EPA
United States
Environmental Protection
Agency
The QTRACER2 Program for
Tracer-Breakthrough Curve
Analysis for Tracer Tests in
Karstic Aquifers and
Other Hydrologic Systems
(Supersedes EPA/600/R-98/156a and 156b, 2/'99)
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EPA/600/R-02/001
May 2002
The QTRACER2 Program for Tracer-
Breakthrough Curve Analysis
for Tracer Tests in Karstic Aquifers
and Other Hydrologic Systems
(Supersedes EPA/600/R-98/156a and 156b, 2/'99)
National Center for Environmental Assessment-Washington Office
Office of Research, and Development
U.S. Environmental Protection Agency
Washington, DC 20460
Recycled/Recyclable
Printed with vegetable-based ink on
paper that contains a minimum of
50% post-consumer fiber content
processed chlorine free.
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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.
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Contents
LIST OF TABLES
LIST OF FIGURES
PREFACE
AUTHOR and REVIEWERS
ABSTRACT
vin
ix
xii
xiii
xiv
1. INTRODUCTION 1
1.1. LIMITATIONS OF THIS REPORT ...... 1
1.1.1. Limitations Related to Type of Tracer 1
1.1.2. • Types of Applicable Hydrological Systems 1
1.1.3. Quantitative Versus Qualitative Tracer Tests 2
1.1.4. Limitations Based on Test Design . . 2
1.2. PURPOSE 2
1.2.1. Quantitative Tracer Tests to Support Ground-Water Monitoring Efforts 3
1.2.2. Quantitative Tracer Tests for Risk Assessments 3
1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation 5
1.3. QUALITATIVE VERSUS QUANTITATIVE TRACING ...... . .... 5
2. TRACER TEST DESIGN FACTORS 8
2.1. TRACER CHARACTERISTICS ........................ 11
2.2. TRACER INJECTION -.,. ..... 13
2.2.1. Methods of Injection 13
2.3. TRACER SAMPLING 18
2.4. SAMPLING EQUIPMENT ........ 19
2.5. SAMPLING LOCATIONS AND FREQUENCIES ............... 19
2.6. TRACER MIXING IN THE FLOW SYSTEM ................. 20
2.7. CORRECTION FOR TIME TO REACH FLOW SYSTEM 20
2.8. CORRECTION FOR BACKGROUND 21
2.9. DISCHARGE MEASUREMENTS ......................... 22
2.10. KARST CONDUIT NETWORKS . . . 23
2.10.1. Network Types I, II, and III .... 23
2.10.2. Network Types IV and V . .\ . . . . 23
2.10.3. Network Types VI and VII 25
2.11. DETERMINATION OF TOPOLOGICAL KARST CONDUIT NETWORK
TYPE . . 25
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3. QUANTITATIVE TRACING METHODOLOGY 26
3.1. ESTIMATION OF HYDRAULIC PARAMETERS 27
3.1.1. Total Tracer Recovery 29
3.2. QUALITY OF TRACER MASS RECOVERY 29
3.2.1. Mean Residence Time '. 30
3.3. Residence Time Skewness and Kurtosis .32
3.3.1. Mean Tracer Velocity 32
3.3.2. Longitudinal Dispersion . , 34
3.3.3. Tracer Dilution 38
3.4. FLOW-CHANNEL GEOMETRIES 39
3.4.1. Aquifer Volume 40
3.4.2. Cross-Sectional Area 41
3.4.3. Flow-Channel Diameter 41
3.4.4. Flow-Channel Hydraulic Depth . . . , 41
3.4.5. Flow-Channel Surface Area 41
3.4.6. Tracer Sorption Estimation 42
3.5. EMPIRICAL FLUID DYNAMICS MODELS . . 42.
3.5.1. Peclet Number 43
3.5.2. Dynamic Flow Equations 43
3.6. BOUNDARY-LAYER EFFECTS 45
3.6.1. Friction Factor Estimation 45
3.6.2. Viscous-Flow Sublayer 46
3.6.3. Hydraulic Head Loss 46
3.6.4. Shear Velocity 47
4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY 48
4.1. SIMPLIFIED EXAMPLE CALCULATION . . . . 50
4.1.1. Mass Recovery Example 51
4.1.2. Mean Residence Time Example 51
4.1.3. Mean Tracer Velocity Example 54
4.1.4. Longitudinal Dispersion Example 54
4.1.5. System Volume 56
5. QTRACER2 COMPUTER PROGRAM DESCRIPTION 58
5.1. DATA INTERPOLATION 58
5.2. DATA EXTRAPOLATION 58
5.2.1. Exponential Decay 58
5.2.2. Piecewise Cubic Hermite 59
5.2.3. Straight-Line Projection 59
5.2.4. Extrapolating Discharge 59
5.3. CHATWIN'S ESTIMATION OF LONGITUDINAL DISPERSION 59
5.4. DATA NORMALIZATION 60
5.5. RANGE OF POSSIBILITIES OF QTRACER2 60
5.6. COMPUTER GRAPHICS 61
IV
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5.6.1. Features of the Interactive Graphics Loop . 61
5.7. QTRACER2 SOURCE •.':.'.'.'.'.'.'.'. '. . 64
6. USING QTRACER2 65
6.1. QTRACER2 PROGRAM AND EXAMPLE DATA-PILES .......... 65
6.1.1. Loading QTRACER2 and Example Data Files . 65
6.2, QTRACER2 EXECUTION 66
6.3. QTRACER2 FUNCTIONING , . 67
6.4. SAMPLE FILES ON DISK 67
6.5. DESCRIPTION OF *.D FILES ......... ....... ^
6.6. DESCRIPTION OF *.DAT FILES . . . . 72
6.6.1. Sampling Frequency ......;. 72
6.6.2. Tracer Mass Recovery 72
6.6.3. Flag for Background ; 72
6.6.4. Measured Discharge 76
6.6.5. Discharge Units 7g
6.6.6. System Volume . 77
6.6.7. Radial Distance ..........,.....: 78
6.6.8. Correction for Sinuosity 7g
6.6.9. Flow Medium ................... 7§
6.6.10. Porous-Media and Fracture Units 79
6.6.11. Output File Name 79
6.6.12. Sample Data Interpolation ....................... 79
6.6.13. Interpolated Data File Name . 80
6.6.14. Sample Data Extrapolation 80
6.6.15. Visualize Original Data . '.-".' 81
6.6.16. Visualize Interpolated Data . : 82
6.6.17. Visualize Chatwin Parameters 83
6.6.18. CXTFIT2.0 Data File Creation ................ . . . . . 83
6.6.19. Normalized Tracer Concentration 84
6.6.20. Normalized Tracer Load .... 85
' 6.6.21. Standardized Data File ............ 86
6.6.22. Screen Display 87
6.6.23. Method for Handling Large Time-Concentration Data Files ... ... 87
6.6.24. Actual Time-Concentration Data 88
7. EXAMPLE ANALYSES FROM QTRACER2 90
7.1. QTRACER.D EXAMPLE OUTPUT '. . 90
7.1.1. QTRACER.DAT Tracer-Breakthrough Curve '.-. . : . . - 91
7.1.2. QTRACER.DAT Chatwin Plot ............ 91
7.1.3. QTRACER.DAT Output File '.'.'.'.'. 91
7.1.4. QTRACER.DAT Normalized Tracer Concentration ' . 91
7.1.5. QTRACER.DAT Normalized Tracer Load ............... 91
,7.1.6. QTRACER.DAT Standardized Time-Concentration Data . ...... 91
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7.2. RCA.D EXAMPLE OUTPUT , 102
7.2.1. RCA.DAT Tracer-Breakthrough Curve
7.2.2. RCA.DAT Chatwin Plot
7.2.3. RCA.DAT Output File ™2
7.2.4. RCA.DAT Normalized Tracer Concentration W2
7.2.5. RCA.DAT Normalized Tracer Load ; • • • • • 102
726 RCA DAT Standardized Time-Concentration Data 112
7.3. ANALYSIS ASSESSMENT OF THE QTRACER AND RCA EXAMPLE
DATA FILES • •" ' ' ' m
7.3.1. Molecular Diffusion Layer Thickness
8 QTRACER ANALYSIS OF OTHER HYDROLOGICAL SETTINGS 115
* 8.1. SURFACE-WATER AND POROUS-MEDIA EXAMPLES 115
8.1.1. Surface-Water Example
8.1.2. Porous-Media Example . . .
9 DATA INTERPOLATION AND EXTRAPOLATION EFFECTS 132
' 9 1. COMPARISON OF QTRACER.DAT OUTPUT FILES 132
9 1.1. Interpolated QTRACER.DAT ETC 1^
9 1 2. Interpolated QTRACER.DAT Chatwin Plot 1^
9.1.3. Extrapolated QTRACER.DAT ETC 13»
914 Extrapolated QTRACER.DAT Chatwin Plot "»
9 2 INTERPOLATED-EXTRAPOLATED QTRACER.DAT DATA 138
9 3. COMPARISON OF RCA.DAT OUTPUT FILES 143
9.3.1. Interpolated RCA.DAT ETC ^6
9.3.2. Interpolated RCA.DAT Chatwin Plot ^±
9.3.3. Extrapolated RCA.DAT ETC • l^
934 Extrapolated RCA.DAT Chatwin Plot 14y
9.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA 149
10. ASSOCIATED COMPUTER PROGRAMS 154
10.1. NDATA COMPUTER PROGRAM •
10.1.1. NDATA Source
10.2. AUTOTIME COMPUTER PROGRAM
10.2.1. AUTOTIME Source '.
10.3. DATFILE COMPUTER PROGRAM
10.3.1. DATFILE Source
10.4. COMBINE COMPUTER PROGRAM
10.4.1. COMBINE Screen Plotting Lt6
10.4.2. COMBINE Processing • •'"''''' i7n
10.4.3. COMBINE Source
1 71
11. CONCLUSIONS
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NOTATION
REFERENCES
172
175
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List of Tables
1 Some commonly used fluorescent dye types '•..•••'• 8
2 Data on some common fluorescent tracer dyes 1°
3 Percent pure dye content for selected fluorescent dyes 18
4 Table representing tracer recovery data for processing 48
5 Table representing tracer recovery data for processing 49
6 Table representing Chatwin values 50
7 Discharge values and tracer recovery values at specific times 53
8 Chatwin parameter values for the RCA data set 55
9 Table of values used to determine the time of travel variance ,. . , • 57
10 Pull-down menu items available in QTRACER2 62
11 Example data files on disk •
12 EstimatedparametersfromBTCsforQTRACER.DAT sampling station 135
13 Estimated parameters from BTCsforRCA.DAT sampling station 146
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List of Figures
1 Contaminant leakage into a sinkhole . • • • • 4
2 A Turner Designs® Model 10AU field filter fluorometer 6
3 Chemical structures for selected fluorescent dyes used for water tracing ... 9
4 Electromagnetic spectrum for tracer dyes .................... 11
5 Reinforced sinkhole receiving plant waste water at RCA del Caribe ..... 14
6 Dissolutionally enlarged fissure in limestone .................. 15
7 Mixing fluorescein powder dye .with water in a 5 L carboy ........... 16
8 Injecting mixture of water and fluorescein dye into an injection well ..... 17
9 Typical response curves observed laterally and downstream 21
10 Seven simple karst network types that describe tracer migration 24
11 Definition sketch of BTCs along a selected tracer streamline 27
12 Lateral mixing and longitudinal dispersion patterns 35
13 Tracer-breakthrough curve for the RCA de Caribe Superfund site 52
14 QTRACER.D header file for QTRACER2 processing 70
15 QTRACER.DAT sampling station data file for QTRACER2 processing 73
16 Tracer-breakthrough curve for the QTRACER, DAT data file 92
17 Plotandstraight-linefitoftheChatwinparameterforQTRACER.DAT 93
18 Output file for the QTRACER.DAT sampling station data file 94
19 Normalized tracer concentration data for the QTRACER.DAT data file 99
20 Normalized tracer load data for the QTRACER.DAT data file 100
21 Standardized time-concentration data for the QTRACER.DAT data file 101
22 Tracer-breakthrough curve for the RCA. DAT sampling station data file .... 103
23 Plot and straight-line fit of the Chatwin parameter for RCA. DAT 104
24 Output file for the RCA. DAT sampling station data file 105
25 Normalized tracer concentration data for the RCA. DAT data file 110
26 Normalized tracer load data for the RCA.DAT data file Ill
27 Standardized time-concentration data for the RCA. DAT data file 113
28 Tracer-breakthroughcurvefortheUVAS281.DAT data file 117
29 Plotandstraight-linefitoftheChatwinparameterforUVAS281.DAT. .... 118
30 Output file for theUVAS281.DAT sampling station data file . . . 119
31 Tracer-breakthrough curve for the MOBILE.DAT data file .125
32 Plotandstraight-linefitoftheChatwinparameterforMOBILE.DAT 126
33 Output-file for the MOBILE.DAT sampling station data file 127
34 Interpolated curve for the QTRACER.DAT sampling station data file 133
35 InterpolateddatafortheChatwinparameterforQTRACER.DAT 134
36 Extrapolated curve for.the QTRACER.DAT sampling station data file . . . . . . 139
37 ExtrapolateddatasetfortheChatwinparameterforQTRACER.DAT 140
38 Interpolated and extrapolated data set for the QTRACER.DAT data file .... 141
39 Interpolated and extrapolated data for the Chatwin parameter for the
QTRACER.DAT data file 142
40 Interpolated curve for the RCA. DAT sampling station data file . 144
41 Interpolated data for the Chatwin parameter for RCA. DAT . 145
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42 Extrapolated curve for the RCA. DAT sampling station data file 148
43 Extrapolated data set for the Chatwin parameter for RCA. DAT 150
44 Interpolated and extrapolated data set for the RCA. DAT data file 151
45 Interpolated and extrapolated data for the Chatwin parameter for RCA. DAT
data file 152
46 Example of a sample time-concentration file to be converted 156
47 Example of a converted sample time-concentration file , 157
48 Example of a measured sample time-concentration file 159
49 Example of a measured sample time-discharge file 162
50 Example of a converted sample time-concentration-discharge file 164
51 Plot of the Combine.out data 169
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PREFACE
The National Center for Environmental Assessment (NCEA) has prepared this document
for the benefit of EPA regional offices, States, and the general public because of the need to
develop a fast and easy method for evaluating tracer-breakthrough-curves (BTCs) generated
from tracing studies conducted in hydrologic systems. Results may then be applied in solute-
transport modeling and risk assessment studies.
The purpose of this document is to serve as a technical guide to various groups who
must address potential and/or existing contamination problems in hydrological systems.
Tracing studies are always appropriate and probably necessary, but analyses can be difficult
and tedious. This document and associated computer programs alleviate some of these
problems.
QTRACER2 is an update of the original QTRACER package (Field, 1999) which
was intentionally limited to fractured-rock and karstic aquifers. QTRACER2 addresses
hydrological-tracer tests conducted in all types of hydrological systems. These hydrological
systems include surface-water streams, granular aquifers, fractured-rock aquifers, and
subsurface-flow channels (e.g., mine tunnels, solution conduits, etc.). By necessity, some
hydrological systems are more amenable to certain types of analyses than are other
hydrological systems for the given information. For example, granular aquifers are not
amenable to head-loss estimation without an estimate for hydraulic conductivity. Much of
the original discussion material contained in QTRACER has been retained here because of
the necessity of emphasizing the value of quantitative tracer tests in general and in karst
aquifers in particular.
Another improvement included in QTRACER2 is the ability to provide correct moment
analyses for pulse and continuous releases. The original QTRACER package was inten-
tionally limited to impulse releases because it was believed that most if not all tracer tests
conducted in fractured-rock and karstic aquifers consist of impulse releases. However, be-
cause short-pulse releases are commonly employed in other systems and long-pulse releases
are sometimes employed, it was deemed appropriate to include analyses for these types of
releases. Continuous releases are much less commonly applied, but the analyses are the
same as for long-pulse releases.
The changes applied in QTRACER2 required modifications to the original input files
read by QTRACER. These changes are documented in this report. Also, to bring
QTRA.CER2 up-to-date with current PC operating systems (e.g., Windows®) it was
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necessary to reformulate much of the "computer graphics which resulted in a loss in some
functionality and an increase in others.
Lastly, minor bugs discovered in the original QTRACER package after publication have
been corrected in QTRACER2. While no guarantee that QTRACER2 is bug free can be
provided, every effort has been made to identify and eliminate any bugs that may exist.
XII
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AUTHOR, AND REVIEWERS
The National Center for Environmental Assessment within the U.S. Environmental Protec-
tion Agency's Office of Research and Development was responsible for the preparation of
this document and provided overall direction and coordination during the production effort.
AUTHOR
Malcolm S. Field, Ph.D.
National Center for Environmental Assessment
U.S. Environmental Protection Agency
Washington, D.C.
REVIEWERS
C. Warren Campbell, Ph.D., P.E.
City Hydrologist
Engineering Department
City of Huntsville
P.O. Box 308
Huntsville, Ala.
Gareth J. Davies, P.G.
Principal Hydrologist
Cambrian Ground Water Co.
109 Dhrie Lane
Oak Ridge, Tenn.
Clifford L. Ng
Environmental Engineer
U.S. Environmental Protection Agency
Region II
290 Broadway '
New York, N.Y.
Robert B. Ambrose, Jr., P.E.
U.S. Environmental Protection Agency
ORD/NERL/ERD-Athens
960 College Station Road
Athens, Ga.
xin
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ABSTRACT
Tracer testing is generally regarded as the most reliable and efficient method of gathering
surface and subsurface hydraulic information. This is especially true for karstic and
fractured-rock aquifers. Qualitative tracing tests have been conventionally employed in
most karst sites in the United States. Quantitative tracing tests are employed sparingly at
karstic sites in the United States, although it is widely recognized that they provide a wealth
of hydraulic and geometric data and are commonly employed in nonkarstic hydrological
systems. Quantitative tracer tests are regarded as more difficult and time-consuming than
qualitative tracing tests, which is a fallacy that needs to be overcome. The benefits of
quantitative tracing far outweigh any additional expenses incurred for all hydrologic systems.
An efficient, reliable, and easy-to-use computer program, QTRACER2, designed to run
on PCs running any version of Microsoft Windows®, has been developed to facilitate tracer-
breakthrough curve (ETC) analysis. It solves the necessary equations from user-generated
data input files using robust integration routines and relies on established hydraulic models.
Additional features include dynamic memory allocation, the ability to extrapolate late-time
data using any one of three different methods, two separate methods for handling oversized
time-concentration data files, and a powerful interactive graphics routine.
Four other programs are included to facilitate the use of QTRACER2. The first,
NDATA, allows users to interpolate either their time-concentration or time-discharge data
files to fill in data gaps. The second program, AUTOTIME, allows users to convert time-
concentration data files recorded using military time (a 24-hour clock) into sequential
decimal time as required by QTRACER2. Files created by these two programs may be
combined and appended to the bottom of a sampling station data file that can then be read
byQTRACER2.
The easiest method for creating a new data-input file for use in QTRACER2 is to modify
an existing data-input file using a standard text editor (e.g., Notepad) and save the revised
file with a new name. However, if desired the user may access the third additional program,
DATFILE, to create or modify a data-input file by answering a series of querries posed by
the program.
Lastly, the fourth program was designed to address the problem of non-matching time-
concentration and time-discharge data. The program, COMBINE, combines two disparate
time-data sets into one time-concentration-discharge data set for use by Qtracer2.
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1. INTRODUCTION
Quantitative tracing studies in hydrological systems are studies designed to provide detailed
information regarding flow dynamics. Such, flow dynamics information generally cannot be
obtained from qualitative ground-water tracing studies (commonly employed in karstic solu-
tion conduits), although some aspects are often inferred (Smart et al, 1986). Quantitative
tracing studies consist of nothing more than the development of a tracer budget, i.e., com-
paring the amount of tracer injected into the aquifer system with the amount of tracer
recovered over time in conjunction with ground-water discharge measurements.
1.1. LIMITATIONS OF THIS REPORT
QTRACER2 was written to be as comprehensive as possible. However, as with any report
of this nature, it is necessarily limited in several areas. For example, one limitation that
will be obvious to modelers is the nonincorporation of solute-transport theory in the form of
transport equations. QTRACER2 was intended for tracer test analysis using the method of
moments the results of which can then be used in any number of solute-transport equations
in either the direct or inverse modes. Other more basic limitations are also evident in this
report.
1.1.1. Limitations Related to Type of Tracer
Although this report is intended to be generic in terms of tracer materials used, much
of the report will focus on the use of fluorescent-tracer dyes because of their inherent
desirabilities (Field et al., 1995). Field and Mushrush (1994) also established the value
of tracing petroleum-contaminated ground water using the common tracer dye fluorescein.
The numerical methods described herein, and the accompanying computer programs are
not tracer specific and may be used with any type of tracer material, provided it does
not degrade or decay. For example, the analyses described do not account for the specific
radioactive decay that will occur with radioactive tracers. -
1.1.2. Types of Applicable Hydrological Systems
While most of this report focuses on tracing karst aquifers to define environmental problems,
other hydrological systems are also considered. Karstic aquifers are commonly considered to
be the aquifers most in need of tracing studies. Many professional hydrologists are beginning
to realize, however, that fractured-rock aquifers are just as much in need of tracing studies
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as are karstic aquifers, but in general, tracing fractured-rock aquifers still receives minimal
acceptance beyond basic research projects. Assessments of surface-water streams, granular
aquifers, and other hydrological systems (e.g., glacial-outwash streams, mine shafts, etc.)
also benefit from tracing studies.
1.1.3. Quantitative Versus Qualitative Tracer Tests
Many aspects of quantitative tracing studies are no different than those of qualitative tracing
studies. The main difference is the level of information desired. The studies by Caspar
(1987a,b), Mull et al. (1988), and Kafi(1998) contain discussions regarding tracer tests.
Readers must decide for themselves if a qualitative tracing test is sufficient or if a the
more detailed quantitative tracing test will better meet their needs. It is the opinion of
the author, and many other tracing professionals, that qualitative tracer tests (and/or the
ridiculous term, semi-quantitative tracer tests) are no longer acceptable and should never
be considered in lieu of quantitative tracer tests.
In those instances where field techniques applicable to quantitative tracing vary from
those applicable to qualitative tracing, an appropriate discussion will ensue. The reader may
want to note that the major difference between quantitative and qualitative tracing studies
is mostly one of mathematical analysis and interpretation based on a more comprehensive
tracer-sampling program, although tracer-injection methodology is also important.
1.1.4. Limitations Based on Test Design
Finally, it is important to note that QTRACER2 (and its predecessor, QTRACER [Field,
1999]) is intended for evaluating the results of tracer tests already conducted. QTRACER2
is wholly dependent on the quality of the data developed during the tracer test, which
requires good tracer-test design and implementation prior to analysis. This report does
not attempt to address either the design or implementation aspects of a tracer test. For
a comprehensive discussion and applicable methodology of tracer-test design, the reader is
referred to Field (2002a,b,c,d). For discussions regarding tracer-test implementation, the
reader should examine several of the references listed at the end of this report.
1.2. PURPOSE
A decision to conduct quantitative tracing studies is based primarily on the need to know
specific attributes of the aquifer being studied or monitored. For example, because of
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the complexity of ground-water flow in karstic and fractured-rock aquifers, ground-water
monitoring can be extremely difficult. The main purpose of this document is to illustrate
the advantages of conducting quantitative tracing tests and to introduce the computer
program, QTRACER2 for tracer-breakthrough curve (ETC) analysis.
QTRACER2 is an efficient, reliable, and easy-to-use computer program designed to run
on PCs running any version of Microsoft Windows®. It was developed to facilitate ETC
analysis. QTRACER2 solves the necessary equations from user-generated data input files
using robust integration routines and by relying on established hydraulic models. Additional
features include dynamic memory allocation, ability to extrapolate late-time data using
any one of three different" methods, two separate methods for handling oversized time-
* ^ - - ' , "
concentration data files, and a powerful'graphics routine. '* •
1.2.1. Quantitative Tracer Tests to Support Ground^ Water Monitoring Efforts
Qualitative ground-water tracing may establish a positive connection between a contamina-
tion source (Figure 1) and the monitoring locations, but probably will-not provide sufficient
evidence as to whether or how'much leachatemay.be escaping past the monitoring points.
Quantitative ground-water tracing provides a measure for determining the effectiveness of
the monitoring system by estimating the tracer loss involved. Inadequate tracer recover-
ies are an indication that losses other than sorption or decay (e.g^ tracer migration to
unmonitored locations) may be significant. :"' . '
1.2.2. Quantitative Tracer Tests for Risk Assessments .,'"' -
When dealing with hazardous-waste- sites (e.g.', SuperfunoT'Sites),-proof of the adequacy of
the existing or slightly modified ground-water monitoring system- may be insufficient when
evaluating the risk posed by_the site; A site risk analysis requires a.e<&mplete description
of the release of the risk agent, "its fate and--transport in ground water-and/or the vadose
zone, and any associated human and ecological exposure. .To this end, it is necessary that
all contaminant-source areas and types of sources be identifies, th'at the actual time of
travel of contaminants to all downgradient receptors be established, and that downgradient
concentrations be properly quantified. Quantitative tracing studies .are an essential part of
any risk assessment of hazardous sites (especially in karstic and fractured-rock terrahes),
because such studies provide much of the necessary information that otherwise could not
be obtained (Field and Nash, 1997; Field, 1997).
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Figure 1. Contaminant leakage from a pesticide storage warehouse into a sinkhole located
in Manati, Puerto Rico. Pollutant stream is yellow in color and black sludge is built up
from past releases.
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1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation
In some instances, it may be desirable to model the hydrologic system using theoretically
based solute-transport models. To calibrate these models to run in the direct mode (time-
concentration estimates), good parameter estimates are essential. Hydraulic and geometric
parameter estimates are most reliably obtained from tracer tests (Field and Nash, 1997).
Theoretically-based models that are run in the inverse mode (parameter optimization) can
and should be used to calibrate the parameters estimated from quantitative tracer tests
prior to evaluating contaminant migration by modeling solute transport in the direct mode
(Maloszewski, pers. coram.).
Field (1997) used parameters estimated from a quantitative tracing test in a solute-
transport model (TOXI5) to effectively calibrate the model for use in estimating the fate
and transport of a hypothetical release of ethyl benzene. The model was run in the direct
mode to produce estimated ethyl benzene concentrations at a downgradient spring used for
drinking water.
Field and Pinsky (2000) used a theoretical two-region nonequilibrium model to optimize
parameters estimated from a series of tracer tests, to demonstrate the effect of immobile-
flow zones (dead zones) on solute migration. Parameter estimation, using the advection-
dispersion equation, the two-region model, or even a three-region model, requires that
reasonably reliable parameter estimates be employed so that a global minimum can be
found during optimization. ; ,
1.3. QUALITATIVE VERSUS QUANTITATIVE TRACING
Many well-head protection studies and landfill investigations/monitoring may be adequately
addressed by qualitative tracing studies. Recharge/discharge areas are routinely established
from successful qualitative dye-tracing studies and are commonly used to establish simple
classes of conduit networks (Atkinson et al., 1973; Brown, 1973; Smart, 1988a). Qualitative
dye-tracing studies are often used to estimate apparent pollutant transport rates from
apparent tracer velocities. Given the potential for additional costs and labor associated
with conducting and interpreting quantitative tracing studies, qualitative tracing studies are
often considered appropriate, but this may not be the case. In other instances, additional
details of the aquifer under investigation need to be established.
It has been suggested that quantitative tracing studies are too expensive because (1)
required sampling at a frequency sufficient to yield reliable results, and (2) the many possible
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places the tracer might go, both situations requiring frequent sample collection at tens or
even hundreds of locations. Neither of these objections are valid.
With the advent of low-cost programmable automatic water samplers, continuous flow-
through filter fluorometers (Figure 2), and recently developed fiber-optic fluorometers
(Barczewski and Marshall, 1992; Benischke and Leitner, 1992) and spectrophotorneters,
adequate sampling frequencies are easily established. The only difficulty is the necessary
power requirements, but automatic water samplers do not draw very much power and can
be run on battery power for long periods.
Figure 2. A Turner Designs® Model 10AU field filter fluorometer operating in the flow-
through mode at Pearl Harbor Naval Base. The red valve is set horizontally to allow inflow
of water from the bottom connector and discharge out the top connector.
Quantitative tracing studies have proved that a generalized estimate for ground-water
flow direction(s), based on potentiometric-surface maps, geological structure, and geological
-------
stratigraphy, can be developed. Therefore, tracing experts can provide a reasonably good
guess where tracers may be recovered without having to sample "everywhere," as has been
advocated in the past. In addition, a "...well-designed tracer test, properly conducted, and
correctly interpreted..." (paraphrased from James F. Quinlan) is likely to provide sufficient
information for a determination as to whether tracer migration to unmonitored locations
has occurred.
