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... Some researches point out that the magnitude of the oscillation will increase as the hydraulic conductivity of the aquifer and the water column height increase (Bredehoeft et al., 1966;Butler & Zhan, 2004). Since Bredehoeft et al. (1966) discussed the role of water-column inertia in hydraulic tests, many researchers also considered inertial effects in their analytical slug test models to interpret the oscillatory head (Butler & Zhan, 2004;Kabala et al., 1985;Kipp, 1985;Malama et al., 2011Malama et al., , 2016McElwee & Zenner, 1998;Springer & Gelhar, 1991;Zurbuchen et al., 2002). Butler and Zhan (2004) presented a homogeneous slug test model for confined aquifers which considers inertial mechanisms both in the observation and test wells. ...

... Butler and Zhan (2004) presented a homogeneous slug test model for confined aquifers which considers inertial mechanisms both in the observation and test wells. Malama et al. (2016) further developed the model for unconfined aquifers. Considering the inertial effects in both wells makes their model more adequate for interpreting cross-well slug tests. ...

The slug test is a common field technique for obtaining local hydraulic parameters near wells, applied, for example, for the hydrogeological investigation at contaminated sites. Although many slug test models have been developed for interpretation of measurements, only a few of them have considered heterogeneous conditions, and water column inertial effects are usually neglected. In this paper, we propose a novel three‐dimensional slug test model (3DHIM) for application in heterogeneous aquifers, considering inertial effects associated with skin effects and linear friction forces. After comparison with existing analytical and numerical solutions of slug tests, the model is applied to an aquifer analog to simulate a series of slug tests. The results from single‐well slug tests show that the well geometry (i.e., the well radius, well depth, and screen length) has an impact on the water level response. For cross‐well slug tests, the results indicate that the water level fluctuations not only include information on the hydraulic signal propagation process in the aquifer but also on well characteristics, such as wellbore storage and inertial effects. These effects cause a phase shift and amplitude change of the water level fluctuation. As the observation and test wells have a good hydraulic connection and similar well geometry, the water level amplitude could be amplified relative to aquifer pressure at the measured position. Therefore, we suggest considering wellbore storage and in‐well inertial effects in slug test‐based subsurface investigations, otherwise the parameter estimates based on well water levels may include errors, particularly in highly permeable layers.

... The nonlinear flow significantly affects this response and may be expressed in terms of a squared velocity term. A substantial number of studies (e.g., Dausse et al., 2021;Hommersen et al., 2021;Kabala et al., 1985;Liu et al., 2020;Malama et al., 2011;Malama et al., 2016;McElwee, 2001;McElwee & Zenner, 1998;McGuire & Zlotnik, 1995;Stone & Clarke, 1993) reported such a nonlinear phenomenon for slug test in a high-conductivity formation. Those studies however mainly focused on investigating the critically damped or underdamped water level response in the wellbore (Wang et al., 2015). ...

This study proposes a new analytical slug test model describing confined flow considering the effects of the formation damage and non-Darcy flow near the wellbore. The former, primarily caused by drilling fluid invasion, introduces an extra wellbore head loss near the well screen. The latter, mainly resulting from the relatively high-velocity flow across the gravel-pack screen, adopts the Forchheimer equation to consider the joint effects of the laminar flow and non-Darcy flow. The proposed model is nonlinear due to the quadratic term for non-Darcy flow in the Forchheimer equation. The new solutions for head responses in the well and formation are derived using the Laplace transform method and integration by parts formula. Furthermore, the present solution is applied to estimate the aquifer parameters via analyzing the water level data from field slug tests conducted in the Minnelusa aquifer near Spearfish, South Dakota. We found that the present solution
provides very good fit to the field data from tests in fractured aquifers, notably the data exhibits a rapid decline at late times on the normalized head vs. logarithmic time plots.

... This method is also convenient for contaminated sites because water does not need to be extracted (i.e., no need to treat water) and negligible movement of contaminants within the system. At some experimental sites where numerous observation wells are located in a relatively small area, slug tests have also been used for cross-hole investigations (e.g., Audouin and Bodin, 2008;Malama et al., 2016;Wang et al., 2018) or hydraulic tomography (e.g., Brauchler et al., 2010;Brauchler et al., 2011;Paradis et al., 2015;Paradis et al., 2016), which provides more confidence in hydraulic property distribution. However, slug test information is generally only available at the tested well due to limitations in both instrumentation and scale of investigation (Butler, 1998;Zhang et al., 2019). ...

Slug tests are one of the most common field methods for estimating local hydraulic conductivity, for fast and low-cost characterization of aquifer heterogeneity. In highly permeable zones, underdamped responses, identified by oscillations of the water level, are generally observed. Several analytical solutions have been developed for modeling underdamped slug test responses. Interpreting these tests in fractured rocks can be challenging due to system complexity, which ultimately raises questions about the appropriate model for interpreting a given dataset. In order to obtain insights on this fundamental problem for slug test analyses in fractured rocks, a complete evaluation on three transient solutions for linear, radial and spherical flow configuration extended to include inertial and wellbore skin effects in a fully penetrating well is proposed. A first comparison between these transient solutions and the classical steady-state model shows that, in some cases, the latter may underestimate hydraulic conductivity. Next, parameter sensitivity and uncertainty analyses were conducted on each solution to evaluate the classical problem of non-uniqueness between models and parameters. As expected, the results from sensitivity analysis show that the hydraulic conductivity parameter is the most sensitive regardless of model configuration. For specific storage, sensitivity is important for the linear model, moderate for the radial model and negligible for the spherical model. For the skin factor, however, sensitivity is negligible for the linear model, moderate for the radial model and most important for the spherical model. These results were next confirmed by performing Bayesian inferences using Markov Chain Monte Carlo technique to evaluate uncertainty on each parameter. Uncertainties appear significant for negligibly sensitive parameters but nearly insignificant for the most sensitive parameters. For all flow configurations, hydraulic conductivity appears however to be accurately estimated. Examples of interpretations for data collected in fractured rocks illustrate the application of these models and provide some recommendations.

... erating unconfined aquifer slug interference test type curves and used the trial and error curve-fitting procedures to estimate aquifer T and S.Sun (2016) developed a semi-analytical solution considering vertical unsaturated flow for analyzing slug test data in an unconfined aquifer and applied the solution to analyze data of three slug test wells.Malama et al. (2016) developed a semi-analytical model to analyze cross-hole slug test data in an unconfined aquifer and the non-linear optimization software PEST(Doherty, 2010) was used to estimate values. s S ...

Specific storage, which represents the aquifer’s capacity to release water from or take into storage when water level changes, is an important aquifer property required for transient groundwater modeling and water resources management. This review synthesizes the published literature on using different methods to estimate field specific storage of aquifers. The field methods include pumping tests, slug tests, and analyses of sea tides, atmospheric loading and earth tides, and seismic waves. The present state of knowledge concerning the analytical and numerical models and parameter estimating procedures are presented and applications of these models are discussed. Specific storage values from 182 different field sites are collected, covering a wide range of aquifer materials, including unconsolidated deposits and rocks. The geometric mean of specific storage for unconsolidated deposits mainly range from 10⁻⁵ to 10⁻⁴ m⁻¹. The geometric mean of specific storage for different types of rocks mainly range from 10⁻⁷ to 10⁻⁶ m⁻¹. The corresponding hydraulic conductivity shows a wider range of variation than the specific storage. There is not a clear relationship between specific storage and hydraulic conductivity for all the data but a positive correlation can be found for some types of aquifer materials. Specific storage is positively correlated with porosity of the aquifer. A comparison of the different field methods is presented and future research directions are recommended.

