Improved Parameter Resolution with Markov Chain Monte Carlo Simulation of Different Aquifer Tests

Hydraulic testing for aquifer characterization at contaminated sites often includes tests of short duration and of different types, such as slug tests and pumping tests, conducted at different phases of investigation. Tests conducted on a well cluster installed in a single aquifer can be combined in aggregate inverse analysis using an analytical model for groundwater flow near a test well. A genetic algorithm performs parallel search of the parameter space and provides starting parameter values for a Markov chain Monte Carlo simulation to estimate the parameter distribution. This sequence of inverse methods avoids guessing of the initial parameter vector and the often encountered difficult convergence of gradient-based methods and estimates the parameter covariance matrix from a distribution rather than from a single point in the parameter space. Combination of different tests improves the resolution of the estimated aquifer properties and allows an assessment of the uniformity of the aquifer. Estimated parameter correlations and standard deviations are used as relative metrics to distinguish well resolved and poorly resolved parameters. The methodology is demonstrated on example field tests in unconfined and leaky aquifers.     

Aquifer Characterization and Uncertainty in Multi-Frequency Oscillatory Flow Tests: Approach and Insights

Characterizing aquifer properties and their associated uncertainty remains a fundamental challenge in hydrogeology. Recent studies demonstrate the use of oscillatory flow interference testing to characterize effective aquifer flow properties. These characterization efforts relate the relative amplitude and phase of an observation signal with a single frequency component to aquifer diffusivity and transmissivity. Here, we present a generalized workflow that relates extracted Fourier coefficients for observation signals with single and multiple frequency components to aquifer flow properties and their associated uncertainty. Through synthetic analytical modeling we show that multi-frequency oscillatory flow interference testing adds information that improves inversion performance and decreases parameter uncertainty. We show increased observation signal length, sampling frequency, and pressure sensor accuracy all produce decreased parameter uncertainty. This work represents the first attempt we are aware of to quantify effective aquifer parameters and their associated uncertainty using multi-frequency oscillatory flow interference testing.     

Understanding the Geometry of Connected Fracture Flow with Multiperiod Oscillatory Hydraulic Tests

An understanding of the spatial and hydraulic properties of fast preferential flow pathways in the subsurface is necessary in applications ranging from contaminant fate and transport modeling to design of energy extraction systems. One method for the characterization of fracture properties over interwellbore scales is Multiperiod Oscillatory Hydraulic (MOH) testing, in which the aquifer response to oscillatory pressure stimulations is observed. MOH tests were conducted on isolated intervals of wells in siliciclastic and carbonate aquifers in southern Wisconsin. The goal was to characterize the spatial properties of discrete fractures over interwellbore scales. MOH tests were conducted on two discrete fractured intervals intersecting two boreholes at one field site, and a nest of three piezometers at another field site. Fracture diffusivity estimates were obtained using analytical solutions that relate diffusivity to observed phase lag and amplitude decay. In addition, MOH tests were used to investigate the spatial extent of flow using different conceptual models of fracture geometry. Results indicated that fracture geometry at both field sites can be approximated by permeable two‐dimensional fracture planes, oriented near‐horizontally at one site, and near‐vertically at the other. The technique used on MOH field data to characterize fracture geometry shows promise in revealing fracture network characteristics important to groundwater flow and transport.     

Identification of Pumping Influences in Long‐Term Water Level Fluctuations

Identification of the pumping influences at monitoring wells caused by spatially and temporally variable water supply pumping can be a challenging, yet an important hydrogeological task. The information that can be obtained can be critical for conceptualization of the hydrogeological conditions and indications of the zone of influence of the individual pumping wells. However, the pumping influences are often intermittent and small in magnitude with variable production rates from multiple pumping wells. While these difficulties may support an inclination to abandon the existing dataset and conduct a dedicated cross‐hole pumping test, that option can be challenging and expensive to coordinate and execute. This paper presents a method that utilizes a simple analytical modeling approach for analysis of a long‐term water level record utilizing an inverse modeling approach. The methodology allows the identification of pumping wells influencing the water level fluctuations. Thus, the analysis provides an efficient and cost‐effective alternative to designed and coordinated cross‐hole pumping tests. We apply this method on a dataset from the Los Alamos National Laboratory site. Our analysis also provides (1) an evaluation of the information content of the transient water level data; (2) indications of potential structures of the aquifer heterogeneity inhibiting or promoting pressure propagation; and (3) guidance for the development of more complicated models requiring detailed specification of the aquifer heterogeneity.     