Quantitative tracing studies can be more valuable than qualitative tracing studies
for answering specific questions. Quantitative tracing studies are often conducted after
qualitative tracing studies have adequately established the ground-water flow trajectories
and apparent ground-water flow velocities so that costs and labor efforts may be minimized.
Ground-water problems, such as pollution migration from hazardous-waste landfills, often
demand more sophisticated quantitative ground-water tracing studies because of the need
to better define subsurface hydraulic processes. Quantitative tracing studies can also
provide significantly better insights into the functioning of the hydrological system than
qualitative tracing tracing studies. Reliable estimates for tracer mass recovery, mean
residence times, mean ground-water flow velocities, longitudinal dispersion, and maximum
volume contact by the tracer allow for useful evaluations of the hydraulic processes of
dispersion, divergence, convergence, dilution, and storage (Atkinson et, al. 1973; Smart,
1988a; Field and Nash, 1997). Such improvements in karst. aquifer evaluation efforts
translate into better ground-water resource management, ground-water monitoring designs,
and ground-water remediation (Smart, 1985).
Finally, it must be noted that qualitative tracing studies can lead to serious misin-
terpretations regarding aquifer connections. Smart et al (1986) compared the results of
qualitative and quantitative tracing for the Traligill Basin in Scotland and determined that
the qualitative tracing results did not properly establish the subsurface connections.
-------
2. TRACER TEST DESIGN FACTORS
Conducting quantitative-tracing studies requires considerable knowledge of the tracer type
employed. Simple measurement errors may occur as a result of tracer-specific effects,
inappropriate sampling, and/or inappropriate analysis (Smart, 1988a). Smart and Laidlaw
(1977), as well as other sections of this document, discuss specific attributes of many of the
fluorescent dyes commonly used for tracing ground-water flow. Field et al. (1995) provide a
comprehensive discussion of the toxicity characteristics of several fluorescent dyes commonly
used for tracing studies. Some typical fluorescent dyes used for tracing are listed in Table 1
and their structures shown in Figure 3.
Table 1. Some commonly used fluorescent dye types, their dye names, and their respective
Colour Index and CAS numbers.
Dye Type and
Common Name
Colour Index
Generic Name
CAS No.
Xanthenes
sodium fluorescein
eosin
Rhodamines
Rliodamine B
Rhodamine WT
Sulpho Rhodamine G
Sulpho Rhodamine B
Stilbenes
Tinopal CBS-X
Tinopal 5BM GX
Phorwite BBH Pure
Diphenyl Brilliant Flavine 7GFF
Functionalized Polycyclic
Aromatic Hydrocarbons
Lissamine Flavine FF
pyranine
amino G acid
Acid Yellow 73 518-47-8
Acid Red 87 17372-87-1
Basic Violet 10 81-88-9
Acid Red 388 37299-86-8'
Acid Red 50 5873-16-5
Acid Red 52 3520-42-1
Fluorescent Brightener 351 54351-85-8
Fluorescent Brightener 22 12224-01-0
Fluorescent Brightener 28 4404-43-7
Direct Yellow 96 61725-08-4
Acid Yellow 7 2391-30-2
Solvent Green 7 • 6358-69-6
— 86-65-7
Appropriate sampling efforts and frequencies for both tracer dye and 'discharge exert
considerable influence on the accuracy of quantitative dye-tracing studies. Analytical
8
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RHODAMINES
XANTHENES
Na+
Na+
H,C N ^^ 0+ ^f N' CH3
CH,
Sodlum Fluoresceln
Cl-
Rhodamine WT
Na+
o-'
Na+
H5C
CH,
Sulpho Rhodamine G
Sulpho Rhodamine B
HO
HO
STILBENES
Tinopal CBS-X
Phorwlle BBH Pure
Tlnopal 5BM GX
V_ HN-/ \
J-fN1, ^
r~/ N=/
™~f~\J—(~~\
^G0:*^
HO-S-0 °' OH
HN
>=N P*
\ >~^
^N^N s
OH
Dlphenyl Brilliant
Flavins 7GFF
FUNCTIONALIZED
POLYCYCLIC
AROMATIC
HYDROCARBONS
Lissamlne Flavlne FF
pyranlne
HO.
o
o-V
OH
S=0
NH,
Amlno G Acid
Figure 3. Chemical structures for selected fluorescent dyes used for water tracing.
-------
methods must yield results with a high degree of precision as well. The fluorescent dyes
listed in Table 1 fluoresce in the visible light spectrum anywhere from about 435 nm
(Tinopal CBS-X) to approximately 584 nm (Sulpho Rhodamine B) (Table 2) (Figure 4).
Table 2. Data on some common fluorescent tracer dyes.
Dye Name Maximum
Excitation A
(nm)
sodium fluorescein
eosin
Rliodamine B
Rhodamine WT
Sulpho Rhodamine G
Sulpho Rhodamine B
Tinopal CBS-X
Phorwite BBH Pure
Diphenyl Brilliant
Flavine 7GFF
Lissamine Flavine FF
pyranine
amino G acid
sodium napthionate
492
515
555
558
535
560
355
349
415
422
4603
4074
359
325
Maximum Fluorescence Detection
Emission1 A Intensity Limit2
(nm) (%) (/*g L-1)
513
535
582
583
555
584
435
439
489
512
512
512
459
420
100
18
60
25
14
30
60
2
?
1.6
18
6
1.0
18
0.002
0.01
0.006
0.006
0.005
0.007
0.01
?
?
r\
7
7
7
0.07
Sorption
Tendency
very low
low
strong
moderate
moderate
moderate
moderate
?
?
?
?
?
?
low
1. Values are approximate only. Different instruments will yield slightly different results.
2. Typical values for tracer detection in clean water using spectrofiuorometric instrumentation.
Values may be adversely affected by augmented fluorescence and/or scattered light back-
ground.
Values will be lower when using filter fluorometric instrumentation.
3. pH>10
4. pH<4.5
Source: Behrens, 1986., Worthington, pers. comm.
Tracer tests in karstic and fractured-rock aquifers may be additionally affected by unknown
subsurface pathways. Different types of solution-conduit and fracture-flow networks will
have a significant effect on tracer mass recovery, but this may be unknown to the tracing
professional. .These factors can be problematic when interpreting either qualitative- or
quantitative-tracing study results and cannot be ignored.
10
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380
450
WAVELENGTH, IN NANOMETERS,
500 570 590 610
760
1
r
UV
Violet
BIU8
Green
» i
01 I
Red
J_J
VISIBLE LIGHT
\ __^_ -*• WAVELENGTH
30mA 0.03A . 3A 30nm ^ 3p — ' 300p 30mm 3m annm
> n ~r I I ||
\ '
Gamma rays | X-rays
I
_ L_ ll i
|l
Ultraviolet 1 1
(UV) . i
1 .J LLJ
I ~~r — r
Infrared | Microwaves 1
(IR) [
1
L_ I.I
— r
1
Radio waves
30km 3000km
~T — 1 1 — I
1 Long L
| electrical 7
i oscillations 'I
1 I , 1
10" 10™ 10"' 10'° 10'
FREQUENCY. IN CYCLES PER SECOND
10"
10* 10'
Figure 4. Electromagnetic spectrum with enlargement of visible spectrum for tracer dyes.
Modified from Wilson et al. (1986, p. 3).
2.1. TRACER CHARACTERISTICS
All chosen tracer substances should exhibit certain "ideal" characteristics, most notably
conservative behavior. 'Unfortunately, no tracer substance is ideal, but fluorescent dyes
are appropriate for tracing hydrologic systems because of their low purchase cost, ease of
use (injection, sampling, and analysis), low toxicity, relatively conservative behavior, high
degree of accuracy of analysis, and low cost of analysis. However, specific aspects of any
particular tracer dye chosen for a tracing study may adversely affect tracer recovery and
thus lead to incorrectly calculated results (e.g., mass-balance errors). For example, sodium
fluorescein (Acid Yellow 73) naturally photodecays, which is problematic for surface-water
tracer tests. - ' - ,.
When conducting qualitative dye-tracing studies, it is usually sufficient to inject a known-
quantity of dye on an "as sold" basis, which means that a considerable amount of diluent
has been added to the dye (i.e., < 100% dye). However, when conducting quantitative
dye-tracing studies, the actual mass of dye injected into the aquifer must be known if the
calculations are to be performed correctly.
Consider, for example, the commonly used fluorescent-tracer dye Rhodamine WT (Acid
11
-------
Red 388). For a qualitative trace, the tracing professional may decide to inject 18 pounds (2
gallons on an as sold basis) into the aquifer and be satisfied with the outcome. A quantitative
trace would, however, require that the actual mass of the dye injected be calculated because
Rhodamine WT is sold as a 20% solution (actually, it is sold as a 17.5% solution, but is
listed as a 20% solution) and because it has a density of 1.19 g cm-3. In this particular
instance, the conversion to mass is developed from the following formula (Mull et al, 1988,
p. 61):
V x p x % =
(1)
where V is volume [cm3], p is density [g cm~3], % is purity, and Mi is mass injected [g].
To determine the actual dye mass injected into the aquifer, the user must perform the.
following calculations:
1. Convert gallons to equivalent SI units (cubic centimeters for this example)
2.0 gal x 3.785 x 10~3 = 7.570 x 103 cm3
where 3.785 x 10"3 is a conversion factor.
2. Next insert the value obtained in step 1 into Equation (1)
7.570 x 103 cm3 x 1.19 g cm-3 x 1.75 x 10"1 ,.= 1.61 x 103 g
= 1.61 kg
Subsequent quantification calculations would then use 1.61 kg for the mass of dye injected
into the aquifer. Similar calculations for other tracer types need to be made using tracer-
specific information.
Tracer sampling also presents some difficulty, depending upon the behavior of the tracer.
All tracers will exhibit some loss due to sorption onto aquifer materials, but other factors
may also cause a loss of tracer mass in the samples. For example, the commonly used tracer
dye, sodium fluorescein (Acid Yellow 73), tends to photodecay so that excess exposure
to sunlight may diminish total mass recovery. Rhodamine WT is temperature dependent
and requires correction of field measurements to a standard temperature. Even worse, it
has recently been shown that Rhodamine WT naturally degrades to.carboxylic fluorescein,
which may substantially interfere with analyses and interpretations if sodium fluorescein
12
-------
was also used during the study (Gareth Davies, pers. comm.). Pyranine (Solvent Green
7) is pH. dependent, which requires careful buffering of the water samples prior to analysis
(Smart and Laidlaw, 1977).
2.2. TRACER INJECTION
Ground-water and surface-water tracing both require labeling or "tagging" the flowing water
with some identifying substance (i.e:\ tracer) for subsequent detection at some distant point.
This can be achieved only by getting the tracer to mix with the water. For surface-water
tracing., this is not difficult.. However, labeling ground water with a tracer can be a fairly
involved process. ->_-..
Typically, for karst systems the tracer substance;, usually a fluorescent dye, is injected
directly into a sinkhole or sinking stream that is believed to be connected to the solution-
conduit system. Figure 5 depicts a reinforced sinkhole located at the RCA del Caribe
Facility. (Barceloneta, Puerto Rico) that was used for plant waste-water injection and for
tracer injection. Although small in appearance, this is a substantial entry point for water
and pollutants. . - . •
Boreholes and wells are often used as injection points, but these are not as effective
as sinkholes and sinking streams. Sinkholes, and sinking streams are directly connected to
the subsurface "plumbing" system of a karstic aquifer. Boreholes and wells, in general, are
rarely connected to the subsurface flow system.
Once injected, the tracer will move through the hydrological system. Figure 6 depicts
a fairly typical solution conduit that may exist in an area. From Figure 6 it is obvious
that if the conduit shown was at a depth of approximately 10 to 30 meters, it would be
nearly impossible to detect it by any known geophysical means, or to intersect it by a well.
Monitoring wells are next to useless in .this instance. However, a slug of tracer dye would
use this conduit to migrate to a point where detection is possible.
2.2.1. Methods of Injection
Tracer injection can be achieved using a variety of methods. For example, it is not atypical to
observe an injection in which a powder or liquid dye is injected ("dumped" and "introduced"
are synonyms) directly into a sinkhole, sinking stream, or monitoring well. However, it
is usually desirable to mix powder tracers with water prior to injection to prevent site
contamination by air currents. The tracer/water mixture is then more easily, poured into
the injection point. Powder tracer mixing is most easily accomplished by adding a measured
13
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Figure 5. Reinforced sinkhole receiving plant waste water at the RCA del Caribe Facility.
Waste water appears as clear water discharging from the rust colored pipe inside the
sinkhole.
quantity of tracer into a large carboy (e.g., 5 L) containing a small quantity of water
(Figure 7).
After the preferred amount of tracer has been added to the carboy, more water is added to
the mixture to bring the level up to about one-half to one-third full. The cap is then screwed
down tightly, and the carboy shaken vigorously to effect a thorough mixing. The carboy
should be weighed before and after all additions and after injection so that a reasonably
accurate estimate of tracer mass can be recorded. The contents of the carboy are then easily
released into the injection point (Figure 8).
Many of the commonly used fluorescent dyes that were previously available in powder
form are now available in liquid form. The liquid form of the powder dyes exhibit
greatly reduced concentrations when compared with the powder form (Table, 3), but the
14
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Figure 6. Dissolutionally enlarged fissure in limestone where most flow will occur. Precipi-
tation of calcium carbonate in fractures appears as white and/or brown streaks.
concentration is insignificant when mass is used to determine the appropriate tracer mass.
Given the availability of liquid dyes there appears to-be no"useful or^valid reason for using
the powder form. -
Prior to tracer injection a-substantial quantity of water (e.g., 1000 gal.) should be
released into the sinkhole or monitoring well (this is unnecessary for sinking streams). This
"primer" of water helps to lubricate the system and to flush out any debris. The tracer may
then be added to the inflowing water. Alternatively, the water injection may be halted for
tracer injection and then restarted after tracer injection.
A large quantity of chaser water (e.g., 3000 gal.) is injected after tracer injection to
help move the tracer along. Chase water helps to prevent the tracer getting stored in large
dead-end pores and behind other obstructions. However, it is necessary in some instances
(e.g., monitoring wells) that care be taken not to raise the head excessively. Experience has
15
-------
Figure 7. Mixing fluorescein powder dye with water in a 5 L carboy. Fluorescein is a
brick-red color when a dry powder.
16
-------
Figure 8. Injecting mixture of water and fluorescein dye into an injection well. Fluorescein
has a dark red color when concentrated as shown here, but becomes a bright fluorescent
green when diluted.
17
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Table 3. Percent pure dye content for selected fluorescent dyes.
Colour Index
Generic Name
Acid Blue 9
Acid Red 52
Acid Red 87
Acid Red 388
Acid Yellow 73
Basic Violet 10
Fluorescent
Brightener 351
Solvent Green 7
Powder Dye
(%)
74.0*
90-92.0
86.0
85.0**
60.0
90.0
,60.0
80.0 ••• .
Liquid Dye
(%)
37.0
18.0
26.0
17.0
30.0
45.0t
— '•
—
Specific Gravity
(gem-3)
—
1.175
—
1.160
1.190
—
—
- —
Values listed are equal to within ±5.0%.
*Acid Blue is also sold with a Food, Drug and Cosmetic (FD&C)
purity equal to 92.0%.
**Acid Red 388 is not commercially available in powder form.
tBasic Violet 10 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.
shown that a slow flow (e.g., < 50 gpm) is more effective than a rapid flow.
2.3. TRACER SAMPLING
Sampling for tracer must be performed in conjunction with discharge measurements for
quantitative tracing because ground-water discharge and tracer-mass recovery are strongly
interconnected. If discharge is not measured during the tracing study, but water samples
are collected, then the tracing study may be considered semi-quantitative. Sampling must
also be of sufficient frequency to avoid the problem of aliasing (Smart, 1988a). Aliasing
occurs when sampling frequencies are inadequate (i.e., time intervals between individual
sampling events are too far apart), which may cause certain aspects of tracer.recovery to
go unobserved.
Additionally, cessation of sampling prior to complete recovery of the tracer mass may
lead to an inadequate estimate of the aquifer characteristics desired. Field and Nash (1997)
demonstrated the efficiency of numerical interpolation/extrapolation algorithms to fill gaps
in the sampling-data record.
18
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2.4. SAMPLING EQUIPMENT
Mull et al. (1988, pp. 38-39) recommend that samples be collected by automatic samplers
using glass sample bottles to minimize losses. Automatic samplers can be programmed to
collect a water sample at appropriate sampling frequencies so that even late-night samples
may be conveniently collected. Glass sample bottles are less likely to sorb the tracer than
are plastic sample bottles, which may distort sample-analysis results. Even if automatic
samplers are not to be used, glass sample bottles are still appropriate for sample collection.
The sample bottles need only be large enough to hold a maximum of approximately 32 mL
of water in most instances.
Grab samples using appropriately sized test tubes with caps (e.g., 25 mm x 150 mm)
minimize handling. Samples should be stored tightly capped in a cool, dark place. Shipping
to the laboratory should be by cooler, with an ice block enclosed.
Packets of activated charcoal may also be collected if fluorescent dyes are used as tracers.
It is believed that activated charcoal will ensure dye recovery because the supposed much
lower dye concentrations found in water samples may not be detected in the water, or
sampling frequencies may not have been adequate. The ability of activated charcoal to
continue sorbing and concentrating fluorescent dye provides a sound means for determining
fluorescent dye occurrence when water samples are ambiguous. However, at best, activated
charcoal will result in a qualitative tracing test only. More seriously, there is considerably
more opportunity for sample contamination from handling. Still more serious is the recently
considered problem of false positives and false negatives associated with activated charcoal
packets (Smart,and Karunaratne, 2001; Smart and Simpson, 2001).
2.5. SAMPLING LOCATIONS AND FREQUENCIES
Sampling locations and frequencies can be based on the results of qualitative dye-tracing
studies so that appropriate sampling locations and frequencies may be determined before
conducting quantitative tracing studies. Preliminary qualitative tracing studies may
help ensure that proper sample collection will occur, while minimizing expenses when
quantitative tracing efforts are undertaken.
Should quantitative ground-water tracing efforts be initiated prior to qualitative tracing
efforts, it is possible that too many or too few sampling locations will be utilized; the
former drives up the cost, while the latter results in incomplete tracer mass recovery.
Sampling frequencies may also be inadequate, resulting in added costs (excessive number
19
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of samples collected) or inadequate tracer mass recovery (too few samples collected too
infrequently). Preliminary simple ground-water tracing studies can be useful for more
difficult and complicated tracing studies. However, as previously, discussed (Section 1.3.
on page 5), recent studies have proven that, with a basic understanding of the local
hydrogeology and the use of automatic water sampling equipment, qualitative tracing efforts
need not be conducted prior to quantitative tracing efforts.
2.6. TRACER MIXING IN THE FLOW SYSTEM
Complete lateral and vertical mixing of the tracer is considered ideal, but, not always
possible. An acceptable mixing length is one in which the travel distance allows for nearly
complete lateral mixing of the tracer, and is considered to be an important factor in tracing
surface-water flows (Kilpatrick and Cobb, 1985, pp. 2-3). Unfortunately, ground-water
tracing does not always ensure that adequate lateral mixing will occur in solution conduits
or fractures because tracing efforts are constrained to the limits of tracer-injection points as
related to tracer-recovery points. Inadequate mixing may result in incorrect tracer-recovery
calculations.
Mull et al. (1988, pp. 43-44) recommend that sampling during preliminary traces occur
(at a minimum) at three places in the cross-section of the spring and the ETC plotted
for each sampling point in the cross-section. Complete lateral mixing is determined to
have occurred when the areas under the BTCs, for each sampling location, are the same
regardless of curve shape or magnitude of the peaks. Optimum results are obtained when
mixing is about 95% complete (Figure 9) (Kilpatrick and Cobb, 1985, p. 3).
2.7. CORRECTION FOR TIME TO REACH FLOW SYSTEM
For some tracer injections, accurate time of travel, velocity, and dispersion estimates require
that the time needed for the tracer to reach the flow system (e.g., infiltration time) be taken
into account for a more accurate estimate. Tracer flow velocity is adjusted for time to reach
and/or exit the flow system by subtracting tinf from the total real time of travel values t;
and integrating. However, this will lead to negative times of travel, so it is easier to subtract
tinf from the mean time of travel t to obtain the true tracer velocity (Dole, 1906, p. 78)
x
v — —
t-t
(2)
'in/
20
-------
Slug
Injection
TIME
Short Distance
Curve areas not the same,
lateral mixing incomplete.
Flow
a •
b •
c •
Definition sketch of
sample points
Optimum Distance
Curve areas about the same,
mixing nearly complete.
Long Distance
Curve areas identical,
perfect mixing.
Figure 9. Typical response curves observed laterally and at different distances downstream
from a slug injection of a tracer in the center of a stream where the symbols are defined in
the Notations section (page 172) (Kilpatrick and Cobb, 1985, p. 3).
The difference between the true velocity and the perceived velocity is then (Dole, 1906,
p. 78)
V =
(3)
(t - *<„/)*
with a consequent correction for dispersion. While this adjustment is usually not necessary
for surface-water tracer tests and many tracer injections into disappearing streams and
sinkholes, it may be absolutely essential for accurate analyses for deep aquifers, or slow
infiltration through the beds of sinking streams.
,2.8. CORRECTION FOR BACKGROUND
All field measurements need to be corrected by subtracting background tracer concentrations
from measured tracer concentrations. For example, sodium fluorescein is used to color
automobile antifreeze. Because there are so many automobiles in existence and so many of
them have leaks in their radiators, fluorescein-colored antifreeze is fairly ubiquitous in the
"environment.
Prior to any tracing efforts, background water samples C^ need to be collected and
analyzed for the tracer of interest. If the values obtained are low enough (e.g., few p,g L"1),
21
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then the chosen tracer may be used. If not, then a different tracer should be chosen. Low
background concentrations in samples will then need to be averaged Cb because it is not
possible to subtract a suite of background concentrations from the measured concentrations.
This final average background concentration is subtracted from every sample of recovered
tracer from subsequent tracing efforts
where
n
(4)
(5)
In addition, instrument calibration (e.g., scanning spectrofluorophotometer and filter
fluorometer) should be performed as described in the appropriate U.S. Geological Survey
Techniques of Water-Resources Investigations publications (Kilpatrick and Cobb, 1985;
Wilson et al, 1986). Proper instrument calibration is essential. Calibration using distilled
water is common, but use of sample water is also acceptable.
2.9. DISCHARGE MEASUREMENTS
As stated previously, tracer sampling must be performed in conjunction with discharge
measurements. If sampling is performed at wells that are being pumped at a constant rate,
then discharge is fairly easily determined. Discharge at springs is considerably more difficult
to estimate. If grab samples are being collected from non-pumping wells, then some estimate
for flux past the well may need to be established.
Estimation of discharge may require special efforts on the part of the tracing professional.
Weirs may need to be built, standpipes installed, flow meters utilized, and losses to
evaporation estimated (for large bodies of water). Numerous documents describing methods
for estimating discharge already exist so the techniques will not be discussed here. Interested
readers should examine the appropriate U.S. Geological Survey Techniques of Water-
Resources Investigations publications for comprehensive discussion of discharge estimates.
Important to note is the possible occurrence of transient high-level overflows in which
normally dry springs may discharge large quantities of water during storm events. Springs
that are normally dry during low- to moderate-flow conditions may function during high-
flow conditions. Efforts to address irregularly functioning springs should be prepared prior
to initiating quantitative-tracing studies so that discharge of tracer at such springs can be
recovered.
22
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Less common is the problem of sampling well screens set at elevations below which
high-flow conditions occur. Such wells may be adequate for recovering tracer during low-
and moderate-flow conditions, but incapable of drawing in and discharging tracer during
high-flow conditions. Presumably, such an occurrence would be addressed by appropriate
sampling at downgradient high-flow springs. •
2.10. KARST CONDUIT NETWORKS
Tracing studies used in the determination of subsurface flow conditions in karst terranes are
greatly influenced by various combinations of subsurface flow networks located between the
inflow and outflow points of the aquifer. Seven types of karst networks are known to exist,
as schematically shown on Figure 10.
The influence of karst networks on tracer quantity present at a recovery site can be
significant. If flow is through the simple Type I network, dye quantity estimates may be
reasonably accurate. The more complex the karst network, however, the less likely it is that
estimates of dye quantity will be adequate. As estimates become more difficult to make, it
becomes tempting to use more dye than necessary. For Types II through VII (but excluding
Type V), the estimate of dye quantity is likely to be low.
2.10.1. Network Types I, II, and III
If flow is through a Type I network, then predictions based on common tracing techniques
may be reasonably accurate. If flow is through a Type II or Type III network, the accuracy
of the predictions will tend to be inversely proportional to the amount of dye that is either
diluted by additional water inflow or diverted to unknown discharge points. Distributary
flow and multidirectional flow are subtypes of Types III and IV.
2.10.2. Network Types IV and V
Types IVa and IVb further complicate the flow determination because of significant loss
of dye and because the identified outflow point will have a discharge rate that may be less
than, greater than, or equal-to the inflow point. Type V presents the worst situation related
to flow prediction because no dye is recovered. This can lead to a false conclusion of a lack
of hydraulic connectivity (i.e., if the dye goes elsewhere, such results indicate there is no
flow to the sites being monitored).
23
-------
m
m,
Figure 10 Seven simple karst network types that describe tracer migration m karst conduits.
Any of these networks may significantly influence tracer tests between the point of inflow
(IN) and the point of outflow (OUT) in a karst system. Discharge into the conduit is q,
discharge out bf the conduit is Q, tracer mass injected into the conduit, is -m*, and tracer
mass recovered is Tr. Note: Any one of these network types may be interconnected with
any of the others. Modified from Atkinson et al. (1973) and Caspar (1987b, p. 64).
24
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2.10.3, Network Types VI and VII
Types VI and VII are situations where either a significant amount of ground- water storage
exists or a separate karst subsystem is connected to the main karst system. These are really
subgroups of any one of Network Types I, II, III, IV, or V. As drawn, Network Types VI
and VII appear only as subgroups of Network Type I, but additional inflows, outflows, or
no connection to the sample-collection station(s) are realistic possibilities. For contaminant
transport in a karst system, Network Types VI and VII may play significant roles.
2.11. DETERMINATION OF TOPOLOGICAL KARST CONDUIT NET-
WORK TYPE
Determination of the karst conduit network type usually requires extensive cave exploration,
but can be roughly estimated from quantitative ground- water tracing studies. This is
achieved by recognizing that each topological type exhibits specific characteristics that
influence the results of tracing studies (Atkinson et al, 1973).
A Type I network (Figure 10) will exhibit such characteristics as inflow discharge equal
to outflow discharge and mass of injected tracer equal to mass of recovered tracer
q = Q
Min =• M
out
This assessment seems intuitively obvious considering that, for both the inflow and
outflow discharges to be equal and for complete tracer recovery to occur, requires that a
simple straight tube be denned. Other topological types become more difficult to assess as
discharges and tracer recoveries become more complex (Figure 10).
It will be noted that Network Types VI and VII may fit into any one of the above
categories, but with the added effect of storage in the system. Storage is not, however,
accounted for in the simple relationships because it is only a delaying mechanism.
25
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3. QUANTITATIVE TRACING METHODOLOGY
Quantitative tracing studies are based on a detailed study of BTCs, which are generated
from quantitative chemical analyses (e.g., fluorescence) of a series of water samples, in
combination with ground-water discharge measurements for each sampling station at which
tracer was recovered. Tracer-breakthrough curve shape for hydrological systems depends
upon:
• Character of the tracer;
« Prevailing flow conditions;
• Structure of the aquifer (Smart, 1988a);
Discussion of these conditions, as related to BTCs, has already been addressed and reviewed
by Smart (1988a). Successful quantitative ground-water tracing studies are dependent upon:
• Conservative behavior of the tracer substance;
• Precise instrument calibration;
• Adequate quantity of tracer substance to be injected;
• Sufficient monitoring frequency at all downgradient receptors;
• Precise discharge measurements at downgradient receptors; and
• Sufficient length of monitoring period for total tracer mass recovery.
These factors may be achieved through good design, implementation, and persistence.
Various problems tend to arise when the above factors are not considered in the design of
a tracing study. Such problems may include no tracer recovery, incomplete tracer recovery,
or aliasing of the ETC (Smart, 1988a). These problems lead to fundamental questions
regarding the tracing study. If none or only some of the injected tracer mass was recovered,
what caused incomplete recovery? What was the mean residence time (mean tracer transit
time) for the tracer in the aquifer? What were the mean and apparent tracer velocities
assuming advection only? How significant was longitudinal dispersion in the aquifer?