... Malama et al. 2016;Mamer and Lowry 2013;Rau et al. 2012), a numerical case was first set up to demonstrate the implementation details of the Bayesian experimental design. The 2-D model domain is shown inFig. ...

Heat tracing methods have been widely employed for subsurface characterization. Nevertheless, there were very few studies regarding the optimal monitoring design for heat tracing in heterogeneous streambeds. In this study, we addressed this issue by proposing an efficient optimal design framework to collect the most informative diurnal temperature signal for Bayesian estimation of streambed hydraulic conductivities. The data worth (DW) was measured by the expected relative entropy between the prior and posterior distributions of the conductivity field. An adaptively refined Gaussian process surrogate was employed to alleviate the computational burden, resulting in at least three orders of magnitude of speed-up. The applicability of the optimal experimental design framework was evaluated by both numerical and sandbox experimental cases. Results showed that, the most informative locations centered in the transition zones among the main patterns of the hydraulic conductivity field, while the most informative times centered in a short period after the minimum/maximum temperature appeared. With the fixed number of measurements, extending the calibration period was more beneficial than increasing the monitoring frequency in improving the estimation results. To our best knowledge, this work is the first study on Bayesian monitoring design for streambed characterization with the heat tracing method. The method and results can provide guidance on selecting monitoring strategies under budget-limited conditions.

... Depending on the type of aquifers being tests, a number of analytical and semi-analytical models for interpreting cross-hole slug tests have been presented in the literature (e.g. Karasaki et al., 1988;Novakowski, 1989;Hyder et al., 1994;Butler and Zhan, 2004;Malama et al., 2016). Among others, the solution of Hyder et al. (1994), also known as the KGS model, is widely used in the hydrogeological community (Belitz and Dripps, 1999). ...

A laboratory analogue experiment platform with an artificial fracture was built to analyze the effect of slug interference tests on the evaluation of the hydraulic properties of fractured rocks. The response of an aquifer to a slug source well was analyzed using type-curve comparisons under the condition of different radial constant-water-head boundaries. The injecting-water, releasing-water, and pneumatic laboratory experiments of the slug interference tests were conducted in an artificial fracture. The relationship between the critical distance of the radial constant-water-head boundary and the dimensionless storage coefficient approximately followed a power function. The empirical formula provides an intuitive and effective reference criterion for considering the influence of the radial constant-water-head boundaries during field slug interference tests. When the radial constant-water-head boundary distances are less than the critical values, the boundary leads to an obvious increase in the recovery rate during the late response period, and the response peaks of the aquifer shift to an earlier time in the low-storage fractured rocks. The monitoring and analysis of the response in fractured rocks can improve the accuracy of the transmissivity and storage coefficient estimations, particularly when the slug interference tests are affected by the radial constant-water-head boundaries.

Specific storage, a basic hydraulic property of an aquifer, is required for transient groundwater studies. Previous investigations have shown that specific storage decreases with depth. Here, we collected field-specific storage-depth data from the literature and proposed an empirical model that describes the decreasing trend of specific storage with depth in the Earth's crust. The results show that the model agrees well with the field-specific storage-depth data. There are three parameters in the proposed model, which is flexible in fitting specific storage-depth data. The model also yields a finite value at the ground surface and a reasonable decay rate with depth. This is the first model describing the decreasing trend of specific storage with depth. The model is simple and can readily be applied to transient numerical models of groundwater flow and solute transport in porous media.

The multi-walled carbon nanotubes (MWCNTs) were synthesized by homemade equipment with the waste alcohol. The synthesized MWCNTs were characterized by scanning electron microscopy (SEM), transmission electron microscope (TEM), and Raman spectroscopy. Moreover, in confirming the synthesized green/eco-friendly technique, MWCNTs were grown on some of the micropunches to show the attractive potential for bioenergy application compellingly and convincingly. Results show that due to the usage of the waste alcohol, not only is this technique definitely green/eco-friendly to the environment, but also MWCNTs as a protective layer on the micropunch can lengthen the service life of the micropunch by up to 35% without directly affecting the size of the punched holes compared with that of without MWCNTs. Moreover, the punched microholes are definitely quite distinct from that of traditional punching. Besides the fracture band is absent, the areas of rollover and burr are also extremely narrow, which implies the attractive punched microhole can be used directly without any posttreatments.

Free enzymes do not possess properties of recovery and reusability, and also they are not stable at wide pH and temperature range. Therefore, new ways which can enhance enzyme stability and reusability should be developed, and hence, the immobilization technique is one such approach. These immobilization techniques offer such materials which have the ability to be active in the much wide range of pH and temperature, and also they are more stable than the free enzymes. Immobilization is carried out on the nanosized material either by adsorption, covalent coupling, entrapment, encapsulation or cross-linking. These nanomaterial-immobilized enzymes show several advances over the free enzymes because of large surface area-to-volume ratio, lower mass transfer resistance and high mobility. Several nanomaterials are used for immobilizing the enzymes; however, their recovery from the reaction mixture is very poor. Therefore, the magnetic nanomaterials are more attractively used in immobilization because the enzyme immobilized through magnetic nanomaterial has the tendency to be easily separated out from the reaction mixture. These nanomaterial-immobilized enzymes show wide range of applications in biotechnology, bioanalysis, biomedicine, pathology and biosensors.

Hydraulic tomography inverse problems, which are solved to estimate aquifer hydraulic properties between wells, are known to be ill-conditioned and a priori information is often added to regularize numerical inversion of head data. Because both head data and a priori information have effects on the inversed solution, assessing the meaningful information contained in head data alone is required to ensure comprehensive interpretation of inverse solutions, whether they are regularized or not. This study thus aims to assess the amount of information contained in tomographic slug tests head data to resolve heterogeneity in Kh, Kv/Kh and Ss. Therefore, a resolution analysis based on truncated singular value decomposition of the sensitivity matrix with a noise level representative of field measurements is applied using synthetic data reflecting a known littoral aquifer. As an approximation of the hydraulic behavior of a real aquifer system, synthetic tomographic experiments and associated sensitivity matrices are generated using a radial flow model accounting for wellbore storage to simulate slug tests in a plane encompassing a stressed well and an observation well. Although fine-scale resolution of heterogeneities is limited by the diffusive nature of the groundwater flow equations, inversion of tomographic slug tests head data holds the potential to uniquely resolve coarse-scale heterogeneity in Kh, Kv/Kh and Ss, as inscribed in the resolution matrix. This implies that tomographic head data can provide key information on aquifer heterogeneity and anisotropy, but that fine-scale information must be supplied by a priori information to obtain finer details.

