Explicit Estimation of Aquifer Diffusivity from Linear Stream Stage

Different approaches are available for estimation of aquifer hydraulic diffusivity from a linear stream-stage variation and corresponding groundwater heads. These approaches require interpolation from tabulated values or computation of hydraulic gradient at the stream aquifer interface. Certain methods use approximation or interpolation of tabulated values for an infinite series. These methods are prone to errors in the estimated aquifer hydraulic diffusivity. An alternative approach is to use a closed-form solution of the problem and develop an explicit expression for the aquifer hydraulic diffusivity, which is free from errors of using infinite series, interpolation, and computation of hydraulic gradient. Such an alternative method is developed for a linearly varying stream stage. The new method can yield the estimate of hydraulic diffusivity even from a single observation. The proposed method would be applicable to practical hydraulic engineering problems keeping in view that most of a rising part of a stream stage hydrograph can be approximated by a linear rise and certain rivers may show a linearly varying stream stage. Use of the new method is demonstrated on published and field data, which shows that the estimates obtained using the new method are comparable to that obtained using an optimization approach.     

Confined Aquifer Parameters from Temporal Derivative of Drawdowns

A simple method that uses the time derivative of drawdowns is proposed for the evaluation of confined aquifer parameters. Explicit expressions are proposed for evaluation of the aquifer parameters as well as a graphical procedure. A reliable and accurate scheme to calculate the numerical derivative of drawdowns is developed based upon an analytical approach. The method requires early drawdown data (u > 0.01, where u is the argument of well function), and is shown to converge to the Cooper-Jacob method for late drawdowns (u ≤ 0.01). It does not require curve matching or an initial guess for the parameters. Calculations for the method can be performed on a hand-held calculator. The method has been applied to published data sets and the results have been compared with those obtained using traditional methods. The method accurately estimates the aquifer parameters using only early drawdown data, thereby indicating savings in time and money.     

Simple Method for Confined-Aquifer Parameter Estimation

Early drawdown data, for which the argument u of the well function is >0.01, have often been considered unimportant in evaluating aquifer parameters. This paper shows that these early drawdown data, especially in the neighborhood of u = 0.43, can yield accurate values of aquifer parameters. A simple method has been presented for explicit determination of aquifer parameters using early drawdown data. The method does not require curve matching, initial guess of the parameters, or special care to check for u < 0.01, and the computations involved can be performed on a calculator. Application of the method on published data sets shows that the estimates of the aquifer parameters using only a few initial drawdowns are as good as those obtained by Theis curve matching when all data, including the late drawdowns (u ≤ 0.01), are used. The new method converges with the Cooper-Jacob method when the late drawdown data are considered. Thus, the late drawdown data also can be analyzed using the new method.     

Analytical Solution for Two-Dimensional Solute Transport in Finite Aquifer with Time-Dependent Source Concentration

Using the Hankel Transform Technique, an analytical solution is derived for two-dimensional solute transport in a homogeneous isotropic aquifer. The aquifer is subjected to time-dependent point source contamination. The solution is derived under two conditions: (1) the flow velocity in the aquifer is a sinusoidally varying function and (2) the flow velocity is an exponentially decreasing function. Initially the aquifer is assumed solute free. The analytical solution is illustrated using an example.     

Aquifer Boundaries and Parameter Identification Simplified

A simple method is proposed for simultaneous and explicit identification of confined aquifer parameters and boundaries from drawdowns measured at an observation well during a constant rate pumping test. The method requires the determination of peaks of unimodal curves. Only a little subjectivity is involved in the method as the peak is a well defined point. The method is applicable even when the first and second straight lines on the semilogarithmic characteristic drawdown curve are not fully developed. The calculations involved can be performed on a calculator. Results have also been presented for small arguments of the well functions defining the development of the straight lines. The times for initiation and development of straight lines are quantified. The minimum duration of a pumping test for a reliable identification of the aquifer parameters and boundaries using the proposed method is also quantified. Use of the new method suggests a much shorter duration pumping test for the accurate identification of aquifer parameters and boundaries. This would save considerable time and money. At least a 100-fold savings in time and money involved in a pumping test to locate a boundary is observed when compared to the use of the law of times in the Cooper-Jacob method. Application of the method to published data sets shows that reliable estimates of the aquifer parameters and distance to a boundary are obtained.     

