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 HVAC systems. In addition, their compatibility with a naturally occurring and very stable thermal reservoir has increased their use in the design of sustainable or green buildings and man-made environments. This paper is concerned with the development of a mathematical model describing the thermal processes that occur in a circulating geothermal well as the water thermally interacts with the surrounding formation. First principles are utilized to develop a general single well model that is able to predict the heating or cooling of a well with time. The single well model is then utilized to build a simulation for an infinite line of adjacent wells that thermally interact with each other over time. The behavior of a single isolated well and a line of evenly spaced wells is discussed and compared with recent experimental data for circulation in an isolated well.

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