# On the use of thermal response tests for deep geothermal exploration in urban areas: A case study made on the Greater Montréal (Canada)

Mafalda Miranda, Madeline Chapelet, Félix-Antoine Comeau, Jasmin

Raymond, J. Christian Dupuis, Philippe Pasquier, Chrystel Dezayes

► To cite this version:

Mafalda Miranda, Madeline Chapelet, Félix-Antoine Comeau, Jasmin Raymond, J. Christian Dupuis, et al.. On the use of thermal response tests for deep geothermal exploration in urban areas: A case study made on the Greater Montréal (Canada). Geothermics, 2026, 134, pp.103523. 10.1016/j.geothermics.2025.103523. hal-05493437

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1 On the use of thermal response tests for deep geothermal exploration in urban areas: A
case study made on the Greater Montreal (Canada)

3 Mafalda M. Miranda¹*, Madeline Chapelet², Félix-Antoine Comeau², Jasmin Raymond², Christian Dupuis³, Philippe Pasquier⁴, Chrystel Dezayes⁵

5 ¹. GRAnalytics Lda. Rua da Alvaneia, 14. 2415-316 Leiria, Portugal. mafalda.a.m.miranda@gmail.com
6 (MMM). Mafalda M. Miranda was formerly working at INRS, to which the study is ascribed.

7 ². INRS-ETE – Institut national de la recherche scientifique, Centre Eau Terre Environnement. 490, rue de la Couronne Québec (QC) G1K 9A9, Canada. felix-antoine.comeau@inrs.ca (FAC),
9 jasmin.raymond@inrs.ca (JR)

10 ³. Département de géologie et de génie géologique, Faculté des sciences et de génie, Université Laval.
11 Pavillon Adrien-Pouliot 1065, avenue de la Médecine, Université Laval Québec (QC) G1V 0A6 Canada.
12 christian.dupuis@ggl.ulaval.ca (CDu)

13 ⁴. Département des génies civil, géologique et des mines, Polytechnique Montréal. 2500, chemin de Polytechnique Montréal (QC) H3T 1J4 Canada. philippe.pasquier@polymtl.ca (PP)

15 ⁵. BRGM – Bureau de recherches géologiques et Minières. 3 avenue Claude Guillemin, BP 36009 45060, Orléans Cedex 2, France. c.dezayes@brgm.fr (CDe)

17 * Corresponding author.

18 Abstract

19 Exploring deep geothermal resources can be challenging in dense urban areas and therefore new tools are needed to de-risk geothermal projects – particularly at the early exploration phase. One potential option is to take advantage of the geothermal heat pump industry and use thermal response tests (TRTs) with initial ground temperature measurements for a first-order assessment of terrestrial heat flux. This does not replace deep geothermal exploration drilling but can help target areas of interest and provide a source of unexploited
24 data. This hypothesis was tested in a study aiming to improve knowledge on deep geothermal resources
25 over the Greater Montreal Area (Canada). TRT datasets were analysed at 22 locations to estimate the
26 terrestrial heat flux. The results were then compared to heat flux estimates made with bottom-hole
27 temperature data and equilibrium temperature profiles from the 6 deep wells available in the area. Both
28 datasets show a certain degree of correlation. To support these findings, a 400 m deep geothermal
29 exploration well was drilled to provide an accurate equilibrium temperature profile in a zone of interest.
30 The data retrieved from this well validated the results and confirmed that, in this setting, TRT can be used
31 as a de-risking tool for deep geothermal exploration.

32 **Keywords:** Bottom-hole temperature, temperature profiling, borehole geophysics, St. Lawrence Lowlands,
33 Canada

34 **1. Introduction**

35 Urban areas located in cold climates, where heating needs account for more than 60% of the energy demand,
36 could benefit from deep geothermal district heating systems as an option to decarbonise energy systems
37 and lessen the need for new electric sources. However, despite the environmental, economic, and social
38 benefits of deep geothermal energy, evaluating the resource potential of urban areas is challenging. High-
39 quality geothermal data in urban centres is commonly limited, with deep wells scattered over vast areas,
40 making assessments uncertain.

41 This limited availability of deep data raises an important question: how to reduce project risk in the early
42 exploration phases before moving onto more complex data acquisition campaigns? In this study, we tested
43 the hypothesis of leveraging data from the geothermal heat pump (GHP) sector to reduce uncertainty about
44 deep geothermal potential.

45 A common practice in the GHP industry is to perform thermal response tests (TRTs). Such tests are used to
46 evaluate the effective ground thermal conductivity over the borehole heat exchanger (BHE) length (Spitler
47 and Gehlin, 2015). This helps the industry to properly design GHP systems, avoiding misconceptions.
A less common application of TRT is to combine the thermal conductivity data with a temperature profile measured before the TRT to infer the terrestrial heat flux (Marquez et al., 2019). Terrestrial heat flux can be solved as a 1D inversion heat conduction problem combining in situ thermal conductivity data with equilibrium temperature profiling and ground surface temperature history. Application of TRTs in this context could be used to inform on deep geothermal resources of urban areas where deep boreholes are sparse but TRTs are common and, in this way, fill important data gaps at early stages of deep geothermal projects.

Therefore, the research question we aim to answer in this study is: Can TRTs be used as an alternative tool to perform a first-order screening of the deep geothermal potential of urban areas before advancing to more complex data acquisition campaigns?

To answer this question, we examined data from different sources such as TRT, bottom-hole temperature (BHT) measured in oil and gas exploration wells, and deep equilibrium temperature profiles measured in geothermal exploration boreholes to investigate the usefulness of TRT data and indicate zones of interest for further deep geothermal exploration. The objective is to evaluate if TRT could be used as a tool to provide a high-level, first-order assessment of the deep geothermal potential of urban areas with important heating energy demands and where deep wells are lacking because exploratory drilling is challenging. Such hypothesis has, to the best of our knowledge, never been verify with regional datasets, highlighting the novelty of the proposed approach to deep geothermal exploration in dense urban areas.

## 1.1. Study site and available data

This study was undertaken in the metropolitan area of Montreal, located in the province of Québec, Canada (Figure 1). This area encompasses what can be considered as the Greater Montreal, including nearby municipalities on the North and South shores of the St. Lawrence River. This area was chosen to carry out this proof-of-concept study since there are 2 oil and gas wells with BHT data, 4 deep wells with equilibrium temperature profiles, 22 TRTs with equilibrium and continuous temperature measurements and 1
geothermal exploration well (LP#1) drilled specifically within the scope of this work to provide an
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equilibrium temperature profile in a zone of interest (Figure 1).
73

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Simplified geological map of the St. Lawrence Lowlands in the province of Quebec and location of the bottom-hole temperature (BHT), deep equilibrium temperature profiles (Eq. T), thermal response test (TRT) and geothermal exploration well (LP#1) data used in this work.</figcaption></figure>

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In terms of geology, the study area is located within the St. Lawrence Lowlands sedimentary basin (Figure 1). This sedimentary basin occupies a land surface area of roughly 20,000 km² and is bounded to the northwest by the Precambrian rocks of the Grenville Province and to the southeast by the Cambro-Ordovician rocks of the Appalachians (Figure 1). The rocks of the St. Lawrence Lowlands lie unconformably on top of the Grenville, while the Appalachians overlie the basin through a large thrust fault called the Logan Line (Figure 1).
Eight thermostratigraphic units were defined within the St. Lawrence Lowlands sedimentary basin (Bédard et al., 2018). The upper caprock unit is composed by rocks of Queenston, Lorraine and Sainte-Rosalie groups, consisting mainly of siltstones, sandstones and shales. These groups lie on top of Utica Shale. Due to their low thermal and hydraulic conductivity values, this upper caprock and Utica Shale are potential thermal blankets and barriers to the terrestrial heat flux (Bédard et al., 2018). The carbonate rocks of the Trenton, Black River and Chazy groups are grouped together in a unit called Tr-BR-Ch. The Beekmantown and Potsdam groups are divided into two units according to their constituent formations: Beauharnois and Theresa for the former, Cairnside and Covey Hill for the latter. The Tr-BR-Ch, Beekmantown and Potsdam groups are mainly composed of limestone, dolomitic rock and sandstone, whose permeability is higher than that of cap rocks (Lavoie, 2009; Tran Ngoc et al., 2014). Given their lithological nature, rocks in the Tr-BR-Ch, Beekmantown and Potsdam groups are therefore considered to be potential reservoir units (Dietrich et al., 2011; Konstantinovskaya et al., 2014; Tran Ngoc et al., 2014; Bédard et al., 2018). Indeed, the dolomitic units of the Beekmantown Group acted as reservoirs for liquid hydrocarbons and natural gas during their burial (Chi et al., 2000), and a gas deposit was exploited in this unit from 1980 to 1994. Furthermore, the low hydraulic conductivity of the Potsdam Group and Grenvillian basement makes these deep rocks potential targets for stimulated geothermal systems (Gauchat, 2017).

