A nonlinear mathematical model for two-phase flow in nanoporous media

Date

2022-02-28

Authors

Melzi, Imane
Atik, Youcef

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

We propose a mathematical model for the two-phase flow nanoporous media. Unlike classical models, our model suppose that the rock permeability depends on the gradient of pressure. Using usual laws of flows in porous media, we obtain a system of two nonlinear partial differential equations: the first is elliptic and the second is parabolic degenerate. We study a regularized version of our model, obtained by adding a ``vanishing'' term to the coefficient causing the degeneracy. We prove the existence of a weak solution of the regularized model. Our approach consists essentially to use the Rothe's method coupled with Galerkin's method.

Description

Keywords

Nonlinear system, Nanoporous media, Rothe's method, Galerkin's method

Citation

Melzi, I., & Atik, Y. (2022). A nonlinear mathematical model for two-phase flow in nanoporous media. <i>Electronic Journal of Differential Equations, 2022</i>(15), pp. 1-33.

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Attribution 4.0 International

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