A tracer test in a shallow heterogeneous aquifer monitored via time-lapse surface electrical resistivity tomography

Transcription

1 GEOPHYSICS, VOL. 75, NO. 4 JULY-AUGUST 21 ; P. WA61 WA73, 18 FIGS., 2 TABLES / A tracer test in a shallow heterogeneous aquifer monitored via time-lapse surface electrical resistivity tomography Martina Monego 1, Giorgio Cassiani 2, Rita Deiana 2, Mario Putti 3, Giulia Passadore 1, and Lorenzo Altissimo 4 ABSTRACT We illustrate a case study of a saline tracer test in a shallow, highly heterogeneous aquifer, monitored by means of surface time-lapse ERT. The test was aimed at identifying the system s hydraulic properties. Some of the expected limitations of the method particularly caused by the strong decrease in ERT resolution with depth and the consequent problems with mass balance and moment calculation could be partly balanced by the use of direct measurements of groundwater electrical conductivity and tracer concentration at one selected location. The vast heterogeneity of the system, ranging in lithology from clay to gravel at a scale of meters to tens of meters, reflects itself in the tracer migration and distribution over time: The tracer is trapped in the low-permeability regions and from these it is slowly released over time. Highresolution surface ERT proves effective at picturing this system behavior over time. The extreme heterogeneity is also a challenge in the attempt to translate bulk electrical conductivity into estimates of groundwater electrical conductivity and, hence, solute concentration because surface conductivity in fine sediments has an important role. The test results could be used to identify some of the key parameters for solute transport, namely, mean groundwater velocity and aquifer dispersivity at the scale of the test by means of transport model calibration. INTRODUCTION Transport of dissolved substances in groundwater is one of the most important mechanisms controlling the migration of pollutants in the subsurface. Transport in the dissolved phase is also a key factor in contaminant remediation processes: Chemical and biochemical reactions occur in the aqueous phase and the required contact between reagents and biota is controlled by transport Mao et al., 26. Transport is strongly controlled by geologic heterogeneity, which plays a key role at a variety of scales. In particular, hydraulic conductivity, one of the key hydrogeologic parameters, can vary by up to 13 orders of magnitude Freeze and Cherry, Solute transport processes are consequently affected by heterogeneity, resulting in strong spatiotemporal variability of solute concentrations. This makes conventional monitoring techniques, based on few boreholes and limited water sampling in space and time, often incapable of capturing the variability and the complexity of transport processes. Only in the presence of the exceptional monitoring infrastructures at a few well-characterized scientific research sites e.g., MacKay et al., 1986; Molz et al., 1986; LeBlanc et al., 1991; Boggs et al., 1992; Kemna et al., 22 is it possible to have enough sampling points many tens to hundreds of multilevel samplers to picture the spacetime evolution of solute plumes. These well-known experiments essentially confirmed the limitations of conventional sampling schemes and the need for additional information. In recent years, increasing attention has been paid to geophysical methods that can provide spatially and temporally dense information on the evolution of solute plumes, particularly during tracer tests Vereecken et al., 22; Hyndman and Tronicke, 25; Rubin and Hubbard, 25; Kemna et al., 26; Vereecken et al., 26. Electrical and electromagnetic techniques have been used predominantly for these purposes because they are sensitive to changes in aqueous-phase electrical conductivity caused by saline tracers, which are most often used for this purpose. Tracer salinity cannot exceed several grams per liter to avoid gravity effects but these concentrations are sufficiently high in most cases to be detectable using surface and borehole geophysical methods. Tomographic techniques offer the possibility of constructing images of the subsurface in Manuscript received by the Editor 31 July 29; revised manuscript received 24 October 29; published online 3 September Università di Padova, Dipartimento IMAGE, Padova, Italy. monego@idra.unipd.it; passadore@idra.unipd.it. 2 Università di Padova, Dipartimento di Geoscienze, Padova, Italy. giorgio.cassiani@unipd.it; rita.deiana@unipd.it. 3 Università di Padova, Dipartimento DMMMSA, Padova, Italy. putti@dimsa.unipd.it. 4 Centro Idrico Novoledo, Villaverla, Italy. altissimo@centroidriconovoledo.it. 21 Society of Exploration Geophysicists. All rights reserved. WA61

2 WA62 Monego et al. two or three dimensions, which are well suited to picture the evolution of solute plumes. Electrical resistivity tomography ERT in particular has been the key methodology applied for saline tracer imaging e.g., Binley et al., 1996 but some notable examples using GPR attenuation for the same purpose have also been made possible due to the increased electrical conductivity of the tracer Day-Lewis et al., 23; Johnson et al., 27. In all cases and in contrast to structural hydrogeologic characterization, in which static properties of the subsurface are explored e.g., delineation of lithological boundaries, estimation of hydraulic conductivity, assessment of aquifer heterogeneity, transport characterization involves the monitoring of dynamic processes associated with spatiotemporal variations of subsurface state variables. The mapping and monitoring of transport processes therefore require the application of time-lapse geophysical methodologies that allow the