## 1.2. Previous work and rationale for geothermal exploration in the St. Lawrence Lowlands

The St. Lawrence Lowlands sedimentary basin has been the target of several studies to understand its deep geothermal potential. Majorowicz and Minea (2012) outlined that there are areas within the St. Lawrence Lowlands and the adjacent Appalachians with significant potential for the development of enhanced geothermal systems (EGS) to generate electricity and produce heat. These authors indicated that temperatures above 120 °C may be found at a depth over 4.5 km in the Trois-Rivières area (Figure 1 for location), around 4.5 km near Rimouski and in the Gaspé Peninsula and around 4 km south of Québec City (Figure 1 for location). Furthermore, Bédard et al. (2018) analysed BHT data from oil and gas wells located within the St. Lawrence Lowlands and suggested the potential existence of three positive geothermal
anomalies where the heat flux is estimated to be greater than the sedimentary basin average. One of those
potential positive geothermal anomalies is located in the south shore of Montréal. However, Saull et al.
(1962) analysed 4 deep wells (> 1 km deep) with equilibrium temperature profiles around the Montreal area
(defined as Eq. T in Figure 1) and estimated geothermal gradients ranging between 6 and 27 °C km⁻¹ and
heat flux ranging between 31 to 34 mW m⁻², which are typical values for this sedimentary basin.

Given these different estimates, and in order to fill the knowledge gap between the scattered data available
in the Montreal region, TRT data were used in this study, albeit at different depths, to obtain information
on the deep geothermal potential of the Montreal metropolitan area. A total of 22 TRTs are available and
were analysed in the Greater Montreal area including the North and South shores (Figure 1). Although the
data are derived from wells that were drilled to a total vertical depth of 500 m or less, their value is attributed
to the fact that they provide an unprecedented access to ground thermal conductivity and equilibrium
temperature profiles in an urban area that has a dense population and high heating energy demands.

However, assessing the deep geothermal potential of a site on the basis of TRT data alone is not
recommended because it implies important assumptions. For this reason, a geothermal exploration well
(LP#1; Figure 1) was drilled in the area of interest to validate the TRT-based estimates.

1.3. Overall objective and novelty of the study

With this study, we wish to demonstrate for the first time how useful TRT data is for a high-level first-order
screening of deep geothermal resources in densely populated urban environments. This proof-of-concept
study shows that the three different data sources used in this work present a good degree of correlation. The
proposed methodology can easily be used in other urban centres where TRT data are available and deep
geothermal resources have the potential to transform the urban energy system. Furthermore, in this work, a
novel approach to estimate heat flux from continuous temperature profiles is put forward. The method
developed estimates heat flux as a 1D inversion heat conduction problem using a solver algorithm to
minimise the sum of least squares between measured and simulated temperature profiles. A third novelty is
the use of the quality assessment protocol developed by the International Heat Flow Commission to evaluate
the estimates obtained by each dataset. This helps assess the reliability of the estimates. Finally, the fourth
novelty is the development of a high-resolution heat flux map for the Greater Montreal Area which can help
de-risking further deep geothermal studies.

## 2. Data description

As illustrated in Figure 1 2 oil and gas wells with bottom-hole temperature (BHT) data, 4 deep wells with
equilibrium temperature profiles, 22 TRTs with equilibrium and continuous temperature measurements and
1 geothermal exploration well (LP#1) drilled specifically within the scope of this work are available in the
study area. These different datasets are key to test the hypothesis of using TRT data as a tool to de-risk deep
geothermal exploration in dense urban areas. The following subsections provide a description of the
different datasets used in this work.

### 2.1. BHT data

The well A157 (Figure 1 for location) is a former oil and gas well located in the town of Brossard. Previous
analysis of BHT measurements in this well suggest an anomalous temperature compared to the others BHT
measurements within the St. Lawrence Lowlands (SNC Inc., 1979; Lefebvre and Trempe, 1980; Bédard et
al., 2016). The well A157 was drilled in 1971, has a true vertical depth of 1449.02 m, and revealed a BHT
of 56.67 °C. This anomalous BHT data point led to the hypothesis that a positive geothermal anomaly may
be present in the area (Bédard et al., 2016). Brossard has a population of 91,525 (Statistics Canada, 2021)
and a temperature of 56 °C at 1400 m depth suggests significant potential for deep geothermal district
heating systems that could be envisioned in this region to offset power consumed for space heating during
the winter season.

Another oil and gas well used in this study is the A263 (Figure 1 for location) that was drilled in 2008 and
is located approximately 15 km southeast of Brossard, in St-Jean-sur-Richelieu. The A263 well reveals a
156 BHT of 20 °C at 413.98 m (Bédard et al., 2016). This well also supports the potential existence of sufficient
157 temperatures for deep geothermal production in the area.

158 These two data points were the target of a detail analysis in this study to estimate a statistical value for the
159 heat flux, which is a new contribution that builds on previous studies (e.g., Bédard et al., 2016). This detail
160 analysis consisted in correcting the BHT data for drilling and paleoclimate disturbances, and in using Monte
161 Carlo-based sensitivity analysis to estimate a range of possible heat flux values. This will be further
162 explained in the Methodology section.

163 **2.2. Deep wells with equilibrium temperature profiles**

164 Saull et al. (1962) analysed 4 deep oil and gas wells with equilibrium temperature profiles in Valleyfield
165 (A001 - Montreal #1, Figure 1), St. Hyacinthe (A112 - St. Rosalie #2, Figure 1), and Lanoraie (A031 -
166 Cartier #5 and A068 - Lounan #1, Figure 1). The A001 well was drilled in 1955 and has a depth of 537 m.
167 The A112 well was drilled in 1956 and has a depth of 823 m. The A031 well was drilled in 1935 and has a
168 depth of 762 m and the A068 well was drilled in 1956 and has a depth of 411 m. Saull et al. (1962) carried
169 out thermal conductivity analyses on core samples retrieved from these wells and estimated the geothermal
170 gradient considering the measured equilibrium temperature profiles. Then, these authors estimated the heat
171 flux for each well, from 31 to 34 mW m⁻². It is important to outline that, despite the fact that the temperature
172 profiles analysed by Saull et al. (1962) show an inversion of the thermal gradient typical of regions affected
173 by paleoclimate history, these authors did not perform any paleoclimate correction to the temperature
174 profiles. However, these authors also highlight that correcting the geothermal gradient for these
175 paleoclimate disturbances of subsurface temperature would lead to an increase of the geothermal gradient
176 values estimated. No further analysis was carried out for these wells within the scope of this study, and the
177 values obtained by Saull et al. (1962) were used for comparison with the remaining datasets.

178 **2.3. TRT data**
Measurements of equilibrium temperature are sometimes performed before carrying out a TRT. In the study area, there are 22 TRT sites with equilibrium temperature profiles that could be analysed to estimate heat flux. TRT data were acquired from various companies, ministries and research organisations that agreed to share their data (Raymond et al., 2019). This includes the temperature profiles and thermal conductivity values used in this work and associated to TRT (Figure 2).
<figure><img src="image_3.png" /><figcaption>Figure 2. TRT temperature profiles with thermal conductivity information. TC – thermal conductivity.</figcaption></figure>

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<figure><img src="image_6.png" /></figure>

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<figure><img src="image_12.png" /><figcaption>187 **Figure 2 (cont.)**. TRT temperature profiles with thermal conductivity information. TC – thermal conductivity.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Figure 2 (cont.)**. TRT temperature profiles with thermal conductivity information. TC – thermal conductivity.</figcaption></figure>

As these temperature profiles are considered in equilibrium, drilling corrections were not performed, but corrections such as measured depth and paleoclimate were applied to the profiles. The measured depth correction is typically applied when the temperature profile is measured inside the U-tube pipe of the borehole heat exchanger and the paleoclimate correction is justified by the gradient inversion observed that is believed to be caused by temperature variations that propagate at depth from the surface. Corrections for groundwater flow also were not performed since the temperature profiles show a linear increase of temperature with depth typical of conductive environments. Further details of these corrections are provided
197 in the Methodology section together with the improved methodology to estimate heat flux that was put
198 forward in the scope of this study.

199 **2.4. Geothermal exploration well (LP#1)**

200 As previously mentioned, LP#1 was drilled with the goal of, on one hand, providing further
201 insights into the deep geothermal potential of an area of interest and, on the other hand, validating
202 the TRT-based heat flux estimates.

203 LP#1 is a vertical slim hole well with 400 m depth and was drilled in 2022. Temperature profiling
204 with an RBR duet probe (Figure 3) and geophysical borehole logging (Figure 4) were performed
205 in this well to further characterise the subsurface.

<figure><img src="image_14.png" /><figcaption>207 **Figure 3.** Continuous temperature profiles measured in LP#1 with an RBR duet probe.</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>**Figure 4.** Mount Sopris logs acquired in LP#1 and geological interpretation of the well.</figcaption></figure>

Further details on the temperature probes are given in the Methodology section. Representative core samples from the different lithologies encountered were collected and analysed in the laboratory to determine their thermal conductivity. Furthermore, thermal conductivity was also estimated based on the natural gamma-ray well log and empirical equations. Information on the geothermal gradient and thermal conductivity made it possible to estimate heat flux, and the methodology used at all steps is explained with details in the Methodology section.

