Reservoir Variability and Modeling with Fractals

Abstract

ABSTRACT An important factor in the simulation of reservoir performance is the input reservoir parameters. Layers are often modeled with constant parameters (porosity, permeability, etc.) or with only minor variations. The failure to incorporate appropriate heterogeneity into reservoir performance predictions can be a significant problem. This paper examines the variability in reservoir parameters as measured with wireline logs. Both vertical and horizontal well data are utilized for this purpose. The nature of the log variability in both a sandstone and a carbonate reservoir are evaluated using rescaled range (R/S) analysis in conjunction with power spectrum analysis, similar to the methodology of Hewett et al. The R/S analysis yields a fractal dimension that can be used to model the reservoir parameters. Both vertical and horizontal well log data can be characterized as fractional Gaussian noise of similar fractal dimension. Fractal reservoir realizations are generated using Fourier transform techniques. This technique is straightforward and successfully maintains the desired spatial dependencies of the data. The fractal dimension is derived from the results of the statistical analysis. Some potential problems with this determination will be highlighted and discussed. Examples of simulation results demonstrate improved reservoir performance predictions using the fractal realizations. Reservoir sweep efficiencies are altered and a different recovery performance is obtained relative to linearly interpolated realizations.