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Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology pp 267–321Cite as

Mathematical Modeling of Filtration Processes in Porous Media

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Part of the book series: Engineering Materials and Processes ((EMP))

Abstract

The current variety of filtration theories suggests that the porous medium and the fluid filling it form some continuous medium. That is, the elements of the porous medium-fluid system, though considered physically infinitesimal, however, are large enough compared to the size of pores and particles (grains, fibers) forming a porous medium. Averaged characteristics of the porous medium, which are introduced for mathematical description, may be sufficiently substantiated only for the volume with a large number of enclosed pores and particles. In terms of the elementary theory of filtration, the meaning of the solid skeleton of the porous medium is, above all, geometric—the skeleton limits the region of space in which the fluid moves. In more complex cases, we have seen strong interaction between the skeleton and the adjacent layers of the fluid. Therefore, the properties of the porous medium in the theory of filtration are usually described by a set of geometric averages. In this chapter, several cell models are considered for calculation of hydrodynamic permeability of porous media. It is assumed that porous media in general may consist of partially porous spherical or cylindrical particles. Different limiting cases are investigated and theoretical results are compared with experimental data.

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Acknowledgment

The support of Russian Science Foundation (RSF) is acknowledged (grant No 14-19-01045).

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Authors and Affiliations

  1. Department of Higher Mathematics, Gubkin Russian State University of Oil and Gas, Moscow, Russia

    Anatoly Nikolaevich Filippov

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  1. Anatoly Nikolaevich Filippov
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Correspondence to Anatoly Nikolaevich Filippov .

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Filippov, A.N. (2014). Mathematical Modeling of Filtration Processes in Porous Media. In: Structural Properties of Porous Materials and Powders Used in Different Fields of Science and Technology. Engineering Materials and Processes. Springer, London. https://doi.org/10.1007/978-1-4471-6377-0_13

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  • DOI: https://doi.org/10.1007/978-1-4471-6377-0_13

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  • Online ISBN: 978-1-4471-6377-0

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