**3. Methodology**

Our workflow is illustrated in Figure 5. First, the different datasets are analysed separately and corrections to the temperature data are made to determine the undisturbed geothermal gradient. Then, for BHT data and LP#1 data, thermal conductivity and radiogenic heat production is estimated based on the methods described in subsection 3.3. For each dataset, the undisturbed geothermal gradient and thermal properties information is used to estimate heat flux according to the methods described in subsection 3.4. Then, a quality assessment protocol is applied according to what is described in section 3.5, and finally, a surface heat flux map is produced.
<figure><img src="image_16.png" /><figcaption>**Figure 5.** Workflow with information of the sections describing the data (Section 2), the methodology and results (Section 3 & 4), and the spatial distribution of the heat flux values estimated and implications for deep geothermal developments (Section 5).</figcaption></figure>

**3.1. Temperature profiling and geophysical borehole logging**

Three temperature profiles were measured in the LP#1 well at different times and using two different temperature probes (Figure 3 and 4). One profile was acquired one day after drilling with an RBR probe, another about 2 weeks after drilling with a Mount Sopris fluid column temperature instrument, and a last profile about 7 months after drilling with an RBR probe.

The RBR probe is a submersible temperature and pressure data logger with an accuracy of ± 0.002 °C and < 0.25 m and a resolution of < 0.00005°C and < 0.005 m, respectively. The probe was inserted in the well about 20 min before beginning of the recording to ensure the thermal equilibrium between the probe and the groundwater in the well. The temperature was recorded in a continuous temperature logging pace of 1 m per 10 seconds.
The Mount Sopris fluid column temperature log measures the temperature of the fluid near the sensor with a temperature accuracy less than 1% and a temperature resolution of 0.004 °C. The temperature was recorded in a continuous temperature logging pace, acquiring temperature measurements at every 0.05 m. Other Mount Sopris logs acquired in the scope of this work for a full characterisation of LP#1 well were resistivity, natural gamma, caliper and fluid column conductivity (Figure 4).

## 3.2. Corrections applied to temperature data

### 3.2.1. Drilling disturbance correction for BHTs

Drilling operations disrupt the thermal equilibrium of the surrounding rock with temporarily cooling (Jessop, 1990). Temperature measurements carried out during logging are generally taken shortly after drilling is completed, which leaves no time for the surrounding rock to return to its equilibrium temperature. Thus, BHT measurements often underestimate the subsurface temperature (Harrison et al., 1983; Jessop, 1990). In order to estimate the undisturbed subsurface temperature, a temperature correction needs to be applied, and several empirical temperature correction methods are available. In this work, the Harrison correction was preferred for the BHT of the well A157 while the Waples and Ramly correction was used for the BHT of the well A263. This was due to the shallow depth of the A263 well.

The Harrison correction is an empirical method used for depths between 600 and 3932 metres. It relates measured depth to temperature according to the following equation (Harrison et al., 1983):

$$T_c = T_{BHT} + (-16.51 + (1.827 \times 10^{-2}z) - (2.345 \times 10^{-6}z^2)) \quad (1)$$

where $T_c$ (°C) is the corrected temperature, $T_{BHT}$ (°C) is the bottom-hole temperature and $z$ (m) is depth.

The correction of Waples and Ramly (2001) is an empirical method that takes into account the time elapsed between the end of drilling operations and the time of temperature measurement:

$$T_c = T_0 + \left( \frac{-0.1462 \times \ln(t_f) + 1.699}{0.572 \times z^{0.075}} \right) (T_{BHT} - T_0) \quad (2)$$

where $T_0$ (°C) is the undisturbed surface temperature and $t_f$ (h) is the time after the end of drilling.
### 3.2.2. Measured depth correction for temperature profiles in borehole heat exchangers

Different methods were used to measure temperature profiles in the closed U-pipe borehole heat exchangers prior to TRTs, including a wired probe and a fixed fibre-optic cable connected to a distributed temperature sensing unit. When a wired temperature probe is lowered in the U-tube pipe to measure the temperature profile, the water level rises. This rise in water level can affect the evaluation of temperature as a function of depth and thus affect geothermal gradient estimates. The real depth can be estimated by subtracting the rise in the water column caused by the probe and its cable from the measured depth (Raymond et al., 2016). This correction was applied to each depth measured in the temperature profiles obtained during TRT according to the following equation (e.g., Raymond et al., 2016; Pambou et al., 2019):

$$z = z_m - \left( \frac{V_{probe} + V_{cable}(z_m)}{2\pi r_{pipe}^2} \right) \quad (3)$$

where $V$ (m³) is volume and $r$ (m) is the internal radius of the pipe. The subscript m stands for measured. The volume of the probe is 8.06×10⁻⁵ m² and the volume of the cable is variable. The internal radius of the pipe is 1.71×10⁻² m (high density polyethylene 1¹/₄ inch nominal diameter, surface dimension ratio 11).

### 3.2.3. Paleoclimate correction applied to all data sets

Temperature profiles are often disturbed by surface temperature variations, such as ice ages and current global warming. These temperature changes propagate in the subsurface over time, altering the subsurface temperature. In order to avoid misestimating temperatures at depth after gradient extrapolation, it is necessary to correct the measured gradient to obtain an equilibrium geothermal gradient.

The equilibrium geothermal gradient is calculated by applying a correction to the measured temperature data points. This paleoclimate correction removes the overall cumulative effect of the various past and present climate events (Birch, 1948; Jessop, 1990). The paleoclimate correction is calculated using the following equation (Birch, 1948; Jessop, 1990):
$$282 \qquad \Delta T = \sum_i T_v \times \left[ erf\left(\frac{z}{\sqrt{4\alpha t_{i1}}}\right) - erf\left(\frac{z}{\sqrt{4\alpha t_{i2}}}\right) \right] \qquad (4)$$

where $\Delta T$ (°C) is the temperature correction to be applied to the measured temperature, $T_v$ (°C) is the average temperature variation between the climate event and today's baseline, $erf(-)$ is the error function, $\alpha$ (m² s⁻¹) is the thermal diffusivity, and $t_{i1}$ and $t_{i2}$ (s) are the end and beginning of the climate event. A thermal diffusivity value for each TRT was determined considering the thermal conductivity evaluated from TRT and literature-based volumetric heat capacity.

The past paleoclimate events that had a significant impact on southern Québec and were considered in this study are the last four ice ages, the Holocene Climatic Optimum, the Roman and Medieval warming periods, and the Little Ice Age (Table 1). Beyond affected by paleoclimate events, the shallow subsurface is also affected by more recent temperature changes, such as global warming. Therefore, temperature data were also corrected for the effect of this recent climate event. A compilation of mean annual surface temperature variations was made for each TRT site based on historical weather station data available. The average temperature measured between 1920 and 1940 was used as the reference temperature (5.40 °C), this period being considered as the period before global warming. Recent global warming (1940 to 2019) has been subdivided into different stages of several decades according to their average temperature increase relative to the reference temperature (Table 1).

<table><caption>**Table 1.** Paleoclimate events considered for Québec's region (Chapelet, 2022).</caption><thead><tr><th>Climate event</th><th>Temperature step (T<sub>v</sub>) (°C)</th><th>Time period (years B.P.)</th></tr></thead><tbody><tr><td>Nebraskan Glaciation</td><td>-5</td><td>300,000 – 265,000</td></tr><tr><td>Kansian Glaciation</td><td>-5</td><td>200,000 – 175,000</td></tr><tr><td>Illinoian Glaciation</td><td>-5</td><td>125,000 – 100,000</td></tr><tr><td>Wisconsin Glaciation</td><td>-5</td><td>65,000 – 12,000</td></tr><tr><td>Holocene Climatic Optimum (or, Holocene Thermal Maximum)</td><td>+2</td><td>7,000 – 5,800</td></tr><tr><td>Roman and Medieval warming periods</td><td>+1</td><td>3,200 – 1,000</td></tr><tr><td>Little Ice Age</td><td>-1</td><td>500 – 270</td></tr><tr><td>1942-1972</td><td>+0.99</td><td>80 – 50</td></tr><tr><td>1973-1995</td><td>+0.72</td><td>49 – 27</td></tr><tr><td>1996-2019</td><td>+1.88</td><td>26 – 3</td></tr></tbody></table>

B.P. – before present
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**3.3. Thermal properties characterization**

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As a reminder, this study is based on three data sources (BHT, TRT and a geothermal exploration well) that were compared with each other and with four equilibrium temperature profiles from the literature. The thermal properties of BHT and geothermal exploration well were therefore characterised by different methodologies, which are described in the following subsections. The equilibrium temperature profiles were analysed by Saull et al. (1962) and the thermal properties values obtained by these authors were used in this work. TRT results were acquired from various companies, ministries and research organisations that agreed to share their data (Raymond et al., 2019) and the thermal conductivity values reported were used in this work.

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**3.3.1. For BHTs**

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Average thermal conductivity for each of the geological units in the St. Lawrence Lowlands Basin was determined by Raymond et al. (2019) who compiled all available data sources. The thermal conductivity values from the 79 TRTs carried out in the basin were considered to be fairly representative of in situ conditions. However, the thermal conductivity data inferred from geophysical logs are more numerous, with 498 data intervals for 72 wells (Nasr et al., 2018; Raymond et al., 2019). For this study, it was therefore decided to consider these two sources of data and the average thermal conductivity from the logs was added to the average thermal conductivity determined by TRT to establish probability functions to geological units. This provided a meaningful distribution of values that can be used to estimate the thermal conductivity of rock units intercepted by wells in which BHT was measured (Table 2).

