A new method for aquifer system identification and parameter estimation

The standard practice for assessing aquifer parameters is to match groundwater drawdown data obtained during pumping tests against theoretical well function curves specific to the aquifer system being tested. The shape of the curve derived from the logarithmic time derivative of the drawdown data is also very frequently used as a diagnostic tool to identify the aquifer system in which the pumping test is being conducted. The present study investigates the incremental area method (IAM) to serve as an alternative diagnostic tool for the aquifer system identification as well as a supplement to the aquifer parameter estimation procedure. The IAM based diagnostic curves for ideal confined, leaky, bounded and unconfined aquifers have been derived as part of this study, and individual features of the plots have been identified. These features were noted to be unique to each aquifer setting, which could be used for rapid evaluation of the aquifer system. The effectiveness of the IAM methodology was investigated by analyzing field data for various aquifer settings including leaky, unconfined, bounded and heterogeneous conditions. The results showed that the proposed approach is a viable method for use as a diagnostic tool to identify the aquifer system characteristics as well as to support the estimation of the hydraulic parameters obtained from standard curve matching procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

A single recovery type curve from Theis'' exact solution

The Theis type curve matching method and the Cooper-Jacob semilog method are commonly used for estimation of transmissivity and storage coefficient of infinite, homogeneous, isotropic, confined aquifers from drawdown data of a constant rate pumping test. Although these methods are based on drawdown data, they are often applied indiscriminately to analyze both drawdown and recovery data. Moreover, the limitations of drawdown type curve to analyze recovery data collected after short pumping times are not well understood by the practicing engineers. This often may result in an erroneous interpretation of such recovery data. In this paper, a novel but simple method is proposed to determine the storage coefficient as well as transmissivity from recovery data measured after the pumping period of an aquifer test. The method eliminates the dependence on pumping time effects and has the advantage of employing only one single recovery type curve. The method based on the conversion of residual drawdown to recovered drawdown (buildup) data plotted versus a new equivalent time (delta(t) x t(p)/t(p) + delta(t)). The method uses the recovery data in one observation point only, and does not need the initial water level h0, which may be unknown. The accuracy of the method is checked with three sets of field data. This method appears to be complementary to the Cooper-Jacob and Theis methods, as it provides values of both storage coefficient and transmissivity from recovery data, regardless of pumping duration.     

Estimation of unconfined aquifer parameters by genetic algorithms

Abstract

Unconfined aquifer parameters, viz. transmissivity, storage coefficient, specific yield and delay index from a pumping test are estimated using the genetic algorithm optimization (GA) technique. The parameter estimation problem is formulated as a least-squares optimization, in which the parameters are optimized by minimizing the deviations between the field-observed and the model-predicted time–drawdown data. Boulton's convolution integral for the determination of drawdown is coupled with the GA optimization technique. The bias induced by three different objective functions: (a) the sum of squares of absolute deviations between the observed and computed drawdown; (b) the sum of squares of normalized deviations with respect to the observed drawdown; and (c) the sum of squares of normalized deviations with respect to the computed drawdown, is statistically analysed. It is observed that, when the time–drawdown data contain no errors, the objective functions do not induce any bias in the parameter estimates and the true parameters are uniquely identified. However, in the presence of noise, these objective functions induce bias in the parameter estimates. For the case considered, defining the objective function as the sum of the squares of absolute deviations between the observed and simulated drawdowns resulted in the best possible estimates. A comparison of the GA technique with the curve-matching procedure and a conventional optimization technique, such as the sequential unconstrained minimization technique (SUMT), is made in estimating the aquifer parameters from a reported field pumping test in an unconfined aquifer. For the case considered, the GA technique performed better than the other two techniques in parameter estimation, with the sum-of-squares errors obtained from the GA about one fourth of those obtained by the curve matching procedure, and about half of those obtained by SUMT.

Citation Rajesh, M., Kashyap, D. & Hari Prasad, K. S. (2010) Estimation of unconfined aquifer parameters by genetic algorithms. Hydrol. Sci. J. 55(3), 403–413.     