In terms of contaminant transport, answers to these questions are essential. Some of
the questions can be answered by only making best professional interpretations of the ETC.
26
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Siten
Site n +1
ELAPSED TIME
Figure 11. Definition sketch of BTCs along a selected tracer streamline from an instanta-
neous tracer injection (Kilpatrick and Wilson, 1989, p. 3).
Others may be answered by careful numerical analysis of the ETC. For example, in instances
of insufficient sampling frequency or cessation of sampling prior to total tracer mass recovery,
good interpolation/extrapolation algorithms may be used to fill gaps in the data. However,
problems of aliasing may not be addressed by such efforts while extrapolation of data beyond
real sampling times may not provide realistic values.
3.1. ESTIMATION OF HYDRAULIC PARAMETERS
Hydraulic parameters may be estimated by the method of moments. The zeroth moment
is used to estimate the tracer mass recovery. The first moment is used to estimate the
mean residence time and mean flow velocity. The second moment is used to estimate the
longitudinal dispersion. However, as will be shown, the second moment may not provide
reliable estimates for dispersion (Field and Pinsky, 2000).
Analysis by the method of moments is nothing more than determining the area under
the ETC generated by plotting time versus measured tracer concentrations (Figure 11).
The following discussion is taken from Kilpatrick and Wilson (1989, p. 3 and 4).
The BTCs along a streamline shown in Figure 11 may be described in terms of elapsed
-------
time after a slug injection. Characteristics pertinent to the ETC analysis are:
• TL, elapsed time to the arrival of the leading edge of the ETC at a sampling point;
• Tp) elapsed time to the peak concentration Cp of the ETC at a point;
• Tc, elapsed time to the centroid of the ETC at a point; and
• Tj, elapsed time to the trailing edge of the response curve at a point.
The mean travel time for the flow along a streamline is the difference in elapsed time of
the centroids of the BTCs defined upstream and downstream on the same streamline given
by
f~i~i rr~\
•*• Cn+l -* Cn
(6)
where n is the number of the sampling site. Similarly, the travel times of the leading edge,
peak concentration, and trailing edge along a given streamline are, respectively
= TLn+l - TLn
(7)
tp =
-Tn
and
The time Td necessary for the tracer mass to pass a sampling point in a section is
Td = Ttn - TLn
(8)
(9)
(10)
As shown in Figure 11, a typical tracer cloud may travel faster in the center of the stream
than along the flow channel walls, where it may also be elongated. Complete definition of
the ETC may involve measurement at more than one point or streamline at several sections
(if possible). Usually, in hydrologic systems other than surface streams, such elaborate
sampling is not possible. Samples are acquired where feasible. It also may not be necessary
if adequate mixing has occurred. However, it is advisable to sample at least three points
along a cross section of a spring, if possible, to ensure adequate mixing.
The duration or time of passage of a tracer response at a section TD is the difference
between the slowest trailing time along a flow channel and the fastest leading edge time,
28
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usually observed in the center. The difference between the values oLTd and TD can be
significant. It is usually assumed that Tb'« T^. ,
The remainder of this document will not rely on Equations (6)-(10) because it is rare for
ground-water tracing studies to provide an opportunity for sampling at multiple locations
along a streamline. Direct access to a cave during a tracer test is one exception.
3.1.1. Total Tracer Recovery
Estimation of tracer recovery for individual sampling stations is given by Equation (11)
(modified from Caspar, 1987b, p. 62) .
- r
Jo
C(t] Q(t] dt
(11)
and total tracer recovery from all downgradient receptors may be estimated from Equa-
tion (12) (Caspar, 1987b, p. 63)
(12)
These models assume complete mixing of the tracer substance with water, negligible
dispersion effects, and that the tracer mass will ultimately exit the aquifer system completely
at one or more downgradient receptors as a function of time.and discharge.
A simple total mass recovery equation for a single sampling station was developed by
Mull et al. (1988, p. 52) that includes a necessary unit conversion factor, because English
and SI units are intermixed in their equation. Other than the necessary unit conversion
factor, this equation yields acceptable results if proper care is taken in the execution of the
tracing study. Their equation is not reproduced here to avoid confusion with Equation (11)
of this section.
3.2. QUALITY OF TRACER MASS RECOVERY
The quality of the tracer experiment may be quantified in terms of mass recovered. Usually,
the quality of the tracer experiment is given as a percent of mass recovered, but this affords
little insight. An accuracy index given by Sukhodolov et al. (1997)
.. Min-MT
(13)
provides more insight into the quality of the tracing experiment. An AI = 0 indicates a
perfect tracing experiment. A positive A/ indicates more mass injected than was recovered,
29
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while a negative A/ suggests more mass recovered than was injected. As AI moves further
away from zero, the quality of the tracing experiment gets poorer.
A high degree of precision for tracer recovery has considerable utility. For evaluation of
ground-water monitoring and contaminant transport, total tracer mass recovery is essential.
Tracer mass recovery should be quantified to ensure that all relevant locations are properly
monitored for ground-water quality. Otherwise, it is likely that important ground-water
discharge locations may be missed. A low-percent recovery of a conservative tracer mass
may be an indication of significant loss of tracer during the study, often a result of improper
determination of downgradient receptors. A high-percent recovery is a probable indication
that most, if not all, relevant downgradient receptors were properly monitored for tracer
recovery. For contaminated sites of a controversial nature (e.g., Superfund sites), this can
be critical.
3.2.1. Mean Residence Time
Mean tracer residence time is the length of time required for the centroid (gravity mass) of
the tracer to traverse the entire length of the aquifer system, representing the turnover time
for the aquifer. The centroid is generally not the same as the peak concentration of the
tracer in the ETC, but the more flow conforms to Pick's law, the less obvious the difference
between the centroid and the peak concentration.
Mean tracer residence time for impulse and short-pulse releases fa < t) is estimated
from Equation (14) (modified from Caspar, 1987a, p. 93)
t =
/oo
tC(t}Q(f)dt
_
/oo
C(t) Q(t] dt
and for long-pulse and continuous releases fa > t) from (Sardin et a/., 1991)
(14)
= ni-
Jo
dt
where
F(t) =
C(t)
(15)
(16)
Travel-time variance for impulse and short-pulse releases fa < i) is estimated from
30
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Equation (17) (modified from Mull et al, 1988, p. 58)
/•oo
(t-t)2 C(t] Q(t] dt
~2 — Jo
/•o
/
Jo
C(t}Q(t}dt
• (17)
and for long-pulse and continuous releases (tz > f) from (Sardin et al, 1991)
[l-F(i)]tdt-t*
/•o
= 2 /
Jo
(18)
It will be noted that for Equations (17) and (18) to be appropriate for long-pulse releases, the
time-concentration data file must be truncated so that the descending time-concentration
data is ignored in the calculations.
Equations (14) to (18) assume that tracer residence time will vary from zero for
instantaneous exit of the tracer mass from the aquifer system to infinity for tracer mass
that is stored in micropores. They provide relevant information on the time required for the
centroid of a nonreactive pollutant mass spilled in the vicinity of the injected tracer mass
to reach a downgradient receptor.
Mean tracer residence time may be estimated by summation algorithms, a simplified
version of which was developed by Mull et al. (1988, p. 56). Their equation provides
good results, but may be confusing to the uninitiated, and may also be confused with
Equation (14). A simplified example calculation is performed later in this report (see
Section 4. on page 48).
A method for estimating mean tracer residence time was also developed by Smart
(1988b) using time-concentration integrals that are based on a routine in Church (1974).
This' method does not include discharge in the calculation, but is generally similar to that
presented in this section. This method has not been tested by this author but may be
regarded as acceptable.
For contamination studies, initial tracer breakthrough (i.e., first arrival) may be consid-
ered more valuable than the tracer residence time, although it may have little theoretical
meaning. Initial tracer breakthrough provides water managers with an indication of the
length of time a contaminant will take to be detected at a downgradient receptor. How-
ever, the effects of longitudinal dispersion and inadequate sensitivity of current analytical
methods at extremely low concentrations render this situation meaningless.
31
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3.3. Residence Time Skewness and Kurtosis
Tracer travel time skewness is a measure of the lateral asymmetry of the ETC and the
kurtosis is a measure of the peakness of the ETC. For impulse and short-pulse releases,
skewness may be determined from (modified from Mull et al., 1988, p. 58)
(t - f)3 Q(t) C(t) dt
~ poo
t3 / Q(t}C(t)dt
Jo
(19)
Kt =
(20)
and the kurtosis may be determined from
/oo
(t - £)4 Q(t) C(t) dt
.
/oo
<5(t) C(t) dt
-
For continuous and long-pulse releases, the calculation of skewness is considerably more
difficult. In this instance skewness may be obtained from (Ravi Subramaniam, pers. comm.)
o
\ - F(t}}& dt - Qt [ [l-F(t)]tdt + 2t(
Jo
(21)
and the kurtosis may be determined from
/oo r°° ~ •?
r - -r-,/ \i 9 7 -,^r2 / r-i T-I/J.M j. jj. o Z4 o I 2\2 /'ooA
[4t — 12t — jP(t)]i dt + Vlt \ [I-F(t)]tdt-3t -3(at) (22)
Jo
A symmetrical curve results in a skewness coefficient equal to zero. Positive number
for the skewness indicates that the ETC is weighted to the right, recedes more gently than
it rises (Mull et al., 1988, p. 59), and reflects both longitudinal dispersion and dead zone
effects. Skewness is used by Qtracer2 only for comparison of dimensionless BTCs generated
from multiple tracer tests conducted from the same injection points to the same recovery
locations as described by Mull et al. (1988). Kurtosis is also used by Qtracer2 for comparison
purposes only for comparison of dimensionless BTCs generated from multiple tracer tests
conducted from the same injection points to the same recovery locations. Application of
skewness and kurtosis estimates is briefly discussed in Section 6.6.21. on page 86
3.3.1. Mean Tracer Velocity
Mean tracer velocity is a measure of the flow rate of the centroid of the tracer mass. For
impulse releases, mean tracer velocity is given by Equation (23) (modified from Caspar,
32
-------
1987b, p. 66)
v =
x
— C(t) Q(t] dt
i
C(t) Q(t] dt
(23)
with a standard deviation for impulse releases given by Equation (24)
\
/oo
C(£) Q(t) dt
.
For short-pulse releases (£2 < £), mean tracer velocity is given by Equation (25)
(24)
2/e
C(t)Q(t)dt
(25)
with a standard deviation given by Equation (26)
\
r i
Jo I
f r r \
1 Xs Xs \
V£-t2/2 t-t2/2j
1 2
C(€)Q(t}dt
/oo
C(t}Q(t)dt
' .
(26)
For long-pulse and continuous releases (£2 > £), mean tracer velocity is given by Equa-
tion (27)
v —
(27)
The standard deviation for long-pulse and continuous releases (£2 > £) cannot be solved
trivially and is not attempted here. '
Tracer migration distance(s) is usually measured as a straight-line distance from the
injection point to the tracer recovery sampling station (radial distance = x [L]). A straight-
line assumption for solution conduits is unrealistic and should be corrected for sinuosity
(Field and Nash, 1997; Worthington, 1991, pp. 85-91) by
xs = Sd x
(28)
33
-------
where 1 < S
-------
responses to a slug of injected tracer are shown with distance downstream from a. single,
center slug injection along selected imaginary streamlines.
SLUG INJECTION
OFTRACER
Vertical and lateral mixing
longitudinal dispersion
(vertical not shown)
IV
LONGDISTANCE
Stream
boundary
III
OPTIMUM
DISTANCE
VERYSHORT
DISTANCE
Figure 12. Lateral mixing and longitudinal dispersion patterns and changes in distribution
of concentration downstream from a single, center slug injection of tracer (Kilpatrick and
Wilson, 1989, p. 2).
As noted by Kilpatrick and Wilson (1989, p. 2), a soluble nonreactive tracer (e.g.,
some fluorescent dyes) released into a stream behaves in the same manner as the actual
water particles. Therefore, a measure of the movement of the tracer and its dispersion
characteristics will, in effect, be a measure of the movement of an element of fluid in the
stream. It may be further noted that the dispersion and mixing of the tracer in the receiving
stream takes place in all three dimensions (Figure 12), although vertical mixing normally
occurs before lateral mixing, depending on the flow characteristics and velocity variations. •
Longitudinal dispersion, having no boundaries, continues indefinitely and is the dispersion
component of principal interest (Kilpatrick and Wilson, 1989, p. 2).
Longitudinal Dispersion by the Method of Moments Longitudinal dispersion is
most commonly estimated using the second moment (Maloszewski and Zuber, 1992), which
when properly weighted for concentration, may be estimated for impulse, long-pulse (£2 > t),
35
-------
and continuous releases by (Kreft and Zuber, 1978)
DL =
2x,
and for short-pulse releases (i2 < t) by (Wolff et al, 1979)
_
12; 2zl
(29)
(30)
It should be recognized here that DL solved by (30) is based on the assumption of a
ETC and does not represent the mean residence time distribution as does (2J3). In some
instances, there will usually not be any major difference in DL estimation from (29) or (30).
Equations (29) and (30) assume that Pick's law is always applicable; that is, there is
no anomalous behavior. In actuality, immobile-flow zones (dead zones) are common, which
cause a long tail to the ETC and invalidates Pick's law.
Longitudinal Dispersion by the Chatwin Method Chatwin (1971) developed a
method for determining longitudinal dispersion intended to address the problem of non-
Fickian behavior. Technically, the Chatwin method is only really valid for impulse releases,
but it does provide a reasonable approximation for longitudinal dispersion for pulse and
continuous releases (see Section 8.1.1. on page 115). Longitudinal dispersion as developed
in Chatwin (1971) is given by Equation (31) as
/tin
CVt
vt
where the proportionality constant, Ap represents (Davis et al, 2000)
M
For symmetrical concentration distributions (Davis et al., 2000),
xs = vt
which may be rearranged to yield
C — Cp — —
Ap —
(31)
(32)
(33)
(34)
(35)
36
-------
Day (1975) showed that Equation (35) results in relatively insignificant errors for asymmet-
rical concentration distributions.
Subject to tK < xs/v, Equation (31) is reduced to the general least-squares problem by
solving
where
A =
(36)
(37)
x=
(38)
b = (&!, 62, ... , bK)
where T represents the transpose of the vector.
The parameters bi are equal to the left-hand side of Equation (31)
(39)
(40)
and the parameters to be determined Xi are equal to the two factors on the right-hand side
of Equation (31)
xs
(41)
V
(42)
'X3
where x± is the y intercept of the straight-line fit to the early-time data and £2 is the slope
of the straight-line fit to the early-time data. Either term on the right-hand side allows
for solution of the longitudinal dispersion coefficient DL, provided that a plot of the left-
hand side of Equation (31) against early-time data reasonably falls as a straight line (Day,
37
-------
1975). The late-time data will depart from the straight line due to non-Fickian dispersion
characteristics (e.g., dead zones).
Equations (29) and (30) tend to overestimate DL, suggesting a greater ETC spread
than is likely to occur as a result of solute dispersion. Alternatively, Equation (31) may to
underestimate DL for systems exhibiting Fickian behavior.
In this report, Equation (31) is always used except in those instances where the Chatwin
method appears to fail or computer memory storage is exceeded. In that case, Equations (29)
and (30) are used as appropriate.
Mull et al. (1988, pp. 59-60) developed two equations designed to estimate the longi-
tudinal dispersion coefficient of a karst conduit from dye-tracing studies. Results of the
two equations on the same data set produce radically different results. Their Equation (17)
appears to be the more reliable estimate for dispersion.
Smart (1988b) developed a relatively simple method of estimating the dispersion
coefficient based on the efforts of Brady and Johnson (1981), who used an equation derived
by Dobbins (1963). Although not described here, this method appears reasonable and
should be considered.
3.3.3. Tracer Dilution
Estimation of tracer dilution is desirable so that effective dilution of pollutant releases
may also be estimated. Given the generally nonconservative behavior of most .tracers and
pollutants in hydrologic systems, as well as their basic differences, estimation of effective
dilution is recognized as a very rough approximation at best. Still, estimation efforts can
provide useful predictions about potential dilution in the system.
Longitudinal dispersion theory for a conservative tracer, released as a slug at t = 0
and x = 0 in densely fissured aquifers where dispersion and advection are assumed to be
one-dimensional, suggests that a uniform Gaussian distribution of the tracer concentration
will occur in the direction of flow as shown in Equation (9) of Dobbins (1963).
-,\2
— (xs — v t)
(43)
Mass Min of the injected tracer is assumed to be small relative to the mass flux rate of the
water, so, in theory, the ETC should approach a Gaussian shape. In fact, the ETC is always
skewed to the right because of the effects of transverse dispersion (ignored in Equation [43]),
38
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nonsteady flow conditions, and storage of tracer in very slow-moving water of small voids
with later release into large voids, which forms the "tail" of the ETC (Atkinson, 1987).
However, tracer behavior is considered to be sufficiently Gaussian-like to allow use of the
property of "complementarity." Complementarity suggests that the effects of dispersion on
two tracer injections at successive times will proceed independently of each other, and that
the combined effect of the two injections will be the sum of their individual effects (Atkinson,
1987). This property was experimentally employed by Smart (1985) to demonstrate the
probable dilution estimation for a large quarry that had been used as a landfill for municipal
wastes.
Smart derived a dilution equation that utilized tracer input/output concentrations by
relating the mass of tracer injected into the aquifer from successive and repeated injections
to tracer recovery
D==CL= M™ . . ... (44)
Cp£ At CJ Opj,
Steady-state concentration Cpi, is a function of tracer recovery from a single tracer
injection and is given as
(45)
where Cj is the tracer concentration at the resurgence at time -j for a single instantaneous
tracer injection. Time tj, represents the time between tracer injection and tracer break-
through at the resurgence. The value n equals d/At, where d is the time between tracer
breakthrough and final tracer detection at the resurgence (pulse duration).
As may be observed from the above discussion, effective estimation of tracer dilution
in an aquifer is very difficult. Smart (1985) points out that as the tracer is not conserved
in the aquifer, dilution will be overestimated in proportion to the amount of tracer loss.
Effective estimation of tracer dilution is necessary, but much research is still needed.
3.4. FLOW-CHANNEL GEOMETRIES
Flow-channel geometries are estimated by evaluating discharge with respect to mean
residence time. This is accomplished for either the continuous or the discrete situation.
Not all the equations described in this section may be applied to analyses of porous-media
systems (e.g., granular aquifers), because of the need to know particle diameter, hydraulic
conductivity, and/or other factors.
39
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3.4.1. Aquifer Volume
Tracer mass recovery, where discharge was measured during each tracer sampling event,
allows for a rough estimate of the maximum volume of flow system traversed by the tracer
cloud using of Equation (46) (Atkinson et aL, 1973)
V= / Qdt
Jo
(46)
If a single discharge value is used as a mean discharge, then the volume may be estimated
by
(47)
and a total maximum volume estimate based on the sum of each individual'transport zone
(e.g., solution conduit or fracture) traversed by the tracer cloud may be determined from
Equation (48)
(48)
It should be noted that aquifer volume calculations will be only a crude approximation
at best. Summing the volumes of individual transport zones to achieve a total maximum
volume estimate should not be expected to produce accurate results, but the, sum of the
individual transport zones do provide some indication of the aquifer volume contacted
by tracer. However, Equations (46) and (47) provide a more realistic estimate of the
system volume than could be obtained from the product of mean discharge and time to
peak concentration, although this theory requires additional data for confirmation (Smart,
1988b).
By far, the majority of volume space will be occupied by micropores, but these contribute
little to the flow of ground water in solution conduits and fractures. As such, it is
recommended that investigators consider a variety of methods for estimating aquifer volume
and use all the data obtained for a better volume estimation. .
Perhaps more valuable is a comparison between inflow rates and outflow rates. If
injection discharge is measured during tracer injection, comparisons may be made between
inflow and outflow that may lead to additional insights into the aquifer. For example,
inflow/outflow evaluations, coupled with comprehensive ETC analyses furnish ;a means, for
assessing the type of karst aquifer under investigation (Atkinson et a/., 1973).
40
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3.4.2. Cross-Sectional Area
The easiest and probably most reliable geometric parameter that can be estimated is cross-
sectional area. Because the volume V could be estimated from Equations (46) or (47), the
cross-sectional area may be estimated from
"-'
(49)
where xs may be a sinuous distance or a straight-line distance. A sinuous distance will
result in a smaller A than a straight-line distance would suggest,
3.4.3. Flow-Channel Diameter
By assuming a cylindrical flow channel, it is possible to estimate a flow-channel diameter
from a BTC. Because the system volume has been estimated, the flow-channel diameter
may be obtained by
(50)
Obviously, Dc/2 can be used to estimate the flow-channel radius that is typically used in
many modeling endeavors.
3.4.4. Flow-Channel Hydraulic Depth
If open channel flow is assumed to occur in the flow channel, then a hydraulic depth may
be estimated by
DH = 4~ (51)
LJct
which is a reasonable approximation.
3.4.5. Flow-Channel Surface Area
If the flow channel is assumed to conform to a cylinder, then it is possible to obtain an
initial estimate of the conduit surface area. (If it is also a solution conduit, then it needs to
conform, to Karst Network Types I, II, VI, and VII) A flow-channel surface area estimate
is obtained by
As =
(52)
41
-------
The roughness correction factor m is necessary because the cylinder concept assumes a
"smooth as glass" cylinder. Roughness factor estimation is not straightforward and requires
some degree of professional judgment, especially if the flow channel of interest cannot be
directly entered to take physical measurements of roughness.
A reasonable estimate for the roughness factor may be obtained by
£
771 =
5/103
(53)
The surface irregularities relief e, taken as 1.0 m, is considered reasonably representative
of typical flow-channel walls. There is some support for this assumption from natural river
beds (Chow, 1959, p. 196). The viscous-flow sublayer 5 is divided by 103 in Equation (53)
to correct for obstructions in the flow regime created by scallops, differential dissolution,
large bends, undercut walls, breakdown, and backwater zones, as well as other possible
flow restrictions. These effects were considered by Atkinson (1977) to explain an estimated
roughness height equal to nearly three times the diameter of the solution conduit he was
investigating.
3.4.6. Tracer Sorption Estimation
Sorption to flow-channel walls can be estimated by considering a laboratory column as
analogous to flow through a channel. Although far from perfect, it can provide useful
information for comparison with more theoretically based models.
Karst conduit sorption is estimated by
__ (Co - Cf)V
CfAs
and for multidischarge systems (e.g., Karst Network Types III and IV)
(54)
(55)
If a multidischarge system is of interest, it is essential to note that any results obtained
by Equation (54) will be erroneous. Only results obtained by Equation (55) should be
considered relevant.
3.5. EMPIRICAL FLUID DYNAMICS MODELS
Experiments on fluid dynamics have led to the development of many models for flow for
specific geometries. These geometries will not necessarily be reproduced by the actual
42
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hydrologic systems and cannot be reliably approximated, whether physical measurements
can be taken or not. However, by making some simple assumptions, reasonable parameter
estimates may be obtained. For solution conduits, it may be assumed that the phreatic
conduit will best be approximated by assuming a cylindrical conduit. Such an assumption
is not unreasonable for phreatic conduits developed in flat-lying sediments and may not be
too unreasonable for other structural and stratigraphic conditions.
3.5.1. Peclet Number
The Peclet number is a measure of the relative contribution of mechanical dispersion and
diffusion to solute transport. It relates the effectiveness of mass transport by advection
V TT^Ir = ~PeihT) to tne effectiveness'of mass transport by either dispersion or diffu-
sion (jjjs\ (Schiesser and Silebi, 1997, p. 372). Peclet numbers below 0.4 indicate diffusion
control; 0.4 — 6.0 suggests that diffusion and advection are in transition and thus approxi-
mately equal to each other; and > 6.0 indicates advection control (Fetter, 1992, pp. 54-55).
In most nonporous media instances of solute transport in karst conduits, Peclet numbers
will be greater than 6.0. Often, the Peclet numbers will be many times greater than 6.0.
Estimation of a Peclet number can be obtained from the calculated dispersion and mean
tracer velocity from
vxs
AT
(56)
It is necessary to note that estimation of the Peclet number by Equation (56) may be too
low. Substitution of the peak flow velocity vp could be considered, but most likely would
result in overestimating the Peclet number.
It should also be noted here that even though xs is listed as representing distance, in
reality, for porous-media flow, it probably will not have been corrected for sinuosity.
3.5.2. Dynamic Flow Equations
Open-channel and closed-conduit flow phenomena are usually described by dimensionless
equations for flow behavior. The Reynolds number furnishes a means for determining if flow
is laminar or turbulent. The Froude number is used to determine if the flow is subcritical
or supercritical.- The equations described in this section are not all applicable to analyses
of porous-media systems (e.g., granular aquifers) because of the need to know particle
diameter. . .
43
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Reynolds Number The resistance of flow depends entirely upon the geometry and
magnitude of the quantity p*^°, where p represents fluid density, d conduit diameter, and v
dynamic viscosity. The Reynolds number NR is the parameter describing the process. The
smaller the Reynolds number, the more resistance to flow. Assuming a cylindrical conduit,
a rough approximation of the Reynolds number for each individual sampling station may
be obtained from
NR=^ (57)
Estimation of the Reynolds number by Equation (57) will be only a crude approximation
because the quantity (V/xs)1/2 is dependent upon a maximum volume estimate and a
straight-line radial distance to the sampling station. Consequently, V is immoderately
large, xs is immoderately small, and (F/a;.,)1/2 is excessively large. Therefore, calculation
of Reynolds number by Equation (14) should be regarded as an upper limit. However,
the quantity V/x3 has been used to reasonably estimate the cross-sectional area of a single
uniform water-filled karst conduit in the Malign karst system (Smart, 1988b).
If the Reynolds number indicates flow to be in the laminar regime, then an equivalent
hydraulic conductivity K for flow within the conduit (or fracture) may be calculated. For
laminar flow in a karst conduit, K is obtained by
K =
8/i
and for laminar flow in a fracture, K is obtained by
K =
!2fJL
(58)
(59)
It should be noted that a hydraulic conductivity estimated by either Equation (58) or (59)
will be extremely large. In truth, K will be approaching infinity (imagine the value of K for
a lake). Hydraulic conductivity cannot be approximated for turbulent conditions because,
by definition, turbulent flow is a nonlinear phenomenon.
For porous-media flow, the Reynolds number uses the hydraulic conductivity in place of
the cylinder diameter (de Marsily, 1986, p. 74)
IK p.
AT
NR =
(60)
although comparisons between Equation (57) and Equation (60) are inappropriate. Using
Equation (60) it may be accepted that laminar flow occurs when 1 < NR < 10, transient
flow occurs when 10 < NR < 100, and turbulent flow occurs when NR > 100.
44
-------
Froude number The ratio of the mean flow velocity to the linear dimension of flow
(hydraulic mean depth) is a measure of the extent to which gravitational acceleration affects
flow. Gravity becomes less important as the ratio increases. Such a ratio is useful for
determining if flow is in the subcritical or supercritical range. The parameter describing the
effect is the Froude number and is given by
NF =
v
(61)
Estimation of the Froude number by Equation (61) will be a rough approximation mainly
for the same reasons that apply to the Reynolds number estimation. The Froude number is
used to explain flow behavior for streams with a free surface, which may increase uncertainty
because subsurface channels may exhibit either open-channel flow, closed-conduit flow, or
both flow types depending on stage.
An estimated .Froude number for a flow channel exhibiting closed-conduit flow (e.g.,
karst conduits) is not appropriate. Also, as presented, the calculation for the Froude number
assumes that the cross-sectional area of the flow channel, divided by the diameter of the
flow channel, is equal to the mean hydraulic depth, which may not always be true.
3.6. BOUNDARY-LAYER EFFECTS
While not generally considered in tracing studies, boundary-layer effects can substantially
impact the study results. In most instances, flow-channel walls are assumed to be smooth,
which is unreasonable. Cave exploration and fractured-rock studies have revealed that
conduit walls are often covered with scallops, making them very rough. Additionally,
sediment coating on cave walls and layering on cave floors greatly adds to roughness and
surface area. Cave breakdown is an extreme case causing significant roughness. The
equations described in this section are not applied to analyses of porous-media systems
(e.g., granular aquifers) because of the need to know particle diameter.
3.6.1. Friction Factor Estimation
When flow is believed to be laminar, a friction factor may be estimated by (White, 1988,
p. 163)
J f '=~ ~~" \ )
and for turbulent flow, a friction factor may be estimated by (White, 1988, p. 163)
1 , DC f/T>\
—= - 2 log h 1.14 (63)
Vff £
45
-------
where the relief of surface irregularities £ is a controlling factor and depends on the nature
of the channel through which flow is occurring.
