The local change of scale method for modelling flow in natural porous media (I): Numerical tools

Abstract

The local change of scale method couples the macroscopic permeability tensor K with the micro-geometry of the porous medium. This procedure, deriving K from first principles has been under theoretical development for more than a decade. In this paper we discuss the successful implementation of this procedure using both the Implicit Finite Element (IFE) and Explicit Finite Volume (EFV) methods. In this implementation it is clear that the classical Representative Elementary Volume (REV) is too small and must be replaced by a larger ‘Darcy Representative Elementary Volume’. The validity of the implementation is demonstrated by producing the correct results on a simple periodic array where analytic solution exists. Maps of local pseudo-velocity and pseudo-pressure fields in analogues of diagenetically perturbed media are realistic. For several cases of diagenetically perturbed media, the EFV method is sufficient. This is important in that EFV method has a straightforward evolutionary path to a three-dimensional mesh.