Dual‐Screened Vertical Circulation Wells for Groundwater Lowering in Unconfined Aquifers

A new type of vertical circulation well (VCW) is used for groundwater dewatering at construction sites. This type of VCW consists of an abstraction screen in the upper part and an injection screen in the lower part of a borehole, whereby drawdown is achieved without net withdrawal of groundwater from the aquifer. The objective of this study is to evaluate the operation of such wells including the identification of relevant factors and parameters based on field data of a test site and comprehensive numerical simulations. The numerical model is able to delineate the drawdown of groundwater table, defined as free‐surface, by coupling the arbitrary Lagrangian–Eulerian algorithm with the groundwater flow equation. Model validation is achieved by comparing the field observations with the model results. Eventually, the influences of selected well operation and aquifer parameters on drawdown and on the groundwater flow field are investigated by means of parameter sensitivity analysis. The results show that the drawdown is proportional to the flow rate, inversely proportional to the aquifer conductivity, and almost independent of the aquifer anisotropy in the direct vicinity of the well. The position of the abstraction screen has a stronger effect on drawdown than the position of the injection screen. The streamline pattern depends strongly on the separation length of the screens and on the aquifer anisotropy, but not on the flow rate and the horizontal hydraulic conductivity.     

Estimating hydraulic parameters when poroelastic effects are significant

For almost 80 years, deformation-induced head changes caused by poroelastic effects have been observed during pumping tests in multilayered aquifer-aquitard systems. As water in the aquifer is released from compressive storage during pumping, the aquifer is deformed both in the horizontal and vertical directions. This deformation in the pumped aquifer causes deformation in the adjacent layers, resulting in changes in pore pressure that may produce drawdown curves that differ significantly from those predicted by traditional groundwater theory. Although these deformation-induced head changes have been analyzed in several studies by poroelasticity theory, there are at present no practical guidelines for the interpretation of pumping test data influenced by these effects. To investigate the impact that poroelastic effects during pumping tests have on the estimation of hydraulic parameters, we generate synthetic data for three different aquifer-aquitard settings using a poroelasticity model, and then analyze the synthetic data using type curves and parameter estimation techniques, both of which are based on traditional groundwater theory and do not account for poroelastic effects. Results show that even when poroelastic effects result in significant deformation-induced head changes, it is possible to obtain reasonable estimates of hydraulic parameters using methods based on traditional groundwater theory, as long as pumping is sufficiently long so that deformation-induced effects have largely dissipated.     

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.     

Analytical model for aquifer response incorporating distributed stream leakage

An analytical model of stream/aquifer interaction is proposed that predicts drawdown in an aquifer with leakage from a finite-width stream induced by pumping from a well. The model is formulated based on the assumptions of stream partial penetration, a semipervious streambed, and distributed recharge across a finite-width stream. Advantages of the analytical solution include its simple structure, consisting of the Theis well function with integral modifications. The solution is derived for the semi-infinite domain between the stream and pumping well, which is of primary interest to hydrogeologists. Previous stream/aquifer analytical models are compared to the analytical solution based on dimensionless drawdown profiles. Drawdown in the aquifer near a wide stream was found to be less than that predicted by a solution that ignored stream width. Deviations between the proposed analytical solutions and previous solutions increase as stream width increases. For a hypothetical stream/aquifer system, the proposed analytical solution was equivalent to prior solutions when the ratio of the distance between the stream and aquifer to the stream width was greater than 25. This analytical solution may provide improved estimates of aquifer and streambed leakage parameters by curve fitting experimental field drawdown data.     

A new method for the interpretation of pumping tests in leaky aquifers

A novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The method is based on the analysis of the first and second derivatives of the drawdown with respect to log time for the estimation of the flow parameters. Like commonly used analysis procedures, such as the type-curve approach developed by Walton (1962) and the inflection point method developed by Hantush (1956), the mathematical development of the DIP method is based on the assumption of homogeneity of the leaky aquifer layers. However, contrary to the two methods developed by Hantush and Walton, the new method does not need any fitting process. In homogeneous media, the two classic methods and the one proposed here provide exact results for transmissivity, storativity, and leakage factor when aquifer storage is neglected and the recharging aquifer is unperturbed. The real advantage of the DIP method comes when applying all methods independently to a test in a heterogeneous aquifer, where each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. Therefore, the methods are complementary and not competitive. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.     

