Resumen
The initial-boundary-value problem for the non-stationary two-dimensional heat conduction equation in a limited region, modeling the unsteady distribution of soil temperature in the vicinity of the main gas pipeline in the permafrost zone, is considered. The parameters of the mathematical model are selected in accordance with experimental data on the transportation of gas in areas of permafrost distribution. Modeling of the temperature field is carried out for 30 years from the start of operation of the gas pipe. The problem is solved numerically by the finite element method with counting parameters selected as a result of methodological calculations. Settlements begin on January 1 of the first year of operation of the gas pipeline. To analyze the temperature field near the pipe at certain points in time, we plotted the temperature dependence along the horizontal axis at a distance of 10 cm from the top of the pipe and 10 cm from the bottom of the pipe. At a distance of 10 cm from the far right point of the pipe, temperature dependences are plotted in depth along the vertical axis. As moments of time, moments are selected that are characteristic of the temperature field of the soil during the summer periods of pipe operation: the middle of the 1st, 5th, 10th, 15th, 20th, and 30th years of observation. It is shown that the operation of the pipe with the selected parameters does not lead to the appearance of areas with a positive temperature in the permafrost soil around the pipe. The established temperature regime ensures trouble-free operation of the main gas pipeline.