user to distinguish between static and dynamic effects. Early applications e.g., Bevc and Morrison, 1991; Daily et al., 1992, 1995; Binley et al., 1996; Slater et al., 1997, 2; Barker and Moore, 1998 are limited to imaging solute transport as accurately as possible. Though important, these applications could not provide estimates of hydraulic parameters and their spatial variability. To quantify the hydraulic parameters of the subsurface, it is essential to make use of hydrologic models. The most complete use of the geophysical data coming from tracer monitoring would be to use these data for hydrologic model calibration e.g., for vadose zone studies, see Binley et al., 22; Deiana et al., 27, 28. In solute tracer experiments, the presence of the tracer is detected by geophysical identification using electrical or EM methods. The corresponding time-lapse data are used as equivalent concentration data to infer the timing and location of the tracer breakthrough. In conjunction with transport models, such data can be directly interpreted in terms of transport parameters such as flow velocity and dispersivity. The recent literature on time-lapse ERT applied to saline tracer tests follows this conceptual pathway to different extents. A simple advective-dispersive transport model is used by Slater et al. 22 to try and match the evidence from time-lapse 3D ERT monitoring of a controlled saline tracer experiment in a tank. Approximate analytical solutions to the transport equation are adopted by Kemna et al. 22 in terms of a classical 3D solution to the transport equation in an equivalently homogeneous medium and as an equivalent stream tube model that can help identify the effect of hydraulic heterogeneity from the time-lapse 2D ERT images collected along a plane roughly perpendicular to the main flow direction. Vanderborght et al. Veneto (ITALY) Province of Vicenza VERONA VICENZA PADOVA ROVIGO BELLUNO TREVISO VENEZIA Lessini Mountains Sochio Thiene Sandrigo Villaverta Dueville Springs zone VICENZA Figure 1. Location of the test site in the Veneto region, northeast Italy. 25 perform a synthetic case study to evaluate the possibility of estimating local-scale dispersion and spatial statistics of hydraulic conductivity from ERT data. Their approach is based on a first-order approximate solution of the stochastic transport equation. Singha and Gorelick 25 use a classical 3D advective-dispersive equation for their synthetics and analyze their experimental results using a moment analysis of the resulting real and synthetic plumes, calculating dispersion from rates of second-moment changes over time. The moment analysis pointed out a severe underestimation of the injected tracer mass recovery only 25%, qualitatively similar to findings in vadose-zone 3D ERT experiments Binley et al., 22, where approximately 5% of the water mass is recovered by ERT, which is attributed to the limited resolution provided by ERT away from electrodes Day-Lewis and Lane, 24; Day-Lewis et al., 25. This fact prompted a series of possible approaches to tackle the limited resolution of ERT Singha and Gorelick, 26a, 26b; Singha and Moysey, 26. However, optimism about the information content of time-lapse ERT has prevailed Day-Lewis and Singha, 28; Pollock and Cirpka, 28; Singha et al., 28 and indeed this methodology confirms itself as a potentially indispensable tool to see the motion of solutes and the water carrying them in the subsurface e.g., Cassiani et al., 26. In this paper, we present the results of a saline-tracer test field experiment conducted in a shallow highly heterogeneous aquifer. The goals of this study were 1 to assess the feasibility of deriving quantitative information on solute concentration and hydraulic parameters from surface ERT measurements and 2 to test the procedure in a rather unfavorable highly heterogeneous environment. SITE DESCRIPTION The area selected for the field experiment is located in northeastern Italy, approximately 13 km from the city of Vicenza Figure 1. The area is a natural reserve that belongs to the company that manages the waterworks of Padova Acegas-Aps. Some deep approximately 1 m supply wells are located in the area Figure 2. This is a flat region with elevations between 5 and 56 m above sea level. Geologically, the site is located in the so-called linea delle risorgive resurgence line, where groundwater flowing from the upper Po river plain recharge zones encounters the fine-grained sediments of the lower plain and eventually comes back to the surface. The points of outflow springs are known as risorgive resurgences. As a result, numerous small streams are produced, eventually flowing into each other to form resurgent rivers. The resurgence line is characterized by an extreme heterogeneity of sediments, varying from coarse gravel to clay in short distances. N Our experiments have been focused on the first few meters below the ground surface in a small area characterized by a very shallow water table approximately 1 m below the ground surface with a fairly regular northeast-southwest slope Figure 3. In this area, various shallow boreholes were drilled and completed. The descriptions of cores extracted from two boreholes GP5 and GP6 down to 5-m depth are shown in Figure 4. Note how heterogeneous the system is, considering that the two boreholes are only 9 m apart Figure 3. The presence of a silty clay clayey silt lens is apparent at the location of borehole GP6 Field site

