and

= = 1 = -T
TE(Z,T) = THs (az-T + %) erfc ad =T
e VAR /Pe
P.T mm, 2Ra\ —PeBaz a?
inRi (Rz+T+ a) 'd
T Ra PR — 7? paz RZ+T
+ [F - | € eric | — (67)
2 2P, 4Ry lap /P,

3.2.2. Tracer Retardation and Tracer Decay

Application of any solution to Equation (43) or Equation (52) for instances where tracer
retardation and tracer decay are significant (Rg > 1; > 0) can have profound effects on
the shape of the BTC. Commonly, increasing R, tends to cause a flattening, lengthening,
and spreading of the BTC, whereas increasing jz causes only a flattening of the BTC.
Conversely, increasing Ry when using Equations (54), (56), or (57) results in a steepening,
lengthening, and spreading of the BTC. An increase in Ry has the effect of reducing the
calculated value for Co, which causes a concomitant increase in estimated mass M so that
the set value for C” can be maintained. A lengthening and spreading of the BTC continues
in a normal manner because the time of travel ¢ is not considered in the root determination.
Increasing 4 when solving for the root also causes a steepening of the BTC because it
also has the effect of reducing the calculated value for GO”. The net effect is to cause an

. . . FE ue
increase in estimated mass M so that the preset value for C’ can be maintained.

3.3. SOLUTE TRANSPORT

Preliminary estimates for tracer mass in conjunction with travel time estimates and related
hydraulic parameters may be applied to any particular solution to Equation (52) to obtain
a BTC. Inverse analysis using the estimated parameters M, Ry, and/or ys and the predicted
BTC can be conducted to observe the sensitivity of the model to any one of the three
parameters.

The primary difficulty with application of any particular solution to the ADE is the
need to estimate not only the tracer mass but the times of travel (f, tp, and t,), which are
related to flow velocity (v, up, v;) and axial dispersion D,. An inability on the part of the

originators of previous tracer mass estimation equations (Field, 2002c) to estimate #, v, and

47



TABLE 3.1. FINAL TRACER-MASS ESTIMATE CALCULATIONS

TRACER-MASS ESTIMATES

TRACER MASS TRACER MASS TRACER MASS TRACER MASS
CINI. EST.) (ADJ. EST.) (REA. EST.) (FIN. EST.)
(g) (g) (g) (g)
2.0723E+03 1.0400E+03 --- 1.0400E+03

ERROR CODE => 4 4

FINAL TRACER-MASS REDUCTION FACTORS

SYSTEM VOL. DILUTION VOL. RETARDATION DECAY
(m73) (m3) (DIMEN. ) (1/h)
1.50E+05 1.50E+05 1.00E+00 0.00E+00

SET CONC. AVERAGE CONC. PEAK CONC.
(ug/L) (ug/L) (ug/L)

1.8300E+01 1.8505E+01

Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.

111



aged 4xou uo ponuruoo

(Lee 4 ‘Zeer ‘z7teY) ve Thing = W (ez)
(6 4 ‘9261 ‘oypye]y pue Adqy) . at Mey = W (zz)
(6961 ‘seeH) (0€ “d ‘9461 ‘s0Y¥91,J pue AoTy) a5 = W (12)
(6g61 ‘seey) TAG6= W (02)
(6c61 ‘seey) o0s= W (61)
(s96r ‘uunq) — (2 -d ‘9461 ‘YH, pL AoTV) Ton = WN (g1)
(6961 ‘UgWIg pue merq) (ToT “d ‘Gg6T “Te 9 seq) a= WN (21)
alg ‘oquoe) (g2z “d ‘ex6T ‘“Suryeomg) in, = W (91)
a(g ‘ous (822 “4 ‘¢26T ‘“Sury00u) Bin, = (a1)
(09 “4 ‘zg61 ‘redsep) vo . Boon = W (v1)
(goer ‘s4oq) (6¥ 4 ‘Ug6r ‘redsexy) Cee = nw (en)
a(6961 ‘oeurdayg) (6p -d ‘2861 ‘redsep) .
2(696T ‘eurdoyg) (9 4 ‘1g61 ‘guoumy) [P+ OS +)]T= we)
(4z¢ ‘4 ‘g66r ‘ges1) (12 4 ‘Zo0z “re 4 jepnyps) *OD°LT = W (11)
(1g61 ‘ourmoypyyog-ourts) (aze ‘d ‘g661 ‘gest TeL= WN (01)
a(é ‘PBIIMD) (6p “4 ‘1961 ‘tedsep) ;
ag ‘PFPIND) (926 “4 ‘1861 ‘graowepy) 76%, = W (6)
aouarajay aoUdoJOY
Axeurlig ghtepuooeg quoryenbyy qequinyy

*(penuryuos) sseui uorpelur eov1y Suryeurryse Joy suoTyenbe suIog “¢ 91qeI,

13



Table 30. Required porous media tracer test _design specifics.
Parameter ‘Test Site Wilerwald Kirchdorf Site* Mobile Site* Chalk River*

Q, mh? 2.59 x 10! 137x102 = 5.6910! 1.62 x 10°
L,m 2.00 x 10? 5.85x 102 3.83 x10! ~—-8.00 x 10°
n 1.50 x 107} 140x107? 3.50 x 107? 3.80 x 107?
bm 1.00 x 10? 8.80x 10° 216x10! 8.20 x 10°
T,m 7.50 x 101 ve

te, h 1.00 x 10° ve 7.6610 7.73 x 10!

ty, m° 9.00 x 10-? ooo 5.69x 10! 1.62 x 10°
CP pg Lt 3.10 x 10° 2.71 x 10° 9.80x 10? 3.06 x 10-4
CS wg Lt 1.84 x 10° 2.66x10° 1.09x104 3.64 1074

@ Transverse tracer spread not estimated for forced-gradient tracer tests.
> Average tracer concentration for nonreactive tracer transport.

© Average tracer concentration for reactive tracer transport.



measured BTC in the sense that the initial sample collection time and sample collection
frequency recommended by EHTD would have resulted in an accurate depiction of the actual
BTC. The occurrence of the long tail may or may not have been detected, depending on
whether sample collection continued after 11 hours.

The Uvas Creek travel times listed in Table 28 show average travel time £ to be less
than the time to peak concentration ty (é < tp), which appears contrary to typical tracer
tests, where £ > tp. The greater t, for the Uvas Creek tracer test is an artifact of the long
ty relative to actual tracer travel times. It should be noted that the measured £ and v were
obtained from Q/A and related to L in Bencala and Walters (1983) is the same method used
by EHTD (Field, 2002c), which explains the exact match by the EHTD-estimated # and
v. Breakthrough-curve analysis using QTRACER (Field, 2002b), modified to account for
short-pulse releases (Wolff et al., 1979) and long-pulse releases (Sardin et al., 1991), resulted
in a Z = 2.08 hours and v = 135 m h7! which quite reasonably match the measured results.
However, QTRACER estimated D = 542 m? h~!, which is midway between the measured
D and the EHTD-estimated D.

Because a relatively insignificant amount of tracer was added directly to the stream
water, Dy = V for both the measured and the EHTD-predicted results (Table 29). The
exact match for both of the EHTD-predicted volumes with the measured V was surprising

and is not expected to occur in other similar instances.

7.3.1.2. Missouri River Tracer Test. Flow in streams similar to the Missouri River
is difficult to assess due to sheer size. The Missouri River tracer test used to evaluate
EHTD probably represents the simplest case tested here because an impulse release of a
large quantity of tracer was recovered sufficiently far from the injection point (243 km)
as to not be adversely influenced by the actual injection. Figure 24 shows the results of
the Missouri River tracer test. The nonreactive case adequately represents the results of
the Missouri River tracer test, although the measured BTC was not ideally realized by the
EHTD prediction because the nonreactive tracer test still suggested appropriate sampling
times that would result in detection of the BTC. In addition, somewhat more tracer than
was required was recommended by EHTD (Table 28) — a result of overestimating dispersion
for such a simple flow system.

The reactive case allowed for a match of the measured BTC peak, but EHTD then
recommended 1.5x more tracer than was actually needed. EHTD-estimated f = 36.6 hours
and v = 6623 mh! reasonably matched the measured values, but required Ry = 1.13

137



Cover Photo

Uranine (Acid Yellow 73) release into the underground river in Sainte Anne Cave, Belgium

(photo courtesy of Philippe Meus).



PROJECT NAME AND TRACER-TEST CONDITIONS

PROJECT NAME

KARST EXAMPLE -- LOST RIVER CAVE SYSTEM

FLOW TYPE STATIONS RELEASE MODE RELEASE TIME
(h)
1 1 IMPULSE, 0.00E+00

FLOWING STREAM TRACER TEST

FECA CAG CIE GCI CIGCIOKIE IGRI SRIOK IERIE AGRI RII ACR I AIR

*
* STATION: LOST RIVER RISE

*

*
*
*

FERRO A IOS AGRE AICO S CRIES BIOSIS SOI IIIa AAA AAA AAA

Figure 15. Standard-form example output file generated by EHTD from a typical input file

(see Figure 12) continued.

107



the hydraulics of the system are approximated, sampling frequency and initial sample
collection time can also be predicted. The computer code, EHTD, facilitates the tracer-
design methodology for typical hydrological settings using measured hydrological field
parameters to calculate functional relationships. The measured parameters and functional
relationships are then applied to a hypothetical CSTR to develop a preliminary BTC that
is then numerically evaluated by the method of moments for tracer mass and hydraulic
parameter estimation. The calculated hydraulic parameters are then used in solving for
estimated tracer mass and sampling times.

The CSTR-generated BTC is solved by the method of moments by developing a piecewise
cubic Hermite function. That is, the interpolant is defined in terms of a set of cubic
polynomials, each of which is defined between a pair of consecutive data points. The
coefficients of these cubic polynomials are chosen so that the interpolant has continuous
first derivatives, and the remaining freedom of choice is used to ensure that the interpolant
is visually acceptable, meaning that monotonicity in the data results in monotonicity in the
interpolant, which is defined by (Kahaner et al., 1989, p. 100-103 and 106-108)

g(t) = A) = > Cihis(t) + dihi(t). (100)
i=l

A piecewise cubic Hermite function in effect produces the most reasonable interpolation
of the data possible with excellent theoretical convergence properties. Integration is then
accomplished by cubic Hermite quadrature as (Kahaner et al., 1989, p. 161-162)

Ts r= f" nioute= 9° f mat) as [i (101)

1 = 1
which is the compound trapezoid rule with appropriate end corrections. The compound
trapezoid rule is exceptionally accurate when the integrand is a smooth periodic function
given by equally spaced data points (Kahaner et al., 1989, p. 162).

Equations (54)-(57) may be solved directly or by using a combination of the bisection
method and the secant method. The bisection method ensures certainty and the secant
method ensures rapid convergence. This is very efficient and accurate and is guaranteed to
produce reasonable results (Kahaner et al., 1989, p. 248-250).

For instances where tracer mass is expected to be adversely affected by retardation
or decay, EHTD employs a constrained nonlinear least-squares optimization routine to
adjust the tracer mass, retardation, and decay estimates relative to the BTC produced
by the hypothetical CSTR. The nonlinear optimization routine searches for a vector y of

56



-o— Measured Data
NonReactive Transport
Reactive Transport

Concentration (ug 1)

Figure 26. Comparison of measured data for the Variegated Glacier tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rg = 1.25
and p = 1.595 h7}.

EHTD-predicted nonreactive results, EHTD was successful in that both nonreactive and
reactive estimates for tracer mass were adequate and the suggested sampling times would
approximate the measured BTC. Using the larger estimate for cross-sectional area obtained
from v would also have been successful in that the suggested sampling times would have
produced the measured BTC when the tracer test was implemented.

Again, a relatively insignificant amount of tracer was added directly to the stream water
at the bottom of the karst window, causing Dy = V for both the EHTD-predicted results
(Table 29). Neither of the predictions for V by EHTD matched the measured V, but
the approximations may be regarded as sufficiently close to the measured value for V to

adequately represent the tracer test.

7.3.1.4. Variegated Glacier Tracer Test. Tracer testing is commonly used to define
the hydraulic parameters associated with glacial outflows. The Variegated Glacier post-
surge tracer test BTC was very reasonably approximated by EHTD for both nonreactive

and reactive considerations (Figure 26). The EHTD-predicted hydraulic parameters ¢ = 4.27

140



FEE GEOG OAC GGO GC CEIO OC GCG GAGGIA IK

MALCOLM S. FIELD
U.S. ENVIRONMENTAL PROTECTION AGENCY

* *
* *
* PROGRAM TO OPTIMIZE TRACER MASS TO BE INJECTED INTO A FLOW +
* SYSTEM TO ENSURE RELIABLE TRACER-MASS RECOVERY AT THE *
* EXPECTED DOWNGRADIENT SAMPLING STATIONS BASED ON THEORY. *
* *
* DEVELOPED *
* *
* BY *
* *
* *
* *
* *

FEI OCC ECA AGHIOS RASS OGG GRIGG IE

ENTER INPUT FILE NAME (DEFAULT = EHTD.IN):
ENTER OUTPUT FILE NAME (DEFAULT = EHTD.OUT):

ENTER PLOT FILE NAME (DEFAULT = NULL):

Figure 8. Initial EHTD screen title which appears at program start.

a

In the Windows Explorer, Left Double-Click the EHTD folder and then Left Double-
Click the EHTD.EXE file to initiate program operation.?

2, At this point, EHTD will open the program initiation screen and title (Figure 8) and
will prompt you to enter an input file name for the file to be evaluated (Figure 8) unless
you specified a file when starting the program using a DOS prompt. One advantage of
a subdirectory on your hard disk is that you will not be required to provide an obscure
path for all subfiles; the program will find them automatically because they are all

at the same location as the executable file. If the data files are in different locations

SIf a command prompt is preferred, then at the C:\> prompt, type “CD\EHTD” without the quotes. You
will then see a new prompt; C:\EHTD>. You may now type “EHTD” to run the program by just responding to
the requested information, assuming that you have also copied the necessary data files or created your own.
You may want to type “EHTD filename” such as “EHTD Ehtd.in”, which will automatically load and begin
running the EHTD default data set described in the journal article (Molz et al., 1986b). You may do the
same with any of the other *. in data files, which will load the appropriate data files and begin processing.



tracer test was deemed responsible for the differing results (Field and Pinsky, 2000).

To alleviate some of the difficulties associated with estimating the mass of tracer to be
released, numerous empirical equations have been developed by various individuals (Field,
2002a). In nearly every instance these equations appear to have been devised without
regard to solute transport theory and, at times, without regard to site hydrology. Rather,
they appear to have been developed solely as a result of the developer’s experience from
one or more tracer tests. Also, in many instances various—and sometimes unexplained—
multipliers are incorporated into the equations to account for potentially inadequate tracer
mass estimates (Field, 2002a).

Initial sample collection times and sampling frequencies are also generally unknown
quantities because solute fluxes are typically unknown. However, application of functional
relationships developed from measured parameters can be used to estimate solute transport
parameters. The determination of solute transport parameters translates into appropriate
sampling frequencies.

The purpose of this paper is to answer three basic questions common at the start of
any hydrologic tracer test: (1) How much tracer mass should be released? (2) When should
sampling start? and (3) At what frequency should samples be collected? In this paper
an efficient hydrologic tracer test design (EHTD) methodology for estimating tracer mass
based on solute transport theory is developed. Use of the methodology developed here leads
to a better understanding of the probable transport processes operating in the system prior
to conducting the tracer test. Improved understanding of the transport processes then leads
to better estimates of tracer mass to be released. In addition, initial sample collection times
and sample collection frequencies are calculated using solute transport theory.

Although this tracer-design methodology is expected to be reliable in most instances, it
does not address the common occurrences of multimodal BTCs and long-tailed BTCs be-
cause such BTCs require much more complex analyses with numerous unknown parameters
(Maloszewski et al., 1992a; Toride et al., 1993). Density-induced sinking effects that may
occur in natural gradient porous-media tracer tests (Oostrom et al., 1992; Barth et al., 2001)
are also not addressed. The methodology introduced here is tracer independent, whereas
density-induced sinking is a tracer-dependent process and requires a separate analysis to

determine how much, if any, tracer sinking may occur.



than either the set or the average concentration. Should the average concentration not equal
the set concentration or the peak concentration be less than either the average or the peak

concentrations, a clear error in either data input or EHTD processing is indicated.

6.1.1.10. Table 4.1. Estimated Sampling Frequency. A particularly useful aspect
of EHTD is its ability to recommend when the first sample should be collected and an
appropriate sampling frequency thereafter. This information is reflected in Table 4.1.

(Figure 15, page 106) in terms of “exact times” (decimal years, decimal weeks, decimal

days, decimal hours, and decimal minutes) and “convenient time” (i.e., 12-hour clock).
This information provides the user with a helpful file for either programming an automatic
data recorder or for determining when to collect grab samples at a sufficient frequency for
adequately defining the BTC.

6.1.1.11. Calculated Tracer-Mass. A boxed final estimate for tracer mass in kilo-
grams, grams, and milligrams (Figure 15, page 106) follows Table 4.1. for each sampling
station listed in the data input file (Figure 12).

6.1.1.12. Error Codes. Following the results of each sampling station calculation, a
list of error codes (Figure 15, page 106) are reprinted and a basic description of each is
provided. Often these will be fairly insignificant, as is the case shown in Figure 15.

6.1.1.13. Recommended Tracer-Mass. Completion of processing of the entire project
(e.g., all listed sampling files in the data input file, Figure 12) will result in a summed es-
timate for tracer mass in kilograms, grams, and milligrams. For multiple sampling station
listings in a data input file, the recommended tracer mass may greatly exceed any individual
sampling station, which can be problematic if subsurface pathways do not connect to all
the listed sampling stations. In this latter instance, it is possible that more tracer than
is desired could be recovered at selected sampling stations although this is much less of a
problem than with the conventional conjecture method (see Section 2.1.1.).

6.1.1.14. Date and Time of Processing. ENTD prints out the time when EHTD
processed the data input file because the results of EHTD are highly temporal-dependent.
That is, flows are likely to be higher in wet seasons than during dry seasons. To obtain

reasonable results, EHTD should be run soon after basic field measurements are taken and

116



OCOWONAOAHh AW

PerPRReER
oP WNROO-

15.

PPE EP RPE EP ee eee eee
OCPNRTUANDNDNODHDOORDANND

Figure 18. Data file generated by EHTD used to produce Figure 19 continued.

122





References

Alexander, Jr., E. C., Quinlan, J. F., 1992. Practical Tracing of Groundwater with Emphasis
on Karst Terranes. Tech. Rep. Short Course Manual, 2nd ed., Geological Society of
America, Boulder, Colorado.

Aley, T. J., 1999. The Ozark Underground Laboratory’s Groundwater Tracing Handbook.
Tech. rep., Ozark Underground Laboratory, Protem, Mo.

Aley, T. J., Fletcher, M. W., 1976. The water tracer’s cookbook. Missouri Speleology 16(3),
1-32.

Barth, G. R., Ilangasekare, T. H., Hill, M. C., Rajaram, H., 2001. A new tracer-density

criterion for heterogeneous porous media. Water Resources Research 37(1), 21-31.

Behrens, H., Beims, U., Dieter, H., Dietze, G., Eikmann, T., Grummt, T., Hanisch, H.,
Henseling, H., Ka8, W., Kerndorff, H., Leibundgut, C., Miiller-Wegener, U., Rénnefahrt,
1, Scharenberg, B., Schleyer, R., Schloz, W., Tilkes, F., 2001. Toxicological and ecotoxi-

cological assessment of water tracers. Hydrogeology Journal 9, 321-325.

Bencala, K. E., Walters, R. A., 1983. Simulation of solute transport in a mountain pool-
and-riffle stream: A transient storage model. Water Resources Research 19(3), 718-724.

Bendel, L., 1948. Ingenieurgeologie, 832 p. Springer, Vienna.

Blower, S. M., Dowlatabadi, H., 1994. Sensitivity and uncertainty analysis of complex
models of disease transmission: An HIV model, as an example. International Statistical
Review 62(2), 229-243.

Bégli, A., 1980. Karst Hydrology and Physical Speleology, 284 p. Springer, Berlin.

Brugman, M. M., 1987. Water Flow at the Base of a Surging Glacier. Ph.D. Dissertation,
267 p., California Institute of Technology, Pasadena, Cal.

Chatwin, P. C., 1971. On the interpretation of some longitudinal dispersion experiments.
Journal of Fluid Mechanics 48(4), 689-702.

Davis, S. N., Campbell, D. J., Bentley, H. W., Flynn, T. J., 1985. Ground water Tracers,
200 p. National Ground water Association, Dublin, Ohio.

166



Table 18. Recommended sampling times for selected tracer reaction conditions
(continued).

Sampling Time, hours

Sample R3=1.0 R8=1.0 R§=10 R{=1.0 R§=20 R= 3.0

Number p=0.0 p=001 w=005 pw=01 w=00 p=0.0
37 29.51 29.33 28.89 28.17 59.01 88.51
38 30.13 29.94 29.49 28.75 60.25 90.38
39 30.75 30.56 30.10 29.34 61.50 92.24
40 31.37 31.17 30.71 29.92 62.74 94.11
41 31.99 31.79 31.32 30.51 63.98 95.97
42 32.61 32.40 31.92 31.09 65.22 97.84
43 33.23 33.02 32.53 31.68 66.47 99.70
44 33.86 33.64 33.14 32.26 67.71 101.56
45 34.48 34.25 33.75 32.85 68.95 103.43
46 35.10 34.87 34.35 33.43 70.20 105.29
47 35.72 35.48 34.96 34.02 71.44 107.16
48 36.34 36.10 35.57 34.60 72.68 109.02
49 36.96 36.72 36.18 35.19 73.92 110.89
50 37.58 37.33 36.78 35.77 75.17 112.75
51 38.21 37.95 37.39 36.36 76.41 114.62
52 38.83 38.56 38.00 36.94 77.65 116.48
53 39.45 39.18 38.60 37.53 78.90 118.34
54 40.07 39.79 39.21 38.11 80.14 120.21
55 40.69 40.41 39.82 38.69 81.38 122.07
56 41.31 41.03 40.43 39.28 82.63 123.94
57 41.93 41.64 41.03 39.86 83.87 125.80
58 42.56 42.26 41.64 40.45 85.11 127.67
59 43.18 42.87 42.25 41.03 86.35 129.53
60 43.80 43.49 42.86 41.62 87.60 131.40
61 44.42 44.11 43.46 42.20 88.84 133.26
62 45.04 44.72 44.07 42.79 90.08 135.12
63 45.66 45.34 44.68 43.37 91.33 136.99
64 16.28 45.95 45.29 43.96 92.57 138.85
65 46.91 46.57 45.89 44.54 93.81 140.72

@Recommended sampling frequency = 37.12 minutes.

>Recommended sampling frequency = 37.29 minutes.
°Recommended sampling frequency = 36.95 minutes.
4Recommended sampling frequency = 36.45 minutes.

©Recommended sampling frequency = 1.24 hours.

fRecommended sampling frequency = 1.86 hours.
Note that tracer decay has units of h~?.



Table 8. Tracer-dye mass per 1000 m of traced distance.

Tracer Material Ty, grams

Na-fluorescein 282
Rhodamine WT 280
Diphenyl Brilliant Flavine 7GFF > 846
Tinopal 5BM GX > 846
Tinopal BBH Pure > 846
Phorwite AR 1694

1976, p. 7-9), although the unsuitability of such a reliance is not clear.

Equations (23)~(27) specifically relate to actual dye mass, they mix English and Metric
units, and they require multiplication by unidentified unit conversion factors. Each of these
four equations requires the use of the specific tracer dye factors of density and purity,
but they were primarily intended for use with liquid Rhodamine WT. Equations (23)—(25)
were intended for discharge measurements in surface-water streams, where Equations (23)
and (24) represent an impulse release and Equation (25) a long-pulse release (e.g., t2 > é).
Equation (25) appears very differently in the three primary references, but application
of consistent units and simplification shows that the original forms of Equation (25) are
identical.

Equation (26) is a slight modification of Equation (24) and is intended for solution
conduits in that it includes the multiplier 1.5 to account for solution conduit sinuosity.
Equation (27) was designed for time-of-travel studies in surface-water streams and will
produce slightly different results from those obtained with Equation (23) (Kilpatrick and
Wilson, 1989, p. 14) and Equation (24).

Equation (28) is identified in the United States as a “rule of thumb” formula for
determining the appropriate mass of Lycopodium spores to release. It relates a percentage
of discharge with a percentage of distance to obtain the mass needed (Ka8, 1998, p. 325).

Equations (29)-(33) are somewhat different from most of the other equations. Equa-
tion (29) has also been generally considered as a rule of thumb in the United States for trac-
ing flow in solution conduits. Unlike most of the previous 28 equations, Equation (29) does
not rely on discharge to determine the appropriate tracer mass to be used. Rather, it relies
on mass associated with a specific tracer dye type required for the expected travel distance

(Table 8). It was originally intended for visual dye confirmation in elutant (J = 1.0), but the

20



UNITS

1 for metric units (meters, square meters, cubic meters per hour).

UNITS = 2 for English units (feet, square feet, cubic feet per hour).

For example, Line 4 in Figure 10 might, for an actual tracer test, appear as:

1 1 0.0 0.0 1

which states that FLOW = 1, RELEAS = 1, RTIME (h) = 0.0 h, INFLOW (m°3/h) =
0.0 m®h-?, and UNITS = 1. It will be noted that the values listed for RTIME and
INFLOW are merely place holders. Alternatively, Line 4 in Figure 10 might appear as:

1 2 3.0 0.0 1
which represents a 3-hour pulse release in which flush or inflow water should be
excluded, such as might occur with a tracer test in a surface-water stream.

As yet another alternative, Line 4 might be the listing for FLOW as any integer greater
than 1 and less than 6 (2 < z < 5), which requires a proper corresponding entry in
Line 9. In this instance, Line 4 in Figure 11 might appear as:

4 2 76.56 5.688E01 1

which represents a porous media, injection/withdrawal tracer test in which tracer was
injected into a well over a period of 76.56 hours coupled with an injection flow rate
and downgradient withdrawal rate equal to 5.688 x 10? m® h-.

NOTE: Time values are always in hours!

Line 5 is also a comment statement provided so that the user may enter a clarifying state-

ment, which is ignored by EHTD. It is generally used as a convenient breaking point

before listing the sample station name(s). For example, Figure 10 lists Line 5 as:

FEE CEOS IOARIS CII OCIO AKG IACI CCI ACI IAAI ACR A AA

which has no real meaning and is ignored by EHTD. Line 5 can be left blank if
desired.

Line 6 is also a comment statement provided so that the user may enter a clarifying state-

ment, which is ignored by EHTD. It is generally used as a convenient indicator that

91



Table 11. Tracer test_design parameters.

Parameter Porous Media Karst

Q, mht 7.20 x 10! 3.60 x 10?
i,m 5.00 x 10? 3.00 x 108
W,m 1.00 x 10? 1.00 x 10?
V, m? 1.00 x 10 3.00 x 10°
b,m 1.00 x 10 1.00 x 10?
Ne 1.00 x 107? 1.00 x 10?
v, mht 4.17 x 107! 4.17 x10!
gm h} 7.20 x 107! 3.60 x 10?
ta, h 3.60 x 10° 2.16 x 10?
tp?h 1.20 x 108 7.20 x 104
C,, mg m=? 1.00 x 10! 1.00 x 10+
Ag, mg m3 1.00 x 10° 1.00 x 10°
05 rad 5.24 x 107? 5.24 x 107!
Sy 1.00 x 10° 1.00 x 10°
toth 1.56 x 10% 9.63 x 10!
To, 5.00 x 10° 2.00 x 10°
Toy 3.00 x 108 5.00 x 108
Te, 2.50 x 1077 2.50 x 107+
To, 2.50 x 10-° 2.50 x 107-9
Tes 5.00 x 1071 5.00 x 1077
Tos 1.00 x 10° 1.00 x 10°
Te, 5.00 x 107? 5.00 x 1071
Tuy; & 2.00 x 108 2.00 x 108
Tup, & 2.40 x 104 2.40 x 104
T,, gem * 1.20 x 10° 1.20 x 10°
Tp 3.00 x 107! 3.00 x 107?
App 5.00 x 10° 1.00 x 10°
I 1.00 x 107? 1.00 x 107!
Sin 1.00 x 10° 1.00 x 10°
* q=Q/100

> t= ta/3

© 6=30°

4 te =13t,

Adapted from Parriaux et al. (1988, p. 9).

27



8. APPLICATION OF EHTD TO SUPPORT RISK ASSESSMENTS

A critical aspect of any contamination investigation (potential or existing) of a given
hydrological system involves the development of a risk assessment to assess the threat to
human health and the environment posed by the contamination. Risk assessments consist
of three components: hazard identification, exposure assessment, and dose response. In
this section, exposure assessments as related to solute transport will be the focus. Hazard
identification (toxicity estimation) and dose-response assessment (estimation of the extent of
increasing hazard as a function of increasing exposure) are not addressed here. In addition,
that aspect of exposure assessment that deals with uptake (e.g., ingestion of contaminated
water) is not addressed here. Rather, solute transport from a source area to a point of
exposure in a hydrological system is the focus of this section. For more complete details

on exposure and risk assessments, the interested reader is referred to Reichard et al. (1990)

for a general overview of risk assessment methodology in ground water, USEPA (1992)

for general exposure methodology, USEPA (1998a) for detailed ecological risk assessment
methods and USEPA (1989) for detailed human health risk assessment methods. USEPA
(1986a,b, 1991, 1996, 1998b) provide detailed risk assessment guidance for the development
of various toxicological methods.

8.1. EXPOSURE ASSESSMENT OVERVIEW

A typical exposure assessment for real and potential contamination usually includes solute-
transport modeling as a means of reducing uncertainties and/or forecasting the effects of
any suggested changes. The exposure pathway (source to exposure point) requires field
investigations which are often enhanced through modeling of the environmental systems
which helps to lessen the impact of uncertainties. Uncertainties in exposure assessments
are always an issue that must be addressed. Typical uncertainties associated with exposure
assessments in hydrological systems are listed in Figure 31.

The value and importance of using a well calibrated model for risk assessment purposes
is widely recognized. For example, McAvoy et al. (2003) used the well-known water quality
model, QUAL2E (after calibration) to conduct a basic risk assessment regarding wastewater
loading to Balatuin River in the Philippines. Rhodamine WT (Acid Red 388) dye tracing
results were used to develop the necessary parameters for model calibration. Interestingly,
the initial dye release included too little dye (9.52 g) and the two subsequent releases required

152



3.5.1. Travel Times and Velocity

For the purpose of determining axial dispersion D., tracer travel time weighted for tracer

mass for impulse and short-pulse releases is estimated from

- [rca
7 [cwa

and tracer travel time variance o? is estimated from

ak (t- 8° C(
“Foo

where C’ is obtained from Equation (84). The CSTR-generated BTC is predicated on the
assumption of an impulse or short-pulse release, so other forms of Equations (86) and (87)

(87)

are not required.

3.5.2. Tracer Dispersion Estimates

Axial dispersion may be determined using the method of moments theory. Although
statistically and theoretically valid, the method of moments has the tendency to overestimate
dispersion. Alternatively, the effects of velocity variations, matrix diffusion, and immobile-
flow regions can create the appearance of significant dispersion. These difficulties require
that dispersion estimates be obtained in a manner that considers the method of moments
while reducing the influence of long tails. This is most easily accomplished using the Chatwin
(1971) method in conjunction with the method of moments.

3.5.2.1. Estimating Dispersion by the Method of Moments. Axial dispersion

properly weighted for concentration may be estimated for an impulse release by

2 3
OU

2z
and for a short-pulse release by (Wolff et al., 1979)

to\ v?
D,= (« ~ “) 2s (89)

It should be recognized here that D, solved by Equation (89) is based on the assumption of

D,= (88)

a BTC and does not represent the mean residence time distribution, as does Equation (88).

52



@-@— Measured Dato
—a-A— NonReactive Transport
Reactive Transport

z
:
3
8

of Loon

10 15
Time (h)

Figure 23. Comparison of measured data for the Uvas Creek site tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Ra = 1.0
and p = 0.08 ho}.

281 (281 m from injection site) and ¢ was 2.11 hours (Table 28).

Reach 281 was chosen to evaluate EHTD because the short travel distance coupled with
the relatively long ta caused a plateau in the BTC (Figure 23). Setting C = 3.12 mL!
for nonreactive transport (‘Table 27) resulted in an almost exact fit visually of the EHTD-
predicted results to the actual BTC, but the EHTD-predicted tracer mass was slightly less
than that injected during the actual tracer test (Figure 23). Setting C = 3.19 mg L~* and
}: = 0.08 h7! for reactive transport also resulted in a nearly exact fit visually of the EHTD-
predicted results to the actual BTC while matching the injected tracer mass (Figure 23).
Only the measured long BTC tail was not predicted by EHTD. Both the nonreactive and the
reactive EHTD-predicted BTC plateaus match the measured BTC plateau. Accounting for
p= 0.08 h-! had no measurable effect on the BTC or the estimated transport parameters.
EHTD substantially underestimated D (Table 28), but any adverse effects appear to be
insignificant because EHTD-recommended sampling times were appropriate for defining the
BTC.

EHTD-generated BTCs for both nonreactive and reactive tracer tests predicted the

136



where sampling times are based on travel distance and lack of timely recovery. In both these
instances sampling frequency was initially determined as a factor of transport distance, but
it is iteratively adjusted to longer times as tracer recovery is delayed.

A simpler but more realistic method uses average expected travel velocity that is based
on current-meter measurements for surface streams. For a porous medium, Darcy’s law
may be used to gain a general sense of tracer time of arrival, provided required parameters
(e.g., effective porosity) are available. For solution conduits, an expected average transport
velocity equal to 0.02 ms"! may be used as the basis for designing a sampling schedule
(Worthington et al., 2000). This average transport velocity of 0.02 ms“! was statistically
determined by regression analyses of 2877 tracing tests between sinking streams and springs
in carbonates in 37 countries (Worthington et al., 2000). It has been suggested that sampling
frequency should not be based on average velocity because the leading edge will be missed
(Kilpatrick and Wilson, 1989, p. 12), but this can be overcome by recognizing that the
average velocity is a rough estimate and represents a rough average travel time. The
suggested sampling frequency can be appropriately adjusted to ensure that initial sample
collection begins prior to likely tracer breakthrough.

2.2, EFFICIENT HYDROLOGIC TRACER-TEST DESIGN (EHTD)

To better facilitate tracer testing in hydrologic systems, the EHTD methodology was
developed (Field, 2002a). Unsuccessful quantitative tracer tests using several of the tracer
mass estimation equations listed in Table 3 and recommended sample collection frequencies
listed in Tables 9 and 10 and previous qualitative tracer test results led to the development
of EHTD. Application of EHTD to the study site resulted in successful tracer tests and

showed that good tracer test design can be developed prior to initiating a tracer test (Field,
2000, p. 26).

2.2.1. Basic Design of EHTD

EHTD is based on the theory that field-measured parameters (e.g., discharge, distance,
cross-sectional area) can be combined in functional relationships that describe solute
transport. processes related to flow velocity and times of travel. EHTD applies these initial
estimates for times of travel and velocity to a hypothetical continuous stirred tank reactor
(CSTR) as an analog for the hydrologic flow system to develop initial estimates for tracer
concentration and axial dispersion based on a preset average tracer concentration. Root
determination of the one-dimensional advection-dispersion equation (ADE) using the preset

23



concentration is changing, so that as the average |dC/dt| increases, sampling frequency
should also increase (Yevjevich, 1972, p. 2).

