Ramp Kernels for Aquifer Responses to Arbitrary Stream Stage

Analytical expressions for ramp kernels (new kernels) for an improved convolution for obtaining aquifer responses, viz, groundwater head, rate, and cumulative volume of groundwater flow, to an arbitrary stage, are obtained. The use of the ramp kernels gives accurate aquifer responses and is superior to the conventional convolution in which numerical integration or pulse kernels are used. The extent of improvement in the results with the use of the ramp kernels is discussed and quantified for three examples, where the results are compared to analytical solutions. For the comparisons, the analytical solutions for linear and sinusoidal stream stages are derived. The use of the ramp kernels reproduces accurately the analytical solutions. The concept of ramp kernels can also be used for obtaining an accurate solution of convolution integrals observed in other fields.     

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.     

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.     

Flow Depletion of Semipervious Streams Due to Pumping

Expressions for the rate and volume of flow depletion of semipervious streams due to pumping are presented in computationally simple forms. Analytical expressions have been proposed to take into account both partial penetration and semipervious bed and banks of the stream. Graphs suitable for engineering applications are presented for siting wells, and the effect of an intermittent pumping cycle on the rate and volume of stream flow depletion has also been discussed. The exclusive volume of flow depletion during a cycle is shown to vary with the selection of the end of the cycle.     

Flow Depletion of Semipervious Streams Due to Unsteady Pumping Discharge

Analytical expressions for rate and volume of flow depletion of semipervious streams due to sinusoidal variation in pumping rate are obtained. An analytical but approximate method is developed for obtaining the rate and volume of stream flow depletion due to arbitrary unsteady pumping discharge. The method uses the ramp kernel and convolution. The use of ramp kernels permits linear interpolation between two consecutive discretized discharge values. The analytical equations for the ramp kernels for the rate and volume of stream flow depletion are derived. The proposed method is applicable for homogeneous and isotropic aquifers that are hydraulically connected to streams.     

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.     

Rate and Volume of Stream Flow Depletion due to Unsteady Pumping

Analytical but approximate methods are developed for obtaining pumping induced rate and volume of stream flow depletion, which can account for unsteady (any variation) pumping discharge and are also applicable for intermittent pumping and recovery. Exact analytical solutions for a sinusoidal variation in the pumping discharge are proposed; the proposed methods are verified using these solutions. The proposed methods use ramp kernels that give results superior to the conventional convolution. These ramp kernels assume the linear variation in pumping discharge between the two consecutive discretized points as opposed to the uniform variation assumed in the conventional convolution. The proposed solutions are applicable for homogeneous and isotropic aquifers hydraulically connected to streams.     

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 Varada Aquifer System for Sustainable Groundwater Development

Groundwater flow modeling has been used extensively worldwide with varying degrees of success. The ability to predict the groundwater flow is critical in planning and implementing groundwater development projects under increasing demand for fresh water resources. This paper presents the simulation of the aquifer system for planning the groundwater development of Varada basin, Karnataka, India using the Galerkin finite-element method. The government of Karnataka State, India is implementing the World Bank assisted project, “Jal Nirmal” for a sustainable development of the region, thereby ensuring a safe supply of drinking water to the northern districts of the state. Varada basin is one of the beneficiaries of the project in Haveri district. Field tests carried out in the study area indicate that the region is predominantly a confined aquifer with transmissivity and storage coefficients ranging from 5.787×10?6?m2/s (0.500?m2/day) to 4.213×10?3?m2/s (3.640×102?m2/day) and 0.011–0.001×10?2, respectively. This study mainly emphasizes the spatial and temporal variability of groundwater potential under different developmental scenarios. The model predictions were reasonably good with correlation coefficients ranging from 0.78 to 0.91 with the root mean square error of about 0.46–0.78 during calibration and validation. The stated accuracies are based on comparisons between measured and calculated heads. The outcome of the study would be a useful input for the conjunctive use of surface water and groundwater planning for the sustainable development of the region.     

Stream Classification System Based on Susceptibility to Algal Growth in Response to Nutrients

We developed a stream classification system that is based on stream’s susceptibility to algal growth using a two-step approach. The model portrays algal biomass as a result of stream’s response to nutrient concentrations and the response is governed by various stream factors. In the first step, a nutrient-chlorophyll a relationship was developed to characterize nutrient’s effects on algal biomass. Residuals of the relationship were attributed to stream’s susceptibility to algal growth in response to nutrients and referred to as “observed” susceptibility. In the second step, conditions of other contributing factors were used to explain the variation in the residuals and the developed relationship was used to generate “predicted” susceptibility. Existing data compiled from various monitoring projects of Illinois streams and rivers were used to illustrate the approach. Streams were classified into three (high, medium, and low) categories based on their observed and predicted susceptibility values, respectively. With the available data, the model showed a 40-50% success rate for classifying the streams based on three observed and predicted susceptibility categories. Model entropy also was calculated for selecting the best model. The results show the important role of both nutrients and other contributing factors in explaining the variation of algal biomass. The study also suggests ways to fine tune the model and improve its accuracy, which would make the presented model a more viable tool for stream classification for establishing nutrient criteria to prevent surface streams from eutrophication.     

