Hydraulic Tomography: Continuity and Discontinuity of High‐K and Low‐K Zones

Hydraulic tomography is an emerging field and modeling method that provides a continuous hydraulic conductivity (K) distribution for an investigated region. Characterization approaches that rely on interpolation between one‐dimensional (1D) profiles have limited ability to accurately identify high‐K channels, juxtapositions of lenses with high K contrast, and breaches in layers or channels between such profiles. However, locating these features is especially important for groundwater flow and transport modeling, and for design and operation of in situ remediation in complex hydrogeologic environments. We use transient hydraulic tomography to estimate 3D K in a volume of 15‐m diameter by 20‐m saturated thickness in a highly heterogeneous unconfined alluvial (clay to sand‐and‐gravel) aquifer with a K range of approximately seven orders of magnitude at an active industrial site in Assemini, Sardinia, Italy. A modified Levenberg‐Marquardt algorithm was used for geostatistical inversion to deal with the nonlinear nature of the highly heterogeneous system. The imaging results are validated with pumping tests not used in the tomographic inversion. These tests were conducted from three of five clusters of continuous multichannel tubing (CMTs) installed for observation in the tomographic testing. Locations of high‐K continuity and discontinuity, juxtaposition of very high‐K and very low‐K lenses, and low‐K “plugs” are evident in regions of the investigated volume where they likely would not have been identified with interpolation from 1D profiles at the positions of the pumping well and five CMT clusters. Quality assessment methods identified a suspect high‐K feature between the tested volume and a lateral boundary of the model.     

Hydraulic Tomography: 3D Hydraulic Conductivity,Fracture Network,and Connectivity in Mudstone

We present the first demonstration of hydraulic tomography (HT) to estimate the three-dimensional (3D) hydraulic conductivity (K) distribution of a fractured aquifer at high-resolution field scale (HRFS), including the fracture network and connectivity through it. We invert drawdown data collected from packer-isolated borehole intervals during 42 pumping tests in a wellfield at the former Naval Air Warfare Center, West Trenton, New Jersey, in the Newark Basin. Five additional tests were reserved for a quality check of HT results. We used an equivalent porous medium forward model and geostatistical inversion to estimate 3D K at high resolution (K blocks <1 m³), using no strict assumptions about K variability or fracture statistics. The resulting 3D K estimate ranges from approximately 0.1 (highest-K fractures) to approximately 10⁻¹³ m/s (unfractured mudstone). Important estimated features include: (1) a highly fractured zone (HFZ) consisting of a sequence of high-K bedding-plane fractures; (2) a low-K zone that disrupts the HFZ; (3) several secondary fractures of limited extent; and (4) regions of very low-K rock matrix. The 3D K estimate explains complex drawdown behavior observed in the field. Drawdown tracing and particle tracking simulations reveal a 3D fracture network within the estimated K distribution, and connectivity routes through the network. Model fit is best in the shallower part of the wellfield, with high density of observations and tests. The capabilities of HT demonstrated for 3D fractured aquifer characterization at HRFS may support improved in situ remediation for contaminant source zones, and applications in mining, repository assessment, or geotechnical engineering.     

A Type-Curve Method for the Analysis of Pumping Tests with Piecewise-Linear Pumping Rates

Aquifer hydraulic parameters are commonly inferred from constant-rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable-rate pumping tests in confined aquifers. In particular, we adopt a piecewise-linear fitting of variable pumping rates and propose a new type-curve method for estimating the hydraulic conductivity (K ) and specific storage (S_s ) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log-log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and S_s values estimated by the new type-curve method are found to be quite close to PEST-based estimates. Parameter estimation results demonstrate the difference in K and S_s values between observation wells. The difference could be attributed to the spatial heterogeneity in K and S_s . A future research topic may focus on the characterization of K and S_s heterogeneity with the currently available drawdown data from variable-rate pumping tests.     

