Manuscript Click here to download Manuscript ENGE-D-15- 02723_R2_TextMarked.docx Click here to view linked References 1 Tomographic Slug and Pumping Tests Comparison 1/22 2 3 4 1 Submitted to Environmental Earth Sciences: NovCare 2015 Thematic Issue 5 6 2 7 8 3 Comparison of slug and pumping tests for hydraulic tomography 9 10 11 4 experiments: A practical perspective 12 13 5 14 1 2 2 2 15 6 Daniel Paradis , René Lefebvre , Erwan Gloaguen , and Bernard Giroux 16 7 17 18 8 1: Geological Survey of Canada, 490 rue de la Couronne, Quebec City, Canada G1K 9A9 19 20 9 2: Institut national de la recherche scientifique, Centre Eau Terre Environnement (INRS-ETE), 21 22 10 490 rue de la Couronne, Quebec City, Canada G1K 9A9 23 24 11 25 26 12 Corresponding author: Daniel Paradis 27 13 Phone: (418) 654-3713 Fax: (418) 654-2604 E-mail: [email protected] 28 29 14 30 31 15 32 33 16 KEYWORDS: Aquifer characterization, Heterogeneity, Hydraulic tomography, Slug tests, 34 35 17 Pumping tests, Resolution analysis, Principle of reciprocity 36 37 18 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 2/22 2 3 4 19 ABSTRACT 5 6 20 7 8 21 Hydraulic tomography is the simultaneous analysis of several hydraulic tests performed in 9 10 22 multiple isolated intervals in adjacent wells to image heterogeneous hydraulic property fields. In 11 12 23 this study, we compare the resolutions associated with hydraulic tomography experiments carried 13 24 out with slug tests and pumping tests for simple configurations with hydraulic property values 14 15 25 representative of an extensively studied littoral aquifer. Associated test designs (e.g., pumping 16 17 26 rates, test durations) and the validity of the principle of reciprocity are also assessed. For this 18 19 27 purpose, synthetic tomography experiments and their associated sensitivity matrices are 20 21 28 generated using a radial flow model accounting for wellbore storage. The resolution analysis is 22 23 29 based on a pseudo-inverse analysis of the sensitivity matrix with a noise level representative of 24 30 field measurements. Synthetic experiments used equivalent perturbations for slug tests and 25 26 31 pumping tests. Even though pumping tests induce a drawdown in observation intervals that is 27 28 32 three times larger than head changes due to slug tests, resolutions for hydraulic conductivities 29 30 33 (horizontal and vertical) are similar for the two tests and slightly lower for specific storage with 31 32 34 pumping. However, experiments with pumping require fifty times more water and are seven 33 34 35 times longer to perform than experiments with slug tests. Furthermore, reducing pumping rates 35 36 to limit disposal of water or test durations to decrease field data acquisition time would 36 37 37 considerably lower resolutions for either scenario. Analyses are done using all available stressed 38 39 38 and observation intervals as required by the non-applicability of the principle of reciprocity for 40 41 39 slug tests and pumping tests with important wellbore storage. This study demonstrates concepts 42 43 40 that have important implications for the performance and analysis of hydraulic tomography 44 45 41 experiments. 46 42 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 3/22 2 3 4 5 43 1 Introduction 6 7 8 44 Knowledge of the hydraulic heterogeneity that controls flow and transport in aquifer systems, 9 10 45 such as preferential flow paths and impermeable barriers, is essential for sound groundwater 11 46 resource protection. Slug tests and pumping tests are common field experiments used to estimate 12 13 47 the hydraulic properties of aquifer systems (Kruseman and de Ridder, 2000). A slug test consists 14 15 48 of inducing an instantaneous change in water level in a well, whereas a pumping test involves 16 17 49 withdrawing water out of a well at a controlled, generally constant, rate. For both kinds of 18 19 50 hydraulic tests, water level response is measured in one or more surrounding observation wells 20 21 51 and in the stressed well itself. The area affected by a hydraulic test is a function of the hydraulic 22 52 diffusivity defined by the ratio of hydraulic conductivity (K) and specific storage (S ). The larger 23 s 24 53 the hydraulic diffusivity, the larger will be the response in the observation well and the farther 25 26 54 from the stressed well will it be possible to measure the response with a good signal to noise 27 28 55 ratio . Several authors have proposed the use of hydraulic tomography to define heterogeneous 29 30 56 hydraulic property fields (e.g., Tosaka et al., 1993; Gottlieb and Dietrich, 1995; Butler et al., 31 32 57 1999; Yeh and Liu, 2000; Bohling et al., 2002; 2007; Brauchler et al., 2003, 2010, 2011, 2013; 33 58 Zhu and Yeh, 2005; Illman et al., 2007, 2008; Fienen et al., 2008; Cardiff et al., 2009; Illman et 34 35 59 al., 2009; Berg and Illman, 2011, 2013, 2015; Cardiff and Barrash, 2011; Huang et al., 2011; 36 37 60 Cardiff et al., 2012; Sun et al., 2013; Paradis et al., 2015; 2016). Hydraulic tomography is the 38 39 61 simultaneous analysis of several hydraulic tests performed in multiple wells or multiple isolated 40 41 62 intervals in wells, which provides a better resolution capability of hydraulic property fields than 42 43 63 conventional hydraulic tests (Butler, 2005). Analysis of hydraulic tomography data is essentially 44 64 related to inverse problems with issues related to non-uniqueness of the solution as the number 45 46 65 of unknown parameters is usually greater than the number of measurements (under-determined 47 48 66 problem) or the data do not contain enough information about the model parameters (rank- 49 50 67 deficient problem) due to the physics of the problem and experimental configuration (e.g., 51 52 68 Carrera and Neuman, 1986; Yeh and Liu, 2000; Tonkin and Doherty, 2005; Illman et al., 2008; 53 69 Bohling, 2009; Xiang et al., 2009; Bohling and Butler, 2010; Huang et al., 2011; Liu and 54 55 70 Kitanidis, 2011; Paradis et al., 2015, 2016). While regularization for constraining the number of 56 57 71 possible solutions is an important topic (e.g., Tikhonov, 1963; Tikhonov and Arsenin, 1977; 58 59 72 Kitanidis, 1995; Vasco et al., 1997; Carrera and Neuman, 1986; Yeh and Liu, 2000; Doherty, 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 4/22 2 3 4 73 2003; Caers, 2005; Rubin and Hubbard, 2005; Tonkin and Doherty, 2005; Carrera et al., 2005; 5 6 74 Fienen et al., 2008; Illman et al., 2008; Berg and Illman, 2011; Cardiff and Barrash, 2011; 7 8 75 Huang et al., 2011; Cardiff et al., 2012; Sun et al., 2013; Soueid Ahmed et al., 2014; Zha et al., 9 10 76 2014), this paper focuses rather on some practical aspects related to hydraulic tomography, 11 12 77 which is of crucial importance to guide practitioners involved in hydraulic property 13 78 characterization either in terms of estimates accuracy or field efficiency. 