A.A. Papin, Y.Y. Podladchikov
Isothermal Motion of Two Immiscible Fluids in a Poroelastic Medium
In this paper, a mathematical model of simultaneous flow of two immiscible liquids in a poroelastic medium are considered. This model is a generalization of the classical Muskat-Leverett model, in which porosity is considered to be a given function of spatial coordinates. The accounting of compressibility of the porous medium is the crucial moment. The proposed model is based on the mass conservation equations for liquids and porous skeleton, Darcy’s law for liquids, the movement of the porous skeleton, the formula for the Laplace capillary pressure, rheological equation for porosity, and the condition of equilibrium “of the system as a whole”. Paragraph 1 provides the formulation of the problem and the conversion of a threedimensional system of equations written in Euler variables. The result is a system of a composite type that, like the classical Muskat-Leverett model, consists of equations with degenerate solutions. A compatibility condition occurs for solid phase velocity. Passing to Lagrange variables results in the closed system of equations free of solid phase velocity.
Key words: two-phase filtration, Darcy’s law, saturation, poroelastic, Lagrange variables
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