Interaction of temperature fields in an unlimited array of soil during the selection of low-grade heat by U-shaped probes of a geothermal heat pump units

Abstract

The methodology and results of mathematical modeling of the unsteady process of selecting low-grade soil heat with a vertical U-shaped geothermal probe placed in a well of heat pump units (HPU), the free space of which is filled with a heat-conducting filler, are presented. The developed mathematical model is based on the joint use of two classical analytical methods: a source-drain adapted to the unsteady process of heat extraction from an unlimited soil mass, and a superposition method that allows one to quantify the effect of the interaction of the temperature fields of the downpipe and the riser pipe laid at a small distance from each other in one well. As a result, the main calculated dependencies underlying the developed mathematical model on which the computational experiment was performed were obtained analytically. The results of a computational experiment, performed on the example of a well with a vertical U-shaped soil probe, designed to select low-grade heat from an unlimited array of dry sand, are presented in graphs. An analysis of the results made it possible to identify the main factors affecting the intensity of heat extraction, justify the conditions for the effective operation of U-shaped probes in the wells of the soil contour of heat pump units, and quantitatively determine the maximum allowable temperature increment of the heated coolant according to the condition of efficient use of the heat transfer surface.