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322
<table><caption>**Table 2.** Probability distribution functions for thermal conductivity and internal heat generation (Chapelet, 2022).</caption><thead><tr><th rowspan="2">Geological unit</th><th colspan="3">Thermal conductivity (W m<sup>-1</sup> K<sup>-1</sup>)</th><th rowspan="2">Statistical distribution</th><th colspan="3">Internal heat generation (&mu;W m<sup>-3</sup>)</th><th rowspan="2">Statistical distribution</th></tr><tr><th>&mu;</th><th>&sigma;</th><th>n</th><th>&mu;</th><th>&sigma;</th><th>n</th></tr></thead><tbody><tr><td>Appalaches</td><td>2.67</td><td>0.90</td><td>13</td><td>Extreme value</td><td>1.61</td><td>0.24</td><td>196</td><td>Logistic</td></tr><tr><td>Caprock</td><td>2.35</td><td>0.54</td><td>250</td><td>Loglogistic</td><td>1.61</td><td>0.24</td><td>196</td><td>Logistic</td></tr><tr><td>Utica</td><td>2.42</td><td>0.38</td><td>77</td><td>Logistic</td><td>0.93</td><td>0.36</td><td>40</td><td>Weibull</td></tr><tr><td>Tr-BR-Ch</td><td>2.64</td><td>0.51</td><td>80</td><td>Weibull</td><td>0.39</td><td>0.20</td><td>36</td><td>Lognormal</td></tr><tr><td>Beauharnois</td><td>4.24</td><td>0.47</td><td>24</td><td>Laplace</td><td>0.70</td><td>0.14</td><td>19</td><td>Normal</td></tr><tr><td>Theresa</td><td>3.62</td><td>0.54</td><td>16</td><td>Laplace</td><td>0.91</td><td>0.17</td><td>9</td><td>Extreme values</td></tr><tr><td>Cairnside</td><td>5.02</td><td>0.50</td><td>23</td><td>Extreme value</td><td>0.22</td><td>0.13</td><td>11</td><td>Exponential</td></tr><tr><td>Covey Hill</td><td>3.41</td><td>0.70</td><td>27</td><td>Extreme value</td><td>0.75</td><td>0.18</td><td>11</td><td>Inverse Gaussian</td></tr></tbody></table>

324

$\mu$ – average, $\sigma$ – standard deviation, $n$ – number of samples.

325

326

327

328

The rock internal heat generation, which was needed to calculate heat flux, was obtained from natural gamma-ray logging data of oil and gas wells in the St. Lawrence Lowlands Basin (Table 2). The density and specific heat capacity values for the geological units in the St. Lawrence Lowlands Basin come from the work of Tran Ngoc et al. (2014) and Nasr (2016), respectively.

329

330

The probability distributions were defined on the basis of the available data and using the @RISK software's built-in distribution fitting function. @RISK is a commercial software for Monte Carlo and risk analysis.

331

332

333

The role of this function is to identify the distribution best suited to the available data. These thermal conductivity and heat generation distributions were used to estimate the statistical distribution of heat flux values of wells A157 and A263.

334

### 3.3.2. For geothermal exploration well LP#1

335

336

Thermal conductivity ($\lambda$; W m$^{-1}$ K$^{-1}$) of the LP#1 well was calculated based on the natural gamma-ray log recording and the empirical equations proposed by Fuchs and Föster (2014):

337

$$ \lambda = 5.281 - 2.961\phi - 2.797V_{\text{shale}} \quad (5) $$

338

$$ \lambda = 5.058 - 0.1\rho - 2.915V_{\text{shale}} \quad (6) $$
where φ (-) is porosity, ρ (kg m⁻³) is density and V<sub>shale</sub> (-) is the volume of shale. Eq. (5) was used to estimate the thermal conductivity of the caprock and Utica Shale geological units and Eq. (6) to estimate the thermal conductivity of the Tr-BR-Ch group.

Porosity and density were taken from literature. Caprock has a porosity ranging between 3.9-5.0%, Utica between 4.0-7.0%, and Tr-BR-Ch between 1.4-9.0% (Bedard et al., 2018). The average values were used. In terms of density, caprock was assumed 2700 kg m⁻³, Utica 2450 kg m⁻³ and Tr-BR-Ch 2700 kg m⁻³ (Bedard et al., 2018).

The volume of shale was estimated based on the Linear GR Index:

$$V_{\text{shale}} = I_{\text{GR}} = \frac{GR_{\text{log}} - GR_{\text{min (clean sand/carbonate)}}}{GR_{\text{max (shale)}} - GR_{\text{min (clean sand/carbonate)}}} \quad (7)$$

where GR (API) is the value from the natural gamma-ray log.

Additionally, thirteen core pieces representative of the main lithologies intercepted by the well were analysed with an optical scanner to calibrate thermal conductivity estimated on the basis of the natural gamma-ray log and the empirical equations. Of these 13 core pieces, 6 belong to the Tr-BR-Ch group and 7 to the Utica Shale formation. The optical scanning technique was developed by Popov and is a transient method widely used to evaluate the thermal conductivity of geological materials using a laser as a heat source (Popov et al., 2016).

Internal heat generation (A; W m⁻³) was estimated as (Bucker and Rybach, 1996):

$$A = 0.0158(GR - 0.8) \quad (8)$$
361 **3.4. Surface heat flux**

362 **3.4.1.For BHTs**

363 The geothermal gradient is the variable used to evaluate heat flux and temperatures at depth and corresponds
to the variation in temperature with depth in the subsurface. Although this variation is not a linear
364
365 phenomenon, it can still be approximated by the following equation for BHT data:

$$
366 \quad \left[ \frac{\Delta T}{\Delta z} \right] = \frac{T_{\text{BHT,c}} - T_0}{z} \qquad (9)
$$

367 where $\left[\frac{\Delta T}{\Delta z}\right]$ (°C m⁻¹) is the geothermal gradient and $T_{\text{BHT,c}}$ (°C) is the corrected BHT for drilling and
368 paleoclimate disturbances. The temperature value $T_0$ (°C) is the undisturbed subsurface temperature ($T_g$; K),
369 which is calculated as (Ouzzane et al., 2015):

$$
370 \quad T_g = 17.898 + 0.951 T_s \tag{10}
$$

371 where T_s (K) is the mean annual ambient air temperature, which was estimated based on climate normal
372 using weather date of the past 15 years (Chapelet, 2022). For the study area, T_s is 7.28 °C and T_g takes the
373 value 11.44 °C.

374 Surface heat flux is then calculated using the following relationship (e.g., Jessop, 1990):

$$
375 \quad Q_0 = \left( \lambda_e \times \frac{\Delta T}{\Delta z} \right) + \left( \frac{A_e \times z}{2} \right) \qquad (11)
$$

376 where $Q_0$ (W m⁻²) is the surface heat flux and the subscript e stands for effective.

377 Surface heat flux from BHT data was estimated using Monte Carlo simulations with @RISK software and
378 the distributions of values assigned to the effective thermal conductivity and internal heat generation
379 (Table 2).

380
381
### 3.4.2. For TRTs and geothermal exploration well LP#1

Terrestrial heat flux estimated based on TRT data and from LP#1 used a different approach because a continuous temperature profile was available. Heat flux was solved as a 1D inverse heat conduction problem to decrease the uncertainty and improve quality.

A generalised reduced gradient (GRG) nonlinear solving method was selected to find the optimal heat flux by minimisation of the sum of the squared residuals:

$$388 \qquad \begin{cases} \min_{Q} RSS(Q) \\ lb_{Q} \le Q \le ub_{Q} \end{cases} \qquad (13)$$

where $lb$ and $ub$ are the lower and upper bound of the heat flux, and

$$390 \qquad RSS = \sum (T_{\text{measured}} - T_{\text{model}})^2 \qquad (14)$$

where RSS (-) is the residual sum of squares.

The simulated temperature profile is given by:

$$393 \qquad T(z, t) = T_0 + \frac{Q}{\lambda}z - \frac{A}{2\lambda}z^2 + T_t(z) \qquad (15)$$

where

$$395 \qquad T_t(z) = \sum_i (T_v) \times \left( erf\left(\frac{z}{\sqrt{4\alpha t_{i1}}}\right) - erf\left(\frac{z}{\sqrt{4\alpha t_{i2}}}\right) \right) \qquad (16)$$

The heat flux inversion approach considered the internal heat generation estimated based on the natural gamma-ray log and calibrated thermal conductivity estimated based on the Linear GR Index model and laboratory analyses. TRT-based estimates neglected the internal heat generation.

## 3.5. Quality assessment of heat flux estimates

An evaluation of the methodological quality of the heat flux estimates was carried out according to the quality assurance protocol developed by the International Heat flux Commission (Table 3; Fuchs et al.,
2023). For each input parameter, i.e., temperature gradient and thermal conductivity, an individual score is determined. This score reflects the accuracy of the temperature gradient and thermal conductivity determination, and the product of the temperature gradient and thermal conductivity scores ranks the quality of the heat flux estimation.