3.6.2. Viscous-Flow Sublayer
It is well documented by empirical studies that turbulent flow occurs as a core that
is surrounded by a viscous-flow sublayer. The thickness of the viscous-flow sublayer is
dependent on the degree of channel-wall roughness. If a typically very rough flow channel
is assumed, then the viscous-flow sublayer may be estimated by (White, 1988, p. 163)
5 32.8
(64)
which is an important parameter for assessing the extent of solute sorption to channel walls
and the possibility of matrix diffusion effects. Matrix diffusion can occur only from the
viscous-flow sublayer.
3.6.3. Hydraulic Head Loss
When flow is laminar, the hydraulic head loss along a channel can be estimated by (modified
from White, 1988, p. 162)
hL =
(65)
and when flow is turbulent, the hydraulic head loss along the channel may be estimated by
(White, 1988, p. 163)
hL-fj^r (66)
which emphasizes the influence of friction on head loss.
Hydraulic head loss in porous media is based on a rearrangement of Darcy's law (modified
from White, 1988, p. 162)
hL =
vxs
(67)
It should be noted here that even though xs is listed here as representing distance, in reality
it probably will not have been corrected for sinuosity.
46
-------
3.6.4. Shear Velocity
The shear velocity for flow through a flow channel is created by'boundary-layer effects
produced by the channel walls. Therefore, it might be expected that the shear velocity will
be somewhat less than the flow velocity in the center of the channel.
Estimation of the shear velocity is obtained by
__
DC xs
(68)
It will be noted that flow velocities produced by Equation (68) will always'be less than
those produced by Equation (23). This makes sense in that the flow channel walls should
impart some negative influence (i.e., resistance) on the flow velocity.
47
-------
4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY
To determine the total mass recovery of tracer injected into a hydrologic system, the follow-
ing steps must be initiated. The example calculations describe a scenario in which time is
measured in hours and discharge calculations are in SI units, to facilitate the explanation.
Simple modifications to the procedure may be made for units that vary from the example.
1. Plot the Concentration Subtract background tracer concentration. Plot the concen-
tration of tracer recovered (e.g., mg L"1) versus time in appropriate units (e.g., h).
Time should be plotted on the x axis.
2. Plot the Discharge If the tracer is being recovered at a sampling location (e.g., spring
or well) where discharge is variable over the time of tracer recovery, then plot discharge
in appropriate units (e.g., m3 s-1) versus time (hours) also. Again, time should be
plotted on the x axis. If discharge is constant there is no need to plot discharge.
3. Integrate Recovery Curve Quantitation of tracer recovery is found by integrating
everywhere underneath the tracer recovery curve according to Equation (11), which
must be integrated numerically. This is done using a simple summation algorithm.
This is most easily accomplished by setting up a table that facilitates the necessary
calculations (Table 4).
Table 4. Table representing tracer recovery data for processing.
Sample t Q C CxQ txCxQ
(T) (L3 T-1) (M L-3) (M T"1) (M)
4. Integrate Recovery Curve Again Integrating the recovery curve a second time, but
this time including time t, and dividing by the mass recovered (step 3 above) according
to Equation (14), will yield the mean residence time. This is most easily accomplished
by using the table created in step 3 above (Table 4), which facilitates the necessary
calculations. Time is recorded in equally spaced increments. If discharge; was constant
during the period of tracer recovery, then the Q column (column 3) of the table has a
48
-------
constant value as well. The C x Q column (column 5) is obtained from the product
of the third and fourth column values. The t x C x Q column (column 6) is obtained
from the product of the C x Q column with the t column (column 1), and by applying
all necessary conversions (e.g., hours vs. seconds).
5. Calculate Tracer Mass Recovery When the table of values is complete, Equa-
tion (11) can be solved by summing column 5 and multiplying by a time conversion to
get units of mass only. Hence, the solution to Equation (11) is acquired in a simplified
manner by
(69)
_
= Q(t)C(t)dt w Y^
i i=i
where tc is any necessary time conversion factor that allows for units of mass.
6. Calculate Mean Tracer Residence Time Mean tracer residence time t is found by
solving Equations (14) and (17). Equations (14) and (17) are solved by the same
method that Equation (11) is solved; by simplified summation of the data. Using
Table 4, summing column 6, and multiplying by the appropriate conversion factor to
get units of concentration-time. Divide the mass obtained in step 5 above into this
number to obtain units of time.
7. Calculate Mean Tracer Velocity Divide the distance traversed by the tracer cloud
by the mean tracer residence time to obtain mean tracer velocity.
8. Calculate Longitudinal Dispersion If the method of moments is used to solve for
longitudinal dispersion the basics of steps 3 and 4 above are repeated to create Table 5.
Columns 4 and 5 are again summed and the results converted to appropriate units.
Then Equations (29) and (30) are applied depending on the type of tracer release.
Alternatively, if the Chatwin method is used, Table 6 is set up using legitimate values
Table 5. Table representing tracer recovery data for processing.
Sample (t-t)2 Q C CxQ (t-t)2xCxQ
(T2) (I^T-1) (ML"3) (MT-1) (MT) .
49
-------
for time (0 < tK < xs/v], and solved parameters for 6; (Equation [40]) representing
the Chatwin designation. A straight line is then drawn through the legitimate values,
and longitudinal dispersion is solved using either Equation (41) or (42).
Table 6. Table representing Chatwin values.
Sample Time Chatwin Fit Residual
(h) (s1/2) (s1/2) (dimen.) .
9. Repeat for Subsequent Sampling Stations Repeat the above steps for all wells
and/or springs in which the tracer was recovered.
10. Calculate Total Tracer Mass Recovery If several wells and/or springs recovered
the tracer, then sum the individual masses obtained for each well and,each spring
together to obtain the total tracer mass recovered.
11. Calculate Percent Mass Recovered Calculate the percentage of mass recovered by
dividing the quantity of tracer mass recovered by the quantity of tracer mass injected
and multiplying the result by 100.
12. Calculate Additional Parameters Calculate the Peclet number, Reynolds number,
etc. as desired and appropriate, using the equations developed in Section 3. on page 26
4.1. SIMPLIFIED EXAMPLE CALCULATION
Four hundred and thirty-five kilograms of sodium chloride, NaCl (264 kg Cr) (RCA, 1992),
were injected into the north coast karst aquifer over a period of 24 minutes (0.4 hour) at the
RCA del Caribe (Barceloneta, Puerto Rico) Superfund site for a tracing study. Injection
occurred at a rate of 13.75 gpm (8.78 x 10~4 m3 s"1) at 940 feet (287 m) below land surface
(BLS), which is also below the confining layer for the bottom of the shallow aquifer.
The leakage rate from the deep aquifer up the annular space to the shallow aquifer was
450 gpm. The total height that the tracer-needed to rise to reach the shallow aquifer was
240 feet (73 m) or 700 feet (213 m), BLS. The time down the well (940 feet) was 11.18
minutes, and the rise up the annular space 240 feet was 1.08 minutes for a total reduction
50
-------
of the time of travel by 12.26 minutes (0.2 hour), and a consequent increase in the flow
velocity according to Equation (2).
Recovery was at an observation well 110 feet (34 meters) from the injection well that
was pumped at a constant rate of 6.0 gpm (3.79 x 10~4 m3 s"1). Figure 13 displays the
ETC for the RCA del Caribe Superfund site, and Table 7 (slightly modified from Table 4)
displays the tracer recovery data and estimation methods for the zeroth and first moments.
4.1.1. Mass Recovery Example
Tracer mass recovery is found by solving Equation (11) or, more simply, by Equation (69).
Equation (69) is solved for tracer mass recovery by multiplying the measured concentration
values by the measured discharge values after correcting for consistent units and then
summing the results. Column 6 of Table 7 lists the products of columns 4 and 5 and
is summed at the end.
The summed results of column 6 of Table 7 must be multiplied by 3,600 seconds because
time is recorded in hours, but the analyses used seconds.
(4.85 x 102 mg s-1) (3.60 x 103 s) = 1.75 x 106 mg
= 1.75 kg •
As shown, 1.75 kg of Cl~ were recovered. Because 264 kg of Cl~ was injected into the
aquifer, it is evident that only 0.66% of the original tracer mass was recovered. Clearly a
serious mass balance problem exists. It may be noted that Equation (69) is not as precise
as Equation (11). However, results obtained by Equation (69) will generally be found to be
more than adequate in most instances.
4.1.2. Mean Residence Time Example
Tracer residence time is found by solving Equation (14) or its equivalent discrete form. This
is accomplished by multiplying column 6 by column 3 in Table 7, and recording the results
in column 7. Summing column 7 of Table 7, and multiplying by 3,600 seconds will yield
results in units of mass-time .
(1.54 x 107 mg) (3.60 x 103 s) = 5.54 x 1010mg s
51
-------
RCA. DAT
400
10 15
Time from Injection (h)
20
25
Figure 13. Tracer-breakthrough curve for the RCA de Caribe Superfund site.
52
-------
Table 7. • Discharge values and tracer recovery values at specific times.
Sample
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
t
(h)
0
1
2
3
.00
.00
.00
.00
4.00
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
,00
Q
(m3 s-1)
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
3.79 x
io-4
ID"4
10~4
io-4
10~4
io-4
io-4
1Q-4
ID"4
ID"4
io-4
io-4
ID"4
io-4
10~4
10~4
io-4'
io-4
io-4
io-4
ID"4
ID"4
ID"4
ID"4
io-4
C
(mgm-3)
0.00
0.00
o.oo
0.00
0.00
5.00
2.50
3.80
2.00
1.25
7.50
5.50
4.00
2.50
2.00
1.50
1.40
1.30
1.20
1.10
1.00
9.00
8.00
7.00
6.00
I
x
x
X
X
X
X
x_
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
X
"\n
si=
10°
10°
10°
10°
10°
IO3
IO5
IO5
IO5
IO5
IO4
IO4
IO4
IO4
IO4
IO4
IO4
IO4
IO4
IO4
IO4
IO3
IO3
IO3
IO3
!
CxQ
(mg s-1)
0.00
0.00
0.00
0.00
0.00
1.89
9.46
1.44
7.57
4.73
2.84
2.08
1.51
9.46
7.57
5.68
5.30
4.92
4.54
4.16
3.79
3.41
3.03
2.65
2.27
4.85
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x IO1
xlO2
x IO1
x IO1
x IO1
x IO1
x IO1
x!0°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x 10°
x IO2
tx C x Q
(mg)
0.00
0.00
0.00
0.00
0.00
3.41
2.04
3.63
2.18
1.53
1.02
8,25
6.54
4.43
3.82
3.07
3.05
3.01
2.94
2.85
2.73
2.58
2.40
.2.19
1.96
1.54
x 10°
x!0°
x 10°
x 10°
xio°
x IO4
x IO6
x IO6
x IO6
x IO6
x IO6
x IO5
x IO5
x IO5
xlO5
x 10s
x IO5
x IO5
x IO5
x IO5
x IO5
x IO5
x IO5
x IO5
x IO5
xlO7
Note: "Sample" arbitrarily assumes that the first sample was collected at the
time of injection.
Time t is listed here in hours, but is converted to seconds before
multiplying with C and Q.
(source: RCA, 1992)
53
-------
Dividing by the mass recovered (1.75 kg) will yield the mean residence time of the tracer in
units of time.
5xl°'°mss
1.75 x 106 mg
- 3.17
= 8.79 x 10° h
This is necessarily corrected for time to reach the flow zone (tinf — 0.2 h)
8.79 x 10° h - 2.0 x 10"1 h = 8.59 x 10° h
Apparently, it took less than 9 hours for the GT tracer to reach the recovery well.
4.1.3. Mean Tracer Velocity Example
Mean tracer velocity is obtained from Equation (25) or, more simply, by dividing the distance
to the sampling station by the time of travel, minus one half the pulse-injection time, which
is a modification of Equation (2)
34n
- - Q4
(8.79 h - 0.2 h) - ^ h
= 4.05 x 10° m
- 1.13 x 10~3 m s
~l
This may then be used to estimate the velocity of a nonreactive pollutant, assuming that
this value is representative of the prevailing ground-water flow velocity. If the tracer used
is of known reactivity with the aquifer, then it may be related to a pollutant of similar
reactivity to estimate retardation.
The difference between the perceived velocity and the actual velocity may then be
obtained from Equation (3)
34m (0.2 h) 2 ' ! ;
(8.79 h - 0.2 h) 8.79 h ~ 9^ x 1U m n
which suggests a relatively insignificant difference of 0.1 m h"1 for this example.
4.1.4. Longitudinal Dispersion Example
Longitudinal dispersion is most accurately estimated by the Chatwin method (Equa-
tion [31]), which can be tedious. Using just the first valid time value, Equation (40) appears
as
bl . Asp x Wi^°5^ _ 284.57 s'/'
x
x
54
-------
Table 8. Chatwin parameter values for the RCA data set.
Sample
6
7
8
9
10
11
12
13
14
25
Time
(t)
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
24.0
Chatwin
(s1/2)
284.57
103.48
0.00
-128.70
-178.75
-228.03
-259.98
-292.60
-335.96
-552.44
Fit
(s1/2)
266.33
132.01
-2.32
-136.65
-270.98
-405.31
-539.64
-673.97
-808.30
-2285.91
Residual
(dimen.)
18.24
-28.52_
2.32
•7.96
92.23
177.28 •
279.66
381.37
472.33
1733.47
after converting the time and concentration values to consistent values (seconds and nig m~3
[/j, Lr1], respectively for this example). Partial results for the RCA example data set are
shown in Table 8. Samples collected prior to t — 5.0 hours were devoid of tracer (C = 0.0
mg Lr1), so the first legitimate sample for consideration for the Chatwin analysis occurs at
5.0 hours. According to the limit tK < 8.40 h (see Section 3.3.2. on page 34), only samples
6-9 listed in Table 8 are considered valid for the Chatwin analysis (assuming that sample
1 [Table 4] represents time zero). A casual inspection of Table 8 will indicate that residual
errors (Chatwin value minus the Fit value) after sample 9 become increasingly large further
indicating the inappropriateness of samples 10-25.
Also, it should be noted that while time values listed in Table 8 are in hours, the Chatwin
and Fit values are listed in seconds to the one-half power. The Fit values are obtained by
fitting a straight line through the Chatwin values plotted against time. The choice of units
does not matter provided, appropriate corrections are made to the final dispersion estimates.
Using samples 6-9, longitudinal dispersion by the Chatwin method is DL =1.15 m2 h""1
and a corresponding Peclet number is obtained, from Equation (56)
If the method of moments are used to solve for longitudinal dispersion (Equation [30]), then
55
-------
where of = 12.75 hours was obtained from Equation (17) in summation form (Table 9)
similar to the method used to obtain the mean resident time (Table 7).
As with Table 7, column 5 in Table 9 is multiplied by column 2 in Table 9 and the results
recorded in column 6. Summing column 6 of Table 9 and multiplying by 3,600 seconds will
yield results in units of mass-time
(2.23 x 107 mgs) (3.60 x 103 s) = 8.03 x 1010mg s2
Dividing by the mass recovered (1.75 kg) will yield the time of travel variance of the tracer
in units of time.
2
8.03 x
mg s
1.75 x 106 mg
= 12.75 x 10° h2
The Peclet number is now obtained as Pe = 11.09.
4.1.5. System Volume
The flow system volume may be estimated using Equation (47). The average discharge for
the RCA del Caribe site, 3.79 x 10~4 m3 s"1 (6 gpm), is multiplied by the mean residence
time, 3.09 x 104 s, to obtain the system volume.
(3.79 x 10-4 m s-1) (3.09 x 104 s) - 1.17 x 101 m3 :
Apparently, only a small volume of the aquifer was utilized by the tracer to arrive at the
recovery well, which was expected, given the poor mass recovery.
56
-------
Table 9. Table of values used to determine the time of travel variance.
Sample
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
(t-f)2
(h2)
7.40 x 101
5.78 x 101
4.36 x.101
3.14 x 101
2.12 x 101
1.30 x 101
6.79x10°
2.58 x 10°
3.66 x ID"1
1.56 x 10"1
1.95 x 10°
5.74 x 10°
1.15 x 101
1.93 x 101
2.91 x 101
4.09 x 101
5.47 x 101
7.05 x 101
8.83 x 101
1.08 x 102
1.30 x 102
1.54 x 102
1.79 x 102
2.07 x 102
2.37 x 102
Q
(m3 s-1)
3.79 x 10~4
3.79 x ID"4
3.79 x 10-4
3.79 x 10~4
3.79 x 10-4
3.79 x ID"4
3.79 x 10~4
3.79 x 10~4
3.79 x 1Q-4
3.79 x 10~4
3.79 x 10-4
3.79 x ID"4
3:79 x 10~4
3.79 x ID"4
3.79 x 10~4
3.79 x 10~4
3.79 x 10~4
3.79 x 10~4
3.79 x 10~4
3.79 x 10~4
3.79 x ID"4
3.79 x 10-4
3.79 x ID"4
3.79 x ID"4
3.79 x ID"4
C
(mg m~3)
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
5.00 x 103
2.50 x 105
3.80 x 105
2.00 x 105
1.25 x 105
7.50 x 104
5.50 x 104
4.00' x 104
2.50 x 104
2.00 x 104
1.50 x 104
1.40 x IP4
1.30 x 104
1.20 x 104
1.10 x 104
1.00 x 104
9.00 x 103
8.00 x 103
7.00 x 103
6.00 x 103
5D?=i -
CxQ
(mg s-1)
0.00 x 10°
0.00 x 10°
0,00 x 10°
0.00 x 10°
0.00 x 10°
1.89 x 10°
9.46 x 101
1.44 x 102
7.57 x 101
4.73 x 101
2.84 x 101
2.08 x 101
1.51 x 101
9.46 x 10°
7.57 x 10°
5.68 x 10°
5.30 x 10°
4.92 x 10°
4.54 x 10°
4.16 x 10°
3.79 x 10°
3.41 x 10°
3.03 x 10°
2.65 x 10°
2.27 x 10°
4.85 x 102
(t-t)2xCxQ
(nigs)
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
8.85 x 104
2.31 x 106
1.33 x 106
9.97 x 104
2.66 x 104
1.99 x 105
4.30 x 105
6.28 x 105
6.58 x 10s
7.93 x 105
8.36 x 105
1.04 x 106
1.25 x 106
1.44 x 106
1.62 x 106
1,77 x 106
1.88 x 106
1.96 x 106
1.98xl06
1.94 x 106
2.23 x 107
Note: "Sample" arbitrarily assumes that the first sample was collected at the
time of injection. . - •
Time (t — i)2 is listed here in hours2, but is converted to seconds2 before
multiplying with C and Q.
57
-------
5. QTRACER2 COMPUTER PROGRAM DESCRIPTION
To facilitate calculation of total tracer recovery and related information, a FORTRAN
computer program has been developed (Field and Nash, 1997). A CD containing the
executable file and data files is contained at the end of this document. The program uses a
reliable and efficient integration algorithm that takes advantage of an efficient interpolation
algorithm (Kahaner et al, 1989, pp. 81-137) and/or extrapolation routines if desired.
5.1. DATA INTERPOLATION
The interpolation algorithm used in the FORTRAN program develops a "piecewise cubic
Hermite" function. The interpolant is defined in terms of a set of cubic polynomials, each
of which is defined between pairs of consecutive data points. The coefficients of these cubic
polynomials are chosen so that the interpolant has continuous first derivatives, which makes
it a "Hermite" interpolant. This is not enough to uniquely determine the interpolant, and
the remaining freedom of choice is used to ensure that the interpolant is "visually pleasing,"
meaning that monotonicity in the data results in monotonicity in the interpolant (i.e., the
interpolant does not have extraneous "wiggles"). A piecewise cubic Hermite function, in
effect, produces the most reasonable interpolation of the data possible.
5.2. DATA EXTRAPOLATION
Data extrapolation may be used if tracer sampling has ceased prior to complete tracer
recovery. Extrapolation may be used to predict the time at which zero (or near zero) tracer
concentration would have occurred had tracer sampling been continued until complete tracer
recovery was accomplished. The program extrapolates the data by three separate methods.
5.2.1. Exponential Decay
The first and most hydrologically based method uses an exponential decay function in which
five additional points are created to produce a reasonably smooth decay curve. This method
is based on the concept that most BTCs, in which complete recovery was obtained, exhibit
exponential decay. Using this method prevents the newly extrapolated data from ever
reaching zero (or background) concentration. In reality, it would go to infinity if allowed.
To overcome this problem, the program approximates the best stopping location.
58
-------
5.2.2. Piecewise Cubic Hermite
The second method relies on the cubic Hermite function to find the single most reasonable
stopping data point for extrapolation. This is achieved by using the entire ETC to
develop a smooth function, based on the shape of the overall curve, and then producing
an appropriately chosen extrapolation point. Unfortunately, because the curve has rising
and descending limbs and at least one peak (multiple peaks are not uncommon), excessive
extrapolation will cause extrapolation to rise incorrectly. A stopping criteria is used to
prevent extrapolation from proceeding in a rising fashion. The net effect is to cause
extrapolation to cease prior to zero concentration being reached in most instances. In
some instances, even an acceptable decrease may not be achieved.
5.2.3. Straight-Line Projection
The third method for data extrapolation is achieved by projecting data for the decreasing
limb of the ETC beyond the last measured time-concentration data point, such that zero
tracer concentration is achieved. This is accomplished by projecting a line from the last
peak value through each of the measured (or interpolated) data points on the decreasing
limb to the x axis and storing the new data point in an array. The greatest cluster of the
new data array is then used to estimate a final time value for zero tracer concentration.
5.2.4. Extrapolating Discharge
Extrapolation of discharge data is a virtual unknown. It is determined here by taking the
midpoint of the measured late-time discharge data limb as the endpoint and extending the
discharge curve to equal the extrapolated late-time data. If the measured discharge data
are decreasing, then the extrapolated discharge data will increase to one-half the original
decreasing value. If the measured discharge data are increasing, then the extrapolated
discharge data will decrease to one-half the original increasing value.
Extrapolating the data beyond measured values is very risky and may lead to serious
errors in the analyses. However, used cautiously, extrapolation of the data may lead to
additional insights into aquifer hydraulics.
5.3. CHATWIN'S ESTIMATION OF LONGITUDINAL DISPERSION
Calculation of longitudinal dispersion is accomplished by fitting a straight line through a
plot of the Chatwin Parameter versus statistically determined early-time data using an
59
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efficient singular value decomposition routine (Kahaner et al., 1989, pp. 218-223), a routine
chosen because degenerate data may prevent a straight-line calculation by either a, least-
squares method or by the normal equations. Singular value decomposition always produces
a straight-line fit to the data (Vetterling et al, 1992, p. 197). Evaluation of the fit is provided
by statistical calculation of the coefficient of determination (/?2), the correlation coefficient
(r), the probability of the fit, and Fisher's z statistic. R"2 should approach a value of 1 for
a good fit, r should approach a value of -1 for a good fit (for the Chatwin Parameter), the
probability of the fit should be a very small value, and Fisher's z statistic may be used in
additional statistical tests if desired (Press et al., 1992, pp. 632-633).
Because of memory limitations typical of PCs, there can be instances in which large data
files exceed the ability of the data arrays to provide sufficient storage for Chatwin's method
of analysis. When this occurs, the method of moments is automatically applied according
to Equations (29) and (30). Using Equations (29) or (30) will almost always result in-an
overestimation of dispersion, which should be realized.
5.4. DATA NORMALIZATION
Individual tracer tests conducted at the same injection/recovery stations under differing
hydrologic conditions should be compared to obtain information regarding aquifer behavior
under varying conditions. Normalized tracer concentration files, normalized tracer load
files, and standardized tracer concentration files can be calculated by QTRACER2 and may
be analyzed according to the method described by Mull et al. (1988). The discussion by
Mull et al. is very comprehensive and, therefore, is not repeated here. Another reaison for
not repeating the Mull et al. discussion here, is because of the probability that in most
instances, the tracing site (1) may have multiple discharge locations, many of which may
not be continuously monitored for tracer; and (2) may require more quantitative tracing
experiments than can be reasonably undertaken. ,
5.5. RANGE OF POSSIBILITIES OF QTRACER2
QTRACER2 can be used on almost any type of tracer test in any kind of geological
environment (e.g., surface water, porous media, fractured-rock aquifer, or karst aquifer).
This may sound strange,'but the statement is true because the basic equations for mass
balance are not dependent on geological conditions.
QTRACER2 was initially designed to be used in karst systems primarily, but it will
handle any other typical hydrological system (e.g., fractured-rock systems) reasonably
60
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well when told to do so in the sampling station data file. It may be used to evaluate
BTCs from tracer tests conducted in surface water and porous media by entering the
relevant information in the sampling station data file(s) and dummy information where
the information is irrelevant. The user will then need to note when the output data make
sense. By exercising some basic judgment, QTRACER2 can be effectively used in a variety
of environments.
5.6. COMPUTER GRAPHICS
A high-quality color graphics algorithm, PGPLOT1 (Pearson, 1997), that allows cascading
of graphics screens, direct printing, creation of screen files, etc., using pull-down menus
in the Windows environment has been included in QTRACER2. (The original interactive
capabilities developed by Kahaner and Anderson (1990), and utilized in QTRACER are
no longer available.) The graphics routine used here also provides for visual examination
of the data files and other relevant information (e.g., statistics when appropriate). 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.
5.6.1. Features of the Interactive Graphics Loop
Running QTRACER2 starts a conventional Windows screen with a series of pull-down
menus (Table 10). Each underlined character in Table 10 indicates that the Alt key plus
the underlined character implements the respective menu item. For example, Alt+F initiates
the pull-down menu items underneath the File heading. Of course, the mouse pointer 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
often. Most of the more useful graphics functions have been built directly into QTRACER2
to alleviate excess work by the user. However, in some instances, the user may find the
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 stack, slightly offset to the lower right.
•"•PGPLOT may be obtained from http://www.astro.caltech.edu/~tjp/pgplot/
61
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62
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File Items listed under this heading 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.
Edit ^ Items listed under this heading 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.
Copy Ctrl-j-Ins Copy selected items to the clipboard.
Paste Paste selected items to the screen.
View Items listed under this heading 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).
State Items listed under this heading are described as follows.
Pause Ctrl+S Pause the graphic display.
Resume Ctrl+Q Resume graphic display.
The two items Pause and Resume appear only as alternates of each other so that only the
one that is not currently functioning is accessible. The item that is currently in operation
is not displayed in the pull-down menu.
63
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Window Items listed under this heading 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 QTRACER2.
Input Automatically displays the input screen (Graphic 1) for data input.
Clear Paste Clears an item pasted onto the screen.
Status 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. ,
2 PGPlot Graphics, # 1 Identifying name/number of all subsequently opened graphics screens
(active when "check marked").
Help Items listed under this heading are described as follows.
Contents Listing of available help contents.
Using Help Describes the use of the Help function.
About Identifies the current version o/QTRACER (Version 2.0).
5.7. QTRACER2 SOURCE
The FORTRAN source for QTRACER2 is included on the CD. It is a very large program
that had to be split into pieces to allow its use on a PC. It is not recommended that users
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. This program is not allowed for use for commercial products.
64
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6. USING QTRACER2
The QTRACER2 program for ETC analysis is an easy-to-use computer package that
requires little more from the user than pressing when requested or manipulating
pull-down menus with a mouse. However, QTRACER2 does require creating data-input
files first for processing. Using data-input files rather than requiring interactive responses
to questions posed by the program facilitates more rapid data processing while minimizing
the opportunities for incorrect data entry.
6.1. QTRACER2 PROGRAM AND EXAMPLE DATA FILES
Before running the program, the user should copy all QTRACER2 files to the hard drive
and put the supplied CD-ROM disk in a safe place. Although the CD-ROM has plenty
of storage space for the creation of data-output files and graphics files, the possibility of
damage to the QTRACER2 program file from excess use cannot be ignored.
6.1.1. Loading QTRACER2 and Example Data Files
1. After "booting" up the computer, place the CD-ROM into the CD-ROM drive.
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 press the
letter "E" on the keyboard.
4. Place the mouse pointer on the CD-ROM 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 press 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 then Left Click on "C_ppy" or just press "C" on the keyboard.
7. Left Click on the preferred hard drive (e.g., C:). .
65
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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 then Left Click on "£aste" or just press "P" on the key board.
A Folder named Qtracer2 will be created on the chosen hard drive and all the appropriate
files copied accordingly to the appropriate file folders2.
6.2. QTRACER2 EXECUTION
QTRACER2 is very easy to use. Once the appropriate data files are created (which are
nearly self-explanatory) QTRACER2, for the most part, requires nothing more than pressing
the () key as requested or manipulation of the mouse and clicking with
the left-mouse button.
