Patent ID: 7983883

Claim:
A computer-implemented method of modeling flow of a fluid within a reservoir comprising: dividing a reservoir into a finite number of grid cells that forms a grid of the reservoir; defining interaction regions contained within adjacent grid cells in the grid, each interaction region being defined by first and second sets of points, the first set of points representing a grid cell center of each of the adjacent grid cells from which said each interaction region is defined, and the second set of points being edge centers defined as midpoints of lines separating adjacent grid cells defining each interaction region; defining subvolumes within each interaction region, each subvolume defined by a grid cell center of a first one of the grid cells, edge centers of lines separating the first one of the grid cells defining each interaction region from others of the grid cells defining said each interaction region, and a vertex representing a point where all grid cells defining said each interaction region meet; performing, using the computer, multipoint flux approximation operations that allow continuous pressure interpolation within one of the interaction regions by for each subvolume, performing piecewise approximation to derive a set of equations in terms of pressures at grid cell centers and edge centers, the set of equations containing an unknown pressure parameter at the vertex, and deriving and solving flux balance equations to eliminate the unknown pressure parameter at the vertex; using pressure values obtained by the multipoint flux approximation operations, modeling the flow of fluid within the reservoir; and outputting the model of fluid flow.