Quantitative temperature monitoring of a heat tracing experiment using cross-borehole ERT 1,2 3 3 3Hermans Thomas , Wildemeersch Samuel , Jamin Pierre , Orban Philippe , Brouyère 3 3 1Serge , Dassargues Alain , Nguyen Frédéric . 1University of Liege, Applied Geophysics, Department ArGEnCo, Engineering Faculty, B52, 4000 Liege, Belgium.  2F.R.S.-FNRS Research Fellow. 3University of Liege, Hydrogeology and Environmental Geology, Aquapole, Departement ArGEnCo, Engineering Faculty, B52, 4000 Liege, Belgium. Corresponding author Hermans Thomas, University of Liege, Applied Geophysics, Department ArGEnCo, Engineering Faculty, B52, Chemin des Chevreuils 1, 4000 Liege, Belgium. Tel : +3243669263, Fax : +3243669520, thomas.hermans@ulg.ac.be  NOTICE: this is the author’s version of a work that was accepted for publication in Geothermics (53), 14-26. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Please cite as :Hermans T., S. Wildemeersch., P. Jamin, P. Orban, S. Brouyère, A. Dassargues and F. Nguyen. 2015. Quantitative temperature monitoring of a heat tracing experiment using cross-borehole ERT. Geothermics, 53, 14-26. doi: http://dx.doi.org/10.1016/j.geothermics.2014.03.013 1  Abstract 1 The growing demand for renewable energy leads to an increase in the development of 2 geothermal energy projects and heat has become a common tracer in hydrology and 3 hydrogeology. Designing geothermal systems requires a multidisciplinary approach including 4 geological and hydrogeological aspects. In this context, electrical resistivity tomography 5 (ERT) can bring relevant, qualitative and quantitative information on the temperature 6 distribution in operating shallow geothermal systems or during heat tracing experiments. We 7 followed a heat tracing experiment in an alluvial aquifer using cross-borehole time-lapse 8 ERT. Heated water was injected in a well while water of the aquifer was extracted at another 9 well. An ERT section was set up across the main flow direction. The results of ERT were 10 transformed into temperature using calibrated petrophysical relationships. These ERT-derived 11 temperatures were then compared to direct temperature measurements in control piezometers 12 collected with distributed temperature sensing (DTS) and groundwater temperature loggers. 13 Spatially, it enabled to map the horizontal and vertical extent of the heated water plume, as 14 well as the zones where maximum temperatures occurred. Quantitatively, the temperatures 15 and breakthrough curves estimated from ERT were in good agreement with the ones observed 16 directly during the rise and maximum of the curve. An overestimation, likely related to 3D 17 effects, was observed for the tail of the heat breakthrough curve. The error made on 18 temperature can be estimated to be between 10 to 20 %, which is a fair value for indirect 19 measurements. From our data, we estimated a quantification threshold for temperature 20 variation of 1.2°C. These results suggest that ERT should be considered when designing heat 21 tracing experiments or geothermal systems. It could help also to assess the geometrical 22 complexity of the concerned reservoirs. It also appears that ERT could be a useful tool to 23 monitor and control geothermal systems once they are in operation. 2  24 Keywords: Heat tracing, geothermal system, time-lapse, cross-borehole electrical resistivity 25 tomography, temperature monitoring 26 3  27  28 1. Introduction 29 Shallow alluvial aquifers constitute potential shallow geothermal energy reservoirs, relatively 30 abundant and easily accessible. In these low temperature systems, groundwater has an average 31 temperature ranging from 5 to 30°C and may be used for domestic or industrial cooling and 32 heating (Allen and Milenic, 2003; Haehnlein et al., 2010). 33 The two main techniques to exploit shallow geothermal energy systems are ground source 34 heat pump (GSHP), which are closed systems with a vertical or horizontal heat exchanger, 35 and groundwater heat pump (GWHP), which are open systems circulating groundwater 36 between production and injection wells. Designing such systems requires a multidisciplinary 37 approach including geological and hydrogeological aspects. The most common approach is to 38 model the system using a coupled groundwater and heat flow simulator. However, such 39 models require estimating parameters governing heat transport such as heat capacity, thermal 40 conductivity and density. Due to a lack of data, authors often have to rely on standard 41 calculation charts, values found in the literature or default values implemented in softwares 42 (e.g. Busby et al., 2009; Lo Russo and Civita, 2009; Liang et al., 2011; de Paly et al., 2012). 43 In-situ tests, such as thermal response tests (Raymond et al., 2011; Mattsson et al., 2008), or 44 laboratory measurements (e.g. Haffen et al., 2013) are sometimes possible but the deduced 45 values may deliver only well-centered information or may not always be representative of in-46 situ conditions. 47 Thermal tracing experiments are performed for decades in hydrogeology (Anderson, 2005; 48 Saar, 2011). Such experiments are used to improve the characterization of hydrogeological 49 parameters (e.g. hydraulic conductivity or dispersivity), but the same methodologies may be 50 used to study the thermal properties of shallow geothermal systems (e.g. Vandenbohede et al., 51 2009, 2011; Giambastiani et al. 2012). However, the heterogeneity of geothermal and 4  52 hydrogeological systems may be too complex to be fully caught by thermal or solute tracer 53 experiments alone (e.g. Brouyère, 2001).  54 In this context, electrical resistivity tomography (ERT) can bring relevant and spatially 55 distributed information both on the heterogeneity of aquifers and on the temporal behavior of 56 tracers. Indeed, ERT has proven its efficiency to image and/or monitor spatial phenomena 57 (Vereecken et al., 2006) such as salt water intrusions (Nguyen et al., 2009; Hermans et al., 58 2012c), variations in moisture content (Binley et al., 2002), biodegradation of hydrocarbons 59 (Atekwana et al., 2000), salt tracer experiments (Kemna et al., 2002 ; Robert et al., 2012) and 60 heat injection experiments (Hermans et al., 2012b). It was also used in the characterization of 61 geological structures, for example in the exploration of geothermal systems, where 62 hydrothermal fluids may generate high contrasts of resistivity (Pérez-Flores and Gomez 63 Trevino, 1997; Bruno et al., 2000; Garg et al., 2007; Arango-Galván et al., 2011). 