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.     

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.     

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.     

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.     

Optimizing Aquifer Parameters from Drawdowns in Large Diameter Wells

An optimization method is proposed for estimating the storage coefficient and transmissivity of an aquifer from drawdowns in large diameter wells consequent to an unsteady pumping. The concept of an optimal time step size is propagated in the proposed method. The estimate of the aquifer parameters corresponding to the optimal time step size is termed final estimate. The estimates for any other time step size are not reliable. The proposed method can also take into account the residual drawdowns. The application of the method is illustrated using an example.     

Estimating Aquifer Parameters from Early Drawdowns in Large-Diameter Wells

The existing equation applicable for large diameter wells in confined aquifers is transformed into a convenient form and a set of semilogarithmic diagnostic curves is developed for identifying the aquifer parameters (storage coefficient and transmissivity) from early drawdowns in large diameter wells. A scaled well function is proposed for the diagnostic curves. The aquifer parameters are estimated by matching the diagnostically plotted drawdowns to one of the diagnostic curves by a parallel shift of only one axis. The substantial curvature of the diagnostic curves and shifting of only one axis facilitate matching and reduce subjectivity. The proposed method is an improvement over the existing matching methods. The new method can reliably identify the aquifer parameters from only early drawdowns and would result in a 100-fold saving in time and money. It is hoped that this method would be helpful to field engineers and practitioners.     

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.     

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.     

Investigation of Boundary Shear Stress and Pollutant Detachment from Impervious Surface during Simulated Urban Storm Runoff

Pollutant detachment rates have been determined for four chloride salts during simulated urban storm runoff. Under rainfall and/or overland flow conditions, chloride mass flux was measured and related to boundary shear stress of the test surface. Washoff coefficients, presumed to depend only on pollutant characteristics, were computed based on the slopes of dimensionless mass flux versus dimensionless time plots. Washoff coefficients were found to vary among and between the chloride compounds studied. In general, higher overland flow rates produced lower boundary shear and lower washoff coefficients. The combination of simulated rainfall and overland flow resulted in an increased boundary shear and an increased washoff coefficient. An empirical washoff coefficient based on a load characteristic curve derived from an exponential washoff relationship was also computed from the runoff data and compared with the previous washoff coefficient. A linear correlation between these two washoff coefficients was observed. The magnitude of the latter coefficient under simulated rainfall was consistent with reported values obtained from field data.     

Identifying Representative Parameters of IUH

A simple procedure is proposed, using a linear transform, for obtaining a single representative effective rainfall hyetograph (ERH) and the corresponding direct runoff hydrograph (DRH) by processing multistorm data. Using these representative ERH and DRH, the representative parameters of the two-parameter gamma distribution instantaneous unit hydrograph (IUH) is determined by either the proposed optimization method or the conventional method of moments. The optimization method is found superior to the method of moments and yields reliable IUH. However, the method of moments is easier to apply and yields acceptable results. A two-parameter gamma distribution is used for the parametric representation of the IUH, which yields a smooth shape of the IUH. A linear programming or a least-squares approach does not yield a IUH and the UH it identifies does not have a smooth shape (oscillations are observed in the tail of the UH). The new method yields a reliable representative IUH. The use of the methods is illustrated using the published data sets.     

Approximation of Well Function and Identification of Leaky Aquifer Parameters

The existing equation for leaky aquifers is transformed into a nondimensional form using new parameters and a scaled well function for leaky aquifers is proposed. A computationally simple function is developed for accurately approximating the scaled well function for the practical range of the parameters. Utilizing this function (approximation), an optimization method is proposed for identifying the leaky-aquifer parameters from observed drawdowns. The new function has an enhanced utility when a repetitive numerical evaluation of the well function for leaky aquifers is needed, e.g., while estimating the aquifer parameters using optimization or Kalman filter or artificial neural network methods. The application of the proposed method is illustrated using a few sets of published data. The proposed method outperforms the extended Kalman filter method, based on the reported results in the literature.     

Identifying Effective Distance to a Recharge Boundary

The solution to the problem of induced recharge where pumping is planned near a stream, requires determining effective distance to the line of recharge. This is generally accomplished by analyzing the drawdowns observed during the pumping test conducted near a recharge boundary. Traditional methods of estimating the distance between observation well and image well either use the concept of fully developed straight lines or make use of the type curves for matching. Hantush's method requires the locating of the inflection point on the drawdown curve. The curve matching or the Hantush method is subjective and hence involves errors due to personal judgment. A long-duration pumping test is required to be conducted in order to obtain a fully developed second straight line. In many situations, such a long-duration pumping test is not feasible. In this paper, a robust optimization method is presented that allows the use of shorter-duration pumping test data, for estimating aquifer parameters, and distance to the effective line of recharge. Thus, it saves time and costs involved in conducting a long-duration pumping test. Application of the method on published data sets shows that the new method yields reliably accurate estimates of the parameters.     

Drawdown due to Temporally Varying Pumping Discharge: Inversely Estimating Aquifer Parameters

A ramp kernel method is proposed for accurately calculating the drawdown due to any temporal variation in pumping discharge. The use of the ramp kernels assumes the linear variation between the two consecutive measured pumping discharges. The prior studies assume a rectangular variation between the two consecutive measured pumping discharges. In the rectangular variation, a uniform pumping rate is assumed during a time span. An analytical equation for calculating the ramp kernel is derived. An optimization method is used with the proposed ramp kernels for inversely estimating the aquifer parameters from drawdown due to an arbitrary unsteady pumping discharge. Unlike the prior methods, the proposed method accurately identifies the parameters even when the sampling interval for the drawdown and pumping discharge is longer than that needed for assuming a linear variation. The proposed method outperforms the prior method. Application of the proposed method is illustrated using examples.