&EPA
United States
Environmental Protection
Agency
Tracer-Test Planning Using the
Efficient Hydrologic Tracer-Test
Design (EHTD) Program
-------
Cover Photo
Uranine (Acid Yellow 73) release into the underground river in Sainte Anne Cave, Belgium
(photo courtesy of Philippe Meus).
-------
EPA/600/R-03/034
April 2003
Tracer-Test Planning Using the
Efficient Hydrologic Tracer-Test
Design (EHTD) Program
National Center for Environmental Assessment-Washington Office
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
-------
DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental Protection Agency
policy and approved for publication. Mention of trade names or commercial products does
not constitute endorsement or recommendation for use.
Preferred citation:
U.S. Environmental Protection Agency (EPA). (2003)Tracer-Test Planning Using the Efficient Hydrologic
Tracer-Test Design (EHTD) Program. National Center for Environmental Assessment, Washington, DC;
EPA/600/R-03/034. Available from: National Technical Information Service, VA; PB2003-103271, and
.
-------
Contents
LIST OF TABLES vii
LIST OF FIGURES viii
PREFACE ix
ORGANIZATION OF THIS DOCUMENT x
AUTHOR and REVIEWERS xi
ABSTRACT xiv
I BACKGROUND 1
1. INTRODUCTION 2
1.1. QUICK START PROGRAM USAGE 4
1.1.1. Simple Program Usage 4
1.1.2. Example Test Files 5
2. REVIEW OF PREVIOUS TRACER TEST DESIGN METHODS 6
2.1. TRACER MASS ESTIMATION AND SAMPLING FREQUENCIES .... 7
2.1.1. Tracer Mass Estimation by Conjecture 7
2.1.1.1. Recent Arguments Opposing Rigorous Tracer Mass Estimation. 10
2.1.2. Tracer Mass Estimation by Mathematical Equation 11
2.1.2.1. Review of Tracer-Mass Estimation Equations 11
2.1.2.2. Review of Sampling Frequencies 22
2.2. EFFICIENT HYDROLOGIC TRACER-TEST DESIGN (EHTD) 23
2.2.1. Basic Design of EHTD 23
2.2.2. Range of Capabilites of EHTD 25
2.3. TRACER-TEST DESIGN RESULTS USING PREVIOUS METHODS ... 25
2.3.1. Examination of Tracer-Mass Estimation Equations 26
2.3.1.1. Porous Media 26
2.3.1.2. Karstic Media 29
2.4. EHTD ANALYSIS OF THE TWO TRACER TESTS 29
2.4.1. EHTD Results 31
2.4.1.1. EHTD Porous-Media Analysis Results 36
2.4.1.2. EHTD Karstic-Media Analysis Results 36
2.4.2. Mass Required as Related to Sorption by Detectors 36
2.5. TRAVEL TIMES AND SAMPLING FREQUENCIES 37
2.5.1. Travel Times 37
2.5.2. Sampling times 37
2.5.2.1. Porous Media Sampling Times 38
in
-------
2.5.2.2. Karstic Media Sampling Times 38
2.6. NOTATIONS FOR SECTION 2 38
II MODEL THEORY AND METHOD DEVELOPMENT 41
3. TRACER-TEST DESIGN METHODOLOGY 42
3.1. SOLUTE-TRANSPORT MODELING 42
3.2. TRACER MASS ESTIMATION 43
3.2.1. Model Solutions 44
3.2.1.1. Impulse Release for BVP 44
3.2.1.2. Pulse Release for BVP 45
3.2.1.3. Uniform Initial Concentration (IVP) 46
3.2.1.4. Exponential Production (PVP) 46
3.2.2. Tracer Retardation and Tracer Decay 47
3.3. SOLUTE TRANSPORT 47
3.4. HYDRAULIC AND GEOMETRIC PARAMETERS 48
3.4.1. Measured Parameters 48
3.4.2. Functional Relationships 48
3.4.3. Travel Time Estimates 50
3.5. CONTINUOUS STIRRED TANK REACTOR (CSTR) 51
3.5.1. Travel Times and Velocity 52
3.5.2. Tracer Dispersion Estimates 52
3.5.2.1. Estimating Dispersion by the Method of Moments 52
3.5.2.2. Estimating Dispersion by the Chatwin Method 53
3.6. TRACER SAMPLE COLLECTION DESIGN 54
3.6.1. Sample Collection 54
3.6.1.1. Sampling Frequency 54
3.6.1.2. Initial Sample Collection 55
3.7. METHODOLOGY EVALUATION 55
3.7.1. Simulation 57
III BASIC PROGRAM USAGE 64
4. USING EHTD TO DESIGN A TRACER TEST 65
4.1. EHTD PROGRAM USAGE AND EXAMPLE DATA FILES 65
4.1.1. Loading EHTD and Example Data Files 65
4.2. EHTD EXECUTION 66
4.3. USER-REQUESTED LATIN HYPERCUBE SAMPLING (LHS) ROUTINE 70
4.4. USER-SUGGESTED SOLUTE MASS 72
4.5. SCREEN OUTPUT 74
4.5.1. Screen Output of Error Messages 75
4.5.1.1. Warning Messages 75
IV
-------
4.5.1.2. Error Messages 75
4.5.2. Screen Output of Optimization Results 77
4.6. COMPUTER GRAPHICS 78
4.6.1. Features of the Interactive Graphics Loop 78
4.6.1.1. File 81
4.6.1.2. Edit 81
4.6.1.3. View 81
4.6.1.4. State 81
4.6.1.5. Window 82
4.6.1.6. Help 82
4.7. EHTD SOURCE 82
5. EHTD USE OF INPUT FILES 83
5.1. DESCRIPTION OF INPUT FILES 83
5.1.1. Line-by-Line Description of Input Files 89
6. EHTD OUTPUT FILES 97
6.1. DESCRIPTION OF OUTPUT FILES 97
6.1.1. EHTD-Produced Data Output Files 105
6.1.1.1. Data Output File Header Material 105
6.1.1.2. Input Data Units 105
6.1.1.3. Initial Data Input Reprise 105
6.1.1.4. Sampling Station Name 105
6.1.1.5. Table 1.1. Input Factors 115
6.1.1.6. Output Data Units 115
6.1.1.7. Table 2.1.1. Initial Hydraulic Factors 115
6.1.1.8. Table 2.1.2. Final Hydraulic Factors 115
6.1.1.9. Table 3.1. Final Tracer Mass Estimate 115
6.1.1.10. Table 4-1- Estimated Sampling Frequency 116
6.1.1.11. Calculated Tracer-Mass 116
6.1.1.12. Error Codes 116
6.1.1.13. Recommended Tracer-Mass 116
6.1.1.14. Date and Time of Processing 116
6.2. THE QUALITY OF EHTD-PREDICTED RESULTS 117
6.3. EFFECT OF INITIAL CONCENTRATION AND EXPONENTIAL PRO-
DUCTION 118
6.3.1. Effect of an Initial Concentration 118
6.3.2. Effect of Exponential Production 118
6.3.3. Breakthrough Curve Shape 118
6.3.4. Average and Peak Concentration Estimates 125
v
-------
7. TRACER TEST DESIGN EXAMINATION DATA SETS 128
7.1. FLOWING STREAMS 128
7.1.1. Small Creek 129
7.1.2. Large River 129
7.1.3. Solution Conduit 129
7.1.4. Meltwater Channel 130
7.2. POROUS MEDIA 130
7.2.1. Natural-Gradient Tracer Test 130
7.2.2. Forced-Gradient Tracer Test 131
7.2.3. Injection-Withdrawal Tracer Test 131
7.2.4. Recirculation 132
7.3. TRACER-TEST DESIGN RESULTS 132
7.3.1. Flowing Streams Results 133
7.3.1.1. Uvas Creek Tracer Test 133
7.3.1.2. Missouri River Tracer Test 137
7.3.1.3. Dyers Spring Tracer Test 138
7.3.1.4. Variegated Glacier Tracer Test 140
7.3.2. Porous Media Results 141
7.3.2.1. Test Site Wilerwald Tracer Test 145
7.3.2.2. Kirchdorf-Unteropfingen Tracer Test 146
7.3.2.3. Mobile Site Tracer Test 148
7.3.2.4. Chalk River Site Tracer Test 149
IV ADDITIONAL APPLICATION OF EHTD 151
8. APPLICATION OF EHTD TO SUPPORT RISK ASSESSMENTS 152
8.1. EXPOSURE ASSESSMENT OVERVIEW 152
8.2. FORECASTING POLLUTION FOR RISK ASSESSMENTS 154
8.2.1. Dimensionless Dye-Recovery Curve 154
8.2.2. EHTD for Forecasting pollution Effects 154
8.2.2.1. Using EHTD Directly to Forecast Pollution 155
8.2.2.2. Using the LHS-Routme m EHTD to Forecast Pollution. . . 156
9. SUMMARY AND CONCLUSIONS 159
NOTATIONS 162
REFERENCES 166
VI
-------
List of Tables
1 Average dye manufacturers' purities for selected powder dyes 9
2 Percent pure dye content for selected fluorescent dyes 10
3 Some equations for estimating tracer injection mass 12
4 Aquifer and tracer-dependent coefficients TCl — TC4 15
5 Aquifer and tracer-dependent coefficient Tc& 17
6 Tracer dependent coefficient TC& 17
7 Prevailing test conditions coefficient Tc7 18
8 Tracer-dye mass per 1000 m of traced distance 20
9 General sampling schedule for a karst terrane 24
10 Specific sampling schedule for a karst terrane 24
11 Tracer test design parameters 27
12 Tracer-mass estimates 28
13 EHTD tracer test design parameters 30
14 EHTD tracer test analysis results 32
15 Tracer-dye mass per 1000 m of traced distance 35
16 Tracer test design parameters 57
17 Predicted tracer mass and tracer concentration 59
18 Recommended sampling times for selected tracer reaction conditions 61
19 Table illustrating the form of the EHTD-created plot file 69
20 Variable parameter types used in the LHS routine 72
21 Screen display of a typical EHTD warning message 75
22 Screen display of a typical EHTD warning message 76
23 Typical screen display of optimization results 77
24 Pull-down menu items available in EHTD 80
25 Description of the input file components listed in Figures 10 and 11 86
26 Example test data sets 128
27 Required flowing stream tracer test design specifics 133
28 EHTD-predicted BTCs versus measured BTCs for the flowing stream tracer
tests 134
29 EHTD-predicted results versus measured results for the flowing stream tracer
tests 135
30 Required porous media tracer test design specifics 142
31 EHTD-Predicted BTCs versus measured BTCs for the porous media tracer
tests 143
32 EHTD-predicted results versus measured results for the porous media tracer
tests 144
vn
-------
List of Figures
1 EHTD results for an impulse release for the porous media test parameters. . 33
2 EHTD results for an impulse release for the karstic test parameters 33
3 EHTD results for a pulse release for the porous media test parameters. ... 34
4 EHTD results for a pulse release for the karstic test parameters 35
5 Preliminary ETC from a hypothetical CSTR 58
6 Predicted ETC for Prospect Hill Spring for retardation effects 59
7 Predicted ETC for Prospect Hill Spring for tracer decay effects 60
8 Initial EHTD screen title 67
9 Equations used to calculate univariate statistics for an input file 73
10 Generic example of an flowing stream input file format 84
11 Generic example of an porous media input file format 85
12 Typical example input file 98
13 Standard-form example ETC 99
14 Data file used to produce Figure 13 100
15 Standard-form example output file 106
16 Comparison of EHTD-predicted ETC to measured ETC 117
17 Example input file with an initial concentration and exponential production
constants 119
18 Data file used to produce Figure 19 120
19 Effect of including an initial concentration and exponential production . . . 125
20 Comparison of the effect of including an initial concentration and exponential
production 126
21 Modified EHTD-produced portion of Table 3.1 127
22 Example EHTD-produced Table 5.1 127
23 Comparison of measured data for the Uvas Creek site tracer test 136
24 Comparison of measured data for the Missouri River tracer test 138
25 Comparison of measured data for the Dyers Spring tracer test 139
26 Comparison of measured data for the Variegated Glacier tracer test 140
27 Comparison of measured data for the Test Site Wilerwald tracer test .... 145
28 Comparison of measured data for the Kirchdorf-Unteropfingen site tracer test 147
29 Comparison of measured data for the Mobile site tracer test 148
30 Comparison of measured data for the Chalk River site tracer test 150
31 Uncertainties associated with exposure assessments 153
32 Seven BTC's developed by the U.S. Geological Survey 155
33 Standardized curve- and EHTD-predicted ETC for Dyers Spring 157
34 LHS-generated input file of means using the Dyers Spring parameters 158
vin
-------
PREFACE
The National Center for Environmental Assessment has prepared this document for the
benefit of the U.S. Environmental Protection Agency regional offices, states, and the general
public because of the need to develop a fast and easy method for designing tracer tests in
hydrologic systems. Application of the methodology described in this document can provide
individuals with the information necessary for designing reliable and safe tracer tests while
eliminating much of the guesswork typical of first time tracer testing in a new environment.
The purpose of this document is to serve as a technical guide to various groups who
must address potential or existing contamination problems in hydrologic systems. Tracing
studies are always appropriate and probably necessary, but initial design work is usually
relegated to guesses as to the amount of tracer to release and when to collect samples. This
document and associated computer programs alleviate some of these problems.
The Efficient ^Hydrologic ^Tracer-test Design (EHTD) program uses a few basic field
measurements combined in functional relationships that are coupled with the concept of a
continuous stirred tank reactor and solute-transport theory to develop the basic design of
a tracer test. Initial solute-transport parameters are produced by EHTD, which although
imprecise because they are only predictive, still provide adequate information for effective
tracer-test design.
EHTD produces a detailed assessment of expected tracer-test results before a tracer
test is ever initiated. It also produces a likely tracer-breakthrough curve for each sampling
station. Preliminary testing of EHTD has shown it to be reliable in most instances. It
is believed that as EHTD is used, improvements in its design will grow as suggestions are
made.
IX
-------
ORGANIZATION OF THIS DOCUMENT
This document serves as a "user's manual" for the computer program EHTD. It is arranged
in four parts:
• Part I Background
• Part II Model Theory and Method Background
• Part III Basic Program Usage
• Part IV Additional Application of EHTD
Part I introduces the program and provides the necessary for the new user to begin
running the program immediately. This is then followed by an in-depth review and
discussion of previous attempts at tracer test design.
Part II consists on a single section that is a comprehensive discussion of the relationship
between solute-transport theory and tracer test design as applied by EHTD. This section
will most likely be of interest to the more academic-type of scientists and engineers. More
practically-oriented individuals will likely want to skip reading this section.
Part III discusses the basic usage of EHTD. Section 4 explains how to run EHTD
including usage of the pull-down menus for manipulating screen display. Section 5 covers the
creation/modification of the input file read by EHTD. Section 6 is a detailed examination
of the output files produced by EHTD. Lastly, Section 7 validates EHTD functioning by
comparing the EHTD predictions for eight selected examples with actual tracer-test results.
Part IV also consists of just a single section that explains how EHTD can be used to
forecast the potential effects of inadvertent or deliberate pollutant releases. In addition, it
briefly illustrates the development of an input file of mean values for parameters created by
a Latin Hypercube Routine.
x
-------
AUTHOR AND REVIEWERS
The National Center for Environmental Assessment within the U.S. Environmental Pro-
tection Agency's Office of Research and Development was responsible for preparing of this
document and provided overall direction and coordination during the production effort.
AUTHOR
Malcolm S. Field, Ph.D.
National Center for Environmental Assessment
Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C.
REVIEWERS
Feike J. Leij, Ph.D.
U.S. Salinity Laboratory
450 West Big Springs Road
Riverside, Ca.
Philippe Meus, Ph.D.
Ministere de la Region wallonne
Direction generale des Ressources naturelles
et de I'Environnement
Division de 1'Eau
Direction des Eaux souterraines
avenue Prince de Liege 15
B-5100 Jambes (Namur)
Belgique
Arthur N. Palmer, Ph.D.
Earth Sciences Department
209 Science Building 1
State University of New York
Oneonta, N.Y.
Michael Verrault, M.Sc.A
Centre d'etudes sur les ressources minerales
Universite du Quebec a Chicoutimi
Chicoutimi, Quebec
Canada
Laboratoire d'Etude des Transferts en
Hydrologie et Environnement (LTHE)
1023 rue de la Piscine
BP 53, Domaine Universitaire
F-38041 Grenoble, Cedex 9, Frnace
European Water Tracing Services
rue de la Chapelle 43
B-4550 Nandrin
Belgique
Les Laboratoires SL
1309, blv St-Paul
Chicoutimi, Quebec
Canada
XI
-------
ABSTRACT
Hydrological tracer testing is the most reliable diagnostic technique available for estab-
lishing flow trajectories and hydrologic connections and for determining basic hydraulic
and geometric parameters necessary for establishing operative solute-transport processes.
Tracer-test design can be difficult because of a lack of prior knowledge of the basic hydraulic
and geometric parameters desired and the appropriate tracer mass to release. A new effi-
cient hydrologic tracer-test design (EHTD) methodology has been developed that combines
basic measured field parameters (e.g., discharge, distance, cross-sectional area) in functional
relationships that describe solute-transport processes related to flow velocity and time of
travel. The new method applies these initial estimates for time of travel and velocity to a
hypothetical continuously stirred tank reactor as an analog for the hydrologic flow system to
develop initial estimates for tracer concentration and axial dispersion, based on a preset av-
erage tracer concentration. Root determination of the one-dimensional advection-dispersion
equation (ADE) using the preset average tracer concentration then provides a theoretical
basis for an estimate of necessary tracer mass.
Application of the predicted tracer mass with the hydraulic and geometric parameters
in the ADE allows for an approximation of initial sample-collection time and subsequent
sample-collection frequency where a maximum of 65 samples were determined to be
necessary for describing the predicted tracer-breakthrough curve (ETC). Inclusion of tracer
retardation and decay cause a net increase in tracer-mass estimates so that the preset
average tracer concentration will be maintained, with a consequent steepening of the ETC,
but retardation also causes ETC spreading and a delay in tracer arrival.
Determining the necessary tracer mass, the initial sample-collection time, and the
subsequent sample-collection frequency for a proposed tracer test are the three most difficult
aspects to estimate prior to conducting the test. To facilitate tracer-mass estimation, 33
mass-estimation equations have been developed over the past century. The 33 equations
are reviewed here; 32 of them were evaluated using previously published tracer-test design
examination parameters. Comparison of the results produced a wide range of estimated
tracer mass, but no means is available by which one equation may be reasonably selected
over the others. Each equation produces a simple approximation for tracer mass. Most
of the equations are based primarily on estimates or measurements of discharge, transport
distance, and suspected transport times.
Although the basic field parameters commonly employed are appropriate for estimating
xn
-------
tracer mass, the 33 equations are problematic in that they were all probably based
on the original developer's experience in a particular field area and not necessarily on
measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies
are typically based primarily on probable transport distance, but with little regard to
expected travel times. This too is problematic in that tracer sampling remains a haphazard
process that tends to result in false negatives or data aliasing.
Simulations from the recently developed EHTD methodology were compared with those
obtained from 32 of the 33 published tracer-mass estimation equations and suggested
sampling frequencies. EHTD applies functional relationships developed from hydrologic
measurements in a solute-transport model to develop a preliminary ETC that has been
shown to reasonably predict actual tracer-test results.
Effective tracer-test design requires that the likely results be predicted in advance of test
initiation to ensure tracer-testing success. EHTD-predicted BTCs for various hydrological
conditions were compared with measured BTCs obtained from actual tracer tests. The
hydrologic conditions for the tracer tests ranged from flowing streams to porous-media
systems. The tracer tests evaluated included flowing streams tracer tests conducted in
small and large surface-water streams, a karst solution conduit, and a glacial-meltwater
stream and porous-media systems conducted as natural-gradient, forced-gradient, injection-
withdrawal, and recirculation tracer tests.
Comparisons of the actual tracer tests and the predicted results showed that tracer
breakthrough, hydraulic characteristics, and sample-collection frequency may be forecasted
sufficiently well in most instances to facilitate good tracer-test design. However, comparisons
were generally improved by including tracer decay and/or retardation in the simulations.
Inclusion of tracer decay in the simulations also tended to require an increase in set average
tracer concentration to facilitate matching peak concentrations in the measured BTCs.
Both nonreactive tracer and reactive tracer predictions produced recommended sample-
collection frequencies that would adequately define the actual BTCs, but estimated tracer-
mass estimates were less precise.
EHTD may also be used to facilitate drinking-water protection strategies. EHTD pro-
vides water managers with the ability to conduct release-scenario simulations by overriding
the set average concentration. The simulations can be used to predict toxic substance ar-
rival times (time to leading edge, time to peak, persistence), axial dispersion, dilution, and
arrival concentrations. By combining the EHTD-simulation results with risk assessment
analyses for acute exposures, water managers can develop a set of alternatives as part of an
xiii
-------
overall strategy for protecting human health. This set of alternatives could range from no
action (i.e., no significant concern) to disconnecting the water-supply system, announcing
a no-contact warning, and arranging for the supply of an alternative water source.
xiv
-------
Part I
BACKGROUND
Flow of diluted uranine (Acid Yellow 73) through Sainte Anne Cave, Belgium. The tracer
release is depicted on the cover of this document (photo courtesy of Philippe Meus).
-------
1. INTRODUCTION
Tracer tests are regularly applied in many hydrologic systems to determine various
hydraulic and geometric parameters. However, the success of a tracer test depends on
the release of sufficient—but not excessive—tracer material into the flow regime for reliable
tracer detection based on appropriate initial sample collection time and sampling frequency.
Determination of the optimal quantity of tracer material to release into a flow system to
maximize the probability of achieving positive results while maintaining safe concentrations
in the environment and minimizing public concern has been of considerable interest for a
long time.
To maintain safe tracer concentrations and to minimize public concerns regarding colored
water, Field et al. (1995) suggested that fluorescent dye concentrations at downstream
receptors be maintained at or below 1-2 mg L"1. They arrived at these concentrations by
conducting an in-depth evaluation of available toxicological information on 12 fluorescent
dyes and one dye intermediate using a U.S. Environmental Protection Agency (EPA)
approved assessment method for cases where actual data were lacking. Field et al. urged
the use of only that quantity of tracer dye actually needed to ensure positive results. The
use of significantly more than is needed might adversely affect the environment and human
health, although the degree of adversity was not quantified. In addition, excessive amounts
of tracer could compromise tracer test interpretations. However, determining the adequate
and safe amounts of tracer substance, dye or otherwise, to use in a tracing study can be
difficult (Kafi, 1998, p. 327).
An optimal tracer mass that meets both hydrologic and environmental criteria is
dependent on a number of relatively indeterminate factors, such as the volume of water that
dilutes the tracer, hydrological conditions during high-flow and low-flow periods, residence
time, number and direction of discharge points, transport distance(s), sorption, decay, and
degree and type of pollution. Therefore, the quantity of tracer needed for release at any
particular site and time may be significantly different from that needed at another site or
at the same site at another time.
For example, a preliminary tracer test at a Superfund site in Tennessee using 0.7g of
Rhodamine WT resulted in a conventional, positively skewed tracer-breakthrough curve
(ETC) and nearly 100% mass recovery (Field and Pinsky, 2000). A subsequent tracer test
at the same site 48 hours later using 71 g of Rhodamine WT produced a very abrupt ETC
with a very long tail and only 28% mass recovery. A large storm that preceeded the second
-------
tracer test was deemed responsible for the differing results (Field and Pinsky, 2000).
To alleviate some of the difficulties associated with estimating the mass of tracer to be
released, numerous empirical equations have been developed by various individuals (Field,
2002a). In nearly every instance these equations appear to have been devised without
regard to solute transport theory and, at times, without regard to site hydrology. Rather,
they appear to have been developed solely as a result of the developer's experience from
one or more tracer tests. Also, in many instances various—and sometimes unexplained—
multipliers are incorporated into the equations to account for potentially inadequate tracer
mass estimates (Field, 2002a).
Initial sample collection times and sampling frequencies are also generally unknown
quantities because solute fluxes are typically unknown. However, application of functional
relationships developed from measured parameters can be used to estimate solute transport
parameters. The determination of solute transport parameters translates into appropriate
sampling frequencies.
The purpose of this paper is to answer three basic questions common at the start of
any hydrologic tracer test: (1) How much tracer mass should be released? (2) When should
sampling start? and (3) At what frequency should samples be collected? In this paper
an efficient hydrologic tracer test design (EHTD) methodology for estimating tracer mass
based on solute transport theory is developed. Use of the methodology developed here leads
to a better understanding of the probable transport processes operating in the system prior
to conducting the tracer test. Improved understanding of the transport processes then leads
to better estimates of tracer mass to be released. In addition, initial sample collection times
and sample collection frequencies are calculated using solute transport theory.
Although this tracer-design methodology is expected to be reliable in most instances, it
does not address the common occurrences of multimodal BTCs and long-tailed BTCs be-
cause such BTCs require much more complex analyses with numerous unknown parameters
(Maloszewski et al., 1992a; Toride et al., 1993). Density-induced sinking effects that may
occur in natural gradient porous-media tracer tests (Oostrom et al., 1992; Barth et al., 2001)
are also not addressed. The methodology introduced here is tracer independent, whereas
density-induced sinking is a tracer-dependent process and requires a separate analysis to
determine how much, if any, tracer sinking may occur.
-------
1.1. QUICK START PROGRAM USAGE
Begin by copying all EHTD files (i.e., Ehtd.exe., Grfont.dat, Rgb.txt, and *.in) to the hard
drive of a computer. (See Section 4.1.1. on page 65 for a detailed discussion on the copying
of EHTD files to a hard drive.) Once stored on the hard drive, EHTD is ready to be run.
(NOTE: EHTD functions best with a display = 1024 x 768 pixels; adequately with a display
= 800 x 600 pixels; and not so well for further reduced display settings.)
1.1.1. Simple Program Usage
To run EHTD, please perform the following:
1. Execute the EHTD.exe file by Left Double-Clicking on it using a mouse.
2. Follow on screen instructions:
(a) Press to run the default input file (i.e.,EHTD. in),
(b) Press to create the default output name (i.e.,EHTD.out),
(c) Press to skip producing a PostScript plot file.
3. Use the pull-down menus to manipulate the plot. For example:
FILE: To save a BITMAP file of the screen plot or print.
VIEW: To change the screen display to view the entire plot all at once.
WINDOW: Move from GRAPHIC2 (plot screen) back to GRAPHIC 1
(text display screen) for additional computation.
In the GRAPHIC 1 (text display screen) screen press for completion of EHTD
(i.e., writing of all output data to the output file). If this step is not completed then
some computational results (e.g., final tracer mass estimate) will not be written to
the output file.
-------
Note: It is essential that the program be ended by moving from the GRAPHIC2 screen
to the GRAPHIC 1 screen using the WINDOW pull-down menu and that be
pressed so that final computational results may be recorded in the output file and that
all requested plot files get created. Also, a date/time stamp is written to the bottom
of the file.
4. Open the output file and/or the plot file created using a standard Windows viewer
(e.g., Notepad) to see the results.
1.1.2. Example Test Files
The following example data files are provided on the CD-ROM that accompanies this docu-
ment so that the user may examine the functioning of EHTD under differing environmental
conditions:
Clarkef .in Single spring discharge site for a complexly folded karst terrane
(Field, 2000)
Clarke2.in1 Multiple spring discharge sites for a complexly folded karst terrane
(Field, 2000)
Mull.in Karst window to spring tracer test (Mull et al., 1988a, pp. 61-66)
Lost.in Lost River Cave System (Field and Pinsky, 2000)
Gl.in Tenn. example from a quarry (Davies, pers. comm.}
G2.in Tenn. example from a quarry (repeat tracer test of above)
Missl.in Surface water tracer test example (Yotsukura et al., 1970, pp. G3-G6)
Miss2.in Surface water tracer test example (repeat tracer test of above)
Step.in Created example for continuous release
Borden.in Borden tracer test (Mackay et al., 1986)
Ehtd.in Injection-withdrawal test example (default)
(Molz et al., 1986a, pp. 52-60, 71)
Chalk.in Recirculation test example (Huyakorn et al., 1986)
1EHTD sums total estimated tracer mass to be released at the end of the program.
-------
2. REVIEW OF PREVIOUS TRACER TEST DESIGN METHODS
Quantitative hydrologic tracer testing is the most reliable method for establishing
solute transport trajectories and for defining solute transport parameters. Determining the
necessary tracer mass to release, when to start collecting samples, and at what frequency
all subsequent samples should be collected can be very difficult to estimate, especially in
karstic terranes. In most tracing studies in karstic terranes, design efforts are focused on
predicting where tracer will arrive and where best to release tracer. The tracer mass released
is typically a guess based on the experience of the practitioner. Although attempting to
predict where the tracer will arrive and where best to release the tracer are important and
valuable aspects of conducting a tracer test, guessing the appropriate tracer mass to release
is a fallacious practice that almost ensures that too much or too little tracer will be released.
To facilitate the determination of necessary tracer mass for a successful tracer test,
at least 33 tracer mass estimation equations have been developed over the last century.
Although a considerable improvement over the typical method of guessing an appropriate
tracer mass to release, these equations are also problematic. With the exception of two
equations, they were all developed on the false assumption that a simple algebraic expression
that appears to function adequately for a selected hydrologic setting will then adequately
function in all hydrologic settings. In addition, these equations fail to properly account for
the important effects of axial dispersion and solute transport theory (Field, 2002a).
Tracer test sample collection frequency in karstic terranes is typically a haphazard pro-
cedure based on expected transport distance and supposed travel time. The haphazardness
of sample collection is further exacerbated when qualitative tracing tests are conducted. In
general, a preliminary sample collection frequency is determined before the tracing test is
initiated but is subject to revision during the tracer test as time passes with or without
tracer recovery.
In this paper, the 33 tracer mass estimation equations are briefly reviewed; 32 were
evaluated using previously published tracer test design-examination parameters. For this
review, unless otherwise indicated, the published tracer mass estimation equations were
all probably intended to estimate the mass of tracer on an "as-sold basis," which often
necessarily includes a large quantity of diluent. In addition, conventional sample collection
frequency determinations are briefly reviewed. The results of the review and examination of
the 33 mass estimation equations and the typical sampling frequencies are compared with
the recently developed EHTD method that has been shown to be theoretically sound and
6
-------
more reliable than previous methods.
2.1. TRACER MASS ESTIMATION AND SAMPLING FREQUENCIES
Hydrologic tracing requires that an appropriate mass of tracer be released such that de-
tectable concentrations of the tracer may be recovered at the sampling stations. Commonly,
an estimate of the mass of tracer to release consists of nothing more than a guess that is
sometimes based on the general experience of particular individuals (Alexander and Quin-
lan, 1992, p. 19; Aley, 1999, p. 14) or on prior experience at the location to be traced (e.g.,
Meigs and Beauheim, 2001). Other times, the guess is whatever sounds good at the time. In
rare instances, a tracer mass estimation equation may be used to determine the appropriate
tracer mass to release. Although general tracing experience is beneficial and specific site
experience is better still for determining the quantities of tracer to release, neither approach
may be regarded as scientifically rigorous. Worse, the former suggests that only select indi-
viduals are adequately qualified to assess tracer needs, and the latter suggests the possibility
of numerous tracer release efforts at a site before success may be obtained.
2.1.1. Tracer Mass Estimation by Conjecture
There are four reasons beyond practical experience that may explain why a guess is used to
estimate the necessary tracer mass to release. The first is the over-reliance on qualitative
tracing in karstic terranes using common fluorescent dyes. Qualitative tracing is the use of
packets of activated carbon (commonly known as "detectors" or "bugs" in North America
and "fluocapteurs" in France) to sorb the fluorescent dye as it exits the underground. This
method is believed to facilitate karst tracing in that these detectors can be distributed
throughout the area where tracer dye is expected to exit the subsurface and may be collected
when convenient.
Although qualitative tracing is commonly applied in Great Britain and the United
States, the method is scientifically untenable because false-positive results (Gunn and
Lowe, 2000; Lutz and Parriaux, 1988) and false-negative results (Smart et al., 1986) are
common. Sorption onto detectors allows for reduced tracer dye concentrations because
activated carbon reportedly increases tracer dye concentrations 400 times the concentration
in water (Aley, 1999, p. 21), although published research suggests that dye concentration
by activated carbon is probably 3 to 4 times the concentration in water but may be as high
as 1000 times the concentration (Kafi, 1998, pp. 100-103).
Unfortunately, activated carbon also enhances background concentrations (fluorescent
7
-------
dyes and other similarly appearing compounds), which may be advantageous for visual de-
termination of dye but which adversely affects the signal-to-noise ratio of modern analytical
instruments (Worthington, pers. comm.}. Excess sorption of background concentrations re-
quires that the estimated tracer dye concentration to be released exceed background concen-
trations at the sampling stations by fO times to ensure detection (Crawford, pers. comm.},
an undesirable practice from both an aesthetic and an ecological perspective (Smart and
Karunaratne, 2001).
Excessive and extensive background sorption also causes ambiguous results, erroneously
suggesting tracer recovery at most or all of the sampling stations (McCann and Krothe,
1992) because the method does not lend itself to establishing that the sorbed and "identified"
compound is in fact the fluorescent dye of interest. Even more basic, it may be regarded as
nonsense on its face. By requiring an injection concentration that results in a downstream
concentration >10 times background, it is assumed that a multitude of background samples
(typically three) have been collected and that the maximum concentration or some statistical
value (e.g., mean, median, etc.) for which a 10-fold increase is intended was used as
a measure. Second, it is very difficult to translate an upstream concentration at a
ground-water injection point into a downstream concentration. Third, the method for
this calculation requires appropriate field measurements and numerical analysis, which are
typically avoided.
More recent research suggests that fluorescent dye sorption by detectors may not be as
straightforward as once thought. Research at the University of Minnesota (Davies, pers.
comm.} suggests that the occurrence of false negatives and false positives may occur far
more frequently than has previously been recognized, primarily because of the vagaries
of fluorescent dye sorption/desorption by the detectors. For example, sodium fluorescein
(uranine [45350 C.I. Acid Yellow 73]) was found to be readily sorbed by activated carbon,
but it was also desorbed almost immediately. Rhodamine WT (C.I. Acid Red 388),
however, was not readily sorbed and was difficult to elute. The rapid sorption-desorption
of short-wavelength dyes and the slow sorption and difficult elution of long-wavelength dyes
compromise the use of activated carbon for detection (Smart and Simpson, 2001).
Other peculiarities related to sorption by activated carbon and sample handling (Smart
and Friederich, 1982; Smart and Zabo, 1997) also prevent replication of the results, a basic
requirement of any scientific endeavor. The difficulties are further exacerbated by the
fluorescence spectra shift caused by the high j>H of the elutants (Kafi, 1998, p. 102). In
addition, specific tracer types may result in varying sorptive behaviors (Sutton et al., 2001).
8
-------
Table 1. Average dye manufacturers' purities for selected powder dyes.
Colour Index
Generic Name
Acid Red 9
Acid Red 52
Acid Red 87
Acid Red 388
Acid Yellow 73
Basic Violet 10
Fluorescent
Brightener 351
Solvent Green 7
Common Name Colour Index
Constitution No.
erioglaucine
Sulpho Rhodamine B
eosin
Rhodamine WT
Na-fluorescein
Rhodamine B
Tinopal CBS-X
pyranine
42090
45100
45380
45350
45170
59040
Average Puritya
Range, %
73-75
85-90
65-70
82-85
75
90
60
80
a Values are for the "crude" form of the dyes only.
The second reason the tracer mass to be released is guessed at stems from the lack
of knowledge regarding the volume and degree of spreading necessary for estimating the
extent of tracer dilution. Sorptive characteristics of the transport medium and tracer are
also typically unknown. Although surface-water volume and degree of spreading can be
reasonably estimated, aquifer volume and degree of spreading remain virtual unknowns
until a quantitative tracer test is conducted and numerically evaluated. Understanding
tracer losses due to tracer sorption generally requires extensive testing and analysis using a
selected tracer and specific materials and the results are not readily transferable.
A third reason why necessary tracer masses are guessed at may relate to the relative
purities of the various fluorescent dyes supplied by different manufacturers. Table 1 lists the
average dye manufacturers' purities of some common fluorescent dyes used for hydrological
tracing and Table 2 lists the average percent pure dye content of the dyes supplied by one
distributor. This range of fluorescent dye purities complicates the determination of dye
mass to release.
The fourth and final reason that the tracer mass to release is guessed is because of the
relative obscurity, confusing nature, and inconsistency surrounding the use of existing tracer
mass estimation equations. In general, these equations have been found to be less exact
than is commonly desired (Kafi, 1998, p. 323).
-------
Table 2. Percent pure dye content for selected fluorescent dyes.
Tracer Dye
(Common Name)
erioglaucinec
Sulpho Rhodamine B
eosin
Rhodamine WTd
Na-fluorescein
Rhodamine Be
Tinopal CBS-X
pyranine
Powder Dyea
Content, %b
74.0
90-92.0
86.0
85.0
60.0
90.0
60.0
80.0
Liquid Dyea
Content, %b
37.0
18.0
26.0
17.0
30.0
45.0
a Values listed are within ±5.0%.
b % = ^^ x 100.
L-o Abs
c Erioglaucine is also sold with a Food, Drug and Cosmetic (FD&C) purity
equal to 92.0%.
d Rhodamine WT is not commercially available in powder form and rarely
exceeds 18% purity in liquid form.
e Rhodamine B as a liquid is mixed with glacial acetic acid.
Note: The values listed are specific to one manufacturer — crude dye
stocks can and will vary significantly with manufacturer.
