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.     

Semianalytical Model for Drawdown due to Pumping a Partially Penetrating Large Diameter Well

A semianalytical model is developed for computing drawdowns in and around a partially penetrating large diameter well. The new model can take into account an unsteady pumping discharge and thus drawdowns during recovery can be computed. This model can also yield the unsteady contributions from well and aquifer storages to the pumped discharge. While developing the model, the flow from the bottom of the well is also accounted.     

Drawdown due to Pumping a Partially Penetrating Large-Diameter Well Using MODFLOW

The approach by the author for modeling the large-diameter wells using MODFLOW is extended to the partially penetrating large-diameter wells. The temporal variation of drawdown due to a steady pumping is presented in the form of diagnostic curves for different penetration. These diagnostic curves can also be used to estimate the aquifer parameters from the observed drawdowns in a partially penetrating large-diameter well.     

Simple Approximation of Well Function for Constant Drawdown Variable Discharge Artesian Wells

A simple approximation of the well function for a constant drawdown is developed. This approximation is used to estimate the storage coefficient and transmissivity of the aquifer from observed unsteady discharge under a constant drawdown condition, using an optimization method. Another simple approximation for calculating the total production volume during a time span is also developed. The developed approximations for the well function and production function are accurate within a maximum error of 0.7% for the practical range of the argument.     

Kernel Method for Transient Rate and Volume of Well Discharge under Constant Drawdown

A kernel method is proposed for calculating transient rate and cumulative volume of well discharge under constant drawdown. The new method can also be used for obtaining the drawdown (in pressure head) in the aquifer at some distance away from the well. Employing the new method, an optimization method is used to estimate the aquifer parameters from transient well discharge or drawdown in the aquifer pressure head. The proposed method can also be used to model the recovery of drawdown (in aquifer pressure head) after the plug-in of the well.     

Diagnostic Curve for Confined Aquifer Parameters from Early Drawdowns

A diagnostic curve of unimodal shape is developed for identifying the confined aquifer parameters from early drawdowns. A scaled well function is proposed for the diagnostic curve and computationally simple functions are developed for its accurate approximation. The diagnostic curve may be viewed as an alteration of the Theis’ curve or as the generalization of a previous approach proposed by the writer. Plotting the pumping test data in a convenient form and matching it to the diagnostic curve with a parallel shift of axes identify the aquifer parameters. The unimodal shape of the diagnostic curve facilitates matching and reduces the personal errors. The proposed method is simple, easy to apply, and yields accurate estimates of aquifer parameters from only early drawdowns, which would save considerable time and money involved in conducting a long-duration pumping test. The estimates obtained using the new method are as good as those obtained from much more complex methods. The new method does not require either the initial guess for the parameter values or repetitive evaluation of the well function.     

Drawdowns due to Intermittent-Pumping Cycles

This paper offers solutions for drawdowns due to intermittent pumping cycles or cyclic pumping, which are high accuracy approximations of the series of Theis functions superimposed in time. The proposed approximation formulas are an improvement over the earlier works. The earlier approximations are valid only if the number of pumping cycles is greater than 10 and involve gamma functions that are less convenient to evaluate than the rational approximation formulas offered in this paper. The proposed approximations are valid for any number of pumping cycles and involve simple functions that can be computed even using a calculator. The drawdown functions are defined for the drawdowns at the end of pumping or shutoff periods. The proposed expressions for these functions are also suitable for the estimation of aquifer parameters by plotting the observed drawdowns on semilogarithmic paper. Procedures for estimation of storage coefficient and head loss at the well from cyclic pumping drawdowns are not available. This paper also offers procedures for the estimation of transmissivity, storage coefficient, and head loss at the pumped well from the observed intermittent (cyclic) pumping drawdowns.     

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.     

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.     

New Methods for Aquifer Parameters from Slug Test Data

An objective method and a diagnostic curve method are developed for estimating the aquifer parameters (storage coefficient and transmissivity) from slug test data on a fully penetrating well. In the objective method, explicit equations are developed for estimating the aquifer parameters. In the diagnostic curve method, a set of unimodal diagnostic curves is developed along with a guiding straight line. The rise or fall in water level of the well is plotted diagnostically on a double logarithmic graph and matched to one of the diagnostic curves plotted on the same scale with a parallel shift of axes, to estimate the aquifer parameters from the dual coordinates of a selected point on the matched portion of the graphs. The unimodal shape of the diagnostic curves and the guiding straight line facilitate the matching and limit the subjectivity. The proposed methods can easily identify a nonideal condition. The estimates of the aquifer parameters obtained using the proposed methods are more accurate than those obtained using the prior curve matching methods. The proposed methods are also able to identify nonideal conditions. It is hoped that the new methods will be of help to field and practicing engineers.     

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.     

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.