Patent Document ID: 20060235667
Application ID: 11106300
Patent Flag: 0

Claim One:
1. A method of computerized simulation of state changes of fluids in underground layered formations in the earth, comprising the steps of: partitioning a formation layer into a 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; 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 into a matrix P representing a matrix diagonal and layer connectivity of the grid cells and another matrix B representing lateral connectivity of the grid cells; performing matrix-vector multiplication operations in the computer as a series expansion to form an approximate inverse matrix M −1 in the computer; applying a conjugate residual interactive solution in the computer to solve the representations of the state changes and obtain a residual; and repeating the steps of performing matrix-vector multiplication and applying a conjugate residual interactive solution in the computer until the obtained residual is within an established tolerance limit of accuracy.