Identification of fractal properties and parameters upscaling of layered heterogeneous medium

UDK: 622.
DOI: 10.24887/0028-2448-2020-1-46-49
Key words: hydrodynamic modeling, identification of parameters, layered inhomogeneous medium, upscaling, permeability, fractals, power laws
Authors: I.N. Abdulin (Ufa State Aviation Technical University, RF, Ufa), V.A. Baikov (RN-BashNIPIneft LLC, RF, Ufa ; Ufa State Aviation Technical University, RF, Ufa)

Coarsening of computational spatial grids is one of the main ways to reduce the cost of computing resources in geological and hydrodynamic modeling of hydrocarbon reservoirs. The procedure of overriding reservoir properties in an upsized cell of the computational grid is called upscaling (averaging). The quality of this procedure is determined by degree of prognostic capability decreasing of applied models. The traditional way for determining the average value as the arithmetic mean is not always applicable in practice, since it does not take into account the spatial heterogeneity of the averaged values distribution. In this paper, we consider the case of a reservoir with formation reservoir properties (permeability and porosity) values close to power functions of the spatial variable. Proximity of reservoir properties to power function indicates to a fractal inhomogeneity of the porous medium. The power-law upscaling procedure is proposed for this case. An initial-boundary-value problem for a one-dimensional fractal model of unsteady-state filtration is considered. The identification procedure of fractal quantities of this model is proposed and investigated. The proposed methods tested on data from one of the fields in Western Siberia. A comparative analysis with the arithmetic mean method is performed on permeability data. The proposed techniques have a potential for use in reservoir engineering and monitoring.


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