Mathematical apparatus for gas pipeline leak detection

The paper proposes a method that enables the calculation of the size and coordinates of an emergency gas leak that occurred as a result of the depressurization of the gas pipeline, based on pressure and flow measurements at the outlet of the gas pipeline. The method is based on a mathematical model of the non-isothermal, steady-state flow of a gas mixture through a gas pipeline of constant cross-section. The method is a modification of the method used for identifying the location of a gas leak in a well. The method allows you to calculate the size and coordinates of the leak with high accuracy over a wide range of changes in the flow rate, pressure, and temperature of the gas at the inlet. The paper provides examples of calculating the coordinates of a leak in gas pipelines using the proposed iterative method, and demonstrates its convergence. An example of the influence of the error in setting the outlet pressure on the error in calculating the coordinates of the leak is given. The proposed mathematical method can be extended to gas leak detection in gas wells and in ultra-high pressure offshore gas pipelines.