The name of the competition under which the program is being implemented: Grant funding competition for young scientists under the project "Zhas Galym" for 2024-2026.

Project Leader: Amankeldy K. Turarov, Specialist in mathematics and numerical solution of gas-hydrodynamic processes.

Identifiers:

• Scopus Author ID: 57190938508 (https://www.scopus.com/authid/detail.uri?authorId=57190938508 ),
• ORCID: 0000-0002-0732-0045 (https://orcid.org/0000-0002-0732-0045 ).

Project Research Group

Project abstract

The study of the processes of field development is of great practical importance in the oil and gas industry due to the need to improve the methods of increasing production. One of the most efficient and economical methods of oil production is the gas lift method, which plays an important role after the fountain process. The main characteristic of gas lift wells is the dependence of the well flow rate on the volume flow rate of the injected gas.

The main approach to conducting research is the use of the variational method, which reduces the problem to solving a conjugate problem. The solution of the conjugate problem determines the dual value of the gradient of the minimizing functional. A gradient iterative method will be used to determine the optimal pressure value. For the numerical solution, a monotone difference scheme of the TVD type for nonlinear hyperbolic equations will be constructed. The issues of approximation, stability and convergence of difference schemes for the main and conjugate problems will be investigated. To study stability, the method of a priori estimates and the harmonic method are used. The developed difference scheme will be numerically implemented on an adaptive curved grid. An algorithm for constructing mobile adaptive grids of gas lift well media thickening on mobile phase boundaries will be constructed. Computational experiments based on the conducted research will be conducted to test two hypotheses. The first hypothesis is related to checking the adequacy of the proposed computational model of fluid and gas movement in a gas lift well. In particular, the efficiency of the algorithm for implementing the difference scheme on adaptive grids with a movable phase boundary will be evaluated. The second hypothesis is related to the verification of the adequacy of the solution of the optimal control problem.

The significance of the project on a national scale is associated with the development of new effective algorithms for determining the optimal parameters of gas injection into the well, which can be used both for oil and gas fields already under development and for the re-development of fields that were already considered undeveloped.

The aim of the project is to improve the mathematical model of the gas lift process for optimizing oil production by secondary methods, as well as the development and theoretical study of computational methods for the task of a multiphase dynamic model of the gas lift process.

Expected and achieved project results:

• Development of a method for finding optimal solutions for a linear problem with boundary control.
• Development of an algorithm for finding a solution to an optimization problem with boundary control in the discrete and continuous case.
• Development of a method for finding a solution for the optimal boundary control problem with an undivided boundary condition in the discrete and continuous case.
• Study of the issues of stability, convergence and solution of discrete analogues of gas lift problems.
• Numerical implementation of the algorithm for solving the problem of gas lift wells and in subdomains.
• Numerical methods for solving one-dimensional and two-dimensional problems and in subdomains.
• Creation of computer programs for numerical implementation of the developed algorithms for solving gas lift problems (including using supercomputer computing technologies).

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