2.1.1.1. Recent Arguments Opposing Rigorous Tracer Mass Estimation. It
has recently been argued that a rigorous approach to estimating tracer mass is unnecessary.
It has further been argued that promoting such an endeavor may lead to uninformed
regulators' deciding the mass of tracer necessary for the proposed experiment. However,
neither of these arguments is justifiable.
The argument suggesting that a rigorous tracer-mass estimation is an unnecessary effort
is promoted by those individuals who have traditionally relied on the method of conjecture
as a means for estimating tracer mass. Conjecture abrogates the need for taking time-
consuming field measurements and it suggests and air of all-knowing by the conjecturer. It
may just be adequate for these individuals because they are uninterested in conducting
a quantitative tracer test. A qualitative trace that only roughly approximates tracer
trajectories and velocities is all that is desired, so a good estimate of tracer mass to release
is not considered because of the vagaries of tracer sorption by activated carbon.
The argument that inexperienced or "know-nothing" regulators will begin deciding
appropriate tracer masses may be regarded as fallacious. It is a useful scare tactic often
10
-------
employed to keep regulators away and to further the perception of the "all-knowing" expert.
More significantly, however, it may be appropriate for regulators to estimate tracer masses
if they are going to be taking the necessary field measurements that the tracer hydrologists
are avoiding. If nothing else, it provides the regulator with a useful check on the conjecturer.
2.1.2. Tracer Mass Estimation by Mathematical Equation
Many equations for calculating the amount of tracer material to release into a flow system
have been published. Thirty-three empirically determined equations are considered here
(Table 3) (see Section 2.6., page 38 for a description of the parameters used in Table 3).
It will be noted that some of the equations listed in Table 3 do not appear in original
form, as they have been modified for consistency of units and to yield mass in grams. An
examination of these equations reveals little about each except that most rely to some extent
on volumetric flow rate (discharge). Presumably, the reliance on discharge by the originators
of the equations was intended to address probable dilution effects. The 33 equations were
developed empirically, so maintaining mass balance appears not to have been an important
consideration. Although not apparent from Table 3, 5 of the 33 equations incorporate
different systems of measurement in their original form.
Sources for the equations were not always specific about which type of tracer a particular
equation was meant for in the design or about whether it even matters, but most were
probably designed for the fluorescent dye Na-fluorescein. Also, it is not always clear whether
an equation was intended for visual tracer detection, instrument detection in water samples,
or sample collectors designed to enhance tracer concentrations (e.g., carbon sorption of
fluorescent dyes via detectors).
Some equations require a "fudge factoring" constant that takes into consideration the
relative detectability of the tracer to be used, the residence time within the aquifer, the type
of sampling done, the method of sample collection, and/or the method of analysis. Specifics
such as tracer type, methods of sampling and analysis, and fudge factor multipliers should
generally be regarded as inappropriate when calculating necessary tracer mass unless a clear
scientific basis for such can be established (e.g., solution-conduit sinuosity <1.5).
2.1.2.1. Review of Tracer-Mass Estimation Equations. Worthington (pers. comm.}
examined more than 3000 tracer tests and was able to fit a straight line through a double-
logarithmic plot in two separate instances. In the first instance a double-logarithmic plot
of Mass injected versus Time x Discharge x Concentration showed a clear relationship
11
-------
Table 3. Some equations for estimating tracer injection mass.
Number
(la)
(Ib)
(2)
(3)
(4)
(5a)
(5b)
(6)
(7a)
(7b)
(8)
Equationa
M — 0 ^fi IQcPtp\
ivi — u.oo ^ 1000 j
M = 0.56 ( i000J )
/ xO.93
M = 17 ( 3 6QX1Q6 )
n/r Tc'i L
M - 10
l\/r T ( QL ~\ 1 V
-"-(^2 V8.64xl04W ' 5.0X104
^ ~~ 3600
MTd Q L
3600
2000
n/r bW[2LCp+Ad2(2L-W)]
M 3731
M 2g
T\/f QL
3600
Secondary13
Reference
(Parriaux et al., 1988, p. 7)
(Parriaux et al., 1988, p. 7)
(Parriaux et al., 1988, p. 8)
(Kafi, 1998, p. 323)
(Milanovic, 1981, p. 276)
(Parriaux et al., 1988, p. 8)
(Caspar, 1987, p. 49)
(Parriaux et al., 1988, p. 8)
(Kafi, 1998, p. 326)
(Kafi, 1998, p. 325)
(Milanovic, 1981, p. 276)
(Caspar, 1987, p. 49)
(Bogli, 1980, p. 139)
Primary
Reference
(Worthington, pers. comm.}c
(Worthington, pers. comm.}c
(Worthington, pers. comm.}c
(UNESCO, 1973-1983)
(UNESCO, 1973-1983)
(Bendel, 1948)
(Dienert, 1913)d
(Dienert, ?)e
(Leibungut, 1974)
(Leibungut, 1974)
(Leibundgut and Wernli, 1982)
(Leibundgut, 1981)
(Leibundgut and Wernli, 1982)
(Martel, 1940)c'e'f
(Martel, 1940)c'e'f
(Thurner, 1967)e
continued on next page
-------
Table 3. Some equations for estimating tracer injection mass (continued).
Number
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
Equationa
— C4 V
MT1 T
— J-Cf, J-1
1\/T T rp /yi
A/r T \(^ i Q \
M L \\L l 1.8x104 J
i\/r ( Q2 L }
V3600g'
T\/f tdQPSf
8.64X104
i\/r TMI Q
3600
l\/r M2 1
3600
M — ^Q
1V± 40
n/r CpTpQL
2500 v
M =5.0Q
M = 9.5V L
M=^
M1 A ^yQ / ^
y 3.6x10° v
1\/T QCptpTp
M 3398
Secondary13
Reference
(Milanovic, 1981, p. 276)
(Caspar, 1987, p. 49)
(Kafi, 1998, p. 325)
(Schudel et al., 2002, p 21)
(Caspar, 1987, p. 49)
(Caspar, 1987, p. 49)
(Sweeting, 1973, p. 228)
(Sweeting, 1973, p. 228)
(Davis et al., 1985, p. 101)
(Aley and Fletcher, 1976, p. 7)
(Aley and Fletcher, 1976, p. 30)
Primary
Reference
(Guillard, ?)e
(Guillard, ?)e
(Siline-Bektchourine, 1951)
(Kafi, 1998, p. 327)
(Stepinac, 1969)e
(Stepinac, 1969)e
(Keys, 1968)
(Caspar, 1987, p. 50)
(Jenko, ?)e
(Jenko, ?)e
(Drew and Smith, 1969)
(Dunn, 1968)
(Haas, 1959)
(Haas, 1959)
(Haas, 1959)
(Aley and Fletcher, 1976, p. 9)
(Rantz, 1982, p. 237)
continued on next page
-------
Table 3. Some equations for estimating tracer injection mass (continued).
Number
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
(33)
M
M
M
M
M
M
M
M
M
Mp
Equationa Secondary13
Reference
_ QCpfTpTp
747.23
O C T £9
1000
_ QCptTpTp
498.15
CpTpTp ( Qf \°'°4
2.94 \^149.53y
_ Q£
~ 20
_ TMzLI App
1000
= SmL (Kafi, 1998, p. 324)
— Sm V fKnfi 1 00C n °^d-}
— i ,-,,-, ^ivajj, ic/yo, p. o£^j
_ y
200
= QtpPh (Kafi, 1998, p. 327)
Primary
Reference
(Kilpatrick and Cobb, 1985, p
(Rathbun, 1979, p. 26)
(Rantz, 1982, p. 236)
(Kilpatrick and Cobb, 1985, p
(Mullet al, 1988a, p. 37)
(Kilpatrick and Wilson, 1989,
(Kafi, 1998, p. 324)
(Alexander and Quinlan, 1992
(Timeus, 1926)e
(Timeus, 1926)e
(Kilpatrick, 1993, p. 14)
(Kinnunen, 1978)
.8)
.17),
p. 14)
, p. 19)
aSome equations slightly modified to allow consistency of units.
bSecondary references do not always correctly reproduce the original equations.
cSee also (Worthington and Smart, 2001).
dDienert (1913) contains no equation for estimating tracer mass (Worthington, pers. comm.)
ePrimary reference not always properly identified or readily available.
fThe correct citation is (Martel, 1913) (Worthington, pers. comm.)
See the Notations list in Section 2.6., page 38.
-------
defined by Equation (1) (Table 3). In the second instance a double-logarithmic plot of Mass
injected versus Length x Discharge x Concentration also resulted in a clear relationship
defined by Equation (2). Equations (1) and (2) provide a means for estimating the mass of
dye to be injected such that positive tracer recoveries are likely.
Table 4. Aquifer and tracer-dependent coefficients TCl — 7c4a-
Aquifer Tracer Tct
Tracer-Dependent Coefficient, TCl
clay • • • 5-20
sand • • • 2-10
fractured rock • • • 2-20
karst • • • 2-10
Tracer-Dependent Coefficient, TC2
porous media • • • 5.0 x 102
fractured rock • • • 3.0 x 103
Tracer-Dependent Coefficient, Tc3
very permeable Na-fluorescein 2.5 x 10"1
aquifers
slightly permeable • • • 1.0 x 10°
aquifers
NaCl 2.5 x 102
Tracer-Dependent Coefficient, Tc4
Na-fluorescein 2.5 x 10~9
a Source: Adapted from Parriaux et al. (1988).
Equations (3)-(7a) were published by Parriaux et al. (1988) in a tracing guide that was
intended to be practical but is obscure and difficult to obtain. Equation (7b) is a slightly
more complicated form of Equation (7a). According to Parriaux et al. (1988), citing Zotl
(1974), Equations (3)-(7a) were developed for Na-fluorescein, but they may be used for
tracing with Lycopodium spores by using 1.5-2.0 times the weight of Na-fluorescein. Zotl
further suggests that higher amounts can only be advantageous. Equations (3)-(5) also
include an aquifer and/or tracer-dependent coefficient TCi (Table 4), which is intended to
adjust the tracer mass to be injected. Equation (4) is valid for Na-fluorescein, but for
15
-------
eosin (45380 C.I. Acid Red 87), five to 10 times more dye is required (Parriaux et al.,
1988, p. 7). Quoting from Zotl (1974), Parriaux et al. (1988, p. 8) suggest that although
Equation (5a) is appropriate for Na-fluorescein sorption onto detectors, two to three times
more dye is required for water samples. Although not stated, Zotl was probably referring to
visual detection of fluorescent dye in water when detectors are not being used. Equation (5b)
appears similar to Equation (5a), but the full citation and primary reference are not provided
in Milanovic (1981, p. 276), and it includes a tracer-dependent coefficient Tc4, which may
be a misprint.
Equations (6) and (7) include a sorption coefficient Adi that is intended to increase
tracer mass for which units are either not clearly provided [Equation (6)] or are inconsistent
with common application [Equation (7)]. For Equation (6), Parriaux et al. (1988, p. 8)
recommend td = 3L/v, suggesting that the tracer test duration is expected to be three
times the mean residence time distribution f. For Equation (7), Ad2 = 1.0 mg m~3 for Na-
fluorescein and Ad2 > 1.0 mg m~3 for all other dyes depending on their respective sorption
characteristics (Kafi, 1998, p. 325).
Equation (7) includes an additional "safety factor" S/ that is not intended to protect
human health or the environment from excessive tracer mass releases. Rather, Sf is intended
to ensure adequate tracer-mass injection by acting as a fudge factor multiplier to increase
the mass of tracer to be released. Equation (7b) is the equivalent of Equation (7a) adjusted
for some tracer entrance angle other than 30°. The original form of Equation (7b) listed in
Kafi (1998, p. 325) includes what appears to be some time value multiplied by gravitational
acceleration g, but these parameters are not identified and no units are provided. It is
probable that Equation (7b) required multiplication by g~l in suitable units (e.g., cm s~2,
m s~2). For this review, Equation (7b) has been appropriately adjusted.
Equations (8)-(28) are generally similar to Equations (3)-(7). Equation (8) was intended
for visual detection of Na-fluorescein. Equations (9), (10), and (11) each include an aquifer-
and/or tracer-dependent coefficient Tci (Tables 4-7).
16
-------
Table 5. Aquifer and tracer-dependent coefficient TCS'
Tracer Dye
Na-fluorescein
eosin
erthrosine
congo red
Methyl blue
Spirit blue
Ponceau red
Clay
0.5
0.5
1.0
2.0
2.0
2.0
1.0
Stone
- 2
- 2
-4.
-8.
-8.
-8.
-4.
.0
.0
.0
.0
.0
.0
.0
Sandstone Fractured
0.2
0.2
1.0
2.0
2.0
2.0
1.0
- 1.
- 1.
- 3.
-6.
-6.
- 7.
- 3.
.0
.0
.0
.0
.0
.0
.0
0.2
0.2
1.0
2.0
2.0
2.0
1.0
- 2.
- 2.
-4.
-8.
-8.
-8.
-4.
Rock Karst
.0
.0
.0
.0
.0
.0
.0
0.2
0.2
1.0
2.0
2.0
2.0
1.0
- 1.0
- 1.0
-4.0
-8.0
-8.0
-8.0
-4.0
Source: Adapted from (Kafi, 1998, p. 325).
Table 6. Tracer dependent coefficient TCea.
Tracer Material
Na-fluorescein
eosin
Sulpho Rhodamine G
Rhodamine B
Sulpho Rhodamine B
Rhodamine WT
Pyranine
Na-Napthionate
Tinopal
Duasyne
NaCl
LiCl
KC1
KBr
spores
surfactants
phages (particle count)
Serratia marcescens
microspheres
indium
Tc6
1.0 x 10°
5.5 x 10°
2.0 x 10°
1.5 x 101
4.0 x 10°
2.0 x 101
5.5 x 10°
1.5 x 101
3.0 x 10°
2.0 x 104
1.0 x 103
1.0 x 104
1.5 x 10°
2.0 x 101
1.0 x 1013
1.0 x 1013
1.0 x 1012
1.0 x ID"1
Tc6b
1.0 x 10°
2.0-3.0 x 10°
2.0 x 10°
4.0 x 10°
5.0 x 10°
1.5 x 101
2.5 x 102
4.0 x 10°
1.0 x 104
1.0 x 103
3.0-5.0 x 103
1.0 x 1012
1.0 x 1012
a Source: Adapted from (Kafi, 1998, p. 327).
b Modifications to TC(3 from (Schudel et al., 2002, p 21).
Equation (11) as listed in Kafi (1998, p. 327) requires two independent coefficients,
17
-------
Table 7. Prevailing test conditions coefficient Tc7a.
Prevailing Condition TCr TCrb
Rapid flow in channels 0.1 - 0.9
Photosensitive decay 2.0 - 4.0
Surface-water flow Q > 3.6 x 106 2.0 - 4.0
River-bank filtration Q < 1.8 x 104 2.0 - 4.0
Ground-water flow K < 0.36 m h"1 • • • 1.00 b
Ground-water flow K < 3.6m h^f?] 2.0- 4.0
Ground-water flow 0.36 < K < 3.6 m tr1 • • • 0.50 b
Ground-water flow K > 3.6 m h"1 • • • 0.25 b
Fractured-rock studies • • • 0.2 - 2.0
Fractured-rock studies with if} > 60° 2.0 - 4.0 2.0 - 4.0
Karstic aquifers in general • • • 0.2-1.0
Karstic aquifers with inflow • • • 10( ® "1°'93
Unsaturated zone 1-30 m thick
Low tracer-background levels
Turbid samples or
samples with natural fluorescence
Unsaturated zone >30 m thick 5.0 - 10.0
Soil zone with cohesive soils 5.0 - 10.0
Studies near a ground-water divide 5.0 - 10.0
Multiple recovery stations likely 5.0 - 10.0
a Source: Adapted from (Kafi, 1998, p. 328).
b Modifications to Tc, from (Schudel et al., 2002, p 21).
and Tc7 (Tables 6 and 7), which requires considerable insight and/or experience on the part
of the practitioner. Modifications to Tc& and TC7 were obtained from Schudel et al. (2002,
p 21) as shown in Tables 6 and 7 but the requirements of insight and experience have not
been alleviated.
Equation (12) is listed as being valid only when Q < 5.0 m3 s"1 and L > 12 km.
Equation (13) uses a ratio of swallet inflow to spring discharge Q/q, although the reasoning
for this is not explained. Equation (13) is expected to overestimate tracer mass for
predominantly vadose systems > 1 km (Caspar, 1987, p. 49).
Equation (14) is intended for use with In-EDTA, and it also includes a loss coefficient
P = 1-3 and a safety factor S/ < 2. The loss coefficient P represents the mass injected to
the mass recovered, and it is justified on the reasoning that some mass of the tracer will
be retained in the system (Caspar, 1987, p. 50). The rationale for setting S/ at < 2 is not
18
-------
explained.
Equations (15) and (16) rely on a set amount of dye to be injected per rate of spring
discharge or swallet inflow, respectively. These two equations are probably intended for
visual detection and, reportedly, reduced amounts of fluorescent dye could be released if
detectors are used for dye sorption (Sweeting, 1973, p. 228).
Equation (17) is described in a very confusing manner in Davis et al. (1985, p. 101).
The description appears as: "They [(Drew and Smith, 1969)] recommended using 60 grams
of dye per kilometer of underground travel, per 0.15 cubic meters per second of discharge,
at the largest likely rising." A more clearly worded statement would have stated that 60
grams of dye is recommended for every kilometer of underground travel for 15% of discharge
(m3 s"1) at the largest likely rising.
Equations (18), (21), and (22) were published by Aley and Fletcher (1976) in a
tracing guide that was also intended to be a practical guide. Equation (18) is listed
as being applicable for surface water and was intended for time-of-travel studies using
Rhodamine WT. It includes an unidentified multiplier that may be a unit conversion
factor, although this is not clear. The original form of Equation (18) is reported as a
volume with units of milliliters (Aley and Fletcher, 1976, p. 7), but this requires that the
unidentified multiplier be a unit conversion factor representing tracer density. The multiplier
appears much too large to solely represent tracer density, so it is likely that it is a combined
conversion factor representing density and a fudge factor. Equation (18) is a modification
of the original equation by Aley and Fletcher (1976, p. 7) to obtain mass in grams, on the
assumption that the original equation really was intended to yield a volume in milliliters.
Equations (19)-(21) represent a progression in development as technology improved
(Haas, 1959) and are really only variants of Equation (8). Equation (19) was intended for
visual detection and relates a specific amount of tracer dye mass to discharge and distance.
Equation (20) was intended for ultraviolet light enhancement and relates tracer dye mass
to system volume and distance. Equation (21) was intended for adsorption onto activated
carbon and relates tracer dye mass to discharge and distance, but it may be expected to
yield excessive amounts of tracer material (Aley and Fletcher, 1976, p. 9).
Equation (22) is intended for tracing ground-water flow using Na-fluorescein and is
applicable to waters of pH > 5.5, transport via solution conduits, and dye sorption by
detectors. Substituting Rhodamine WT for Na-fluorescein requires 2 to 10 times more
tracer dye (Aley and Fletcher, 1976, p. 9). This equation supposedly results in reduced
tracer quantities because it does not rely on proposed downstream Cp (Aley and Fletcher,
19
-------
Table 8. Tracer-dye mass per 1000 m of traced distance.
Tracer Material TMa, grams
Na-fluorescein 282
Rhodamine WT 280
Diphenyl Brilliant Flavine 7GFF > 846
Tinopal 5BM GX > 846
Tinopal BBH Pure > 846
Phorwite AR 1694
1976, p. 7-9), although the unsuitability of such a reliance is not clear.
Equations (23)-(27) specifically relate to actual dye mass, they mix English and Metric
units, and they require multiplication by unidentified unit conversion factors. Each of these
four equations requires the use of the specific tracer dye factors of density and purity,
but they were primarily intended for use with liquid Rhodamine WT. Equations (23)-(25)
were intended for discharge measurements in surface-water streams, where Equations (23)
and (24) represent an impulse release and Equation (25) a long-pulse release (e.g., t2 > t).
Equation (25) appears very differently in the three primary references, but application
of consistent units and simplification shows that the original forms of Equation (25) are
identical.
Equation (26) is a slight modification of Equation (24) and is intended for solution
conduits in that it includes the multiplier 1.5 to account for solution conduit sinuosity.
Equation (27) was designed for time-of-travel studies in surface-water streams and will
produce slightly different results from those obtained with Equation (23) (Kilpatrick and
Wilson, 1989, p. 14) and Equation (24).
Equation (28) is identified in the United States as a "rule of thumb" formula for
determining the appropriate mass of Lycopodium spores to release. It relates a percentage
of discharge with a percentage of distance to obtain the mass needed (Kafi, 1998, p. 325).
Equations (29)-(33) are somewhat different from most of the other equations. Equa-
tion (29) has also been generally considered as a rule of thumb in the United States for trac-
ing flow in solution conduits. Unlike most of the previous 28 equations, Equation (29) does
not rely on discharge to determine the appropriate tracer mass to be used. Rather, it relies
on mass associated with a specific tracer dye type required for the expected travel distance
(Table 8). It was originally intended for visual dye confirmation in elutant (/ = 1.0), but the
20
-------
use of analytical instruments has allowed a reduction in required tracer mass (/ = 0.01 to
/ = 0.1). For tracing in the Appalachians, approximately five times as much dye is needed
for success (Quinlan, pers. comm.}.
Equations (30) and (31) are considered valid for tracing water flow in solution conduits
using Na-fluorescein (Kafi, 1998, p. 324). For Equation (30), Sm = 1.0 for L > 100 m up
to some unspecified upper limit and Sm = 2.0 for L > 1000 m also up to some unspecified
upper limit. Equation (31) suggests 1 to 2 grams of dye per 100 m3 of water to be traced.
Equations (32) and (33) are for conditions different from those of the previous 30
equations. Equation (32) was designed to estimate tracer mass for lakes and estuaries
with a 1 |j.g L"1 average concentration at the expected sampling locations. Equation (33)
was designed for phage tracing and includes a phage factor. It appears to be little different
from the other equations in that it also relies on discharge and peak arrival. However, it
utilizes a phage factor and rather than having units of mass in grams it has units of Np m3
where Np represents the number of phage.
Flow discharge is clearly the main factor for the majority of the 33 equations listed,
suggesting that tracer dilution estimates were an overriding concern during development.
Expected transport distance or transport time are also generally common elements. All
other factors included in the equations were intended to address either known complications
(e.g., transport distance) or unknown complications (e.g., sorption) that are expected to
influence final downstream concentrations.
It should be noted that many of the parameters listed in Table 3 require preliminary
calculations. For example, td = 3f (Parriaux et al., 1988, p. 8) for tracer tests in solution
conduits may be estimated from
3L 3LA
— —^-,
v Q
and td for forced-gradient tracer tests in porous media may be estimated from
3L 3L27r6ne
. .
34
(35)
Such essential calculations are not immediately obvious, however.
It is also necessary to point out that any equations that require tracer purity Tp in the
calculations, for example, Equations (18) and (23)-(27), will be greatly affected by minor
changes in the value of Tp. For these equations, fluorescent dye type can profoundly affect
how much tracer will be recommended because of the varying concentrations of different
dyes and their form, liquids or powders.
21
-------
2.1.2.2. Review of Sampling Frequencies. The most uncertain aspect of any
tracing study is the schedule for sample collection (Kilpatrick and Wilson, 1989, p. 16).
Whereas much effort has gone into estimating tracer mass for a tracing study, very little
appears to have been done in terms of determining sample collection frequency. Sampling
frequencies are generally based on travel distances, which suggests a direct relationship
between travel distance and expected time of arrival. This relationship is obviously correct,
but it is ambiguous because transport velocity as a function of residence time is unknown.
Transport velocities can achieve extreme ranges, rendering invalid sampling schedules based
on transport distances that are devoid of residence time estimates.
Tracer test sampling frequencies are typically based on two approaches. In the first
instance, for transport via solution conduits, tracer recovery from qualitative tracing tests
(e.g., sorption of fluorescent dyes onto detectors) that are sampled every few hours, days,
or weeks (Alexander and Quinlan, 1992, p. 21) (most commonly every 1 to 2 weeks) serves
as a basis for determining appropriate sampling frequencies for quantitative-tracing tests.
Sampling schedules based on qualitative tracing tests have been found to result in false
positive results (Field, 2000, pp. 11-14) and false negative results (Smart et al., 1986) and
cannot be relied upon for predicting sampling times.
In the second instance, sampling frequencies may be based on transport distances from
tracer injection points to expected tracer recovery stations with due consideration to travel
times. For surface-water streams, Kilpatrick and Wilson (1989, p. 16) suggest that
tp = 2.78 x 10~4— (36)
vp
can be used to determine when to initiate sampling for detection of the tracer leading edge
and 10% of the trailing edge. Leading edge is given by (Kilpatrick and Wilson, 1989, p. 18)
+ + dl° (17\
ti = tp — (67)
and 10% of the tracer trailing edge by (Kilpatrick and Wilson, 1989, p. 18)
feio = tp + ^ (38)
Although no criteria were specified, (Kilpatrick and Wilson, 1989, p. 18) suggest that the
number of samples to be collected can be determined by dividing tdw by 30, which will
result in an appropriate sampling frequency necessary for describing the ETC.
A general sampling schedule is shown in Table 9, where sampling times are based on
travel distance and daily lack of tracer recovery. A specific schedule is shown in Table 10,
22
-------
where sampling times are based on travel distance and lack of timely recovery. In both these
instances sampling frequency was initially determined as a factor of transport distance, but
it is iteratively adjusted to longer times as tracer recovery is delayed.
A simpler but more realistic method uses average expected travel velocity that is based
on current-meter measurements for surface streams. For a porous medium, Darcy's law
may be used to gain a general sense of tracer time of arrival, provided required parameters
(e.g., effective porosity) are available. For solution conduits, an expected average transport
velocity equal to 0.02 m s~l may be used as the basis for designing a sampling schedule
(Worthington et al., 2000). This average transport velocity of 0.02 m s"1 was statistically
determined by regression analyses of 2877 tracing tests between sinking streams and springs
in carbonates in 37 countries (Worthington et al., 2000). It has been suggested that sampling
frequency should not be based on average velocity because the leading edge will be missed
(Kilpatrick and Wilson, 1989, p. 12), but this can be overcome by recognizing that the
average velocity is a rough estimate and represents a rough average travel time. The
suggested sampling frequency can be appropriately adjusted to ensure that initial sample
collection begins prior to likely tracer breakthrough.
2.2. EFFICIENT HYDROLOGIC TRACER-TEST DESIGN (EHTD)
To better facilitate tracer testing in hydrologic systems, the EHTD methodology was
developed (Field, 2002a). Unsuccessful quantitative tracer tests using several of the tracer
mass estimation equations listed in Table 3 and recommended sample collection frequencies
listed in Tables 9 and 10 and previous qualitative tracer test results led to the development
of EHTD. Application of EHTD to the study site resulted in successful tracer tests and
showed that good tracer test design can be developed prior to initiating a tracer test (Field,
2000, p. 26).
2.2.1. Basic Design of EHTD
EHTD is based on the theory that field-measured parameters (e.g., discharge, distance,
cross-sectional area) can be combined in functional relationships that describe solute
transport processes related to flow velocity and times of travel. EHTD applies these initial
estimates for times of travel and velocity to a hypothetical continuous stirred tank reactor
(CSTR) as an analog for the hydrologic flow system to develop initial estimates for tracer
concentration and axial dispersion based on a preset average tracer concentration. Root
determination of the one-dimensional advection-dispersion equation (ADE) using the preset
23
-------
to
Table 9. General sampling schedule for a karst terranea.
Sampling
Distance, km
1
1-10
>10
Day 1
2
4
12
Day 2
3
6
12
Day 3
4-6
8
12
Interval, hours
Days 4-6
8-12
12
12
Day 6
24
24
24
Day 15
24
48
48
Source: Adapted from (Milanovic, 1981, p. 275) and (Caspar, 1987, p. 57).
Table 10. Specific sampling schedule for a karst terranea.
Site No.
1
2
3
4
5
6
Distance, km I
0.60
0.95
1.40
2.90
5.00
11.00
3ays 1-2
2
2
4
4
4
12
Days 3-4
4
4
6
6
6
12
Sampling
Days 5-7
6
6
12
12
12
24
Interval, hours
Days 8-14
12
12
24
24
24
24
Days 15-21
24
24
24
24
24
24
Days 22-49
56
56
56
56
56
56
a Source: Adapted from Kafi (1998, p. 333).
-------
average concentration then provides a theoretical basis for an estimate of necessary tracer
mass. Application of the predicted tracer mass with the hydraulic and geometric parameters
in the ADE allows for an approximation of initial sample-collection time and subsequent
sample collection frequency where 65 samples have been empirically determined to best
describe the predicted ETC.
2.2.2. Range of Capabilites of EHTD
Although most of the tracer mass estimation equations listed in Table 3 were designed
for tracing in solution conduits in karstic terranes, there appears to be no logical reason
to exclude porous media systems. The fact that solute transport processes in hydrologic
systems all follow the same basic theoretical principles suggests that an appropriate model
for estimating tracer mass would function effectively for all hydrological systems. However,
such a model would need to be able to account for slight differences in the nature of the
flow systems (e.g., effective porosity) and the manner in which the tracer test is conducted
(e.g., tracer release mode).
Breakthrough curves predicted using the tracer test design program EHTD for various
hydrological conditions have been shown to be very reliable (Field, 2002c). The hydrologic
conditions used to evaluate EHTD ranged from flowing streams to porous media systems
so that the range of capabilities of EHTD could be assessed. The flowing streams used to
evaluate EHTD included tracer tests conducted in small and large surface-water streams,
a solution conduit, and a glacial-meltwater stream. The porous media systems used
to evaluate EHTD included natural gradient, forced gradient, injection withdrawal, and
recirculation tracer tests. Comparisons between the actual tracer tests and the results
predicted by EHTD showed that EHTD adequately predicted tracer breakthrough, hydraulic
characteristics, and sample collection frequency in most instances.
2.3. TRACER-TEST DESIGN RESULTS USING PREVIOUS METHODS
Tracer-test design examination parameters provided by Parriaux et al. (1988) and reprinted
in Kafi (1998, p. 324) have previously been applied to a small set of the 33 equations listed
in Table 3. Unfortunately, only a few of these equations were examined using the test
examination parameters. Although not stated it is likely that one of the reasons for the
limited examination is that additional parameters are necessary for testing the equations.
25
-------
2.3.1. Examination of Tracer-Mass Estimation Equations
The tracer-test design examination parameters originally listed in Parriaux et al. (1988)—
and reprinted in Table 11 with additional parameters—were applied to 32 of the 33
equations in Table 3. Liquid Na-fluorescein, which is considered to be the tracer material
used, is conventionally available as a 30% solution (Tp = 0.3) and has a density of
1.2 g cm~3. Equation (33) was not evaluated because it was designed for conditions other
than those listed in Table 11. Tracer mass estimates using the tracer test design examination
parameters and Equations (l)-(32) resulted in tracer mass estimates that ranged from a
fraction of a gram of tracer to tens of thousands of grams of tracer (Table 12). Large tracer
mass ranges are probable using the same equation when variable hydrologic conditions
and/or tracer-dependent coefficients TQ are applied. Equation (25) is expected to produce
greater tracer mass estimates than the other equations because it is based on a long-pulse
release (t2 > i), which will also cause a much later real value for tp than the one listed in
Table 11.
For perspective, the results of Equations (l)-(32) may be compared to similar results
produced by
T O 106
M ^ -^ (39)
for an impulse release and
M = TpQt2W6 (40)
for a pulse release. Although Equations (39) and (40) were not found in any of the references
listed in Table 3, it is likely that they are commonly used because they exhibit mass balance.
However, there appears to be no reason to believe that either would yield reasonable results
because Q is the only included flow system parameter.
2.3.1.1. Porous Media. Application of Equations (l)-(32) to the porous media ex-
amination parameters listed in Table 11 resulted in tracer mass estimates that ranged from
2.5 x 10~8 g to 4.75 x 108 g, or a difference of >16 orders of magnitude (Table 12). If
Equations (5b), (9), and (20) are removed from consideration, the difference is 3 orders of
magnitude. Equations (5b) and (9) may legitimately be removed from consideration on the
assumption that Tc4 was misprinted in Milanovic (1981, p. 276). Equation (20) may also
include a misprint (volume rather than discharge). A range of 3 orders of magnitude for
tracer mass is difficult to resolve without additional information or site-specific experience.
26
-------
Table 11. Tracer test design parameters.
Parameter
Q, m3 tr1
L, m
W, m
V, m3
6, m
ne
v, m h"1
gam3 n-l
id; n
%» ft
Cp, mg m~3
Ad, mg m
0? rad
sf
t^ h
TCl
/T~I
/T~I
/T~I
/T~I
/T~I
/T~I
^Mi, g
^ M2 ) g
Tp, g cm"3
T
J-P
App
I
Sm
a q=Q/10Q
k t = t/7/3
c 6* = 30°
d t2 = 1.3tB
Porous Media
7.20 x 101
5.00 x 102
1.00 x 102
1.00 x 105
1.00 x 101
1.00 x 10~2
4.17 x 1Q-1
7.20 x 1Q-1
3.60 x 103
1.20 x 103
1.00 x 101
1.00 x 10°
5.24x ID'1
1.00 x 10°
1.56 x 103
5.00 x 10°
3.00 x 103
2.50 x ID"1
2.50 x 10~9
5.00 x ID"1
1.00 x 10°
5.00 x ID"1
2.00 x 103
2.40 x 104
1.20 x 10°
3.00 x 1Q-1
5.00 x 10°
1.00 x ID"1
1.00 x 10°
Karst
3.60 x 102
3.00 x 103
1.00 x 102
3.00 x 105
1.00 x 102
1.00 x 101
4.17 x 101
3.60 x 101
2.16 x 102
7.20 x 101
1.00 x 101
1.00 x 10°
5.24x ID'1
1.00 x 10°
9.63 x 101
2.00 x 10°
5.00 x 103
2.50 x ID'1
2.50 x 10~9
5.00 x 10-1
1.00 x 10°
5.00 x 10-1
2.00 x 103
2.40 x 104
1.20 x 10°
3.00 x 1Q-1
1.00 x 10°
1.00 x ID"1
1.00 x 10°
Adapted from Parriaux et al. (1988, p. 9).
27
-------
Table 12. Tracer-mass estimates.
Equationa
(la)
(2)
(3)
(4)
(5a)
(5b)
(6)
(7a)
(7b)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
(18)
(19)
(20)
(21)
(22)
(23)
(24)
(25)
(26)
(27)
(28)
(29)
(30)
(31)
(32)
Porous Media, g
2.63 x 102
2.00 x 10°
2.50 x 102
3.00 x 103
2.50 x 10°
2.50 x 10~8
1.30 x 103
2.92 x 103
2.92 x 103
1.00 x 101
1.25 x 10~4
2.50 x 102
3.50 x 103
5.12 x 102
1.00 x 103
3.00 x 10°
4.00 x 101
4.80 x 10°
9.00 x 102
4.15 x 102
3.60 x 102
4.75 x 10s
9.84 x 101
2.29 x 102
3.05 x 102
4.16 x 102
1.35 x 103
6.24 x 102
4.83 x 102
1.80 x 103
7.05 x 101
5.00 x 102
1.00 x 103
5.00 x 102
Karst, g
8.80 x 101
4.72 x 101
6.00 x 102
1.56 x 102
7.50 x 101
7.50 x 10~7
3.89 x 102
1.77 x 105
1.76 x 105
3.00 x 102
7.50 x 10~4
1.50 x 103
1.50 x 103
3.36 x 103
3.00 x 104
9.00 x 10-1
2.00 x 102
2.40 x 101
2.70 x 104
1.24 x 102
1.80 x 103
8.55 x 109
2.95 x 103
1.25 x 102
9.15 x 101
1.24 x 102
4.04 x 102
1.87 x 102
1.56 x 102
5.40 x 104
8.46 x 101
3.00 x 103
3.00 x 103
1.50 x 103
a Prom Table 3.
-------
For comparison purposes, Equations (39) and (40) would yield 2.16 x 107 g and 3.37 x
1010 g for the impulse and pulse releases, respectively. The results of Equation (39) appear
to be the greatest of all except for those of Equation (20) and the results of Equation (40) are
greater than those of all 32 examined equations (Table 12). Equations (20), (39), and (40)
likely represent an absolute upper range of tracer mass to release, and releases in this range
would probably be excessive and possibly harmful (Field et al., 1995; Behrens et al., 2001).
2.3.1.2. Karstic Media. Results of the karstic media examination parameters listed
in Table 11 in Equations (l)-(29) produced tracer mass estimates that ranged from
7.50 x 10~7 g to 8.55 x 109 g, a difference also of >16 orders of magnitude. Removing
Equations (5b), (9), and (20) results in a difference of 5 orders of magnitude. As in the case
with porous media, such a large range is difficult to resolve without additional information
or site-specific experience.
Equations (39) and (40) resulted in l.OSx 10s g and 1.01 x 1010 g for the impulse and pulse
releases, respectively. Equation (39) resulted in an estimated mass greater than all but that
of Equation (20) (Table 12) and the results of Equation (40) are greater than those of all 32
examined equations (Table 12). As with the porous media estimates, Equations (20), (39),
and (40) likely represent an upper limit for tracer mass to release, and such a release would
probably be excessive and possibly harmful (Field et al., 1995; Behrens et al., 2001).
