ABSTRACT
Block successive overrelaxation is used to solve the pressure equations of large 3-dimensional reservoir models with limited or zero permeability between layers. Each block consists of several vertical planes of the model. Composing the blocks of vertical planes allows wellbore pressure equations to be included along with the reservoir cell block equations to implicitly couple wellbore pressure to reservoir grid block pressure. The equations for each block are solved simultaneously using sparse elimination techniques. The work of factorization, forward and backward substitution is transferred from the host computer to an attached array processor. The host computer is an IBM 168 or a VAX 11/780, and the attached processor an FPS 190L or FPS 120B.
For large anisotropic multi-layer models with limited vertical permeability between layers, the block technique shows two or three times better convergence than plane SOR. Convergence may be further improved by overlapping a few planes in adjacent blocks. Host computer CPU time and cost may be reduced by up to a factor of two to five for these models. Two hypothetical test problems and three reservoir problems are described.
