Sensitivity-based upscaling for history matching of reservoir models

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.