Providing a sound basis for aquifer management or remediation requires that hydrogeological investigations carried out to understand groundwater flow and contaminant transport be based on representative data that capture the heterogeneous spatial distribution of aquifer hydraulic properties. This paper describes a general workflow allowing the characterization of the heterogeneity of the hydraulic properties of granular aquifers at an intermediate scale of a few km2. The workflow involves characterization and data integration steps that were applied on a 12 km2 study area encompassing a decommissioned landfill emitting a leachate plume and its main surface water receptors. The sediments composing the aquifer were deposited in a littoral-sublittoral environment and show evidence of small-scale transitional heterogeneities. Cone penetrometer tests (CPT) combined with soil moisture and electrical resistivity (SMR) measurements were thus used to identify and characterize spatial heterogeneities in hydraulic properties over the study area. Site-specific statistical relationships were needed to infer hydrofacies units and to estimate hydraulic properties from high-resolution CPT/SMR soundings distributed all over the study area. A learning machine approach was used due to the complex statistical relationships between colocated hydraulic and CPT/SMR data covering the full range of aquifer materials. Application of this workflow allowed the identification of hydrofacies units and the estimation of horizontal hydraulic conductivity, vertical hydraulic conductivity and porosity over the study area. The paper describes and discusses data acquisition and integration methodologies that can be adapted to different field situations, while making the aquifer characterization process more time-efficient and less labour-intensive.

The streaming potential method has emerged as a promising technology for
indirect acquisition of spatially dense measurements of the hydraulic
system state response to pumping aquifers. The method relies on
measurements of electric potentials generated by groundwater flow due to
the existence of the electric double layer at the rock--water interface.
Mathematical solutions describing the transient electric potentials
associated with pumping tests have been recently developed and
demonstrated to yield reasonable estimates of hydraulic parameters
(Malama et al., 2009b,a). We present results of laboratory experiments
conducted to investigate the applicability of the unconfined aquifer
model under controlled conditions in a sand tank instrumented with
pressure transducers and non-polarizable electrodes. The measured
pressure and streaming potential changes under various pumping rates are
presented and discussed. Measurements show unambiguous transient
streaming potential responses to groundwater flow in bounded cylindrical
system. Parameters estimated from streaming potential data are compared
to those from drawdown data. Sandia National Laboratories is a
multi-program laboratory managed and operated by Sandia Corporation, a
wholly owned subsidiary of Lockheed Martin Corporation, for the U.S.
Department of Energy's National Nuclear Security Administration under
contract DE-AC04-94AL85000.

We consider parameters determined by the inversion of slug-test head recovery data with the homogeneous-parameter model of Cooper et al. [1967] to be weighted spatial averages of transmissivity and storage defined at a smaller scale. We quantify the spatial averaging using a power-average spatial filter expression. We determine the form of the filter function and the power exponent using numerically simulated slug-test data. The filter function that describes how smaller-scale transmissivity is weighted by slug tests displays an approximate 1/r2 behavior, with r the radial distance from the well. The radius of the cylinderical volume that is averaged by the slug test is inversely proportional to the square root of the storage coefficient (larger averaging volume with smaller storage). The power exponent grows from −0.19 to 0.345 as the ratio of the characteristic scale of the heterogeneity to the characteristic scale of the averaging volume grows, although a power exponent of zero, corresponding to geometric averaging, provides good results for most simulations. Our results show that while slug tests are useful to estimate transmissivity, they have dubious value for estimating storage coefficients. We find that the transmissivity estimate is unbiased and does not appear to be strongly influenced by storage properties. The storage coefficient estimate is, however, strongly influenced by the transmissivity and is biased. We investigate the interaction between storage coefficient and transmissivity by examining an analytical slug-test model that contains two annular zones, each with distinct transmissivity and storage coefficient.

A semianalytical solution is presented to a mathematical model describing the flow of groundwater in response to a slug test in a confined or unconfined porous formation. The model incorporates the effects of partial penetration, anisotropy, finiteradius well skins, and upper and lower boundaries of either a constant-head or an impermeable form. This model is employed to investigate the error that is introduced into hydraulic conductivity estimates through use of currently accepted practices (i.e., Hvorslev, 1951; Cooper et al., 1967) for the analysis of slug-test response data. The magnitude of the error arising in a variety of commonly faced field configurations is the basis for practical guidelines for the analysis of slug-test data that can be utilized by field practitioners.

A semianalytical solution is presented for a mathematical model describing the flow of groundwater in response to a slug or pumping test in a highly permeable, confined aquifer. This solution, which is appropriate for wells of any degree of penetration and incorporates inertial mechanisms at both the test and observation wells, can be used to gain new insights into hydraulic tests in highly permeable settings. The oscillatory character of slug- and pumping-induced responses will vary considerably across a site, even in an essentially homogeneous formation, when wells of different radii, depths, and screen lengths are used. Thus variations in the oscillatory character of responses do not necessarily indicate variations in hydraulic conductivity (K). Existing models for slug tests in partially penetrating wells in high-K aquifers neglect the storage properties of the media. That assumption, however, appears reasonable for a wide range of common conditions. Unlike in less permeable formations, drawdown at an observation well in a high-K aquifer will be affected by head losses in the pumping well. Those losses, which affect the form of the pumping-induced oscillations, can be difficult to characterize. Thus analyses of observation-well drawdown should utilize data from the period after the oscillations have dissipated whenever possible. Although inertial mechanisms can have a large impact on early-time drawdown, that impact decreases rapidly with duration of pumping and distance to the observation well. Conventional methods that do not consider inertial mechanisms should therefore be viable options for the analysis of drawdown data at moderate to large times.

Hydraulic tomography (i.e., a sequential aquifer test) has recently been
proposed as a method for characterizing aquifer heterogeneity. During a
hydraulic tomography experiment, water is sequentially pumped from or
injected into an aquifer at different vertical portions or intervals of
the aquifer. During each pumping or injection, hydraulic head responses
of the aquifer at other intervals are monitored, yielding a set of
head/discharge (or recharge) data. By sequentially pumping (or
injecting) water at one interval and monitoring the steady state head
responses at others, many head/discharge (recharge) data sets are
obtained. In this study a sequential inverse approach is developed to
interpret results of hydraulic tomography. The approach uses an
iterative geostatistical inverse method to yield the effective hydraulic
conductivity of an aquifer, conditioned on each set of head/discharge
data. To efficiently include all the head/discharge data sets, a
sequential conditioning method is employed. It uses the estimated
hydraulic conductivity field and covariances, conditioned on the
previous head/discharge data set, as prior information for next
estimations using a new set of pumping data. This inverse approach was
first applied to hypothetical, two-dimensional, heterogeneous aquifers
to investigate the optimal sampling scheme for the hydraulic tomography,
i.e., the design of well spacing, pumping, and monitoring locations. The
effects of measurement errors and uncertainties in statistical
parameters required by the inverse model were also investigated.
Finally, the robustness of this inverse approach was demonstrated
through its application to a hypothetical, three-dimensional,
heterogeneous aquifer.

