A numerical study of fluids with pressure dependent viscosity flowing through a rigid porous medium

Abstract

In this paper we consider modifications to Darcy's equation wherein the drag coefficient is a function of pressure, which is a realistic model for technological applications like enhanced oil recovery and geological carbon sequestration. We first outline the approximations behind Darcy's equation and the modifications that we propose to Darcy's equation, and derive the governing equations through a systematic approach using mixture theory. We then propose a stabilized mixed finite element formulation for the modified Darcy's equation. To solve the resulting nonlinear equations we present a solution procedure based on the consistent Newton-Raphson method. We solve representative test problems to illustrate the performance of the proposed stabilized formulation. One of the objectives of this paper is also to show that the dependence of viscosity on the pressure can have a significant effect both on the qualitative and quantitative nature of the solution.