<table><caption>**Table 3.** Definition of the methodological classes and respective ranking descriptions (Fuchs et al., 2023).</caption><thead><tr><td>Quality score</td><td>Ranking description</td></tr></thead><tbody><tr><td>1 – 0.75</td><td>Excellent</td></tr><tr><td>0.75 – 0.50</td><td>Good</td></tr><tr><td>0.50 – 0.25</td><td>Ok</td></tr><tr><td>0.25 – 0</td><td>Poor</td></tr></tbody></table>

Temperature gradient individual scoring includes three evaluation criteria depending on the measurement type (continuous log, multiple temperature points or BHT). Each type is also differentiated into equilibrium/corrected or perturbed measurements (Table 4).

<table><caption>**Table 4.** Methodological evaluation scheme for temperature gradient determination (Fuchs et al., 2023).</caption><thead><tr><th>Measurement type</th><th></th><th>Penalty</th></tr></thead><tbody><tr><td rowspan="2">Continuous temperature log</td><td>Equilibrium/corrected</td><td>+0.1</td></tr><tr><td>Perturbed</td><td>-0.1</td></tr><tr><td rowspan="3">Multiple single temperature point</td><td>Equilibrium/corrected</td><td>-0.1</td></tr><tr><td>Perturbed</td><td>-0.3</td></tr><tr><td>Estimated</td><td>-0.5</td></tr><tr><td rowspan="3">BHT + surface temperature</td><td>Equilibrium/corrected</td><td>-0.3</td></tr><tr><td>Perturbed</td><td>-0.5</td></tr><tr><td>Estimated</td><td>-0.6</td></tr></tbody></table>

Thermal conductivity individual scoring is more complex and depends on the location, source type, number of measurement points, saturation, and pressure and temperature conditions (Table 5). The location score reflects where the thermal conductivity data was obtained, i.e., from actual heat flux location, from nearby or other location, or from literature. The source type score is related with the measurement type, i.e., in situ probe, core-log integration, core measurements, cutting measurements, outcrop measurements, log interpretation, mineral calculation or lithology/textbook.
<table><caption>**Table 5.** Methodological evaluation scheme for thermal conductivity determination (modified from Fuchs et al., 2023).</caption><thead><tr><th>Thermal conductivity</th><th>Penalty</th></tr></thead><tbody><tr><td><strong>Location</strong></td><td></td></tr><tr><td>Thermal conductivity data from actual heat flux location</td><td>0</td></tr><tr><td>Thermal conductivity data from nearby or other location</td><td>-0.1</td></tr><tr><td>Thermal conductivity assumed from literature</td><td>-0.2</td></tr><tr><td><strong>Source type</strong></td><td></td></tr><tr><td>In situ probe</td><td>+0.1</td></tr><tr><td>Core-log integration</td><td>+0.1</td></tr><tr><td>Core measurements</td><td>0</td></tr><tr><td>Cutting measurements</td><td>-0.1</td></tr><tr><td>Outcrop measurements</td><td>-0.1</td></tr><tr><td>Log interpretation</td><td>-0.1</td></tr><tr><td>Mineral calculation (mixing model)</td><td>-0.2</td></tr><tr><td>Lithology/Textbook</td><td>-0.2</td></tr><tr><td><strong>Number of conductivity points</strong></td><td></td></tr><tr><td>&gt; 15</td><td>0</td></tr><tr><td>1 – 15</td><td>-0.1</td></tr><tr><td><strong>Saturation status</strong></td><td></td></tr><tr><td>Saturated measured</td><td>0</td></tr><tr><td>Calculated or recovered</td><td>-0.1</td></tr><tr><td>Dry measured</td><td>-0.2</td></tr><tr><td><strong>Pressure-temperature conditions</strong></td><td></td></tr><tr><td>In situ</td><td>0</td></tr><tr><td>Replicated in situ</td><td>-0.1</td></tr><tr><td>Ambient conditions</td><td>-0.2</td></tr></tbody></table>

# 4. Results

## 4.1. Heat flux estimates from BHT data

BHT measured in the well A157 and in the well A263 were corrected for drilling and paleoclimate disturbances (Table 6). The corrected temperature for the well A157 is 63.69 °C and for the well A263 is 24.40 °C. Application of drilling and paleoclimate correction led to a temperature increase of 11% for the well A157 and 18% for the well A263. The average effective thermal conductivity estimated from the lithologies for well A157 and A263 are 3.1 W m⁻¹ K⁻¹ and 2.3 W m⁻¹ K⁻¹, respectively (Table 6). The average effective internal heat generation was evaluated to be 0.77 µW m⁻³ for well A157 and 1.44 µW m⁻³ for well A263 (Table 6). These results and the undisturbed ground surface temperature estimated based on Ouzanne et al. (2015) empirical equation (i.e., 11.44 °C) resulted in an average geothermal gradient and surface heat flux of 35 °C km⁻¹ and 109 mW m⁻² for well A157 (Table 3). The well A263, in turn, reveals an average geothermal gradient of 31 °C km⁻¹ and an average surface heat flux of 73 mW m⁻² (Table 6).
Table 6. BHT data corrected for drilling and paleoclimate effects, effective thermal conductivity and internal heat generation and geothermal gradient and surface heat flux.

<table><thead><tr><th rowspan="2">Parameters</th><th rowspan="2"></th><th colspan="2">Well</th></tr><tr><th>A157</th><th>A263</th></tr></thead><tbody><tr><td>TVD (m)</td><td></td><td>1445.7</td><td>414.0</td></tr><tr><td>Measured temperature (°C)</td><td></td><td>56.67</td><td>20.00</td></tr><tr><td rowspan="2">Corrected temperature (°C)</td><td>Drilling</td><td>61.67</td><td>23.35</td></tr><tr><td>Paleoclimate</td><td>63.96</td><td>24.40</td></tr><tr><td rowspan="5">Effective thermal conductivity (W m<sup>-1</sup> K<sup>-1</sup>)</td><td>Average</td><td>3.09</td><td>2.34</td></tr><tr><td>5<sup>th</sup> percentile</td><td>2.58</td><td>1.84</td></tr><tr><td>95<sup>th</sup> percentile</td><td>3.44</td><td>3.04</td></tr><tr><td>Mode</td><td>3.21</td><td>2.20</td></tr><tr><td>Median</td><td>3.13</td><td>2.27</td></tr><tr><td rowspan="5">Effective internal heat generation (μW m<sup>-3</sup>)</td><td>Standard deviation</td><td>0.27</td><td>0.40</td></tr><tr><td>Average</td><td>0.77</td><td>1.44</td></tr><tr><td>5<sup>th</sup> percentile</td><td>0.65</td><td>1.11</td></tr><tr><td>95<sup>th</sup> percentile</td><td>0.91</td><td>1.77</td></tr><tr><td>Mode</td><td>0.75</td><td>1.44</td></tr><tr><td rowspan="5">Geothermal gradient (°C km<sup>-1</sup>)</td><td>Median</td><td>0.76</td><td>1.44</td></tr><tr><td>Standard deviation</td><td>0.08</td><td>0.20</td></tr><tr><td>Average</td><td>35.1</td><td>31.0</td></tr><tr><td>5<sup>th</sup> percentile</td><td>32.5</td><td>23.8</td></tr><tr><td>95<sup>th</sup> percentile</td><td>37.8</td><td>38.2</td></tr><tr><td rowspan="5">Surface heat flux (mW m<sup>-2</sup>)</td><td>Mode</td><td>35.1</td><td>30.5</td></tr><tr><td>Median</td><td>35.1</td><td>31.0</td></tr><tr><td>Standard deviation</td><td>1.6</td><td>4.2</td></tr><tr><td>Average</td><td>108.8</td><td>72.8</td></tr><tr><td>5<sup>th</sup> percentile</td><td>89.0</td><td>50.7</td></tr><tr><td rowspan="5"></td><td>95<sup>th</sup> percentile</td><td>124.1</td><td>102.2</td></tr><tr><td>Mode</td><td>112.8</td><td>66.7</td></tr><tr><td>Median</td><td>110.2</td><td>70.6</td></tr><tr><td>Standard deviation</td><td>10.8</td><td>16.1</td></tr></tbody></table>

## 4.2. Heat flux estimates from TRTs

Terrestrial heat flux from TRT data suggest that values over the Greater Montreal Area are generally low (Table 7). The highest values are obtained in a specific area of the South Shore of Montreal where TRT 11, TRT 13 and TRT17 were drilled (Table 7). Here, heat flux was estimated to range between 58.6 mW m<sup>-2</sup> (TRT 13) to 78.7 mW m<sup>-2</sup> (TRT 11). These heat flux values have some degree of correlation with the heat flux estimated in A157 and A263 wells (Table 6). The reader is referred to Appendix 1 where the temperature profiles and the results of the inversion approach are shown. The quality of the fit between measured and simulated temperature profiles for TRT1 to 13 varies between 0.00 and 0.03 but the
441 temperature profiles of these TRTs have a relatively small number of temperature data points (between 4 and 7). The quality of the fit for TRT14 to 22 is more variable, between 0.17 and 7.64. However, the temperature profiles measured in these TRTs are continuous and more data points were used to fit the simulated to the measured temperature profile.

