Sean Andrew McKenna

On the late‐time behavior of tracer test breakthrough curves

The authors investigated the late-time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate-limited mass transfer (e.g., in dual or multi-porosity systems) and found that the late-time concentration, c, is given by the simple expression: c = t{sub ad} (c{sub 0}g {minus} m{sub 0}{partial_derivative}g/{partial_derivative}t), for t >> t{sub ad} and t{sub a} >> t{sub ad} where t{sub ad} is the advection time, c{sub 0} is the initial concentration in the medium, m{sub 0} is the 0th moment of the injection pulse; and t{sub a} is the mean residence time in the immobile domain (i.e., the characteristic mass transfer time). The function g is proportional to the residence time distribution in the immobile domain, the authors tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression they examine the behavior of late-time concentration for a number of mass transfer models. One key results is that if rate-limited mass transfer causes the BTC to behave as a power-law at late-time (i.e., c {approximately} t{sup {minus}k}), then the underlying density function of rate coefficients must also be a power-law with the form a{sup k{minus}}, as a {r_arrow}0. This is true for both density functions of first-order and diffusion rate coefficients. BTCs with k < 3 persisting to the end of the experiment indicate a mean residence time longer than the experiment and possibly infinite, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. They apply their analysis to breakthrough curves from Single-Well Injection-Withdrawal tests at the Waste Isolation Pilot Plant, New Mexico.

Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single‐well injection‐withdrawal tests

We investigated multiple-rate diffusion as a possible explanation for observed behavior in a suite of single-well injection-withdrawal (SWIW) tests conducted in a fractured dolomite. We first investigated the ability of a conventional double-porosity model and a multirate diffusion model to explain the data. This revealed that the multirate diffusion hypothesis/model is consistent with available data and is capable of matching all of the recovery curves. Second, we studied the sensitivity of the SWIW recovery curves to the distribution of diffusion rate coefficients and other parameters. We concluded that the SWIW test is very sensitive to the distribution of rate coefficients but is relatively insensitive to other flow and transport parameters such as advective porosity and dispersivity. Third, we examined the significance of the constant double-log late time slopes (−2.1 to −2.8), which are present in several data sets. The observed late time slopes are significantly different than would be predicted by either conventional double-porosity or single-porosity models and are believed to be a distinctive feature of multirate diffusion. Fourth, we found that the estimated distributions of diffusion rate coefficients are very broad, with the distributions spanning a range of up to 3.6 orders of magnitude. Fifth, when both heterogeneity and solute drift are present, late time behavior similar to multirate mass transfer can occur. Although it is clear that multirate diffusion occurs in the Culebra, the number of orders of magnitude of variability may be overestimated because of the combined effects of drift and heterogeneity.

Field example of data fusion in site characterization

Application of data fusion to characterization of the Fountain and Lyons Formations at a field site incorporates geologic knowledge, geophysical log data, cross-hole seismic tomography, hydraulic test data, and observations of head to reduce uncertainty associated with subsurface interpretation. These formations consist of channel and overbank deposits that have undergone variable diagenesis, resulting in more hydrofacies than would have been encountered in the original, unaltered deposits. The disparate types of available data are integrated to yield a coherent hydrofacies classification through use of discriminant analysis and soft data techniques. This data fusion improves definition of the complex hydrofacies and increases knowledge of their spatial correlation. Two hundred multiple-indicator, conditional, stochastic simulations of the site are generated, 100 with only hard data and 100 with both hard and soft data. Forward groundwater flow modeling using estimates of hydraulic conductivity from field testing yields smaller head residuals for realizations which include soft data. Inverse modeling is used to eliminate hydrofacies realizations that do not honor hydraulic data and to estimate hydrofacies hydraulic conductivity ranges for the hard and hard/soft data ensembles. Inverse parameter estimation substantially decreases head residuals for both ensembles. Standard deviations of hydraulic conductivities estimated through inverse modeling are smaller when both hard and soft data are used to generate the simulations, even though head residuals are similar within the two ensembles when these estimated hydraulic conductivities are used.