14 15 79 16 17 80 The ability of a hydraulic experiment to resolve hydraulic property fields from observations can 18 19 81 be understood through the analysis of the sensitivity of head or drawdown to the parameters 20 21 82 associated with the aquifer system to characterize (Menke, 1989; Aster, 2005). Sensitivity 22 23 83 magnitudes and correlations indicate which parameters can be better resolved. For example, it 24 84 has been recognized by Butler and McElwee (1990) that varying the magnitude and frequency of 25 26 85 the pumping rate scheme of a pumping test can increase parameter resolutions by increasing 27 28 86 sensitivity magnitudes while simultaneously constraining sensitivity correlations. While constant 29 30 87 rate pumping tests are the most used tests for hydraulic tomography (see the comprehensive 31 32 88 summary of previously published studies dedicated to hydraulic tomography provided by Cardiff 33 34 89 and Barrash, 2011), few efforts have been dedicated to understanding the impact of test initiation 35 90 methods on the resolution of hydraulic property fields. Actually, since slug and pumping tests 36 37 91 generate very different hydraulic perturbations, it would be worth assessing whether those tests 38 39 92 produce different parameter resolution characteristics for hydraulic tomography experiments. 40 41 93 Indeed, early times hydraulic response for a pumping test is known to be mostly sensitive to 42 43 94 parameters between the stressed and observation wells, whereas the relative influence of 44 45 95 parameters outside the inter-well region increases as the drawdown spreads away from the 46 96 observation well (Oliver, 1993; Leven et al., 2006). On the other hand, it is generally considered 47 48 97 that only the immediate vicinity of the stressed well can be resolved with a slug test because the 49 50 98 change in hydraulic head pulse is sharply vanishing away from the stressed well (Ferris and 51 52 99 Knowles, 1963; Rovey and Cherkauer, 1995). 53 54 100 55 101 The main objective of this study is then to compare the resolutions associated with tomography 56 57 102 experiments carried out with slug tests and pumping tests. In particular, we are interested by the 58 59 103 resolution of horizontal hydraulic conductivity (Kh), K anisotropy (ratio of vertical and horizontal 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 5/22 2 3 4 104 K, Kv/Kh), and Ss. Moreover, choices in hydraulic test design (e.g., test stress: pumping rate and 5 6 105 initial head, test duration) are often made to get around some technical difficulties often 7 8 106 encountered during field tomography experiments, such as desaturation of the stressed interval, 9 10 107 noisy measurements and excessive test durations. Thus, in an effort to maximize the quality of 11 12 108 the information contained in field data, often-acquired at large expenses, we also assess the 13 109 impact of some field practices associated to the realization of hydraulic tests and verify the 14 15 110 validity of the principle of reciprocity for both kinds of tests. 16 17 111 18 19 112 After presenting the general approach followed to evaluate the resolution matrix of a tomography 20 21 113 experiment in Section 2, we verify the applicability of the principle of reciprocity for slug and 22 23 114 pumping tests and we discuss the implications for acquisition and analysis of tomography data in 24 115 Section 3. Then, Section 4 presents a comparison of resolution for tomography experiments 25 26 116 using slug tests and pumping tests as well as the impact of reduced test stresses (pumping rates 27 28 117 and initial heads) and test durations. Finally, we summarize and discuss the main findings of this 29 30 118 study in Section 5. 31 32 33 119 2 General approach for the evaluation of the resolution matrix 34 35 36 120 The observations (head or drawdown) made during a hydraulic test are sensitive to the hydraulic 37 38 121 properties or parameters of the aquifer system at locations reached by the perturbation induced 39 40 122 by the test (Vasco et al., 1997). Parameter sensitivity is the ratio of the change in the 41 42 123 observations to a unit relative change in a parameter value. The relative magnitude of the 43 44 124 sensitivity for different parameters indicates which parameters can be better resolved from the 45 125 observations. Also, parameters that have dissimilar (non-correlated) temporal sensitivity patterns 46 47 126 throughout a test can be resolved separately because they have different effects on observations. 48 49 127 A resolution matrix combines sensitivities from a number of observations and for a number of 50 51 128 parameters into a single measure related to each parameter, which integrates the effects of 52 53 129 sensitivity magnitudes and correlations, and that can be analyzed to assess the ability to resolve 54 55 130 parameters from tomography experiments. Figure 1 illustrates the general approach followed to 56 131 evaluate the resolution matrix of a tomography experiment carried out with slug tests or pumping 57 58 132 tests. Further details about this approach proposed by Clemo et al. (2003) that is summarized 59 60 133 below can be found in Bohling (2009) and Paradis et al. (2015). 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 6/22 2 3 4 134 5 6 135 1. Forward modeling and sensitivity calculation. To simulate hydraulic tests (slug and 7 8 136 pumping tests) and to compute sensitivities of the synthetic tomography experiments, we used 9 10 137 the numerical simulator lr2dinv (Bohling and Butler, 2001). This simulator is a two-dimensional 11 12 138 (2D) axisymmetric finite-difference model that describes flow to a partially penetrating well in 13 139 response to an instantaneous change in water level (e.g., slug test) or to a pumping stress in a 14 15 140 confined aquifer through the radial groundwater flow equation. The simulator also allows the 16 17 141 explicit simulation of wellbore storage effects and placement of packer intervals in the stressed 18 19 142 well. 20 21 143 22 23 144 Using lr2dinv, the sensitivity matrix elements are constructed by a sequence of groundwater flow 24 145 simulations, one simulation per parameter grid cell, in which each hydraulic property in a single 25 26 146 cell is slightly perturbed (1%) from its original value and the differences in head or drawdown 27 28 147 are noted. Each Jm,n element in the sensitivity matrix represents the normalized sensitivity of the 29 30 148 head or drawdown at a given time and location, hm, to one of the model parameter, pn: 31 32 149 33 ∂h 34 m J = Jm,n = pn (1) 35 ∂pn 36 37 150 38 39 151 The head or drawdown index m runs over all observation times and locations for all simulated 40 41 152 tests, and pn represents either the Kh, Kv/Kh or Ss value associated with each cell in the parameter 42 153 grid. It should be noted that groundwater flow associated with each tomography experiment is 43 44 154 nonlinear, and we thus assume that the sensitivity matrix with its elements given by (1) provides 45 46 155 a close approximation of the behavior of the nonlinear flow in the vicinity of the model 47 48 156 parameters used for each synthetic simulations given the fact that small perturbations are used to 49 50 157 compute sensitivities (Bohling, 2009). Details about mathematical formulation and numerical 51 52 158 implementation can be found in Bohling and Butler (2001) and Butler and McElwee (1995). 