Simulation of reservoir flow processes at the
finest scale is computationally expensive and in some cases
impractical. Consequently, upscaling of several fine-scale
grid blocks into fewer coarse-scale grids has become an
integral part of reservoir simulation for most reservoirs.
This is because as the number of grid blocks increases, the
number of flow equations increases and this increases, in
large proportion, the time required for solving flow problems.
Although we can adopt parallel computation to share
the load, a large number of grid blocks still pose significant
computational challenges. Thus, upscaling acts as a bridge
between the reservoir scale and the simulation scale.
However as the upscaling ratio is increased, the accuracy
of the numerical simulation is reduced; hence, there is a
need to keep a balance between the two. In this work, we
present a sensitivity-based upscaling technique that is
applicable during history matching. This method involves
partial homogenization of the reservoir model based on the
model reduction pattern obtained from analysis of the
sensitivity matrix. The technique is based on wavelet
transformation and reduction of the data and model spaces
as presented in the 2Dwp–wk approach. In the 2Dwp–wk
approach, a set of wavelets of measured data is first
selected and then a reduced model space composed of
important wavelets is gradually built during the first few
iterations of nonlinear regression. The building of the
reduced model space is done by thresholding the full
wavelet sensitivity matrix. The pattern of permeability
distribution in the reservoir resulting from the thresholding
of the full wavelet sensitivity matrix is used to determine
the neighboring grids that are upscaled. In essence,
neighboring grid blocks having the same permeability
values due to model space reduction are combined into a
single grid block in the simulation model, thus integrating
upscaling with wavelet multiscale inverse modeling. We
apply the method to estimate the parameters of two synthetic
reservoirs. The history matching results obtained
using this sensitivity-based upscaling are in very close
agreement with the match provided by fine-scale inverse
analysis. The reliability of the technique is evaluated using
various scenarios and almost all the cases considered have
shown very good results. The technique speeds up the
history matching process without seriously compromising
the accuracy of the estimates.