Optimization of Parameters of a Vertical Ground Heat Exchanger in a Geothermal Heating System

This study presents the results of an original study on the influence of selected parameters on the thermal efficiency of a vertical ground heat exchanger (VGHE) in a ground-source heat pump (GSHP) system. The research objective was an analysis of the specific thermal efficiency of a vertical ground heat exchanger q, received by a U-shaped element made of plastic pipes placed in a borehole, depending on seven direct influencing factors: the ground temperature Tg; the soil thermal conductivity coefficient λg; the thermal conductivity coefficient of the well material λm; the temperature of the heating medium (glycol) Tw at the feed to the ground heat exchanger and its flow rate M; the internal diameter of the pipes of the ground heat exchanger dw; and the distances between the external walls of the pipes of the ground heat exchanger L. The analysis was carried out for the climatic conditions of the Podlasie Voivodeship (Poland). Based on the results of the computational experiment obtained using the TRNSYS numerical environment, a deterministic mathematical model of this relationship was developed, and the effects of the influence of selected factors on the specific thermal efficiency q of the vertical ground heat exchanger, received by the U-shaped element, were analysed. Based on the model, the contribution of each parameter to the efficiency of the heat exchanger was determined. It turned out that changes in the values of the factors Tg (X1), λg (X2), λm (X3), M (X5), dw (X6) and L (X7) from the lower to the upper level caused an increase in the specific efficiency q of the heat exchanger by 34.04, 7.90, 15.20, 55.42, 6.58 and 24.26%. Only factor Tw (X4), with such a change, caused a decrease in the thermal efficiency of the tested heat exchanger by 44.22%. The parameters of the tested element of the geothermal heating system were also optimized according to the energy criterion using a numerical method in the Matlab environment. The information may be useful for scientists, designers, producers and consumers of heating systems based on heat pumps with a vertical ground heat exchanger as the lower heat source.