53 159 54 55 160 For all synthetic simulations, we use a 2D simulation grid with 43 cells of logarithmically 56 57 161 increasing dimension along the radial axis encompassing the stressed and observation wells and 58 59 162 26 cells of dimension equal to 0.3048 m (1 foot) along the vertical axis. This discretization 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 7/22 2 3 4 163 places the zero-head outer boundary of the model very far from the stressed well (about 111 m), 5 6 164 so that it has negligible effects on simulated heads or drawdown at the stressed and observation 7 8 165 wells. Confined conditions are also assumed to define lower and upper boundary conditions. 9 10 166 Slug tests are simulated by modifying the initial head condition at the cells representing the 11 12 167 stressed interval, with all other heads in the model set to zero, in order to produce an 13 168 instantaneous head perturbation into the aquifer. And, pumping tests are simulated through the 14 15 169 boundary condition by specifying the pumping rate in the stressed interval. Note that to avoid 16 17 170 desaturation of the stressed interval (water level below the top of the screen) slug tests and 18 19 171 pumping tests are simulated by injecting water into the synthetic aquifer. Specific parameter grid 20 21 172 discretization and parameter values for each synthetic experiment discussed in this study are 22 23 173 presented later in their respective section. 24 174 25 26 175 2. Moore-Penrose pseudo-inverse and resolution matrix. Given a vector m of n parameters to 27 28 † 176 be estimated, the Moore-Penrose pseudo-inverse Jp (Moore, 1920; Penrose, 1955) can be used in 29 30 177 computing a least-squares and minimum length solution m† from a data vector d of m 31 32 178 observations (head or drawdown) as (Menke, 1989; Aster, 2005): 33 34 179 35 † 36 m† = Jpd (2) 37 38 180 39 † 40 181 where Jp is the sensitivity matrix J retaining the p largest singular values and vectors of its 41 42 182 singular value decomposition corresponding to the most strongly resolved parameters. Note that 43 44 183 the Moore-Penrose pseudo-inverse is a convenient way of analyzing the information content of 45 46 184 least-squares inverse problems (e.g., Bohling, 2009; Paradis et al, 2015) without having to 47 185 optimize an objective function that could be computationally intensive. If the true model of 48 49 186 parameters are represented by the vector m and the corresponding true data vector is represented 50 51 187 by d=Jm, then the estimated parameter vector from the pseudo-inverse m† can be expressed 52 53 188 from (2) as (Menke, 1989; Aster, 2005): 54 55 189 56 † 57 m† = JpJm = Rm (3) 58 59 190 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 8/22 2 3 4 191 The matrix multiplying the true model of parameters m is called the resolution matrix: 5 6 192 7 † 8 R = JpJ (4) 9 10 193 11 12 194 where the elements of R are indicators of the relative magnitude and correlation between 13 14 195 parameter sensitivities resulting from the pseudo-inverse. For this study, only the diagonal 15 16 196 elements of R that indicate the resolution of each parameter are analyzed. The values of diagonal 17 197 elements are between 0 and 1: a value of 0 means that a parameter cannot be resolved from the 18 19 198 observations, whereas a value of 1 means it can be perfectly resolved. Discussion about the 20 21 199 information contained in the entire resolution matrix can be found in Menke (1989) and Aster 22 23 200 (2005). 24 25 201 26 27 202 To get a common basis of comparison among the different tomography experiments using slug 28 203 tests and pumping tests, we select for each experiment the number of p singular values and 29 30 204 vectors in (4) according to a predefined level of error in parameter estimates resulting from the 31 32 205 pseudo-inverse. As proposed by Clemo et al. (2003), p can indeed be selected by considering d 33 34 206 in (2) as the random noise in the observations η and m as the error in the parameter estimates 35 36 207 Δm†, which leads to the following: 37 38 208 39 † 40 Δm† = Jpη (5) 41 42 209 43 210 Thus, for a given level of parameter error, defined here as the root-mean-square of the norm of 44 45 211 Δm†, the number of p singular values and vectors to retain for the evaluation of the resolution 46 47 212 matrix in (4) is selected using (5) (see Bohling, 2009). For this study, we choose an error Δm† of 48 49 213 0.1 (average relative error of 10%) and define a Gaussian noise η (mean of zero; standard 50 51 214 deviation of 2x10-4 m) realistic of field experimentations (e.g., Bohling, 2009; Paradis et al., 52 53 215 2015). 54 55 216 56 57 217 Figure 1 58 59 60 218 3 Verification of the principle of reciprocity 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 9/22 2 3 4 219 In this section, we investigate the applicability of the principle of reciprocity for slug tests and 5 6 220 pumping tests as it may have implications for the acquisition and analysis of tomographic data, 7 8 221 and consequently on parameter resolutions as well. The principle of reciprocity states that, as 9 10 222 long as wellbore storage effects can be neglected, reciprocal tests for which the role of the 11 12 223 stressed and observation intervals are interchanged produce identical observation interval 13 224 responses regardless of the degree of heterogeneity (see proof in McKinley et al., 1968). To 14 15 225 verify this principle, we simulate head and drawdown for reciprocal tests that are symmetrical 16 17 226 (Figure 2a) and asymmetrical (Figure 3a) with respect to the heterogeneity in Kh, Kv and Ss. Thus 18 19 227 for both models, reciprocal tests are simulated by varying each hydraulic property of layer 2 one 20 21 228 at a time (black layers in Figures 2a and 3a) while holding all other properties unchanged (Table 22 23 229 1). We note also that stressed and observation interval locations in Figures 2a and 3a are 24 230 symmetrical to the upper and lower no-flow boundaries to avoid misinterpretation of the 25 26 231 reciprocal tests. Wellbore storage is also only simulated in the stressed intervals as we assume 27 28 232 that wellbore storage effects in straddled observation intervals with packers can be neglected 29 30 233 (Sageev, 1986; Novakowski, 1989). 31 32 234 33 34 235 Figures 2b and 2c present results of the reciprocal slug tests and pumping tests, respectively, for 35 236 the symmetrical cases. Obviously, reciprocal responses are indistinguishable whether the test is 36 37 237 initiated in well 1 or well 2 since those tests are performed under identical conditions (note that 38 39 238 reciprocal curves are superposed in Figure 2). Figures 3b and 3c show however that for the 40 41 239 asymmetrical cases, that the reciprocal head and drawdown responses in the observation 42 43 240 intervals are different when Kh and Kv are varied, which refutes the principle of reciprocity. 