A closed form slug test theory for high permeability aquifers

We incorporate a linear estimate of casing friction into the analytical slug test theory of Springer and Gelhar (1991) for high permeability aquifers. The modified theory elucidates the influence of inertia and casing friction on consistent, closed form equations for the free surface, pressure, and velocity fluctuations for overdamped and underdamped conditions. A consistent, but small, correction for kinetic energy is included as well. A characteristic velocity linearizes the turbulent casing shear stress so that an analytical solution for attenuated, phase shifted pressure fluctuations fits a single parameter (damping frequency) to transducer data from any depth in the casing. Underdamped slug tests of 0.3, 0.6, and 1 m amplitudes at five transducer depths in a 5.1 cm diameter PVC well 21 m deep in the Plymouth-Carver Aquifer yield a consistent hydraulic conductivity of 1.5 x 10(-3) m/s. The Springer and Gelhar (1991) model underestimates the hydraulic conductivity for these tests by as much as 25% by improperly ascribing smooth turbulent casing friction to the aquifer. The match point normalization of Butler (1998) agrees with our fitted hydraulic conductivity, however, when friction is included in the damping frequency. Zurbuchen et al. (2002) use a numerical model to establish a similar sensitivity of hydraulic conductivity to nonlinear casing friction.     

A simple approach using Bouwer and Rice's method for slug test data analysis

Slug test data obtained from tests performed in an unconfined aquifer are commonly analyzed by graphical or numerical approaches to determine the aquifer parameters. This paper derives three fourth-degree polynomials to represent the relationship between Bouwer and Rice's coefficients and the ratio of the screen length to the radius of the gravel envelope. A numerical approach using the nonlinear least squares and Newton's method is used to determine hydraulic conductivity from the best fit of the slug test data. The method of nonlinear least squares minimizes the sum of the squares of the differences between the predicted and observed water levels inside the well. With the polynomials, the hydraulic conductivity can be obtained by simply solving the nonlinear least squares equation by Newton's method. A computer code, SLUGBR, was developed from the derived polynomials using the proposed numerical approach. The results of analyzing two slug test datasets show that SLUGBR can determine hydraulic conductivity with very good accuracy.     

Salinity‐induced increase of the hydraulic conductivity in the hyporheic zone of coastal wetlands

In coastal zones globally, salinization is rapidly taking place due to the combined effects of sea level rise, land subsidence, altered hydrology, and climate change. Although increased salinity levels are known to have a great impact on both biogeochemical and hydrological processes in aquatic sediments, only few studies have included both types of processes and their potential interactions. In the present paper, we used a controlled 3‐year experimental mesocosm approach to test salinity induced interactions and discuss mechanisms explaining the observed hydrological changes. Surface water salinity was experimentally increased from 14 to 140 mmol Cl per L (0.9 and 9 PSU) by adding sea salt which increased pore water salinity but also increased sulfate reduction rates, leading to higher sulfide, and lower methane concentrations. By analyzing slug test data with different slug test analysis methods, we were able to show that hydraulic conductivity of the hyporheic zone increased 2.8 times by salinization. Based on our hydrological and biogeochemical measurements, we conclude that the combination of pore dilation and decreased methane production rates were major controls on the observed increase in hydraulic conductivity. The slug test analysis method comparison allowed to conclude that the adjusted Bouwer and Rice method results in the most reliable estimate of the hydraulic conductivity for hyporheic zones. Our work shows that both physical and biogeochemical processes are vital to explain and predict hydrological changes related to the salinization of hyporheic zones in coastal wetlands and provides a robust methodological approach for doing so.     

Using data assimilation method to calibrate a heterogeneous conductivity field and improve solute transport prediction with an unknown contamination source

Hydraulic conductivity distribution and plume initial source condition are two important factors affecting solute transport in heterogeneous media. Since hydraulic conductivity can only be measured at limited locations in a field, its spatial distribution in a complex heterogeneous medium is generally uncertain. In many groundwater contamination sites, transport initial conditions are generally unknown, as plume distributions are available only after the contaminations occurred. In this study, a data assimilation method is developed for calibrating a hydraulic conductivity field and improving solute transport prediction with unknown initial solute source condition. Ensemble Kalman filter (EnKF) is used to update the model parameter (i.e., hydraulic conductivity) and state variables (hydraulic head and solute concentration), when data are available. Two-dimensional numerical experiments are designed to assess the performance of the EnKF method on data assimilation for solute transport prediction. The study results indicate that the EnKF method can significantly improve the estimation of the hydraulic conductivity distribution and solute transport prediction by assimilating hydraulic head measurements with a known solute initial condition. When solute source is unknown, solute prediction by assimilating continuous measurements of solute concentration at a few points in the plume well captures the plume evolution downstream of the measurement points.     