64 Besides the characterization of shallow geothermal systems themselves, their impact on the 65 groundwater temperatures in the aquifer may be important since their exploitation yields cold 66 and heat plumes (Molson et al., 1992; Palmer et al., 1992 ; Warner and Algan, 1984) which 67 may influence aquifer properties and groundwater chemistry (e.g. Jesuβek et al., 2013) and 68 microbiology (Brielmann et al., 2009). Haehnlein et al. (2010) pointed out that, if laws and 69 rules exist in some countries to limit the temperature difference caused by the use of 70 geothermal systems, the development of anomalies is rarely monitored. With the growth of 71 the demand for renewable energy, we can expect that regulations will become stricter and 72 controls of installations more common. New monitoring technologies will be needed and ERT 73 may play an important role to monitor spatially, i.e. not only in wells, the variations of 74 temperature in the aquifer. For example, the temperature changes observed on operating 75 GWHP systems (e.g. Vanhoudt et al., 2011) are typically in the range of temperature that 76 could be detected by ERT. 5  77 ERT aims at imaging the electrical resistivity distribution of the subsurface. Using 78 petrophysical relationships such as Archie’s law, one may recover indirect parameters such as 79 saturation, water electrical conductivity or total dissolved solid content. Bulk electrical 80 resistivity also decreases with temperature (e.g. Revil et al., 1998). In most studies, 81 temperature effects are undesirable and may create artifacts in the interpretation, a correction 82 term is applied to remove the influence of temperature variations (Hayley et al., 2007; 83 Sherrod et al., 2012). Few studies used time-lapse ERT to monitor directly temperature 84 changes (Ramirez et al., 1993 ; Labrecque et al., 1996b), generally in a context quite different 85 from GWHP or GSHP systems. 86 Hermans et al. (2012b) monitored with time-lapse surface ERT a heat injection experiment at 87 a relatively small scale (45 m) and at shallow depth (2 to 4.5 m). Their results show that ERT 88 is a reliable tool to monitor temperature changes and may be a method of choice for the 89 design and the monitoring of geothermal systems. However, the results need to be extended to 90 deeper and more complex, heterogeneous reservoirs, as it will be considered in this paper. 91 ERT-derived temperatures were very close to temperatures modeled using a calibrated 92 coupled groundwater and heat flow and transport model bringing additional constraints on the 93 thermal properties of the aquifer.  94 For deeper reservoirs, the rapid decrease in resolution and sensitivity of surface ERT becomes 95 a major drawback (Caterina et al., 2013). It is then necessary to consider borehole ERT to 96 improve resolution (Perri et al., 2012). For example, Prevedel et al. (2009) installed deep (600 97 to 750 m) borehole electrodes to monitor the migration of CO2 within a storage reservoir 98 (Bergmann et al., 2012). For cross-hole ERT, the results obtained for a specific study are 99 more easily extendable than for surface ERT because resolution patterns are not depth 100 dependent.  6  101 In borehole ERT, electrodes are located under the ground surface, either fixed at the outer-102 edge of the casing or mounted on cables with the borehole fluid ensuring the electrical contact 103 with the surrounding rock. In the latter case, borehole fluid is generally more conductive than 104 the rock and may influence resistance measurements (Doetsch et al., 2010). Using time-lapse 105 ERT, the relative fluid effect will be almost similar at each time-step and should be 106 insignificant in inversion results (Nimmer et al., 2008). 107 In this paper, we study the ability of ERT to monitor temperature changes in a heterogeneous 108 aquifer and follow thermal tracing experiments. We pumped water from a gravel aquifer, 109 heated it and reinjected it in a second well, similar to a GWHP system operation. 110 The paper is organized as follows: first, the field site is described; second, the methodology is 111 presented; then, the results of the ERT monitoring are compared with direct measurements in 112 wells; finally, conclusions are presented. 113 2. Field Site 114 The study site is located in Hermalle-sous-Argenteau in Belgium near the Belgian-Dutch 115 border (Figure 1). It lies on the alluvial aquifer of the Meuse River. A pumping well and 8 116 piezometers were already present on the site since the 1980’s and 11 new piezometers were 117 drilled in June 2012 together with an injection well. They were arranged in three different 118 panels crossing the main flow direction between the injection well and the pumping well in 119 order to study the spatial variability during tracing experiments (Pz10 to 20, Figure 2). 120 Borehole logs enabled to divide the deposits in four different units. The first layer consists of 121 loam and clay with a thickness between 1 and 1.5m. The second layer is composed of gravel 122 in a clayey matrix. The bottom of this layer is found at depth between 2 and 3.2m. These two 123 first layers have little importance in this study because they are located in the unsaturated 124 zone. The water table lies at approximately 3.2m depth, with a very small gradient towards 7  125 the northeast which is the main direction of flow (Figure 2). The third unit is composed of 126 gravel and pebbles in a sandy matrix. The quantity of sand decreases with depth, whereas the 127 size of the pebbles increases with depth, a vertical variability is thus present. Lateral 128 variability in the grain size distribution of the deposits is also expected in this heterogeneous 129 aquifer, leading to variable hydrogeological parameters. Between 9.7 and 10.1 m, the 130 Carboniferous bedrock composed of folded shales and sandstones is found. 131 In the middle panel, the outer piezometers are screened on the whole thickness of the alluvial 132 aquifer. This is also the case for the injection and pumping wells. Except for the latter, they 133 were equipped with a distributed temperature sensing (DTS) system to monitor the 134 temperature during the experiment (Leaf et al., 2012 and references therein) with a spatial 135 resolution of 0.5m. Pz14 and Pz16 were screened at two different levels, with a 2m long 136 screen between 4 and 6m depth and 1m screen between 8.5 and 9.5m. All other piezometers 137 were screened at two different levels, with a 1m screen between 4.5 and 5.5m depth and a 2m 138 screen between 8 and 10m depth. In the middle of each screened zone, a groundwater 139 temperature logger was placed to monitor the temperature and the pressure during all the 140 experiment. 141 Previous studies have shown that the gravel aquifer is very permeable. Calibrated hydraulic 142 -1 -3conductivity values were found previously between 1.2 10  and 2 10  m/s (Dassargues, 143 1997; Derouane & Dassargues, 1998; Brouyère, 2001).  With such values, it is possible to 144 inject at a rate much higher than Hermans et al. (2012b) who were limited by the low 145 hydraulic conductivity of fine sands and the small thickness of the aquifer. 146 3. Methodology 147 3.1.  Heating and injection procedure 8  148 The experiment consists of an injection and pumping test. The groundwater is pumped from 149 the pumping well, located in the northeastern part of the site, downstream from the injection 150 well. We used a pumping rate of 30 m³/h. Given the high hydraulic conductivity values of the 151 aquifer, the corresponding drawdown is only 5 cm in the pumping well and 4 cm in Pz19 (5 m 152 upgradient from the well). The pumping process ensures that the main direction of flow will 153 cross the three intermediate panels. Pumping was started one day before the beginning of the 154 injection of heated water, far early enough to reach a steady-state flow, and continued after 155 the end of injection.  