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The QTRACER Program for
Tracer-Breakthrough Curve
Analysis for Karst and
Fractured-Rock Aquifers
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EPA/600/R-98/156a
February 1999
The QTRACER Program for Tracer-
Breakthrough Curve Analysis
for Karst and Fractured-Rock Aquifers
National Center for Environmental Assessment-Washington Office
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
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DISCLAIMER
The 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 constitue endorsement or recommendation for use.
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Contents
LIST OF TABLES vii
LIST OF FIGURES viii
PREFACE x
AUTHOR and REVIEWERS xi
ABSTRACT xii
1. INTRODUCTION 1
1.1. LIMITATIONS OF THIS REPORT 1
1.2. PURPOSE 2
1.2.1. Quantitative Tracer Tests to Support Ground-Water Monitoring Efforts 2
1.2.2. Quantitative Tracer Tests for Risk Assessments 2
1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation 4
1.3. QUALITATIVE VERSUS QUANTITATIVE TRACING 4
2. TRACER TEST DESIGN FACTORS 8
2.1. TRACER CHARACTERISTICS 12
2.2. TRACER INJECTION 13
2.2.1. Methods of Injection 16
2.3. TRACER SAMPLING 16
2.4. SAMPLING EQUIPMENT 19
2.5. SAMPLING LOCATIONS AND FREQUENCIES 19
2.6. TRACER MIXING IN THE CONDUIT 20
2.7. CORRECTION FOR BACKGROUND 20
2.8. DISCHARGE MEASUREMENTS 22
2.9. KARST CONDUIT NETWORKS 23
2.9.1. Network Types I, II, and III 23
2.9.2. Network Types IV and V 23
2.9.3. Network Types VI and VII 23
2.10. DETERMINATION OF TOPOLOGICAL KARST CONDUIT NETWORK
TYPE 25
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 30
3.2.1. Mean Residence Time 31
3.2.2. Mean Tracer Velocity 32
3.2.3. Longitudinal Dispersion 33
3.2.4. Tracer Dilution 35
in
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KARST CONDUIT AND FRACTURED-ROCK GEOMETRIES 37
3.3.1. Aquifer Volume 37
3.3.2. Cross-Sectional Area 38
3.3.3. Karst Conduit Diameter 38
3.3.4. Karst Conduit Hydraulic Depth 38
3.3.5. Karst Conduit Surface Area 38
3.3.6. Tracer Sorption Estimation 39
3.4. EMPIRICAL FLUID DYNAMICS MODELS 40
3.4.1. Peclet Number 40
3.4.2. Dynamic Flow Equations 40
3.5. BOUNDARY-LAYER EFFECTS 42
3.5.1. Friction Factor Estimation 42
3.5.2. Laminar Flow Sublayer 42
3.5.3. Hydraulic Head Loss 43
3.5.4. Shear Velocity 43
4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY 44
4.1. SIMPLIFIED EXAMPLE CALCULATION 46
4.1.1. Mass Recovery Example 46
4.1.2. Mean Residence Time Example 46
4.1.3. Mean Tracer Velocity Example 49
4.1.4. Longitudinal Dispersion Example 49
4.1.5. System Volume 49
5. QTRACER COMPUTER PROGRAM DESCRIPTION 50
5.1. DATA INTERPOLATION 50
5.2. DATA EXTRAPOLATION 50
5.2.1. Exponential Decay 50
5.2.2. Piecewise Cubic Hermite 51
5.2.3. Straight-Line Projection 51
5.2.4. Extrapolating Discharge 51
5.3. CHATWIN'S ESTIMATION OF LONGITUDINAL DISPERSION .... 52
5.4. DATA NORMALIZATION 52
5.5. RANGE OF POSSIBILITIES OF QTRACER 52
5.6. COMPUTER GRAPHICS 53
5.6.1. Features of the Interactive Graphics Loop 53
5.7. QTRACER SOURCE 57
6. USING QTRACER 58
6.1. QTRACER PROGRAM AND DATA FILES 58
6.2. QTRACER EXECUTION 58
6.3. QTRACER FUNCTIONING 59
6.4. SAMPLE FILES ON DISK 59
6.5. DESCRIPTION OF *.D FILES 62
IV
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6.6. DESCRIPTION OF *.DAT FILES 63
6.6.1. Sampling Frequency 63
6.6.2. Tracer Mass Recovery 67
6.6.3. Flag for Background 67
6.6.4. Measured Discharge 68
6.6.5. Discharge Units 68
6.6.6. Aquifer Volume 69
6.6.7. Radial Distance 69
6.6.8. Correction for Sinuosity 69
6.6.9. Conduit or Fracture Flow 70
6.6.10. Fracture Geometry Units 70
6.6.11. Output File Name 70
6.6.12. Sample Data Interpolation 71
6.6.13. Interpolated Data File Name 71
6.6.14. Sample Data Extrapolation 71
6.6.15. Visualize Original Data 72
6.6.16. Visualize Interpolated Data 74
6.6.17. Visualize Chatwin Parameters 74
6.6.18. CXTFIT2.0 Data File Creation 75
6.6.19. Normalized Tracer Mass 76
6.6.20. Normalized Tracer Load 77
6.6.21. Standardized Data File 78
6.6.22. Screen Display 79
6.6.23. Method for Handling Large Time-Concentration Data Files 79
6.6.24. Actual Time-Concentration Data 80
7. EXAMPLE ANALYSES FROM QTRACER 82
7.1. ATKIN.D EXAMPLE OUTPUT 82
7.1.1. ATKIN.DAT Tracer-Breakthrough Curve 82
7.1.2. ATKIN.DAT Chatwin Plot 84
7.1.3. ATKIN.DAT Output File 84
7.1.4. ATKIN.DAT Normalized Tracer Concentration 84
7.1.5. ATKIN.DAT Normalized Tracer Load 84
7.1.6. ATKIN.DAT Standardized Time-Concentration Data 84
7.2. RCA.D EXAMPLE OUTPUT 84
7.2.1. RCA.DAT Tracer-Breakthrough Curve 93
7.2.2. RCA.DAT Chatwin Plot 93
7.2.3. RCA.DAT Output File 93
7.2.4. RCA.DAT Normalized Tracer Concentration 93
7.2.5. RCA.DAT Normalized Tracer Load 93
7.2.6. RCA.DAT Standardized Time-Concentration Data 93
7.3. ANALYSIS ASSESSMENT OF THE TWO EXAMPLE DATA FILES . . 103
7.3.1. Molecular Diffusion Layer Thickness 103
v
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8. DATA INTERPOLATION AND EXTRAPOLATION EFFECTS 104
8.1. COMPARISON OF ATKIN.DAT OUTPUT FILES 104
8.1.1. Interpolated ATKIN.DAT Tracer-Breakthrough Curve 104
8.1.2. Interpolated ATKIN.DAT Chatwin Plot 104
8.1.3. Extrapolated ATKIN.DAT Tracer-Breakthrough Curve 107
8.1.4. Extrapolated ATKIN.DAT Chatwin Plot 107
8.2. INTERPOLATED-EXTRAPOLATED ATKIN.DAT DATA 112
8.3. COMPARISON OF RCA.DAT OUTPUT FILES 112
8.3.1. Interpolated RCA.DAT Tracer-Breakthrough Curve 112
8.3.2. Interpolated RCA.DAT Chatwin Plot 112
8.3.3. Extrapolated RCA.DAT Tracer-Breakthrough Curve 116
8.3.4. Extrapolated RCA.DAT Chatwin Plot 116
8.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA 116
9. ASSOCIATED COMPUTER PROGRAMS 125
9.1. NDATA COMPUTER PROGRAM 125
9.1.1. NDATA Source 126
9.2. AUTOTIME COMPUTER PROGRAM 126
9.2.1. AUTOTIME Source 126
9.3. DATFILE COMPUTER PROGRAM 129
9.3.1. DATFILE Source 129
10.CONCLUSIONS 130
NOTATION 131
REFERENCES 133
VI
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List of Tables
1 Some commonly used fluorescent dye types and their dye names with their
respective Colour Index and CAS numbers 8
2 Data on some common fluorescent tracer dyes 10
3 Table representing tracer recovery data for processing 44
4 Spring discharge values and tracer recovery values at specific times 48
5 Example data files on disk 60
6 Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for ATKIN.DAT sampling station 108
7 Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for RCA.DAT sampling station 118
vn
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List of Figures
1 Contaminant leakage from a pesticide storage warehouse into a sinkhole
located in Manati, Puerto Rico. Pollutant stream is yellow color and black
sludge is buildup from past releases 3
2 A Turner Designs® Model 10AU field filter fluorometer operating in the flow-
through mode at Pearl Harbor Naval Base. Red valve is set horizontal to
allow inflow of water from the bottom connector and discharge out the top
connector 6
3 Chemical structures for selected fluorescent dyes used for water tracing. . . 9
4 Electromagnetic spectrum with enlargement of visible spectrum for tracer
dyes 11
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 14
6 Dissolutionally enlarged fissure in limestone where most flow will occur.
Precipitation of calcium carbonate in fractures appears as white and/or
brown streaks 15
7 Mixing fluorescein powder dye with water in a 5 L carboy. Fluorescein is a
brick red color when a dry powder 17
8 Injecting mixture of water and fluorescein dye into an injection well. Fluo-
rescein has as a very dark red color when concentrated as shown here, but
becomes a bright fluorescent green when diluted 18
9 Typical response curves observed laterally and at different distances down-
stream 21
10 Seven simple karst network types that describe tracer migration in karst
onduits 24
11 Definition sketch of tracer-breakthrough curves along a selected tracer
streamline 28
12 Lateral mixing and longitudinal dispersion patterns and changes in distribution 34
13 Tracer-breakthrough curve for the RCA de Caribe Superfund site 47
14 ATKIN.D header file for QTRACER processing 62
15 ATKIN.DAT sampling station data file for QTRACER processing 64
16 Tracer-breakthrough curve for the ATKIN.DAT sampling station data file. 83
17 Plot and straight-line fit of the Chatwin parameter for the ATKIN.DAT
sampling station data file 85
18 Output file for the ATKIN.DAT sampling station data file 86
19 Normalized tracer concentration data for the ATKIN.DAT sampling station
data file 90
20 Normalized tracer load data for the ATKIN.DAT sampling station data file. 91
21 Standardized time-concentration data for the ATKIN.DAT sampling station
data file 92
22 Tracer-breakthrough curve for the RCA.DAT sampling station data file. . . 94
vin
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23 Plot and straight-line fit of the Chatwin parameter for the RCA.DAT
sampling station data file 95
24 Output file for the RCA. DAT sampling station data file 96
25 Normalized tracer concentration data for the RCA.DAT sampling station
data file 100
26 Normalized tracer load data for the RCA.DAT sampling station data file. . 101
27 Standardized time-concentration data for the RCA.DAT sampling station
data file 102
28 Interpolated curve for the ATKIN.DAT sampling station data file 105
29 Interpolated data set for the Chatwin parameter for the ATKIN.DAT
sampling station data file 106
30 Extrapolated curve for the ATKIN.DAT sampling station data file 110
31 Extrapolated data set for the Chatwin parameter for the ATKIN.DAT
sampling station data file Ill
32 Interpolated and extrapolated data set for the ATKIN.DAT sampling station
data file 113
33 Interpolated and extrapolated data for the Chatwin parameter for ATKIN.DAT
sampling station data file 114
34 Interpolated curve for the RCA.DAT sampling station data file 115
35 Interpolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file 117
36 Extrapolated curve for the RCA.DAT sampling station data file 120
37 Extrapolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file 121
38 Interpolated and extrapolated data set for the RCA.DAT sampling station
data file 122
39 Interpolated and extrapolated data for the Chatwin parameter for RCA.DAT
sampling station data file 124
40 Example of a sample time-concentration file using military time for conversion!27
41 Example of a converted sample time-concentration file created by AUTOTIME128
IX
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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 generated
from tracing studies conducted in karst and fractured-rock aquifers. 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 ground-water contamination problems in karst and
fractured-rock terranes. 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.
x
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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
Gareth J. Davies, P.G.
Cambrian Ground Water Co.
109 Dixie Lane
Oak Ridge, Tenn.
Arthur N. Palmer, Ph.D.
Earth Sciences Department
209 Science Building 1
State University of New York
Oneonta, N.Y.
XI
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ABSTRACT
Tracer tests are generally regarded as being the most reliable and efficient means of
gathering subsurface hydraulic information. This is true for all types of aquifers, but
especially so for karst 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 karst sites in the United States, although it is widely
recognized that they provide a wealth of hydraulic and geometric data on subsurface
conditions. Quantitative tracer tests are regarded as more difficult and time-consuming
than qualitative tracing tests, which is a fallacy to be overcome. The benefits of quantitative
tracing far outweigh any additional expenses that are incurred.
An efficient, reliable, and easy-to-use computer program, QTRACER, designed to run
on PCs running any version of MS-DOS® or Windows®, has been developed to facilitate
tracer-breakthrough curve analysis. It solves the necessary equations from user-generated
data input files using robust integration routines and by relying on established hydraulic
models. Additional features include dynamical 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 interactive graphics routine.
Two other programs are included to facilitate the use of QTRACER. The first, NDATA,
allows the user to interpolate either their time-concentration or time-discharge data files to
fill in data gaps. The second program, AUTOTIME, allows the user to convert time-
concentration data files recorded using military time into sequential decimal time as
required by QTRACER. Files created by these two programs may be appended to the
bottom of a sampling station data file that can be read by QTRACER.
xn
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1. INTRODUCTION
Quantitative tracing studies in karst and fractured-rock aquifers are ground-water tracing
studies designed to provide detailed information regarding the subsurface-flow dynamics of
the aquifers. Such flow-dynamics information generally cannot be obtained from qualitative
ground-water tracing studies, 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., comparing 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
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 thus 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.
Additionally, most of this report will focus on tracing karst aquifers to define environ-
mental problems. Karst aquifers are commonly considered to be the types of aquifers most
in need of tracing studies. Many professional hydrologists are beginning to realize that
fractured-rock aquifers are just as much in need of tracing studies as are karst aquifers, but
in general tracing fractured-rock aquifers still receives minimal acceptance.
Many aspects of quantitative tracing studies are no different than those of qualitative
tracing studies. The main difference is the level of information desired. As a consequence,
the reader is referred to the work by Caspar (1987a,b) and Mull et al. (1988) for good
discussions regarding tracer tests in karst and fractured-rock terranes. Readers must decide
for themselves if a qualitative tracing test is all they need or if a quantitative tracing test
will better meet their needs.
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
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studies is mostly one of mathematical analysis and interpretation based on a more
comprehensive tracer-sampling program.
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
the complexity of ground-water flow in karst and fractured-rock aquifers, ground-water
monitoring can be very difficult. The main purposes of this document is to illustrate the
advantages of conducting quantitative tracing tests and to introduce the computer program,
QTRACER for tracer-breakthrough curve analysis.
QTRACER is an efficient, reliable, and easy-to-use computer program designed to run
on PCs running any version of MS-DOS® or Windows®. It was developed to facilitate
tracer-breakthrough curve analysis. QTRACER solves the necessary equations from user-
generated data input files using robust integration routines and by relying on established
hydraulic models. Additional features include dynamical 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 interactive 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 f) and the monitoring locations, but probably will not provide sufficient
evidence as to whether or how much leachate may 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., Superfund 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 complete description of
the release of the risk agent, its fate and transport in ground water and/or the epikarstic
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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 color and black sludge is buildup from
past releases.
