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This article has developed and verified a mathematical aggregated approximate model of developing a gas condensate field using a cyclic process. The essence of the cyclic process is to pump the drained gas into the productive formation to reduce the pressure drop into the deposit. This process allows for increased condensate recovery in the future. The model discussed in this article is a continuous dynamic system with control parameters. It is a modification of the dynamic aggregated model of a purely gas field, designed for planning for a sufficiently long period with limited information about the state of the reservoir (the initial flow rate of wells, the initial recoverable gas reserves, the initial reservoir pressure, the dependence of potential condensate content per unit volume of fatty gas on the reservoir pressure). A non-standard approach underlies the model construction. Logical simplifications and a priori assumptions about the processes occurring in the field during its development are at its core. The instruments in the model are the increase in production and injection wells and the proportion of injection wells involved in the production. The purpose of the article is to calculate various variants of the dynamics of the fundamental indicators of the development of a gas condensate field for a sufficiently long-term period at the stage of preliminary design.

The authors consider a continuous dynamic approximating model of a gas fields group and, on its basis, set maximum and minimum issues. The tasks proposed for research are optimal control problems with mixed constraints with free-final-time and moving right end. We analytically solve the rapid-action problem. The central mathematical apparatus is Pontryagin maximum principle in Arrow form, using Lagrange multipliers. The theoretically obtained results of the analysis are of particular interest.

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