156 We used a mobile water heater (AQUAMOBIL DH6 system) to heat the water injected in the 157 aquifer. It can work at a maximum rate of 3 m³/h with a difference in temperature of about 158 30°C. Given the high hydraulic conductivity of the aquifer, we decided to inject at this 159 maximal rate. During the injection phase, 3 m³/h of the pumped water were derived in a 160 stocking tank, passed through the water heater and injected in the injection well. The mean 161 temperature of the extracted water at the time of the experiment (October-November 2012) 162 was 13°C. With the maximum injection rate, the temperature of the injected water reached a 163 stabilized mean value of 38°C. 164 thInjection started on October 30  and lasted for 1 day, resulting in the injection of 72 m³ of 165 heated water. Using groundwater also for injection, the transformation of ERT results into 166 temperatures will be direct and only require a unique petrophysical relationship. However, the 167 heterogeneity of the aquifer and the advection component make the experimental set-up quite 168 complex. 169 3.2.  Petrophysical relationship linking temperature and conductivity 170 The aim of the petrophysical relationships is to quantify the link between bulk electrical 171 conductivity and temperature. Bulk electrical conductivity is generally expressed as a function 9  172 of porosity, grain size and tortuosity (often joined in a term called formation factor), 173 saturation, fluid electrical conductivity and surface conductivity. In this case, we are 174 interested in the saturated zone (saturation = 1) where the grain size distribution is dominated 175 by gravel with very few fine elements. We can thus neglect the surface conductivity which is 176 very low for coarse grains (Revil and Linde, 2006). With this assumption, the link between 177 bulk electrical conductivity σb and fluid electrical conductivity σf is  178 f    (1) bF179 where F is the formation factor (Archie, 1942). The latter is variable spatially, depending on 180 the lithology. In the case of a monitoring study, we measure bulk electrical resistivity at 181 different time steps and compare it to a reference state, called the background. If we take the 182 ratio of equation 1 between a specific time-step, representing state 2, and the reference 183 background, representing state 1, we have  184 b 2 f 2   (2)  b 1 f 1185 and the relation is not dependent on the formation factor anymore. In equation 2, σb1 and σb2 186 are determined with ERT after inversion of resistance data and σf1 is either measured on the 187 field directly or deduced from the temperature of the formation water in the aquifer. The only 188 unknown in equation 2 is the fluid electrical conductivity at state 2, which can be expressed as 189 b 2     (3) f 2 f 1b 1190 Through equations 1 to 3, we see that the variation in bulk electrical conductivity in the 191 saturated zone is related to a variation of the fluid electrical conductivity only. The latter can 192 be caused by a change in fluid salinity or by a change in temperature. If we assume that the 10  193 salinity of the fluid remains constant during the experiment, the water electrical conductivity 194 depends only on temperature. 195 Hermans et al. (2012a) have shown that for long term experiments (storage phase) at 196 relatively high temperature, the link between temperature and electrical resistivity may be 197 more complex, due to precipitation/dissolution effects related to temperature changes, as 198 shown by Robert et al. (2013). However, in this case, the temperature difference is about 199 25°C and should rapidly decrease due to dispersion effects. The variation of salinity with 200 changing chemical equilibrium should be relatively small. If this effect is not negligible, an 201 additional term in equation 5 should be added and calibrated to derive temperatures. 202 In the temperature interval considered in this experiment (10 to 40°C globally, and 10 to 20°C 203 for the panel monitored with ERT), a linear dependence can be assumed between temperature 204 and fluid electrical conductivity (e.g. Sen and Goode 1992 and Hayley et al. 2007 or Hermans 205 et al. 2012b for applications). This relation can be expressed as f ,T206  m (T  2 5)  1   (4) ff , 2 5207 where σf,T is water electrical conductivity at temperature T in °C, σf,25 is the conductivity at 208 25°C, considered as the reference temperature (another reference could be chosen as well) and 209 mf is the fractional change in electrical conductivity per degree Celsius at the reference 210 temperature.  211 A water sample was taken on the site and relation 4 was verified experimentally in the 212 laboratory (Figure 3). Figure 3 shows the results up to 20°C (temperature encountered in the 213 middle panel), but the trends remains the same until 40°C. Fitting a linear curve to the 214 experimental points, we found mf equal to 0.0194 and the conductivity at the reference 11  215 temperature (25°C) is equal to 0.0791 S/m. The value for the fractional change per degree 216 Celsius is in the same range as observed by Hayley et al. (2007) and Hermans et al. (2012b). 217 Introducing equation 4 into equation 3, we can express the temperature T (in °C) according to 218 bulk electrical conductivity, water electrical conductivity at the temperature of reference and 219 at the temperature of the background and the fractional change per degree Celsius 1   b 2 ,T  220 f 1T    1  2 5  (5) m  f  b 1 f , 2 5 221 where σb2,T represents the bulk electrical conductivity at the time-step for which we try to 222 determine the temperature. 223 3.3.  Electrical resistivity measurements 224 The two outer piezometers of the middle panel (Pz13 and Pz17 on Figure 2) were equipped 225 with borehole electrode cables with 0.5m spacing. Each borehole has thus 13 electrodes made 226 of stainless steel located from 3.5 to 9.5 m depth. The first electrode is located just below the 227 water table whereas the last electrode is located just above the bedrock. 228 The two boreholes are separated horizontally by 4.5 m. The thickness covered by the 229 electrodes is 6 m. The aspect ratio, i.e. the ratio of the separation between boreholes and the 230 length of the equipped borehole is thus equal to 0.75. This value is often considered as the 231 maximum acceptable value to obtain a sufficient resolution. Optimal resolution is generally 232 achieved with an aspect ratio of 0.5 (LaBrecque et al., 1996b). 233 We used a combination of bipole-bipole (also called AM-BN) and dipole-dipole (AB-MN) 234 configurations as measuring sequence. The first one has a better signal-to-noise, but a lower 235 resolution (Zhou and Greenhalgh, 2000). For bipole-bipole measurements, we measured 236 every possible configuration. For the dipole-dipole, we kept only the cross-borehole 12  237 measurements, using a dipole spacing ranging from 0.5 to 5m and measuring dipoles sharing 238 one electrode. The complete data set contains 969 possible measurements. 239 We used an ABEM Terrameter LS to acquire the data with an acquisition delay of 0.5s and an 240 acquisition time of 1s. We used a standard deviation limit of 1% on the repeatability error 241 after 3 stacks to filter the data. For almost each time step, we collected both normal and 242 reciprocal measurements to assess the error level on the data. The latter are obtained by 243 swapping current and potential electrodes (LaBrecque et al., 1996a). Acquiring a complete 244 data set took about 45 minutes (normal and reciprocal measurements). 