<table><caption>Table 7. Geothermal gradient and heat flux values obtained for each TRT in Montreal region.</caption><thead><tr><th>ID<br>TRT</th><th>Location</th><th>Depth<br>(m)</th><th>Geological<br>unit</th><th>Thermal<br>conductivity<br>(W m<sup>-1</sup> K<sup>-1</sup>)</th><th>Heat flux<br>(mW m<sup>-2</sup>)</th><th>RSS<br>(-)</th><th>Temperature<br>data points used<br>for fit / total<br>data points</th></tr></thead><tbody><tr><td>1</td><td>North Shore</td><td>145</td><td>Basement</td><td>2.61</td><td>32.6</td><td>0.00</td><td>2 / 6</td></tr><tr><td>3</td><td>North Shore</td><td>145</td><td>Tr-BR-Ch</td><td>2.40</td><td>28.4</td><td>0.00</td><td>4 / 5</td></tr><tr><td>4</td><td>North Shore</td><td>120</td><td>Theresa</td><td>4.90</td><td>26.0</td><td>0.00</td><td>3 / 6</td></tr><tr><td>5</td><td>North Shore</td><td>115</td><td>Tr-BR-Ch</td><td>2.76</td><td>42.6</td><td>0.00</td><td>3 / 4</td></tr><tr><td>6</td><td>North Shore</td><td>145</td><td>Caprock</td><td>2.37</td><td>49.5</td><td>0.03</td><td>5 / 6</td></tr><tr><td>7</td><td>North Shore</td><td>145</td><td>Beauharnois</td><td>3.68</td><td>30.0</td><td>0.01</td><td>5 / 5</td></tr><tr><td>8</td><td>North Shore</td><td>145</td><td>Beauharnois</td><td>3.61</td><td>15.3</td><td>0.00</td><td>4 / 6</td></tr><tr><td>9</td><td>North Shore</td><td>115</td><td>Beauharnois</td><td>3.45</td><td>18.6</td><td>0.01</td><td>5 / 5</td></tr><tr><td>15</td><td>North Shore</td><td>330</td><td>Tr-BR-Ch<br>Beekmantown</td><td>3.48</td><td>41.5</td><td>0.17</td><td>181 / 326</td></tr><tr><td>21</td><td>North Shore</td><td>433</td><td>Tr-BR-Ch<br>Beekmantown</td><td>3.40</td><td>23.7</td><td>0.31</td><td>284 / 420</td></tr><tr><td>10</td><td>Greater<br>Montreal</td><td>145</td><td>Tr-BR-Ch</td><td>1.86</td><td>20.1</td><td>0.00</td><td>3 / 5</td></tr><tr><td>14</td><td>Greater<br>Montreal</td><td>500</td><td>Tr-BR-Ch</td><td>2.95</td><td>41.6</td><td>1.24</td><td>351 / 491</td></tr><tr><td>16</td><td>Greater<br>Montreal</td><td>360</td><td>Tr-BR-Ch<br>Beekmantown<br>Tr-BR-Ch</td><td>3.08</td><td>47.6</td><td>1.64</td><td>161 / 356</td></tr><tr><td>18</td><td>Greater<br>Montreal</td><td>500</td><td>Beekmantown<br>Potsdam<br>Tr-BR-Ch</td><td>4.05</td><td>42.4</td><td>0.22</td><td>343 / 483</td></tr><tr><td>19</td><td>Greater<br>Montreal</td><td>500</td><td>Beekmantown</td><td>2.70</td><td>46.3</td><td>5.97</td><td>401 / 492</td></tr><tr><td>20</td><td>Greater<br>Montreal</td><td>475</td><td>Basement</td><td>2.58</td><td>37.1</td><td>7.64</td><td>376 / 470</td></tr><tr><td>2</td><td>South Shore</td><td>140</td><td>Caprock</td><td>1.98</td><td>47.4</td><td>0.02</td><td>6 / 6</td></tr><tr><td>11</td><td>South Shore</td><td>150</td><td>Caprock</td><td>2.27</td><td>78.9</td><td>0.05</td><td>6 / 6</td></tr><tr><td>12</td><td>South Shore</td><td>145</td><td>Beauharnois</td><td>3.42</td><td>28.8</td><td>0.00</td><td>5 / 5</td></tr><tr><td>13</td><td>South Shore</td><td>150</td><td>Utica<br>Caprock</td><td>2.23</td><td>61.3</td><td>0.01</td><td>6 / 7</td></tr><tr><td>17</td><td>South Shore</td><td>500</td><td>Utica Shale<br>Tr-BR-Ch</td><td>2.72</td><td>67.0</td><td>5.19</td><td>496 / 496</td></tr><tr><td>22</td><td>South Shore</td><td>142</td><td>Caprock</td><td>2.74</td><td>75.9</td><td>0.20</td><td>45 / 64</td></tr></tbody></table>

4.3. Heat flux estimates from geothermal exploration well LP#1
The first temperature profile, measured one day after drilling with a RBR probe, suggests an uncorrected geothermal gradient of about 24.5 °C km⁻¹ (Figure 6). The second profile, measured with a Mount Sopris fluid column temperature instrument 2 weeks after drilling, indicates an uncorrected geothermal gradient of 23.7 °C km⁻¹ (Figure 6). The last measured profile 7 months after drilling with an RBR probe suggests an uncorrected geothermal gradient of 23.0 °C km⁻¹ (Figure 6). This last measured temperature profile was considered no longer disturbed by drilling activities and therefore was in equilibrium and was used to estimate surface heat flux based on the 1D heat conduction inversion approach.

<figure><img src="image_17.png" /><figcaption>**Figure 6.** Temperature gradient profiles measured in LP#1 well, interpreted stratigraphy, thermal conductivity profile estimated based on the natural gamma-ray log, thermal conductivity evaluated in the lab with a thermal conductivity scanner, and calibrated thermal conductivity curve, and radiogenic heat production estimated based on the natural gamma-ray log. RBR#1 - temperature profile measured one day after drilling with an RBR probe, Mount Sopris log - temperature profile measured about 2 weeks after drilling with a Mount Sopris fluid column temperature, RBR#2 - temperature profile measured about 7 months after drilling with an RBR probe.</figcaption></figure>

As previously explained, thermal conductivity was estimated from the natural gamma-ray log (yellow curve in Figure 6) and empirical equations and from laboratory analyses (black points in Figure 6). Since the
thermal conductivity evaluated by these two methods shows a difference of 19% for Utica and 35% for the Tr-BR-Ch group, an equation was developed to calibrate the thermal conductivity estimated from well logs against laboratory analyses for each lithology (orange curve in Figure 6). The difference between calculated thermal conductivity and measured thermal conductivity is illustrated in Figure 7 along with the calibration equation developed in this study.

<figure><img src="image_18.png" /><figcaption>**Figure 7.** Relationship between laboratory analyses and calculated thermal conductivity from natural gamma-ray log and empirical equations. Orange dots – Utica shale, blue dots – Tr-BR-Ch group.</figcaption></figure>

Figure 6 illustrates the radiogenic heat production estimated on the basis of the natural gamma-ray log as explained in the methodology section, subsection 3.3.2.

This information was then combined to estimate heat flux as described in subsection 3.4.2. Heat flux was solved as a 1D inverse heat conduction problem to decrease uncertainties on how to correctly apply paleoclimate correction and interpret the corrected geothermal gradient. The heat flux value that minimises the sum of the objective function (least-squares residuals) is 68 mW m⁻² (Figure 8). The objective function has an RSS value of 47.38 when trying to reproduce 2030 of 3295 temperature measurements, and the heat flux was estimated considering the calibrated thermal conductivity. The surface temperature was also optimised, and the value is 7.79 °C. Figure 8 illustrates the measured (black line) and the simulated (red line) temperature profile showing the quality of the fit particularly in the conductive section of the measured temperature profile.
<figure><img src="image_19.png" /><figcaption>Figure 8. Measured (black line) and simulated (red line) temperature profiles for well LP#1.</figcaption></figure>

## 4.4. Quality assessment of heat flux estimates

### 4.4.1. Temperature score

The lowest temperature score for quality assessment is obtained for the BHT data followed by the shallow TRTs with multiple single temperature points (Table 8). The highest score was obtained for the deeper TRTs with continuous temperature profiles and for the geothermal exploration well LP#1 where the temperature profile was also acquired in a continuous manner (Table 8).

<table><caption>Table 8. Methodological evaluation scheme for temperature gradient determination.</caption><thead><tr><th>Measurement type</th><th></th><th>Penalty</th><th>BHT</th><th>TRT (1 – 13)</th><th>TRT (14 – 22)</th><th>LP#1</th></tr></thead><tbody><tr><td rowspan="2">Continuous temperature log</td><td>Equilibrium/corrected</td><td>+0.1</td><td>---</td><td>---</td><td>0.0<sup>1</sup></td><td>0.0<sup>1</sup></td></tr><tr><td>Perturbed</td><td>-0.1</td><td>---</td><td>---</td><td>---</td><td>---</td></tr><tr><td rowspan="3">Multiple single temperature point</td><td>Equilibrium/corrected</td><td>-0.1</td><td>---</td><td>-0.2<sup>1</sup></td><td>---</td><td>---</td></tr><tr><td>Perturbed</td><td>-0.3</td><td>---</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Estimated</td><td>-0.5</td><td>---</td><td>---</td><td>---</td><td>---</td></tr><tr><td rowspan="3">BHT + surface temperature</td><td>Equilibrium/corrected</td><td>-0.3</td><td>-0.4<sup>1</sup></td><td>---</td><td>---</td><td>---</td></tr><tr><td>Perturbed</td><td>-0.5</td><td>---</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Estimated</td><td>-0.6</td><td>---</td><td>---</td><td>---</td><td>---</td></tr><tr><td colspan="2">T Score</td><td></td><td>0.6</td><td>0.8</td><td>1.0</td><td>1.0</td></tr></tbody></table>
Although temperature data was corrected for drilling and paleoclimate, a high penalty is used to reflect the uncertainty imposed by a literature-based paleoclimate history and by a ground surface temperature estimated from meteorological data and empirical equation.