Asymptotic analysis of cross-hole hydraulic tests in fractured granite

Illman and Tartakovsky (2005a, 2005b) developed a new approach for the interpretation of three-dimensional pneumatic well tests conducted in porous or fractured geologic media, which is based on a straight-line analysis of late-time data. We modify this approach to interpret three-dimensional well tests in the saturated zone and use it to analyze the cross-hole hydraulic test data collected in the Full-Scale Engineered Barrier Experiment gallery at the Grimsel Test Site in Switzerland. The equivalent hydraulic conductivity and specific storage obtained from our analysis increase with the radial distance between the centroids of the pumping and monitoring intervals. Since this scale effect is observed from a single test type (cross-hole tests), it is less ambiguous than scale effects typically inferred from laboratory and multiple types of hydraulic tests (e.g., slug, single- and cross-hole tests). The statistical analysis of the estimated hydraulic parameters shows a strong correlation between equivalent hydraulic conductivity and specific storage.     

Steady- and transient-state inversion in hydrogeology by successive flux estimation

A calibration method to solve the groundwater inverse problem under steady- and transient-state conditions is presented. The method compares kriged and numerical head field gradients to modify hydraulic conductivity without the use of non-linear optimization techniques. The process is repeated iteratively until a close match with piezometric data is reached. The approach includes a damping factor to avoid divergence and oscillation of the solution in areas of low hydraulic gradient and a weighting factor to account for temporal head variation in transient simulations. The efficiency of the method in terms of computing time and calibration results is demonstrated with a synthetic field. It is shown that the proposed method provides parameter fields that reproduce both hydraulic conductivity and piezometric data in few forward model solutions. Stochastic numerical experiments are conducted to evaluate the sensitivity of the method to the damping function and to the head field estimation errors.     

Using data assimilation method to calibrate a heterogeneous conductivity field conditioning on transient flow test data

A data assimilation method is developed to calibrate a heterogeneous hydraulic conductivity field conditioning on transient pumping test data. The ensemble Kalman filter (EnKF) approach is used to update model parameters such as hydraulic conductivity and model variables such as hydraulic head using available data. A synthetical two-dimensional flow case is used to assess the capability of the EnKF method to calibrate a heterogeneous conductivity field by assimilating transient flow data from observation wells under different hydraulic boundary conditions. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating continuous hydraulic head measurements and the hydraulic boundary condition will significantly affect the simulation results. For our cases, after a few data assimilation steps, the assimilated conductivity field with four Neumann boundaries matches the real field well while the assimilated conductivity field with mixed Dirichlet and Neumann boundaries does not. We found in our cases that the ensemble size should be 300 or larger for the numerical simulation. The number and the locations of the observation wells will significantly affect the hydraulic conductivity field calibration.     

Slug test analysis to evaluate permeability of compressible materials

The line-fitting methods such as the Hvorslev method and the Bouwer and Rice method provide a rapid and simple means to analyze slug test data for estimating in situ hydraulic conductivity ( k ) of geologic materials. However, when analyzing a slug test in a relatively compressible geologic formation, these conventional methods may have difficulties fitting a straight line to the semilogarithmic plot of the test data. Data from relatively compressible geologic formations frequently show a concave-upward curvature because of the effect of the compressibility or specific storage ( S _s). To take into account the compressibility of geologic formations, a modified line-fitting method is introduced, which expands on Chirlin's (1989) approach to the case of a partially penetrating well with the basic-time-lag fitting method. A case study for a compressible till is made to verify the proposed method by comparing the results from the proposed methods with those obtained using a type-curve method (Kansas Geological Survey method [ Hyder et al. 1994 ]).     

Modification of the Bouwer and Rice Method to a Cutoff Wall with a Filter Cake

The Bouwer and Rice method is a line-fitting method used to estimate the hydraulic conductivity of an aquifer by means of a slug test. When considering a relatively impermeable layer, called a filter cake, which may form at the interface between a cutoff wall and the natural soil formation, the assumptions of the Bouwer and Rice method are violated. A modification of the Bouwer and Rice method is proposed that incorporates the concept of a flow net, whereby the geometry of the cutoff wall and filter cake is effectively considered in estimating the hydraulic conductivity of a vertical cutoff wall.     