1. In Windows Explorer, Left Double-Click the QTRACER2 folder and then Left Double-
Click the QTR.EXE file which will initiate program operation.3
2. The program prompts the user to enter the file to be evaluated (unless a file was
specified when starting the program using a DOS prompt). Press XENTER> to
automatically run the default file, QTRACER. D, which calls QTRACER. DAT (these two files
correspond with ATKIN.D and ATKIN.DAT from the original QTRACER Version 1.0,
respectively). However, if the data files are in different locations from QTRACER2,
the user must provide the correct path to the *.D and *.DAT files. One advantage
of creating a subdirectory on the hard disk is that the program will find all files
automatically because they are all at the same location as the executable file.
2The first version of Qtracer was designed for MSDOS®use and required that the files be moved according
to the following instructions which may still be used:
• At the C: \> prompt, type "MKDIR QTRACER2" (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 Qtr.dos on the CD to your hard disk. For
example, you might type (if C is your disk drive): "COPY D: \*. * C: \QTRACER2\*. *."
• Repeat the above commands for the other files on the CD.
• Put your CD in a safe location.
3If a command prompt is preferred then at the C: \> prompt, type "CD\QTRACER2" without the quotes.
The user will then see a new prompt; C:\QTRACER2>. Assuming the user also copied the necessary data
files or created your own, the user may now type "QTR" to run the program by responding to the requested
information. The user may want to type "QTR /Rename" such as "QTR QTRACER. D", which will automatically
load and run the Atkinson data set described in the journal article (Field and Nash, 1997).. The user may
do the same with the Mull et al. (1988) data by typing "QTRACER2 MULL.D" to load the appropriate data
files and begin processing.
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Additional information regarding QTRACER2 execution is presented in Section 7. on
page 901 However, the really important information (files creation) is listed in this section.
6.3. QTRACER2 FUNCTIONING
QTRACER2 runs by processing two types of files at once. The first file processed is a
header file, which identifies the amount of tracer injected into the hydrologic system and
ALL appropriate subfiles. Subfiles are data files, each of which represents a sampling
station where tracer was recovered for the particular study. The subfiles must include all
necessary information for the program to run. They also allow the user to run the program
without interaction with the user (batch mode), pause processing to allow the user to observe
numerical output, and display high-quality graphics. What follows are seven sets of data
files that may be used to test the QTRACER2 program. The data files may also be reviewed
directly, as they are simple ASCII files.
Run QTRACER2 on each of the supplied files and compare the results with the
results provided in the publication "Risk Assessment Methodology for Karst Aquifers:
, (1) Estimating Karst Conduit-Flow Parameters" (Field and Nash, 1997) [qTRACER.D and
MULL.D only]. Preferably, you will be able to test the program on your own data sets, where
you may already know the results.
6.4. SAMPLE FILES ON DISK
The following nine "header" data files (*.D) and their respective sample station data files
(*.DAT) are included on the disk (Table 11). Each header file must reference at least one
corresponding sample station data file. However, the number of sample station data files
that correspond to a header file is limited only by your computer's capabilities.
Note: There is no specific requirement that the data files end with the extensions "D"
or "DAT" (e.g., QTRACER.D; QTRACER.DAT). The "D" and "DAT" extensions are simply
conventions used in this manual and in the example data file.
Descriptions of data files listed in Table 11 follow.
1. QTRACER.D and QTRACER.DAT are hypothetical data sets provided by Dr. Timothy
Atkinson (Atkinson, 1987) for educating students (of which this author was one) on
the proper methodology for analyzing and Interpreting BTCs. Analysis of these data
sets using QTRACER2 is presented in considerable detail in Field and Nash (1997).
67
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Table 11. Example data files on disk.
Header Data Sample Station
File Data File
QTRACER.D
MULL.D
LOST.D
RCA.D
TOPLITA.D
GAR2.D
MUUL.D
UVAS281.D
MOBILE.D
QTRACER.DAT
MULL.DAT
LOST.DAT
RCA.DAT
TOPLITA.DAT
GAR2.DAT
MUUL.DAT
UVAS281.DAT
MOBILE.DAT
2. MULL.D and MULL.DAT are data sets taken from a U.S. EPA Region IV report (Mull
et al, 1988) in which very comprehensive ETC analysis is described. ;The MULL.D
and MULL.DAT data sets appear slightly modified from the original in that data has
been recorded in SI units on the disks. The original Mull et al. data set mixed SI and
English units that QTRACER2 allows for and corrects. Analysis of these da,ta sets
• using QTRACER2 is presented in considerable detail in Field-and Nash (1997).
3. LOST.D and LOST.DAT are data sets listing the results of a ETC. They were generated
by the senior author (and other students) when Dr. Atkinson was instructing proper
methodology for conducting tracer tests and analyzing and interpreting the results.
It was obtained for the Lost River Cave System in Kentucky.
4. RCA.D and RCA.DAT are the data sets that originally inspired the effort to de-
velop QTRACER2. A tracer test conducted at an RCA del Caribe Superfund site
(Barceloneta, P.R.) supposedly provided substantial information on the functioning
of the karst aquifer and on some solute-transport processes in the aquifer. However,
only about 0.7% of the Cl~ tracer (injected as NaCl) was recovered. Questions re-
garding the simple calculations and other factors illustrated in Section 4.1. on page 50
of this report warranted a more refined approach. This computer program estimates
recovery at 0.7%, indicating an extremely poor recovery effort at the site.
5. TOPLITA.D and TOPLITA.DAT are modified data sets.(Caspar, 1987a, p. 58) that serve
to demonstrate that an "ideal" ETC is not necessary for QTRACER2 to function
68
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properly. The Toplita data sets are also excellent for demonstrating QTRACER2's
data extrapolation capabilities because of the shape of the curve and the position of
the last measured data point.
6. GAR2. D and GAR2. DAT are modified data sets from a Superfund site in Tennessee.
The original data sets were subjected to extensive data interpolation by the computer
program NDATA (see Section 10.1. on page 154 for a description of NDATA). A
deliberately "huge" data set was constructed to demonstrate QTRACER2's capability
of handling data sets that are too large for most PCs. The data set also intended to
test the reliability of NDATA's interpolation capability.
7. MUUL. D and MUUL. DAT are modified data sets of MULL. D and MULL. DAT, respectively.
They were created using NDATA to again assess QTRACER2's capabilities of handling
"huge" data sets, but with a "variable" discharge (GAR2 .DAT has a constant discharge).
8. UVAS281 .D and UVAS281 .DAT consists of original surface-water tracing data published
by Zand et al. (1976) and republished in Bencala and Walters (1983). It is available
from the U.S. Geological Survey and is provided here to illustrate QTRACER2's ability
to evaluate surface-water tracing data (see Section 8. on page 115).
9. MOBILE. D and MOBILE. DAT consists of slightly modified data from Molz et al. (1986a,b).
It is reprinted here to illustrate QTRACER2's ability to evaluate tracer tests con-
ducted in porous media (see Section 8. on page 115).
NOTE: EDIT ONE OF THE *.D FILES AND SAVE AS A NEW FILE WITH A NEW
FILE NAME. THEN EDIT ONE OF THE *.DAT FILES AS OFTEN AS NECESSARY
FOR EACH SAMPLING STATION TO BE ANALYZED. SAVE EACH *.DAT FILE AS
A NEW FILE WITH A NEW FILE NAME.
6.5. DESCRIPTION OF *.D FILES
All descriptions in this section use QTRACER.D as sample input. An example header file,
QTRACER.D, appears in Figure 14.
A *.D file (e.g., QTRACER.D) is very small. A typical *.D file begins with a requestor
for the mass of tracer injected, which should be followed by a value input by the user.
69
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QUANTITY OF TRACER INJECTED
450
UNITS OF MEASURE (1-lbs, 2-kg, 3-g, 4-mg)
3
TYPE OF RELEASE AND TIME FOR RELEASE (1-impulse, 2-pulse, 3-step) [HOURS]
1 0.0
TIME FOR TRACER TO REACH FLOW ZONE [HOURS]
0.0
SAMPLING DATA FILES LIST
QTRACER.DAT
Figure 14. QTRACER.D header file for QTRACER2 processing.
Subsequent requestors appear in the same manner as can be seen in Figure 14. That is,
a requestor appears, usually with some options that are allowed, so the user will know
what can be entered, and on the next line the user enters the appropriate response that
QTRACER2 will read. So the first requestor in Figure 14 appears as
QUANTITY OF TRACER INJECTED
450
which is simply asking for the quantity of tracer material injected into the system. For
the QTRACER.D example 450 is listed by the user because this was the hypothetical tracer
quantity injected into the system.
The file next requests information on the unit of measure for the tracer mass injected,
because obviously the number 450 has no meaning without any units.
UNITS OF MEASURE (1-lbs, 2-kg, 3-g, 4-mg)
3
The numbers enclosed in parentheses represent the valid units allowed by QTRACER2.
The user responds with the appropriate units. For the QTRACER.D example the number 3 is
listed to indicate grams (g) as the unit of measure.
Next is a request for a brief description of the type and time required for tracer injection.
TYPE OF RELEASE AND TIME FOR RELEASE (1-impulse, 2-pulse, 3-step) [HOURS]
1 0.0
The numbers enclosed in parentheses represent valid choices for the type of injection used
70
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for the tracer test where impulse represents an instantaneous injection, pulse represents
an injection that occurred over some period of measurable time, and step represents a
continuous injection for the length of the tracer test period. The listed units [HOURS]
is a required entry only for a pulse and step (continuous) releases. An impulse release
demands that the time for release be left blank or set to zero; anything greater than zero
will precipitate QTRACER2 resetting the release time to zero.
The file now requires some entry for the time taken to reach the flow zone. TIME FOR
TRACER TO REACH FLOW ZONE [HOURS]
0.0
Typically this value will be zero, which must be entered (not left blank) for QTRACER2 to
properly function. The importance of this value is described by Equations (2) and (3) and
is used to properly determine t, upsilon, and DXa.
Lastly, the program asks for the name of all subfiles to be called by QTRACER2 for
processing as part of the *.D file. As previously explained, each header file describing the
initial tracer injection conditions must reference at least one sampling station data file,
which will be listed here as *.DAT files (e.g., QTRACER.DAT). The subfiles correspond to
each sampling station at which tracer was recovered.
SAMPLING DATA FILES LIST
QTRACER.DAT
For the QTRACER. D example, only one station is listed as having recovered tracer, QTRACER. DAT,
because that is the only station at which this hypothetical trace recovered the tracer.
However; if 23 sampling stations had recovered tracer, then all 23 sample files would
be recorded here — one above the other, but in no particular order. For example, tracer
recovery at 23 sampling stations for the QTRACER. D tracer test might be listed as:
QTRACER.l '
QTRACER.2
QTRACER.3
QTRACER.23
Any other appropriate names such as the names of various monitoring wells or monitored
springs are acceptable. The only requirement is that the user be able to recognize the names
after QTRACER2 has been run, as it is most advantageous to run QTRACER2 in batch
mode for large data sets.
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6.6. DESCRIPTION OF *.DAT FILES
All descriptions in this section use QTRACER.DAT as sample input except as otherwise listed.
An example sampling station data file, QTRACER.DAT, appears in Figure 15.
The *.DAT files (e.g., QTRACER.DAT) are fairly long and detailed. They must be detailed
so that the program can properly process all the necessary site information.
6.6.1. Sampling Frequency
A *.DAT file begins by requesting the units used for listing the time data, which must
be consistent. The actual time data are listed at the very end of this file along with the
concentration data and discharge data when appropriate. The first item for a *.DAT file is
SAMPLING FREQUENCY: UNITS (l=days, 2=hrs, 3=min3 4=sec) ;
2
in which a value of 2 is listed because time was recorded in hours.
NOTE: SAMPLING FREQUENCY does NOT mean that there must be an even time span
between sampling events, only consistent units.
6.6.2. Tracer Mass Recovery
The tracer recovery data must also have consistent units, which follows the same convention
as sampling frequency.
TRACER RECOVERY CONCENTRATION: UNITS (l=g/L, 2=mg/L, 3=ug/L, 4=ng/L)
3
So for the QTRACER.DAT example, 3 was recorded because tracer concentration is recorded
at the end of this file (corresponding to time data) in units of /ig L"1. :
6.6.3. Flag for Background
Quite commonly, a background concentration value is measured prior to initiating a tracer
test. This value must be subtracted from the measured concentration values tp allow for a
more accurate mass balance estimation.
FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) [VALUE]
0 ' ' '
The word "FLAG" is a marker that acts like an on/off switch. It informs QTRACER2 how
to respond. The number 0 for the QTRACER.DAT data set tells QTRACER2 that no value
for background is available — no "value" is required. The number 1 tells QTRACER2 that
a background value is available for subtracting from the data set,— a number; 1 MUST be
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SAMPLING FREQUENCY: UNITS (l=days, 2=hrs, 3=min, 4=sec)
2
TRACER RECOVERY CONCENTRATION: UNITS (l=g/L, 2=mg/L, 3=ug/L, 4=ng/L)
3
FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) AND [VALUE]
00
DISCHARGE IN DATA FILE OR CONSTANT: (1-data file, 2=constant)
1
DISCHARGE: UNITS (l=nT3/d, 2=m~3/hr, 3=nT3/min, 4=m"3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ft~3/hr, 9=ft~3/min, 10=ft'N3/sec) [VALUE]
40 . .
ESTIMATE SYSTEM VOLUME (l=yes, 0=no)
1
RADIAL DISTANCE TO SAMPLING STATION: UNITS (l=m, 2=ft, 3=km, 4=miles) [VALUE]
3 1.8
CORRECTION FOR SINUOSITY (l=yes, 0=no) [VALUE, def=1.0]
1 1.5
FLOW ME1DIUM: POROSITY (l=subsurface channel, 2=surface channel,
3=porous medium, 4=fractured medium) [VALUE, def=1.0]
1 1.0
IF POROUS FLOW: UNITS, HYDR. COND. (l=m/s, 2=m/hr, 3=ft/s, 4=m/hr, 0=null)
IF FRACTURE(S) FLOW: UNITS, HEIGHT (l=m, 2=ft, 0=null) [VALUE]
0 0.0
NAME OF THE FILE OF INPUT/OUTPUT VALUES
Ql.OUT .
INTERPOLATE DATA (l=yes, 0=no) [NUMBER OF KNOTS]
0 1000 .
NAME OF THE INTERPOLATED OUTPUT VALUES FILE
qi.INT
Figure 15. QTRACER.DAT sampling station data file for QTRACER2 processing.
73
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EXTRAPOLATE DATA (l=yeSj 0=no) [1=EXP. DECAY, 2=CUBIC HERMITE, 3=STAT. METH.]
01
VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)
0110
VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT)
0110 ;
VISUALIZATION: CHATWIN PARAMETERS (CHECK PRINT PLOT QPLOT)
0010
FLAG FOR FILE OF DATA FOR CXTFIT MODELING (CXTFIT Min Mont)
000
NAME OF FILE FOR SOLUTE-TRANSPORT MODELING (VALID IF FLAG=1)
C:\VANGENU\CXT\Q1.ADV
FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0)
1 '[
NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1)
Ql.NRM
VISUALIZATION: NORMALIZED CONCENTRATION (CHECK PLOT JOIN OPLOT)
0010
FLAG FOR NORMALIZED TRACER LOAD FILE (1/0)
1
NAME OF FILE FOR NORMALIZED TRACER LOAD VALUES (VALID IF FLAG=1)
Ql.LOD
VISUALIZATION: NORMALIZED TRACER LOAD (CHECK PLOT JOIN OPLOT) ;
0010
FLAG FOR STANDARDIZED TIME AND CONCENTRATION VALUES FILE (1/0)
1
NAME OF FILE FOR STANDARDIZED TIME AND CONCENTRATION' (VALID IF FLAG=1)
Ql.STN
VISUALIZATION: STANDARDIZED TIME AND CONCENTRATION (CHECK PLOT JOIN OPLOT)
0010
Figure 15. QTRACER.DAT sampling station data file for QTRACER2 processing (con-
tinued).
74
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FLAG
1
FLAG
3
TIME
0.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10
11
12
13
14
15
16
17
18
19
20
0
0
0
0
0
0
0
0
0
0
.
.
.
.
.
.
.
.
.
.
0
0
0
0
0
0
0
0
0
0
0
FOR OUTPUT TO SCREEN AND PAUSE AS NECESSARY (1/0)
FOR DATA ANALYSIS METHOD (1,ALL DATA; 2 .BLOCK AVE; 3,BLOCK SKIP)
CONCENTRATION DISCHARGE (CONDITIONAL)
0
0
0
0
0
0
0
6
7
4
2
1
0
0
0
0
0
p
0
0
0
.00
.00
.00
.00
.00
.00
.00
.50
.50
.60
.10
.10
.93
.88
.83
.75
.63
.40
.18
.08
.03
4
4
4
4
4
4
4
4
4
4
4
'4
4
4
4
4
4
4
4
3
3
.10
.20
.27
.35
.42
.50
.57
.67
.75
.82
.90
.80
.68
.56
.46
.33
.22
.12
.00
.90
.80
Figure 15.
tinued).
QTRACER.DAT sampling station data file for QTRACER2 processing (con-
75
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followed by a number [VALUE] (i.e., concentration) in the SAME units as those in which
the concentration data set is recorded.
The [VALUE] is a requestor that applies only when the FLAG is set to ;1, in which
case the user MUST supply a background concentration for subtraction from the measured
concentration values. The user is asked to supply a number only if appropriate. However,
this number may be zero.
For example, in the MULL.DAT example, the flag for background appears as
FLAG FOR BACKGROUND TRACER CONCENTRATION (1/0) [VALUE]
1 0.01
because a background tracer concentration of 0.01 yug Lr1 is available. This value will
automatically be subtracted from all concentration values in the time-concentration data
file prior to processing (but after data interpolation and/or extrapolation). Note that the
MULL. DAT data set has already been identified as having tracer recovery concentration values
recorded in units equal to fj,g Lr1.
6.6.4. Measured Discharge
Discharge is typically measured as a single occurrence during a tracer test and taken as a
constant value, or measured periodically throughout the tracing experiment. QTRACER2
needs to know which way discharge was measured for proper processing.
DISCHARGE IN DATA FILE OR CONSTANT: (l=data file, 2=constant)
1
means that for l=data file, the time-concentration listing at the end of the *.DAT file must
also contain a third column of discharge values. The 2=constant means that discharge is a
constant, the value for which must be included in the next section with the discharge units
of measure. So for the QTRACER. DAT file, a variable discharge 1 is listed, which means that
there MUST be a third column of data at the end of the QTRACER. DAT data file, (Figure 15).
If a single (e.g., constant) discharge was recorded, then the user would enter 2 on the
appropriate line.
6.6.5. Discharge Units
As with all the other data listed, QTRACER2 needs to know in which units discharge was
measured so that an appropriate correction to allow for consistent units can be made. A
considerable range of discharge unit measures is allowed by QTRACER2, so the requestor
actually takes up two lines in the data file. ;
76
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DISCHARGE: UNITS (I=ur3/d, 2=nT3/hr, 3=m~3/min, 4=m~3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ff3/hrJ 9=ft~3/min, 10=ft~3/sec) [VALUE]
4
A number 4 by itself indicates that a variable discharge is recorded in nTS/sec (m3 s"1), the
values for which are listed at the end of the data file (QTRACER.DAT). (QTRACER2 converts
all other discharge choices to m3 s~l prior to processing the file.)
If a constant discharge is to be used (e.g., LOST.DAT) then the user would record
DISCHARGE: UNITS (l=nT3/d, 2=nT3/lir3 3=nT3/min, 4=nT3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ff3/hr5 9=ft~3/min, 10=ft~3/sec) [VALUE]
4 1.78
to indicate that a constant discharge in nTS/sec (m3 s"1) with a value of 1.78 is to be used
in the analysis.
If sampling was performed at a nonpumping well by withdrawing an aliquot of water
from the well by use of a bailer, "then discharge is unknown (although there is clearly some
flux of water flowing past the well). The user should enter a very small flux value unless
the flux: can be guessed. For example, the user might enter:
DISCHARGE: UNITS (l=nT3/d, 2=m~3/hr, 3=m~3/min, 4=nT3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ft~3/hr, 9=ft"3/miii, 10=ft~3/sec) [VALUE]
4 l.OE-10
By entering "4 l.OE-10" (entering the value 4, a blank space, and then l.OE-10) into the
program, the user is multiplying the tracer concentration data file by a very small value
so a minimal effect might be applied assuming very, little flux past the well (e.g., for tight
fissures). Mathematically this works; physically, this suggests that discharge is known and
is negligible, which may not be correct and may create a fairly substantial error in data
analysis.
6.6.6. System Volume
The system volume can be estimated by QTRACER2 provided the time-concentration data
file begins at zero time. (QTRAGER2 now automatically adds zero time when zero time is
absent from the time-concentration data file.) A simple on/off switch informs QTRACER2
to estimate volume. If the switched is set to off, then subsequent geometries (e.g., cross-
.sectional area) will also not be estimated.
ESTIMATE SYSTEM VOLUME (l=yes, 0=no)
1
The switch value 1 for the QTRACER. DAT example informs QTRACER2 that system volume
should be estimated. .
77
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6.6.7. Radial Distance
QTRACER2 needs to know the straight-line distance to the sampling station from the in-
jection site and the units by which distance was measured.
RADIAL DISTANCE TO SAMPLING STATION: UNITS (l=m, 2=ft, 3=km, 4=miles) [VALUE]
3 1.8
A distance equal to 1.8 kilometers is entered for the QTRACER.DAT example.
6.6.8. Correction for Sinuosity
Because most solution conduits and fractures are not straight-line features, a sinuosity factor
may be included for QTRACER2 to use in processing the data.
CORRECTION FOR SINUOSITY (l=yes, 0=no) [VALUE, def=1.0]
1 1.5
A listing of 1 1.5 tells QTRACER2 to correct the radial distance for sinuosity by a, factor
of 1.5x. However, if no value is listed, a default equal to 1.0 is supplied. The sinuosity
factor is limited to a range of 1.0 < 3.0.
6.6.9. Flow Medium
QTRACER2 allows the user to decide if the flow system conforms to a subsurface channel
such as a typical karst solution-conduit or mine tunnel (e.g., tubular), surface channel
such as a small stream or large river (e.g., Missouri River), porous medium (e.g., granular
aquifer), or fracture opening (e.g., planar) or set of fractures. If it is a fractured-rock system,
a porosity value will need to be entered by the user as per the VALUE request. A default
of 1.0 (100%) porosity is used if no value is listed, which suggests that all flow occurred
via a single fracture. A porosity value has no effect for flow through subsurface channels
or surface channels. A porosity value also has no effect on a porous-media flow system in
QTRACER2 if a hydraulic conductivity value is missing.
FLOW MEDIUM: POROSITY (l=subsurface channel, 2=surface channel,
3=porous medium, 4=fractured medium) [VALUE, def=1.0] :
1
For QTRACER. DAT, a value of 1 tells QTRACER2 to consider subsurface-channel flow only;
a porosity value does not need to be entered because QTRACER2 automatically sets a
default value of 1.0.
78
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6.6.10. Porous-Media and Fracture Units
If tracer migrated through a porous medium, then the user would list the estimated
hydraulic conductivity by first recording a units identifier (e.g., 1) and then an actual
value representing the hydraulic conductivity.
Alternatively, if the tracer migrated through a fractured-rock system, then the user
would list the fracture(s) measured or estimated height units. Otherwise, QTRACER2 will
do its best to estimate the height, although the estimated value may not be very reliable.
IF POROUS FLOW: UNITS, HYDR. COND. (l=m/s, 2=m/hr, 3=ft/s, 4=m/hr, 0=null)
IF FRACTURE(S) FLOW: UNITS, HEIGHT (l=m, 2=ft, 0=null) [VALUE]
0 0.0
The flag 0 is irrelevant here because flow is a subsurface channel. However, for porous media
or fracture flow, the flag 0 tells QTRACER2 that fracture height is unknown and must be
estimated by QTRACER2.
6.6.11. Output File Name
QTRACER2 requires that an output filename be given so that the results may be written
to an "output file." The requestor is listed as INPUT/OUTPUT because much of the output
information is a repeat of input information.
NAME OF THE FILE OF INPUT/OUTPUT VALUES
Ql.OUT
The output file name Ql.OUT is used here because it allows for easy deletion without
inadvertently deleting the original input files. Any filename is allowed by QTRACER2,
although the user may not want to use a name that is excessively long.
6.6.12. Sample Data Interpolation
QTRACER2 is very good at data interpolation. It relies on a piecewise cubic Hermite to
determine the best possible interpolant for the given data.
INTERPOLATE DATA (l=yes, 0=no) and [NUMBER OF KNOTS]
0
This requestor is asking if the user would like to interpolate the data. A 0 means NO and the
user may move on. A 1 (QTRACER.DAT example) means YES and the user then must inform
QTRACER2 of the MINIMUM number of knot points to be created by the interpolation
algorithm.
To create an interpolated data file, the user might record the following.
INTERPOLATE DATA (l=yes, 0=no) and [NUMBER OF KNOTS]
79
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1 200
The flag and value 1 200, respectively, inform QTRACER2 that data interpolation is desired
and that > 200 knots points (interpolated data points) are required. Any value other than
200 could be used as computer memory allows.
6.6.13. Interpolated Data File Name
If an interpolated data file is to be created for processing, it must be given a name. This
file is then stored and can be viewed later or deleted as desired.
NAME OF THE INTERPOLATED OUTPUT VALUES FILE
Ql.INT
The output filename Ql.INT is used here because it allows for easy deletion without
inadvertently deleting the original input files. Any file name is allowed by QTRACER2,
although the user may not want to use a name that is excessively long. If data interpolation
is not requested above, this requestor is ignored by QTRACER2.
6.6.14. Sample Data Extrapolation
QTRACER2 is also very good at data extrapolation, but it is up to the user to determine
the method preferred. That is, the user must decide if an exponential decay function, a
piecewise cubic Hermite, or a straight-line projection from the last peak value through the
descending limb is most reasonable. Data extrapolation requires that the peak tracer con-
centration be obtained and that the descending limb of the breakthrough curve be started.
EXTRAPOLATE DATA (l=yes, 0=no) [1=EXP. DECAY, 2=CUBIC HERMITE, 3=STAT. METH.]
0 1
The 0 1 means that no extrapolation for the QTRACER.DAT file is requested (the second flag,
1, has no effect in this instance).
A 1=EXP. DECAY means that data extrapolation will be an exponential decay function,
a 2=CUBIC HERMITE means that data extrapolation will be by means of a piecewise cubic
Hermite, and a 3=STAT. METH. means that data extrapolation will be by the statistical
method of projecting lines from the peak concentration through the late-time data onto the
x axis and determining the greatest cluster. ;
QTRACER2 allows the user to extrapolate data to zero or near zero concentration (after
subtracting any background tracer concentration) without data interpolation. The user will
know the extent of data extrapolation by (1) examining the interpolation data file created
if the interpolation flag is switched on, or (2) by simply observing the "upper limit" to
80
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integration displayed at the top of the final output screen/file. The latter can be observed
whether a data interpolation file has been created or not.
6.6.15. Visualize Original Data
The original data may be visually examined before full processing by the user (CHECK),
plotted as points (PLOT), joined by a line (JOIN), and directly sent as a PostScript plot to
a file for later printing (OPLOT). Any one of these four items may be requested or not as
desired.
VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)
0110
The requestors CHECK PLOT JOIN OPLOT are asking if the user would like to:
1. Examine the concentration data file (CHECK).
2. Plot the data on the screen (PLOT).
3. Draw a smooth line through the data points (JOIN).
4. Automatically create a PostScript output file for plotting (OPLOT).
A number 1 answers YES to a requestor, a number 0 answers NO to a requestor. So for the
QTRACER.DAT example:
VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)
0 1 10 ,
tells the program to:
1. Not show the data file (CHECK = 0).
2. Plot the data on the.screen (PLOT = 1).
3. Draw a smooth curve through all the points (JOIN = 1).
4. Not create a PostScript output file automatically (OPLOT = 0).
Data Plotting Each individual plot screen allows for considerable interactive graphics
so that the user may customize the plots as desired. The interactive graphics are explained
in Section 5.6.1. on page 61 using the pull-down menus.
Sometimes the curve may look somewhat odd; this occurs because the interpolation
algorithm used for smooth plotting sometimes has difficulty jumping to oddly placed data
81
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points4. Data interpolation by QTRACER2 will help overcome this effect. Also, fewer than
three data points will result in no data smoothing.
More importantly, the shape of the curve drawn through the data points does not
necessarily represent the integration. QTRACER2 will perform a much better integration of
the curve than appears on the screen, in that it will seamlessly connect the points smoothly
even though this function cannot be observed by the user. So the user need not be troubled
by lihe smooth line drawn on screen not appearing to be entirely "perfect."