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zone, and any associated human and ecological exposure. To this end, it is necessary
that all contaminant source areas and types of sources be identified, that 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 located in karst and fractured-rock terranes because
such studies provide much of the necessary information that otherwise could not be obtained
(Field and Nash, 1997; Field, 1997).
1.2.3. Quantitative Tracer Tests for Solute-Transport Parameter Estimation
In other instances it may be desirable to model the aquifer 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 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. comm.}.
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 et al. (1998) 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 ade-
quately addressed by qualitative tracing studies. Recharge/discharge areas are routinely
established from successful qualitative dye-tracing studies and are commonly used to estab-
lish simple classes of conduit networks (Atkinson et al., 1973; Brown, 1973; Smart, 1988a).
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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 trac-
ing studies are often considered appropriate, but this may not be true. In other instances,
however, additional details of the aquifer under investigation need to be established.
It has been suggested that quantitative tracing studies are too expensive because of (1)
required sampling at a frequency sufficient to yield reliable results and (2) there are too
many possible places the tracer might go, which would require frequent sample collection
at tens or even hundreds of locations. Neither of these two items are valid, however.
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 spectrophotometers,
adequate sampling frequencies are easily established. The only difficulty is the necessary
power options, but automatic water samplers do not draw very much power and can be
run on battery power for long periods.
Quantitative tracing studies have proved that a generalized estimate for ground-water
flow directions 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, although 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. They can also provide significantly more
and better insights into the functioning of the aquifer than can qualitative tracing studies.
Reliable estimates for tracer mass recovery, mean residence times, mean ground-water flow
velocities, longitudinal dispersion, and maximum volume of aquifer conduits allow for useful
evaluations of the hydraulic processes of dispersion, divergence, convergence, dilution, and
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Figure 2. A Turner Designs® Model 10AU field filter fluorometer operating in the flow-
through mode at Pearl Harbor Naval Base. Red valve is set horizontal to allow inflow of
water from the bottom connector and discharge out the top connector.
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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.
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2. TRACER TEST DESIGN FACTORS
Conducting quantitative tracing studies requires considerable knowledge of the tracer type
employed, because simple measurement errors may occur as a result of tracer-specific
effects, inappropriate sampling, and/or inappropriate analysis (Smart, 1988a). Smart and
Laidlaw (1977) and 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 and their dye names with their
respective Colour Index and CAS numbers.
Dye Type and
Common Name
Colour Index
Generic Name
CAS No.
Xanthenes
sodium fluorescein
eosin
Rhodamines
Rhodamine B
Rhodamine WT
Sulpho Rhodamine G
Sulpho Rhodamine B
Stilbenes
Tinopal CBS-X
Tinopal 5BM GX
Phorwite BBH Pure
Diphenyl Brilliant Flavine 7GFF
Functionalized Polycydic
Aromatic Hydrocarbons
Acid Yellow 73
Acid Red 87
518-47-8
17372-87-1
Basic Violet 10 81-88-9
Acid Red 388 37299-86-^
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
Lissamine Flavine FF
pyranine
amino G acid
Acid Yellow 7
Solvent Green 7
2391-30-2
6358-69-6
86-65-7
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RHODAMINES
XANTHENES
o-' ^f "o' "*^ o
Sodium Fluorescein
Na+
Eosln
H,C
H,C' "CH,
Sulpho Rhodamine G
Sulpho Rhodamine B
STILBENES
Tinopal CBS-X
HO'
Phorwite BBH Pure
Tinopal 5BM GX
Dlphenyl Brilliant
Flavlne 7GFF
FUNCTIONALIZED
POLYCYCLIC
AROMATIC
HYDROCARBONS
Lissamine Flavine FF
Pyranine
OH
Amino G Acid
Figure 3. Chemical structures for selected fluorescent dyes used for water tracing.
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Appropriate sampling efforts and frequencies for both tracer dye and ground-water
discharge exert considerable influence on the accuracy of quantitative dye-tracing studies.
Analytical 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
Rhodamine 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) (%) Gug 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
?
?
?
?
?
?
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 spectrofluorometric 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. pR > 10
4. pR < 4.5
Source: Behrens, 1986., Worthington, pers. comm.
10
-------
WAVELENGTH, IN NANOMETERS
380 450 500 570 590 610 760
/UV
Violet
Blue
Green
|
*o3
01
c
ro
0
i
Red i IR /
H
1
VISIBLE LIGHT
\ ^, -*•-* WAVELENGTH
30mA 0.03A 3A 30nm ^ 3^ -**" 300p 30mm 3m 300m 30km 3000kr
\
1 1
' Gamma rays
X-rays
1
ii
r
Ultraviolet
1 (UV) i
1
1
1
1
Infrared | Microwaves
(IR)
1 I
1
1 1
Radio waves
1 I
1 ' 1
Long j
electrical /
oscillations
1 1
10" 10" 10" 10" 10" 1012 10'°
FREQUENCY, IN CYCLES PER SECOND
10"
10*
10*
101
Figure 4. Electromagnetic spectrum with enlargement of visible spectrum for tracer dyes.
Modified from Wilson et al. (1986, p. 3).
11
-------
Lastly, different types of karst-conduit and fracture-flow networks will have a significant
effect on tracer mass recovery, but such knowledge 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.
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 subsurface flow 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).
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
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 1.16 g cm~3. In
this particular instance, the conversion to mass is developed from the following formula
(Mullet al., 1988, p. 61):
Vxpx% = Mm (I)
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
12
-------
where 3.785 x 10 is a conversion factor.
2. Next insert the value obtained in step 1 into Equation (1)
7.570 x 103 cm3 x 1.16 g cm"3 x 1.75 x 10"1 = 1.54 x 103 g
= 1.54 kg
Subsequent quantification calculations would then use 1.54 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, a commonly used
dye for ground-water tracing, 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 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 only be achieved 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
fairly involved.
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 karst
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.
13
-------
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.
14
-------
Figure 6. Dissolutionally enlarged fissure in limestone where most flow will occur.
Precipitation of calcium carbonate in fractures appears as white and/or brown streaks.
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 karst aquifer. Boreholes and wells, in general, are rarely
connected to the subsurface flow system.
Once injected, the tracer will move through the conduit system. Figure 6 depicts two
fairly typical karst conduits that may exist in an area. From Figure 6 it is obvious that if
the two conduits shown were at a depth of approximately 10-30 meters, it would be nearly
impossible to detect them by any known geophysical means or to intersect them by a well.
Monitoring wells are next to useless in this instance. However, a slug of tracer dye will use
these conduits to migrate to a point where detection is possible.
15
-------
2.2.1. Methods of Injection
Tracer injection can use 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
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 accomplished. The contents of the
carboy are then easily released into the injection point (Figure 8).
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 flush out the system of any debris and to lubricate the system.
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.
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 semiquantitative. Sampling must
also be of sufficient frequency so as 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
16
-------
Figure 7. Mixing fluorescein powder dye with water in a 5 L carboy. Fluorescein is a brick
red color when a dry powder.
17
-------
Figure 8. Injecting mixture of water and fluorescein dye into an injection well. Fluorescein
has as a very dark red color when concentrated as shown here, but becomes a bright
fluorescent green when diluted.
18
-------
not be observed.
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.
2.4. SAMPLING EQUIPMENT
Mull et al. (1988, pp. 38-39) recommend that samples be collected by automatic samplers
using glass sample bottles so as to minimize losses. Automatic samplers can be programmed
to collect a water sample at appropriate sampling frequencies so that even midnight 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 need to be collected if fluorescent dyes are used
as tracers. It is believed that activated charcoal will ensure dye recovery because the
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.
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 in
advance of conducting quantitative tracing studies. Preliminary qualitative tracing studies
19
-------
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, with the result being added costs (excessive number of
samples collected) or inadequate tracer mass recovery (not enough samples collected often
enough). Preliminary simple ground-water tracing studies can be useful for more difficult
and complicated tracing studies. However, as previously discussed (Section 1.3.), 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 CONDUIT
Complete lateral and vertical mixing of the tracer in a conduit or fracture(s) 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 in karst and fractured-rock aquifers does not always
ensure that adequate lateral mixing will occur in karst 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 spring and the tracer-breakthrough
curves plotted for each sampling point in the cross-section. Complete lateral mixing is
determined to have occurred when the areas under the tracer-breakthrough curves 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 BACKGROUND
All field measurements need to be corrected by subtracting background tracer concentra-
tions 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
20
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Slug
Injection
f
ILJ
0
2
o
0
I \
I V.
;/*v.
TIME *-
T
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 (Kilpatrick and Cobb, 1985, p.
3).
21
-------
them have leaks in their radiators, fluorescein-colored antifreeze is fairly ubiquitous in the
environment.
Prior to any tracing efforts, background water samples need to be collected and analyzed
for the tracer of interest. If the values obtained are low enough (e.g., few //g L"1), 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. This final value is then subtracted
from every sample of recovered tracer from subsequent tracing efforts.
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, f985;
Wilson et al., 1986). Proper instrument calibration is essential. Calibration using distilled
water is common, but use of sample water is also acceptable.
2.8. 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 nonpumping 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 profes-
sional. Weirs may need to be built, standpipes installed, flow meters utilized, and losses to
evaporation estimated (for large bodies of water). Numerous documents describing meth-
ods 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 es-
timates.
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.
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-
22
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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.
2.9. 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 dye 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.
2.9.1. 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.
2.9.2. 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 sense of a
lack of hydraulic conductivity (i.e., if the dye goes elsewhere, such results indicate there is
no flow to the sites being monitored).
2.9.3. 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
23
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' OUT
1 OUT
TYPE II
q < Q
m. =TT
OUT
" T
GROUND-WATER
STORAGE
MAIN KARST
SYSTEM
Figure 10. Seven simple karst network types that describe tracer migration in karst onduits.
Any of there 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 of the conduit is Q, tracer mass injected into the conduit is mi, and tracer
mass recovered is TT- 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
-------
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.
2.10. 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
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 defined. 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 tracer-breakthrough curves,
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 conduit-
dominated karst aquifers depends upon:
• Character of the tracer.
• Prevailing flow conditions.
• Structure of the aquifer (Smart, 1988a) and similarly for fractured-rock aquifers.
Discussion of these conditions as related to tracer-breakthrough curves has already been
addressed and also 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.
• 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 tracer-breakthrough curve (Smart, 1988a). These problems
lead to some 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?
26
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In terms of contaminant transport, answers to these questions are essential. Some
of the questions can only be answered by making best professional interpretations of the
tracer-breakthrough curve. Others may be answered by careful numerical analysis of the
tracer-breakthrough curve. 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 for karst conduits and fractures are 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, and the
second moment is used to estimate the longitudinal dispersion. However, as will be shown,
the second moment should not be relied upon for reliable estimates for dispersion.
Analysis by the method of moments is really nothing more than determining the area
under the tracer-breakthrough curve generated by plotting time verses measured tracer
concentrations (Figure ff).
The following discussion is taken from Kilpatrick and Wilson (1989, p. 3 and 4) because
it is so eloquently stated and straightforward.
The tracer-breakthrough curves along a streamline shown in Figure 11 may be described
in terms of elapsed time after a slug injection. Characteristics pertinent to the tracer-
breakthrough curve analysis are
• TL, elapsed time to the arrival of the leading edge of the tracer-breakthrough curve
at a sampling point.
• TP} elapsed time to the peak concentration Cp of the tracer-breakthrough curve at a
point.
• Tc, elapsed time to the centroid of the tracer-breakthrough curve at a point.
• Tt, 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 tracer-breakthrough curves defined upstream and downstream on the
27
-------
o
<
DC
h-
z
UJ
o
2
O
o
Site n
Site n + 1
ELAPSED TIME
7,
Figure 11. Definition sketch of tracer-breakthrough curves along a selected tracer streamline
from an instantaneous tracer injection (Kilpatrick and Wilson, 1989, p. 3).
28
-------
same streamline given by
tc = TC(B+1) - TCn (2)
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
IL = TL(n+1) ~ TLn (3)
tP = TP(n+i) ~ TPn (4)
and
tt = T*, + 1) - T*n (5)
The time Td necessary for the tracer mass to pass a sampling point in a section is
Td = Ttn - TLn (6)
As shown in Figure 11, a typical tracer cloud may travel faster in the center of the
stream than along the karst conduit or fracture walls, where it may also be more elongated.
Complete definition of the tracer-breakthrough curve to a slug injection therefore may
involve measurement at more than one point or streamline in several sections (if possible).
Usually in karst and fractured-rock aquifer tracing, 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 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 conduit or fracture wall and the fastest leading
edge time, usually observed in the center. The difference between the values of Td and TD
can be significant. It is usually assumed that TD f« Td.
The remainder of this document will not rely on Equations (2)-(6) because it is rare
for ground-water tracing studies to provide an opportunity to sample at multiple locations
along a streamline. Direct access to a cave during a tracer test is one exception, however.
3.1.1. Total Tracer Recovery
Estimation of tracer recovery for individual sampling stations is given by Equation (7)
(modified from Caspar, 1987b, p. 62)
oo
M0 = I'c(t)Q(t)dt (7)
o
29
-------
and total tracer recovery from all downgradient receptors may be estimated from Equa-
tion (8) (Caspar, 1987b, p. 63)
MT = Ł M0i (8)
i=\
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 dye recovery equation for a single sampling station was developed by
Mull et al. (f988, 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 (7)
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 percent of mass recovered, but this affords
little insight. An accuracy index given by Sukhodolov et al. (f997)
A, = *^L (9)
IVlin
provides more insight into the quality of the tracing experiment. An AI = 0 indicates a
perfect tracing experiment. A positive AI indicates more mass injected than was recovered,
while a negative Aj suggests more mass recovered than was injected. As Aj 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 so as 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.
30
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3.2.1. Mean Residence Time
Mean tracer residence time is the length of time required for the centroid (gravity mass) of
the tracer mass 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 mass in the tracer-breakthrough curve, but the more ground-water flow conforms to
Pick's law the less obvious the difference between the centroid and the peak concentration.
Mean tracer residence time is estimated from Equation (10) (modified from Caspar,
1987a, p. 93)
oo
jtC(t}Q(t}dt
f=^ (10)
jC(t}Q(t}dt
o
with a standard deviation given by Equation (11) (modified from Mull et al., 1988, p. 58)
1/2
o
C(t}Q(i)dt
fC(t)Q(t)dt
(11)
Equations (10) and (11) 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 be confused with Equation (10).
A simplified example calculation is performed later in this report.
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
considered more valuable than the tracer residence time, although it may have little
theoretical meaning. Initial tracer breakthrough provides ground-water managers with an
indication of the length of time a contaminant will take to be detected at a downgradient
31
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receptor. However, because of the effects of longitudinal dispersion, and inadequate
sensitivity of current analytical methods at extremely low concentrations renders this
situation meaningless.
3.2.2. Mean Tracer Velocity
Mean tracer velocity is a measure of the flow rate of the centroid of the tracer mass and is
given by Equation (12) (modified from Caspar, 1987b, p. 66)
oo
f^C(t)Q(t)dt
(12)
fC(t)Q(t)dt
o
with a standard deviation given by Equation (13)
oo
fC(t)Q(t)dt
0
1/2
(13)
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 karst conduits is unrealistic and should be corrected for sinuosity (Field
and Nash, 1997; Worthington, 1991, pp. 85-91) by
xs = 1.5x (14)
Estimation of the mean tracer velocity is an appropriate measure of the rate at which
the bulk of a nonreactive pollutant mass will migrate in a karst conduit. It also provides a
useful insight into the flow hydraulics of the conduit. Equations (12) and (13) also assume
that tracer residence time will vary from zero to instantaneous exit of the tracer mass from
the aquifer system.
