Thermal Attenuation and Lag Time in Fractured Rock: Theory and Field Measurements From Joint Heat and Solute Tracer Tests

The modeling and prediction of heat transfer in fractured media is particularly challenging as hydraulic and transport properties depend on a multiscale structure that is difficult to resolve. In addition to advection and dispersion, heat transfer is also impacted by thermal attenuation and lag time, which results from fracture-matrix thermal exchanges. Here we derive analytical expressions for thermal lag time and attenuation coefficient in fractured media, which quantify the effect of fracture geometry on these key factors. We use the developed expressions to interpret the results of single-well thermal and solute tracer tests performed in a crystalline rock aquifer at the experimental site of Ploemeur (H+ observatory network). Thermal breakthrough was monitored with fiber-optic distributed temperature sensing (FO-DTS), which allows temperature monitoring at high spatial and temporal resolution. The observed thermal response departs from the conventional parallel plate fracture model but is consistent with a channel model representing highly channelized fracture flow. These findings, which point to a strong reduction of fracture-matrix exchange by flow channeling, show the impact of fracture geometry on heat recovery in geothermal systems. This study also highlights the advantages to conduct both thermal and solute tracer tests to infer fracture aperture and geometry.