Regulations of the Formation of the Thermal Influence Zone of Underground Heat Exchanger as an Environmental Risk Factor for the Soil Environment

The task of establishing the regularities of creating a thermal area in the soil when using heat exchangers of secondary energy sources is considered. The characteristics of the non-stationary process of spreading thermal energy in the soil and related information about the degree of cooling of the energy carrier in the process of forming the temperature range and the duration of the process are important issues considered in the process of implementing the task. The study of these regularities makes it possible to assess not only the energy efficiency of the use of secondary energy sources, but also their environmental safety for the under-ground environment. An analytical approach to solving a problem requires the creation of a mathematical model and a methodology for its implementation. A mathematical model is proposed, which is based on the differential equation of non-stationary thermal conductivity in a two-dimensional formulation and is supplemented with initial and boundary conditions that characterize the real process of thermal area formation. The implementation of the mathematical model was carried out by the method of using integral transformations, in particular, Lapass and Fourier transformations were applied. As a result, an analytical solution was obtained, which made it possible to evaluate the characteristic regularities of the process. To obtain numerical solutions and their analysis, we will use the concept of dimensionless time. Numerical implementation of the problem for various conditions allows to establish the degree of dissipation of heat energy in the soil, which is estimated by the coefficient of the useful effect of the system, and to establish the duration of the process of formation of the thermal area.