Apparent tracer velocity is a measure of the rate of tracer migration as a function
of initial tracer breakthrough; it is obtained by dividing the distance traversed by the
tracer cloud by the time of first arrival of the tracer dye. Mean tracer velocity provides
substantially improved insight into aquifer functioning over apparent velocity.
Mull et al. (1988, p. 58) provide a simple equation for calculating mean tracer velocity.
Their equation is also not reproduced here to avoid confusion. An example of its use is
presented later in this report.
32
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3.2.3. Longitudinal Dispersion
Longitudinal dispersion in karst conduits is similar to dispersion in closed conduits and open
channels because conduit flow ranges from slow and laminar to rapid and turbulent in karst
aquifers that may exhibit either closed-conduit flow or open-channel flow characteristics and
similarly for fractured-rock aquifers. The longitudinal dispersion coefficient is a measure
of the rate at which a concentrated dye mass spreads out along the flow path (Mull et
al., 1988, p. 59). It is defined as the temporal rate of change of the variance of the tracer
cloud (Fisher, 1968). It is relevant to the analysis of karst conduits because it provides an
indication of the amount of possible spreading of a pollutant mass in terms of increasing
persistence and decreasing concentration over time.
Hydrodynamic dispersion, typical of porous media aquifers, may be regarded as not
relevant to flow within karst conduits and fractures. Numerous studies on longitudinal
dispersion have been conducted over the past few decades (Chatwin, 1971; Sullivan, 1971;
Day, 1975; Nordin and Troutman, 1980; Jobson, 1987; Reichert and Wanner, 1991), mostly
with respect to open-channel flow. Longitudinal and lateral dispersion for a slug release of
tracer or pollutant in a karst conduit (and less so for a fracture) will generally appear as
shown in Figure 12. In Figure 12, the responses to a slug of injected tracer are shown with
distance downstream along selected imaginary streamlines.
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 will in effect be a measure of
the movement of an element of fluid in the stream and its dispersion characteristics. 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 is most commonly estimated using the second moment. Dis-
persion is obtained using Equation (15) (Maloszewski and Zuber, 1992)
DL - \i d5)
v xs
Equation (15) assumes that Fick's law is always applicable; that is, there is no anomalous
behavior. In actuality immobile zones (dead zones) are common, which cause a long tail
33
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SLUG INJECTION
OFTRACER
Lateral mixing
and longitudinal
dispersion
Vertical and lateral mixing
longitudinal dispersion
(vertical not shown)
IV
LONG DISTANCE
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).
34
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to the breakthrough curve and invalidates Pick's law.
Chatwin (1971) developed a method for determining longitudinal dispersion that applies
to both closed-conduit flow and open-channel flow. Longitudinal dispersion is given by
Equation (16) (Chatwin, 1971) as
An M1/2
5 - ^p] (16)
The constant of proportionality Ap can be estimated from (Day, 1975)
(17)
The first term on the right-hand side of Equation (16) is the y intercept; the second
term on the right-hand side of Equation (16) is the gradient of the line. Either term on the
right-hand side allows for solution for the longitudinal dispersion coefficient (Ł>L) provided
that a plot of the left-hand side of Equation (16) against early-time data reasonably falls
as a straight line (Day, 1975). The late time data will depart from the straight line due to
non-Fickian dispersion characteristics (e.g., dead zones).
Mull et al. (1988, pp. 59-60) developed two equations designed to estimate the
longitudinal 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.
3.2.4. Tracer Dilution
Estimation of tracer dilution in a karst conduit is desirable so that effective dilution of
pollutant releases may also be estimated. Given the generally nonconservative behavior of
fluorescent tracer dyes and of most pollutants in aquifers 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
35
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one-dimensional, suggests that a uniform Gaussian distribution of the tracer concentration
will occur in the direction of flow as shown in Equation (9) (Dobbins, 1963)
•• exp
(Xs-Vt}^
(18)
Mass Min of the injected tracer is assumed to be small relative to the mass flux rate of
the ground water so, in theory, the tracer-breakthrough curve should approach a Gaussian
shape. In fact the tracer-recovery curve is always skewed to the right because of the effects
of transverse dispersion (ignored in Equation [18]), 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 tracer-breakthrough curve (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
Mm
PL PL
Steady-state concentration CPL is a function of tracer recovery from a single tracer
injection and is given as
j=tb+nA.t
CPL= E Q (20)
3=tb
where Cj is the tracer concentration at the resurgence at time j for a single instantaneous
tracer injection. Time if, 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
a karst aquifer is very difficult. Smart (1985) points out that as the tracer is not conserved
in the aquifer, then 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.
36
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3.3. KARST CONDUIT AND FRACTURED-ROCK GEOMETRIES
Karst conduit and fracture geometries are estimated by evaluating discharge with respect
to mean residence time. This is accomplished for either the continuous or for the discrete
situation.
3.3.1. Aquifer Volume
Tracer mass recovery at a spring where discharge was measured during each tracer sampling
event allows for a rough estimate of the maximum volume of the conduit or fracture
traversed by the tracer cloud by use of Equation (21) (Atkinson et al., 1973)
t
V=JQdt (21)
J
o
If a single discharge value is used as a mean spring discharge then the karst-conduit volume
may be estimated by
V = Qf (22)
and a total maximum volume estimate based on the sum of each individual conduit or
fracture traversed by the tracer cloud may be determined from Equation (23)
VT = f^Vi (23)
i=l
It should be noted that aquifer volume calculations will be only a crude approximation at
best. Summing the volumes of individual conduits or fractures to achieve a total maximum
volume estimate should not be expected to produce accurate results, but the sum of the
individual conduits or fractures does provide some indication of the aquifer volume occupied
by conduits or fractures. However, Equations (21) and (22) 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 conduit-dominated karst aquifers. 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
37
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inflow and outflow that may lead to additional insights into the aquifer. For example,
inflow/outflow evaluations coupled with comprehensive tracer breakthrough curve analyses
furnish a means for assessing the type of karst aquifer under investigation (Atkinson et al.,
1973).
3.3.2. 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 (21) or (22) the
cross-sectional area may be estimated from
A = ^- (24)
xs
which is based on a sinuous distance and hence is less than the straight-line distance would
suggest.
3.3.3. Karst Conduit Diameter
By assuming a cylindrical karst conduit it is possible to estimate a karst conduit diameter
from a tracer-breakthrough curve. Because the system volume has been estimated the karst
conduit diameter may be obtained by
DC = 2^ (25)
Obviously Dc/2 can be used to estimate the karst conduit radius which is typically used
in many modeling endeavors.
3.3.4. Karst Conduit Hydraulic Depth
If open channel flow is assumed to occur in the karst conduit then a hydraulic depth may
be estimated by
DH = ^ (26)
L>C
which is a reasonable approximation.
3.3.5. Karst Conduit Surface Area
If the karst conduit is assumed to conform to a cylinder and conforms to Karst Network
Types I, II, VI, and VII, then it is possible to obtain an initial estimate of the conduit
38
-------
surface area. A karst conduit surface area estimate is obtained by
As =
s
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 karst conduit of interest cannot be
directly entered for physical measurements of roughness to be taken.
A reasonable estimate for the roughness factor may be obtained by
(28)
The surface irregularities relief e, taken as 1.0 m, is considered reasonably representative
of typical karst conduit walls. There is some support for this assumption from natural river
beds (Chow, 1959, p. 196). The laminar flow sublayer 6 is divided by 103 in Equation (28)
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 karst conduit he was
investigating.
3.3.6. Tracer Sorption Estimation
Sorption to karst conduit walls can be estimated by considering a laboratory column as
analogous to flow through a karst conduit. Although far from perfect, it can provide useful
information for comparison with more theoretically based models.
Karst conduit sorption is estimated by
_ (C0 - Cf}V
and for multidischarge karst aquifers (Karst Network Types III and IV)
Ka = (C°c^Vl (30)
If a multidischarge karst aquifer is of interest it is essential to note that any results
obtained by Equation (29) will be erroneous. Only those results obtained by Equation (30)
should be considered relevant.
39
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3.4. 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
karst conduits or fracture 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 karst 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.
3.4.1. 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
(~W^^x~ = ~-^ei^) t° the effectiveness of mass transport by either dispersion or
diffusion (^-r) (Schiesser and Silebi, 1997, p. 372). Peclet numbers below 0.4 indicate
oxs
diffusion control; 0.4 — 6.0 suggests that diffusion and advection are in transition and thus
approximately equal to each other; and > 6.0 indicates advection control (Fetter, 1992,
pp. 54-55). In most 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
Pe = ^ (31)
It is necessary to note that estimation of the Peclet number by Equation (31) will
probably be too low. Substitution of the peak flow velocity vp could be considered, but
most likely would result in overestimating the Peclet number.
3.4.2. 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.
40
-------
Reynolds Number The resistance of flow depends entirely upon the geometry and
magnitude of the quantity Ł^, where p represents fluid density, d conduit diameter, and
v dynamic viscosity. The Reynolds number 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 = ^Ł (32)
Estimation of the Reynolds number by Equation (32) 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 (V/xs}1/2 is excessively large. Therefore, calculation
of Reynolds number by Equation (14) should be regarded as an upper limit. However, the
quantity, V/xs, 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 conduit) may be calculated. For
laminar flow in a karst conduit K is obtained by
K = ° (33)
8JL V '
and for laminar flow in a fracture K is obtained by
It should be noted that a hydraulic conductivity estimated by either Equation (33) or (34)
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.
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
(35)
-------
Estimation of the Froude number by Equation (35) 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 karst conduits may exhibit either open-channel flow, closed-conduit
flow, or both flow types depending on stage. An estimated Froude number for karst conduits
exhibiting closed-conduit flow is not appropriate. Also, as presented the calculation for the
Froude number assumes that the cross-sectional area of the karst conduit divided by the
diameter of the karst conduit is equal to the mean hydraulic depth, which may not always
be true.
3.5. BOUNDARY-LAYER EFFECTS
While not generally considered in tracing studies, boundary-layer effects can substantially
impact the study results. In most instances, karst conduit and fracture 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.
3.5.1. Friction Factor Estimation
When flow is believed to be laminar, a friction factor may be estimated by (White, 1988,
p. 163)
and for when flow is turbulent, a friction factor may be estimated by (White, 1988, p. 163)
1 Dr
= 2 log— + 1.14 (37)
Ł
where the relief of surface irregularities e is a controlling factor and depends on the nature
of the conduit through which flow is occurring.
3.5.2. Laminar Flow Sublayer
It is well documented by empirical studies that turbulent flow occurs as a core that is
surrounded by a laminar flow sublayer. The thickness of the laminar flow sublayer is
42
-------
dependent on the degree of conduit wall roughness. If a typically very rough karst conduit
is assumed, then the laminar flow sublayer may be estimated by (White, 1988, p. 163)
6 32-8 mi
( '
which is an important parameter for assessing the extent of solute sorption to conduit walls
and the possibility of matrix diffusion effects. Matrix diffusion can only occur from the
laminar flow sublayer.
3.5.3. Hydraulic Head Loss
When flow is laminar, the hydraulic head loss along the conduit can be estimated by
(modified from White, 1988, p. 162)
/,, = (39)
pgr2
and for when flow is turbulent, the hydraulic head loss along the conduit may be estimated
by (White, 1988, p. 163)
hL = l^ (40)
40r
which emphasizes the influence of friction on head loss.
3.5.4. Shear Velocity
The shear velocity for flow through a karst conduit is created by boundary-layer effects
produced by the conduit walls. Therefore it might be expected that the shear velocity will
be somewhat less than the flow velocity in the center of the conduit.
Estimation of the shear velocity is obtained by
"• = Pw- <41>
V DC xs
It will be noted that flow velocities produce by Equation (41) will always be less than
those produced by Equation (12). This makes sense in that the karst conduit walls should
impart some negative influence on the flow velocity.
43
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4. EXAMPLE CALCULATIONS FOR TOTAL TRACER RECOVERY
To determine the total recovery of tracer injected into an aquifer, the following 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 shown.
f. Plot the Concentration
Subtract background tracer concentration. Plot the concentration of tracer recovered (e.g.,
mg L"1) verses 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 spring or well where discharge is variable over the
time of tracer recovery, then plot discharge in appropriate units (e.g., m3 s"1) verses time
(hours) also. Again, time should be plotted on the x axis. If discharge is constant, then
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 (7), which must be integrated numerically. This is
done using a simple summation algorithm. This is most easily accomplished by setting up
a table which facilitates the necessary calculations (Table 3).
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 (10), will yield the mean residence
time. This is most easily accomplished by using the table created in step 3 above, which
facilitates the necessary calculations (Table 3).
Table 3. Table representing tracer recovery data for processing.
t Q C C xQ txC xQ
(T) (L3 T-1) (M L-3) (M T-1) (M)
Time is recorded in equally spaced increments. If discharge was constant during the
44
-------
period of tracer recovery, then the Q column of the table has a constant value as well. The
C Q column is obtained from the product of the second and third column values. The t C Q
column is obtained from the product of the C Q column with the t column and by applying
appropriate conversions as necessary (e.g., hours vs. seconds).
5. Calculate Tracer Mass Recovery
When the table of values is complete, Equation (7) can be solved by summing column 4
and multiplying by a time conversion to get units of mass only. Hence, the solution to
Equation (7) is acquired in a simplified manner by
00 n n
M0= f Q(t)C(t)dt « Ł Q^C^&t^ « tc ^(Qid) (42)
0 i=l i=l
where tc is any necessary time conversion factor to allow for units of mass.
6. Calculate Mean Tracer Residence Time
Mean tracer residence time f is found by solving Equation (10). Equation (10) is solved by
the same method that Equation (7) is solved; by simplified summation of the data. From
Table 3 sum the values in column five and multiply this value 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. Repeat for Subsequent Sampling Stations
Repeat the above steps for all wells and/or springs in which the tracer was recovered.
9. 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.
10. 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 by 100.
45
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4.1. SIMPLIFIED EXAMPLE CALCULATION
Four hundred and thirty-five kilograms of sodium chloride, NaCl, (264 kg Cl~) (RCA, 1992)
were injected into the north coast karst aquifer at the RCA del Caribe (Barceloneta, Puerto
Rico) Superfund site for a tracing study. Recovery was at an observation well 120 feet from
the injection well that was pumped at a constant rate of 6.0 gpm. Figure 13 displays the
tracer-breakthrough curve for the RCA del Caribe Superfund site and 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 (7) or more simply by Equation (42).
Equation (42) 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 4 of Table 4 lists the products of columns 2 and 3 and is
summed at the end.
The summed results of column 4 of Table 4 must be multiplied by 3600 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 (42) is not as precise
as Equation (7). However, results obtained by Equation (42) 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 (10) or its equivalent discrete form.
This is accomplished by multiplying column 4 by column 1 in Table 4 and recording the
results in column 5. Summing column 5 of Table 4 and multiplying by 3600 seconds will
yield results in units of mass-time
1.55 x 107 mg) (3.60 x 103 s) = 5.58 x 1010mg s
46
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RCA.DAT
400
350
300
250
o
'- 200
o
9 150
o
c
o
o
100
50
Data =
25
6 8 10 12 14 16 18
Tfme from Injection (hours)
20
22
24
Figure 13. Tracer-breakthrough curve for the RCA de Caribe Superfund site.
