Solution method and apparatus for large-scale simulation of layered formations

A data processing system for computerized simulation of state changes of fluids in underground layered formations in the earth, the data processing system comprising:

• a processor for performing 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;
• 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;
• and
• a memory for storing the results obtained by the processor.

A computer program stored in signal bearing media for causing a data processor to simulate state changes of fluids in underground layered formations in the earth, the computer program product containing instructions stored in machine-readable code and causing the processor to perform the following steps:

• 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.