A Second-Order Mimetic Approach for Tracer Flow in Oil Reservoirs

Abstract

fax 01-972-952-9435. AbstractA new mimetic method for solving tracer flow equations in oil reservoirs is presented. This mimetic method is a formal extension and an improved version of standard finite differences schemes and it has three main advantages. First, its grid is a hybrid version of point center and point distributed grids, so the new method does not require ghost points in its formulation and implementation. Second, boundary conditions approximations achieves same order of convergence as inner nodes, it is well known that standard finite difference schemes convergence rate deteriorates at boundaries. Third, the new scheme satisfies Green-Gauss-Stokes identity at the discrete level, which guarantee that the scheme is fully conservative and represents correctly the physics properties of the problem. The new scheme was implemented to solve tracer flow equations in a reservoir and it was tested in a set of five spot problems. Numerical results show that the new scheme produces better approximations than standard finite difference simulators on coarse grids.

A New Analysis of an Implicit Mimetic Scheme for the Heat Equation

“…In this article, a second order mimetic operators described in [8] [9] will be analyzed in the context of the transient diffusivity equation. This version of the mimetic operators has been successfully applied to elliptic equations [9] [10], transient diffusivity equations [11]- [19], reservoir flow problems [20] [21], the acoustic wave equation [22] [23], the biharmonic equation [24] and the biharmonic wave equation [25]. From all these references, the more relevant to this article are [11]- [18] [20] [21], which presents mimetic schemes for the heat or diffusivity equations, and a brief review of their content will be described.…”