Patent ID: 8346523

Claim:
A computer-implemented method for use in modeling fluid flow in a subsurface reservoir using a model, the method comprising: (a) creating a fine grid defining a plurality of fine cells associated with the subsurface reservoir, a coarse grid defining a plurality of coarse cells having interfaces between the coarse cells, the coarse cells being aggregates of the fine cells, and a dual coarse grid defining a plurality of dual coarse control volumes, the dual coarse control volumes being aggregates of the fine cells and having boundaries bounding the dual coarse control volumes; (b) calculating dual basis functions on the dual coarse control volumes by solving local elliptic problems; and (c) computing the model, on a computer system, over the coarse grid in a plurality of timesteps; wherein: the model comprises one or more variables representative of fluid flow in the subsurface reservoir, at least one of the one or more variables representative of fluid flow being responsive to the calculated dual basis functions; the computing comprises, for each timestep: (i) partitioning the coarse cells into regions by applying at least one adaptivity criteria to variables of the model; wherein: the regions comprise a first region corresponding to coarse cells in which a displacing fluid injected into the subsurface reservoir has not invaded, and a second region corresponding to coarse cells in which the displacing fluid has invaded; and a boundary between the first region and the second region is established at the interface between coarse cells which satisfy a first adaptivity criterion; and (ii) updating at least one coarse-scale variable of the model in the second region with at least one respective fine-scale variable that is reconstructed over the second region and is associated with the fine cells; and the computed model, comprising the updated at least one coarse-scale variable, models fluid flow in the subsurface reservoir for each timestep.