Corner Point Geometry in Reservoir Simulation

Hydrocarbon reservoirs commonly possess a geometry which incorporates both dip and faulting. In order to distinguish depth variations due to these two effects, it is useful to specify a simulation cell through the positions of its eight corner points. The faces of such a cell may be bilinear surfaces, and may form part of a distorted grid. Such a grid may be chosen such that cell boundaries lie along faults, which may be vertical or sloping. Normal and fault connections may be treated on an equivalent basis. A system of 'coordinate lines' and corner point depths used to construct such a model is described. An exact analytic expression is obtained for the cell volume. Transmissibility values are calculated in terms of three-vector mutual interface areas, which automatically incorporate corrections for dip and inclined flow. The application of calculated transmissibilities to a simple five point model can lead to an inconsistent finite difference scheme, and to significant errors if the grid is highly distorted. A method of avoiding such errors is presented, which more accurately reflects the interaction between pressures and cell geometry to produce flows. This is derived from basic finite element type principles, and results are presented for test cases, comparing the corrected scheme with a simple five point model.