This paper (SPE 52637) was revised for publication from paper SPE 38002, first presented at the 1997 SPE Reservoir Simulation Symposium, Dallas, 8-11 June. Original manuscript received for review 1 July 1997. Revised manuscript received 5 August 1998. Paper peer approved 3 September 1998.
Summary
The gridblock permeabilities used in reservoir simulation are commonly determined through the upscaling of a fine scale geostatistical reservoir description. Though it is well established that permeabilities computed in this manner are, in general, full tensor quantities, most finite difference reservoir simulators still treat permeability as a diagonal tensor. In this paper, we implement a capability to handle full tensor permeabilities in a general purpose finite difference simulator and apply this capability to the modeling of several complex geological systems. We formulate a flux continuous approach for the pressure equation by use of a method analogous to that of previous researchers (Edwards and Rogers; Aavatsmark et al.), consider methods for upwinding in multiphase flow problems, and additionally discuss some relevant implementation and reservoir characterization issues. The accuracy of the finite difference formulation, assessed through comparisons to an accurate finite element approach, is shown to be generally good, particularly for immiscible displacements in heterogeneous systems. The formulation is then applied to the simulation of upscaled descriptions of several geologically complex reservoirs involving crossbedding and extensive fracturing. The method performs quite well for these systems and is shown to capture the effects of the underlying geology accurately. Finally, the significant errors that can be incurred through inaccurate representation of the full permeability tensor are demonstrated for several cases.
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Operator-based linearization for general purpose reservoir simulation