### 4.4.2. Thermal conductivity score

The lowest thermal conductivity score was obtained for the BHT data since thermal conductivity from TRTs, outcrops, and well logs were combined to estimate heat flux (Table 9). The highest score was obtained for the TRT data since thermal conductivity was measured in situ (Table 9).

<table><caption>**Table 9.** Methodological evaluation scheme for thermal conductivity determination.</caption><thead><tr><th></th><th>Thermal conductivity</th><th>Penalty</th><th>BHT</th><th>TRT</th><th>LP#1</th></tr></thead><tbody><tr><td rowspan="6">Location</td><td>Thermal conductivity data from actual heat flux location</td><td>0.0</td><td>---</td><td>0.0</td><td>0.0</td></tr><tr><td>Thermal conductivity data from nearby or other location</td><td>-0.1</td><td>-0.1</td><td>---</td><td>---</td></tr><tr><td>Thermal conductivity assumed from literature</td><td>-0.2</td><td>---</td><td>---</td><td>---</td></tr><tr><td>In situ probe</td><td>+0.1</td><td>+0.1</td><td>+0.1</td><td>---</td></tr><tr><td>Core-log integration</td><td>+0.1</td><td>+0.1</td><td>---</td><td>+0.1</td></tr><tr><td>Core measurements</td><td>0.0</td><td>---</td><td>---</td><td>0.0</td></tr><tr><td rowspan="6">Source type</td><td>Cutting measurements</td><td>-0.1</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Outcrop measurements</td><td>-0.1</td><td>-0.1</td><td>---</td><td>---</td></tr><tr><td>Log interpretation</td><td>-0.1</td><td>-0.1</td><td>---</td><td>---</td></tr><tr><td>Mineral calculation (mixing model)</td><td>-0.2</td><td>-0.1</td><td>---</td><td>---</td></tr><tr><td>Lithology/Textbook</td><td>-0.2</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Number of conductivity points</td><td>&gt; 15</td><td>0.0</td><td>0.0</td><td>0.0</td><td>0.0</td></tr><tr><td rowspan="3">Saturation status</td><td>1 – 15</td><td>-0.1</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Saturated measured</td><td>0.0</td><td>0.0</td><td>0.0</td><td>---</td></tr><tr><td>Calculated or recovered</td><td>-0.1</td><td>---</td><td>---</td><td>---</td></tr><tr><td rowspan="4">Pressure-temperature conditions</td><td>Dry measured</td><td>-0.2</td><td>-0.2</td><td>---</td><td>-0.2</td></tr><tr><td>In situ</td><td>0.0</td><td>0.0</td><td>0.0</td><td>---</td></tr><tr><td>Replicated in situ</td><td>-0.1</td><td>---</td><td>---</td><td>---</td></tr><tr><td>Ambient conditions</td><td>-0.2</td><td>-0.2</td><td>---</td><td>-0.2</td></tr><tr><td colspan="2">TC Score</td><td></td><td>0.4</td><td>1.1</td><td>0.7</td></tr></tbody></table>

### 4.4.3. Quality score

The overall quality score for the heat flux estimated from BHT is 0.24, meaning that these estimates are classified as of poor quality. Heat flux estimated from TRT, on the other hand, has an overall quality score ranging between 0.88 and 1.0, meaning that these estimates can be classified as of excellent quality. Finally,
503 heat flux estimated from the geothermal exploration well LP#1 has an overall quality score of 0.7, meaning
504 that these estimates are of good quality

505 **5. Spatial distribution of heat flux in the Montreal region and implications for deep geothermal developments**
506

507 Compiling the data from the three different sources analysed and the available literature reveals that in
508 general the South Shore of Montréal area has a greater terrestrial heat flux than the region average (61 vs.
509 34 mW m⁻² excluding the BHT data; Figure 9). This observation agrees with the hypothesis made by
510 previous authors who suggested the existence of a positive geothermal anomaly in this area (Bédard et al.,
511 2016, 2020). The greater than average terrestrial heat flux estimated in this work suggests that the South
512 Shore of Montréal could be a potential target for deep geothermal district heating systems and further
513 research is worthwhile to assess the techno-economic potential of developing such networks. In fact, a
514 preliminary techno-economic modelling suggests that deep geothermal resources could be exploited at a
515 competitive cost compared to individual electrical heaters common in the Montréal area (Miranda et al.,
516 2024). Therefore, more in-depth data acquisition involving expensive deep drilling exploratory campaigns
517 could be envisioned.
<figure><img src="image_20.png" /><figcaption>**Figure 9.** Spatial distribution of heat flux in the Greater Montreal region. Refer to Figure 1 for geographical location and association of colors with geological units.</figcaption></figure>

**6. Discussion**

The energy system in urban centres is changing, and geothermal resources could play an important role in reshaping the way energy is supplied to the building stock for heating and cooling around the world. Many European countries are developing district heating systems to supply space heating with deep geothermal resources. Nevertheless, assessing the deep geothermal potential of urban areas is difficult, particularly where deep geothermal exploration wells are non-existent.
Commonly, the deep geothermal potential of a site is evaluated from temperature measurements in deep wells. BHT measurements in oil and gas wells are an example of a common exploration tool for deep geothermal assessments (Bédard et al., 2016; Huang et al., 2020; Batir and Richards, 2022). However, in many urban areas like Montréal, oil and gas wells are limited in number and thus often scattered over vast areas, making the assessments uncertain. This raises an important question: Can TRTs be used as alternative tools for a first-order screening of the deep geothermal potential of urban areas before advancing for more complex data acquisition campaigns?

This work demonstrated that, when combined to an equilibrium temperature profile, TRT data can be used for a high-level, first-order assessment of the deep geothermal potential of urban areas. However, it is important to keep in mind that TRT data does not replace the need for deep drilling campaigns for an accurate assessment. TRT data can be used as an indicator of a potential favourable area but not be used to provide an absolute evaluation. The advantages and limitations of using TRT data are discussed below.

One of the main advantages of TRT is that they are commonly made in urban areas, unlike deep wells, which require a certain amount of space and accessibility. The GHP industry commonly conducts TRT not facing space constraints and heavy regulations to comply with, thanks to the shallow depth of the borehole heat exchangers. Furthermore, the areas to be covered by the data are mostly concentrated in urban areas where the need for heat is important. The inventory of TRT made by the GHP industry therefore enables the collection of a greater number of data within these zones, and thus offers a certain degree of completeness when it comes to estimating the geothermal potential of a region.

Another advantage of using TRT for deep geothermal assessments is that the heat flux assessment relies on in situ thermal conductivity determined directly from heat injection tests. These thermal conductivity values obtained are thus more representative of the in situ conditions than those obtained from laboratory analysis of core and hand samples and well logs although a single equivalent value is generally obtained along the borehole length.
Similarly, estimating a site's geothermal potential should not be based on a single BHT measurement, as is the case when the data comes from oil and gas wells. Temperature profiles from TRTs, measured at regular intervals in borehole heat exchangers, therefore appear to be an alternative method for a more accurate interpretation of the temperature profile.

Estimating surface heat flux on the basis of TRT data, although tested by others at specific sites (e.g., Raymond et al., 2016; Marquez et al., 2019), still remains an innovative method that can be further improved, especially when interested in regional geothermal resources assessment like in this work. In fact, routinely analysing TRT to estimate the terrestrial heat flux could have a significant impact in urban areas that are in continuous growth where heating energy demand is becoming more and more important. Developing renewable energies, such as geothermal resources, could help reduce greenhouse gas emissions and meeting these growing heating energy needs.

Developing geothermal resources requires an exploration phase to define the geological potential of the sites of interest. In such a case, the use of TRT data appears to be more suitable than deep drilling for a first order assessment because of the limited number of deep boreholes in the Montréal area. Thus, in view of the potential benefits, it is important to consider and advance this method in future research.

Although many advantages, TRT data also has certain limitations. One of the main weaknesses of using TRT data for estimating the geothermal gradient is their shallow depths. Since TRTs commonly reach an average depth of 100-200 m, they can only provide temperature data impacted by near-surface disturbances. The shallow subsurface is disturbed by surface events that propagate at depth. For example, climate variations at the surface constantly influence the subsurface temperature. Past glacial periods led to a drop in the subsurface temperature while the present-day global warming is causing temperature to rise. This means that the temperature profile measured in the borehole heat exchanger is disturbed, and corrections are necessary to counteract the effects of various climate events and estimate an undisturbed geothermal gradient.
The application of these paleoclimate corrections is time consuming and demanding. A literature review on climate proxies needs to be completed to reconstruct the appropriate ground surface temperature history. Furthermore, the current global warming episode requires compiling historical meteorological data for each TRT studied in order to estimate the variation in mean annual surface temperature. Access to this historical data can be difficult, depending on the country or region targeted. Despite the precautions taken, the paleoclimate correction method is not perfect, and the results obtained are approximate. It is therefore important to bear in mind that absolute temperature values measured prior to a TRT should be treated with caution when assessing the geothermal gradient.

