Analytical solutions for predicting thermal plumes of groundwater heat pump systems

Abstract

Groundwater heat pump (GWHP) systems have gained attention for space heating and cooling due to their efficiency and low installation costs. Their number is growing in many countries, and therefore in some areas, dense installations are expected. This might lead to thermal interferences between neighbouring groundwater wells and a decrease in efficiency. In the presented study, three analytical formulations are inspected for the prediction of the thermal plume around such open-loop systems under various hydrogeological conditions. A thermal radial transport scenario without background groundwater flow and two advective scenarios with moderate to significant ambient flow velocities (1 and 10 m d−1) are analytically simulated and compared with numerical simulations. Two-dimensional (2D) numerical models are used to estimate the validity of analytical results for a homogeneous confined aquifer, without considering heat transfer in upper and lower layers of the aquifer. In order to represent more realistic aquifer conditions of limited vertical extension, an additional three-dimensional numerical model (3D) is deployed to account for vertical heat losses. The estimated relative errors indicate that the analytical solution of the radial heat transport is in good agreement with both numerical model results. For the advective scenarios, the suitability of the linear and planar advective heat transport models strongly depend on ambient groundwater flow velocity and well injection rate. For low groundwater velocities (1 m d−1), the planar model fits both numerical model results better than the linear advective model. However, the planar model's ability to estimate thermal plumes considerably decreases for high injection rates (>0.6 l s−1). In contrast, the linear advective model shows a good agreement with the two-dimensional numerical results for high groundwater flow conditions (≥10 m d−1). The comparison with the three-dimensional numerical models indicates that the vertical heat transfer is challenging for all of the selected analytical solutions. Despite this, there is a wide range of applicability for the provided analytical solutions in studying the thermal impact of GWHP systems. Hence, the inspected solutions prove to be useful candidates for first-tier impact assessment in crowded areas with potential thermal interferences.