44 45 241 46 242 As suggested by the comparison of Figures 3c and 3d for reciprocal pumping tests considering 47 48 243 and neglecting wellbore storage, respectively, the refutation of the principle of reciprocity for 49 50 244 observation interval responses could be explained by a wellbore storage effect. Note that stressed 51 52 245 interval responses differ regardless of the degree of heterogeneity. In fact, for a pumping test in a 53 54 246 well with a large diameter, the total pumping rate (Q) set by the pump is the combined 55 247 contributions of flow rates coming from the wellbore (Q ) and the aquifer system (Q ) 56 w a 57 248 (Dougherty and Babu, 1984). Wellbore storage supplies most of the initial pumped water, which 58 59 249 initially equals to Q and gradually decreases to zero when pumping continues. In contrast, the 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 10/22 2 3 4 250 contribution from the aquifer system is initially zero and gradually approaches Q when 5 6 251 drawdown is reaching steady-state. Also, the relative contributions of Qw and Qa that must 7 8 252 balance with Q vary according to the hydraulic properties surrounding the stressed well 9 10 253 (Q=Qa+Qw). Note here that we only consider wellbore storage due to water level change and not 11 12 254 from water compressibility. Thus, as the drawdown in an observation interval is controlled by the 13 255 flow at this location Q , which depends on Q at the stressed interval and the heterogeneity 14 obs a 15 256 travelled by the hydraulic perturbation, reciprocal drawdown responses in Figure 3c differ 16 17 257 because Qa is different for each reciprocal test while the heterogeneity seen in reverse order by 18 19 258 the hydraulic perturbations is the same in the two directions of testing. For pumping tests where 20 21 259 wellbore storage can be neglected (Qw=0), Qa is independent of the heterogeneity surrounding 22 23 260 the stressed well and is equal to the same constant value of Q for the two reciprocal tests (Qa=Q), 24 261 which explains the identical reciprocal observation interval responses in Figure 3d. We note in 25 26 262 Figure 3c that reciprocal observation interval responses are identical at steady-state when 27 28 263 wellbore storage effect becomes negligible. Finally, a similar reasoning can be applied for slug 29 30 264 tests in Figure 3a where Qa is proportional to the decline of the water level in the the stressed 31 32 265 interval (Qa=Qw; Q=0), which is also controlled by the hydraulic properties surrounding the 33 34 266 stressed interval. 35 267 36 37 268 In summary, the principle of reciprocity as applied to observation interval responses is valid for 38 39 269 cases where wellbore storage effects can be neglected. This is not the case for slug tests or 40 41 270 pumping tests with large diameter boreholes. As a consequence, stressed and observation interval 42 43 271 responses must be recorded during field testing and used together in the analysis of hydraulic 44 45 272 tomography experiments. 46 273 47 48 274 Table 1 49 50 275 51 52 276 Figure 2 53 54 277 55 278 Figure 3 56 57 58 59 279 4 Comparison of resolutions for different hydraulic test designs 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 11/22 2 3 4 280 This section explores the effects of different hydraulic test designs used for tomography 5 6 281 experiments on parameter resolutions. In particular, we assess the effects of test initiation 7 8 282 methods (slug and pumping tests), reduced test stresses (initial heads and pumping rates) and 9 10 283 reduced test durations. 11 12 13 284 4.1 Effect of test initiation methods 14 15 16 285 In this section, we compare the resolutions of two tomography experiments that use slug tests 17 18 286 and pumping tests, respectively. To compare parameter resolutions on a common basis over the 19 20 287 domain, we use a parameter grid with similar cell sizes. The simulation grid was thus divided 21 288 into 143 cells of 0.61 m in height, that corresponds to the length of the stressed interval, and, due 22 23 289 the logarithmic change in cell dimensions in the radial direction, the cells of the simulation grid 24 25 290 were merged laterally to obtain cell widths of approximately equal size (Figures 4a and 4b). 26 27 291 Sensitivities for the resolution analysis are also computed from a homogeneous and anisotropic 28 -5 -1 -5 -1 29 292 model with bulk average Kh, Kv/Kh and Ss values of 1×10 ms , 0.1 and 1×10 m , respectively. 30 293 Those values are representative of the hydrogeological conditions present at the St-Lambert site 31 32 294 in Canada where field tomographic experiments were already carried out and documented by 33 34 295 Paradis et al. (2016). Although aquifers are inherently heterogeneous in nature, using a 35 36 296 homogeneous model eases the resolution comparison by isolating the effects of the spatial 37 38 297 structure of hydraulic properties. The later has been already discussed by Paradis et al. (2015) for 39 40 298 tomographic slug tests. For each of the two tomography experiments, we simulate 13 tests 41 299 carried out in 0.61-m long stressed intervals located at different depths along the stressed well. 42 43 300 For each test, hydraulic responses in the stressed interval itself and in 3 observation intervals 44 45 301 (except for the uppermost and lowermost stressed intervals that use 2 observation intervals; see 46 47 302 Figures 4a and 4b) distributed along the observation well are simultaneously recorded. A total of 48 49 303 13 stressed and 37 observation interval responses are thus available for the resolution analysis of 50 51 304 each tomography experiment. As discussed later, both stressed and observation interval 52 305 responses are needed in the analysis due to the non-applicability of the principle of reciprocity. 53 54 306 Each slug test is initiated using an initial head of 4.5 m in the stressed interval. And, to fairly 55 56 307 compare resolutions between slug tests and pumping tests, we calculate an equivalent pumping 57 58 308 rate that produces a steady-state drawdown of 4.5 m in the stressed interval, which is identical to 59 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 12/22 2 3 4 309 the initial head used for slug tests (Peres et al., 1989). For the present model this corresponds to a 5 6 310 pumping rate of 4.0x10-5 m3/s (2.4 LPM). 7 8 311 9 10 312 To compare the spatial resolution fields of the two tomography experiments, Figures 4a and 4b 11 12 313 show the diagonal elements of the resolution matrix at the corresponding parameter grid cells for 13 314 experiments with slug tests and pumping tests, respectively. Mean resolution values for cells 14 15 315 within the inter-well region are also presented in Table 2 for this comparison. We note that this 16 17 316 resolution analysis is based on the 10,000 s records of head or drawdown, which correspond to 18 19 317 the termination of each slug test or to the time to reach steady-state conditions. Figures 4a and 4b 20 21 318 thus show that independently of the test initiation method, resolutions for Kh, Kv/Kh and Ss are 22 23 319 strongly focused on the stressed and observation wells with higher resolutions near the stressed 24 320 well where sensitivities are larger. This agree with previous studies using both kind of tests 25 26 321 (Vasco et al., 1997; Bohling, 2009; Paradis et al., 2015). Moreover, we see that resolution fields 27 28 322 for Kh in Figures 4a and 4b are almost identical for the two experiments, as also expressed by 29 30 323 similar mean resolution values (Experiments 1 and 2 in Table 2). Mean resolution values are also 31 32 324 similar for Kv/Kh despite resolutions that appear much higher near the pumping well, whereas 33 34 325 resolutions for Ss are definitely much lower for pumping than for slug tests. 