245 The error level was estimated using both the methods of Slater et al. (2000) and Koestel et al. 246 (2008). They both used the reciprocal error to derive a linear relationship between the mean 247 measured resistance Rm (mean between normal and reciprocal resistance, in Ohm) and error e 248 (in Ohm) defined as the difference between normal and reciprocal measurements  249 e  a  b R  (6) m250 where a is an absolute error (Ohm) and b is a relative error. Slater et al. (2000) considered the 251 envelope curve as error model, which can be considered as conservative, since the mean error 252 is overestimated. Koestel et al. (2008) worked with standard deviation of logarithmic bins to 253 determine the coefficients. This method may result in a mean error model, less conservative. 254 Nguyen et al. (2011) have shown that the noise level characterization is of great importance in 255 time-lapse studies and should always be investigated carefully. If the noise levels are too 256 different between time-steps, it may prevent a quantitative interpretation of monitoring data. 257 If noise levels are almost similar, one should choose a common error model to invert all data 258 sets. We calculated error models for both methods and each time-step. We chose a common 259 error model with an absolute error of 0.002 Ohm and a relative error of 0.5%. We tested 13  260 different error level around these values, with few differences in the final images, both 261 qualitatively and quantitatively.  262 The aim of cross-hole electrical resistivity was to detect the first arrival of the tracer, the 263 maximum temperature reached in the middle panel and, to image vertical and lateral 264 variations in the temperature distribution. Data sets were collected about every six hours 265 during the injection and the day after. For the next days, we increased the time-steps to about 266 18h, with one or two sections per day. The total monitoring time was 6 days, time at which 267 the resistivity distribution had almost returned to the background distribution. For 268 comparison, a DTS system was set in both boreholes to control the temperature directly and 269 assess the ability of ERT to derive reliable temperatures. 270 3.4.  Inversion procedure 271 In electrical resistivity tomography, the solution of the inverse problem is non-unique. A 272 common way to solve such inverse problems is to add a regularization constraint to the least-273 square problem (Tikhonov and Arsenin, 1977). The problem is then to minimize, through an 274 iterative process an objective function of the form 2 2275  (m )  W (d  f (m ))   W m  (7) d m276 where λ balances between the data misfit (first term of the right hand side of equation 7) and 277 the model a priori characteristic (second term), d represents the vector containing the data, 278 expressed as the logarithm of measured impedance, m is the model of the logarithm of 279 subsurface electrical conductivity, f(m) is the forward operator, Wd is the data weighting 280 matrix using the reciprocal error as estimate (equation 6) and Wm is a matrix describing an a 281 priori characteristic of the conductivity model. Several forms are possible for Wm, for 282 example to include prior information (e.g. Hermans et al. 2014). The most common method, 14  283 used in this study, is to penalize roughness to describe smooth model variations (deGroot-284 Hedlin and Constable, 1990).  285 With time-lapse data sets, we are more interested in the change in electrical conductivity than 286 in the absolute value of conductivity. Generally, the process of inversion is adapted in order to 287 improve inversion results. In this paper, we do not consider coupled inversion of time-lapse 288 ERT data and hydrogeological models (e.g. Irving and Singha 2010). Three main procedures, 289 with several variants, exist to invert for time-lapse ERT data (e.g. Miller et al. 2008), namely 290 independent inversion, time-constrained or reference model inversion and difference 291 inversion. In the first one, inversion results obtained separately are simply substracted, which 292 should eliminate systematic errors but amplify uncertainties in the data. For temporally 293 constrained schemes, a regularization operator is added in the time dimension in addition to 294 the space dimensions, to minimize changes between successive sections (e.g. Karaoulis et al., 295 2011, 2014). This enables 4D inversions of ERT time-lapse data sets and has already shown 296 to be efficient in tracer tests (Revil et al., 2013). In this study, we used the difference 297 inversion scheme (Kemna et al., 2002) where the problem is formulated in terms of variations 298 for both data and model. Equation 7 becomes 2 2299  (m )  W (d  d  f (m )  f (m ))   W (m  m )  (8) d 0 0 m 0300 where d0 and m0 are respectively the data set and the model corresponding to the background 301 state. The results obtained for the background are thus used as reference for subsequent 302 inversions. This method should reduce the systematic error and provide a faster convergence. 303 (LaBrecque and Yang, 2000). 304 To compare the successive models in the monitoring study, it is important that all data sets are 305 inverted with the same level of data misfit corresponding to the expected noise level. Indeed, 306 over-fitting the data may create artifacts of inversion in the corresponding image, whereas the 15  307 contrary would results in an over-smoothed inverted section (LaBrecque et al., 1996a). To 308 achieve this, the iteration process is stopped when the root-mean-square (RMS) value of 309 error-weighted data misfit  2W (d  f (m ))d310    (9) R M SN311 with N representing the number of data, reaches the value 1 for a maximum possible value of 312 λ, corresponding to data fitted to its error level. At each iteration, λ is optimized to obtain the 313 minimum value of εRMS.  When, εRMS is inferior to 1, we looked for the unique value of λ that 314 satisfies the data misfit criterion (εRMS = 1). 315 We used the code CRTomo (Kemna, 2000) to invert our data. This code is a 2.5D inversion 316 code; it means that the electrical conductivity distribution is assumed to be constant in the 317 direction perpendicular to the section and that the effect of boreholes themselves cannot be 318 taken into account (Nimmer et al., 2008; Doetsch et al., 2010). Effects caused by boreholes 319 are of more concern when the investigated site is located in high resistive rocks. They may 320 also be, at least partly, avoided with time-lapse inversion. Indeed, we can expect that, if 321 present, 3D artifacts will be compensated because present in both background and monitoring 322 states (Nimmer et al., 2008). However, a possible 3D effect when imaging a contrasting 323 plume, also called shadow effect, is that the plume is imaged even if it is outside the image 324 plane, because the 3D heterogeneity caused by the moving tracer is not taken into account in 325 the 2.5D inversion scheme (Nimmer et al., 2008). This may result in bias in the breakthrough 326 curve, leading to an apparent more diffuse behavior of tracers (Vandenborght et al., 2005). 