## JMI2011C-7 Numerical simulation of multicomponent compressible flow in porous medium (pp.53-60)

Author(s)： Ondřej Polívka and Jiří Mikyška

J. Math-for-Ind. **3C** (2011) 53-60.

- File： JMI2011C-7.pdf (539KB)

Abstract

The paper deals with the numerical modeling of compressible single-phase flow of a mixture composed of several components in a porous medium. The mathematical model is formulated by means of Darcy's law, components continuity equations, constitutive relations, and appropriate initial and boundary conditions. The problem is solved numerically using a combination of the mixed-hybrid finite element method for Darcy's law discretization and the finite volume method for the discretization of the transport equations. This approach provides exact local mass balance. The time discretization is carried out by the Euler method. The resulting large system of nonlinear algebraic equations is solved by the Newton-Raphson iterative method. The dimensions of obtained system of linear algebraic equations are significantly reduced so that they do not depend on the number of mixture components. The convergence of the numerical scheme is verified on two problems of methane injection into a homogeneous 2D reservoir filled with propane which is horizontally or vertically oriented.

Keyword(s). Mixed-hybrid finite element method, finite volume method, Newton-Raphson method, single-phase compressible multicomponent flow, miscible displacement