On Taylor dispersion effects for transient solutions in geothermal heating systems

Residential geothermal heating systems have been developed over the past few decades as an alternative to fossil-fuel based heating. Through mathematical modeling the relationship between the operating parameters of the heat pump and the piping length of the geothermal system, which is directly correlated to the cost of the system is investigated. The effect of Taylor dispersion of heat in the fluid which is not yet addressed in the literature with respect to geothermal systems is included. A model of a simple configuration of a single pipe surrounded concentrically by grout and then by soil is considered, where the soil region has a constant ambient temperature. The conduction between the two regions is modeled with a classical thermal resistance. Taylor dispersion effects are significant at higher Peclet numbers associated with this system, and Taylor dispersion in the fluid and thermostat frequency dictate the minimum tubing length needed for successful operation in an insulated subsystem. We consider both steady state and transient (cyclic operation) analyses and find that the axial dispersion increases linearly in the cycle rate for large flow rates. We find that the estimated tubing length for complete energy transport is increased when Taylor dispersion is included, but that this effect can be mitigated with an appropriate choice of the borehole radius.