Analytical methods for transient flow to a well in a confined-unconfined aquifer

Concurrent existence of confined and unconfined zones of an aquifer can arise owing to ground water withdrawal by pumping. Using Girinskii's potential function, Chen (1974, 1983) developed an approximate analytical solution to analyze transient ground water flow to a pumping well in an aquifer that changes from an initially confined system to a system with both unconfined and confined regimes. This article presents the details of the Chen model and then compares it with the analytical model developed by Moench and Prickett (1972) for the same problem. Hypothetical pumping test examples in which the aquifer undergoes conversion from confined to water table conditions are solved by the two analytical models and also a numerical model based on MODFLOW. Comparison of the results suggests that the solutions of the Chen model give better results than the Moench and Prickett model except when the radial distance is very large or aquifer thickness is large compared with drawdown.     

Combining pump-and-treat and physical barriers for contaminant plume control

A detailed analysis is presented of the hydraulic efficiency of plume management alternatives that combine a conventional pump-and-treat system with vertical, physical hydraulic barriers such as slurry walls or sheet piles. Various design settings are examined for their potential to reduce the pumping rate needed to obtain a complete capture of a given contaminated area. Using established modeling techniques for flow and transport, those barrier configurations (specified by location, shape, and length) that yield a maximum reduction of the pumping rate are identified assuming homogeneous aquifer conditions. Selected configurations are further analyzed concerning their hydraulic performance under heterogeneous aquifer conditions by means of a stochastic approach (Monte Carlo simulations) with aquifer transmissivity as a random space function. The results show that physical barriers are an appropriate means to decrease expected (mean) pumping rates, as well as the variance of the corresponding pumping rate distribution at any given degree of heterogeneity. The methodology presented can be transferred easily to other aquifer scenarios, provided some basic premises are fulfilled, and may serve as a basis for reducing the pumping rate in existing pump-and-treat systems.     

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.     

Analytical model for computing residence times near a pumping well

An analytical solution for calculating the residence time of fluid flowing toward a pumping well in an unconfined aquifer has been developed. The analytical solution was derived based on a radial, steady-state, Dupuit-Forchheimer flow model. The resulting integral expression involved computing the imaginary error function, for which a simple series expansion is proposed. The validity of the analytical expression is demonstrated by testing its results against numerical results for an example problem. The analytical solution compared favorably with the numerical approximation.     

Estimating aquifer properties using groundwater hydrograph modelling

Estimation of aquifer hydraulic properties is essential for predicting the response of an aquifer to extractions and hence estimating the availability of the groundwater resources. Aquifer tests are commonly used for the estimation of aquifer properties; however, they can be expensive and often only characterize the short‐term response of the aquifer. This paper presents a time series modelling approach to estimating aquifer hydraulic properties. It is applied to 42 bores monitoring an unconfined aquifer within an irrigation region of south‐eastern Australia, and the resulting probabilistic estimate of hydraulic properties are evaluated against pumping test estimates. It is demonstrated that the time series modelling can provide a reliable estimate of the hydraulic properties that are typical of a very long‐term pumping test. Furthermore, the application of the time series modelling to 42 bores provided novel insights into the aquifer heterogeneity. We encourage others to further test the approach and the source code is available from: http://www.mathworks.com/matlabcentral/fileexchange/48546‐peterson‐tim‐j‐groundwater‐statistics‐toolbox Copyright © 2015 John Wiley & Sons, Ltd.     

Generalized Radial Flow in Synthetic Flow Systems

Traditional analysis methods used to determine hydraulic properties from pumping tests work well in many porous media aquifers, but they often do not work in heterogeneous and fractured‐rock aquifers, producing non‐plausible and erroneous results. The generalized radial flow model developed by Barker (1988) can reveal information about heterogeneity characteristics and aquifer geometry from pumping test data by way of a flow dimension parameter. The physical meaning of non‐integer flow dimensions has long been a subject of debate and research. We focus on understanding and interpreting non‐radial flow through high permeability conduits within fractured aquifers. We develop and simulate flow within idealized non‐radial flow conduits and expand on this concept by simulating pumping in non‐fractal random fields with specific properties that mimic persistent sub‐radial flow responses. Our results demonstrate that non‐integer flow dimensions can arise from non‐fractal geometries within aquifers. We expand on these geometric concepts and successfully simulate pumping in random fields that mimic well‐test responses seen in the Culebra Dolomite above the Waste Isolation Pilot Plant.     

