  An initial-boundary value problem for an unsteady two-dimensional heat
conduction equation in a bounded domain modeling the unsteady temperature
distribution of permafrost soil in the vicinity of a main gas pipeline, taking
into account climate warming, is investigated. The parameters of the
mathematical model are selected in accordance with experimental data on gas
transportation in permafrost areas. The problem is solved numerically by the
finite element method. Modeling of the temperature field has been carried out
for 30 years since the start of the gas pipeline operation. Calculations are
carried out until the periodic temperature regime of the soil around the gas
pipeline is practically established. Under the initial conditions adopted in
the work, a periodic temperature regime at the top and bottom of the pipe is
established in approximately 12 years, and a periodic temperature regime in
depth is established in approximately 22 years. Two scenarios of climate
warming are considered: moderate RCP2.6 and more negative RCP8.5. It is shown
that significant changes in the ground temperature regime occur in the vicinity
of the pipe under both warming scenarios. Nevertheless, the calculations
demonstrate the preservation of permafrost even in a negative scenario of
climate warming.
