Assessment of heat transfer in an aquifer utilizing fractal theory

The thermal conductivity of a formation, which is a basic parameter in well logging, is difficult to measure when the formation is porous or fractured and filled with water. In order to describe the heat transfer in an aquifer, a notion of overall thermal conductivity was proposed, which includes the thermal conduction of the soil or rock and the advection of groundwater. This paper adopts the fractal theory to establish a geometric model of the aquifer, which helps with the analysis of the heat transfer mechanism in an irregular configuration, and derives a correlation of the overall thermal conductivity from the thermal resistance structure. The overall thermal conductivity of typical aquifers indicates that the advection in the aquifer cannot be ignored even if the Reynolds number (Re) of the groundwater is less than 1. However, when the velocity and temperature of groundwater are determined, the advection does not depend on the porosity of the aquifer and therefore can be regarded as a constant. Furthermore, this parameter provides an easy but effective way to analyze the heat exchange between the wellbore and the surrounding formation, especially in the ground source heat pump (GSHP) system.