Interaction of temperature fields in soil massif during abstraction of low-grade heat by U-shaped probes of geothermal heat pump units

Research in the field of alternative energy sources use is of relevance due to the limited reserves of fossil fuels, the constant cost increase and flue gas emissions generated by power plants along with fuel combustion. The use of low-grade ground energy with the help of geothermal heat pump stations makes it possible to save fossil fuel and reduce environmental pollution. Since about 50 % of the one-time capital investment is spent on the construction of ground loop, the issues on improving the efficiency of ground heat abstraction are of particular relevance. However, until now there is no unified normative technique to calculate ground probes and to create ground loops of optimal constructions. The absence of calculation methods and intelligible practical dependencies does not allow one to quantify the influence of various factors on the heat extraction process, the intensity of which varies significantly over time. The authors have applied two analytical methods in the developed mathematical model. The first one is a source-sink method adapted to the non-stationary process of heat abstraction away from the soil mass. And the second one is the superposition method which made it possible to quantify the effect of the interaction of temperature fields in the well. The mathematical model has been developed, and calculated dependences have been obtained. The authors have presented a calculation method and the results of mathematical modeling of the non-stationary process of soil heat abstraction by a vertical U-shaped geothermal probe and the internal interaction of the temperature fields of the downcomer and riser pipes. The results of the computational experiment are presented in the form of graphs. The authors have determined three key particular cases of the operation of a ground probe and formulas to define the maximum allowable increment of the temperature of the heated coolant under the condition of maximum efficient use of the heat-receiving surface applicable to various types of soil. The analysis of the obtained results makes it possible to identify the main factors affecting the heat-absorption efficiency (actual heat transfer coefficients and specific heat inflows) for each of the pipes and for the entire probe, considering the interaction of temperature fields around the downcomer and riser pipes during the heating period.