3 Tracer test monitored via ERT WA63 whereas at the same depth we have gravel with sandy silt in borehole GP5. This evidence is fully consistent with the highly heterogeneous nature of the resurgence area and is expected to strongly impact the flow and transport behavior of the system. Consequently, it is not surprising that the groundwater electrical conductivity shows some nonnegligible spatial variation Table 1 even at small distances, with a general decrease southwest Figure 2, where shallow groundwater mixes with water flowing in the ditch. N Marenda Bevarara PA PB Acegas-APS area Piezometers Public wells EXPERIMENTAL SETUP Tracer test and ERT data acquisition To test the hydraulic characteristics of the shallow part of the system, we performed a saline tracer test monitored via shallow high-resolution surface ERT. Figure 3 shows the water table as measured on July 14, 28. The mean groundwater flow direction from northeast to southwest suggests that a tracer test could be conducted by injecting a saline tracer in borehole GP6 with a reasonable expectation of retrieving the tracer at borehole GP5 see Figure 4 for the corresponding stratigraphy. Therefore, we concentrated our attention on a small rectangular area at the intersection between two ditches, corresponding to a rectangle of 18.8 m x-direction by 1 m y-direction; Figure 5. The area was defined by the need to allocate 14 ERT lines of 48 electrodes each. The selected electrode spacing was.4 m in the x-direction and.25 m in the y-direction so that each intersection is marked by one electrode. We used 2-cm-long stainless steel electrodes. The depth of investigation of ERT depends on the nonlinear manner of the electrical resistivity distribution and on the survey line extent. A priori only a rough estimate of the depth of investigation can be made, ranging between 1/5 and 1/4 of the survey line length. For the case at hand, we estimated that a maximum reliable investigation depth is 4 m for the x lines and approximately 3 m for the shorter y lines. The saline tracer was prepared using 5 m 3 of water from the nearby ditches and NaCl to achieve a concentration of 6 g/l with a resulting electrical conductivity of approximately 11 ms/ cm. Larger concentrations of NaCl could lead to gravitative sinking and are not necessary to achieve the required increase in bulk conductivity to be detected from the ground surface see Cassiani et al., 26. The average background electrical conductivity of the pore water on site is 55 ms/cm. The injection of the 5 m 3 of aqueous solution took place on July 14, 28 in borehole GP6, which is screened between 1 and 4 m below Rizzi GP1 GP2 15 m 3 m "La Boiona" spring Figure 2. Larger-scale view of the test site. The triangles indicate the shallow boreholes and the circles show the location of the deep wells extracting water for the Padova waterworks. N GP 3 PZ 13 PZ 12 PZ 14 GP 4 GP 5 GP8 PZ11 PZ 9 PZ 1a PZ 1 GP 6 GP 7 PZ 8 PZ 7 PZ 6 Irrigation ditch Field site Piezometric levels equidistance:.2m 5 m Figure 3. Setup of the test site. The arrow indicates the expected prevailing groundwater flow direction. The water-table contour lines correspond to the piezometric survey run on July 14, 28, the same day the tracer test began.

4 WA64 Monego et al. ground. The system returned quickly to hydraulic equilibrium after tracer injection, as testified by the return of the water-table elevation to the original level in the injection borehole. Electrical resistivity tomography monitoring only started after this transient; therefore, this phase could be safely ignored in the hydraulic modeling see below. The ERT acquisition was planned as a sequence of 2D lines. For each line, a complete skip dipole-dipole scheme was adopted, acquiring direct and reciprocal swapping potential with current electrodes measurements to have an estimate of measurement errors Daily et al., 24. An on time for the current of 25 ms was chosen for each cycle and a target 5 mv potential reading was set as a criterion for current injection. The sequence was optimized to take full advantage of the ten physical channels of the IRIS Syscal Pro resistivity meter so that each sequence was composed of 1925 measurements, requiring approximately 2 minutes for acquisition. One ground level.5 m 1. m 1.5 m 2. m 2.5 m 3. m 3.5 m 4. m 4.5 m 5. m depth (m) Table 1. Background electrical conductivity of groundwater at the experimental site prior to saline tracer injection (July 7, 28). Note the fairly large natural variability of background conditions partly controlled by the flowing irrigation ditches (Figure 5), particularly on boreholes PZ12 and PZ14. Borehole see Figure 5 bottom ground soil with silt and gravely elements fine gravel with sandy silt silty clay clayey silt silty clay silty gravel with sand silty sand fine sand silty clay fine sand silty clay fine sand clay sandy silt fine sand with silt silt GP6 stratigraphy description.5 m Groundwater electrical conductivity w S/m GP5.568 GP6.583 GP7.643 GP8.515 PZ PZ groundwater level groundwater level July m 1.1 July 2 26 sandy silt clayey silt sandy silt ground level 1.5 m 2. m 2.5 m 3. m 3.5 m 4. m 4.5 m 5. m depth (m) bottom ground soil with clayey silt gravel with silty sand gravel with sandy silt fine silty sand coarse sand sandy silt silty sand with gravel fine sand sand fine sand with silt fine sand fine sand with silt clay sandy silt sandy silt with clay complete survey 14 lines was possible in one day. One background survey was run prior to tracer injection to estimate background bulk conductivity. Six complete surveys followed the injection July 15, July 17, July 29,August 1,August 7, andaugust 28. Direct measurements of groundwater electrical conductivity supplemented the ERT data sets: Continuous monitoring of electrical conductivity and automated groundwater sampling every two hours were performed in borehole GP5 at 2.5 m from the ground surface. Samples were analyzed for Na and Cl concentrations. The monitoring at borehole GP5 started at 6 p.m. on