A node-centred finite volume formulation for the solution of two-phase flows in non-homogeneous porous media

摘要

The simulation of two-phase flow of oil and water in inhomogeneous porous media represents a great challenge because rock properties such as porosity and permeability can change abruptly throughout the reservoir. This fact can produce velocities which vary several orders of magnitude within very short distances. The presence of complex geometrical features such as faults and deviated wells is quite common in reservoir modelling, and unstructured mesh procedures, such as finite elements (FE) and finite volume (FV) methods can offer advantages relative to standard finite differences (FD) due to their ability to deal with complex geometries and the easiness of incorporating mesh adaptation procedures. In fluid flow problems FV formulations are particularly attractive as they are naturally conservative in a local basis. In this paper, we present an unstructured edge-based finite volume formulation which is used to solve the partial differential equations resulting from the modelling of the immiscible displacement of oil by water in inhomogeneous porous media. This FV formulation is similar to the edge-based finite element formulation when linear triangular elements are employed. Flow equations are modelled using a fractional flux approach in a segregated manner through an IMplicit Pressure-Explicit Saturation (IMPES) procedure. The elliptic pressure equation is solved using a two-step approach and the hyperbolic saturation equation is approximated through an artificial diffusion method adapted for use on unstructured meshes. Some representative examples are shown in order to illustrate the potential of the method to solve fluid flows in porous media with highly discontinuous properties.