Implicit linearization method for non-standard two-phase flow in porous media

TL;DR

This paper introduces a monotone fixed-point linearization scheme for a non-local two-phase flow model in porous media, effectively handling dynamic capillary pressure and heterogeneity with proven convergence and efficient numerical performance.

Contribution

It presents a novel linearization scheme for non-standard two-phase flow models with non-local effects, including convergence proof and numerical validation.

Findings

The scheme converges under physically reasonable assumptions.

It efficiently handles reservoir heterogeneity and dynamic capillary pressure.

Performance surpasses traditional iterative schemes in convergence speed.

Abstract

In this paper, we consider a non-local (in time) two-phase flow model. The non-locality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed-point iterative linearization scheme for the resulting non-standard model. The scheme treats the dynamic capillary pressure functions semi-implicitly and introduces an $L$-scheme type \cite{List2016, Radu2015} 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 heterogeneity in addition to the dynamic change of the capillary pressure function. The proposed scheme satisfies the predefined stopping criterion within a few numbers of iterations. We also compared the performance of the proposed scheme against the iterative IMplicit Pressure Explicit Saturation scheme