2.4. EHTD ANALYSIS OF THE TWO TRACER TESTS
As with the 33 equations listed in Table 3, use of the EHTD methodology requires
that specific flow-system parameters be measured or reasonably estimated. A subset of
parameters from Table 11 that represent the required parameters necessary for evaluation
by EHTD are shown in Table 13. From Table 13 it is apparent that only measurable
parameters related to the hydraulics of the flow system are required for EHTD analysis.
However, the two tracer-specific parameters, retardation and decay, and the sinuosity factor
are not required. The sinuosity factor is an adjustable multiplier <1.5 that is similar
to the one used in Equation (26) except that Equation (26) requires the inclusion of
Sn = 1.5. It is also used by EHTD to increase the measured straight-line distance by
an appropriate distance, because natural solution conduits are not constrained to perfectly
straight channels.
Although not presented in Table 13, EHTD also requires identification of the type of
flow system tracer test, the type of release, and the time for tracer injection, in an attempt
29
-------
Table 13. EHTD tracer test design parameters.
Parameter
Q, m3 h-1
Afm2
L, m
W, m
6, m
ne
q, m3 h"1
Cp, mg m-3
t2^h
Ci° mg m~3
7i° dimen.
72^ dimen.
snc
Rd
^h-1
Porous Media
7.20 x 101
5.00 x 102
1.00 x 102
1.00 x 101
1.00 x 10~2
7.20 x ID'1
1.00 x 101
1.56 x 103
0.00 x 10°
0.00 x 10°
0.00 x 10°
1.00 x 10°
0.00 x 10°
Karst
3.60 x 102
8.63 x 10°
3.00 x 103
3.60 x 10°
1.00 x 101
9.63 x 101
0.00 x 10°
0.00 x 10°
0.00 x 10°
1.00 x 10°
1.00 x 10°
0.00 x 10°
a For this analysis, A = Q/v for the karstic spring.
Normally Q and A would be measured concurrently
and the solution v = Q/A used by EHTD.
b Parameter required by EHTD for pulse and continu-
ous releases.
c These parameters not required by EHTD but must be
listed in the input file.
to ensure universality. The type of flow system tracer test can be simply a flowing stream
(open-channel or closed-conduit flow = surface-water stream or solution conduit) or it can be
porous media. EHTD analysis of porous media systems additionally requires consideration
of any one of the following hydraulic conditions:
1. Natural gradient tracer test,
2. Forced gradient tracer test (extraction well),
3. Injection/withdrawal test (injection well rate = pumping well rate), or
4. Recirculation test (injection well rate = pumping well rate while recirculating the
tracer back to the injection well).
The tracer test parameters listed in Table 13 relate to a solution conduit tracer test and a
30
-------
forced gradient porous media tracer test, the latter assumed because of the relatively high
discharge rate (72 m3 h"1) provided by Parriaux et al. (1988, p. 9).
Type of tracer release refers to three methods of tracer injection; impulse, pulse, and
continuous. Impulse (instantaneous) releases are the most common tracer injection method
for karstic systems, whereas pulse releases (slow releases over some period of time) are the
most common tracer injection method for porous media systems. Continuous releases are
rarely employed in either system, primarily because of cost. For the porous media and
karstic tracer test parameters listed in Tables 11 and 13, impulse releases were assumed
except for Equation (22), in which a long-pulse release was assumed.
Time for tracer injection refers specifically to tracer injection time, but it also may
include pre- and post-tracer injection flush water to account for additional dilution effects.
Total dilution volume VD is obtained from
VD = (q + Q)t, (41)
which should not be considered a technically correct approach. However, it does yield good
approximations for dilution effects, which will usually be equal to or greater than the system
volume V calculated from the total discharge for the duration of the tracer test. For this
analysis, VD was of some significance because q was fairly significant.
2.4.1. EHTD Results
Application of EHTD to the parameters listed in Table 13 resulted in tracer mass estimates
of 525 g for the impulse release and 1950 g for the pulse release for the porous media tracer
test and 102 g for the impulse release and 631 g for the pulse release for the karstic tracer
test (Table 14). To obtain these results, EHTD uses an average concentration C rather than
a peak concentration Cp. For this analysis, the peak concentration used in Equations (1)-
(32) was taken as the average concentration. The effect of taking Cp = C was relatively
insignificant, because Rd = 1.0 and fi = 0.0 h"1 (Field, 2002a).
Hydraulic parameters from EHTD simulations of the porous media and karstic tracer
tests are shown in Table 14. Tracer breakthrough curves for the porous media and karstic
systems tracer tests are shown in Figures 1 and 2, respectively. All the parameters listed
in Table 14 were calculated by EHTD using the parameters listed in Table 13. Some of the
EHTD-calculated parameters listed in Table 14 (e.g., v] approximate the same parameters
listed in Table 11. However, important transport parameters such as axial dispersion DL
and Peclet number Pe are uniquely calculated by EHTD. Although these parameters may
31
-------
Table 14. EHTD tracer test analysis results.
Parameter
Mf g
Af!?g
t, h
tpfh
tp^h
^,'mh-1
i^nitr1
t^mh-1
DLfm2 h~l
D^m2 h~l
af m
o^m
p a
-* e
Peb
tifh
ti^h
t/fh
tfih
£
-------
TRACER MASS = 516.54 g
— Breakthrough Curve
n Sampling Times
20
Figure 1. EHTD results for an impulse release for the porous media test parameters.
§
o
TRACER MASS = 101.43 g
Breakthrough Curve
Sampling Times
50
100 150
Time (h)
200
Figure 2. EHTD results for an impulse release for the karstic test parameters.
33
-------
I
§
20
15
10
TRACER MASS =2.30E+00 kg
Breakthrough Curve
O Sampling Times
10
20 30
Time (wk)
40
Figure 3. EHTD results for a pulse release for the porous media test parameters.
be only crudely approximated by EHTD, it has been shown that these parameter estimates
are generally reasonable (Field, 2002c). Also, although t remained unchanged regardless
of the type of tracer release employed, tp and Cp were greatly increased when a long-pulse
release was employed (Table 14) (Figures 3 and 4) for the respective hydrologic systems.
A long-pulse release also causes an earlier t\ but a greater t/ (Table 14).
It will be noted that V = 7.85 x 104 m3 and V = 2.59 x 104 m3 for the porous media and
karstic tracer tests, respectively. These volumes are much greater than the volumes listed
in Table 11. The difference is a result of arbitrarily choosing of V (Parriaux et al., 1988,
p. 9) as opposed to calculating V using an accepted approach such as
QL
V =
(42)
Applying Equation (42) results in V = 8.64 x 104 m3 and V = 2.59 x 104 m3 for the
porous media and karstic tracer tests, respectively. Using these recalculated volumes in the
equations listed in Table 3 did not significantly change the results of Equation (4), but it
caused a slight decrease in the results of Equations (20) and (31) and a substantial decrease
in the results of Equation (32) (Table 15). Although not expected, the estimated mass
using Equation (32) with the improved estimates for V was in better agreement with the
EHTD-predicted mass for the karstic media tracer test.
34
-------
TRACER MASS = 681.65 g
Breakthrough Curve
Sampling Times
Figure 4. EHTD results for a pulse release for the karstic test parameters.
Table 15. Tracer-dye mass per 1000 m of traced distance.
Equationa
(4)
(20)
(31)
(32)
Porous Media, g
3.00 x 103
4.10 x 10s
8.64 x 102
4.32 x 102
Karst, g
1.51 x 102
7.38 x 108
2.59 x 102
1.30 x 102
From Table 3.
35
-------
2.4.1.1. EHTD Porous-Media Analysis Results. Comparisons with EHTD-estimated
tracer mass for the impulse release for the porous media tracer test suggest that only Equa-
tions (12), (18), (23), (26), (30), and (32) can reasonably be considered for estimating tracer
mass. Of these, only Equation (26) gave a greater result that was greater than the EHTD-
estimated tracer mass, the other values being relatively low. Interestingly, Equation (12) is
considered invalid for these conditions (L < 12 km), whereas Equation (30) is considered
valid for tracing solution conduits. Equations (18), (23), (26), and (32) were all intended
for tracing surface water. For the pulse release, Equation (25) underestimated M slightly
relative to EHTD, probably as a result of the lack of consideration for additional dilution
effects caused by q.
2.4.1.2. EHTD Karstic-Media Analysis Results. Comparisons with EHTD-estimated
tracer mass for the karstic tracer test suggest that only Equations (la), (4), (5a), (18), (22),
(23), (26), (27), and (29) reasonably estimate the appropriate mass of tracer to release.
The results of equations (la), (5a), and (29) are low relative to the EHTD-estimated tracer
mass, whereas those for Equations (4) and (18), (22), (23), (26), (27) are relatively high.
Equations (4), (5a), and (29) all require the use of multipliers representing tracer-dependent
factors controlled by aquifer conditions. These multipliers may also assume a range of val-
ues, but only Equation (29) is reasonably specific regarding which multiplier value to use
for the given conditions. As with the porous media tracer test, the pulse release described
by Equation (25) underestimated M slightly relative to EHTD, again probably as a result
of the lack of consideration for additional dilution effects caused by q.
2.4.2. Mass Required as Related to Sorption by Detectors
Several of the 33 equations listed in Table 3, for example, Equations (5a), (21), (22), and
(29), were specifically intended for sorption onto detectors, allowing for reduced tracer-dye
concentrations. For the porous media tracer test, Equation (5a), (19), (22), and (29) all
resulted in a lower estimated tracer mass than the mass suggested by EHTD. For the karstic
tracer test, Equations (5a), (19)-(22), (29) all resulted in greater tracer mass estimates than
suggested by EHTD.
In general, the vast majority of the 32 of 33 equations listed in Table 3 and tested resulted
in much greater tracer mass estimates than suggested by EHTD for either the porous media
system or the karstic system. Tracer dye concentration enhancement by activated carbon
should allow for much lower tracer mass estimates than predicted by EHTD. However,
36
-------
the lack of a measurable and distinct ETC that is normally obtained when water samples
are collected and analyzed prevents clear determination that the dye of interest has been
recovered.
2.5. TRAVEL TIMES AND SAMPLING FREQUENCIES
Typically, users of Equations (l)-(33) would initiate sample collection frequencies according
to flow rates estimated using Darcy's law for porous-media aquifers. Unfortunately, because
hydraulic conductivity, hydraulic gradient, and effective porosity may not be available,
Darcy's law is difficult to apply. For karstic aquifers, weekly or biweekly sample collection
schedules for qualitative tracer tests are conventionally employed. Alternatively, schedules
shown in Tables 9 and 10 may be considered if water samples are to be collected. Rarely,
an assumed karstic-flow velocity of 0.02 m s"1 may be considered in defining a sampling
schedule.
2.5.1. Travel Times
The suggested time of arrival for peak concentration tp for the tracer test design examination
parameters (Table 11) of 50 days and 72 hours for the porous media case and the karstic
media case, respectively, really represent t. Because of the difficulty in estimating tp prior to
conducting a tracer test, tp ~ f was taken as a necessary approximation. EHTD predicted
tp = 41 days and 81 days for the impulse release and the pulse release for the porous media
tracer test, respectively, and tp = 70 hours (3 days) and 131 hours (6 days) for the pulse
release and the impulse release for the karstic media tracer test, respectively (Table 14).
Clearly the tp was very well approximated by EHTD for both example tracer tests.
The use of td = 3 L/v suggests durations of 150 days and 9 days for the porous media
and karstic system, respectively (Table 11). EHTD, however, suggested 136 and 8 days
for the porous-media and karstic system tracer tests, respectively, for an impulse release
(Figs. 1 and 2) and 274 and 14 days for the porous-media and karstic system tracer tests,
respectively, for a pulse release (Figs. 3 and 4) (Table 14). These differences occurred
because EHTD employs a slightly different process for estimating td- These latter times are
relatively insignificant.
2.5.2. Sampling times
EHTD suggests appropriate sampling frequencies based on the type of flow system and
the type of release. In all instances, sampling-frequency suggestions are determined by the
37
-------
expected times of travel and the need to adequately define the ETC. Early detection of
tracer breakthrough requires that sampling be initiated prior to initial tracer breakthrough.
Sixty-five samples are recommended for adequate ETC definition, especially for instances
in which BTCs may be multimodal or long tailed (Field 200la). Application of weekly or
biweekly sampling schedules or the sampling schedules listed in Tables 9 and 10 would fail
to adequately define either ETC.
Collecting samples for the EHTD-suggested durations td listed in Table 14 would clearly
define the entire ETC should the tracer tests conform to the ADE. If tracer recoveries
were still strong beyond the EHTD-suggested durations, sampling analyses could continue
unimpeded at the EHTD-suggested frequencies.
2.5.2.1. Porous Media Sampling Times. Figures 1 and 3 depict the recommended
sampling times for 65 samples that correspond, for impulse and pulse releases, respectively
for the porous-media case. Suggested sampling frequencies were 48 hours for the impulse
case and 96 hours for a pulse release (Table 14). Initial suggested sample-collection times
were eight days and nine days after tracer injection for the impulse and pulse releases,
respectively (Table 14).
2.5.2.2. Karstic Media Sampling Times. Recommended sampling times for the
karstic test, for impulse and pulse releases are shown in Figures 2 and 4. Suggested sampling
frequencies were three hours for the impulse case and five hours for a pulse release (Table 14).
Initial suggested sample-collection times were 29 hours and 18 hours after tracer injection
for the impulse and pulse releases, respectively (Table 14).
2.6. NOTATIONS FOR SECTION 2.
A cross-sectional area of a spring (m2)
Abd absorbance of dye sample (nm)
Abs absorbance of dye at 100% strength (nm)
Adl tracer adsorption coefficient >1.0 (mgm~3[?]) (Note: adsorption is normally identi-
fied as a distribution coefficient in niL3 g"1)
Ad2 tracer adsorption coefficient >1.0 (mg m~3) (Note: adsorption is normally identified
as a distribution coefficient in niL3 g"1)
App multiplier for Appalachian karst = 5.0
a dispersivity = ^ (m)
38
-------
b aquifer thickness (m)
C0 initial (stock) dye concentration (g m~3)
Cp expected peak tracer concentration (mg m~3)
DL axial dispersion (m2 h"1)
g gravitational acceleration = 978.039 at 0° Latitude[?] (cm s~2[?])
/ multiplier for instrumental analysis = 0.01 to 1.0
K aquifer hydraulic conductivity (mh"^?])
L expected tracer transport distance (m)
M calculated tracer mass to inject (g)
Mp number of phage to be release (Np m3)
ne effective porosity (dimen.)
9 expected tracer entrance angle for transverse spread (degrees)
P expected ratio of injected tracer to recovered tracer (In-EDTA) representing tracer
loss = 1.0 to 3.0 (dimen.)
Pe Peclet number = ^j (dimen.)
Ph phage factor and count & 2.0 x 1010 to 5.0 x 1010 (dimen.)
-0 tracer scattering angle (degrees)
q inflow rate at injection point (m3 h"1)
Q well or spring discharge (m3 h"1)
Rd tracer retardation (dimen.)
Sf safety factor to ensure adequate peak concentration for detection (dimen.)
Sm multiplier for tracer mass = 1.0 to 2.0 (dimen.)
Sn sinuosity factor = l.Ox to 1.5x (dimen.)
td expected duration of tracer test (h)
tdw expected tracer test duration at 10% of the peak concentration (s)
ti time for first sample to be collected (h)
t<2 tracer injection time for a pulse injection (h)
tf time interval for sample collection (h)
tp expected time to peak tracer arrival (h)
ttw trailing edge to 10% level (h)
Td aquifer and tracer-dependent coefficients [Tables 4-7] (dimen.)
TM-L tracer dye (Na-fluorescein) mass to inject per spring discharge = 2.0 x 103 to 5.0 x 103
(g)
TM2 tracer dye (Na-fluorescein) mass to inject per inflow rate at injection point = 2.4 x 104
39
-------
(g)
Mg tracer dye [Table 8] mass for 1000 m transport distance (g)
Ah
Tv tracer purity = n / x 100 (dimen.)
1 ^o-^bs
Tp tracer density (g c^m)
H tracer decay (h"1)
v average velocity for tracer migration (m h"1)
vp expected velocity for peak tracer migration (m s"1)
V flow system volume (m3)
VD dilution volume for a spring or well (m3)
W transverse spread of tracer (m)
40
-------
Part II
MODEL THEORY AND METHOD
DEVELOPMENT
. '•
Controlled release of slightly diluted uranine (Acid Yellow 73) into a storm drain to test
for leakage. Tracer release is accomplished using a small, valveless, variable-rate, positive-
displacement, fluid-metering pump operating on a 12-volt dc battery withdrawing fluid from
a graduated cylinder. The decline in tracer in the graduated cylinder with respect to time
provides a check on the rate of tracer release.
41
-------
3. TRACER-TEST DESIGN METHODOLOGY
Previous efforts aimed at estimating tracer mass to be released for a tracer test focused
primarily on expected dilution and drew upon the originators experience. None of the
previous efforts appear to have been derived according to solute-transport theory. It would
also appear that solute-transport theory was seldom considered in designing tracer-sampling
schedules. Solute-transport theory in natural and controlled systems has been investigated
extensively and is well-understood. It would seem appropriate then to consider solute-
transport theory as a tool for determining the optimal tracer mass for release and sample-
collection frequency.
3.1. SOLUTE-TRANSPORT MODELING
Numerous model variations designed to describe solute transport have been developed.
A general one-dimensional advection-dispersion equation (ADE) typically appears as (see
Notations section)
R^ = D^-^-vC + ^(z} (43)
The retardation factor Rd can represent retardation in porous media by (Freeze and Cherry,
1979, p. 404)
Rd=l + ^ (44)
v
or Rd can represent retardation in fractured media by (Freeze and Cherry, 1979, p. 411)
Rd = I + ^ (45)
bf
or Rd can represent retardation in a solution conduit by (Field and Pinsky, 2000)
Rd = l + (46)
The first-order rate coefficient for tracer decay // in porous media is given as (Toride
et al., 1995, p. 3)
Pb^dP's (A>7\
» = » + —j- (^
in fractured media may be taken as
H = M+ atl8 (48)
bf
42
-------
and in solution conduits may be taken as
, 1Kavs
H = Hi -\ -- (49)
r
If tracer decay for the liquid phase Hi equals tracer decay for the sorbed phase ns then the
combined first-order decay n is equal to HiRd (Toride et al., 1995, p. 4) which is a reasonable
assumption commonly employed (Toride et al., 1995, p. 35).
The zero-order production coefficient 7(2) in porous media is given as (Toride et al.,
1995, p. 3)
(50)
It is applicable to fractured media and solution conduits with 9=1 (100%).
3.2. TRACER MASS ESTIMATION
The most straightforward method for estimating tracer mass is to obtain a solution to
Equation (43) and then solve for average concentration or its real root /(#*) ~ 0. As a
basic control, it is necessary to include a desired average concentration C that corresponds
to average time for peak concentration Cp that corresponds to peak time tp.
A simple solution to Equation (43) for a Dirac (6) function for obtaining the maximum
tracer concentration that ignores tracer retardation and decay is
f(x*) = CP -- M (51)
•) \ / P A /~t T^( 7 ' V /
which may be solved explicitly for tracer mass M. Equation (51) will generally provide
a reasonable estimate for M, provided reasonable estimates are available for the other
parameters. However, Equation (51) may be oversimplified for many applications because
it deals only with peak concentration and lacks consideration of tracer retardation and
tracer decay. Applying Equation (51) may result in excessive tracer mass estimates, which
is neither desirable from a hydrologic, aesthetic, economic, human health, or ecological
perspective, nor is it necessary to achieve positive tracer recovery. Alternatively, actual
tracer retardation and/or tracer decay may result in tracer mass estimates that are too
small for adequate tracer recovery.
Application of more comprehensive solutions to Equation (43) will provide a more
reasonable and reliable estimate for the tracer mass to be injected. Some solutions to
Equation (43) can be evaluated explicity for M, but other solutions for (43) may require
evaluation for its real root for some x* e [ai,a2], where x* represents the estimated mass
M.
43
-------
3.2.1. Model Solutions
Solutions for Equation (43) for impulse and pulse releases are most appropriate for
estimating tracer mass. A continuous release is less relevant because most tracer tests
involve a finite time period for release. Although not a physical reality, it is probable that
most tracer tests, especially in karstic aquifers, attempt to achieve an impulse release that
may be described as a Dirac (S) pulse. However, many attempts at an impulse release are
actually pulse releases due to the time involved for the tracer to reach the flow system under
investigation (Field, 1997; Field and Pinsky, 2000).
Applying the dimensionless parameters listed in the Notations section to Equation (43)
result in (Toride et al., 1995, p. 4)
1^%- —-^a + 7E(^), (52)
which may be solved for the boundary value problem (BVP), the initial value problem
(IVP), and the production value problem (PVP) by the law of superposition for resident
concentration using a third-type inlet condition as (Toride et al., 1995, p. 6)
CE(Z, T) = CB(Z, T) + CT(Z, T) + CP(Z, T), (53)
where the B, /, and P superscripts denote boundary, initial, and production value problems,
respectively. A third-type inlet boundary condition for resident concentration is used
because it conserves mass (Toride et al., 1995, p. 5) and it is the most physically realistic
(Silebi and Schiesser, 1992, pp. 418-431).
EHTD considers only uniform constant initial concentration C1 (Z, T) for background
concentrations. EHTD considers only exponential production for CP(Z, T} and is intended
to relate only to bacterial growth for release of a living bacterial agent. For tracer mass
estimation, CT(Z, T) and CP(Z, T) can usually be taken as zero, so that CE(Z, T) =
CB(Z, T).
3.2.1.1. Impulse Release for BVP. which when solved for the boundary value
problem is (modified from Toride et al., 1995, p. 13)
Z,T), (54)
771
where C (Z, T) is a preset mean volume-aver aged concentration that corresponds to
dimensionless distance Z and dimensionless mean residence time T. The auxiliary function
44
-------
Tf is defined as (Toride et al., 1993, 1995, p. 14)
P -pe(RdZ-T)2 p / R,Z-\-T \
^K ( ry rr\ —"5 / e AD T e PZ C I ^^^I-L \ / r r \
,(Z,T) = e Rd \l^j^e 4RdT ^e erfc | = . (55)
J
Solving Equation (54) explicitly for M or for its real root as it relates to C (Z, T) limits
the solution to the concentration corresponding with average travel time, which will be less
than the peak concentration.
3.2.1.2. Pulse Release /or BVP. The solution to Equation (52) for a pulse release
for the case where HE = 0 is (modified from Toride et al., 1995, p. 14)
/(**) = CE(Z, T) - V & - #_!) If (Z,T - ft), (56)
and for the case where //E ^ 0 is (modified from Toride et al., 1995, p. 14)
2
/(**) = CE(Z, T) - - #_i) rf (Z,T - TO, (57)
_ t1 _
where (56) and (57) are again solved for the real root as related to C (Z,T~), in which
the result will be less than the peak concentration. The auxiliary functions F^ and F.f are
defined as (Toride et al., 1993, 1995, p. 14)
rf(Z, T) = ^erfcl -^^^= I W^^e
(58)
Z V ^ y \^RdT/Pe]
x \ '
when p,E = 0 and
EdZ - wT
RdZ + uT
e 2 erfc
d
erfc _ = (59)
'4RdT/Pe
where tt = \/l + -p- when /^ 7^ 0 (i.e., // > 0).
45
-------
3.2.1.3. Uniform Initial Concentration (IVP). The IVP may be solved for uni-
form initial concentration by (Toride et al., 1995, p. 10)
(60)
The auxiliary function Ff is defined as
rf(Z, T) = e Rd { l--erfc
Ed(Z - Zi) - T
+ S
l + Pe(Z + Zi)
ePeZ erfc
PT p 7 Pe[fld(Z + ^) + T]2
^ PsZ U^T
(61)
3.2.1.4. Exponential Production (PVP). The PVP may be solved for solute pro-
duction that changes exponentially with distance by (Toride et al., 1995, p. 12)
= 7i + 72e-A^, (62)
which gives the solution as (Toride et al., 1995, p. 12)
CP(Z, T} =
T
71 If (Z, T- 0) + 72 If (Z, T- Xp)dT
71
[1 - Ff (Z, T- 0) - TJ(Z, T- fjL
(HE > o)
pE( 7 rr. \P\ rl-.
1 4 [Zjj 1 , A J a/
(^E = o)
where the auxiliary functions Ff and TE are defined as
T
if (z, T- \p) dt
TE(Z, T) = e
- - erfc
2Xp/Pe)T
e Rd erfc
(63)
(64)
(65)
(66)
46
-------
and
1 / \Z-T + ^\ erfc
T
2 1Pe ma
(67)
3.2.2. Tracer Retardation and Tracer Decay
Application of any solution to Equation (43) or Equation (52) for instances where tracer
retardation and tracer decay are significant (Rd > 1; p > 0) can have profound effects on
the shape of the ETC. Commonly, increasing Rd tends to cause a flattening, lengthening,
and spreading of the ETC, whereas increasing p causes only a flattening of the ETC.
Conversely, increasing Rd when using Equations (54), (56), or (57) results in a steepening,
lengthening, and spreading of the ETC. An increase in Rd has the effect of reducing the
calculated value for C , which causes a concomitant increase in estimated mass M so that
the set value for C can be maintained. A lengthening and spreading of the ETC continues
in a normal manner because the time of travel t is not considered in the root determination.
Increasing p when solving for the root also causes a steepening of the ETC because it
also has the effect of reducing the calculated value for C . The net effect is to cause an
increase in estimated mass M so that the preset value for C can be maintained.
3.3. SOLUTE TRANSPORT
Preliminary estimates for tracer mass in conjunction with travel time estimates and related
hydraulic parameters may be applied to any particular solution to Equation (52) to obtain
a ETC. Inverse analysis using the estimated parameters M, Rd, and/or p and the predicted
ETC can be conducted to observe the sensitivity of the model to any one of the three
parameters.
The primary difficulty with application of any particular solution to the ADE is the
need to estimate not only the tracer mass but the times of travel (t, tpl and tj), which are
related to flow velocity (v, VP} Vi) and axial dispersion Dz. An inability on the part of the
originators of previous tracer mass estimation equations (Field, 2002c) to estimate f, v, and
47
-------
Dz prior to initiating a tracer test is the most likely reason why solute transport theory was
ignored when developing tracer mass estimation methods. Because t and Dz can take on
a wide range even when assuming steady-flow conditions, reasonable initial estimates for t
and Dz can be difficult to obtain and are most commonly acquired from a tracer test.
Estimates for hydraulic parameters can, however, be obtained from some basic flow-
system measurements, functional relationships, and consideration of a simple conceptual
model of the flow system. Although the simple model and functional relationships may
be only approximations, they are likely to be sufficiently reliable as to lead to a good
approximation of some basic hydraulic parameters that are necessary for a successful tracer
test.
3.4. HYDRAULIC AND GEOMETRIC PARAMETERS
The use of Equations (54), (56), or (57) for assessing transport processes and predicting
tracer mass requires that specific hydraulic and geometric parameters measured in the field
be combined in simple functional relationships. These measured parameters and functional
relationships can then be applied in a simple hypothetical model as a precursor to application
of the ADE.
3.4.1. Measured Parameters
For flowing streams in surface channels or solution conduits, measurements for discharge
Q, cross-sectional area A, and transport distance L need to be taken. These three
parameters are the most important measurable field parameters necessary for establishing
basic hydraulic and geometric controls in any hydrologic system.
For porous media, additional measurements or estimates for specific parameters must
also be taken. These additional parameters are expected transverse spread W and vertical
spread H of the tracer plume and effective porosity ne. Moreover, it is necessary that the
type of tracer test be identified as either a natural gradient test or a forced gradient test in
which a radially symmetric flow field is created by an extraction well.
3.4.2. Functional Relationships
Discharge, cross-sectional area, and transport distance can each be measured at a down-
stream location such as a spring if a karst aquifer or estimated from Darcy's law if a porous-
media aquifer. Transport distance in solution conduits may be corrected for sinuosity by
48
-------
multiplying by a sinuosity factor < 1.5 (Sweeting, 1973, p. 231). Surface stream or solution
conduit volume V may be estimated by
V = AL. (68)
Aquifer volume for porous media with regional gradient is estimated by
V = LWH, (69)
and aquifer volume for porous media under forced-gradient conditions is estimated by
. (70)
Average flow velocity v for a surface stream or solution conduit may be estimated from
or, for a natural gradient tracer test in porous media, by application of Darcy's law. Initial
average flow velocity for a natural gradient tracer test will conform to the basic form of
Equation (71) when ne is included
(72)
although width W may be difficult to estimate. If W cannot reasonably be estimated, then
velocity is estimated from
/o
(73)
L/2Hne'
which is not theoretically correct but may result in an acceptable approximation.
For a forced gradient tracer test in porous media in which the gradient is influenced by
either a single extraction well or by a combination of an injection well and a withdrawal
well, velocity may be estimated from (Kafi, 1998, p. 377)
/o
(74)
and for an injection-withdrawal tracer test with recirculation from (Webster et al., 1970)
(75)
49
-------
3.4.3. Travel Time Estimates
Estimates for transport velocities translate directly into transport times. Initial average
time of travel f is estimated from
f=l (76)
and tracer test duration from
*„ = ^ (77)
where 2 < nm < 3, depending on the type of tracer release. Parriaux et al. (1988, p. 8)
recommend nm = 3, but it has been experimentally established that setting nm = 2 for
impulse releases and nm = 3 for pulse releases produces the best results.
Individual tracer travel time data points must also be estimated. A base time value tb
for initial time t\ and subsequent time spacing At may be estimated up to t by
n
and a base time value tm for subsequent time spacing nm At from f may be estimated by
(79)
By assuming f = tp, individual time values tj may be calculated up to f from
n/2
tm, (80)
i=l
and individual time values U from t from
n
" *»*, (81)
i=n/2
where n is a reasonable number of data points for obtaining a smooth ETC. Combining the
values obtained from Equation (80) and Equation (81) results in a series of appropriately
spaced time values that approximates initial tracer arrival and final tracer detection.
Doubling or tripling time spacing after f is not really necessary. However, it is essential
that sufficiently early and late times be established to ensure adequate consideration of
actual flow conditions.
50
-------
3.5. CONTINUOUS STIRRED TANK REACTOR (CSTR)
Obtaining an estimate for M and Dz can be achieved for a predicted ETC on the basis of
the theory of a completely mixed CSTR. A mass balance model that describes the dynamics
of a simplified CSTR is (Silebi and Schiesser, 1992, p. 49-50)
d^^ = qCQ-QC-VkC. (82)
Setting q = Q and using initial condition
C(0) = Cp, (83)
the solution to Equation (82) is (Silebi and Schiesser, 1992, p. 50)
(84)
Equation (84) will produce an exponentially decaying ETC starting at the peak concen-
tration Cp with a gradient that is dependent on the value of the reaction rate constant k
and the space velocity Q/V (Levenspiel, 1999, p. 93). It is apparent from Equation (84)
that whereas Cp may be preset, prior knowledge of discharge Q, reactor volume V , and
transport times t must be determined.
Equation (84) is evaluated for C from t ~ tp in a descending manner using 0.25 < k <
1.0, although k = 0 would adequately suffice. The concentration values C obtained from
Equation (84) leading from f are then reversed to achieve an ascending limb leading to t.
Equation (84) is then resolved for C from f in a descending manner using a k ^C 1.0. For
n = 200, k = 1/200 represents a reasonable exponential decay for the descending limb.
The values for k were empirically determined such that 0.25 < k < 1.0 represents a
steeply ascending limb, whereas k ^C 1.0 represents a more gently decaying descending limb
controlled by the number of data points. The result is a good approximation of a typically
positively skewed ETC in which a cusp forms the peak concentration at the peak time of
arrival. Although the values for k were empirically determined, the resulting ETC appears
to reasonably represent a typical ETC based on observation and experience.
The ETC produced by the CSTR model is subsequently evaluated by
/oo
C(i) dt (85)
.
to obtain the area under the ETC. The area represents an initial estimate for the tracer
mass to be adjusted as required by Equations (54), (56), or (57).
51
-------
3.5.1. Travel Times and Velocity
For the purpose of determining axial dispersion Dz, tracer travel time weighted for tracer
mass for impulse and short-pulse releases is estimated from
j
t C(t) dt
-c , (86)
C(t) dt
o
and tracer travel time variance of is estimated from
oo
(t - tf C(i) dt
"t--9—TOO , (87)
/ C(t] dt
Jo
where C is obtained from Equation (84). The CSTR-generated ETC is predicated on the
assumption of an impulse or short-pulse release, so other forms of Equations (86) and (87)
are not required.
3.5.2. Tracer Dispersion Estimates
Axial dispersion may be determined using the method of moments theory. Although
statistically and theoretically valid, the method of moments has the tendency to overestimate
dispersion. Alternatively, the effects of velocity variations, matrix diffusion, and immobile-
flow regions can create the appearance of significant dispersion. These difficulties require
that dispersion estimates be obtained in a manner that considers the method of moments
while reducing the influence of long tails. This is most easily accomplished using the Chatwin
(1971) method in conjunction with the method of moments.
3.5.2.1. Estimating Dispersion by the Method of Moments. Axial dispersion
properly weighted for concentration may be estimated for an impulse release by
Dz = ^- (88)
and for a short-pulse release by (Wolff et al., 1979)
It should be recognized here that Dz solved by Equation (89) is based on the assumption of
a ETC and does not represent the mean residence time distribution, as does Equation (88).
52
-------
There will usually not be any major difference between Dz estimated from Equation (88)
and Dz estimated from Equation (89). In addition, because the CSTR-generated ETC is
based on an impulse release, Equation (89) may reasonably be ignored even though the
subsequent tracer test may be a pulse or step test.
3.5.2.2. Estimating Dispersion by the Chatwin Method. Axial dispersion may
be estimated using a modification of the method developed by Chatwin (1971), given by
'tin
vt
Subject to tK < z/v} Equation (90) is reduced to the general least-squares problem by
solving
where
(91)
(92)
T
X= (Xi, X2)
b =(6i,62, ... ,6K)T.
The parameters 6» are equal to the left-hand side of Equation (90)
t In
i=
(93)
(94)
(95)
and the parameters to be determined X
of Equation (90)
are equal to the two factors on the right-hand side
(96)
vt
53
-------
where x\ is the y intercept of the straight-line fit to the early-time data and x2 is the gradient
of the straight-line fit to the early-time data.
Equations (88) and (89) tend to overestimate Dz for nonporous-medium flow systems,
which will generally result in an overestimation of tracer mass needed and a greater ETC
spread than is likely to occur as a result of solute dispersion. Alternatively, Equation (90)
tends to underestimate Dz for porous-medium flow systems, which will have an effect
opposite that obtained from Equations (88) and (89).
For these two reasons, Equation (90) is used to estimate Dz for a nonporous-medium flow
system and Equation (88) and/or Equation (89) are used to estimate Dz for porous-medium
flow systems. Although not precise measures of Dz, these estimates are believed to be
adequate for the purpose of obtaining an approximation of Dz for use in Equations (54), (56),
or (57).
3.6. TRACER SAMPLE COLLECTION DESIGN
Solute transport parameter estimates are used in Equations (54), (56), or (57) with the
initial estimate for tracer mass. Adjustments to the initial estimate for tracer mass are
made iteratively on the basis of the estimated solute transport parameters, preset mean
P
volume-averaged concentration C , and any effects created by suggested tracer reactions.
Final estimates are then used in the ADE to generate a ETC representative of the flow
system to be traced.
3.6.1. Sample Collection
The ADE-generated ETC serves as the basis for determining an appropriate sampling
frequency and an initial sample collection time. Rather than using guesswork, transport
distance, or unmeasured estimates for tracer velocity, as is common (Field, 2002c), the ETC
allows for realistic consideration of the times of travel.
3.6.1.1. Sampling Frequency. Sample collection frequency is based on an arbitrary
number of samples to be collected that balances the cost of sample collection and analysis
with the value of an ever—increasing number of samples. An adequate sampling frequency
necessary for representing a continuous series by a discrete series must be determined for
extracting optimal information while maximizing the accuracy of the results and minimizing
the computational costs. The sampling frequency then is based on how rapidly tracer
54
-------
concentration is changing, so that as the average \dC/dt\ increases, sampling frequency
should also increase (Yevjevich, 1972, p. 2).
The number of samples ns to be collected can be arbitrarily chosen initially. Novakowski
(1992) suggested that ns equal at least 20 to 30 samples, with the greatest concentration
of samples occurring around Cp, which assumes that Cp is known, whereas (Kilpatrick
and Wilson, 1989, p. 18) suggest that ns = 30 samples will generally be necessary as a
minimum for defining the ETC. To properly define rapid changes in the ETC, ns = 60
was experimentally found to be more reliable if aliasing effects are to be avoided (Smart,
1988). Aliasing of a multimodal ETC is a common problem when an inadequate sampling
frequency is applied to a tracer test that exhibits complex behavior.
Sampling frequency may then be determined from
ns
where tsm corresponds to C > 1.0~3 |j.g L"1 for all tracer tests except recirculation tracer
tests where C > 1.0~6 \ig L"1. These values for tsm are used on the assumption that lower
concentrations are not readily detectable or necessarily relevant.
