An extended Krylov subspace method to simulate single-phase fluid flow phenomena in axisymmetric and anisotropic porous media

Abstract

We develop and validate a novel numerical algorithm for the simulation of axisymmetric single-phase fluid flow phenomena in porous and permeable media. In this new algorithm, the two-dimensional parabolic partial differential equation for fluid flow is transformed into an explicit finite-difference operator problem. The latter is solved by making use of an extended Krylov subspace method (EKSM) constructed with both positive and inverse powers of the finite-difference operator. A significant advantage of the method of solution presented in this paper is that simulations of pressure can be obtained at a multitude of times with practically the same efficiency as that of a single-time simulation. Moreover, the usage of inverse powers of the finite-difference operator provides a substantial increase in efficiency with respect to that of standard Krylov subspace methods. Tests of numerical performance with respect to analytical solutions for point and line sources validate the accuracy of the developed method of solution. We also validate the algorithm by making comparisons between analytical and numerical solutions in the Laplace transform domain. Additional tests of accuracy and efficiency are performed against a commercial simulator for spatially complex and anisotropic models of permeable media.