MATHEMATICAL MODELING OF NON-STATIONARY GAS FLOW PROCESS IN A GAS PIPELINE CAUSED BY AN EMERGENCY GAS LEAK - Zapukhliak, V. B.; Prokopiv, I. В. (PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, 2025)
The article addresses the pressing issue of estimating gas losses during pipeline transportation, the importance of which has increased during the period of military action due to the risk of external destructive influences. The purpose of the study is to create a mathematical model of the non-stationary gas flow process in a gas pipeline caused by an emergency leak. A model based on the equations of motion and continuity was developed to describe the pressure and mass flow rate oscillations of the gas that occur during leak formation. The system of differential equations is reduced to a linearized equation, which includes the Dirac delta function for modeling concentrated gas withdrawal at the leak point. The solution to the equation is found using the integral sine transformation under initial (stationary linear pressure distribution) and boundary conditions (constant pressure at the beginning and end of the section). Based on the resulting dependencies for pressure and mass flow rate, a methodology for quantitative determination of total gas losses is formulated as the sum of the initial mass of gas in the emergency section and gas overflows from adjacent sections during the time until the linear valves are closed. Numerical calculations of the relative value of gas flow rates are performed, taking into account the overflows. Graphs show that the mass flow rate of gas at valve No. 1's cross-section instantly increases after a leak and then smoothly declines, while at valve No. 2's cross-section, a sharp drop is observed, followed by stabilization and a possible reverse flow. The modeling results ensure improved accuracy in estimating gas losses. The obtained results can be used to improve methods for diagnosing and predicting gas losses in gas transportation systems.