Application and analysis of a new method for calculating tensor permeability
Michael J.E. Sternberg · Geological Society London Special Publications · 1995
Abstract Geostatistical techniques generate multi-million gridblock reservoir descriptions which must be scaled up to coarser models before being utilized in standard reservoir simulators. When the underlying structure is cross-bedded, and the imposed pressure drop does not follow the layering, the effective permeability must be represented as a full tensor to capture the flow properties of the system. We present a novel method of computation for effective permeability, which preserves tensorial cross-flow effects while remaining compatible with standard (non-tensor) simulation. The resulting mixed finite element formulation, periodic boundary conditions and ‘self-consistent’ inlet and outlet pressures provide an unique non-linear scale-up computation. The method is applied to a synthetic data set drawn from a North Sea reservoir. For a typical value of Kv/Kh — about 5% — the cross-terms dominate over the diagonal in the computation of vertical permeability. In overall response, the use of the standard diagonal tensor and five-point finite difference scheme is in error by about 15%, and in error by a factor of 100% in the evaluation of Kv/Kh. The results are especially important in evaluating the productivity from horizontal wells, where vertical flow dominates.