The number of samples n, to be collected can be arbitrarily chosen initially. Novakowski
(1992) suggested that n, equal at least 20 to 30 samples, with the greatest concentration
of samples occurring around Cy, which assumes that C, is known, whereas (Kilpatrick
and Wilson, 1989, p. 18) suggest that n, = 30 samples will generally be necessary as a
minimum for defining the BTC. To properly define rapid changes in the BTC, n, — 60
was experimentally found to be more reliable if aliasing effects are to be avoided (Smart,
1988). Aliasing of a multimodal BTC is a common problem when an inadequate sampling
frequency is applied to a tracer test that exhibits complex behavior.

Sampling frequency may then be determined from

tay = Sa, (98)

where t. corresponds to C > 1.0-° yg L7? for all tracer tests except recirculation tracer
tests where C’> 1.0- pg L~!. These values for t,, are used on the assumption that lower

concentrations are not readily detectable or necessarily relevant.

3.6.1.2. Initial Sample Collection. Once the sampling frequency has been deter-
mined, the initial sample collection time is adjusted backwards by an additional number of
selected samples ny. Initial sample collection time t,, is then obtained by subtracting ty
from tsm for a selected number of additional samples n. For most instances, ny = 5 may
be taken as a reasonable number of additional samples to collect prior to the occurrence of

ts, =tsm. All subsequent sampling times are found from

ta = tes + Do te, (99)
i=1

The total number of samples to be collected with an associated sampling time spacing
ts¢ can be subsequently divided into fractions thereof as desired. Earlier sample collection
than the recommended t,, may be considered as appropriate. Sample collection ending
times other than tg may also be determined, depending on whether tracer detection has

ceased prior to reaching tg or is continuing beyond ty.

3.7. METHODOLOGY EVALUATION

Application of this tracer estimation methodology provides a general sense of the appropriate
tracer mass to release and the general hydraulics of the system to be traced. Because

55





Line 7 will contain the sample station name. For example, Figure 10 lists Line 6 as:

STATION NAME

which is ignored by EHTD but is useful for recognizing Line 7, which is READ by
EHTD. Line 6 can be left blank if desired.

Line 7 is a user-supplied name that is required and is READ by EHTD. It intended to be

an identifier for a specific sample station. For example, Figure 10 lists Line 7 as:

Name of Sample Station 1

where the number 1 is used in this example as an indicator that there is more than
one sampling station for the example tracer test. The actual name can be anything,

but one must be listed.

Line 8 is another comment statement provided so that the user may enter a clarifying
statement, which is ignored by EHTD. It is intended as a convenient indicator for
appropriate input to be listed on Line 8. For example, Figure 10 lists Line 8 as:

DISCHARGE (m~3/h) DISTANCE (m) AREA (m72) SINUOSITY FACTOR

Alternatively, Figure 11 lists Line 8 as:

DISCHARGE (m*3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)

Both of these examples serve as indicators of data input for Line 9 and to be READ
by EHTD. Line 8 best serves as a header listing for Line 9.

Line 9 is a series of user-supplied data representing either field measurements or estimates
for the parameters identified on Line 8 of Figure 10 or Figure 11, as appropriate. For
example, Line 9 (with Line 8 added for clarity) in Figure 10 might, for an actual

tracer test, appear as:

DISCHARGE (m~3/h) DISTANCE (m) AREA (m72) SINUOSITY FACTOR
6.408E3 8000.0 18.8 1.0

which states that DISCHARGE (m*3/h) = 6.40810? m* h7!, DISTANCE (m) = 8000.0

92



T T T T —-

+ February 28, 1985 4
= 985

Concentration (ug L7")

a

Time (h)

Figure 32. Seven BTC’s developed by the U.S. Geological Survey between Dyers Spring
and a nearby karst window over one year (1985) (Mull et al., 1988a, p. 73). Note that the
May 30, 1985 curve is the Dyers Spring BTC that is examined in detail in Section 7. on
page 128 and graphically as Figure 25 on page 139.

capable of approximating the environmental conditions for the given time period. This may
be accomplished using EHTD provided it is recognized that EHTD may only be considered

a screening-level model when used in this manner.

8.2.2.1. Using EHTD Directly to Forecast Pollution. Given some degree of
confidence regarding the ability of EHTD to suggest the appropriate mass of tracer to
release and sampling times, EHTD can be used as a quick screening model for addressing
pollutant releases. Consider the Dyers Spring example developed in Section 7.3.1.3. on
page 138 where EHTD was used to produce an acceptable estimate for time of travel and
tracer mass released.

The USGS standardized curve for this site was applied to a hypothetical release of
0.19 m® (50 gallons) of a 5% solution of copper sulfate (1.13 kg copper) into the karst
window from which the original tracer tests were conducted. Assuming a spring discharge
= 91.74 m® ho! (3.24 x 10° ft ho) the standardized curve method suggested (Mull et al.,
1988a, pp. 77-78):

155



- 0496E+01
-1352E+01
- 2209E+01
-3066E+01
.3922E+01
-4779E+01

FESO EOC O GIGS GE CG CISOEGI GCI GCI SI IOI ORCA ACE AA

CALCULATED TRACER-MASS: 1.040E+00 kg
1.040E+03 g
1.040E+06 mg

FESR COE OR ROR CG OGRE IGOR IOS EI AGIIOK AICI IEA ACK A a A

ERROR CODE DESCRIPTION

No change in sign of F(X*) was found although
the interval (A,B) collapsed to the requested
tolerance. The user must examine this case and
decide whether A is near a local minimum of F(X*)
or A is near a zero of even multiplicity, or
neither of these.

FAIA AAA GCI ICCAD GEICO CIS IOS AICI II ICA

RECOMMENDED TRACER-MASS: 1.040E+00 kg
1.040E+03 g
1.040E+06 mg

FESO CGC GOCE OGIO EOR IORI ICI ACACIA II

TRACER-TEST DESIGN PROGRAM RESULTS AS OF: 1/18/2002
2:39:20:30 pm

Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.

114



Concentration (ug L-!)
oa

Time (wk)

TRACER MASS = 516.54 g

— Breakthrough Curve
Sampling Times

Concentration (ug L-*)
o

33

T 7

TRACER MASS = 101.43 g

— Breakthrough Curve
¢ Sompiing Times

Figure 2. EHTD results for an impulse release for the karstic test parameters.



Table 21. Screen display of a typical EHTD warning message.

*** WARNING -- END OF FILE ASSUMED BECAUSE OF MISSING "END OF RUNS" FILE TERMINATOR ***
WARNING MESSAGE...THIS MESSAGE WILL ONLY BE PRINTED ONCE.

RECOVERABLE ERROR IN INPUT FILE
ERROR NUMBER = -t

Press <RETURN> to continue program

In instances where the user is interested in the effects created by solute retardation
and/or solute decay, the user may have EHTD run an optimization routine, which may
result in a slight modification of the estimated tracer mass and/or retardation and decay,
depending on whether one or the other or both are to be adjusted by EHTD. (See Section 3.7.
on page 55, Line Numbers 10-14 listed in Table 25 on page 86, and related discussion on
pages 93-95 for discussions related to EHTD optimization of the selected parameters.)

4.5.1. Screen Output of Error Messages

As EHTD progresses, various error messages may pop up from time to time. For the most
part, these can be ignored if they are only listed as warnings. More serious errors will stop
EHTD from any additional data processing.

4.5.1.1. Warning Messages. Warning messages are fairly common and are primarily
an indication of some abnormality in the user-specified input file that EHTD has recognized.
Usually, these warning messages can be ignored. For example, should the user construct an
input file that is missing the last three lines (two comment lines and the input file ending
command END OF RUNS), the warning message shown in Table 21 will appear. This message
is stating nothing more than that the user inadvertently did not complete the input file in
standard form (see Section 5. on page 83 for a detailed discussion of input file standard
forms), but EHTD has recognized this error and will process the input file anyway, so the
user is instructed to press <RETURN> to continue. The ERROR NUMBER = -1 will appear in

the output file with an explanation. Other basic warning messages are possible.

4.5.1.2. Error Messages. A more serious error, identified as fatal by EHTD, will also
occur if a critical item is missing from the user-specified input file. For example, should
the input file be missing the sampling station name (a required field), then EHTD will

75



ORGANIZATION OF THIS DOCUMENT

This document serves as a “user’s manual” for the computer program EHTD. It is arranged
in four parts:
e Part I Background

e Part II Model Theory and Method Background
e Part III Basic Program Usage
e Part IV Additional Application of EHTD

Part I introduces the program and provides the necessary for the new user to begin
running the program immediately. This is then followed by an in-depth review and
discussion of previous attempts at tracer test design.

Part II consists on a single section that is a comprehensive discussion of the relationship
between solute-transport theory and tracer test design as applied by EHTD. This section

will most likely be of interest to the more academic-type of scientists and engineers. More

practically-oriented individuals will likely want to skip reading this section.

Part III discusses the basic usage of EHTD. Section 4 explains how to run EHTD
including usage of the pull-down menus for manipulating screen display. Section 5 covers the
creation/modification of the input file read by EHTD. Section 6 is a detailed examination
of the output files produced by EHTD. Lastly, Section 7 validates EHTD functioning by
comparing the EHTD predictions for eight selected examples with actual tracer-test results.

Part IV also consists of just a single section that explains how EHTD can be used to
forecast the potential effects of inadvertent or deliberate pollutant releases. In addition, it
briefly illustrates the development of an input file of mean values for parameters created by
a Latin Hypercube Routine.



Contents
LIST OF TABLES

LIST OF FIGURES

PREFACE

ORGANIZATION OF THIS DOCUMENT
AUTHOR and REVIEWERS

ABSTRACT

I BACKGROUND
1. INTRODUCTION

1.1. QUICK START PROGRAM USAGE...........-...00004
1.1.1. Simple Program Usage... 2.2. ..-.0.0.000 00000004
1.1.2, Example Test Files 2... ee eee

2. REVIEW OF PREVIOUS TRACER TEST DESIGN METHODS
2.1. TRACER MASS ESTIMATION AND SAMPLING FREQUENCIES
2.1.1. Tracer Mass Estimation by Conjecture

a

2.1.1.1. Recent Arguments Opposing Rigorous Tracer Mass Estimation. 10

2.1.2. Tracer Mass Estimation by Mathematical Equation ........
2.1.2.1. Review of Tracer-Mass Estimation Equations. ......
2.1.2.2. Review of Sampling Frequencies. .............

2.2. EFFICIENT HYDROLOGIC TRACER-TEST DESIGN (EHTD) ....
2.2.1. Basic Design of EHTD ............. 2000000000.
2.2.2. Range of Capabilites of EHTD....................

2.3. TRACER-TEST DESIGN RESULTS USING PREVIOUS METHODS .. .

2.3.1. Examination of Tracer-Mass Estimation Equations ........
2.3.1.1. Porous Media. .. 1.0... ee ee

2.3.1.2. Karstic Media.

2.4.1.1. EHTD Porous-Media Analysis Results

2.5.1. Travel Times
2.5.2. Sampling times

iii

2.4, EHTD ANALYSIS OF THE TWO TRACER TESTS ...........
24.1. EHTD Results 2.2.2.2... 20... ee ee ee
2.4.1.2. EHTD Karstic-Media Analysis Results...........

2.4.2. Mass Required as Related to Sorption by Detectors ........

2.5. TRAVEL TIMES AND SAMPLING FREQUENCIES...........

2.5.2.1. Porous Media Sampling Times. .... 2.0.0.0...

11



Measured Data
NonReactive Transport
Reactive Transport

Concentration (ug L7’)

Time (h)

Figure 24. Comparison of measured data for the Missouri River tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rg = 1.13
and p= 0.0 ho}.

to obtain a better match to the measured BTC and tracer mass injected. The EHTD-

estimated D = 1.90 x 10’ m? h7! is clearly overestimated (Table 28), but this inaccuracy

would not appear to adversely affect the tracer test because the measured BTC would have
been defined if the EHTD-recommended sampling schedules were implemented.

As with the Uvas Creek tracer test, a relatively insignificant amount of tracer was added
directly to the stream water, resulting in Dy = V for both of the EHTD-predicted results
(Table 29). Interestingly, although the EHTD-predicted V and Dy reasonably approximated
the measured V, the EHTD-predicted V and Dy for the reactive case very nearly matches
the measured V.

7.3.1.3. Dyers Spring Tracer Test. Ground-water flow and solute transport through
solution conduits are commonly assessed by conducting quantitative tracer tests because
conventional methods, such as pumping tests, are generally insufficient for adequately
defining hydraulic parameters. Designing quantitative tracer tests in previously untraced
karstic terranes can be very difficult. Typically, a trial-and-error approach that relies on

138



Table 13. EHTD tracer test design parameters.

Parameter Porous Media Karst

Q, m3 ho 7.20 x 10! 3.60 x 10?
A? m? see 8.63 x 10°
L,m 5.00 x 10? 3.00 x 10°
Wim 1.00 x 10? ee
b,m 1.00 x 10!
Ne 1.00 x 10-? tee
gq, mh? 7.20 x 1071 3.60 x 10°
Cy, mg m=? 1.00 x 10? 1.00 x 10+
to?h 1.56 x 10° 9.63 x 10?
Cs mg m=? 0.00 x 10° 0.00 x 10°
~a$ dimen. 0.00 x 10° 0.00 x 10°
25 dimen. 0.00 x 10° 0.00 x 10°
on 1.00 x 10°
1.00 x 10° 1.00 x 10°
0.00 x 10° 0.00 x 10°

* For this analysis, A = Q/v for the karstic spring.
Normally Q and A would be measured concurrently
and the solution v = Q/A used by EHTD.

> Parameter required by EHTD for pulse and continu-
ous releases.

© These parameters not required by EHTD but must be
listed in the input file.

to ensure universality. The type of flow system tracer test can be simply a flowing stream

(open-channel or closed-conduit flow = surface-water stream or solution conduit) or it can be

porous media. EHTD analysis of porous media systems additionally requires consideration
of any one of the following hydraulic conditions:

1. Natural gradient tracer test,
2. Forced gradient tracer test (extraction well),
. Injection/withdrawal test (injection well rate = pumping well rate), or

. Recirculation test (injection well rate = pumping well rate while recirculating the
tracer back to the injection well).

The tracer test parameters listed in Table 13 relate to a solution conduit tracer test and a

30



for tracer mass enough to match the actual mass released and for predicted injection
concentration to match the actual injection concentration. However, the increase in tracer
mass also caused a slight negative shift of the descending limb of the predicted BTC because
of the required steepening of the BTC to maintain the desired C. Setting 4 = 0.0075 h-?
and Ry = 1.1 allowed for a good estimate for tracer mass and a slight positive shift in the
BTC, but with a slight decrease in predicted tp, a 2-hour increase for t; and ty (Table 31),
and a l-hour increase for C, (Table 32).

EHTD-suggested sampling times may be regarded as adequate for defining the measured
BTC. The multimodal measured BTC for the Mobile Site clearly illustrates the need for
frequent sampling if the BTC is to be properly defined (Figure 29). Although not as
frequent as the average sample collection frequency t '¢ of 5 hours for the measured BTC, a
t7 = 19 hours is probably reasonable for defining the BTC while not being excessive. Tracer
sampling ceased prior to complete tracer recovery, so it is difficult to determine whether
EHTD adequately predicted final tracer recovery.

Predicted dilution volumes for the Mobile Site tracer test exceeded the predicted system
volumes, but the dilution volumes reasonably matched the measured system volumes
(Table 32). The good estimation for Dy would have enhanced the predictions for M,
but the poor match of the predicted V to the measured V was unexpected, although it

appears not to have adversely influenced the tracer mass prediction for the reactive case.

7.3.2.4. Chalk River Site Tracer Test. Recirculation tracer tests are rarely em-
ployed to evaluate transport parameters in porous media systems. A recirculation tracer
test conducted at the Chalk River Site was very well predicted by EHTD for both the non-
reactive and reactive cases (Figure 30). The EHTD-predicted results for the nonreactive
case produced a good fit to the measured BTC and a nearly exact match of the predicted
# to the measured é but a very poor match for predicted ty to the measured t, (Table 31).
The incorrectly estimated tp was caused by recirculating the recovered tracer back into the
injection well while tracer recovery from the start of the tracer test was still occurring.
Average velocity, D, and P, were also very well matched.

EHTD-estimated tracer mass for the nonreactive case was four times less than the actual
tracer mass released. Setting 4. = 0.011 h7! resulted in a close match to the actual tracer
mass released and injection concentration, but it also produced a slight negative shift in
the BTC. Setting Ry = 1.1 caused a positive shift of the BTC that matched the measured
BTC and the mass released. Allowing for tracer decay caused the EHTD-predicted BTC to

149



Table 18. Recommended sampling times for selected tracer reaction conditions.

Sampling Time, hours

Sample AZ=1.0 RR=10 RZ=10 RI=1.0 RE=20 Ri =30

Number p=0.0 p=0.01 p=005 p=01 p=00 u=0.0
1 7.13 7.15 7.02 7.il 14.26 21.39
2 7.75 7.77 7.63 7.69 15.51 23.26
3 8.37 8.39 8.23 8.28 16.75 25.12
4 9.00 9.00 8.84 8.86 17.99 26.99
5 9.62 9.62 9.45 9.45 19.24 28.85
6 10.24 10.23 10.06 10.03 20.48 30.72
7 10.86 10.85 10.66 10.62 21.72 32.58
8 11.48 11.47 11.27 11.20 22.96 34.45
9 12.10 12.08 11.88 11.79 24.21 36.31
10 12.73 12.70 12.49 12.37 25.45 38.17
il 13.35 13.31 13.09 12.96 26.69 40.04
12 13.97 13.93 13.70 13.54 27.94 41.90
13 14.59 14.54 14.31 14.13 29.18 43.77
4 15.21 15.16 14.92 14.71 30.42 45.63
15 15.83 15.78 15.52 15.30 31.66 47.50
16 16.45 16.39 16.13 15.88 32.91 49.36
17 17.08 17.01 16.74 16.47 34.15 51.23
18 17.70 17.62 17.35 17.05 35.39 53.09
19 18.32 18.24 17.95 17.64 36.64 54.95
20 18.94 18.86 18.56 18.22 37.88 56.82
21 19.57 19.47 19.17 18.81 39.12 58.68
22 20.18 20.09 19.78 19.39 40.37 60.55,
23 20.80 20.70 20.38 19.98 41.61 62.41
24 21.43 21.32 20.99 20.56 42.86 64.28
25 22.05 21.93 21.60 21.15 44.09 66.14
26 22.67 22.55 22.20 21.73 45.34 68.01
27 23.29 23.17 22.81 22.32 46.58 69.87
28 23.91 23.78 23.42 22.90 47.82 71.73
29 24.53 24.40 24.03 23.49 49.07 73.60
30 25.15 25.01 24.63 24.07 50.31 75.46
31 25.78 25.63 25.24 24.66 51.55 77.33
32 26.40 26.25 25.85 25.24 52.79 79.19
33 27.02 26.86 26.46 25.83 54.04 81.06
34 27.64 27.48 27.06 26.41 55.28 82.92
35 28.26 28.09 27.67 27.00 56.52 84.79
28.88 28.71 28.28 27.58 57.77 86.65

61

continued on next page



NO PLOT FILE SPECIFIED, RESULTS WILL NOT BE WRITTEN TO A PLOT FILE!
followed by:

FILE NAMES HAVE BEEN READ

4.3. USER-REQUESTED LATIN HYPERCUBE SAMPLING (LHS) ROU-
TINE

After the last file name has been read, EHTD will ask if you want to generate a series
of input files using a Latin Hypercube Sampling (LHS) routine and the original input file
parameters as initial parameters to be randomly selected within an appropriate range. This
routine was added to allow the user to consider the effect of conditions that may differ from
the measured conditions. At the end of each LHS-generated input file, a suggested solute
mass to manually enter is provided (see Section 4.4.). A comprehensive discussion of LHS
is provided in Iman and Helton (1988) and McKay et al. (1979).
The actual LHS query appears as:

DO YOU WANT TO RUN THE LATIN HYPERCUBE SAMPLING ROUTINE (Y=YES, N=NQ)?

Pressing N causes the LHS routine to be ignored only for the particular sampling station

currently being evaluated by EHTD. Subsequent sampling stations that are part of the

overall input file will each be queried as to whether the user would like to run the LHS
routine.

Pressing Y causes a second query:
DO YOU WANT TO GENERATE A SERIES OF INPUT FILES OR ONE FILE OF MEAN VALUES?
1=INPUT FILES
2=FILE OF MEANS

Entering 1 causes the following request:

ENTER THE NUMBER OF LHS-DEVELOPED INPUT FILES DESIRED (N > 12):



SEPA Beste
Tracer-Test Planning Using the

Efficient Hydrologic Tracer-Test
Design (EHTD) Program

x xX



Line 18 as:

STOP PROCESSING

which is ignored by EHTD but is useful for recognizing Line 19, which is READ by
EHTD if included. Line 18 can be left blank if desired.

Line 19 is a stopping criterion that is specifically listed End of Runs and that is READ by
EHTD. It intended to facilitate EHTD processing, but it is not required. Line 19 may

be left blank without any expected processing difficulties, but a warning message to

the user is returned. Using the stopping criterion End of Runs is useful for allowing
the inclusion of file notes to be included at the end of the data input file. For example,
Figure 10 lists Line 19 as:

End of Runs

Karstic site

Tracer injection to occur in a sinking stream
Tracer recovery expected at two springs
Discharge measurements made on date

where the informational statements following Line 19 are not processed by EHTD
but are useful notes. In particular, the date when discharge measurements were taken

is very valuable, because discharges can change radically over very short time periods.

96



Levenspiel, O., 1999. Chemical Reaction Engineering, 668 p. John Wiley & Sons, New York.

Lutz, T., Parriaux, A., 1988. The Identification of Uranine in Natural Water by High
Pressure Liquid Chromatography (HPLC). In: Goldbrunner, J. (Ed.), Steirische Beitrage
zur Hydrogeologie. Vol. 39. Joanneum Research, Graz, Germany, pp. 141-148.

Mackay, D. M., Freyberg, D. L., Roberts, P. V., Cherry, J. A., 1986. A natural gradient
experiment on solute transport in a sand aquifer: 1. Approach and overview of plume
management. Water Resour. Res. 22(13), 2017-2029.

Matoszewski, P., Harum, T., Benischke, R., 1992a. Mathematical modelling of tracer
experiments in the karst of lurbach system. In: Behrens, H., Benischke, R., Bricelj,
M., Harum, T., Ké8, W., Kosi, G., Leditzky, H. P., Leibundgut, C., Matoszewski, P.,
Maurin, V., Rajner, V., Rank, D., Reichert, B., Stadler, H., Stichler, W., Trimborn,
P., Zojer, H., Zupan, M. (Eds.), Investigations with natural and artificial tracers in the
karst aquifer of the Lurbach system (Peggau~Tanneben-Semriach, Austria), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 116-136.

Matoszewski, P., Leibundgut, C., Schneider, J., 1992b. Mathematical Modelling of the
Tracer Experiment Performed in the Test Site Wilerwald. In: Leibundgut, C., De Car-
valho Dill, A., Matoszewski, P., Miiller, I., Schneider, J. (Eds.), Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitriige zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.

Martel, 1913. Sur les expériences de fluorescéine & grandes distances. C. R. Academy Sciences
157, 1102-1104.

McAvoy, D. C., Masscheleyn, P., Peng, C., Morrall, S. W., Casilla, A. B., Lim, J. M. U.,
Gregorio, E. G., 2003. Risk assessment approach for untreated wastewater using the
QUAL2E water quality model. Chemosphere , in press.

McCann, M. R., Krothe, N. C., 1992. Development of a monitoring program at a superfund

site in a karst terrane near Bloomington, Indiana. In: Quinlan, J. (Ed.), Proceedings of

170



PROJECT NAME

KARST EXAMPLE -- LOST RIVER CAVE SYSTEM

FLOW RELEAS RTIM (h) INFLOW (m*3/h) UNITS

1 1 0.0 0.0 1

ZERO RAO ACSA AIEEE AKIGBE ASE OSES TIES SAI SEE I AAA A
STATION NAME

LOST RIVER RISE

DISCHARGE (m73/h) DISTANCE (m) AREA (m*2) SINUOSITY FACTOR

6 .408E3 8000.0 18.8 41.0

INIT. CONC. (ug/L) GAMMA1 GAMMA2

0.3 0.5 0.5

RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)
1.0 0.0 0 18.3

1 1

1.0 0.0

10.0 5.0

JESS ABCC OO OIOS SBS EGE SE SI IC IARIGIGSIO IGE IGA AR A A
STOP PROCESSING
END OF RUNS

Figure 17. Example input file with an initial concentration and exponential production

constants.

119



3 T T T T T T

Bs e-o— Measured Data
ra —A-4— NonReactive Transport
=.~ Reactive Transport

Concentration (ug L71)

Time (d)

Figure 28. Comparison of measured data for the Kirchdorf-Unteropfingen site tracer test

with EHTD-predicted results for nonreactive and reactive transport. For reactive transport,
Ra = 1.0 and p = 0.0003 h-!.

the incorrectly estimated n, obtained from the pumping test.

The tracer test design used an ne = 0.14, which is the value of the specific yield obtained
from the pumping test. This n. was later found to be significantly in error. Tracer test
analysis resulted in an n. = 0.08 (Ka8, 1998, pp. 515-516), which when applied to EHTD
produces much better BTC fits to the measured BTC.

Estimated tracer mass for the nonreactive case closely matched the actual tracer mass
released. Setting = 0.0003 h~! produced a slightly greater estimate for tracer mass than
was released. However, this slight increase in tracer mass also resulted in a slight shift in
the decreasing limb of the BTC.

Although the EHTD-predicted BTCs failed to adequately match the measured BTC,
EHTD did reasonably predict the appropriate tracer mass to release. EHTD-recommmended
sample collection times for the Kirchdorf-Unteropfingen tracer test were generally adequate
for defining the BTC, although initial tracer breakthrough was not predicted by EHTD.

For the Kirchdorf-Unteropfingen tracer test, tracer occurred as an impulse release, the
effect of which was an insignificant amount, so Dy = V for both of the EHTD-predicted

147



DISCLAIMER

This document has been reviewed in accordance with U.S. Environmental Protection Agency
policy and approved for publication. Mention of trade names or commercial products does
not constitute endorsement or recommendation for use.

Preferred citation:

U.S. Environmental Protection Agency (EPA). (2003)Tracer-Test Planning Using the Efficient Hydrologic
Tracer-Test Design (EHTD) Program. National Center for Environmental Assessment, Washington, DC;
EPA/600/R-03/034. Available from: National Technical Information Service, VA; PB2003-103271, and
<http: //www.epa.gov/ncea>.

ii





6. EHTD OUTPUT FILES

EHTD produces only minimal screen output. For the most part, screen output is limited
to estimates for tracer mass and warning and/or error messages related to the respective
input file and processing. Most of this information can be ignored by the user, as all of the
screen text output is reproduced in much greater detail in the EHTD output file.

Upon completion of input file processing, EHTD automatically develops a screen plot of
the likely BTC according to the data contained in the input file. As noted in Section 3.1.
the BTC developed by EHTD is based on the conventional ADE using any one of the three
solutions listed in Section 3.2.1., Equations (54) - (57). It will be noted that unless the
user specifically informs EHTD to produce a Plot File during program initiation or saves
the screen plot as a *.bmp file (see Section 4.6.1.), no final'screen plot will be produced for

later viewing.
6.1. DESCRIPTION OF OUTPUT FILES

Entering the name of a typical EHTD data input file when requested by EHTD (see
Section 4.2.), the requested data output file name, and the requested plot file name, if
desired, results in rapid data processing by EHTD. Figure 12 represents a typical data input
file. It consists of measured data developed for the Lost River Cave System in Kentucky, in
which recovery was expected at the Lost River Rise [see Field and Pinsky (2000) for a brief
discussion of the site]. Upon completion of input file processing by EHTD, a conventional
BTC is plotted on the CRT screen (Figure 13). This plot displays the recommended tracer
mass necessary to generate the particular BTC displayed. If multiple recovery stations were
listed in the input file (see Figure 10 for a general example), then the final output file will
recommend a tracer mass that is developed by summing the masses recommended for each
individual sampling station.

If a plot file is requested of EHTD by the user, then a standard plot file in ASCII
format will be produced. Figure 14 depicts the plot file developed by EHTD from the Lost
River Cave System data input file (Figure 12). The first two columns of data in Figure 14
are much longer than the second two columns and represent the data points generated by
EHTD to produce the BTC. The second two columns of data never exceed 65 data points
and represent the recommended sampling times and likely concentration values.

Data processing completion by EHTD also completes the development of data output
files that describe the results of EHTD analysis. The data output files are quite long because

97



Table 7. Prevailing test conditions coefficient To,*.

Prevailing Condition Teo, To,»

Rapid flow in channels 0.1- 09
Photosensitive decay 2.0- 4.0
Surface-water flow Q > 3.6 x 10® 2.0- 4.0
River-bank filtration Q < 1.8 x 104 2.0- 4.0 tee
Ground-water flow K < 0.36 m hu" oe 1.006
Ground-water flow K < 3.6m hTM}[?] 2.0- 4.0 ve
Ground-water flow 0.36 < K < 3.6mh7 ee 0.505
Ground-water flow K > 3.6m h7+ cee 0.256
Fractured-rock studies ee 0.2 — 2.0
Fractured-rock studies with w > 60° 2.0- 4. 2.0 - 4.0
Karstic aquifers in general ut 0.2 - 1.0
Karstic aquifers with inflow ee 10 (sees)? 93
Unsaturated zone 1-30 m thick 2.0— 4.0 oe
Low tracer-background levels 2.0- 4.0
Turbid samples or 2.0- 4.0

samples with natural fluorescence
Unsaturated zone >30 m thick 5.0 — 10.0
Soil zone with cohesive soils 5.0 — 10.0
Studies near a ground-water divide 5.0 — 10.0
Multiple recovery stations likely 5.0 - 10.0

@ Source: Adapted from (Ka, 1998, p. 328).
> Modifications to Tc, from (Schudel et al., 2002, p 21).

and Tc, (Tables 6 and 7), which requires considerable insight and/or experience on the part
of the practitioner. Modifications to To, and Tc, were obtained from Schudel et al. (2002,
p 21) as shown in Tables 6 and 7 but the requirements of insight and experience have not
been alleviated.

Equation (12) is listed as being valid only when Q < 5.0m*s7! and L > 12km.
Equation (13) uses a ratio of swallet inflow to spring discharge Q/g, although the reasoning
for this is not explained. Equation (13) is expected to overestimate tracer mass for
predominantly vadose systems > 1 km (Gaspar, 1987, p. 49).

Equation (14) is intended for use with In-EDTA, and it also includes a loss coefficient
P = 1-3 anda safety factor Ss < 2. The loss coefficient P represents the mass injected to
the mass recovered, and it is justified on the reasoning that some mass of the tracer will
be retained in the system (Gaspar, 1987, p. 50). The rationale for setting S; at < 2 is not

18



Table 23. Typical screen display of optimization results.

I INITIAL X(I) D(I)

1 0. 183887D+09 0.600D+00

2 0. 100000D+01 0.521D+05,
3 0..000000D+00 0. 206D+05,
IT WF F RELDF PRELDF RELDX MODEL STPPAR D*STEP = NPRELDF.

0 1 0.152D-70
1 2 0.152D-70 0.00D+00:0.44D-77 0. 0D+00 G 0.0D+00  0.3D-71 0.44D-77

seeeex K- AND RELATIVE FUNCTION CONVERGENCE +*4#x

FUNCTION 0.151871D-70  RELDX 0.000D+00
FUNC. EVALS 2 GRAD. EVALS 3
PRELDF 0.440D-77 ‘NPRELRF 0.440D-77
I FINAL X(I) DCL) GC)
1 0.183887D+09 0.600D+00 0.165D-78
2 — 0.100000D+014 0.521D+05, -0.306D-68
3 0,000000D+00 0.206D+05 0.199D-69

FINAL TRACER MASS ESTIMATE

MASS = 1.84E+05 g

Press <RETURN> to initiate plot routine

4.5.2. Screen Output of Optimization Results

Selecting the optimization routine may result in a slight alteration of the estimated tracer
mass, the tracer retardation, and/or the tracer decay. Prior to displaying the final tracer
mass estimate, EHTD will display the results of the optimization routine, which will appear
similar to the one shown in Table 23.

Most of the information provided in Table 23 will be of little use and may be ignored.
However, at the top of Table 23 is a list of the parameter values (I) selected for optimization,
their initial values (INITIAL X(I)), and the derivative of each (D(I)). For this example,
three parameters are shown; the order will always be MASS, RETARDATION, and DECAY unless
retardation is not included in the optimization routine, in which case the order would be
MASS and DECAY.

The next row (IT NF F...) is an indication of the optimization iterations that

will follow and related operations (only one iteration after an initial value for this example).

77



Table 20. Variable parameter types used in the LHS routine.
Variable Porous Media Flowing Stream

Mass Mass

Discharge Discharge

Effective Porosity Cross-Sectional Area
Aquifer Thickness Lateral Transport Distance
Lateral Transport Distance Initial Concentration
Transverse Transport Distance First Production Coefficient
Initial Concentration Second Production Coefficient
First Production Coefficient Retardation

Second Production Coefficient Decay

Retardation

Decay

FPOMODNANRwWNH

PR

original input file. This one file will contain all of the LHS-generated input files, which the
user may then selectively enter into EHTD by copying and pasting the desired input file as
a new file.

Alternatively, if one input file of mean values was selected (2=FILE OF MEANS), a single

input file consisting of the mean values of the required parameters (e.g., discharge, Q)

will be developed followed by a comprehensive set of univariate statistics that describe the
parameters. The statistics listing is ignored by EHTD when this file is later processed (if
processing is initiated by the user) because it appears after the “END OF FILES” input file
statement. The univariate statistics, developed using the equations shown in the box in
Figure 9 on the next page, provide a sense of the range and distribution of values produced
by the LHS routine. Substitution of, for example, the minimum or maximum value of a
selected parameter (e.g., Stat(6,*) and Stat(7, +), respectively in Figure 9 on the following
page) may be a desirable change in some instances. It is necessary to note here that the
parameters used in the univariate statistics are listed as individual variables identified in
Table 20.

4.4. USER-SUGGESTED SOLUTE MASS

At this point the user will be queried by EHTD as to whether the user would like to suggest
a solute mass (tracer or pollutant) for EHTD to use. This feature is useful for predicting
the outcome of an accidental spill or a deliberate release of a highly toxic substance, as

might occur from a terrorist attack. A similar type of approach was developed by Taylor

72



overall strategy for protecting human health. This set of alternatives could range from no

action (i.e., no significant concern) to disconnecting the water-supply system, announcing

a no-contact warning, and arranging for the supply of an alternative water source.



