IMPROVED METHODS FOR PERFORMING RESERVOIR SIMULATION

摘要

A method for performing reservoir simulation by solving a mixed implicit-IMPES matrix (MIIM) equation. The variable implicit reservoir model comprises a plurality of cells including both implicit cells and IMPES cells. The MIIM equation includes a first scalar IMPES equation for each of the IMPES cells and a set of implicit equations for each of the implicit cells. The reservoir simulation method comprises the following operations: (a) constructing a global IMPES pressure equation from the MIIM equation; (b) solving the global IMPES pressure equation for pressure changes; (c) computing first residuals at the implicit cells in response to the pressure changes; (d) determining improved saturations by solving the total velocity sequential equations at the implicit cells using the first residuals; (e) computing second residuals at the implicit cells and at a subset of the IMPES cells that are in flow communication with any of the implicit cells in response to the improved saturations; (f) determining if a convergence condition based on the second residuals is satisfied; and (g) repeating steps (b) through (f) until the convergence condition is satisfied. After the convergence condition is satisfied, a final solution estimate for the MIIM equation is computed from the pressures changes and the improved saturations. The final solution estimate may be applied to determine the behavior of the reservoir model at a future discrete time value. Alternative to step (d), improved saturations and improved pressures may be computed by performing one or more iterations with a selected preconditioner at the implicit cells.