Published: Sept. 4, 2020

Béatrice M. Rivière, Noah Harding Chair and Professor of Computational and Applied Mathematics, Rice University

Diffuse Interface Methods for Two-Phase Flows in Digital Rock

Modeling multicomponent flows in porous media is important for many applications relevant to energy and environment. Advances in pore-scale imaging, increasing availability of computational resources, and developments in numerical algorithms have started rendering direct pore-scale numerical simulations of multiphase flow on pore structures feasible.  I will present a pore-scale flow model based on the coupling of Cahn-Hilliard and Navier-Stokes equations. At the micro-meter scale, the rock structure is given and the fluid flows through the connected pores. The three-dimensional computational domain is the union of voxels, obtained from the micro-CT scanning of real rock samples. A priori error estimates show convergence of the numerical scheme for sufficiently smooth solutions.  Simulations on Berea sandstones show the robustness of the algorithm. Extensions of the diffuse interface method for a system of two-phase flows with soluble surfactant is introduced.