3. TRACER-TEST DESIGN METHODOLOGY

Previous efforts aimed at estimating tracer mass to be released for a tracer test focused
primarily on expected dilution and drew upon the originators experience. None of the
previous efforts appear to have been derived according to solute-transport theory. It would
also appear that solute-transport theory was seldom considered in designing tracer-sampling
schedules. Solute-transport theory in natural and controlled systems has been investigated
extensively and is well-understood. It would seem appropriate then to consider solute-
transport theory as a tool for determining the optimal tracer mass for release and sample-

collection frequency.
3.1. SOLUTE-TRANSPORT MODELING

Numerous model variations designed to describe solute transport have been developed.
A general one-dimensional advection-dispersion equation (ADE) typically appears as (see

Notations section)

oC PC aC
Rasy = Dap UR uc + 72) (43)

The retardation factor Rg can represent retardation in porous media by (Freeze and Cherry,
1979, p. 404)

pPoKa

Rg=1+ 0 (44)
or Ra can represent retardation in fractured media by (Freeze and Cherry, 1979, p. 411)
2K,
Rg=1+ (45)
by
or Rg can represent retardation in a solution conduit by (Field and Pinsky, 2000)
2K,
Ra=1+——% (46)

Tr

The first-order rate coefficient for tracer decay in porous media is given as (Toride
et al., 1995, p. 3)

Kapts
po=mt Pb ih (47)
in fractured media may be taken as
2Kabs
w= int ae (48)
f

42



9. SUMMARY AND CONCLUSIONS

Hydrologic tracer testing is an essential method of study for evaluating solute transport
processes. However, the initial design of most tracer tests can be problematic due to
a lack of prior knowledge concerning the hydrologic transport properties for which the
tracer test is intended. A simple, reliable method for designing tracer tests has been
developed by solving the one-dimensional advection-dispersion equation (ADE) for a preset
average tracer concentration. This tracer design method provides a sound theoretical
basis for estimating tracer mass and sample collection frequency by combining basic field
measurements for hydraulic and geometric parameters in functional relationships that
describe solute transport processes to estimate flow velocity and times of travel.

These relationships are then applied to a hypothetical continuous stirred tank reactor
(CSTR) as an analog for the hydrologic flow system to develop estimates for tracer
concentration and axial dispersion based on the preset average tracer concentration.
Solution of the one-dimensional ADE using the preset average tracer concentration then
allows for an estimate of necessary tracer mass. Application of the predicted tracer mass
with the hydraulic and geometric parameters in the ADE further allows for an approximation
of initial sample-collection time and subsequent sample collection frequency.

Tracer retardation and decay cause an increase in tracer mass estimates because the set
average tracer concentration is maintained by the method. Retardation has the added effect
of delaying tracer breakthrough and causing more spread in the tracer-breakthrough curve
(BTC), which can have significant consequences for determining when to initiate sample
collection and at what frequency all subsequent samples should be collected. However,
experience with common tracers in various environments serves to trivialize this problem.
Prior evaluations of distribution coefficients and simulations using selected values for
retardation and decay can further limit the errors that may occur from tracer reactions
with solids.

The method does not attempt to physically predict the conditions that may cause
multimodal or long-tailed BTCs because it is not possible or necessary to add such
complexity. It also does not address the possible occurrence of density-induced sinking. Not
only would estimates for unknown parameters be required (e.g., mass transfer coefficient),
but the effect of adding such complexity would not greatly improve the estimates for required
tracer mass or recommended sampling frequency.

159



Generic Flowing Stream Input File

PROJECT NAME
Name of Planned Tracer Test
FLOW RELEAS RTIM (h) INFLOW (m73/h) UNITS

FIO IIR AR OI ICR ROR IO Ra aC aa a Kk 2k ai a ak ke a 2k ko ak a ak a ko eo ak a ak ok ak ek ak ak a a ak ok ake ae
STATION NAME

Name of Sample Station 1

DISCHARGE (m73/h) DISTANCE (m) AREA (m~2) SINUOSITY FACTOR

INIT. CONC. (ug73/L) GAMMA1 GAMMA2

RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)

FEA AAO GIGS E OIA SIS IG CIOIIAOIII OI AII I AA IA.
STATION NAME

Name of sample station 2

DISCHARGE (m73/h) DISTANCE (m) AREA (m2) SINUOSITY FACTOR

INIT. CONC. (ug~3/L) GAMMA1 GAMMA2

RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)

FOC AIC IGOR IO AC A IGOR IO IR IG RR a 2 aR a ak a a a a
18 STOP PROCESSING
19 End of Runs

Figure 10. Generic example of an flowing stream input file illustrating the basic format used
by EHTD for processing. Note that the Line numbers are not part of a typical input file
and are listed here only for reference purposes for Table 25. Also note that Lines 6-17 are
repeated for each individual sampling station considered for the particular study.

84



Silebi, C. A., Schiesser, W. E., 1992. Dynamic Modeling of Transport Process Systems, 518
p. Academic Press, San Diego, Calif.

Siline-Bektchourine, A. I., 1951. Hydrogéologie Spéciale, 394 p. Gossendarctvennoe Iz-
datelctvo Geologitcheshoi Litertouri, Moscow.

Smart, C., Zabo, L., 1997. Experimental design, technique and protocol in fluorometric
tracing of ground water. In: Proceedings of the 12th International Congress of Speleology;
6th Conference on Limestone Hydrology and Fissured Media. Vol. 2. International Union
of Speleology and Swiss Speleological Society, La Chaux de Fonds, Switzerland, pp. 51-54.

Smart, C. C., 1988. Artificial tracer techniques for the determination of the structure of
conduit aquifers. Ground Water 26(4), 445-453.

Smart, C. C., Karunaratne, K. C., 2001. Statistical characterization of natural background
fluorescence as an aid to dye tracer test design. In: Beck, B. F., Herring, J. G. (Eds.),
Proceedings of the Eighth Multidisciplinary Conference on Sinkholes and the Engineering
and Environmental Applications of Karst Geology and Hydrology. Lamoreau and Assoc.,
Oak Ridge, Tenn., pp. 271-276.

Smart, C. C., Simpson, B., 2001. An evaluation of the performance of activated charcoal in
detection of fluorescent compounds in the environment. In: Beck, B. F., Herring, J. G.
(Eds.), Proceedings of the Eighth Multidisciplinary Conference on Sinkholes and the
Engineering and Environmental Applications of Karst Geology and Hydrology. Lamoreau
and Assoc., Oak Ridge, Tenn., pp. 265-270.

Smart, P. L., Atkinson, T. C., Laidlaw, I. M. S., Newson, M. D., Trudgill, S. T.,
1986. Comparison of the results of quantitative and nonquantitative tracer tests for
determination of karst conduit networks: An example from the Traligil] Basin, Scotland.
Earth Surface Processes 11, 249-261.

Smart, P. L., Friederich, H., 1982. An assessment of the methods and results of water-
tracing experiments in the Gunung Mulu National Park, Sarawak. British Cave Research
Association, Transactions 9, 100-112.

Sutton, D. J., Kabala, Z. J., Francisco, A., Vasudevan, D., 2001. Limitations and potential
of commercially available rhodamine WT as a groundwater tracer. Water Resources
Research 37(6), 1641-1656.

173



NAME OF DATA FILE

LATIN HYPERCUBE FILE NUMBER 1

FLOW RELEAS RTIM (bh) INFLOW (m3/h) UNITS
1 1 0.0 0.0 1

poprrreprevernrrccrem@enrecenrrtrrrrreno © Soo oc rs Soto
STATION NAME

DYERS SPRING

DISCHARGE (m*3/h) DISTANCE (m) AREA (m*2) SINUOSITY FACTOR
2.499E+02 9. 195E+02 1.991E+00 1.0

INIT. CONC. (ug/L) GAMMAL GAMMA2

5.000E-01 5.000E-01 5 .000E-01

RETARDATION DECAY (1/h) opTIM AVE. CONC. (ug/L)
1.483E+00 9.000E-02 1 4.120E+00

1 1

1.0 0.0

10.0 5.0

eR EH HH nero BEER E EEO EEA EIA RRA
RUNS

STOP PROCESSING
LHS SUGGESTED USER INPUT SOLUTE MASS = 7.662E+00 g

Univariate Statistics from UVSTA

Variable Mean Variance Std. Dev. Skewness
1 7.66154 79.211682 -90009 1.4285
249.88990  0.8427E+05 29028670 1.4285

1.99133 0.615789 -T8AT2 0.4743

919.47539  9349.850234 -69462 0.1262

0.50000 0.083358
0.50000 0.083358
1.48261 0.099951
0.09000 0.002701

28872 -0.5487E-16
28872 0.3864E-16
31615 0.2561
.05197 0. 6316E-16

8
10
0)
16
0.50000 0.083358 0.28872 -0.7563E-16
°
°
°
0.

Minimum Maximum Range Coef. Var.
0.3563 35.6343 36.2779 -1617
11.6225  1162.2528 150.6303 -1617
0.9202 3.6807 2.7605 3944
762.0000 1097. 2800 335.2800 1052
0.0000 1.0000 1.0000 “8774
0.0000 1.0000 1.0000 S774
0.0000 1.0000 1.0000 5774
1.0000 2.1000 1.1000 2132
0.0000 0.1800 0.1800 8774

Variable Lower CIM Upper CLM = Lower CLV —Upper CLV
748108 7.83600 7.061028 © 81.454079

244.19970  255.58010 0.8198E+05 86651 .8540

1.97595 2.00671 0.599069 0.633221

917.57999 37080 9095.994980 9614.534266

0.49434 0.50566 0.081095 -088718

0.49434 0.50566 0.081095 088718

0.49434 0.50566 0.081095 -085718
1.47641 1.48881 0.097237 -102780
0.08898 0.09102 0.002627 .002777

Figure 34. LHS-generated input file of means using the Dyers Spring parameters. Note
CLM and CLV represent the confidence levels for the mean and the variance, respectively. All
other table headings should be readily apparent.



Sixty-five sampling times were developed to adequately determine when the first sample
should be collected and to properly define the BTC. Breakthrough curve definition requires
that the BTC peak be correctly identified and that a potentially long tail be detected.
Further, in order to avoid the effects of data aliasing, a substantial number of samples
are required (Smart, 1988). Although 20 to 30 samples have been suggested by others as
adequate for BTC definition (Novakowski, 1992; Kilpatrick and Wilson, 1989, p. 18), these
researchers were not concerned with problems associated with long tails or data aliasing.
To ensure that data aliasing is avoided, 60 sample-collection times are developed by EHTD
which allows for better BTC definition without excessive sampling. However, should 60
samples prove to be excessive, it is always possible to choose to collect some fraction of
60. To ensure that initial tracer breakthrough is not missed, n, = 5 was included as an

appropriate number of samples to collect prior to expected tracer breakthrough.

63



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9S ve <4 er 9 v 00'S S
9¢ 114 <4 car 9 v 06% v
9g ve Vo rai 9 v ort £
9g <4 ral 9 v 4 S60 4
9g Ve al 9 v 4 09°0 T

60s SMe 1% GT she pI-gsheq L-Gskeq p-Esheq ZT skeq uly ‘sowEysIG. “ON A4IS

sinoy ‘[easequy Surjdureg

“puvdle) Jsrey @ JOY a[npayos Suydures oytoedg “QT equi,

24

“(4g 'd ‘Ug6T “redsep) pur (G2z “d ‘TR6T ‘plAoueTA)) Wor pordepy ‘oomog y

8h Ve ol ras rai rai 0I<
8h ve fai 8 9 v OI-T
Ve Ve er-8 oF ts z T

gt Aeq gheq 9 + skeq gkeq ZAeq | Aeq wry ‘aoueysig.
sanoy ‘Teasojuy Suydureg
“PURITY JSIVY B IO} o[Npoyps Suydures pesouory “G aqey,



Kilpatrick, F. A., Cobb, E. D., 1985. Measurement of Discharge Using Tracers. Tech.
Rep. Techniques of Water-Resources Investigations, Book 3, Chapter A16, 52 p., US.
Geological Survey.

Kilpatrick, F. A., Taylor, K. R., 1986. Generalization and Application of Tracer Dispersion
Data. Water Resources Bulletin 22(4), 537-548.

Kilpatrick, F. A., Wilson, Jr., J. F., 1989. Measurement of Time of Travel in Streams by
Dye Tracing. Tech. Rep. 27 Techniques of Water-Resources Investigations of the U.S.
Geological Survey, Book 3, Chapter A9, 27 p., U.S. Geological Survey.

Kinnunen, K., 1978. Tracing Water Movement by Means of eschericia coli bacteriophages.
Tech. Rep. Publication of Water Research Institute, 25, 50 p., National Board of Waters,
Finland.

Leibundgut, C., 1981. Zum Anwendung Kiistlicher Tracerin Gletscher, 85 p. Publikation
Gewasserkde, No. 85, Unversity of Bern.

Leibundgut, C., 1992. Test Site. In: Leibundgut, C., De Carvalho Dill, A., Matoszewski, P.,
Miiller, I., Schneider, J. (Eds.), Investigation of Solute Transport in the Porous Aquifer
of the Test Site Wilerwald (Switzerland), Steirische Beitrage zur Hydrogeologie, 6th
International Symposium on Water Tracing, Transport Phenomena in Different Aquifers
(Investigations 1987-1992). Vol. 43. Joanneum Research, Graz, Germany, pp. 229-250.

Leibundgut, C., De Carvalho Dill, A., 1992. Tracer Tests. In: Leibundgut, C., De Car-
valho Dill, A., Matoszewski, P., Miiller, I., Schneider, J. (Eds.}, Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport
Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.

Leibundgut, C., Wernli, H. R., 1982. Zur Frage der Einspeisemengenberechnung fiir
Fluoreszenztracer. In: Leibundgut, C., Weingartner, R. (Eds.), Tracermethoden in der
Hydrologie, Beitrage Geologie Schweiz — Hydrologie. Vol. 28(I). Geographischer Vrlag,
Bern, Switzerland, pp. 119-130.

Leibungut, C., 1974. Fluoreszierende markierfarbstoffe in der hydrologie. In: Mitt. Natur-
forsh. Ges. Bern, N.F. Vol. 31. Bern, Switzerland, pp. 63-84.

169



2.4.1.1. EHTD Porous-Media Analysis Results. Comparisons with EHTD-estimated
tracer mass for the impulse release for the porous media tracer test suggest that only Equa-
tions (12), (18), (23), (26), (30), and (32) can reasonably be considered for estimating tracer
mass. Of these, only Equation (26) gave a greater result that was greater than the EHTD-
estimated tracer mass, the other values being relatively low. Interestingly, Equation (12) is
considered invalid for these conditions (Z < 12 km), whereas Equation (30) is considered
valid for tracing solution conduits. Equations (18), (23), (26), and (32) were all intended
for tracing surface water. For the pulse release, Equation (25) underestimated M slightly
relative to EHTD, probably as a result of the lack of consideration for additional dilution

effects caused by q.

2.4.1.2. EHTD Karstic-Media Analysis Results. Comparisons with EHTD-estimated
tracer mass for the karstic tracer test suggest that only Equations (1a), (4), (5a), (18), (22),
(23), (26), (27), and (29) reasonably estimate the appropriate mass of tracer to release.
The results of equations (1a), (5a), and (29) are low relative to the EHTD-estimated tracer
mass, whereas those for Equations (4) and (18), (22), (23), (26), (27) are relatively high.
Equations (4), (5a), and (29) all require the use of multipliers representing tracer-dependent
factors controlled by aquifer conditions. These multipliers may also assume a range of val-
ues, but only Equation (29) is reasonably specific regarding which multiplier value to use
for the given conditions. As with the porous media tracer test, the pulse release described
by Equation (25) underestimated M slightly relative to EHTD, again probably as a result

of the lack of consideration for additional dilution effects caused by q.

2.4.2. Mass Required as Related to Sorption by Detectors

Several of the 33 equations listed in Table 3, for example, Equations (5a), (21), (22), and
(29), were specifically intended for sorption onto detectors, allowing for reduced tracer-dye
concentrations. For the porous media tracer test, Equation (5a), (19), (22), and (29) all
resulted in a lower estimated tracer mass than the mass suggested by EHTD. For the karstic
tracer test, Equations (5a), (19)—-(22), (29) all resulted in greater tracer mass estimates than
suggested by EHTD.

In general, the vast majority of the 32 of 33 equations listed in Table 3 and tested resulted
in much greater tracer mass estimates than suggested by EHTD for either the porous media
system or the karstic system. Tracer dye concentration enhancement by activated carbon

should allow for much lower tracer mass estimates than predicted by EHTD. However,

36



of the large amount of information developed by EHTD to produce a reliable prediction of

results.

6.1.1. EHTD-Produced Data Output Files

EHTD-produced data output files are very detailed and organized. Each data output file is
organized in a manner that allows the user to follow how EHTD progressed from initial input
data to preliminary transport estimates to final transport estimates. Consistency of output
in terms of units (SI only) and form are maintained regardless of type of trace planned
or input units (English vs. SI). Using a typical input file (Figure 12), EHTD generates a
standard-form data output file, which is shown in Figures 15.

6.1.1.1. Data Output File Header Material. Initial output by EHTD is a boxed file
(Figure 15, page 106) that identifies the file and developer, when the file was last modified,
and the data input file read by EHTD to produce the output file. The critical information
listed is the last modified data, because this ensures that the most up-to-date version is
being used, and the input file name, because this ensures identification of which data input
file conforms with which data output file.

6.1.1.2. Input Data Units. A typical data input file allows both English and SI units
(Figure 15, page 106). However, EHTD data-output files only appear with SI units because

of convenience, consistency, and the fact that SI units represent “better” science.

6.1.1.3. Initial Data Input Reprise. EHTD next repeats the initial design data
(Figure 15, page 106) listed in the data input file (see Figure 15). This ensures that the
opportunity to review the input data is provided so that the user can check that the tracer
test design matches expected field conditions. This information is not repeated regardless
of how many sampling stations are listed in the data input file because this information

represents the tracer injection aspects of the project.

6.1.1.4. Sampling Station Name. EHTD identifies the expected tracer recovery
station to which the following data refer (Figure 15, page 106). As a new sampling station
is read by EHTD, new expected recovery data are produced in the data output file.

105



Part IT

MODEL THEORY AND METHOD
DEVELOPMENT

wet . “€ » -

Controlled release of slightly diluted uranine (Acid Yellow 73) into a storm drain to test
for leakage. Tracer release is accomplished using a small, valveless, variable-rate, positive-
displacement, fluid-metering pump operating on a 12-volt de battery withdrawing fluid from
a graduated cylinder. The decline in tracer in the graduated cylinder with respect to time
provides a check on the rate of tracer release.

41



T T T T T T t

20+ 4
a o— Meosured Data

1-4 - No Additional Conditions
=... Additional Conditions

a BF ] 4
4 !
$s f
§ !
z 10+ é 4
i
H
: }
Sr } 4
a :
oeeric: seit URI EERETE
° 70 20 30 40 50 60 70
Time (b)

Figure 20. Comparison of the effect of including an initial concentration and exponential
production to the Lost River Cave System data. The label No Additional Conditions
indicates just the tracer release data and the label Additional Conditions indicates that
an initial concentration and exponential production are included with the tracer release
data.

126



the lack of a measurable and distinct BTC that is normally obtained when water samples

are collected and analyzed prevents clear determination that the dye of interest has been
recovered.

2.5. TRAVEL TIMES AND SAMPLING FREQUENCIES

Typically, users of Equations (1)-(33) would initiate sample collection frequencies according
to flow rates estimated using Darcy’s law for porous-media aquifers. Unfortunately, because
hydraulic conductivity, hydraulic gradient, and effective porosity may not be available,
Darcy’s law is difficult to apply. For karstic aquifers, weekly or biweekly sample collection
schedules for qualitative tracer tests are conventionally employed. Alternatively, schedules
shown in Tables 9 and 10 may be considered if water samples are to be collected. Rarely,
an assumed karstic-flow velocity of 0.02 ms~! may be considered in defining a sampling
schedule.

2.5.1. Travel Times

The suggested time of arrival for peak concentration t, for the tracer test design examination
parameters (Table 11) of 50 days and 72 hours for the porous media case and the karstic
media case, respectively, really represent t. Because of the difficulty in estimating t, prior to
conducting a tracer test, ¢, © £ was taken as a necessary approximation. EHTD predicted
tp = 41 days and 81 days for the impulse release and the pulse release for the porous media,
tracer test, respectively, and tp = 70 hours (3 days) and 131 hours (6 days) for the pulse
release and the impulse release for the karstic media tracer test, respectively (Table 14).
Clearly the t, was very well approximated by EHTD for both example tracer tests.

The use of fg = 3L/v suggests durations of 150 days and 9 days for the porous media
and karstic system, respectively (Table 11). EHTD, however, suggested 136 and 8 days
for the porous-media and karstic system tracer tests, respectively, for an impulse release
(Figs. 1 and 2) and 274 and 14 days for the porous-media and karstic system tracer tests,
respectively, for a pulse release (Figs. 3 and 4) (Table 14). These differences occurred
because EHTD employs a slightly different process for estimating tg. These latter times are
relatively insignificant.

2.5.2. Sampling times

EHTD suggests appropriate sampling frequencies based on the type of flow system and
the type of release. In all instances, sampling-frequency suggestions are determined by the

37



. At the computer desk top, place the mouse pointer (arrow) on the “My Computer”
icon and click the Right mouse button (Right Click).

. Left Click on the word “Explore” in the pop-up menu. Alternatively, just hit the
letter “E” on the keyboard.

. Place the mouse pointer on the CD-ROM disk drive icon (e.g., D: or E:) and Left
Double-Click.

. Left Click “Edit” at the top of the Window Screen and Left Click on “Select All” in
the pull-down menu. Alternatively, just hit the letter “A” on the keyboard.

. Left Click on the “Copy” icon on the “Tool Bar” near the top of the Window Screen
(second row). Alternatively, Left Click on “Edit” at the top of the Window Screen
and Left Click on “Copy” or just hit “C” on the keyboard.

. Left Click on the preferred hard drive (e.g., C:).

. Left Click on the “Paste” icon on the “Tool Bar” near the top of the Window Screen
(second row). Alternatively, Left Click on “Edit” at the top of the Window Screen
and Left Click on “Paste” or just hit “P” on the keyboard.

A folder named EHTD will be created on the chosen hard drive and all the appropriate
files copied accordingly to the appropriate file folders.

4.2. EHTD EXECUTION

EHTD is very easy to use. After the appropriate data files are created (which are nearly

self-explanatory), EHTD, for the most part, requires nothing more than hitting <ENTER>
as requested or manipulating the mouse and clicking with the left mouse button. (See
Section 5. on page 83 for a detailed discussion of EHTD data-input files.)

?EHTD was not designed for MSDOS® use, which requires that the files be moved according to the
following instructions:

e At the C:\> prompt, type “MKDIR EHTD” (without the quotes — whenever quotes appear in this section
type the requested information without the quotes).

e Next, copy the executable and data files stored in the file Ehtd_dos on the CD to the hard disk (for
example, if C is the disk drive: “COPY D:\*.* C:\EHTD\*.*”).

« Repeat the above commands for the other files on the CD.

e Put the CD in a safe location.



respond with a screen display similar to the one shown in Table 22. The first line shown
in Table 22 indicates that either the sampling station name or the ‘‘END OF RUNS’? file
terminator is missing. From the second line it is apparent that the sampling station name is
missing, because this line indicates that the last sampling station name identified by EHTD
(STATION NAME READ WAS:) appears nonsensical (i.e., DISCHARGE (m*3/h)...). The listed
station name on line 2 of Table 22 is actually just a comment line that should normally be
ignored by EHTD (see Section 5. on page 83 for an description of comment lines in input
files).

Also apparent from the first line in Table 22 is that a missing ‘‘END OF RUNS’? file
terminator may still cause a fatal error rather than just a warning error as shown in Table 21.
This may sometimes occur if EHTD is unable to distinguish a “true end” to the user-supplied
input file.

All the information shown in Table 22 up to the statement FATAL ERROR IN... will
be printed in the named output file. The ERROR NUMBER = -5 will not appear in the
output file because the necessary information will already have been produced. Following
the listed error number, the statement, JOB ABORT DUE TO FATAL ERROR., is the last
significant statement for a typical user. The additional information listed (i.e, MESSAGE
START NERR...) are of no consequence to the user; this information is useful to

programmers only. Other basic error messages are possible.

Table 22. Screen display of a typical EHTD warning message.
MISSING STATION NAME OR "END OF RUNS" FILE TERMINATOR

LAST STATION NAME READ WAS: DISCHARGE (m~3/h) DISTANCE (m) AREA (m*2) SINUOSITY FACTOR

PROGRAM STOPPED DUE TO ERROR IN INPUT FILE

CHECK INPUT FILE INCONSISTENT ERRORS

FOR EXAMPLE --- DOES THE NUMBER OF RECOVERY STATIONS
MATCH THE ACTUAL NUMBER OF RECORDED RECOVERY STATIONS?

FATAL ERROR IN...
FATAL ERROR IN INPUT FILE

ERROR NUMBER = 5

JOB ABORT DUE TO FATAL ERROR.

° ERROR MESSAGE SUMMARY

MESSAGE START NERR LEVEL COUNT.
FATAL ERROR -5 2 1



forced gradient porous media tracer test, the latter assumed because of the relatively high
discharge rate (72 m* h7") provided by Parriaux et al. (1988, p. 9).

Type of tracer release refers to three methods of tracer injection; impulse, pulse, and
continuous. Impulse (instantaneous) releases are the most common tracer injection method
for karstic systems, whereas pulse releases (slow releases over some period of time) are the
most common tracer injection method for porous media systems. Continuous releases are
rarely employed in either system, primarily because of cost. For the porous media and
karstic tracer test parameters listed in Tables 11 and 13, impulse releases were assumed
except for Equation (22), in which a long-pulse release was assumed.

Time for tracer injection refers specifically to tracer injection time, but it also may
include pre- and post-tracer injection flush water to account for additional dilution effects.
Total dilution volume Vp is obtained from

Vo = (9+ Q)E, (41)

which should not be considered a technically correct approach. However, it does yield good
approximations for dilution effects, which will usually be equal to or greater than the system
volume V calculated from the total discharge for the duration of the tracer test. For this

analysis, Vp was of some significance because q was fairly significant.

2.4.1. EHTD Results

Application of EHTD to the parameters listed in Table 13 resulted in tracer mass estimates
of 525 g for the impulse release and 1950 g for the pulse release for the porous media tracer
test and 102 g for the impulse release and 631 g for the pulse release for the karstic tracer
test (Table 14). To obtain these results, EHTD uses an average concentration C rather than
a peak concentration Cp. For this analysis, the peak concentration used in Equations (1)-
(32) was taken as the average concentration. The effect of taking Cy = C was relatively
insignificant, because Ry = 1.0 and y = 0.0 hTM! (Field, 2002a).

Hydraulic parameters from EHTD simulations of the porous media and karstic tracer
tests are shown in Table 14. Tracer breakthrough curves for the porous media and karstic
systems tracer tests are shown in Figures 1 and 2, respectively. All the parameters listed
in Table 14 were calculated by EHTD using the parameters listed in Table 13. Some of the
EHTD-calculated parameters listed in Table 14 (e.g., v) approximate the same parameters
listed in Table 11. However, important transport parameters such as axial dispersion Dr
and Péclet number P. are uniquely calculated by EHTD. Although these parameters may

31



20 F T T T T T T 74

" -6-@- Measured Breakthrough Curve
AX “4-4 - Predicted Breakthrough Curve

a

Concentration (ug L~')
3

Time (h)

Figure 16. Comparison of EHTD-predicted BTC to measured BTC for the Lost River Rise
using a typical input file (see Figure 12). Note the good prediction for tracer arrival times
developed by EHTD.

EHTD-suggested recommendations implemented shortly thereafter. Significant errors in
calculations and in implementation are likely to occur if there is a delay in following up on

field measuremenis.

6.2. THE QUALITY OF EHTD-PREDICTED RESULTS

A comparison of the EHTD-predicted BTC to the measured BTC for the Lost River Rise
is shown in Figure 16. It will be noted that whereas EHTD predicted a greater spread
than was actually measured, the estimated times for tracer arrival were very well predicted;
therefore, it is likely that the measured BTC would have been given better definition had
sampling proceeded according to the recommended sampling times (frequency) developed
by EHTD.

Of particular significance is the estimate for tracer mass versus the actual tracer mass
injected. EHTD recommended approximately twice as much tracer as was actually used
for the project. The excess mass recommendation in this instance reflects the greater-than-

expected longitudinal dispersion calculated by EHTD.

117



-2147
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- 28266E-05
- 70494E-05
.16710E-04
.37773E-04
.81676E-04
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-64959E-03
. 12065E-02
-21689E-02
.37810E-02
-64030E-02
. 10550E-01
.16937E-01
-26531E-01
-40602E-01
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39.
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43.
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46.
47.
48.
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50.
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52.
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59.
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64.

079
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075
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786
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926
782
639
496
352
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779

-55912E-01
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.19294F-01
-11138E-01
- 63619E-02
- 35976E-02
- 20154E-02
- 11191E-02
-61624E-03
- 33669E-03
- 18260E-03
- 98335E-04
-52608E-04
- 27968E-04
.14781E-04
- 7T675E-05
-40601E-05
-21115E-05
-10928E-05
-56295E-06
-28874E-06
-14748E-06
« 75026E-07
-38023E-07
. 19200E-07
- 96614E-08
-48455E-08
+ 24224E-08
-12074E-08
- 60003E-09
- 29736E-09
. 14697E-09

Figure 14. Data file generated by EHTD used to produce Figure 13 continued.



TABLE 2.1.2. FINAL ESTIMATED HYDRAULIC FACTORS WITHOUT RETARDATION
(NONREACTIVE TRANSPORT)

ESTIMATED STATISTICAL TIMES OF TRAVEL

DISPERSION

3.1336E+04

PECLET NUMBER DISPERSIVITY
(DIMEN. )

Figure 15. Standard-form example output file generated by EHTD from a typical input file

(see Figure 12) continued.

110



6.1.1.5. Table 1.1. Input Factors. EHTD prints results in a standardized tabular
form, the first of which is labeled TABLE 1.1 INPUT FACTORS THAT INFLUENCE TRACER-MASS
ESTIMATION (Figure 15, page 106). This table represents a reprise of specific sampling sta-

tion measured or input data listed in Table 12.

6.1.1.6. Output Data Units. The results of a typical data output file are only in
SI units (Figure 15, page 106). EHTD data output files appear only with SI units for
convenience and consistency and because SI units represent “better” science.

6.1.1.7. Table 2.1.1. Initial Hydraulic Factors. The next output table (TABLE
2.1.1. INITIAL ESTIMATED HYDRAULIC FACTORS) (Figure 15, page 106) describes the
initial calculations essential for developing the preliminary BTC (see Figure 5, page 58).
Although mostly self-explanatory, some items do need to be clarified. For example, AVERAGE
TIME is listed twice, once as an “initial estimate” and once as an “adjusted estimate.” The
initial estimate relates directly to the measured discharge and expected travel distance.
The adjusted estimate relates to moment analysis of the preliminary BTC, which has a
“connecting bar” to the AVERAGE TIME VARIANCE to show that these two are related only
to each other.

6.1.1.8. Table 2.1.2. Final Hydraulic Factors. This table reflects final calculations
developed by EHTD. Figure 15, page 106 does not show any significant differences from
Table 2.1.1. (Figure 15, page 106) because ‘ ‘NONREACTIVE TRANSPORT?’ was specified, the
result of which is no retardation effects.

6.1.1.9. Table 3.1. Final Tracer Mass Estimate. Table 3.1. (Figure 15, page 106)
reflects the “initial tracer mass estimate” obtained from the preliminary BTC (see Figure 5,
page 58), the “adjusted tracer mass estimate” obtained from the BTC and developed
according to Equations (54) — (57), the “readjusted tracer mass estimate” obtained when
OPTIMIZATION is requested, and the “final tracer-mass estimate” resulting from the complete
EHTD processing. An ERROR CODE is included as appropriate; its meaning is described at
the end of the output file.

This table also lists the “set,” “average,” and “peak” tracer concentrations (Figure 15,
page 106) associated with the data input file (Figure 12). Very rarely will the average

concentration not match the set concentration and the peak concentration not be greater

115



Measured Data
4b aw NonReactive Transport | 4
\ Reactive Transport
4
3p
€
3
£ at
5
8
2
8
oe
it
°
°

Time (h)

Figure 25. Comparison of measured data for the Dyers Spring tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rg = 1.05
and ys = 0.018 h-}.

more common qualitative tracer tests and past professional experience are used as a means
for designing a quantitative tracer test (Mull et al., 1988a, pp. 26, 28).

Measured C, at Dyers Spring occurred later than the nonreactive EHTD-predicted
results when A is estimated from peak velocity vp (Figure 25). No prior estimates for
the Dyers Spring A coupled with the measured Q were available. Typically, conduit A is
estimated using v calculated from the BTC, but the long BTC tails associated with Dyers
Spring (Mull et al., 1988a, p. 69) as a result of immobile flow regions tends to skew v (Field
and Pinsky, 2000). The long tails for the measured BTCs adversely affect the v calculation
by inferring slower transport, which results in a smaller calculated cross-sectional area and
consequently causes a later tracer breakthrough (Field, 2002c). Substituting vp for v results
in an earlier tracer breakthrough than that of the measured recovery, which suggests that
Up and vu bracket the true velocity, as was shown to be the case by Field and Pinsky (2000).

Allowing for tracer retardation Rg = 1.05 and tracer decay ys = 0.018 h-! results in a
BTC that adequately matches the measured BTC and a tracer-mass estimate that matches
the actual tracer mass released (Table 29). Although the measured C, was missed by the

139



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“$}80} 1odeI} VIpoul snoiod ayy 10j SOL. poses snss9a SO T.q pePrperg-G.LHA ‘TE AqeT,

143



EPA/600/R-03/034
April 2003

Tracer-Test Planning Using the
Efficient Hydrologic Tracer-Test

Design (EHTD) Program

National Center for Environmental Assessment-Washington Office
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460

RecycledRecyclable
OY Printed with vegetable-based ink on

paper that contains a minimum of
50% post-consumer fiber content
Processed chlorine tree.



Table 27. Required flowing stream tracer test design specifics.

Parameter Uvas Creek Missouri River Dyers Spring Variegated Glacier

Q,m?h7! 4.79 x 10! 3.47 x 10° 1.16 x 10? > 1.44 x 108
L,m 2.81 x 10? 2.43 x 108 9.14 x 10? 1.00 x 104
A, m? 3.60x 1071 5.23 x 10? 1.84 x 10° 6.15 x 10?
to, h 3.00 x 10° oon vee 1.67 x 1071
ty, m® see wee wee vee
C#pugL 3.12 x 103 1.62 x 10° 4.14 x 10° 3.69 x 101
C’ugL? 3.19 x 103 1.62 x 10° 4.12 x 10° 1.94 x 10!

* Average tracer concentration for nonreactive tracer transport.
> Average tracer concentration for reactive tracer transport.

7.3.1. Flowing Streams Results

Flowing stream tracer tests make up the first four tracer tests listed in Table 26. These
four tests include small and large surface-water streams, karst solution conduit, and glacial-
meltwater stream. The parameters required for EHTD simulation for these tests are listed
in Table 27. EHTD simulation of flowing streams requires only measurement or estimates
for discharge Q, longitudinal distance L, cross-sectional area A, tracer release mode ta, and
set average tracer concentration C. Two listings for C appear in Table 27 because p: may
cause the predicted C; to fall below the measured C, that occurs with no tracer decay. Of
the four tracer tests listed in Table 27, a slightly decreased C, was a problem only for the
Uvas Creek tracer test.