New graphical methods for estimating aquifer hydraulic parameters using pumping tests with exponentially decreasing rates

Actual pumping tests may involve continuously decreasing rates over a certain period of time, and the hydraulic conductivity (K) and specific storage (S_s) of the tested confined aquifer cannot be interpreted from the classical constant‐rate test model. In this study, we revisit the aquifer drawdown characteristics of a pumping test with an exponentially decreasing rate using the dimensionless analytical solution for such a variable‐rate model. The drawdown may decrease with time for a short period of time at intermediate pumping times for such pumping tests. A larger ratio of initial to final pumping rate and a smaller radial distance of the observation well will enhance the decreasing feature. A larger decay constant results in an earlier decrease, but it weakens the extent of such a decrease. Based on the proposed dimensionless transformation, we have proposed two graphical methods for estimating K and S_s of the tested aquifer. The first is a new type curve method that does not employ the well function as commonly done in standard type curve analysis. Another is a new analytic method that takes advantage of the decreasing features of aquifer drawdown during the intermediate pumping stage. We have demonstrated the applicability and robustness of the two new graphical methods for aquifer characterization through a synthetic pumping test.     

Assessing radial transmissivity variation in heterogeneous aquifers using analytical techniques

Pumping tests are one of the most commonly used in situ testing techniques for assessing aquifer hydraulic properties. Numerous researches have been conducted to predict the effects of aquifer heterogeneity on the groundwater levels during pumping tests. The objectives of the present work were as follows: (1) to predict drawdown conditions and to estimate aquifer properties during pumping tests undertaken in radially symmetric heterogeneous aquifers, and (2) to identify a method for assessing the transmissivity field along the radial coordinate in radially symmetric and fully heterogeneous transmissivity fields. The first objective was achieved by expanding an existing analytical drawdown formulation that was valid for a radially symmetric confined aquifer with two concentric zones around the pumping well to an N concentric zone confined aquifer having a constant transmissivity value within each zone. The formulation was evaluated for aquifers with three and four concentric zones to assess the effects of the transmissivity field on the drawdown conditions. The specific conditions under which aquifer properties could be identified using traditional methods of analysis were also evaluated. The second objective was achieved by implementing the inverse solution algorithm (ISA), which was developed for petroleum reservoirs to groundwater aquifer settings. The results showed that the drawdown values are influenced by a volumetric integral of a weighting function and the transmissivity field within the cone of depression. The weighting function migrates in tandem with the expanding cone of depression. The ability of the ISA to predict radially symmetric and log‐normally distributed transmissivity fields was assessed against analytical and numerical benchmarks. The results of this investigation indicated that the ISA method is a viable technique for evaluating the radial transmissivity variations of heterogeneous aquifer settings. Copyright © 2013 John Wiley & Sons, Ltd.     

Non-Darcian groundwater flow in leaky aquifers

Abstract

A simplified method has been developed for solving leaky aquifer non-Darcian flow hydraulics. The principle of volumetric approach is combined with the confined-aquifer, time-dependent drawdown equation in an observation well. The groundwater flow in the leaky aquifer is assumed to obey a non-Darcian flow law of exponential type. The results are obtained in the form of type-curve expressions from which the necessary bundles of curves are drawn for a set of selective non-Darcian flow aquifer parameters. Although application of the methodology appears as rather limited but it provides a scientific contribution and extension of leaky aquifer theory towards nonlinear flow conditions. The methodology developed herein is applied to some actual field data from the eastern sedimentary basin in the Kingdom of Saudi Arabia.     