35 326 36 37 327 Explanation of those similarities in parameter resolution can be found in Figures 5a, 5b and 5c. 38 39 328 In Figure 5a, we plot as a reference the stressed interval responses for the equivalent slug and 40 41 329 pumping tests, as previously discussed. In Figures 5b and 5c, we see that while drawdown due to 42 43 330 pumping in the observation interval is three times larger than the head change induced by the 44 45 331 slug test, the magnitude of the sensitivity for each hydraulic property is quite similar. Thus, 46 332 assuming that correlation between sensitivity for each hydraulic property is almost identical for 47 48 333 the two tests, comparable parameter resolutions are explained by the similarity in sensitivity 49 50 334 magnitudes. Then, head changes due to slug tests are more efficient than drawdowns produced 51 52 335 by pumping tests at resolving parameters, as head changes much lower than drawdowns produce 53 54 336 similar sensitivity magnitudes. This is due to the sharper form of the head perturbation caused by 55 337 the instantaneous slug of water applied in the stressed interval that produces larger spatial and 56 57 338 temporal hydraulic gradients. Also, this explain why Ss is lower for pumping tests because 58 59 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 13/22 2 3 4 339 temporal hydraulic gradients are smaller with pumping, which can be deduced from Figure 5c 5 6 340 with Ss sensitivities for pumping about the third of the sensitivities for slug tests. 7 8 341 9 10 342 Table 2 11 12 343 13 344 Figure 4 14 15 345 16 17 346 Figure 5 18 19 20 347 4.2 Effect of reduced test stresses 21 22 23 348 In this section, we first illustrate the effects of reducing the pumping rate of each pumping test 24 25 349 used for the tomography experiment. Indeed, as pumping tests use much more water than 26 27 350 equivalent slug tests, such a reduction would be desirable at sites where the storage or injection 28 29 351 of a large volume of water may be an issue (e.g., contaminated sites). For our previous 30 352 tomography experiment, we used 9 L of water to initiate each slug test, whereas 400 L per 31 32 353 pumping test was needed to reach steady-state conditions. We note that pneumatic slug test 33 34 354 initiation method using air pressure to lower or raise the water level in the stressed interval could 35 36 355 also be chosen to avoid using water at sensitive sites. Because a pumping test that would use 37 38 356 only 9 L of water would produce non-significant drawdown in the observation intervals, we 39 40 357 rather reduce pumping rates by four (experiment 4 in Table 2); thus 100 L of water is used 41 358 instead of 400 L. We note that at this reduced rate, the peak head from the original slug test and 42 43 359 steady-state drawdown of the 100 L pumping test recorded in the stressed intervals have the 44 45 360 same magnitudes (Figure 6a). 46 47 361 48 49 362 As expected from the previous section, Figure 6b shows that reduced pumping rates decrease 50 51 363 sensitivity magnitudes, which results in lower parameter resolutions as depicted in Table 2 52 364 (Experiment 4). Note that reducing initial heads by half leads to a similar decrease in resolutions 53 54 365 for tomographic slug tests (Experiment 3 in Table 2). For those particular cases, the effect of 55 56 366 reduced initial heads with respect to pumping rates is more pronounced (half the initial heads for 57 58 367 a quarter of the original pumping rates) likely due to the head in the observation intervals that are 59 60 368 closer to the level of noise, which increases parameter sensitivity correlations. 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 14/22 2 3 4 369 5 6 370 Figure 6 7 8 9 371 4.3 Effect of reduced test durations 10 11 12 372 In this section, we discuss the effects of reducing test durations of both slug tests and pumping 13 14 373 tests in order to reduce data acquisition time of tomographic experiments that by design required 15 16 374 numerous tests. For our previous synthetic experiment with pumping tests, each test in the field 17 18 375 required as much as 2.75 h (10,000 s) to reach steady-state drawdown in the observation 19 20 376 intervals. By considering that after each pumping test a recovery period equivalent to the 21 377 pumping period is needed before conducting the next test, the 13 tests of this experiment would 22 23 378 require more than 72 h of testing in the field. For those simulations, we consider recording head 24 25 379 and drawdown for each test for a period of 1,000 s (17 min) instead of 10,000 s (2.75 h) (Figure 26 27 380 7a), which is considered more realistic for actual field applications. 28 29 381 30 382 As shown in Table 2 (Experiments 5 and 6), both experiments with slug tests and pumping tests 31 32 383 see a reduction in resolutions. Examination of Figure 7b suggests that reduced test durations 33 34 384 increase sensitivity correlations. In particular, we see that the sensitivity curves for Kv/Kh, and Ss 35 36 385 of the pumping test are pretty similar for much of the duration of the test, which implies that 37 38 386 their individual effect on drawdown cannot be resolved separately. Moreover, we see in Table 2 39 40 387 that the reduction in resolution is more severe with pumping because drawdown at 1,000 s are far 41 388 from steady-state and still provide important information on parameters, whereas heads related to 42 43 389 slug tests are close to their equilibrium state. Further reducing slug test durations long before 44 45 390 heads reach their equilibrium state, at 400 s (7 min) for example (Experiment 7 in Table 2; 46 47 391 Figures 7a and 7b), also reduces considerably resolutions to values close to pumping tests at 48 49 392 1,000 s. We note that pumping tests are longer due to wellbore storage that delays the aquifer 50 51 393 response (see Figures 3c and 3d). 52 394 53 54 395 Figure 7 55 56 57 396 58 5 Summary and discussion 59 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 15/22 2 3 4 397 In this study, we assessed test initiation methods (slug and pumping tests) and some related field 5 6 398 practices on parameter resolutions of tomography experiments. For this purpose, synthetic 7 8 399 tomography experiments and their associated sensitivity matrices were generated using a radial 9 10 400 flow model accounting for wellbore storage. The resolution analysis was based on a pseudo- 11 12 401 inverse analysis of the sensitivity matrix with a noise level representative of field measurements. 13 402 The main findings of this study are summarized and discussed below. 