327 We used a grid with square elements of 0.25 m x 0.25 m, to have two elements between 328 electrodes, extended laterally and in depth for inversion. ERT-borehole 1 is located at 329 abscissa 1 m and ERT-borehole 2 at abscissa 5.5 m on the grid.  16  330 To assess the quality of the ERT image, we used the error weighted cumulative sensitivity 331 matrix (Kemna, 2000; Caterina et al., 2013). The cumulative sensitivity S is defined as 332 T TS  d ia g ( J W W J )  (10) d d333 where J is the Jacobian matrix and T denotes the transpose operator. S depends on both the 334 distribution of resistivity in the model parameters and the data weighting matrix which 335 depends on the error assessment. A high value of sensitivity for a parameter signifies that a 336 change of its resistivity would strongly influence the data. In contrast, a low value of 337 sensitivity is characteristic of a parameter having less influence on the predicted data. Such a 338 low sensitivity zone will most likely be badly resolved in the inverted section. However, it has 339 to be noted that high sensitivity does not necessarily mean high resolution.  340 4. Results and discussion 341 4.1.  Cross-borehole ERT background 342 The background image was obtained using equation 7, corresponding to the smoothness-343 constrained solution (Figure 4). In the zone between the boreholes, we see that the resistivity 344 lies between 100 and 200 Ohm-m, with lower resistivities at the bottom of the section. These 345 resistivity values are characteristic of saturated sand and gravel. The lower resistivity 346 observed at the bottom of the aquifer corresponds with coarser gravel and a lower sand 347 content.  348 The resistivity tends to increase towards the unsaturated zone (above – 3.5m), but there was 349 no electrode in this part of the section (the electrode at – 3 m was modeled but not used for 350 any configuration).  However, we do not expect these absolute values to be accurate due to 351 borehole and 3D effects in the inversion (Nimmer et al., 2008).  352 The sensitivity pattern is typical of cross-borehole measurements (Figure 5). The sensitivity is 353 high in the neighborhood of the boreholes and decreases towards the middle part of the 17  354 section. The sensitivity is lower in two opposite triangles in the upper and bottom part of the 355 saturated zone, due to a smaller coverage of data points in this zone. The lowest sensitivity 356 values are found in the unsaturated zone. The electrical contact through borehole electrodes 357 was not possible because the borehole is not filled with water in this part; no surface 358 electrodes were used to improve the resolution, because the aim is to image temperature 359 changes in the saturated zone. Given the sensitivity values and the aspect ratio, we assume 360 that the chosen configuration is sufficient to monitor temperature changes within the section. 361 4.2.  Cross-borehole ERT monitoring results 362 Before looking at inverted data, it is important to qualitatively check if the acquired data 363 contains some information about the monitored process. We calculated the mean resistance of 364 each data set after removing data with repeatability error higher than 1% (870 points 365 remaining). The mean resistance for the background data set is 14.31 Ohm. The first 366 monitoring set was taken after 7h of injection, the mean resistance slightly increases, but not 367 significantly (Figure 6). This is likely an effect of noise on the data. We can state that 368 temperature changes are too small to influence the measured resistance. The same effect can 369 be observed on individual measurements. The mean resistance then decreases with time to 370 reach a minimum value of 13.76 Ohm after 30 to 35 hours after the beginning of injection, 371 which corresponds to 6 to 11 hours after the end of injection. After the minimum, the mean 372 resistance starts to increase and slightly tends to its initial state, even if it is not totally reached 373 at the end of the monitoring process. 374 Figure 6 can be seen as a qualitative mean breakthrough curve of the heat tracing experiment. 375 It enables to derive two important parameters: the first detected arrival of heat, which occurs 376 between 7 and 12 hours, and the maximum changes, which occurs between 30 and 35 hours. 377 The time-lapse data sets were inverted using equation 8, i.e. the results of Figure 4 are used as 378 a reference and we inverted data differences to derive model perturbations. We kept the same 18  379 error model for all inversions and we reached a value of εRMS equal to 1 for all inversions, 380 ensuring that all models are fitted to the same level of noise. The results are presented as 381 percentage change of resistivity    382 i B G    1 0 0  (11) B G383 where ρi is the resistivity of the time-lapse section and ρBG is the resistivity of the background 384 section. A negative value corresponds to a decrease in resistivity (or increase of conductivity) 385 and a positive value corresponds to an increase in resistivity. 386 Given the process that is monitored, only negative changes related to an increase in 387 temperature are expected. However, in the inverted time-lapse sections (Figure 7) positive 388 changes of resistivity appear. They are limited in absolute value to +5% in the unsaturated 389 zone which suffers from a very poor resolution, and +3% in the saturated zone. We relate 390 these positive changes to the propagation of data noise in the inversion process (Robert et al. 391 2012). Consequently, we consider that variations in the range -3% to +3% cannot be directly 392 related to temperature variations. They are whitened in the figure. If -3% is the minimum 393 change in resistivity that can be correctly imaged, the limit of detection of ERT for 394 temperature at 13°C for temperature is about 1.2°C (equation 5). 395 The inverted time-lapse sections (Figure 7) show a general behavior of the plume similar to 396 the one observed from the mean resistance. After 7h (not shown), changes in resistance are 397 low and under the level of noise, yielding a section with no changes, i.e. the background 398 model is sufficient to explain the data. After 12h, changes of resistivity about - 5% appear. 399 Then, the decrease in resistivity becomes stronger and reaches a maximum between 25 and 35 400 h. Afterwards, the contrast becomes less strong and after 90 h, almost all changes are below 401 5%. It signifies that their level becomes low to be interpreted quantitatively (close to the limit 402 of detection). However, their spatial distribution is coherent with previous time steps, so it 19  403 means that the aquifer has not returned to its initial state yet, which is confirmed by the mean 404 resistance.  405 The apparent decrease in resistivity observed in the 101 h section is likely due to an artifact of 406 inversion since it is not physically plausible and does not appear in any other sections. The 407 fact that all other anomalies observed in the sections are recurrent for all time steps and that 408 their amplitude variation follows the trend of classical breakthrough curves validate 409 qualitatively the results of inversion. If some anomalies were related to artifacts of inversion, 410 they would be more randomly distributed for the different time-steps. 