3.6.1.2. Initial Sample Collection. Once the sampling frequency has been deter-
mined, the initial sample collection time is adjusted backwards by an additional number of
selected samples rib- Initial sample collection time tsi is then obtained by subtracting tsf
from tsm for a selected number of additional samples rib- For most instances, rib = 5 may
be taken as a reasonable number of additional samples to collect prior to the occurrence of
tsi = tsm- All subsequent sampling times are found from
i. (99)
The total number of samples to be collected with an associated sampling time spacing
tsf can be subsequently divided into fractions thereof as desired. Earlier sample collection
than the recommended tsi may be considered as appropriate. Sample collection ending
times other than td may also be determined, depending on whether tracer detection has
ceased prior to reaching td or is continuing beyond td-
3.7. METHODOLOGY EVALUATION
Application of this tracer estimation methodology provides a general sense of the appropriate
tracer mass to release and the general hydraulics of the system to be traced. Because
55
-------
the hydraulics of the system are approximated, sampling frequency and initial sample
collection time can also be predicted. The computer code, EHTD, facilitates the tracer-
design methodology for typical hydrological settings using measured hydrological field
parameters to calculate functional relationships. The measured parameters and functional
relationships are then applied to a hypothetical CSTR to develop a preliminary ETC that
is then numerically evaluated by the method of moments for tracer mass and hydraulic
parameter estimation. The calculated hydraulic parameters are then used in solving for
estimated tracer mass and sampling times.
The CSTR-generated ETC is solved by the method of moments by developing a piecewise
cubic Hermite function. That is, the interpolant is defined in terms of a set of cubic
polynomials, each of which is defined between a pair of consecutive data points. The
coefficients of these cubic polynomials are chosen so that the interpolant has continuous
first derivatives, and the remaining freedom of choice is used to ensure that the interpolant
is visually acceptable, meaning that monotonicity in the data results in monotonicity in the
interpolant, which is defined by (Kahaner et al., 1989, p. 100-103 and 106-108)
g(t) = h(t) = Cihi(t) + d%%(t}. (100)
A piecewise cubic Hermite function in effect produces the most reasonable interpolation
of the data possible with excellent theoretical convergence properties. Integration is then
accomplished by cubic Hermite quadrature as (Kahaner et al., 1989, p. 161-162)
/ » /' = !" n(t}dt = Y^ d I d hi(t) + di ! d hi(t), (101)
Jti i=l Jti Jti
which is the compound trapezoid rule with appropriate end corrections. The compound
trapezoid rule is exceptionally accurate when the integrand is a smooth periodic function
given by equally spaced data points (Kahaner et al., 1989, p. 162).
Equations (54)-(57) may be solved directly or by using a combination of the bisection
method and the secant method. The bisection method ensures certainty and the secant
method ensures rapid convergence. This is very efficient and accurate and is guaranteed to
produce reasonable results (Kahaner et al., 1989, p. 248-250).
For instances where tracer mass is expected to be adversely affected by retardation
or decay, EHTD employs a constrained nonlinear least-squares optimization routine to
adjust the tracer mass, retardation, and decay estimates relative to the ETC produced
by the hypothetical CSTR. The nonlinear optimization routine searches for a vector y of
56
-------
Table 16. Tracer test design parameters.
Parameter Value
Release Mode
Q, m3 h-1
zfra
A, m2
CE, Hg L-1
Measured Parameters
Impulse
3.63 x 102
2.74 x 103
2.23 x 10°
5.00 x 101
Functional Relationships
tp, h 1.64 x 101
f, h 1.69 x 101
vp, mh-1 1.68 x 102
v, mh-1 1.63 x 102
V, m3 6.12 x 103
Axial Dispersion
DZJ m2 h-1 4.50 x 103
Pe 9.90 x 101
Tracer Reaction
Rd 1.00 x 10°
fi, h-1 0.00 x 10°
a Transport distance = straight-line distance, 1.83 x 103 m x
sinuosity factor, 1.5.
p components that minimizes the sum of the squares function f(y) = | J^™=1 fi(y}2 that is
constrained by 7. < yi < %, 1 < i < p where the fi(y) are twice continuously differentiable
functions of y (Dennis et al., 1981).
3.7.1. Simulation
The methodology described was tested for Prospect Hill Spring located in Clarke County,
Va., using the measured field parameters and functional relationships listed in Table 16.
Figure 5 is a plot of time versus concentration produced by a hypothetical CSTR using
the measured field parameters and functional relationships listed in Table 16. Integrating
Figure 5 produced a preliminary estimate for tracer mass of M = 111 g. Of particular
57
-------
40
I
§
20
TRACER MASS = 188.01 g
Breakthrough Curve
(Preliminary)
10
20 30
Time (h)
40
50
Figure 5. Preliminary tracer-breakthrough curve generated from a hypothetical CSTR.
significance are the variable effects created by the measured field parameters when combined
in functional relationships. Increasing Q, decreasing A, or decreasing L all have the effect
of shifting the curve to the left and decreasing the mass estimate. Decreasing Q, increasing
A, or increasing L all have the effect of shifting the curve to the right and increasing the
mass estimate.
Figure 6 is a plot of time versus concentration produced by the ADE using the
measured field parameters and functional relationships listed in Table f 6 with varying tracer
retardation (Rd = I, Rd = 2, Rd = 3) and no tracer decay (// = 0 h"1). The predicted
tracer mass necessary for a successful tracing test and the resulting average and peak tracer
concentrations are shown in Table 17 for varying tracer reaction conditions. From Figure 6
P
and Table 17 it is apparent that although C remains the same for each ETC for varying
values of Rd, t and Dz appear to increase and v to decrease as Rd increases. In fact, these
hydrologic parameters have not physically changed, but increasing Rd creates just such an
appearance.
Table 17 also includes four instances of tracer decay (n > Oh"1) without retardation
(Rd = 1-0), the effects of which are shown in Figure 7 for three of the instances (// = 0.0 h"1,
H = 0.05 h"1, n = 0.1 h"1), because // = 0.01 h"1 would not be readily distinguishable from
58
-------
40
20
I
1
1
1
1
1
1
4
1
A
/
A
i / i
1*
' \
* ' \
1 ,
' ' I
*' \
i! i
f' \
i \
/I \
• i
' . \
Q Q Retardation = 1.0
_^^_ Retardation = 2.0
. _ Retardation = 3.0
50
100
150
Time (h)
Figure 6. Predicted ETC for Prospect Hill Spring for increasing values for retardation.
Symbols represent recommended sampling times.
Table 17. Predicted tracer mass and tracer concentration.
Tracer Reaction
Rd
1.0
1.0
1.0
1.0
2.0
3.0
X^m
0.0
0.0
0.0
0.0
0.42
0.84
^h-1
0.0
0.01
0.05
0.1
0.0
0.0
M, g
113.99
134.94
265.00
616.07
227.98
341.97
CE, HgL-1
50.00
50.00
50.00
50.00
50.00
50.00
(-SPI M-g L>
50.59
50.77
51.92
54.02
50.59
50.59
Ka obtained for an assumed cylindrical solution conduit using
Equations (46) and (68).
59
-------
^ 40 -
s
g
Tracer Decay = 0.0
_A_A - Tracer Decay = 0.05
Tracer Decay = 0.1
20
30
40
Time (h)
Figure 7. Predicted ETC for Prospect Hill Spring for increasing values for tracer decay.
Symbols represent recommended sampling times.
H = 0.0 h"1. It is obvious from Figure 7 that as tracer decay is allowed to increase, Cp
P
also increases (Table 17) because of the necessity of maintaining C . This effect was not
observed for increasing tracer retardation. In addition, because Cp increases, the ETC
is steepened, causing an apparent decrease in tracer transport times. However, whereas tp
clearly decreases (Figure 7), t remains unchanged regardless of the proposed tracer reactions.
Increasing tracer reaction effects causes a concomitant increase in tracer-mass estimates.
—E
The increase in tracer mass estimates reflects the need to match the set value for C while
including factors that have the net effect of decreasing tracer mass estimates, so that the
overall effect is an estimate for tracer mass that approximates that which should be used in
a tracer test.
Included in Figures 6 and 7 is an indication of appropriate sampling times for each ETC
(Table 18).
60
-------
Table 18. Recommended sampling times for selected tracer reaction conditions.
Sampling Time, hours
Sample
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Rd = l-°
n = o.o
7.13
7.75
8.37
9.00
9.62
10.24
10.86
11.48
12.10
12.73
13.35
13.97
14.59
15.21
15.83
16.45
17.08
17.70
18.32
18.94
19.57
20.18
20.80
21.43
22.05
22.67
23.29
23.91
24.53
25.15
25.78
26.40
27.02
27.64
28.26
28.88
Rbd = i-o
fJL = 0.01
7.15
7.77
8.39
9.00
9.62
10.23
10.85
11.47
12.08
12.70
13.31
13.93
14.54
15.16
15.78
16.39
17.01
17.62
18.24
18.86
19.47
20.09
20.70
21.32
21.93
22.55
23.17
23.78
24.40
25.01
25.63
26.25
26.86
27.48
28.09
28.71
Rcd = i-o
fj, = 0.05
7.02
7.63
8.23
8.84
9.45
10.06
10.66
11.27
11.88
12.49
13.09
13.70
14.31
14.92
15.52
16.13
16.74
17.35
17.95
18.56
19.17
19.78
20.38
20.99
21.60
22.20
22.81
23.42
24.03
24.63
25.24
25.85
26.46
27.06
27.67
28.28
Rdd = i-o
7.11
7.69
8.28
8.86
9.45
10.03
10.62
11.20
11.79
12.37
12.96
13.54
14.13
14.71
15.30
15.88
16.47
17.05
17.64
18.22
18.81
19.39
19.98
20.56
21.15
21.73
22.32
22.90
23.49
24.07
24.66
25.24
25.83
26.41
27.00
27.58
Red = 2.0
fJL = 0.0
14.26
15.51
16.75
17.99
19.24
20.48
21.72
22.96
24.21
25.45
26.69
27.94
29.18
30.42
31.66
32.91
34.15
35.39
36.64
37.88
39.12
40.37
41.61
42.86
44.09
45.34
46.58
47.82
49.07
50.31
51.55
52.79
54.04
55.28
56.52
57.77
Rfd = 3.0
n = o.o
21.39
23.26
25.12
26.99
28.85
30.72
32.58
34.45
36.31
38.17
40.04
41.90
43.77
45.63
47.50
49.36
51.23
53.09
54.95
56.82
58.68
60.55
62.41
64.28
66.14
68.01
69.87
71.73
73.60
75.46
77.33
79.19
81.06
82.92
84.79
86.65
continued on next page
61
-------
Table 18. Recommended sampling times for selected tracer reaction conditions
(continued).
Sampling Time, hours
Sample
Number
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
)U = 0.0
29.51
30.13
30.75
31.37
31.99
32.61
33.23
33.86
34.48
35.10
35.72
36.34
36.96
37.58
38.21
38.83
39.45
40.07
40.69
41.31
41.93
42.56
43.18
43.80
44.42
45.04
45.66
46.28
46.91
)U = 0.01
29.33
29.94
30.56
31.17
31.79
32.40
33.02
33.64
34.25
34.87
35.48
36.10
36.72
37.33
37.95
38.56
39.18
39.79
40.41
41.03
41.64
42.26
42.87
43.49
44.11
44.72
45.34
45.95
46.57
RC — 1 n
nd — x-u
p. = 0.05
28.89
29.49
30.10
30.71
31.32
31.92
32.53
33.14
33.75
34.35
34.96
35.57
36.18
36.78
37.39
38.00
38.60
39.21
39.82
40.43
41.03
41.64
42.25
42.86
43.46
44.07
44.68
45.29
45.89
Rdd = 1.0
28.17
28.75
29.34
29.92
30.51
31.09
31.68
32.26
32.85
33.43
34.02
34.60
35.19
35.77
36.36
36.94
37.53
38.11
38.69
39.28
39.86
40.45
41.03
41.62
42.20
42.79
43.37
43.96
44.54
Rl = 2-0
59.01
60.25
61.50
62.74
63.98
65.22
66.47
67.71
68.95
70.20
71.44
72.68
73.92
75.17
76.41
77.65
78.90
80.14
81.38
82.63
83.87
85.11
86.35
87.60
88.84
90.08
91.33
92.57
93.81
Rfd = 3.0
n = o.o
88.51
90.38
92.24
94.11
95.97
97.84
99.70
101.56
103.43
105.29
107.16
109.02
110.89
112.75
114.62
116.48
118.34
120.21
122.07
123.94
125.80
127.67
129.53
131.40
133.26
135.12
136.99
138.85
140.72
aRecommended sampling frequency = 37.12 minutes.
bRecommended sampling frequency = 37.29 minutes.
cRecommended sampling frequency = 36.95 minutes.
dRecommended sampling frequency = 36.45 minutes.
eRecommended sampling frequency = 1.24 hours.
fRecommended sampling frequency = 1.86 hours.
Note that tracer decay has units of h"1.
62
-------
Sixty-five sampling times were developed to adequately determine when the first sample
should be collected and to properly define the ETC. Breakthrough curve definition requires
that the ETC peak be correctly identified and that a potentially long tail be detected.
Further, in order to avoid the effects of data aliasing, a substantial number of samples
are required (Smart, 1988). Although 20 to 30 samples have been suggested by others as
adequate for ETC definition (Novakowski, 1992; Kilpatrick and Wilson, 1989, p. 18), these
researchers were not concerned with problems associated with long tails or data aliasing.
To ensure that data aliasing is avoided, 60 sample-collection times are developed by EHTD
which allows for better ETC definition without excessive sampling. However, should 60
samples prove to be excessive, it is always possible to choose to collect some fraction of
60. To ensure that initial tracer breakthrough is not missed, n\> = 5 was included as an
appropriate number of samples to collect prior to expected tracer breakthrough.
63
-------
Part III
BASIC PROGRAM USAGE
Injection of 1 kg of uranine (Acid Yellow 73) at a sinkhole that receives flow from Bebec
Creek on the Norville chalk plateau of Haute-Normandie, France. Dye recoveries were
obtained ~2200 m away at a spring and well located in the Seine river alluvial plain (photo
courtesy of Nicolas Massei).
64
-------
4. USING EHTD TO DESIGN A TRACER TEST
EHTD is an easy-to-use program for the design of tracer tests in flowing water (e.g.,
open-channel flow or closed-conduit flow in surface streams, caves, sewers, etc.) and porous
media (e.g., gravel aquifer). Using just a few field hydrological measurements, it estimates
the "correct" tracer mass to release for a tracer study and predicts the hydraulic parameters
that define solute migration. It also provides a reasonable sampling schedule for the proposed
tracer test. A graphic ETC and A detailed output file provide substantial details necessary
for implementing the proposed tracer test.
As with published (and some unpublished) tracer mass estimation equations, this
program relies primarily on perceived travel distance, flow discharge, and flow cross-sectional
area to estimate tracer mass. Unlike previously published equations, this program is
somewhat more elaborate in that it attempts to rigorously apply solute transport theory
by use of various forms of the advection-dispersion (equilibrium) model. Attempts at mass
conservation and mass balance were essential to the method. Initial estimates for times of
travel, related factors, and tracer mass are based on the concept of a hypothetical CSTR as
a surrogate for the flow system.
Selected error messages appear toward the end of the whereas output file. Many of these
error messages will not be of any great significance to the user, others are important. It is
recommended that the error messages be checked to ensure proper EHTD functioning.
4.1. EHTD PROGRAM USAGE AND EXAMPLE DATA FILES
NOTE: This program functions best with a display equal to 1024 x 768 pixels, adequately
with a display equal to 800 x 600 pixels, and not so well for further reduced display settings.
Before running the program, all EHTD files to his (her) should be copied to the PC's
hard drive and the supplied CD-ROM disk stored in a safe location. Although plenty of
storage space is available on the CD-ROM disk for the creation of data-output files and
graphics files, the possibility of damage to the EHTD program file from excess use cannot
be ignored.
4.1.1. Loading EHTD and Example Data Files
1. After booting up the computer, place the CD-ROM disk into the computer's CD-ROM
disk drive.
65
-------
2. At the computer desk top, place the mouse pointer (arrow) on the "My Computer"
icon and click the Right mouse button (Right Click).
3. Left Click on the word "Explore" in the pop-up menu. Alternatively, just hit the
letter "E" on the keyboard.
4. Place the mouse pointer on the CD-ROM disk drive icon (e.g., D: or E:) and Left
Double-Click.
5. Left Click "Edit" at the top of the Window Screen and Left Click on "Select All" in
the pull-down menu. Alternatively, just hit the letter "A" on the keyboard.
6. Left Click on the "Copy" icon on the "Tool Bar" near the top of the Window Screen
(second row). Alternatively, Left Click on "Edit" at the top of the Window Screen
and Left Click on ".Copy" or just hit "C" on the keyboard.
7. Left Click on the preferred hard drive (e.g., C:).
8. Left Click on the "Paste" icon on the "Tool Bar" near the top of the Window Screen
(second row). Alternatively, Left Click on "Edit" at the top of the Window Screen
and Left Click on "Paste" or just hit "P" on the keyboard.
A folder named EHTD will be created on the chosen hard drive and all the appropriate
files copied accordingly to the appropriate file folders2.
4.2. EHTD EXECUTION
EHTD is very easy to use. After the appropriate data files are created (which are nearly
self-explanatory), EHTD, for the most part, requires nothing more than hitting
as requested or manipulating the mouse and clicking with the left mouse button. (See
Section 5. on page 83 for a detailed discussion of EHTD data-input files.)
2EHTD was not designed for MSDOS® use, which requires that the files be moved according to the
following instructions:
• At the C: \> prompt, type "MKDIR EHTD" (without the quotes — whenever quotes appear in this section
type the requested information without the quotes).
• Next, copy the executable and data files stored in the file Ehtd_dos on the CD to the hard disk (for
example, if C is the disk drive: "COPY D: \*. * C: \EHTD\*. *").
• Repeat the above commands for the other files on the CD.
• Put the CD in a safe location.
66
-------
* *
* *
* PROGRAM TO OPTIMIZE TRACER MASS TO BE INJECTED INTO A FLOW *
* SYSTEM TO ENSURE RELIABLE TRACER-MASS RECOVERY AT THE *
* EXPECTED DOWNGRADIENT SAMPLING STATIONS BASED ON THEORY. *
* *
* DEVELOPED *
* *
* BY *
* *
* MALCOLM S. FIELD *
* U.S. ENVIRONMENTAL PROTECTION AGENCY *
* *
ENTER INPUT FILE NAME (DEFAULT = EHTD.IN):
ENTER OUTPUT FILE NAME (DEFAULT = EHTD.OUT):
ENTER PLOT FILE NAME (DEFAULT = NULL):
Figure 8. Initial EHTD screen title which appears at program start.
1. In the Windows Explorer, Left Double-Click the EHTD folder and then Left Double-
Click the EHTD.EXE file to initiate program operation.3
2. At this point, EHTD will open the program initiation screen and title (Figure 8) and
will prompt you to enter an input file name for the file to be evaluated (Figure 8) unless
you specified a file when starting the program using a DOS prompt. One advantage of
a subdirectory on your hard disk is that you will not be required to provide an obscure
path for all subfiles; the program will find them automatically because they are all
at the same location as the executable file. If the data files are in different locations
3If a command prompt is preferred, then at the C:\> prompt, type "CD\EHTD" without the quotes. You
will then see a new prompt; C: \EHTD>. You may now type "EHTD" to run the program by just responding to
the requested information, assuming that you have also copied the necessary data files or created your own.
You may want to type "EHTD filename" such as "EHTD Ehtd. in", which will automatically load and begin
running the EHTD default data set described in the journal article (Molz et al., 1986b). You may do the
same with any of the other *. in data files, which will load the appropriate data files and begin processing.
67
-------
from EHTD, you will need to provide the correct path to the * . in files. Alternatively,
pressing will automatically run the default file, Ehtd.in.
3. Now enter a data output file name to be written or press for default name
(EHTD.out) as requested (Figure 8). Be aware that previous output files can be
overwritten if the same name is used for more than one. However, an input file cannot
be overwritten if one is mistakenly entered.
4. Enter a plot file name to be written or press for NULL, which means that
no plot file is to be written (Figure 8). As with the output file name, duplicate usage
of plot file names will result in the overwriting of previous plot files, but exiting input
file names will not be accepted. There is no default plot file name used (the default is
no plot file). If a plot file name is given, then two plot files will be created; a TIME-
CONCENTRATION data file and a PostScript plot file. The latter will have an
appropriate name assigned (e.g., sampling station name) and a .ps extension added.
The TIME-CONCENTRATION data file will consist of four columns of data as shown
in Table 19.
It will be noted from Table 19 that much more data will appear in the first two
columns than in the second two columns. This is because the first two columns
define the ETC, whereas the second two columns represent suggested sampling times,
which are necessarily reduced to a workable recommendation. It will also be noted
that multiple sampling stations will necessarily be recorded in the same plot file one
right after the other in the order in which they appear in the input file but with
the header information separating each new sampling station data set. Individual
sampling station PostScript files are created, however. A single sampling station file
listing will result in just one set of data being recorded.
After the last file name has been entered, EHTD will respond for approximately one
second with:
FILE NAMES HAVE BEEN READ
unless NULL was specified for no plot file to be generated in which case EHTD will
respond for approximately on second with:
-------
Table 19. Table illustrating the form of the EHTD-created plot file.
PLOT FILE: Sampling Station File Name
TIME CONG. TIME CONG.
(h) (^g/1) (h)
PLOT FILE: Sampling Station File Name
TIME CONG. TIME
(h) (^g/1) (h)
CONG.
PLOT FILE: Sampling Station File Name
TIME CONG. TIME
(h) 0/g/l) (h)
CONG.
69
-------
NO PLOT FILE SPECIFIED, RESULTS WILL NOT BE WRITTEN TO A PLOT FILE!
followed by:
FILE NAMES HAVE BEEN READ
4.3. USER-REQUESTED LATIN HYPERCUBE SAMPLING (LHS) ROU-
TINE
After the last file name has been read, EHTD will ask if you want to generate a series
of input files using a Latin Hypercube Sampling (LHS) routine and the original input file
parameters as initial parameters to be randomly selected within an appropriate range. This
routine was added to allow the user to consider the effect of conditions that may differ from
the measured conditions. At the end of each LHS-generated input file, a suggested solute
mass to manually enter is provided (see Section 4.4.). A comprehensive discussion of LHS
is provided in Iman and Helton (1988) and McKay et al. (1979).
The actual LHS query appears as:
DO YOU WANT TO RUN THE LATIN HYPERCUBE SAMPLING ROUTINE (Y=YES, N=NO)?
Pressing N causes the LHS routine to be ignored only for the particular sampling station
currently being evaluated by EHTD. Subsequent sampling stations that are part of the
overall input file will each be queried as to whether the user would like to run the LHS
routine.
Pressing Y causes a second query:
DO YOU WANT TO GENERATE A SERIES OF INPUT FILES OR ONE FILE OF MEAN VALUES?
1=INPUT FILES
2=FILE OF MEANS
Entering 1 causes the following request:
ENTER THE NUMBER OF LHS-DEVELOPED INPUT FILES DESIRED (N > 12) :
70
-------
for a flowing stream system or:
ENTER THE NUMBER OF LHS-DEVELOPED INPUT FILES DESIRED (N > 14) :
for a porous media system. The generation of LHS input files requires that a specific mini-
mum number of input files be generated to satisfy the inequality (Blower and Dowlatabadi,
1994; McKay et al., 1979)
N>. (102)
Alternatively, entering 2 causes the following request:
ENTER THE NUMBER OF LHS-DEVELOPED CALCULATIONS DESIRED (e.g., N = 1000):
which means that the LHS routine is expecting entry of a "large" number for develop-
ment of a set of mean values for use in a single input file. Note, however, values in the
range of > 10, 000 will necessitate patience on the part of the user as EHTD runs the LHS
routine. Also, note that for porous media systems with "DIST-Y" set to zero will cause a
an insignificant error report to the screen which can be ignored. (See Table 25 on page 86
for a discussion of "DIST-Y".)
After determining whether a LHS routine is to be run, EHTD informs the user that
input data are being read and that input errors are being evaluated:
INPUT FILE READ AND AND ERROR AND INPUT-ERROR CHECK PROCEEDING
from which the program quickly moves on to either informing the user of any data en-
try errors or processing the input file. Later in the program, if the user has requested that
the LHS routine be run, EHTD will query the user for a LHS-generated output file name:
ENTER LATIN HYPERCUBE OUTPUT FILE NAME (DEFAULT = LHS_n . OUT) :
where n represents the number of the LHS-generated output files or set of calculations
to be developed. If a series of input files was selected above (1=INPUT FILES), one file is
developed for each sampling station evaluated by the LHS routine. If the default is used,
then n will increment automatically to correspond with each sampling station listed in the
71
-------
Table 20. Variable parameter types used in the LHS routine.
Variable Porous Media Flowing Stream
1 Mass Mass
2 Discharge Discharge
3 Effective Porosity Cross-Sectional Area
4 Aquifer Thickness Lateral Transport Distance
5 Lateral Transport Distance Initial Concentration
6 Transverse Transport Distance First Production Coefficient
7 Initial Concentration Second Production Coefficient
8 First Production Coefficient Retardation
9 Second Production Coefficient Decay
10 Retardation
11 Decay
original input file. This one file will contain all of the LHS-generated input files, which the
user may then selectively enter into EHTD by copying and pasting the desired input file as
a new file.
Alternatively, if one input file of mean values was selected (2=FILE OF MEANS), a single
input file consisting of the mean values of the required parameters (e.g., discharge, Q)
will be developed followed by a comprehensive set of univariate statistics that describe the
parameters. The statistics listing is ignored by EHTD when this file is later processed (if
processing is initiated by the user) because it appears after the "END OF FILES" input file
statement. The univariate statistics, developed using the equations shown in the box in
Figure 9 on the next page, provide a sense of the range and distribution of values produced
by the LHS routine. Substitution of, for example, the minimum or maximum value of a
selected parameter (e.g., Stat(6, *) and Stat(7, *), respectively in Figure 9 on the following
page) may be a desirable change in some instances. It is necessary to note here that the
parameters used in the univariate statistics are listed as individual variables identified in
Table 20.
4.4. USER-SUGGESTED SOLUTE MASS
At this point the user will be queried by EHTD as to whether the user would like to suggest
a solute mass (tracer or pollutant) for EHTD to use. This feature is useful for predicting
the outcome of an accidental spill or a deliberate release of a highly toxic substance, as
might occur from a terrorist attack. A similar type of approach was developed by Taylor
72
-------
1. Mean, Stat(l,*)
2. Variance, Stat(2,*)
3. Standard Deviation, Stat(3, *)
4. Skewness, Stat(4, *)
5. Kurtosis, Stat(5,*) ««„ = n"^f " ~ 3
U^E/i^iO^i-*™) ] J
6. Minimum, Stat(6,*) xmin =
7. Maximum, Stat(7, *) xmax =
8. Range, Stat(8, *) xr = xmax - x
9. Coefficient of Variation, Stat(9, *) xcv = jr1 for xw ^ 0
10. Number of values processed, Stat(10,*) n
min
where the statistics are given in terms of a single variable x. The z-th datum is Xj, with
corresponding frequencies set to unity (/» = 1) and weights also set to unity (wi = l).a
"Note that none of the variables shown in this box are intended in any way to match similar variables
used elsewhere in this document. For example, Xj here represents any required input parameter (e.g.,
discharge, Q) and n represents the the number of values requested (processed) by the LHS routine to
develop the mean values for each of the required parameters.
Figure 9. Equations used to calculate the univariate statistics used to describe the LHS-
generated mean values used in a single input file.
et al. (1986, p. 41-54), Kilpatrick and Taylor (1986), and Mull et al. (1988a, p. 75-79),
but these methods are much more difficult to implement, they require a great deal more
measured data acquired over a very long timeframe, and they tend to overestimate the peak
downstream concentration. EHTD does not suffer from the limitations listed and reliably
reproduces peak concentration. However, the previously developed methods do provide a
better visual fit to an expected long ETC tail than does EHTD, but this better tail fit is
useful primarily in estimating solute persistence.
This first EHTD query appears as:
DO YOU WANT TO SUGGEST AN INITIAL SOLUTE MASS (Y=YES, N=NO)?
73
-------
Entering N represents a "no," and EHTD will continue processing by adjusting the in-
ternally estimated solute mass to achieve the desired downstream C. Entering Y represents
a "yes," which causes EHTD to pause a second time for the user to be further queried as
to the actual solute mass to be considered. This second EHTD query appears as:
ENTER A SUGGESTED SOLUTE MASS IN GRAMS (g):
where the user would enter a solute mass that EHTD is to use for processing. The originally
desired C will be ignored by EHTD. EHTD will bypass all tracer mass estimation routines
and proceed directly to the basic solute-transport modeling routine using the estimated
hydraulic parameters (see Section 3.4.) and the user-supplied solute mass.
EHTD will respond by noting the user-suggested solute mass to be used in processing
in milligrams (mg) and an appropriate error code, an explanation of which appears at the
end of the EHTD output file. The EHTD response will appear as:
USER-SUGGESTED MASS = • • • mg
ERROR CODE AVERAGE CONCENTRATION ESTIMATE = • • •
where • • • represents an appropriate numerical value.
4.5. SCREEN OUTPUT
Further processing by EHTD will result in a screen display of
1. INITIAL TRACER MASS ESTIMATE is an initial tracer mass estimate based on the CSTR
analogy.
2. ADJUSTED TRACER MASS ESTIMATE is an adjusted tracer mass estimate based on factors
such as tracer-reactivity effects such as tracer retardation and tracer decay.
3. FINAL TRACER MASS ESTIMATE is the final tracer mass estimate based on the use of the
selected optimization routine.
These are presented so that the user can gain a sense of the workings produced by
EHTD prior to going to a screen plot of the resulting ETC or reviewing the output file.
(See Section 6. on page 97 for a detailed discussion of EHTD data output files.)
74
-------
Table 21. Screen display of a typical EHTD warning message.
*** WARNING — END OF FILE ASSUMED BECAUSE OF MISSING "END OF RUNS" FILE TERMINATOR ***
WARNING MESSAGE...THIS MESSAGE WILL ONLY BE PRINTED ONCE.
RECOVERABLE ERROR IN INPUT FILE
ERROR NUMBER = -1
Press to continue program
In instances where the user is interested in the effects created by solute retardation
and/or solute decay, the user may have EHTD run an optimization routine, which may
result in a slight modification of the estimated tracer mass and/or retardation and decay,
depending on whether one or the other or both are to be adjusted by EHTD. (See Section 3.7.
on page 55, Line Numbers 10-14 listed in Table 25 on page 86, and related discussion on
pages 93-95 for discussions related to EHTD optimization of the selected parameters.)
4.5.1. Screen Output of Error Messages
As EHTD progresses, various error messages may pop up from time to time. For the most
part, these can be ignored if they are only listed as warnings. More serious errors will stop
EHTD from any additional data processing.
4.5.1.1. Warning Messages. Warning messages are fairly common and are primarily
an indication of some abnormality in the user-specified input file that EHTD has recognized.
Usually, these warning messages can be ignored. For example, should the user construct an
input file that is missing the last three lines (two comment lines and the input file ending
command END OF RUNS), the warning message shown in Table 21 will appear. This message
is stating nothing more than that the user inadvertently did not complete the input file in
standard form (see Section 5. on page 83 for a detailed discussion of input file standard
forms), but EHTD has recognized this error and will process the input file anyway, so the
user is instructed to press to continue. The ERROR NUMBER = -1 will appear in
the output file with an explanation. Other basic warning messages are possible.
4.5.1.2. Error Messages. A more serious error, identified as fatal by EHTD, will also
occur if a critical item is missing from the user-specified input file. For example, should
the input file be missing the sampling station name (a required field), then EHTD will
75
-------
respond with a screen display similar to the one shown in Table 22. The first line shown
in Table 22 indicates that either the sampling station name or the ' 'END OF RUNS'' file
terminator is missing. From the second line it is apparent that the sampling station name is
missing, because this line indicates that the last sampling station name identified by EHTD
(STATION NAME READ WAS:) appears nonsensical (i.e., DISCHARGE (m~3/h) . . .)- The listed
station name on line 2 of Table 22 is actually just a comment line that should normally be
ignored by EHTD (see Section 5. on page 83 for an description of comment lines in input
files).
Also apparent from the first line in Table 22 is that a missing ' 'END OF RUNS'' file
terminator may still cause a fatal error rather than just a warning error as shown in Table 21.
This may sometimes occur if EHTD is unable to distinguish a "true end" to the user-supplied
input file.
All the information shown in Table 22 up to the statement FATAL ERROR IN. . . will
be printed in the named output file. The ERROR NUMBER = -5 will not appear in the
output file because the necessary information will already have been produced. Following
the listed error number, the statement, JOB ABORT DUE TO FATAL ERROR., is the last
significant statement for a typical user. The additional information listed (i.e., MESSAGE
START NERR. . .) are of no consequence to the user; this information is useful to
programmers only. Other basic error messages are possible.
Table 22. Screen display of a typical EHTD warning message.
MISSING STATION NAME OR "END OF RUNS" FILE TERMINATOR
LAST STATION NAME READ MAS: DISCHARGE (m'S/h) DISTANCE (m) AREA (nT2) SINUOSITY FACTOR
PROGRAM STOPPED DUE TO ERROR IN INPUT FILE
CHECK INPUT FILE INCONSISTENT ERRORS
FOR EXAMPLE DOES THE NUMBER OF RECOVERY STATIONS
MATCH THE ACTUAL NUMBER OF RECORDED RECOVERY STATIONS?
FATAL ERROR IN...
FATAL ERROR IN INPUT FILE
ERROR NUMBER = -5
JOB ABORT DUE TO FATAL ERROR.
0 ERROR MESSAGE SUMMARY
MESSAGE START NERR LEVEL COUNT
FATAL ERROR -521
76
-------
Table 23. Typical screen display of optimization results.
I INITIAL X(I) D(I)
1 0.
2 0.
3 0.
IT NF
0 1
1 2
. 183887D+09
.1000000+01
.0000000+00
F
0.152D-70
0.1520-70 0
0 . 6000+00
0.521D+05
0 . 2060+05
RELDF PRELDF RELDX MODEL STPPAR D*STEP NPRELDF
.000+00 0.44D-77 0.00+00 G 0. OD+00 0.30-71 0.44D-77
***** x- AND RELATIVE FUNCTION CONVERGENCE *****
FUNCTION
FUNC. EVALS
PRELDF
I
1 0.
2 0.
3 0.
0.151871D-70
2
0 . 4400-77
FINAL X(I)
183887D+09
1000000+01
OOOOOOD+00
RELDX O.OOOD+00
GRAD. EVALS 3
NPRELRF 0.440D-77
0(1) G(I)
0 . 600D+00 0 . 1650-78
0.521D+05 -0.3060-68
0 . 206D+05 0 . 1990-69
FINAL TRACER MASS ESTIMATE
MASS = 1.84E+05 g
Press to initiate plot routine
4.5.2. Screen Output of Optimization Results
Selecting the optimization routine may result in a slight alteration of the estimated tracer
mass, the tracer retardation, and/or the tracer decay. Prior to displaying the final tracer
mass estimate, EHTD will display the results of the optimization routine, which will appear
similar to the one shown in Table 23.
Most of the information provided in Table 23 will be of little use and may be ignored.
However, at the top of Table 23 is a list of the parameter values (I) selected for optimization,
their initial values (INITIAL X(I)), and the derivative of each (D(I)). For this example,
three parameters are shown; the order will always be MASS, RETARDATION, and DECAY unless
retardation is not included in the optimization routine, in which case the order would be
MASS and DECAY.
The next row (IT NF F. . .) is an indication of the optimization iterations that
will follow and related operations (only one iteration after an initial value for this example).
77
-------
This can be a very large set of iterations if radical changes to the values are required, but
this is unlikely.
Next is an indication of how well the optimization routine performed; in this instance
the statement:
***** X- AND RELATIVE FUNCTION CONVERGENCE *****
indicates very positive optimization results. This same line appears in the final output file
as an error message so that the user has a documented record of how well the optimization
routine performed.
The next three rows also will not be of much use to the user, as they only indicate the
function evaluations, gradient evaluations, etc. However, the next four rows are very useful,
as they represent the final outcome of the optimization routine. The FINAL X(I) and D(I)
are similar to those listed at the top of Table 23, and the G(I) represents the final gradient
estimates.
Lastly, the screen displays the FINAL TRACER MASS ESTIMATE just as though the opti-
mization routine had not been run. EHTD then informs the user to continue on to the plot
routine to visualize the predicted ETC.
4.6. COMPUTER GRAPHICS
A high-quality color graphics algorithm, PGPLOT4 (Pearson, 1997) that allows cascading
of graphics screens, direct printing, creation of screen files, and more using pull-down menus
in the Windows environment is included in EHTD. It is particularly useful for evaluating
the effect of interpolating and/or extrapolating the original data. Publication-quality plots
may be generated as PostScript files from the graphics screen incorporated into the program.
Alternatively, a screen dump using any type of printer is possible.
4.6.1. Features of the Interactive Graphics Loop
Running EHTD will start a conventional Windows screen with a series of pull-down menus
(Table 24). Each underlined character in Table 24 indicates that the key plus the
underlined character implements the respective menu item. For example, will
initiate the pull-down menu items underneath the File heading. Of course the mouse pointer
4PGPLOT may be obtained from http://www.astro.caltech.edu/~tjp/pgplot/
78
-------
can be used to access the menu items.
It is necessary to point out here that most users will not use the pull-down menus very
often. Most of the more useful graphics functions have been built directly into EHTD so
as to alleviate excess work on the part of the user. However, in some instances, the user
may find particular functions of value. For example, selecting the (Cascade function under
the Window pull-down menu after a total five or six graphics plots have been produced in
a series of child windows will cause the child windows to become stacked, but slightly offset
to the right and down.