Field Study of Subsurface Heterogeneity with Steady‐State Hydraulic Tomography

Remediation of subsurface contamination requires an understanding of the contaminant (history, source location, plume extent and concentration, etc.), and, knowledge of the spatial distribution of hydraulic conductivity (K) that governs groundwater flow and solute transport. Many methods exist for characterizing K heterogeneity, but most if not all methods require the collection of a large number of small‐scale data and its interpolation. In this study, we conduct a hydraulic tomography survey at a highly heterogeneous glaciofluvial deposit at the North Campus Research Site (NCRS) located at the University of Waterloo, Waterloo, Ontario, Canada to sequentially interpret four pumping tests using the steady‐state form of the Sequential Successive Linear Estimator (SSLE) ( Yeh and Liu 2000 ). The resulting three‐dimensional (3D) K distribution (or K‐tomogram) is compared against: ( 1 ) K distributions obtained through the inverse modeling of individual pumping tests using SSLE, and ( 2 ) effective hydraulic conductivity (K_eff) estimates obtained by automatically calibrating a groundwater flow model while treating the medium to be homogeneous. Such a K_eff is often used for designing remediation operations, and thus is used as the basis for comparison with the K‐tomogram. Our results clearly show that hydraulic tomography is superior to the inversions of single pumping tests or K_eff estimates. This is particularly significant for contaminated sites where an accurate representation of the flow field is critical for simulating contaminant transport and injection of chemical and biological agents used for active remediation of contaminant source zones and plumes.     

Comparison of Hydraulic Tomography with Traditional Methods at a Highly Heterogeneous Site

Over the past several decades, different groundwater modeling approaches of various complexities and data use have been developed. A recently developed approach for mapping hydraulic conductivity (K) and specific storage (S_s) heterogeneity is hydraulic tomography, the performance of which has not been compared to other more “traditional” methods that have been utilized over the past several decades. In this study, we compare seven methods of modeling heterogeneity which are (1) kriging, (2) effective parameter models, (3) transition probability/Markov Chain geostatistics models, (4) geological models, (5) stochastic inverse models conditioned to local K data, (6) hydraulic tomography, and (7) hydraulic tomography conditioned to local K data using data collected in five boreholes at a field site on the University of Waterloo (UW) campus, in Waterloo, Ontario, Canada. The performance of each heterogeneity model is first assessed during model calibration. In particular, the correspondence between simulated and observed drawdowns is assessed using the mean absolute error norm, (L₁), mean square error norm (L₂), and correlation coefficient (R) as well as through scatterplots. We also assess the various models on their ability to predict drawdown data not used in the calibration effort from nine pumping tests. Results reveal that hydraulic tomography is best able to reproduce these tests in terms of the smallest discrepancy and highest correlation between simulated and observed drawdowns. However, conditioning of hydraulic tomography results with permeameter K data caused a slight deterioration in accuracy of drawdown predictions which suggests that data integration may need to be conducted carefully.     

Hydraulic Tomography Offers Improved Imaging of Heterogeneity in Fractured Rocks

Fractured rocks have presented formidable challenges for accurately predicting groundwater flow and contaminant transport. This is mainly due to our difficulty in mapping the fracture‐rock matrix system, their hydraulic properties and connectivity at resolutions that are meaningful for groundwater modeling. Over the last several decades, considerable effort has gone into creating maps of subsurface heterogeneity in hydraulic conductivity (K) and specific storage (S_s) of fractured rocks. Developed methods include kriging, stochastic simulation, stochastic inverse modeling, and hydraulic tomography. In this article, I review the evolution of various heterogeneity mapping approaches and contend that hydraulic tomography, a recently developed aquifer characterization technique for unconsolidated deposits, is also a promising approach in yielding robust maps (or tomograms) of K and S_s heterogeneity for fractured rocks. While hydraulic tomography has recently been shown to be a robust technique, the resolution of the K and S_s tomograms mainly depends on the density of pumping and monitoring locations and the quality of data. The resolution will be improved through the development of new devices for higher density monitoring of pressure responses at discrete intervals in boreholes and potentially through the integration of other data from single‐hole tests, borehole flowmeter profiling, and tracer tests. Other data from temperature and geophysical surveys as well as geological investigations may improve the accuracy of the maps, but more research is needed. Technological advances will undoubtedly lead to more accurate maps. However, more effort should go into evaluating these maps so that one can gain more confidence in their reliability.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

