Optimization Problems with Periodic Boundary Conditions and Boundary Control for Gas-Lift Wells

We consider a gas-lift process averaged over time. It is assumed that the gas-liquid mixture formed in the mixing zone on the boundary of the annular space and the oil pool is delivered to the lift via impulsive systems. Since the gas-liquid mixture directed from the mixture zone to the exit of the well is not completely transferred, in order to get the maximum output of the well for the minimum initial volume of the gas, we assume that the volumes of gas-liquid mixture at the entrance and exit of the lift are identical, i.e., impose the conditions of periodicity. We propose an algorithm for the solution of this problem based on the method of finding extrema with the use of numerical quasilinearization and Euler procedures realized in the MATLAB package. The results are illustrated by an example showing that the proposed approach results in a significant increase in the output of the well.