The hydrogeological properties and responses of a productive aquifer in northeastern Switzerland are investigated. For this purpose, 3D crosshole electrical resistivity tomography (ERT) is used to define the main lithological structures within the aquifer (through static inversion) and to monitor the water infiltration from an adjacent river. During precipitation events and subsequent river flooding, the river water resistivity increases. As a consequence, the electrical characteristics of the infiltrating water can be used as a natural tracer to delineate preferential flow paths and flow velocities. The focus is primarily on the experiment installation, data collection strategy, and the structural characterization of the site and a brief overview of the ERT monitoring results. The monitoring system comprises 18 boreholes each equipped with 10 electrodes straddling the entire thickness of the gravel aquifer. A multichannel resistivity system programmed to cycle through various four-point electrode configurations of the 180 electrodes in a rolling sequence allows for the measurement of approximately 15,500 apparent resistivity values every 7 h on a continuous basis. The 3D static ERT inversion of data acquired under stable hydrological conditions provides a base model for future time-lapse inversion studies and the means to investigate the resolving capability of our acquisition scheme. In particular, it enables definition of the main lithological structures within the aquifer. The final ERT static model delineates a relatively high-resistivity, low-porosity, intermediate-depth layer throughout the investigated aquifer volume that is consistent with results from well logging and seismic and radar tomography models. The next step will be to define and implement an appropriate time-lapse ERT inversion scheme using the river water as a natural tracer. The main challenge will be to separate the superposed time-varying effects of water table height, temperature, and salinity variations associated with the infiltrating water.

Modern developments in theoretical and applied science depend on knowledge of the properties of mathematical functions, from elementary trigonometric functions to the multitude of special functions. These functions appear whenever natural phenomena are studied, engineering problems are formulated, and numerical simulations are performed. They also crop up in statistics, financial models, and economic analysis. Using them effectively requires practitioners to have ready access to a reliable collection of their properties. This handbook results from a 10-year project conducted by the National Institute of Standards and Technology with an international group of expert authors and validators. Printed in full color, it is destined to replace its predecessor, the classic but long-outdated Handbook of Mathematical Functions, edited by Abramowitz and Stegun. Included with every copy of the book is a CD with a searchable PDF of each chapter.

Meaningful understanding of flow and solute transport in general requires the knowledge of hydraulic conductivity and its anisotropy. Various field methods allow the measurement of the horizontal component (Kh), but vertical hydraulic conductivity (Kv) is rarely measured, for lack of practical field tests. This paper proposes vertical interference slug tests, an adaptation of inter-well interference slug tests to a single well, for the efficient field measurement of Kv. The test is carried out in a single well between a stress and an observation interval that are vertically isolated with a three-packer assembly. An instantaneous pressure pulse is induced in the stress interval and resulting drawdowns are recorded in both the stress and the observation intervals. In a proof-of-concept field study, 12 vertical interference tests were carried out sequentially along a fully-screened well across a moderately heterogeneous and highly anisotropic
aquifer made up of littoral silts and sands. A direct-push method was used to install the well, which was completed without sand-pack to allow the natural collapse of sediments in the thin annular space around the screen. Direct-push wells allow the measurement of in situ hydraulic properties of sediments and minimize well construction interferences with hydraulic tests. Drawdowns measured in stress and observation intervals of multiple tests were simultaneously inverted numerically to reconstruct heterogeneous profiles of Kh, hydraulic conductivity anisotropy (Kv/Kh), and specific storage (Ss). Results were validated by comparison of observed versus predicted drawdowns and with field and laboratory measurements of Kh and Kv made along the tested well. Results indicate that the profile of Kv values obtained with vertical interference slug tests follows a similar pattern with depth than the profile with lab measurements made with a permeameter on soil samples collected in the same intervals as the interference tests, which demonstrates that vertical interference slug tests could provide an efficient method for the field measurement of well-scale Kv values.

1] Considerable progress has been made in developing a theoretical framework for modeling slug test responses in formations with high hydraulic conductivity K. However, several questions of practical significance remain unresolved. Given the rapid and often oscillatory nature of test responses, the traditional hydrostatic relationship between the water level and the transducer-measured head in the water column may not be appropriate. A general dynamic interpretation is proposed that describes the relationship between water level response and transducer-measured head. This theory is utilized to develop a procedure for transforming model-generated water level responses to transducer readings. The magnitude of the difference between the actual water level position and the apparent position based on the transducer measurement is a function of the acceleration and velocity of the water column, test geometry, and depth of the transducer. The dynamic approach explains the entire slug test response, including the often-noted discrepancy between the actual initial water level displacement and that measured by a transducer in the water column. Failure to use this approach can lead to a significant underestimation of K when the transducer is a considerable distance below the static water level. Previous investigators have noted a dependence of test responses on the magnitude of the initial water level displacement and have developed various approximate methods for analyzing such data. These methods are re-examined and their limitations clarified. Practical field guidelines are proposed on the basis of findings of this work. The soundness of the dynamic approach is demonstrated through a comparison of K profiles from a series of multilevel slug tests with those from dipole-flow tests performed in the same wells.

Two models for slug tests conducted in unconfined aquifers are developed by (a) extending the uncon-fined KGS solution to oscillatory responses, yielding a model referred to herein as the unified model, and (b) replacing the constant head condition with the linearized kinematic condition at the water table. The models can be used to analyze the full range of responses from highly oscillatory to overdamped. The second model, refered to as the moving water table (MWT) model, is only applicable when effects of well bore skin are negligible. The models are validated by comparison with published solutions, and by appli-cation to a published case study of field tests conducted in wells without skin in an unconfined aquifer at the MSEA site in Nebraska. In this regard (a) the MWT model essentially yields the same results as the confined KGS model, except very close to the water table, and (b) the unified model yields slightly smaller aquifer K-values relative to the MWT model at all positions in the well. All model solutions yield compa-rable results when fitted to published field data obtained in an unconfined fluvial aquifer at the MSEA site in Nebraska. The unified model is fitted to field data collected in wells known to exhibit positive skin effects at the Boise Hydrogeophysical Research Site (BHRS) in Boise, Idaho. It is shown to yield hydraulic conductivity estimates of comparable magnitude to those obtained with the KGS model for overdamped responses, and the Springer–Gelhar model for oscillatory responses. Sensitivity of the MWT model to spe-cific yield, S y , and hydraulic anisotropy, j is evaluated and the results, when plotted in log–log space and with consideration of log-scale time derivatives of the response, indicate that these two parameters should be estimable from slug test data, though challenges still remain.