47
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Table 4. Spring discharge values and tracer recovery values at specific times.
t
(h)
0.00 x 10°
1.00 x 10°
2.00 x 10°
3.00 x 10°
4.00 x 10°
5.00 x 10°
6.00 x 10°
7.00 x 10°
8.00 x 10°
9.00 x 10°
10.00 x 10°
11.00 x 10°
12.00 x 10°
13.00 x 10°
14.00 x 10°
15.00 x 10°
16.00 x 10°
17.00 x 10°
18.00 x 10°
19.00 x 10°
20.00 x 10°
21.00 x 10°
22.00 x 10°
23.00 x 10°
24.00 x 10°
Q
(m3 s-1)
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 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 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 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 10~4
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 104
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
^n
^i=l
CxQ
(mg s-1)
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
0.00 x 10°
1.90 x 10°
9.48 x 101
1.44 x 102
7.58 x 101
4.74 x 101
2.84 x 101
2.09 x 101
1.52 x 101
9.48 x 10°
7.58 x 10°
5.69 x 10°
5.31 x 10°
4.93 x 10°
4.55 x 10°
4.17 x 10°
3.79 x 10°
3.41 x 10°
3.03 x 10°
2.65 x 10°
2.27x 10°
4.85 x 102
t x C x Q
(mg)
0.00 x 104
0.00 x 106
0.00 x 106
0.00 x 106
0.00 x 106
3.42 x 106
2.05 x 105
3.63 x 105
2.18 x 105
1.54 x 105
1.02 x 105
8.28 x 105
6.57 x 105
4.44 x 105
3.82 x 105
3.07 x 105
3.06 x 105
3.02 x 105
2.95 x 105
2.85 x 105
2.73 x 105
2.58 x 105
2.40 x 105
2.19 x 105
1.96 x 105
1.55 x 107
(source: RCA, 1992)
48
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and dividing by the mass recovered (1.75 kg) will yield the mean residence time of the
tracer in units of time.
5-58 >< 1Q1° m§ s _ 3 19 x 104 8
1.75 xlO6 mg ~ 3'19xl° s
= 8.86 x 10° h
Apparently, it took less than 9 hours for the Cl~ tracer to reach the recovery well.
4.1.3. Mean Tracer Velocity Example
Mean tracer velocity is obtained from Equation (12) or, more simply, by dividing the
distance to the sampling station by the time of travel
3.66 x 101 m 0 !
— = 4.13 x 10 m h 1
8.86 x 10° h
= 1.15 x 10~3 m s'1
which may then 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.
4.1.4. Longitudinal Dispersion Example
Longitudinal dispersion is most accurately estimated by the Chatwin method in Equa-
tion (16), which can be tedious.
4.1.5. System Volume
The flow system volume may be estimated using Equation (22). 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, 3.19 x 104 s, to obtain the system volume.
3.79 x 10~4 m s'1} (3.19 x 104 s) = 1.21 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.
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5. QTRACER 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 disk 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 datapoints. 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 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 tracer-breakthrough curves 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.
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5.2.2. Piecewise Cubic Hermite
The second method relies on the cubic Hermite function to find the single most reason-
able stopping datapoint for extrapolation. This is achieved by using the entire tracer-
breakthrough curve 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, but 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 developed by projecting data for the decreasing
limb of the tracer-breakthrough curve 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 will be 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
were decreasing, then the extrapolated discharge data will increase to one-half the original
decreasing value. If the measured discharge data were 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.
51
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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
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 (R2}, the correlation
coefficient (r), the probability of the fit, and Fisher's z statistic. R2 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 Equation (15). Using Equation (15) 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 QTRACER and may
be analyzed according to the method described by Mull et al. (1988). The discussion by
Mull et al. is very comprehensive and as such is not repeated here. Another reason for
not repeating the Mull et al. discussion here is because of the probability that in most
instances, the ground-water tracing site will (1) have multiple discharge locations, many of
which may not be continuously monitored for tracer; and (2) will require more quantitative
tracing experiments than can be reasonably undertaken.
5.5. RANGE OF POSSIBILITIES OF QTRACER
QTRACER 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).
52
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This may sound strange, but the statement is true because the basic equations for mass
balance are not dependent on geological conditions.
QTRACER was designed to be used in karst systems primarily, but it will handle
fractured-rock systems reasonably well when told to do so in the sampling station data
file. However, it may be used to evaluate tracer-breakthrough curves 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 that only some of the output data will make sense.
For example, it would be considered ridiculous to accept the tube diameter output for
a tracer test conducted in porous media. However, by exercising some basic judgment,
QTRACER can be effectively used in a variety of environments.
5.6. COMPUTER GRAPHICS
A high-quality color graphics algorithm (Kahaner and Anderson, 1990) that includes useful
interactive capabilities is included in QTRACER. It 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 a dot-matrix printer is
possible.
5.6.1. Features of the Interactive Graphics Loop
QTRACER takes advantage of a very powerful and useful interactive graphics loop. It is
used when a graphics screen is displayed and the user would like to customize the display
as desired. The following discussion comes from the user's manual to "Volksgrapher" —
Volksgrapher: A FORTRAN Plotting Package User's Guide, Version 3.0 (Kahaner and
Anderson, 1990).
Zooming Type z (for "zoom") to enter the zoom mode. Four "zoom corners" will appear
for the graph on the screen. The zoom box corners appear on the "current" graph. Use
the cursor control keys (arrow keys) to translate the zoom box. To move the zoom box in
finer increments, type f; to go back to coarse movement, type c.
This translates the zoom box; i.e., "whole-moving" mode. Type s to enter "side-
moving" mode. Typing a cursor control key causes one side of the box to move outward.
53
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To move a side INWARD, type a SHIFTED cursor control key: e.g., a shifted up arrow
moves the top edge down. To get back to "whole-moving" mode, type w.
Once the zoom box has been satisfactorily specified, type z again to accomplish the
zoom. Type r to "restore" or "zoom out" to the previous graph (i.e., the one prior to the
last zoom). You may zoom in or out several levels.
Press the Esc key to remove the zoom box without zooming and return to the normal
interactive mode.
Note that zooming will change the mode of all text associated with the graph in mode
2 ("sticking to a point") to mode 1 ("staying a distance from the lower left corner").
Rearranging Graphs Typing a (for "arrange") causes four corners to momentarily flash
around the "current" graph and places the graphics package into the arrange mode. The
space bar, cursor keys, shift keys, and f, c, w, and s work as in zoom mode. The current
graph will be erased, its new position and shape being indicated only by the corners. To
draw the graph in its new position, type d. This shifts the graphics package back into
"normal" mode.
Typing x redraws the entire screen. This is useful when numerous changes have resulted
in a cluttered screen. Press Esc to leave the arrange mode without changing the graph.
Moving Legends Type 1 (for "legend") to enter the legend moving mode. Corners
will briefly flash around the "current" legend. Select legend using the space bar or the
backspace key and move the legend around as in the zoom mode. The size of the legend
box cannot be changed. Type d to draw the currently selected legend, x to clean up the
screen, or v to toggle the current legend between visible and invisible. Press Esc to leave
the legend mode without changing any legends.
Editing a Graph's Axes Type e (for "edit") to change the min/max values on a
graph's axes, to switch between linear and logarithmic axes, or to number/unnumber axes.
Move the pointer < using the cursor keys to select items to change and type c to change
them. Exit edit mode with Esc, which ignores the changes, or type u (for "update") to
redraw the screen incorporating the changes.
Altering and Adding Text Text strings can be manipulated interactively. New text
can be added, even if none of the necessary routines were originally called in the program.
54
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Type t to enter text mode; a star will flash at the first letter of the "current" text string.
Use the spacebar or backspace to select a different string. Translate it using the cursor
control keys, or rotate it right (clockwise) with r or left (counterclockwise) with 1. The size
of the characters can also be changed; they can be made larger by typing "+" and smaller
by typing "-." Type > to increase the text's color code and < to decrease it. Typing ! will
delete the current text line. To edit the current line, type e; you will be prompted for the
new contents.
The fineness of translation, rotation and resizing of text can be changed. To go to "fine"
movement, type f; for "ultrafine," type u; to return to "coarse," type c.
To change a current string's mode to "keep a distance" mode, type d. To change it to
"stick to a point" mode, type p. To center the current string horizontally, and change its
mode to horizontal centering, type h. To center the current string vertically, and change
its mode to vertical centering, type v. To change a string's mode between normal (left)
vertical centering and right vertical centering or normal horizontal (bottom) centering and
top horizontal centering, type @.
To display the current line's color code, number, and positioning mode, type s (for
"status"). Type s again to stop displaying status.
To make the current centered line into an axis label that will act like one entered via
the program, type a. The current line will then be "owned" by the current graph. The
label it becomes depends on its positioning mode: a top-centered line becomes a title, and
so forth. If the current line is not centered, it will not become a label.
To add new text, type n (for "new"). A prompt will appear, asking for the new line.
Entry of the new text line is terminated by pressing the enter key. The new line will have
the same size, color, and rotation as the current one and be positioned to line up as the
next line "under" it. The new line will have the same positioning mode as the current one,
unless the current one is centered. In that case, the new line will have "keep a distance"
mode. The new line will be owned by the current graph, NOT the current line's owner.
The new line becomes the current line, so that blocks of text may be added easily. Note
that each page (screen) cannot have more than 50 lines of text. The maximum number of
characters in a text string is 70.
To draw a Greek character, precede the letter by I. Thus I a will draw an a. To
subscript or superscript a character, precede it with _ or ~. Thus H2O is the formula for
water. Use ""to get super-superscript, like ex (represents e to the x squared). To generate
a Greek subscript, such as a, use _| a. To generate I, _ , or ~ precede it with I as in I I sin
55
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(x) I I, which will display the absolute value of sin(x) as | sin(x)|.
Some special characters of occasional use (e.g., integral, square root, or arrow) are also
available. To access them first look up their THREE-digit ASCII code, then enter the code
preceded by a \. For example \202 will produce an integral symbol. To get a backslash,
use \220.
Type x to clean up the screen and return to normal mode. Type Esc to leave text mode
without redrawing the screen.
Printing The graphics package can produce an output file for PostScript-quality output
or dot matrix (Epson-compatible printer). To print a graphics screen to an Epson printer,
hit d; the screen will be "dumped" to the printer. The default format for high-quality
printing is PostScript. This format can be changed in the interactive loop by typing h,
which then prompts for a device name (those available are listed below):
1. "tek" = Tektronix
2. "hpg" = HPGL-Plotter
3. "pos" = Postscript
4. "qms" = QMS-Lasergrafix
To print the screen, type p and provide a filename. This file can be sent to an appropriate
printer. To send the output directly to a printer on a PC, give the name of the printer port
(e.g., Iptl) instead of a file name.
Additionally, if the user has requested that the screen display a plot (either data or line
or both) and that a PostScript file be generated, a plot file will be created upon exiting
the plot screen as occurs when hitting the ENTER key.
The Cursor The graphics package has a graphics cursor for finding the position of items
on graphs and extracting those values into your program. Type s to show the cursor. Then
type w to display the cursor position in coordinates of the current graph.
Leaving the Interactive Loop Leave the interactive loop by pressing the ENTER key.
QTRACER will continue after resetting the screen to text mode.
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5.7. QTRACER SOURCE
The FORTRAN source for QTRACER is included on the disk. It is a very large program
that had to be split into pieces to allow its use on a PC. It is also not recommended that
for a user to attempt to follow the logic or to modify the program. Questions regarding
the program's functioning can be addressed to the author.
In addition, the graphics routine developed at the National Institute of Standards and
Technology includes one C source and one ASSEMBLY source. The ASSEMBLY source is
very complicated and not amenable to general manipulation.
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6. USING QTRACER
The QTRACER program for tracer-breakthrough curve analysis is an easy-to-use computer
package that requires little more of the user than to hit ENTER when requested. However,
QTRACER requires that data input files be created first for processing. The use of data
input files for processing, rather than allowing the user to respond to questions posed by
the program, facilitates more rapid data processing while minimizing the opportunities for
inputting incorrect data.
6.1. QTRACER PROGRAM AND DATA FILES
Before running the program, you should create a subdirectory on your hard disk for data
storage and to protect the original disk. To begin with, please perform the following:
1. At the C:\> prompt, type "MKDIR QTRACER" (without the quotes — whenever quotes
appear in this section type the requested information without the quotes).
2. Next copy the executable and data files from your disk to your hard disk. For example,
you might type (if E is your disk drive):
"COPY E:\*.EXE C:\QTRACER\*.EXE"
"COPY E:\*.DAT C:\QTRACER\*.D"
"COPY E:\*.D C:\QTRACER\*.DAT"
3. Put your disk in a safe location.
6.2. QTRACER EXECUTION
QTRACER is very easy to use. Once the appropriate data files are created (which are
nearly self-explanatory) QTRACER, for the most part, requires nothing more than hitting
the ENTER (RETURN) key as requested.
1. At the C:\> prompt, type "CD\QTRACER" without the quotes. You will then see a
new prompt; C: \QTRACER>.
2. You may now type "QTRACER" to run the program by just responding to the requested
information and assuming that you have also copied the necessary data files or created
your own. You may want to type "QTRACER filename" such as "QTRACER ATKIN.D",
which will automatically load and begin running the Atkinson data set described in
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the journal article (Field and Nash, 1997). You may do the same with the Mull et al.
(1988) data by typing "QTRACER MULL.D" which will load the appropriate data files
and begin processing.
3. At this point, you will be prompted by the program to enter the file to be evaluated
(unless you specified a file when starting the program). One advantage of a
subdirectory on your hard disk is that you will not be required to provide an obscure
path for all subfiles; the program will find them automatically because they are all
at the same location as the executable file. If the data files are in different locations
from QTRACER, you will need to provide the correct path to the *.D and *.DAT
files.
Additional information will be presented in Section 7. regarding QTRACER execution.
However, the really important information (files creation) is listed in this section.
6.3. QTRACER FUNCTIONING
QTRACER runs by processing two types of files at once. The first file called is a header
file, which identifies the amount of tracer injected into the aquifer 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 include all necessary information to
allow the program to run. They also allow the user to run the program independently of
the user (batch mode) or to pause processing to allow the user to observe numerical output
and the opportunity to display high-quality graphics. What follows are seven sets of data
files that may be used to test the QTRACER Program. If the user so desires, the data files
may be reviewed directly, as they are simple ASCII files.
Run QTRACER 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) [ATKIN.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. Hopefully your results will compare favorably with those
produced by this program.
6.4. SAMPLE FILES ON DISK
The following five "header" data files (*.D) and their respective sample station data files
(*.DAT) are included on the disk (Table 5). Each header file must have at least one
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corresponding sample station data file that is referenced by the header file. However, the
number of sample station data files that correspond to a header file is basically unlimited
except as by your computer capabilities.
Note: There is no specific requirement that the data files end with the extensions "D" or
"DAT" (e.g., ATKIN.D; ATKIN.DAT). The "D" and "DAT" extensions are just the convention
used in this manual and on the example data file.
Table 5. Example data files on disk.
Header Data Sample Station
File Data File
ATKIN.D ATKIN.DAT
MULL.D MULL.DAT
LOST.D LOST.DAT
RCA.D RCA.DAT
TOPLITA.D TOPLITA.DAT
GAR2.D GAR2.DAT
MUUL.D MUUL.DAT
The data files listed in Table 5 are described as follows.
1. ATKIN.D and ATKIN.DAT are hypothetical data sets provided Dr. Timothy Atkinson
(Atkinson, 1987) for educating a group of students (of which this author was one) on
the proper methodology for analyzing and interpreting tracer-breakthrough curves.
Analysis of these data sets using QTRACER is presented in considerable detail in
Field and Nash (1997).
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 tracer-breakthrough curve 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 which QTRACER allows for and corrects.