411 The advantage of crosshole ERT compared to direct measurements is to provide a spatial 412 distribution of the changes occurring in the aquifer. Figure 7 clearly shows that the changes in 413 resistivity are not homogeneously distributed in the aquifer. Most important changes are 414 observed below -7.5 m depth. This part of the alluvial aquifer is dominated by very coarse 415 gravel with pebbles and a limited amount of sandy matrix, as was observed during drilling. 416 The hydraulic conductivity of the bottom part is higher and the flux is greater, so a major part 417 of heat is flowing in this zone of the aquifer. In the upper part, the convection velocity is slow 418 and the maximum change in temperature is much lower, below the minimum change that 419 ERT can detect. Laterally, we also see variations. The maximum change does not occur in the 420 middle of the section, along the supposed main flow direction. It is located closer to ERT-421 borehole 1. The resistivity changes are smaller in the middle part, whereas there are a little bit 422 higher in the neighborhood of ERT-borehole 2. Since sensitivity is smaller in the middle 423 section, there is more uncertainty related to those parameters. However, this trend will be 424 confirmed by direct measurements in boreholes (section 4.4). 425 The lateral variations observed in the ERT sections suggest a degree of heterogeneity that was 426 not clearly distinguishable on borehole logs. Zones of preferential flows modify the expected 20  427 flow direction and result in sections showing a complex spatial behavior. We will see later 428 that these observations are confirmed by direct measurements in borehole. 429 4.3.  ERT-derived temperatures 430 For simplicity, we decided to use a constant value of σf1 (equation 5) to transform the ERT 431 images into temperature sections.  432 Equation 4 proposes a linear relationship between water electrical conductivity and 433 temperature. We thus deduce σf1 based on our direct measurements of temperature. Theyshow 434 that the temperature profile is not constant everywhere in the aquifer and in the ERT section 435 (Figure 8). In ERT-borehole 1, a maximum temperature difference of 1.3°C is observed 436 between the top and the bottom of the aquifer. It is slightly less in ERT-borehole 2. The mean 437 temperature in the two boreholes is also different: 12.8 °C in ERT-borehole 1 (Pz13) and 438 13.6°C in ERT-borehole 2 (Pz17). We took the mean temperature of both ERT-boreholes 439 (13.2°C) and derived with equation 4 a water electrical conductivity of 0.061 S/m. Another 440 solution would have been to interpolate temperatures between boreholes, but it would have 441 made the process more complex without ensuring an improvement of the results.  442 This process has two additional assumptions. First, the specific electrical conductivity of 443 water is constant with time. This was controlled using water samples collected in Pz15 during 444 the test. The changes in the specific conductivity of water are smaller than 1%. The increase 445 in temperature does not seem to favor precipitation or dissolution of minerals. The second 446 assumption is that, at a given temperature, the ratio σf1/ σf,25 (equation 5) is constant in space, 447 or similarly that mf is constant in the whole section. Indeed, if the specific conductivity of 448 water varies in the section, the conductivity at a given temperature varies in the same 449 proportion and the influence on the calculation of temperature is limited. Given the values 450 generally observed in the literature, this assumption is not too severe. 21  451 The spatial distribution of temperature (Figure 9) is similar to electrical resistivity changes 452 (Figure 7). Maximum changes of temperature are observed in the neighborhood of ERT-453 borehole 1, with a maximum temperature of 21°C, which corresponds to an increase around 454 8°C. However, we know that the background temperature in ERT-borehole 1 is slightly below 455 the mean value chosen to draw these sections. Considering the limit of detection of 1.2°C at 456 13°C, temperatures in the range 13.2-14.4°C are only indicative of a small raise in 457 temperature, but the exact value cannot be derived. In addition, we have an error related to the 458 mean water electrical conductivity used in equation 5. 459 4.4.  Comparison with direct measurements 460 The layout of the study site enabled to make a lot of direct measurements in piezometers, at 461 different levels in the aquifer. To compare with ERT results, we have DTS measurements in 462 ERT-boreholes 1 and 2, and groundwater temperature loggers at two levels in the three 463 intermediate piezometers Pz14 to Pz16. 464 The quicker arrival of heat in the bottom part of the aquifer (figures 7 and 9) is confirmed in 465 intermediate piezometers (Figure 10 for Pz15). In the upper part, the arrival is very slow and a 466 clear increase in temperature is only visible after 2 days. The oscillations in the signal are 467 disturbances due to sampling of water by pumping from the piezometer. The amplitude of the 468 signal remains very small, below 1°C at the end of the test. Actually, the peak would only be 469 observed after 10 days with an amplitude of about 1.15°C. The same is observed in Pz16 (1°C 470 after 10 days). In Pz14, the change is slightly higher (2°C after 4 days). In the bottom part, the 471 arrival of heat is quicker, after a few hours, with a range of temperature slightly above the 472 limit of detection of ERT. This is totally in agreement with the ERT sections. Spatially, the 473 temperatures observed with ERT are also coherent with direct measurements. The 474 temperatures observed in the bottom part of Pz14 to 16 have a decreasing trend from Pz14 to 475 Pz16, which is also evident from ERT sections where the zone near ERT-borehole 1 is hotter 22  476 than the middle of the section. As an example, the maximum ΔT in Pz14 is 4.2°C, whereas it 477 is only 2.9°C in Pz15. We can conclude that the qualitative observations on the spatial and 478 temporal distribution of temperature are confirmed by direct measurements. 479 To verify the ability of ERT measurements to quantify temperature, we rely on two different 480 indicators. First, we can draw breakthrough curves at the locations of groundwater 481 temperature loggers to compare the direct measured curve with the ERT-derived curve. This 482 will give insights on the ability to quantify temporally temperature changes. Secondly, we 483 may compare temperature logs at ERT-borehole 1 and 2, to investigate quantitatively the 484 spatial distribution of temperature. 485 Figure 11 shows the breakthrough curves in the bottom part of Pz14 (A) and Pz15 (B) for 486 both direct measurements and ERT. We used the temperatures measured in the corresponding 487 boreholes to determine σf1 in equation 5. For both piezometers, ERT does not detect directly 488 that heat is arrived, because the changes are small, below the sensitivity of the method. 