Academic Editor: Ben T. Nohara
Copyright © 2010 Fikrat A. Aliev et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.