A simple constant-head injection test for streambed hydraulic conductivity estimation

A fast, efficient constant-head injection test (CHIT) for in situ estimation of hydraulic conductivity (K) of sandy streambeds is presented. This test uses constant-head hydraulic injection through a manually driven piezometer. Results from CHIT compare favorably to estimates from slug testing and grain-size analysis. The CHIT combines simplicity of field performance, data interpretation, and accuracy of K estimation in flowing streams.     

Analytical Interpretation of Slug Test in a Vertical Cutoff Wall

An analysis method for slug tests performed in a partially penetrating well within a vertical cutoff wall is presented. A steady‐state shape factor for evaluating hydraulic conductivity of the material within the wall was derived by applying the method of images to the previously developed analytical solution of Zlotnik et al. (2010) for an infinite aquifer. Two distinct boundary conditions were considered: constant‐head boundary for the case of direct contact between the wall and the aquifer, and no‐flux boundary representing an impermeable filter cake on the sides of the wall. The constant‐head and no‐flux boundary conditions yield significantly higher and lower shape factors, respectively, than those for the infinite aquifer. Consequently the conventional line‐fitting method for slug test analysis would yield an inaccurate estimate of the hydraulic conductivity of a vertical cutoff wall.     

A simple correction for slug tests in small-diameter wells

A simple procedure is presented for correcting hydraulic conductivity (K) estimates obtained from slug tests performed in small-diameter installations screened in highly permeable aquifers. Previously reported discrepancies between results from slug tests in small-diameter installations and those from tests in nearby larger-diameter wells are primarily a product of frictional losses within the small-diameter pipe. These frictional losses are readily incorporated into existing models for slug tests in high-K aquifers, which then serve as the basis of a straightforward procedure for correcting previously obtained K estimates. A demonstration of the proposed procedure using data from a series of slug tests performed in a controlled field setting confirms the validity of the approach. The results of this demonstration also reveal the detailed view of spatial variations in K that can be obtained using slug tests in small-diameter installations.     

Low‐Flow Hydraulic Conductivity Tests at Wells that Cross the Water Table

Wells with screens and sand packs that cross the water table represent a challenging problem for determining hydraulic conductivity by slug testing due to sand pack drainage and resaturation. Sand pack drainage results in a multisegmented recovery curve. One must then subjectively pick a portion of the curve to analyze. Sand pack drainage also results in a change in the effective radius of the well which requires a guess at the porosity or specific yield in analyzing the test. In the study of Robbins et al. (2009) , a method was introduced to obtain hydraulic conductivity in monitoring wells using the steady‐state drawdown and flow rate obtained during low‐flow sampling. The method was tested in this study in wells whose screens cross the water table and shown to avoid sand pack drainage problems that complicate analyzing slug tests. In applying the method to low‐flow sampling, only a single pair of steady‐state flow rate and drawdown are needed; hence, to derive meaningful results, an accurate determination of these parameters is required.     

Estimation of anisotropic hydraulic conductivity using geophysical data in a coastal aquifer of Karnataka,India

Estimation of hydraulic parameters is essential to understand the interaction between groundwater flow and seawater intrusion. Though several studies have addressed hydraulic parameter estimation, based on pumping tests as well as geophysical methods, not many studies have addressed the problem with clayey formations being present. In this study, a methodology is proposed to estimate anisotropic hydraulic conductivity and porosity values for the coastal aquifer with unconsolidated formations. For this purpose, the one-dimensional resistivity of the aquifer and the groundwater conductivity data are used to estimate porosity at discrete points. The hydraulic conductivity values are estimated by its mutual dependence with porosity and petrophysical parameters. From these estimated values, the bilinear relationship between hydraulic conductivity and aquifer resistivity is established based on the clay content of the sampled formation. The methodology is applied on a coastal aquifer along with the coastal Karnataka, India, which has significant clayey formations embedded in unconsolidated rock. The estimation of hydraulic conductivity values from the established correlations has a correlation coefficient of 0.83 with pumping test data, indicating good reliability of the methodology. The established correlations also enable the estimation of horizontal hydraulic conductivity on two-dimensional resistivity sections, which was not addressed by earlier studies. The inventive approach of using the established bilinear correlations at one-dimensional to two-dimensional resistivity sections is verified by the comparison method. The horizontal hydraulic conductivity agrees with previous findings from inverse modelling. Additionally, this study provides critical insights into the estimation of vertical hydraulic conductivity and an equation is formulated which relates vertical hydraulic conductivity with horizontal. Based on the approach presented, the anisotropic hydraulic conductivity of any type aquifer with embedded clayey formations can be estimated. The anisotropic hydraulic conductivity has the potential to be used as an important input to the groundwater models.     

