Adaptive Local Mesh Refinement and Multi-Grid Solution Methods in Numerical Reservoir Simulation

Flexible gridding has the potential of increasing the accuracy in numerical simulation of flow through hydrocarbon reservoirs within limitations in computing time and memory space. The adaptive gridding method presented here follows general concepts given by Brandt. For the pressure and the total velocity fields mixed finite elements are used, which give high accuracy particularly for the velocity field. A multi-grid solution method is stated for the indefinite set of equations associated with the mixed-finite-element discretisatiOn. The use of this accurate velocity field in Buckley-Leverett theory (2 - or 3-D) and in more comprehensive reservoir models is outlined.