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

• Published in: International journal for numerical methods in fluids 2021-02, Vol.93 (2), p.445-461
• Main Authors: Kassa, Abay Molla, Kumar, Kundan, Gasda, Sarah E., Radu, Florin A.
• Format: Article
• Language: English
• Subjects: Capillary pressure; dynamic capillary pressure; iterative coupling; Iterative methods; Linearization; Mathematical models; Porous media; Pressure; Saturation; Theoretical analysis; Transport equations; two‐phase flow; Wettability
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.4891

Summary In 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. In this article, we propose a pseudo‐monolithic linearization scheme for two‐phase flow in a porous medium. The scheme treats the capillary pressure function implicitly in time. We give a theoretical convergence analysis of the proposed scheme. Furthermore, the scheme is tested for a variety of numerical examples.