On the estimation of thermal resistance in borehole thermal conductivity test

Sizing of ground-coupled loop heat exchangers (GLHE) depends on the ground thermal conductivity and capacity, and the borehole thermal resistance. One popular method to estimate the thermal parameters is the interpretation of in situ thermal response tests. The modeled response is Tm=(Tin+Tout)/2, the average temperature of the fluid entering and leaving the ground. The Tm response corresponds to the physically unrealistic hypothesis of constant heat flux along a borehole. Using a 3D finite element model of the borehole, we show that Tm does not correspond to the fluid mean temperature within the borehole. Accordingly, with Tm, an overestimation of the borehole thermal resistance results. The resistance overestimation has a noticeable economic impact. We propose instead a new estimator we name “p-linear” average of Tin and Tout with parameter p→-1, as determined by numerical simulations. We show that the p-linear average closely fits the average fluid temperature computed with the numerical model, hence avoiding bias in estimation of borehole thermal resistance. Finally, we discuss the problem of collinearity arising in the estimation of thermal parameters.