Numerical modeling of the gas lift process of oil production by optimization methods

This paper presents a detailed method for the numerical solution of direct and inverse problems arising in the framework of the gas lift process of oil production, which are described by a hyperbolic system of differential equations. The direct problem is solved using high-precision second-order difference schemes that ensure stability and accuracy of calculations in the space-time domain. The inverse problem, in turn, is formulated as an optimal control problem, where minimizing the target functional is implemented using the gradient method. To find the gradient of the conjugate function, a conjugate problem is used, the construction of which is based on the principles of Lagrangian identities and duality, which provides strict mathematical validity. Numerical experiments have confirmed the high efficiency of the proposed method in solving inverse problems and optimizing key parameters of the gas lift process. The results show that the use of the conjugate equation method contributes to a significant increase in oil recovery while minimizing the cost of injected gas, which makes the method economically and technologically advantageous. Additionally, it is demonstrated that the method makes it possible to correctly approximate the initial conditions even in difficult conditions associated with changes in the physical parameters of the process.