Hydraulic results of the EHTD-predicted BTCs for the four flowing stream tracer tests
are compared with the actual BTC results in Table 28. Tracer injection specifics are
listed in Table 29 and include consideration tracer mass, injection concentration C;, pulse
injection volume ty, injection rate q, flow system volume V, and dilution volume Dy, which

represents the combined effect of the injection flow rate q with discharge Q.

7.3.1.1. Uvas Creek Tracer Test. The tracer test conducted at Uvas Creek was
chosen as a test case to evaluate the ability of EHTD to predict tracer tests results in very
small streams when fz is large. For instances where tz > t, Yu et al. (1999) recommend the
BTC be solved for a Heaviside condition up to C, of the BTC. For the Uvas Creek injection,

tz was 3.00 hours (Table 27), but tracer recovery occurred within several minutes at reach

133



input to be listed on Line 13. For example, Figure 10 lists Line 12 as:

RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)

Line 13 is a series of user-supplied input representing a desire on the part of the user
to allow for tracer retardation in the system, tracer-specific decay (in reciprocal
hours only), to turn on program optimization, and to set a required average tracer
concentration. Retardation values to be entered must always conform to > 1.0, decay

values must always conform to > 0.0, and average concentration must conform to

> 0.0 for obvious reasons (i.e., from solute transport theory, retardation can never be
less than one, decay can never be negative, and average concentration can never be

less than or equal to zero). So, for example, Line 13 in Figure 10 might appear as:

1.0 0.0 0 20.0

which states that RETARDATION = 1.0, DECAY (1/h) = 0.0 h-}, OPTIM = 0, AVE.
CONC. (ug/L) = 20.0 pg L7!. Note that setting optimization to zero (OPTIM = 0)
informs EHTD not to perform an optimization routine. However, setting optimization
to one (OPTIM = 1) informs EHTD to perform an optimization on the estimated tracer
mass, retardation, and decay if appropriate (see Lime 14 description in Table 25 and
below.

It is essential that estimated values for retardation > 1.0 and decay > 0.0 h7! not
be excessively large. Very large values for either retardation or decay may result in
nonsense results from EHTD.

Line 14 is aseries of two user-supplied input switches to inform EHTD whether retardation

and/or decay estimates are to be estimated. For example, if OPTIM = 1 (Line 13)

and Line 14 in Figure 10 is represented by

1 1

EHTD, is informed to perform a full optimization (mass, retardation, and decay).
Setting Line 14 to

0 1

informs EHTD to optimize mass and decay only, whereas

94



where x; is the y intercept of the straight-line fit to the early-time data and 2 is the gradient
of the straight-line fit to the early-time data.

Equations (88) and (89) tend to overestimate D, for nonporous-medium flow systems,
which will generally result in an overestimation of tracer mass needed and a greater BTC
spread than is likely to occur as a result of solute dispersion. Alternatively, Equation (90)
tends to underestimate D, for porous-medium flow systems, which will have an effect
opposite that obtained from Equations (88) and (89).

For these two reasons, Equation (90) is used to estimate D. for a nonporous-medium flow
system and Equation (88) and/or Equation (89) are used to estimate D. for porous-medium
flow systems. Although not precise measures of D,, these estimates are believed to be
adequate for the purpose of obtaining an approximation of D, for use in Equations (54), (56),
or (57).

3.6. TRACER SAMPLE COLLECTION DESIGN

Solute transport parameter estimates are used in Equations (54), (56), or (57) with the
initial estimate for tracer mass. Adjustments to the initial estimate for tracer mass are

made iteratively on the basis of the estimated solute transport parameters, preset mean

«aE .
volume-averaged concentration C’’, and any effects created by suggested tracer reactions.

Final estimates are then used in the ADE to generate a BTC representative of the fow
system to be traced.

3.6.1. Sample Collection

The ADE-generated BTC serves as the basis for determining an appropriate sampling
frequency and an initial sample collection time. Rather than using guesswork, transport
distance, or unmeasured estimates for tracer velocity, as is common (Field, 2002c), the BTC
allows for realistic consideration of the times of travel.

3.6.1.1. Sampling Frequency. Sample collection frequency is based on an arbitrary
number of samples to be collected that balances the cost of sample collection and analysis
with the value of an ever—increasing number of samples. An adequate sampling frequency
necessary for representing a continuous series by a discrete series must be determined for
extracting optimal information while maximizing the accuracy of the results and minimizing
the computational costs. The sampling frequency then is based on how rapidly tracer

54



(g)

tracer dye [Table 8] mass for 1000 m transport distance (g)

tracer purity = ae x 100 (dimen.)

tracer density (g c~!m)

tracer decay (h~')

average velocity for tracer migration (m h7?)
expected velocity for peak tracer migration (m s~')
flow system volume (m°)

dilution volume for a spring or well (m*)

transverse spread of tracer (m)



estimate for the Test Site Wilerwald tracer test was seriously problematic, although tracer
mass estimates for all the porous media tracer tests were underestimated. Prior knowledge
of the behavior of the type of system being traced and the type of tracer to be used can
provide some indication of necessary estimates for retardation and decay.

EHTD simulations for the eight tracer tests evaluated resulted in very reasonable ap-
proximations for seven of the tracer tests. In some instances, (e.g., Test Site Wilerwald and
Kirchrdorf Unteropfingen) expected time to peak arrival (tp) was inaccurately reproduced.
In other instances (e.g., Uvas Creek, Missouri River, Test: Site Wilerwald, and Kirchrdorf
Unteropfingen) axial dispersion (D,) was inaccurately reproduced. However, in all these in-
stances the results of EHTD for both the reactive and the nonreactive simulations resulted
in adequate approximations for the hydraulic parameters of interest.

Future work should focus on refining EHTD to better approximate tracer mass estimates
and transport parameters. Improvements may include consideration of the longer transport
times associated with the longer transport crescents created by injection and the effects of
stagnant regions. Although these improvements are not necessary for EHTD to develop a
sampling schedule that will define a BTC, they will result in improved tracer mass estimates
and some transport parameter estimates. Application of EHTD in its current form prior
to initiating a tracer test leads to a more efficient design, fewer trial-and-error efforts, less
expense related to excess tracer use and excess sample collection and analysis, and greater
likelihood of tracer test success.

161



Table 22. Description of the input file components (continued).

Line Type Identifier Description

19 Character END OF RUNS Program termination code:
Not required, but allows file notes to be included
at the end of the input file (e.g., references).

*Lines 6-17 may be repeated for any number of sampling stations.

because of the generic aspect of each is that the value to be entered for type of flow, FLOW,
on Line 4 must correspond to the listing on Line 9. Correct representation of Line 9 is
not required, but it is useful for clarity purposes, as pointed out in Table 25. Section 5.1.1.
provides a detailed line-by-line explanation of Figures 10 and 11 in reference to Table 25.

5.1.1, Line-by-Line Description of Input Files

Figure 10, Figure 11, and Table 25 each include a Line number to identify the line on which
a particular item must be supplied in a data input file. These Line numbers are provided
here only as a guide to the user and are never to be included in any actual data input file.
Below is a detailed description of each line for a typical data input file. In most instances,
the description provided refers to Figure 10 and refers specifically to Figure 11 only when
necessary because of the similarity of most data entry lines for the two types of data input
files.

Line 1 is a comment statement provided to the user to enter a clarifying statement that
is ignored by EHTD. It is generally used as a convenient label for Line 2, which is
READ by the program. For example, Figure 10 lists Line 1 as:

PROJECT NAME

which is stating that the Lime 2 is a name to be READ by EHTD. Line 1 can be left
blank if desired.

Line 2 is a user-supplied name that is required and is READ by EHTD. It intended to be
an identifier for the specific tracer test being designed. For example, Figure 10 lists
Line 2 as:

Name of Planned Tracer Test

89



“gg oded “9'Z WOIJOIg UT ysl] SUOIJUION OY} 005
(wuios -ssad ‘uoySuryza0 AA) (ETET ‘TXTEP) St WOLYeI9 yoouI00 YT, ,
-oyqereae Ayrpeor 0 pogrquopt Ayiodoad sKemye you oouosojor Arewd,
(‘uwoa ‘suad ‘uoySuryyiog) sseul LoowIy BuyyeUITyso JOZ UoTyenbo ou suyeyUOD (161) OUI p
“(100% “q1eUIg pu u0}SUTYyZI0A\) OST? og,
‘suoryenbo yeurso oy} oonpoadar Apyoor100 sAemye you Op soouoIOJoI ATYpUOdIgG
‘syan jo AovoysIsuoo More 07 poylpour ApYFI[s suoryenbo outog,

(g26T ‘vountutyy) (az¢ “4 ‘g66T ‘geM) 40 ="N (9)

(pT 4 ‘E661 Suyedryy) = Ww (ze)

a(9@6I ‘snauty,) (rze “4 ‘ge6t ‘geM) ws = W (18)

o(9Z6T ‘snoury,) (vee “d ‘g66T ‘geM) T“s= WN (oe)

(61 ‘4 ‘Z66T ‘uepUINy pue sepuexety) tee ay =W (62)

(oze “4 ‘9661 ‘ges 7b = NW (82)

(ot 4 ‘Gg61 ‘uosTAA pur yryEedqyy) ain NW (te)

(ze “d ‘egget “Te 99 TIN) ve Tie = W (92)
“(21 “4 ‘S861 ‘qqop pue yLyed]ry)
(ge “4 ‘Zg6T ‘zqUey)

(92 “4 “6261 ‘unquyey) me airing = W ($2)

(g--d ‘eg6r ‘qqog pue youyedqry7) o mime WV)

aoualojoy aouadejoy
Avewig qStepuosag quolyenbyy Jaquiny,

*(panurjuoa) sseur uorofur Ja9e14 Suryeuttyse Joy suoryenba ourog “¢ a]qz,
ponuy b yeuly J t S “€ PIVeL

14



Table 2. Percent pure dye content for selected fluorescent dyes.

Tracer Dye Powder Dye* Liquid Dye*
(Common Name) Content, %P Content, %>

erioglaucine® 74.0 37.0
Sulpho Rhodamine B 90-92.0 18.0
eosin 86.0 26.0
Rhodamine WT* 85.0 17.0
Na-fluorescein 60.0 30.0

Rhodamine B* 90.0 45.0
Tinopal CBS-X 60.0 ot
pyranine 80.0

* Values listed are within +5.0%.

> % = Gate x 100.

© Erioglaucine is also sold with a Food, Drug and Cosmetic (FD&C) purity
equal to 92.0%.

4 Rhodamine WT is not commercially available in powder form and rarely
exceeds 18% purity in liquid form.

© Rhodamine B as a liquid is mixed with glacial acetic acid.

Note: The values listed are specific to one manufacturer — crude dye
stocks can and will vary significantly with manufacturer.

2.1.1.1. Recent Arguments Opposing Rigorous Tracer Mass Estimation. It
has recently been argued that a rigorous approach to estimating tracer mass is unnecessary.
It has further been argued that promoting such an endeavor may lead to uninformed
regulators’ deciding the mass of tracer necessary for the proposed experiment. However,
neither of these arguments is justifiable.

The argument suggesting that a rigorous tracer-mass estimation is an unnecessary effort
is promoted by those individuals who have traditionally relied on the method of conjecture
as a means for estimating tracer mass. Conjecture abrogates the need for taking time-
consuming field measurements and it suggests and air of all-knowing by the conjecturer. It
may just be adequate for these individuals because they are uninterested in conducting
a quantitative tracer test. A qualitative trace that only roughly approximates tracer
trajectories and velocities is all that is desired, so a good estimate of tracer mass to release
is not considered because of the vagaries of tracer sorption by activated carbon.

The argument that inexperienced or “know-nothing” regulators will begin deciding

appropriate tracer masses may be regarded as fallacious. It is a useful scare tactic often

10



m, AREA (m*2) = 18.8 m?, and SINUOSITY = 1.0 or no sinuosity adjustment. Al-
ternatively, Line 9 (with Line 8 added for clarity) in Figure 11 might appear as:

DISCHARGE (m*3/h) POROSITY THICKNESS (m) DIST-X (m)  DIST-Y (m)
5.688E1 0.35 21.6 38.3 0.0

which states that DISCHARGE (m*3/h)
THICKNESS (m) = 21.6 m, DIST-X (m)

5.688 x 10' m?h-!, POROSITY = 0.35,
38.3 m, and DIST-Y (m) = 0.0m.

Of particular significance in the second example is the lack of an estimated transverse
spread (DIST-Y (m) = 0.0). Transverse spread needs to be estimated only for a
natural-gradient porous media tracer test (FLOW = 2). All subsequent cases (FLOW =
3-5) will result in an automatic transverse spread estimate by EHTD according to
Equations (72) - (75).

Line 10 is a comment statement provided so the user may enter a clarifying statement,

which is ignored by EHTD. It is intended as a convenient indicator for appropriate
input to be listed on Line 11. For example, Figure 10 lists Line 10 as:

INIT. CONC. (ug/L) GAMMA1 GAMMA2

Line 11 is a series of user-supplied input representing a desire on the part of the user

to allow for initial (background) tracer concentration and exponential (growth)
production. Initial concentration and production values to be entered must always
conform to > 0.0. So, for example, Line 11 in Figure 10 might appear as:

0.02 0.1 0.2

which states that INIT. CONC. (ug/L) = 0.02 ug L-?, GAMMA1 = 0.1, GAMMA2 =
0.2.

It is essential that estimated values for initial concentration > 0.0 and the exponential
production parameters > 0.0 not be excessively large. Very large values for either
initial concentration (relative to set average concentration) or exponential production

parameters may result in nonsense results from EHTD.

Line 12 is a comment statement provided so the user may enter a clarifying statement,

which is ignored by EHTD. It is intended as a convenient indicator for appropriate

93



~ee@— Measured Data
a4  NonReactive Transport
ass. Reoctive Transport

Concentration (ng L~')

20
Time (d)

Figure 30. Comparison of measured data for the Chalk River site tracer test with EHTD-
predicted results for nonreactive and reactive transport. For reactive transport, Rg = 1.1
and w= 0.011 ho}.

develop a slight peak at ~ 8 days and a consequent decreasing limb. The EHTD-predicted
BTC for the reactive case produced a visually better fit than have previous modeling efforts

(Huyakorn et al., 1986), because G was adjusted as necessary to obtain a C, that matched
the measured C, (Table 30).

As with the Mobile Site tracer test, the EHTD-suggested sampling times may be regarded
as ideal for defining the measured BTC. The multimodal measured BTC for the Chalk River
Site also illustrates the need for frequent sampling if the BTC is to be properly defined

(Figure 30). A ty = 12 hours is sufficient for defining the BTC. However, tracer sampling
ceased prior to complete tracer recovery, so it is not possible to determine whether EHTD-
recommended sampling ended too soon.

Unlike the Mobile Site tracer test, the predicted system volumes for the Chalk River
tracer test match the measured V quite well, especially for the nonreactive case. (Table 32).
Predicted Dy was twice the predicted V, reflecting the recirculation aspect of this tracer
test. The effect of Dy = 2V was to increase the suggested tracer mass necessary for

achieving a positive tracer test.



Source-Related Uncertainties

e Will release(s) of contaminants occur?
[Probability of release(s).|

e When will the release(s) occur and for how long?
[Timing and duration of release(s).]

e What contaminants will or are being released?
(Chemical, biological, or radiological contaminant releases.]

¢ How much will be or is being released?
[Mass loading.]

Pathway-Related Uncertainties

« Will contaminants reach exposure point?
{Flow trajectory and proximity of source to point of contact.]

e@ When will contaminants reach point of exposure?
(Time of travel and duration of exposure.]

e What contaminants will reach the point of exposure?
{Environmental fate of contaminants.]

e How much contamination will reach the point of exposure?
[Contaminant concentration at the point of exposure.|

Use-Related Uncertainties

e Water used for drinking and/or bathing and by whom?
[Exposure route, number, and sensitivity of exposed population.]

¢ How long will user be affected by the contamination?
{Duration and continuity of exposure.|

e What monitoring program is in place?
[Potential to avert exposure.]

e What dilution and/or treatment prior to exposure?
[Reduced exposure levels due to reduced contaminant concentrations.}

Figure 31. Uncertainties associated with exposure assessments in hydrological systems
{adapted from Reichard et al. (1990, p. 6)].

slightly greater amounts of dye (14.28 g each) for a total release of (38.08 g). Analysis using
EHTD suggested that even greater quantities of dye (100.11 g) would have been appropriate.

153



—— Standardized Breakthrough Curve
5 -4 - EHTD~Predicted Breakthrough Curve|

Concentration (ug L-1)

. 10 20 "0
Time (h)

Figure 33. Standardized curve- and EHTD-predicted BTC for a hypothetical copper sulfate
release to the karst window shown by dye tracing to be connected to Dyers Spring.

includes a slight overestimate for transport distance, a large overestimate for discharge and
retardation, and other incorrect values. However, adjustments to this file are easily made.
The file can then be run as often as necessary to gain a sense of those factors that are most
influential to the transport of a solute.

One significant point to make about the LHS routine used in EHTD is that it will always
create an input file with optimization “turned on” (Figure 34). Because optimization is
requested, EHTD will ignore any user-entered tracer or solute mass and will optimize for
the best mass for the listed conditions. If the user prefers to use a desired mass, then
optimization must be reset. to zero.



2.1.2.2. Review of Sampling Frequencies. The most uncertain aspect of any
tracing study is the schedule for sample collection (Kilpatrick and Wilson, 1989. p. 16).
Whereas much effort has gone into estimating tracer mass for a tracing study, very little
appears to have been done in terms of determining sample collection frequency. Sampling
frequencies are generally based on travel distances, which suggests a direct relationship
between travel distance and expected time of arrival. This relationship is obviously correct,
but it is ambiguous because transport velocity as a function of residence time is unknown.
Transport velocities can achieve extreme ranges, rendering invalid sampling schedules based
on transport distances that are devoid of residence time estimates.

Tracer test sampling frequencies are typically based on two approaches. In the first
instance, for transport via solution conduits, tracer recovery from qualitative tracing tests
(e.g., sorption of fluorescent dyes onto detectors) that are sampled every few hours, days,
or weeks (Alexander and Quinlan, 1992, p. 21) (most commonly every 1 to 2 weeks) serves
as a basis for determining appropriate sampling frequencies for quantitative-tracing tests.
Sampling schedules based on qualitative tracing tests have been found to result in false
positive results (Field, 2000, pp. 11-14) and false negative results (Smart et al., 1986) and
cannot be relied upon for predicting sampling times.

In the second instance, sampling frequencies may be based on transport distances from
tracer injection points to expected tracer recovery stations with due consideration to travel
times. For surface-water streams, Kilpatrick and Wilson (1989, p. 16) suggest that

tp = 2.78 x = 36
‘P

Up

can be used to determine when to initiate sampling for detection of the tracer leading edge
and 10% of the trailing edge. Leading edge is given by (Kilpatrick and Wilson, 1989, p. 18)

ta,
t= ty- 3 (37)
and 10% of the tracer trailing edge by (Kilpatrick and Wilson, 1989, p. 18)
2t,
tye = tp +S (38)

Although no criteria were specified, (Kilpatrick and Wilson, 1989, p. 18) suggest that the
number of samples to be collected can be determined by dividing tg,, by 30, which will
result in an appropriate sampling frequency necessary for describing the BTC.

A general sampling schedule is shown in Table 9, where sampling times are based on

travel distance and daily lack of tracer recovery. A specific schedule is shown in Table 10,

22



Mp
M,
My
i)
Ne

Nn

Ns
Noo
Nio

zero-order production coefficient for the liquid phase (M L~$ T-1)
zero-order production coefficient for the adsorbed (solid) phase (M M7! T-!)
auxiliary functions for equilibrium transport [see Section 3.2.1.4]

Hermite cubic basis function

Hermite cubic basis function

solute-migration zone thickness (L)

hazard index for all pathways (dimen.)

hazard quotient for ingestion (dimen.)

hazard quotient for inhalation (dimen.)

hazard quotient for dermal contact (dimen.)

integrand of a function

approximate integrand of a function

amount of water ingested per day (L? T+)

inhalation rate (L? T-1)

CSTR reaction rate constant (T~')

number of uncertain variables to be developed by Latin Hypercube Sampling routine
fracture and/or solution conduit distribution coefficient (L)

solute distribution coefficient (L? M7!)

volumetric conversion for water (L3 L~’)

characteristic distance from point of injection to point of recovery (L)
dimensionless constant for exponential production (growth) profile

tracer mass (M)

dimensionless mass of applied tracer for a Dirac input = ua

particle mass (M)

mass of total number of particles (M)

number of evaluation points (dimen.)

number of additional sample to be collected prior to expected tracer breakthrough
effective porosity (dimen.)

number of evaluation points for Chatwin analysis (dimen.)

multiplier for estimating tracer test duration (dimen.)

number of samples to be collected

median infectious dose (# T-1)

median morbidity dose (# T-)

concentration of particles (# L~)

163



29.
29.
30.
30.
30.
31.
31.
32.
32.
33.
33.
34.
34.
35.
35.
36.
36.
37.
37.
38.
38.
38.
39.
39.
40.
40.
41.
41.
42.
42.
43.
43.
44,
44.
45.
45.
46.
46.

Figure 14. Data file generated by EHTD used to produce Figure 13 continued.

104
573
042
512
981
451
920
390
859
328
798
267
737
206
675
145
614
084
553
022
492
961
431
900
370
839
308
778
247
717
186
655
125
594
064
533
002
472

+3482
- 4967
+7489
- 1001
-5439
.0722
-6760
-3465
-0748
-85268
- 67246
- 52733
-41128
-81911
- 24635
. 18927
.14475
-11021
-83550E-01
-63081E-01
-47439E-01
.35539E-01
-26527E-01
-19730E-01
-14625E-01
- 10805E-01
« T9569E-02
.58418E-02
-42762E-02
-31212E-02
-22719E-02
-16492E-02
.11941E-02
-86240E-03
-62133E-03
-44659E-03
-32026E-03
+ 22916E-03

PRENN WW HO

103



- 56840
- 56835
- 56832
- 56830
- 56828
. 56827
- 56826
- 56825
- 56825
- 56824
-56824
-56824
-56824
-56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
. 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
- 56824
.779 -56824

Figure 18. Data file generated by EHTD used to produce Figure 19 continued.

124



SDA

at

Nue ye Se XsoS sacks

dimensionless time = 4

dimensionless mean residence time = 4

dimensionless pulse time = 4%; (i = 1, 2; T, =0)
solute decay (T~1)

. . ie L(ne, K, Li 2Ko ps Li ajts
dimensionless equilibrium decay = 2@# Lape Rept e); Cot us). (me FX Hs)

liquid phase solute decay (T-')

sorbed phase solute decay (T~1)

mean tracer velocity (L T-+)

mean tracer velocity for the CSTR-generated BTC (L T~!)
measured tracer velocities for each sampling time (L T-?)

peak tracer velocity (L T-!)

flow system volume (L*)

shower stall volume (L’)

concentration of particulate matter for a concentrated volume (%)
width of solute-migration zone (L)

water usage (L*)

vector of straight-line parameters used in the Chatwin analysis (T!/)
vector of p components (M, Ra, and 4) to be optimized

distance (L)

dimensionless distance = 2

165



3.2.1.3. Uniform Initial Concentration (IVP). The IVP may be solved for uni-
form initial concentration by (Toride et al., 1995, p. 10)

CMZ, T) = O72 (Z, T). (60)

The auxiliary function Pf is defined as

P.T et Palate gy yeT*
aRa”

Pesos) (61)

\/4R,-T/Pe

3.2.1.4. Exponential Production (PVP). The PVP may be solved for solute pro-
duction that changes exponentially with distance by (Toride et al., 1995, p. 12)

PZ=n+new4, (62)

which gives the solution as (Toride et al., 1995, p. 12)

il
CM a.T) =F f wThZ. 7:0) + ur. 7 Mar (63)
a JO

T
% [1 -P8(z, T; 0) ~ TF (2,7; w®)| +B [ TE(Z,T; 2”) dt (64)
0
(u® > 0)
T
BIe(Z,T) + z [ V2 (Z, T; X”) dt (65)
0
(u* = 0)

where the auxiliary functions [¥ and If are defined as

-aET P. P
TH(Z,T) = e ee ge ae PON 2 {4 = erfc ieee (14 2a0/P)T Bea pepinT|

\/ARaT/P.

(1+ 5). PrZ+INPZ bee +(1+2A?/P.) aan

AP /4RaT/P.

_ _
— Fe THe oe, Fea (66)

\/4RiT/P.

46



PLOT FILE: LOST RIVER RISE

NANNMAADMRAOKNTHTH PAP ARP WWWAWNNNNHFHHH:

BREAKTHROUGH CURVE

TIME CONC.
(h) (ug/L)
23471 0.0000
46941 0.0000
70412 0.0000
93883 0.0000
1735 0.0000
4082 0.0000
6429 0.0000
8777 0.0000
1124 0.0000
3471 0.0000
5818 0.0000
8165 9.0000
0512 0.0000
2859 0.0000
5206 0.0000
7553 0.0000
9900 0.0000
2247 0.0000
4594 0.0000
6941 0.0000
9288 0.0000
1635 0.0000
3983 0.0000
6330 0.0000
8677 0.0000
1024 0.0000
3371 0.0000
5718 0.0000
8065 0.0000
0412 0.0000
2759 0.0000
5106 0.0000
7453 0.0000

SAMPLE TIMES AND CONC.

TIME

CONC.
(ug/L)
.15918E-05
. 839299E-04
.53591E-03
-45611E-02
- 26531E-01
«11300
. 37166
- 98432
2.1701
4.0911
6.7403
9.8809
13.082
15.839
17.723
18.492
18.130
16.813
14.830
12.505
10.123
7.8980
5.9579
4.3585
3.1001
2.1490
1.4548
- 96361
-62552
+39855
«24959
-15381
-93383E-01

Figure 14. Data file generated by EHTD used to produce Figure 13.

100



Part III
BASIC PROGRAM USAGE

Injection of 1 kg of uranine (Acid Yellow 73) at a sinkhole that receives flow from Bebec
Creek on the Norville chalk plateau of Haute-Normandie, France. Dye recoveries were
obtained ~2200 m away at a spring and well located in the Seine river alluvial plain (photo
courtesy of Nicolas Massei).



eosin (45380 C.I. Acid Red 87), five to 10 times more dye is required (Parriaux et: al.,
1988, p. 7). Quoting from Zétl (1974), Parriaux et al. (1988, p. 8) suggest that although
Equation (5a) is appropriate for Na-fluorescein sorption onto detectors, two to three times
more dye is required for water samples. Although not stated, Zétl was probably referring to
visual detection of fluorescent dye in water when detectors are not being used. Equation (5b)
appears similar to Equation (5a), but the full citation and primary reference are not provided
in Milanovié (1981, p. 276), and it includes a tracer-dependent coefficient Tc,, which may
be a misprint.

Equations (6) and (7) include a sorption coefficient Ag, that is intended to increase
tracer mass for which units are either not clearly provided [Equation (6)] or are inconsistent
with common application [Equation (7)]. For Equation (6), Parriaux et al. (1988, p. 8)
recommend t; = 3L/v, suggesting that the tracer test duration is expected to be three
times the mean residence time distribution #. For Equation (7), Ag = 1.0 mg mTM* for Na-
fluorescein and Ag, > 1.0 mg m~° for all other dyes depending on their respective sorption
characteristics (K&B, 1998, p. 325).

Equation (7) includes an additional “safety factor” Sy that is not intended to protect
human health or the environment from excessive tracer mass releases. Rather, S¢ is intended
to ensure adequate tracer-mass injection by acting as a fudge factor multiplier to increase
the mass of tracer to be released. Equation (7b) is the equivalent of Equation (7a) adjusted
for some tracer entrance angle other than 30°. The original form of Equation (7b) listed in
K&B (1998, p. 325) includes what appears to be some time value multiplied by gravitational
acceleration g, but these parameters are not identified and no units are provided. It is

1 2

probable that Equation (7b) required multiplication by gTM in suitable units (e.g., cm s~*,

ms**). For this review, Equation (7b) has been appropriately adjusted.
Equations (8)—-(28) are generally similar to Equations (3)-(7). Equation (8) was intended
for visual detection of Na-fluorescein. Equations (9), (10), and (11) each include an aquifer-

and/or tracer-dependent coefficient To, (Tables 4 — 7).



4.6.1.5. Window. Items listed under this heading in Table 24 are described as follows.

Cascade Allows for a cascading view of multiple child windows at one time.
Tile Allows for a tile display of multiple child windows at one time.
Arrange Icons Not currently used in EHTD.

Input Automatically displays the input screen (Graphic 1) for data input.
Clear Paste Clears an item pasted onto the screen.

Status Bar Displays the current operating mode of the displayed graphics screen in a bar at the
bottom of the screen (when “check marked”).

1 Graphic 1 Name of the data input screen (“check marked”) if active.

2 PGPlot Graphics, # 1 Identifying name/number of all subsequently opened graphics screens
(active when “check marked”).

4.6.1.6. Help. Items listed under this heading in Table 24 are described as follows.

Contents Listing of available help contents.
Using Help Description on the use of the Help.
About Identifies the EHTD program.

4.7, EHTD SOURCE

The FORTRAN source for EHTD is included on the CD. It is a very large program and
it had to be split into pieces to allow its use on a PC. It is not recommended that users
to attempt to follow the logic or modify the program. Questions regarding the program’s
“functioning can be addressed to the author.

In addition, the graphics routine developed at the California Institute of Technology is

included. However, it is not allowed for use in commercial products.

82



AUTHOR AND REVIEWERS

The National Center for Environmental Assessment within the U.S. Environmental Pro-

tection Agency’s Office of Research and Development was responsible for preparing of this

document and provided overall direction and coordination during the production effort.

AUTHOR
Malcolm S. Field, Ph.D.

National Center for Environmental Assessment

Office of Research and Development
U.S. Environmental Protection Agency
Washington, D.C.

REVIEWERS

Feike J. Leij, Ph.D.

U.S. Salinity Laboratory
450 West Big Springs Road
Riverside, Ca.

Philippe Meus, Ph.D.

Ministére de la Région wallonne

Direction générale des Ressources naturelles
et de l'Environnement

Division de ’Eau

Direction des Eaux souterraines

avenue Prince de Liége 15

B-5100 Jambes (Namur)

Belgique

Arthur N. Palmer, Ph.D.
Earth Sciences Department
209 Science Building 1

State University of New York
Oneonta, N.Y.

Michaél Verrault, M.Sc.A

Centre d’études sur les ressources minérales
Université du Québec & Chicoutimi
Chicoutimi, Québec

Canada

Laboratoire d’Etude des Transferts en
Hydrologie et Environnement (LTHE)
1023 rue de la Piscine

BP 53, Domaine Universitaire
F-38041 Grenoble, Cedex 9, Frnace

European Water Tracing Services
rue de la Chapelle 43

B-4550 Nandrin

Belgique

Les Laboratoires SL
1309, blv St-Paul
Chicoutimi, Québec
Canada



4, USING EHTD TO DESIGN A TRACER TEST

EHTD is an easy-to-use program for the design of tracer tests in flowing water (e.g.,
open-channel flow or closed-conduit flow in surface streams, caves, sewers, etc.) and porous
media (e.g., gravel aquifer). Using just a few field hydrological measurements, it estimates
the “correct” tracer mass to release for a tracer study and predicts the hydraulic parameters
that define solute migration. It also provides a reasonable sampling schedule for the proposed
tracer test. A graphic BTC and A detailed output file provide substantial details necessary
for implementing the proposed tracer test.

As with published (and some unpublished) tracer mass estimation equations, this
program relies primarily on perceived travel distance, flow discharge, and flow cross-sectional
area to estimate tracer mass. Unlike previously published equations, this program is
somewhat more elaborate in that it attempts to rigorously apply solute transport theory
by use of various forms of the advection-dispersion (equilibrium) model. Attempts at mass
conservation and mass balance were essential to the method. Initial estimates for times of
travel, related factors, and tracer mass are based on the concept of a hypothetical CSTR as
a surrogate for the flow system.

Selected error messages appear toward the end of the whereas output file. Many of these
error messages will not be of any great significance to the user, others are important. It is
recommended that the error messages be checked to ensure proper EHTD functioning.

4.1. EHTD PROGRAM USAGE AND EXAMPLE DATA FILES

NOTE: This program functions best with a display equal to 1024 x 768 pixels, adequately
with a display equal to 800 x 600 pixels, and not so well for further reduced display settings.

Before running the program, all EHTD files to his(her) should be copied to the PC’s
hard drive and the supplied CD-ROM disk stored in a safe location. Although plenty of
storage space is available on the CD-ROM disk for the creation of data-output files and
graphics files, the possibility of damage to the EHTD program file from excess use cannot
be ignored.

4.1.1. Loading EHTD and Example Data Files

1. After booting up the computer, place the CD-ROM disk into the computer’s CD-ROM
disk drive.

65



for a flowing stream system or:
ENTER THE NUMBER OF LHS-DEVELOPED INPUT FILES DESIRED (N > 14):

for a porous media system. The generation of LHS input files requires that a specific mini-

mum number of input files be generated to satisfy the inequality (Blower and Dowlatabadi,

1994; McKay et al., 1979)

4ky
3"

Alternatively, entering 2 causes the following request:

N> (102)

ENTER THE NUMBER OF LHS-DEVELOPED CALCULATIONS DESIRED (e.g., N = 1000):

which means that the LHS routine is expecting entry of a “large” number for develop-
ment of a set of mean values for use in a single input file. Note, however, values in the
range of > 10,000 will necessitate patience on the part of the user as EHTD runs the LHS
routine. Also, note that for porous media systems with “DIST-Y” set to zero will cause a
an insignificant error report to the screen which can be ignored. (See Table 25 on page 86
for a discussion of “DIST-Y”.)