The items shown in Table 24 works whether the program is currently at the text-only
screen (Graphic 1) where the user responds to queries posed by EHTD or if the program
is currently at the data-plot screen (PGPlot Graphics, #1). However, there is little point
in accessing any of the pull-down items from the text-only screen whereas in the data-plot
screen the user may find some items of value. For example, the color data-plot screen can
be printed as it appears, saved as it appears, resized to fit the whole screen, etc.
A brief description of each pull-down item shown in Table 24 is provided in the next six
subsections. Because the items listed in Table 24 are relatively self explanatory, the items
are only briefly described.
79
-------
Table 24. Pull-down menu items available in EHTD.
oo
o
File
Print...
Save...
Exit Ctrl+C
Edit
Select Text
Select Graphics
Select All
Copy Ctrl+Ins
Paste
View
Size To Fit
Full Screen Alt Enter
State Window
Pause Ctrl+S (Cascade
Tile
Arrange Icons
Input
Clear Paste
Status Bar
IGraphic 1
2PGPlot Graphics, # 1
Help
(Contents
Using Help
About
-------
4.6.1.1. File. Items listed under this heading in Table 24 are described as follows.
Print... A screen dump to the local printer attached to the respective PC.
Save... Save the screen as a bitmapped (*.BMP) file.
Exit Ctrl+C Exit the program.
4.6.1.2. Edit. Items listed under this heading in Table 24 are described as follows.
Select Text Select text for pasting to the clipboard.
Select Graphics Select graphics for pasting to the clipboard.
Select All Select both text and graphics for pasting to the clipboard.
Ctopy Ctrl+Ins Copy selected items to the clipboard.
Paste Paste selected items to the screen.
4.6.1.3. View. Items listed under this heading in Table 24 are described as follows.
Size To Fit Fit the graphics screen to the view surface without scroll bars.
Full Screen Alt+Enter Fit the entire graphics screen to the view surface without the menu
items displayed (a left-mouse click returns to the original screen).
4.6.1.4. §tate. Items listed under this heading in Table 24 are described as follows.
Pause Ctrl+S Pause the graphic display.
Resume Ctrl+Q Resume graphic display.
Pause and Resume appear only as alternates of each other, so that only the one that is not
currently functioning is accessible. The one that is currently in operation is not displayed
in the pull-down menu.
81
-------
4.6.1.5. ^Window. Items listed under this heading in Table 24 are described as follows.
Cascade Allows for a cascading view of multiple child windows at one time.
Tile Allows for a tile display of multiple child windows at one time.
Arrange Icons Not currently used in EHTD.
Input Automatically displays the input screen (Graphic 1) for data input.
Clear Paste Clears an item pasted onto the screen.
^tatus Bar Displays the current operating mode of the displayed graphics screen in a bar at the
bottom of the screen (when "check marked").
1 Graphic 1 Name of the data input screen ("check marked") if active.
^ PGPlot Graphics, # 1 Identifying name/number of all subsequently opened graphics screens
(active when "check marked").
4.6.1.6. Help. Items listed under this heading in Table 24 are described as follows.
Contents Listing of available help contents.
Using Help Description on the use of the Help.
About Identifies the EHTD program.
4.7. EHTD SOURCE
The FORTRAN source for EHTD is included on the CD. It is a very large program and
it had to be split into pieces to allow its use on a PC. It is not recommended that users
to attempt to follow the logic or modify the program. Questions regarding the program's
functioning can be addressed to the author.
In addition, the graphics routine developed at the California Institute of Technology is
included. However, it is not allowed for use in commercial products.
82
-------
5. EHTD USE OF INPUT FILES
EHTD is written to work only with prepared data files because there is too much
important data that needs to be entered correctly. Keyboard entry is typically very
frustrating and usually results in typographical errors that are difficult to correct. If these
errors are caught, it usually indicates that it is time to repeat the entire data entry process.
Good computer programs allow for created data files to be read directly by the program.
These files can easily be corrected or modified as desired without a great deal of effort on
the part of the user.
EHTD data files have been developed in a relatively simple manner to be as straight-
forward as possible. Each data file consists of a leading part that identifies the planned
tracer test followed by any number of likely sample recovery stations. If more than a single
sample recovery station is listed in the data file, then the projected tracer mass calculated
by EHTD is an additive process.
This additive process is correct only if the multiple sample recovery stations are
independent of each other. If the multiple sample recovery stations are in line with each other
(e.g., they occur along the same stream line), then twice as much tracer will be estimated
than may be necessary. This situation must be evaluated by the user on a case-by-case
5.1. DESCRIPTION OF INPUT FILES
EHTD uses a straight-forward, standard format for data input files. Unnecessary "com-
ment" or blank lines are interspersed with necessary lines that EHTD reads and processes.
Although the comment lines may be left blank, adding descriptive comments is useful for
keeping the file well organized.
Figure fO illustrates the general form of a typical flowing stream input file, the
components of which are briefly described, and Figure ff illustrates the general form of
a typical porous media input file, the components of which are briefly described in Table 25.
Note that the Line numbers listed in Figures fO and ff correspond to the Line numbers
listed in Table 25. No column numbers are provided because free format input is permitted
(i.e., the placement of input items is irrelevant).
A cursory inspection of Figures fO and f f will show that the only significant difference
between the two occurs at Line(s) 8 and ultimately Line(s) 9 (repeated as necessary in
both figures and any real data-input file). Although not apparent in Figures fO and ff
83
-------
Line Generic Flowing Stream Input File
1 PROJECT NAME
2 Name of Planned Tracer Test
3 FLOW RELEAS RTIM (h) INFLOW (m~3/h) UNITS
4
6 STATION NAME
7 Name of Sample Station 1
8 DISCHARGE (m~3/h) DISTANCE (m) AREA (m~2) SINUOSITY FACTOR
9
10 INIT. CONG. (ug"3/L) GAMMA1 GAMMA2
H
12 RETARDATION DECAY (1/h) OPTIM AVE. CONG. (ug/L)
13
14
15
16
6 STATION NAME
7 Name of sample station 2
8 DISCHARGE (m~3/h) DISTANCE (m) AREA (m~2) SINUOSITY FACTOR
9
10 INIT. CONG. (ug"3/L) GAMMA1 GAMMA2
11
12 RETARDATION DECAY (1/h) OPTIM AVE. CONG. (ug/L)
13
14
15
16
17
18 STOP PROCESSING
19 End of Runs
Figure 10. Generic example of an flowing stream input file illustrating the basic format used
by EHTD for processing. Note that the Line numbers are not part of a typical input file
and are listed here only for reference purposes for Table 25. Also note that Lines 6-17 are
repeated for each individual sampling station considered for the particular study.
84
-------
Line
Generic Porous Media Input File
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
6
7
8
9
10
11
12
13
14
15
16
17
18
19
PROJECT NAME
Name of Planned Tracer Test
FLOW RELEAS RTIM (h)
INFLOW (m~3/h)
UNITS
STATION NAME
Name of Sample Station 1
DISCHARGE (m~3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
INIT. CONG. (ug"3/L) GAMMA1 GAMMA2
RETARDATION DECAY (1/h) OPTIM
AVE. CONG. (ug/L)
STATION NAME
Name of sample station 2
DISCHARGE (m~3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
INIT. CONG. (ug"3/L) GAMMA1 GAMMA2
RETARDATION DECAY (1/h) OPTIM
AVE. CONG. (ug/L)
STOP PROCESSING
End of -Runs
Figure 11. Generic example of an porous media input file illustrating the basic format used
by EHTD for processing. Note that the Line numbers are not part of a typical input file
and are listed here only for reference purposes for Table 25. Also note that Lines 6-17 are
repeated for each individual sampling station considered for the particular study.
85
-------
Table 25. Description of the input file components listed in Figures 10 and 11.
Line Type Identifier
Description
1
2 Character TITLE1
3
4 Integer FLOW
Integer
RELEAS
Real
RTIME (h)
Comment line.
Descriptive title for planned tracer test.
Comment line.
Type of flow data code:
1 Open-channel or closed-conduit flow.
2 Porous media flow and a natural-gradient
tracer test.
3 Porous media flow and a forced-gradient
tracer test.
4 Porous media flow and a injection/withdrawal
test.
5 Porous media flow and a recirculation test.
Tracer release method data code:
1 Impulse tracer release (i.e., Dirac 6 function).
2 Pulse tracer release (time dependent).
3 Continuous tracer (step) release.
Time in hours for pulse release (RELEAS = 2)
only, but a place holder is required (automatically
converted to zero for RELEAS / 2).
4 Real INFLOW (m"3/t)
or Real INFLOW (ft"3/t)
4 Integer UNITS
5
6
7 Character TITLE2
8
Injection flow rate (m3
h-1 or ft3 h-1).
Units used in the input file.
1 Metric units (e.g., m, m2, m3 h"1).
2 English units (e.g., ft, ft2, ft3 tr1).
Comment line.
Comment line.
Descriptive title for sampling station.
Comment line (Note the Line 8 differences
between Figure 10 and Figure 11).
continued on next page
-------
Table 22. Description of the input file components (continued).
Line Type
9 Real
or Real
9
or
9
or
9
or
Real
Real
Real
Real
Real
Real
Real
Real
Identifier
Description
Flowing Stream Entry for Line 9 (see Figure 10)
DISCHARGE (m"3/T) Sampling station discharge (m3 h"1 or ft3 h"1).
DISCHARGE (ft~3/T) estimated from surface discharge (e.g., spring[s];
surface-water stream) if FLOW = 1.
Estimated from Darcy's law for porous media
discharge if FLOW = 2.
Estimated from pumping well if FLOW = 3 or 4.
DISTANCE (m)
DISTANCE (ft)
AREA (m~2)
AREA (ft"2)
SINUOSITY FACTOR
Estimated longitudinal distance from release point
to expected recovery point (m or ft).
Cross-sectional area of discharge point (e.g., spring
or surface-water stream cross-sectional area) (m2 or ft2).
DISTANCE multiplier (< 1.5) to account for sinuosity.
Applicable to solution conduits primarily when a
straight-line distance between tracer injection and
recovery points is listed for DISTANCE.
Porous Media Entry for Line 9 (see Figure 11)
DISCHARGE (m"3/T) Sampling station discharge (m3 h"1 or ft3 h"1).
DISCHARGE (ft"3/T) estimated from surface discharge (e.g., spring[s];
surface-water stream) if FLOW = 1.
Estimated from Darcy's law for porous media
discharge if FLOW = 2.
Estimated from pumping well if FLOW = 3 or 4.
POROSITY
Estimated effective porosity of the porous medium.
9
or
9
or
9
or
Real
Real
Real
Real
Real
Real
THICKNESS (m)
THICKNESS (ft)
DIST-X (m)
DIST-X (ft)
DIST-Y (m)
DIST-Y (ft)
Estimated porous medium thickness (m or ft).
Estimated longitudinal distance from release point
to expected recovery point (m or ft).
Estimated transverse spread of tracer at the
expected recovery point (m or ft).
continued on next page
87
-------
Table 22. Description of the input file components (continued).
Line
10
11
11
11
Type
Real
Real
Real
Identifier
INIT. CONG. (ug/L)
GAMMA 1
GAMMA2
Description
Comment line.
Initial (background) tracer concentration
First exponential production (growth) constant
(> 0.0).
Second exponential production (growth)
constant
12
13
13
13
15
15
16
16
17
18
Real
Real
Integer
13 Real
14 Integer
14 Integer
Real
Real
Real
Real
RETARDATION
DECAY
OPTIM
AVE. CONG. (ug/L)
(> 0.0).
Comment line.
Factor to account for possible tracer retardation
(> 1.0).
Factor to account for possible tracer decay (> 0.0).
Global program optimization data code:
0 No optimization.
1 Optimization.
Desired average concentration at the sampling
station (\ig L"1).
Optimization for tracer retardation.
0 No optimization.
1 Optimization.
Optimization for tracer decay.
0 No optimization.
1 Optimization.
Minimum bound on tracer retardation optimization.
Minimum bound on tracer decay optimization.
Maximum bound on tracer retardation optimization.
Maximum bound on tracer decay optimization.
Comment line.
Comment line.
continued on next page
-------
Table 22. Description of the input file components (continued).
Line Type
Identifier
Description
19 Character END OF RUNS
Program termination code:
Not required, but allows file notes to be included
at the end of the input file (e.g., references).
aLines 6-17 may be repeated for any number of sampling stations.
because of the generic aspect of each is that the value to be entered for type of flow, FLOW,
on Line 4 must correspond to the listing on Line 9. Correct representation of Line 9 is
not required, but it is useful for clarity purposes, as pointed out in Table 25. Section 5.1.1.
provides a detailed line-by-line explanation of Figures 10 and 11 in reference to Table 25.
5.1.1. Line-by-Line Description of Input Files
Figure 10, Figure 11, and Table 25 each include a Line number to identify the line on which
a particular item must be supplied in a data input file. These Line numbers are provided
here only as a guide to the user and are never to be included in any actual data input file.
Below is a detailed description of each line for a typical data input file. In most instances,
the description provided refers to Figure 10 and refers specifically to Figure 11 only when
necessary because of the similarity of most data entry lines for the two types of data input
files.
Line 1 is a comment statement provided to the user to enter a clarifying statement that
is ignored by EHTD. It is generally used as a convenient label for Line 2, which is
READ by the program. For example, Figure 10 lists Line I as:
PROJECT NAME
which is stating that the Line 2 is a name to be READ by EHTD. Line I can be left
blank if desired.
Line 2 is a user-supplied name that is required and is READ by EHTD. It intended to be
an identifier for the specific tracer test being designed. For example, Figure 10 lists
Line 2 as:
Name of Planned Tracer Test
-------
which should match all references to the eventual tracer test.
Line 3 is also a comment statement provided so that the user may enter a clarifying
statement, which is ignored by EHTD. It is generally used as a convenient label for
Line 4 which is READ by the program. For example, Figure 10 lists Line 3 as:
FLOW RELEAS RTIME (h) INFLOW (m~3/h) UNITS
which is stating that control codes and data listed on Line 4 are to be READ by EHTD.
Line 3 best serves as a header listing for Line 4.
Line 4 is a user-specified input, the specifics of which are as follows:
FLOW = 1 if open-channel or closed-conduit flow (surface-water stream or solution
conduit).
FLOW = 2 if porous media flow and a natural-gradient tracer test.
FLOW = 3 if porous media flow and a forced-gradient tracer test (extraction well).
FLOW = 4 if porous media flow and an injection/withdrawal test (injection well rate
= pumping well rate).
FLOW = 5 if porous media flow and a recirculation test (injection well rate = pumping
well rate).
RELEAS = 1 for impulse (instantaneous) tracer release (i.e., Dirac S function).
RELEAS = 2 for pulse tracer release (time dependent).
RELEAS = 3 for continuous (step) tracer release.
RTIME (h) is time for a pulse release (RELEAS = 2). It is meaningless for a nonpulse
tracer release (i.e., RELEAS =£ 2), but some value must be entered as a place
holder (automatically converted to zero for RELEAS ^ 2).
INFLOW (m~3/h) or (ft~3/h) is the rate of injection, and it can have significant effects
on the extent of predicted dilution. For pulse and continuous releases into porous
media systems, a value for INFLOW should definitely be included. No value should
be listed for impulse releases. The user must also decide whether pre- and post-
tracer injection flush water should be included to account for additional dilution
effects. However, for flowing streams (e.g., surface-water streams), upstream
discharges entering the injection point should not be included as INFLOW.
90
-------
UNITS = 1 for metric units (meters, square meters, cubic meters per hour).
UNITS = 2 for English units (feet, square feet, cubic feet per hour).
For example, Line 4 in Figure 10 might, for an actual tracer test, appear as:
1 1 0.0 0.0 1
which states that FLOW = 1, RELEAS = 1, RTIME (h) = 0.0 h, INFLOW (m~3/h) =
0.0m3 h"1, and UNITS = 1. It will be noted that the values listed for RTIME and
INFLOW are merely place holders. Alternatively, Line 4 in Figure 10 might appear as:
1 2 3.0 0.0 1
which represents a 3-hour pulse release in which flush or inflow water should be
excluded, such as might occur with a tracer test in a surface-water stream.
As yet another alternative, Line 4 might be the listing for FLOW as any integer greater
than 1 and less than 6 (2 < x < 5), which requires a proper corresponding entry in
Line 9. In this instance, Line 4 in Figure 11 might appear as:
4 2 76.56 5.688E01 1
which represents a porous media injection/withdrawal tracer test in which tracer was
injected into a well over a period of 76.56 hours coupled with an injection flow rate
and downgradient withdrawal rate equal to 5.688 x 101 m3 h"1.
NOTE: Time values are always in hours!
Line 5 is also a comment statement provided so that the user may enter a clarifying state-
ment, which is ignored by EHTD. It is generally used as a convenient breaking point
before listing the sample station name(s). For example, Figure 10 lists Line 5 as:
which has no real meaning and is ignored by EHTD. Line 5 can be left blank if
desired.
Line 6 is also a comment statement provided so that the user may enter a clarifying state-
ment, which is ignored by EHTD. It is generally used as a convenient indicator that
91
-------
Line 7 will contain the sample station name. For example, Figure 10 lists Line 6 as:
STATION NAME
which is ignored by EHTD but is useful for recognizing Line 7, which is READ by
EHTD. Line 6 can be left blank if desired.
Line 7 is a user-supplied name that is required and is READ by EHTD. It intended to be
an identifier for a specific sample station. For example, Figure fO lists Line 7 as:
Name of Sample Station 1
where the number f is used in this example as an indicator that there is more than
one sampling station for the example tracer test. The actual name can be anything,
but one must be listed.
Line 8 is another comment statement provided so that the user may enter a clarifying
statement, which is ignored by EHTD. It is intended as a convenient indicator for
appropriate input to be listed on Line 8. For example, Figure 10 lists Line 8 as:
DISCHARGE (m~3/h) DISTANCE (m) AREA (nT2) SINUOSITY FACTOR
Alternatively, Figure 11 lists Line 8 as:
DISCHARGE (m~3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
Both of these examples serve as indicators of data input for Line 9 and to be READ
by EHTD. Line 8 best serves as a header listing for Line 9.
Line 9 is a series of user-supplied data representing either field measurements or estimates
for the parameters identified on Line 8 of Figure 10 or Figure 11, as appropriate. For
example, Line 9 (with Line 8 added for clarity) in Figure 10 might, for an actual
tracer test, appear as:
DISCHARGE (m~3/h) DISTANCE (m) AREA (m~2) SINUOSITY FACTOR
6.408E3 8000.0 18.8 1.0
which states that DISCHARGE (m~3/h) = 6.408x 103 m3 h"1, DISTANCE (m) = 8000.0
92
-------
m, AREA (m~2) =18.8 m2, and SINUOSITY = 1.0 or no sinuosity adjustment. Al-
ternatively, Line 9 (with Line 8 added for clarity) in Figure 11 might appear as:
DISCHARGE (m~3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
5.688E1 0.35 21.6 38.3 0.0
which states that DISCHARGE (m~3/h) = 5.688 x 101 m3 h"1, POROSITY = 0.35,
THICKNESS (m) = 21.6m, DIST-X (m) = 38.3 m, and DIST-Y (m) = 0.0m.
Of particular significance in the second example is the lack of an estimated transverse
spread (DIST-Y (m) = 0.0). Transverse spread needs to be estimated only for a
natural-gradient porous media tracer test (FLOW = 2). All subsequent cases (FLOW =
3—5) will result in an automatic transverse spread estimate by EHTD according to
Equations (72) - (75).
Line 10 is a comment statement provided so the user may enter a clarifying statement,
which is ignored by EHTD. It is intended as a convenient indicator for appropriate
input to be listed on Line 11. For example, Figure 10 lists Line 10 as:
INIT. CONC. (ug/L) GAMMA1 GAMMA2
Line 11 is a series of user-supplied input representing a desire on the part of the user
to allow for initial (background) tracer concentration and exponential (growth)
production. Initial concentration and production values to be entered must always
conform to > 0.0. So, for example, Line 11 in Figure 10 might appear as:
0.02 0.1 0.2
which states that INIT. CONC. (ug/L) =0.02 |j.g Lr1, GAMMA1 = 0.1, GAMMA2 =
0.2.
It is essential that estimated values for initial concentration > 0.0 and the exponential
production parameters > 0.0 not be excessively large. Very large values for either
initial concentration (relative to set average concentration) or exponential production
parameters may result in nonsense results from EHTD.
Line 12 is a comment statement provided so the user may enter a clarifying statement,
which is ignored by EHTD. It is intended as a convenient indicator for appropriate
93
-------
input to be listed on Line 13. For example, Figure 10 lists Line 12 as:
RETARDATION DECAY (1/h) OPTIM AVE. CONG. (ug/L)
Line 13 is a series of user-supplied input representing a desire on the part of the user
to allow for tracer retardation in the system, tracer-specific decay (in reciprocal
hours only), to turn on program optimization, and to set a required average tracer
concentration. Retardation values to be entered must always conform to > 1.0, decay
values must always conform to > 0.0, and average concentration must conform to
> 0.0 for obvious reasons (i.e., from solute transport theory, retardation can never be
less than one, decay can never be negative, and average concentration can never be
less than or equal to zero). So, for example, Line 13 in Figure 10 might appear as:
1.0 0.0 0 20.0
which states that RETARDATION = 1.0, DECAY (1/h) =0.0 h"1, OPTIM = 0, AVE.
CONG. (ug/L) =20.0 M-g L"1. Note that setting optimization to zero (OPTIM = 0)
informs EHTD not to perform an optimization routine. However, setting optimization
to one (OPTIM = 1) informs EHTD to perform an optimization on the estimated tracer
mass, retardation, and decay if appropriate (see Line 14 description in Table 25 and
below.
It is essential that estimated values for retardation > 1.0 and decay > 0.0 h"1 not
be excessively large. Very large values for either retardation or decay may result in
nonsense results from EHTD.
Line 14 is a series of two user-supplied input switches to inform EHTD whether retardation
and/or decay estimates are to be estimated. For example, if OPTIM = 1 (Line 13)
and Line 14 in Figure 10 is represented by
1 1
EHTD, is informed to perform a full optimization (mass, retardation, and decay).
Setting Line 14 to
0 1
informs EHTD to optimize mass and decay only, whereas
94
-------
1 0
informs EHTD to optimize mass and retardation only. If OPTIM = 0 (Line 13) and
Line 14 is represented by
1 1
EHTD is informed to not perform any optimization because the main optimization
control switch is set to off.
Line 15 sets the minimum bounds to be considered by EHTD on the optimization of
retardation and decay. Values for Line 15 for retardation cannot be less than one,
and for decay they cannot be less than zero. For example, Line 15 in Figure 10 will
commonly appear as
1.0 0.0
which informs EHTD of the minimum bounds allowed according to the user.
Line 16 sets the maximum bounds to be considered by EHTD on the optimization of
retardation and decay. Values for Line 15 for retardation can be any number greater
than one, and for decay they can be any number greater than zero. For example,
Line 15 in Figure 10 will commonly appear as
10.0 5.0
which informs EHTD of the maximum bounds allowed according to the user.
Line 17 is a comment statement provided so that the user may enter a clarifying state-
ment, which is ignored by EHTD. It is generally used as a convenient breaking point
before listing the sample station name(s). For example, Figure 10 lists Line 17 as:
which has no real meaning and is ignored by EHTD. Line 17 can be left blank if
desired.
Line 18 is also a comment statement provided so that the user may enter a clarifying
statement, which is ignored by EHTD. It is generally used as a convenient indicator
that Line 17 will contain the End of Runs indicator. For example, Figure 10 lists
95
-------
Line 18 as:
STOP PROCESSING
which is ignored by EHTD but is useful for recognizing Line 19, which is READ by
EHTD if included. Line 18 can be left blank if desired.
Line 19 is a stopping criterion that is specifically listed End of Runs and that is READ by
EHTD. It intended to facilitate EHTD processing, but it is not required. Line 19 may
be left blank without any expected processing difficulties, but a warning message to
the user is returned. Using the stopping criterion End of Runs is useful for allowing
the inclusion of file notes to be included at the end of the data input file. For example,
Figure 10 lists Line 19 as:
End of Runs
Karstic site
Tracer injection to occur in a sinking stream
Tracer recovery expected at two springs
Discharge measurements made on date
where the informational statements following Line 19 are not processed by EHTD
but are useful notes. In particular, the date when discharge measurements were taken
is very valuable, because discharges can change radically over very short time periods.
96
-------
6. EHTD OUTPUT FILES
EHTD produces only minimal screen output. For the most part, screen output is limited
to estimates for tracer mass and warning and/or error messages related to the respective
input file and processing. Most of this information can be ignored by the user, as all of the
screen text output is reproduced in much greater detail in the EHTD output file.
Upon completion of input file processing, EHTD automatically develops a screen plot of
the likely ETC according to the data contained in the input file. As noted in Section 3.1.
the ETC developed by EHTD is based on the conventional ADE using any one of the three
solutions listed in Section 3.2.1., Equations (54) - (57). It will be noted that unless the
user specifically informs EHTD to produce a Plot File during program initiation or saves
the screen plot as a *.bmp file (see Section 4.6.1.), no final screen plot will be produced for
later viewing.
6.1. DESCRIPTION OF OUTPUT FILES
Entering the name of a typical EHTD data input file when requested by EHTD (see
Section 4.2.), the requested data output file name, and the requested plot file name, if
desired, results in rapid data processing by EHTD. Figure 12 represents a typical data input
file. It consists of measured data developed for the Lost River Cave System in Kentucky, in
which recovery was expected at the Lost River Rise [see Field and Pinsky (2000) for a brief
discussion of the site]. Upon completion of input file processing by EHTD, a conventional
ETC is plotted on the CRT screen (Figure 13). This plot displays the recommended tracer
mass necessary to generate the particular ETC displayed. If multiple recovery stations were
listed in the input file (see Figure 10 for a general example), then the final output file will
recommend a tracer mass that is developed by summing the masses recommended for each
individual sampling station.
If a plot file is requested of EHTD by the user, then a standard plot file in ASCII
format will be produced. Figure 14 depicts the plot file developed by EHTD from the Lost
River Cave System data input file (Figure 12). The first two columns of data in Figure 14
are much longer than the second two columns and represent the data points generated by
EHTD to produce the ETC. The second two columns of data never exceed 65 data points
and represent the recommended sampling times and likely concentration values.
Data processing completion by EHTD also completes the development of data output
files that describe the results of EHTD analysis. The data output files are quite long because
97
-------
PROJECT NAME
KARST EXAMPLE — LOST RIVER CAVE SYSTEM
FLOW RELEAS RTIM (h) INFLOW (m~3/h)
1 1 0.0 0.0
UNITS
1
STATION NAME
LOST RIVER RISE
DISCHARGE (m~3/h)
6.408E3
INIT. CONC. (ug/L)
0.0
RETARDATION
1.0
1
1.0
10.0
DISTANCE (m)
8000.0
GAMMA 1
0.0
DECAY (1/h)
0.0
1
0.0
5.0
AREA (m~
18.8
GAMMA2
0.0
OPTIM
0
2)
SINUOSITY FACTOR
1.0
AVE. CONC. (ug/L)
18.3
STOP PROCESSING
END OF RUNS
Figure 12. Typical example input file to illustrate how an example EHTD-generated output
file appears after processing.
-------
TRACER MASS =1.04E+00 kg
— Breakthrough Curve
n Sampling Times
40
50
60
70
Time (h)
Figure 13. Standard-form example ETC generated by EHTD from a typical input file
(see Figure 12). Note that recommended sampling times are shown (open circles), as is
recommended tracer mass to inject. In addition, time and concentration units are adjusted
automatically to their most readable values according to the tracer test design parameters.
99
-------
PLOT FILE: LOST RIVER RISE
BREAKTHROUGH CURVE
TIME
(h)
.23471
.46941
.70412
.93883
1.1735
1.4082
1.6429
1.8777
2.1124
2.3471
2.5818
2.8165
3.0512
3.2859
3.5206
3.7553
3.9900
4.2247
4.4594
4.6941
4.9288
5.1635
5.3983
5.6330
5.8677
6.1024
6.3371
6.5718
6.8065
7.0412
7.2759
7.5106
7.7453
CONG.
(Hg/D
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
0.0000
SAMPLE TIMES AND CONG.
TIME CONG.
(h)
9.9516
10.808
11.665
12.522
13.378
14.235
15.092
15.948
16.805
17.662
18.518
19.375
20.232
21.088
21.945
22.802
23.658
24.515
25.372
26.228
27.085
27.942
28.799
29.655
30.512
31.369
32.225
33.082
33.939
34.795
35.652
36.509
37.365
.15918E-05
.39299E-04
.53591E-03
.45611E-02
.26531E-01
.11300
.37166
.98432
2.1701
4.0911
6.7403
9.8809
13.082
15.839
17.723
18.492
18.130
16.813
14.830
12.505
10.123
7.8980
5.9579
4.3585
3.1001
2.1490
1.4548
.96361
.62552
.39855
.24959
.15381
.93383E-01
Figure 14. Data file generated by EHTD used to produce Figure 13.
100
-------
7.9800
8.2147
8 . 4494
8.6841
8.9189
9.1536
9.3883
9.6230
9.8577
10.092
10.327
10.562
10.797
11.031
11.266
11.501
11.735
11.970
12.205
12.439
12.674
12.909
13.144
13.378
13.613
13.848
14.082
14.317
14.552
14.787
15.021
15.256
15.491
15.725
15.960
16.195
16.429
16.664
16.899
0.0000
.17967E-09
.79528E-09
.32080E-08
.11880E-07
.40652E-07
.12931E-06
. 38444E-06
.10733E-05
.28266E-05
.70494E-05
.16710E-04
.37773E-04
.81676E-04
.16940E-03
.33788E-03
.64959E-03
.12065E-02
.21689E-02
.37810E-02
.64030E-02
.10550E-01
.16937E-01
.26531E-01
.40602E-01
.60777E-01
.89084E-01
.12800
. 18044
.24981
.33995
.45506
.59966
.77846
.99620
1.2575
1.5667
1.9275
2.3431
38.222
39.079
39.935
40.792
41.649
42.505
43.362
44.219
45.075
45.932
46.789
47 . 645
48.502
49.359
50.215
51.072
51.929
52.786
53.642
54.499
55.356
56.212
57.069
57.926
58.782
59.639
60.496
61.352
62.209
63.066
63.922
64.779
.55912E-01
.33045E-01
.19294E-01
.11138E-01
.63619E-02
.35976E-02
.20154E-02
.11191E-02
.61624E-03
.33669E-03
.18260E-03
.98335E-04
.52608E-04
.27968E-04
.14781E-04
.77675E-05
.40601E-05
.21115E-05
.10928E-05
.56295E-06
. 28874E-06
. 14748E-06
.75026E-07
.38023E-07
.19200E-07
.96614E-08
.48455E-08
.24224E-08
. 12074E-08
.60003E-09
.29736E-09
. 14697E-09
Figure 14. Data file generated by EHTD used to produce Figure 13 continued.
101
-------
17.134
17.368
17.603
17.838
18.072
18.307
18.542
18.777
19.011
19.246
19.481
19.715
19.950
20.185
20.419
20.654
20.889
21.124
21.358
21.593
21.828
22.062
22.297
22.532
22.767
23.001
23.236
23.471
23.940
24.409
24.879
25.348
25.818
26.287
26.757
27.226
27.695
28.165
28.634
2.8157
3.3463
3.9350
4.5803
5.2795
6.0284
6.8214
7.6518
8.5115
9.3916
10.282
11.173
12.054
12.913
13.741
14.527
15.262
15.936
16.543
17.075
17.528
17.897
18.180
18.376
18.484
18.505
18.443
18.300
17.790
17.018
16.033
14.891
13.643
12.341
11.028
9.7425
8.5131
7.3621
6 . 3044
Figure 14. Data file generated by EHTD used to produce Figure 13 continued.
102
-------
29.104
29.573
30.042
30.512
30.981
31.451
31.920
32.390
32.859
33.328
33.798
34.267
34.737
35.206
35.675
36.145
36.614
37.084
37.553
38.022
38.492
38.961
39.431
39.900
40.370
40.839
41.308
41.778
42 . 247
42.717
43.186
43.655
44.125
44.594
45.064
45.533
46.002
46 . 472
5 . 3482
4.4967
3 . 7489
3.1001
2.5439
2.0722
1.6760
1 . 3465
1 . 0748
.85268
.67246
.52733
.41128
.31911
.24635
.18927
. 14475
.11021
.83550E-01
.63081E-01
.47439E-01
.35539E-01
.26527E-01
.19730E-01
.14625E-01
.10805E-01
.79569E-02
.58418E-02
.42762E-02
.31212E-02
.22719E-02
.16492E-02
.11941E-02
.86240E-03
.62133E-03
.44659E-03
.32026E-03
.22916E-03
Figure 14. Data file generated by EHTD used to produce Figure 13 continued.
103
-------
46.941 .16362E-03
47.411 .11658E-03
47.880 .82901E-04
48.350 .58834E-04
48.819 .41675E-04
49.288 .29465E-04
49.758 .20796E-04
50.227 .14652E-04
50.697 .10305E-04
51.166 .72362E-05
51.635 .50731E-05
52.105 .35511E-05
52.574 .24820E-05
53.044 .17322E-05
53.513 .12071E-05
53.983 .84008E-06
54.452 .58385E-06
54.921 .40523E-06
55.391 .28089E-06
55.860 .19447E-06
56.330 .13447E-06
56.799 .92868E-07
57.268 .64064E-07
57.738 .44144E-07
58.207 .30384E-07
58.677 .20891E-07
59.146 .14349E-07
59.615 .98452E-08
60.085 .67484E-08
60.554 .46212E-08
61.024 .31615E-08
61.493 .21608E-08
61.963 .14756E-08
62.432 .10067E-08
62.901 .68627E-09
63.371 .46742E-09
63.840 .31809E-09
64.310 .21630E-09
64.779 .14696E-09
Figure 14. Data file generated by EHTD used to produce Figure 13 continued.
104
-------
of the large amount of information developed by EHTD to produce a reliable prediction of
results.
6.1.1. EHTD-Produced Data Output Files
EHTD-produced data output files are very detailed and organized. Each data output file is
organized in a manner that allows the user to follow how EHTD progressed from initial input
data to preliminary transport estimates to final transport estimates. Consistency of output
in terms of units (SI only) and form are maintained regardless of type of trace planned
or input units (English vs. SI). Using a typical input file (Figure 12), EHTD generates a
standard-form data output file, which is shown in Figures 15.
6.1.1.1. Data Output File Header Material. Initial output by EHTD is a boxed file
(Figure 15, page 106) that identifies the file and developer, when the file was last modified,
and the data input file read by EHTD to produce the output file. The critical information
listed is the last modified data, because this ensures that the most up-to-date version is
being used, and the input file name, because this ensures identification of which data input
file conforms with which data output file.
6.1.1.2. Input Data Units. A typical data input file allows both English and SI units
(Figure 15, page 106). However, EHTD data-output files only appear with SI units because
of convenience, consistency, and the fact that SI units represent "better" science.
6.1.1.3. Initial Data Input Reprise. EHTD next repeats the initial design data
(Figure 15, page 106) listed in the data input file (see Figure 15). This ensures that the
opportunity to review the input data is provided so that the user can check that the tracer
test design matches expected field conditions. This information is not repeated regardless
of how many sampling stations are listed in the data input file because this information
represents the tracer injection aspects of the project.
6.1.1.4. Sampling Station Name. EHTD identifies the expected tracer recovery
station to which the following data refer (Figure 15, page 106). As a new sampling station
is read by EHTD, new expected recovery data are produced in the data output file.
105
-------
* *
* TRACER-TEST DESIGN PROGRAM *
* *
* *
* LAST MODIFIED: JUNE 19 2002 *
* *
* EQUILIBRIUM MODEL FOR ROOTS AND NONLINEAR OPTIMIZATION *
* FOR TRACER MASS, TRACER RETARDATION, TRACER DECAY, INITIAL *
* SAMPLE COLLECTION TIME, AND SUBSEQUENT SAMPLING FREQUENCY *
* *
* MALCOLM S. FIELD *
* USEPA — NCEA-W *
* WASHINGTON, DC 20460 *
* *
* *
* DATA INPUT FILE: LOST.IN *
* *
INPUT DATA
ALL DATA ARE IN "CONSISTENT UNITS'
LENGTH [L] (m)
TIME [T] (h)
CONC. [M/T] (mg/m~3 = (J-g/L)
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12).
106
-------
PROJECT NAME AND TRACER-TEST CONDITIONS
PROJECT NAME
KARST EXAMPLE — LOST RIVER CAVE SYSTEM
FLOW TYPE STATIONS RELEASE MODE RELEASE TIME
(h)
1 1 IMPULSE O.OOE+00
FLOWING STREAM TRACER TEST
* STATION: LOST RIVER RISE
*
*
*
*
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
107
-------
TABLE 1.1. INPUT FACTORS THAT INFLUENCE TRACER MASS ESTIMATION
MEASURED PARAMETERS OF INFLUENCE
DISCHARGE DISTANCE X-SEC. AREA SINUOUS FACTOR
(m~3/h) (m) (nT2)
6.4080E+03 8.00E+03 1.88E+01 l.OOE+00
TRACER-SPECIFIC FACTORS OF INFLUENCE
FACTOR VALUE LOWER UPPER ADJUSTABLE
BOUND BOUND
RETARDATION l.OOE+00 O.OOE+00 O.OOE+00 0
DECAY (1/h) O.OOE+00 O.OOE+00 O.OOE+00 0
SET AVERAGE CONCENTRATION
= mg/m~3)
1.83E+01
OUTPUT DATA
ALL DATA ARE IN "CONSISTENT UNITS"
LENGTH [L] (m)
TIME [T] (h)
CONC. [M/T] (mg/m~3 = (J-g/L)
MASS [M] (mg, g, kg)
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
-------
TABLE 2.1.1. INITIAL ESTIMATED HYDRAULIC FACTORS
ESTIMATED STATISTICAL TIMES OF TRAVEL
AVERAGE TIME AVERAGE TIME AVERAGE TIME PEAK TIME
(INI. EST.) (ADJ. EST.) VARIANCE (INI. EST.)
