Implicit linearization scheme for nonstandard two‐phase flow in porous media

Abstract

SummaryIn this article, we consider a nonlocal (in time) two‐phase flow model. The nonlocality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed‐point iterative linearization scheme for the resulting nonstandard model. The scheme treats the dynamic capillary pressure functions semiimplicitly and introduces an L‐scheme type stabilization term in the pressure as well as the transport equations. We prove the convergence of the proposed scheme theoretically under physically acceptable assumptions, and verify the theoretical analysis with numerical simulations. The scheme is implemented and tested for a variety of reservoir heterogeneities in addition to the dynamic change of the capillary pressure function. The proposed scheme satisfies the predefined stopping criterion within a few number of iterations. We also compared the performance of the proposed scheme against the iterative implicit pressure explicit saturation scheme.

Field-scale impacts of long-term wettability alteration in geological CO$_2$ storage

“…On the one hand, a caprock that becomes intermediate-wet or hydrophobic is less effective than a water-wet caprock in providing an effective capillary barrier. On the other hand, capillary diffusion may be reduced in the storage reservoir through long-term WA, which can be beneficial to injectivity and capacity by causing the CO 2 to displace the resident fluid efficiently [Kassa et al, 2021a]. A wettability change, in general, affects the space-time evolution of CO 2 plume in the formation in ways that has not been fully understood yet.…”