Estimating Thermal Response Test Coefficients: Choosing Coordinate Space of The Random Function
- PDF / 3,276,609 Bytes
- 21 Pages / 439.37 x 666.142 pts Page_size
- 78 Downloads / 150 Views
Estimating Thermal Response Test Coefficients: Choosing Coordinate Space of The Random Function Roberto Bruno1 · Francesco Tinti1 · Sara Focaccia1,2
Received: 6 October 2014 / Accepted: 1 August 2015 / Published online: 28 August 2015 © International Association for Mathematical Geosciences 2015
Abstract In shallow geothermal systems, the main equivalent underground thermal properties are commonly calculated with a thermal response test (TRT). This is a borehole heat exchanger production test where the temperature of a heat transfer fluid is recorded over time at constant power heat injection/extraction. The equivalent thermal parameters (thermal conductivity, heat capacity) are simply deduced from temperature data regression analysis that theoretically is a logarithmic function in the time domain, or else a linear function in the log-time domain. 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. If the autocorrelation function (variogram, covariance) of residuals is known, coefficient variance can be directly deduced. Coefficient estimates are independent of the drift form adopted, and the residuals are the same in the same points. The random function is different in the time domain, however, and in the log-time domain. In fact, residual
The work was presented to GeoEnv 2014 Conference on Geostatistics for Environmental Applications, held in Paris, 9-11/07/2014.
B
Francesco Tinti [email protected] Roberto Bruno [email protected] http://www.dicam.unibo.it/ Sara Focaccia [email protected] http://tecnico.ulisboa.pt/
1
Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, via Terracini 28, 40131 Bologna, Italy
2
CERENA, Instituto Superior Técnico de Lisboa, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal
123
4
Math Geosci (2016) 48:3–23
variograms are different due to the transformation of the coordinate space. This paper uses a TRT case study to examine the consequences of coordinate space transformation for a random function, namely its variogram. The specific question addressed is the choice of coordinate space and variogram. Keywords Thermal response test · Random function · Geothermal energy · Pseudo-variogram models · Non-linear transformation
1 Thermal Response Test Data Analysis: Introduction In the shallow geothermal sector, the main thermal properties of a reservoir are usually deduced by the production test, known as the thermal response test (TRT), which is based on thermally stimulating a borehole heat exchanger (BHE) and then recording the average fluid temperature evolution over time T (t) (Mogensen 1983). The aim is to evaluate the equivalent thermal parameters (thermal conductivity, heat capacity) of the volume of ground affected by the heat exchange, with contemporary verification of BHE thermal properties (Eklof and Gehlin 1996). In a homogeneous and isotropic medium, the ground volume is a central cylind
Data Loading...
