Simulation of Thermal Fields in the Permafrost With Seasonal Cooling Devices

Abstract

A new mathematical model of heat distribution in permafrost soils is considered taking into account different climatic and physical factors. The first group of factors includes consideration of solar radiation, seasonal changes of air temperature, leading to periodic thawing (freezing) of soil, and possible snow layers. The second group of factors is the heterogeneity of the soil, the presence of a number of piles, or foundation structures, seasonal cooling devices. Seasonal cooling devices are vapor-fluid devices consisting of a hermetically sealed and seasoned with coolant, metal pipe with diameter 57 mm, length up to 10 meters or more, consisting of aerial parts (condenser fins) up to 2.5 meters and an underground part. These devices operate without external power sources only by the laws of physics. Taking into account these factors leads to solution of three-dimensional quasilinear heat distribution equation (quasi-linear equation due to the dependence of the thermophysical parameters on temperature) of the Stefan problem in a rectangular parallelepiped, but also with a nonlinear boundary condition at the soil surface associated with solar radiation. It is assumed that the lateral faces of the computational domain are insulated and are chosen sufficiently far from the location of engineering structures, and a computational grid of large dimension to be used, with adaptation to the heat (cold) sources. Software product is designed for numerical simulation of thermal fields in permafrost and melted soil, taking into account thermal diffusion properties of the soil and heat exchange between the soil and air, including also due to heat loss by radiation. The paper is devoted to the results of numerical simulations carried out for the project work in several oil and gas fields in Russia, located in the permafrost zone.