Tracer tests in a fractured dolomite: 3. Double‐porosity, multiple‐rate mass transfer processes in convergent flow tracer tests

Convergent flow tracer tests conducted in the Culebra dolomite (Rustler Formation, New Mexico) are analyzed with both single- and multiple-rate, double-porosity models. Parameter estimation is used to determine the mean and standard deviation of a lognormal distribution of diffusion rate coefficients as well as the advective porosity and longitudinal dispersivity. At two different test sites both multirate and single-rate models are capable of accurately modeling the observed data. The single-well injection-sswithdrawal test provides more precise estimates of the mass transfer parameters than the convergent flow tracer tests. Estimation of the multirate distribution parameters is consistent across locations for the two types of tests. Limits of resolution are calculated for the multirate distribution, and these limits explain the precision with which the standard deviation of the multirate distribution can be estimated. These limits also explain the necessary increase in the advective porosity for the single-rate model at one location and not the other. Implications of the multirate mass transfer model at time and length scales greater than those of the tracer tests include the instantaneous equilibrium of a significant fraction of the matrix and the possibility of a fraction of the diffusive porosity not reaching an equilibrium solute concentration at long times.

UNCERT: geostatistics, uncertainty analysis and visualization software applied to groundwater flow and contaminant transport modeling

UNCERT is a 2D and 3D geostatistics, uncertainty analysis and visualization software package applied to ground water flow and contaminant transport modeling. It is a collection of modules that provides tools for linear regression, univariate statistics, semivariogram analysis, inverse-distance gridding, trend-surface analysis, simple and ordinary kriging and discrete conditional indicator simulation. Graphical user interfaces for MODFLOW and MT3D, ground water flow and contaminant transport models, are provided for streamlined data input and result analysis. Visualization tools are included for displaying data input and output. These include, but are not limited to, 2D and 3D scatter plots, histograms, box and whisker plots, 2D contour maps, surface renderings of 2D gridded data and 3D views of gridded data. By design, UNCERT’s graphical user interface and visualization tools facilitate model design and analysis. There are few built in restrictions on data set sizes and each module (with two exceptions) can be run in either graphical or batch mode. UNCERT is in the public domain and is available from the World Wide Web with complete on-line and printable (PDF) documentation. UNCERT is written in ANSI-C with a small amount of FORTRAN77, for UNIX workstations running X-Windows and Motif (or Lesstif). This article discusses the features of each module and demonstrates how they can be used individually and in combination. The tools are applicable to a wide range of fields and are currently used by researchers in the ground water, mining, mathematics, chemistry and geophysics, to name a few disciplines. # 1999 Elsevier Science Ltd. All rights reserved.

Multivariate Applications for Detecting Anomalous Water Quality

The ability to detect deliberate or accidental contamination of a water distribution system is of real concern to the safety and security of our nation’s drinking water. To address these concerns, increased attention has been placed on sophisticated monitoring of water distribution systems and the use of robust statistical analysis. Using existing data from in-situ water quality sensors, this paper explores the ability to detect anomalies in water quality using multivariate techniques. The algorithm developed in this study uses a multivariate distance measure between the current water quality measurement and the closest observation in multivariate space within a moving window of previous observations. To discriminate between normal and anomalous water quality, the distance measure is compared to a constant threshold. To test the algorithm, we utilize both simulated anomalous events and laboratory based events that correspond to real contaminants. These events are superimposed onto in-situ water quality recorded at four different locations within a single utility network. Measured water quality parameters include free chlorine, pH, temperature and electrical conductivity. Robust discrimination methods have a high probability of detecting anomalies with a low false alarm rate. Here, receiver operating characteristic (ROC) curves are used to test the ability of the multivariate classification algorithm to detect anomalous water quality while keeping false alarms low. This analysis explores the false alarm rate associated with detecting a range of anomalous water quality observations.

