Geoffrey C. Bohling

Pumping tests in networks of multilevel sampling wells: Motivation and methodology

The identification of spatial variations in hydraulic conductivity (K) on a scale of relevance for transport investigations has proven to be a considerable challenge. Recently, a new field method for the estimation of interwell variations in K has been proposed. This method, hydraulic tomography, essentially consists of a series of short-term pumping tests performed in a tomographic-like arrangement. In order to fully realize the potential of this approach, information about lateral and vertical variations in pumping-induced head changes (drawdown) is required with detail that has previously been unobtainable in the field. Pumping tests performed in networks of multilevel sampling (MLS) wells can provide data of the needed density if drawdown can accurately and rapidly be measured in the small-diameter tubing used in such wells. Field and laboratory experiments show that accurate transient drawdown data can be obtained in the small-diameter MLS tubing either directly with miniature fiber-optic pressure sensors or indirectly using air-pressure transducers. As with data from many types of hydraulic tests, the quality of drawdown measurements from MLS tubing is quite dependent on the effectiveness of well development activities. Since MLS ports of the standard design are prone to clogging and are difficult to develop, alternate designs are necessary to ensure accurate drawdown measurements. Initial field experiments indicate that drawdown measurements obtained from pumping tests performed in MLS networks have considerable potential for providing valuable information about spatial variations in hydraulic conductivity.

Inherent Limitations of Hydraulic Tomography

We offer a cautionary note in response to an increasing level of enthusiasm regarding high-resolution aquifer characterization with hydraulic tomography. We use synthetic examples based on two recent field experiments to demonstrate that a high degree of nonuniqueness remains in estimates of hydraulic parameter fields even when those estimates are based on simultaneous analysis of a number of carefully controlled hydraulic tests. We must, therefore, be careful not to oversell the technique to the community of practicing hydrogeologists, promising a degree of accuracy and resolution that, in many settings, will remain unattainable, regardless of the amount of effort invested in the field investigation. No practically feasible amount of hydraulic tomography data will ever remove the need to regularize or bias the inverse problem in some fashion in order to obtain a unique solution. Thus, along with improving the resolution of hydraulic tomography techniques, we must also strive to couple those techniques with procedures for experimental design and uncertainty assessment and with other more cost-effective field methods, such as geophysical surveying and, in unconsolidated formations, direct-push profiling, in order to develop methods for subsurface characterization with the resolution and accuracy needed for practical field applications.

The use of slug tests to describe vertical variations in hydraulic conductivity

Abstract Multilevel slug tests provide one means of obtaining estimates of hydraulic conductivity on a scale of relevance for contaminant transport investigations. A numerical model is employed here to assess the potential of multilevel slug tests to provide information about vertical variations in hydraulic conductivity under conditions commonly faced in field settings. The results of the numerical simulations raise several important issues concerning the effectiveness of this technique. If the length of the test interval is of the order of the average layer thickness, considerable error may be introduced into the conductivity estimates owing to the effects of adjoining layers. The influence of adjoining layers is dependent on the aspect ratio (length of test interval/well radius) of the tesy interval and the flow properties of the individual layers. If a low-permeability skin is present at the well, the measured vertical variations will be much less than the actual variations, owing to the influence of the skin conductivity on the parameter estimates. A high-permeability skin can also produce apparent vertical variations that are much less than the actual, owing to water flowing vertically along the conductive skin. In cases where the test interval spans a number of layers, a slug test will yield an approximate thickness-weighted average of the hydraulic conductivities of the intersected layers. In most cases, packer circumvention should not be a major concern when packers of 0.75 m or longer are employed. Results of this study are substantiated by recently reported field tests that demonstrate the importance of well emplacement and development activities for obtaining meaningful estimates from a program of multilevel slug tests.

Sensitivity analysis of slug tests. Part 1. The slugged well

Abstract In this paper, we apply the techniques of sensitivity analysis to the Cooper et al. model for slug tests in confined aquifers. A sensitivity analysis of slug-test responses can provide valuable information concerning optimal test design (within the limitations of the chosen model). The sensitivity analysis enables a family of generic sensitivity coefficients for transmissivity (T) and storage coefficient (S) to be defined by two parameters a (related to S) and β (related to time and T). Two facts stand out from this family of curves. First, the sensitivity to S is much lower than that to T; second, the sensitivity curves for T and S are very similar in shape (i.e. the correlation is high) making it difficult to reliably estimate both T and S. Sensitivity analysis shows that the estimated standard errors of the parameters are inversely proportional to the initial head (H0), so large initial heads should be used when possible. Generally, an increased number of measurements improves parameter estimation, if properly placed in time. Early time measurements are important for defining H0 accurately. The best estimates for T and S are obtained by minimizing the correlation between the sensitivity coefficients for T and S and sampling at points of maximum sensitivity.