July 15 and lasted until 11 a.m. onaugust 11, 28. Inversion of electrical data sets The tomographic inversion of electrical data sets was performed using an Occam inversion approach LaBrecque et al., 1996 using the code ProfileR Binley, GP5 stratigraphy description fine sand with silt sandy silt find silty sand Figure 4. Stratigraphic logs of injection GP6 and monitoring GP5 boreholes see Figures 3 and 5 for location The data processing consisted of rejecting data for which the difference between direct and reciprocal values exceeded a threshold error equal to 5% of the average of the same two measurements. On average, this criterion implied a loss of approximately 1% of the data points. The number of valid quadripoles averaged approximately 9 values taken as averages of valid direct and reciprocal data points. Changes in ERT images with time could have been assessed by carrying out independent data inversions, each representing a snapshot in time, and subtracting values pixel by pixel from the background image. However, when time changes are small relative to the natural spatial variability within the region of interest and because of the 2D geometry in the monitoring of 3D processes such as a tracer injection, pixel-by-pixel subtraction is often ineffective in providing clear images of tracer motion with time. In this paper, the analysis of the resistivity variations with time was performed following the method of Daily et al. 1992, which uses the ratio of the resistance measured at the same quadripole at different times. Thus, for each quadripole, the data to be inverted at each time step following the first one is derived from the current and background resistance values as R R hom R i R, where R hom is the resistance of the same quadripole for a homogeneous reference medium, R is the resistance of the quadripole in the background survey, and R i is the resistance of the quadripole in the current ith survey. The same 5% data error level adopted in the background inversion was assumed in the resistance ratio inversion. In principle, 3D inversion of the same data set might be possible even though the acquisition is indeed in two dimensions on each line. However, considering the large number of data points approximately 12,5 per time step and the large number of cells that would be required for 3D inversion approximately 3, we elected to take a simplified approach and analyze individual 2D inversion results. 1

5 Tracer test monitored via ERT WA65 Time-lapse ERT results RESULTS AND DISCUSSION The results of the background ERT survey are shown in Figure 6. One striking feature of this background image is the presence of a distinct low-resistivity body roughly aligned with lines y 1, y 2, and y 3 and as deep as approximately 3 m from the ground surface. A comparison with the available core analysis in borehole GP6 Figure 4 located very close to line y 2 confirms that this body is a lens of silt and clay. Similarly, a comparison of lines y 5 and x 3 with the stratigraphic column in borehole GP5 Figure 4 also confirms that the high-resistivity regions are mostly saturated gravel. The shallow and generally conductive part of all ERT lines is the silty soil extending to approximately.5 m from the ground surface Figure 4. Resistivity ratio inversion was conducted for all six surveys following the tracer injection. The corresponding results relevant to x lines are shown in Figure 7 of course, only for the region below the water table at approximately 1-m depth. Because x is nearly parallel to the prevailing flow direction see Figures 3 and 5, we limited the display to the profiles that show the patterns of tracer transport more directly; the y lines show results consistent with the x lines at all times. Several features can be noted in Figure 7: Right after tracer injection July 15, the tracer is clearly concentrated around the injection point and extends more in the direction perpendicular to flow than longitudinally. This is a relatively strange feature that can be explained only by the strong control exerted by the system heterogeneity Figure 6 on the flow and transport patterns; note that injection in borehole GP6 took place in a low-permeability region under a transient local gradient that pushed the tracer along the maximum permeability patterns. Three days after injection July 17, the tracer shows a fast migration forward, practically reaching the end of the 18.8-m section but a large anomaly remains in the injection zone. This is an indication that tracer outflow from the low-permeability region is slow. Consequently, the tracer plume is split into more than one body, as is clearly seen in sections x 2 and x 3. As time progresses, a quasi-steady situation is reached when the tracer continuously flows out of the low-permeability region and samples the high-permeability regions downgradient; effectively, the low-permeability region takes the role of a continuous source of tracer for the rest of the aquifer. These results confirm that the system is highly heterogeneous and that this heterogeneity strongly impacts the distribution and migration of the tracer during and after injection. Groundwater electrical conductivity from bulk electrical resistivity changes Figure 7 shows the behavior of the tracer migration only in qualitative terms. To translate the resistivity ratio values into quantitative estimates of solute concentration, two steps must be taken. First, bulk resistivity as measured by ERT must be translated into aqueous-phase resistivity below the water table ; and second, aqueous-phase resistivity must be converted into solute concentration. Generally, step 1 is conducted in clay-free, fully saturated sediments using Archie s law 1942 m 2m 2m 2m 2m 2m y PZ 7 