Features of mathematical modeling of natural gas production and transport systems in the Russia’s arctic zone

The necessity of accounting for real gas properties, thermal interaction with permafrost rocks and the possibility of formation (dissociation) of gas hydrates in these objects for adequate description of the operation of gas wells and main gas pipelines in the regions of the Far North by appropriate mathematical models is shown. Mathematical models that take into account the non-isothermal gas flow within the framework of pipe hydraulics, the change of the area of tube cross-section due to the formation of hydrates and the dependence of the heat transfer coefficient between gas and hydrate layer on the varying flow area over time are proposed. The corresponding conjugate problem of heat exchange between the imperfect gas in the well and the environment (rocks) is reduced to solving differential equations describing the non-isothermal flow of gas in the pipes and the heat transfer equations in rocks with the corresponding conjugation conditions. In the quasi-stationary mathematical model of hydrate formation (dissociation), the dependence of the gas-hydrate transition temperature on the pressure of gas is taken into account. Established that the formation of hydrates in wells, even at low reservoir temperatures and a thick layer of permafrost, takes a fairly long period of time, which allows to quickly prevent the creation of emergency situations in gas supply systems. Some decisions taken in the design of the first section of the main gas pipeline «Power of Siberia» have been analyzed by methods of mathematical modeling. In particular, it is shown that if the gas is not dried sufficiently, the outlet pressure may drop below the allowable limit in about 6-7 hours. At the same time, for completely dry gas, it is possible to reduce the cost of thermal insulation of the pipeline at least two fold