(h) (h) (IT 2) (h)
2.3471E+01 3.6943E+01 1.3812E+02 2.3471E+01
ESTIMATED TRANSPORT VELOCITIES AND DISCHARGE VOLUME
AVE. VELOCITY AVE. VELOCITY PEAK VELOCITY SYSTEM VOLUME
(INI. EST.) (ADJ. EST.) (INI. EST.) (INI. EST.)
(m/h) (m/h) (m/h) (m~3)
3.4085E+02 2.3685E+02 3.3417E+02 3.0080E+05
ESTIMATED DISPERSION PARAMETERS
DISPERSION PECLET NUMBER DISPERSIVITY
(m~2/h) (DIMEN.) (m)
3.1336E+04 8.7018E+01 9.1935E+01
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
109
-------
TABLE 2.1.2. FINAL ESTIMATED HYDRAULIC FACTORS WITHOUT RETARDATION
(NONREACTIVE TRANSPORT)
ESTIMATED STATISTICAL TIMES OF TRAVEL
AVERAGE TIME TIME VARIANCE PEAK TIME
(h) (IT 2) (h)
2.3471E+01 1.3812E+02 2.2767E+01
ESTIMATED TRANSPORT VELOCITIES AND DISCHARGE VOLUME
AVE. VELOCITY PEAK VELOCITY
(m/h) (m/h)
3.4085E+02 3.5139E+02
ESTIMATED DISPERSION PARAMETERS
DISPERSION PECLET NUMBER DISPERSIVITY
(nT2/h) (DIMEN.) (m)
3.1336E+04 8.7018E+01 9.1935E+01
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
110
-------
TABLE 3.1. FINAL TRACER-MASS ESTIMATE CALCULATIONS
TRACER-MASS ESTIMATES
TRACER MASS
(INI. EST.)
(g)
TRACER MASS
(ADJ. EST.)
(g)
TRACER MASS
(REA. EST.)
TRACER MASS
(FIN. EST.)
(g)
2.0723E+03
ERROR CODE =>
1.0400E+03
4
1.0400E+03
4
FINAL TRACER-MASS REDUCTION FACTORS
SYSTEM VOL.
(m~3)
DILUTION VOL.
(m~3)
RETARDATION
(DIMEN.)
DECAY
(1/h)
1.50E+05
1.50E+05
l.OOE+00
O.OOE+00
TRACER CONCENTRATIONS
SET CONC.
AVERAGE CONC.
PEAK CONC.
1.83E+01
1.8300E+01
1.8505E+01
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
Ill
-------
TABLE 4.1. ESTIMATED SAMPLING FREQUENCY
SAMPLING TIME INTERVAL
EXACT CONVENIENT
(min) (min)
5.1401E+01 51.
RECOMMENDED SAMPLING TIMES SINCE TRACER RELEASE
SAMPLE EXACT CONVENIENT
NUMBER (h) (h) (min)
1 9.9516E+00 9. 57.
2 1.0808E+01 10. 48.
3 1.1665E+01 11. 40.
4 1.2522E+01 12. 31.
5 1.3378E+01 13. 23.
6 1.4235E+01 14. 14.
7 1.5092E+01 15. 5.
8 1.5948E+01 15. 57.
9 1.6805E+01 16. 48.
10 1.7662E+01 17. 40.
11 1.8518E+01 18. 31.
12 1.9375E+01 19. 23.
13 2.0232E+01 20. 14.
14 2.1088E+01 21. 5.
15 2.1945E+01 21. 57.
16 2.2802E+01 22. 48.
17 2.3658E+01 23. 40.
18 2.4515E+01 24. 31.
19 2.5372E+01 25. 22.
20 2.6228E+01 26. 14.
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
112
-------
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
2.7085E+01
2.7942E+01
2.8799E+01
2.9655E+01
3.0512E+01
3.1369E+01
3.2225E+01
3.3082E+01
3.3939E+01
3.4795E+01
3.5652E+01
3.6509E+01
3.7365E+01
3.8222E+01
3.9079E+01
3.9935E+01
4.0792E+01
4.1649E+01
4.2505E+01
4.3362E+01
4.4219E+01
4.5075E+01
4.5932E+01
4.6789E+01
4.7645E+01
4.8502E+01
4.9359E+01
5.0215E+01
5.1072E+01
5.1929E+01
5.2786E+01
5.3642E+01
5.4499E+01
5.5356E+01
5.6212E+01
5.7069E+01
5.7926E+01
5.8782E+01
5.9639E+01
27.
27.
28.
29.
30.
31.
32.
33.
33.
34.
35.
36.
37.
38.
39.
39.
40.
41.
42.
43.
44.
45.
45.
46.
47.
48.
49.
50.
51.
51.
52.
53.
54.
55.
56.
57.
57.
58.
59.
5
57
48
39
31
22
14
5
56
48
39
31
22
13
5
56
48
39
30
22
13
5
56
47
39
30
22
13
4
56
47
39
30
21
13
4
56
47
38
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
113
-------
60
61
62
63
64
65
6.0496E+01
6.1352E+01
6.2209E+01
6.3066E+01
6.3922E+01
6.4779E+01
60.
61.
62.
63.
63.
64.
30.
21.
13.
4.
55.
47.
*
*
*
*
*
CALCULATED TRACER-MASS:
1.040E+00 kg
1.040E+03 g
1.040E+06 mg
*
*
*
*
*
ERROR CODE
4
DESCRIPTION
No change in sign of F(X*) was found although
the interval (A,B) collapsed to the requested
tolerance. The user must examine this case and
decide whether A is near a local minimum of F(X*)
or A is near a zero of even multiplicity, or
neither of these.
*
*
*
*
*
RECOMMENDED TRACER-MASS:
1.040E+00 kg
1.040E+03 g
1.040E+06 mg
*
*
*
*
*
TRACER-TEST DESIGN PROGRAM RESULTS AS OF: 1/18/2002
2:39:20:30 pm
Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.
114
-------
6.1.1.5. Table 1.1. Input Factors. EHTD prints results in a standardized tabular
form, the first of which is labeled TABLE 1.1 INPUT FACTORS THAT INFLUENCE TRACER-MASS
ESTIMATION (Figure 15, page 106). This table represents a reprise of specific sampling sta-
tion measured or input data listed in Table 12.
6.1.1.6. Output Data Units. The results of a typical data output file are only in
SI units (Figure 15, page 106). EHTD data output files appear only with SI units for
convenience and consistency and because SI units represent "better" science.
6.1.1.7. Table 2.1.1. Initial Hydraulic Factors. The next output table (TABLE
2.1.1. INITIAL ESTIMATED HYDRAULIC FACTORS) (Figure 15, page 106) describes the
initial calculations essential for developing the preliminary ETC (see Figure 5, page 58).
Although mostly self-explanatory, some items do need to be clarified. For example, AVERAGE
TIME is listed twice, once as an "initial estimate" and once as an "adjusted estimate." The
initial estimate relates directly to the measured discharge and expected travel distance.
The adjusted estimate relates to moment analysis of the preliminary ETC, which has a
"connecting bar" to the AVERAGE TIME VARIANCE to show that these two are related only
to each other.
6.1.1.8. Table 2.1.2. Final Hydraulic Factors. This table reflects final calculations
developed by EHTD. Figure 15, page 106 does not show any significant differences from
Table 2.1.1. (Figure 15, page 106) because ' 'NONREACTIVE TRANSPORT'' was specified, the
result of which is no retardation effects.
6.1.1.9. Table 3.1. Final Tracer Mass Estimate. Table 3.1. (Figure 15, page 106)
reflects the "initial tracer mass estimate" obtained from the preliminary ETC (see Figure 5,
page 58), the "adjusted tracer mass estimate" obtained from the ETC and developed
according to Equations (54) - (57), the "readjusted tracer mass estimate" obtained when
OPTIMIZATION is requested, and the "final tracer-mass estimate" resulting from the complete
EHTD processing. An ERROR CODE is included as appropriate; its meaning is described at
the end of the output file.
This table also lists the "set," "average," and "peak" tracer concentrations (Figure 15,
page 106) associated with the data input file (Figure 12). Very rarely will the average
concentration not match the set concentration and the peak concentration not be greater
115
-------
than either the set or the average concentration. Should the average concentration not equal
the set concentration or the peak concentration be less than either the average or the peak
concentrations, a clear error in either data input or EHTD processing is indicated.
6.1.1.10. Table 4-1- Estimated Sampling Frequency. A particularly useful aspect
of EHTD is its ability to recommend when the first sample should be collected and an
appropriate sampling frequency thereafter. This information is reflected in Table 4.1.
(Figure 15, page 106) in terms of "exact times" (decimal years, decimal weeks, decimal
days, decimal hours, and decimal minutes) and "convenient time" (i.e., 12-hour clock).
This information provides the user with a helpful file for either programming an automatic
data recorder or for determining when to collect grab samples at a sufficient frequency for
adequately defining the ETC.
6.1.1.11. Calculated Tracer-Mass. A boxed final estimate for tracer mass in kilo-
grams, grams, and milligrams (Figure 15, page 106) follows Table 4.1. for each sampling
station listed in the data input file (Figure 12).
6.1.1.12. Error Codes. Following the results of each sampling station calculation, a
list of error codes (Figure 15, page 106) are reprinted and a basic description of each is
provided. Often these will be fairly insignificant, as is the case shown in Figure 15.
6.1.1.13. Recommended Tracer-Mass. Completion of processing of the entire project
(e.g., all listed sampling files in the data input file, Figure 12) will result in a summed es-
timate for tracer mass in kilograms, grams, and milligrams. For multiple sampling station
listings in a data input file, the recommended tracer mass may greatly exceed any individual
sampling station, which can be problematic if subsurface pathways do not connect to all
the listed sampling stations. In this latter instance, it is possible that more tracer than
is desired could be recovered at selected sampling stations although this is much less of a
problem than with the conventional conjecture method (see Section 2.1.1.).
6.1.1.14. Date and Time of Processing. EHTD prints out the time when EHTD
processed the data input file because the results of EHTD are highly temporal-dependent.
That is, flows are likely to be higher in wet seasons than during dry seasons. To obtain
reasonable results, EHTD should be run soon after basic field measurements are taken and
116
-------
s
g
20
15
10
Measured Breakthrough Curve
-A -A - Predicted Breakthrough Curve
10
20
30 40
Time (h)
50
60
70
Figure 16. Comparison of EHTD-predicted ETC to measured ETC for the Lost River Rise
using a typical input file (see Figure 12). Note the good prediction for tracer arrival times
developed by EHTD.
EHTD-suggested recommendations implemented shortly thereafter. Significant errors in
calculations and in implementation are likely to occur if there is a delay in following up on
field measurements.
6.2. THE QUALITY OF EHTD-PREDICTED RESULTS
A comparison of the EHTD-predicted ETC to the measured ETC for the Lost River Rise
is shown in Figure 16. It will be noted that whereas EHTD predicted a greater spread
than was actually measured, the estimated times for tracer arrival were very well predicted;
therefore, it is likely that the measured ETC would have been given better definition had
sampling proceeded according to the recommended sampling times (frequency) developed
by EHTD.
Of particular significance is the estimate for tracer mass versus the actual tracer mass
injected. EHTD recommended approximately twice as much tracer as was actually used
for the project. The excess mass recommendation in this instance reflects the greater-than-
expected longitudinal dispersion calculated by EHTD.
117
-------
Section 7. contains a detailed examination of how well EHTD functions under a variety
of conditions. It will be noted from Section 7. that EHTD appears to work extremely well
for any the environmental condition or design consideration.
6.3. EFFECT OF INITIAL CONCENTRATION AND EXPONENTIAL PRO-
DUCTION
The inclusion of an initial (background) concentration and exponential (growth) production
can greatly influence the shape of the ETC and two final estimated parameters: average
concentration and peak concentration. However, the EHTD-suggested tracer mass is not
affected.
These two additional conditions will generally be most beneficial when used in conjunc-
tion with a user-supplied solute mass (see Section 4.4., page 72) and EHTD is used as a
counterterrorism tool (see Section 8.). This may be especially true for exponential produc-
tion for the release of a bacteria if adequate nutrients and respiratory conditions exist.
6.3.1. Effect of an Initial Concentration
An initial concentration will cause the ETC to begin at a concentration that is equal to
the value entered by the user. This effect may or may not be evident depending upon the
initial concentration entered relative to the final peak concentration (see Lines 10 and 11 of
Table 25 and explanation on page 93).
6.3.2. Effect of Exponential Production
Exponential growth will cause the entire ETC to continue rising even as concentration is
decreasing because of the growth factors included. This effect may or may not be evident, de-
pending on the dimensionless exponential production constants (GAMMA 1, GAMMA2) entered
relative to the final peak concentration (see Lines 10 and 11 of Table 25 and explanation on
page 93).
6.3.3. Breakthrough Curve Shape
The influence of an initial concentration (Ci = 0.3 |j.g L"1) and exponential production
(71 = 72 = 0.5) (Figure 17) is reflected in Figure 18. A comparison of the data listed
in Figure 18 with the data listed in Figure 14 (pages 100-104) shows that ETC time data
and sample time data (columns 1 and 3 of Figures 14 and 18) are identical, but that ETC
118
-------
PROJECT NAME
KARST EXAMPLE — LOST RIVER CAVE SYSTEM
FLOW RELEAS RTIM (h) INFLOW (m~3/h)
1 1 0.0 0.0
UNITS
1
STATION NAME
LOST RIVER RISE
DISCHARGE (m~3/h)
6.408E3
INIT. CONC. (ug/L)
0.3
RETARDATION
1.0
1
1.0
10.0
DISTANCE (m)
8000.0
GAMMA 1
0.5
DECAY (1/h)
0.0
1
0.0
5.0
AREA (m~
18.8
GAMMA2
0.5
OPTIM
0
2)
SINUOSITY FACTOR
1.0
AVE. CONC. (ug/L)
18.3
STOP PROCESSING
END OF RUNS
Figure 17. Example input file with an initial concentration and exponential production
constants.
119
-------
PLOT FILE: LOST RIVER RISE
BREAKTHROUGH
TIME
(h)
.23471
.46941
.70412
.93883
1.1735
1.4082
1.6429
1.8777
2.1124
2.3471
2.5818
2.8165
3.0512
3.2859
3.5206
3.7553
3.9900
4.2247
4.4594
4.6941
4.9288
5.1635
5.3983
5.6330
5.8677
6.1024
6.3371
6.5718
6.8065
7.0412
7.2759
7.5106
7.7453
CURVE
CONG.
(Hg/D
30500
31000
31501
32001
32501
33001
33502
34002
34502
35003
35503
36004
36504
37005
37505
38006
38507
39007
39508
40009
40510
41011
41513
42014
42515
43017
43519
44020
44523
45025
45527
46030
46533
SAMPLE TIMES AND CONG.
TIME CONG.
(h)
9.9516
10.808
11.665
12.522
13.378
14.235
15.092
15.948
16.805
17.662
18.518
19.375
20.232
21.088
21.945
22.802
23.658
24.515
25.372
26.228
27.085
27.942
28.799
29.655
30.512
31.369
32.225
33.082
33.939
34.795
35.652
36.509
37.365
.51277
.53135
.55050
.57332
.61428
.71994
.99791
1.6297
2.8337
4.7708
7.4328
10.582
13.785
16.539
18.415
19.171
18.794
17.461
15.463
13.123
10.729
8.4939
6.5459
4.9405
3.6778
2.7235
.0271
.5345
.1954
.96782
.81845
.72243
.66184
2.
1
1
Figure 18. Data file generated by EHTD used to produce Figure 19.
120
-------
7.9800
8.2147
8 . 4494
8.6841
8.9189
9.1536
9.3883
9.6230
9.8577
10.092
10.327
10.562
10.797
11.031
11.266
11.501
11.735
11.970
12.205
12.439
12.674
12.909
13.144
13.378
13.613
13.848
14.082
14.317
14.552
14.787
15.021
15.256
15.491
15.725
15.960
16.195
16.429
16.664
16.899
.47036
.47539
.48043
. 48547
.49052
.49556
.50062
.50567
.51074
.51581
.52089
.52598
.53109
.53623
.54143
.54671
.55215
.55784
.56396
.57073
.57853
. 58787
.59947
.61428
.63359
.65902
.69260
.73679
.79452
.86919
.96461
1.0850
1 . 2349
1.4189
1.6418
1.9082
2.2224
2 . 5882
3.0085
38.222
39.079
39.935
40.792
41.649
42.505
43.362
44.219
45.075
45.932
46.789
47 . 645
48.502
49.359
50.215
51.072
51.929
52.786
53.642
54.499
55.356
56.212
57.069
57.926
58.782
59.639
60.496
61.352
62.209
63.066
63.922
64.779
.62428
.60136
.58757
.57940
.57461
.57184
.57025
.56936
.56885
.56857
. 56842
.56833
.56829
.56826
.56825
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
Figure 18. Data file generated by EHTD used to produce Figure 19 continued.
121
-------
17.134
17.368
17.603
17.838
18.072
18.307
18.542
18.777
19.011
19.246
19.481
19.715
19.950
20.185
20.419
20.654
20.889
21.124
21.358
21.593
21.828
22.062
22.297
22.532
22.767
23.001
23.236
23.471
23.940
24.409
24.879
25.348
25.818
26.287
26.757
27.226
27.695
28.165
28.634
3 . 4857
4.0208
4.6137
5.2630
5.9659
6.7181
7.5142
8.3473
9.2094
10.091
10.984
11.876
12.757
13.617
14.444
15.230
15.963
16.636
17.241
17.771
18.221
18.587
18.867
19.059
19.163
19.181
19.115
18.967
18.449
17.667
16.674
15.523
14.268
12.958
11.639
10.347
9.1117
7.9558
6.8937
Figure 18. Data file generated by EHTD used to produce Figure 19 continued.
122
-------
29.104
29.573
30.042
30.512
30.981
31.451
31.920
32.390
32.859
33.328
33.798
34.267
34.737
35.206
35.675
36.145
36.614
37.084
37.553
38.022
38.492
38.961
39.431
39.900
40.370
40.839
41.308
41.778
42 . 247
42.717
43.186
43.655
44.125
44.594
45.064
45.533
46.002
46 . 472
5.9339
5.0793
4.3287
3.6778
3.1197
2 . 6464
2.2490
1.9185
1 . 6460
1.4232
1 . 2425
1.0970
.98058
.88816
.81521
.75798
.71334
.67871
.65199
.63147
.61579
.60386
.59482
.58801
.58289
.57906
.57621
.57409
.57252
.57136
.57051
.56989
.56943
.56910
.56886
.56868
.56856
. 56847
Figure 18. Data file generated by EHTD used to produce Figure 19 continued.
123
-------
46.941
47.411
47 . 880
48.350
48.819
49 . 288
49.758
50.227
50.697
51.166
51.635
52.105
52.574
53.044
53.513
53.983
54.452
54.921
55.391
55.860
56.330
56.799
57.268
57.738
58.207
58.677
59.146
59.615
60.085
60.554
61.024
61.493
61.963
62.432
62.901
63.371
63.840
64.310
64.779
.56840
.56835
.56832
.56830
.56828
.56827
.56826
.56825
.56825
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
.56824
Figure 18. Data file generated by EHTD used to produce Figure 19 continued.
124
-------
I
§
TRACER MASS =1.04E+00 kg
Breakthrough Curve
Sampling Times
70
Figure 19. Effect of including an initial concentration and exponential production to the
Lost River Cave System data. Note that the ETC does not begin at zero concentration and
exhibits a gently rising slope prior to initiating a steep rise in response to tracer release.
concentration data and sample concentration data (columns 2 and 4 of Figures 14 and 18)
are very different.
Using the data listed in Figure 18, Figure 19 depicts the Lost River Cave System with
an Ci = 0.3 |j.g L"1 and exponential production (ji = 72 = 0.5) applied. It is evident from
Figure 19 that these conditions have a significant influence on the final ETC when compared
with the conditions of Figure 13, as shown in Figure 20.
6.3.4. Average and Peak Concentration Estimates
The general output file (Figure 15) will be slightly altered when an initial concentration
and/or exponential production are supplied in an input file to specifically reflect changes in
the estimated C and Cp. Providing an initial concentration and/or exponential production
will cause the bottom of EHTD-produced Table 3.1 to be altered to appear as Figure 21
(see Figure 15 on page 111 for comparison). In addition to producing a modified Table 3.1,
EHTD will also produce a Table 5.1 immediately after Table 4.1. The EHTD-produced
Table 5.1 will provide an estimate of C and Cp (Figure 22).
125
-------
20
15
10
Q Q Measured Data
_A-A - No Additional Conditions
_ Additional Conditions
10
20
30 40
Time (h)
50
60
70
Figure 20. Comparison of the effect of including an initial concentration and exponential
production to the Lost River Cave System data. The label No Additional Conditions
indicates just the tracer release data and the label Additional Conditions indicates that
an initial concentration and exponential production are included with the tracer release
data.
126
-------
FINAL TRACER-MASS REDUCTION FACTORS
SYSTEM VOL. DILUTION VOL. RETARDATION DECAY
(nT3) (nT3) (DIMEN.)
1.50E+05 1.50E+05 l.OOE+00 O.OOE+00
TRACER CONCENTRATIONS
SET CONC. AVERAGE CONG. PEAK CONG.
1.83E+01 1.8300E+01* 1.8505E+01*
*PRELIMINARY ESTIMATES FOR AVERAGE CONC. AND PEAK CONC.
SEE REVISED ESTIMATES LISTED IN TABLE 5.1.
Figure 21. Modified EHTD-produced portion of Table 3.1 to reflect influence of an initial
concentration and/or exponential production.
*** TABLE 5.1. REVISED TRACER CONCENTRATIONS ***
SET CONC. AVERAGE CONC. PEAK CONC.
1.83E+01 1.8967E+01 1.9181E+01
Figure 22. Example EHTD-produced Table 5.1 to reflect influence of an initial concentration
and/or exponential production.
127
-------
7. TRACER TEST DESIGN EXAMINATION DATA SETS
Several hydrological tracer tests representing various environmental and design condi-
tions are listed in Table 26. The results of each of the measured eight tracer tests were
Table 26. Example test data sets.
Test Name Test Type
Flowing Stream
Uvas Creek Small Creek
Missouri River Large River
Dyers Spring Solution Conduit
Variegated Glacier Meltwater Channel
Porous Media
Test Site Wilerwald Natural Gradient
Kirchdorf-Unteropfingen Site Forced Gradient
Mobile Site Injection Withdrawal
Chalk River Recirculation
compared with forecasted results. For purposes of the type of analysis, flow through a so-
lution conduit and glacial-melt water channel are listed under the flowing stream category
along with small surface-water creeks and large rivers. This is because flow through a so-
lution conduit behaves more like surface-water flow than porous media flow even though
flow through solution conduits is correctly classed as ground-water flow. Prediction of flow
through solution conduits and glacial-meltwater channels requires treatment similar to that
of surface-water flow.
7.1. FLOWING STREAMS
Two surface-water streams representing small and large flows were examined to evaluate
the effect of extreme flow discharge ranges on prediction capabilities. Uvas Creek is a small
stream that was traced in the mid 1970s. The Missouri River is a large river that was traced
in the mid 1960s. Dyers Spring was chosen as a representative tracer test through a solution
conduit to a potable-water spring. All three tracer tests were conducted and analyzed by
the U.S. Geological Survey. A glacial-meltwater channel (Variegated Glacier) was also listed
as a flowing stream because water flow through glacial meltwater channels behaves similarly
to flow in surface-water streams.
128
-------
7.1.1. Small Creek
Uvas Creek was traced in 1976 using a steady 3-hour injection of 1068 g of chloride in
late summer during a low flow period (Bencala and Walters, 1983; Zand et al., 1976). The
emphasis of the tracing test was to investigate the mass transport processes in a small
stream. The experimental study was limited to a 610 m reach, with widths ranging from
0.3 to 4 m. Flow rate at the time of the study was 45.0 m3 h"1. Tracer concentration
measurements were taken at selected reaches where measured flow rates varied slightly from
45.0 m3 h"1. For this evaluation, tracer recovery at reach 281 m was used. The channel was
composed of a rough bed with alternating pools and riffles and a steep slope (0.03 m m"1).
7.1.2. Large River
The Missouri River was traced along a 243 km reach between Sioux City, Iowa and
Plattsmouth, Nebraska, in 1967. The purpose of the tracer test was to obtain sufficient
data to simultaneously define axial dispersion, transverse mixing, cross-sectional geometry,
and transverse velocity distribution. Approximately 54 kg of Rhodamine WT (C.I. Acid
Red 388) were injected as a line source extending across the middle half of the channel
(Yotsukura et al., 1970, pp. G3-G5).
Sampling stations were located in a manner such that cross-sectional areas could be
divided into four increments with approximately equal discharges. Discharge measurements
were taken at the four cross-sections by the current meter method. Sampling frequency
varied from 15 minutes to 2 hours, depending on the expected rate of change of concentration
(Yotsukura et al., 1970, pp. G5-G6).
7.1.3. Solution Conduit
Dyers Spring is a blue-hole rise pit that connects an impenetrable solution-conduit system
with a nearby karst window developed in the St. Louis Limestone. It is an important water-
supply spring in Elizabethtown, Kentucky (Mull and Lyverse, 1984, p. 21). Limestone
is exposed at the bottom of the karst window, where a stream reportedly flows into a
swallet. No other external drainage has been observed, so all water entering the karst
window eventually drains into the swallet (Mull et al., 1988b, p. 58).
Several tracer tests to Dyers Spring using the karst window were performed by the U.S.
Geological Survey with varying degrees of tracer mass recovery (Mull et al., 1988b, p. 71).
The primary intent of the tracer tests was to assess the solute transport processes operative
129
-------
in the system. Recoveries ranged from 54 to 172%, which is probably a function of flow
conditions when the tracer tests were undertaken and discharge measurement errors.
The Dyers Spring tracer test considered here consisted of an impulse injection of 3.57 g
of Rhodamine WT, which resulted in 63% mass recovery. Errors in discharge estimation,
Rhodamine WT deaminoalkylation (Kafi, 1998, pp. 33-35), and/or isomer-specific sorption
(Sutton et al., 2001) may have partially affected tracer-mass recovery estimates. Moderate-
flow conditions (Mull et al., 1988b, pp. 25, 69) may also have caused unknown tributary
flow to or from the solution conduit and a consequent reduced tracer mass recovery (Field
and Nash, 1997).
7.1.4. Meltwater Channel
A tracer test was conducted in 1983 at Variegated Glacier in southeastern Alaska immedi-
ately post-glacial surge, when meltwater discharge from the glacier increased greatly. An
approximately 5.2 kg pulse (£2 = 10 minutes) of Rhodamine WT was injected through a
borehole at the base of the glacier (Brugman, 1987, p. 93) and recovered at Lower Stream,
10 km downstream. Hot water was injected into the borehole prior to dye injection to en-
sure good hydraulic connection with the basal water system (Brugman, 1987, pp. 91-91).
Discrete samples were collected at the glacier terminus. Sample-collection frequency was
initially set at 40 minutes but was lengthened after 8 hours (Brugman, 1987, p. 93).
7.2. POROUS MEDIA
Tracer tests are commonly conducted in porous media aquifers in a variety of forms. These
tracer tests rarely include natural-gradient tracer tests because of the typically long travel
times involved. To increase the rate of transport, forced-gradient tracer tests, injection-
withdrawal tracer tests, and recirculation tracer tests are often employed. Table 26 lists
four tracer tests representing each of these types of tracer tests.
7.2.1. Natural-Gradient Tracer Test
Natural-gradient tracer tests in porous media are difficult and generally aggravating to
implement because of the design information required and the very long tracer transport
times involved. Even so, natural-gradient tracer tests are desirable because the flow field
is not distorted, as occurs with forced-gradient tracer tests. Test Site Wilerwald, located
northeast of Berne, Switzerland, in the Swiss Central Plateau, was established to evaluate
130
-------
solute transport processes in a porous media aquifer. The aquifer is in the Emme Valley and
consists of postglacial Holocene sandy gravels that vary in thickness from a few meters to
88 m with ground-water depths that vary from 0.5 to 3 m (Leibundgut, 1992, pp. 230-231).
In September, 1985, 1 kg of sodium fluorescein (C.I. Acid Yellow 73) dissolved in 90 L
of water was released over a one hour period into an injection well. Sampling commenced
almost immediately and continued for 24 weeks at several downgradient wells. The furthest
well sampled for tracer from the injection well was approximately 200 m to the northwest
(Leibundgut and De Carvalho Dill, 1992, pp. 232-233). The basic transport parameters
used to describe the aquifer consisted of a hydraulic conductivity K = 8.64 m h"1, aquifer
thickness b = 10 m, effective porosity ne = 12 — 17%, and hydraulic gradient i = 0.4%
(Maloszewski et al., 1992b, p. 239).
7.2.2. Forced-Gradient Tracer Test
A tracer and aquifer test were simultaneously conducted over a period of several months at
the Kirchdorf-Unteropfingen area within the Iller Valley in Germany. Alpine Rhine glacial
materials consisting of well-rounded, stratified, fine to coarse gravel with intercalated sand
fractions make up the valley aquifer. The extraction well was pumped at a rate of 1368
m3 h"1. During the pumping test, 3 kg of sodium fluorescein were released immediately
into an observation well situated 585 m from the extraction well. Initial tracer recovery
occurred at the extraction well within about 3 days and continued for more than 100 days
(Kafi, 1998, pp. 515-516). The pump test yielded a transmissivity of 1019 m2 h"1 (K = 116
m h"1) and specific yield = 0.14, which was taken to be the same as effective porosity (Kafi,
1998, pp. 515-516) for this evaluation.
7.2.3. Injection-Withdrawal Tracer Test
An injection withdrawal two-well tracer test consists of injecting water containing tracer
into an injection well and withdrawing water from an extraction well at an equal rate so
that equilibrium may be established. Such a test was conducted in a soil borrow area at
the Barry Steam Plant of the Alabama Power Company near Mobile, Alabama, in the late
summer of 1984. The surface is composed of Quaternary-age, low-terrace deposits consisting
of interbedded sands and clays down to a depth of 61 m. Below these deposits a Miocene
series of undifferentiated sands, silty clays, and thin-bedded limestones extend to a depth
of 305 m (Molz et al., 1986a, p. 38).
131
-------
At the Mobile site bromide was injected into a well over a period of 3.19 days. The
entire tracer test lasted 32.5 days (Molz et al., 1986b). The injection and withdrawal
wells, separated by a distance of 38.3 m, were operated continuously at 57 m3 h"1 (Molz
et al., 1986a, p. 55) to cause steady-state conditions between the injection-withdrawal wells.
Details of the test are described in Molz et al. (1986b) and Molz et al. (1986a, pp. 52-60,
71).
7.2.4. Recirculation
A two-well recirculation tracer test is the same as an injection/withdrawal tracer test except
that the extracted water is recirculated back into the injection well. Such a tracer test
was conducted at the Chalk River site. The basic tracer test design parameters for a
recirculation tracer test conducted at the Chalk River site are listed in Huyakorn et al.
(1986) and described in detail in Pickens and Grisak (1981). Two glaciofluvial sand aquifers
are separated by a 1 m layer of silty clay, which was taken as the bottom confining layer
for the aquifer being traced. This sand aquifer is 8.2 m thick and is confined above by a
17 cm-thick silty-clay layer. Aquifer tests at the site resulted in a K that ranged from 720
to 7200 m h"1, but a single-well tracer test suggests K = 5040 m h"1 (Pickens and Grisak,
1981).
The recirculation tracer test consisted of two wells 8 m apart that were operated at
a flow rate of 1.62 m3 h"1. Tracer was injected for a period of 3.22 days with an initial
concentration of 4.1 x 10~3 |J,g L"1 (Huyakorn et al., 1986), which translates into a tracer
mass of 521 |j,g.
7.3. TRACER-TEST DESIGN RESULTS
The eight tracer tests listed in Table 26 were used to test EHTD. Because these tests
represent a range of tracer test types, the robustness of EHTD could be examined.
Simulations using these eight data sets consisted of using only those measured or estimated
field parameters necessary for application of EHTD while excluding specific tracer test-
determined parameters. Set average tracer concentration C and possible tracer reactions,
tracer retardation Rd and tracer decay /j, were adjustable parameters so that measured
peak tracer concentration Cp and measured tracer mass M could be matched. Normal
use of EHTD to predict tracer test results prior to test implementation would not require
adjustment to match Cp or M except as may be desired.
132
-------
Table 27. Required flowing stream tracer test design specifics.
Parameter
Q,
L,
A,
i2,
tv,
Ly ,
Ly j
m3h-l
m
m2
h
m3
M-gL"1
HgL-1
Uvas Creek
4.79 x
2.81 x
3.60 x
3.00 x
3.12 x
3.19 x
101
102
lo-1
10°
103
103
Missouri
3.47
2.43
5.23
1.62
1.62
x
x
X
X
X
River
106
105
102
10°
10°
Dyers
1.16
9.14
1.84
4.14
4.12
Spring Variegated Glacier
x
x
x
x
x
102
102
10°
10°
10°
1.44
1.00
6.15
1.67
3.69
1.94
x 105
x 104
x 101
x ID'1
x 101
x 101
a Average tracer concentration for nonreactive tracer transport.
b Average tracer concentration for reactive tracer transport.
7.3.1. Flowing Streams Results
Flowing stream tracer tests make up the first four tracer tests listed in Table 26. These
four tests include small and large surface-water streams, karst solution conduit, and glacial-
meltwater stream. The parameters required for EHTD simulation for these tests are listed
in Table 27. EHTD simulation of flowing streams requires only measurement or estimates
for discharge Q, longitudinal distance L, cross-sectional area A, tracer release mode £2, and
set average tracer concentration C. Two listings for C appear in Table 27 because n may
cause the predicted Cp to fall below the measured Cp that occurs with no tracer decay. Of
the four tracer tests listed in Table 27, a slightly decreased Cp was a problem only for the
Uvas Creek tracer test.
Hydraulic results of the EHTD-predicted BTCs for the four flowing stream tracer tests
are compared with the actual ETC results in Table 28. Tracer injection specifics are
listed in Table 29 and include consideration tracer mass, injection concentration d, pulse
injection volume ty, injection rate q, flow system volume V, and dilution volume Dy, which
represents the combined effect of the injection flow rate q with discharge Q.
7.3.1.1. Uvas Creek Tracer Test. The tracer test conducted at Uvas Creek was
chosen as a test case to evaluate the ability of EHTD to predict tracer tests results in very
small streams when t2 is large. For instances where t2 > t, Yu et al. (1999) recommend the
ETC be solved for a Heaviside condition up to Cp of the ETC. For the Uvas Creek injection,
t2 was 3.00 hours (Table 27), but tracer recovery occurred within several minutes at reach
133
-------
Table 28. EHTD-predicted BTCs versus measured BTCs for the flowing stream tracer tests.
Data Seta'b t, hours
tp, hours
v, m h l
D, m2 h-1
Pe, dirnen.
ti, hours
tf, hours
Uvas Creek Tracer Test
Measured
EHTD-N
EHTD-R
2.11 x
2.11 x
2.11 x
10°
10°
10°
4.33 x
4.03 x
4.03 x
10°
10°
10°
1.33 x 102
1.33 x 102
1.33 x 102
8.64 x 102
4.52 x 102
4.52 x 102
4.33 x
8.26 x
8.26 x
101
102
102
5.33 x 10-1
7.56 x 1Q-1
7.63 x 10-1
1.67 x
1.36 x
1.34 x
lo-1
lo-1
lo-1
Missouri River Tracer Test
Measured
EHTD-N
EHTD-R
4.20 x
3.66 x
3.66 x
101
101
101
4.00 x
3.59 x
3.59 x
101
101
101
5.78 x 103
6.62 x 103
6.62 x 103
5.35 x 106
1.90 x 107
1.90 x 107
2.62 x
8.46 x
8.46 x
102
101
101
3.40 x 101
1.53 x 101
1.73 x 101
1.00 x
1.29 x
1.46 x
10°
10°
10°
Dyers Spring Tracer Test
Measured
EHTD-N
EHTD-R
1.72 x
1.45 x
1.45 x
101
101
101
1.45 x
1.42 x
1.41 x
101
101
101
5.38 x 101
6.32 x 101
6.32 x 101
3.28 x 102
6.61 x 102
6.61 x 102
Variegated Glacier Tracer
Measured
EHTD-N
EHTD-R
5.00 x
4.27 x
4.27 x
10°
10°
10°
4.30 x
4.23 x
3.59 x
10°
10°
10°
2.00 x 103
2.34 x 103
2.34 x 103
2.09 x 105
3.58 x 105
3.58 x 105
1.50 x
8.73x
8.73x
Test
9.57 x
6.55 x
6.55 x
102
101
101
101
101
101
1.15 x 101
6.22 x 10°
6.39 x 10°
1.90 x 10°
1.53 x 10°
1.76 x 10°
5.00 x
5.09 x
5.32 x
7.00 x
1.93 x
1.80 x
lo-1
lo-1
lo-1
lo-1
lo-1
lo-1
a EHTD-N = nonreactive tracer test results. EHTD-R = reactive tracer test results.
b Reactive results are listed as though no tracer reactions have occurred.