Remediation of TCE-Contaminated Groundwater in a Sandy Aquifer Using Pulsed Air Sparging: Laboratory and Numerical Studies

The objective of this study was to investigate, through laboratory and numerical investigations, the effectiveness of a pulsed air sparging system for remediation of groundwater contaminated with trichloroethylene (TCE) in a sandy aquifer. In laboratory experiments, air was pulsed into TCE source zone on a daily basis in order to remediate TCE-contaminated groundwater. Most dissolved TCE was removed at the end of experiments although its concentrations fluctuated due to the air pulsing. The measured gaseous phase TCE concentration increased whereas the aqueous phase TCE concentration decreased during air sparging pulses. Experimental data were assessed by using a numerical code STOMP (subsurface transport over multiphases) with some modification based on the TCE dissolution kinetics. The unmeasured residual TCE mass was predicted through numerical simulations. Results show that aqueous concentrations for TCE are still much higher than the maximum contaminant level in spite of successful removal of 95% of residual TCE. It may imply that it would be more appropriate to apply air sparging combined with other remediation technologies such as bioremediation for remediation of TCE-contaminated groundwater.     

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.     

Analytical Model to Quantify Crude Oil Spill Volume in Sandy Layered Aquifers

Crude oil spills have far-reaching consequences not only from the point of view of economic considerations but also from the point of view of environmental pollution. This is particularly important in oil-producing countries like Saudi Arabia. In an attempt to study this phenomenon further, an analytical and experimental study was undertaken. In this study analytical estimation of crude oil spills in layered sandy soils was performed by vertically integrating the oil content function. This function exhibits discontinuities at the interfaces of different soil layers. The influence of layering on the estimation process was examined by comparing the analytical results with and without the layering. An experimental setup was used to assess the predictions of the analytical model formulated. The experimental results, for homogeneous soils, were compared with predictions of previous analytical and empirical models. This study shows that analytical as well as empirical models consistently underestimate the actual spill volume in soils. Furthermore, analytical predictions were shown to depend on how close the system was to hydrostatic equilibrium. It also shows that soil layering is a very significant factor that should be incorporated in quantifying the extent of aquifer contamination.     

Diagnostic Curves for Identifying Leaky Aquifer Parameters with or without Aquitard Storage

Two sets of unimodal diagnostic curves, one set assumes no aquitard storage and the other set assumes aquitard storage, are developed for identifying the parameter of leaky aquifers from early drawdowns, which yields accurate estimates of the parameters and lessens the subjectivity due to personal errors. The proposed diagnostic curve method is simple, easy to apply, and is based on matching of the diagnostically plotted observed drawdowns to an appropriate diagnostic curve. The new method is simple, easy to apply, does not require either the initial guess for the parameter values or repetitive evaluation of the leaky aquifer well function, and outperforms the conventional curve-matching, optimization, extended Kalman filter, and artificial neural network methods. The proposed set of diagnostic curves has a good diagnostic property and is able to easily identify nonideal conditions. The new method suggests a shorter duration pumping test, which would save time, money, and water. It is hoped that the proposed method would be useful to the field engineers and practitioners.     

Flow Depletion Induced by Pumping Well from Finite Length of Stream

A procedure for calculating the flow depletion from a finite length of a stream induced by a pumping well in an adjacent aquifer is developed. Four management cases of finite length of the stream including a basic case are considered. A “basic flow depletion factor” is defined, in terms of which the flow depletion factors for all cases are expressed. The basic flow depletion factor is twice the Hantush M function. A computationally simple and accurate practical approximation of the basic flow depletion factor is presented that encompasses the full practical range of the solutions. Using this approximation, an optimization method is proposed for the estimation of the aquifer hydraulic diffusivity and effective distance from the pumping well to the line of recharge from the measured temporal variation of stream flow depletion between two sections. During optimization, repeated computation of stream flow depletion is required; use of the proposed approximation simplifies the computation.     

Generalized Analytical Solutions for Groundwater Head in a Horizontal Aquifer in the Presence of Subsurface Drains

Generalized analytical solutions for groundwater head in horizontal aquifers in the presence of parallel subsurface drains are obtained considering a transient rate of recharge as a power series (polynomial) function and depth-dependent rate of evapotranspiration. A function, new to analytical drainage studies, is proposed for correctly representing the depth-dependent rate of evapotranspiration. The solutions are obtained considering the practical situation of drains placed at a shallow depth in a considerable depth of aquifer. Two conditions of large and small saturated thicknesses in comparison to the changes in groundwater head are considered. A mathematical criterion is proposed to distinguish between large and small saturated thicknesses.     

Simple Equations for Aquifer Parameters from Drawdowns in Large-Diameter Wells

Simple equations are proposed for estimating storage coefficient and transmissivity of an aquifer from drawdowns in large- diameter wells. The proposed method requires determination of the peak and time to peak of a unimodal curve. Using these values and utilizing the provided set of equations, the aquifer parameters are estimated through an iterative procedure. The proposed method is void of subjectivity involved in the previously proposed curve matching methods. Also, the new method can be used when the conventional curve matching methods cannot be applied to estimate the aquifer parameters. The new method can be used to estimate the aquifer parameters from the drawdown data observed only up to a time so that the peak could be determined.     

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.