A pseudospectral matrix element (PSME) method which extended the formulation of the pseudospectral matrix (PSM) method to a multi-element scheme, has been applied by the authors to the studies of miscible displacement of fluids in porous media. The resulting pressure Poisson equation which satisfies the differential mass conservation (incompressible flow) is a non-separable self-adjoint operator with Neumann boundary contions in each direction. A separable preconditioner which is constructed from the original operator, in conjuction with the conjugate residual method, provides an efficient iteration scheme to the solution of pressure field. At the high mobility ratio (M = 100), an adaptive method following the idea of minimizing a functional is adopted to resolve the steep fingered front. In the diagonal five-spot model problem, a domain decomposition with the Schwarz Alternating Procedure (SAP) is used to iteratively solve two quarter concentric circles with overlapping area.

The phenomea of fingers’ growing and shielding can be observed in a horizontal slab when a small disturbance in the permeability is subject to the unfavorable mobility ratio (M = 10, 100) between oil and solvent, while in a five-spot reservoir simulation visous fingering still exists even without any permeability perturbation under the mobility ratio M = 10.

You can access this article if you purchase or spend a download.