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.