Flow Depletion Induced by Pumping Well from Stream Perpendicularly Intersecting Impermeable/Recharge Boundary

Analytical solutions for rate and volume of flow depletion induced by pumping a well from a stream that intersects an impermeable or a recharge boundary at right angles are derived using the basic flow depletion factor defined earlier by the author. A new concept of directly obtaining stream flow depletion using the method of images is proposed. The solutions are derived for five different management cases of a stream and boundary intersecting at right-angles, assuming the aquifer to be confined with semi-infinite areal extent. A computationally simple function is proposed for accurately approximating the error function. The existing analytical solution in the case of a right-angle bend of stream given by Hantush was obtained for unconfined aquifers using a linearization of the governing partial differential equation. The solution for this case obtained using the proposed method for confined aquifer is the same as obtained by Hantush for unconfined aquifers, which shows that the linearization adopted by Hantush does not actually solve this problem for unconfined aquifers.     

Estimation of the Maximum Consumption of Permanganate by Aquifer Solids Using a Modified Chemical Oxygen Demand Test

Knowledge of the consumption of permanganate by naturally occurring reduced species associated with aquifer materials is required for site screening and design purposes to support permanganate in situ chemical oxidation (ISCO) applications. It has been established that this consumption is not a singled-valued quantity, but rather is kinetically controlled. Current methods to determine this permanganate natural oxidant demand (NOD) involve the use of well-mixed batch tests, which are time consuming and subject to test variables (e.g., concentration, mass of oxidant to solid ratio, reaction duration, and mixing conditions) that significantly affect the results. In this paper, we propose a modified chemical oxygen demand (COD) test using permanganate, which can be used to determine the maximum permanganate NOD of an aquifer material. As an initial point of comparison, we tested aquifer materials collected from eight potential ISCO sites using this modified or permanganate COD method, the traditional dichromate COD method, and a method based on well-mixed batch reactors. The results from this comparison indicated that there was no statistically significant difference (α = 5%) between the results of the permanganate COD test and the maximum NOD from the well-mixed batch reactors, while on average the dichromate COD test overestimated the maximum NOD by 100%. The permanganate COD test results were highly correlated to the batch-test maximum NOD data (r = 0.996), and to the total organic carbon and amorphous Fe content of the aquifer materials (r = 0.91). A limited sensitivity investigation of this proposed permanganate COD test revealed that the suspected formation of manganese oxides, a reaction byproduct, may lead to increased experimental variability. However, in spite of this concern we recommend that this proposed permanganate COD method is a quick and economical approach for estimating the maximum permanganate NOD for aquifer materials to support permanganate ISCO site screening and initial design purposes.     

Simulation of Radial Collector Well in Shallow Alluvial Riverbed Aquifer Using Analytic Element Method

To withdraw large quantities of groundwater from the alluvial aquifers for various uses near riverbeds, radial collector (RC) wells are often preferable to the installation of several small diameter tube wells. In regions where rivers are not perennial or have low flow conditions during most part of the year, the RC wells are placed in the riverbed to obtain uninterrupted supply of naturally filtered groundwater through highly permeable saturated riverbed aquifers. Due to the complexities of flow, no exact analytical solution exists to provide steady state discharge drawdown relationship for RC well. Numerical model construction using finite difference or finite element method is quite cumbersome because of the radial orientation of laterals. To overcome these difficulties, in this study a steady state simulation model based on analytic element method (AEM) is developed to simulate the discharge-drawdown relation for RC well in an unconfined riverbed aquifer. In the model, line-sink elements are used to represent stream as well as radial laterals with specified conductance. The model is used to study the effects of different lateral configurations, hydraulic conductivity of riverbed aquifer, radius of influence and conductance of laterals on the well discharge, and consequent drawdown. Further based on the results of simulations using the AEM model, an approximate empirical equation is developed to obtain the discharge of RC well readily for design purpose. Further, the developed model has been applied to a field study and results are obtained for different plausible configurations of radial wells. The proposed methodology based on the application of AEM modeling tool, has been found to be efficient in constructing riverbed aquifer model with RC well. The proposed model is recommended in designing new collector well by providing minimum length of laterals for the sustained yield.     

Calculation of Inflow and Outflow in Phreatic Aquifers

Computer algebraic routines are applied for determination of the phreatic surface from standard boundary-value problems for ordinary differential equations. The method does not require iterative steps as other methods do and therefore may be readily used by engineers. The problem of seepage from (into) an unconfined semiinfinite aquifer into (from) an adjacent reservoir that has a sudden change of water level is revised. Comparisons with the Polubarinova-Kochina series expansion are done. Superelevation of the water table in a wetting regime compared to a drainage regime is quantified by the value of sorptivity (desorptivity). The absolute values of sorptivity and desorptivity diverge as the amplitude of the reservoir level change increases. A problem of a steady flow into (from) a constant head well from (into) an unconfined leaky aquifer is also examined. The water table elevation, well rate, and volume of the cone of depression (injection) are calculated.     