A method for evaluating horizontal well pumping tests

Predicting the future performance of horizontal wells under varying pumping conditions requires estimates of basic aquifer parameters, notably transmissivity and storativity. For vertical wells, there are well-established methods for estimating these parameters, typically based on either the recovery from induced head changes in a well or from the head response in observation wells to pumping in a test well. Comparable aquifer parameter estimation methods for horizontal wells have not been presented in the ground water literature. Formation parameter estimation methods based on measurements of pressure in horizontal wells have been presented in the petroleum industry literature, but these methods have limited applicability for ground water evaluation and are based on pressure measurements in only the horizontal well borehole, rather than in observation wells. This paper presents a simple and versatile method by which pumping test procedures developed for vertical wells can be applied to horizontal well pumping tests. The method presented here uses the principle of superposition to represent the horizontal well as a series of partially penetrating vertical wells. This concept is used to estimate a distance from an observation well at which a vertical well that has the same total pumping rate as the horizontal well will produce the same drawdown as the horizontal well. This equivalent distance may then be associated with an observation well for use in pumping test algorithms and type curves developed for vertical wells. The method is shown to produce good results for confined aquifers and unconfined aquifers in the absence of delayed yield response. For unconfined aquifers, the presence of delayed yield response increases the method error.     

Effect of wellbore storage and finite thickness skin on flow to a partially penetrating well in a phreatic aquifer

An analytical model is presented for the analysis of constant flux tests conducted in a phreatic aquifer having a partially penetrating well with a finite thickness skin. The solution is derived in the Laplace transform domain for the drawdown in the pumping well, skin and formation regions. The time-domain solution in terms of the aquifer drawdown is then obtained from the numerical inversion of the Laplace transform and presented as dimensionless drawdown–time curves. The derived solution is used to investigate the effects of the hydraulic conductivity contrast between the skin and formation, in addition to wellbore storage, skin thickness, delayed yield, partial penetration and distance to the observation well. The results of the developed solution were compared with those from an existing solution for the case of an infinitesimally thin skin. The latter solution can never approximate that for the developed finite skin. Dimensionless drawdown–time curves were compared with the other published results for a confined aquifer. Positive skin effects are reflected in the early time and disappear in the intermediate and late time aquifer responses. But in the case of negative skin this is reversed and the negative skin also tends to disguise the wellbore storage effect. A thick negative skin lowers the overall drawdown in the aquifer and leads to more persistent delayed drainage. Partial penetration increases the drawdown in the case of a positive skin; however its effect is masked by the negative skin. The influence of a negative skin is pronounced over a broad range of radial distances. At distant observation points the influence of a positive skin is too small to be reflected in early and intermediate time pumping test data and consequently the type curve takes its asymptotic form.     

Use of Computers in the Field

Performing long-term pump tests, single-well aquifer tests and long-term ground water monitoring were, in the past, considered costly and labor-intensive tasks. However, because of recent advances in portable data acquisition systems, these field tests can be performed in a relatively cost-effective and efficient manner. Certain data acquisition systems (DAS) have unique options available. Recently developed and commonly used computers are the Envirolab®, the Paroscientific®, and the In-Situ®. The use of implementing DAS in ground water field studies has proved to be successful when compared to the many disadvantages of performing those tasks manually. Successful acquisition of aquifer characterization data using computerized methods is highly dependent on the implementation of proper field programming and operational procedures. In order to provide high qualify and meaningful data, the field operator must be familiar with proper equipment implementation and programming instructions. Once familiar with these procedures, the use of DAS in the field provides a cost-effective and efficient tool for aquifer testing.     

Steady state flow with hydraulic conductivity change around large diameter wells

Darcian flow law in aquifers assumes that the aquifer hydraulic conductivity is constant and the groundwater movement is due only to the piezometric level changes through hydraulic gradient. In practice, after the well development the aquifer just around the well has comparatively larger hydraulic conductivity and gradient. Patchy aquifer solutions in the literature consider sudden hydraulic conductivity changes with distance for the steady state flow. The change of transmissivity is demonstrated by the application of slope‐matching procedure to actual field data. It is the main purpose of this paper to derive simple analytical expressions for aquifer parameter evaluations with steadily decreasing hydraulic conductivity around the well. Spatial nonlinear hydraulic conductivity changes around a large‐diameter well within the depression cone of a confined aquifer are considered as exponentially decreasing functions of the radial distance. Copyright © 2010 John Wiley & Sons, Ltd.     