Automatic Postscript Files Automatic PostScript file creation of the plot files is very
advantageous when numerous data files must be processed as a batch operation. However,
these files will not be produced if the program is set to NOT create a file. This item will
usually be set to zero except when QTRACER2 is run in batch mode, because the PostScript
files can be quite large and printing them is unnecessary until a final version based on user
modifications is desired.
Using QTRACER2 for automatic PostScript output does NOT REQUIRE that the
data filenames be shorter than six characters. For the initial data file, the new name
adds underscores and extensions as appropriate. For example, the Qtracer.dat data file
would result in a PostScript plot file named Qtracer-dat.ps to identify it jas a plot of
the actual data file as recorded by the user. Likewise, an interpolated data file would
be named Qtracer-int.ps and a Chatwin data file would be named Qtracer-cht.ps. However,
all subsequent PostScript plot data file would conform to user chosen output file names. For
example, a normalized tracer mass file would be named Ql-.nrm.ps.
Manual Bitmapped Files Bitmapped files of all screen plots can be created very easily
by QTRACER2. These will usually be done when QTRACER2 is not being run in batch
mode. This is accomplished using the File pull-down menu described in Section 5.6.1. on
page 61
6.6.16. Visualize Interpolated Data
This requestor is used in the same manner as the previous visualization requestor. The only
difference is that it deals with interpolated data only. It functions when data interpolation
4This problem was evident in Version 1.0 of QTRACER mainly due to the bezier algorithm used for
data smoothing. Version 2 of QTRACER (QTRACER2) does not exhibit this problem so readily because
the bezier algorithm has been replaced by a cubic Hermite algorithm.
82
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was requested by the user.
VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT)
0110
This example 0 I1 1 0 tells QTRACER2 to do nothing for the QTRACER.DAT data file
'because no data interpolation was requested. If interpolation data had been requested,
then 0110 would tell QTRACER2 to not display the interpolated data, plot the data
with a line on screen, and not produce a PostScript plot file.
6.6.17. Visualize Chatwin Parameters
For longitudinal dispersion estimation, QTRACER2 will first attempt the Chatwin method.
If the storage arrays are exceeded, it will go to the method of moments.
The Chatwin parameters are visualized in the same manner as the previous items except
for connecting the data points with a line. That is, the Chatwin parameters may be
examined (CHECK), printed to a file (PRINT), plotted (PLOT), and sent to a file as a PostScript
plot file (OPLOT). There is no JOIN function because the Chatwin method automatically relies
on fitting a straight line through the early-time data.
VISUALIZATION: CHATWIN PARAMETERS (CHECK PRINT PLOT OPLOT)
0010
The switches, 0 0 1 0 for the QTRACER.DAT example, inform QTRACER2 that the data is
to be plotted on the screen only.
6.6.18. CXTFIT2.0 Data File Creation
In some instances, it is possible and desirable to use CXTFIT2.0 (Toride et al, 1995) to
model the data. QTRACER2 facilitates this by allowing the user to automatically create
an input file for use with CXTFIT2.0.
Form of CXTFIT2.0 File This option allows the user to request creation of a CXTFIT
file (CXTFIT) and use the original injected tracer mass (Min) or the recovered tracer mass
(Mout) for processing. Determining whether to use the mass injected or the mass recovered
is more than just a preference item. It is related to the functioning of the system and the
number of recovery stations (e.g., more than one recovery station will usually require Mout),
and greatly affects mass balances.
FLAG FOR FILE OF DATA FOR CXTFIT MODELING (CXTFIT Min Mout)
000
The three switches 000 tell QTRACER2 not to create a CXTFIT2.0 file and not to use
83
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either the mass injected or mass recovered in file creation. If a CXTFIT2.0 file option was
set to 1 and the other two options set to 0, then a default of mass injected (Min) would be
used.
If a CXTFIT2.0 file is to be created for use in the CXTFIT2.0 model, then the user
should:
1. Obtain a copy of the program and the user's manual. CXTFIT2.0 is a very complicated
program and requires considerable reading of the manual to understand its functioning.
2. IGNORE all FIRST line data after the first item of the CXTFIT2.0 cheated file —
QTRACER2 adds some additional information for user examination that is not read
byCXTFIT2.0.
3. QUESTION initial values for .the selected parameters. For example, if QTRACER2
was forced to use the method of moments to estimate dispersion, then the "D"
parameter listed in the CXTFIT2.0 created file could be too large for a global minimum
to be found.
These three items are essential before embarking on the use of CXTFIT2.0.
CXTFIT File Name and Location If a CXTFIT2.0 input file is to be created, then
the user must give the file a name. Also, if the CXTFIT2.0 program is not stored in the
same location as QTRACER2, then it is desirable to give it a path to where: it should be
created so that the user will not need to type in the path to the CXTFIT2.0 file.
NAME OF FILE FOR SOLUTE-TRANSPORT MODELING (VALID IF FLAG=1) :
C:\VANGENU\CXT\Q1.ADV
The data line, C: \VANGENU\CXT\qi. ADV, tells QTRACER2 to create the CXTFIT2.0 file at
the above listed path where the executable version of CXTFIT2.0 is stored. Actually, the
requestor is ignored in this instance because QTRACER2 was informed above not to create
a CXTFIT2.0 file. ;
Any of the files that QTRACER2 creates (except as by OPLOT) can be given a path for
file storage.
6.6.19. Normalized Tracer Concentration
The time-concentration data may be normalized for mass according to the Mull et al (1988)
method. That is, the concentration data may be rewritten into consistent units (mg Lr1)
84
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kg 1 injected to allow for comparison of multiple BTCs conducted at the same tracer
injection-recovery location. This newly created data may also be examined.
Flag to Create Normalized Data File for Mass The creation of a normalized
concentration data file is performed by the on/off switch described earlier (l=on, 0=off).
FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0)
1 -.•-•..'.
Name of Normalized Concentration File for Mass As with all other files created
by QTRACER2, a filename must be provided before QTRACER2 can create the file.
NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1)
Ql.NRM
A filename with an extension (*.NRM) is not required. Any name is acceptable. The "VALID
IF FLAG=1" requestor refers to the above on/off switch.
Visualize Normalized Concentration The newly created normalized concentration
file can be visualized in the same manner as the original data. That is, the data can be
examined (CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to a
file in PostScript form for PostScript plotting (OPLOT).
VISUALIZATION: NORMALIZED CONCENTRATION (CHECK PLOT JOIN OPLOT)
0010
Setting the four switches to 0 0 1 0 tells QTRACER2 to display a smooth line on the
screen.
6.6.20. Normalized Tracer Load
The tracer concentration data may be normalized for loading according to the Mull et
al. (1988) method. That is, the concentration data may be rewritten into consistent units
of (mg s"1) kg"1 injected to allow for comparison of multiple BTCs conducted at the same
tracer injection-recovery location. This newly created, data may also be examined.
Flag to Create Normalized Data File for Loading The creation of a normalized
concentration data file is again performed by the on/off switch described earlier (l=on,
0=off).
FLAG FOR NORMALIZED TRACER LOAD FILE (1/0)
85
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Name of Normalized Concentration File for Load As with all other files created
by QTRACER2, a filename must be provided before QTRACER2 can create the file.
NAME OF FILE FOR NORMALIZED TRACER LOAD VALUES (VALID IF FLAG=1)
Ql.LOD
A filename with an extension (*.LOD) is not required. Any name is acceptable.
Visualize Normalized Tracer Load The newly created normalized load file can be
visualized hi the same manner as the original data. That is, the data can be examined
(CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to a file in
PostScript form for PostScript plotting (OPLOT). ;
VISUALIZATION: NORMALIZED TRACER LOAD (CHECK PLOT JOIN OPLOT)
0010
Setting the four switches to 0 0 1 0 tells QTRACER2 to display a smooth line on the
screen.
6.6.21. Standardized Data File
The tracer concentration data may be standardized for dimensionless time and concentration
according to the Mull et al. (1988) method. That is, time may be rewritten by •
(* - *)
and concentration data may be rewritten by
C_
a
(70)
(71)
to create a completely dimensionless tracer-recovery curve that may be used as a "type
curve" for future contaminant release problems (see Mull et al. [1988] for a comprehensive
discussion). This newly created data may also be examined.
Breakthrough curves generated by multiple tracer tests conducted from the same
tracer-release point to the same tracer-recovery point conducted under differing hyrdologic
conditions may be examined by plotting each standardized ETC on the same graph. When
comparing the BTCs, it is useful to note the skewness and kurtosis (see Section 3.3.
on page 32) as well as visually noting similarities in the curves of each ETC- Apparent
differences between plotted BTCs, skewness, and/or kurtosis must be critically examined
to determine if the differences may be judged significant.
86
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Flag to Create Standardized Data File The creation of a standardized dimensionless
data file is again performed by the on/off switch described earlier (l=on, 0=off).
FLAG FOR STANDARDIZED TIME AND CONCENTRATION VALUES FILE (1/0)
I
Name of Standardized Data File As with all other files created by QTRACER2, a
filename must be provided before QTRACER2 can create the file.
NAME OF FILE FOR STANDARDIZED TIME AND CONCENTRATION (VALID IF FLAG=1)
Ql.STN
A filename with an extension (*.STN) is not required. Any name is acceptable.
Visualize Standardized Data File The newly created standardized time-concentra-
tion file can be visualized in the same manner as the original data. That is, the data can
be examined (CHECK), plotted (PLOT), joined with a line (JOIN), and automatically sent to
a file in PostScript form for PostScript plotting (OPLOT).
VISUALIZATION: STANDARDIZED TIME AND CONCENTRATION (CHECK PLOT JOIN OPLOT)
0010
Setting the four switches to 0 0 1 0 tells QTRACER2 to display a smooth line on the
screen.
6.6.22. Screen Display
QTRACER2 allows for processing interruption for displaying results by use of the on/off
switch (l=on, 0=off). If the user would like to view the program results as they become
available, then the switch should be set to l=on. QTRACER2 will pause periodically to
allow the user to view the results; RETURN will inform QTRACER2 to continue.
Setting the switch to 0=off allows QTRACER2 to run in the batch mode. This is
preferable when many sample station data files must be processed for a single header file.
FLAG FOR OUTPUT TO SCREEN AND PAUSE AS NECESSARY (1/0)
1
6.6.23. Method for Handling Large Time-Concentration Data Files
With the advent of automatic data loggers, incredibly large time-concentration data files
are being recorded. Often these files are much too large for conventional computer memory
allocation. Because of this problem, QTRACER2 has been programmed to allow for
adjustment accordingly by:
87
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1. Using all the time-concentration data, provided computer memory is not exceeded.
2. Averaging blocks of data to create a single data point for each block.
3. Skipping blocks of data.
The more measured data that QTRACER2 can handle the better. Therefore, if QTRACER2
must use less than all the data it will attempt to minimize the size of the blocks it must
average or skip.
FLAG FOR DATA ANALYSIS METHOD (1,ALL DATA; 2,BLOCK AVE; 3,BLOCK SKIP)
1
Two sets of data files were created to be "huge" are included on the disk. The first set,
GAR2.D and GAR2.DAT, were created by interpolation data collected at a Superfund site with
constant discharge. The second set, MUUL.D and MUUL.DAT, was created from the MULL
data set by interpolation and include a "variable" discharge (although discharge did not
always vary while being measured). \ •
6.6.24. Actual Time-Concentration Data
The last item to be listed for each *.DAT file is the actual time-concentratipn da,ta and
discharge data if these were not constant. The actual time-concentration data set (and
discharge data, if relevant) are recorded in the UNITS identified at the top of the *.DAT
file. Discharge must only be listed if a variable discharge was measured at each sampling
interval. For the QTRACER.DAT example: '.
TIME CONCENTRATION DISCHARGE (CONDITIONAL)
0.0 0.00 4.10
20.0 0.03 3.80
is listed to correspond with TIME CONCENTRATION DISCHARGE measurements. The paren-
thetical CONDITIONAL relates to whether discharge was variable or constant., If discharge
was earlier identified as a variable, then a discharge column must be recorded; if discharge
was earlier identified as a constant, then a discharge column must not appear.
If a single or average (constant) discharge was measured for the site, a constant discharge
value should have been identified earlier in the data file where appropriate. So for the
RCA.DAT example, only the TIME CONCENTRATION values are recorded as: ;
88
-------
TIME CONCENTRATION DISCHARGE (CONDITIONAL)
0.0 0.0
24.0 6.0
Earlier in the RCA.DAT data file (near the top), discharge had been identified as being a
CONSTANT (flag = 2) with UNITS and VALUE equal:
66
which indicates that discharge was recorded in "gpm" (flag = 6) and the actual discharge
value is 6 (the second 6 listed). -
Be advised that the TIME CONCENTRATION files do not need to list all the occurrences
of zero tracer recovery at the beginning of the tracer study. However, the time 0.0 should
be listed at the very top of the data file to indicate' the time of tracer injection.- If system
volumes are to be estimated for a variable discharge, TIME must begin with 0.0. As noted
above, zero time is now automatically added when missing from the time-concentration data
file. :
Conduit volume and Reynolds number can only be calculated if discharge is measured
at a SPRING, not a well. If a well is analyzed and the appropriate flags turned on to
indicate a desire to calculate conduit volume and Reynolds number, both will be calculated,
but significant uncertainties should be expected in the results, making calculations for the
RCA.DAT data sets suspect.
89
-------
7. EXAMPLE ANALYSES FROM QTRACER2
i
QTRACER2 is very easy and fast to use once the necessary header file and sampling station
data files have been created (see Section 6. on page 65). As described in Section 6.2. on
page 66, the user need only place the pointer on the QTR icon and Left Double-Click
to initiate QTRACER2, which introduces the program and prompts for the name of a
header file (tracing project file). At this point the user may type any valid header filename
(e.g., Qtracer.D) or just press to automatically run the QTRACER2 default file
(Qtracer.D) and observe proper functioning of QTRACER2.
At this point, QTRACER2 will proceed until finished if the batch mode has been
specified (see Section 6.6.22. on page 87). Alternatively, if the user requested screen display,
QTRACER2 will pause periodically to allow the user to observe the analytical results as
they become available. Simply pressing as directed by QTRACER2 will cause
QTRACER2 to move to the next available display screen except for the data plot screens.
The plot screens require the user to click the Left Click anywhere on any particular child
window to highlight that window for interactive manipulation using the pulldown menus
and for viewing. Left Clicking on the Graphicl screen returns the user to the; data-display
screen.
Lastly, if multiple sampling station data files are to be processed by QTRACER2 for
a single tracing project file or header file (see Section 6.5. on page 69), then QTRACER2
will enter a loop mode. Upon completion of processing a single sampling station data file,
QTRACER2 will clear most of its memory and loop back to read and process the next
sequentially listed sampling station data file in the header file list. Upon processing all
the sampling station data files, QTRACER2 will then develop a final total output of some
specific information (e.g., total mass recovery) and append this small output subfile to the
LAST specified sampling station output file.
7.1. QTRACER.D EXAMPLE OUTPUT
In Section 6.5. on page 69 QTRACER.D was used as a sample tracing project file or header file.
QTRACER.D referenced the sampling station data file, QTRACER.DAT (Section 6.6. on page 72,
and Table 11), that provided all the information necessary for QTRACER2 processing of
the data for that sampling station.
90
-------
7.1.1. QTRACER.DAT Tracer-Breakthrough Curve
Figure 16 depicts the basic tracer-breakthrough curve generated and analyzed by QTRACER2.
Note that discharge was measured each time a water sample was collected.
7.1.2. QTRACER.DAT Chatwin Plot
Figure 17 depicts the data plot and straight-line fit of the Chatwin parameter for longitudinal
dispersion generated and analyzed by QTRACER2. Note that the equation for the straight-
line and the relevant statistics describing the straight-line fit were generated by QTRACER2
where Y = 747.901 + -95.3754 is of the form y = mx + b and Equations (41) and (42) are:
xi = 747.901 and x2 = -95.3754.
7.1.3. QTRACER.DAT Output File
Figure 18 depicts the final analytical output generated by QTRACER2. Besides observing
the analytical results, note the end of the output file, which depicts the complete results
of the analysis.- QTRACER2 performs this function even though only a single sampling
station data file was analyzed. As such, the total results are the same as those listed in the
main part of the output file.
7.1.4. QTRACER.DAT Normalized Tracer Concentration
Figure 19 depicts the normalized tracer concentration data generated by QTRACER2
according to the method described by Mull -et al. (1988). Note the concentration units
for the y axis.
7.1.5. QTRACER.DAT Normalized Tracer Load
Figure 20 depicts the normalized tracer load data generated by QTRACER2 according to
the method described by Mull et al. (1988). Note the concentration units for the y axis.
7.1.6. QTRACER.DAT Standardized Time-Concentration Data
Figure 21 depicts the standardized-time concentration data generated by QTRACER2
according to the method described by Mull et al. (1988). Note the time units on the x
axis and the concentration units on the y axis.
91
-------
QTRACER.DAT
10 15
Time from Injection (h)
- 4.5
CD
E1
D
-C
o
to
a
- 4
Figure 16. Tracer-breakthrough curve for the QTRACER.DAT sampling station data file.
92
-------
QTRACER.DAT
-l • 1 ' 1 -1 r-
Y = 747.901 + -95.3754 X
CO
," 8
R^ =0.9815
r =-.9907'
z =-2.685
PROS =0.8676E-01
Chotwin Parameter
8
10
12
14
16
18
20
Time from Injection (h)
Figure 17. Plot and straight-line fit of the Chatwin parameter for the QTRACER. DAT sampling
station data file.
93
-------
********************************************************************
* *
* Listing of output for: QTRACER.DAT ' *
Limits to integration for the data file: QTRACER.DAT
Lower integration limit
Upper integration limit
.00000
20.000
hrs
hrs
The quantity of tracer recovered
.44798 kg
447.98 g
.44798E+06 mg
.44798E+09 ug
Distance from input to outflow point
Corrected for sinuosity = 1.50X
2.7000 km
Time to leading edge (first arrival)
7.0000 hrs
Time to peak tracer concentration
For a peak tracer concentration
8.0000 hrs
7.5000 ug/L
Figure 18. Output file for the QTRACER.DAT sampling station data file.
94
-------
The mean tracer transit time
.38629
9.2711
556.26
d
hrs
min
Variance for mean tracer time
.11515E-01 d~2
6.6325 hrs "2
23877. min~2
Standard deviation for tracer time
.10731
2.5754
154.52
d
hrs
min
The mean tracer velocity
Standard deviation for tracer velocity
6989.5 m/d
291.23 m/hr
.80897E-01 m/s
1637.7 m/d
68.238 ' m/hr
.18955E-01 m/s
Dispersion coefficient
Longitudinal dispersivity
3.2582
40.276
m~2/s
m
Peclet number
67.037
Advection > Diffusion
Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).
95
-------
The maximum tracer velocity
9257.1 m/d
385.71 m/hr
.10714 m/s
Flow-channel volume estimate
Based on a lower integration limit
and on an upper integration limit
Flow-channel cross-sectional area
.14941E+06 nT3
.00000 hrs
9.2711 hrs
55.338
m~2
Flow-channel surface area
Tracer sorption coefficient (channel)
Hydraulic head loss along channel
Based on a friction factor
.51674E+08 ;m~2
.13016E-04 m
.12078E-01 m
.11254
Viscous-flow sublayer along walls
Estimated Reynolds number
Based on an estimated tube diameter
1.3779 'mm
.59564E+06
8.3939 m
Estimated Froude number
Based on an estimated hydraulic depth
.10061E-01 ;
6.5926 m
Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).
96
-------
Molecular mass transport parameters
Shear velocity
.17006E-01 m/s
Estimated Schmidt number
1140.0
Estimated Sherwood number
14926.
Mass transfer coef. from wall to flow
.17782E-05 m/s
Molecular diffusion layer thickness
.56238 mm
Percent recovery of tracer injected
99.552 '/.
Accuracy index (0.0 = Perfect Recov.)
.4481E-02
Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).
97
-------
* Listing of output for: QTRACER.DAT
*
*
*
*
Total quantity of tracer recovered
.44798
447.98
kg
'S
Total aquifer volume estimate
Total aquifer surface area estimate
Final tracer sorption coefficient
. 14941E+06 ,nT3
.51674E+08 m
. 13016E-04 .m
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
99.552 %
.4481E-02 ,
Figure 18. Output file for the QTRACER.DAT sampling station data file (continued).
98
-------
QTRACER.DAT
m
q
d
•«.
"E"
'o, 5
-* c>
0>
E
o
c
o
o
ro
O
m
Cl
Q1 .NRM
Normalized Concentration
10 15
Time from Injection (hours)
Figure 19. Normalized tracer concentration data for the QTRACER.DAT sampling station
data file.
99
-------
QTRACER.DAT
80
J°
°E"
'
60
w 40
en
E
o
<§
20
t = 9.271
at = 2.575
jt = 1.561
Kt = 1.838
hrs
hrs
hrs
hrs
0
10 15
Time from Injection (hours)
20
Figure 20. Normalized tracer load data for the QTRACER.DAT sampling station data file.
100
-------
QTRACER.DAT
^0.8
c.
o
c
-------
7.2. RCA.D EXAMPLE OUTPUT
In Section 4.1. on page 50 a tracer test conducted at the RCA del Caribe Superfund site
(Barceloneta, P.R.) was used as an example for analysis. RCA.D is the header file read by
QTRACER2 and references the sampling station data file, RCA. DAT (Table 11), that provides
all the relevant information necessary for QTRACER2 processing of the data obtained for
that sampling station. !
7.2.1. RCA.DAT Tracer-Breakthrough Curve
Figure 22 depicts the basic tracer-breakthrough curve generated by QTRACER2 and
analyzed by QTRACER2. Note that discharge was measured each time a water sample
was collected.
7.2.2. RCA.DAT Chatwin Plot
Figure 23 depicts the data plot and straight-line fit of the Chatwin parameter for longitudinal
dispersion generated by QTRACER2 and analyzed by QTRACER2. Note that the equation
for the straight-line and the relevant statistics describing the straight-line fit were generated
by QTRACER2.
7.2.3. RCA.DAT Output File
Figure 24 depicts the final analytical output generated by QTRACER2. Besides observing
the analytical results, note the end of the output file, which depicts the complete results
of the analysis. QTRACER2 performs this function even though only a single sampling
station data file was analyzed. As such, the total results are the same as those listed in the
main part of the output file.
7.2.4. RCA.DAT Normalized Tracer Concentration
Figure 25 depicts the normalized tracer concentration data generated by QTRACER2
according to the method described by Mull et al. (1988). Note the concentration units
for the y axis.
7.2.5. RCA.DAT Normalized Tracer Load
Figure 26 depicts the normalized tracer load data generated by QTRACER2; according to
the method described by Mull et al. (1988). Note the concentration units for the y axis.
102
-------
RCA.DAT
400 -
10 15
Time from Injection (h)
20
25
Figure 22. Tracer-breakthrough curve for the RCA .DAT sampling station data file.
103
-------
RCA. DAT
O
T
Y = 937.976 + -134.329 X
R2 =0.9867
r =-.9933
z =-2.850
PROB =0.6665E-02
Chatwin Parameter
10
15
Time from Injection (h)
20
25
Figure 23. Plot and straight-line fit of the Chatwin parameter for the RCA.DAT sampling
station data file.
104
-------
********************************************************************
* *
* Listing of output for: RCA.DAT *
Limits to integration for the data file: RCA.DAT
Lower integration limit
Upper integration limit
.00000
24.000
hrs
hrs
The quantity of tracer recovered
1.7403 kg
1740.3 g
.17403E+07 mg
.17403E+10 ug
Distance from input to outflow point
Uncorrected for sinuosity
33.528 m
(110.00 ft)
Time to leading edge (first arrival)
5.0000 hrs
Time to peak tracer concentration
For a peak tracer concentration
6.9999 hrs
380.00 ug/L
Figure 24. Output file for the RCA. DAT sampling station data file.
105
-------
The mean tracer transit time
.35853 d
8.6048 hrs
516.24 min
Variance for mean tracer time
.21200E-01 d"2
12.211 ;hrs~2
43961. min"2
Standard deviation for tracer time
.14560 d
3,4945 hrs
209.67 • min
The mean tracer velocity
Standard deviation for tracer velocity
93.753 m/d
3.9064 : m/hr
.11111E-02 :m/s
29.204 m/d
1.2168 .m/hr
.33801E-03 m/s
Dispersion coefficient
Longitudinal dispersivity
.31943E-03 nT2/s
.29437 m
Peclet number
113.90
Advection > Diffusion
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
106
-------
The maximum tracer velocity
160.94 m/d
6.7057 m/hr
.18627E-02 m/s
Flow-channel volume estimate
11.726
m~3
Flow-channel cross-sectional area
Flow-channel surface area
Tracer sorption coefficient (channel)
Hydraulic head loss along channel
Based on a friction factor
.34974
m"2
21237. m~2
.83208E-01 m
.30391E-06 m
.10076E-01
Estimated Reynolds number
Based on an estimated tube diameter
and an hydraulic conductivity
635.17
.66731
m
.11971E+06 m/s
Estimated Froude number
Based on an estimated hydraulic depth
.47862E-03
.52411 m
.Figure 24. Output file for the RCA.DAT sampling station data file (continued).
107
-------
Molecular mass transport parameters
Shear velocity
.21585E-03 m/s
Estimated Schmidt number
1140.0
Estimated Sherwood number
139.57
Mass transfer coef. from wall to flow
.20915E-06 m/s
Molecular diffusion layer thickness
4.7813 mm
Percent recovery of tracer injected
.65922
Accuracy index (0.0 = Perfect Recov.)
.9934
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
108
-------
********************************************************************
* " -.-•••••-" ' *
* Listing of output for: RCA.DAT *
* *
********************************************************************
Total quantity of tracer recovered
1.7403
1740.3
kg
g
Total aquifer volume estimate
Total aquifer surface area estimate
Final tracer sorption coefficient
11.726
21237.
nT3
m
.83208E-01 m
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
.65922 %
.9934
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
109
-------
RCA.DAT
200
Q)
if 150
CT
L
c 100
o
o
o
50
t = 8.605
= 3.494
7t = 2.104
10 15
Time from Injection (hours)
20
25
Figure 25. Normalized tracer concentration data for the RCA. DAT sampling station data file.
110
-------
RCA.DAT
80
8 60
40
o
c
o
O
20
t = 8.605
= 3.494
= 2.104
= 4.412
0
10 15
Time from Injection (hours)
20
25
Figure 26. Normalized tracer load data for the RCA.DAT sampling station data file.
Ill
-------
7.2.6. RCA.DAT Standardized Time-Concentration Data
Figure 27 depicts the standardized-time concentration data generated by QTRACER2
according to the method described by Mull et al. (1988). Note the time units on the x
axis and the concentration units on the y axis.
7.3. ANALYSIS ASSESSMENT OF THE QTRACER AND RCA EXAMPLE
DATA FILES
From the two examples (QTRACER and RCA), it is apparent that QTRACER2 is not
affected by variable discharges versus a constant discharge. QTRACER2 is also' not affected
by recovery at a spring versus recovery at a monitoring well. ;
The QTRACER data set resulted in nearly perfect mass recovery. Had the QTRACER
data set been analyzed according to the description given in Section 4. on page 48, the user
would have noted a mass recovery > 100%. The efficient integration algorithms used by
QTRACER2 results in a more reliable mass balance. • ;
QTRACER2 results for the RCA data set were quite similar to those presented in
Section 4.1.1. on page 51 QTRACER2 performs equally well on less ideal sites (e.g.,
TOPLITA).
7.3.1. Molecular Diffusion Layer Thickness
An estimate of the molecular diffusion layer thickness 5m appears at the end of Figures 18
and 24. It is useful for understanding mass transfer from the walls of a karst .conduit into
the main flow stream. Estimation of 5m may be achieved from (Dreybrodt, 1988, p. 172)
Nsh = Dc/5
'm
(72)
where the Sherwood number Nsh for turbulent flow is obtained from (Dreybrodt, 1988, p.
172)
Nsh =
(73)
which is valid for 0.6 < Nsc < 2500 and 2000 < NR < 35000. For laminar flow conditions
Nsh may be estimated from
Q.668(Dc/xs}NRNsc
Nsh = 3.65 +
(74)
112
-------
RCA.DAT
c
o
c
-------
A mass transfer coefficient kf is obtained from the Sherwood number by using the
relationship (Dreybrodt, 1988, p. 171)
(75)
Dr,
where the molecular diffusivity is on the order of 10 9 m2 s 1 (Neretnieks, 1993, p. 109).
