STOCHASTIC INTERPOLATION OF AQUIFER PROPERTIES OF HETEROGENEOUS GEOLOGIC MEDIA USING FRACTAL PROCESSES

The relevance of the work is conditioned by the need to use random processes based on Levi-distribution in describing the process of filtration of fluid flow in oil reservoirs and groundwater. These processes describe the filtration process more accurately than the fractal Brownian motion (fBm) and fractal Gaussian noise (fGn), especially with sharp changes in the geological environment. The purpose of the work is to show the advantages of using stochastic interpolation methods in geostatistics as compared to deterministic methods (in particular, the creaking method). Research methodology: theoretical analysis and experimental study of methods for probabilistic modeling of aquifer properties of geological media under conditions of uncertainty and limited availability of information on permeability and porosity of reservoirs. Results. It is shown that stochastic interpolation is most suitable for modeling dispersion characteristics of heterogeneous geological formations. The use of the assumption of Gaussian distribution in describing the process of fluid filtration is unreasonable. It is especially unreasonable in the presence of abrupt changes inherent in geological stratifications. Such changes are more adequately described by fractal Levi-motion (fLm). Stable Levidistribution of increments of the studied filtration characteristics of oil-saturated deposits showed a good coincidence with empirical data of numerous physical changes of geological structures in a wide range of spatial variables vertically and horizontally. Conclusions. The use of fLm – models represents a fundamentally new approach in geostatistics. The presence of heavy tails of the Levi-distribution of increments of the filtration characteristics of the layers and scaling the distribution parameters of this distribution allows us to react to sudden and sharp changes in rock properties. This effectively reproduces the strata and sedimentary deposits on the reservoir surface and characterizes heterogeneity in a wide range of distribution of spatial variables