An existing closed form model is modified to describe the damped response of groundwater in a fractured bedrock borehole with variable apertures and dips to a slug test. The existing theory, which requires single sized horizontal fractures, is accurately calibrated by slug test data from three uncased bedrock boreholes in the Dedham Granite and an observation well screened just below the contact surface with a till drumlin. Apertures and dips vary however, so the ability of the modified theory to accommodate different sizes and inclinations improves upon the physical validity of its predecessor when fracture information accompanies slug test data. Geophysical logs identify a large number and dip of fractures in the uncased boreholes in the Dedham Granite in this regard. A lognormally distributed, horizontal aperture calibration of the slug tests in the uncased boreholes retains the accuracy of the single size model, and yields aperture statistics more consistent with literature values. The slug test in the screened observation well is accurately calibrated with the modified horizontal theory for discrete (two) sizes, based upon the average fracture spacing found in the uncased boreholes. All four results yield comparable compressibility estimates, which depend on fracture spacing but not size or dip. The calibrated aperture size and calculated fracture porosity and permeability decrease with length of the borehole into the Dedham Granite. The measured dip and aperture for flowing and nonflowing fractures in one of the boreholes accurately calibrates the modified theory. The inclusion of dip reduces the calibrated permeability because of the increased ellipsoidal area at the interface of the borehole and the inclined fractures.

For groundwater transport modelling on a scale of 10-100 m, detailed information about the spatial distribution of hydraulic conductivity is of great importance. At a test site (10 × 20 m) in the alluvial gravel-and-sand aquifer of the perialpine Thur valley (Switzerland), four different methods were applied on different scales. The comparison of the results showed that multilevel slug tests give the most reliable results at the required scale. For their analysis, a plausible value of the anisotropy ratio (K vertical/ K horizontal) is needed. For alpine and perialpine aquifers, a range of 0.1-0.2 can be expected. Flowmeter logs are recommended, if the relative distribution of hydraulic conductivity is of primary importance. Sieve analyses should be used, if an accuracy of a factor of 3 is acceptable. Pumping test results indicate the upper boundary of the natural spectrum of hydraulic conductivity at the scale of the test site.

Slug test has been commonly applied to determine the near-well aquifer properties because of its logistical and economic advantages over other aquifer tests. Instantaneously increasing or decreasing the water level inside a slug test well will generate a significant hydraulic gradient near the well screen-aquifer interface (particularly at early stage of slug test), which may result in near-well aquifer flow deviated from Darcian behavior. However, previous studies on slug test rarely considered non-Darcian flow process associated with the slug test. In this study, a transient model of slug test in a leaky confined aquifer was established considering non-Darcian horizontal flow in the aquifer, and Darcian and vertical flow in the aquitard. The non-Darcian flow in the aquifer was described by the Izbash (power-law) equation. A finite-difference solution was presented for solving the non-linear model of slug test, the accuracy of which was tested through comparison with a previous analytical solution. By analyzing the sensitivities of dimensionless aquitard leakance (αD), non-Darcian index (n), and ratio of well screen radius versus well casing radius (χ) on the water level recovery (WLR) of slug test, one could conclude that the rate of WLR increased with the decrease of n for a given time. The WLR curve of Darcian flow (n = 1) was above the curves of non-Darcian flow, including fully developed turbulent flow. There was a deflection point for each WLR curve without the aquitard leakance in log–log scales, and the slope of the curve approached a constant after such a point. The effects of aquitard leakance on WLR for non-Darcian case appeared later than Darcian case. The normalized sensitivity coefficients of WLR with respect to n, αD and χ were negative, and they were most sensitive to n and least to αD.

In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot unveil the distribution of hydraulic conductivity. Jointly inverting geophysical and hydrological data allows us to benefit from the advantages of geophysical imaging and, at the same time, recover the hydrological parameters of interest. We have applied a coupling strategy between geophysical and hydrological models that is based on structural similarity constraints. Model combinations, for which the spatial gradients of the inferred parameter fields are not aligned in parallel, are penalized in the inversion. This structural coupling does not require introducing a potentially weak, unknown, and nonstationary petrophysical relation to link the models. The method was first tested on synthetic data sets and then applied to two combinations of geophysical/hydrological data sets from a saturated gravel aquifer in northern Switzerland. Crosshole ground-penetrating radar (GPR) traveltimes were jointly inverted with hydraulic tomography data, as well as with tracer mean arrival times, to retrieve the 2D distribution of GPR velocities and hydraulic conductivities. In the synthetic case, incorporating the GPR data through a joint inversion framework improved the resolution and localization properties of the estimated hydraulic conductivity field. For the field study, recovered hydraulic conductivities were in general agreement with flowmeter data.

A procedure is presented for calculating the hydraulic conductivity of an aquifer near a well from the rate of rise of the water level in the well after a certain volume of water is suddenly removed. The calculation is based on the Thiem equation of steady state flow to a well. The effective radius over which the head difference between the equilibrium water table in the aquifer and the water level in the well is dissipated was evaluated with a resistance network analog for a wide range of system geometries. The technique is applicable to completely or partially penetrating wells in unconfined aquifers. It can also be used for confined aquifers that receive water from the upper confining layer.

Mishra and Neuman (2010) developed an analytical solution for flow to a partially penetrating well of zero radius in a compressible unconfined aquifer that allows inferring its saturated and unsaturated hydraulic properties from responses recorded in the saturated and/or unsaturated zones. Their solution accounts for horizontal as well as vertical flows in each zone. It represents unsaturated zone constitutive properties in a manner that is at once mathematically tractable and sufficiently flexible to provide much improved fits to standard constitutive models. In this paper we extend the solution of Mishra and Neuman [2010] to the case of a finite diameter pumping well with storage; investigate the effects of storage in the pumping well and delayed piezometer response on drawdowns in the saturated and unsaturated zones as functions of position and time; validate our solution against numerical simulations of drawdown in a synthetic aquifer having unsaturated properties described by the van Genuchten [1980]-Mualem [1976] model; use our solution to analyze 11 transducer-measured drawdown records from a seven-day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada; validate our parameter estimates against manually-measured drawdown records in 14 other piezometers at Borden; and compare (a) our estimates of aquifer parameters with those obtained on the basis of all these records by Moench [2008], (b) on the basis of 11 transducer-measured drawdown records by Endres et al. [2007], (c) our estimates of van Genuchten-Mualem parameters with those obtained on the basis of laboratory drainage data from the site by Akindunni and Gillham [1992], and (d) our corresponding prediction of how effective saturation varies with elevation above the initial water table under static conditions with a profile based on water contents measured in a neutron access tube at a radial distance of about 5 m from the center of the pumping well. We also use our solution to analyze 11 transducer-measured drawdown records from a 7 day pumping test conducted by University of Waterloo researchers at the Canadian Forces Base Borden in Ontario, Canada. We validate our parameter estimates against manually measured drawdown records in 14 other piezometers at Borden. We compare our estimates of aquifer parameters with those obtained on the basis of all these records by Moench (2008) and on the basis of 11 transducer-measured drawdown records by Endres et al. (2007), and we compare our estimates of van Genuchten-Mualem parameters with those obtained on the basis of laboratory drainage data from the site by Akindunni and Gillham (1992); finally, we compare our corresponding prediction of how effective saturation varies with elevation above the initial water table under static conditions with a profile based on water contents measured in a neutron access tube at a radial distance of about 5 m from the center of the pumping well.

A solution is presented for the change in water level in a well of finite diameter after a known volume of water is suddenly injected or withdrawn. A set of type curves computed from this solution permits a determination of the transmissibility of the aquifer.

