Features of liquid filtration in heterogeneous formations with random permeability. Part 2. Estimation of the uncertainty of the well flow rate with variations in the statistical parameters of the reservoir permeability field

UDK: 622.276.031:532.5.001

DOI: 10.24887/0028-2448-2025-10-54-58

Key words: filtration, permeability, dispersion, correlation length, current lines, channels, probability, stochastics media, random porous media

Authors: L.A. Gaydukov (Moscow Institute of Physics and Technology, RF, Moscow); D.V. Posvyanskii (Kotelnikov Institute of Radioengeeniring and Electronics of the RAS, RF, Moscow); T.A. Abramov (Oil and Gas Research Institute of the RAS, RF, Moscow)

The statistical parameters of the random permeability field have a significant impact on the nature of fluid flow in a porous medium and reservoir development indicators. These parameters have high uncertainty, and their values are in a wide range. With a strong heterogeneity of the permeability of the formation, the liquid flows through the formed channels of preferential filtration, which are not caused by the presence of extended geological inhomogeneities, but are a consequence of focusing the filtration flow by fluctuations in the permeability field. In this article, the issue of the possibility of determining the statistical parameters of the reservoir permeability field for subsequent use in analytical models for calculating the well flow rate dispersion is investigated. It is shown that the synthetic pressure recovery curves of a vertical well in an inhomogeneous reservoir with a lognormal random permeability distribution are characterized by the presence of a pronounced «ramp» effect. The radius of the study at which the pressure curves enters the «ramp» area is comparable to the correlation length of the permeability field. Analytical models are proposed that make it possible to calculate the well flow rate variance for various correlation lengths of the permeability field in a wide range of the coefficient of variation.

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