After determining whether a LHS routine is to be run, EHTD informs the user that
input data are being read and that input errors are being evaluated:

INPUT FILE READ AND AND ERROR AND INPUT-ERROR CHECK PROCEEDING

from which the program quickly moves on to either informing the user of any data en-
try errors or processing the input file. Later in the program, if the user has requested that
the LHS routine be run, EHTD will query the user for a LHS-generated output file name:

ENTER LATIN HYPERCUBE OUTPUT FILE NAME (DEFAULT = LHS.n .OUT):

where n represents the number of the LHS-generated output files or set of calculations
to be developed. If a series of input files was selected above (1=INPUT FILES), one file is
developed for each sampling station evaluated by the LHS routine. If the default is used,
then n will increment automatically to correspond with each sampling station listed in the

71



OIAARWNH

NWNNYNYNYONNNYEP EE EPP ee HEH eo
BAAARONHF SCOWIAMRARANES

29

30
31

List of Tables

Average dye manufacturers’ purities for selected powder dyes. ........ 9
Percent pure dye content for selected fluorescent dyes... ........... 10
Some equations for estimating tracer injection mass............... 12
Aquifer and tracer-dependent coefficients To, —To,..- 0 ee 15
Aquifer and tracer-dependent coefficient To... . 0. eee 17
Tracer dependent coefficient To,. 17
Prevailing test conditions coefficient To,. ......-... 18
Tracer-dye mass per 1000 m of traced distance. 20
General sampling schedule for a karst terrane. 24
Specific sampling schedule for a karst terrane. 24

Tracer test design parameters... 2... ee ee 27

Tracer-mass estimates. ........ 28
EHTD tracer test design parameters. 30
EHTD tracer test analysis results... 20... ee 32
Tracer-dye mass per 1000 m of traced distance. .............0-. 35
Tracer test design parameters... 2.2... ee ee 57
Predicted tracer mass and tracer concentration. .............0.. 59
Recommended sampling times for selected tracer reaction conditions. .... 61
Table illustrating the form of the EHTD-created plot file... ......... 69
Variable parameter types used in the LHS routine... . . 72
Screen display of a typical EHTD warning message. 75
Screen display of a typical EHTD warning message. .............. 76
Typical screen display of optimization results. ..............00. 77
Pull-down menu items availablein EHTD. ...............0..0. 80
Description of the input file components listed in Figures 10 and 1l...... 86

Example test data sets... 2.2... 22... ee
Required flowing stream tracer test design specifics.
EHTD-predicted BTCs versus measured BTCs for the flowing stream tracer

tests. ee ee 134
EHTD-predicted results versus measured results for the flowing stream tracer

tests. ee ee 135
Required porous media tracer test design specifics... .............. 142

EHTD-Predicted BTCs versus measured BTCs for the porous media tracer

vii



20F T T T \ T T 7—
TRACER MASS =1.04E+00 kg

—— Breakthrough Curve
o Sampiing Times

15>

Concentration (ug L~')
r)
T

Time (h)

Figure 13. Standard-form example BTC generated by EHTD from a typical input file
(see Figure 12). Note that recommended sampling times are shown (open circles), as is
recommended tracer mass to inject. In addition, time and concentration units are adjusted
automatically to their most readable values according to the tracer test design parameters.

99



Table 19. Table illustrating the form of the EHTD-created plot file.

PLOT FILE: Sampling Station File Name
TIME CONC. TIME
(h) (ug/l) (h)

PLOT FILE: Sampling Station File Name
TIME CONC. TIME
(h) (ug/1) (h)

PLOT FILE: Sampling Station File Name
TIME CONC. TIME
(h) (ug/l) (h)

conc.
(ug/1)

69





1 0
informs EHTD to optimize mass and retardation only. If OPTIM = 0 (Line 13) and
Line 14 is represented by

1 1
EHTD is informed to not perform any optimization because the main optimization

control switch is set to off.

Line 15 sets the minimum bounds to be considered by EHTD on the optimization of
retardation and decay. Values for Line 15 for retardation cannot be less than one,
and for decay they cannot be less than zero. For example, Zine 15 in Figure 10 will
commonly appear as

1.0 0.0

which informs EHTD of the minimum bounds allowed according to the user.

Line 16 sets the maximum bounds to be considered by EHTD on the optimization of
retardation and decay. Values for Line 15 for retardation can be any number greater
than one, and for decay they can be any number greater than zero. For example,

Line 15 in Figure 10 will commonly appear as

10.0 5.0
which informs EHTD of the maximum bounds allowed according to the user.

Line 17 is a comment statement provided so that the user may enter a clarifying state-
ment, which is ignored by EHTD. It is generally used as a convenient breaking point
before listing the sample station name(s). For example, Figure 10 lists Line 17 as:

FESS FIGO GORI CORIO IERIE OCIGEIGRICICIGEZI ACIS AGI AGIA ICR AAI AAA

which has no real meaning and is ignored by EHTD. Line 17 can be left blank if
desired.

Line 18 is also a comment statement provided so that the user may enter a clarifying
statement, which is ignored by EHTD. It is generally used as a convenient indicator
that Line 17 will contain the End of Runs indicator. For example, Figure 10 lists

95



T # ‘sorpdery yord dz
T orqderpy

Jeg snyeyg
aqseg 1ea[D aysed o
qynduy suy+i9 Adop %
qnoqy suooy osuvy IV Peps O+MIO IR
dye] 3uisy OIL Joy WY Woosog [NJ sorpdesr) yooyag “OABG
squaquod, apeoseg §§+]119 osneg WA OI, 921g 4x9], qa[ag quia
qe aopuly yeas MOA wpa ond

"CLLHa UT O[qePeAe SUIT Nom UMOP-NG pe qe,



Field, M. S., Pinsky, P. F., 2000. A two-region nonequilibrium model for solute transport
in solution conduits in karstic aquifers. Journal of Contaminant Hydrology 44, 329-351.

Field, M. S., Wilhelm, R. G., Quinlan, J. F., Aley, T. J., 1995. An assessment of the potential
adverse properties of fluorescent tracer dyes for groundwater tracing. Environmental
Monitoring and Assessment 38, 75-96.

Freeze, R. A., Cherry, J. A., 1979. Groundwater, 604 p. Prentice-Hall, Engelwood Cliffs,
N.J.

Gaspar, E., 1987. Modern Trends in Tracer Hydrology, 145 p. CRC Press, Inc., Boca Raton,
Fla.

Gunn, J., Lowe, D., 2000. Editorial. Journal of Cave and Karst Science (Transactions of the
British Cave Research Association) 26, 99-100.

Haas, J. L., 1959. Evaluation of ground water tracing methods used in speleology. National
Speleological Society Bulletin 21(2), 67-76.

Heys, B., 1968. Closing address. Transaction of Cave Research Group, Great Britain 10(2),
121.

Huyakorn, P. S., Andersen, P. F., Molz, F. J., Giiven, O., Melville, J. G., 1986. Simulations
of two-well tracer tests in stratified aquifers at the Chalk River and the Mobile sites.
Water Resources Research 22(7), 1016-1030.

Iman, R. L., Helton, J. C., 1988. An investigation of uncertainty and sensitivity analysis
techniques for computer models. Risk Analysis 8, 71-90.

Kahaner, D. K., Moler, C., Nash, S. G., 1989. Numerical Methods and Software, 581 p.
Prentice-Hall, Engelwood Cliffs, N.J.

K&8, W., 1998. Tracing Technique in Geohydrology, 581 p. A.A. Balkema, Rotterdam, The
Netherlands.

Kilpatrick, F. A., 1993. Simulation of Soluble Waste Transport and Buildup in Surface
Wwaters Using Tracers. Tech. Rep. Techniques of Water-Resources Investigations, Book
3, Chapter A20, 37 p., U.S. Geological Survey.



the Third Conference on Hydrogeology, Ecology, Monitoring, and Management of Ground
Water in Karst Terranes. National Ground Water Association, Dublin, Ohio, pp. 349-370.

McKay, M. D., Conover, W. J., Beckman, R. J., 1979. A comparison of three methods
for selecting values of input variables in the analysis of output from a computer code.
Technometrics 21, 239-245.

Meigs, L. C., Beauheim, R. L., 2001. Tracer tests in a fractured dolomite, 1, Experimental
design and observed tracer recoveries. Water Resources Research 37(5), 1113-1128.

Milanovié, P., 1981. Karst Hydrogeology, 434 p. Water Resources Publications, Littleton,
Col.

Molz, F. J., Giiven, O., Melville, J. G., Crocker, R. D., Matteson, K. T., 1986a. Performance,
analysis, and simulation of a two-well tracer test at the Mobile site. Water Resources
Research 22(7), 1031-1037.

Molz, F. J., Giiven, O., Melville, J. G., Keely, J. F., 1986b. Performance and Analysis of
Aquifer Tracer Tests with Implications for Contaminant Transport Modeling. Tech. Rep.
EPA/600/2-86/062, 88 p., U.S. Envir. Prot. Agency, Washington, D.C.

Mull, D. S., Liebermann, T. D., Smoot, J. L., Woosley, Jr., L. H., 1988a. Application
of Dye-Tracing Techniques for Determining Solute-Transport Characteristics of Ground
Water in Karst Terranes. Tech. Rep. EPA/904/9-88-001, 103 p., U.S. Envir. Prot. Agency,
Region IV, Atlanta, Ga.

Mull, D. S., Lyverse, M. A., 1984. Ground Water Hydrology of the Elizabethtown Area,
Kentucky. Tech. Rep. WRI 84-4057, 59 p., U.S. Geol. Surv. Geol. Surv. Water-Resour.
Tnvest., Washington, D.C.

Mull, D. S., Smoot, J. L., Liebermann, T. D., 1988b. Dye Tracing Techniques Used to
Determine Ground-Water Flow in a Carbonate Aquifer System Near Elizabethtown,
Kentucky. Tech. Rep. WRI 87-4174, 95 p., U.S. Geol. Surv. Water-Resour. Invest.,
Washington, D.C.

Novakowski, K. S., 1992. The analysis of tracer experiments conducted in divergent radial
flow fields. Water Resources Research 28(12), 3215-3225.

171



D, prior to initiating a tracer test is the most likely reason why solute transport theory was
ignored when developing tracer mass estimation methods. Because t and D, can take on
a wide range even when assuming steady-flow conditions, reasonable initial estimates for =
and D, can be difficult to obtain and are most commonly acquired from a tracer test.

Estimates for hydraulic parameters can, however, be obtained from some basic flow-
system measurements, functional relationships, and consideration of a simple conceptual
model of the flow system. Although the simple model and functional relationships may
be only approximations, they are likely to be sufficiently reliable as to lead to a good
approximation of some basic hydraulic parameters that are necessary for a successful tracer
test.

3.4. HYDRAULIC AND GEOMETRIC PARAMETERS

The use of Equations (54), (56), or (57) for assessing transport processes and predicting
tracer mass requires that specific hydraulic and geometric parameters measured in the field
be combined in simple functional relationships. These measured parameters and functional

relationships can then be applied in a simple hypothetical model as a precursor to application
of the ADE.

3.4.1. Measured Parameters

For flowing streams in surface channels or solution conduits, measurements for discharge

Q, cross-sectional area A, and transport distance L need to be taken. These three
parameters are the most important measurable field parameters necessary for establishing
basic hydraulic and geometric controls in any hydrologic system.

For porous media, additional measurements or estimates for specific parameters must
also be taken. These additional parameters are expected transverse spread W and vertical
spread H of the tracer plume and effective porosity n,. Moreover, it is necessary that the
type of tracer test be identified as either a natural gradient test or a forced gradient test in
which a radially symmetric flow field is created by an extraction well.

3.4.2. Functional Relationships

Discharge, cross-sectional area, and transport distance can each be measured at a down-
stream location such as a spring if a karst aquifer or estimated from Darcy's law if a porous-

media aquifer. Transport distance in solution conduits may be corrected for sinuosity by

48



3.2.1. Model Solutions

Solutions for Equation (43) for impulse and pulse releases are most appropriate for
estimating tracer mass. A continuous release is less relevant because most tracer tests
involve a finite time period for release. Although not a physical reality, it is probable that
most tracer tests, especially in karstic aquifers, attempt to achieve an impulse release that
may be described as a Dirac (5) pulse. However, many attempts at an impulse release are
actually pulse releases due to the time involved for the tracer to reach the flow system under
investigation (Field, 1997; Field and Pinsky, 2000).

Applying the dimensionless parameters listed in the Notations section to Equation (43)
result in (Toride et al., 1995, p. 4)

(52)

which may be solved for the boundary value problem (BVP), the initial value problem
(IVP), and the production value problem (PVP) by the law of superposition for resident

concentration using a third-type inlet condition as (Toride et al., 1995, p. 6)
C®(Z, T) = C?(Z, T)+C'(Z, T)+C?(Z, 7), (53)

where the B, J, and P superscripts denote boundary, initial, and production value problems,
respectively. A third-type inlet boundary condition for resident concentration is used
because it conserves mass (Toride et al., 1995, p. 5) and it is the most physically realistic
(Silebi and Schiesser, 1992, pp. 418-431).

EHTD considers only uniform constant initial concentration C/(Z, T) for background
concentrations. EHTD considers only exponential production for C?(Z, T) and is intended
to relate only to bacterial growth for release of a living bacterial agent. For tracer mass
estimation, C!(Z, T) and C?(Z, T) can usually be taken as zero, so that C#(Z, T) =
C®(Z, T)

3.2.1.1. Impulse Release for BVP. which when solved for the boundary value
problem is (modified from Toride et al., 1995, p. 13)

f(a*) =O" (Z,T) — Mgl?(Z,7), (54)

mE mh: :
where C (Z,T) is a preset mean volume-averaged concentration that corresponds to

dimensionless distance Z and dimensionless mean residence time T. The auxiliary function

44



2. REVIEW OF PREVIOUS TRACER TEST DESIGN METHODS

Quantitative hydrologic tracer testing is the most reliable method for establishing
solute transport trajectories and for defining solute transport parameters. Determining the
necessary tracer mass to release, when to start collecting samples, and at what frequency
all subsequent samples should be collected can be very difficult to estimate, especially in
karstic terranes. In most tracing studies in karstic terranes, design efforts are focused on
predicting where tracer will arrive and where best to release tracer. The tracer mass released
is typically a guess based on the experience of the practitioner. Although attempting to
predict where the tracer will arrive and where best to release the tracer are important and
valuable aspects of conducting a tracer test, guessing the appropriate tracer mass to release
is a fallacious practice that almost ensures that too much or too little tracer will be released.

To facilitate the determination of necessary tracer mass for a successful tracer test,
at least 33 tracer mass estimation equations have been developed over the last century.
Although a considerable improvement over the typical method of guessing an appropriate
tracer mass to release, these equations are also problematic. With the exception of two
equations, they were all developed on the false assumption that a simple algebraic expression
that appears to function adequately for a selected hydrologic setting will then adequately
function in all hydrologic settings. In addition, these equations fail to properly account for
the important effects of axial dispersion and solute transport theory (Field, 2002a).

Tracer test sample collection frequency in karstic terranes is typically a haphazard pro-
cedure based on expected transport distance and supposed travel time. The haphazardness
of sample collection is further exacerbated when qualitative tracing tests are conducted. In
general, a preliminary sample collection frequency is determined before the tracing test is
initiated but is subject to revision during the tracer test as time passes with or without
tracer recovery.

In this paper, the 33 tracer mass estimation equations are briefly reviewed; 32 were
evaluated using previously published tracer test design-examination parameters. For this
review, unless otherwise indicated, the published tracer mass estimation equations were
all probably intended to estimate the mass of tracer on an “as-sold basis,” which often
necessarily includes a large quantity of diluent. In addition, conventional sample collection
frequency determinations are briefly reviewed. The results of the review and examination of
the 33 mass estimation equations and the typical sampling frequencies are compared with
the recently developed EHTD method that has been shown to be theoretically sound and

6



a

Concentration (ug t7')
3

TRACER MASS = 681.65.

9g 4

o_Sompling Times

—_ Breakthrough Curve

Figure 4. EHTD results for a pulse release for the karstic test parameters.

Time (h)

Table 15. Tracer-dye mass per 1000 m of traced distance.

Equation* Porous Media, g¢ Karst, g
(4) 3.00 x 108 1.51 x 10?
(20) 4.10 x 108 7.38 x 108
(31) 8.64 x 10? 2.59 x 10?
(32) 4.32 x 10? 1.30 x 10?

* From Table 3.

35



aquifer thickness (m)
initial (stock) dye concentration (g m~)

expected peak tracer concentration (mg m7)

axial dispersion (m? h~')

gravitational acceleration = 978.039 at 0° Latitude[?] (cm s~?[?])
multiplier for instrumental analysis = 0.01 to 1.0

aquifer hydraulic conductivity (m h71[?])

expected tracer transport distance (m)

calculated tracer mass to inject (g)

number of phage to be release (N, m°)

effective porosity (dimen.)

expected tracer entrance angle for transverse spread (degrees)

expected ratio of injected tracer to recovered tracer (In-EDTA) representing tracer
loss = 1.0 to 3.0 (dimen.)

Péclet number = 4 (dimen.)

phage factor and count ~ 2.0 x 10" to 5.0 x 10° (dimen.)

tracer scattering angle (degrees)

inflow rate at injection point (m? h-')

well or spring discharge (m? h~!)

tracer retardation (dimen.)

safety factor to ensure adequate peak concentration for detection (dimen.)
multiplier for tracer mass = 1.0 to 2.0 (dimen.)

sinuosity factor = 1.0x to 1.5x (dimen.)

expected duration of tracer test (h)

expected tracer test duration at 10% of the peak concentration (s)

time for first sample to be collected (h)

tracer injection time for a pulse injection (h)

time interval for sample collection (h)

expected time to peak tracer arrival (h)

trailing edge to 10% level (h)

aquifer and tracer-dependent coefficients [Tables 4-7] (dimen.)

tracer dye (Na-fluorescein) mass to inject per spring discharge = 2.0 x 10° to 5.0 x 108

(g)

tracer dye (Na-fluorescein) mass to inject per inflow rate at injection point = 2.4 x 104

39



from EHTD, you will need to provide the correct path to the *. in files. Alternatively,
pressing <ENTER> will automatically run the default file, Ehtd.in.

. Now enter a data output file name to be written or press <ENTER> for default name
(EHTD.out) as requested (Figure 8). Be aware that previous output files can be
overwritten if the same name is used for more than one. However, an input file cannot

be overwritten if one is mistakenly entered.

. Enter a plot file name to be written or press <ENTER> for NULL, which means that

no plot file is to be written (Figure 8). As with the output file name, duplicate usage

of plot file names will result in the overwriting of previous plot files, but exiting input
file names will not be accepted. There is no default plot file name used (the default is
no plot file). If a plot file name is given, then two plot files will be created; a TIME-
CONCENTRATION data file and a PostScript plot file. The latter will have an
appropriate name assigned (e.g., sampling station name) and a .ps extension added.
The TIME-CONCENTRATION data file will consist of four columns of data as shown
in Table 19.

It will be noted from Table 19 that much more data will appear in the first two
columns than in the second two columns. This is because the first two columns
define the BTC, whereas the second two columns represent suggested sampling times,
which are necessarily reduced to a workable recommendation. It will also be noted
that multiple sampling stations will necessarily be recorded in the same plot file one
right after the other in the order in which they appear in the input file but with
the header information separating each new sampling station data set. Individual
sampling station PostScript files are created, however. A single sampling station file

listing will result in just one set of data being recorded.

After the last file name has been entered, EHTD will respond for approximately one
second with:

FILE NAMES HAVE BEEN READ

unless NULL was specified for no plot file to be generated in which case EHTD will
respond for approximately on second with:



in the system. Recoveries ranged from 54 to 172%, which is probably a function of flow
conditions when the tracer tests were undertaken and discharge measurement errors.

The Dyers Spring tracer test considered here consisted of an impulse injection of 3.57 ¢
of Rhodamine WT, which resulted in 63% mass recovery. Errors in discharge estimation,
Rhodamine WT deaminoalkylation (K48, 1998, pp. 33-35), and/or isomer-specific sorption
(Sutton et al., 2001) may have partially affected tracer-mass recovery estimates. Moderate-
flow conditions (Mull et al., 1988b, pp. 25, 69) may also have caused unknown tributary
flow to or from the solution conduit and a consequent reduced tracer mass recovery (Field
and Nash, 1997).

7.1.4. Meltwater Channel

A tracer test was conducted in 1983 at Variegated Glacier in southeastern Alaska immedi-
ately post-glacial surge, when meltwater discharge from the glacier increased greatly. An
approximately 5.2 kg pulse (tg = 10 minutes) of Rhodamine WT was injected through a
borehole at the base of the glacier (Brugman, 1987, p. 93) and recovered at Lower Stream,
10 km downstream. Hot water was injected into the borehole prior to dye injection to en-
sure good hydraulic connection with the basal water system (Brugman, 1987, pp. 91-91).
Discrete samples were collected at the glacier terminus. Sample-collection frequency was

initially set at 40 minutes but was lengthened after 8 hours (Brugman, 1987, p. 93).

7.2. POROUS MEDIA

Tracer tests are commonly conducted in porous media aquifers in a variety of forms. These
tracer tests rarely include natural-gradient tracer tests because of the typically long travel
times involved. To increase the rate of transport, forced-gradient tracer tests, injection-
withdrawal tracer tests, and recirculation tracer tests are often employed. Table 26 lists

four tracer tests representing each of these types of tracer tests.

7.2.1. Natural-Gradient Tracer Test

Natural-gradient tracer tests in porous media are difficult and generally aggravating to
implement because of the design information required and the very long tracer transport
times involved. Even so, natural-gradient tracer tests are desirable because the flow field
is not distorted, as occurs with forced-gradient tracer tests. Test Site Wilerwald, located

northeast of Berne, Switzerland, in the Swiss Central Plateau, was established to evaluate



29.
29.
30.
30.
30.
31.
31.
32.
32.
33.
«798
- 267
-737
- 206
35.
36.
36.
37.
37.
38.
38.
38.
39.
39.
40.
40.
41.
41.
42.
42.
43.
«655
+125
+594
- 064
45.
46.
46.

BeRB

BEG

Figure 18. Data file generated by EHTD used to produce Figure 19 continued.

104
873
042
512
981
451
920
390
859
328

675
145
614
084
553
022
492
961
431
900
370
839
308
778
247
717
186

533
002
472

PRRRENNWWHhOO

+9339
.0793
- 3287
6778
-1197
6464
. 2490
-9185
-6460
-4232
- 2425
.0970

- 98058
-88816
-81521
- 75798
- 71334
- 67871
-65199
-63147
-61579
- 60386
-59482
-58801
- 58289
- 57906
-57621
- 57409
-57252
. 57136
»57051
- 56989
- 56943
- 56910
- 56886
- 56868
- 56856
- 56847

123



Part I
BACKGROUND

Flow of diluted uranine (Acid Yellow 73) through Sainte Anne Cave, Belgium. The tracer
release is depicted on the cover of this document (photo courtesy of Philippe Meus).



TRACER MASS =1.04E+00 kg

Breakthrough Curve
co _Sompling Times

a

Concentration (ug L-")
3

Time (h)

Figure 19. Effect of including an initial concentration and exponential production to the
Lost River Cave System data. Note that the BTC does not begin at zero concentration and
exhibits a gently rising slope prior to initiating a steep rise in response to tracer release.

concentration data and sample concentration data (columns 2 and 4 of Figures 14 and 18)
are very different.

Using the data listed in Figure 18, Figure 19 depicts the Lost River Cave System with
an C; = 0.3 ug L~! and exponential production (y, = 72 = 0.5) applied. It is evident from
Figure 19 that these conditions have a significant influence on the final BTC when compared
with the conditions of Figure 13, as shown in Figure 20.

6.3.4. Average and Peak Concentration Estimates

The general output file (Figure 15) will be slightly altered when an initial concentration
and/or exponential production are supplied in an input file to specifically reflect changes in
the estimated C and C). Providing an initial concentration and/or exponential production
will cause the bottom of EHTD-produced Table 3.1 to be altered to appear as Figure 21
(see Figure 15 on page 111 for comparison). In addition to producing a modified Table 3.1,
EHTD will also produce a Table 5.1 immediately after Table 4.1. The EHTD-produced
Table 5.1 will provide an estimate of C and C, (Figure 22).

125



and in solution conduits may be taken as

2K,
Bb=iat ate (49)

If tracer decay for the liquid phase s, equals tracer decay for the sorbed phase yz, then the
combined first-order decay yz is equal to Ra (Toride et al., 1995, p. 4) which is a reasonable
assumption commonly employed (Toride et al., 1995, p. 35).

The zero-order production coefficient 7(z) in porous media is given as (Toride et al.,
1995, p. 3)

ne) = (2) + OE) (50)

It is applicable to fractured media and solution conduits with 6 = 1 (100%).

3.2. TRACER MASS ESTIMATION

The most straightforward method for estimating tracer mass is to obtain a solution to
Equation (43) and then solve for average concentration or its real root f (c*) +0. Asa
basic control, it is necessary to include a desired average concentration C that corresponds
to average time ¢ or peak concentration C, that corresponds to peak time tp.

A simple solution to Equation (43) for a Dirac (6) function for obtaining the maximum

tracer concentration that ignores tracer retardation and decay is

f(a") =C, M

~ Ane /4xDit,'

which may be solved explicitly for tracer mass M. Equation (51) will generally provide

(51)

a reasonable estimate for M, provided reasonable estimates are available for the other
parameters. However, Equation (51) may be oversimplified for many applications because
it deals only with peak concentration and lacks consideration of tracer retardation and
tracer decay. Applying Equation (51) may result in excessive tracer mass estimates, which
is neither desirable from a hydrologic, aesthetic, economic, human health, or ecological
perspective, nor is it necessary to achieve positive tracer recovery. Alternatively, actual
tracer retardation and/or tracer decay may result in tracer mass estimates that are too
small for adequate tracer recovery.

Application of more comprehensive solutions to Equation (43) will provide a more
reasonable and reliable estimate for the tracer mass to be injected. Some solutions to
Equation (43) can be evaluated explicity for M, but other solutions for (43) may require

evaluation for its real root for some x* € [a1, a2], where z* represents the estimated mass
M.

43



2.6.

Ir

2.5.2.2. Karstic Media Sampling Times.
NOTATIONS FOR SECTION 2.

MODEL THEORY AND METHOD DEVELOPMENT 41

3. TRACER-TEST DESIGN METHODOLOGY

3.1.
3.2.

SOLUTE-TRANSPORT MODELING
TRACER MASS ESTIMATION
3.2.1. Model Solutions
3.2.1.1. Impulse Release for BVP. .. 2... 2 ee
3.2.1.2. Pulse Release for BVP.
3.2.1.3. Uniform Initial Concentration (IVP)
3.2.1.4. Exponential Production (PVP)
3.2.2. Tracer Retardation and Tracer Decay

. SOLUTE TRANSPORT
. HYDRAULIC AND GEOMETRIC PARAMETERS

3.4.1. Measured Parameters
3.4.2. Functional Relationships
3.4.3. Travel Time Estimates

. CONTINUOUS STIRRED TANK REACTOR (CSTR)

3.5.1. Travel Times and Velocity

3.5.2. Tracer Dispersion Estimates
3.5.2.1. Estimating Dispersion by the Method of Moments.
3.5.2.2. Estimating Dispersion by the Chatwin Method.

. TRACER SAMPLE COLLECTION DESIGN

3.6.1. Sample Collection
3.6.1.1. Sampling Frequency. .. 2... 6 ee ee
3.6.1.2. Initial Sample Collection.

. METHODOLOGY EVALUATION

3.7.1. Simulation

III BASIC PROGRAM USAGE

4. USING EHTD TO DESIGN A TRACER TEST 65
4.1. EHTD PROGRAM USAGE AND EXAMPLE DATA FILES........- 65
4.1.1. Loading EHTD and Example Data Files .....---.-------- 65

4.2. EHTD EXECUTION ... 2.0.2... e ee 66
4.3. USER-REQUESTED LATIN HYPERCUBE SAMPLING (LHS) ROUTINE 70
4.4. USER-SUGGESTED SOLUTE MASS ........--.--220+005- 72
4.5. SCREEN OUTPUT .. 1.2.2.2... 200 00002 eee 74

4.5.1. Screen Output of Error Messages .... 2... ------+2000- 7
4.5.1.1. Warning Messages... . 2... 6 0 ee ee 75

iv



NOTATION

long dimension of rod-shaped particle (L)
slope parameter for median infection estimate
slope parameter for median morbidity estimate
cross-sectional area of flow system (L?)

matrix of time values used in the Chatwin analysis (T)

interval of data points that bracket the function f(x*); (¢ = 1,2)
adsorption effiency (dimen.)

short dimension of rod-shaped particle (L)

one half fracture width (L)

maximum allowable Chatwin parameter corresponding to ¢, (T’/?)
vector of concentration parameters for the Chatwin analysis (T’/?)
tracer concentration (M L~*)

average tracer concentration (M L7%)

equilibrium tracer concentration (M L~*)

mean volume-averaged equilibrium tracer concentration (M L~*)

dimensionless resident tracer concentration = g

dimensionless concentration for BVP
dimensionless concentration for IVP
dimensionless concentration for PVP
characteristic tracer concentration (M L-*)
volume-averaged input concentration (M L~*)
peak tracer concentration (M L~*)

data value derivatives

axial dispersion (L? T-1)

function representing the real root of the ADE
input concentrations for pulse injection; (i = 1, 2; go = go = 0)
function of values such that 9{t:) = C;

zero-order production coefficient (M L~? T-?)

LinentpoKars). Ubgut2Kas), L(rwt2Kays)
Tevco , byuco , ruco

dimensionless exponential production (growth) constants for the PVP [i = 1, 2]

dimensionless production =

upper bounds on y
lower bounds on y



Part IV
ADDITIONAL APPLICATION OF
EHTD

Release of slightly diluted uranine (Acid Yellow 73) into flow of water for tracer test. Note
the contrast between the uranine color (fluorescent green) and the algae build-up on the
sides of the stream flow. This tracer test was conducted in order to verify the integrity of
the local production well from infiltration by toxic substances that may be accidentally or
deliberately released in the future.

151



r : r 1
a
we -e-6g— Tracer Decay = 0.0
4-8 - Tracer Decay = 0.05
Ls.- Tracer Decay = 0.1
a TF 1
u
.
E
H
|
& 2b J
8
0 herons
° 40

Time (h)

Figure 7. Predicted BTC for Prospect Hill Spring for increasing values for tracer decay.
Symbols represent recommended sampling times.

y= 0.0h7?. It is obvious from Figure 7 that as tracer decay is allowed to increase, Cp
also increases (Table 17) because of the necessity of maintaining G”. This effect was not
observed for increasing tracer retardation. In addition, because Cp increases, the BTC
is steepened, causing an apparent decrease in tracer transport times. However, whereas tp
clearly decreases (Figure 7), f remains unchanged regardless of the proposed tracer reactions.

Increasing tracer reaction effects causes a concomitant increase in tracer-mass estimates.
The increase in tracer mass estimates reflects the need to match the set value for O* while
including factors that have the net effect of decreasing tracer mass estimates, so that the
overall effect is an estimate for tracer mass that approximates that which should be used in
a tracer test.

Included in Figures 6 and 7 is an indication of appropriate sampling times for each BTC
(Table 18).

60



defined by Equation (1) (Table 3). In the second instance a double-logarithmic plot of Mass
injected versus Length x Discharge x Concentration also resulted in a clear relationship
defined by Equation (2). Equations (1) and (2) provide a means for estimating the mass of
dye to be injected such that positive tracer recoveries are likely.

Table 4. Aquifer and tracer-dependent coefficients To, —To,*.

Aquifer Tracer To,

Tracer-Dependent Coefficient, To,

clay tee 5-20
sand tee 2-10
fractured rock oe 2-20
karst ee 2-10

Tracer-Dependent Coefficient, Tc,

porous media oo 5.0 x 10?
fractured rock oo 3.0 x 108

Tracer-Dependent Coefficient, To,

very permeable Na-fluorescein 2.5 x 107+
aquifers
slightly permeable ee 1.0 x 10°
aquifers
nes NaCl 2.5 x 10?

Tracer-Dependent Coefficient, To,

Na-fluorescein 2.5 x 10-°

* Source: Adapted from Parriaux et al. (1988).

Equations (3)-(7a) were published by Parriaux et al. (1988) in a tracing guide that was
intended to be practical but is obscure and difficult to obtain. Equation (7b) is a slightly
more complicated form of Equation (7a). According to Parriaux et al. (1988), citing Zétl
(1974), Equations (3)-(7a) were developed for Na-fluorescein, but they may be used for
tracing with Lycopodium spores by using 1.5-2.0 times the weight of Na-fluorescein. Zétl
further suggests that higher amounts can only be advantageous. Equations (3)-(5) also
include an aquifer and/or tracer-dependent coefficient Tc, (Table 4), which is intended to

adjust the tracer mass to be injected. Equation (4) is valid for Na-fluorescein, but for

15



TRACER MASS = 188.01 9

— Breakthrough Curve
(Preliminary)

&

20

E
3
8

Time (h)

Figure 5. Preliminary tracer-breakthrough curve generated from a hypothetical CSTR.

significance are the variable effects created by the measured field parameters when combined
in functional relationships. Increasing Q, decreasing A, or decreasing L all have the effect
of shifting the curve to the left and decreasing the mass estimate. Decreasing Q, increasing
A, or increasing L all have the effect of shifting the curve to the right and increasing the
mass estimate.

Figure 6 is a plot of time versus concentration produced by the ADE using the
measured field parameters and functional relationships listed in Table 16 with varying tracer
retardation (Ry = 1, Ra = 2, Ra = 3) and no tracer decay (u = Oh-!). The predicted
tracer mass necessary for a successful tracing test and the resulting average and peak tracer
concentrations are shown in Table 17 for varying tracer reaction conditions. From Figure 6
and Table 17 it is apparent that although CG” remains the same for each BTC for varying
values of Ry, ? and D, appear to increase and v to decrease as aq increases. In fact, these
hydrologic parameters have not physically changed, but increasing Rg creates just such an
appearance.

Table 17 also includes four instances of tracer decay (4 > 0 h7') without retardation
(Ra = 1.0), the effects of which are shown in Figure 7 for three of the instances (u=0.0h-+,
“= 0.05 bh, w= 0.1 h-"), because # = 0.01 h7! would not be readily distinguishable from

58



“poranodO0 OAVY SUOTJOLOI LOTT] OU YHNOYY SE Pops] OIL S]NSOI OATVDY g

“s}]NsoI 9809 JOOwIY OATJOWOI = Y-G.LHM 'S3Ns0r 4s09 o9wI} oATOWOIUOU = N-GLHA wv

y-OLXO8T (OTX9LT OLX GG9 OT XBsGe IX Pes OI X6ge PLX4ey UAL

OL XeeT OLXeGt OLXSgo OTXsce OLX Peet OTXxesry OLx2er NALHA

OT X00L gOEXO6T OTXL96 OL X60 OT X00% POT XOEF —O1L X00 pomsvoyy

qSa], 409V4T, 4aroD] poyobarv,

OLX ZS (OL X689 OL XeLs8 OIXI99 OT XZE9 OLX IPT ,OLXSVT UOLHY

1-01 X 60S OL X2@z9 OL XELs COIXI99 OLXZE9 OLXe@Pl ,O1Xxehl N-GLHA

OLX 00S OT XSTT OTXOGT TXsee OLXseg OT XGPT OLX Z2T  pommsvoy
ysay, doov4y, Gurudg sua

oOLXOVT jOLXELT OL X98 {OT XO06T ,~OTX799 OL X6GE Ol x99 WALA

oOTX6ZT jOLXEGT jO1X9F8 {OT XOBT ~OTXZ99 OTX6GE OI x99E NGL

oOTXOOT OTXOFE OL XZ9% OT XGES TX8LS OT X00 OL XO  pomsvo
qsa], La0v4T, any wnoss~pyy

OLX PET {OLX e9'L 1X 9e8 OIXear OLXeel OlxXeoy OTXxIT@ UWaLHA

1-01 X9ET 101 X9GL LX978 OTXZor OIXeel pl xeOr ~OIXTL@ N-CLHY

OLX LZ9T ;OTX€eS OLXeey PIX 9's OIXeeT OTXcer OX Ils Ppomseop

Pa, 4a, YOK say
simoy ‘2 smoy ‘yy ‘wounp “gq jy gu‘gq ,_yu‘a sinoy ‘7 ge} VIE

"S]S9} JooBI] UIRdI}S SUIMOY OY} JOF SO,.],q poinseow snsIaa sO,L.qg peyrpeaid-qLHA ‘8% dL

134



3.5. CONTINUOUS STIRRED TANK REACTOR (CSTR)

Obtaining an estimate for M and D, can be achieved for a predicted BTC on the basis of
the theory of a completely mixed CSTR. A mass balance model that describes the dynamics
of a simplified CSTR is (Silebi and Schiesser, 1992, p. 49-50)
d(VC)
dt

Setting g = Q and using initial condition

= qCy — QC ~ VEC. (82)

C(0) = O,, (83)
the solution to Equation (82) is (Silebi and Schiesser, 1992, p. 50)
C(t) = Cre (O+V OV], (84)

Equation (84) will produce an exponentially decaying BTC starting at the peak concen-
tration C, with a gradient that is dependent on the value of the reaction rate constant k
and the space velocity Q/V (Levenspiel, 1999, p. 93). It is apparent from Equation (84)
that whereas C, may be preset, prior knowledge of discharge Q, reactor volume V, and
transport times ¢ must be determined.