Application of an Analytical Solution as a Screening Tool for Sea Water Intrusion

Sea water intrusion into aquifers is problematic in many coastal areas. The physics and chemistry of this issue are complex, and sea water intrusion remains challenging to quantify. Simple assessment tools like analytical models offer advantages of rapid application, but their applicability to field situations is unclear. This study examines the reliability of a popular sharp‐interface analytical approach for estimating the extent of sea water in a homogeneous coastal aquifer subjected to pumping and regional flow effects and under steady‐state conditions. The analytical model is tested against observations from Canada, the United States, and Australia to assess its utility as an initial approximation of sea water extent for the purposes of rapid groundwater management decision making. The occurrence of sea water intrusion resulting in increased salinity at pumping wells was correctly predicted in approximately 60% of cases. Application of a correction to account for dispersion did not markedly improve the results. Failure of the analytical model to provide correct predictions can be attributed to mismatches between its simplifying assumptions and more complex field settings. The best results occurred where the toe of the salt water wedge is expected to be the closest to the coast under predevelopment conditions. Predictions were the poorest for aquifers where the salt water wedge was expected to extend further inland under predevelopment conditions and was therefore more dispersive prior to pumping. Sharp‐interface solutions remain useful tools to screen for the vulnerability of coastal aquifers to sea water intrusion, although the significant sources of uncertainty identified in this study require careful consideration to avoid misinterpreting sharp‐interface results.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

Discontinuous Steady‐State Analytical Solutions of the Boussinesq Equation and Their Numerical Representation by Modflow

Known analytical solutions of groundwater flow equations are routinely used for verification of computer codes. However, these analytical solutions (e.g., the Dupuit solution for the steady‐state unconfined unidirectional flow in a uniform aquifer with a flat bottom) represent smooth and continuous water table configurations, simulating which does not pose any significant problems for the numerical groundwater flow models, like MODFLOW. One of the most challenging numerical cases for MODFLOW arises from drying‐rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. Numerical solutions of groundwater flow equations cannot be rigorously verified for such cases due to the lack of corresponding exact analytical solutions. Analytical solutions of the steady‐state Boussinesq equation, associated with the discontinuous water table configurations over a stairway impervious base, are presented in this article. Conditions resulting in such configurations are analyzed and discussed. These solutions appear to be well suited for testing and verification of computer codes. Numerical solutions, obtained by the latest versions of MODFLOW (MODFLOW‐2005 and MODFLOW‐NWT), are compared with the presented discontinuous analytical solutions. It is shown that standard MODFLOW‐2005 code (as well as MODFLOW‐2000 and older versions) has significant convergence problems simulating such cases. The problems manifest themselves either in a total convergence failure or erroneous results. Alternatively, MODFLOW‐NWT, providing a good match to the presented discontinuous analytical solutions, appears to be a more reliable and appropriate code for simulating abrupt changes in water table elevations.     

Hydrogeology of the Brunswick (Passaic) Formation and Implications for Ground Water Monitoring Practice

Fractured shales of the Brunswick Formation provide a major aquifer in the most industrialized region of New Jersey. Numerous cases of ground water contamination have been documented in this formation. However, effectiveness of monitoring and remediation efforts is often hampered by the use of inappropriate concepts regarding ground water flow controls in this complex aquifer system. One such concept presumes that near-vertical fractures parallel to the strike of beds provide principal passages for the flow and produce an anisotropic response to pumping stress. Field evidence presented in this paper confirms that the Brunswick Formation hosts a gently dipping, multiunit, leaky aquifer system that consists of thin water-bearing units and thick intervening aquitards. The water-bearing units are associated with major bedding partings and/or intensely fractured seams. Layered heterogeneity of such a dipping multiunit aquifer system produces an anisotropic flow pattern with preferential flow along the strike of beds. Within the weathered zone, the permeability of the water-bearing units can be greatly reduced. The commonly used hydrogeologic model of the Brunswick as a one-aquifer system, sometimes with vaguely defined "shallow" and "deep" zones, often leads to the development of inadvertent cross-flows within monitoring wells. If undetected, cross-flows may promote contaminant spread into deeper units and impair the quality of hydrogeologic data. Hydrogeologic characterization of the Brunswick shales at any given site should be aimed primarily at identification of the major water-bearing and aquitard units. Recommended techniques for this characterization include fluid logging and other in-well tests.     

Analysis of the water content in an unconfined aquifer with a partially penetrated pumping well

Most methods developed to represent water flow phenomena in an unconfined aquifer with a fully penetrated pumping well are either numerical, such as the well‐known FEMWTER model, or experimental; analytical models of a partially penetrated pumping well are rare. This study employs the linearized Richards equation as the governing equation, with the aid of Fourier Integral Transformation, to obtain an analytical solution of the water content distribution in an unconfined aquifer with a partially penetrated pumping well. The results from this study could serve to substantiate in some sense results from numerical models. In addition, the theory developed herein can be modified to simulate a vacuum‐pressured pumping well since it is derived by considering, among others, the location and length of a well screen with fluxes. Copyright © 2008 John Wiley & Sons, Ltd.     

