Multiscale Wavelet and Upscaling-Downscaling for Reservoir Simulation

The unfortunate case of hydrocarbon reservoirs being often too large and filled with uncertain details in a large range of scales has been the main reason for developments of upscaling methods to overcome computational expenses. In this field lots of approaches have been suggested, amongst which the wavelets application has come to our attention. The wavelets have a mathematically multiscalar nature which is a desirable property for the reservoir upscaling purposes. While such a property has been previously used in permeability upscaling, a more recent approach uses the wavelets in an operator-coarsening- based upscaling approach. We are interested in enhancing the efficiency in implementation of the second approach. the performance of an wavelet-based operator coarsening is compared with several other upscaling methods such as the group renormalization, the pressure solver and local-global upscaling methods. An issue with upscaling, indifferent to the choice of the method, is encountered while the 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 is to downscale the results of upscaling (that is to keep the computational benefit of the pressure equation upscaling) and solve the saturation at the original un-upscaled scale. For the saturation efficient solution on this scale, streamline method can then be used. Our contribution here is to develop a computationally advantageous downscaling procedure that saves considerable time compared to the original proposed scheme in the literature. This is achieved by designing basis functions similar to multiscale methods used to obtain a velocity distribution. Application of our upscaling-downscaling method on EOR processes and also comparing it with non-uniform quadtree gridding will be further subjects of this study