In laminated clastic reservoirs, the difference in permeability at the bed scale could be several orders of magnitude across the various facies. In addition, cross-bedding and pinched-out geological surfaces give rise to tortuous flow paths. Incorporation of such flow-relevant fine-scale heterogeneities into reservoir-scale models is accomplished through an effective two-stage multiphase upscaling technique. The two stages of scale-up involve (1) bed to genetic-unit scale upscaling and (2) genetic-unit to reservoir scale upscaling. In the bed to genetic-unit scale upscaling step, full tensor permeabilities are computed using a fast flow-based upscaling procedure taking advantage of a multipoint flux approximation method. A novel iterative quasi-global pseudoization method is used in the genetic-unit to reservoir scale upscaling process. The fundamental idea of iterative pseudoization relies on the calibration of effective properties that govern coarse-scale flows to non-local regional interwell-scale flows in the underlying fine-scale model. The calibration is performed through the minimization of an objective function that computes the mismatch in flow responses between fine-scale and coarse-scale models. The pseudoization procedure is formulated as a constrained optimization problem, which is iteratively solved by estimating the variables that parameterize the pseudo-relative permeabilities and pseudo-capillary pressures.

The effectiveness of the two-stage upscaling technique is demonstrated in an intuitive example case featuring the scale-up of a stratigraphically complex Aeolian outcrop-scale reservoir-sector model for a waterflooding scenario. This proof-of-concept example is designed to validate the accuracy and efficacy of the two-stage upscaling method where the full-detail two-dimensional fine-scale model is affordable to simulate and serves as the “true” model for verification. Results indicate that the two-stage upscaling method renders practically intractable high-geologic resolution simulation problems tractable and delivers good accuracy.

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