Irrigation ditch PZ 8 PZ 9 PZ 1 x 6 x 4 x 3 x 2 GP7 x 6 GP8 x 4 x 3 GP6 GP5 x 2 x1y 1 y 2 y 3 y 4 y 5 y 6 y 7 Ωm GP7 approximate expected groundwater flow direction saline trace injection GP6 sampler GP5 GP8 PZ 14 PZ 12 x 1 y 1 y 2 y 3 y 4 y 5 y 6 y m 3.2 m 3.2 m 3.2 m 3.2 m 3.2 m N x Figure 5. Geometry of the 2D surface ERT lines covering the area impacted by the saline trace injection in borehole GP6. In the x- and y-directions, the lines are composed of 48 electrodes, spaced.4 inches and.25 m apart, respectively. Continuous groundwater sampling was performed in borehole GP y 1 y2 y 3 y 4 Figure 6. Background resistivity images along the x- and y-directions. Note the presence of a well-identified lens of silt and clay to the northeast, confirmed by the stratigraphic log of borehole GP6 Figure 4 and detected as a very conductive body by ERT lines in both directions resistivity of this body is approximately 2 m and lower. Saturated sand and gravel have resistivity values of approximately 1 m. x 1 x 2 x 3 y 5 x 4 y6 x 6 y 7 Irrigation ditch

6 WA66 Monego et al. a) July 15th, 28 July 17th, 28 x x x x x b) x x x x x c) Depth (m) July 29th, 28 August 1st, 28 August 7th, 28 x x x x x Depth (m) Depth (m) August 28th, Resistivity ratio with respect to background (%) Resistivity ratio with respect to background (%) Resistivity ratio with respect to background (%) Figure 7. a Resistivity ratios with respect to background in the x-direction on July 15 and July 17. Injection took place on July 14. b Resistivity ratios with respect to background in the x-direction on July 29 and August 1. c Resistivity ratios with respect to background in the x-direction onaugust 7 andaugust b w F w m, where s b is bulk electrical conductivity s b 1/r b, r b is bulk electrical resistivity e.g., as shown in Figure 6, s w is water electrical conductivity, and F is named the formation factor that is a function of porosity f and an empirically derived cementation exponent m. For the case presented in this paper, it is expected that Archie s law equation 2 cannot be applied for the entire domain, given the presence of regions with important clay fractions. We computed the apparent formation factor F using equation 2 and a spatially interpolated groundwater electrical conductivity derived from the data in Table 1. The result Figure 8 confirms that Archie s law cannot be applied everywhere because in the silt-clay lens we have very low F values close to one or even lower, indicating an important contribution from surface conductivity s s that in a first approximation Brovelli et al., 25 can be considered as acting in parallel with conduction within the saturated pore space b w F w F s. Waxman and Smits 1968 propose a classical model to describe surface conductivity s BQ v F, where Q v is the volume concentration of clay exchange cations meq/cm 3 and B is the equivalent conductance of the clay counterions cm 2 S/meq, which is related to their mobility. The empirical parameter B is a function of s w given in S/m and of the cementation exponent m according to Sen et al B 1.93m 1.7/ w. To quantify the electrical conductivity of the aqueous phase in the region where Archie s law is not applicable, we need to estimate the parameters in equation 4, particularly Q v. We made a few assumptions: We identified the clayey region on the basis of a threshold value of the apparent formation factor F Figure 8, consistent with the stratigraphic log of borehole GP6. We considered Archie s law applicable if F 2 clay-free region. In the region where F 2 clayey region, we applied the Waxman and Smits relationship equation 4; Waxman and Smits, 1968 with an assumption equation 5. We assumed that inside the clayey region the true formation factor F is equal to the average formation factor in the F 2 region, i.e., F a 4. According to core evidence, we set porosity f.3 so that the cementation exponent to be used in equation 5 is m By substituting the corresponding values in equation 4, we could estimate the value of Q v for all locations in the clayey region Q v F a b w, m 1.7/ w

7 Tracer test monitored via ERT WA67 where s b measured from ERT and s w interpolated from data in Table 1 correspond to background conditions. The resulting estimated Q v distribution is shown in Figure 9 for the x sections below the water table at approximately 1-m depth. The corresponding range for Q v.3.8 meq/cm 3 is within literature values Lesmes and Friedman, 25. Once the parameters of Archie s law equation 2 in the clay-free region F and the parameters of Waxman and Smits relationship equation 4 in the clayey region F a, m, and Q v are identified on the basis of the background measurements, it is possible to estimate the electrical conductivity of the aqueous phase at time t from the bulk electrical conductivity measured by ERT. For the clayey region, it is necessary to iterate to find s w t as the zero of equation 7 for every location F a b t w t 1.93mQ v / w t x 1 x 2 x 3 x 4 x 6 Figure 1 shows the corresponding estimated variation of groundwater electrical conductivity with respect to background for one date July 17. Analogous results are available for all dates. The quantitative estimation of groundwater electrical conductivity is a key step toward the use of ERT-monitored tracer test data for hydraulic characterization. However, several caveats must be kept in mind; in particular, we know that resolution in the ERT image varies dramatically in space Day-Lewis et al., 25 and this generally leads to a severe underestimation of the tracer total mass. We approached the problem by making two substantial simplifying assumptions: The bias is introduced by ERT inversion and due to resolution issues is not strongly space dependent; consequently, the