A GENERAL PURPOSE MICROCOMPUTER AQUIFER TEST EVALUATION TECHNIQUE

Abstract. Although determination of aquifer characteristics from pumping test data is generally carried out using type curves or other graphical techniques, a number of computer methods have been developed recently for this purpose. Based on the principle of least squares, these methods of nonlinear regression analysis can be applied to any flow system for which analytical expressions of the drawdown distribution are known. In view of the growing general interest in the application of microcomputers in ground-water hydrology, a BASIC routine has been developed for estimating any number of aquifer parameters. The least squares solution is calculated by Marquardt's algorithm, using the singular-value decomposition of the Jacobian matrix. The robust computing method obtained can be applied to all kinds of pumping tests. Aquifer characteristics as well as their standard deviations are computed with optimal speed and accuracy. The technique is demonstrated by a simple application to steady flow in a leaky aquifer and an example is provided. Other applications are easily implemented and programs for unsteady-state aquifer tests, recovery tests and multiple aquifer tests are available.     

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.     

Air and water flows induced by pumping tests in unconfined aquifers with low‐permeability zones

Air flows from the atmosphere into an unconfined aquifer when the water table falls during pumping tests. Pumping test results in unconfined aquifers may be significantly affected by low‐permeability zones (LPZs) near the initial water table position, because they restrict the downward movement of air. A transient, three‐dimensional air–water two‐phase flow model is employed to investigate numerically the effects of local heterogeneity on pumping test results in unconfined aquifers. Two cases of local heterogeneities are considered herein: a LPZ around the pumping well and on one side of the pumping well. Results show that the drawdown with the LPZ is significantly greater than that of the homogeneous aquifer. The differences in drawdown are the most significant at intermediate times and gradually diminish at later times. The LPZ significantly reduces air flow from the atmosphere to the aquifer. The pore air velocity in the LPZ is very low. The air pressure at the observation point under the LPZ when air begins to enter is significantly lower than the air pressure of the homogeneous aquifer at the same point. After that, the air pressure increases quickly and then increases slowly. The time for the air pressure to reach the atmospheric pressure is significantly longer. Copyright © 2013 John Wiley & Sons, Ltd.     

Underdamped slug tests with unsaturated‐saturated flows by considering effects of wellbore skins

An analytical solution is presented for the slug tests conducted in a partially penetrating well in an unconfined aquifer affected from above by an unsaturated zone. The solution considers the effects of wellbore skin and oscillatory responses on underdamped slug tests. The flow in the saturated zone is described by a two‐dimensional, axially symmetric governing equation, and the flow in the unsaturated zone above the water table by a linearized one‐dimensional Richards' equation. The unsaturated medium properties are represented by the exponential constitutive relationships. A Laplace domain solution is derived using the Laplace and finite Fourier transform and the solution in the real‐time domain is evaluated using the numerical inverse Laplace transform method. The solution derived in this study is more general and reduces to the most commonly used solutions for slug tests in their specified conditions. It is found that the unsaturated flow has a significant impact on the slug test conducted in an unconfined aquifer. The impact of unsaturated flow on such a slug test is enhanced with a larger anisotropy ratio, a shorter well screen length, a shorter distance between the well screen and the water table, or a larger well screen radius. The impact of unsaturated flow on slug tests decreases as the degree of penetration (the length of well screen) increases. For a fixed well screen length, the impact of unsaturated flow on slug tests decreases as the distance between the centre of screen and the water table increases. A large dimensionless well screen radius (>0.01) leads to significant effects of unsaturated flow on slug tests. The unsaturated flow reduces the oscillatory responses to underdamped slug tests. The unsaturated zone has significant impact on slug test under high‐permeability wellbore skin.     

Steady flow to a partially penetrating blind‐wall well in a confined aquifer

Wells in aquifers of loose collapsible sediment are cased so that they have a blind wall and gain water only from the bottom. The hydraulic gradient established at the bottom of these wells during pumping brings the aquifer materials in a quicksand state, which may cause abrasion of pipes and pumps and even the destruction of well structure. To examine the quicksand occurrence, an analytical solution for the steady flow to a partially penetrating blind‐wall well in a confined aquifer is developed. The validity of the proposed solution is evaluated numerically. The sensitivity of maximum vertical gradient along the well bottom in response to aquifer and well parameters is examined. The solution is presented in the form of dimensionless‐type curves and equations that can be easily used to design the safe pumping rate and optimum well geometry to protect the well against sand production. The solution incorporates the anisotropy of aquifer materials and can also be used to determine the hydraulic conductivity of the aquifer. Copyright © 2012 John Wiley & Sons, Ltd.