Mixed Finite Element Method for Miscible Displacement Problems in Porous Media

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Abstract
Effective numerical simulation of many EOR problems requires very accurate approximation of the Darcy velocities of the respective fluids. In this paper we describe a new method for the accurate determination of the Darcy velocity of the total fluid in the miscible displacement of one incompressible fluid by another in a porous medium. The new mixed finite-element procedure solves for both the pressure and velocity of the total fluid simultaneously as a system of first-order partial differential equations. By solving for u = (− k/μ) ∇p as one term, we minimize the difficulties occurring in standard methods caused by differentiation or differencing of p and multiplication by rough coefficients k/μ. By using mixed finite elements for the pressure equation coupled in a sequential method with a finite element procedure for the concentration of the invading fluid, we are able to treat a variety of problems with variable permeabilities, different mobility ratios, and a fairly general location of injection and production wells. Mixed finite-element methods also produce minimal grid-orientation effect. Computational results on a variety of two-dimensional (2D) problems are presented.