Implicit Hybrid Upwind scheme for coupled multiphase flow and transport with buoyancy

Numerical simulation of coupled multiphase flow and transport in porous media is used in many scientific and industrial applications, such as groundwater management and oil recovery. To solve the governing partial differential equations, we focus on the fully-implicit (backward-Euler) finite-volume method (FIM). In this numerical scheme, large algebraic systems must be solved at each time step using Newton's method. This can be quite expensive, especially for highly nonlinear problems with buoyancy. In this work, we present a new first-order approximation of the flux in the FIM leading to improved nonlinear convergence rate and radius. This approximation is based on Implicit Hybrid Upwinding and relies on separate treatments of the viscous and buoyancy parts of the numerical flux. Moreover, in the viscous part, the total velocity discretization is key, as it controls the coupling between the elliptic flow problem and the hyperbolic multiphase transport problem. To achieve robustness and efficiency, we propose a differentiable total velocity discretization that adapts to the balance of forces at each interface. We analyze the theoretical properties of the resulting numerical scheme and prove that saturations remain between physical bounds. Challenging two- and three-phase test cases illustrate that our numerical scheme brings a significant reduction in the number of nonlinear iterations compared to a finite-volume discretization relying on the widely used phase-per-phase upstream weighting. Our numerical scheme therefore reduces the simulation cost while providing similar accuracy. (C) 2016 Elsevier B.V. All rights reserved.