14 15 403 16 17 404 1. Parameter resolutions are similar for tomography experiments using equivalent slug tests 18 19 405 and pumping tests. Using either slug tests or pumping tests that induce identical initial head 20 21 406 and steady-state drawdown in the stressed interval lead to similar mean resolutions in 22 23 407 hydraulic properties, except for Ss resolution that is slightly lower with pumping. Also, while 24 408 there are slight differences, parameter resolution fields of tomography experiments 25 26 409 simulated with a noise level representative of field conditions are essentially focused on the 27 28 410 stressed and observation wells. Thus, for the two different test initiation methods, the same 29 30 411 general limitations apply on the resolution of hydraulic properties because hydraulic tests are 31 32 412 more sensitive to hydraulic properties in the immediate vicinity of the wells (Vasco et al., 33 34 413 1997). 35 414 36 37 415 2. A slug test is more efficient at resolving parameters for the same magnitude in hydraulic 38 39 416 perturbations induced in the observation intervals. For instance, for the same values of head 40 41 417 changes due to a slug test and drawdown induced by pumping in observation intervals, a 42 43 418 slug test is more efficient at resolving parameters due to the sharper form of the induced 44 45 419 head perturbation that produces larger sensitivities. So, in the field, one will try to maximize 46 420 pumping rates even if the drawdown measured in the observation intervals appears 47 48 421 “reasonably large”. That could however be difficult as each pumping rate should be 49 50 422 adjusted, generally by a trial-and-error process, according to the hydraulic properties 51 52 423 surrounding the tested interval that can vary considerably for heterogeneous aquifer systems. 53 54 424 In that respect, slug tests could be easier to perform because the initial head is set 55 425 independently of the materials surrounding the well. However, large initial heads should be 56 57 426 initiated in order to induce head changes in observation intervals that are larger than the 58 59 427 noise level of the measurements, which may require a slightly more complex testing 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 16/22 2 3 4 428 equipment than a single pump (e.g., Paradis et al., 2016). Then, even if large head changes at 5 6 429 a distance from a stressed well could be harder to produce with a slug test than drawdowns 7 8 430 by pumping, the magnitude of the hydraulic perturbation alone is not a condition sufficient 9 10 431 to assess the resolution potential of a tomographic experiment, and the sensitivities 11 12 432 associated with each type of test should also be considered. 13 433 14 15 434 3. Wellbore storage leads to the refutation of the principle of reciprocity for both slug tests and 16 17 435 transient responses of pumping tests in wells with large diameters. As a consequence of the 18 19 436 non-applicability of the principle of reciprocity shown by synthetic experiments, the 20 21 437 observation interval response does not provide a unique description of the heterogeneity 22 23 438 because it is impossible to tell from this response whether the head change or the drawdown 24 439 observed result from the flow rate induced by the test at the stressed interval, which is 25 26 440 controlled by the surrounding heterogeneity, or the heterogeneity travelled by the hydraulic 27 28 441 perturbation to the observation interval location. To obtain this information, stressed and 29 30 442 observation interval responses for each test must be recorded in the field and used in the 31 32 443 tomographic analysis to isolate the influence of the stressed interval response. Reciprocal 33 34 444 tests using only observation interval responses could also be considered, but this alternative 35 445 is less efficient as it requires twice the number of tests per tomographic experiment. From a 36 37 446 practical perspective, head changes in stressed intervals caused by slug tests are generally 38 39 447 easier to record with accuracy than drawdown due to pumping that are often influenced by 40 41 448 pumping rate variations associated to the equipment itself. Large pumping rates can also 42 43 449 induce important head losses in the stressed interval, which should be carefully considered 44 45 450 in the analysis to avoid misinterpretation of the recorded water levels. Finally, it should be 46 451 noted that using stressed and observation interval responses is also important to get better 47 48 452 parameter resolutions as the different temporal sensitivity patterns for the different intervals 49 50 453 contribute to decrease sensitivity correlations (Paradis et al., 2015). 51 52 454 53 54 455 4. Reduced test durations produce lower resolutions regardless of the test initiation methods. 55 456 This finding implies that the recording of slug tests until heads have recovered their initial 56 57 457 levels or pumping tests until steady-state is reached should be the preferred practice. 58 59 458 However, this practice increases the overall acquisition time of tomography data. In this 60 61 62 63 64 65 1 Tomographic Slug and Pumping Tests Comparison 17/22 2 3 4 459 regard, a slug test offers an important advantage over a pumping test for tomography 5 6 460 experiments that generally need many tests since it requires less time per test. For the 7 8 461 synthetic tomography experiments discussed in this paper, each slug test requires less than 9 10 462 one-third of the time of a pumping test for the same hydrogeological conditions. 11 12 463 Furthermore, since slug tests do not require a recovery period (heads are back to their initial 13 464 levels) before testing the next interval as required after each pumping test, we estimate that 14 15 465 an equivalent tomography experiment with slug tests is approximately seven times shorter to 16 17 466 carry out in the field than an experiment with the same number of pumping tests. 18 19 467 20 21 468 Overall, this study demonstrates that tomographic slug tests are an interesting alternative to more 22 23 469 commonly used tomographic pumping tests. Indeed, the same level of parameter resolutions 24 470 could be achieved for a much shorter field effort. This means, that this could foster the use of 25 26 471 hydraulic tomography by a larger community of scientists or practitioners outside of the current 27 28 472 research community. For future work it would be interesting to assess resolutions and field- 29 30 473 efficiency of periodic pumping tests and slug tests as proposed by Cardiff et al. (2013) and 31 32 474 Guiltinan and Becker (2015), respectively. 33 34 35 475 6 Acknowledgements 36 37 38 476 This study was supported by the Geological Survey of Canada as part of the Groundwater 39 40 477 Geoscience Program and by NSERC Discovery Grants held by R.L. and E.G. The authors would 41 42 478 like to thank the four anonymous reviewers that provided constructive reviews. 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Water Resour Res 41:W07028 doi:10.1029/2004WR003790 38 39 626 40 41 627 42 43 628 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 Figure captions

