Patent ID: 7596480

Claim:
In a computerized reservoir simulation, the improved method of computerized simulation of state changes of fluids in an underground layered formation of the reservoir in the earth, comprising the steps of: partitioning a formation layer into an unstructured grid formed of a number of laterally contiguous grid cells; establishing for the grid cells representations of state changes for the grid cells with contiguous grid cells of the unstructured grid of the formation layer; arranging the established representations of state changes for the grid cells into a matrix A according to the position in the formation of the grid cells; partitioning the matrix A into a matrix P representing a diagonal plus layered component of the matrix A of the grid cells of the unstructured grid of the formation layer and another matrix B representing lateral connectivity of the matrix A of the laterally contiguous grid cells of the partitioned formation layer; forming a matrix product E in the computer representing the matrix multiplication product of a negative inverse matrix −P −1 of the matrix P with the matrix B; performing series preconditioner matrix-vector multiplication operations in the computer as a series expansion based on the matrix product E; applying a conjugate residual interactive matrix solution in the computer to solve the representations of the state changes of the fluids in the partitioned grid cells and obtain a residual; repeating the steps of performing series preconditioner matrix-vector multiplication operations and applying a conjugate residual interactive matrix solution in the computer to solve for the representations of the state changes for the fluids of the partitioned grid cells until the obtained residual is within an established tolerance limit of accuracy; storing the computerized simulation of representations of the state changes for the partitioned grid cells when the obtained residual is within the established tolerance limit of accuracy; and forming an output display of the stored computerized simulation of representations for the state changes of fluids in the underground layered formation of the reservoir.