Multi-level solution of large-scale linear systems in simulation of porous media in giant reservoirs

摘要

In solving linear systems of billions of equations resulting from reservoir simulator pressure equations for giant reservoirs organized into fine-grid models, a multi-level methodology acquires a fast and coarser grid solution to be used as a more accurate initial estimate for the fine grid problem. Solver iterations performed on the coarser grid in reduced processing time generate a better initial estimate, resulting in fewer of the more expensive iterations at the fine-grid level.

主权项

1. A method of computerized simulation of a giant subsurface reservoir in a data processing system of a plurality of data processors, the computerized simulation being an iterative linear solution of equations for reservoir parameters of a giant subsurface reservoir, the giant subsurface reservoir being simulated as a model partitioned into a number of cells arranged in an organized system of cells, the simulation further being based on geological and fluid characterization information for the cells of the reservoir, the method comprising the computer processing steps of:
(a) mapping information from the organized system of cells of the reservoir from an original fine grid scale into a coarse cell grid of a reduced number from the original grid; (b) initializing a postulated system solution matrix in the computer system for reservoir parameters for the coarse cell grid; (c) performing a preconditioned conjugate-gradient extrapolation in the computer system on the initialized postulated system solution matrix received for reservoir parameters for the coarse cell grid by determining a preconditioned matrix-vector product; (d) transforming in the computer system the results of the preconditioned conjugate-gradient extrapolation for the coarse cell grid to the original cell grid; and (e) performing an iterative linear solution in the computer system for reservoir parameters for the original grid of cells.