Kaminska A. Mathematical modeling and numerical analysis for nonstationary modes of multi-line linear sections of the gas transportation system

The object of study - nonstationary and nonisothermal processes of gas flow in multi-line linear sections of the gas transportation system. Goal of research - the improvement of the existing mathematical model of nonstationary, including emergency, operation modes of multi-line linear sections of the gas transportation system and development of efficient numerical methods to calculate these modes with the required accuracy. Methods of research - numerical methods for solving boundary value problems for systems of partial differential equations and methods of solving linear and nonlinear systems of equations, methods of probability theory and mathematical statistics to identify emergency situations of a multi-line linear sections. Hardware - Personal computer. The theoretical and practical research results - improved model and developed numerical methods for calculation of nonstationary modes of operation of multi-line linear sections of the gas transportation system allow to calculate the gas flow parameters (pressure, mass flow rate and temperature) with the required accuracy, the analysis of which is used in the planning of technological modes of operation of a multi-line sections and when taking decisions in systems of the supervisory control. The method of identification of emergency situations allows to prevent possible accidents on the multi-line linear sections and to obtain estimates of the parameters of gas leaks, that increases the safety and reliability of the gas transportation system elements and reduces the potential economic damage from the accident. Scientific novelty - improved existing mathematical models of nonstationary non-isothermal operation modes of multi-line linear sections of the gas transportation system by introducing algebraic equations (including nonlinear) to the model, that take into account impact of the switching elements of the gas transportation system (valves), which allows to take into account changes in the structure of the gas transportation system; for the first time a numerical method introduce to calculate nonstationary non-isothermal modes of operation of multi-line linear sections of the gas transportation system that is different from existing by method of solving the system of nonlinear equations, and allowing with higher accuracy calculate and predict the actual processes of gas flow; for the first time proposed method for identifying emergency situations related to gas leaks, which is based on improved mathematical model and allowing with higher speed and accuracy detect and localize an fault section of the pipeline. The results of the thesis are used in the manufacturing process on the branch of "Scientific Research and Design Institute for Gas Transportation" (R&D Institute for Gas Transportation) "Ukrtransgas" as part of the project development 393.10-DP " "Implementation dispatch center of Kharkov linear production department of main gas pipeline." The research results are used in educational and research processes at the Department of Applied Mathematics, Kharkov National University of Radio Electronics when reading the course "Mathematical modeling of systems with distributed parameters" as well as in the graduation design.