A Leaky Aquifer below Champlain Sea Clay: Closed‐Form Solutions for Natural Seepage

Closed‐form solutions are proposed for natural seepage in semiconfined (leaky) aquifers such as those existing below the massive Champlain Sea clay layers in the Saint‐Lawrence River Valley. The solutions are for an ideal horizontal leaky aquifer below an ideal aquitard that may have either a constant thickness and a constant hydraulic head at its surface, or a variable thickness and a variable hydraulic head at its surface. A few simplifying assumptions were needed to obtain the closed‐form solutions. These have been verified using a finite element method, which did not make any of the assumptions but gave an excellent agreement for hydraulic heads and groundwater velocities. For example, the difference between the two solutions was smaller than 1 mm for variations in the 5 to 8 m range for the hydraulic head in the semiconfined aquifer. Note that fitting the hydraulic head data of monitoring wells to the theoretical solutions gives only the ratio of the aquifer and aquitard hydraulic conductivities, a clear case of multiple solutions for an inverse problem. Consequently, field permeability tests in the aquitard and the aquifer, and pumping tests in the aquifer, are still needed to determine the hydraulic conductivity values.     

The usefulness of outcrop analogue air permeameter measurements for analyzing aquifer heterogeneity: quantifying outcrop hydraulic conductivity and its spatial variability

Saturated hydraulic conductivity (K) is one of the most important parameters determining groundwater flow and contaminant transport in both unsaturated and saturated porous media. Although several well‐established laboratory methods exist for determining K, in situ measurements of this parameter remain very complex and scale dependent. Often, the limited accessibility of subsurface sediments for sampling means an additional impediment to our ability to quantify subsurface K heterogeneity. One potential solution is the use of outcrops as analogues for subsurface sediments. This paper investigates the use of air permeameter measurements on outcrops of unconsolidated sediments to quantify K and its spatial heterogeneity on a broad range of sediment types. The Neogene aquifer in northern Belgium is used as a case study for this purpose. To characterize the variability in K, 511 small‐scale air permeability measurements were performed on outcrop sediments representative over five of the aquifer's lithostratigraphic units. From these measurements, outcrop‐scale equivalent K tensors were calculated using numerical upscaling techniques. Validation of the air permeameter‐based K values by comparison with laboratory constant head K measurements reveals a correlation of 0.93. Overall, the results indicate that hand‐held air permeameters are very efficient and accurate tools to characterize saturated K, as well as its small‐scale variability and anisotropy on a broad range of unconsolidated sediments. The studied outcrops further provided a qualitative understanding of aquifer hydrostratigraphy and quantitative estimates about K variability at the centimetre‐scale to metre‐scale. Copyright © 2013 John Wiley & Sons, Ltd.     

Geologic heterogeneity and a comparison of two geostatistical models: Sequential Gaussian and transition probability-based geostatistical simulation

A covariance-based model-fitting approach is often considered valid to represent field spatial variability of hydraulic properties. This study examines the representation of geologic heterogeneity in two types of geostatistical models under the same mean and spatial covariance structure, and subsequently its effect on the hydraulic response to a pumping test based on 3D high-resolution numerical simulation and field data. Two geostatistical simulation methods, sequential Gaussian simulation (SGS) and transition probability indicator simulation (TPROGS) were applied to create conditional realizations of alluvial fan aquifer systems in the Lawrence Livermore National Laboratory (LLNL) area. The simulated K fields were then used in a numerical groundwater flow model to simulate a pumping test performed at the LLNL site. Spatial connectivity measures of high-K materials (channel facies) captured connectivity characteristics of each geostatistical model and revealed that the TPROGS model created an aquifer (channel) network having greater lateral connectivity. SGS realizations neglected important geologic structures associated with channel and overbank (levee) facies, even though the covariance model used to create these realizations provided excellent fits to sample covariances computed from exhaustive samplings of TPROGS realizations. Observed drawdown response in monitoring wells during a pumping test and its numerical simulation shows that in an aquifer system with strongly connected network of high-K materials, the Gaussian approach could not reproduce a similar behavior in simulated drawdown response found in TPROGS case. Overall, the simulated drawdown responses demonstrate significant disagreement between TPROGS and SGS realizations. This study showed that important geologic characteristics may not be captured by a spatial covariance model, even if that model is exhaustively determined and closely fits the exponential function.     