Groundwater also plays a role in the thermal regime of the subsurface. Certain rocks are likely to promote the circulation of groundwater, which in turn influences subsurface temperature. In recharge areas, for example, subsurface temperature tends to decrease, while in areas of warm groundwater upwelling, temperature tends to increase (Saar, 2011; Anderson, 2005). The geothermal gradient can thus be disrupted when conditions favourable to water circulation are met. These include porous, permeable rock, high topographic variation and water infiltration.

The use of TRTs to assess the deep geothermal potential requires a certain amount of caution, as the superficial nature of the data collected can lead to a misestimation of heat flux. Thus, if a TRT analysis identifies a thermal anomaly, this anomaly could be larger or smaller than indicated by the TRT results, depending on near-surface phenomena affecting the measured geothermal gradient. The TRT therefore provides a preliminary characterisation of the study area.

Lastly, it should be noted that the TRT data used in this work were not publicly recorded and come from GHP industrials, ministries and research organisations that accepted to share the information. Access to this private information may be difficult, which constitutes a barrier to the use of TRT in the study of the geothermal potential of urban areas and hinders the development of this new method.
In conclusion, the use of TRT to estimate the geothermal gradient and surface heat flux can provide a greater number of data whose origin differs from the data commonly used to date. As a result, TRT can be used to complement other sources of subsurface thermal information and detect geothermal anomalies in urban areas before deep drilling is justified. Despite the uncertain nature of TRT data, this new approach makes it possible to achieve a degree of completeness in assessing the geothermal potential of a region by combining the different data sources (TRT and deep drilling). It is a relatively new approach that offers prospects for future research.

## 7. Conclusions

The population of urban areas is expected to grow, and this will consequently increase the heating energy demand. Deep geothermal resources could be a game changer to transform the energy system of urban centres. However, assessing the deep geothermal potential of urban areas is difficult, and alternative exploration tools are needed to surpass this challenge, especially at the early exploration phase.

With this in mind, we tested the hypothesis of using temperature profiles measured before TRT to screen and assess the deep geothermal energy potential of urban areas, using the Greater Montreal Area (Canada) as a case study.

Terrestrial heat flux values estimated from 22 TRT of 120 to 500 m in depth were compared to 2 BHT recorded at 413.98 and 1400 m depth, 4 heat flux assessments available from the literature and taken from borehole ranging from 411 to 823 m in depth and to a 400 m deep geothermal exploration well specifically drilled for this project. The different data source showed some correlation, indicating that a specific region within the South Shore of Montréal has greater heat flux values compared to the average of the region under study (61 vs. 32 mW m⁻²). This area seems to be most interesting for deep geothermal exploration in the Greater Montreal and therefore more detailed and complex data acquisition campaigns may be worth to decrease uncertainty and plan future deep geothermal developments. On the other hand, the terrestrial heat flux on the Montreal Island seems less important, on average 39 mW m⁻², and the expenses associated with
deep geothermal exploration may not be worthwhile. This recommendation could only be made after analysing temperature information from available TRT as there were previously not sufficient deep borehole temperature measurements to support such a science-based decision-making process.

Although this research work does not provide any insights into why the South Shore of Montréal is positively anomalous in terms of heat flux values, it corroborates the existence of that positive geothermal anomaly on the South Shore of Montreal. Furthermore, it demonstrates the significance of using TRT data from the GHP industry for a high-level, first-order screening of the deep geothermal potential of urban areas. Despite the limitations highlighted in this work, TRT data offers unprecedented access to data that would otherwise be difficult to collect in urban environments.

## 631 Nomenclature

<table><tr><td>A</td><td>W m<sup>-3</sup></td><td>Internal heat generation</td></tr><tr><td>A<sub>e</sub></td><td>W m<sup>-3</sup></td><td>Effective internal heat generation</td></tr><tr><td>erf</td><td>-</td><td>Error function</td></tr><tr><td>GR</td><td>API</td><td>Natural gamma-raylog</td></tr><tr><td>lb</td><td>W m<sup>2</sup></td><td>Lower bound of heat flux</td></tr><tr><td>l<sub>GR</sub></td><td>-</td><td>Linear GR Index</td></tr><tr><td>Q<sub>0</sub></td><td>W m<sup>-2</sup></td><td>Surface heat flux</td></tr><tr><td>Q</td><td>W m<sup>-2</sup></td><td>Heat flux</td></tr><tr><td>RSS</td><td>-</td><td>Residual sum of squares</td></tr><tr><td>r</td><td>m</td><td>Internal radius of the pipe</td></tr><tr><td>T<sub>0</sub></td><td>°C</td><td>Undisturbed surface temperature</td></tr><tr><td>T<sub>BHT</sub></td><td>°C</td><td>Bottom-hole temperature</td></tr><tr><td>T<sub>BHT,c</sub></td><td>°C</td><td>Corrected BHT for drilling and paleoclimate disturbances</td></tr><tr><td>T<sub>c</sub></td><td>°C</td><td>Corrected temperature</td></tr><tr><td>T<sub>g</sub></td><td>K</td><td>Undisturbed subsurface temperature</td></tr><tr><td>T<sub>measured</sub></td><td>°C</td><td>Measured temperature</td></tr><tr><td>T<sub>model</sub></td><td>°C</td><td>Simulated temperature</td></tr><tr><td>T<sub>s</sub></td><td>K</td><td>Mean annual ambient air temperature</td></tr><tr><td>T<sub>v</sub></td><td>°C</td><td>Average temperature variation between the climate event and today's baseline</td></tr><tr><td>t<sub>i1</sub></td><td>s</td><td>End of the climate event</td></tr><tr><td>t<sub>i2</sub></td><td>s</td><td>Beginning of the climate event</td></tr><tr><td>t<sub>f</sub></td><td>h</td><td>Time after end of drilling</td></tr></table>
<table><tr><td>ub</td><td>W m<sup>-2</sup></td><td>Upper bound of heat flux</td></tr><tr><td>V</td><td>m<sup>3</sup></td><td>Volume</td></tr><tr><td>V<sub>shale</sub></td><td>-</td><td>Volume of shale</td></tr><tr><td>z</td><td>m</td><td>Depth</td></tr><tr><td>z<sub>m</sub></td><td>m</td><td>Measured depth</td></tr><tr><td>α</td><td>m<sup>2</sup> s<sup>-1</sup></td><td>Thermal diffusivity</td></tr><tr><td>ΔT</td><td>°C</td><td>Temperature correction to be applied to the measured temperature</td></tr><tr><td>ΔT/Δz</td><td>°C m<sup>-1</sup></td><td>geothermal gradient</td></tr><tr><td>λ</td><td>W m<sup>-1</sup> K<sup>-1</sup></td><td>Thermal conductivity</td></tr><tr><td>λ<sub>e</sub></td><td>W m<sup>-1</sup> K<sup>-1</sup></td><td>Effective thermal conductivity</td></tr><tr><td>φ</td><td>%</td><td>Porosity</td></tr><tr><td>ρ</td><td>kg m<sup>-3</sup></td><td>Density</td></tr></table>

632

633 **Statements and Declarations**

634 **Acknowledgements:** Acti-Cité and Groupe Poirier were partners of this project and are acknowledged for
635 making possible the drilling of the 400 m-deep geothermal exploration well which contributed validating
636 the TRT-based estimates.

637 **Funding:** This research was funded by an NSERC Alliance grant awarded to Jasmin Raymond.

638 **Availability of data and materials:** All data is provided in the manuscript.

639 **Contributions:** Conceptualisation MMM; methodology, MMM; validation, MMM; formal analysis,
640 MMM and MC; investigation, MMM and MC; resources, MC, FAC, JR, CD, PP and CD; data curation,
641 MMM and MC; writing—original draft preparation, MMM; writing—review and editing, MMM, FAC, JR,
642 CD, PP and CD; visualisation, MMM; supervision, JR; project administration, JR; funding acquisition, JR.
643 All authors have read and agreed to the published version of the manuscript.

644 **Competing interests:** The authors declare no conflict of interest.

645 **Consent to publish:** The authors agree with the publication of the manuscript.

646 **Appendix 1**
647 The results of the 1D inversion approach used to estimate the terrestrial heat flux from the temperature

648 profiles measured before each TRT are illustrated in the figures below (Figure A1). The location of each

649 TRT is shown on Figure 1.
<figure><img src="image_21.png" /><figcaption>Figure A1. Measured (black line) and simulated (red line) temperature profiles.</figcaption></figure>
<figure><img src="image_22.png" /><figcaption>Figure A1 (cont.). Measured (black line) and simulated (red line) temperature profiles.</figcaption></figure>
<figure><img src="image_23.png" /><figcaption>Figure A1 (cont.). Measured (black line) and simulated (red line) temperature profiles.</figcaption></figure>

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