Equation (84) is evaluated for C from ¢ ~ t, in a descending manner using 0.25 < k <
1.0, although k = 0 would adequately suffice. The concentration values C’ obtained from
Equation (84) leading from @ are then reversed to achieve an ascending limb leading to é.
Equation (84) is then resolved for C’ from # in a descending manner using a k < 1.0. For
n = 200, k = 1/200 represents a reasonable exponential decay for the descending limb.

The values for k were empirically determined such that 0.25 < k < 1.0 represents a
steeply ascending limb, whereas k < 1.0 represents a more gently decaying descending limb
controlled by the number of data points. The result is a good approximation of a typically
positively skewed BTC in which a cusp forms the peak concentration at the peak time of
arrival. Although the values for k were empirically determined, the resulting BTC appears
to reasonably represent a typical BTC based on observation and experience.

The BTC produced by the CSTR model is subsequently evaluated by

M=Q fr C(t) dt (85)

to obtain the area under the BTC. The area represents an initial estimate for the tracer
mass to be adjusted as required by Equations (54), (56), or (57).

51



dyes and other similarly appearing compounds), which may be advantageous for visual de-

termination of dye but which adversely affects the signal-to-noise ratio of modern analytical
instruments (Worthington, pers. comm.). Excess sorption of background concentrations re-
quires that the estimated tracer dye concentration to be released exceed background concen-
trations at the sampling stations by 10 times to ensure detection (Crawford, pers. comm.),
an undesirable practice from both an aesthetic and an ecological perspective (Smart and
Karunaratne, 2001).

Excessive and extensive background sorption also causes ambiguous results, erroneously
suggesting tracer recovery at most or all of the sampling stations (McCann and Krothe,
1992) because the method does not lend itself to establishing that the sorbed and “identified”
compound is in fact the fluorescent dye of interest. Even more basic, it may be regarded as
nonsense on its face. By requiring an injection concentration that results in a downstream
concentration >10 times background, it is assumed that a multitude of background samples
(typically three) have been collected and that the maximum concentration or some statistical
value (e.g., mean, median, etc.) for which a 10-fold increase is intended was used as
a measure. Second, it is very difficult to translate an upstream concentration at a
ground-water injection point into a downstream concentration. Third, the method for
this calculation requires appropriate field measurements and numerical analysis, which are
typically avoided.

More recent research suggests that fluorescent dye sorption by detectors may not be as
straightforward as once thought. Research at the University of Minnesota (Davies, pers.
comm.) suggests that the occurrence of false negatives and false positives may occur far
more frequently than has previously been recognized, primarily because of the vagaries
of fluorescent dye sorption/desorption by the detectors. For example, sodium fluorescein
(uranine [45350 C.I. Acid Yellow 73]) was found to be readily sorbed by activated carbon,
but it was also desorbed almost immediately. Rhodamine WT (CI. Acid Red 388),
however, was not readily sorbed and was difficult to elute. The rapid sorption-desorption
of short-wavelength dyes and the slow sorption and difficult elution of long-wavelength dyes
compromise the use of activated carbon for detection (Smart and Simpson, 2001).

Other peculiarities related to sorption by activated carbon and sample handling (Smart
and Friederich, 1982; Smart and Zabo, 1997) also prevent replication of the results, a basic
requirement of any scientific endeavor. The difficulties are further exacerbated by the
fluorescence spectra shift caused by the high pH of the elutants (Ka8, 1998, p. 102). In
addition, specific tracer types may result in varying sorptive behaviors (Sutton et al., 2001).

8



average concentration then provides a theoretical basis for an estimate of necessary tracer
mass. Application of the predicted tracer mass with the hydraulic and geometric parameters
in the ADE allows for an approximation of initial sample-collection time and subsequent
sample collection frequency where 65 samples have been empirically determined to best
describe the predicted BTC.

2.2.2. Range of Capabilites of EHTD

Although most of the tracer mass estimation equations listed in Table 3 were designed
for tracing in solution conduits in karstic terranes, there appears to be no logical reason
to exclude porous media systems. The fact that solute transport processes in hydrologic
systems all follow the same basic theoretical principles suggests that an appropriate model
for estimating tracer mass would function effectively for all hydrological systems. However,
such a model would need to be able to account for slight differences in the nature of the
flow systems (e.g., effective porosity) and the manner in which the tracer test is conducted
(e.g., tracer release mode).

Breakthrough curves predicted using the tracer test design program EHTD for various
hydrological conditions have been shown to be very reliable (Field, 2002c). The hydrologic
conditions used to evaluate EHTD ranged from flowing streams to porous media systems
so that the range of capabilities of EHTD could be assessed. The flowing streams used to
evaluate EHTD included tracer tests conducted in small and large surface-water streams,
a solution conduit, and a glacial-meltwater stream. The porous media systems used
to evaluate EHTD included natural gradient, forced gradient, injection withdrawal, and
recirculation tracer tests. Comparisons between the actual tracer tests and the results
predicted by EHTD showed that EHTD adequately predicted tracer breakthrough, hydraulic
characteristics, and sample collection frequency in most instances.

2.3. TRACER-TEST DESIGN RESULTS USING PREVIOUS METHODS

Tracer-test design examination parameters provided by Parriaux et al. (1988) and reprinted
in Ka (1998, p. 324) have previously been applied to a small set of the 33 equations listed
in Table 3. Unfortunately, only a few of these equations were examined using the test
examination parameters. Although not stated it is likely that one of the reasons for the

limited examination is that additional parameters are necessary for testing the equations.

25



—S-o— Measured Data
—a-4 — NonReactive Transport
= x-- Reactive Transport

Concentration (ug L7*)

Time (d)

Figure 27. Comparison of measured data for the Test Site Wilerwald tracer test with EHTD

predicted results for nonreactive and reactive transport. For reactive transport, Rg = 1.80
and p = 0.0044 h7!.

in Table 32.

7.3.2.1. Test Site Wilerwald Tracer Test. Natural-gradient tracer tests in porous
media can be frustrating because of the time involved, the number and type of field
measurements necessary, and the construction of injection and recovery sites. Unlike with
karstic terranes, some basic transport parameters can be approximated prior to initiating
the tracer test, which minimizes some of the design difficulties. However, errors in estimates
for parameters that are difficult to estimate prior to conducting a tracer test (e.g., effective
porosity) can result in substantial errors in the tracer test design.

The tracer test design parameters for Test Site Wilerwald were carefully measured and/or
estimated by geophysics, which helped facilitate a good tracer test design (De Carvalho Dill
and Miiller, 1992, pp. 234-239). Using these same parameters in EHTD resulted in
satisfactory fits to the measured BTC (Figure 27) with — = 868 hours, t, = 794 hours,
v = 0.23 mh7}, and D = 1.46 m? h~!, which do not approximate the measured results as
well as desired (Table 31). Using the data provided and an estimate for discharge according

145



TF is defined as (Toride et al., 1993, 1995, p. 14)

_ —Pe(R, oe val
TP(Z,T) = z “A ear P. ec?” erfe Ral = f . (55)
a mRa Ra \/4RaT/Pz

Solving Equation (54) explicitly for M or for its real root as it relates to Oz , T) limits
the solution to the concentration corresponding with average travel time, which will be less
than the peak concentration.

3.2.1.2, Pulse Release for BVP. The solution to Equation (52) for a pulse release

for the case where yu” = 0 is (modified from Toride et al., 1995, p. 14)
2
* Reig rH
f(a") =O'Z,T) - 2G: - ga) F(ZT -T), (56)
i=1
and for the case where ® + 0 is (modified from Toride et al., 1995, p. 14)

2

F(a") =O'(2,7) — 7: — ga) PR(Z,T - TB), (67)

i=1
where (56) and (57) are again solved for the real root as related to Cz, T), in which
the result will be less than the peak concentration. The auxiliary functions Pf and TF are
defined as (Toride et al., 1993, 1995, p. 14)

as 2-7
TF(Z,T) = 1 oof Tene T \= aha?
Vara/P.
( +PZ+ =) oP? enfe | HaZ EF (58)
4 \/4RaT/P.
when py” = 0 and

T¥(Z,T) = a oF erte (24,7 au

1+ \/4RgT/P.

1 pate RaZ +ul
+ ae? erfe | ——>—

V4Ral/P.
2 ebere Pelee erfe RaZ +uT
— y2 —_
lou 4/4RaT/Pz
where u = 4/1+ ue when p” £0 (ie, w? > 0).

45

N



employed to keep regulators away and to further the perception of the “all-knowing” expert.

More significantly, however, it may be appropriate for regulators to estimate tracer masses
if they are going to be taking the necessary field measurements that the tracer hydrologists
are avoiding. If nothing else, it provides the regulator with a useful check on the conjecturer.

2.1.2. Tracer Mass Estimation by Mathematical Equation

Many equations for calculating the amount of tracer material to release into a flow system
have been published. Thirty-three empirically determined equations are considered here
(Table 3) (see Section 2.6., page 38 for a description of the parameters used in Table 3).
It will be noted that some of the equations listed in Table 3 do not appear in original
form, as they have been modified for consistency of units and to yield mass in grams. An
examination of these equations reveals little about each except that most rely to some extent
on volumetric flow rate (discharge). Presumably, the reliance on discharge by the originators
of the equations was intended to address probable dilution effects. The 33 equations were
developed empirically, so maintaining mass balance appears not to have been an important
consideration. Although not apparent from Table 3, 5 of the 33 equations incorporate
different systems of measurement in their original form.

Sources for the equations were not always specific about which type of tracer a particular
equation was meant for in the design or about whether it even matters, but most were
probably designed for the fluorescent dye Na-fluorescein. Also, it is not always clear whether
an equation was intended for visual tracer detection, instrument detection in water samples,
or sample collectors designed to enhance tracer concentrations (e.g., carbon sorption of
fluorescent dyes via detectors).

Some equations require a “fudge factoring” constant that takes into consideration the
relative detectability of the tracer to be used, the residence time within the aquifer, the type
of sampling done, the method of sample collection, and/or the method of analysis. Specifics
such as tracer type, methods of sampling and analysis, and fudge factor multipliers should
generally be regarded as inappropriate when calculating necessary tracer mass unless a clear

scientific basis for such can be established (e.g., solution-conduit sinuosity <1.5).

2.1.2.1. Review of Tracer-Mass Estimation Equations. Worthington (pers. comm.)
examined more than 3000 tracer tests and was able to fit a straight line through a double-
logarithmic plot in two separate instances. In the first instance a double-logarithmic plot
of Mass injected versus Time x Discharge x Concentration showed a clear relationship

11



At the Mobile site bromide was injected into a well over a period of 3.19 days. The
entire tracer test lasted 32.5 days (Molz et al., 1986b). The injection and withdrawal
wells, separated by a distance of 38.3 m, were operated continuously at 57 m® h7) (Molz
et al., 1986a, p. 55) to cause steady-state conditions between the injection-withdrawal wells.
Details of the test are described in Molz et al. (1986b) and Molz et al. (1986a, pp. 52-60,
71).

7.2.4. Recirculation

A two-well recirculation tracer test is the same as an injection/withdrawal tracer test except
that the extracted water is recirculated back into the injection well. Such a tracer test
was conducted at the Chalk River site. The basic tracer test design parameters for a
recirculation tracer test conducted at the Chalk River site are listed in Huyakorn et al.
(1986) and described in detail in Pickens and Grisak (1981). Two glaciofluvial sand aquifers
are separated by a 1 m layer of silty clay, which was taken as the bottom confining layer
for the aquifer being traced. This sand aquifer is 8.2 m thick and is confined above by a
17 em-thick silty-clay layer. Aquifer tests at the site resulted in a K that ranged from 720
to 7200 m hTM, but a single-well tracer test suggests K = 5040 mh! (Pickens and Grisak,
1981).

The recirculation tracer test consisted of two wells 8 m apart that were operated at

a flow rate of 1.62 m*?h-!. Tracer was injected for a period of 3.22 days with an initial

concentration of 4.1 x 1073 yg L~! (Huyakorn et al., 1986), which translates into a tracer

mass of 521 ug.

7.3. TRACER-TEST DESIGN RESULTS

The eight tracer tests listed in Table 26 were used to test EHTD. Because these tests
represent a range of tracer test types, the robustness of EHTD could be examined.
Simulations using these eight data setis consisted of using only those measured or estimated
field parameters necessary for application of EHTD while excluding specific tracer test-
determined parameters. Set average tracer concentration C and possible tracer reactions,
tracer retardation Rg and tracer decay were adjustable parameters so that measured
peak tracer concentration C, and measured tracer mass M could be matched. Normal
use of EHTD to predict tracer test results prior to test implementation would not require
adjustment to match C, or M except as may be desired.



This can be a very large set of iterations if radical changes to the values are required, but
this is unlikely.

Next is an indication of how well the optimization routine performed; in this instance
the statement:

#ee%% X- AND RELATIVE FUNCTION CONVERGENCE +****

indicates very positive optimization results. This same line appears in the final output file
as an error message so that the user has a documented record of how well the optimization
routine performed.

The next three rows also will not be of much use to the user, as they only indicate the
function evaluations, gradient evaluations, etc. However, the next four rows are very useful,
as they represent the final outcome of the optimization routine. The FINAL X(I) and D(I)
are similar to those listed at the top of Table 23, and the G(I) represents the final gradient
estimates.

Lastly, the screen displays the FINAL TRACER MASS ESTIMATE just as though the opti-
mization routine had not been run. EHTD then informs the user to continue on to the plot

routine to visualize the predicted BTC.

4.6. COMPUTER GRAPHICS

A high-quality color graphics algorithm, PGPLOT* (Pearson, 1997) that allows cascading

of graphics screens, direct printing, creation of screen files, and more using pull-down menus
in the Windows environment is included in EHTD. It is particularly useful for evaluating
the effect of interpolating and/or extrapolating the original data. Publication-quality plots
may be generated as PostScript files from the graphics screen incorporated into the program.
Alternatively, a screen dump using any type of printer is possible.

4.6.1. Features of the Interactive Graphics Loop

Running EHTD will start a conventional Windows screen with a series of pull-down menus
(Table 24). Each underlined character in Table 24 indicates that the <Alt> key plus the
underlined character implements the respective menu item. For example, <Alt+F> will
initiate the pull-down menu items underneath the File heading. Of course the mouse pointer

4PGPLOT may be obtained from http: //www.astro.caltech.edu/~tjp/pgplot/



Thirty-three tracer mass estimation equations and the computer program efficient hy-
drologic tracer-test design (EHTD) methodology were reviewed and tested using published
test criteria. Testing 32 of the 33 equations and EHTD produced extreme ranges in the
results. EHTD is the only method that was developed using established solute transport
theory. The other 33 equations were all developed empirically. Although the review and
testing described does not provide a means for determining the best tracer mass estimation
method and sampling frequency method to employ, recent tracer testing successes using
EHTD suggests that EHTD may be more reliable than the other methods (Field, 2000).

Sample collection schemes were also reviewed and shown to be difficult to implement
and unreliable because of their haphazard nature. Darcy’s law for porous media cases was

not applied because of insufficient test data, but Darcy’s law is believed to be a reasonable

model for designing a sampling schedule, provided that difficult-to-obtain parameters (e.g.,

effective porosity) can be adequately estimated. For karstic media, application of an assumed
average velocity equal to 0.02ms~} for designing a sampling schedule can be effective,
provided tracer release and transport occur via solution conduits.

Given the complexities and difficulties associated with the published 33 tracer mass
estimation equations and conventional sampling schemes, their continued use must remain
suspect at best. As shown by EHTD, these previously developed equations/methods fail to
yield consistent results. Application of the more scientifically sound method developed in
EHTD is more likely to ensure successful tracer test results (Field, 2002a) and is suggested
as a more reliable alternative.

A total of eight tracer tests representing a wide range of conditions and a minimum of pre-
tracer test design parameters were used to evaluate EHTD. In all but the Test Site Wilerwald
and Kirchdorf-Unteropfingen tracer tests, the measured BTC curves were approximated by
EHTD for both nonreactive and reactive instances. Recommended sampling times were
found to be adequate for defining the measured BTCs for all eight tracer tests. Only the
initial tracer breakthrough times for the Test Site Wilerwald and Kirchdorf-Unteropfingen
were inadequately predicted, which was directly related to the unreliability of Darcy’s law
in the first case and the use of an incorrectly determined effective porosity in the latter.

Most of the EHTD-predicted tracer mass estimates for nonreactive conditions were
mostly fairly to the actual tracer masses released. For the flowing stream tracer tests,
tracer mass estimates were inadequate only for the Uvas Creek and Variegated Glacier tracer
tests. The tracer mass estimates for the Missouri River tracer test were slightly greater than

the actual tracer mass released. For the porous media tracer tests, only the tracer mass

160



Table 14. EHTD tracer test analysis results.
Parameter Porous Media Karst

Meg 5.25 x 10? 1.02 x 10?
Mg 1.95 x 10° 6.31 x 10?
ih 1.09 x 108 7.19 x 10
teh 9.82 x 10? 6.90 x 10!
toh 1.93 x 103 1.31 x 10?
v,mh-} 4.58 x 1071 4.17 x 10!
vp? m h7 5.09 x 107? 4.35 x 10)
pe m ho? 2.59 x 107? 2.30 x 10!
Di? mh? 7.99 x 10° 1.52 x 10?
D,?m? bh 2.09 x 10! 2.44 x 108
om 1.74 x 10! 3.64 x 10!
o>m 4.56 x 10! 5.86 x 10
P 2.87 x 104 8.25 x 10
P» 1.10 x 10? 5.12 x 107
ti2h 1.92 x 10? 2.90 x 10!
t?h 2.16 x 10? 1.80 x 10!
teh 4.80 x 10! 3.00 x 10°
teh 9.60 x 10 5.00 x 10°
tah 3.27 x 108 2.00 x 10?
tah 6.56 x 108 3.41 x 10?
C, mg m~3 1.09 x 104 1.04 x 10
Cp? mg mTM* 1.63 x 10+ 1.87 x 10+
Vp, m3 7.93 x 104 2.61 x 104
V, m3 7.85 x 104 2.59 x 104

® Impulse release results.
» Pulse release results.



1. Mean, Stat(1, *) Ey = fewer

hw

2. Variance, Stat(2, +) a= Ehiwe (esta)

3. Standard Deviation, Stat(3, «) Ow = Jo,

4, Skewness, Stat(4, x) ew = ne

5. Kurtosis, Stat(5, *) Key = {geet} 3

6. Minimum, Stat(6, +) Lmin = min(x;)

7. Maximum, Stat(7, «) max = max(z;)

8. Range, Stat(8, +) Lp = Imax — min

9. Coefficient of Variation, Stat(9, «) Ly =F for Ty #0
10. Number of values processed, Stat (10, «) n=DNfi

where the statistics are given in terms of a single variable x. The i-th datum is 2;, with
corresponding frequencies set to unity (f; = 1) and weights also set to unity (w; = 1).*

“Note that none of the variables shown in this box are intended in any way to match similar variables
used elsewhere in this document. For example, x; here represents any required input parameter (e.g.,
discharge, Q) and n represents the the number of values requested (processed) by the LHS routine to
develop the mean values for each of the required parameters.

Figure 9. Equations used to calculate the univariate statistics used to describe the LHS-
generated mean values used in a single input file.

et al. (1986, p. 41-54), Kilpatrick and Taylor (1986), and Mull et al. (1988, p. 75-79),
but these methods are much more difficult to implement, they require a great deal more
measured data acquired over a very long timeframe, and they tend to overestimate the peak
downstream concentration. EHTD does not suffer from the limitations listed and reliably
reproduces peak concentration. However, the previously developed methods do provide a
better visual fit to an expected long BTC tail than does EHTD, but this better tail fit is
useful primarily in estimating solute persistence.
This first EHTD query appears as:

DO YOU WANT TO SUGGEST AN INITIAL SOLUTE MASS (Y=YES, N=NO)?

73



components M, Ra, and pz of vector y to be optimized

Péclet number = 3% (dimen.)

skin permeability constant (L T~')
probability of infection (dimen.)
probability of morbidity (dimen.)
probability of mortality (dimen.)
porosity (dimen.)

bulk density (M L~°)

particle density (M L-%)

inflow into injection point at time of injection (L* T~')
flow system discharge (L? T-‘)

solute conduit radius (L)

twice continuously differentiable functions of y

solute retardation (dimen.)

reference concentration (M M7?)

reference dose (M M-! T~')

skin surface area (L?)

shower duration (T)

sinuosity factor (dimen.)

travel time variance (T?)

time (T)

average time of travel (T)

base time value for At time spacing (T)

tracer-test duration corresponding to last detectable tracer breakthrough (T)
individual tracer sampling times (T)

maximum allowable time for Chatwin analysis t,, < 2 (T)
base time value for n,,At time spacing (T)

time for pulse release (T)

expected time to peak arrival (T)

tracer release control (dimen.)

sample-collection times (T)

sampling frequency (T)

time corresponding to minimum concentration for sample collection (T)
time spacing for CSTR-generated BTC (T)

164



3.4.3. Travel Time Estimates

Estimates for transport velocities translate directly into transport times. Initial average
time of travel ¢ is estimated from

zak (76)
v
and tracer test duration from
tg — Tmt (77)
Uv

where 2 < n, < 3, depending on the type of tracer release. Parriaux et al. (1988, p. 8)
recommend n», = 3, but it has been experimentally established that setting n,, = 2 for
impulse releases and n,, = 3 for pulse releases produces the best results.

Individual tracer travel time data points must also be estimated. A base time value t,

for initial time ¢, and subsequent time spacing At may be estimated up to ¢ by

n,

3
oF]

ho, (78)

>|

and a base time value t,, for subsequent time spacing n,,At from ¢ may be estimated by
tm = Mm to. (79)

By assuming ¢ = tp, individual time values ¢; may be calculated up to ¢ from

n/2
i=tet tre (80)
i=l
and individual time values t; from # from
n
ti=tm+ > tris (81)
i=n/2

where 7 is a reasonable number of data points for obtaining a smooth BTC. Combining the
values obtained from Equation (80) and Equation (81) results in a series of appropriately
spaced time values that approximates initial tracer arrival and final tracer detection.
Doubling or tripling time spacing after f is not really necessary. However, it is essential
that sufficiently early and late times be established to ensure adequate consideration of

actual flow conditions.

50



Entering N represents a “no,” and EHTD will continue processing by adjusting the in-
ternally estimated solute mass to achieve the desired downstream C. Entering Y represents
a “yes,” which causes EHTD to pause a second time for the user to be further queried as
to the actual solute mass to be considered. This second EHTD query appears as:

ENTER A SUGGESTED SOLUTE MASS IN GRAMS (g):

where the user would enter a solute mass that EHTD is to use for processing. The originally

desired C will be ignored by EHTD. EHTD will bypass all tracer mass estimation routines

and proceed directly to the basic solute-transport modeling routine using the estimated
hydraulic parameters (see Section 3.4.) and the user-supplied solute mass.

EHTD will respond by noting the user-suggested solute mass to be used in processing
in milligrams (mg) and an appropriate error code, an explanation of which appears at the
end of the EHTD output file. The EHTD response will appear as:

USER-SUGGESTED MASS = --- mg
ERROR CODE AVERAGE CONCENTRATION ESTIMATE = ---

where --- represents an appropriate numerical value.
4.5. SCREEN OUTPUT
Further processing by EHTD will result in a screen display of

1. INITIAL TRACER MASS ESTIMATE is an initial tracer mass estimate based on the CSTR

analogy.

2. ADJUSTED TRACER MASS ESTIMATE is an adjusted tracer mass estimate based on factors

such as tracer-reactivity effects such as tracer retardation and tracer decay.

3. FINAL TRACER MASS ESTIMATE is the final tracer mass estimate based on the use of the

selected optimization routine.

These are presented so that the user can gain a sense of the workings produced by
EHTD prior to going to a screen plot of the resulting BTC or reviewing the output file.
(See Section 6. on page 97 for a detailed discussion of EHTD data output files.)

74



TABLE 2.1.1. INITIAL ESTIMATED HYDRAULIC FACTORS

AVERAGE TIME AVERAGE TIME AVERAGE TIME PEAK TIME
CINI. EST.) (ADJ. EST.) VARIANCE (INI. EST.)
(h) (h) (h72) (h)
2.3471E+01 3.6943E+01 1.3812E+02 2.3471E+01
J |
Lo

AVE. VELOCITY AVE. VELOCITY PEAK VELOCITY SYSTEM VOLUME

(INI. EST.) (ADJ. EST.) (INI. EST.) (INI. EST.)
(m/h) (m/h) (m/h) (m*3)
3.4085E+02 2.3685E+02 3.3417E+02 3.0080E+05

DISPERSION PECLET NUMBER DISPERSIVITY
(m*2/h) (DIMEN. ) (m)
3.1336E+04 8.7018E+01 9.1935E+01

Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued.

109



TABLE 4.1. ESTIMATED SAMPLING FREQUENCY

SAMPLING TIME INTERVAL

CONVENIENT

(min)

Figure 15. Standard-form example output file generated by EHTD from a typical input file

(see Figure 12) continued.

NVNNNNYONNPERBRP BBB BERBER O

-9516E+00
- 0808E+01
-1665E+01
-2522E+01
- 3378E+01
-4235E+01
-5092E+01
-5948E+01
-6805E+01
- 7662E+01
-8518E+01
-9375E+01
-0232E+01
- 1088E+01
-1945E+01
-2802E+01
-3658E+01
-4515E+01
-5372E+01
-6228E+01

112

CONVENIENT
(h) (min)
9. 57.
10. 48.
11. 40.
12. 31.
13. 23.
14. 14.
15. 5.
15. 57.
16. 48.
17. 40.
18. 31.
19. 23.
20. 14.
21. 5.
21. 57.
22. 48.
23. 40.
24, 31.
25. 22.
26. 14.



explained.

Equations (15) and (16) rely on a set amount of dye to be injected per rate of spring
discharge or swallet inflow, respectively. These two equations are probably intended for
visual detection and, reportedly, reduced amounts of fluorescent dye could be released if
detectors are used for dye sorption (Sweeting, 1973, p. 228).

Equation (17) is described in a very confusing manner in Davis et al. (1985, p. 101).
The description appears as: “They [(Drew and Smith, 1969)] recommended using 60 grams
of dye per kilometer of underground travel, per 0.15 cubic meters per second of discharge,
at the largest likely rising.” A more clearly worded statement would have stated that 60
grams of dye is recommended for every kilometer of underground travel for 15% of discharge
(m* s~!) at the largest likely rising.

Equations (18), (21), and (22) were published by Aley and Fletcher (1976) in a
tracing guide that was also intended to be a practical guide. Equation (18) is listed
as being applicable for surface water and was intended for time-of-travel studies using
Rhodamine WT. It includes an unidentified multiplier that may be a unit conversion
factor, although this is not clear. The original form of Equation (18) is reported as a
volume with units of milliliters (Aley and Fletcher, 1976, p. 7), but this requires that the
unidentified multiplier be a unit conversion factor representing tracer density. The multiplier
appears much too large to solely represent tracer density, so it is likely that it is a combined
conversion factor representing density and a fudge factor. Equation (18) is a modification
of the original equation by Aley and Fletcher (1976, p. 7) to obtain mass in grams, on the
assumption that the original equation really was intended to yield a volume in milliliters.

Equations (19)-(21) represent a progression in development as technology improved
(Haas, 1959) and are really only variants of Equation (8). Equation (19) was intended for
visual detection and relates a specific amount of tracer dye mass to discharge and distance.
Equation (20) was intended for ultraviolet light enhancement and relates tracer dye mass
to system volume and distance. Equation (21) was intended for adsorption onto activated
carbon and relates tracer dye mass to discharge and distance, but it may be expected to
yield excessive amounts of tracer material (Aley and Fletcher, 1976, p. 9).

Equation (22) is intended for tracing ground-water flow using Na-fluorescein and is
applicable to waters of pH > 5.5, transport via solution conduits, and dye sorption by
detectors. Substituting Rhodamine WT for Na-fluorescein requires 2 to 10 times more
tracer dye (Aley and Fletcher, 1976, p. 9). This equation supposedly results in reduced
tracer quantities because it does not rely on proposed downstream C, (Aley and Fletcher,

19



“Sy]NsaI Ys} JO9eIy OATJOVOI = Y-C.LHY

“s}]Ns0r 4S9} 109BI} OAIJOVOIUOU = N-C.LHA eo

OLX 6Sb OEX0E% oOTXZIT OLxXSet ,OLXre8 ¢OlXLTh 4-01 X1@G UdLHA
Or xXsly OT X60% OTX2Ol OI XG@T ,-O1 Xe ¢OlX€@T ,O1X PGT N-GLHA
uu EX PO% OTXZL LXSet ,-Ol X28 ¢OLXOT'P 4-01 X 1g pomsvoyy
78a], 40004], ANG sonny yyoYD
yOT X99 ,OLX8ST O1X69S OTX98h ,OTX6TS@ OIXTIZT Ol1XSh2 WaLHa
OLX Ze% ~OLXOTT OTX69S OL X9EV OT X0B% OLX PEP OI X68T N-GLHA
os pOlXS0% jOTX69S OL X9EP 01 X0¢% OI X69T OT X tr, Ppomsvoyy
SAL, 490D47, 94S OPLQOW
9T X EET OT X €ET o0T X 18°% sOTX10€ UCLA
oT X GET OLX CET OT X 08% OLX res NOL
aa OT X 0L°2, OT X 08°% e0E X 00'E = pansvoyyy
pay, saov4y, uabuydosaquy ~fsopyaury
pOTX9BS ~OTXGZ% 2-01 X006 2-OTX006 OTXO7E {OL XZTT O1xX00T Wala
Ol X9ZS OT XGZ% z-01 X006 201X006 O1X0ZE OLXxesr Olx98% N-CLAA
wo yOTX€V6 2-01 X 006 2-01 X006 OTXO@E OT XITT O01 X00T Ppomseayy
q89], Ld004], PyeMnsaqtimM ang 9],
gui ‘Aq et A gua UA Tan 49 |g Bn ‘97 3'‘W 29g Bye

"s}80] 19081} vIpauT snoiod ay} Joy S}{NseI Poinsvoul snsiea syNser poyrpold-G.LHA “ce qe

144



De Carvalho Dill, A., Miiller, I., 1992. Geophysical Prospecting. In: Leibundgut, C., De Car-
valho Dill, A., Matoszewski, P., Miiller, 1., Schneider, J. (Eds.}, Investigation of Solute
Transport in the Porous Aquifer of the Test Site Wilerwald (Switzerland), Steirische
Beitrage zur Hydrogeologie, 6th International Symposium on Water Tracing, Transport

Phenomena in Different Aquifers (Investigations 1987-1992). Vol. 43. Joanneum Research,
Graz, Germany, pp. 229-250.

Dennis, J. E., Gay, D. M., Welsch, R. E., 1981. An adaptive nonlinear least-aquares
algorithm. toms 7(3), 348-383.

Dienert, F., 1913. Rémarques au sujet des expériences avec la fluorescéine. C. R. Academy
Sciences 157, 660-661.

Drew, D. P., Smith, D. 1., 1969. Techniques for the Tracing of Subterranean Drainage. Tech.
Rep. 2, British Geomorphological Research Group Technical Bulletin, Great Britain.

Dunn, B., 1968. Nomographs for determining amount of Rhodamine B dye for time-of-
travel studies. In: In Selected Techniques in water Resources Investigations, 1966-67.
U.S. Geological Survey Water Supply Paper 1892, pp. 9-14.

Field, M. S., 1997. Risk assessment methodology for karst aquifers: (2) Solute-transport
modeling. Environ. Monit. Assess. 47, 23-37.

Field, M. 8., 2000. Ground-water tracing and drainage basin delineation for risk assessment
mapping for spring protection in clarke county, virginia. Tech. Rep. NCEA-W-0936, 36
p., U.S. Environmental Protection Agency, Washington, D.C.

Field, M. S., 2002a. Efficient hydrologic tracer-test design for tracer-mass estimation and

sample-collection frequency, 1, method development. Environmental Geology in press.

Field, M. §., 2002b. The QTRACER2 Program for Tracer-Breakthrough Curve Analysis
for Hydrological Tracer Tests in Karstic Aquifers and Other Hydrologic Systems. Tech.
Rep. EPA/600/R-02/001, 179 p., U.S. Envir. Prot. Agency, Washington, D.C.

Field, M. S., 2002c. A review of some tracer-design equations for tracer~mass estimation

and sample collection frequency. Environmental Geology in press.

Field, M. S., Nash, S. G., 1997. Risk assessment methodology for karst aquifers, 1,
Estimating karst conduit-flow parameters. Environ. Monit. Assess. 47, 1-21.

167



PREFACE

The National Center for Environmental Assessment has prepared this document for the
benefit of the U.S. Environmental Protection Agency regional offices, states, and the general
public because of the need to develop a fast and easy method for designing tracer tests in
hydrologic systems. Application of the methodology described in this document can provide
individuals with the information necessary for designing reliable and safe tracer tests while
eliminating much of the guesswork typical of first time tracer testing in a new environment.

The purpose of this document is to serve as a technical guide to various groups who
must address potential or existing contamination problems in hydrologic systems. Tracing
studies are always appropriate and probably necessary, but initial design work is usually
relegated to guesses as to the amount of tracer to release and when to collect samples. This
document and associated computer programs alleviate some of these problems.

The Efficient Hydrologic Tracer-test Design (EHTD) program uses a few basic field
measurements combined in functional relationships that are coupled with the concept of a
continuous stirred tank reactor and solute-transport theory to develop the basic design of
a tracer test. Initial solute-transport parameters are produced by EHTD, which although
imprecise because they are only predictive, still provide adequate information for effective
tracer-test design.

EHTD produces a detailed assessment of expected tracer-test results before a tracer
test is ever initiated. It also produces a likely tracer-breakthrough curve for each sampling
station. Preliminary testing of EHTD has shown it to be reliable in most instances. It

is believed that as EHTD is used, improvements in its design will grow as suggestions are
made.

ix



FINAL TRACER-MASS REDUCTION FACTORS

SYSTEM VOL. DILUTION VOL. RETARDATION DECAY
(73) (m73) (DIMEN . ) (1/h)

1.50E+05 1.50E+05 1.00E+00 0.00E+00

SET CONC. AVERAGE CONC. PEAK CONC.
(ug/L) (ug/L) (ug/L)
1.83E+01 1.8300E+01* 1.8505E+01*

“PRELIMINARY ESTIMATES FOR AVERAGE CONC. AND PEAK CONC.
SEE REVISED ESTIMATES LISTED IN TABLE 5.1.