Prediction of Remediation of a Heterogeneous Aquifer: A Case Study

Contaminant plumes whose characteristic length is smaller than the horizontal integral scale of the hydraulic conductivity, K, are abundant in shallow, phreatic aquifers. In such cases, the aquifer can be regarded as layered, with K being only a function of the vertical coordinate. The heterogeneity of K has a critical role upon the efficiency of remediation of such sites, for example, by Pump and Treat schemes. The expected efficiency is a random variable, with uncertainty. Quantifying this uncertainty can be of great importance to decision making. In this study, we focus on a case study in the coastal aquifer of Israel and compare two different approaches for constructing realizations of K: continuous and indicator. We observe a significant difference between the constructed realizations, which results in a considerable difference in the predicted remediation efficiency and its uncertainty. Furthermore, we study the effect of conditioning the realizations by a rather limited number of K data points. We find that the conditioning results in a major reduction of the uncertainty. In addition, we compare the results of the transport model to a simplified semi‐analytical solution that is based on assuming radial flow. We find a good agreement with the three‐dimensional numerical model. This result illustrates that the simplified solution can be used for prediction of the remediation efficiency when the flow at the plume vicinity can be regarded as radial.     

Evaluation of Hydraulic Conductivity Estimates from Various Approaches with Groundwater Flow Models

Significant efforts have been expended for improved characterization of hydraulic conductivity (K) and specific storage (S_s) to better understand groundwater flow and contaminant transport processes. Conventional methods including grain size analyses (GSA), permeameter, slug, and pumping tests have been utilized extensively, while Direct Push-based Hydraulic Profiling Tool (HPT) surveys have been developed to obtain high-resolution K estimates. Moreover, inverse modeling approaches based on geology-based zonations, and highly parameterized Hydraulic Tomography (HT) have also been advanced to map spatial variations of K and S_s between and beyond boreholes. While different methods are available, it is unclear which one yields K estimates that are most useful for high resolution predictions of groundwater flow. Therefore, the main objective of this study is to evaluate various K estimates at a highly heterogeneous field site obtained with three categories of characterization techniques including: (1) conventional methods (GSA, permeameter, and slug tests); (2) HPT surveys; and (3) inverse modeling based on geology-based zonations and highly parameterized approaches. The performance of each approach is first qualitatively analyzed by comparing K estimates to site geology. Then, steady-state and transient groundwater flow models are employed to quantitatively assess various K estimates by simulating pumping tests not used for parameter estimation. Results reveal that inverse modeling approaches yield the best drawdown predictions under both steady and transient conditions. In contrast, conventional methods and HPT surveys yield biased predictions. Based on our research, it appears that inverse modeling and data fusion are necessary steps in predicting accurate groundwater flow behavior.     

Depth‐dependent hydraulic conductivity distribution patterns of a streambed

Characterization of streambed hydraulic conductivity from the channel surface to a great depth below the channel surface can provide needed information for the determination of stream‐aquifer hydrologic connectedness, and it is also important to river restoration. However, knowledge on the streambed hydraulic conductivity for sediments 1 m below the channel surface is scarce. This study describes a method that was used to determine the distribution patterns of streambed hydraulic conductivity for sediments from channel surface to a depth of 15 m below. The method includes Geoprobe's direct‐push techniques and Permeameter tests. Direct‐push techniques were used to generate the electrical conductivity (EC) logs and to collect sequences of continuous sediment cores from river channels, as well as from the alluvial aquifer connected to the river. Permeameter tests on these sediment cores give the profiles of vertical hydraulic conductivity (K_v) of the channel sediments and the aquifer materials. This method was applied to produce K_v profiles for a streambed and an alluvial aquifer in the Platte River Valley of Nebraska, USA. Comparison and statistical analysis of the K_v profiles from the river channel and from the proximate alluvial aquifer indicates a special pattern of K_v in the channel sediments. This depth‐dependent pattern of K_v distribution for the channel sediments is considered to be produced by hyporheic processes. This K_v‐distribution pattern implied that the effect of hyporheic processes on streambed hydraulic conductivity can reach the sediments about 9 m below the channel surface. Copyright © 2010 John Wiley & Sons, Ltd.     

