In this paper, we employ a new multiresolution upscaling method for the data in porous media. The method employs an adaptive bandwidth of the kernel function as the multiresolution upscaling operator. We have implemented a hierarchical multiresolution upscaling strategy, which is based on maintaining the important fine scale model structures of the reservoir. In this method, bandwidth is a function of the variability of cell, which controls the upscaling process. In areas with a high variability of the considered feature, small bandwidth leads to maintaining the fine scale structures; and in homogeneous reservoir areas, large bandwidths will lead to coarse-sized cells. In this paper, we have used this proposed method for simultaneous upscaling of two features: density and neutron logs. Determination of optimal bandwidth or threshold for each feature is an important challenge in the bandwidth method. Due to different variabilities of two properties or features, simultaneous upscaling should be performed to capture the variability of both features in the model. The concept of simultaneous upscaling provides a common coarse model for two properties. To prepare the SUTF model, two minimum and maximum bandwidth approaches are used. The upscaling algorithm has been applied for density and neutron logs. Although the fine scale model contains 2290 cells, the number of coarsened cells in SUTF model based on the minimum bandwidth and maximum bandwidth approaches are 402 and 110, respectively. In addition to this new proposed method, the method of wavelet transform has also been used as a well-known method for upscaling, and finally, the results of the two methods are compared. By comparing the results of the two methods, we observe that the upscaling error in the kernel bandwidth method is less than that in the wavelet transform method. The advantage of the kernel bandwidth method over the wavelet transform is the reduction of the loss of the main information as well as the reduction of the numerical dispersion in the new proposed method compared to the wavelet transform method. These benefits have appeared at the upscaling error that is less in the proposed method.

Keywords