Bayesian inference for thermal response test parameter estimation and uncertainty assessment

Abstract

The effective ground thermal conductivity and borehole thermal resistance constitute information needed to design a ground-source heat pump (GSHP). In situ thermal response tests (TRTs) are considered reliable to obtain these parameters, but interpreting TRT data by a deterministic approach may result in significant uncertainties in the estimates. In light of the impact of the two parameters on GSHP applications, the quantification of uncertainties is necessary. For this purpose, in this study, we develop a stochastic method based on Bayesian inference to estimate the two parameters and associated uncertainties. Numerically generated noisy TRT data and reference sandbox TRT data were used to verify the proposed method. The posterior probability density functions obtained were used to extract the point estimates of the parameters and their credible intervals. Following its verification, the proposed method was applied to in situ TRT data, and the relationship between test time and estimation accuracy was examined. The minimum TRT time of 36 h recommended by ASHRAE produced an uncertainty of ~±21% for effective thermal conductivity. However, the uncertainty of estimation decreased exponentially with increasing TRT time, and was ±8.3% after a TRT time of 54 h, lower than the generally acceptable range of uncertainty of ±10%. Based on the obtained results, a minimum TRT time of 50 h is suggested and that of 72 h is expected to produce sufficiently accurate estimates for most cases.

Bayesian inference of structural error in inverse models of thermal response tests

“…Because TRT1 dataset was also used in Ref. [43], in which Bayesian inference was conducted by considering only the random error term, it would be interesting to compare the inferred posteriors of and of the previous and current studies. The comparison and discussion between two results are in Appendix A.…”

“…This large is due to the overfitting of the ILS model to the measured data, whereas the large is due to the positive correlation between and when two parameters are estimated simultaneously as discussed in Ref. [43]. Therefore, whilst the model bias function does not fully capture the convection mode of subsurface heat transfer, it does prevent overfitting between the measured data and computer model outputs, yielding improved estimates of parameter values.…”

“…In our previous work [43], we developed a Bayesian inference technique for the TRT parameter estimation in which the inference was conducted by considering only the random error term. Thus, it would be interesting to compare the inferred posteriors of and from the previous and current studies.…”

Sequential estimation of borehole resistance and ground thermal properties through thermal response test

“…31,32 The stochastic methods for TRT analysis were found to improve the parameters estimation by producing credible intervals of the parameters to reduce operational risks. 33,34 Therefore, for improving the thermal properties estimation of borehole and ground in GSHP, especially for the parameters with low sensitivity, this paper presented a novel parameter estimation method to estimate the borehole resistance, ground thermal conductivity and heat capacity in sequence applying to TRT data. Firstly, based on the classical ILS model, a special sensitivity analysis method was adopted to specify the correlation between the parameters and fluid temperature, then the sequential estimation of the three parameters was determined by the correlations.…”

Comparative Analysis of Different Methodologies Used to Estimate the Ground Thermal Conductivity in Low Enthalpy Geothermal Systems

“…This first approach to linearize the infinite line source model requires rejecting the early measurements for the subsequent test interpretation. TRT duration is usually established between 36-72 h, but this duration has been thoroughly discussed in the past [10] and at the moment is an area of active research [11][12][13][14][15]. Despite the errors these test could involve [4], the high accuracy of ground thermal conductivity results represent essential information in the corresponding geothermal loop sizing.…”