Accounting for Aquifer Heterogeneity from Geological Data to Management Tools

A nested workflow of multiple‐point geostatistics (MPG) and sequential Gaussian simulation (SGS) was tested on a study area of 6 km² located about 20 km northwest of Quebec City, Canada. In order to assess its geological and hydrogeological parameter heterogeneity and to provide tools to evaluate uncertainties in aquifer management, direct and indirect field measurements are used as inputs in the geostatistical simulations to reproduce large and small‐scale heterogeneities. To do so, the lithological information is first associated to equivalent hydrogeological facies (hydrofacies) according to hydraulic properties measured at several wells. Then, heterogeneous hydrofacies (HF) realizations are generated using a prior geological model as training image (TI) with the MPG algorithm. The hydraulic conductivity (K) heterogeneity modeling within each HF is finally computed using SGS algorithm. Different K models are integrated in a finite‐element hydrogeological model to calculate multiple transport simulations. Different scenarios exhibit variations in mass transport path and dispersion associated with the large‐ and small‐scale heterogeneity respectively. Three‐dimensional maps showing the probability of overpassing different thresholds are presented as examples of management tools.     

Redundant and Nonredundant Information for Model Calibration or Hydraulic Tomography

Drawdown data from independent pumping tests have widely been used to validate the estimated hydraulic parameters from inverse modeling or hydraulic tomography (HT). Yet, the independent pumping test has not been clearly defined. Therefore, the goal of this paper is to define this independent pumping test concept, based on the redundant or nonredundant information about aquifer heterogeneity embedded in the observed heads during cross-hole pumping tests. The definition of complete, moderate redundancy and high nonredundancy of information are stipulated using cross-correlation analysis of the relationship between the head and heterogeneity. Afterward, data from numerical experiments and field sequential pumping test campaigns reinforce the concept and the definition.     

Bootstrap Calibration and Uncertainty Estimation of Downhole NMR Hydraulic Conductivity Estimates in an Unconsolidated Aquifer

Characterization of hydraulic conductivity (K) in aquifers is critical for evaluation, management, and remediation of groundwater resources. While estimates of K have been traditionally obtained using hydraulic tests over discrete intervals in wells, geophysical measurements are emerging as an alternative way to estimate this parameter. Nuclear magnetic resonance (NMR) logging, a technology once largely applied to characterization of deep consolidated rock petroleum reservoirs, is beginning to see use in near‐surface unconsolidated aquifers. Using a well‐known rock physics relationship—the Schlumberger Doll Research (SDR) equation—K and porosity can be estimated from NMR water content and relaxation time. Calibration of SDR parameters is necessary for this transformation because NMR relaxation properties are, in part, a function of magnetic mineralization and pore space geometry, which are locally variable quantities. Here, we present a statistically based method for calibrating SDR parameters that establishes a range for the estimated parameters and simultaneously estimates the uncertainty of the resulting K values. We used co‐located logging NMR and direct K measurements in an unconsolidated fluvial aquifer in Lawrence, Kansas, USA to demonstrate that K can be estimated using logging NMR to a similar level of uncertainty as with traditional direct hydraulic measurements in unconsolidated sediments under field conditions. Results of this study provide a benchmark for future calibrations of NMR to obtain K in unconsolidated sediments and suggest a method for evaluating uncertainty in both K and SDR parameter values.     