489 However, the rising part of the curve is well resolved with an ERT-derived temperature 490 almost exactly the same as measured directly. The maximum is overestimated, with an error 491 of about 0.5°C in Pz14. The maximum change being 4°C, it represents an error of about 492 12.5%. In Pz15, the fit is less good, but the maximum change is lower and the spatial 493 smoothing of the inversion process may yield an overestimation of the temperature. For both 494 cases, the tail of the curve is overestimated by ERT-derived temperatures. This effect would 495 lead to an overestimation of the thermal dispersivity of the aquifer if ERT results were used 496 alone. This could be related to a 3D effect (shadow effect), because the maximum of the 497 plume, even if not in the section anymore, is still influencing measurements.  498 It must also be kept in mind that the volume investigated by ERT and direct measurements is 499 not the same. Groundwater temperature loggers give a very local measurement inside the 500 piezometer which is itself a singularity inside the aquifer. ERT inversion results give a mean 23  501 resistivity over the surface of the corresponding cell (here 0.25 cm x 0.25 cm). Another 502 possibility would be an increase of the specific conductivity of formation water due to 503 dissolution of minerals related to the increase of temperature. However, given the quick 504 decrease of temperature when we move away from the injection well, this effect is negligible. 505 This is confirmed by the samples collected in Pz15 which shows an almost constant specific 506 conductivity. 507 Temporally, the results are very satisfactory because the raising part, the maximum and the 508 tailing of the curve are imaged at correct times. In this specific case, the time resolution of 509 ERT is only of a few hours. It signifies that we cannot expect to detect the first arrival with 510 precision. Given the material used, we could achieve a time resolution of half an hour, by 511 reducing acquisition time and acquisition delay which were chosen conservative. 512 The comparison of ERT-derived temperatures with DTS measurement in the two ERT-513 boreholes yields contrasted results and conclusions (Figure 12). In contrast with figure 9, 514 where we used a constant value of σf1, the temperatures measured with the DTS for the 515 background profile were here used to derive a specific value of σf1 for each depth level. In 516 addition, DTS measurements were averaged on the time interval corresponding to the 517 duration of a complete ERT data acquisition. Consequently, the match would be perfect if we 518 would derive temperatures for the background ERT profile using equation 5.  519 In ERT-borehole 1 (Figure 12A), ERT results show the same behavior as observed in Figure 520 7, with higher temperatures in the bottom part of the aquifer, and smaller in the upper part. In 521 contrast, DTS measurements yield an almost constant temperature on the whole thickness of 522 the aquifer. This is a quite surprising observation, because all direct measurements made on 523 the site have shown a clear contrast in temperature distribution between the bottom and upper 524 parts of the aquifer. We think that DTS measurements are influenced by specific borehole 525 conditions and do not reflect the true formation temperature. A possible explanation is that the 24  526 water suffers from some mixing in and around the well.. ERT measurements, even if 527 influenced by the borehole fluid, are sensitive to the variations outside the borehole itself. 528 This effect may also explain why temperature near ERT-borehole 1 seems to be higher in 529 Figure 9 in the upper part of the aquifer whereas it is not the case in the middle part of the 530 section. 531 In ERT-borehole 2 (Figure 12 B, C and D), the agreement between ERT-derived temperatures 532 and DTS logs is better. It confirms that the hot spot observed near this borehole in Figure 9 is 533 not an artifact of inversion but is related to an increase in temperature. Globally, DTS 534 measurements show slightly less contrast than ERT, maybe also due to borehole conditions as 535 observed in ERT-borehole 1. Quantitatively, ERT-derived temperatures are close to DTS 536 temperatures for the rising and maximum part of the breakthrough curve (Figure 12 B and C), 537 but suffer from an overestimation for the tail (Figure 12 D), as it was observed in Figure 11. 538 Such an effect would be reduced in a storage experiment with conditions of no flow. 539 The comparison of ERT results with direct measurements and their good agreement confirm 540 that the alluvial aquifer is heterogeneous and complex. Instead of a unique heat plume in the 541 middle part of the section, we observed two separated arrivals with a minimum temperature 542 observed in the middle. 543 5. Conclusion 544 The growing demand for renewable energy leads to an increase in the development of 545 geothermal energy projects. Heat storage has become a common energy storage technology 546 and heat is a common tracer in hydrology and hydrogeology. The variation of electrical 547 resistivity/conductivity of water, soils and rocks is a well-known phenomenon and has been 548 studied for several decades. However, the potential of ERT, a method mapping the electrical 25  549 resistivity of the subsurface, to monitor and quantify temperature was barely approached in 550 the literature.  551 In this paper, we investigated the ability of crosshole ERT to monitor a heat tracing 552 experiment in a complex heterogeneous alluvial aquifer. The studied section was located 553 perpendicular to the main direction of flow to cross the plume of heated water. The results, 554 corroborated by direct measurements in several control piezometers, highlight the ability of 555 ERT to qualitatively monitor the variations of temperature in the aquifer. Spatially, it enabled 556 to map the horizontal and vertical extent of the plume, as well as the zones of maximum 557 temperatures, what would not be feasible with costly and limited direct measurements.  558 If information on the initial fluid conductivity is available, ERT results may be interpreted 559 quantitatively in terms of temperature. The temperatures estimated from ERT were relatively 560 close the ones observed directly during the rise and maximum part of the curve. An 561 overestimation, likely related to 3D effects, was observed for the tail of the breakthrough 562 curve. The error made can be estimated to be between 10 to 20 %, which is a fair value for 563 indirect measurements. The precision of the method may be better in more favorable cases, 564 for example in no or low flow conditions. 3D imaging procedure using more than two wells 565 should also improve the reliability of electrical resistivity monitoring results, yielding a better 566 characterization of temperature distribution. 567 The limit of quantification of temperature changes depends on the noise level observed on the 568 site. ERT requires for an error assessment in order to avoid artifacts in the inverted sections. 569 The higher the noise level, the lower the resolution of ERT to derive temperature changes. In 570 this case, we observed after inversion positive changes of electrical resistivity up to 3% in the 571 saturated zone. Those changes were not physically related to the tracing experiments and 26  572 enabled us to estimate a limit of quantification for ERT around 1.2°C for temperature 573 changes. 