Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions

An analytical study is carried out to examine the effect of thermal dispersion on the simulation of temperature plumes in aquifers that evolve from vertical ground source heat pump (GSHP) systems. Analytical solutions for the simulation of heat transport in aquifers often ignore thermal dispersion. In this study an existing two-dimensional analytical approach for transient conditions is used. Moreover, an equation to calculate the length of the temperature plume for steady state conditions is developed. To study the interplay between thermal dispersion and hydraulic conductivity, Darcy velocities are varied from 10−8 m/s to 10−5 m/s and thermal dispersivities are varied based on two assumptions: 1) thermal dispersion is assumed to be only dependent on the Darcy velocity and 2) thermal dispersion is assumed to be scale-dependent. The results are discussed with respect to their implications for typical legal regulations and operation of such GSHP systems. In general, the effect of thermal dispersion on the temperature plume around the borehole heat exchanger (BHE) is minor when thermal dispersion is assumed to be depending solely on the magnitude of groundwater flow (e.g., in a homogeneous aquifer). On the other hand, based on a field scale of 10 m and assuming thermal dispersion to be scale-dependent, thermal dispersion can be neglected only for conditions typical for fine sands, clays, and silts with q < 10−8 m/s. For aquifers where medium sands and gravels (with Darcy velocities q > 10−8 m/s) dominate, thermal dispersion has a larger effect on the temperature plume distribution around the borehole heat exchanger.