Tomographic Slug and Pumping Tests Comparison 1/2

1 Figures Captions 2 3 Figure 1. Schematic diagram illustrating the general approach used for the evaluation of the 4 resolution matrix of a tomography experiment. 1) Starting from an idealized aquifer system and a 5 test configuration, sensitivities are calculated using the numerical flow simulator through a 6 perturbation approach. 2) A Moore-Penrose pseudo-inverse approach is then applied on the 7 resulting sensitivity matrix to evaluate the associated resolution matrix. 3) Resolution 8 characteristics of the tomography experiment is finally analyzed through inspection of the 9 diagonal elements of the resolution matrix. 10 11 Figure 2. Head and drawdown for reciprocal slug tests and pumping tests, respectively, for the

12 case with a test configuration symmetrical with respect to layering in Kh, Kv and Ss. (a) Aquifer 13 model and test configuration; (b) Head for reciprocal slug tests; (c) Drawdown for reciprocal 14 pumping tests considering wellbore storage in the stressed well; and (d) Drawdown for 15 reciprocal pumping tests neglecting wellbore storage in the stressed interval. Note that reciprocal 16 tests are simulated by mirroring the vertical locations of the stressed and observation intervals to

17 represent the two different testing directions. Values of Kh, Kv and Ss for the different simulations 18 are compiled in Table 1. 19 20 Figure 3. Head and drawdown for reciprocal slug tests and pumping tests, respectively, for the

21 case with a test configuration asymmetrical with respect to layering in Kh, Kv and Ss. (a) Aquifer 22 model and test configuration; (b) Head for reciprocal slug tests; (c) Drawdown for reciprocal 23 pumping tests considering wellbore storage in the stressed well; and (d) Drawdown for 24 reciprocal pumping tests neglecting wellbore storage in the stressed interval. Note that reciprocal 25 tests are simulated by mirroring the vertical locations of the stressed and observation intervals to

26 represent the two different testing directions. Values of Kh, Kv and Ss for the different simulations 27 are compiled in Table 1. 28

29 Figure 4. Diagonal elements of the resolution matrix for Kh, Kv/Kh, and Ss associated with the 30 analysis of the synthetic 10,000 s head (a) and drawdown (b) records for a homogeneous and 31 anisotropic model. Resolutions are based on a Moore-Penrose pseudo-inverse of the sensitivity Tomographic Slug and Pumping Tests Comparison 2/2

32 matrix for a relative parameter error of 10% and a random noise with a standard deviation of 33 2x10-4 m (see Supplementary Material for supportive information). 34 35 Figure 5. Head and drawdown in (a) stressed and (b) observation intervals for a single test.

36 Sensitivities in Kh, Kv/Kh, and Ss for the observation interval in (c) are computed for the entire 37 inter-well region. Stressed and observation intervals are located in the middle of the wells. 38

39 Figure 6. (a) Head and drawdown as well as (b) sensitivities in Kh, Kv/Kh, and Ss for the 40 observation interval of a single test considering a reduced pumping rate of 1.0x10-5 m3/s (0.6 41 LPM). Head and sensitivities for the slug test in gray are from Figure 5 for reference. Head and 42 sensitivities for reduced initial slug test head of 2.25 m (Table 2) are not shown, but their 43 magnitudes are half those of Figure 5 (gray lines). 44

45 Figure 7. (a) Head and drawdown as well as (b) sensitivities in Kh, Kv/Kh, and Ss for the 46 observation interval of a single test considering a reduced test duration lasting 1,000 s instead of 47 10,000 s. 48 Figure 1

Numerical Model Tomographic Experiment

Observation Stressed Observation Stressed Well Well Well Well

1. Sensitivity 1 2 3 Observation Computation 4 5 Intervals 6 7 + 8 9 10 Stressed 11 12 Interval 13

Sensitivity Matrix n 2. Moore-Penrose J11 ... J1n Pseudo-Inverse m ...... m: number of measurements n ...... : number of parameters

Jm1 ... Jmn

Resolution Matrix 3. Resolution Matrix n Diagonal Elements Analysis R11 ... R1n n ......

Rn1 ... Rnn Figure 2 corrected

(A) Symmetrical reciprocal test configuration with respect to heterogeneity well 1 well 2 8 Unchanged 1 6 well 1 well 2 4 Kh , Kv or Ss Varied 2 well 1 well 2 2 Elevation(m) Unchanged 3 0 0 2 4 6 8 10 12 14 16 18 Distance (m) (B) Slug tests 5 5 5 0.1 Kh varied Kv varied Ss varied (m)-Obs.Head 4 4 4 stres. stres. stres. 3 3 3 0.05 2 2 2 obs. obs. 1 1 1

Head(m)-Stres. obs. 0 0 0 0 10 0 10 1 10 2 10 3 10 4 10 0 10 1 10 2 10 3 10 4 10 0 10 1 10 2 10 3 10 4 Time (sec) Time (sec) Time (sec) (C) Pumping tests considering wellbore storage

