Transformation of motion equations in the oil extraction process into Roesser-type equations and their solution using the Laplace transform

Aliyev F.A. Tagiyev R.M. Namazov O.Z. Turarov A.K.
October 2025 University of Tabriz

Computational Methods for Differential Equations
2025 #13 Issue 4 1085 - 1094 pp.

In the article, the method of solving Roesser-type equations with the Laplace transformation for modeling and analysis of oil extraction processes is analyzed. Roesser-type equations are widely used to describe the dynamics of multidimensional systems, and their solution is important in improving the efficiency of oil extraction processes. First, the structure and properties of Roesser-type equations are presented. Later, the process of solving these equations is presented step by step by applying the Laplace transform method. By converting the special differential equations given by this method to simpler algebraic equations, both analytical and computer calculations can be significantly simplified. Based on the calculations and examples, it is shown that the proposed method provides high accuracy and efficiency. The research results enable the application of new approaches in the optimization and management of oil extraction processes.

34K06 , 34K28 , 65L05 , Boundary problem , Cauchy problem , Differential equations of hyperbolic type , Gas-lift , Laplace transform , Roesser model

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Institute of Applied Mathematics, Baku State University, Baku, Azerbaijan
Azerbaijan State Oil and Industry University, Baku, Azerbaijan
Western Caspian University, Baku, Azerbaijan
Sumgayit State University, Sumgayit, Azerbaijan
East Kazakhstan State Technical University, Ust-Kamenogorsk, Kazakhstan

Institute of Applied Mathematics
Azerbaijan State Oil and Industry University
Western Caspian University
Sumgayit State University
East Kazakhstan State Technical University

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