RESERVOIR SIMULATION WITH PRESSURE SOLVER FOR NON-DIAGONALLY DOMINANT INDEFINITE COEFFICIENT MATRICES

Performance of computers is improved during determination of pressure distribution among grid cells of a reservoir model during reservoir simulation by computer processing. Convergence can prove difficult to obtain when conditions cause a coefficient matrix involved in the processing to become indefinite. An indefinite coefficient matrix can occur either due to physical conditions in the reservoir related to vapor liquid equilibria, or due to nonphysical conditions created numerically due to improper derivatives. The conventional previously taken corrective action of time step cutting is avoided when convergence becomes difficult during reservoir simulation. Time step cutting has proven to be very costly, in terms of computer usage and time, for very large reservoirs having models involving millions, billions or more number of unknown parameter values.