Non-Linear Finite Volume discretization for Subsurface Flow and Mechanics problem

Abstract

Energy transition extends the range of geological settings and physical processes to be taken into account in subsurface reservoir modelling. Many of these applications consider essentially anisotropic reservoir or require advanced gridding that can not be resolved consistently by conventionally used Two Point Flux Approximation (TPFA). In this project we present a Nonlinear Two Point Flux Approximation (NTPFA) based on gradient reconstruction and homogenization function. The approximation provides consistent solution for full permeability tensor on various grids. The approach combines flux guesses in a nonlinear way such that the obtained approximation is essentially monotone that guarantees the positivity of solution. We demonstrate the consistency of approach on several examples. We also use the multi-physics capabilities to test the simulator on saturation transport of dead oil when displaced with water. The developed approximation was implemented within Delft Advanced Research Terra Simulator (DARTS). Next we propose a new Nonlinear Two Point Stress Approximation technique which follows the collocated finite volume scheme for mechanical problem. In this section we try to discretize the linear elasticity equation by using nonlinear traction flux at interfaces similar to the setup used in fluid flow problem. This is done by balancing each component of traction individually and using the weighting scheme suggested in flux approximations.