System and method for performing reservoir simulation using preconditioning

摘要

A computer-implemented system, method, and software are provided for solving linear systems of equations arising in reservoir simulation. A linear system of fluid flow equations, including a plurality of unknown variables, is provided that represents fluid flow properties in a geological formation of a subterranean reservoir. Block diagonal scaling is applied to the linear system of fluid flow equations. Threshold incomplete lower-upper approximate factorization is applied to obtain a preconditioning matrix, which can be used to iteratively solve unknown variables associated with the system of fluid flow equations. Preconditioning can be used directly as part of a preconditioned Krylov subspace method or alternatively as a 2nd stage preconditioner in a CPR algorithm.

主权项

1. A computer-implemented method for solving linear systems of equations arising in reservoir simulation, the method comprising:
(a) providing a linear system of fluid flow equations that represents fluid flow properties in a geological formation of a subterranean reservoir, the linear system of fluid flow equations comprising a plurality of unknown variables; (b) applying, with a processor, block diagonal scaling to the linear system of fluid flow equations to obtain a block diagonal matrix; (c) applying at least one of Sinkhorn-Knopp Column-Row equilibration, Sinkhorn-Knopp Row-Column equilibration, or Ruiz Row-Column equilibration; (d) applying threshold incomplete lower-upper approximate factorization to the block diagonal matrix to obtain a preconditioning matrix; and (e) iteratively solving the linear system of fluid flow equations for the unknown variables using the preconditioning matrix.