Objective Identification of the Stabilized Regime in Thermal Response Tests: A Log-Derivative Alternative to Semilog Slope Fitting
Updated: Aug 24
A practical approach to identifying when a Thermal Response Test has reached a sufficiently stable regime for reliable thermal conductivity and borehole thermal resistance estimation.
TECHNICAL PAPER
Fabrice Toussaint,MSEng., Voraggo Limited — Sofia, Bulgaria
Why the Interpretation of a TRT Matters
Thermal Response Tests (TRTs) are widely used to characterize the thermal properties of the ground and the thermal resistance of a borehole before designing a ground-source heat pump system. In conventional TRT interpretation, the mean fluid temperature is plotted against the logarithm of time, and the thermal conductivity and borehole thermal resistance are derived from the slope and intercept of the resulting linear relationship.
The reliability of this approach, however, depends on selecting an appropriate time interval over which the thermal response has reached a sufficiently stable regime. In practice, the beginning of this interval can be selected subjectively, and different reasonable choices may lead to materially different estimates of ground thermal conductivity and borehole thermal resistance.
This Technical Paper examines whether a logarithmic temperature derivative can provide a more objective indication of when the stabilized regime has been reached. Rather than replacing the conventional semilogarithmic interpretation, the proposed approach is intended to provide an independent diagnostic for identifying and justifying the fitting interval.
The choice of the fitting window can materially affect the estimated ground thermal conductivity and borehole thermal resistance.
In the synthetic case examined in the paper, two plausible semilogarithmic fitting windows produced significantly different results. An early fitting window estimated the ground thermal conductivity at 3.02 W/m·K, compared with the reference value of 2.50 W/m·K — an overestimation of approximately 21%.
≈ 21%
Potential overestimation of ground thermal conductivity from an early, but plausible, semilogarithmic fitting window.
When the fitting interval was anchored to the stabilized regime identified from the logarithmic derivative, the estimated thermal conductivity was 2.52 W/m·K, within approximately 1% of the reference value. The corresponding borehole thermal resistance estimate was 0.101 m·K/W, compared with the reference value of 0.100 m·K/W.
≈ 1%
Deviation of estimated ground thermal conductivity from the reference value when the fitting interval is anchored to the identified stabilized regime.
What the Paper Examines
Conventional semilogarithmic TRT interpretation and the dependence of calculated thermal properties on the selected fitting interval.
Logarithmic temperature derivatives as a diagnostic for identifying the onset of the stabilized thermal response.
Derivative plateau behaviour and its relationship to the validity of the conventional semilogarithmic fitting approach.
The effect of fitting-window selection on estimated ground thermal conductivity and borehole thermal resistance.
Uncertainty associated with the identification of the stabilized regime and the practical limitations of the proposed diagnostic approach.
The proposed derivative analysis is not presented as a replacement for conventional TRT interpretation, but as an additional diagnostic tool for making the selection of the fitting regime more objective and transparent.
Access the Technical Paper
Download the complete Technical Paper to review the methodology, derivative analysis, synthetic test case, numerical results and discussion of the practical implications for Thermal Response Test interpretation.