Unmatched Multiblock Grids for Simulation of Geometrically Complex Reservoirs

A simulator with hexahedral multiblock grids has been developed to simulate flow in reservoirs with geometrically complex features (i.e., faults and wells). A reservoir model can always be gridded with multiblock grids with matching grid lines between blocks. However, this matching requirement may introduce many small cells that have little impact on the simulation results as well as unnecessarily increase the number of blocks. We thus relax the matching requirement by allowing for nonmatching grid lines at block boundaries. This generalization simplifies the construction of multiblock grids greatly as each block can now be gridded independently and patched together afterwards. For instance, a new grid around a well can be inserted into an existing stratigraphic grid. The result is much simpler grids with fewer blocks and/or cells as compared to original matched multiblock grids. The complexity shifts from the grid construction to the calculation of transmissibilities. To this end, we need an accurate, consistent discretization scheme for nonmatching grids. We first derive a flux continuous discretization scheme for convex polyhedra grids. For general geometries a prismatic interface grid is constructed that establishes cell connectivities across the unmatched interface. Applying a piecewise constant approximation, we compute transmissibilities for this interface grid and map them back to the original hexahedral cells. We analyze the accuracy of this method via comparisons to matched fine grids. The effectiveness and applicability of this new method is demonstrated with reservoir models with wells and faults.