bias can be removed at least to a first-order approximation by scaling the solute concentration values derived from ERT using a proportionality coefficient derived from a single point where solute concentration is known. The assumptions above are apparently very strong but they are justified by the acquisition geometry and the subsequent data use. First, ERT acquisition takes place from the surface only. This geometry leads to a sensitivity/resolution spatial distribution that has a strong depth variation with depth and small variations in the horizontal direction. Second, in view of the above, it makes perfect sense not to try and derive 3D distributions of solute concentration because resolution is dramatically lost at depth and the corresponding solute concentration estimates would be strongly biased in the vertical direction. Therefore, we elected to take vertical averages of the estimated solute concentrations and compare such averages with a 2D transport model. This is also justified by the prevalent horizontal direction of the hydraulic gradient. In the following section, we tackled this problem mainly with the help of direct chemical measurements at one location borehole GP Depth (m) F y 1 y y y y y 6 y Figure 8. Apparent formation factor F computed according to Archie s law for the 14 ERT sections x and y, on the basis of the background resistivity images from surface ERT Figure 6 and of the interpolated background groundwater electrical conductivity values Table 1. Note how in correspondence with the lens of silt and clay identified in Figure 6 the F values are unreasonably low close to one or even lower, thus showing that Archie s law is not applicable there, for which an important surface conduction contribution must be accounted. x 1 x 2 x 3 x 4 x Depth (m) 3 Q (meq/cm ) v Figure 9. Cation exchange capacity per unit pore volume expressed in meq/cm 3 estimated along the x ERT profiles using Waxman and Smits 1968 model and the procedure described in the text.

8 WA68 Monego et al. Direct chemical measurements and groundwater tracer concentration Groundwater samples from borehole GP5 at 2.5-m depth allowed for direct measurements of Na C Na and Cl C Cl concentrations during the experiment, accompanied by downhole monitoring of groundwater electrical conductivity s w. The dependence of s w on C Cl is notably linear Figure 11. Interestingly, a comparison between Na and Cl concentrations divided by their respective molecular weights Cl 35.45, Na clearly shows Figure 12 that Na is removed with respect to Cl the equivalent weights will be equal. This is another strong indication that significant cation exchange takes place over the clayey sediments prior to groundwater arrival at the monitoring borehole GP5. The peak concentration of Na and Cl is approximately t peak 4 days after injection. However, the peak does not coincide with the traveltime of the center of mass, as calculated from x y y x2 2 σ w (s/m).34 y x y 4 x y x x.8 y x 7 y Depth (m) Figure 1. Variation of aqueous-phase electrical conductivity on July 17 with respect to background, as estimated from Waxman and Smits 1968 in the clayey region and fromarchie s law 1942 elsewhere. 12 tc t dt T, 8 TC t dt where T is the total sampling time from July 15 toaugust 11 note that in Figure 12 only the data to July 27 are shown. We obtain t 9.5 days. The discrepancy between t peak and t is to be attributed to the very long tail of the breakthrough curves at GP5. Because the distance between boreholes GP6 and GP5 is approximately 9 m, the average groundwater velocity can be estimated between 1 and 2.25 m/day, depending on whether we take into account t or t peak. We used the direct measurements at GP5 to find an in situ relationship between groundwater electrical conductivity changes from ERT and groundwater Cl concentration. This approach is in line with the idea that resolution limitations in ERT lead to the need for in situ petrophysical relationships Singha and Gorelick, 26a, 26b; Singha and Moysey, 26 even though we use a far more simplified but practical approach than the above authors. We basically use a single-point calibration to derive the necessary correction, which is then applied to the entire data set. Figure 13 shows the relationship between measured C Cl in borehole GP5 and the corresponding excess groundwater electrical conductivity at approximately the same location as derived from ERT section y 2 at 2.5-m depth, the same depth of groundwater sampling at GP5. The relationship is fitted with a linear regression consistent with direct evidence at borehole GP5 Figure 11, assuming that the resolution loss away from the electrodes i.e., at depth does not alter linearity between groundwater electrical conductivity and Cl concentration. The derived linear relationship is then used to convert the entire data set of excess groundwater electrical conductivity Ds w into estimated Cl concentrations. As ERT resolution is rapidly degraded with depth, we decided to combine the information along the vertical direction and analyze the tracer Fluid electrical conductivity σ w (S/m) Chloride concentration (g/l) Figure 11. Relationship between Cl concentration and groundwater electrical conductivity monitored by direct measurements in borehole GP5 see Figure 5. The relationship is notably linear over the considered range. Equivalent weight Chloride Sodium 7/15 7/16 7/17 7/18 7/19 7/2 7/21 7/22 7/23 7/24 7/25 7/26 7/27 7/28 Date (month/day) Figure 12. Breakthrough curves of Na and Cl at borehole GP5 see Figure 5 in equivalent parts. Note that Na is selectively removed with respect to Cl they should be in a one to one relationship due to exchange over the clayey sediments Na is probably exchanged with Ca.

