Multigrid Methods Applied to Near-Well Modelling in Reservoir Simulation

A new approach to multigrid computation for three-phase black-oil reservoir simulation is presented. The approach employs patch refinement techniques developed within the context of multigrid and domain decomposition methods. In this study, the approach developed involves using the coarse grid as a predictor for the fine grid in any given timestep. The fine grid solution is calculated using the coarse grid as Dirichlet boundary conditions. The fine grid is used to update the coarse grid equations in order to match fine grid behavior. Multigrid convergence techniques are applied. The method is described first in a general setting including a novel approach to local timestepping. An application of the method, employing multiple grids but not local timestepping, to a specific multigrid patch refinement problem (Collins et al 1991a) based on the Seventh SPE Comparative Solution Project on modelling horizontal wells (Nghiem et al 1991) is described.