-------
CO
Oi
Table 29. EHTD-predicted results versus measured results for the flowing stream tracer tests.
Data Seta
M, g
I
^p,
-i
m
/, m h
V, m3
m
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
1.
8.
1.
5.
7.
8.
3.
2.
3.
5.
9.
5.
07
97
07
44
88
91
57
63
56
24
76
23
X
X
X
X
X
X
X
X
X
X
X
X
103
102
103
104
104
104
10°
10°
10°
106
103
106
Uvas Creek Tracer Test
6.25 x 103
6.24 x 103 6.24 x 103 1.44 x 102 4.79 x 101
6.255 x 103 6.25 x 103 1.70 x 102 5.68 x 101
Missouri River Tracer Test
1.64x10°
1.64x10°
1.64x10°
Dyers Spring Tracer Test
4.19 x 10°
4.19 x 10°
4.19x10°
Variegated Glacier Tracer Test
2.38 x 1011 3.70 x 101 2.20 x 10~2 1.32 x 10'1
4.43 x 108 3.70 x 101 2.20 x 10~2 1.32 x 10'1
2.37xlOn 3.72 x 101 2.20 x 10~2 1.32 x 10'1
1.
1.
1.
1.
1.
1.
2.
1.
1.
7.
6.
7.
.01
.01
.01
.46
.27
.44
.00
.68
.77
.20
.15
.69
x
x
X
X
X
X
X
X
X
X
X
X
102
102
102
10s
10s
10s
103
103
103
105
105
105
1.01 x
1.01 x
1.27 x
1.44 x
1.68 x
1.77 x
6.15 x
7.69 x
102
102
108
108
103
103
105
105
EHTD-N = nonreactive tracer test results. EHTD-R = reactive tracer test results.
-------
o>
Measured Data
— NonReactive Transport
—H-g.- Reactive Transport
2 -
O O -Q
15 20
Time (h)
25
30
Figure 23. Comparison of measured data for the Uvas Creek site tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.0
and n = 0.08 h~l.
281 (281 m from injection site) and f was 2.11 hours (Table 28).
Reach 281 was chosen to evaluate EHTD because the short travel distance coupled with
the relatively long t2 caused a plateau in the ETC (Figure 23). Setting C = 3.12 mg L"1
for nonreactive transport (Table 27) resulted in an almost exact fit visually of the EHTD-
predicted results to the actual ETC, but the EHTD-predicted tracer mass was slightly less
than that injected during the actual tracer test (Figure 23). Setting C = 3.19 mg L"1 and
H = 0.08 h"1 for reactive transport also resulted in a nearly exact fit visually of the EHTD-
predicted results to the actual ETC while matching the injected tracer mass (Figure 23).
Only the measured long ETC tail was not predicted by EHTD. Both the nonreactive and the
reactive EHTD-predicted ETC plateaus match the measured ETC plateau. Accounting for
IJL = 0.08 h"1 had no measurable effect on the ETC or the estimated transport parameters.
EHTD substantially underestimated D (Table 28), but any adverse effects appear to be
insignificant because EHTD-recommended sampling times were appropriate for defining the
ETC.
EHTD-generated BTCs for both nonreactive and reactive tracer tests predicted the
136
-------
measured ETC in the sense that the initial sample collection time and sample collection
frequency recommended by EHTD would have resulted in an accurate depiction of the actual
ETC. The occurrence of the long tail may or may not have been detected, depending on
whether sample collection continued after 11 hours.
The Uvas Creek travel times listed in Table 28 show average travel time t to be less
than the time to peak concentration tp (t < tp), which appears contrary to typical tracer
tests, where t > tp. The greater tp for the Uvas Creek tracer test is an artifact of the long
ti relative to actual tracer travel times. It should be noted that the measured f and v were
obtained from Q/A and related to L in Bencala and Walters (1983) is the same method used
by EHTD (Field, 2002c), which explains the exact match by the EHTD-estimated t and
v. Breakthrough-curve analysis using QTRACER (Field, 2002b), modified to account for
short-pulse releases (Wolff et al., 1979) and long-pulse releases (Sardin et al., 1991), resulted
in a t = 2.08 hours and v = 135 m h"1 which quite reasonably match the measured results.
However, QTRACER estimated D = 542 m2 h"1, which is midway between the measured
D and the EHTD-estimated D.
Because a relatively insignificant amount of tracer was added directly to the stream
water, Dv = V for both the measured and the EHTD-predicted results (Table 29). The
exact match for both of the EHTD-predicted volumes with the measured V was surprising
and is not expected to occur in other similar instances.
7.3.1.2. Missouri River Tracer Test. Flow in streams similar to the Missouri River
is difficult to assess due to sheer size. The Missouri River tracer test used to evaluate
EHTD probably represents the simplest case tested here because an impulse release of a
large quantity of tracer was recovered sufficiently far from the injection point (243 km)
as to not be adversely influenced by the actual injection. Figure 24 shows the results of
the Missouri River tracer test. The nonreactive case adequately represents the results of
the Missouri River tracer test, although the measured ETC was not ideally realized by the
EHTD prediction because the nonreactive tracer test still suggested appropriate sampling
times that would result in detection of the ETC. In addition, somewhat more tracer than
was required was recommended by EHTD (Table 28) — a result of overestimating dispersion
for such a simple flow system.
The reactive case allowed for a match of the measured ETC peak, but EHTD then
recommended 1.5x more tracer than was actually needed. EHTD-estimated f = 36.6 hours
and v = 6623 m h"1 reasonably matched the measured values, but required Rd = 1.13
137
-------
1.5
0.5
Q Q Measured Data
_A-A — NonReactive Transport
. _ Reactive Transport
20
40
60
Time (h)
80
100
120
Figure 24. Comparison of measured data for the Missouri River tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.13
and n = 0.0 h'1.
to obtain a better match to the measured ETC and tracer mass injected. The EHTD-
estimated D = 1.90 x 107 m2 h"1 is clearly overestimated (Table 28), but this inaccuracy
would not appear to adversely affect the tracer test because the measured ETC would have
been defined if the EHTD-recommended sampling schedules were implemented.
As with the Uvas Creek tracer test, a relatively insignificant amount of tracer was added
directly to the stream water, resulting in Dy = V for both of the EHTD-predicted results
(Table 29). Interestingly, although the EHTD-predicted V and Dy reasonably approximated
the measured V, the EHTD-predicted V and Dv for the reactive case very nearly matches
the measured V.
7.3.1.3. Dyers Spring Tracer Test. Ground-water flow and solute transport through
solution conduits are commonly assessed by conducting quantitative tracer tests because
conventional methods, such as pumping tests, are generally insufficient for adequately
defining hydraulic parameters. Designing quantitative tracer tests in previously untraced
karstic terranes can be very difficult. Typically, a trial-and-error approach that relies on
138
-------
4 -
3 -
s
g
Measured Data
— NonReactive Transport
|T]-fT._ Reactive Transport
Od
Figure 25. Comparison of measured data for the Dyers Spring tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.05
and n = 0.018 h~l.
more common qualitative tracer tests and past professional experience are used as a means
for designing a quantitative tracer test (Mull et al., 1988a, pp. 26, 28).
Measured Cp at Dyers Spring occurred later than the nonreactive EHTD-predicted
results when A is estimated from peak velocity vp (Figure 25). No prior estimates for
the Dyers Spring A coupled with the measured Q were available. Typically, conduit A is
estimated using v calculated from the ETC, but the long ETC tails associated with Dyers
Spring (Mull et al., 1988a, p. 69) as a result of immobile flow regions tends to skew v (Field
and Finsky, 2000). The long tails for the measured BTCs adversely affect the v calculation
by inferring slower transport, which results in a smaller calculated cross-sectional area and
consequently causes a later tracer breakthrough (Field, 2002c). Substituting vp for v results
in an earlier tracer breakthrough than that of the measured recovery, which suggests that
vp and v bracket the true velocity, as was shown to be the case by Field and Pinsky (2000).
Allowing for tracer retardation Rd = 1.05 and tracer decay p, = 0.018 h"1 results in a
ETC that adequately matches the measured ETC and a tracer-mass estimate that matches
the actual tracer mass released (Table 29). Although the measured Cp was missed by the
139
-------
40 -
30 -
s
g
Q Q— Measured Data
_A-A - NonReactive Transport
—H-H. . Reactive Transport
10
15
Time (h)
Figure 26. Comparison of measured data for the Variegated Glacier tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.25
and n = 1.595 h~l.
EHTD-predicted nonreactive results, EHTD was successful in that both nonreactive and
reactive estimates for tracer mass were adequate and the suggested sampling times would
approximate the measured ETC. Using the larger estimate for cross-sectional area obtained
from v would also have been successful in that the suggested sampling times would have
produced the measured ETC when the tracer test was implemented.
Again, a relatively insignificant amount of tracer was added directly to the stream water
at the bottom of the karst window, causing Dy = V for both the EHTD-predicted results
(Table 29). Neither of the predictions for V by EHTD matched the measured V, but
the approximations may be regarded as sufficiently close to the measured value for V to
adequately represent the tracer test.
7.3.1.4. Variegated Glacier Tracer Test. Tracer testing is commonly used to define
the hydraulic parameters associated with glacial outflows. The Variegated Glacier post-
surge tracer test ETC was very reasonably approximated by EHTD for both nonreactive
and reactive considerations (Figure 26). The EHTD-predicted hydraulic parameters t = 4.27
140
-------
hours, tp = 4.23 hours, v = 2342mb-1, D = 3.58xl05 m2 tr^andPe = 65.5 are close to the
approximations obtained from the measured ETC. However, the EHTD prediction for the
nonreactive case resulted in an earlier tracer breakthrough than that of the measured result
(Table 28) and underestimated tracer mass by nearly three orders of magnitude (Table 29).
Increasing tracer mass using EHTD required considerable tracer loss (// = 1.595 h"1) and
some retardation (Rd = 1.25).
Accounting for retardation causes a slight shift in the EHTD-predicted ETC, allowing for
a reasonable match with the measured ETC. Other than the inadequate estimate for tracer
mass for the nonreactive case, the EHTD-predicted results for the Variegated Glacier tracer
test were sufficient for defining the ETC. Prior knowledge of the nature of glacial outflows
and the tracer used (Rhodamine WT for this tracer test) should allow for an approximation
of the appropriate estimates to use for tracer decay and retardation.
For the Variegated Glacier tracer test, a relatively insignificant amount of tracer was
added directly to the stream water as a small, short-duration pulse with the effect resulting
in Dv = V for both of the EHTD-predicted results (Table 29). The EHTD-predicted
volumes bracket the measured value for V, suggesting that the EHTD-predicted volumes
are reasonable, especially for the reactive case.
7.3.2. Porous Media Results
The second set of the four tracer tests listed in Table 26 represents a typical range of tests
conducted in porous media aquifers. The tests included a natural-gradient tracer test, a
forced-gradient tracer test, an injection/withdrawal tracer test, and a recirculation tracer
test. EHTD prediction of tracer test results in porous media requires more measured and/or
estimated parameters than is required for flowing streams. The parameters necessary for
EHTD simulation of porous media systems are listed in Table 30. For porous media aquifers,
EHTD requires measurements or estimates for Q, L, effective porosity ne, thickness 6,
transverse spread T, t2, and C. For all but natural-gradient tracer tests, EHTD estimates T
(Field, 2002a). As with the flowing stream tracer tests, two listings for C appear in Table 30.
Tracer decay tends to cause predicted Cp to fall below the predicted Cp that occurs with
no tracer decay and the measured Cp unless specific adjustments (e.g., increased C) are
incorporated. Decreases in Cp was a problem in each of the four porous media tracer tests
listed in Table 30.
Hydraulic results of the EHTD-predicted BTCs for the four porous media tracer tests
are compared with the actual ETC results in Table 31. Tracer injection specifics are listed
141
-------
Table 30. Required porous media tracer test design specifics.
Parameter Test Site Wilerwald Kirchdorf Sitea Mobile Sitea
Q, m3 tr1
L, m
n
b, m
T, m
*2, h
tv, m3
C^ n-g L"1
~CC UE L"1
2.59 x IO1
2.00 x IO2
1.50 x 1Q-1
1.00 x IO1
7.50 x IO1
1.00 x 10°
9.00 x 10~2
3.10 x 10°
1.84 x 10°
1.37 x IO3
5.85 x IO2
1.40 x 1Q-1
8.80 x 10°
2.71 x 10°
2.66 x 10°
5.69 x IO1
3.83 x IO1
3.50 x ID'1
2.16 x IO1
7.66 x IO1
5.69 x IO1
9.80 x IO3
1.09 x IO4
Chalk Rivera
1.62 x 10°
8.00 x 10°
3.80 x ID'1
8.20 x 10°
7.73 x IO1
1.62 x 10°
3.06 x IO-4
3.64 x 1Q-4
a Transverse tracer spread not estimated for forced-gradient tracer tests.
b Average tracer concentration for nonreactive tracer transport.
c Average tracer concentration for reactive tracer transport.
142
-------
Table 31. EHTD-Predicted BTCs versus measured BTCs for the porous media tracer tests.
CO
Data Seta>b t, hours
Measured
EHTD-N
EHTD-R
5.38 x
8.68 x
8.68 x
102
102
102
tp, hours
1.50 x
8.20x
6.90 x
102
102
102
v , m h l D, m2 h l
Wilerwald Tracer Test
3.47 x ID"1 5.76 x 10°
2.30 x 1Q-1 1.46 x 10°
2.30 x 1Q-1 1.46 x 10°
Kirchdorf- Unteropfingen Tracer
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
5.62 x
9.68 x
9.68 x
3.60 x
2.04 x
2.04 x
102
102
102
102
102
102
4.06 x
9.00 x
8.91 x
2.10 x
2.30x
2.08 x
102
102
102
102
102
102
5.22 x ID'1 3.82 x 101
6.04 xlQ-1 1.23X101
6.04 xlQ-1 1.23X101
Mobile Site Tracer Test
1.24X1Q-1 3.77X1Q-1
1.88 x 10"1 2.97 x 10"1
1.88 x ID"1 2.97 x 10"1
Pe, dimen.
1.21 x
3.16 x
3.16 x
Test
8.00 x
2.86 x
2.86 x
1.80 x
2.42 x
2.42 x
101
101
101
10°
101
101
101
101
101
ti, hours
3.00 x
1.22 x
1.23 x
6.00 x
1.89 x
1.89 x
6.30 x
3.82 x
4.18 x
101
102
102
101
102
102
101
101
101
tf, hours
3.00 x
6.10 x
4.41 x
2.00 x
4.24 x
4.24 x
5.00 x
1.91 x
2.09 x
101
101
101
101
101
101
10°
101
101
Chalk River Site Tracer Test
Measured
EHTD-N
EHTD-R
1.26 x
1.29 x
1.29 x
102
102
102
1.80 x
7.74 x
1.68 x
102
102
102
6.36 x 10~2 1.04 x 10~2
6.21 x 10~2 2.46 x 10~2
6.21 x 10~2 2.46 x 10~2
4.90 x
2.02 x
2.02 x
101
101
101
8.40 x
2.42 x
2.67 x
101
101
101
1.80 x
1.21 x
1.34 x
101
101
101
a EHTD-N = nonreactive tracer test results. EHTD-R = reactive tracer test results.
b Reactive results are listed as though no tracer reactions have occurred.
-------
Table 32. EHTD-predicted results versus measured results for the porous media tracer tests.
Data Seta
M, g
IG, M-g
-i
C,
m
q, m3 h
3 L,-l
V, m3
A/,m3
Test Site Wilerwald Tracer Test
Measured
EHTD-N
EHTD-R
1.00
4.36
1.00
x
x
X
IO3
IO1
IO3
1.11 x
4.83 x
1.12 x
IO4 3.20 x 10° 9.00 x 10~2
IO5 3.20 x 10° 9.00 x 10~2
IO7 3.20 x 10° 9.00 x 10~2
9.00 x
9.00 x
9.00 x
io-2
io-2
io-2
9.43 x
2.25 x
2.25 x
IO4
IO4
IO4
2.26 x
2.26 x
IO4
IO4
Kirchdorf-Unteropfingen Tracer Test
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
Measured
EHTD-N
EHTD-R
3.00
2.34
3.01
7.42
1.89
7.45
5.21
1.54
5.21
X
X
X
X
X
X
X
X
X
IO3
IO3
IO3
IO5
IO5
IO5
10~4
10~4
10~4
1.69 x
4.34 x
1.71 x
4.10 x
1.23 x
4.17 x
2.80 x 10°
2.80 x 10°
2.81x10°
Mobile Site Tracer Test
IO5 2.20 x IO4 4.36 x IO3
IO4 2.20 x IO4 4.36 x IO3
IO5 2.19 x IO4 4.36 x IO3
Chalk River Site Tracer Test
10~3 8.32 x 10~4 1.25 x IO2
10~3 8.33 x 10~4 1.25 x IO2
10~3 8.34 x 10~4 1.25 x IO2
5.69 x
5.69 x
5.69 x
1.62 x
1.62 x
1.62 x
IO1
IO1
IO1
10°
10°
10°
7.70x
1.32 x
1.33 x
2.05 x
1.16 x
1.28 x
2.04 x
2.09 x
2.30 x
IO5
IO6
IO6
IO4
IO4
IO4
IO2
IO2
IO2
1.32 x
1.33 x
2.32 x
2.56 x
4.18 x
4.59 x
IO6
IO6
IO4
IO4
IO2
IO2
EHTD-N = nonreactive tracer test results. EHTD-R = reactive tracer test results.
-------
S 2
g
O Q— Measured Data
_A-A - NonReactive Transport
—H-H. - Reactive Transport
50
100
Time (d)
150
Figure 27. Comparison of measured data for the Test Site Wilerwald tracer test with EHTD
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.80
and n = 0.0044 h~l.
in Table 32.
7.3.2.1. Test Site Wilerwald Tracer Test. Natural-gradient tracer tests in porous
media can be frustrating because of the time involved, the number and type of field
measurements necessary, and the construction of injection and recovery sites. Unlike with
karstic terranes, some basic transport parameters can be approximated prior to initiating
the tracer test, which minimizes some of the design difficulties. However, errors in estimates
for parameters that are difficult to estimate prior to conducting a tracer test (e.g., effective
porosity) can result in substantial errors in the tracer test design.
The tracer test design parameters for Test Site Wilerwald were carefully measured and/or
estimated by geophysics, which helped facilitate a good tracer test design (De Carvalho Dill
and Miiller, 1992, pp. 234-239). Using these same parameters in EHTD resulted in
satisfactory fits to the measured ETC (Figure 27) with t = 868 hours, tp = 794 hours,
v = 0.23 m h 1, and D = 1.46 m2 h 1, which do not approximate the measured results as
well as desired (Table 31). Using the data provided and an estimate for discharge according
145
-------
to Darcy's law, estimated tracer travel times (Table 31) could not be improved, but an
improvement in calculated tracer mass to release (Table 32) could be improved by providing
an estimate for tracer decay. Evident from Figure 27 and Table 31 is that the estimated
times of travel t and tp were underestimated by EHTD, which is a direct result of the
application of Darcy's law.
The actual tracer mass released was 24 x more than the EHTD-nonreactive recommended
estimate. Setting // to 0.0044 h"1 raised the tracer mass estimate to the actual amount
released, but a consequent and significant decrease in estimated Cp was required (Table 30).
The tracer used for the Test Site Wilerwald tracer test was fluorescein, which is generally
regarded as being slightly retarded in granular aquifers and not very sensitive to degradation
in the subsurface. For this test, fluorescein appears not to have been significantly retarded,
but it may have been severely degraded according to EHTD. This contention is supported by
the actual tracer test, which indicates that only about 77 g of fluorescein were recovered [85
g when evaluated using QTRACER2 and a straight-line projection for data extrapolation
(Field, 2002b, pp. 57-58)].
Figure 27 shows that EHTD inadequately predicted the measured ETC for both the
nonreactive and the reactive cases but that most of the ETC, including the long, relatively
gently sloping ETC tail, would be identified during the sampling process even though
EHTD failed to accurately predict the ETC when Darcy's law is applied. For the Test
Site Wilerwald tracer test, tracer was added as a small, short-duration pulse, the effect of
which was a relatively insignificant amount so Dv = V for both of the EHTD-predicted
results (Table 32). The EHTD-predicted volumes only slightly exceeded the measured value
for V, suggesting that the EHTD-predicted volumes are reasonable.
7.3.2.2. Kirchdorf-Unteropfingen Tracer Test. In porous media systems, forced-
gradient tracer tests are prefered because the length of time for the test is greatly reduced
and the transport parameters necessary for designing the tracer test are more easily
estimated. However, errors in estimated parameters may still result in a poor tracer test
design. The Kirchdorf-Unteropfingen tracer test was designed using parameters that were
determined from a pumping test.
The EHTD-predicted BTCs poorly match the measured ETC, and initial tracer break-
through was not adequately predicted (Figure 28). Peak concentration for the measured
ETC was missed by both EHTD-predicted cases by more than 17 days (Table 31). The
poor EHTD predictions for the Kirchdorf-Unteropfingen tracer test are directly related to
146
-------
Measured Data
_A-A — NonReactive Transport
_ Reactive Transport
Figure 28. Comparison of measured data for the Kirchdorf-Unteropfingen site tracer test
with EHTD-predicted results for nonreactive and reactive transport. For reactive transport,
Rd = 1.0 and n = 0.0003 h~l.
the incorrectly estimated ne obtained from the pumping test.
The tracer test design used an ne = 0.14, which is the value of the specific yield obtained
from the pumping test. This ne was later found to be significantly in error. Tracer test
analysis resulted in an ne = 0.08 (Kafi, 1998, pp. 515-516), which when applied to EHTD
produces much better ETC fits to the measured ETC.
Estimated tracer mass for the nonreactive case closely matched the actual tracer mass
released. Setting // = 0.0003 h"1 produced a slightly greater estimate for tracer mass than
was released. However, this slight increase in tracer mass also resulted in a slight shift in
the decreasing limb of the ETC.
Although the EHTD-predicted BTCs failed to adequately match the measured ETC,
EHTD did reasonably predict the appropriate tracer mass to release. EHTD-recommended
sample collection times for the Kirchdorf-Unteropfingen tracer test were generally adequate
for defining the ETC, although initial tracer breakthrough was not predicted by EHTD.
For the Kirchdorf-Unteropfingen tracer test, tracer occurred as an impulse release, the
effect of which was an insignificant amount, so Dy = V for both of the EHTD-predicted
147
-------
•1
20
15
10
Od
Measured Data
NonReactive Transport
.- Reactive Transport
10
20
30
Time (d)
40
50
60
Figure 29. Comparison of measured data for the Mobile site tracer test with EHTD
predicted-results for nonreactive and reactive transport. For reactive transport, Rd = 1.1
and n = 0.0075 h~l.
results (Table 32). Both of the EHTD-predicted volumes exceeded the measured value for
V, reflecting the effect of the incorrect effective porosity.
7.3.2.3. Mobile Site Tracer Test. Injection/withdrawal tracer tests provide an op-
portunity to establish equilibrium conditions during ground-water extraction prior to ini-
tiating a tracer test. The Mobile Site tracer test was designed using transport parameters
that were carefully determined from pumping tests and single-well tracer tests, which led to
better estimates for the parameters necessary for designing the injection/withdrawal tracer
test.
The EHTD-predicted BTCs closely matched the measured ETC (Figure 29). Only the
long, somewhat multimodal erratic tail of the measured ETC was not adequately predicted
by EHTD. The long tail is suspected to have occurred as a result of longer flow lines
causing longer transport times, which occurs during well injection (Molz et al., 1986a,
pp. 22, 58). Because EHTD does not predict long ETC tails the estimates for t and v
were incorrectly estimated by approximately 3 days, but tp, D, and Pe were very well
approximated (Table 31). Setting // = 0.0075 h"1 and Rd = 1.1 increased the estimate
148
-------
for tracer mass enough to match the actual mass released and for predicted injection
concentration to match the actual injection concentration. However, the increase in tracer
mass also caused a slight negative shift of the descending limb of the predicted ETC because
of the required steepening of the ETC to maintain the desired C. Setting // = 0.0075 h"1
and Rd= 1-1 allowed for a good estimate for tracer mass and a slight positive shift in the
ETC, but with a slight decrease in predicted tp} a 2-hour increase for t\ and t/ (Table 31),
and a 1-hour increase for Cp (Table 32).
EHTD-suggested sampling times may be regarded as adequate for defining the measured
ETC. The multimodal measured ETC for the Mobile Site clearly illustrates the need for
frequent sampling if the ETC is to be properly defined (Figure 29). Although not as
frequent as the average sample collection frequency t/ of 5 hours for the measured ETC, a
tf = 19 hours is probably reasonable for defining the ETC while not being excessive. Tracer
sampling ceased prior to complete tracer recovery, so it is difficult to determine whether
EHTD adequately predicted final tracer recovery.
Predicted dilution volumes for the Mobile Site tracer test exceeded the predicted system
volumes, but the dilution volumes reasonably matched the measured system volumes
(Table 32). The good estimation for Dv would have enhanced the predictions for M,
but the poor match of the predicted V to the measured V was unexpected, although it
appears not to have adversely influenced the tracer mass prediction for the reactive case.
7.3.2.4. Chalk River Site Tracer Test. Recirculation tracer tests are rarely em-
ployed to evaluate transport parameters in porous media systems. A recirculation tracer
test conducted at the Chalk River Site was very well predicted by EHTD for both the non-
reactive and reactive cases (Figure 30). The EHTD-predicted results for the nonreactive
case produced a good fit to the measured ETC and a nearly exact match of the predicted
f to the measured t but a very poor match for predicted tp to the measured tp (Table 31).
The incorrectly estimated tp was caused by recirculating the recovered tracer back into the
injection well while tracer recovery from the start of the tracer test was still occurring.
Average velocity, D, and Pe were also very well matched.
EHTD-estimated tracer mass for the nonreactive case was four times less than the actual
tracer mass released. Setting // = 0.011 h"1 resulted in a close match to the actual tracer
mass released and injection concentration, but it also produced a slight negative shift in
the ETC. Setting Rd = 1.1 caused a positive shift of the ETC that matched the measured
ETC and the mass released. Allowing for tracer decay caused the EHTD-predicted ETC to
149
-------
0.8
0.6
c
o
o
o
o
0.2
Measured Data
_A A- NonReactive Transport
_o g.. Reactive Transport
10
20
Time (d)
30
Figure 30. Comparison of measured data for the Chalk River site tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rd = 1.1
= 0.011 h~l.
develop a slight peak at ~ 8 days and a consequent decreasing limb. The EHTD-predicted
ETC for the reactive case produced a visually better fit than have previous modeling efforts
(Huyakorn et al., 1986), because C was adjusted as necessary to obtain a Cp that matched
the measured Cp (Table 30).
As with the Mobile Site tracer test, the EHTD-suggested sampling times may be regarded
as ideal for defining the measured ETC. The multimodal measured ETC for the Chalk River
Site also illustrates the need for frequent sampling if the ETC is to be properly defined
(Figure 30). A t/ = 12 hours is sufficient for defining the ETC. However, tracer sampling
ceased prior to complete tracer recovery, so it is not possible to determine whether EHTD-
recommended sampling ended too soon.
Unlike the Mobile Site tracer test, the predicted system volumes for the Chalk River
tracer test match the measured V quite well, especially for the nonreactive case. (Table 32).
Predicted Dv was twice the predicted V, reflecting the recirculation aspect of this tracer
test. The effect of DV = 2 V was to increase the suggested tracer mass necessary for
achieving a positive tracer test.
150
-------
Part IV
ADDITIONAL APPLICATION OF
EHTD
Release of slightly diluted uranine (Acid Yellow 73) into flow of water for tracer test. Note
the contrast between the uranine color (fluorescent green) and the algae build-up on the
sides of the stream flow. This tracer test was conducted in order to verify the integrity of
the local production well from infiltration by toxic substances that may be accidentally or
deliberately released in the future.
151
-------
8. APPLICATION OF EHTD TO SUPPORT RISK ASSESSMENTS
A critical aspect of any contamination investigation (potential or existing) of a given
hydrological system involves the development of a risk assessment to assess the threat to
human health and the environment posed by the contamination. Risk assessments consist
of three components: hazard identification, exposure assessment, and dose response. In
this section, exposure assessments as related to solute transport will be the focus. Hazard
identification (toxicity estimation) and dose-response assessment (estimation of the extent of
increasing hazard as a function of increasing exposure) are not addressed here. In addition,
that aspect of exposure assessment that deals with uptake (e.g., ingestion of contaminated
water) is not addressed here. Rather, solute transport from a source area to a point of
exposure in a hydrological system is the focus of this section. For more complete details
on exposure and risk assessments, the interested reader is referred to Reichard et al. (1990)
for a general overview of risk assessment methodology in ground water, USEPA (1992)
for general exposure methodology, USEPA (1998a) for detailed ecological risk assessment
methods and USEPA (1989) for detailed human health risk assessment methods. USEPA
(1986a,b, 1991, 1996, 1998b) provide detailed risk assessment guidance for the development
of various toxicological methods.
8.1. EXPOSURE ASSESSMENT OVERVIEW
A typical exposure assessment for real and potential contamination usually includes solute-
transport modeling as a means of reducing uncertainties and/or forecasting the effects of
any suggested changes. The exposure pathway (source to exposure point) requires field
investigations which are often enhanced through modeling of the environmental systems
which helps to lessen the impact of uncertainties. Uncertainties in exposure assessments
are always an issue that must be addressed. Typical uncertainties associated with exposure
assessments in hydrological systems are listed in Figure 31.
The value and importance of using a well calibrated model for risk assessment purposes
is widely recognized. For example, McAvoy et al. (2003) used the well-known water quality
model, QUAL2E (after calibration) to conduct a basic risk assessment regarding wastewater
loading to Balatuin River in the Philippines. Rhodamine WT (Acid Red 388) dye tracing
results were used to develop the necessary parameters for model calibration. Interestingly,
the initial dye release included too little dye (9.52 g) and the two subsequent releases required
152
-------
Source-Related Uncertainties
• Will release(s) of contaminants occur?
[Probability of release(s).]
• When will the release(s) occur and for how long?
[Timing and duration of release(s).]
• What contaminants will or are being released?
[Chemical, biological, or radiological contaminant releases.]
• How much will be or is being released?
[Mass loading.]
Pathway-Related Uncertainties
• Will contaminants reach exposure point?
[Flow trajectory and proximity of source to point of contact.]
• When will contaminants reach point of exposure?
[Time of travel and duration of exposure.]
• What contaminants will reach the point of exposure?
[Environmental fate of contaminants.]
• How much contamination will reach the point of exposure?
[Contaminant concentration at the point of exposure.]
Use-Related Uncertainties
• Water used for drinking and/or bathing and by whom?
[Exposure route, number, and sensitivity of exposed population.]
• How long will user be affected by the contamination?
[Duration and continuity of exposure.]
• What monitoring program is in place?
[Potential to avert exposure.]
• What dilution and/or treatment prior to exposure?
[Reduced exposure levels due to reduced contaminant concentrations.]
Figure 31. Uncertainties associated with exposure assessments in hydrological systems
[adapted from Reichard et al. (1990, p. 6)].
slightly greater amounts of dye (14.28 g each) for a total release of (38.08 g). Analysis using
EHTD suggested that even greater quantities of dye (100.11 g) would have been appropriate.
153
-------
8.2. FORECASTING POLLUTION FOR RISK ASSESSMENTS
The appropriateness of EHTD for determining acceptable tracer mass and sampling times
for proposed tracer tests has already been documented. However, after tracer tests have been
conducted EHTD may be used for screening-level pollution forecasting. The EHTD-results
may then be applied in a risk assessment at a rough screening level. Such an endeavor,
the value of which not being immediately apparent, is useful because of the difficulty and
expense of conducting multiple tracer tests several times during any given year and over
several years. A single tracer test provides only a temporal "snapshot" of the hydrological
system the results of which may not be relevant other periods.
8.2.1. Dimensionless Dye-Recovery Curve
The tracer testing conducted by McAvoy et al. (2003) was conducted during the dry season
only. In their work, the authors assumed that greater dilution would occur during the
wet months which may be true but is undocumented. For this reason, the U.S. Geological
Survey (USGS) conducted several tracer tests in the same system over at least a year's time
to address temporal differences in flow (Mull et al., f 988b). A plot of the seven tracer tests
conducted by the USGS indicates considerable real-time differences and real-concentration
differences in the BTC's (Mull et al., f988a, p. 55). Figure 32 on the next page depicts
the seven BTC's. The differences in the BTC's were muted by converting the BTC's to
dimensionless form, plotting the dimensionless BTC's at the same scales and then developing
a single standardized dimensionless dye-recovery curve or "type curve" (Mull et al., f988a,
pp. 68-75). Development of the standardized curve is a very slow tedious process where a
ETC is drawn by eye and appropriate statistics calculated. This process is repeated several
times until the calculated statistics meet some arbitrary level of acceptance.
After development of the standardized curve the effects of a given release into the
hydrologic system could be forecast with some degree of confidence provided discharge
was available (Mull et al., f988a, pp. 75-79). Although useful and relevant, the method
devised is a trial-and-error procedure requiring considerable subjective analysis. A simpler
less expensive method is desirable.
8.2.2. EHTD for Forecasting pollution Effects
To be able to forecast the effects of any contaminant releases in any given hydrological
system, a chosen model must either be properly calibrated for the given time period or be
154
-------
15 -
February 28, 1985
March 1. 1985
May 23. 1985
May 30. 1985
July 16. 1985
August 12. 1985
February 26. 1986
50
Figure 32. Seven BTC's developed by the U.S. Geological Survey between Dyers Spring
and a nearby karst window over one year (1985) (Mull et al., 1988a, p. 73). Note that the
May 30, 1985 curve is the Dyers Spring ETC that is examined in detail in Section 7. on
page 128 and graphically as Figure 25 on page 139.
capable of approximating the environmental conditions for the given time period. This may
be accomplished using EHTD provided it is recognized that EHTD may only be considered
a screening-level model when used in this manner.
8.2.2.1. Using EHTD Directly to Forecast Pollution. Given some degree of
confidence regarding the ability of EHTD to suggest the appropriate mass of tracer to
release and sampling times, EHTD can be used as a quick screening model for addressing
pollutant releases. Consider the Dyers Spring example developed in Section 7.3.1.3. on
page 138 where EHTD was used to produce an acceptable estimate for time of travel and
tracer mass released.
The USGS standardized curve for this site was applied to a hypothetical release of
0.19m3 (50 gallons) of a 5% solution of copper sulfate (1.13kg copper) into the karst
window from which the original tracer tests were conducted. Assuming a spring discharge
= 91.74 m3 h"1 (3.24 x 103 ft3 h"1) the standardized curve method suggested (Mull et al.,
1988a, pp. 77-78):
155
-------
1. Cp= 2.61 mgL-1
2. ti = 14.0 h
3. tp = 18.0 h
4. tf ~ 40.0 h
Applying EHTD with assuming no pollutant reactivity to this hypothetical example and
using a reasonable estimate for cross-section area to be 1.65 m2 (17.73 ft2) resulted in:
1. Cp= 2.04 mgL-1
2. t\ = 7.39 h (measurable)
3. tp = 16.09 h
4. tf ~ 40.0 h
Including a pollutant decay factor would have caused a reduction in the EHTD-predicted
peak concentration while including a pollutant retardation factor would have caused both
a reduction in the peak concentration and later travel times. A comparison of the
standardized-predicted ETC and EHTD-predicted ETC is shown in Figure 33 on the next
page. Although there is no definitive way in which one ETC shown in Figure 33 can
be selected over the other it will be noted that the standardized curve method tends to
overestimate peak concentration (Mull et al., 1988a, p. 76) while it is likely that EHTD
will underestimate peak concentration if a good measure or estimate for discharge, cross-
sectional area (or transverse spread for porous media), and transport distance are not
sufficiently accurate.
8.2.2.2. Using the LHS-Routine in EHTD to Forecast Pollution. As explained
in Section 4.3. on page 70 a LHS-input file of mean values (see page 72) can be developed
from any input file of measured values. Using the Dyers Spring data a LHS-developed file
was created from 10,000 randomly-generated parameter values (Figure 34 on page 158).
Note that Figure 34 on page 158 also includes the univariate statistics that describe the
input parameters (see Table 20 on page 72 for identification of the variables). Using the
EHTD-generated file (Figure 34) will not produce correct results because it in no way was
intended to match the conditions identified (e.g., Q ^ 91.74m3h-1). For example, it
156
-------
s
g
Standardized Breakthrough Curve
-A -A - EHTD-Predicted Breakthrough Curve
10
20
30
40
50
Time (h)
Figure 33. Standardized curve- and EHTD-predicted ETC for a hypothetical copper sulfate
release to the karst window shown by dye tracing to be connected to Dyers Spring.
includes a slight overestimate for transport distance, a large overestimate for discharge and
retardation, and other incorrect values. However, adjustments to this file are easily made.
The file can then be run as often as necessary to gain a sense of those factors that are most
influential to the transport of a solute.
One significant point to make about the LHS routine used in EHTD is that it will always
create an input file with optimization "turned on" (Figure 34). Because optimization is
requested, EHTD will ignore any user-entered tracer or solute mass and will optimize for
the best mass for the listed conditions. If the user prefers to use a desired mass, then
optimization must be reset to zero.
