On the numerical simulation of waterflooding of heterogeneous petroleum reservoirs

We present a new, naturally parallelizable, accurate numerical method for the solution of transport-dominated diffusion processes in heterogeneous porous media. For the discretization in time of one of the governing partial differential equations, we introduce a new characteristics-based procedure which is mass conservative, the modified method of characteristics with adjusted advection (MMOCAA). Hybridized mixed finite elements are used for the spatial discretization of the equations and a new strip-based domain decomposition procedure is applied towards the solution of the resulting algebraic problems.