The thermal response of an infinite line of open loop wells for ground coupled heat pump systems

Ground thermal energy storage is a means of storing thermal energy underground during the summer and utilizing it during the winter. The main use of such a technology is in the heating, ventilating and air conditioning sector where the ground provides a stable temperature reservoir for a heat pump system. Heat pumps are mechanical systems that provide heating to a space in the winter, and cooling in the summer. They are increasingly popular because the same system provides both heating modes, depending on the direction of the cycle upon which they operate. The stable temperature reservoir allows the heat pump system to run at a higher efficiency. Thermal energy is transmitted to and from the ground by circulation of water through standing column geothermal wells. In commercial applications, the ground storage is enabled by a field of multiple wells; hence proper well spacing is important for optimum performance for a fixed land area and required storage capacity. If wells are too closely spaced, one system may thermally encroach on another thereby lowering the efficiency of both.This paper presents a comprehensive analysis of the thermal response of a line of evenly spaced wells, operating concurrently. A numerical model is developed, validated using empirical data, and compared to an approximate analytical model that allows for the assessment of coefficient of performance degradation. The analytical model is solved by separating the problem into three time regimes. First, for small values of time, heat is absorbed predominantly by the thermal capacity of the well water. Second, for intermediate times, heat flow through an infinite cylinder dictates the thermal response. Third, for late times, planar conduction dominates due to thermal encroachment between adjacent wells. The transition times between these regimes are derived from characteristic times distinct to the driving physics. Using the analytical model, the temperature response of the well in a line is compared to an isolated well showing the degradation in well performance with time. This degradation in performance is then related to the coefficient of performance of a reversible heat pump system to assess the impact on efficiency. The results quantify the decrease in coefficient of performance of a ground coupled heat pump system sourced by a line of wells as a function of time and decreasing well spacing. The coefficient of performance figure is a figure of merit for geothermal well field designers to properly assess the financial benefits of a ground coupled heat pump system compared to conventional systems.