Patent ID: 7765091

Claim:
A method for simulating the properties of a fluid-containing subterranean reservoir, the method comprising: (a) providing a reservoir model of a subterranean reservoir partitioned into a grid of fine cells and respective grids of primal coarse cells and dual coarse cells which overlie the grid of fine cells; (b) constructing a first pressure equation comprising 1) a homogenous equation component p h ; 2) a gravity and capillarity equation component p g ; and 3) an inhomogenous equation component p p associated with at least one of sources and sinks and accumulation; (i) solving the homogenous equation component p h to obtain dual basis functions utilizing local boundary conditions on the dual coarse cells; (ii) solving the gravity and capillarity equation component p g to arrive at a summation of products of primal coarse cell pressures and dual basis functions and a correction term; (iii) solving the inhomogenous equation component p p to arrive at primal coarse cell pressure equations utilizing the basis functions in conjunction with the correction term; (c) solving the primal coarse cell pressure equations for primal coarse cell pressures; (d) constructing pressures in the fine cells which are a combination of products of primal coarse cell pressures and basis functions augmented by the correction term from the p g equation; and (e) outputting or displaying, through a computer system, the pressure in the fine cells for use as a variable in simulating the properties of the fluid-containing subterranean reservoir.