Fractal-wavelet neural-network approach to characterization and upscaling of fractured reservoirs

Characterization of field-scale porous media (FSPM), such as oil, gas and geothermal reservoirs, is a complex problem. Field data are often difficult to analyze because they exhibit complex patterns of behavior. The problem is even more complex when one has to deal with fractured porous media. In this paper we describe a new hybrid approach to comprehensive characterization of FSPM, development of accurate fine-grid geological models for them, and their upscaling. First, we describe the fractal approach to analyzing the porosity logs, the permeability distributions, and other properties of FSPM. We show that an accurate and efficient method of analyzing such data is provided by wavelet transformations. These transformations can also be used for the analysis of the patterns of fracture networks of FSPM, and processing of seismic data, and therefore they provide a unified approach to the treatment of practically all types of data for FSPM. We then propose a fractal neural network that can recognize fractal data and construct accurate correlations for estimating those properties of FSPM for which the data are scarce, e.g., their permeability distribution. Next, the results of the fractal-wavelet neural-network model are combined with stochastic conditional simulations to generate an accurate geological (fine-grid) model for FSPM, including their fracture network. A wavelet transformation method is then described for upscaling of the geological model of FSPM. Thus, one has a unified approach to reservoir characterization and modeling in which three key concepts play prominent roles: fractal analysis, wavelet transformations, and fractal neural networks.

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