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Reservoir Characterization |
BP International Ltd, Chertsey Road, Sunbury-on-Thames TW16 7LN, UK
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.
