One of the key parameters of a reservoir that determines well productivity and the dynamics of development indicators is its permeability. The statistical parameters of the reservoir permeability field have high uncertainty, and their values lie in a wide range. In this regard, the formation is considered as a spatial body, the local permeability of which in the inter-well space is a random field, the correlation scales of which are small compared to the characteristic dimensions of the entire system. Using the method of multivariate numerical hydrodynamic modeling and the method of equations for stochastic moments of the pressure field, the influence of the statistical characteristics of the permeability field on the patterns of fluid filtration in porous media is investigated. It is shown that the statistical characteristics of the random permeability field have a noticeable effect on the nature of the fluid flow in a porous medium. It was revealed that with a strong heterogeneity of the reservoir permeability, the flow of liquid occurs through the formed channels, and the distribution of the well flow rate obeys Poisson statistics. Channels of preferential filtration change the dynamics of well watering and significantly affect the performance of reservoir development. The use of the tool for variation of statistical parameters of the permeability field makes it possible in some cases to exclude non-physical modification of the initial parameters of the hydrodynamic model, thereby increasing its predictive ability.
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