The Schmidt number Nsc relates momentum and mass transfer. It is estimated by
relating the molecular diffusivity of the tracer to the kinematic viscosity of the water
according to the relationship
(76)
It will be noted here that Dm = 1.0 x 10 9 (L2 T l) is taken as a general value for
all tracer tests in QTRACER2 because it is too demanding that every possible tracer
diffusion coefficient be identified in QTRACER2. It is also assumed that the average user
of QTRACER2 will be unfamiliar with the appropriate value for Dm, making it impractical
to expect a user to provide an accurate value. For these reasons, any calculations using Dm
should be regarded as being only rough approximations.
114
-------
8. QTRACER ANALYSIS OF OTHER HYDROLOGICAL SETTINGS
The previous version of QTRACER2 (QTRACER) was primarily designed for analysis of
BTCs from tracing tests conducted in karstic terranes (e.g., solution conduits) and fractured-
rock terranes. The previous version noted that BTCs conducted in other hydrological
systems could be analyzed as well, but that much of the latter results may not be relevant
(e.g., Froude number for a porous-media tracer test) and the user had to know which
'parameters to ignore. However, as explained in Section 6.6. on page 72 (see also Figure 15
on page 73) a new sampling station data file entry addressing the type of hydrological system
is provided for in QTRACER2.
8.1. SURFACE-WATER AND POROUS-MEDIA EXAMPLES
QTRACER2 now allows an entry for the type "FLOW MEDIUM" with an additional entry
for the,"POROSITY": .
Subsurface Channel = 1 A subsurface channel is considered representative of any type
of karstic-solution conduit, mine shaft or tunnel, or any other type of submerged
conduit. ' '
Surface Channel = 2 A surface channel is considered'representative of any surface-water
flow from a very small creek to a large river. :
Porous Medium = 3 Porous medium is exactly what it sounds like; any type of flow
through porous media. This can be a granular aquifer (e.g., alluvial aquifer) that
flows through a packed column in the laboratory. If porous-media flow is chosen, then
the user has the option of including a porosity value and a hydraulic conductivity
value.
Fractured Medium = 4 This last item addresses flow through a fractured-rock aquifer in
which a fracture porosity is important or flow through a single linear fracture (porosity
— 100%). If fracture flow is chosen, the user, has the option of including an estimated
porosity value and an estimated fracture height value.
8.1.1. Surface-Water Example
A small stream, Uvas Creek, was traced in 1976 using a steady three hour injection of 1068 g
of Cl— in late summer during a low-flow period (Bencala and Walters, 1983; Zand, et al,
115
-------
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. Time-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).
This study included several sampling stations along the entire reach of the study. In this
particular case, individual runs for each sampling station should be run by QTRACER2
because summation function built into QTRACER2 would incorrectly sum the results for
the same tracer-recovery data.
Figure 28 and Figure 29 are the ETC and Chatwin plots of the UVAS Creek data set,
respectively. Figure 30 is the output file generated by QTRACER2 on the Uvas Creek data
set.
A cursory inspection of Figure 28 will show that plotting was initiated at some value
greater than zero. Background Cl~ concentrations at the site were taken as 3.71 rng Lr1
and axe included in the data file for plotting. The background concentration is subtracted
from the actual data file prior to any actual data analysis. :
It will be noted that Figure 30 differs in some unique ways from Figures 18 and 24
(pages 94 and 105, respectively). For example, both Figures 18 and 24 provide an estimate
for the standard deviation for the mean tracer velocity, but no such listing is provided
in Figure 30. No standard deviation for mean tracer velocity could be estimated for the
UVAS281.DAT data set because the pulse-injection time exceeded the mean time of travel.
As indicated in Section 3.3.1. on page 32, this calculation is not trivial. More significant is
the fact that the upper limit to integration was necessarily changed from 29.867 hours to
4.3333 hrs (Figure 30) because tracer release was of a long-pulse type. I
Transport-parameter estimates by QTRACER2 appears to be excellent. For example,
QTRACER2 estimated flow velocity to be 0.038 m s"1 which compares exceptionally well
with the published velocity of 0.037 m s"1 (Zand et al, 1976; Bencala and Walters, 1983)
obtained from Q/A. From Section 3.3.2. (page 36) it will be noted that in general, the
Chatwin method should provide a reasonable estimate for longitudinal dispersion even
though it is an incorrect method for pulse and continuous releases. Interestingly, by using
the Chatwin method, QTRACER2 estimated longitudinal dispersion to be 0.15 m s"1 which
compares favorably with the published longitudinal dispersion values of 0.24 m2 s"1 (Bencala
and Walters, 1983) and 0.25 m2 s"1 (Zand et al, 1976). ;
116
-------
Uvas281.DAT
10 15 20
Time from Injection (h)
25
30
Figure 28. Tracer-breakthrough, curve for the UVAS281 .DAT sampling station data file.
117
-------
Uvas281.DAT
= O
Y = 362.002 + -136.888 X
R* =0.9913
r =-.9956
z =-3.062
PROB =0.4368E-02
O O o
Chatwin Parameter
10 15 20
Time from Injection (h)
25
30
Figure 29. Plot and straight-line fit of the Chatwin parameter for the UVAS281 .D:AT sampling
station data file. •
118
-------
********************************************************************
* *
* Listing of output for: UVAS281.DAT *
* *
********************************************************************
Limits to integration for the data file: UVAS281.DAT
Lower integration limit
Upper integration limit
.00000
29.867
hrs
hrs
The quantity of tracer recovered
1.3191 kg
1391.1 g
.13191E+07 mg
.13191E+10 ug
Distance from input to outflow point
Uncorrected for sinuosity
281.00
m
Time to leading edge (first arrival)
.16667
hrs
Time to peak tracer concentration
For a peak tracer concentration
4.3333
6.2500
hrs
mg/L
Figure 30. Output file for the UVAS281 .DAT sampling station data file.
119
-------
Upper Limit to integration necessarily changed!
Lower integration limit
Upper integration limit
.00000 hrs
4.3333 hrs
The mean tracer transit time
.86625E-01
2.0790
124.74
d
hrs
min
Variance for mean tracer time
.27233E-03
.15686
564.71
d"2
hrs~2
min" 2
Standard deviation for tracer time
.16502E-01
.39606
23.764
d
hrs
min
The mean tracer velocity
3243.9
135.16
.37545E-01
m/d
m/hr
m/s
Dispersion coefficient
Longitudinal dispersivity
.15064
4.0122
m"2/s
m
Peclet number
70.037 :
Advection > Diffusion
Figure 30. Output file for the UVAS281 .DAT sampling station data file (continued).
120
-------
The maximum tracer velocity
40464.
1686.0
.46833
m/d
m/hr
m/s
Flow-channel volume estimate
Flow-channel cross-sectional area
Flow-channel,surface area
Tracer sorption coefficient (channel)
Hydraulic head loss along channel
Based on a friction factor
104.78
.37289
m"3
m~2
.75270E+06 nT2
0.0000 m
.44516E-01 m
1.5189
Viscous-flow sublayer along walls
Estimated Reynolds number
Based on an estimated tube diameter
.80813
22692.
.68904
mm
m
Estimated Froude number
Based on an estimated hydraulic depth
.16297E-01
.54117 m
Figure 30. Output file for the UVAS281.DAT sampling station data file (continued).
121
-------
Molecular mass transport parameters
Shear velocity
..28996E-01 m/s
Estimated Schmidt number
1140.0
Estimated Sherwood number
991.01
Mass transfer coef. from wall to flow
.14383E-05 m/s
Molecular diffusion layer thickness
.69529 mm
Percent recovery of tracer injected
123.51
Accuracy index (0.0 = Perfect Recov.)
-.2351
*******************************************************************
*
*
*
*
*
*
*
*
*
*
AN IMPOSSIBLE CONDITION EXISTS! CHECK YOUR UNITS FOR
CORRECTNESS OR CHECK TO SEE IF SAMPLE CONTAMINATION
HAS OCCURRED (i.e., HAS,SOMEONE ELSE BEEN INJECTING
THE SAME TRACER MATERIAL IN THE AREA?). ALSO CHECK
YOUR LIMITS TO INTEGRATION AND YOUR DISCHARGE ESTIMATES.
DISCHARGE ESTIMATION ERRORS ARE VERY COMMON. TRACER ,
RECOVERY SHOULD NOT BE GREATER THAN 100% AND THE
ACCURACY INDEX SHOULD NOT BE LESS THAN ZERO.
*
*
*
*
*
*
*
*
*
*
*******************************************************************
Figure 30. Output file for the UVAS281 .DAT sampling station data file (continued).
:122
-------
* Listing of output for: UVAS281.DAT
Total quantity of tracer recovered
1.3191
1391.1
kg
g
Total aquifer volume estimate
Total aquifer surface area estimate
Final tracer sorption coefficient
104.78 m'
.75270E+06 m
0.0000 m
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
123.51
-.2351
"I
h
*
*
*
*
*
*
.*
*
.*
*
AN IMPOSSIBLE CONDITION EXISTS! CHECK YOUR UNITS FOR
CORRECTNESS OR CHECK TO SEE IF SAMPLE CONTAMINATION
HAS OCCURRED (i.e., HAS SOMEONE ELSE BEEN INJECTING
THE SAME TRACER MATERIAL IN THE AREA?). ALSO CHECK
YOUR LIMITS TO INTEGRATION AND YOUR DISCHARGE ESTIMATES.
DISCHARGE ESTIMATION ERRORS ARE VERY COMMON. TRACER
RECOVERY SHOULD NOT BE GREATER THAN 100% AND THE
ACCURACY INDEX SHOULD NOT BE LESS THAN ZERO.
*
*
*
*
'*
*
*
*
*
*
Figure 30. Output file for the UVAS281.DAT sampling station data file (continued).
123
-------
Even more significant in Figure 30 is an error message that appears twice. This error
message indicates that more tracer mass was recovered than was injected. Although it
appears twice in Figure 30, it only appears in the case when > 100% tracer-mass is recovered.
In the case of Figure 30, excess tracer-mass recovery occurred at the single sampling station
that was considered. It is possible that individual sampling stations may result in < 100%,
but that their sum could result in > 100%.
8.1.2. Porous-Media Example
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).
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. 1986a, p. 52-60, 71) and (Molz, et al.
1986b).
Figure 31 and Figure 32 are the BTC and Chatwin plots of the WAS Creek data set,
respectively. Figure 33 is the output file generated by QTRACER2 on the Uvas Creek data
set.
As with Figure 30, Figure 33 also differs in some unique ways from Figures 18 and 24
(pages 94 and 105, respectively). For example, both Figures 18 and 24 provide an estimate
for the surface area and sorption coefficient, but no such listing is provided in Figure 33. No
surface area or sorption coefficient could be estimated for the MOBILE.DAT data set because
the porous-media systems require some knowledge regarding particle diameter that is not
provided for in QTRACER2. In addition, a Froude number is not estimated because a
Froude number is not relevant to porous-media systems.
124
-------
Mobile.DAT
20
15
g 10
o
o
o
Data = 62
200
400
Time from Injection (h)
600
800
Figure 31. Tracer-breakthrough curve for the MOBILE.DAT sampling station data file.
125
-------
Mobile.DAT
o
o
• o
£. g
CM
Y = 1870.97 + -8.19140 X
R2 =0.9590
r =-.9793
z =-2.280
PROS =0.1217E-13
. i .... i .
Chatwin Parameter
100 200 300 400 500 600
Time from Injection (h)
700
800
Figure 32. Plot and straight-line fit of the Chatwin parameter for the MOBILE.DAT sampling
station data file.
126
-------
* . *
* Listing of output for: MOBILE.DAT *
*'.-'.' *
********************************************************************
Limits to integration for the data file: MOBILE.DAT
Lower integration limit
Upper integration limit
.00000
760.00
hrs
hrs
The quantity of tracer recovered
362.29 kg
.36229E+06 g
.36229E+09 mg
.36229E+12 ug
Distance from input to outflow point
Uncorrected for sinuosity
38.300
m
Time to leading edge (first arrival)
9.8000 hrs
Time to peak tracer concentration
For a peak tracer concentration
209.00 hrs
22.000 mg/L
Figure 33. Output file for the MOBILE.DAT sampling station data file.
127
-------
The mean tracer transit time
14.985
359.64
21579.
d
hrs
min
Variance for mean tracer time
50.094 d"2
28854. hrs "2
.10387E+09 nmT2
Standard deviation for tracer time
7.0777 d
169.86 hrs
10192. min
The mean tracer velocity
Standard deviation for tracer velocity
2.9720 m/d
.12383 m/hr
.34398E-04 m/s
2.6669 m/d
.11112 in/hr
.30867E-04 m/s
Dispersion coefficient
Longitudinal dispersivity
.10476E-03 nT2/s
3.0456 m
Peclet number
12.576
Advection > Diffusion
Figure 33. Output file for the MOBILE.DAT sampling station data file (continued).
128
-------
The maximum tracer velocity
Transport-zone volume estimate
Transport zone cross-sectional area
Hydraulic head loss along channel
Estimated Reynolds number
9.3796 m/d
.39082 m/hr
.10856E-03 m/s
20456. nT3
534.11
nT2
.26349E-04 m
.72743E-01
Figure 33. Output file for the MOBILE.DAT sampling station data file (continued).
129
-------
Molecular mass transport parameters
Estimated Schmidt number
1140-0
Estimated Sherwood number
1.8708
Percent recovery of tracer injected
46.388
Accuracy index (0.0 = Perfect Recov.)
0.5361
Figure 33. Output file for the MOBILE.DAT sampling station data file (continued).
130
-------
* Listing of output for: MOBILE.DAT
*
*
*
*
********************************************************
Total quantity of tracer recovered
362.29 kg
.36229E+06 g
Total aquifer volume estimate
20456.
m~3
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
46.388
0.5361
Figure 33. Output file for the MOBILE.DAT sampling station data file (continued)
131
-------
9. DATA INTERPOLATION AND EXTRAPOLATION EFFECTS
As explained in Section 5.1. on page 58, QTRACER2 uses a very efficient data interpolation
routine. The primary use of the data interpolation routine is when the user believes that
missing data points can be reasonably approximated by data interpolation. For example, if
the user believes that unaltered BTCs suggest that data aliasing may have occurred, then
data interpolation may be able to confirm or deny if aliasing has actually occurred.
9.1. COMPARISON OF QTRACER.DAT OUTPUT FILES
To illustrate the effect of data interpolation, data extrapolation, and the combined effect of
both on a data set exhibiting good mass recovery, the QTRACER. DAT data set was subjected
to each of these three algorithms. In some instances, the effect is fairly noticeable while in
other instances there are no differences. : . .
9.1.1. Interpolated QTRACER.DAT ETC
Figure 34 depicts the interpolated ETC generated and analyzed by QTRACER2. Note that ;
discharge has an interpolated value for each time an interpolated tracer concentration value ;
was created.
9.1.2. Interpolated QTRACER.DAT Chatwin Plot
Figure 35 depicts the interpolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER2. Note that the equation
for the straight-line and the relevant statistics describing the straight-line fit were generated ,
byQTRACER2.
Some difference will be noted between Figure 35 and Figure 17 (page 93), but not a
significant difference. Interpolation results in more data points falling on the necessary
straight line; 'the equation of the straight line has different values for the y intercept and
slope. As such, a slightly different estimate for longitudinal dispersion results.
Table 12 compares the final analytical output for the unaltered ETC for the QTRACER.DAT
data set, the interpolated QTRACER.DAT data set, and the Interpolated-extrapolated
QTRACER.DAT data set. Note how each file's results are closely matched with the oth-
ers.
132
-------
01.INT
o
c
0)
o
o
o
Knots = 100
nterpolated Data
Time from Injection (h)
D
O
in
Figure 34. Interpolated curve for the QTRACER.DAT sampling station data file.
133
-------
Q1.INT
o
o
in
Y = 875.168 + -110.475
°°00000
OOOOOOOOOOOOOOO
ooooo
°°oc
R2 =0.9691
r =-.9844
z =-2.424
PROB =0.5685E-11
' 1 1
J L
Chatwin Parpmeter
i ' • '
8
10
12 14 16
Time from Injection (h)
18 20
Figure 35. Interpolated data set for the Chatwin parameter for the QTRACER.DAT sampling
station data file.
134
-------
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9.1.3. Extrapolated QTRACER.DAT ETC
Figure 36 depicts the extrapolated ETC generated and analyzed by QTRACER2. Note
that discharge has an interpolated value for each time an extrapolated tracer concentration
value is created.
Graphically, the user will note that the ETC shown in Figure 36 appears relatively
unchanged from Figure 16. The only apparent difference is that the elapsed tracer travel
time has been extended from 20 hours to > 22 hours and that one additional data point
(total data = 22) has been included. ;
More obvious is the effect of data extrapolation on the discharge curve when data
extrapolation routines 1 (exponential decay) and 3 (statistical fit) are employed (3 =
statistical fit for-Figure 36). Extrapolation routine 2 (piecewise cubic Hermite) uses the
shape of the entire existing data curve to determine the "most reasonable" extrapolation
data point possible for the extrapolated discharge. ;
Extrapolation routines 1 and 3, however, have no mathematical basis for consideration.
For example, there is no reason to assume that discharge will behave as an, exponential
decay function, so extrapolation routine 1 = exponential decay would make no physical
sense. Therefore, when extrapolation routines 1 or 3 are requested and a variable discharge
is measured, QTRACER2 will automatically extend the discharge curve in ;the opposite
vertical direction (along the y axis) to one-half its previous range. It is up to the user to
decide on its reasonableness. '
9.1.4. Extrapolated QTRACER.DAT Chatwin Plot
Figure 37 depicts the extrapolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER2. Note that the straight-
line fit, the equation for the straight line, and the relevant statistics describing; the straight-
line fit generated by QTRACER2 are identical to Figure 17. Data extrapolation had no
effect on the Chatwin method analysis because the original sample had resulted in nearly
"complete" tracer recovery. :
9,2. INTERPOLATED-EXTRAPOLATED QTRACER.DAT DATA
Figures 38 and 39 illustrate how the interpolation and extrapolation routines provided in
QTRACER2 can be used in ETC analyses. Table 12 illustrates that there are jio significant
differences hi any of the analyses provided by QTRACER2 for the QTRACER.DAT data set.
138
-------
QTRACER.DAT
D
O
CO
Q
10 15
Time from Injection (h)
Figure 36. Extrapolated curve for the QTRACER. DAT sampling station data file.
139
-------
QTRACER.DAT
W
o
o
o
Y = 747.901 + -95.3754 X
R2 =0.9815
r =-.9907
z =-2.685
PROB =0.8676E-01
Chatwin Parameter
8
10
12 14 16
Time from Injection (h)
18
20
Figure 37. Extrapolated data set for the Chatwin parameter for the QTRACER.DAT sampling
station data file. :
140
-------
Q1.INT
- 5
Knots = 232
nterp/Extrap Data
0
10 15
Time from Injection (h)
Figure 38. Interpolated and extrapolated data set for the QTRACER.DAT sampling station
data, file. . .
141
-------
Q1.INT
o
8
w
o
s
'
«_«
8
8
in
o
o
Rz =0.9236
r =-.9610
z =-1.959
PROB =0.6660E-14
Y = 924.127 + -116.842 X
Chatwin Parameter
10
, 15
Time from Injection (h)
20
Figure 39. Interpolated and extrapolated data for the Chatwin parameter for QTRACER.DAT
sampling station data file.
142
-------
A more erratic BTC, or one that was ended leaving a significant mass.of tracer in the
system, would result in large differences when data interpolation and/or extrapolation is
employed. The user should note that when data extrapolation are employed without data
interpolation, the graphics may appear incorrect (i.e., a straight-line connection from the
last measured data point to the extrapolated data point). This apparent inaccuracy is not
a problem, however, as it is strictly an artifact of the plotting algorithm. The integration
routine used by QTRACER2 will develop a smooth curve between all provided data points
regardless of BTC appearance.
9.3. COMPARISON OF RCA.DAT OUTPUT FILES
To further illustrate the effect of data interpolation, data extrapolation, and the combined
effects of both on a data set exhibiting poor mass recovery, the RCA. DAT data set was
subjected to each of these three algorithms. In some instances, the effect is fairly noticeable,
while in other instances there are no differences.
9.3.1. Interpolated RCA.DAT BTC
Figure 40 depicts the interpolated BTC generated and analyzed by QTRACER2. Note that
discharge has no interpolated value. This is because discharge was considered a constant,
so there are no data to interpolate.
Graphically, the user will note that Figure 40 is little changed from the curve shown in
Figure 22. The slight improvement is most evident at the peak, where the interpolated file
more correctly matches the peak concentration data point. In Figure 22, the graphics line
slightly exceeds the time to peak concentration. However, the apparent inaccurate plotting
is NOT reflected in the actual data analysis by QTRACER2.
9.3.2. Interpolated RCA.DAT Chatwin Plot
Figure 41 depicts the interpolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER2. Note that the equation
for the straight-line and the relevant statistics describing the straight-line fit were generated
byQTRACER2.
Some difference will be noted between Figure 41 and Figure 23, but not a greatly
significant difference. Interpolation results in more data points falling on the necessary
straight line, and the equation of the straight line has different values for the y intercept
and slope. As such, a slightly different estimate for longitudinal dispersion will result.
143 . ' .
-------
, R1.INT
400 -
Knots = 101
Interpolated Data
10 15
Time from Injection (h)
Figure 40. Interpolated curve for the RCA.DAT sampling station data file.
144
-------
RUNT
o
8
c o
— 10
.*>. I
o
o
o
Y = 885.469 + -127.254 X
°0°°°°oo,
°°o0
°°00oo
'OOOOOOOOi
oooooooo
100°oooo0ooooo
'Ooo°oooo
R^ =0.9922
r =-.9961
z =-3.120
PROB =0.2626E-17
Chatwin Parameter
10 15
Time from Injection (h)
20
25
Figure 41. Interpolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file.
145
-------
Table 13. Estimated hydraulic flow and geometric parameters from BTCs for RCA. DAT
sampling station. . ;
Parameter
Tracer Mass
Recovered, g
Percent Mass
Recovered
Accuracy
Index
Initial Tracer
Breakthrough, h
Time to Peak
Concentration, h
Mean Tracer
Residence Time, h
Elapsed Tracer
Travel Time, h
Maximum Tracer
Flow Velocity, m h"1
Peak Tracer
Plow Velocity, m h"1
Mean Tracer
Flow Velocity, m h"1
Shear
Velocity, m h"1
Longitudinal
Dispersion, m2 s"1
Hydraulic
Head Loss, m
Flow-Channel
Volume, m3
Flow-Channel Cross-
Sectional Area, m2
Flow-Channel
Surface Area, m2
Tracer Sorption
Coefficient, m
Tube
Diameter, m
RCA.DAT
(unaltered)
1.74 x 103
6.59 x HT1
9.93 x ID"1
5.00 x 10°
7.00 x 10°
8.61 x 10°
2.40 x 101
6.71 x 10°
4.79 x 10°
3.91 x 10°
7.77 x ID"1
1.15 x 10°
3.04 x ID"7
1.17X101
3.50 x ID"1
2.12 x 104
8.32 x 10~2
6.67 x 10-1
RCA.DAT
(interpolated)
1.74 x 103
6.59 x 10-1
9.93 x ID"1
4.08 x 10°
6.96 x 10°
8.60 x 10°
2.40 x 101
8.22 x 10°
4.82 x 10°
3.91 x 10°
7.77 x 1.0-1
1.29 x 10°
3.04 x 10~7
1.17X101
3.50 x ID"1
2.12 x 104
8.32 x 10-2
6.67 x 10"1
RCA.DAT1
(extrapolated)
1.77 x 103
6.70 x ID"1
9.93 x 10-1
5.00 x 10°
7.00 x 10°
8.90 x 10°
3.17 x 101
6.71 x 10°
4.79 x 10°
3.78 x 10°
7.58 x ID"1
1.15 x 10°
2.85 x 10~7
1.21 x 101
3.62 x 10-1
2.11 x 104
8.53 x 10~2
6.79 x 10"1
RCA.DAT2
(inter. /extra.)
1.77 x 103
6.71 x 101
9.93 x 10-1
4.08 x 10°
6.96 x 10°
8.95 x 10°
5.20 x 101
8.22 x 10°
4.82 x 10°
3.76 x 10°
7.55 x lO"1
1.38 x 10°
2.81 x 1Q-7
1.22 x 101
3.64 x 10-1
2.10 x 104
8.57 x 1Q-2
6.80 x ID"1
continued on next page
l
146
mm^m^m
-------
Table 13. Estimated hydraulic flow and geometric parameters from BTCs for RCA. DAT
sampling station (continued).
Parameter
RCA.DAT RCA.DAT
(unaltered) (interpolated)
RCA.DAT1-
(extrapolated)
RCA.DAT2
(inter./extra.)
Friction
Factor
Laminar Hydraulic
Conductivity, m s"1
Reynolds
Number
Froude
Number
Peclet
Number
Schmidt
Number
Sherwood
Number
Mass Transfer
Coefficient, m s"1
Molecular diffusion
layer, m
1.01 x 1CT1 1.01 x ID"1
1.20 x 105 1.20 x 105
6.35 x 102 6.35 x 102
4.79 x 10~4 4.79 x 10~4
1.14xl02 1.02 x 102
1.14 x 103 1.14 x 103
1.40 x 102 1.40 x 102
2.09 x 10
,-7
2.09 x 10
-7
4.78 x 1Q-3 4.78 x W~3
1.02 x 1Q-1
1.24 x 105
6.25 x 102
4.59 x ID"4
1.10 x 102
1.14 x 103
1.40 x 102
2,06 x ID"7
4.86 x ID"3
1.03 x ID"1
1.25 x 105
6.23 x 102
4.56 x ID"4
9.16 x 101
1.14 x 103
1.40 x 102
2.05 x ID"2
4.87 x ID"3
Listed parameters without dimensions are dimensionless.
Extrapolated using a statistical straight line fit.
2Extrapolated using a cubic Hermite function.
Table 13 compares the final analytical output for the unaltered ETC for the RCA. DAT
data set, the interpolated RCA.DAT data set, and the interpolated-extrapolated RCA.DAT
data set. Note how each file's results are closely matched with the others.
9.3.3. Extrapolated RCA.DAT ETC
Figure 42 depicts the extrapolated ETC generated and analyzed by QTRACER2. Note
that discharge has no extrapolated value because discharge was constant.
Graphically, the user will note that Figure 42 is more reasonable than Figure 22. The
improvement is most evident in the elapsed time of travel. In Figure 22, the elapsed time of
travel (24 hours) is reflected in a cessation of sample collection prior to "complete" tracer
recovery. However, Figure 42 suggests nearly "complete" tracer recovery at > 30 hours.
147
-------
RCA.DAT
400 -
Data = 26
Extrapolated Data
0
0
10 15 20 25
Time from Injection (h)
Figure 42. Extrapolated curve for the RCA. DAT sampling station data, file.
148
-------
9.3.4. Extrapolated RCA.DAT Chatwin Plot
Figure 43 depicts the extrapolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER2. Note that the straight-
line fit, equation for the straight-line, and relevant statistics describing the straight-line fit
generated by QTRACER2 are slightly different from-the results shown in Figure 23.
The obvious differences between Figure 43 and Figure 23 are a result of not having
continued actual data collection until near "complete" tracer recovery. Because sampling
ceased before adequate tracer recovery, data extrapolation exerts considerable influence on
the Chatwin analysis; in this instance, a straight-line fit to the data that is not as good.
9.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA
Figures 44 'and 45 illustrate how the interpolation and extrapolation routines provided in
QTRACER2 can be used in ETC analyses. Table 13 illustrates that there are no significant
differences in any of the analyses provided by QTRACER2 for the RCA.DAT data set.
The user will note in Figure 44 that the exponential decay equation :
y = 660.115 e
-0.215973z
(77)
has been produced along with the correlation coefficient r (-0.9418) and the standard error
of the estimated fit (50.87). QTRACER2 provides this information to the user to assist in
assessing the effect of an exponential decay on a BTC. Whereas extrapolation methods 2
(piecewise cubic Hermite) and 3 (statistical method) produce a single extrapolated point,
method 1 (exponential decay) produces five additional data points and thus has a great deal
more influence on the final results.
Exponential decay extrapolation has more influence because the integration routine
employed by QTRACER2 is forced to conform to the shape of the exponentially decaying
curve. It is therefore incumbent upon the user to determine how appropriate it is to use
an exponential decay model for extrapolation. For example, applying an exponential decay
model for extrapolation to the QTRACER'. DAT data set results in tracer mass recovery that
is, greater than what was injected. Clearly this is an impossibility that suggests major field
errors, laboratory errors, numerical errors, or some combination of all three.