Analysis of these data sets using QTRACER is presented in considerable detail in
Field and Nash (1997).
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3. LOST.D and LOST.DAT are data sets listing the results of a tracer-breakthrough curve
generated by the senior author (and other students) when Dr. Timothy Atkin-
son was instructing proper methodology for conducting tracer tests and analyz-
ing/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 QTRACER. 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 regard-
ing the simple calculations and other factors illustrated in Section 4.1. 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, f987a, p. 58), the intent
of which is to demonstrate that an "ideal" tracer-breakthrough curve is not necessary
for QTRACER to function properly. The Toplita data sets are also excellent for
demonstrating QTRACER's data extrapolation capabilities because of the shape of
the curve and the position of the last measured datapoint.
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 9.f. for a description of NDATA). A deliberately "huge"
data set was constructed to demonstrate QTRACER'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 QTRACER's capabilities of han-
dling "huge" data sets, but with a "variable" discharge (GAR2.DAT has a constant
discharge).
NOTE: JUST EDIT ONE OF THE *.D FILES AND SAVE AS A NEW FILE WITH
A NEW FILE NAME. NEXT EDIT ONE OF THE *.DAT FILES AS OFTEN AS
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NECESSARY FOR EACH SAMPLING STATION TO BE ANALYZED AND SAVE
EACH AS A NEW FILE WITH AN APPROPRIATELY CHOSEN NEW FILE NAME.
6.5. DESCRIPTION OF *.D FILES
All descriptions in this section use ATKIN.D as an example input. An example header file,
ATKIN.D, appears in Figure 14.
A *.D file (e.g., ATKIN .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. 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 the next line is where the user will then enter the appropriate response which
will be read by QTRACER. 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 aquifer. For
the ATKIN.D example 450 is listed by the user because this was the hypothetical tracer
quantity injected into the aquifer.
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 the parentheses represent the valid units allowed by QTRACER.
QUANTITY OF TRACER INJECTED
450
UNITS OF MEASURE (1-lbs, 2-kg, 3-g, 4-mg)
3
SAMPLING DATA FILES LIST
ATKIN.DAT
Figure 14. ATKIN.D header file for QTRACER processing.
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The user should respond with the appropriate units. For the ATKIN.D example a number
3 is listed to indicate grams (g) as the unit of measure.
Lastly, the program asks for the name of all subfiles to be called by QTRACER 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., ATKIN.DAT). Thus the subfiles correspond to
each sampling station at which tracer was recovered.
SAMPLING DATA FILES LIST
ATKIN.DAT
For the ATKIN.D example only one station is listed as having recovered tracer, ATKIN.DAT,
because that is the only station at which this hypothetical trace recovered the tracer.
If, however, 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 ATKIN.D tracer test might be listed as:
ATKIN.l
ATKIN.2
ATKIN.3
ATKIN.23
Any other appropriate names such as the names of various monitoring wells or monitored
springs are acceptable. The only requirement for the user is that the user be able
to recognize the names some time after QTRACER has been run as it will be most
advantageous to run QTRACER in the batch mode for large data sets.
6.6. DESCRIPTION OF *.DAT FILES
All descriptions in this section use ATKIN.DAT as example input except as otherwise listed.
An example sampling station data file ATKIN.DAT appears in Figure 15.
The *.DAT files (e.g., ATKIN.DAT) are fairly long and detailed. They must be detailed
so that the program can properly process all the site information necessary.
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. So the first item for a *.DAT file
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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]
0
DISCHARGE IN DATA FILE OR CONSTANT: (l=data file, 2=constant)
1
DISCHARGE: UNITS (l=m"3/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"3/sec) [VALUE]
4
ESTIMATE AQUIFER 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=1.5]
1 1.5
CONDUIT OR FRACTURE(S) FLOW,POROSITY (l=conduit, 0=fracture) [VALUE, def=1.0]
1
IF FRACTURE(S) FLOW: UNITS,HEIGHT (l=m, 2=ft, 0=null) [VALUE]
0
NAME OF THE FILE OF INPUT/OUTPUT VALUES
Al.OUT
INTERPOLATE DATA (l=yes, 0=no) [NUMBER OF KNOTS]
0
NAME OF THE INTERPOLATED OUTPUT VALUES FILE
Al.INT
Figure 15. ATKIN.DAT sampling station data file for QTRACER processing.
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EXTRAPOLATE DATA (l=yes, 0=no) [1=EXP. DECAY, 2=CUBIC HERMITE, 3=STAT. METH.]
0 1
VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)
0110
VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT)
0110
VISUALIZATION: CHATWIN PARAMETERS (CHECK PLOT OPLOT)
010
FLAG FOR FILE OF DATA FOR CXTFIT MODELING (CXTFIT Min Mout)
000
NAME OF FILE FOR SOLUTE-TRANSPORT MODELING (VALID IF FLAG=1)
C:\VANGENU\CXT\A1.ADV
FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0)
1
NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1)
Al.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)
Al.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)
Al.STN
VISUALIZATION: STANDARDIZED TIME AND CONCENTRATION (CHECK PLOT JOIN OPLOT)
0010
Figure 15. ATKIN.DAT sampling station data file for QTRACER processing (continued).
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FLAG FOR OUTPUT TO SCREEN AND PAUSE AS NECESSARY (1/0)
1
FLAG FOR DATA ANALYSIS METHOD (1,ALL DATA; 2,BLOCK AVE; 3,BLOCK SKIP)
3
TIME CONCENTRATION DISCHARGE (CONDITIONAL)
0.0 0.00 4.10
1.0 0.00 4.20
2.0 0.00 4.27
3.0 0.00 4.35
4.0 0.00 4.42
5.0 0.00 4.50
6.0 0.00 4.57
7.0 6.50 4.67
8.0 7.50 4.75
9.0 4.60 4.82
10.0 2.10 4.90
11.0 1.10 4.80
12.0 0.93 4.68
13.0 0.88 4.56
14.0 0.83 4.46
15.0 0.75 4.33
16.0 0.63 4.22
17.0 0.40 4.12
18.0 0.18 4.00
19.0 0.08 3.90
20.0 0.03 3.80
Figure 15. ATKIN.DAT sampling station data file for QTRACER processing (continued).
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IS
SAMPLING FREQUENCY: UNITS (l=days, 2=hrs, 3=min, 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 ATKIN.DAT example, 3 was recorded because tracer concentration is recorded at
the end of this file (corresponding to time data) in units of //g 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 to 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 QTRACER how
to respond. The number 0 for the ATKIN.DAT data set tells QTRACER that no value for
background is available — no "value" is required. The number 1 tells QTRACER that a
background value is available for subtracting from the data set — a number 1 MUST be
followed by a number [VALUE] (i.e., concentration) in the SAME units as 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 IF appropriate.
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 //g L"1 is available. This value will
automatically be subtracted from all concentration values in the time-concentration data
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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 //g L"1.
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. QTRACER
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 whose value must be included in the next section with the discharge units of
measure. So for the ATKIN.DAT file a variable discharge 1 is listed, which means that there
MUST be a third column of data at the end of the ATKIN.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, QTRACER needs to know what units discharge was
measured in so that an appropriate correction can be made to allow for consistent units. A
considerable range of discharge unit measures is allowed by QTRACER, so the requestor
actually takes up two lines in the data file.
DISCHARGE: UNITS (l=m~3/d, 2=m~3/hr, 3=m~3/min, 4=m~3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ft~3/hr, 9=ft~3/min, 10=ft~3/sec) [VALUE]
4
A number 4 by itself indicates that a variable discharge is recorded in m~3/sec (m3 s"1),
the values of which are listed at the end of the data file (ATKIN .DAT). (QTRACER converts
all discharges to m3 s"1.)
If a constant discharge is to be used (e.g., LOST.DAT) then the user would record
DISCHARGE: UNITS (l=m~3/d, 2=m~3/hr, 3=m~3/min, 4=m~3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ft~3/hr, 9=ft~3/min, 10=ft~3/sec) [VALUE]
4 1.78
to indicate that a constant discharge in m~3/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=nT3/min, 4=m~3/sec, 5=gpd, 6=gpm,
7=ft~3/d, 8=ft~3/hr, 9=ft~3/min, 10=ft~3/sec) [VALUE]
4 l.OE-10
By entering "4 1. OE-10" (entering the value 4, a blank space, and then 1. 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. Aquifer Volume
The aquifer (or flow zone) volume can be estimated by QTRACER provided the time-
concentration data file begins at zero time. A simple on/off switch informs QTRACER
to estimate volume. If the switched is set to off, then subsequent geometries (e.g., cross-
sectional area) also will not be estimated.
ESTIMATE AQUIFER VOLUME (l=yes, 0=no)
1
The switch value 1 for the ATKIN.DAT example informs QTRACER that aquifer volume
should be estimated.
6.6.7. Radial Distance
QTRACER needs to know the straight-line distance to the sampling station from the in-
jection site and the units by which it 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 ATKIN.DAT example.
6.6.8. Correction for Sinuosity
Because most karst conduits and fractures are not straight-line features, a sinuosity factor
may be included for QTRACER to use in processing the data.
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CORRECTION FOR SINUOSITY (l=yes, 0=no) [VALUE, def=1.5]
1 1.5
A listing of 1 1.5 tells QTRACER to correct the radial distance for sinuosity by a factor
of 1.5x. However, because the default is 1.5, a value does not need to be entered in this
case. The sinuosity factor is limited to a range that is 1.0 < 3.0.
6.6.9. Conduit or Fracture Flow
QTRACER allows the user to decide if the geometry of the system conforms more to a
typical karst conduit (e.g., tubular) or as a fracture (e.g., planar) or set of fractures. If
it is a fractured-rock system, then 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 occured via a single fracture. A porosity values has no effect for flow
through karst conduits.
CONDUIT OR FRACTURE(S) FLOW,POROSITY (l=conduit, 0=fracture) [VALUE, def=1.0]
1
For the ATKIN.DAT a value of 1 tells QTRACER to consider conduit flow only.
6.6.10. Fracture Geometry Units
If the tracer migrated through a fractured-rock system then the user may want to list
the fracture(s) height and the units that the fracture(s) height was recorded. Otherwise,
QTRACER will do its best to estimate the height, although the user should not expect the
estimated value to be very reliable.
IF FRACTURE(S) FLOW: UNITS,HEIGHT (l=m, 2=ft, 0=null) [VALUE]
0
The flag 0 is irrelevant here because flow is through a conduit. However, for fracture flow
the flag 0 tells QTRACER that fracture height is unknown and must be estimated by
QTRACER.
6.6.11. Output File Name
QTRACER requires that an output filename be given so that the results may be written
to an "out 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
Al.OUT
The output file name Al.OUT is used here because it allows for easy deletion without
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inadvertently deleting the original input files. Any file name is allowed by QTRACER,
although the user may not want to use a name that is excessively long, as PCs do not like
long file names.
6.6.12. Sample Data Interpolation
QTRACER is very good at data interpolation. It relies on a piecewise cubic Hermit to
determine the best possible interpolant for the given data.
INTERPOLATE DATA (l=yes, 0=no) and [NUMBER OF KNOTS]
0
This requestor is obviously asking if the user would like to interpolate the data. A 0 means
NO and the user may move on. A 1 (ATKIN.DAT example) means YES and the user then
must inform QTRACER of the MINIMUM number of knot points to be created by the
interpolation algorithm.
If the user would like to have an interpolated data file created the user might record
the following.
INTERPOLATE DATA (l=yes, 0=no) and [NUMBER OF KNOTS]
1 200
The flag and value 1 200, respectively, inform QTRACER that data interpolation is desired
and that > 200 knots points (interpolated data points) are required. Any value other than
200 could be used as your PC 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 will be stored and can be viewed later or deleted as desired.
NAME OF THE INTERPOLATED OUTPUT VALUES FILE
Al.INT
The output file name Al. INT is used here because it allows for easy deletion without
inadvertently deleting the original input files. Any file name is allowed by QTRACER,
although the user may not want to use a name that is excessively long, as PCs do not like
long file names. If data interpolation is not requested above, this requestor is ignored by
QTRACER.
6.6.14. Sample Data Extrapolation
QTRACER is also very good at data extrapolation, but it is up to the user to determine
which method is preferred. That is, the user must decide if an exponential decay function,
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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 ATKIN.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.
QTRACER 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 interpolation flag was switched on, or (2) by simply observing the "upper limit"
to 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). Anyone 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 datapoints (JOIN).
4. Automatically create a postscript output file for plotting (OPLOT).
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A number 1 answers YES to a requestor, a number 0 answers NO to a requestor. So for
the ATKIN.DAT example:
VISUALIZATION: STRAIGHT DATA (CHECK PLOT JOIN OPLOT)
0110
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..
Sometimes the curve looks somewhat odd (note odd tip at on the concentration peak
for the MULL.DAT data set when plotted); this occurs because the Bezier algorithm used
for smooth plotting sometimes has difficulty jumping to oddly placed datapoints. Data
interpolation by QTRACER will help overcome this effect. Also, fewer than 3 or more
than 847 data points will result in no data smoothing.
More importantly, the shape of the curve drawn through the datapoints does not
necessarily represent the integration. QTRACER will perform a much better integration
of the curve that appears on the screen, in that it will seamlessly connect the points very
smoothly even though this function cannot be observed by the user. So the user need not
be troubled by the 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 QTRACER is being 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.
Be advised automatic postscript output REQUIRES that the data filenames be NO
longer than six characters. A filename extension can cause some problems (e.g., *.DAT),
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so the automatically created postscript files will be renamed with an underscore (e.g.,
ATKIN_01.POS). The extension *.DAT was not replaced, it just did not fit here because of
the name length limitation.
If several postscript files are to be produced (identified in various places in the *.DAT
file, QTRACER will number them accordingly. So for the ATKIN.DAT example QTRACER
might produce six separate postscript files as
ATKIN_01.POS, . . ., ATKIN_06.POS
Actually, a long filename with or without an extension can be used, but the designated
name of the new data file to be created and listed in the data file must not exceed six
characters. In this instance, the program will then create a name VGnn.pos where nn =
01 to 06.
Manual Postscript Files Postscript files of all screen plots can be created very easily
by QTRACER. These will usually be done when QTRACER is not being run in batch
mode and after some modifications have been made to the plots to meet a user specified
appearance. This is described in considerable detail in a later section.
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
was requested by the user.
VISUALIZATION: INTERPOLATED DATA (CHECK PLOT JOIN OPLOT)
0110
This example 0110 tells QTRACER absolutely nothing for the ATKIN.DAT data file
because no data interpolation was requested. If data interpolated had been requested,
then 0110 would tell QTRACER 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, QTRACER 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 datapoints with a line. That is, the Chatwin parameters may be
examined (CHECK), plotted (PLOT), and sent to a file as a postscript plot file (OPLOT). There
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is no JOIN function because the Chatwin method automatically relies on fitting a straight
line through the early-time data.
VISUALIZATION: CHATWIN PARAMETERS (CHECK PLOT OPLOT)
010
The switches, 0 1 0 for the ATKIN.DAT example, inform QTRACER 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. QTRACER 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 that a CXTFIT
file be created (CXTFIT) and that the original injected tracer mass (Min), or the recovered
tracer mass (Mout) be used 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 QTRACER to not create a CXTFIT2.0 file, and obviously
not to use either the mass injected or mass recovered in file creation. If a CXTFIT2.0 file
option was set to and the other two options set to zero, 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 created file —
QTRACER adds some additional information for user examination that is not read
by CXTFIT2.0.
