A Multigrid Procedure for Local Grid Refinement in Oil Reservoir Simulation

Abstract We discuss local grid refinement procedures for reservoir simulation, including local timestepping, which means the use of different time step sizes in the coarse and refined regions. A non-linear multigrid algorithm is proposed for solving the coupling between coarse and fine meshes. This approach does not need to solve for matrices with complex structure, it does not employ any relaxation parameters, it is well suited for parallel processing and it can be easily implemented in existing simulators. The proposed techniques were implemented in a black-oil simulator and tested in complex problems described in the literature. The results show the ability local grid refinement has to model the behaviour in the vicinity of wells. The coupling algorithm has shown to be robust and efficient, allowing a significant reduction in CPU time when compared to regular and fine meshes. The local timestepping procedure has shown to be attractive specially in cases where the number of grid blocks in the coarse mesh is large when compared to the refined regions. This situation is typical of field studies.