9 Tracer test monitored via ERT WA69 movement in the horizontal plane. Before averaging along the vertical direction, we removed the top meter of each section corresponding to the vadose zone, we considered only the trapezoidal central part of each ERT profile as usually shown in commercial ERT codes, and we limited ourselves for x and y lines to a maximum depth of 3.5 m below ground. In this way, we kept only results that are more reliable in terms of ERT resolution. The vertically averaged ERT-derived Cl concentrations along the 14 2D lines were subsequently combined to give a map in plan view, using an interpolation scheme based on weighted averages at each point in which weights are inversely proportional to the distance squared. Figure 14 shows the results of this procedure for the six postinjection surveys. The figure clearly shows the main mechanisms of tracer injection with elongation in the y-direction July 15 and the following release of the tracer and migration predominantly in the x-direction. Already on July 17, two tracer bodies separate: One is migrating fast in the x-direction whereas the other is trapped in the clayey region close to the injection point. Figure 15 shows the same vertically averaged Cl concentration in which only the values outside the clayey regions are considered for horizontal interpolation. Moment analysis and modeling results A basic moment analysis was conducted on the results in Figures 14 and 15. The zeroth order moment was defined as M AC x,y dxdy, 9 motion of the center of mass Figures 15 and 16 is on average extremely slow approximately.12 m/day, totally incompatible with the observed t and t peak, see above. This is not surprising because the mass spatial distribution is controlled mainly by the slow release from the clayey regions, particularly at late times. In fact, if we consider only the data of July 15 and July 17, when the slow tail release from the trapped mass is not predominant, the groundwater velocity is approximately 1 m/ day, compatible with direct evidence from samples at borehole GP5. Considering only the mass in the nonclayey region Table 2, last column, we observed that mass increases between July 15 and July 17 and then steadily decreases. Because the sampling data at borehole GP5 confirm that the arrival time is between July 18 and July 23 considering either t peak or t, we can assume that tracer mass started to leave our control volume Figure 5 from the downstream boundary between July 23 and July 29. This early mass loss in the horizontal direction as well prevents us from computing meaningful estimates of second-order moments, from which aquifer dispersion characteristics could be inferred. In exchange, we concentrated our attention on the time evolution of Cl concentration as directly measured at the GP5 sampling point and as estimated at transversal control lines such as y 5 and y 6 Figure 5. To exploit the information contained in the breakthrough curves shown in Figure 12, we adopted a simplified 2D solution of the transport equation for a point release of mass M per unit thickness at location x,y in a horizontal velocity field V x,v y with dispersion tensor components D x and D y where A is the overall area monitored with ERT Figure 5. The total Cl mass is derived as the product of M Dzf, where f is porosity.3 and Dz is the vertically averaging thickness 2.5 m. Table 2 shows the total Cl mass computed over the entire domain Figure 14 and restricted to the clay-free region Figure 15. Considering that 3 kg of NaCl was used to spike the 5 m 3 of injected water and that this amounts to approximately 18 kg of Cl, we conclude that in our procedure we recover approximately between 65% and 8% of the total injected Cl mass. The lack of mass balance, albeit not as dramatic as in other studies, can still be attributed to ERT resolution issues but might also depend on some downward migration of the tracer below the chosen 3.5-m depth used as the bottom of our control volume note that the injection borehole GP6 is screened to 4-m depth. We also computed first-order moments in x- and y-directions x c,y c. The locations of the center of mass considering the entire tracer distribution or only the distribution outside the clayey region are shown in Figures 14 and 15. Note that when the entire mass is considered, the center of mass is basically stationary because a considerable mass is held back in the clayey region 5.1 kg of the total 6.3 kg onaugust 28 see Table 2. However, even neglecting the mass contribution from within the clayey region, the overall a) Chloride concentration (g/l) from direct measurements in GP5 b) Chloride concentration C cl(g/l) C cl = δσ w.16 2 R = δσ w (S/m) from geophysics surveys direct measurements in GP5 values estimated with the relation (starting from δσw measured in geophysics surveys /7 19/7 23/7 27/7 31/7 4/8 8/8 12/8 16/8 2/8 24/8 28/8 Date (day/month) Figure 13. a Relationship between measured Cl concentration at borehole GP5 and the variation of groundwater electrical conductivity with respect to background estimated from ERT at the same location; a linear relationship is fitted, which is then used to convert the ERT results into in situ estimates of Cl concentration. b Comparison between actual Cl concentration in GP5 and the corresponding estimates from ERT using the relationship in a.

