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Equations of the mechanics of porous media saturated with liquid and gas

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Abstract

The approach proposed by Podil'chuk [1] is used to derive a system of equations of motion for saturated porous media, allowance being made for the mutual influence of the solid, liquid, and gas phases. The permeabilities of the anisotropic porous medium are assumed to depend on the direction. It is shown that when there are no gas phases and the liquid is incompressible the system of equations reduces to the general equations of the theory of elasticity of an anisotropic body with fictitious stress components. For a porous medium saturated with liquid, the relationships between the permeabilities and the anisotropy constants are obtained. The motion of liquid in an elastic porous medium in the form of an orthotropic cylindrical region with a cavity in the form of a circular cylinder is considered as an example.

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Literature cited

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Authors and Affiliations

  1. Donetsk

    N. V. Bondarenko

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  1. N. V. Bondarenko
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 82–87, July–August, 1981.

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Bondarenko, N.V. Equations of the mechanics of porous media saturated with liquid and gas. Fluid Dyn 16, 554–559 (1981). https://doi.org/10.1007/BF01094599

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  • DOI: https://doi.org/10.1007/BF01094599

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