Two-Phase Incompressible Flow with Dynamic Capillary Pressure in a Heterogeneous Porous Media

Mohamed Lamine Mostefai, Abdelbaki Choucha, Salah Boulaaras () and Mufda Alrawashdeh
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Mohamed Lamine Mostefai: Department of Mathematics, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
Abdelbaki Choucha: Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
Salah Boulaaras: Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia
Mufda Alrawashdeh: Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia

Mathematics, 2024, vol. 12, issue 19, 1-22

Abstract: We prove the existence of weak solutions of a two-incompressible immiscible wetting and non-wetting fluids phase flow model in porous media with dynamic capillary pressure. This model is a coupled system which includes a nonlinear parabolic saturation equation and an elliptic pressure–velocity equation. In the regularized case, the existence and uniqueness of the weak solution are obtained. We let the regularization parameter be η → 0 to prove the existence of weak solutions.

Keywords: nonlinear parabolic elliptic system; incompressible flow; dynamic capillary pressure; heterogeneous porous media; nonlinear equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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