Full Approximation Scheme for Reservoir Simulation

Abstract

Simulation of multiphase flow and transport in porous rock formations give rise to large systems of strongly coupled nonlinear equations. Solving these equations is computationally challenging because of orders of magnitude local variations in parameters, mixed hyperbolic-elliptic governing equations, grids with high aspect ratios and strong coupling between local and global flow effects. 

The state-of-the-art solution approach is to use a Newton-type solver with a algebraic multigrid preconditioner for the elliptic part of a linearized system. Herein, we discuss the use and implementation of a Full Approximation Scheme (FAS) in which algebraic multigrid is applied on a nonlinear level. By use of this method, global and semi-global nonlinearities can be resolved on the appropriate coarse scale. 

Improved nonlinear convergence is demonstrated on standard benchmark cases from the petroleum literature. The method is implemented in the solver framework of the open-source Matlab Reservoir Simulation Toolbox (MRST).