A simple model of a slug test in a fissured aquifer has been studied in order to gain insight into the difficulties of interpreting data from such tests. The model is used to estimate the errors that would result from applying the standard type curve analysis to fissured aquifers. It is found that the derived aquifer transmissivity will always be overestimated, but by a factor which is unlikely to exceed 3. By contrast, the derived storage coefficient can be in error by a factor ranging from 10−6 to 105. The volume of the aquifer influenced by a slug test is investigated, and a simple formula for estimating the range of a test is suggested.

In this study the potential of an inversion approach based on hydraulic travel time and hydraulic attenuation tomography was assessed. Both hydraulic travel time and hydraulic attenuation tomography are based on the transformation of the transient groundwater flow equation into the eikonal equation using an asymptotic approach. The eikonal equation allows the calculation of pressure propagation and attenuation along trajectories, which is computationally efficient. The attenuation and travel time-based inversion approaches are naturally complementary: hydraulic travel times are determined by the hydraulic diffusivity, a combination of hydraulic conductivity and specific storage, whereas the attenuation is determined solely by specific storage. The potential of our hydraulic tomographical approach was investigated at a well-characterized sand and gravel aquifer located in the Leine River valley near Göttingen, Germany. The database for the hydraulic inversion consists of 392 cross-well slug interference tests performed between five wells, in which the positions of the sources (injection ports) and the receivers (observation ports), isolated with double packer systems, were varied between tests. The results have shown that the combination of hydraulic travel time and hydraulic attenuation tomography allows the reconstruction of the diffusivity and storage distribution in two and three dimensions with a resolution and accuracy superior to that possible with type curve analysis.

A new multilevel ground water monitoring system has been developed that uses custom-extruded flexible 1.6-inch (4.1 cm) outside-diameter (O.D.) multichannel HOPE tubing (referred to as Continuous Multichannel Tubing or CMT) to monitor as many as seven discrete zones within a single borehole in either unconsolidated sediments or bedrock. Prior to inserting the tubing in the borehole, ports are created that allow ground water to enter six outer pie-shaped channels (nominal diameter = 0.5 inch [1.3 cm]) and a central hexagonal center channel (nominal diameter = 0.4 inch [1 cm]) at different depths, facilitating the measurement of depth-discrete piezometric heads and the collection of depth-discrete ground water samples. Sand packs and annular seals between the various monitored zones can be installed using conventional tremie methods. Alternatively, bentonite packers and prepacked sand packs have been developed that are attached to the tubing at the ground surface, facilitating precise positioning of annular seals and sand packs. Inflatable rubber packers for permanent or temporary installations in bedrock aquifers are currently undergoing site trials. Hydraulic heads are measured with conventional water-level meters or electronic pressure transducers to generate vertical profiles of hydraulic head. Ground water samples are collected using peristaltic pumps, small-diameter bailers, inertial lift pumps, or small-diameter canister samplers.

The water level response to a slug or bailer test in a well completed in
a confined aquifer has been evaluated taking into account well-bore
storage and inertial effects of the water column in the well. The
response range, from overdamped with negligible inertial effects to
damped oscillation, was covered employing numerical inversions of the
Laplace-transform solution. By scaling the time with respect to the
undamped natural period of the well-aquifer system and by using the
damping parameter for a second-order damped, inertial-elastic system, a
set of type curves was constructed that enables water level response
data from a slug or bailer test to be analyzed under conditions where
the inertial parameter is large. Values of transmissivity and effective
static water column length can be determined when an estimate of storage
coefficient is available. The numerical solution and resulting type
curves cover the transition range between the limiting cases of
negligible inertial effects and of damped oscillation that have been
treated by others. Two examples of slug test analysis show that precise
results depend on accurate measurements of water level displacement
(±1% of initial value).

A new analytical model is proposed for the delayed response process
characterizing flow to a well in an unconfined aquifer. The present
approach differs from that of Boulton [1954b, 1963, 1970] and Boulton
and Pontin [1971] in that it is based only on well-defined physical
parameters of the aquifer system. Therefore it provides a possible
physical explanation for the mechanism of delayed water table response
and eliminates the conceptual difficulties encountered with Boulton's
theory of `delayed yield from storage above the water table.' Contrary
to prevailing belief the process of delayed response in a homogeneous
anisotropic phreatic aquifer can be simulated by using constant values
of specific storage and specific yield without recourse to unsaturated
flow theory. The results suggest that, in the absence of significant
infiltration at the ground surface, compressibility may often be a much
more important factor than unsaturated flow above the water table.
Current methods of analyzing field data from unconfined aquifers do not
usually consider compressibility. The present theory shows that such
methods are limited in their application to relatively large values of
time.

In this study the potential of cross-well slug interference tests for high resolution aquifer characterization of hydraulic heterogeneity was assessed. The cross-well slug interference tests were performed at the research site "Stegemuhle", located in the Leine River valley near Gottingen, Germany. The geological composition of the subsurface, consisting mainly of 3.5 m silt and clay overlying 2.5 m sand and gravel, was determined by geophysical well logging and bore core data. To account for lateral changes a refraction seismic survey was conducted. Based on these data an area, characterized by an aquifer thickness of approximately 2 m and an average hydraulic conductivity of 5.0 x 10(-4) m/s (determined by pumping tests), most appropriate for cross-well slug interference tests, was chosen. Altogether 196 cross-well slug interference tests were performed using a tomographic measurement array. The cross-well slug interference tests were evaluated using type curve analysis, which provided detailed information concerning the vertical changes of hydraulic conductivity and specific storage. To assess hydraulic strata connectivity a travel time based tomographic inversion approach was utilized. The potential of the inversion approach to determine lateral changes could be successfully demonstrated by the reconstruction of the pinch out of a high diffusivity layer close to the bottom of the aquifer. The results demonstrate that the combined evaluation of cross-well slug interference tests based on type curve analysis and travel time inversion allows for the development of a detailed model about subsurface hydraulic heterogeneity.

The concept of observation-well response time is introduced in the context of aquifer pump tests. Previous work on hydrostatic time lag and slug tests is considered together with the precise way in which an observation well responds during an aquifer test. Using the concepts of Hvorslev an equation is produced linking observation-well response time, α, and a dimensionless response-time factor β. The Theis equation is then modified by various values of β to derive a set of type curves. The two parameters α and β are related by a simple equation involving aquifer transmissivity, T, and storativity, S. Both α and β can be obtained from an aquifer test whilst α alone can be obtained independently from a slug test. An example is given showing the effect of β upon aquifer test results and the value of α calculated from the aquifer test analysis is corroborated by slug test results. The definition of β is used to show in what circumstances it will be important and how its effect can be reduced to a minimum. The introduction of slug testing of observation wells as standard practice for all aquifer tests is suggested.

A method for testing formations of very low permeability is presented. The method is based on an analytical solution that describes the decay of a head change caused by pressurizing the volume of water stored in a shut-in well. Type curves prepared from this solution are matched with observed data to determine the hydraulic properties of the formation tested. The test is similar to the conventional slug test; however, its much shorter duration makes the testing of extremely tight formations feasible.

