Finite-Analytic Cubature Based Numerical Method for Reservoir Simulation

This paper presents the application of the method of integro-differential cubature for efficient solution of reservoir models. The application of this method is illustrated by solving the Buckley-Leverett model for water flooding of naturally fractured oil reservoirs. It is shown that the cubature method yields accurate solutions even using 10 times less number of grid blocks and 3000 times larger time steps than the finite difference method. In addition, the numerical dispersion problem that is apparent in the finite difference solution is eliminated.