The unfortunate case of hydrocarbon reservoirs being often too large and filled withuduncertain details in a large range of scales has been the main reason for developments ofudupscaling methods to overcome computational expenses. In this field lots of approachesudhave been suggested, amongst which the wavelets application has come to our attention.udThe wavelets have a mathematically multiscalar nature which is a desirable propertyudfor the reservoir upscaling purposes. While such a property has been previously usedudin permeability upscaling, a more recent approach uses the wavelets in an operator-coarsening-udbased upscaling approach. We are interested in enhancing the efficiency inudimplementation of the second approach. the performance of an wavelet-based operatorudcoarsening is compared with several other upscaling methods such as the groupudrenormalization, the pressure solver and local-global upscaling methods.udAn issue with upscaling, indifferent to the choice of the method, is encountered whileudthe saturation is obtained at coarse scale. Due to the scale discrepancy the saturation profiles are too much averaged out, leading to unreliable production curves. An idea isudto downscale the results of upscaling (that is to keep the computational benefit of theudpressure equation upscaling) and solve the saturation at the original un-upscaled scale.udFor the saturation efficient solution on this scale, streamline method can then be used.udOur contribution here is to develop a computationally advantageous downscalingudprocedure that saves considerable time compared to the original proposed scheme in theudliterature. This is achieved by designing basis functions similar to multiscale methodsudused to obtain a velocity distribution.udApplication of our upscaling-downscaling method on EOR processes and also comparingudit with non-uniform quadtree gridding will be further subjects of this study.
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