Operator-Based Linearization Approach for Modeling of Multiphase Flow with Buoyancy and Capillarity

Numerical simulation of coupled multiphase multicomponent flow and transport in porous media is a crucial tool for understanding and forecasting of complex industrial applications related to the subsurface. The discretized governing equations are highly nonlinear and usually need to be solved with Newton's method, which corresponds with high computational cost and complexity. With the presence of capillary and gravity forces, the nonlinearity of the problem is amplified even further, which usually leads to a higher numerical cost. A recently proposed operator-based linearization (OBL) approach effectively improves the performance of complex physical modeling by transforming the discretized nonlinear conservation equations into a quasilinear form according to state-dependent operators. These operators are approximated by means of a discrete representation on a uniform mesh in physical parameter space. Continuous representation is achieved through the multilinear interpolation. This approach provides a unique framework for the multifidelity representation of physics in general-purpose simulation. The applicability of the OBL approach was demonstrated for various energy subsurface applications with multiphase flow of mass and heat in the presence of buoyancy and diffusive forces. In this work, the OBL approach is extended for multiphase multicomponent systems with capillarity. Through the comparisons with a legacy commercial simulator using a set of benchmark tests, we demonstrate that the extended OBL scheme significantly improves the computational efficiency with the controlled accuracy of approximation and converges to the results of the conventional continuous approach with an increased resolution of parametrization.

Automated summary

The study proposes an effective method to improve the performance of complex physical modeling in numerical simulation of coupled multiphase multicomponent flow and transport in porous media by transforming discretized nonlinear conservation equations into a quasilinear form and achieving continuous representation through multilinear interpolation. The approach demonstrates significant improvement in computational efficiency with controlled accuracy of approximation and convergence to traditional continuous methods with increased resolution of parametrization through comparisons with a legacy commercial simulator in benchmark tests.