How to Find Aquifer Statistics Utilizing Pumping Tests? Two Field Studies Using welltestpy

We present a workflow to estimate geostatistical aquifer parameters from pumping test data using the Python package welltestpy . The procedure of pumping test analysis is exemplified for two data sets from the Horkheimer Insel site and from the Lauswiesen site, Germany. The analysis is based on a semi-analytical drawdown solution from the upscaling approach Radial Coarse Graining, which enables to infer log-transmissivity variance and horizontal correlation length, beside mean transmissivity, and storativity, from pumping test data. We estimate these parameters of aquifer heterogeneity from type-curve analysis and determine their sensitivity. This procedure, implemented in welltestpy , is a template for analyzing any pumping test. It goes beyond the possibilities of standard methods, for example, based on Theis' equation, which are limited to mean transmissivity and storativity. A sensitivity study showed the impact of observation well positions on the parameter estimation quality. The insights of this study help to optimize future test setups for geostatistical aquifer analysis and provides guidance for investigating pumping tests with regard to aquifer statistics using the open-source software package welltestpy .     

A Computerized Ground Water Monitoring System

This article describes a computer automated, hydrologic analysis system designed to allow the collection of high quality, long-term pumping test data. The instrument solves two of the major problems encountered in the field during aquifer tests: insufficient data, particularly during the early part of a test when drawdown is rapid; and high labor costs associated with long-term monitoring.
To illustrate the system's application, results are presented from the test of a highly transmissive aquifer. The aquifer's drawdown response was rapid; thus the time-drawdown curve was essentially flat after the first two minutes of the test, and correspondingly rapid data acquisition was essential for a unique solution of the aquifer's three-dimensional hydraulic conductivities.     

A Type-Curve Method for the Analysis of Pumping Tests with Piecewise-Linear Pumping Rates

Aquifer hydraulic parameters are commonly inferred from constant-rate pumping tests, while variable pumping rates are frequently encountered in actual field conditions. In this study, we propose a generally applicable dimensionless form of the analytical solution for variable-rate pumping tests in confined aquifers. In particular, we adopt a piecewise-linear fitting of variable pumping rates and propose a new type-curve method for estimating the hydraulic conductivity (K ) and specific storage (S_s ) of the investigated confined aquifer. For each test, a series of type curves, which depend on the variable pumping rates, the location of observation wells and the introduced first dimensionless inflection time, need to be provided for matching the observed drawdown data on a log-log graph. We first demonstrate the applicability and robustness of this method through a synthetic pumping test. Subsequently, we apply this method to analyze drawdown data from four pumping tests conducted within a multilayered aquifer/aquitard system in Wuxi city, Jiangsu Province, China. The parameter estimates are then compared with those reported by PEST. The K and S_s values estimated by the new type-curve method are found to be quite close to PEST-based estimates. Parameter estimation results demonstrate the difference in K and S_s values between observation wells. The difference could be attributed to the spatial heterogeneity in K and S_s . A future research topic may focus on the characterization of K and S_s heterogeneity with the currently available drawdown data from variable-rate pumping tests.     

Flowing partially penetrating well: solution to a mixed-type boundary value problem

A new semi-analytic solution to the mixed-type boundary value problem for a flowing partially penetrating well with infinitesimal skin situated in an anisotropic aquifer is developed. The solution is suited to aquifers having a semi-infinite vertical extent or to packer tests with aquifer horizontal boundaries far enough from the tested area. The problem reduces to a system of dual integral equations (DE) and further to a deconvolution problem. Unlike the analogous Dagan's steady-state solution [Water Resour. Res. 1978; 14:929–34], our DE solution does not suffer from numerical oscillations. The new solution is validated by matching the corresponding finite-difference solution and is computationally much more efficient. An automated (Newton–Raphson) parameter identification algorithm is proposed for field test inversion, utilizing the DE solution for the forward model. The procedure is computationally efficient and converges to correct parameter values. A solution for the partially penetrating flowing well with no skin and a drawdown–drawdown discontinuous boundary condition, analogous to that by Novakowski [Can. Geotech. J. 1993; 30:600–6], is compared to the DE solution. The D–D solution leads to physically inconsistent infinite total flow rate to the well, when no skin effect is considered. The DE solution, on the other hand, produces accurate results.