Mathematical Model of Accidental Gas Leakage from Underwater Pipelines

The paper deals with the problem of determining the parameters of the transported gas in case of partial destruction of subsea sections of gas pipelines. The solution to this problem is proposed to be obtained on the basis of creating a mathematical model describing the relationship of pressure, velocity and gas temperature at each point of the subsea main pipeline, including at the place of emergency outflow. To build such a model, the equations of the continuity of the gas flow in all sections of the gas pipeline, the equations characterizing the change in the momentum of this flow, as well as the equations of heat content for the molar gas flow rate for the pipeline sections before and after the rupture were used. The process of submerged gas outflow through a partially destroyed pipeline wall is considered as an adiabatic process obeying Saint-Venant's law and occurring at the local speed of sound. For the case of the location of the rupture in the deep-water section of the main pipeline, a mode of subsonic gas outflow is provided as its adiabatic movement through a short pipe without friction. A numerical check of the performance of the proposed model was carried out for a subsea gas pipeline with a variable profile. Quantitative distributions of the characteristics of the gas flow along the main pipeline with fractures with different areas are also obtained. The combination of these distributions makes it possible to automatically identify the parameters of emergency gas outflows in subsea gas pipelines. According to the values of gas pressure, velocity and temperature at the inlet and outlet of the controlled section, the area of local destruction of the main pipeline and the location of the rupture on the route are calculated. These parameters make it possible to form such a control of the compressor stations, which is adequate to the current abnormal state of the pipeline.