Ir2dinv: a finite-difference model for inverse analysis of two-dimensional linear or radial groundwater flow

Abstract We have developed a program for inverse analysis of two-dimensional linear or radial groundwater flow problems. The program, lr2dinv, uses standard finite difference techniques to solve the groundwater flow equation for a horizontal or vertical plane with heterogeneous properties. In radial mode, the program simulates flow to a well in a vertical plane, transforming the radial flow equation into an equivalent problem in Cartesian coordinates. The physical parameters in the model are horizontal or x-direction hydraulic conductivity, anisotropy ratio (vertical to horizontal conductivity in a vertical model, y-direction to x-direction in a horizontal model), and specific storage. The program allows the user to specify arbitrary and independent zonations of these three parameters and also to specify which zonal parameter values are known and which are unknown. The Levenberg–Marquardt algorithm is used to estimate parameters from observed head values. Particularly powerful features of the program are the ability to perform simultaneous analysis of heads from different tests and the inclusion of the wellbore in the radial mode. These capabilities allow the program to be used for analysis of suites of well tests, such as multilevel slug tests or pumping tests in a tomographic format. The combination of information from tests stressing different vertical levels in an aquifer provides the means for accurately estimating vertical variations in conductivity, a factor profoundly influencing contaminant transport in the subsurface.

Sensitivity analysis of slug tests Part 2. Observation wells

Abstract An earlier paper (Part 1, this issue) dealt with the use of sensitivity analysis for the design of a slug test that would give reasonably accurate estimates of the aquifer parameters by an informed choice of the number and times of measurements. An investigation of the radial dependence of the Cooper et al. analytical solution for a slug test in a confined aquifer shows that the use of one or more observation wells can vastly improve the parameter estimates, particularly the estimate of the storage parameter. Generally, the observation well must be fairly close (about 10 m or less) to the slugged well to be effective. The storage coefficient must be small in order to see the effect of the slug at greater distances from the stressed well. Since the temporal and spatial dependence of the sensitivities for transmissivity and storage are considerably different, the addition of one or more observation wells will substantially reduce the correlation between these two parameters, which will result in much better estimates than are usually obtained in slug tests. These ideas are illustrated using typical data representative of our research sites.

Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.

GSLIB-style programs for discriminant analysis and regionalized classification

Abstract Discriminant analysis is a statistical technique used to predict the group membership of a set of multivariate observations, each of which is assumed to arise from one of a set of distinct classes or groups. Each group is characterized by a certain distribution in multivariate space, and group allocations are based on the similarity of each sample to each group. Assuming multivariate normality, generalized distance measures based on the squared Mahalanobis distance from each sample to each group centroid arise as the natural measure of similarity. One can allocate samples to groups either on the basis of minimum generalized distance or, equivalently, maximum posterior probability of group membership. In earth science applications samples are often associated with geographic locations. In this situation regionalized classification can be used to produce a map representing group membership throughout the sampled domain. This can be accomplished by interpolating either generalized distances or membership probabilities from sample locations to regularly spaced grid nodes and comparing resulting grids to produce a classification map. This paper presents a set of GSLIB-style FORTRAN programs for performing discriminant analysis and regionalized classification. The program disco performs discriminant analysis and the programs xmd2cls and prb2cls combine interpolated distances and probabilities, respectively, to create a grid of predicted classifications. In addition, the utility program colbind allows the user to combine selected columns from different GSLIB-style data files into one file.

Gaussian or non-Gaussian logconductivity distribution at the MADE site: What is its impact on the breakthrough curve?

The impact of the logconductivity (Y=ln K) distribution fY on transport at the MADE site is analyzed. Our principal interest is in non-Gaussian fY characterized by heavier tails than the Gaussian. Both the logconductivity moments and fY itself are inferred, taking advantage of the detailed measurements of Bohling et al. (2012). The resulting logconductivity distribution displays heavier tails than the Gaussian, although the departure from Gaussianity is not significant. The effect of the logconductivity distribution on the breakthrough curve (BTC) is studied through an analytical, physically based model. It is found that the non-Gaussianity of the MADE logconductivity distribution does not strongly affect the BTC. Counterintuitively, assuming heavier tailed distributions for Y, with same variance, leads to BTCs which are more symmetrical than those for the Gaussian fY, with less pronounced preferential flow. Results indicate that the impact of strongly non-Gaussian, heavy tailed distributions on solute transport in heterogeneous porous formations can be significant, especially in the presence of high heterogeneity, resulting in reduced preferential flow and retarded peak arrivals.

Reassessing the MADE direct-push hydraulic conductivity data using a revised calibration procedure

In earlier work, we presented a geostatistical assessment of high-resolution hydraulic conductivity (K) profiles obtained at the MADE site using direct-push (DP) methods. The profiles are derived from direct-push injection logger (DPIL) measurements that provide a relative indicator of vertical variations in K with a sample spacing of 1.5 cm. The DPIL profiles are converted to K profiles by calibrating to the results of direct-push permeameter (DPP) tests performed at selected depths in some of the profiles. Our original calibration used a linear transform that failed to adequately account for an upper limit on DPIL responses in high-K zones and noise in the DPIL data. Here we present a revised calibration procedure that accounts for the upper limit and noise, leading to DPIL K values that display a somewhat different univariate distribution and a lower lnK variance (5.9±1.5) than the original calibration values (6.9±1.8), although each variance estimate falls within the others 95% confidence interval. Despite the change in the univariate distribution, the autocorrelation structure and large-scale patterns exhibited by the revised DPIL K values still agree well with those exhibited by the flowmeter data from the site. We provide the DPIL and DPP data, along with our calibrated DPIL K values, in the supplemental materials. This article is protected by copyright. All rights reserved.