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.     

Semi‐analytical solution for a slug test in partially penetrating wells including the effect of finite‐thickness skin

This paper presents a new semi‐analytical solution for a slug test in a well partially penetrating a confined aquifer, accounting for the skin effect. This solution is developed based on the solution for a constant‐flux pumping test and a formula given by Peres and co‐workers in 1989. The solution agrees with that of Cooper and co‐workers and the KGS model when the well is fully penetrating. The present solution can be applied to simulate the temporal and spatial head distributions in both the skin and formation zones. It can also be used to demonstrate the influences of skin type or skin thickness on the well water level and to estimate the hydraulic parameters of the skin and formation zones using a least‐squares approach. The results of this study indicate that the determination of hydraulic conductivity using a conventional slug‐test data analysis that neglects the presence of a skin zone will give an incorrect result if the aquifer has a skin zone. Copyright © 2008 John Wiley & Sons, Ltd.     

Influence of aquifer heterogeneity and return flow on pumping test data interpretation

Analytical solutions of drawdown in unconfined aquifers are widely applied for determining the specific yield, S_y, and the horizontal and the vertical hydraulic conductivity K_r and K_z, respectively. In many previous studies, estimates of S_y and K_z were observed to be highly variable and physically unrealistic. This has been attributed to the conceptualization of flow above the declining water table and aquifer heterogeneity in the applied models. We present the analysis of time-drawdown data from a pumping test instrumented with depth-differentiated observation piezometers arranged in clusters. Applying homogeneous anisotropic aquifer models in combination with nonlinear least squares parameter identification techniques, the data were analyzed in different groups: analysis of data from individual piezometer clusters and simultaneous analysis of the entire data set from all piezometer clusters (global analysis). From the cluster analyses, estimates of S_y and K_z exhibit large variances and depart from a priori estimates inferred from the hydrostratigraphy. Parameter estimates from the global analysis do not fall within the parameter bounds (minimum and maximum values) defined by the cluster analyses. While heterogeneity appears to be the important reason for large parameter variances, we discuss the influence of rarely considered aquifer return flow on drawdown and the inconsistent results from the cluster and global analyses. We corroborate our findings with data on hydraulic gradients, slug test data, and results from the application of a more realistic numerical flow model.     

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.     

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.     

High-resolution slug testing

The hydraulic conductivity (K) variation has important ramifications for ground water flow and the transport of contaminants in ground water. The delineation of the nature of that variation can be critical to complete characterization of a site and the planning of effective and efficient remedial measures. Site-specific features (such as high-conductivity zones) need to be quantified. Our alluvial field site in the Kansas River valley exhibits spatial variability, very high conductivities, and nonlinear behavior for slug tests in the sand and gravel aquifer. High-resolution, multilevel slug tests have been performed in a number of wells that are fully screened. 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 used to analyze the data, employing an automated processing system that runs within the Excel spreadsheet program. It is concluded that slug tests can provide the necessary data to identify the nature of both horizontal and vertical K variation in an aquifer and that improved delineation or higher resolution of K structure is possible with shorter test intervals. The gradation into zones of higher conductivity is sharper than seen previously, and the maximum conductivity observed is greater than previously measured. However, data from this project indicate that well development, the presence of fines, and the antecedent history of the well are important interrelated factors in regard to slug-test response and can prevent obtaining consistent results in some cases.     

Parameter identification for leaky aquifers using global optimization methods

In the past, graphical or computer methods were usually employed to determine the aquifer parameters of the observed data obtained from field pumping tests. Since we employed the computer methods to determine the aquifer parameters, an analytical aquifer model was required to estimate the predicted drawdown. Following this, the gradient‐type approach was used to solve the nonlinear least‐squares equations to obtain the aquifer parameters. This paper proposes a novel approach based on a drawdown model and a global optimization method of simulated annealing (SA) or a genetic algorithm (GA) to determine the best‐fit aquifer parameters for leaky aquifer systems. The aquifer parameters obtained from SA and the GA almost agree with those obtained from the extended Kalman filter and gradient‐type method. Moreover, all results indicate that the SA and GA are robust and yield consistent results when dealing with the parameter identification problems. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Evaluation of Combined Direct-Push Methods Used for Aquifer Model Generation

Most established methods to characterize aquifer structure and hydraulic conductivities of hydrostratigraphical units are not capable of delivering sufficient information in the spatial resolution that is desired for sophisticated numerical contaminant transport modeling and adapted remediation design. With hydraulic investigation methods based on the direct-push (DP) technology such as DP slug tests, DP injection logging, and the hydraulic profiling tool, it is possible to rapidly delineate hydrogeological structures and estimate their hydraulic conductivity in shallow unconsolidated aquifers without the need for wells. A combined application of these tools was used for the investigation of a contaminated German refinery site and for the setup of hydraulic aquifer models. The quality of DP investigation and the models was evaluated by comparisons of tracer transport simulations using these models and measured breakthroughs of two natural gradient tracer tests. Model scenarios considering the information of all tools together showed good reproduction of the measured breakthroughs, indicating the suitability of the approach and a minor impact of potential technical limitations. Using the DP slug tests alone yielded significantly higher deviations for the determined hydraulic conductivities compared to considering two or three of the tools. Realistic aquifer models developed on basis of such combined DP investigation approaches can help optimize remediation concepts or identify flow regimes for aquifers with a complex structure.     

