Numerical analysis of thermal response tests with a groundwater ﬂow and heat transfer model J. Raymond a, * , R. Therrien a , L. Gosselin b , R. Lefebvre c a Département de géologie et de génie géologique, Université Laval, 1065 avenue de la médecine, Québec (Qc) G1V 0A6, Canada b Département de génie mécanique, Université Laval, 1065 avenue de la médecine, Québec (Qc) G1V 0A6, Canada c Institut national de la recherche scientiﬁque, Centre Eau Terre Environnement, 490 de la Couronne, Québec (Qc) G1K 9A9, Canada article info Article history: Received 30 November 2009 Accepted 25 June 2010 Available online 3 August 2010 Keywords: Geothermal Heat pump Ground heat exchanger Thermal response test Thermal conductivity Waste rock abstract The Kelvin line-source equation, used to analyze thermal response tests, describes conductive heat transfer in a homogeneous medium with a constant temperature at inﬁnite boundaries. The equation is based on assumptions that are valid for most ground-coupled heat pump environments with the exception of geological settings where there is signiﬁcant groundwater ﬂow, heterogeneous distribution of subsurface properties, a high geothermal gradient or signiﬁcant atmospheric temperature variations. To address these speciﬁc cases, an alternative method to analyze thermal response tests was developed. The method consists in estimating parameters by reproducing the output temperature signal recorded during a test with a numerical groundwater ﬂow and heat transfer model. The input temperature signal is speciﬁed at the entrance of the ground heat exchanger, where ﬂow and heat transfer are computed in 2D planes representing piping and whose contributions are added to the 3D porous medium. Results obtained with this method are compared to those of the line-source model for a test performed under standard conditions. A second test conducted in waste rock at the South Dump of the Doyon Mine, where conditions deviate from the line-source assumptions, is analyzed with the numerical model. The numerical model improves the representation of the physical processes involved during a thermal response test compared to the line-source equation, without a signiﬁcant increase in computational time. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction In situ thermal response tests (TRTs) [1], also called borehole thermal conductivity tests, are used in the design of ground-coupled heat pump systems. The tests generally consist in circulating heated water in a closed loop made of a vertical ground heat exchanger and a testing unit. The water temperature is measured at the heat exchanger inlet and outlet, along with water ﬂow rate. Using these data, thermal properties of the subsurface and borehole are calculated with analytical or numerical models [2]. Since it is mathematically simple and generally provides a satisfying ﬁt to observations, the analytical line-source model has been the most popular method to analyze TRTs. The line-source model, which is based on the Kelvin line-source equation [3], solves for radial heat transfer form a linear source embedded in an inﬁnite medium, assuming that:  The surrounding medium is homogeneous and isotropic;  The line source is inﬁnite and has a constant heat ﬂux per unit length;  Heat transfer from the source is radial and purely conductive;  The initial temperature is uniform;  The temperature at an inﬁnite radial distance from the source remains constant. These assumptions may not be always valid for some geological settings. For example, in layered sedimentary rocks, the thermal properties of individual layers can be variable and a homogeneous medium might not adequately represent the thermal properties of the layered system [4]. Heterogeneities of subsurface thermal properties can further inﬂuence heat transfer such that the radial direction assumption is no longer valid. When the permeability of the subsurface is sufﬁciently high, signiﬁcant groundwater ﬂow can lead to advective heat transfer, which is not accounted for in the line-source model [5]. Finally, a strong geothermal gradient or signiﬁcant atmospheric temperature variations during a shallow test can inﬂuence observed temperatures. Our hypothesis is that numerical models could be used as alternatives to analytical solutions to analyze TRTs for cases where * Corresponding author. Tel.: þ1 418 656 2131; fax: þ 1 418 656 7339. E-mail address: jasmin.raymond.1@ulaval.ca (J. Raymond). Contents lists available at ScienceDirect Renewable Energy journal homepage: www.elsevier.com/locate/renene 0960-1481/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.renene.2010.06.044 Renewable Energy 36 (2011) 315e324