As a rule, the basis for engineering calculations for monitoring the productivity of wells is the model of stationary and unsteady inflow in homogeneous formations or formations with a given type of zonal heterogeneity. This is due to the presence of analytical models for these cases with a high calculation speed. The approaches proposed in the article on the use of field theory methods, on the one hand, being analytical, have a high calculation speed, and, on the other hand, allow one to take into account an arbitrarily distributed inhomogeneity in filtration-capacitive properties. This advantage can become the basis for the development of new engineering tools in assessing the flow in heterogeneous reservoirs.

The main goal of this work is to develop a methodology for calculating well productivity and rapid assessment of pressure distribution in heterogeneous reservoirs. In contrast to the traditional approach to modeling filtration in inhomogeneous media using numerical finite-difference and finite-element methods, the article investigates the applicability of computational algorithms based on the use of the mathematical apparatus of perturbation methods and composite asymptotics.

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