Geometrically complex geological features, such as faults, cross stratified beds and large scale inclined strata, can have very significant effects on the flow of reservoir fluids. Standard finite difference methodology lacks the geometric flexibility required for modeling flow through or around such structures. Triangle based discretization methods, by contrast, offer an attractive means to discretize and simulate flow through geometrically complex features accurately.
In this paper, a triangle based mixed finite element – finite volume technique for compositional reservoir simulation is developed. The formulation is of IMPES type and is applicable to three phase, multicomponent systems in two dimensions. Most previous mixed finite element formulations were restricted to two phase or fully miscible systems. The compositional approach presented here extends these earlier techniques though it retains the general structure of the more limited formulations. Specifically, the governing equations are cast in terms of a pressure equation and a series of component mass balance equations expressed in terms of the ‘total’ velocity. A triangle based mixed finite element method is applied to the solution of the pressure equation while a finite volume technique is employed for solution of the component mass balance equations. The overall methodology is particularly well suited for the modeling of flow through complex geological strata characterized by heterogeneous, generally anisotropic permeability fields. This is demonstrated explicitly through application of a preliminary implementation of the method to the simulation of flow through a faulted cross section with a complex permeability description. Extension of the formulation to the three dimensional case is also discussed.