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Mathematical Models for Poroelastic Flows

  • Book
  • © 2014

Overview

Authors:
  1. Anvarbek Meirmanov

    1. Mathematics and Cybernetics, Kazakh-British Technical University, Almaty, Kazakhstan

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  • For each underground physical process the reader finds a set of mathematical models depending on the dimensionless criteria of the given process and describing the process with different degrees of exactness
  • The reader may apply the suggested approach to solve many other important problems in filtration and acoustics and obtain macroscopic mathematical models, which are asymptotically exact
  • First volume in a new series

Part of the book series: Atlantis Studies in Differential Equations (ASDE, volume 1)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxxviii
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  2. Isothermal Liquid Filtration

    • Anvarbek Meirmanov
    Pages 1-65

  3. Filtration of a Compressible Thermo-Fluid

    • Anvarbek Meirmanov
    Pages 67-87

  4. Hydraulic Shock in Incompressible Poroelastic Media

    • Anvarbek Meirmanov
    Pages 89-134

  5. Double Porosity Models for a Liquid Filtration

    • Anvarbek Meirmanov
    Pages 135-167

  6. Filtration in Composite Incompressible Media

    • Anvarbek Meirmanov
    Pages 169-239

  7. Isothermal Liquid Filtration

    • Anvarbek Meirmanov
    Pages 241-263

  8. Non-isothermal Acoustics in Poroelastic Media

    • Anvarbek Meirmanov
    Pages 265-283

  9. Isothermal Acoustics in Composite Media

    • Anvarbek Meirmanov
    Pages 285-316

  10. Double Porosity Models for Acoustics

    • Anvarbek Meirmanov
    Pages 317-325

  11. Diffusion and Convection in Porous Media

    • Anvarbek Meirmanov
    Pages 327-365

  12. The Muskat Problem

    • Anvarbek Meirmanov
    Pages 367-381

  13. Back Matter

    Pages 383-449
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Keywords

About this book

The book is devoted to rigorous derivation of macroscopic mathematical models as a homogenization of exact mathematical models at the microscopic level. The idea is quite natural: one first must describe the joint motion of the elastic skeleton and the fluid in pores at the microscopic level by means of classical continuum mechanics, and then use homogenization to find appropriate approximation models (homogenized equations). The Navier-Stokes equations still hold at this scale of the pore size in the order of 5 – 15 microns. Thus, as we have mentioned above, the macroscopic mathematical models obtained are still within the limits of physical applicability. These mathematical models describe different physical processes of liquid filtration and acoustics in poroelastic media, such as isothermal or non-isothermal filtration, hydraulic shock, isothermal or non-isothermal acoustics, diffusion-convection, filtration and acoustics in composite media or in porous fractured reservoirs. Our research is based upon the Nguetseng two-scale convergent method.

Authors and Affiliations

  • Mathematics and Cybernetics, Kazakh-British Technical University, Almaty, Kazakhstan

    Anvarbek Meirmanov

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