A spectral method aimed at explaining the role of the heat transfer rate when the Infinite Line Source model is applied to Thermal Response Test analyses

Abstract

The present paper introduces new concepts related to the modeling of vertical Borehole Heat Exchangers for Ground Coupled Heat Pump applications. A sensitivity analysis on how specific parameters affect the ground thermal conductivity kgr estimation when the Infinite Line Source model is used to interpret a Thermal Response Test has been performed. The study has been conducted considering shallow and deep BHEs, with and without geothermal gradient, and for homogeneous and stratified ground thermal conductivities. The qratio parameter scales the external heat rate to a natural heat rate associated with the geothermal gradient. The effect of qratio on the TRT analysis has been related to a specific dimensionless g-transfer function called g0, which incorporates the geothermal gradient. Three in-house built Fortran90 codes implementing the finite-difference models related to coaxial, single and double U-BHE geometries are exploited to evaluate the dimensionless g-transfer functions related to each fluid volume. A spectral method aimed to reconstruct the fluid temperature profiles by superposing two separated convolutions in the time domain exploiting the Fast Fourier Transform leads to considering qratio as the dominant parameter when the ILS model is used to estimate kgr. In the case of a single-layered subsurface, qratio >>1 guarantees the correct ILS-based kgr estimation for any BHE geometry. In the coaxial center-pipe inlet case with a single-layered subsurface and qratio<1, the ILS-based kgr estimation when the g0-function is taken into account can differ by -14% from the correct ILS-based kgr estimation without taking into account the g0-function. In the case of a multilayered subsurface, the qratio parameter indicates when the effective kgr estimated by the ILS model departs from the weighted-thickness average. A departure of 10% occurs for qratio between 2 and 2.5 for the coaxial center-pipe inlet cases considered and the departure increases with decreasing qratio.