Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 191053, 11 pages
doi:10.1155/2010/191053
Research Article

Asymptotic Method of Solution for a Problem of Construction of Optimal Gas-Lift Process Modes

Fikrat A. Aliev,1 Mutallim M. Mutallimov,1 Idrak M. Askerov,1 and Iouldouz S. Raguimov2

1Institute of Applied Mathematics, Baku State University, Baku 1148, Azerbaijan
2Department of Mathematics and Statistics, York University, Toronto, ON , M3J 1P3, Canada

Received 22 December 2009; Revised 16 April 2010; Accepted 16 April 2010

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.

Abstract

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.