Experimental validation of a lumped parameter model for geothermal systems based on Downhole Heat Exchanger

Downhole Heat Exchangers provide a sustainable solution for geothermal energy extraction without fluid production and reinjection. However, the design of these systems remains challenging because of the coupled heat and mass transfer phenomena occurring between the heat exchanger, the geothermal well, and the surrounding aquifer under natural convection conditions. This study presents an experimentally validated lumped-parameter model for geothermal aquifer-well-Downhole Heat Exchanger systems. The proposed framework combines internal forced convection, external natural convection, and porous-medium thermal resistance within a unified thermal resistance network. Different natural convection correlations available in the literature are systematically compared against experimental measurements in order to identify the most suitable formulation for confined annular geothermal configurations. In addition, a methodology for estimating the geothermal fluid mass flow rate induced by natural convection is introduced together with a modified effectiveness-NTU representation adapted to geothermal systems. The model is validated using experimental data from a real geothermal installation located on the island of Ischia, Italy, and further tested on an additional geothermal dataset. The results show good agreement between model predictions and experimental measurements of heat transfer coefficients and global thermal performance over a thermal power range up to approximately 45 kW. The modified effectiveness-NTU representation successfully collapses the experimental data into a single trend and allows estimation of a maximum extractable thermal power of approximately 75 kW for the investigated geothermal system. The proposed methodology provides an engineering tool for the design and performance evaluation of geothermal Downhole Heat Exchanger systems operating under natural convection conditions.