6 6 6 0.6 (m)-Obs.Drawdown Kh varied Kv varied Ss varied 5 5 5 0.5 4 stres. 4 stres. 4 stres. 0.4 3 obs. 3 3 0.3 obs. 2 2 2 obs. 0.2 1 1 1 0.1

Drawdown(m)-Stres. 0 0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Time (sec) (D) Pumping tests without wellbore storage 6 6 6 0.6 (m)-Obs.Drawdown Kh Kv Ss 5 varied 5 varied 5 varied 0.5 4 stres. 4 stres. 4 stres. 0.4 3 3 3 0.3 2 obs. 2 2 0.2 1 1 obs. 1 obs. 0.1

Drawdown(m)-Stres. 0 0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Time (sec) Figure 3 modified

(A) Asymmetrical reciprocal test configuration with respect to heterogeneity well 1 well 2 8 6 well 1 well 2 Unchanged 1 4 well 1 well 2 2 Elevation(m) Kh , Kv or Ss Varied 2 0 0 2 4 6 8 10 12 14 16 18 Distance (m) (B) Slug tests 5 5 5 0.1 Kh varied Kv varied Ss varied (m)-Obs.Head 4 4 4 stres. stres. 3 stres. 3 3 0.05 2 2 2 obs. obs. 1 obs. 1 1 Head(m)-Stres. 0 0 0 0 10 0 10 1 10 2 10 3 10 4 10 0 10 1 10 2 10 3 10 4 10 0 10 1 10 2 10 3 10 4 Time (sec) Time (sec) Time (sec) (C) Pumping tests considering wellbore storage

6 6 6 0.6 (m)-Obs.Drawdown Kh varied Kv varied Ss varied 5 5 5 0.5 4 stres. 4 stres. 4 stres. 0.4 3 3 3 0.3 obs. obs. 2 obs. 2 2 0.2 1 1 1 0.1

Drawdown(m)-Stres. 0 0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Time (sec) (D) Pumping tests without wellbore storage 6 6 6 0.6 (m)-Obs.Drawdown Kh varied Kv varied Ss varied 5 stres. 5 5 stres. 0.5 4 4 stres. 4 0.4 3 3 3 0.3 2 obs. 2 obs. 2 0.2 obs. 1 1 1 0.1

Drawdown(m)-Stres. 0 0 0 0 0 1 2 3 4 5 0 1 2 3 4 5 0 1 2 3 4 5 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Time (sec) Figure 4

(A) Slug: 10000 sec, Kh Resolution (B) Pumping: 10000 sec, Kh Resolution str. obs. str. obs. 1 1

6 0.8 6 0.8 0.6 0.6 4 4 0.4 0.4

Elevation(m) 2 Elevation(m) 2 0.2 0.2 0 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18

Slug: 10000 sec, Kv /Kh Resolution Pumping: 10000 sec, Kv /Kh Resolution 1 1

6 0.8 6 0.8 0.6 0.6 4 4 0.4 0.4

Elevation(m) 2 Elevation(m) 2 0.2 0.2 0 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18

Slug: 10000 sec, Ss Resolution Pumping: 10000 sec, Ss Resolution 1 1

6 0.8 6 0.8 0.6 0.6 4 4 0.4 0.4

Elevation(m) 2 Elevation(m) 2 0.2 0.2 0 0 2 4 6 8 10 12 14 16 18 2 4 6 8 10 12 14 16 18 Distance (m) Distance (m) Figure 5

(A) (B) (C) Stressed Interval Observation Interval Observation Interval 5 0.3 Drawdown Pumping 0.04 (m) sensitivity Normalized 4 Drawdown from Head pumping test 0.2 0.02 3 0 2 0.1 Head from slug test -0.02

Head/Drawdow(m) 1 Head/Drawdown(m) Slug Kh Kv /Kh Ss -0.04 0 0 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Time (sec) Figure 6

(A) (B) Observation Interval Observation Interval 0.3

Slug (from Figure 5c) 0.04 (m) sensitivity Normalized

Steady-state 0.2 drawdown from Pumping 0.02 Peak head pumping from 0 Figure 5b 0.1 -0.02 Kh Head/Drawdown(m) Kv /Kh Ss -0.04 0 0 1 2 3 4 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Figure 7

(A) (B) Observation Interval Observation Interval 0.3

0.04 (m) sensitivity Normalized Slug Pumping Drawdown from pumping test 0.2 0.02 17 min 7 min 0

Head from 2.5 h 0.1 -0.02 slug test 2.5 h 17 min Head/Drawdown(m) Kh Kv /Kh 7 min Ss -0.04 0 0 1 2 3 4 0 1 2 3 4 10 10 10 10 10 10 10 10 10 10 Time (sec) Time (sec) Table

Tomographic Slug and Pumping Tests Comparison 1/2

1 Table 1. Hydraulic properties of each layer in the model used for the verification of the principle 2 of reciprocity for slug tests and pumping tests. 3

Kh Kv Ss Simulation Layer (ms-1) (ms-1) (m-1)

-6 -6 -5 Kh varied 2 1x10 1x10 1x10

-5 -5 -5 Kv varied 2 1x10 1x10 1x10

-5 -6 -6 Ss varied 2 1x10 1x10 1x10

For all simulations 1 and 3 1x10-5 1x10-6 1x10-5

4 5 Tomographic Slug and Pumping Tests Comparison 2/2

6 Table 2. Mean resolution for cells within the inter-well region for different tomography 7 experiments using different test initiation methods (slug and pumping), test durations and 8 pumping rates. 9

Pumping Mean Resolution for Test Initial Rate Inter-Well Region Experiment Duration Head (x10-5 (s) (m) Kh Kv/Kh Ss 3 m /s) (ms-1) (-) (m-1)

1.Slug tests 10,000 4.5 - 0.57 0.30 0.48

2.Pumping tests 10,000 - 4.0 0.54 0.33 0.36

3.Reduced initial slug test heads 10,000 2.25 - 0.52 0.24 0.36

4.Reduced pumping rates 10,000 - 1.0 0.49 0.23 0.26

5.Reduced slug test durations 1,000 4.5 - 0.50 0.24 0.37

6.Reduced pumping test durations 1,000 - 4.0 0.41 0.21 0.21

7.Reduced slug test durations 400 4.5 - 0.41 0.20 0.24

10 Supplementary Material

Click here to access/download Supplementary Material ENGE-D-15-02723_R2_SuppData.docx