ESTIMATION OF COEFFICIENTS OF THERMAL RESPONSE TEST: THE CHOICE OF THE COORDINATES SPACE OF THE RANDOM FUNCTION

In the shallow geothermal sector, the main equivalent underground thermal properties are commonly deduced by a Thermal Response Test. It is the production test of a Borehole Heat Exchanger, where temperature of a heat transfer fluid over time, T(t_α ) is recorded, following an heat injection / extraction by constant power. The evaluation of equivalent thermal parameters (thermal conductivity, heat capacity) is simply deduced by a regression of the temperature data, which theoretically is a logarithmic function in the time domain: m_T (t)=a+b ln⁡t; or a linear function in the domain of the time logarithm τ=ln⁡t: m_T (τ)=a+bτ. By interpreting the recorded temperatures as a regionalized variable whose drift is the regression function, in both cases the formal problem is a linear estimation of the mean (the coefficients a,b). By knowing the autocorrelation function (variogram, covariance) of residuals, the estimation variance of coefficients is straight deduced. The estimates of coefficients are independent on the drift form adopted and also the residuals are the same in the same points, Y(t_α )=Y(τ_α ). However, the Random Function is different in the time domain, and in the domain of time logarithm, and in fact, residuals’ variograms are different γ(t_α-t_β ),≠γ(τ_α-τ_β ) due to the transformation of the coordinates’ space. This work examines and comments the consequences of the transformation of the coordinates’ space for a random function, namely on its variogram, through a TRT case study. The actual problem considered is the choice of the coordinates’ space and variogram to adopt.