A more erratic BTC or one that was ended leaving a significant mass of tracer in the
system would result in large differences when data interpolation and/or extrapolation are
employed. The user should note that when data extrapolation is employed without data
149
-------
RCA.DAT
8
in
§
—I—i—i—I—1—I—1—
Y = 937.976 + -134.329 X
R2 =0.9867
r =-.9933
z =-2.850
PROB =0.6665E-02
'
Chatwin Parameter
10
15
Time from Injection (h)
20
25
Figure 43. Extrapolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file. i
150
-------
RUNT
400 -
0
10
Knots = 434
Interp/Extrap Data
-0.215973 X
Y = 690.115 e
Sy. X = 50.87
r =-.9418
20 30 40
Time from Injection (h)
50
Figure 44. Interpolated and extrapolated data set for the RCA.DAT sampling station data
file.
151
-------
RUNT
o
8
7
T 1 T
FT =0.9901
r =-.9950
•L =-2.999
PROS =0.1072E-37
Y = 857.357 + -122.270 X
10
20 30
Time from Injection (h)
40
50
Figure 45. Interpolated and extrapolated data for the Chatwin parameter. for RCA.DAT
sampling station data file. ;
152
-------
interpolation, the graphics may appear incorrect (i.e., a straight-line connection from the
last measured data point to the extrapolated data point). This apparent inaccuracy is not
a problem, however, as it is strictly an artifact of the plotting algorithm. The integration
routine used by QTRACER2 will develop a smooth curve between all provided data points
regardless of ETC appearance.
153
-------
10. ASSOCIATED COMPUTER PROGRAMS
To facilitate the efficient use of QTRACER2,! three additional programs have been developed
and included with this package. The first, NDATA, allows the user to run, an efficient
interpolation program to fill missing data in either the time-concentration or the time-
discharge data files. The second program, AUTOTIME, converts time-concentration data
files using military time into sequential decimal time as required by QTRACER2. The
third program, DATFILE, provides a straightforward interface for the creation of a sample
station data file. ;
The results of these three programs are:easily appended or copied to a *.DAT file (see
Section 6.6.24. on page 88 and the end of Figure 15). By judicious use of these programs,
QTRACER2 can be made more efficient because the data can be quickly and easily placed
in required form.
10.1. NDATA COMPUTER PROGRAM
Typically, discharge is not measured as frequently or at the same time as tracer concentra-
tion. Hence, the time concentration data file might appear as (no specific data file example):
4.10 i
0.0 0.00
1.0 2.05
5.0 4.50
10.0 4.10
15.0 4.33
20.0 0.03
3.96
3.80
The data file cannot be processed because values for discharge and corresponding values
for concentration must also be recorded in the file (unless a constant discharge was listed
above), To resolve this problem, NDATA.EXE, a very good data interpolation algorithm
has been programmed (it is the same one used in QTRACER2). To use this program,.Left
Double-Click on NDATA and follow the instructions. Note that this program ONLY works on
a time-concentration file or time-discharge file without any other headers. The algorithm
must therefore be used on the original data set(s) and the results copied to the bottom of
the final data file to be processed. ;
When using NDATA only X/Y data is recognized by the program as a data file. So if
you were missing some discharge values, create a set of X/Y values in which time values
correspond to X and discharge values correspond with Y. Do not use the concentration
values. The program can then be used to fill in missing discharge values. When typing in
154
-------
the data, OMIT all time values for which a corresponding discharge or concentration value
is missing. Using the example above, if the concentration value corresponds to time=15.0,
the user would exclude the entire line from the data set to be processed. The greater the
number of missing data pairs, the greater the interpolation errors.
Note that NDATA is to be used to fill data gaps in both concentration data and discharge,
but only where corresponding values are missing. It is better to allow QTRACER2 to
perform data interpolation on a complete data file.
10.1.1. NDATA Source
The FORTRAN source code is included on the NDATA disk. Modification of the NDATA
main file can be relatively easily accomplished if desired, but is not recommended. The user
should not attempt to modify the included subroutines.
10.2. AUTOTIME COMPUTER PROGRAM
Tracer-breakthrough curve data is often recorded in military time as opposed to sequentially
from 0 to infinity. AUTOTIME will convert data recorded in military time into sequentially
listed time in terms of decimal seconds, decimal minutes, decimal hours, or decimal days
depending on the user's preference. -.
The user must first create a time-concentration file such as that shown in Figure 46.
Left Double-Click AUTOTIME and then follow the instructions to create a new file of
time-concentration data that can then be copied to the end of a *.DAT file and read
by QTRACER2. Note that the concentration and discharge values are not altered by
AUTOTIME. Also note that a variable discharge recorded by the user is allowed in a third
column that is read by AUTOTIME. The third column is not necessary, however.
Running AUTOTIME on the data listed in Figure 46 for conversion to decimal hours
will result the file listed in Figure 47. As stated previously, that QTRACER2 allows for free-
format data entry, so a nicely formatted data column is unnecessary. All that is necessary
is that the two data columns be separated by at least one blank space or a comma.
10.2.1. AUTOTIME Source
The FORTRAN source code is included on the AUTOTIME disk. Modification of
the AUTOTIME main file can be relatively easily accomplished if desired, but is not
recommended.
155
-------
10 15
21 45
22 15
22 45
23 15
23 45
0 15
0 45
1 15
1 45
2 15
2 45
3 15
3 45
4 15
4 45
5 15
5 45
6 15
6 45
7 15
7 45
8 15
8 45
13 45
22 45
0.010
0.010
0.060
0.500
1.320
2.050
3.900
4.200
4.200
3.400
3.050
2.450
2.000
1.500
1.200
0.950
0.800
0.600
0.550
0.500
0.420
0.370
0.350
0.300
0.200
0.010
3 . 23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
3.23E-2
3 . 23E-2
3.23E-2
3.23E-2
3 . 23E-2
3 . 23E-2
3.23E-2
3.23E-2-
3 . 23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
3.23E-2
3.23E-2
3.23E-2
3.23E-2
3 . 23E-2
3 . 23E-2
3 . 23E-2
Figure 46. Example of a sample time-concentration file using military time for conversion
(Mull et al., 1988). : ;
156
-------
0.0000
11.5000
12.0000
12.5000
13 . 0000
13 . 5000
14.0000
14.5000
15.0000
15.5000
16.0000
16 . 5000
17.0000
17.5000
18.0000
18.5000
19.0000
19.5000
20 . 0000
20.5000
21.0000
21.5000
22 . 0000
22.5000
27.5000
36.5000
0.0100
0.0100
0 . 0600
0,5000
1.3200
2 . 0500
3.9000
4.2000
4.2000
3.4000
3.0500
2 . 4500
2.0000
1.5000
1 . 2000
0 . 9500
0 . 8000
0.6000
0.5500
0 . 5000
0 . 4200
0.3700
0.3500
0.3000
0 . 2000
0.0100
0 . 0323
0 . 0323
0.0323
0.0323
0 . 0323
0 . 0323
0.0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0.0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0 . 0323
0.0323
Figure 47. Example of a converted sample time-concentration file created by AUTOTIME
(Mull et al, 1988).
157
-------
10.3. DATFILE COMPUTER PROGRAM
The easiest method for creating a sample station data file (Figure 15) may be accomplished
by using a text editor to edit an existing sample station data file and saving the altered file
using a new filename. However, if desired, the user may use DATFILE to create a sample
station data file. In addition, DATFILE may be used to read in a QTRACER file (either a
*.D file or a *.DAT file) for quick conversion to a QTRACER2-readable file ;
To use DATFILE, the user need only Left Double-Click DATFILE and respond to each
requestor in turn. In the create mode, DATFILE only produces the upper portion of
a sampling station data file. The actual TIME CONCENTRATION DISCHARGE data
must be appended to the end of the data file created by DATFILE. In the conversion mode,
DATFILE attempts to automatically identify the type of file to be converted by recognizing
the first word of the file (QUANTITY = *.D file; SAMPLING - *.Dat file). If DATFILE
cannot identify the file, the user is requested to provide identification for DATFILE. Upon
recognition, the user then responds to a few appropriate requestors.
A sample station data file created or converted from a QTRACER-file | form using
DATFILE will not appear exactly in the form of Figure 15 because of some formatting
differences. This is not a concern because QTRACER2 uses free format for input.
10.3.1. DATFILE Source
The FORTRAN source code is included on the DATFILE disk. Modification of the
DATFILE main file can be relatively easily accomplished if desired, but is not recommended.
10.4. COMBINE COMPUTER PROGRAM
Typically, as mentioned in Section 10.1. on page 154 discharge is not measured as frequently
or at the same time as tracer concentration. With the advent of continuous-flow filter
fluorometers, pressure transducers, and data loggers, automatic data recording is now
normally conducted. However, if the time settings on these various instruments are not
synchronized or one automatic recording device takes readings less frequently than the a
different recording device, then use of QTRACER in which one "universal" set of TIME
data is used is problematic. For example, consider the following time-concentration data set
(Combinel.dat; modified from the QTRACER.DAT file using the interpolation function of
QTRACER) shown in Figure 48 and the time-discharge data set (Combine2.dat; unmodifed
from the QTRACER.DAT file) shown in Figure 49.
158
-------
0.000000000
0.2000000030
0.4000000060
0.6000000238
0.8000000119
1.000000000
1.200000048
1.399999976
1.600000024
1.799999952
2.000000000
2.200000048
2.400000095
2.599999905
2.799999952
3.000000000
3.200000048
3.399999857
3.599999905
3.799999952
4.000000000
4.199999809
4.399999619
4.599999905
4.799999714
5.000000000
5.199999809
5.399999619
5.599999905
5.799999714
6.000000000
6.199999809
6.400000095
6.599999905
6.799999714
7.000000000
7.199999809
7.400000095
7.599999905
7.800000191
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.000000000
0.6205322146
2.121600866
3.962399006
5.602131367
6.500000000
6.825866222
7.101600170
7.314399719
7.451466560
Figure 48. Example of a measured sample time-concentration file as recorded by an
automatic data recorded (modified from the QTRACER.DAT).
159
-------
8.000000000
8.199999809
8.399999619
8.599999428
8.799999237
9.000000000
9.199999809
9.399999619
9.599999428
9.799999237
9.999999046
10.19999886
10.39999962
10.59999943
10.79999924
10.99999905
11.19999886
11.39999866
11.59999847
11.79999924
11.99999905
12.19999886
12.39999866
12.59999847
12.79999828
12.99999809
13.19999886
13.39999866
13.59999847
13.79999828
13.99999809
14.19999790
14.39999771
14.59999847
14.79999828
14.99999809
15.19999790
15.39999771
15.59999752
15.79999733
7.500000000
7.284326077
6.736979008
6.007468700
5.245306492
4.599999905
4.042011261
3.470477104
2.927937984
2.456932783
2.100001335
1.822443485
1.570183516
1.356703877
1.195482850
1.100000262
1.047596455
1.005732298
0.9730700850
0.9482718706
0.9300000668
0.9165091515
0.9060727954
0.8973819017
0.8891273141
0.8800001144
0.8703692555
0.8611077666
0.8516616225
0.8414769769
0.8300001025
0.8168752193
0.8021946549
0.7860764265
0.7686389089
0.7500001788
0.7302790880
0.7090768218
0.6857351661
0.6595957875
Figure 48. Example of a measured sample time-concentration file as recorded by an
automatic data recorded (modified from the QTRACER.DAT) (continued).
160
-------
15.99999809
16.19999695
16.39999771
16.59999847
16.79999733
16.99999809
17.19999695
17.39999771
17.59999657
17.79999733
17.99999809
18.19999695
18.39999771
18.59999657
18.79999733
18.99999619
19.19999695
19.39999771
19.59999657
20.00000000
0.6300002933
0.5930896401
0.5479190350
0.4982038140
0.4476595819
0.4000004232
0.3527349830
0.3033765852
0.2556514442
0.2132840753
0.1800002754
0.1541337073
0.1314002424
0.1116003171
0.9453354031E-01
0.8000025153E-01
0.6706685573E-01
0.5520012602E-01
0.4480016232E-01
0.2999999933E-01
Figure 48. Example of a measured sample time-concentration file as recorded by an
automatic data recorded (modified from the QTRACER.DAT) (continued).
161
-------
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
4.10
4.20
4.27
4.35
4.42
4.50
4.57
4.67
4.75
4.82
4.90
4.80
4.68
4.56
4.46
4.33
4.22
4.12
4.00
3.90
3.80
Figure 49. Example of a measured sample time-discharge file as recorded by an automatic
data recorded (unmodified from the QTRACER.DAT).
162
-------
The two data files do not correspond because, assuming these appear as recorded by
automatic recording devices, there are only 21 time-discharge data values, while there are
100 time-concentration data values. In this instance, each of the time values for the time-
discharge data set has a matching time value in the time-concentration data set. However,
even if there were no matching time values between the two disparate data sets, COMBINE
would do a tolerable job of making a match.
To use COMBINE, the user need only start the program (Left Double-Click on the
COMBINE icon) and select units for time, concentration, and discharge which can be
arbitrary and are not necessary for the program to run. Next the user enters the time-
concentration data file to be considered, then the time-discharge data file to be considered,
then an output name for the resulting time-concentration-discharge data file, and a plot
file name if a PostScript file of the screen plot is desired, A screen plot of the resulting
time-concentration-discharge data file will be displayed if the chosen interpolation step is
not too small. A selected interpolation step of 0.1 is recommended as an initial value, but
the user is free to pretty much choose any value. However, a very small interpolation step
(e.g., 0.0001) will result in a massively huge file that may exceed the memory stack on the
local computer.
Processing the two data files shown above, Combinel.dat and Combine2.dat, using
COMBINE results in the following time-concentration-discharge data file shown in Fig-
ure 50.
10.4.1. COMBINE Screen Plotting
If the size of the created time-concentration-discharge file is of a reasonable size, COMBINE
will display a screen plot from which a bitmapped file may be created. A screen plot was
added so that the user may examine the results of the COMBINE-created file in relation
to the original time-concentration and time-discharge data files. Although only a visual
inpection, the screen plot allows the user the ability to verify that the COMBINE-created
file is acceptable.
Figure 51 (page 169) depicts the results of Figure 50. The open circles in Figure 51
represent measured time-concentration data points from Figure 48 and the open triangles
in'Figure 51 represent measured time-discharge data points from Figure 49. The solid line
in Figure 51 represents the interpolated time-concentration data shown in Figure 50 and the
dashed line in Figure 51 represents the interpolated time-discharge data shown in Figure 50.
Although it is not readily apparent from Figure 51, the data listed in Figure 50 results
163
-------
TIME
CONCENTRATION
DISCHARGE
O.OOOOOOOE+00
0.2000000
0 . 3000000
0 . 4000000
0.5000000
0.6000000
0.7000000
0.8000000
1 . 100000
1.200000
1.300000
1.400000
1.500000
1.600000
1.700000
1.800000
1.900000
2.000000
2.100000
2.200000
2.300000
2.400000
2.500000
2.600000
2.700000
2.800000
2.900000
3.000000
3.100000
3.200000
3.300000
3.400000
3.500000
3.600000
3.700000
3.800000
3 . 900000
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
O.OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+OQ
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
O.OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
0 . OOOOOOOE+00
4.100000
4.122500
4.133300
4.143900
4.154100
4.164000
4.173500
4.182700
4.208000
4.215400
' 4.222500
4.229300
4.236000
4.242500
4.249100
4.255800
4.262700
4.270000
4 . 277600
4.285500
; 4.293600
! 4.301700
4.310000
4.318300
4.326400
4.334500
4 . 342400
4.350000
4.357300
4.364400
4.371400
4 . 378200
4.385000
4.391800
4.398600
4.405600
4.412700
Figure 50. Example of a converted sample time-concentration-discharge file created by
COMBINE for use in QTRACER.
164
-------
4,
4.
000000
100000
4.200000
4.300000
4.400000
4.500000
4.600000
4.700000
4.800000
4.900000
5.000000
5.100000
5.200000
5.300000
5.400000
5.500000
5.600000
5.700000
5.800000
5.900000
6.000000
6.100000
6.200000
6.300000
6.400000
6.500000
6.600000
6.700000
6.800000
6.900000
7.000000
7.100000
7.200000
7.300000
7.400000
7.500000
7.600000
7.700000
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.OOOOOOOE+00
0.2003800
0.6203800
1.273800
2.121300
3.031500
3.962100
4.853700
5.601900
6.136200
6.499900
6.685300
6.825800
6.971000
7.101500
7.217100
7.314400
7.394800
4.420000
4.427600
4.435500
4.443600
4.451700
4.460000
4.468300
4.476400
4.484500
4.492400
4.500000
4.507300
4.514200
4.520900
4.527500
4.534000
4.540700
4.547500
4.554600
4.562000
4.570000
4.578700
4.588100
4.598100
4.608500
4.619200
4.629900
4.640500
4.650900
4.660700
4.670000
4.678800
4.687300
4.695600
4.703800
4.711800
4.719600
4.727300
Figure 50. Example of a converted sample time-concentration-discharge file created by
COMBINE for use in QTRACER (continued).
165
-------
7.800000
7.900000
8.000000
8.100000
8.200000
8.300000
8.400000
8 . 500000
8.600000
8.700000
10.10000
10.20000
10.30000
10.40000
10.50000
10 . 60000
10.70000
10.80000
10 . 90000
11.00000
11.10000
11.20000
11.30000
11.40000
11.50000
11.60000
11.70000
11.80000
11.90000
12.00000
12.10000
12.20000
12.30000
12.40000
12.50000
12.60000
12.70000
12.80000
7.451500
7.484700
7.500000
7.430900
7 . 284400
7.050300
6.737100
6 . 387400
6.007600
5.620800
1 . 955300
1.822500
1.692300
' 1 . 570300
1.457600
1 . 356800
1.268200
1.195500
1 . 141200
1.100000
1.071200
1 . 047600
1 . 025400
1.005700
0 . 9883500
0 . 9730800
0.9597900
0 . 9482800
0 . 9384500
0.9300100
0 . 9227900
0.9165100
0.9110100
0.9060800
0.9016000
0 . 8973800
0 . 8932800
0.8891300
4.735000
4.742500
4.750000
4.757300
4.764400
4.771400
4.778200
4.785000
4.791800
4.798600
4.898200
4.893100
4.885300
4.875300
4.863600
4.850900
4 . 837600
4.824400
4.811600
4.800000
4.788900
4.777400
4.765600
4.753600
4.741400
4.729000
4.716700
4.704300
4.692100
4.680000
4.667900
4.655700
4.643300
4.631000
4.618600
4.606400
4.594400
4.582600
Figure 50. Example of a converted sample time-concentration-discharge file created by
COMBINE for use in QTRACER (continued).
166
-------
12 . 90000
13.00000
13.10000
13.20000
13.30000
13.40000
13.50000
13.60000
13.70000
13.80000
13 . 90000
14.00000
14.10000
14.20000
14.30000
14 . 40000
14.50000
14.60000
14 . 70000
14.80000
14.90000
15.00000
15.10000
15.20000
15.30000
15.40000
15.50000
15.60000
15.70000
15.80000
15.90000
16.00000
16.10000
16.20000
16 . 30000
16.40000
16.50000
16.60000
0 . 8846500
0.8800000
0.8752000
0.8703700
0 . 8657300
0.8611100
0 . 8564400
0.8516700
0 . 8467000
0.8414800
0.8359200
0.8300000
0 . 8236400
0.8168800
0 . 8097300
0.8022000
0.7943200
0 . 7860800
0 . 7775200
0.7686500
0 . 7594700
0.7500100
0.7403100
0 . 7302900
0.7199100
0.7090900
0 . 6977200
0.6857500
0 . 6730600
0.6596100
0.6454500
0.6300200
0.6125300
0.5931100
0.5713600
0 . 5479400
0.5234300
0.4982300
4/571100
4.560000
4 . 549400
4.539300
4.529500
4.519900
4.510500
4.501000
4.491300
4.481400
4.471000
4.460000
4.448300
4.435800
4.422800
4.409400
4.395800
4.382100
4.368500
4.355200
4.342300
4.330000
4.318200
4.306700
4.295300
4 . 284200
4.273200
4.262400
4.251700
. 4.241000
4.230500
4.220000
4.209700
4.199700
4.189900
4.180200
4.170500
4.160900
Figure 50. Example of a converted sample time-concentration-discharge file created by
COMBINE for use in QTRACER (continued).
167
-------
16.70000
16.80000
16.90000
17.00000
17.10000
17.20000
17.30000
17.40000
17.50000
17 . 60000
17.70000
17.80000
17.90000
18.00000
18.10000
18.20000
18.30000
18,40000
18.50000
18.60000
18.70000
18.80000
18 . 90000
19.00000
19.10000
19.20000
19.30000
19.40000
19.50000
19.60000
19.70000
19.80000
19.90000
20.00000
0.4728200
0.4476800
0.4236500
0.4000200
0.3764900
0 . 3527600
0.3281100
0 . 3034000
0.2790800
0.2556700
0 . 2335400
0.2133000
0 . 1956400
0.1800100
0 . 1664700
0.1541500
0 . 1424000
0.1314100
0.1211600
0.1116100
0 . 1027500
9.4541997E-02
8.7022997E-02
8 . 0007002E-02
7 . 3376998E-02
6.7073002E-02
6.0977999E-02
5.5206001E-02
4.9722001E-02
4.4805001E-02
4.0520001E-02
3.6550999E-02
3.3009000E-02
3.0003000E-02
4.151000
4.141000
4.130700
4.120000
4.108800
4.097000
4 . 084900
4.072500
4.060000
4.047500
4.035100
4.023000
4.011200
4.000000
3.989300
1 3. 978800
•3.968700
3.958700
: 3. 948900
3.939100
3 . 929400
3.919700
3.909900
3.900000
'3.890000
3.880000
! 3. 870000
|3.860000
3.850000
3 . 840000
3.830000
3.820000
; 3. 810000
3.800000
Figure 50. Example of a converted sample time-concentration-discharge file created by
COMBINE for use in QTRACER (continued).
168
-------
COMBINE.OUT
c
o
V»
I
0)
u
c
o
o
Breakthrough Curve
Discharge Curve
10
Time (h)
15
20
4.8
4.6
D
A A °
4.4 ra
"a
4.2
Figure 51. Plot of the Combine, out data listed in Figure 50.
169
-------
in a very large file with a very small time spacing. This small time spacing results in a
total of 185 data values (using a 0.1 interpolation step). Therefore, the solid and dashed
lines actually plot as smooth curves rather than as a series of straight-line segments between
data points. Prom this perspective the quality of the plot indicates that the data listed in
Figure 50 would be acceptable for analysis by QTRACER.
10.4.2. COMBINE Processing
To be able to produce matching time-concentration and time-discharge data files COMBINE
interpolates both data sets independently to produce two new, very large data files. These
are then written to temporary storage and read back into the program in truncated form.
The temporary storage can occupy considerable storage space so it is necessary that the user
ensure that adequate storage space exists on,the hard drive prior to running COMBINE.
By truncating the actual data, it is more .likely that matching time values for the time-
concentration and time-discharge data files will be obtained than if the entire data record
were to be read. If the entire data record were to be read, it is proba,ble that extraneous
decimal places in the time-concentration and time-discharge data files could not be found
to match. The new time-concentration-discharge file is then written to the hard drive and
the temporary files deleted.
10.4.3. COMBINE Source
The FORTRAN source code is included on the COMBINE disk. Modification of the COM-
BINE main file can be relatively easily accomplished if desired, but is not recommended.
The user should not attempt to modify the included subroutines. ,
170
-------
11. CONCLUSIONS
Tracer-breakthrough curves developed from quantitative hydrological tracer tests can be
evaluated given the present high level of accuracy of analytical fluorescence chemistry (and
other tracer substances) and efficiency of numerical algorithms available. Ground-water
flow directions, velocities, and related hydraulic processes such as dispersion, divergence,
convergence, dilution, and storage can be properly established from tracer studies and can
be used to devise better structural models of the karst aquifer. Because of the lack.of
physical access to caves at many karst sites, these structural models, can be valuable for
predicting ground-water flow and contaminant transport in the aquifer.
From a human health perspective, quantitative ground-water tracing studies can assist in
demonstrating real connections between tracer injection sites and downgradient receptors.
Residence times and tracer velocities can provide ground-water managers with potential
time-of-travel estimates likely to occur for nonreactive pollutant spills in the vicinity of
tracer injection sites. Pollutant mass dispersion, dilution, and related processes can also
be estimated by such studies. Until such time that conduit accessibility becomes a reality,
ground-water tracing studies provide the best alternative to acquiring hydraulic data for
karst and fractured-rock aquifers.
A robust, efficient, easy-to-use computer program, QTRACER2, and two related com-
puter programs, NDATA and AUTOTIME, facilitate the analysis of tracer-breakthrough
curves. All three programs are well documented. It is expected that in the future, quan-
titative tracing of contaminated sites will become more and more important for parameter
estimation. QTRACER2 will enhance the necessary analyses and lead to improved site
evaluations.
171
-------
NOTATION
A
A
Aj
Ap
As
b
C
Co
Cb
C
Of
d,
C(xa,t)
D
Dc
DH
DL
Dm
ff
F
9
hL
kf
K
Ka
m
bulk flow region cross-sectional area (L2)
matrix of time values used in the Chatwin analysis (T)
accuracy index (dimensionless)
constant of proportionality for amount of diffusing material (M T1/2* L~3)
karst conduit surface (L2)
vector of concentration parameters for the Chatwin analysis (T1/2)
tracer concentration (M L~3)
initial tracer concentration (M L~3)
average tracer background concentration (M L~3)
average solute (tracer) concentration (M L~3)
final tracer concentration (M L~3)
final measured tracer concentration corrected for background (M L~3)
initial measured tracer concentration uncorrected for background (M L~3)
average concentration of tracer input over time interval (M L~3) :
peak tracer concentration (M Lr3) ;
steady-state (plateau) tracer concentration at a resurgence
for repeated instantaneous injections (M L~3)
mass of recovered tracer over distance (s), xs and time(s), t [M L"~3];
steady-state tracer dilution for multiple injections (dimensionless)
karst conduit diameter (L)
karst conduit hydraulic depth (L)
longitudinal dispersion coefficient (L2 T"1)
molecular diffusion coefficient (L2 T"1)
friction factor (dimensionless) :
cumulative residence time distribution (dimensionless)
gravitational acceleration (L T~2)
hydraulic head loss (L)
mass transfer coefficient (L T"1)
equivalent hydraulic conductivity for laminar flow (L T""1)
karst conduit sorption coefficient (L)
karst conduit roughness correction factor (dimensionless) ;
172
-------
NOTATION cant.
Min
Mm
Mo
MT
n
ne
NF
NR
Nsc
Nsh
Pe
Q
Q
r
Sd
t
tc
Td
TD
Te
Tf
t
At
v
vp
vs
xs
mass of tracer injected (M)
mass of multiple tracer injections (M)
mass of tracer recovered (M)
total tracer mass recovered from all sampling stations (M)
number of measured data points (dimensionless) • .
effective fracture porosity (dimensionless)
Proude number (dimensionless) ...... _
Reynolds number (dimensionless)
Schmidt number (dimensionless)
Sherwood number number (dimensionless)
Peclet number (dimensionless)
ground-water discharge (L3 T"1)
mean ground-water discharge (L3 T"1) :
karst conduit radius (L)
sinuosity factor (dimen.)
time of sample collection (T)
time conversion factor (T)
duration in time for tracer cloud to pass any one point in the flow section (T)
duration in time required for entire tracer cloud to pass a flow section (T)
elapsed time to leading edge of tracer cloud (T)
elapsed time to trailing edge of tracer cloud (T)
time tracer takes to reach the flow system (T)
time for tracer injection for a pulse injection (T)
maximum allowable time for Chatwin analysis (T)
time to peak concentration (T)
mean tracer residence time (T)
time interval between multiple tracer injections (T)
mean tracer velocity (L T""1)
peak tracer velocity (L T""1)
shear tracer velocity (L T"1)
radial distance to, sampling station (L)
173
-------
NOTATION cont.
V volume of individual karst conduits or fractures (L3)
VT total volume space occupied by open space used for tracer migration L3)
w fracture width (L)
x straight-line tracer migration distance (L)
x vector of straight-line parameters used in the Chatwin analysis (T1/2) ;
x vector of straight-line parameters used in the Chatwin analysis (T1/2) •
xa sinuous tracer migration distance (L) ;
5 laminar flow sublayer (L)
6m molecular diffusion layer thickness (L)
7t skewness coefficient (T3)
Kt kurtosis coefficient (T4) ;
e relief of karst conduit wall surface irregularities (L)
IJ, dynamic viscosity (M L~1T~1)
TT pi (dimensionless) :
p fluid density (M L~3)
<7t standard deviation for mean residence time (T)
-------
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