Cross-hole pneumatic injection tests have been conducted in 16 vertical and inclined boreholes in unsaturated fractured tuffs at the Apache Leap Research Site (ALRS) near Superior, Arizona. Their purpose was to characterize the bulk pneumatic properties and connectivity of fractures at the site on scales ranging from meters to several tens of meters. We describe the design, conduct, and type curve interpretation of one of these tests. Our cross-hole type curves are modified after Hsieh and Neuman [1985] to consider single-phase airflow and extended to consider the effects of storage and skin in monitoring intervals. Cross-hole type curves of pressure derivatives and recovery are included for improved pneumatic characterization of the site. We analyze recorded pressures in each monitoring interval separately from those in other intervals while treating the fractured rock as a uniform, isotropic porous continuum. Each record yields an equivalent directional air permeability and air-filled porosity for fractures that connect the corresponding monitoring and injection intervals. Both parameters are found to vary considerably from one monitoring interval to another, reflecting the nonuniform nature of pneumatic rock properties at the ALRS. The geometric mean of these equivalent permeabilities is found to be larger by a factor of 50 than that obtained from single-hole pneumatic injection tests on a nominal scale of 1–3 m (single-hole tests yield only limited information about porosities, which therefore cannot be meaningfully compared with cross-hole results). Our results find support in numerical inverse modeling of cross-hole tests at the site by Vesselinov [2000; see also Illman et al., 1998; Vesselinov et al., 2000]. Vesselinov [2000] has further demonstrated [see also Chen et al., 2000] that a similar scale effect is exhibited by fracture porosity at the ALRS and that both scale effects disappear when cross-hole tests at the site are interpreted by means of a numerical inverse model, which resolves heterogeneities down to a scale of 1 m. When considered jointly with these and other studies of the site, our analysis implies that the pneumatic pressure behavior of unsaturated fractured tuffs at the ALRS can be described quite accurately by means of linearized single-phase airflow equations; this behavior can be interpreted by treating the rock as a continuum on scales ranging from meters to tens of meters: the continuum is representative primarily of interconnected fractures; as these fractures are filled primarily with air, their pneumatic permeabilities and porosities are close to the bulk intrinsic properties of fractures at the site: these intrinsic properties vary randomly with location and direction across the ALRS, and they depend strongly on the scale at which they are determined.

Two large-scale cross-hole pumping tests were conducted at depths of
191-226 m and 662-706 m in deep boreholes at the Mizunami Underground
Research Laboratory (MIU) construction site in central Japan. During
these two tests, induced groundwater responses were monitored at many
observation intervals at various depths in different boreholes at the
site. We analyze the two cross-hole pumping tests using transient
hydraulic tomography (THT) based on an efficient sequential successive
linear estimator to compute the hydraulic conductivity (K) and specific
storage (Ss) tomograms, as well as their uncertainties in
three dimensions. The equivalent K and Ss estimates obtained
using asymptotic analysis treating the medium to be homogeneous served
as the mean parameter estimates for the 3-D stochastic inverse modeling
effort. Results show several, distinct, high K and low Ss
zones that are continuous over hundreds of meters, which appear to
delineate fault zones and their connectivity. The THT analysis of the
tests also identified a low K zone which corresponds with a known fault
zone trending NNW and has been found to compartmentalize groundwater
flow at the site. These results corroborate well with observed water
level records, available fault information, and coseismic groundwater
level responses during several large earthquakes. The successful
application of THT to cross-hole pumping tests conducted in fractured
granite at this site suggests that THT is a promising approach to
delineate large-scale K and Ss heterogeneities, fracture
connectivity, and to quantify uncertainty of the estimated fields.

An improved procedure for numerical inversion of Laplace transforms is proposed based on accelerating the convergence of the Fourier series obtained from the inversion integral using the trapezoidal rule. When the full complex series is used, at each time-value the epsilon-algorithm computes a .(trigonometric) Pade approximation which gives better results than existing acceleration methods. The quotient-difference algorithm is used to compute the coefficients of the corresponding continued fraction, which is evaluated at each time-value, greatly improving efficiency. The convergence of the continued fraction can in turn be accelerated, leading to a further improvement in accuracy.

In paper 1 of this two-part series we described a three-dimensional
numerical inverse model for the interpretation of cross-hole pneumatic
tests in unsaturated fractured tuffs at the Apache Leap Research Site
(ALRS) near Superior, Arizona. Our model is designed to analyze these
data in two ways: (1) by considering pressure records from individual
borehole monitoring intervals one at a time, while treating the rock as
being spatially uniform, and (2) by considering pressure records from
multiple tests and borehole monitoring intervals simultaneously, while
treating the rock as being randomly heterogeneous. The first approach
yields a series of equivalent air permeabilities and air- filled
porosities for rock volumes having length scales ranging from meters to
tens of meters, represented nominally by radius vectors extending from
injection to monitoring intervals. The second approach yields a
high-resolution geostatistical estimate of how air permeability and
air-filled porosity, defined on grid blocks having a length scale of 1
m, vary spatially throughout the tested rock volume. It amounts to
three-dimensional pneumatic "tomography" or stochastic imaging of the
rock. Paper 1 described the field data, the model, and the effect of
boreholes on pressure propagation through the rock. This second paper
implements our inverse model on pressure data from five cross-hole tests
at ALRS. We compare our cross-hole test interpretations by means of the
two approaches with earlier interpretations by means of type curves and
with geostatistical interpretations of single-hole test data. The
comparisons show internal consistency between all pneumatic test
interpretations and reveal a very pronounced scale effect in
permeability and porosity at ALRS.

The hydrogeological properties and responses of a productive aquifer in northeastern Switzerland are investigated. For this purpose, 3D crosshole electrical resistivity tomography (ERT) is used to define the main lithological structures within the aquifer (through static inversion) and to monitor the water infiltration from an adjacent river. During precipitation events and subsequent river flooding, the river water resistivity increases. As a consequence, the electrical characteristics of the infiltrating water can be used as a natural tracer to delineate preferential flow paths and flow velocities. The focus is primarily on the experiment installation, data collection strategy, and the structural characterization of the site and a brief overview of the ERT monitoring results. The monitoring system comprises 18 boreholes each equipped with 10 electrodes straddling the entire thickness of the gravel aquifer. A multi-channel resistivity system programmed to cycle through various four-point electrode configurations of the 180 electrodes in a rolling sequence allows for the measurement of approximately 15,500 apparent resistivity values every 7 h on a continuous basis. The 3D static ERT inversion of data acquired under stable hydrological conditions provides a base model for future time-lapse inversion studies and the means to investigate the resolving capability of our acquisition scheme. In particular, it enables definition of the main lithological structures within the aquifer. The final ERT static model delineates a relatively high-resistivity, low-porosity, intermediate-depth layer throughout the investigated aquifer volume that is consistent with results from well logging and seismic and radar tomography models. The next step will be to define and implement an appropriate time-lapse ERT inversion scheme using the river water as a natural tracer. The main challenge will be to separate the superposed time-varying effects of water table height, temperature, and salinity variations associated with the infiltrating water.