Constraints on hydraulic parameters and implications for groundwater flux across the upland–estuary interface

Analyses of independent laboratory- and field-scale measurements from two sites on Sapelo Island, Georgia reveal heterogeneity in hydraulic parameters across the upland–estuary interface. Regardless of the method used (short-duration pumping tests, amplitude attenuation of tidal pumping data, sediment grain size distributions, and falling head permeameter tests), we obtain hydraulic conductivity of 10⁻⁴ m s⁻¹ for the fine-grained, well-sorted, clean sands that make up the upland areas. Proximal to the upland–estuary boundary, the tidal pumping analyses and permeameter tests suggest that hydraulic conductivities decrease by more than two orders of magnitude, a result consistent with the presence of a clogging layer. Such a clogging layer may arise due to a variety of physical, chemical, or biological processes. The extent and orientation of the layers of reduced hydraulic conductivity near the upland–estuary boundary influence the nature of the aquifer's response to tidal forcing. Where the lower conductivity layer forms a relatively flat creek bank, tidal pumping produces a primarily mechanical response in the adjacent aquifer. Where the creek bank is nearly vertical, there is a more direct hydraulic connection between the tidal creek and the adjacent aquifer. The clogging layer likely contributes to the development of complicated flow pathways across the upland–estuary boundary. Effective flow paths calculated from tidal pumping data terminate within the marsh, beyond the boundary of the upland aquifer, suggesting a diffuse regime of groundwater discharge in the marsh. We postulate that, in many settings, submarsh flow may be as important as seepage faces for groundwater discharge into the marsh–estuary complex.     

Boundary depletion rate and drawdown in leaky wedge‐shaped aquifers

This study presents analytical solutions of the three‐dimensional groundwater flow to a well in leaky confined and leaky water table wedge‐shaped aquifers. Leaky wedge‐shaped aquifers with and without storage in the aquitard are considered, and both transient and steady‐state drawdown solutions are derived. Unlike the previous solutions of the wedge‐shaped aquifers, the leakages from aquitard are considered in these solutions and unlike similar previous work for leaky aquifers, leakage from aquitards and from the water table are treated as the lower and upper boundary conditions. A special form of finite Fourier transforms is used to transform the z‐coordinate in deriving the solutions. The leakage induced by a partially penetrating pumping well in a wedge‐shaped aquifer depends on aquitard hydraulic parameters, the wedge‐shaped aquifer parameters, as well as the pumping well parameters. We calculate lateral boundary dimensionless flux at a representative line and investigate its sensitivity to the aquitard hydraulic parameters. We also investigate the effects of wedge angle, partial penetration, screen location and piezometer location on the steady‐state dimensionless drawdown for different leakage parameters. Results of our study are presented in the form of dimensionless flux‐dimensionless time and dimensionless drawdown‐leakage parameter type curves. The results are useful for evaluating the relative role of lateral wedge boundaries and leakage source on flow in wedge‐shaped aquifers. This is very useful for water management problems and for assessing groundwater pollution. The presented analytical solutions can also be used in parameter identification and in calculating stream depletion rate and volume. Copyright © 2011 John Wiley & Sons, Ltd.     

Two‐dimensional flow response to tidal fluctuation in a heterogeneous aquifer‐aquitard system

In alluvial coastal aquifers, finer sediments are preferentially deposited along the downstream direction, so the hydraulic conductivity is generally heterogeneous and changes with distance from the coastline. To investigate the influence of aquifer heterogeneity on seawater‐groundwater interaction, a new two‐dimensional model characterising groundwater flow in an aquifer‐aquitard system was developed assuming that the hydraulic conductivity of the aquifer linearly increases with the distance from the coastline along the inland direction. A closed‐form analytical solution was derived using the separation‐of‐variables method. Comparing the new solution with the numerical solution by comsol Multiphysics (Sweden) based on the finite‐element method, one can see that the new solution agreed with the numerical solution very well except at the early time. We found that both aquitard leakance and the heterogeneity factor (b) could result in the propagation bias. The propagation bias represents the inconsistency between the theoretical calculation and the observed strong attenuation and small time lag between the head and tide fluctuations. The attenuation decreased with perpendicular distance from the coastline (x‐axis), whereas the time lag increased with distance along the x‐axis. The relationship between the time lag and the distance along the x‐axis seemed to be linear when b was 0.001 m^?1, whereas it obeyed a power function when b was greater than 0.01 m^?1. Copyright © 2014 John Wiley & Sons, Ltd.     

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

Pumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.