Spreadsheet Modeling of Slug Tests Using the van der Kamp Method

Slug testing is frequently employed to calculate aquifer transmissivity and hydraulic conductivity. The van der Kamp technique for interpreting slug test data which experience force-free water level oscillations is not routinely employed because it requires adjusting equations to match the observed well response data. This adjustment can be rapid and convenient when a commercial spreadsheet is employed.     

Evaluation of vertical variations in hydraulic conductivity in unconsolidated sediments

Detailed information on vertical variations in hydraulic conductivity (K) is essential to describe the dynamics of groundwater movement at contaminated sites or as input data used for modeling. K values in high vertical resolution should be determined because K tends to be more continuous in the horizontal than in the vertical direction. To determine K in shallow unconsolidated sediments and in the vertical direction, the recently developed direct-push injection logger can be used. The information obtained by this method serves as a proxy for K and has to be calibrated to obtain quantitative K values of measured vertical profiles. In this study, we performed direct-push soil sampling, sieve analyses and direct-push slug tests to obtain K values in vertical high resolution. Using the results of direct-push slug tests, quantitative K values obtained by the direct-push injection logger could be determined successfully. The results of sieve analyses provided lower accordance with the logs due to the inherent limitations of the sieving method.     

Numerical Modeling of Slug Tests with MODFLOW Using Equivalent Well Blocks

Slug tests are a widely used technique to estimate aquifer hydraulic parameters and the test data are generally interpreted with analytical solutions under various assumptions. However, these solutions are not convenient when slug tests are required to be analyzed in a three‐dimensional model for complex aquifer‐aquitard systems. In this study, equivalent well blocks (EWB) are proposed in numerical modeling of slug test data with MODFLOW. Multi‐well slug tests in partially penetrating wells with skin zones can be simulated. Accuracy of the numerical method is demonstrated by benchmarking with analytical solutions. The EWB method is applied in a case study on slug tests in aquitards in the Pearl River Delta, China.     

SlugIn 1.0: A Free Tool for Automated Slug Test Analysis

The correct characterization of aquifer parameters is essential for water‐supply and water‐quality investigations. Slug tests are widely used for these purposes. While free software is available to interpret slug tests, some codes are not user‐friendly, or do not include a wide range of methods to interpret the results, or do not include automatic, inverse solutions to the test data. The private sector has also generated several good programs to interpret slug test data, but they are not free of charge. The computer program SlugIn 1.0 is available online for free download, and is demonstrated to aid in the analysis of slug tests to estimate hydraulic parameters. The program provides an easy‐to‐use Graphical User Interface. SlugIn 1.0 incorporates automated parameter estimation and facilitates the visualization of several interpretations of the same test. It incorporates solutions for confined and unconfined aquifers, partially penetrating wells, skin effects, shape factor, anisotropy, high hydraulic conductivity formations and the Mace test for large‐diameter wells. It is available in English and Spanish and can be downloaded from the web site of the Geological Survey of Spain. Two field examples are presented to illustrate how the software operates.     

Application of a nonlinear slug test model

Knowledge of the hydraulic conductivity distribution is of utmost importance in understanding the dynamics of an aquifer and in planning the consequences of any action taken upon that aquifer. Slug tests have been used extensively to measure hydraulic conductivity in the last 50 years since Hvorslev's (1951) work. A general nonlinear model based on the Navier-Stokes equation, nonlinear frictional loss, non-Darcian flow, acceleration effects, radius changes in the wellbore, and a Hvorslev model for the aquifer has been implemented in this work. The nonlinear model has three parameters: beta, which is related primarily to radius changes in the water column; A, which is related to the nonlinear head losses; and K, the hydraulic conductivity. An additional parameter has been added representing the initial velocity of the water column at slug initiation and is incorporated into an analytical solution to generate the first time step before a sequential numerical solution generates the remainder of the time solution. Corrections are made to the model output for acceleration before it is compared to the experimental data. Sensitivity analysis and least squares fitting are used to estimate the aquifer parameters and produce some diagnostic results, which indicate the accuracy of the fit. Finally, an example of field data has been presented to illustrate the application of the model to data sets that exhibit nonlinear behavior. Multiple slug tests should be taken at a given location to test for nonlinear effects and to determine repeatability.