TESTING WATER QUALITY CHANGE DETECTION ALGORITHMS.

Rapid detection of anomalous operating conditions within a water distribution network is desirable for the protection of the network against both accidental and malevolent contamination events. In the absence of a suite of in-situ, real-time sensors that can accurately identify a wide range of contaminants, we focus on detecting changes in water quality through analysis of existing data streams from in-situ water quality sensors. Three different change detection algorithms are tested: time series increments, linear filter and multivariate distance. Each of these three algorithms uses previous observations of the water quality to predict future water quality values. Large deviations between the predicted or previously measured values and observed values at future times indicate a change in the expected water quality. The definition of what constitutes a large deviation is quantified by a threshold value applied to the observed differences. Both simulated time series of water quality as well as measured chlorine residual values from two different locations within a distribution network are used as the background water quality values. The simulated time series are created specifically to challenge the change detection algorithms with bimodally distributed water quality values having a square wave and sin wave time series, with and without correlated noise. Additionally, a simulated time series resembling observed water quality time series is created with different levels of variability. The algorithms are tested in two different ways. First, background water quality without any anomalous events are used to test the ability of each algorithm to identify the water quality value at the next time step. Summary statistics on the prediction errors as well as the number of false positive detections quantify the ability of each algorithm to predict the background water quality. The performance of the algorithms with respect to limiting false positives is also compared against a simpler “set point” approach to detecting water quality changes. The second mode of testing employs events in the form of square waves superimposed on top of modeled/measured background water quality data. Three different event strengths are examined and the event detection capabilities of each algorithm are evaluated through the use of receiver operating characteristic (ROC) curves. The area under the ROC curve provides a quantitative basis of comparison across the three algorithms. Results show that the multivariate algorithm produces the lowest prediction errors for all cases of background water quality. A comparison of the number of false positives reported from the change detection algorithms and a set point approach highlights the efficiency of the change detection algorithms. Across all three algorithms, most prediction errors are within one standard deviation of the mean water quality. The event detection results show that the best performing algorithm varies across different background water quality models and simulated event strength.

Improving groundwater project analysis with geophysical data

When interpreting the earth’s subsurface for groundwater contamination, we face a fundamental problem — we typically sample one‐millionth of the relevant material. If only these data are used to determine the material between boreholes and the continuity of high hydraulic conductivity units, the answers will be ambiguous For example, consider a site where three boreholes intersect two hydrofacies (Figure 1). If no other information is available, all of the interpretations shown (and many more not shown) are equally likely.

COMBINING WATER QUALITY AND OPERATIONAL DATA FOR IMPROVED EVENT DETECTION

Water quality signals from sensors provide a snapshot of the water quality at the monitoring station at discrete sample times. These data are typically processed by event detection systems to determine the probability of a water quality event occurring at each sample time. Inherent noise in sensor data and rapid changes in water quality due to operational actions can cause false alarms in event detection systems. While the event determination can be made solely on the data from each signal at the current time step, combining data across signals and backwards in time can provide a richer set of data for event detection. Here we examine the ability of algebraic combinations and other transformations of the raw signals to further decrease false alarms. As an example, using operational events such as one or more pumps turning on or off to define a period of decreased detection sensitivity is one approach to limiting false alarms. This method is effective when lag times are known or when the sensors are co-located with the equipment causing the change. The CANARY software was used to test and demonstrate these combinatorial techniques for improving sensitivity and decreasing false alarms on both background data and data with simulated events.

STAMMT-R Solute Transport and Multirate Mass Transfer in Radial Coordinates

An automatic boat docking system for guiding and docking a boat in a boat slip; including a pair of laterally spaced dock structures defining a boat slip therebetween and having a pair of pivoted retaining booms at the outer ends of the dock structures adjacent the entrance to the slip movable between a closed position transversely spanning the slip entrance and an open position. A cross-rope movable along the slip and a harness rope are engaged by an entering boat to swing the booms to the closed position behind the boat and wrap the boat in transversely centered position by the harness rope.