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.     

An analytic data analysis method for oscillatory slug tests

An analytical data analysis method is developed for slug tests in partially penetrating wells in confined or unconfined aquifers of high hydraulic conductivity. As adapted from the van der Kamp method, the determination of the hydraulic conductivity is based on the occurrence times and the displacements of the extreme points measured from the oscillatory data and their theoretical counterparts available in the literature. This method is applied to two sets of slug test response data presented by Butler et al.: one set shows slow damping with seven discernable extremities, and the other shows rapid damping with three extreme points. The estimates of the hydraulic conductivity obtained by the analytic method are in good agreement with those determined by an available curve-matching technique.     

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.     

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 ]).     

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.     

Identification of hydraulic conductivity distributions in density dependent flow fields of submarine groundwater discharge modeling using adjoint-state sensitivities

A mathematical optimal control method is developed to identify a hydraulic conductivity distribution in a density dependent flow field. Using a variational method, the adjoint partial differential equations are obtained for the density- dependent state equations used for the saline aquifer water flow. The adjoint equations are numerically solved in through a finite difference method. The developed method is applied to identify the hydraulic conductivity distribution through the numerical solution of an optimal control problem. To demonstrate the effectiveness of the optimal control method, three numerical experiments are conducted with artificial observation data. The results indicate that the developed method has the potential to accurately identify the hydraulic conductivity distribution in a saline water aquifer flow system.     

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.     

Aquifer Properties Determined from Two Analytical Solutions

In the analysis of pumping test data, the quality of the determined aquifer parameters can be greatly improved by using a proper model of the aquifer system. Moench (1995) provided an analytical solution for flow to a well partially penetrating an unconfined aquifer. His solution, in contrast to the Neuman solution (1974), accounts for the noninstantaneous decline of the water table (delayed yield). Consequently, the calculated drawdown in these two solutions is different under certain circumstances, and this difference may therefore affect the computation of aquifer properties from pumping test data. This paper uses an inverse computational method to calculate four aquifer parameters as well as a delayed yield parameter, α₁ from pumping test data using both the Neuman (1974) and Moench (1995) solutions. Time-drawdown data sets from a pumping test in an unconfined alluvial aquifer near Grand Island, Nebraska, were analyzed. In single-well analyses, horizontal hydraulic conductivity values derived from the Moench solution are lower, but vertical hydraulic conductivity values are higher than those calculated from the Neuman solution. However, the hydraulic conductivity values in composite-well analyses from both solutions become very close. Furthermore, the Neuman solution produces similar hydraulic conductivity values in the single-well and composite-well analyses, but the Moench solution does not. While variable α₁, seems to play a role in affecting the computation of aquifer parameters in the single-well analysis, a much smaller effect was observed in the composite-well analysis. In general, specific yield determined using the Moench solution could be slightly higher than the values from the Neuman solution; however, they are still lower than the realistic values for sand and gravel aquifers.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

Using direct current resistivity sounding and geostatistics to aid in hydrogeological studies in the Choshuichi alluvial fan, Taiwan

Ground water reservoirs in the Choshuichi alluvial fan, central western Taiwan, were investigated using direct-current (DC) resistivity soundings at 190 locations, combined with hydrogeological measurements from 37 wells. In addition, attempts were made to calculate aquifer transmissivity from both surface DC resistivity measurements and geostatistically derived predictions of aquifer properties. DC resistivity sounding data are highly correlated to the hydraulic parameters in the Choshuichi alluvial fan. By estimating the spatial distribution of hydraulic conductivity from the kriged well data and the cokriged thickness of the correlative aquifer from both resistivity sounding data and well information, the transmissivity of the aquifer at each location can be obtained from the product of kriged hydraulic conductivity and computed thickness of the geoelectric layer. Thus, the spatial variation of the transmissivities in the study area is obtained. Our work is more comparable to Ahmed et al. (1988) than to the work of Niwas and Singhal (1981). The first "constraint" from Niwas and Singhal's work is a result of their use of linear regression. The geostatistical approach taken here (and by Ahmed et al. [1988]) is a natural improvement on the linear regression approach.     

A novel analytical solution for a slug test conducted in a well with a finite-thickness skin

An aquifer containing a skin zone is considered as a two-zone system. A mathematical model describing the head distribution is presented for a slug test performed in a two-zone confined aquifer system. A closed-form solution for the model is derived by Laplace transforms and Bromwich integral. This new solution is used to investigate the effects of skin type, skin thickness, and the contrast of skin transmissivity to formation transmissivity on the distributions of dimensionless hydraulic head. The results indicate that the effect of skin type is marked if the slug-test data is obtained from a radial two-zone aquifer system. The dimensionless well water level increases with the dimensionless positive skin thickness and decreases as the dimensionless negative skin thickness increases. In addition, the distribution of dimensionless well water level due to the slug test depends on the hydraulic properties of both the wellbore skin and formation zones.