The unsteady flow of a weakly compressible fluid in a thin porous layer III: three-dimensional computations

We describe a novel method for determining the pressure and velocity fields for a weakly compressible fluid flowing in a thin three-dimensional layer composed of an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting and/or extracting fluid. Our approach uses the method of matched asymptotic expansions to derive expressions for all significant process quantities, the computation of which requires only the solution of linear, elliptic, two-dimensional boundary value and eigenvalue problems. In this article, we provide full implementation details and present numerical results demonstrating the efficiency and accuracy of our scheme.