Аңдатпа
The problem of synthesizing optimal stabilization of oil production is formulated within the framework of a linear-quadratic optimization problem using a mathematical model of the gas-lift process. This formulation captures the essential dynamics of the interaction between injected gas and produced fluids, allowing for a systematic analysis of the gas-liquid mixture (GLM) flow behavior. It is shown that the construction of optimal controllers can be reduced to the problem of partial periodic optimal stabilization of the GLM flow in the gas-lift process. The problem is considered in a time-averaged linear-quadratic approximation, where the control variable is restricted to the initial value, namely the injected gas. Under this assumption, it is demonstrated that the solution of the control problem reduces to solving a periodic matrix Riccati equation. Furthermore, this periodic problem can be transformed into an equivalent matrix algebraic Riccati equation, whose positive definite solution ensures system stability and optimality. Since the gas-lift process aims at maximizing the extraction of the GLM formed at the bottom of the well, particularly the mixture accumulated at the lift shoe, it is reasonable to impose a periodicity condition in this region. Additionally, a periodicity condition is introduced at the midpoint of the interval, corresponding to the rising phase of the GLM. It is also shown that, in certain cases, the matrix algebraic Riccati equation reduces to a matrix Lyapunov equation. Keywords: synthesis problem; optimal stabilization; gas lift method; Euler-Lagrange equations; matrix algebraic Riccati equation.