3. QUESTION initial values for the selected parameters. For example, if QTRACER
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was forced to use the method of moments to estimate dispersion, then the "D"
parameter listed in the CXTFIT2.0 created file will probably 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 QTRACER, 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\A1.ADV
The data line, C:\VANGENU\CXT\A1 .ADV, tells QTRACER to create the CXTFIT2.0 file at
the above listed path where the executable version of CXTFIT2.0 is stored. Actually, this
requestor is ignored in this instance because QTRACER was informed above to not create
a CXTFIT2.0 file.
It should be noted that any of the files to be created by QTRACER (except as by
OPLOT) can be given a path for file storage.
6.6.19. Normalized Tracer Mass
The tracer 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 L"1) kg"1 injected to allow for comparison of multiple tracer-breakthrough curves
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. A switch of
l=on and a switch of 2=off.
FLAG FOR NORMALIZED CONCENTRATION VALUES FILE (1/0)
1
Name of Normalized Concentration File for Mass As with all other files created
by QTRACER, a file name must be provided before QTRACER can create the file.
NAME OF FILE FOR NORMALIZED CONCENTRATION VALUES (VALID IF FLAG=1)
Al.NRM
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A file name 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 QTRACER to just 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 tracer-breakthrough curves
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. A switch
of l=on and a switch of 2=off.
FLAG FOR NORMALIZED TRACER LOAD FILE (1/0)
1
Name of Normalized Concentration File for Load As with all other files created
by QTRACER, a file name must be provided before QTRACER can create the file.
NAME OF FILE FOR NORMALIZED TRACER LOAD VALUES (VALID IF FLAG=1)
Al.LOD
A file name with an extension (*.LOD) is not required. Any name is acceptable.
Visualize Normalized Tracer Load The newly created normalized load 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).
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VISUALIZATION: NORMALIZED TRACER LOAD (CHECK PLOT JOIN OPLOT)
0010
Setting the four switches to 0 0 1 0 tells QTRACER to just display a smooth line on the
screen.
6.6.21. Standardized Data File
The tracer concentration data may be standardized for dimensionless time and concentra-
tion according to the Mull et al. (1988) method. That is, time may be rewritten by
(^T <43)
and concentration data may be rewritten by
7T (44)
Up
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.
Flag to Create Standardized Data File The creation of a standardized dimensionless
data file is again performed by the on/off switch described earlier. A switch of l=on and
a switch of 2=off.
FLAG FOR STANDARDIZED TIME AND CONCENTRATION VALUES FILE (1/0)
1
Name of Standardized Data File As with all other files created by QTRACER, a
file name must be provided before QTRACER can create the file.
NAME OF FILE FOR STANDARDIZED TIME AND CONCENTRATION (VALID IF FLAG=1)
Al.STN
A file name 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
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Setting the four switches to 0 0 1 0 tells QTRACER to just display a smooth line on the
screen.
6.6.22. Screen Display
QTRACER 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. QTRACER will pause periodically to
allow the user to view the results; RETURN will inform QTRACER to continue.
Setting the switch to 0=off allows QTRACER to run in the batch mode. This 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 PC memory allocation.
Because of this problem, QTRACER has been programmed to adjust accordingly by:
1. Using all the time-concentration data, provided PC memory is not exceeded.
2. Averaging blocks of data to create a single datapoint for each block.
3. Skipping blocks of data.
Obviously the more measured data that QTRACER can handle the better. Therefore, if
QTRACER must use less than all the data it will attempt to minimize the size of the blocks
it must either average or skip.
FLAG FOR DATA ANALYSIS METHOD (l.ALL DATA; 2,BLOCK AVE; 3,BLOCK SKIP)
1
Two sets of data files that were created to be "huge" are included on the disk. The first
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, were created from the
MULL data set by interpolation and include a "variable" discharge (actually, discharge did
not vary all the while that it was measured).
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6.6.24. Actual Time-Concentration Data
The last item to be listed for each *.DAT file is the actual time-concentration data 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 is only required to be listed if a variable discharge was measured at each
sampling interval. For the ATKIN.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 identified as a variable earlier, then a discharge column must be recorded; if discharge
was identified as a constant earlier, then a discharge column must not appear.
If a single or average (constant) discharge was measured for the site, a constant dis-
charge 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:
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:
6 6
which indicates that discharge was recorded in "gpm" (flag = 6) and the actual discharge
value = 6 (second number 6 listed).
Please 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 aquifer volumes are to be estimated for a variable discharge TIME must begin
with 0.0.
Conduit volume and Reynolds number can only be calculated if discharge was measured
at a SPRING, not a well. If a well is analyzed and the appropriate flags turned on to indicate
80
-------
a desire to calculate conduit volume and Reynolds number, both will be calculated, but
significant uncertainties should be expected in the results. So for the RCA.DAT data sets,
these calculations are suspect.
81
-------
7. EXAMPLE ANALYSES FROM QTRACER
QTRACER is very easy and fast to use once the necessary header file and sampling station
data files have been created (see Section 6.). As described in Section 6.2., the user need
only type QTRACER and hit ENTER to initiate QTRACER, which will introduce the program
and then ask for the name of a header file (tracing project file). Alternatively, the user
could type QTRACER filename, which will introduce the program and automatically load and
begin running the specified header file and subsequent data files.
At this point, QTRACER will proceed along until finished if the batch mode has been
specified (see Section 6.6.22.). Alternatively, if the screen display has been requested,
QTRACER will pause periodically to allow the user to observe the analytical results as they
become available. Simply hitting ENTER as directed by QTRACER will cause QTRACER
to move on to the next available display screen.
Lastly, if multiple sampling station data files are to be processed by QTRACER for a
single tracing project file or header file (see Section 6.5.), then QTRACER will enter a loop
mode. Upon completion of processing a single sampling station data file, QTRACER 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, QTRACER 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. ATKIN.D EXAMPLE OUTPUT
In Section 6.5. ATKIN.D was used as an example tracing project file or header file.
ATKIN.D referenced the sampling station data file, ATKIN.DAT (Section 6.6., and Table 5)
that provided all the information necessary for QTRACER processing of the data obtained
for that sampling station.
7.1.1. ATKIN.DAT Tracer-Breakthrough Curve
Figure 16 depicts the basic tracer-breakthrough curve generated by QTRACER and
analyzed by QTRACER. Note that discharge was measured each time a water sample
was collected.
82
-------
ATKIN.DAT
— — — Discharge
6 8 10 12 14 16 18 20
Time from Injection (hours)
Figure 16. Tracer-breakthrough curve for the ATKIN.DAT sampling station data file.
83
-------
7.1.2. ATKIN.DAT Chatwin Plot
Figure 17 depicts the data plot and straight-line fit of the Chatwin parameter for longi-
tudinal dispersion generated and analyzed by QTRACER. Note that the equation for the
straight-line and the relevant statistics describing the straight-line fit were generated by
QTRACER.
7.1.3. ATKIN.DAT Output File
Figure 18 depicts the final analytical output generated by QTRACER. Besides observing
the analytical results, note the end of the output file, which depicts the "total" results of
the analysis. QTRACER 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. ATKIN.DAT Normalized Tracer Concentration
Figure 19 depicts the normalized tracer concentration data generated by QTRACER
according to the method described by Mull et al. (1988). Note the concentration units
for the y axis.
7.1.5. ATKIN.DAT Normalized Tracer Load
Figure 20 depicts the normalized tracer load data generated by QTRACER according to
the method described by Mull et al. (1988). Note the concentration units for the y axis.
7.1.6. ATKIN.DAT Standardized Time-Concentration Data
Figure 21 depicts the standardized-time concentration data generated by QTRACER
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.
7.2. RCA.D EXAMPLE OUTPUT
In Section 4.1. 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 QTRACER
and references the sampling station data file, RCA.DAT (Table 5), that provides all the
relevant information necessary for QTRACER processing of the data obtained for that
sampling station.
84
-------
ATKIN.DAT
100
0
-100
M -200
v.
i—i
^ -300
o
^ -400
c
Z, -500
-600
-700
-800
-900
FT
r
PROB
7.
.9815
-.9907
.8676E-01
-2.685
Y = 747.901 + -95.3754 X
9 10 11 12 13 14 15 16 17
Time from Injection (hours)
18
19 20
Figure 17. Plot and straight-line fit of the Chatwin parameter for the ATKIN.DAT sampling
station data file.
85
-------
Listing of output for: ATKIN.DAT
Limits to integration for the data file:ATKIN.DAT
Lower integration limit .00000 hrs
Upper integration limit 20.000 hrs
The quantity of tracer recovered .44798 kg
447.98 g
.44798E+06 mg
.44798E+09 ug
Distance from input to outflow point 2.7000 km
Corrected for sinuosity = 1.50X
Time to leading edge (first arrival) 7.0000 hrs
Time to peak tracer concentration 8.0000 hrs
For a peak tracer concentration 7.5000 ug/L
Figure 18. Output file for the ATKIN.DAT sampling station data file.
-------
The mean tracer transit time
.38629 d
9.271070 hrs
556.2642000 min
Standard deviation for tracer time
.10731 d
2.5754 hrs
154.5220000 min
The mean tracer velocity
Standard deviation for tracer velocity
6989.484000 m/d
291.2285 m/hr
.80897E-01 m/s
134.51 m/d
5.6047 m/hr
.15569E-02 m/s
Dispersion coefficient
Longitudinal dispersivity
3.2582
40.276
m~2/s
m
Peclet number
77.688
Advection > Diffusion
The maximum tracer velocity
9257.143000 m/d
385.7143 m/hr
.10714 m/s
Figure 18. Output file for the ATKIN.DAT sampling station data file (continued).
87
-------
Karst-conduit volume estimate
Based on a lower integration limit
and on an upper integration limit
Karst-conduit cross-sectional area
Karst-conduit surface area
Tracer sorption coefficient (conduit)
Hydraulic head loss along conduit
Based on a friction factor
.14941E+06 m~3
.00000 hrs
9.2711 hrs
55.338 m~2
51552650. m~2
.13046E-04 m
.12021E-01 m
.11201
Laminar flow sublayer along walls
Estimated Reynolds number
Based on an estimated tube diameter
1.3811 mm
595636.9000
8.3939 m
Estimated Froude number
Based on an estimated hydraulic depth
.10061E-01
6.5926 m
Shear velocity
.16966E-01 m/s
Molecular mass transport parameters
Estimated Schmidt number
Estimated Sherwood number
Mass transfer coef. from wall to flow
Molecular diffusion layer thickness
1140.026000
14925.68000
.17782E-05 m/s
.56238 mm
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
99.55 %
.4481E-02
Figure 18. Output file for the ATKIN.DAT sampling station data file (continued).
-------
Listing of total estimates for: atkin.d
Total quantity of tracer recovered
.44798
447.98
kg
g
Total aquifer volume estimate
Total aquifer surface area estimate
Final tracer sorption coefficient
.14941E+06 m~3
51552650. m
.13046E-04 m
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
99.55 %
.4481E-02
Figure 18. Output file for the ATKIN.DAT sampling station data file (continued).
-------
ATKIN.DAT
.018
.016
.014
u
-" .012
c
'o. -010
en
E
.008
.006
0 .004
.002
.000
t =
7t =
9.271 hrs
2.575 hrs
1 .561
1 .838
6 8 10 12 14 16 18 20
Time from Injection (hours)
Figure 19. Normalized tracer concentration data for the ATKIN.DAT sampling station
data file.
90
-------
ATKIN.DAT
9.271 hrs
2.575 hrs
1 .561
1 .838
6 8 10 12 14
Ttme from Injection (hours)
16
20
Figure 20. Normalized tracer load data for the ATKIN.DAT sampling station data file.
91
-------
ATKIN.DAT
1,1
1,0
/*•»*
o.
x. -9
^^
c -8
o
'•S .7
» .6
u
J ,5
TJ
q>
N .4
5 -3
c
D
•*• 9
w •-*
,1
.0
t
CTt
7t
Cp
.0000
1 .000
1 .561
1 .000
dtzed Curve
-4-3-2-1 0 1 _ 2
Standardized Time (t-t)/at
Figure 21. Standardized time-concentration data for the ATKIN.DAT sampling station
data file.
92
-------
7.2.1. RCA.DAT Tracer-Breakthrough Curve
Figure 22 depicts the basic tracer-breakthrough curve generated by QTRACER and
analyzed by QTRACER. 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 longi-
tudinal dispersion generated by QTRACER and analyzed by QTRACER. Note that the
equation for the straight-line and the relevant statistics describing the straight-line fit were
generated by QTRACER.
7.2.3. RCA.DAT Output File
Figure 24 depicts the final analytical output generated by QTRACER. Besides observing
the analytical results, note the end of the output file, which depicts the "total" results of
the analysis. QTRACER 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 QTRACER
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 QTRACER according to
the method described by Mull et al. (1988). Note the concentration units for the y axis.
7.2.6. RCA.DAT Standardized Time-Concentration Data
Figure 27 depicts the standardized-time concentration data generated by QTRACER
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.
93
-------
RCA.DAT
400
350
300
250
o
'- 200
o
9 150
o
c
o
o
100
50
Data =
25
6 8 10 12 14 16 18
Tfme from Injection (hours)
20
22
24
Figure 22. Tracer-breakthrough curve for the RCA.DAT sampling station data file.
94
-------
RCA.DAT
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
-1600
-1800
PROB =
z =
.9867
-.9933
.6665E-02
-2.850
Y = 937.977 + -134.329 X
6 8 10 12 14 16 18
Time from Injection (hours)
20
22
24
Figure 23. Plot and straight-line fit of the Chatwin parameter for the RCA.DAT sampling
station data file.
95
-------
Listing of output for: RCA.DAT
Limits to integration for the data file:RCA.DAT
Lower integration limit .00000 hrs
Upper integration limit 24.000 hrs
The quantity of tracer recovered 1.7403 kg
1740.3 g
.17403E+07 mg
.17403E+10 ug
Distance from input to outflow point 50.292 km
( 165.00 ft)
Corrected for sinuosity = 1.50X
Time to leading edge (first arrival) 5.0000 hrs
Time to peak tracer concentration 7.0000 hrs
For a peak tracer concentration 380.00 ug/L
Figure 24. Output file for the RCA.DAT sampling station data file.
96
-------
The mean tracer transit time
.36687 d
8.804829 hrs
528.2897000 min
Standard deviation for tracer time
.14560 d
3.4945 hrs
209.6686000 min
The mean tracer velocity
Standard deviation for tracer velocity
137.0848000 m/d
5.711866 m/hr
0.15866E-02 m/s
19.330 m/d
.80543 m/hr
.22373E-03 m/s
Dispersion coefficient
Longitudinal dispersivity
.71871E-03 m~2/s
.45298 m
Peclet number
139.65
Advection > Diffusion
The maximum tracer velocity
241.4016000 m/d
10.05840 m/hr
.27940E-02 m/s
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
97
-------
Karst-conduit volume estimate
.11.999
m~3
Karst-conduit cross-sectional area
Karst-conduit surface area
Tracer sorption coefficient (conduit)
Hydraulic head loss along conduit
Based on a friction factor
.23858 m~2
35007.070 m~2
.51651E-01 m
.98203E-06 m
.83435E-01
Estimated Reynolds number
Based on an estimated tube diameter
and an hydraulic conductivity
767.0682000
.55115 m
81662. m/s
Estimated Froude number
Based on an estimated hydraulic depth
.77006E-03
.43288 m
Shear velocity
.28791E-03 m/s
Molecular mass transport parameters
Estimated Schmidt number
Estimated Sherwood number
Mass transfer coef. from wall to flow
Molecular diffusion layer thickness
1140.026000
122.374600
.22203E-06 m/s
4.5038 mm
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
.6592
.9934
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
-------
Listing of total estimates for: rca.d
Total quantity of tracer recovered
1.7403
1740.3
kg
g
Total aquifer volume estimate
Total aquifer surface area estimate
Final tracer sorption coefficient
11.999
m~3
35007.070 m
.51651E-01 m
Percent recovery of tracer injected
Accuracy index (0.0 = Perfect Recov.)
