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.
Highlights
Unsaturated groundwater flow, enhanced oil recovery, and subsurface carbon dioxide (CO2) storage[1,2,3,4,5] are typical applications of multiphase porous media flow with high societal relevance
We focus on the two-phase flow that considers dynamic pore-scale wettability alteration (WA) processes
We propose and analyse an iterative linearization scheme for the designed nonstandard model above based on an iterative implicit pressure explicit saturation (IMPES) approach, typically we followed the work of Kvashchuk and Radu.[18]
Summary
Unsaturated groundwater flow, enhanced oil recovery, and subsurface carbon dioxide (CO2) storage[1,2,3,4,5] are typical applications of multiphase porous media flow with high societal relevance. Numerical simulations including mathematical modeling and numerical methods have been applied to understand such flow processes. The governing mathematical models are highly nonlinear and possibly degenerate systems of partial differential equations. The nonlinearities are introduced through constitutive models such as relative permeabilities—and capillary pressure—saturation relations. We describe these relations by either van Genuchten[6] or Brooks and Corey[3,7] parametrizations. These parameterizations are only suited for rock surfaces that experience a static and uniform wetting property
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