The Karhunen-Loéve transform, which optimally extracts coherent information from multichannel input data in a least-squares sense, is used for two specific problems in seismic data processing.The first is the enhancement of stacked seismic sections by a reconstruction procedure which increases the signal-to-noise ratio by removing from the data that information which is incoherent trace-to-trace. The technique is demonstrated on synthetic data examples and works well on real data. The Karhunen-Loéve transform is useful for data compression for the transmission and storage of stacked seismic data.The second problem is the suppression of multiples in CMP or CDP gathers. After moveout correction with the velocity associated with the multiples, the gather is reconstructed using the Karhunen-Loéve procedure, and the information associated with the multiples omitted. Examples of this technique for synthetic and real data are presented.

Slug interference testing may be particularly useful for characterizing hydraulic properties of aquifer sites where disposal of contaminated ground water makes pumping tests undesirable. The design, performance, and analysis of slug interference tests for two field test examples are presented. Results were compared with standard constant-rate pumping tests. The comparison indicates that slug interference tests provide estimates comparable to those obtained from short duration pumping tests for the determination of transmissivity, storativity, and vertical anisotropy.The close agreement in hydraulic property values obtained using the two test methods suggests that slug interference testing, under favorable test conditions (for example, observation well distances ≤ 30 m), can provide representative aquifer characterization results. The quality and extent of test data obtained also indicate the potential use of slug interference testing for three-dimensional hydrologic characterization investigations, when conducted using multilevel monitoring facilities.

Normally, slug test measurements are limited to the well in which the water level is perturbed. Consequently, it is often difficult to obtain reliable estimates of hydraulic properties, particularly if the aquifer is anisotropic or if there is a wellbore skin. In this investigation, we use partially penetrating stress and observation wells to evaluate specific storage, radial hydraulic conductivity and anisotropy of the aquifer, and the hydraulic conductivity of the borehole skin. The study site is located in the W9 subbasin of the Sleepers River Research Watershed, Vermont. At the site, ∼3 m of saturated till are partially penetrated by a stress well located in the center of the unconfined aquifer and six observation wells located above, below, and at the depth of the stress well at radial distances of 1.2 and 2.4 m. The observation wells were shut in with inflatable packers.
The semianalytical solution of Butler (1995) was used to conduct a sensitivity analysis and to interpret slug test results. The sensitivity analysis indicates that the response of the stress well is primarily sensitive to radial hydraulic conductivity, less sensitiive to anisotropy and the conductivity of the borehole skin, and nearly insensitive to specific storage. In contrast, the responses of the observation wells are sensitive to all four parameters. Interpretation of the field data was facilitated by generating type curves in a manner analogous to the method of Cooper et al. (1967). Because the value of radial hydraulic conductivty is obtained from a match point, the number of unknowns is reduced to three. The estimated values of radial hydraulic conductivity and specific storage are comparable to those derived from the methods of Bouwer and Rice (1976) and Cooper et al. (1967). The values and skin conductivity, however, could not have been obtained without the use of observation wells.

Slug tests in fractured rock usually are interpreted with models that assume homogeneous formation properties, even though hydraulic properties of fractures can vary by many orders of magnitude over the length of boreholes. To investigate the impact of heterogeneity on the interpretation of slug tests in fractured rock, slug tests were conducted over large intervals of boreholes in crystalline rock in central New Hampshire, and interpreted using a homogeneous model. The results of the slug tests were then compared with estimates of transmissivity from fluid-injection tests conducted over shorter intervals in the same boreholes. The fluid-injection tests showed transmissivity to vary more than six orders of magnitude over the length of the boreholes; however, the sum of the transmissivities from the fluid-injection tests were within an order of magnitude of the transmissivity estimated from the slug tests. Although the two estimates of transmissivity were within an order of magnitude of each other, the water level responses during the slug tests did not exactly match the responses predicted by the homogeneous model. To investigate the effect of heterogeneity on water level responses during slug tests, a Laplace-transform solution was developed for slug tests conducted in boreholes containing multiple fractures with hydraulic properties that vary over the length of the borehole. A comparison of this solution with the homogeneous model shows no difference between the shape of water level responses in a homogeneous formation and a (layered) heterogeneous formation. Furthermore, the transmissivity estimated using a homogeneous model is within an order of magnitude of the prescribed transmissivity in the heterogeneous model. Thus, differences between responses predicted from a homogeneous model and measured water levels during slug tests can be attributed to phenomena such as nonradial flow in the vicinity of the borehole, and not heterogeneous hydraulic properties over the length of the borehole. The experimental results of this investigation show that even when conditions such as nonradial flow are present in the vicinity of the borehole, interpretations of slug tests using a homogeneous model provided order-of-magnitude estimates of transmissivity in the crystalline rock terrane under consideration.

Slug interference responses within unconfined aquifers are characterized by an initial wave or “hump,” which is followed by a flat transitional plateau region and then by a declining, recessional limb segment. The shape and amplitude of the initial wave are primarily controlled by the elastic characteristics (i.e., S) and degree of anisotropy within the aquifer, while transmissivity is the principal parameter affecting the transmission (i.e., arrival time) of the slug interference response. Wellbore storage and delayed-yield effects tend to attenuate the test response. The transitional and late-time recessional segments are significantly influenced by the aquifer's specific yield. In addition, test well/aquifer relationships, e.g., observation well distance, aquifer thickness, and well depth/aquifer penetration, also strongly affect slug interference characteristics. The sensitivity of the propagated response to test well/aquifer relationships indicates that slug interference tests can be designed to maximize the expected response for aquifer property characterization.

For groundwater transport modeling on a scale of 10–100 m, detailed information about the spatial distribution of hydraulic conductivity is of great importance. At a test site (10×20 m) in the alluvial gravel-and-sand aquifer of the perialpine Thur valley (Switzerland), four different methods were applied on different scales to assess this parameter. A comparison of the results showed that multilevel slug tests give reliable results at the required scale. For its analysis, a plausible value of the anisotropy ratio of hydraulic conductivity (K
v
/K
h
) is needed, which was calculated using a pumping test. The integral results of pumping tests provide an upper boundary of the natural spectrum of hydraulic conductivity at the scale of the test site. Flowmeter logs are recommended if the relative distribution of hydraulic conductivity is of primary importance, while sieve analyses can be used if only a rough estimate of hydraulic conductivity is acceptable.

Virtually every hydrogeologic investigation requires an estimate of hydraulic conductivity (K), the parameter used to characterize
the ease with which water flows in the subsurface. For water-supply investigations, a single estimate of K averaged over a
relatively large volume of an aquifer will usually suffice. However, for water-quality investigations, such an estimate is
often of limited value. A large body of work has demonstrated that spatial variations in K play an important role in controlling
solute movement in saturated flow systems (e.g., Sudicky and Huyakorn, 1991; Zheng and Gorelick, 2003). Numerous studies have shown that information about such variations is required to obtain reliable predictions of contaminant
transport and to design effective remediation systems. Varieties of methods have been used in efforts to acquire this information.
The primary purpose of this chapter is to describe these methods and assess the quality of the information that they can provide.
Later chapters will discuss how geophysics can augment the information obtained with these approaches.