.6592
.9934
Figure 24. Output file for the RCA.DAT sampling station data file (continued).
99
-------
RCA.DAT
220
200
180
160
u
o
= 140
o. 120
L 100
en
~ 80
u
c
o
u
60
40
20
t =
CT =
7t =
8.805 hrs
3.494 hrs
2. 104
4.412
6 8 10 12 14 16 18
Time from Injection (hours)
20 22
24
Figure 25. Normalized tracer concentration data for the RCA.DAT sampling station data
file.
100
-------
RCA,DAT
90
80
V 70
o
4-1
O
Z 60
o»
50
• 40
01
^ 30
o
c
o
0 20
10
0
t =
7i =
8.805 hrs
3.494 hrs
2. 104
4.412
8 10 12 14 16
Ttme from Injection (hours)
18
20
22
24
Figure 26. Normalized tracer load data for the RCA.DAT sampling station data file.
101
-------
RCA.DAT
1,1
1,0
/*•»*
o.
x. -9
^^
c -8
o
'•S .7
» .6
u
J ,5
TJ
q>
N .4
5 -3
c
D
•*• 9
w •-*
,1
.0
-3
.0
t =
CTt =
7t =
CP =
.0000
1 .000
2. 104
1 .000
-1 ,5 .0 1 ,5 _
Standardized Time (t-t)/at
3.0
4.5
Figure 27. Standardized time-concentration data for the RCA.DAT sampling station data
file.
102
-------
7.3. ANALYSIS ASSESSMENT OF THE TWO EXAMPLE DATA FILES
From the two examples ( ATKIN and RCA) , it is apparent that QTRACER is not affected
by variable discharges versus a constant discharge. QTRACER is also not affected by
recovery at a spring versus recovery at a monitoring well.
It will be noted that the ATKIN data set resulted in nearly perfect mass recovery. Had
the ATKIN data set been analyzed according to the description given in Section 4., the
user would have noted that mass recovery was > f 00%. The efficient integration algorithms
used by QTRACER results in a more reliable mass balance.
QTRACER results for the RCA data set were quite similar to those presented in
Section 4.1.1.. QTRACER 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 Sm 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 6m may be achieved from (Dreybrodt, 1988, p. 172)
Nah = Dc/8m (45)
where the Sherwood number Nsh for turbulent flow is obtained from (Dreybrodt, 1988, p.
172)
Nah = 0.023A^83A^C/3 (46)
which is valid for 0.6 < Nsc < 2500 and 2000 < NR < 35000. For laminar flow conditions
Nsh niay be estimated from
,, OMS(Dc/x,)NRN,c
"- = 3-65+l + 0.04[(D0/*.)AW^ (47)
A mass transfer coeficient k/ is obtained from the Sherwood number by using the
relationship (Dreybrodt, 1988, p. 171)
N,k = (48)
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
Nsc = -- (49)
103
-------
8. DATA INTERPOLATION AND EXTRAPOLATION EFFECTS
As explained in Section 5.1., QTRACER utilizes a very efficient data interpolation routine.
The primary use of the data interpolation routine would be if the user believes that missing
datapoints can be reasonably approximated by data interpolation. For example, if the user
believes that unaltered tracer-breakthrough curves suggest that data aliasing may have
occurred, then data interpolation may be able to confirm or deny if aliasing really has
occurred.
8.1. COMPARISON OF ATKIN.DAT OUTPUT FILES
To illustrate the effect of data interpolation, data extrapolation, and the combined effect
of data interpolation and extrapolation on a data set exhibiting good mass recovery, the
ATKIN.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.
8.1.1. Interpolated ATKIN.DAT Tracer-Breakthrough Curve
Figure 28 depicts the interpolated tracer-breakthrough curve generated by QTRACER and
analyzed by QTRACER. Note that discharge has an interpolated value for each time an
interpolated tracer concentration value was created.
Graphically, the user will note that Figure 28 is more reasonable than Figure 16. The
improvement is most evident at the peak, where the interpolated file more correctly matches
the peak concentration datapoint. In Figure f6, the peak concentration is actually exceeded
by the graphics line. However, the apparent inaccurate plotting is NOT reflected in the
actual data analysis by QTRACER.
8.1.2. Interpolated ATKIN.DAT Chatwin Plot
Figure 29 depicts the interpolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER. Note that the equation
for the straight-line and the relevant statistics describing the straight-line fit were generated
by QTRACER.
Some difference will be noted between Figure 29 and Figure f7, but not a significant
difference. Interpolation results in more datapoints 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.
104
-------
ATKIN.DAT
o
z
o
S 3
u
c
o
u
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
2 4 6 8 10 12 14 16 18
Time from Injection (hours)
3.7
20
Figure 28. Interpolated curve for the ATKIN.DAT sampling station data file.
105
-------
ATKIN.DAT
O
300
200
100
0
-100
-200
-300
-400
-500
-600
-700
-800
-900
-1000
Y = 875.168 + -110.475 X
°000
°°oooooo
°°ooooo
000
°00
°or
PROB =
z =
.9691
-.9844
.5685E-11
-2.424
I nterpoIated Data
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Time from Injection (hours)
Figure 29. Interpolated data set for the Chatwin parameter for the ATKIN.DAT sampling
station data file.
106
-------
Table 6 compares the final analytical output for the unaltered tracer-breakthrough curve
for the ATKIN.DAT data set, the interpolated ATKIN.DAT data set, and the Interpolated-
extrapolated ATKIN.DAT data set. Note how each file's results are closely matched with
the others.
8.1.3. Extrapolated ATKIN.DAT Tracer-Breakthrough Curve
Figure 30 depicts the extrapolated tracer-breakthrough curve generated and analyzed by
QTRACER. Note that discharge has an interpolated value for each time an extrapolated
tracer concentration value was created.
Graphically, the user will note that the tracer-breakthrough curve shown in Figure 30
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 datapoint (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 30). Extrapolation routine 2 (piecewise cubic Hermite) uses the
shape of the entire existing data curve to determine the "most reasonable" extrapolation
datapoint 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
was measured, QTRACER 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.
8.1.4. Extrapolated ATKIN.DAT Chatwin Plot
Figure 31 depicts the extrapolated data plot and straight-line fit of the Chatwin parameter
for longitudinal dispersion generated and analyzed by QTRACER. Note that the straight-
line fit, the equation for the straight-line, and the relevant statistics describing the straight-
line fit generated by QTRACER are identical to Figure 17. Data extrapolation had no effect
on the Chatwin method analysis because original sample had resulted in nearly "complete"
tracer recovery.
107
-------
Table 6. Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for ATKIN.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 s"1
Peak Tracer
Flow Velocity, m s"1
Mean Tracer
Flow Velocity, m s"1
Shear
Velocity, m s"1
Longitudinal
Dispersion, m2 s"1
Hydraulic
Head Loss, m
ATKIN.DAT
(unaltered)
4.48 x IO2
9.96 x IO1
4.48 x 1Q-3
7.00 x 10°
8.00 x 10°
9.27 x 10°
2.00 x IO1
1.07 x 1Q-1
9.38 x IO-2
8.09 x 1Q-2
1.70 x 1Q-2
3.26 x 10°
1.20 x 1Q-2
ATKIN.DAT
(interpolated)
4.48 x IO2
9.95 x IO1
4.75 x 1Q-3
6.20 x 10°
8.00 x 10°
9.26 x 10°
2.00 x IO1
1.21 x 1Q-1
9.38 x 1Q-2
8.10 x 1Q-2
1.70 x 1Q-2
2.38 x 10°
1.21 x 10~2
ATKIN.DAT1
(extrapolated)
4.48 x IO2
9.96 x IO1
3.67 x IO-3
7.00 x 10°
8.00 x 10°
9.28 x 10°
2.26x IO1
1.07 x 1Q-1
9.38 x IO-2
8.08 x 1Q-2
1.70 x 1Q-2
3.26 x 10°
1.20 x 1Q-2
ATKIN.DAT2
(inter. /extra.)
4.48 x IO2
9.96 x IO1
3.80 x IO-3
6.10 x 10°
8.00 x 10°
9.27x 10°
2.32 x IO1
1.23 x 1Q-1
9.38 x IO-2
8.09 x 1Q-2
1.70 x 1Q-2
2.13 x 10°
1.20 x 1Q-2
Listed parameters without dimensions are dimensionless.
1 Extrapolated using a statistical straight line fit.
2Extrapolated using a cubic Hermite function.
108
-------
Table 6. Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for ATKIN.DAT sampling station (cont.).
Parameter
Conduit
Volume, m3
Conduit Cross-
Sectional Area, m2
Conduit
Surface Area, m2
Tracer Sorption
Coefficient, m
Conduit
Diameter, m
Hydraulic
Depth, m
Friction
Factor
Laminar Flow
Sublayer, m
Reynolds
Number
Froude
Number
Peclet
Number
Schmidt
Number
Sherwood
Number
Mass Transfer
Coefficient, m s"1
Molecular diffusion
layer, m
ATKIN.DAT
(unaltered)
1.49 x IO5
5.53 x IO1
5.16 x IO7
1.31 x 1Q-5
8.39 x 10°
6.59 x 10°
1.12 x 1Q-1
1.38 x 1Q-3
5.96 x IO5
1.01 x 10~2
7.77 x IO1
1.14 x IO3
1.49 x IO4
1.78 x 1Q-6
5.62 x 1Q-4
ATKIN.DAT
(interpolated)
1.49 x IO5
5.53 x IO1
5.16 x IO7
1.38 x 1Q-5
8.40 x 10°
6.59 x 10°
1.12 x 1Q-1
1.38 x 1Q-3
5.96 x IO5
1.01 x 10~2
1.06 x IO2
1.14 x IO3
1.49 x IO4
1.78 x 1Q-6
5.62 x 1Q-4
ATKIN.DAT1
(extrapolated)
1.50 x IO3
5.54 x IO1
5.15 x IO7
1.07 x 1Q-5
8.40 x 10°
6.60 x 10°
1.12 x 1Q-1
1.38 x 1Q-3
5.95 x IO5
1.01 x 10~2
7.77 x IO1
1.14 x IO3
1.49 x IO4
1.78 x 1Q-6
5.62 x 1Q-4
ATKIN.DAT2
(inter. /extra.)
1.50 x IO3
5.54 x IO1
5.15 x IO7
1.11 x 1Q-5
8.40 x 10°
6.59 x 10°
1.12 x 1Q-1
1.38 x 1Q-3
5.96 x IO5
1.01 x 10~2
1.19 x IO2
1.14 x IO3
1.49 x IO4
1.78 x 1Q-2
5.63 x 1Q-4
Listed parameters without dimensions are dimensionless.
Extrapolated using a statistical straight line fit.
2Extrapolated using a cubic Hermite function.
109
-------
ATKIN.DAT
u
c
o
u
Cone .
— — — Discharge
Data = 22
Ex t rapoIated Data
6 8 10 12 14 16 18 20
Time from Injection (hours)
22
5.0
4.9
4.8
4.7
4.6
4.5
4.4
4.3
4.2
4.1
4.0
3.9
3.8
3.7
24
Figure 30. Extrapolated curve for the ATKIN.DAT sampling station data file.
110
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ATKIN.DAT
100
0
-100
M -200
v.
i—i
^ -300
o
^ -400
c
Z, -500
-600
-700
-800
-900
FT
r
PROB
7.
.9815
-.9907
.8676E-01
-2.685
Y = 747.901 + -95.3754 X
Ext rapoIated Data
9 10 11 12 13 14 15 16 17 18 19 20
Time from Injection (hours)
Figure 31. Extrapolated data set for the Chatwin parameter for the ATKIN.DAT sampling
station data file.
Ill
-------
8.2. INTERPOLATED-EXTRAPOLATED ATKIN.DAT DATA
Figures 32 and 33 illustrates how the interpolation and extrapolation routines provided in
QTRACER can be used to in tracer-breakthrough curve analyses. Table 6 illustrates that
there are no significant differences in any of the analyses provided by QTRACER for the
ATKIN.DAT data set.
A more erratic tracer-breakthrough curve, 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 is
employed without data interpolation, the graphics may appear incorrect (i.e., a straight-line
connection from the last measured datapoint to the extrapolated datapoint). This apparent
inaccuracy is not a problem, however, as it is strictly an artifact of the plotting algorithm.
The integration routine used by QTRACER will develop a smooth curve between all
provided datapoints regardless of tracer-breakthrough curve appearance.
8.3. COMPARISON OF RCA.DAT OUTPUT FILES
To further illustrate the effect of data interpolation, data extrapolation, and the combined
effects of data interpolation and extrapolation 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.
8.3.1. Interpolated RCA.DAT Tracer-Breakthrough Curve
Figure 34 depicts the interpolated tracer-breakthrough curve generated and analyzed by
QTRACER. 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 34 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 datapoint. 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 QTRACER.
8.3.2. Interpolated RCA.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 QTRACER. Note that the equation
112
-------
ATKIN.DAT
8 10 12 14 16 18 20
Time from Injection (hours)
22
3.2
24
Figure 32. Interpolated and extrapolated data set for the ATKIN.DAT sampling station
data file.
113
-------
ATKIN.DAT
o
400
200
0
-200
-400
-600
Z, -800
$.
-1000
-1200
-1400
-1600
Y = 924.127 + -116.842 X
r
PROB
z
.9236
-.9610
.6660E-14
-1 .959
I nterp/Ext rap Data
6 8 10 12 14 16 18
Time from Injection (hours)
20
22
24
Figure 33. Interpolated and extrapolated data for the Chatwin parameter for ATKIN.DAT
sampling station data file.
114
-------
RCA.DAT
400
350
300
250
o
'- 200
o
9 150
o
c
o
o
100
50
Knots = 101
I nterpoIated Data
0 2 4 6 8 10 12 14 16 18 20 22 24
Tfme from Injection (hours)
Figure 34. Interpolated curve for the RCA.DAT sampling station data file.
115
-------
for the straight-line and the relevant statistics describing the straight-line fit were generated
by QTRACER.
Some difference will be noted between Figure 35 and Figure 23, but not a greatly
significant difference. Interpolation results in more datapoints 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.
Table 7 compares the final analytical output for the unaltered tracer-breakthrough curve
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.
8.3.3. Extrapolated RCA.DAT Tracer-Breakthrough Curve
Figure 36 depicts the extrapolated tracer-breakthrough curve generated and analyzed by
QTRACER. Note that discharge has no extrapolated value because discharge was constant.
Graphically, the user will note that Figure 36 is more reasonable than Figure 22. The
improvement is most evident at 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 36 suggests nearly "complete" tracer recovery at > 30 hours.
8.3.4. Extrapolated RCA.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 QTRACER. Note that the straight-
line fit, equation for the straight-line, and relevant statistics describing the straight-line fit
generated by QTRACER are slightly different from the results shown in Figure 23.
The obvious differences in between Figure 37 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 less good straight-line fit to the data.
8.4. INTERPOLATED-EXTRAPOLATED RCA.DAT DATA
Figures 38 and 39 illustrate how the interpolation and extrapolation routines provided in
QTRACER can be used in tracer-breakthrough curve analyses. Table 7 illustrates that
there are no significant differences in any of the analyses provided by QTRACER for the
RCA.DAT data set.
