Comparing transient and steady-state methods for the thermal conductivity characterization of a borehole heat exchanger field in Bergen, Norway

  • Nicolò GiordanoEmail author
  • Jessica Chicco
  • Giuseppe Mandrone
  • Massimo Verdoya
  • Walter H. Wheeler
Original Article


A comparative study was carried out aiming at characterizing the thermal conductivity of rocks sampled in a borehole heat exchanger field. Twenty-three samples were analysed with four different methods based on both steady-state and transient approaches: transient divided bar (TDB), transient line source (TLS), optical scanning (OS), and guarded hot plate (GHP). Moreover, mineral composition (from XRD analyses), P-wave velocity, and density were investigated to assess the petro-physical heterogeneity and to investigate possible causes of divergence between the methods. The results of thermal conductivity showed that TLS systematically underestimates thermal conductivity on rock samples by 10–30% compared to the other devices. The differences between TDB and OS, and GHP and OS are smaller (about 6% and 10%, respectively). The average deviation between TDB and GHP, for which the specimen preparation and the measurement procedure were similar, is about 10%. In general, the differences are ascribable to sample preparation, heterogeneity and anisotropy of the rocks, and contact thermal resistance, rather than the intrinsic accuracy of the device. In case of good-quality and homogeneous samples, uncertainty can be as low as 5%, but, due to the above-mentioned factors, usually uncertainty is as large as 10%. Opposite relationships between thermal conductivity and P-wave velocity were observed when analysing parallel and perpendicular to the main rock foliation. Perpendicular conductivity values grow with increasing perpendicular sonic velocity, while parallel values exhibit an inverse trend. Thermal conductivity also appears to be inversely correlated to density. In quartz-rich samples, high thermal conductivity and low density were observed. In samples with calcite or other likely dense mineral phases, we noticed that lower thermal conductivity corresponds to higher density. The presence of micas is likely to mask major differences between silicate and carbonate samples.


Petro-physical properties Thermal conductivity P-wave velocity Density Borehole heat exchangers 



The authors would like to thank the laboratory of the University of Bergen, in particular Niels Bo Jensen, for carrying out measurements and processing the data with the TCS. Thanks to Eivind Bastesen (NORCE) for field relations fruitful discussions about fieldwork. Giorgia Confalonieri (University of Milano) and Alessandro Pavese (University of Torino) are also warmly thanked for the XRD analyses. The authors are extremely grateful to Jasmin Raymond for the use of the GHP in the Geothermal Open Lab ( at the Institut national de la recherche scientifique of Québec, Canada.

Author contributions

NG collected the samples and took care of the sample preparation for OS (with WHW) and TLS, measurements, and data processing of thermal conductivity with TLS; he also performed P-wave analyses and processed the data. JC prepared the samples, carried out analyses, and processed the data for TDB and GHP; she also took care of XRD processing and density analyses. NG and JC wrote together the original draft paper, finalizing figures and tables. WHW and GM conceptualized the original idea of the study, and together with MV advised on the rigorous experimental analyses and revised the manuscript.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institut national de la recherche scientifiqueCentre Eau Terre EnvironnementQuébecCanada
  2. 2.Dipartimento di Scienze della TerraUniversità di TorinoTorinoItaly
  3. 3.Dipartimento di Scienze della Terra, dell’Ambiente e della VitaUniversità di GenovaGenovaItaly
  4. 4.Energy DepartmentNORCE Norwegian Research CentreBergenNorway

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