Identifying Impervious Boundary and Aquifer Parameters from Pump-Test Data

The common field problem of identifying and locating impervious aquifer boundaries is generally solved by analyzing the pump-test data. The estimate of the distance between the image well and the observation well (r′) is required for locating the boundary. Popular methods of estimating r′ either use the concept of fully developed two straight lines or rely on curve matching. Curve-matching methods are subjective and involve errors due to personal judgment. A very long duration pump test is required in order that the second straight line is developed. In many cases, the first straight line is not developed at all, especially when the observation well is at a greater distance from the pumped well. In this paper, a derivative-based robust optimization method has been proposed for the identification of aquifer parameters (transmissivity, T and storage coefficient, S) and r′ from the drawdowns observed at an observation well. It returns unbiased estimates of the parameters (T, S, and r′) even with a poor initial guess. The method can yield the estimates of the parameters from shorter duration pump-test data, thus saving time and money involved in conducting the pump test with the purpose of identifying r′. It is observed that the hydraulic diffusivity (T∕S) of the aquifer and r′ can be estimated even when the constant rate of pumping is not known.     

Aquifer Response to Sinusoidal or Arbitrary Stage of Semipervious Stream

Analytical expressions for the aquifer responses, viz., groundwater head, rate of flow and cumulative volume of flow, to a generalized sinusoidal stage of semipervious streams considering the stream boundary resistance, are derived. The analytical aquifer responses to a linear stream stage and to a typical analytical flood wave that was used by Cooper and Rorabaugh, are also derived. For a zero-stream resistance, the aquifer responses converge to those for a fully penetrating stream. Also, two analytical methods, a “ramp kernel method” and a “Fourier series method,” for obtaining the aquifer responses to an arbitrary temporal stage of sempervious stream, are developed. The analytical expressions of the ramp kernels for different aquifer responses are developed. The ramp kernel method is found superior to the conventional convolution that uses numerical integration or pulse kernels for obtaining the convolution integral. In the Fourier series method, the aquifer responses to sinusoidal stage are used along with Fourier series. The results obtained using both methods are in close agreement. The new methods are also applicable to fully penetrating streams by assigning a zero value to the stream resistance.     

Storage Coefficient and Transmissivity from Residual Drawdowns

A computationally simple method is proposed for the estimation of transmissivity and storage coefficient from only residual drawdowns at an observation well, the calculations for which can be performed using a calculator. The method does not require the last pumping drawdown, however, duration of pumping is required. Different estimates of storage coefficient during pumping and recovery can be obtained using the new method if applied on such data sets affected by the hysteresis in storage coefficient during pumping versus recovery. The new method may be suited for advanced analysis of pumping/residual drawdowns, such as storage coefficient increasing with recovery. It is able to identify the nonideal aquifer condition (other than infinite confined aquifer) from only residual drawdowns if applied on such data. It can yield reliable estimates of aquifer parameters, which are as good as that obtained using an optimization approach developed previously by the author.     

Approximation of M Function for Partially Penetrating Wells

A computationally simple approximation of the Hantush M function is proposed. Using this approximation, an optimization method is proposed for identifying the aquifer parameters from early drawdowns around partially penetrating wells. The aquifer parameters are hydraulic conductivity and specific storage. The application of the method is illustrated using a field example. The proposed method results in a 120-fold saving in time when compared to the prior method. It is hoped that the proposed approximation and method will be of help to the field engineers and practitioners.     

Subsurface Characterization Using Artificial Neural Network and GIS

A method for characterizing the subsurface is developed using an artificial neural network (ANN) and geographic information system (GIS). Data on the distribution of aquifer materials from monitoring well lithologic logs are used to train a multilayer perceptron using the back-propagation algorithm. The trained ANN predicts using an appropriate prediction scale, the subsurface formation materials at each point on a discretized grid of the model area. GIS is then used to develop subsurface profiles from the data generated using the ANN. These subsurface profiles are then compared with available geological sections to check the accuracy of the ANN-GIS generated profiles. This methodology is applied to determine the aquifer extent and calculate aquifer parameters for input to ground-water models for the multiaquifer system underlying the city of Bangkok, Thailand. A selected portion of the model domain is used for illustration. The integrated approach of ANN and GIS is shown to be a powerful tool for characterizing complex aquifer geometry, and for calculating aquifer parameters for ground-water flow modeling.     