116
-------
RCA.DAT
«<
-•J
o
400
200
0
-200
-400
-600
-800
-1000
-1200
-1400
-1600
Y = 858.595 + -122.354 X
I0°ooooo,
I00°ooo0l
'000(
PROB =
z =
.9894
-.9947
.3033E-18
-2.966
I nterpoIated Data
6 8 10 12 14 16 18
Time from Injection (hours)
20
22
24
Figure 35. Interpolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file.
117
-------
Table 7. Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for RCA.DAT sampling station.
Parameter RCA.DAT RCA.DAT RCA.DAT1 RCA.DAT2
(unaltered) (interpolated) (extrapolated) (inter./extra.)
Tracer Mass 1.74 x 103 1.74 x 103 1.77 x 103 1.77 x 103
Recovered, g
Percent Mass 6.59 x 1CT1 6.59 x 1CT1 6.70 x 1CT1 6.71 x 101
Recovered
Accuracy 9.93 x KT1 9.93 x 1CT1 9.93 x KT1 9.93 x KT1
Index
Initial Tracer 5.00 x 10° 4.08 x 10° 5.00 x 10° 4.08 x 10°
Breakthrough, h
Time to Peak 7.00 x 10° 6.96 x 10° 7.00 x 10° 6.96 x 10°
Concentration, h
Mean Tracer 8.81 x 10° 8.80 x 10° 9.10 x 10° 9.15 x 10°
Residence Time, h
Elapsed Tracer 2.40 x 101 2.40 x 101 3.17 x 101 5.20 x 101
Travel Time, h
Maximum Tracer 2.79 x 10~3 3.42 x 10~3 2.79 x 10~3 3.42 x 10~3
Flow Velocity, m s"1
Peak Tracer 2.00 x 10~3 2.01 x 10~3 2.00 x 10~3 2.01 x 10~3
Flow Velocity, m s"1
Mean Tracer 1.59 x 10~3 1.59 x 10~3 1.54 x 10~3 1.53 x 10~3
Flow Velocity, m s"1
Shear 2.88 x 10~4 2.88 x 10~4 2.81 x 10~4 2.80 x 10~4
Velocity, m s"1
Longitudinal 7.19 x 10~4 8.58 x 10~4 9.24 x 10~4 9.32 x 10~4
Dispersion, m2 s"1
Hydraulic 9.82 x 10~7 9.83 x 10~7 9.20 x 10~7 9.10 x 10~7
Head Loss, m
Listed parameters without dimensions are dimensionless.
1 Extrapolated using a cubic Hermite function.
2Extrapolated using an exponential decay function.
118
-------
Table 7. Estimated hydraulic flow and geometric parameters from tracer-breakthrough
curves for RCA.DAT sampling station (cont.).
Parameter RCA.DAT RCA.DAT RCA.DAT1 RCA.DAT2
(unaltered) (interpolated) (extrapolated) (inter./extra.)
Conduit 1.20 x 101 1.20 x 101 1.24 x 101 1.25 x 101
Volume, m3
Conduit Cross- 2.39 x 10'1 2.39 x 10'1 2.47 x 10'1 2.48 x 10'1
Sectional Area, m2
Conduit 3.50 x 104 3.50 x 104 3.47 x 104 3.47 x 104
Surface Area, m2
Tracer Sorption 5.17 x 10~2 5.16 x 10~2 5.29 x 10~2 5.32 x 10~2
Coefficient, m
Conduit 5.51 x 10"1 5.51 x 10"1 5.60 x 10"1 5.62 x 10"1
Diameter, m
Friction 8.34 x 10~2 8.34 x 10~2 8.48 x 10~2 8.50 x 10~2
Factor
Laminar Hydraulic 8.17 x 104 8.16 x 104 8.44 x 104 8.48 x 104
Conductivity, m s"1
Reynolds 7.67 x 102 7.67 x 102 7.55 x 102 7.53 x 102
Number
Froude 7.70 x 10~4 7.71 x 10~4 7.40 x 10~4 7.34 x 10~4
Number
Peclet 1.40 x 102 1.18 x 102 1.09 x 102 1.08 x 102
Number
Schmidt 1.14 x 103 1.14 x 103 1.14 x 103 1.14 x 103
Number
Sherwood 1.22 x 102 1.22 x 102 1.22 x 102 1.22 x 102
Number
Mass Transfer 2.22 x 10~7 2.22 x 10~7 2.19 x 10~7 2.18 x 10~2
Coefficient, m s"1
Molecular diffusion 4.50 x 10~3 4.50 x 10~3 4.58 x 10~3 4.59 x 10~3
layer, m
Listed parameters without dimensions are dimensionless.
1 Extrapolated using a cubic Hermite function.
2Extrapolated using an exponential decay function.
119
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RCA.DAT
400
350
Data = 26
Ext rapoIated Data
10 15 20 25
Tfme from Injection (hours)
30
35
Figure 36. Extrapolated curve for the RCA.DAT sampling station data file.
120
-------
400
200
> -200
o
^^
c
-400
-600
^ -800
-1000
-1200
-1400
RCA.DAT
Y = 827.304 + -115.883 X
PROB =
z =
.9668
-.9832
.2598E-02
-2.387
6 8 10 12 14 16 18
Time from Injection (hours)
Extrapolated Data
20 22
24
Figure 37. Extrapolated data set for the Chatwin parameter for the RCA.DAT sampling
station data file.
121
-------
RCA.DAT
400
350
300
250
~ 200
o
9 150
u
o
o
100
50
Knots = 434
I nterp/Extrap Data
-.215973 X
Y = 690.115 e
r = -.9418
Sy.X = 50.87
15 20 25 30 35 40
Time from Injection (hours)
45 50 55
Figure 38. Interpolated and extrapolated data set for the RCA.DAT sampling station data
file.
122
-------
The user will note in Figures 38 that the exponential decay equation
y = 690.115e-°-21597a; (50)
has been produced along with the correlation coefficient r (-0.9418) and the standard error
of the estimated fit (50.87). QTRACER provides this information to the user to assist
in assessing the effect of an exponential decay on a tracer-breakthrough curve. It will be
noted that whereas extrapolation methods 2 (piecewise cubic Hermite) and 3 (statistical
method) produce a single extrapolated point, method 1 (exponential decay) produces five
additional datapoints and thus has a great deal more influence on the final results.
Exponential decay extrapolation has more influence because the integration routine
employed by QTRACER is forced to conform to the shape of the exponentially decaying
curve. It is therefore incumbent upon the user to determine the appropriateness of using
an exponential decay model for extrapolation. For example, applying an exponential decay
for extrapolation to the ATKIN.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 tracer-breakthrough curve 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 is
employed without data interpolation, the graphics may appear incorrect (i.e., a straight-line
connection from the last measured datapoint to the extrapolated datapoint). This apparent
inaccuracy is not a problem, however, as it is strictly an artifact of the plotting algorithm.
The integration routine used by QTRACER will develop a smooth curve between all
provided datapoints regardless of tracer-breakthrough curve appearance.
123
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RCA.DAT
500
0
-500
$• -1000
^ -1500
o
-2000
^ -2500
-3000
-3500
-4000
Y = 823.652 + -116.316 X
PROB =
.9842
-.9921
. 1518E-37
-2.762
I nterp/Ext rap Data
10 15 20 25 30 35 40
Time from Injection (hours)
45
50
55
Figure 39. Interpolated and extrapolated data for the Chatwin parameter for RCA.DAT
sampling station data file.
124
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9. ASSOCIATED COMPUTER PROGRAMS
To facilitate the efficient use of QTRACER, 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 QTRACER. The third
program, DATFILE, provides a straightforward interface for the creation of a sample station
datafile.
The results of these three programs are easily appended or copied to a *.DAT file (see
Section 6.6.24. and the end of Figure 15). By judicious use of these programs QTRACER
can be made more efficient because the data can be so quickly and easily placed in required
form.
9.1. NDATA COMPUTER PROGRAM
Typically, discharge is not measured as frequently or at the same time as tracer concen-
tration. Hence, the time concentration data file might appear as (no specific data file
example):
0.0 0.00 4.10
1.0 2.05
5.0 4.50 3.96
10.0 4.10
15.0 4.33
20.0 0.03 3.80
Clearly 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 a very good data interpolation algorithm has been
programmed (same one used in QTRACER) as NDATA.EXE. To use this program just
type NDATA at the DOS prompt and follow the instructions. However, it will ONLY
work on a straight time-concentration file or time-discharge file without any other headers.
Therefore the algorithm must be used on the original data set(s) and the results copied to
the bottom on the final data file to be processed.
When using NDATA only X/Y data can be read in 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
125
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values. The program can then be used to fill in missing discharge values. When typing in
the data OMIT all time values for which a corresponding discharge or concentration value
is missing. Using the example above, if concentration value corresponds to time=15.0 the
user would exclude the entire line from the data set to be processed. Obviously, 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 QTRACER
to perform data interpolation on a complete data file.
9.1.1. 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.
9.2. 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 is shown in Figure 40.
Type AUTOTIME and then follow the instructions to create a new file of time-concentration
data that can then be copied to the bottom of a *.DAT file to be read by QTRACER. 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 40 for conversion to decimal hours
will result the file listed in Figure 41. It will be remembered that QTRACER allows for
free-format data entry so a nicely lined up data column is unnecessary. All that is necessary
is that the two data columns be separated by at least one blank space or one comma.
9.2.1. 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.
126
-------
10 15 0.010 3.23E-2
21 45 0.010 3.23E-2
22 15 0.060 3.23E-2
22 45 0.500 3.23E-2
23 15 1.320 3.23E-2
23 45 2.050 3.23E-2
0 15 3.900 3.23E-2
0 45 4.200 3.23E-2
1 15 4.200 3.23E-2
1 45 3.400 3.23E-2
2 15 3.050 3.23E-2
2 45 2.450 3.23E-2
3 15 2.000 3.23E-2
3 45 1.500 3.23E-2
4 15 1.200 3.23E-2
4 45 0.950 3.23E-2
5 15 0.800 3.23E-2
5 45 0.600 3.23E-2
6 15 0.550 3.23E-2
6 45 0.500 3.23E-2
7 15 0.420 3.23E-2
7 45 0.370 3.23E-2
8 15 0.350 3.23E-2
8 45 0.300 3.23E-2
13 45 0.200 3.23E-2
22 45 0.010 3.23E-2
Figure 40. Example of a sample time-concentration file using military time for conversion
(Mull et aL, 1988).
127
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O.OOOOOOE+00 l.OOOOOOE-02 3.230000E-02
11.500000 l.OOOOOOE-02 3.230000E-02
12.000000 6.000000E-02 3.230000E-02
12.500000 5.000000E-01 3.230000E-02
13.000000 1.320000 3.230000E-02
13.500000 2.050000 3.230000E-02
14.000000 3.900000 3.230000E-02
14.500000 4.200000 3.230000E-02
15.000000 4.200000 3.230000E-02
15.500000 3.400000 3.230000E-02
16.000000 3.050000 3.230000E-02
16.500000 2.450000 3.230000E-02
17.000000 2.000000 3.230000E-02
17.500000 1.500000 3.230000E-02
18.000000 1.200000 3.230000E-02
18.500000 9.500000E-01 3.230000E-02
19.000000 8.000000E-01 3.230000E-02
19.500000 6.000000E-01 3.230000E-02
20.000000 5.500000E-01 3.230000E-02
20.500000 5.000000E-01 3.230000E-02
21.000000 4.200000E-01 3.230000E-02
21.500000 3.700000E-01 3.230000E-02
22.000000 3.500000E-01 3.230000E-02
22.500000 3.000000E-01 3.230000E-02
27.500000 2.000000E-01 3.230000E-02
36.500000 l.OOOOOOE-02 3.230000E-02
Figure 41. Example of a converted sample time-concentration file created by AUTOTIME
(Mullet al, 1988).
128
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9.3. DATFILE COMPUTER PROGRAM
The easiest method of creating a sample station data file (Figure 15) may be accomplished
by using a PC 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.
To use DATFILE the user need only type DATFILE and respond to each requestor in turn.
DATFILE incorporates AUTOTIME so that data listed in military time may be directly
converted to sequential decimal time. It also allows the user to enter an existing file of time-
concentration data (using military time or sequential decimal time) to be incorporated in
the sample station data file to be created.
It will be noted that a sample station data file created using DATFILE will not appear
exactly in the form of Figure 15 because of some formatting differences. This is not a
problem because QTRACER uses free format for input.
9.3.1. DATFILE Source
The FORTRAN source code is included on the DATFILE disk. Modification of the DAT-
FILE main file can be relatively easily accomplished if desired, but is not recommended.
129
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10. CONCLUSIONS
Tracer-breakthrough curves developed from quantitative ground-water tracing studies in
karst and fractured-rock aquifers can be evaluated given the present high level of accuracy of
analytical fluorescence chemistry 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, QTRACER, 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, quanti-
tative tracing of contaminated sites will become more and more important for parameter
estimation. QTRACER will enhance the necessary analyses and lead to improved site
evaluations.
130
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NOTATION
A cross-sectional area (L2)
AI accuracy index (dimensionless)
Ap constant of proportionality for amount of diffusing material (M T1/2 L~3)
As karst conduit surface (L2)
C tracer concentration (M L~3)
Co initial tracer concentration (M L~3)
Cf final tracer concentration (M L~3)
Cj average concentration of tracer input over time interval (M L~3)
Cp peak tracer concentration (M L~3)
CPL steady-state (plateau) tracer concentration at a resurgence
for repeated instantaneous injections (M L~3)
C (xs,i) mass of recovered tracer over distance(s), xs and time(s), t [M L~3];
d pipe diameter (L)
D steady-state tracer dilution for multiple injections (dimensionless)
DC karst conduit diameter (L)
DH karst conduit hydraulic depth (L)
DL longitudinal dispersion coefficient (L2 T"1)
Dm molecular diffusion coefficient (L2 T"1)
// friction factor (dimensionless)
g gravitational acceleration (L T~2)
HL hydraulic head loss (L)
kf mass transfer coefficient (L T"1)
K equivalent hydraulic conductivity for laminar flow (L T"1)
Ka karst conduit sorption coefficient (L)
m karst conduit roughness correction factor (dimensionless)
Min mass of tracer injected (M)
Mm mass of multiple tracer injections (M)
MQ mass of tracer recovered (M)
MT total tracer mass recovered from all sampling stations (M)
ne effective fracture porosity (dimensionless)
Np Froude number (dimensionless)
NR Reynolds number (dimensionless)
131
-------
Nsc Schmidt number (dimensionless)
Nsh Sherwood number number (dimensionless)
Pe Peclet number (dimensionless)
Q ground-water discharge (L3 T"1)
Q mean ground-water discharge (L3 T"1)
r karst conduit radius (L)
t time of sample collection (T)
tp time to peak concentration (T)
t mean tracer residence time (T)
At time interval between multiple tracer injections (T) and
v mean tracer velocity (L T"1)
vp peak tracer velocity (L T"1)
vs shear tracer velocity (L T"1)
xs radial distance to sampling station (L)
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)
xs sinuous tracer migration distance = 1.5x (L)
Greek
5 laminar flow sublayer (L)
5m molecular diffusion layer thickness (L)
e relief of karst conduit wall surface irregularities (L)
p, dynamic viscosity (M L~1T~1}
TT pi (dimensionless)
p fluid density (M L~3)
at standard deviation for mean residence time (T)
av standard deviation for mean flow velocity (L T"1)
132
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