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.
Rights
Attribution 4.0 International