A Model for a Geothermal Well in a Hydraulic Groundwater Flow for Ground Source Heat Pump Systems

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 cooling modes, depending on the direction of the cycle upon which they operate. For proper operation, the heat pump must be connected to a constant temperature thermal reservoir which in traditional systems is the ambient air. In ground source heat pumps however, subterranean ground water is used as the thermal reservoir. To access the subterranean groundwater, “geothermal” wells are drilled into the formation. Water from the building heating or cooling system is circulated through the wells thereby promoting heat exchange between the coolant water and the subterranean formation. The potential for higher efficiency heating and cooling has increased the utilization of ground source heating ventilating and air conditioning systems. In addition, their compatibility with a naturally occurring and stable thermal reservoir has increased their use in the design of sustainable or green buildings and man-made environments. Groundwater flow affects the temperature response of thermal wells due to advection of heat by physical movement of groundwater through the aquifer. Research on this subject is scarce in the geothermal literature. This paper presents the derivation of an analytical solution for thermal dispersion by conduction and advection from hydraulic groundwater flow for a “geothermal” well. This analytical solution is validated against asymptotic analytical solutions. The traditional constant linear heat source solution is dependent on the ground formation thermal properties; the most dominant of which is the thermal conductivity. The results show that as hydraulic groundwater flow increases, the influence of the ground formation thermal conductivity on the temperature response of the well diminishes. The diminishing influence is evident in the Peclet number parameter; a comparison of thermal advection from hydraulic groundwater flow to thermal conduction by molecular diffusion.