Mathematical model in oil extraction by gas-lift method for the case when the reciprocal value of well's depth represents a small parameter is considered. Problem of optimal mode construction i.e., construction of optimal program trajectories and controls is reduced to the linear-quadratic optimal control problem with a small parameter. Analytic formulae for determining the solutions at the first-order approximation with respect to the small parameter are obtained. Comparison of the obtained results with known ones on a specific example is provided, which makes it, in particular, possible to use obtained results in realizations of oil extraction problems by gas-lift method.

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