Application of Wavelet Analysis to Upscaling of Rock Properties

Abstract

Summary Although numerous upscaling techniques are reported in the literature, efficiently computing reasonably accurate equivalent rock properties from geological data at fine scale remains difficult. This is especially true for facies with multiple lithologies under multiphase-flow conditions. Because of the nature of multiscale heterogeneity inherent in petroleum reservoirs, the equivalent rock and flow properties will vary with the scales of heterogeneity. Therefore, upscaled properties under multiphase-flow conditions cannot be estimated without reference to the absolute scales of heterogeneity. Wavelet analysis is a multiresolution framework; thus, it is well suited for upscaling rock and flow properties in a multiscale heterogeneous reservoir. The compact support property of the wavelet transform assures efficient computation. Choice of regularity provides a flexible way to control the smoothness of the resulting up-scaling properties. In this study, we developed a new procedure to improve significantly the computational efficiency and accuracy of upscaling for generating equivalent rock and rock-fluid properties under various geological and flow conditions based on multiresolution analysis of wavelet transforms. Additionally, we explored a wavelet reconstruction method to provide a basis for downsampling fine-scale rock property fields from information at various levels of coarser scale. The beauty of the method is that because the equivalent properties at different length scales are computed recursively, the interdependent influences of the heterogeneities on the scales are included effectively. We demonstrate the method by successfully applying it to upscale interbedset and interfacies reservoir properties of Almond formation outcrops under multiphase-flow conditions.