10 WA7 Monego et al. C x,y,t M/ 4 Dx t 4 Dy t e x x V x t 4D x t e y y V y t 4D y t dxdy. 1 In equation 1, we assumed v x 1.1 m/d and V y, compatible with evidence of arrivals at borehole GP5 and assuming that the prevailing groundwater direction is exactly parallel to the GP6-GP5 line Figure 5. Because M in equation 1 is mass per unit thickness, it could be considered as an unknown to our problem. Fitting equation 1 to the Cl breakthrough data at GP5 leads to the conclusion that D y and M trade off because they both control the concentration values in opposite directions. On the contrary, D x is fairly uniquely identified to a value of m 2 /s, which corresponds to a longitudinal dispersivity a L 2.9 m D x a L V x. If we assume that the total injected Cl mass 18 kg was distributed over the monitored 2.5-m thickness, we obtain a mass per unit thickness M equal to 7.2 kg/m and a corresponding transverse dispersivity a T.4 m Figure 14. Maps showing the distribution of Cl concentration averaged along the vertical direction as estimated from ERT at the times of the six surveys. The center of mass relevant to the entire concentration distribution is shown as a blue square July 15th survey 1 1 July 17th survey 2 1 July 29th survey 3 August 1st survey 4 August 7th survey 5 August 28th survey 6 C cl (g/l) Extent of clayey lens Center of mass location Figure 15. Maps showing the distribution of Cl concentration averaged along the vertical direction as estimated from ERT at the times of the six surveys; here, unlike in Figure 14, the concentration distribution within the clayey lens is not considered. The center of mass relevant to the concentration distribution outside the clay is shown as a blue square July 15th survey 1 1 July 17th survey 2 1 July 29th survey 3 August 1st survey 4 August 7th survey 5 August 28th survey 6 C cl (g/l) Extent of clayey lens Center of mass location

11 Tracer test monitored via ERT WA71 Table 2. Mass of Cl estimated from ERT within the control volume (Figure 5) Date Total mass kg Mass outside the clayey region kg July July July August August August Mass (kg/m) mass in section y 5 mass in section y 6 simulated mass in y 5 simulated mass in y Time (days) x c (m) -coordinate of center of mass x = 1. t +6 c x =.124 t c R 2 = Time (days from injection) Figure 16. The x-coordinate of the center of mass as a function of time, as estimated from Figure 15. The resulting mean groundwater velocity is.124 m/day. If we consider only the data of July 15 and July 17, the groundwater velocity is approximately 1 m/day, compatible with direct evidence from samples at borehole GP5. Chloride concentration C cl (g/l) Observed concentration simulated value Time (days) Figure 17. Comparison between measured red and simulated blue Cl concentrations using the calibrated solution to the 2D advective-dispersive equation 1. D y a T V x. The corresponding calculated breakthrough curve is shown in Figure 17 together with the observed Cl breakthrough curve at GP5, showing a good agreement with a Nash-Sutcliffe coefficient.97. Note that we limited our analysis to estimating horizontal dispersivities because vertical dispersivity cannot be retrieved reliably due to the resolution loss in the vertical direction. This makes our modeling approach perfectly consistent with the information content of the acquired ERT data. Figure 18. Comparison between ERT-estimated symbols and simulated lines Cl concentrations averaged along vertical sections y 5 and y 6 see Figure 5. For simulations, we used a numerical solution to the 1D advective-dispersive equation 11. A further confirmation that the retrieved hydraulic parameters are meaningful comes from the analysis of the total mass per unit length perpendicular to the ERT section estimated in correspondence with the transverse ERT lines and particularly y 5 and y 6. A comparison was made between these measured data and the predictions obtained from a numerical solution to the 1D transport equation C x,t C x,t 2 C x,t V x D x t x x 2, 11 where C is the concentration averaged along the y-direction. For this solution, we used the same parameters as identified by fitting equation 1 to breakthrough curves in GP5, i.e., V x 1.1 m/d and a L 2.9 m. The corresponding comparison between predictions and measured data are shown in Figure 18. Considering that the predicted curves are obtained here with no further calibration, the results are very satisfactory and by using the ERT data confirm the robustness of the hydraulic parameter estimation. However, from Figure 18, it is apparent how the available ERT data miss the most significant dates approximately 1 days after injection. CONCLUSION This case study is a successful example of the use of surface ERT to monitor a tracer test in a complex environment. In spite of some limitations inherent to the method caused by the strong decrease in ERT resolution with depth, the results are meaningful from a hydraulic point of view and could be used to identify some of the key parameters for solute transport, namely, mean groundwater velocity and aquifer dispersivity at the scale of the test. Key to the effective use of ERT data is the exploitation of direct measurements of groundwater electrical conductivity and tracer concentration at one selected location throughout the test. These auxiliary data help correct the otherwise problematic mass-balance error inherent to ERT monitoring of saline tracer tests and consequently add confidence to the test results. Furthermore, these more traditional data are used in addition to the ERT data to calibrate transport models and identify their governing parameters. One key characteristic of the case study is the extreme heterogeneity of the system, which is reflected in the tracer migration and dis-

12 WA72 Monego et al. tribution over time: The tracer is trapped in the low-permeability regions and from these it is slowly released over time. High-resolution surface ERT proves effective at picturing this system behavior over time and adds substantial information to an otherwise blind test. The presence of strong heterogeneities also has a severe effect on the quantitative transformation of bulk resistivity data into estimates of groundwater electrical conductivity and, hence, solute concentration because in clayey regions Archie s law must be substituted by a more complex model accounting for surface conductivity. We presented a possible approach to tackle this problem that is at least partly corroborated by the overall consistency of data and results. 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