Patent ID: 6662146
Filing Date: 2003-12-09
Classification: E21B

Abstract:
A method for performing reservoir simulation by solving a mixed implicit-IMPES matrix (MIIM) equation, wherein the MIIM equation arises from a Newton iteration of a variable implicit reservoir model, wherein the variable implicit reservoir model comprises a plurality of cells including implicit cells and IMPES cells, wherein the MIIM equation includes a first scalar IMPES pressure equation for each of the IMPES cells and a first set of implicit equations for each of the implicit cells, the method comprising:a) constructing a global IMPES pressure matrix equation from the MIIM equation, wherein said constructing the global IMPES pressure matrix equation comprises: constructing a second IMPES pressure equation for each of the implicit cells from the first set of implicit equations corresponding to the implicit cell; and concatenating the first scalar IMPES pressure equations for the IMPES cells and the second IMPES pressure equations for the implicit cells; b) determining coefficients for a second set of saturation equations at the implicit cells by using a total velocity constraint at the implicit cells; c) solving the global IMPES pressure matrix equation for pressure changes; d) computing first residuals at the implicit cells in response to the pressure changes; e) solving the second set of saturation equations for saturation changes at the implicit cells, wherein the second set of saturation equations are formed with the coefficients and the first residuals at the implicit cells; f) 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 saturation changes; g) determining if a convergence condition based on the second residuals is satisfied; h) repeating b) through g) until the convergence condition is satisfied; i) computing a final solution estimate for the MIIM equation from the pressures changes and the saturation changes after the convergence condition is satisfied; j) applying the final solution estimate to determine behavior of the reservoir model at a future discrete time value.