Estimation of Aquifer Parameters from Pumping Test Data by Genetic Algorithm Optimization Technique

Adequate and reliable estimates of aquifer parameters are of utmost importance for proper management of vital groundwater resources. The pumping (aquifer) test is the standard technique for estimating various hydraulic properties of aquifer systems, viz., transmissivity (T), hydraulic conductivity (K), storage coefficient (S), and leakance (L), for which the graphical method is widely used. In the present study, the efficacy of the genetic algorithm (GA) optimization technique is assessed in estimating aquifer parameters from the time-drawdown pumping test data. Computer codes were developed to optimize various aquifer parameters under different hydrogeologic conditions by using the GA technique. Applicability, adequacy, and robustness of the developed codes were tested using 12 sets of the published and unpublished aquifer test data. The aquifer parameters were also estimated by the graphical method using AquiferTest software, and were compared with those obtained by the GA technique. The GA technique yielded significantly low values of the sum of square errors (SSE) for almost all the datasets under study. The results revealed that the GA technique is an efficient and reliable method for estimating various aquifer parameters, especially in the situation when the graphical matching is poor. Also, it was found that because of its inherent characteristics, GA avoids the subjectivity, long computation time and ill-posedness often associated with conventional optimization techniques. Furthermore, the performance evaluation of the developed GA-based computer codes showed that the fitness value (SSE) of the best point in a population reduces with increasing generation number and population size. The analysis of the sensitivity of the parameters during the performance of GA indicated that a unique set of aquifer parameters was obtained for all three aquifer systems. The GA-based computer programs with interactive windows developed in this study are user-friendly and can serve as a teaching and research tool, which could also be useful for practicing hydrologists and hydrogeologists.     

Multicriteria Analysis in an Irrigation District in Mexico

The Alto Rio Lerma Irrigation District, located in the state of Guanajuato in Mexico, is an agricultural area whose sustainability depends partially upon groundwater withdrawal for crop irrigation. Because of high pumping demands and current land-management practices, groundwater levels have declined severely, resulting in aquifer overdraft. In order to analyze economic, environmental, and water use problems in this region, 12 potential cropping patterns were generated for different groundwater withdrawals using linear programming. Then, simulation of the agricultural system was performed using GLEAMS to estimate the amounts of water, nitrate, and pesticides in both runoff and percolation for each cropping pattern. Pumping costs and an aquifer exploitation coefficient account for the economic and environmental impacts of aquifer overdraft. Finally, the Range of Value Method (multicriteria method) was applied to rank and identify the best cropping pattern. The results show the best alternative for effectively balancing environmental with economic considerations was the farming practice, consisting of land leveling, growing vegetables such as red tomato, and controlled groundwater withdrawals to preserve aquifer sustainability.     

Stream Multiaquifer Well Interactions

In this paper, unsteady flow into a multiaquifer well due to stream stage changes and varying pumping rate is analyzed. The well is located at such a distance that the radius of influence touches the stream boundary; hence, pumping induces seepage from the stream to the aquifer. The discrete kernel approach, which is based on Duhamel’s principle, has been applied to find the interaction among stream, aquifers, and pumping well for constant as well as varying stream stage. The analytical expression for a damped sinusoidal flood wave passing in a fully penetrating stream has been used for obtaining the aquifer response. By applying image-well theory, the finite aquifer and well system has been transformed into an infinite aquifer and well system. The principle of superposition, which is applicable to a linear system, has been used to analyze the interaction processes among the three components of the system. The interaction of the stream, aquifers, and well with each other are analyzed during pumping, after stoppage of pumping, as well as during passage of a flood wave in the stream.     

Aquifer Diffusivity and Stream Resistance from Varying Stream Stage

An efficient method that uses discrete ramp kernel is proposed for obtaining the piezometric head in an aquifer due to an arbitrary variation in stream stage considering stream resistance. The method assumes straight line variation between two consecutive points in representing the arbitrary stream stage variation. Expression for the ramp kernel is derived for homogeneous and isotropic aquifer conditions. Using the method, the stream resistance and hydraulic diffusivity of the aquifer are estimated for a set of published data. It is observed that the hydraulic diffusivity should be estimated along with the stream resistance for a better estimation of aquifer diffusivity.     

Aquifer Parameter Estimation for a Constant-Flux Test Performed in a Radial Two-Zone Aquifer

A patchy aquifer or an aquifer with a finite thickness skin can be considered as a radial two-zone aquifer system, which can be characterized by five parameters, i.e., the thickness of the first zone and four aquifer parameters including the transmissivity and storage coefficient for each of the first and second zones. This paper proposes an approach based on an analytical solution of a constant-flux pumping in a confined two-zone aquifer and the simulated annealing algorithm to determine the five parameters simultaneously. The estimated results for the five parameters are fairly good even assuming the aquifer as a single-zone system at the beginning of the data analysis. The estimated results indicate that the first-zone parameters are much more difficult to accurately identify than the second-zone parameters due to insufficient early-time data and high correlation of the sensitivities among the first-zone parameters. However, the problem of inaccurate results obtained at the first-zone can be significantly improved if more densely temporal drawdown measurements are used.