Figure 21. Modified EHTD-produced portion of Table 3.1 to reflect influence of an initial
concentration and/or exponential production.

x TABLE 5.1. REVISED TRACER CONCENTRATIONS ***

SET CONC. AVERAGE CONC. PEAK CONC.
(ug/L) (ug/L) (ug/L)

Figure 22. Example EHTD-produced Table 5.1 to reflect influence of an initial concentration
and/or exponential production.

127



“s][Nser 480} 19081] DAOVEL = Y-C.LHA ‘Si[Nsor 4so4 1098] eaTOwoIUOU = N-CLLHA we

oT X69L gOLX69L ;-OTXZET 2-01 X0@% OLXWwE pOLXLze% OlX ese WALHA
OLX STO OLX STO OLX z-OlxX0% OLX OLS OT XEPh OL X9L6 N-CLHY
ue eOEXOCL 7-OLXZET 2-01 X0@% OT XOLE OLX 8E% OLX FSG posnseoyy

ISA], LIODLE sarov1E) payobarsv,

c0T XLL°T OT X LT ut ut o0L X 6 ot o0T X 99° Y-GLHA
e0EX89T OT X 89T a ut o0E X 6T'P aa o0T X €9'% ~~ N-CLHA
uo 201 X 00% a uo Ol X 61'7 ut o0T X LEE pornseoyy
say, saovsy, Guisdg ssahige
s0IX WPT OLX PPT os 001 X P9'T pOlX 168 U-GLHA 8
g0T XL2BT OE X LeT a a OL X P9'T pOI X 88° N-C.LHA
aa g0T X OPT vee tee o0T X POT yOLX brs pornseay

8A], LOODLE, sonny wnossry

2OL xX TOT 2OTX TOT O1X89S OT XOLT OLX S79 OLX S979 OLX LOT U-OLHY
OLX TOT ,OLX TOT OLX6Lh OLXFHT OLX P29 OL X#Z9 201X268 N-GLHA
a 201 X 10'T oo e0T X SZ°9 a 201 X LOT parmsvoyy

789], LOODLL, Yoao4gQ svayy

oun Aq lA 1-4 gut BD uu IA 11 3n 45 | Br 07 3'Ww eleg Be
8380} JOOWI} WWROIYS TULMOY OY} 1OJ S}MSoI PoMsvat SNSIEA synser poyiperd-G.LHA 62 aL



hours, tp = 4.23 hours, v = 2342 m h7!, D = 3.58x10° m? h-, and P, = 65.5 are close to the
approximations obtained from the measured BTC. However, the EHTD prediction for the
nonreactive case resulted in an earlier tracer breakthrough than that of the measured result
(Table 28) and underestimated tracer mass by nearly three orders of magnitude (Table 29).
Increasing tracer mass using EHTD required considerable tracer loss (4 = 1.595 h~') and
some retardation (Ra = 1.25).

Accounting for retardation causes a slight shift in the EHTD-predicted BTC, allowing for
a reasonable match with the measured BTC. Other than the inadequate estimate for tracer
mass for the nonreactive case, the EHTD-predicted results for the Variegated Glacier tracer
test were sufficient for defining the BTC. Prior knowledge of the nature of glacial outflows
and the tracer used (Rhodamine WT for this tracer test) should allow for an approximation
of the appropriate estimates to use for tracer decay and retardation.

For the Variegated Glacier tracer test, a relatively insignificant amount of tracer was
added directly to the stream water as a small, short-duration pulse with the effect resulting
in Dy = V for both of the EHTD-predicted results (Table 29). The EHTD-predicted
volumes bracket the measured value for V, suggesting that the EHTD-predicted volumes

are reasonable, especially for the reactive case.

7.3.2. Porous Media Results

The second set, of the four tracer tests listed in Table 26 represents a typical range of tests
conducted in porous media aquifers. The tests included a natural-gradient tracer test, a
forced-gradient tracer test, an injection/withdrawal tracer test, and a recirculation tracer
test. EHTD prediction of tracer test results in porous media requires more measured and/or
estimated parameters than is required for flowing streams. The parameters necessary for
EHTD simulation of porous media systems are listed in Table 30. For porous media aquifers,
EHTD requires measurements or estimates for Q, L, effective porosity ne, thickness 6,
transverse spread T, to, and C. For all but natural-gradient tracer tests, EHTD estimates T
(Field, 2002a). As with the flowing stream tracer tests, two listings for C appear in Table 30.
Tracer decay tends to cause predicted Cp to fall below the predicted C, that occurs with
no tracer decay and the measured C, unless specific adjustments (e.g., increased C) are
incorporated. Decreases in C, was a problem in each of the four porous media tracer tests
listed in Table 30.

Hydraulic results of the EHTD-predicted BTCs for the four porous media tracer tests
are compared with the actual BTC results in Table 31. Tracer injection specifics are listed

141



TRACER MASS =2.30E+00 kg

—— Breakthrough Curve
Sampling Times

g
|

Time (wk)
Figure 3. EHTD results for a pulse release for the porous media test parameters.

be only crudely approximated by EHTD, it has been shown that these parameter estimates
are generally reasonable (Field, 2002c). Also, although ¢ remained unchanged regardless
of the type of tracer release employed, tp and C, were greatly increased when a long-pulse
release was employed (Table 14) (Figures 3 and 4) for the respective hydrologic systems.
A long-pulse release also causes an earlier t; but a greater ty (Table 14).

It will be noted that V = 7.85 x 104 m® and V = 2.59 x 10‘ m® for the porous media and
karstic tracer tests, respectively. These volumes are much greater than the volumes listed
in Table 11. The difference is a result of arbitrarily choosing of V (Parriaux et al., 1988,
p. 9) as opposed to calculating V using an accepted approach such as

_@t
va (42)

Applying Equation (42) results in V = 8.64 x 104m? and V = 2.59 x 104m? for the
porous media and karstic tracer tests, respectively. Using these recalculated volumes in the
equations listed in Table 3 did not significantly change the results of Equation (4), but it
caused a slight decrease in the results of Equations (20) and (31) and a substantial decrease
in the results of Equation (32) (Table 15). Although not expected, the estimated mass
using Equation (32) with the improved estimates for V was in better agreement with the
EHTD-predicted mass for the karstic media tracer test.

34



CMNOARwWHe

List of Figures

EHTD results for an impulse release for the porous media test parameters.
EHTD results for an impulse release for the karstic test parameters.

EHTD results for a pulse release for the porous media test, parameters.
EHTD results for a pulse release for the karstic test parameters. .......
Preliminary BTC from a hypothetical CSTR.

Predicted BTC for Prospect Hill Spring for retardation effects

Predicted BTC for Prospect Hill Spring for tracer decay effects

Initial EHTD screen title

Equations used to calculate univariate statistics for an input file

Generic example of an flowing stream input file format

Generic example of an porous media input file format

Typical example input file

Standard-form example BTC

Data file used to produce Figure 13

Standard-form example output file

Comparison of EHTD-predicted BTC to measured BTC

Example input file with an initial concentration and exponential production
constants

Data file used to produce Figure 19

Effect of including an initial concentration and exponential production
Comparison of the effect of including an initial concentration and exponential
production

Modified EHTD-produced portion of Table 3.1

Example EHTD-produced Table 5.1

Comparison of measured data for the Uvas Creek site tracer test . . .
Comparison of measured data for the Missouri River tracer test

Comparison of measured data for the Dyers Spring tracer test

Comparison of measured data for the Variegated Glacier tracer test
Comparison of measured data for the Test Site Wilerwald tracer test
Comparison of measured data for the Kirchdorf-Unteropfingen site tracer test 147
Comparison of measured data for the Mobile site tracer test

Comparison of measured data for the Chalk River site tracer test . . . 150
Uncertainties associated with exposure assessments

Seven BTC’s developed by the U.S. Geological Survey

Standardized curve- and EHTD-predicted BTC for Dyers Spring
LHS-generated input file of means using the Dyers Spring parameters... . .



Table 12. Tracer-mass estimates.
Equation* Porous Media, g Karst, g

(1a) 2.63 x 10? 8.80 x 10!
(2) 2.00 x 10° 4.72 x 107
2.50 x 10? 6.00 x 10?
3.00 x 10% 1.56 x 10?
2.50 x 10° 7.50 x 10
2.50 x 1078 7.50 x 10-77
1.30 x 10° 3.89 x 10?
2.92 x 108 1.77 x 10°
2.92 x 10° 1.76 x 10°
1.00 x 104 3.00 x 10?
1.25 x 1074 7.50 x 1074
2.50 x 10? 1.50 x 103
3.50 x 108 1.50 x 10°
(12) 5.12 x 10? 3.36 x 108
(13) 1.00 x 10° 3.00 x 104
(14) 3.00 x 10° 9.00 x 107?
(15) 4.00 x 10! 2.00 x 10?
(16) 4.80 x 10° 2.40 x 10+
(17) 9.00 x 10? 2.70 x 104
(18) 4.15 x 10? 1.24 x 10?
(19) 3.60 x 10? 1.80 x 10°
(20) 4.75 x 108 8.55 x 10°
(21) 9.84 x 10! 2.95 x 103
(22) 2.29 x 10? 1.25 x 10?
(23) 3.05 x 10? 9.15 x 10+
(24) 4.16 x 10? 1.24 x 10?
(25) 1.35 x 10° 4.04 x 10?
(26) 6.24 x 10” 1.87 x 10?
(27) 4.83 x 10? 1.56 x 10?
(28) 1.80 x 10° 5.40 x 104
(29) 7.05 x 10! 8.46 x 10!
(30) 5.00 x 10? 3.00 x 108
(31) 1.00 x 10° 3.00 x 103
(32) 5.00 x 10? 1.50 x 108

® From Table 3.



TABLE 1.1. INPUT FACTORS THAT INFLUENCE TRACER MASS ESTIMATION

MEASURED PARAMETERS OF INFLUENCE

DISCHARGE DISTANCE X-SEC. AREA

6.4080E+03 8.00E+03 1.88E+01

RETARDATION 1.00E+00 0.00E+00 0.00E+00
DECAY (1/h) 0.00E+00 0. 00E+00 0.00E+00

SET AVERAGE CONCENTRATION
(ug/L = mg/m-3)

1.83E+01

ALL DATA ARE IN "CONSISTENT UNITS"

LENGTH [L] (m)

TIME [T] ()

CONC. [M/T] (mg/m73 = pg/L)
MASS [M] (mg, g, kg)

Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12) continued. 108



more reliable than previous methods.

2.1. TRACER MASS ESTIMATION AND SAMPLING FREQUENCIES

Hydrologic tracing requires that an appropriate mass of tracer be released such that de-
tectable concentrations of the tracer may be recovered at the sampling stations. Commonly,
an estimate of the mass of tracer to release consists of nothing more than a guess that is
sometimes based on the general experience of particular individuals (Alexander and Quin-
lan, 1992, p. 19; Aley, 1999, p. 14) or on prior experience at the location to be traced (e.g.,
Meigs and Beauheim, 2001). Other times, the guess is whatever sounds good at the time. In
rare instances, a tracer mass estimation equation may be used to determine the appropriate
tracer mass to release. Although general tracing experience is beneficial and specific site
experience is better still for determining the quantities of tracer to release, neither approach
may be regarded as scientifically rigorous. Worse, the former suggests that only select indi-
viduals are adequately qualified to assess tracer needs, and the latter suggests the possibility
of numerous tracer release efforts at a site before success may be obtained.

2.1.1. Tracer Mass Estimation by Conjecture

There are four reasons beyond practical experience that may explain why a guess is used to
estimate the necessary tracer mass to release. The first is the over-reliance on qualitative
tracing in karstic terranes using common fluorescent dyes. Qualitative tracing is the use of
packets of activated carbon (commonly known as “detectors” or “bugs” in North America
and “fluocapteurs” in France) to sorb the fluorescent dye as it exits the underground. This
method is believed to facilitate karst tracing in that these detectors can be distributed
throughout the area where tracer dye is expected to exit the subsurface and may be collected
when convenient.

Although qualitative tracing is commonly applied in Great Britain and the United
States, the method is scientifically untenable because false-positive results (Gunn and
Lowe, 2000; Lutz and Parriaux, 1988) and false-negative results (Smart et al., 1986) are
common. Sorption onto detectors allows for reduced tracer dye concentrations because
activated carbon reportedly increases tracer dye concentrations 400 times the concentration
in water (Aley, 1999, p. 21), although published research suggests that dye concentration
by activated carbon is probably 3 to 4 times the concentration in water but may be as high
as 1000 times the concentration (K&B, 1998, pp. 100-103).

Unfortunately, activated carbon also enhances background concentrations (fluorescent

7



1. INTRODUCTION

Tracer tests are regularly applied in many hydrologic systems to determine various
hydraulic and geometric parameters. However, the success of a tracer test depends on
the release of sufficient—but not excessive—tracer material into the flow regime for reliable
tracer detection based on appropriate initial sample collection time and sampling frequency.
Determination of the optimal quantity of tracer material to release into a flow system to
maximize the probability of achieving positive results while maintaining safe concentrations
in the environment and minimizing public concern has been of considerable interest for a
long time.

To maintain safe tracer concentrations and to minimize public concerns regarding colored
water, Field et al. (1995) suggested that fluorescent dye concentrations at downstream
receptors be maintained at or below 1-2 mg L-!. They arrived at these concentrations by
conducting an in-depth evaluation of available toxicological information on 12 fluorescent
dyes and one dye intermediate using a U.S. Environmental Protection Agency (EPA)
approved assessment method for cases where actual data were lacking. Field et al. urged
the use of only that quantity of tracer dye actually needed to ensure positive results. The
use of significantly more than is needed might adversely affect the environment and human
health, although the degree of adversity was not quantified. In addition, excessive amounts
of tracer could compromise tracer test interpretations. However, determining the adequate
and safe amounts of tracer substance, dye or otherwise, to use in a tracing study can be
difficult (K&B, 1998, p. 327).

An optimal tracer mass that meets both hydrologic and environmental criteria is
dependent on a number of relatively indeterminate factors, such as the volume of water that
dilutes the tracer, hydrological conditions during high-flow and low-flow periods, residence
time, number and direction of discharge points, transport distance(s), sorption, decay, and
degree and type of pollution. Therefore, the quantity of tracer needed for release at any
particular site and time may be significantly different from that needed at another site or
at the same site at another time.

For example, a preliminary tracer test at a Superfund site in Tennessee using 0.7 g of
Rhodamine WT resulted in a conventional, positively skewed tracer-breakthrough curve
(BTC) and nearly 100% mass recovery (Field and Pinsky, 2000). A ‘subsequent tracer test
at the same site 48 hours later using 71 g of Rhodamine WT produced a very abrupt BTC
with a very long tail and only 28% mass recovery. A large storm that: preceeded the second



4.5.1.2. Error Messages. . 0... 0 ee 75

4.5.2. Screen Output of Optimization Results... ..........00.. 77

4.6. COMPUTER GRAPHICS ..........0.0 000000000 cee eee 78

4.6.1. Features of the Interactive Graphics Loop ...........0.0. 78

4611. File 0.0.00. 0.0 0000000 eee eee 81

46.1.2. Edit... ee eee 81

4.6.1.3. Views 2... ee 81

46.14. State 2... ee ee 81

46.1.5. Window. 2.2.2... ee ee 82

46.1.6. Help. oo... 0. eee ee eee 82

4.7, EHTD SOURCE .... 0.2.0.0... ee 82

. EHTD USE OF INPUT FILES 83

5.1. DESCRIPTION OF INPUT FILES................ 02.0004 83

5.1.1. Line-by-Line Description of Input Files... ...........0.. 89

. EHTD OUTPUT FILES 97

6.1. DESCRIPTION OF OUTPUT FILES ..................00. 97

6.1.1. EHTD-Produced Data Output Files... .......-2....... 105

6.1.1.1. Data Output File Header Material. ..........2.2.. 105

6.1.1.2. Input Data Units... 2. ee 105

6.1.1.3. Initial Data Input Reprise... . 0... 2 ee ee 105

6.1.1.4. Sampling Station Name... 2.0.00. ee 105

6.1.1.5. Table 1.1. Input Factors. 2.2... ee ee 115

6.1.1.6. Output Data Units... ee 115

6.1.1.7. Table 2.1.1. Initial Hydraulic Factors. ............ 115

6.1.1.8. Table 2.1.2. Final Hydraulic Factors.............. 115

6.1.1.9. Table 3.1. Final Tracer Mass Estimate. ........... 115

6.1.1.10. Table 4.1. Estimated Sampling Frequency. .......... 116

6.1.1.11. Calculated Tracer-Mass. .. 1... ee 116

6.1.1.12. Error Codes. 2... 0 ee 116

6.1.1.18. Recommended Tracer-Mass. . 2... 0. 0 ee 116

6.1.1.14. Date and Time of Processing. ............0..005 116

6.2. THE QUALITY OF EHTD-PREDICTED RESULTS ............. 117
6.3. EFFECT OF INITIAL CONCENTRATION AND EXPONENTIAL PRO-

DUCTION. ................0-.

6.3.1. Effect of an Initial Concentration . .
6.3.2. Effect of Exponential Production
6.3.3. Breakthrough Curve Shape ..............2.2.00004

6.3.4. Average and Peak Concentration Estimates .............. 125



PLOT FILE: LOST RIVER RISE

BREAKTHROUGH CURVE SAMPLE TIMES AND CONC.

cONCc. CONC.

1.1735 32501 13.378 61428
1.4082 33001 14.235 71994
1.6429 33502 15.092 99791
1.8777 34002 15.948 1.6297
2.1124 34502 16.805 2.8337
2.3471 35003 17.662 4.7708
2.5818 - 35503 18.518 7.4328
2.8165 36004 19.375 10.582
3.0512 36504 20.232 13.785
3.2859 37005 21.088 16.539
3.5206 37505 21.945 18.415
3.7553 38006 22.802 19.171
3.9900 38507 23.658 18.794
4.2247 39007 24.515 17.461
4.4594 39508 25.372 15.463
4.6941 40009 26.228 13.123
4.9288 40510 27.085 10.729
5.1635 41011 27.942 8.4939
5.3983 41513 28.799 6.5459
5.6330 42014 29.655 4.9405
5.8677 42515 30.512 3.6778
6.1024 43017 31.369 2.7235
6.3371 43519 32,225 2.0271
6.5718 44020 33.082 1.5345
6.8065 44523 33.939 1.1954
7.0412 45025 34.795 96782
7.2759 45527 35.652 81845
7.5106 46030 36.509 72243
7.7453 46533 37.365 66184

Figure 18. Data file generated by EHTD used to produce Figure 19.

120



PROJECT NAME

KARST EXAMPLE -- LOST RIVER CAVE SYSTEM

FLOW RELEAS RTIM (h) INFLOW (m~3/h) UNITS

1 1 0.0 0.0 1

2 fe oe of fe ake 2 fe ak 2 oe 2 i 2 2 2 26 2 2 af 2c 2c 2 2k 2 2 af ake fe fe ke 2k ae i ak 2 ae a 2 ie a of 2 2 2 2 2 2 i of ak ce ie ic a ake 2k 2c akc
STATION NAME

LOST RIVER RISE

DISCHARGE (m73/h) DISTANCE (m) AREA (m2) SINUOSITY FACTOR
6.408E3 8000.0 18.8 1.0

INIT. CONC. (ug/L) GAMMA1 GAMMA2

0.0 0.0 0.0

RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)
1.0 0.0 ) 18.3

1 1

1.0 0.0

10.0 5.0

2 IR CCC Io OK OK a a ee 9 2 a 9 2 2 2 af 2 2 2 2 2 i ae a i 2c 2 fe 2 2 2 2k 2 a a 2 a ak kk a
STOP PROCESSING

END OF RUNS

Figure 12. Typical example input file to illustrate how an example EHTD-generated output
file appears after processing.



Table 16. Tracer test design parameters.

Parameter Value
Measured Parameters

Release Mode Impulse

Q, m3 h7? 3.63 x 10?

am 2.74 x 108

A, m? 2.23 x 10°

Oo" uel 5.00 x 10?

Functional Relationships

tp h 1.64 x 10!

ih 1.69 x 10"

Up, mb 1.68 x 10?

v,m ho? 1.63 x 10?

V, m3 6.12 x 10°
Axial Dispersion

D,, mht 4.50 x 108

P. 9.90 x 10!
Tracer Reaction

Ra 1.00 x 10°

ho 0.00 x 10°

® Transport distance = straight-line distance, 1.83 x 10? m x

sinuosity factor, 1.5.

Simulation

57

p components that minimizes the sum of the squares function f(y) = 4 07.1 7:(y)? that is
constrained by 7, <yi <7j,1 Sit Sp where the f(y) are twice continuously differentiable
functions of y (Dennis et al., 1981).

The methodology described was tested for Prospect Hill Spring located in Clarke County,
Va., using the measured field parameters and functional relationships listed in Table 16.
Figure 5 is a plot of time versus concentration produced by a hypothetical CSTR using
the measured field parameters and functional relationships listed in Table 16. Integrating
Figure 5 produced a preliminary estimate for tracer mass of M = 11lg. Of particular



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a(Z961 ‘Joumnyy,)
soro(OPGT ‘MB)
)
)

(6g1 “4 ‘Oger ‘I80q)
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yoo(OP6T ‘TOME (o2@ ‘4 ‘Tg6T ‘prscuRTY) OS = WN (8)
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(p26T “MBunqyo"]) (gd ‘gg61 “Te 99 xnetted) Iphyomh — W (9)
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(sv6r ‘Tepueg) (gd ‘gg6r ‘Te 4 xneIeq) jet, NW (8)
(€861-£261 ‘OOSANA) (2d ‘ger ‘ye yo xneqareg) HLROS 4 (ches) “a Ww (r)
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‘wwuoo ‘siad ‘noySutyyI0\) oa 18 6 m8) 1 = W (2)
p(‘wwuos ‘sxad ‘uoy8umy,I0\\) : (=a apt Mt) 96-9 9¢0= W (qt)
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12



solute transport processes in a porous media aquifer. The aquifer is in the Emme Valley and

consists of postglacial Holocene sandy gravels that vary in thickness from a few meters to
88 m with ground-water depths that vary from 0.5 to 3 m (Leibundgut, 1992, pp. 230-231).

In September, 1985, 1 kg of sodium fluorescein (C.I. Acid Yellow 73) dissolved in 90 L
of water was released over a one hour period into an injection well. Sampling commenced
almost immediately and continued for 24 weeks at several downgradient wells. The furthest
well sampled for tracer from the injection well was approximately 200 m to the northwest
(Leibundgut and De Carvalho Dill, 1992, pp. 232-233). The basic transport parameters
used to describe the aquifer consisted of a hydraulic conductivity K = 8.64 m h7?, aquifer
thickness b = 10 m, effective porosity n, = 12 — 17%, and hydraulic gradient i = 0.4%
(Matoszewski et al., 1992b, p. 239).

7.2.2, Forced-Gradient Tracer Test

A tracer and aquifer test were simultaneously conducted over a period of several months at
the Kirchdorf-Unteropfingen area within the Iller Valley in Germany. Alpine Rhine glacial
materials consisting of well-rounded, stratified, fine to coarse gravel with intercalated sand
fractions make up the valley aquifer. The extraction well was pumped at a rate of 1368
m?h-!, During the pumping test, 3 kg of sodium fluorescein were released immediately
into an observation well situated 585 m from the extraction well. Initial tracer recovery
occurred at the extraction well within about 3 days and continued for more than 100 days
(K&B, 1998, pp. 515-516). The pump test yielded a transmissivity of 1019 m? h~! (K = 116
m h“*) and specific yield = 0.14, which was taken to be the same as effective porosity (K&B,
1998, pp. 515-516) for this evaluation.

7.2.3. Injection-Withdrawal Tracer Test

An injection withdrawal two-well tracer test consists of injecting water containing tracer
into an injection well and withdrawing water from an extraction well at an equal rate so
that equilibrium may be established. Such a test was conducted in a soil borrow area at
the Barry Steam Plant of the Alabama Power Company near Mobile, Alabama, in the late
summer of 1984, The surface is composed of Quaternary-age, low-terrace deposits consisting
of interbedded sands and clays down to a depth of 61 m. Below these deposits a Miocene
series of undifferentiated sands, silty clays, and thin-bedded limestones extend to a depth
of 305 m (Molz et al., 1986a, p. 38).

131



ABSTRACT

Hydrological tracer testing is the most reliable diagnostic technique available for estab-
lishing flow trajectories and hydrologic connections and for determining basic hydraulic
and geometric parameters necessary for establishing operative solute-transport processes.
Tracer-test: design can be difficult because of a lack of prior knowledge of the basic hydraulic
and geometric parameters desired and the appropriate tracer mass to release. A new effi-
cient hydrologic tracer-test design (EHTD) methodology has been developed that combines
basic measured field parameters (e.g., discharge, distance, cross-sectional area) in functional
relationships that describe solute-transport processes related to flow velocity and time of
travel. The new method applies these initial estimates for time of travel and velocity to a
hypothetical continuously stirred tank reactor as an analog for the hydrologic flow system to
develop initial estimates for tracer concentration and axial dispersion, based on a preset av-
erage tracer concentration. Root determination of the one-dimensional advection-dispersion
equation (ADE) using the preset average tracer concentration then provides a theoretical
basis for an estimate of necessary tracer mass.

Application of the predicted tracer mass with the hydraulic and geometric parameters
in the ADE allows for an approximation of initial sample-collection time and subsequent
sample-collection frequency where a maximum of 65 samples were determined to be
necessary for describing the predicted tracer-breakthrough curve (BTC). Inclusion of tracer
retardation and decay cause a net increase in tracer-mass estimates so that the preset
average tracer concentration will be maintained, with a consequent steepening of the BTC,
but retardation also causes BTC spreading and a delay in tracer arrival.

Determining the necessary tracer mass, the initial sample-collection time, and the
subsequent sample-collection frequency for a proposed tracer test are the three most difficult
aspects to estimate prior to conducting the test. To facilitate tracer-mass estimation, 33
mass-estimation equations have been developed over the past century. The 33 equations
are reviewed here; 32 of them were evaluated using previously published tracer-test design
examination parameters. Comparison of the results produced a wide range of estimated
tracer mass, but no means is available by which one equation may be reasonably selected
over the others. Each equation produces a simple approximation for tracer mass. Most
of the equations are based primarily on estimates or measurements of discharge, transport
distance, and suspected transport times.

Although the basic field parameters commonly employed are appropriate for estimating

xii



7.1.1. Small Creek

Uvas Creek was traced in 1976 using a steady 3-hour injection of 1068 g of chloride in
late summer during a low flow period (Bencala and Walters, 1983; Zand et al., 1976). The
emphasis of the tracing test was to investigate the mass transport processes in a small
stream. The experimental study was limited to a 610 m reach, with widths ranging from
0.3 to 4 m. Flow rate at the time of the study was 45.0 m*h7!. Tracer concentration
measurements were taken at selected reaches where measured flow rates varied slightly from
45.0 m’ h71. For this evaluation, tracer recovery at reach 281 m was used. The channel was

composed of a rough bed with alternating pools and riffles and a steep slope (0.03 m m7).

7.1.2. Large River

The Missouri River was traced along a 243 km reach between Sioux City, Iowa and
Plattsmouth, Nebraska, in 1967. The purpose of the tracer test was to obtain sufficient
data to simultaneously define axial dispersion, transverse mixing, cross-sectional geometry,
and transverse velocity distribution. Approximately 54 kg of Rhodamine WT (C.I. Acid
Red 388) were injected as a line source extending across the middle half of the channel
(Yotsukura et al., 1970, pp. G3-G5).

Sampling stations were located in a manner such that cross-sectional areas could be
divided into four increments with approximately equal discharges. Discharge measurements
were taken at the four cross-sections by the current meter method. Sampling frequency
varied from 15 minutes to 2 hours, depending on the expected rate of change of concentration
(Yotsukura et al., 1970, pp. G5-G6).

7.1.3. Solution Conduit

Dyers Spring is a blue-hole rise pit that connects an impenetrable solution-conduit system
with a nearby karst window developed in the St. Louis Limestone. It is an important water-
supply spring in Elizabethtown, Kentucky (Mull and Lyverse, 1984, p. 21). Limestone
is exposed at the bottom of the karst window, where a stream reportedly flows into a
swallet. No other external drainage has been observed, so all water entering the karst
window eventually drains into the swallet (Mull et al., 1988b, p. 58).

Several tracer tests to Dyers Spring using the karst window were performed by the U.S.
Geological Survey with varying degrees of tracer mass recovery (Mull et al., 1988b, p. 71).
The primary intent of the tracer tests was to assess the solute transport processes operative

129



Oostrom, M., Hayworth, J. S., Dane, J. H., Giiven, O., 1992. Behavior of dense aqueous
phase leachate plumes in homogenous porous media. Water Resources Research 28(8)
2123-2134.

Parriaux, A., Liskay, M., Miiller, I., della Valle, G., 1988. Guide practique pour l’usage des
traceurs artificiels en hydrologéologues (Bilingual; also published in the same manual as:
Leitfaden fiir den gebrauch kunstlicher tracer in der hydrogeologie]. Tech. Rep. GEOLEP
EPFL 51 p. [49 p.], Société Géologigue Suisse, Groupe des Hydrologéogie [Schweizerische
Gruppe der Hydrogeologen, Arbeitsgruppe ‘Tracer’], Lausanne, Switzerland.

Pearson, T. J., 1997. Pgplot graphics subroutine library. Tech. rep., California Institute of
Technology, Pasadena.

Pickens, J. F., Grisak, G. E., 1981. Scale-dependent dispersion in a stratified granular

aquifer. Water Resources Research 17(4), 1191-1211.

Rantz, S. E., 1982. Measurement and Computation of Streamflow: Volume 1. Measurement
of Stage and Discharge. Tech. Rep. U.S. Geological Survey Water-Supply Paper 2175, 284
p., U.S. Geological Survey.

Rathbun, R. E., 1979. Estimating and Gas and Dye Quantity for Modified Tracer Technique
Measurements of Stream Reaeration Coefficients. Tech. Rep. U.S. Geological Survey
Water-Resoruces Investigations 79-27, 42 p., U.S. Geological Survey.

Reichard, E., Cranor, C., Raucher, R., Zapponi, G., 1990. Groundwater Contamination
Risk Assessment: A Guide to Understanding and Managing the Uncertainties, 204 p.
Vol. [AHS Publ. No. 196. International Association of Hydrological Sciences, Wallingford,
Oxfordshire, U.K.

Sardin, M., Schweich, D., Leij, F. J., van Genuchten, M. T., 1991. Modeling the nonequilib-
rium transport of linearly interacting solutes in porous media: A review. Water Resources
Research 27, 2287-2307.

Schudel, B., Biaggi, D., Dervey, T., Kozel, R., Miiller, L, Ross, J. H., Schindler, U.,
2002. Utilisation des Traceurs Artificiels an Hydrogéologie: Guide Practique, Rapports
de ’OFEG, Série Géologie. Tech. Rep. No. 3, 77 p., Groupe de Travail Tracage de la
Société Suisse d’Hydrogéologie; SSH, Berne, Switzerland.

172



Table 5. Aquifer and tracer-dependent coefficient Ty,*.
Tracer Dye Clay Stone Sandstone Fractured Rock Karst

Na-fluorescein 0.5 — 2.0 0.2-1.0 0.2 — 2.0 0.2 - 1.0
eosin 0.5 ~ 2.0 0.2-1.0 0.2 ~ 2.0 0.2-1.0
erthrosine 1.0- 4.0 1.0 - 3.0 1.0 - 4.0 1.0 - 4.0
congo red 2.0-8.0 20-60 2.0 — 8.0 2.0 - 8.0
Methy] blue 2.0-80 20-60 2.0 — 8.0 2.0 — 8.0
Spirit blue 2.0 - 8.0 2.0 - 7.0 2.0 — 8.0 2.0 - 8.0
Ponceau red 10-40 1.0 - 3.0 1.0 - 4.0 1.0- 4.0

* Source: Adapted from (K&B, 1998, p. 325).

Table 6. Tracer dependent coefficient To,*.

Tracer Material Tos Tog”
Na-fluorescein 1.0 x 10° 1.0 x 10°
eosin. 5.5x10° 2.0—3.0 x 10°
Sulpho Rhodamine G 2.0 x 10° 2.0 x 10°
Rhodamine B 1.5 x 104 ooo
Sulpho Rhodamine B 4.0 x 10° 4.0 x 10°
Rhodamine WT 2.0 x 10! oo
Pyranine 5.5 x 10° 5.0 x 10°
Na-Napthionate 1.5 x 10! 1.5 x 10+
Tinopal 3.0 x 10° 2.5 x 10?
Duasyne wee 4.0 x 10°
NaCl 2.0 x 104 1.0 x 104
LiCl 1.0 x 108 1.0 x 10%
KCI 1.0 x 104 te
KBr ee 3.0 — 5.0 x 108
spores 1.5 x 10° tee
surfactants 2.0 x 10! tee
phages (particle count) 1.0 x 10% 1.0 x 10”
Serratia marcescens 1.0 x 108 oo
microspheres 1.0 x 101? 1.0 x 10!
indium 1.0 x 107 tee

* Source: Adapted from (Ka, 1998, p. 327).
> Modifications to Tc, from (Schudel et al., 2002, p 21).

Equation (11) as listed in Ka® (1998, p. 327) requires two independent coefficients, Tes

17



8.2, FORECASTING POLLUTION FOR RISK ASSESSMENTS

The appropriateness of EHTD for determining acceptable tracer mass and sampling times
for proposed tracer tests has already been documented. However, after tracer tests have been
conducted EHTD may be used for screening-level pollution forecasting. The EHTD-results

may then be applied in a risk assessment at a rough screening level. Such an endeavor,

the value of which not being immediately apparent, is useful because of the difficulty and
expense of conducting multiple tracer tests several times during any given year and over
several years. A single tracer test provides only a temporal “snapshot” of the hydrological
system the results of which may not be relevant other periods.

8.2.1. Dimensionless Dye-Recovery Curve

The tracer testing conducted by McAvoy et al. (2003) was conducted during the dry season
only. In their work, the authors assumed that greater dilution would occur during the
wet months which may be true but is undocumented. For this reason, the U.S. Geological
Survey (USGS) conducted several tracer tests in the same system over at least a year’s time
to address temporal differences in flow (Mull et al., 1988b). A plot of the seven tracer tests
conducted by the USGS indicates considerable real-time differences and real-concentration
differences in the BTC’s (Mull et al., 1988a, p. 55). Figure 32 on the next page depicts
the seven BTC’s. The differences in the BTC’s were muted by converting the BTC’s to
dimensionless form, plotting the dimensionless BTC’s at the same scales and then developing
a single standardized dimensionless dye-recovery curve or “type curve” (Mull et al., 1988a,
pp. 68-75). Development of the standardized curve is a very slow tedious process where a
BTC is drawn by eye and appropriate statistics calculated. This process is repeated several
times until the calculated statistics meet some arbitrary level of acceptance.