574 In contrast with surface ERT, the resolution of crosshole ERT is not depth-dependent but 575 depends mostly on the aspect ratio, the electrode spacing and the distance to the boreholes. In 576 this case, we achieve an aspect ratio of 0.75 with 13 electrodes. A greater distance between 577 boreholes would require a greater electrode spacing or the use of more electrodes. Standard 578 measurement devices generally accept 24 to 32 electrodes per borehole. Considering an 579 electrode spacing a=0.5 m, we successfully imaged a heterogeneous heat plume with a 580 thickness about 5a and a width of about 4a. The results obtained in this study could be easily 581 extended to other experiment keeping similar parameters. The resolution could even be 582 refined using better aspect ratio or more electrodes. The scale of this experiment could be 583 applied for the control of aquifer thermal energy storage (ATES) located in alluvial plains. 584 For deeper and larger systems, it would require larger distances between electrodes and 585 boreholes or the use of set-up with more than two boreholes. 586 In this experiment, we only achieve a time resolution of a few hours. Our measuring 587 procedure takes about 45 minutes. However, it is possible to reduce acquisition delay and 588 acquisition time of each measurement. It would allow to achieve a time resolution of less than 589 30 minutes. Avoiding the complete collection of reciprocal at each time step would further 590 divide the time to collect the data by two. 591 The results presented in this paper suggest that ERT should be considered when designing 592 heat tracing experiments to derive the parameters governing heat flow and transport in the 593 subsurface or geothermal systems. It should also be used to assess the complexity of the 594 concerned reservoirs. It also appears that ERT could be a useful tool to monitor and control 595 geothermal systems once they are in operation. A proper configuration of ERT wells, 27  596 depending on the installed configuration, should enable to control the temperature distribution 597 in the reservoir. This may be of crucial importance to better describe the thermal affected 598 zone or assess the possible influence of the system on groundwater chemistry or 599 microbiology. 600 Acknowledgement 601 We would like to thank the associate editor and two anonymous reviewers for their pertinent 602 comments and suggestions which have helped to improve the manuscript. We also thank the 603 F.R.S.-FNRS and the « Fondation Roi Baudouin – Ernest Dubois Award » for their financial 604 support during the PhD of Thomas Hermans.  605 28  606  607 References 608 Allen, A., Milenic, D., 2003. 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Shallow heat 784 injection and storage experiment: heat transport simulation and sensitivity analysis. 785 Journal of hydrology, 409, 262-272. 786 Vandenborght, J., Kemna, A., Hardelauf, H., Vereecken, H., 2005. Potential of 787 electrical resistivity tomography to infer aquifer transport characteristics from tracer 788 studies: A synthetic case study. Water Resources research, 41, W06013. 789 doi:10.1029/2004WR003774. 790 Vanhoudt, D., Desmedt, J., Van Bael, J., Robeyn, N., Hoes, H., 2011. An aquifer 791 thermal storage system in a Belgian hospital: Long-term experimental evaluation of 792 energy and cost savings. Energy and Buildings, 43, 3657-3665. doi: 793 10.1016/j.enbuild.2011.09.040. 794 Vereecken, H., Binley, A., Cassiani, G., Revil, A., Titov, K., 2006, Applied 795 Hydrogeophysics, Nato Science Series, IV Earth and Environmental Sciences, 71, Springer. 36  796 Warner, D.L., Algan, U., 1984. Thermal impact of residential ground-water heat pumps. 797 Ground water, 22, 6-12. 798 Zhou, B., Greenhalgh, S.A., 2000. Cross-hole resistivity tomography using different 799 electrode configurations. Geophysical Prospecting, 48, 887-912.37  800 FIGURE  801  802 Figure 1. The site of Hermalle-sous-Argenteau is located at the northern part of the Meuse 803 River  in Belgium (Wallonia) near the Dutch boarder. It is located almost at mid-distance 804 between the Meuse River and the Albert Canal. 38  805  806 Figure 2. The new piezometers are arranged in three different panels crossing the expected 807 flow direction between an injection and a pumping well. Pz 10-12, Pz, 14-16 and Pz 18-20 are 808 equipped with groundwater temperature loggers at two different levels. On the middle panel, 809 the outer piezometers were equipped with a DTS system and with electrodes. 39  810  811 Figure 3. The water electrical conductivity of formation water increases linearly with 812 temperature (points). Parameters of equation 4 were fitted with a fractional change per degree 813 -1Celsius, mf, equal to 0.0194 °C  and the electrical conductivity at 25°C is 0.0791 S/m. 40  814  815 Figure 4. The background inverted section shows resistivity values (Ohm-m) varying 816 between 100 and 200 Ohm-m. The section seems slightly heterogeneous. 41  817  818 Figure 5. The relative sensitivity pattern is typical of cross-borehole measurements, with 819 smaller sensitivity values in the middle part of the section, especially at the position of top 820 and bottom electrodes. 42  821  822 Figure 6. The mean resistance (in Ohm) of the global data set first decreases with depth as the 823 plume of heated water approaches, it reaches a minimum after 30 to 35 hours and then starts 824 to increase slightly. 43  825  826 Figure 7. The inverted sections (% change in resistivity) evolve in time with the arrival of the 827 plume. Maximum changes are observed between 30 and 35 h in the surrounding of ERT 828 borehole 1. These sections highlight the spatial heterogeneity of the aquifer. Time is given 829 from the beginning of injection. 44  830  831 Figure 8. DTS temperature profiles in the two ERT boreholes before the test are not similar. 832 The temperature varies with depth and the mean temperature is different in the two boreholes: 833 12.8°C in ERT-borehole 1 and 13.6°C in ERT borehole-2. 45  834  835 Figure 9. The ERT-derived temperature sections show that the maximum temperature 836 reached is around 21°C in the neighborhood of ERT-borehole 1. The sections are limited to 837 the saturated zone, because equation 5 is not valid in the unsaturated zone. 46  838  839 Figure 10. The temperature monitored at two different levels in Pz15 shows that the arrival of 840 the tracers is much quicker and with much higher amplitude in the bottom part of the aquifer 841 than in the upper part. 842  843 Figure 11. Breakthrough curves for ERT-derived temperatures and direct measurements in 844 Pz14 (A) and Pz15 (B) show a good temporal agreement, but temperature are overestimated 845 for the maximum and the tail of the curve. 47  846  847 Figure 12. ERT-derived temperature profiles are not consistent with DTS measurements in 848 ERT-borehole 1 (A), but show a very good agreement in ERT-borehole 2 (B, C and D). The 849 almost constant temperature observed with DTS in ERT-borehole 1 may be due to some 850 mixing of water in and around the well.  48