In the shallow geothermal sector, the main thermal properties of a reservoir are usually deduced by the well – known production test known as Thermal Response Test (TRT), that is based on thermally stimulating a Borehole Heat Exchanger (BHE) and then recording the fluid average temperature evolution over time, T(t). The aim is the evaluation of equivalent thermal parameters (thermal conductivity, thermal capacity) of the volume of ground interested by the heat exchange, with contemporary verification of BHE thermal properties, as well. In a homogeneous and isotropic medium, the ground volume is a cylinder centered in the BHE, with height equal to the thermo active part of the BHE, and with radius increasing as much as the thermal stimulation lasts. The TRT’s common duration varies from a minimum of one day to a maximum of five days, depending on boundary conditions and test’s aims and scopes. Among all several possibilities to deduce equivalent thermal parameters, the simplest and most popular way is the application of the simplified version of the Infinite Linear Source (ILS) solution [1, 2]. This approach assumes the BHE as a borehole of infinite length in a homogeneous and isotropic medium and it expresses the temporal evolution of fluid temperature by (1): T (t)=b∙ln⁡(t)+a (1) The slope b and the intercept a are estimated by operating a classical linear regression on the vector of the experimental fluid data registered at different times. Once identified the slope b, the equivalent underground thermal conductivity λ_g is deduced on the basis of the injected/extracted power rate Q and of the borehole active length, H : λ_g= Q/(4∙π ∙b∙H). By the use of the intercept a, similar procedure allows to deduce the ground volumetric heat capacity c_g and the borehole thermal resistance R_b, linked to one another. The authors in the last years have introduced a geostatistical analysis of the TRT data starting from the ILS theory [3, 4]. They pointed out the limits of ILS basic assumptions, among which: 1) the vectorial nature of the Regionalized Variable “thermal conductivity”, 2) the meaning of “equivalent thermal conductivity”, 3) the continuous change of support during the test. Nevertheless, the approximated results of TRT given by ILS are useful and currently used to understand and design a shallow geothermal field and the research focus is almost on the quality of parameters’ estimations in two approaches (traditional and geostatistical), which are compared by the use of the estimation variance on the regressions of a and b.

Estimation of coefficients of Thermal response test: the choice of the coordinates space of the random function

BRUNO, ROBERTO;TINTI, FRANCESCO
2014

Abstract

In the shallow geothermal sector, the main thermal properties of a reservoir are usually deduced by the well – known production test known as Thermal Response Test (TRT), that is based on thermally stimulating a Borehole Heat Exchanger (BHE) and then recording the fluid average temperature evolution over time, T(t). The aim is the evaluation of equivalent thermal parameters (thermal conductivity, thermal capacity) of the volume of ground interested by the heat exchange, with contemporary verification of BHE thermal properties, as well. In a homogeneous and isotropic medium, the ground volume is a cylinder centered in the BHE, with height equal to the thermo active part of the BHE, and with radius increasing as much as the thermal stimulation lasts. The TRT’s common duration varies from a minimum of one day to a maximum of five days, depending on boundary conditions and test’s aims and scopes. Among all several possibilities to deduce equivalent thermal parameters, the simplest and most popular way is the application of the simplified version of the Infinite Linear Source (ILS) solution [1, 2]. This approach assumes the BHE as a borehole of infinite length in a homogeneous and isotropic medium and it expresses the temporal evolution of fluid temperature by (1): T (t)=b∙ln⁡(t)+a (1) The slope b and the intercept a are estimated by operating a classical linear regression on the vector of the experimental fluid data registered at different times. Once identified the slope b, the equivalent underground thermal conductivity λ_g is deduced on the basis of the injected/extracted power rate Q and of the borehole active length, H : λ_g= Q/(4∙π ∙b∙H). By the use of the intercept a, similar procedure allows to deduce the ground volumetric heat capacity c_g and the borehole thermal resistance R_b, linked to one another. The authors in the last years have introduced a geostatistical analysis of the TRT data starting from the ILS theory [3, 4]. They pointed out the limits of ILS basic assumptions, among which: 1) the vectorial nature of the Regionalized Variable “thermal conductivity”, 2) the meaning of “equivalent thermal conductivity”, 3) the continuous change of support during the test. Nevertheless, the approximated results of TRT given by ILS are useful and currently used to understand and design a shallow geothermal field and the research focus is almost on the quality of parameters’ estimations in two approaches (traditional and geostatistical), which are compared by the use of the estimation variance on the regressions of a and b.
2014
Geostatistics for Environmental Applications - geoEnv 2014 - Book of Abstracts
28
28
Roberto Bruno; Francesco Tinti
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/315715
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact