Convection in a Horizontal Porous Layer.- 7.5 Mixed Convection in a Horizontal Porous Layer.- 7.6 Thermal Boundary Layer Approximation.- 7.7 Conclusion.- 8 Poroelastic Media.- 8.1 Acoustics of an Empty Porous Medium.- 8.2 A Priori Estimates for a Saturated Porous Medium.- 8.3 Local Description of a Saturated Porous Medium.- 8.4 Acoustics of a Fluid in a Rigid Porous Medium.- 8.5 Diphasic Macroscopic Behavior.- 8.6 Monophasic Elastic Macroscopic Behavior.- 8.7 Monophasic Viscoelastic Macroscopic Behavior.- 8.8 Acoustics of Double-Porosity Media.- 8.9 Conclusion.- 9 Microstructure Models of Porous Media.- 9.1 Introduction.- 9.2 Parallel Flow Models.- 9.3 Distributed Microstructure Models.- 9.4 A Variational Formulation.- 9.5 Remarks.- 10 Computational Aspects of Dual-Porosity Models.- 10.1 Single-Phase Flow.- 10.2 Two-Phase Flow.- 10.3 Some Computational Results.- A Mathematical Approaches and Methods.- A.1.1 F-Convergence.- A.1.2 G-Convergence.- A.1.3 H-Convergence.- A.2 The Energy Method.- A.2.1 Setting of a Model Problem.- A.2.2 Proof of the Results.- A.3 Two-Scale Convergence.- A.3.1 A Brief Presentation.- A.3.2 Statement of the Principal Results.- A.3.3 Application to a Model Problem.- A.4 Iterated Homogenization.- B Mathematical Symbols and Definitions.- B.1 List of Symbols.- B.2 Function Spaces.- B.2.1 Macroscopic Function Spaces.- B.2.2 Micro-and Mesoscopic Function Spaces.- B.2.3 Two-Scale Function Spaces.- B.2.4 Time-Dependent Function Spaces.- C References.

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The methods and results of the theory of homogenization and their applications to flow and transport in porous media are discussed in this book. It offers a systematic and rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso-, and macro-scales. The chapters are devoted to percolation, Newtonian and non-Newtonian phenomena, two-phase flow, miscible displacement, and thermal and elastic effects. Detailed studies of micro-structure systems and computational results for dual-porosity models are presented. This book will be of interest to readers who want to learn the principal underlying ideas and concepts of modern mathematical theory, including the most recently obtained results and applications. Mathematicians, soil physicists, geo-hydrologists, chemical engineers, and researchers working in oil reservoir simulation or in the environmental sciences will find this book of particular interest.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 1996
• Sprache: Englisch
• ISBN 10: 0387947868
• ISBN 13: 9780387947860
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 295
• Herausgeber: Hornung Ulrich
• Kontakt zum Hersteller: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Deutschland