157
-------
NAME OF DATA FILE
LATIN HYPERCUBE FILE NUMBER
FLOW RELEAS
1 1
STATION NAME
DYERS SPRING
DISCHARGE (m'S/h)
2.499E+02
INIT. CONC. (ug/L)
5.000E-01
RETARDATION
1.483E+00
1
1.0
10.0
RTIM (h)
0.0
DISTANCE (m)
9.195E+02
GAMMA1
5.000E-01
DECAY (1/h)
9 . OOOE-02
1
0.0
5.0
INFLOW (m-3/h)
0.0
AREA (nT2)
1.991E+00
GAMMA2
5.000E-01
OPTIM
1
UNITS
1
SINUOSITY FACTOR
1.0
AVE. CONC. (ug/L)
4.120E+00
END OF RUNS
STOP PROCESSING
LHS SUGGESTED USER INPUT SOLUTE MASS = 7.662E+00 g
Univariate Statistics from UVSTA
Variable
1
2
3
4
5
6
7
8
9
7
249
1
919
0
0
0
1
0
Mean
.66154
.88990
.99133
.47539
. 50000
. 50000
. 50000
.48261
.09000
Variance
79.
.211682
0 . 8427E+05
0.
9349.
0.
0.
0.
0.
0.
.615789
.850234
.083358
.083358
.083358
.099951
.002701
Std.
8
290
0
96
0
0
0
0
0
Dev.
.90009
. 28670
.78472
.69462
.28872
.28872
.28872
.31615
.05197
-0
-0
0
0
Skewness
1.4285
1.4285
0 . 4743
0.1262
.7563E-16
.5487E-16
.3864E-16
0.2561
.6316E-16
Kurt os is
1
1
-0
-1
-1
-1
-1
-1
-1
.0497
.0497
.9535
.1826
.2000
.2000
.2000
.1282
.2000
Variable
1
2
3
4
5
6
7
8
9
Minimum
0.3563
11.6225
0.9202
762.0000
0.0000
0.0000
0.0000
1.0000
0.0000
Maximum
35.6343
1162.2528
3.6807
1097.2800
1.0000
1.0000
1.0000
2 . 1000
0.1800
Range
35.2779
1150.6303
2.7605
335.2800
1 . 0000
1 . 0000
1 . 0000
1 . 1000
0.1800
Coef . Var .
1.1617
1.1617
0.3941
0.1052
0 . 5774
0 . 5774
0 . 5774
0.2132
0 . 5774
Count
10000.0000
10000.0000
10000.0000
10000.0000
10000.0000
10000.0000
10000.0000
10000.0000
10000.0000
Variable
1
2
3
4
5
6
7
8
9
Lower CLM
7.48708
244 . 19970
1.97595
917.57999
0.49434
0.49434
0.49434
1.47641
0.08898
Upper CLM
7.83600
255.58010
2.00671
921.37080
0.50566
0.50566
0.50566
1.48881
0.09102
Lower CLV
77.061028
0.8198E+05
0 . 599069
9095.994980
0.081095
0.081095
0.081095
0.097237
0.002627
Upper CLV
81.454079
86651.8540
0.633221
9614.534266
0.085718
0.085718
0.085718
0.102780
0.002777
Figure 34. LHS-generated input file of means using the Dyers Spring parameters. Note
CLM and CLV represent the confidence levels for the mean and the variance, respectively. All
other table headings should be readily apparent.
158
-------
9. SUMMARY AND CONCLUSIONS
Hydrologic tracer testing is an essential method of study for evaluating solute transport
processes. However, the initial design of most tracer tests can be problematic due to
a lack of prior knowledge concerning the hydrologic transport properties for which the
tracer test is intended. A simple, reliable method for designing tracer tests has been
developed by solving the one-dimensional advection-dispersion equation (ADE) for a preset
average tracer concentration. This tracer design method provides a sound theoretical
basis for estimating tracer mass and sample collection frequency by combining basic field
measurements for hydraulic and geometric parameters in functional relationships that
describe solute transport processes to estimate flow velocity and times of travel.
These relationships are then applied to a hypothetical continuous stirred tank reactor
(CSTR) as an analog for the hydrologic flow system to develop estimates for tracer
concentration and axial dispersion based on the preset average tracer concentration.
Solution of the one-dimensional ADE using the preset average tracer concentration then
allows for an estimate of necessary tracer mass. Application of the predicted tracer mass
with the hydraulic and geometric parameters in the ADE further allows for an approximation
of initial sample-collection time and subsequent sample collection frequency.
Tracer retardation and decay cause an increase in tracer mass estimates because the set
average tracer concentration is maintained by the method. Retardation has the added effect
of delaying tracer breakthrough and causing more spread in the tracer-breakthrough curve
(ETC), which can have significant consequences for determining when to initiate sample
collection and at what frequency all subsequent samples should be collected. However,
experience with common tracers in various environments serves to trivialize this problem.
Prior evaluations of distribution coefficients and simulations using selected values for
retardation and decay can further limit the errors that may occur from tracer reactions
with solids.
The method does not attempt to physically predict the conditions that may cause
multimodal or long-tailed BTCs because it is not possible or necessary to add such
complexity. It also does not address the possible occurrence of density-induced sinking. Not
only would estimates for unknown parameters be required (e.g., mass transfer coefficient),
but the effect of adding such complexity would not greatly improve the estimates for required
tracer mass or recommended sampling frequency.
159
-------
Thirty-three tracer mass estimation equations and the computer program efficient hy-
drologic tracer-test design (EHTD) methodology were reviewed and tested using published
test criteria. Testing 32 of the 33 equations and EHTD produced extreme ranges in the
results. EHTD is the only method that was developed using established solute transport
theory. The other 33 equations were all developed empirically. Although the review and
testing described does not provide a means for determining the best tracer mass estimation
method and sampling frequency method to employ, recent tracer testing successes using
EHTD suggests that EHTD may be more reliable than the other methods (Field, 2000).
Sample collection schemes were also reviewed and shown to be difficult to implement
and unreliable because of their haphazard nature. Darcy's law for porous media cases was
not applied because of insufficient test data, but Darcy's law is believed to be a reasonable
model for designing a sampling schedule, provided that difficult-to-obtain parameters (e.g.,
effective porosity) can be adequately estimated. For karstic media, application of an assumed
average velocity equal to 0.02 m s~l for designing a sampling schedule can be effective,
provided tracer release and transport occur via solution conduits.
Given the complexities and difficulties associated with the published 33 tracer mass
estimation equations and conventional sampling schemes, their continued use must remain
suspect at best. As shown by EHTD, these previously developed equations/methods fail to
yield consistent results. Application of the more scientifically sound method developed in
EHTD is more likely to ensure successful tracer test results (Field, 2002a) and is suggested
as a more reliable alternative.
A total of eight tracer tests representing a wide range of conditions and a minimum of pre-
tracer test design parameters were used to evaluate EHTD. In all but the Test Site Wilerwald
and Kirchdorf-Unteropfingen tracer tests, the measured ETC curves were approximated by
EHTD for both nonreactive and reactive instances. Recommended sampling times were
found to be adequate for defining the measured BTCs for all eight tracer tests. Only the
initial tracer breakthrough times for the Test Site Wilerwald and Kirchdorf-Unteropfingen
were inadequately predicted, which was directly related to the unreliability of Darcy's law
in the first case and the use of an incorrectly determined effective porosity in the latter.
Most of the EHTD-predicted tracer mass estimates for nonreactive conditions were
mostly fairly to the actual tracer masses released. For the flowing stream tracer tests,
tracer mass estimates were inadequate only for the Uvas Creek and Variegated Glacier tracer
tests. The tracer mass estimates for the Missouri River tracer test were slightly greater than
the actual tracer mass released. For the porous media tracer tests, only the tracer mass
160
-------
estimate for the Test Site Wilerwald tracer test was seriously problematic, although tracer
mass estimates for all the porous media tracer tests were underestimated. Prior knowledge
of the behavior of the type of system being traced and the type of tracer to be used can
provide some indication of necessary estimates for retardation and decay.
EHTD simulations for the eight tracer tests evaluated resulted in very reasonable ap-
proximations for seven of the tracer tests. In some instances, (e.g., Test Site Wilerwald and
Kirchrdorf Unteropfingen) expected time to peak arrival (tp} was inaccurately reproduced.
In other instances (e.g., Uvas Creek, Missouri River, Test Site Wilerwald, and Kirchrdorf
Unteropfingen) axial dispersion (Dz) was inaccurately reproduced. However, in all these in-
stances the results of EHTD for both the reactive and the nonreactive simulations resulted
in adequate approximations for the hydraulic parameters of interest.
Future work should focus on refining EHTD to better approximate tracer mass estimates
and transport parameters. Improvements may include consideration of the longer transport
times associated with the longer transport crescents created by injection and the effects of
stagnant regions. Although these improvements are not necessary for EHTD to develop a
sampling schedule that will define a ETC, they will result in improved tracer mass estimates
and some transport parameter estimates. Application of EHTD in its current form prior
to initiating a tracer test leads to a more efficient design, fewer trial-and-error efforts, less
expense related to excess tracer use and excess sample collection and analysis, and greater
likelihood of tracer test success.
161
-------
NOTATION
a long dimension of rod-shaped particle (L)
a slope parameter for median infection estimate
a* slope parameter for median morbidity estimate
A cross-sectional area of flow system (L2)
A matrix of time values used in the Chatwin analysis (T)
a,i interval of data points that bracket the function /(#*); (i = 1,2)
Ae adsorption effiency (dimen.)
b short dimension of rod-shaped particle (L)
bf one half fracture width (L)
bk maximum allowable Chatwin parameter corresponding to tk (T1/2)
b vector of concentration parameters for the Chatwin analysis (T1/2)
C tracer concentration (M L~3)
C average tracer concentration (M L~3)
CE equilibrium tracer concentration (M L~3)
_ 771
C mean volume-averaged equilibrium tracer concentration (M L~3)
Cr dimensionless resident tracer concentration = —
T c0
CB dimensionless concentration for BVP
C1 dimensionless concentration for IVP
Cp dimensionless concentration for PVP
CQ characteristic tracer concentration (M L~3)
Co volume- averaged input concentration (M L~3)
Cp peak tracer concentration (M L~3)
di data value derivatives
Dz axial dispersion (L2 T"1)
f(x*} function representing the real root of the ADE
Qi input concentrations for pulse injection; (i = 1, 2; g0 = g% = 0)
g(t) function of values such that g(ti) = Ci
7 zero-order production coefficient (M L~3 T"1)
7E dimensionless production =
' I-
nevco ' bfvco ' rvco
dimensionless exponential production (growth) constants for the PVP [i = 1,2]
upper bounds on y
lower bounds on y
162
-------
7z zero-order production coefficient for the liquid phase (M L 3 T l)
7S zero-order production coefficient for the adsorbed (solid) phase (M M"1 T"1)
rf auxiliary functions for equilibrium transport [see Section 3.2.1.4.]
h Hermite cubic basis function
h Hermite cubic basis function
H solute-migration zone thickness (L)
HI hazard index for all pathways (dimen.)
HQI hazard quotient for ingestion (dimen.)
Hq2 hazard quotient for inhalation (dimen.)
Hq3 hazard quotient for dermal contact (dimen.)
/ integrand of a function
/' approximate integrand of a function
Ig amount of water ingested per day (L3 T"1)
Ih inhalation rate (L3 T"1)
k CSTR reaction rate constant (T"1)
ki, number of uncertain variables to be developed by Latin Hypercube Sampling routine
Ka fracture and/or solution conduit distribution coefficient (L)
Kd solute distribution coefficient (L3 M"1)
Kf volumetric conversion for water (L3 L~3)
L characteristic distance from point of injection to point of recovery (L)
Ap dimensionless constant for exponential production (growth) profile
M tracer mass (M)
MB dimensionless mass of applied tracer for a Dirac input = -^-
Mp particle mass (M)
Mp mass of total number of particles (M)
n number of evaluation points (dimen.)
rib number of additional sample to be collected prior to expected tracer breakthrough
ne effective porosity (dimen.)
nK number of evaluation points for Chatwin analysis (dimen.)
nm multiplier for estimating tracer test duration (dimen.)
ns number of samples to be collected
NW median infectious dose (# T"1)
7Vg0 median morbidity dose (# T"1)
Np concentration of particles (# L~3)
163
-------
p components M, Rd, and p, of vector y to be optimized
Pe Peclet number = jy- (dimen.)
Pc skin permeability constant (L T"1)
PI probability of infection (dimen.)
PD-.I probability of morbidity (dimen.)
PM-.D probability of mortality (dimen.)
0 porosity (dimen.)
pb bulk density (M L~3)
pp particle density (M L~3)
q inflow into injection point at time of injection (L3 T"1)
Q flow system discharge (L3 T"1)
r solute conduit radius (L)
fi(y) twice continuously differentiable functions of y
Rd solute retardation (dimen.)
RfC reference concentration (M M"1)
RfD reference dose (M M~l T'1)
Sa skin surface area (L2)
Sd shower duration (T)
Sf sinuosity factor (dimen.)
of travel time variance (T2)
t time (T)
f average time of travel (T)
tb base time value for At time spacing (T)
td tracer-test duration corresponding to last detectable tracer breakthrough (T)
ti individual tracer sampling times (T)
tK maximum allowable time for Chatwin analysis tK < ^ (T)
tm base time value for nmAt time spacing (T)
to time for pulse release (T)
tp expected time to peak arrival (T)
IR tracer release control (dimen.)
ts sample-collection times (T)
tsf sampling frequency (T)
tsm time corresponding to minimum concentration for sample collection (T)
At time spacing for CSTR-generated ETC (T)
164
-------
T dimensionless time = ^
L
T dimensionless mean residence time = ^
Tj dimensionless pulse time = ^; (i = 1, 2; Ti = 0)
)U solute decay (T"1)
ue dimensionless equilibrium decay = L(n^i+nKd^.
r^ T- ^ nev ' bv ' rv
Hi liquid phase solute decay (T"1)
p,s sorbed phase solute decay (T"1)
v mean tracer velocity (L T"1)
v mean tracer velocity for the CSTR-generated ETC (L T"1)
Vi measured tracer velocities for each sampling time (L T"1)
vp peak tracer velocity (L T"1)
V flow system volume (L3)
Va shower stall volume (L3)
uj concentration of particulate matter for a concentrated volume (%)
W width of solute-migration zone (L)
Wu water usage (L3)
x vector of straight-line parameters used in the Chatwin analysis (T1/2)
y vector of p components (M, R^ and jj) to be optimized
z distance (L)
Z dimensionless distance = f
165
-------
References
Alexander, Jr., E. C., Quinlan, J. F., 1992. Practical Tracing of Groundwater with Emphasis
on Karst Terranes. Tech. Rep. Short Course Manual, 2nd ed., Geological Society of
America, Boulder, Colorado.
Aley, T. J., 1999. The Ozark Underground Laboratory's Groundwater Tracing Handbook.
Tech. rep., Ozark Underground Laboratory, Protem, Mo.
Aley, T. J., Fletcher, M. W., 1976. The water tracer's cookbook. Missouri Speleology 16(3),
1-32.
Barth, G. R., Illangasekare, T. H., Hill, M. C., Rajaram, H., 2001. A new tracer-density
criterion for heterogeneous porous media. Water Resources Research 37(1), 21-31.
Behrens, H., Beims, U., Dieter, H., Dietze, G., Eikmann, T., Grummt, T., Hanisch, H.,
Henseling, H., Kafi, W., Kerndorff, H., Leibundgut, C., M tiller-Wegener, U., Ronnefahrt,
I., Scharenberg, B., Schleyer, R., Schloz, W., Tilkes, F., 2001. Toxicological and ecotoxi-
cological assessment of water tracers. Hydrogeology Journal 9, 321-325.
Bencala, K. E., Walters, R. A., 1983. Simulation of solute transport in a mountain pool-
and-rifne stream: A transient storage model. Water Resources Research 19(3), 718-724.
Bendel, L., 1948. Ingenieurgeologie, 832 p. Springer, Vienna.
Blower, S. M., Dowlatabadi, H., 1994. Sensitivity and uncertainty analysis of complex
models of disease transmission: An HIV model, as an example. International Statistical
Review 62(2), 229-243.
Bogli, A., 1980. Karst Hydrology and Physical Speleology, 284 p. Springer, Berlin.
Brugman, M. M., 1987. Water Flow at the Base of a Surging Glacier. Ph.D. Dissertation,
267 p., California Institute of Technology, Pasadena, Gal.
Chatwin, P. C., 1971. On the interpretation of some longitudinal dispersion experiments.
Journal of Fluid Mechanics 48(4), 689-702.
Davis, S. N., Campbell, D. J., Bentley, H. W., Flynn, T. J., 1985. Ground water Tracers,
200 p. National Ground water Association, Dublin, Ohio.
166
-------
De Carvalho Dill, A., Miiller, L, 1992. Geophysical Prospecting. In: Leibundgut, C., De Car-
valho Dill, A., Maloszewski, P., Miiller, L, Schneider, J. (Eds.), Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations f 987-f992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.
Dennis, J. E., Gay, D. M., Welsch, R. E., f98f. An adaptive nonlinear least-aquares
algorithm, toms 7(3), 348-383.
Dienert, F., f9f3. Remarques au sujet des experiences avec la fluoresceine. C. R. Academy
Sciences f57, 660-66f.
Drew, D. P., Smith, D. L, f969. Techniques for the Tracing of Subterranean Drainage. Tech.
Rep. 2, British Geomorphological Research Group Technical Bulletin, Great Britain.
Dunn, B., f968. Nomographs for determining amount of Rhodamine B dye for time-of-
travel studies. In: In Selected Techniques in water Resources Investigations, 1966-67.
U.S. Geological Survey Water Supply Paper 1892, pp. 9-14.
Field, M. S., 1997. Risk assessment methodology for karst aquifers: (2) Solute-transport
modeling. Environ. Monit. Assess. 47, 23-37.
Field, M. S., 2000. Ground-water tracing and drainage basin delineation for risk assessment
mapping for spring protection in clarke county, Virginia. Tech. Rep. NCEA-W-0936, 36
p., U.S. Environmental Protection Agency, Washington, D.C.
Field, M. S., 2002a. Efficient hydrologic tracer-test design for tracer-mass estimation and
sample-collection frequency, 1, method development. Environmental Geology in press.
Field, M. S., 2002b. The QTRACER2 Program for Tracer-Breakthrough Curve Analysis
for Hydrological Tracer Tests in Karstic Aquifers and Other Hydrologic Systems. Tech.
Rep. EPA/600/R-02/001, 179 p., U.S. Envir. Prot. Agency, Washington, D.C.
Field, M. S., 2002c. A review of some tracer-design equations for tracer-mass estimation
and sample collection frequency. Environmental Geology in press.
Field, M. S., Nash, S. G., 1997. Risk assessment methodology for karst aquifers, 1,
Estimating karst conduit-flow parameters. Environ. Monit. Assess. 47, 1-21.
167
-------
Field, M. S., Pinsky, P. F., 2000. A two-region nonequilibrium model for solute transport
in solution conduits in karstic aquifers. Journal of Contaminant Hydrology 44, 329-351.
Field, M. S., Wilhelm, R. G., Quinlan, J. F., Aley, T. J., 1995. An assessment of the potential
adverse properties of fluorescent tracer dyes for groundwater tracing. Environmental
Monitoring and Assessment 38, 75-96.
Freeze, R. A., Cherry, J. A., 1979. Groundwater, 604 p. Prentice-Hall, Engelwood Cliffs,
N.J.
Caspar, E., 1987. Modern Trends in Tracer Hydrology, 145 p. CRC Press, Inc., Boca Raton,
Fla.
Gunn, J., Lowe, D., 2000. Editorial. Journal of Cave and Karst Science (Transactions of the
British Cave Research Association) 26, 99-100.
Haas, J. L., 1959. Evaluation of ground water tracing methods used in speleology. National
Speleological Society Bulletin 21(2), 67-76.
Keys, B., 1968. Closing address. Transaction of Cave Research Group, Great Britain 10(2),
121.
Huyakorn, P. S., Andersen, P. F., Molz, F. J., Giiven, O., Melville, J. G., 1986. Simulations
of two-well tracer tests in stratified aquifers at the Chalk River and the Mobile sites.
Water Resources Research 22(7), 1016-1030.
Iman, R. L., Helton, J. C., 1988. An investigation of uncertainty and sensitivity analysis
techniques for computer models. Risk Analysis 8, 71-90.
Kahaner, D. K., Moler, C., Nash, S. G., 1989. Numerical Methods and Software, 581 p.
Prentice-Hall, Engelwood Cliffs, N.J.
Kafi, W., 1998. Tracing Technique in Geohydrology, 581 p. A.A. Balkema, Rotterdam, The
Netherlands.
Kilpatrick, F. A., 1993. Simulation of Soluble Waste Transport and Buildup in Surface
Wwaters Using Tracers. Tech. Rep. Techniques of Water-Resources Investigations, Book
3, Chapter A20, 37 p., U.S. Geological Survey.
168
-------
Kilpatrick, F. A., Cobb, E. D., 1985. Measurement of Discharge Using Tracers. Tech.
Rep. Techniques of Water-Resources Investigations, Book 3, Chapter A16, 52 p., U.S.
Geological Survey.
Kilpatrick, F. A., Taylor, K. R., 1986. Generalization and Application of Tracer Dispersion
Data. Water Resources Bulletin 22(4), 537-548.
Kilpatrick, F. A., Wilson, Jr., J. F., 1989. Measurement of Time of Travel in Streams by
Dye Tracing. Tech. Rep. 27 Techniques of Water-Resources Investigations of the U.S.
Geological Survey, Book 3, Chapter A9, 27 p., U.S. Geological Survey.
Kinnunen, K., 1978. Tracing Water Movement by Means of eschericia coli bacteriophages.
Tech. Rep. Publication of Water Research Institute, 25, 50 p., National Board of Waters,
Finland.
Leibundgut, C., 1981. Zum Anwendung Kiistlicher Tracerin Gletscher, 85 p. Publikation
Gewasserkde, No. 85, Unversity of Bern.
Leibundgut, C., 1992. Test Site. In: Leibundgut, C., De Carvalho Dill, A., Maloszewski, P.,
Miiller, I., Schneider, J. (Eds.), Investigation of Solute Transport in the Porous Aquifer
of the Test Site Wilerwald (Switzerland), Steirische Beitrage zur Hydrogeologie, 6th
International Symposium on Water Tracing, Transport Phenomena in Different Aquifers
(Investigations 1987-1992). Vol. 43. Joanneum Research, Graz, Germany, pp. 229-250.
Leibundgut, C., De Carvalho Dill, A., 1992. Tracer Tests. In: Leibundgut, C., De Car-
valho Dill, A., Maloszewski, P., Miiller, I., Schneider, J. (Eds.), Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.
Leibundgut, C., Wernli, H. R., 1982. Zur Frage der Einspeisemengenberechnung fur
Fluoreszenztracer. In: Leibundgut, C., Weingartner, R. (Eds.), Tracermethoden in der
Hydrologie, Beitrage Geologie Schweiz - Hydrologie. Vol. 28(1). Geographischer Vrlag,
Bern, Switzerland, pp. 119-130.
Leibungut, C., 1974. Fluoreszierende markierfarbstoffe in der hydrologie. In: Mitt. Natur-
forsh. Ges. Bern, N.F. Vol. 31. Bern, Switzerland, pp. 63-84.
169
-------
Levenspiel, O., 1999. Chemical Reaction Engineering, 668 p. John Wiley & Sons, New York.
Lutz, T., Parriaux, A., 1988. The Identification of Uranine in Natural Water by High
Pressure Liquid Chromatography (HPLC). In: Goldbrunner, J. (Ed.), Steirische Beitrage
zur Hydrogeologie. Vol. 39. Joanneum Research, Graz, Germany, pp. 141-148.
Mackay, D. M., Freyberg, D. L., Roberts, P. V., Cherry, J. A., 1986. A natural gradient
experiment on solute transport in a sand aquifer: 1. Approach and overview of plume
management. Water Resour. Res. 22(13), 2017-2029.
Maloszewski, P., Harum, T., Benischke, R., 1992a. Mathematical modelling of tracer
experiments in the karst of lurbach system. In: Behrens, H., Benischke, R., Bricelj,
M., Harum, T., Kafi, W., Kosi, G., Leditzky, H. P., Leibundgut, C., Maloszewski, P.,
Maurin, V., Rajner, V., Rank, D., Reichert, B., Stadler, H., Stichler, W., Trimborn,
P., Zojer, H., Zupan, M. (Eds.), Investigations with natural and artificial tracers in the
karst aquifer of the Lurbach system (Peggau-Tanneben-Semriach, Austria), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 116-136.
Maloszewski, P., Leibundgut, C., Schneider, J., 1992b. Mathematical Modelling of the
Tracer Experiment Performed in the Test Site Wilerwald. In: Leibundgut, C., De Car-
valho Dill, A., Maloszewski, P., Miiller, L, Schneider, J. (Eds.), Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.
Martel, 1913. Sur les experiences de fluoresceine a grandes distances. C. R. Academy Sciences
157, 1102-1104.
McAvoy, D. C., Masscheleyn, P., Peng, C., Morrall, S. W., Casilla, A. B., Lim, J. M. U.,
Gregorio, E. G., 2003. Risk assessment approach for untreated wastewater using the
QUAL2E water quality model. Chemosphere , in press.
McCann, M. R., Krothe, N. C., 1992. Development of a monitoring program at a superfund
site in a karst terrane near Bloomington, Indiana. In: Quinlan, J. (Ed.), Proceedings of
170
-------
the Third Conference on Hydrogeology, Ecology, Monitoring, and Management of Ground
Water in Karst Terranes. National Ground Water Association, Dublin, Ohio, pp. 349-370.
McKay, M. D., Conover, W. J., Beckman, R. J., 1979. A comparison of three methods
for selecting values of input variables in the analysis of output from a computer code.
Technometrics 21, 239-245.
Meigs, L. C., Beauheim, R. L., 2001. Tracer tests in a fractured dolomite, 1, Experimental
design and observed tracer recoveries. Water Resources Research 37(5), 1113-1128.
Milanovic, P., 1981. Karst Hydrogeology, 434 p. Water Resources Publications, Littleton,
Col.
Molz, F. J., Giiven, O., Melville, J. G., Crocker, R. D., Matteson, K. T., 1986a. Performance,
analysis, and simulation of a two-well tracer test at the Mobile site. Water Resources
Research 22(7), 1031-1037.
Molz, F. J., Giiven, O., Melville, J. G., Keely, J. F., 1986b. Performance and Analysis of
Aquifer Tracer Tests with Implications for Contaminant Transport Modeling. Tech. Rep.
EPA/600/2-86/062, 88 p., U.S. Envir. Prot. Agency, Washington, B.C.
Mull, B. S., Liebermann, T. B., Smoot, J. L., Woosley, Jr., L. H., 1988a. Application
of Bye-Tracing Techniques for Betermining Solute-Transport Characteristics of Ground
Water in Karst Terranes. Tech. Rep. EPA/904/9-88-001, 103 p., U.S. Envir. Prot. Agency,
Region IV, Atlanta, Ga.
Mull, B. S., Lyverse, M. A., 1984. Ground Water Hydrology of the Elizabethtown Area,
Kentucky. Tech. Rep. WRI 84-4057, 59 p., U.S. Geol. Surv. Geol. Surv. Water-Resour.
Invest., Washington, B.C.
Mull, B. S., Smoot, J. L., Liebermann, T. B., 1988b. Bye Tracing Techniques Used to
Betermine Ground-Water Flow in a Carbonate Aquifer System Near Elizabethtown,
Kentucky. Tech. Rep. WRI 87-4174, 95 p., U.S. Geol. Surv. Water-Resour. Invest.,
Washington, B.C.
Novakowski, K. S., 1992. The analysis of tracer experiments conducted in divergent radial
flow fields. Water Resources Research 28(12), 3215-3225.
171
-------
Oostrom, M., Hayworth, J. S., Dane, J. H., Giiven, O., 1992. Behavior of dense aqueous
phase leachate plumes in homogenous porous media. Water Resources Research 28(8),
2123-2134.
Parriaux, A., Liskay, M., Miiller, I., della Valle, G., 1988. Guide practique pour 1'usage des
traceurs artificiels en hydrologeologues [Bilingual; also published in the same manual as:
Leitfaden fiir den gebrauch kunstlicher tracer in der hydrogeologie]. Tech. Rep. GEOLEP
EPFL 51 p. [49 p.], Societe Geologigue Suisse, Groupe des Hydrologeogie [Schweizerische
Gruppe der Hydrogeologen, Arbeitsgruppe 'Tracer'], Lausanne, Switzerland.
Pearson, T. J., 1997. Pgplot graphics subroutine library. Tech. rep., California Institute of
Technology, Pasadena.
Pickens, J. F., Grisak, G. E., 1981. Scale-dependent dispersion in a stratified granular
aquifer. Water Resources Research 17(4), 1191-1211.
Rantz, S. E., 1982. Measurement and Computation of Streamflow: Volume 1. Measurement
of Stage and Discharge. Tech. Rep. U.S. Geological Survey Water-Supply Paper 2175, 284
p., U.S. Geological Survey.
Rathbun, R. E., 1979. Estimating and Gas and Dye Quantity for Modified Tracer Technique
Measurements of Stream Reaeration Coefficients. Tech. Rep. U.S. Geological Survey
Water-Resoruces Investigations 79-27, 42 p., U.S. Geological Survey.
Reichard, E., Cranor, C., Raucher, R., Zapponi, G., 1990. Groundwater Contamination
Risk Assessment: A Guide to Understanding and Managing the Uncertainties, 204 p.
Vol. IAHS Publ. No. 196. International Association of Hydrological Sciences, Wallingford,
Oxfordshire, U.K.
Sardin, M., Schweich, D., Leij, F. J., van Genuchten, M. T., 1991. Modeling the nonequilib-
rium transport of linearly interacting solutes in porous media: A review. Water Resources
Research 27, 2287-2307.
Schudel, B., Biaggi, D., Dervey, T., Kozel, R., Miiller, I., Ross, J. H., Schindler, U.,
2002. Utilisation des Traceurs Artificiels an Hydrogeologie: Guide Practique, Rapports
de 1'OFEG, Serie Geologic. Tech. Rep. No. 3, 77 p., Groupe de Travail Tragage de la
Societe Suisse d'Hydrogeologie; SSH, Berne, Switzerland.
172
-------
Silebi, C. A., Schiesser, W. E., 1992. Dynamic Modeling of Transport Process Systems, 518
p. Academic Press, San Diego, Calif.
Siline-Bektchourine, A. I., 1951. Hydrogeologie Speciale, 394 p. Gossendarctvennoe Iz-
datelctvo Geologitcheshoi Litertouri, Moscow.
Smart, C., Zabo, L., 1997. Experimental design, technique and protocol in fluorometric
tracing of ground water. In: Proceedings of the 12th International Congress of Speleology;
6th Conference on Limestone Hydrology and Fissured Media. Vol. 2. International Union
of Speleology and Swiss Speleological Society, La Chaux de Fonds, Switzerland, pp. 51-54.
Smart, C. C., 1988. Artificial tracer techniques for the determination of the structure of
conduit aquifers. Ground Water 26(4), 445-453.
Smart, C. C., Karunaratne, K. C., 2001. Statistical characterization of natural background
fluorescence as an aid to dye tracer test design. In: Beck, B. F., Herring, J. G. (Eds.),
Proceedings of the Eighth Multidisciplinary Conference on Sinkholes and the Engineering
and Environmental Applications of Karst Geology and Hydrology. Lamoreau and Assoc.,
Oak Ridge, Tenn., pp. 271-276.
Smart, C. C., Simpson, B., 2001. An evaluation of the performance of activated charcoal in
detection of fluorescent compounds in the environment. In: Beck, B. F., Herring, J. G.
(Eds.), Proceedings of the Eighth Multidisciplinary Conference on Sinkholes and the
Engineering and Environmental Applications of Karst Geology and Hydrology. Lamoreau
and Assoc., Oak Ridge, Tenn., pp. 265-270.
Smart, P. L., Atkinson, T. C., Laidlaw, I. M. S., Newson, M. D., Trudgill, S. T.,
1986. Comparison of the results of quantitative and nonquantitative tracer tests for
determination of karst conduit networks: An example from the Traligill Basin, Scotland.
Earth Surface Processes 11, 249-261.
Smart, P. L., Friederich, H., 1982. An assessment of the methods and results of water-
tracing experiments in the Gunung Mulu National Park, Sarawak. British Cave Research
Association, Transactions 9, 100-112.
Sutton, D. J., Kabala, Z. J., Francisco, A., Vasudevan, D., 2001. Limitations and potential
of commercially available rhodamine WT as a groundwater tracer. Water Resources
Research 37(6), 1641-1656.
173
-------
Sweeting, M. M., 1973. Karst Landforms, 362 p. Columbia University Press, New York.
Taylor, K. R., James, R. W., Helinsky, B. M., 1986. Traveltime and Dispersion in the
Shenandoah River and its Tributaries, Waynesboro, Virgina, to Harpers Ferry, West,
Virginia. Tech. Rep. WRI 86-4065, 60 p., U.S. Geol. Surv. Water-Resour. Invest.,
Washington, D.C.
Timeus, G., 1926. Le indagini sull'origini delle acque sotterrane. In: Bertarelli, I. V., Timeus,
E. (Eds.), In, Duemila Grotte. pp. 153-166.
Toride, N., Leij, F. J., van Genuchten, M. T., 1993. A comprehensive set of analytical solu-
tions for nonequilibrium solute transport with first-order decay and zero-order production.
Water Resources Research 29(7), 2167-2182.
Toride, N., Leij, F. J., van Genuchten, M. T., 1995. The CXTFIT Code for Estimating
Transport Parameters from the Laboratory or Field Tracer Experiments; Version 2.0.
Tech. Rep. 137, 121 p., U.S. Salinity Lab., Riverside, Calif.
UNESCO, 1973-1983. Groundwater Studies; An International Guide for Research and
Practice (with Supplements 1975, 1977, and 1983). United Nations.
USEPA, 1986a. Guidelines for Health Risk Assessment of Chemical Mixtures. Tech. Rep.
EPA/630/R-98/002, 28 p., U.S. Environ. Protect. Agency, Washington, D.C.
USEPA, 1986b. Guidelines for Mutagenicity Risk Assessment. Tech. Rep. EPA/630/R-
98/003, 17 p., U.S. Environ. Protect. Agency, Washington, D.C.
USEPA, 1989. Risk Assessment Guidance for Superfund, Volume I, Human Health
Evaluation Manual, (Part A). Tech. Rep. EPA/540/1-89/002, http://www.epa.gov/
superfund/programs/risk/ragsa/index.htm, U.S. Environ. Protect. Agency, Washing-
ton, D.C.
USEPA, 1991. Guidelines for Developmental Toxicity Risk Assessment. Tech. Rep.
EPA/600/FR-91/001, 67 p., U.S. Environ. Protect. Agency, Washington, D.C.
USEPA, 1992. Guidelines for Exposure Assessment. Tech. Rep. EPA/600/Z-92/001, 127 p.,
U.S. Environ. Protect. Agency, Washington, D.C.
USEPA, 1996. Guidelines for Reproductive Toxicity Risk Assessment. Tech. Rep.
EPA/630/R-96/009, 118 p., U.S. Environ. Protect. Agency, Washington, D.C.
174
-------
USEPA, 1998a. Guidelines for Ecological Risk Assessment. Tech. Rep. EPA/630/R-
95/002F, 114 p., U.S. Environ. Protect. Agency, Washington, B.C.
USEPA, 1998b. Guidelines for Neurotoxicity Risk Assessment. Tech. Rep. EPA/630/R-
95/001F, 77 p., U.S. Environ. Protect. Agency, Washington, B.C.
Webster, B. S., Proctor, J. F., Marine, I. W., 1970. Two-Well Tracer Test in Fractured
Crystalline Rock. Tech. Rep. U.S. Geological Survey Water-Supply Paper 1544-1, 22 p.,
U.S. Geological Survey.
Wolff, H. J., Radeke, K. H., Gelbin, B., 1979. Heat and mass transfer in packed beds—iv:
Use of weighted moments to determine axial dispersion coefficients. Chemical Engineering
Science 34, 101-107.
Worthington, S. R. H., Bavies, G. J., Ford, B. C., 2000. Matrix, fracture and channel
components of storage and flow in a Paleozoic limestone aquifer. In: Wicks, C., Sasowski,
I. (Eds.), Groundwater flow and contaminant transport in carbonate aquifers. A.A.
Balkema, Rotterdam, The Netherlands, pp. 113-128.
Worthington, S. R. H., Smart, C. C., 2001. Evaluation of equations estimating mass needed
for sink to spring tracer testing in karst. Journal of Cave and Karst Studies 63, 115.
Yevjevich, V., 1972. Stochastic Processes in Hydrology, 276 p. Water Resources Publications,
Fort Collins, Col.
Yotsukura, N., Fischer, H. B., Sayer, W. W., 1970. Measurement of Mixing Characteristics
of the Missouri River Between Sioux City, Iowa, and Plattsmouth, Nebraska. Tech. Rep.
1899-G, 29 p., U.S. Geol. Surv. Water-Supply Paper, Washington, B.C.
Yu, C., Warrick, A. W., Conklin, M. H., 1999. A moment method for analyzing breakthrough
curves of step inputs. Water Resources Research 35(11), 3567-3572.
Zand, S. M., Kennedy, V. C., Zellweger, G. W., Avanzino, R. J., 1976. Solute Transport
and Modeling of Water Quality in a Small Stream. J. Res. U.S. Geol. Surv. 4(2), 233-240.
Zotl, A., 1974. Karsthydrogeologie, 291 p. Springer, Vienna.
175
------- |