The =
gaslift method is of special importance at the initial period after the flo=
wing of the oil fields [1,2, 3]. The motion in the gaslift process is known=
to obey the hyperbolic nonlinear partial differential equations. Therefore=
, at gaslift operation of the borehole cavity the problem of optimization w=
ith boundary control is of special interest. However, with the original for=
mulation of the problem of optimal control one encounters certain difficult=
ies. The averagings of the hyperbolic equation describing the time profile =
of motion by the gaslift method are given here [1, 3]. It rearranges a part=
ial derivative equation in the nonlinear ordinary differential equations. T=
he strategy of constructing the objective quadratic functional with the use=
of the weight coefficients lies in minimizing the volume of the gas inject=
ed in the annular space and maximizing the desired volume of the gas-liquid=
mixture (GLM) at the end of the lifter. In this case, the aim lies in solv=
ing the corresponding optimization problem where the volume of the injected=
gas which is used as the initial data and plays the role of the control ac=
tion.

The impossibility of using the standard methods to construct the =
corresponding controllers is a disadvantage of this approach. Yet, since at=
certain time intervals the boundary control is constant, the numerical dat=
a obtained can be readily compared with the production data.

Using the =
method of time averaging, the partial derivative equations of motion of gas=
and GLM motion proposed in [1] are rearranged in the ordinary differential=
equations. The problem of optimal boundary control with the quadratic func=
tional is formulated on the basis of the above considerations. The results =
obtained can be used to control the gaslift borehole cavity at oil extracti=
on. For solution of the considered problem of boundary controls, the gradie=
nt method [3] is modified by describing the corresponding Euler=E2=80=93Lag=
range equations [4].

**References**

F. A. Aliev, M. K. Ilyiasov, M. A. Dzhamelbekov, M= odelling of operation of the gaslift borehole cavity. Dokl. NANA, 2008, 4, = 107-116.

F. A. Aliev, N. A. Ismailov, N. S. Mukhtarova, Alg= orithm to determine the optimal solution of a boundary control problem. Aut= omation and Remote Control, 2015, 4, 627-633.

A. H. Mirzadzhanzade, I. M. Ametov, A. M.Khasaev, = Technology and Machinery of Oil Extraction. Moscow, Nauka, 1986.

A. Bryson, Yu Chi Ho, Applied Optimal Control, Wal= tham, Blaisdell, 1969.

**Contributor:**

Prof. Jaan Lellep, U=
niversity of Tartu