Inclusion of advection in fractures in the line source equation for analysis of thermal response tests

Abstract

Proper design of larger ground source heat pump installations, and borehole thermal energy storages (BTES) requires determination of on-site thermal properties of the ground by performing a thermal response test (TRT). The effective thermal conductivity is an important design parameter from TRT that is determined from the line source equation. The line source equation does not include advection and may give incorrect results when groundwater flow is present. This study describes the development and application of a new analytical equation where advective heat in fractured, nonporous rock is accounted for. Including advective heat improves the fit to the measurement data (1.2–77 % better) when applying reasonable values for the thermal conductivity of the ground. The new analytical equation is applicable to all TRTs. Previous studies recommend comprehensive numerical modelling of boreholes affected by groundwater flow. The equation proposed here is an analytical alternative which does not require modelling and is a recommended and cost-effective alternative when groundwater flow affects the thermal properties measured in a borehole heat exchanger in fractured rock.