After development of the standardized curve the effects of a given release into the
hydrologic system could be forecast with some degree of confidence provided discharge
was available (Mull et al., 1988a, pp. 75-79). Although useful and relevant, the method
devised is a trial-and-error procedure requiring considerable subjective analysis. A simpler

less expensive method is desirable.

8.2.2, EHTD for Forecasting pollution Effects

To be able to forecast the effects of any contaminant releases in any given hydrological

system, a chosen model must either be properly calibrated for the given time period or be

154



Sweeting, M. M., 1973. Karst Landforms, 362 p. Columbia University Press, New York.

Taylor, K. R., James, R. W., Helinsky, B. M., 1986. Traveltime and Dispersion in the
Shenandoah River and its Tributaries, Waynesboro, Virgina, to Harpers Ferry, West,
Virginia. Tech. Rep. WRI 86-4065, 60 p., U.S. Geol. Surv. Water-Resour. Invest.,
Washington, D.C.

Timeus, G., 1926. Le indagini sull’origini delle acque sotterrane. In: Bertarelli, I. V., Timeus,
E. (Eds.), In, Duemila Grotte. pp. 153-166.

Toride, N., Leij, F. J., van Genuchten, M. T., 1993. A comprehensive set of analytical solu-
tions for nonequilibrium solute transport with first-order decay and zero-order production.
Water Resources Research 29(7), 2167-2182.

Toride, N., Leij, F. J., van Genuchten, M. T., 1995. The CXTFIT Code for Estimating
Transport Parameters from the Laboratory or Field Tracer Experiments; Version 2.0.
Tech. Rep. 137, 121 p., U.S. Salinity Lab., Riverside, Calif.

UNESCO, 1973-1983. Groundwater Studies; An International Guide for Research and
Practice (with Supplements 1975, 1977, and 1983). United Nations.

USEPA, 1986a. Guidelines for Health Risk Assessment of Chemical Mixtures. Tech. Rep.
EPA/630/R-98/002, 28 p., U.S. Environ. Protect. Agency, Washington, D.C.

USEPA, 1986b. Guidelines for Mutagenicity Risk Assessment. Tech. Rep. EPA/630/R-
98/003, 17 p., U.S. Environ. Protect. Agency, Washington, D.C.

USEPA, 1989. Risk Assessment Guidance for Superfund, Volume I, Human Health
Evaluation Manual, (Part A). Tech. Rep. EPA/540/1-89/002, http: //www.epa.gov/

superfund/programs/risk/ragsa/index htm, U.S. Environ. Protect. Agency, Washing-
ton, D.C.

USEPA, 1991. Guidelines for Developmental Toxicity Risk Assessment. Tech. Rep.
EPA/600/FR-91/001, 67 p., U.S. Environ. Protect. Agency, Washington, D.C.

USEPA, 1992. Guidelines for Exposure Assessment. Tech. Rep. EPA/600/Z-92/001, 127 p.,
U.S. Environ. Protect. Agency, Washington, D.C.

USEPA, 1996. Guidelines for Reproductive Toxicity Risk Assessment. Tech. Rep.
EPA/630/R-96/009, 118 p., U.S. Environ. Protect. Agency, Washington, D.C.

174



Table 25. Description of the input file components listed in Figures 10 and 11.

Line Type Identifier Description

Comment line.
Character TITLE1 Descriptive title for planned tracer test.
Comment line.

Integer FLOW Type of flow data code:

1 = Open-channel or closed-conduit flow.

2 Porous media flow and a natural-gradient
tracer test.

3 Porous media flow and a forced-gradient
tracer test.

4 Porous media flow and a injection/withdrawal
test.

5 Porous media flow and a recirculation test.

Tracer release method data code:

1 Impulse tracer release (i.e., Dirac 6 function).
2 Pulse tracer release (time dependent).

3 Continuous tracer (step) release.

RTIME (h) Time in hours for pulse release (RELEAS = 2)
only, but a place holder is required (automatically
converted to zero for RELEAS # 2).

INFLOW (m73/t) Injection flow rate (m° h7 or ft? ho).
INFLOW (£t73/t)

UNITS Units used in the input file.
1 = Metric units (e.g., m, m?, m? h-').
2 English units (e.g., ft, ft?, ft? h-?).
Comment line.

Comment line.

7 Character TITLE2 Descriptive title for sampling station.

8 oo tt Comment line (Note the Line 8 differences
between Figure 10 and Figure 11).

continued on next page

86



7. TRACER TEST DESIGN EXAMINATION DATA SETS

Several hydrological tracer tests representing various environmental and design condi-

tions are listed in Table 26. The results of each of the measured eight tracer tests were

Table 26. Example test data sets.
Test Name Test Type

Flowing Stream
Uvas Creek Small Creek
Missouri River Large River
Dyers Spring Solution Conduit
Variegated Glacier Meltwater Channel
Porous Media
Test Site Wilerwald Natural Gradient
Kirchdorf-Unteropfingen Site Forced Gradient
Mobile Site Injection Withdrawal
Chalk River Recirculation

compared with forecasted results. For purposes of the type of analysis, flow through a so-
lution conduit and glacial-meltwater channel are listed under the flowing stream category
along with smail surface-water creeks and large rivers. This is because flow through a so-
lution conduit behaves more like surface-water flow than porous media flow even though

flow through solution conduits is correctly classed as ground-water flow. Prediction of flow

through solution conduits and glacial-meltwater channels requires treatment, similar to that

of surface-water flow.

7.1. FLOWING STREAMS

Two surface-water streams representing small and large flows were examined to evaluate
the effect of extreme flow discharge ranges on prediction capabilities. Uvas Creek is a small
stream that was traced in the mid 1970s. The Missouri River is a large river that was traced
in the mid 1960s. Dyers Spring was chosen as a representative tracer test through a solution
conduit to a potable-water spring. All three tracer tests were conducted and analyzed by
the U.S. Geological Survey. A glacial-meltwater channel (Variegated Glacier) was also listed
as a flowing stream because water flow through glacial meltwater channels behaves similarly

to flow in surface-water streams.

128



can be used to access the menu items.

It is necessary to point out here that most users will not use the pull-down menus very
often. Most of the more useful graphics functions have been built directly into EHTD so
as to alleviate excess work on the part of the user. However, in some instances, the user
may find particular functions of value. For example, selecting the Cascade function under
the Window pull-down menu after a total five or six graphics plots have been produced in
a series of child windows will cause the child windows to become stacked, but slightly offset
to the right and down.

The items shown in Table 24 works whether the program is currently at the text-only
screen (Graphic 1) where the user responds to queries posed by EHTD or if the program
is currently at the data-plot screen (PGPlot Graphics, #1). However, there is little point
in accessing any of the pull-down items from the text-only screen whereas in the data-plot
screen the user may find some items of value. For example, the color data-plot screen can
be printed as it appears, saved as it appears, resized to fit the whole screen, etc.

A brief description of each pull-down item shown in Table 24 is provided in the next six
subsections. Because the items listed in Table 24 are relatively self explanatory, the items
are only briefly described.

79



tracer mass, the 33 equations are problematic in that they were all probably based
on the original developer’s experience in a particular field area and not necessarily on
measured hydraulic parameters or solute-transport theory. Suggested sampling frequencies
are typically based primarily on probable transport distance, but with little regard to
expected travel times. This too is problematic in that tracer sampling remains a haphazard
process that tends to result in false negatives or data aliasing.

Simulations from the recently developed EHTD methodology were compared with those
obtained from 32 of the 33 published tracer-mass estimation equations and suggested
sampling frequencies. EHTD applies functional relationships developed from hydrologic
measurements in a solute-transport model to develop a preliminary BTC that has been
shown to reasonably predict actual tracer-test results.

Effective tracer-test design requires that the likely results be predicted in advance of test
initiation to ensure tracer-testing success. EHTD-predicted BT‘Cs for various hydrological
conditions were compared with measured BTCs obtained from actual tracer tests. The
hydrologic conditions for the tracer tests ranged from flowing streams to porous-media
systems. The tracer tests evaluated included flowing streams tracer tests conducted in
small and large surface-water streams, a karst solution conduit, and a glacial-meltwater
stream and porous-media systems conducted as natural-gradient, forced-gradient, injection-
withdrawal, and recirculation tracer tests.

Comparisons of the actual tracer tests and the predicted results showed that tracer
breakthrough, hydraulic characteristics, and sample-collection frequency may be forecasted
sufficiently well in most instances to facilitate good tracer-test design. However, comparisons
were generally improved by including tracer decay and/or retardation in the simulations.
Inclusion of tracer decay in the simulations also tended to require an increase in set average
tracer concentration to facilitate matching peak concentrations in the measured BTCs.
Both nonreactive tracer and reactive tracer predictions produced recommended sample-
collection frequencies that would adequately define the actual BTCs, but estimated tracer-
mass estimates were less precise.

EHTD may also be used to facilitate drinking-water protection strategies. EHTD pro-
vides water managers with the ability to conduct release-scenario simulations by overriding
the set average concentration. The simulations can be used to predict toxic substance ar-
rival times (time to leading edge, time to peak, persistence), axial dispersion, dilution, and
arrival concentrations. By combining the EHTD-simulation results with risk assessment

analyses for acute exposures, water managers can develop a set of alternatives as part of an

xdii



Line Generic Porous Media Input File

1 PROJECT NAME
2 Name of Planned Tracer Test
3 FLOW RELEAS RTIM (h) INFLOW (m73/h) UNITS
5 FESO IC EOI IGA OA OO ICD ACOSO SOCORRO OIC IOSD O IATA
6 STATION NAME
7 Name of Sample Station 1
8 DISCHARGE (m~3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
10 INIT. CONC. (ugTM3/L) GAMMA1 GAMMA2
il tee see tee
12 RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)
13 tee ses wee see
14
15
16 :
17 FESS OOO IO IIa AI I I OI TCC ACI AR ORR TAI ITAA A.
6 STATION NAME
7 Name of sample station 2
8 DISCHARGE (m*3/h) POROSITY THICKNESS (m) DIST-X (m) DIST-Y (m)
10 INIT. CONC. (ug*3/L) GAMMA1 GAMMA2
ae see wee see
12 RETARDATION DECAY (1/h) OPTIM AVE. CONC. (ug/L)
13 see _ wee cee
14
15
16
17 FREES GIOIA IG IRGC AC ICCC GIO EI CIC IAG ACR AK
18 STOP PROCESSING
19 End of Runs

Figure 11. Generic example of an porous media input file illustrating the basic format used
by EHTD for processing. Note that the Line numbers are not part of a typical input file
and are listed here only for reference purposes for Table 25. Also note that Lines 6-17 are
repeated for each individual sampling station considered for the particular study.

85



USEPA, 1998a. Guidelines for Ecological Risk Assessment. Tech. Rep. EPA/630/R-
95/002F, 114 p., U.S. Environ. Protect. Agency, Washington, D.C.

USEPA, 1998b. Guidelines for Neurotoxicity Risk Assessment. Tech. Rep. EPA/630/R-
95/001F, 77 p., U.S. Environ. Protect. Agency, Washington, D.C.

Webster, D. S., Proctor, J. F., Marine, I. W., 1970. Two-Well Tracer Test in Fractured
Crystalline Rock. Tech. Rep. U.S. Geological Survey Water-Supply Paper 1544-I, 22 p.,
US. Geological Survey.

Wolff, H. J., Radeke, K. H., Gelbin, D., 1979. Heat and mass transfer in packed beds—iv:
Use of weighted moments to determine axial dispersion coefficients. Chemical Engineering
Science 34, 101-107.

Worthington, S. R. H., Davies, G. J., Ford, D. C., 2000. Matrix, fracture and channel
components of storage and flow in a Paleozoic limestone aquifer. In: Wicks, C., Sasowski,
I. (Eds.), Groundwater flow and contaminant transport in carbonate aquifers. A.A.
Balkema, Rotterdam, The Netherlands, pp. 113-128.

Worthington, 8. R. H., Smart, C. C., 2001. Evaluation of equations estimating mass needed
for sink to spring tracer testing in karst. Journal of Cave and Karst Studies 63, 115.

Yevjevich, V., 1972. Stochastic Processes in Hydrology, 276 p. Water Resources Publications,
Fort Collins, Col.

Yotsukura, N., Fischer, H. B., Sayer, W. W., 1970. Measurement of Mixing Characteristics
of the Missouri River Between Sioux City, Iowa, and Plattsmouth, Nebraska. Tech. Rep.
1899-G, 29 p., U.S. Geol. Surv. Water-Supply Paper, Washington, D.C.

Yu, C., Warrick, A. W., Conklin, M. H., 1999. A moment method for analyzing breakthrough
curves of step inputs. Water Resources Research 35(11), 3567-3572. ,

Zand, 8. M., Kennedy, V. C., Zellweger, G. W., Avanzino, R. J., 1976. Solute Transport
and Modeling of Water Quality in a Small Stream. J. Res. U.S. Geol. Surv. 4(2), 233-240.

Zotl, A., 1974. Karsthydrogeologie, 291 p. Springer, Vienna.

175



which should match all references to the eventual tracer test.

Line 3 is also a comment statement provided so that the user may enter a clarifying

statement, which is ignored by EHTD. It is generally used as a convenient label for
Line 4 which is READ by the program. For example, Figure 10 lists Line 3 as:

FLOW RELEAS RTIME (h) INFLOW (m73/h) UNITS

which is stating that control codes and data listed on Line 4 are to be READ by EHTD.

Line 3 best serves as a header listing for Line 4.

Line 4 is a user-specified input, the specifics of which are as follows:

FLOW = 1 if open-channel or closed-conduit flow (surface-water stream or solution

conduit).
FLOW = 2 if porous media flow and a natural-gradient tracer test.
FLOW = 3 if porous media flow and a forced-gradient tracer test (extraction well).
FLOW = 4 if porous media flow and an injection/withdrawal test (injection well rate

= pumping well rate).

FLOW = 5 if porous media flow and a recirculation test (injection well rate = pumping

well rate).
RELEAS = 1 for impulse (instantaneous) tracer release (i.e., Dirac 6 function).

RELEAS

2 for pulse tracer release (time dependent).

RELEAS

"

3 for continuous (step) tracer release.

RTIME (h) is time for a pulse release (RELEAS = 2). It is meaningless for a nonpulse
tracer release (i.e., RELEAS # 2), but some value must be entered as a place
holder (automatically converted to zero for RELEAS # 2).

INFLOW (m*3/h) or (£t*3/h) is the rate of injection, and it can have significant effects
on the extent of predicted dilution. For pulse and continuous releases into porous
media systems, a value for INFLOW should definitely be included. No value should
be listed for impulse releases. The user must also decide whether pre- and post-
tracer injection flush water should be included to account for additional dilution
effects. However, for flowing streams (e.g., surface-water streams), upstream

discharges entering the injection point should not be included as INFLOW.

90



SEPA

United States
Environmental Protection
Agency

National Center for
Environmental Assessment
Washington, DC 20460 ©

Official Business
Penalty for Private Use
$300

EPA/600/R-03/034
April 2003

Please make ali necessary changes on the below label,
detach or copy, and return to the address in the upper
lefthand comer.

If you do not wish to receive these reports CHECK HERE];
detach, or copy this cover, and return to the address in the
upper left-hand comer.

PRESORTED STANDARD
POSTAGE & FEES PAID
EPA
PERMIT No. G-35



FES OEIC BGO CIC IGG IIRC IIA I OA I AA

TRACER-TEST DESIGN PROGRAM

LAST MODIFIED: JUNE 19 2002

EQUILIBRIUM MODEL FOR ROOTS AND NONLINEAR OPTIMIZATION
FOR TRACER MASS, TRACER RETARDATION, TRACER DECAY, INITIAL
SAMPLE COLLECTION TIME, AND SUBSEQUENT SAMPLING FREQUENCY

MALCOLM S. FIELD
USEPA -- NCEA-W
WASHINGTON, DC 20460

DATA INPUT FILE: LOST.IN

He HH HH HH HH HH HH HHH

FESO GG GIORC GOES CICIGCISCIORIOR IORI COG I II ACA

ALL DATA ARE IN “CONSISTENT UNITS"

LENGTH [L] (m)
TIME [T] (hb)
CONC. [M/T] (mg/m73 = pg/L)

Figure 15. Standard-form example output file generated by EHTD from a typical input file
(see Figure 12).

106



There will usually not be any major difference between D, estimated from Equation (88)
and D, estimated from Equation (89). In addition, because the CSTR-generated BTC is
based on an impulse release, Equation (89) may reasonably be ignored even though the

subsequent tracer test may be a pulse or step test.

3.5.2.2. Estimating Dispersion by the Chatwin Method. Axial dispersion may
be estimated using a modification of the method developed by Chatwin (1971), given by

C, z vt
th P =—>=- >=. 90
=( cyt) 2VD. VD. ©)
Subject to t, < z/v, Equation (90) is reduced to the general least-squares problem by
solving
mini — Ax (91)
where
1h
1 ¢
A=]. 2 (92)
1 ty
X= (1, a2)" (98)
b = (bj, ba, .-. 5 Dy)? (94)

The parameters b; are equal to the left-hand side of Equation (90)

b= 4/t;in ( : (95)

and the parameters to be determined 2; are equal to the two factors on the right-hand side
of Equation (90)

a-(cin) TM

53



&

Concentration (ug L-")
8

ee Retardation = 1.0
tb Retardation = 2.0
<i. Retardation = 3.0

Time (h)

Figure 6. Predicted BTC for Prospect Hill Spring for increasing values for retardation.
Symbols represent recommended sampling times.

Table 17. Predicted tracer mass and tracer concentration.

Tracer Reaction

Ra Km p,h Mg co", pg L-! C,, wg Lot
1.0 0.0 0.0 113.99 50.00 50.59
10 0.0 0.01 134.94 50.00 50.77
10 0.0 0.05 265.00 50.00 51.92
1.0 0.0 0.1 616.07 50.00 54.02
2.0 0.42 0.0 227.98 50.00 50.59
3.0 0.84 0.0 341.97 50.00 50.59

59

* Ka obtained for an assumed cylindrical solution conduit using
Equations (46) and (68).



1.1. QUICK START PROGRAM USAGE

Begin by copying all EHTD files (i.e., Ehtd.exe., Grfont.dat, Rgb.txt, and *.in) to the hard
drive of a computer. (See Section 4.1.1. on page 65 for a detailed discussion on the copying
of EHTD files to a hard drive.) Once stored on the hard drive, EHTD is ready to be run.
(NOTE: EHTD functions best with a display = 1024 x 768 pixels; adequately with a display
= 800 x 600 pixels; and not so well for further reduced display settings.)

1.1.1. Simple Program Usage

To run EHTD, please perform the following:
1. Execute the EHTD.exe file by Left Double-Clicking on it using a mouse.
2. Follow on screen instructions:

(a) Press <ENTER> to run the default input file (i.e.,EHTD.in),

(b) Press <ENTER> to create the default output name (i.e.,EHTD. out),

(c) Press <ENTER> to skip producing a PostScript plot file.

3. Use the pull-down menus to manipulate the plot. For example:

FILE: To save a BITMAP file of the screen plot or print.
VIEW: To change the screen display to view the entire plot all at once.
WINDOW: Move from GRAPHIC2 (plot screen) back to GRAPHIC1

(text display screen) for additional computation.

In the GRAPHIC] (text display screen) screen press <ENTER> for completion of EHTD
(i.e., writing of all output data to the output file). If this step is not completed then
some computational results (e.g., final tracer mass estimate) will not be written to
the output file.



-ee— Measured Data
NonReactive Transport
Reactive Transport

Concentration (mg L-')

Figure 29. Comparison of measured data for the Mobile site tracer test with EHTD
predicted-results for nonreactive and reactive transport. For reactive transport, Ra = 1.1
and p = 0.0075 hv}.

results (Table 32). Both of the EHTD-predicted volumes exceeded the measured value for

V, reflecting the effect of the incorrect effective porosity.

7.3.2.3. Mobile Site Tracer Test. Injection/withdrawal tracer tests provide an op-
portunity to establish equilibrium conditions during ground-water extraction prior to ini-
tiating a tracer test. The Mobile Site tracer test was designed using transport parameters
that were carefully determined from pumping tests and single-well tracer tests, which led to
better estimates for the parameters necessary for designing the injection/withdrawal tracer
test.

The EHTD-predicted BT'Cs closely matched the measured BTC (Figure 29). Only the
long, somewhat multimodal erratic tail of the measured BTC was not adequately predicted
by EHTD. The long tail is suspected to have occurred as a result of longer flow lines
causing longer transport times, which occurs during well injection (Molz et al., 1986a,
pp. 22, 58). Because EHTD does not predict long BTC tails the estimates for i and v

were incorrectly estimated by approximately 3 days, but tp, D, and P. were very well
approximated (Table 31). Setting » = 0.0075 h7! and Ry = 1.1 increased the estimate

148



Table 22. Description of the input file components (continued).

Line Type Identifier Description
Flowing Stream Entry for Line 9 (see Figure 10)
9 Real DISCHARGE (m~3/T) Sampling station discharge (m* h~? or ft? h~!).
or Real DISCHARGE (ft~3/T) estimated from surface discharge (e.g., spring|s];
surface-water stream) if FLOW = 1.
Estimated from Darcy’s law for porous media
discharge if FLOW = 2.
Estimated from pumping well if FLOW = 3 or 4.
9 Real DISTANCE (m) Estimated longitudinal distance from release point
or Real DISTANCE (ft) to expected recovery point (m or ft).
9 Real AREA (m"2) Cross-sectional area of discharge point (e.g., spring
or Real AREA (£t72) or surface-water stream cross-sectional area) (m? or ft?).
9 Real SINUOSITY FACTOR DISTANCE multiplier (< 1.5) to account for sinuosity.
Applicable to solution conduits primarily when a
straight-line distance between tracer injection and
recovery points is listed for DISTANCE.
Porous Media Entry for Line 9 (see Figure 11)
9 Real DISCHARGE (m*3/T) Sampling station discharge (m° h7! or ft? h7!).
or Real DISCHARGE (ft"3/T) estimated from surface discharge (e.g., spring|s];
surface-water stream) if FLOW = 1.
Estimated from Darcy’s law for porous media
discharge if FLOW = 2.
Estimated from pumping well if FLOW = 3 or 4.
9 Real POROSITY Estimated effective porosity of the porous medium.
9 Real THICKNESS (m) Estimated porous medium thickness (m or ft).
or Real THICKNESS (ft)
9 Real DIST-X (m) Estimated longitudinal distance from release point
or Real DIST-X (ft) to expected recovery point (m or ft).
9 Real DIST-Y (m) Estimated transverse spread of tracer at the
or Real DIST-Y (ft) expected recovery point (m or ft).

continued on next page

87



Table 1. Average dye manufacturers’ purities for selected powder dyes.

Colour Index Common Name Colour Index —s Average Purity*

Generic Name Constitution No. Range, %
Acid Red 9 erioglaucine 42090 73-75
Acid Red 52 Sulpho Rhodamine B 45100 85-90
Acid Red 87 eosin 45380 65-70
Acid Red 388 Rhodamine WT vee 82-85
Acid Yellow 73 Na-fluorescein 45350 75
Basic Violet 10 Rhodamine B 45170 90
Fluorescent Tinopal CBS-X ote 60

Brightener 351
Solvent Green 7 _ pyranine 59040 80

* Values are for the “crude” form of the dyes only.

The second reason the tracer mass to be released is guessed at stems from the lack
of knowledge regarding the volume and degree of spreading necessary for estimating the
extent of tracer dilution. Sorptive characteristics of the transport medium and tracer are
also typically unknown. Although surface-water volume and degree of spreading can be
reasonably estimated, aquifer volume and degree of spreading remain virtual unknowns
until a quantitative tracer test is conducted and numerically evaluated. Understanding
tracer losses due to tracer sorption generally requires extensive testing and analysis using a
selected tracer and specific materials and the results are not readily transferable.

A third reason why necessary tracer masses are guessed at may relate to the relative
purities of the various fluorescent dyes supplied by different manufacturers. Table 1 lists the
average dye manufacturers’ purities of some common fluorescent dyes used for hydrological
tracing and Table 2 lists the average percent pure dye content of the dyes supplied by one
distributor. This range of fluorescent dye purities complicates the determination of dye
mass to release.

The fourth and final reason that the tracer. mass to release is guessed is because of the
relative obscurity, confusing nature, and inconsistency surrounding the use of existing tracer
mass estimation equations. In general, these equations have been found to be less exact
than is commonly desired (Ka8, 1998, p. 323).



expected times of travel and the need to adequately define the BTC. Early detection of
tracer breakthrough requires that sampling be initiated prior to initial tracer breakthrough.
Sixty-five samples are recommended for adequate BTC definition, especially for instances
in which BTCs may be multimodal or long tailed (Field 2001a). Application of weekly or
biweekly sampling schedules or the sampling schedules listed in Tables 9 and 10 would fail
to adequately define either BTC.

Collecting samples for the EHTD-suggested durations t, listed in Table 14 would clearly
define the entire BTC should the tracer tests conform to the ADE. If tracer recoveries
were still strong beyond the EHTD-suggestied durations, sampling analyses could continue
unimpeded at the EHTD-suggested frequencies.

2.5.2.1. Porous Media Sampling Times. Figures 1 and 3 depict the recommended
sampling times for 65 samples that correspond, for impulse and pulse releases, respectively
for the porous-media case. Suggested sampling frequencies were 48 hours for the impulse
case and 96 hours for a pulse release (Table 14). Initial suggested sample-collection times
were eight days and nine days after tracer injection for the impulse and pulse releases,
respectively (Table 14).

2.5.2.2. Karstic Media Sampling Times. Recommended sampling times for the
karstic test, for impulse and pulse releases are shown in Figures 2 and 4. Suggested sampling
frequencies were three hours for the impulse case and five hours for a pulse release (Table 14).
Initial suggested sample-collection times were 29 hours and 18 hours after tracer injection
for the impulse and pulse releases, respectively (Table 14).

2.6. NOTATIONS FOR SECTION 2.

A cross-sectional area of a spring (m?)

A;, absorbance of dye sample (nm)

Ap, absorbance of dye at 100% strength (nm)
tracer adsorption coefficient >1.0 (mg m~*[?}) (Note: adsorption is normally identi-
fied as a distribution coefficient in mL? g71)
tracer adsorption coefficient >1.0 (mg m~*) (Note: adsorption is normally identified
as a distribution coefficient in mL* g~)
multiplier for Appalachian karst = 5.0

dispersivity = 2 (m)

v



5. EHTD USE OF INPUT FILES

EHTD is written to work only with prepared data files because there is too much
important data that needs to be entered correctly. Keyboard entry is typically very
frustrating and usually results in typographical errors that are difficult to correct. If these
errors are caught, it usually indicates that it is time to repeat the entire data entry process.

Good computer programs allow for created data files to be read directly by the program.
These files can easily be corrected or modified as desired without a great deal of effort on
the part of the user.

EHTD data files have been developed in a relatively simple manner to be as straight-
forward as possible. Each data file consists of a leading part that identifies the planned
tracer test followed by any number of likely sample recovery stations. If more than a single
sample recovery station is listed in the data file, then the projected tracer mass calculated
by EHTD is an additive process.

This additive process is correct only if the multiple sample recovery stations are
independent of each other. If the multiple sample recovery stations are in line with each other
(e.g., they occur along the same stream line), then twice as much tracer will be estimated
than may be necessary. This situation must be evaluated by the user on a case-by-case

basis.
5.1. DESCRIPTION OF INPUT FILES

EHTD uses a straight-forward, standard format for data input files. Unnecessary “com-
ment” or blank lines are interspersed with necessary lines that EHTD reads and processes.
Although the comment lines may be left blank, adding descriptive comments is useful for
keeping the file well organized.

Figure 10 illustrates the general form of a typical flowing stream input file, the
components of which are briefly described, and Figure 11 illustrates the general form of
a typical porous media input file, the components of which are briefly described in Table 25.
Note that the Line numbers listed in Figures 10 and 11 correspond to the Line numbers
listed in Table 25. No column numbers are provided because free format input is permitted
(i.e., the placement of input items is irrelevant).

A cursory inspection of Figures 10 and 11 will show that the only significant difference
between the two occurs at Line(s) 8 and ultimately Line(s) 9 (repeated as necessary in
both figures and any real data-input file), Although not apparent in Figures 10 and 11

83



use of analytical instruments has allowed a reduction in required tracer mass (I = 0.01 to
I = 0.1). For tracing in the Appalachians, approximately five times as much dye is needed
for success (Quinlan, pers. comm.).

Equations (30) and (31) are considered valid for tracing water flow in solution conduits
using Na-fluorescein (K&B, 1998, p. 324). For Equation (30), Sm = 1.0 for L > 100m up
to some unspecified upper limit and S,, = 2.0 for L > 1000 m also up to some unspecified
upper limit. Equation (31) suggests 1 to 2 grams of dye per 100 m? of water to be traced.

Equations (32) and (33) are for conditions different from those of the previous 30
equations. Equation (32) was designed to estimate tracer mass for lakes and estuaries
with a 1 ug L-! average concentration at the expected sampling locations. Equation (33)
was designed for phage tracing and includes a phage factor. It appears to be little different
from the other equations in that it also relies on discharge and peak arrival. However, it
utilizes a phage factor and rather than having units of mass in grams it has units of N, m?
where N, represents the number of phage.

Flow discharge is clearly the main factor for the majority of the 33 equations listed,
suggesting that tracer dilution estimates were an overriding concern during development.
Expected transport distance or transport time are also generally common elements. All
other factors included in the equations were intended to address either known complications
(e.g., transport distance) or unknown complications (e.g., sorption) that are expected to
influence final downstream concentrations.

It should be noted that many of the parameters listed in Table 3 require preliminary
calculations. For example, tg = 3¢ (Parriaux et al., 1988, p. 8) for tracer tests in solution
conduits may be estimated from
_3L _3LA

=— 4
ta D O° (34)
and tg for forced-gradient tracer tests in porous media may be estimated from
3L  3L?rbn.
ta= > —e (35)

Such essential calculations are not immediately obvious, however.

It is also necessary to point out that any equations that require tracer purity 7, in the
calculations, for example, Equations (18) and (23)-(27), will be greatly affected by minor
changes in the value of T,. For these equations, fluorescent dye type can profoundly affect
how much tracer will be recommended because of the varying concentrations of different
dyes and their form, liquids or powders.

21



1. Cy = 2.61 mg L-?
2. t=140h
3. ty = 18.0h
4. ty ~ 40.0

Applying EHTD with assuming no pollutant reactivity to this hypothetical example and

using a reasonable estimate for cross-section area to be 1.65 m? (17.73 ft) resulted in:

1. Cy = 2.04 mg L7

2. t= 7.39h (measurable)
3. tp = 16.09h

4. ty ~ 40.0h

Including a pollutant decay factor would have caused a reduction in the EHTD-predicted
peak concentration while including a pollutant retardation factor would have caused both
a reduction in the peak concentration and later travel times. A comparison of the
standardized-predicted BTC and EHTD-predicted BTC is shown in Figure 33 on the next
page. Although there is no definitive way in which one BTC shown in Figure 33 can
be selected over the other it will be noted that the standardized curve method tends to
overestimate peak concentration (Mull et al., 1988a, p. 76) while it is likely that EHTD
will underestimate peak concentration if a good measure or estimate for discharge, cross-
sectional area (or transverse spread for porous media), and transport distance are not

sufficiently accurate.

8.2.2.2. Using the LHS-Routine in EHTD to Forecast Pollution. As explained
in Section 4.3. on page 70 a LHS-input file of mean values (see page 72) can be developed
from any input file of measured values. Using the Dyers Spring data a LHS-developed file
was created from 10,000 randomly-generated parameter values (Figure 34 on page 158).
Note that Figure 34 on page 158 also includes the univariate statistics that describe the
input parameters (see Table 20 on page 72 for identification of the variables). Using the
EHTD-generated file (Figure 34) will not produce correct results because it in no way was
intended to match the conditions identified (e.g., @ # 91.74m*h7?). For example, it

156



7.9800 -47036 38.222 -62428

8.2147 -47539 39.079 -60136
8.4494 -48043 39.935 -58757
8.6841 -48547 40.792 -57940
8.9189 -49052 41.649 -57461
9.1536 -49556 42.505 .57184
9.3883 - 50062 43.362 -57025
9.6230 . 50567 44,219 - 56936
9.8577 -51074 45.075 - 56885
10.092 -51581 45.932 - 56857
10.327 -52089 46.789 - 56842
10.562 - 52598 47.645 -56833
10.797 -53109 48.502 - 56829
11.031 -53623 49.359 -56826
11.266 -54143 50.215 -56825
11.501 . 54671 51.072 . 56824
11.735 .55215 51.929 - 56824
11.970 -55784 52.786 . 56824
12.205 - 56396 53.642 - 56824
12.439 .57073 54.499 - 56824
12.674 -57853 55.356 -56824
12.909 .58787 56.212 -56824
13.144 .59947 57.069 -56824
13.378 -61428 57.926 -56824
13.613 - 63359 58.782 - 56824
13.848 -65902 59.639 - 56824
14.082 -69260 60.496 - 56824
14.317 - 73679 61.352 -56824
14.552 - 79452 62.209 - 56824
14.787 - 86919 63.066 -56824
15.021 - 96461 63.922 - 56824
15.256 1.0850 64.779 -56824
15.491 1.2349

15.725 1.4189

15.960 1.6418

16.195 1.9082

16.429 2.2224

16.664 2.5882

16.899 3.0085

Figure 18. Data file generated by EHTD used to produce Figure 19 continued.

121



BE GOOG IG KG RI I IOK A a fei
Note: It is essential that the program be ended by moving from the GRAPHIC2 screen
to the GRAPHIC screen using the WINDOW pull-down menu and that <ENTER> be
pressed so that final computational results may be recorded in the output file and that
all requested plot files get created. Also, a date/time stamp is written to the bottom
of the file.

FEB GIB KIO EIOKICCCCCOCFOSCRIGOCORIOGRIO IG ICE AIC III aI

4, Open the output file and/or the plot file created using a standard Windows viewer
(e.g., Notepad) to see the results.

1.1.2. Example Test Files

The following example data files are provided on the CD-ROM that accompanies this docu-
ment so that the user may examine the functioning of EHTD under differing environmental
conditions:

Clarkel.in Single spring discharge site for a complexly folded karst terrane
(Field, 2000)

Clarke2.in? Multiple spring discharge sites for a complexly folded karst terrane
(Field, 2000)

Mullin Karst window to spring tracer test (Mull et al., 1988a, pp. 61-66)
Lost.in Lost River Cave System (Field and Pinsky, 2000)
G1.in : Tenn. example from a quarry (Davies, pers. comm.)
G2.in Tenn. example from a quarry (repeat tracer test of above)
Miss1.in Surface water tracer test example (Yotsukura et al., 1970, pp. G3-G6)
Miss2.in Surface water tracer test example (repeat tracer test of above)
Step.in Created example for continuous release
Borden.in Borden tracer test (Mackay et al., 1986)
Ehtd.in Injection-withdrawal test example (default)

(Molz et al., 1986a, pp. 52-60, 71)
Chalk.in Recirculation test example (Huyakorn et al., 1986)

1EHTD sums total estimated tracer mass to be released at the end of the program.



multiplying by a sinuosity factor < 1.5 (Sweeting, 1973, p. 231). Surface stream or solution

conduit volume V may be estimated by
V =AL. (68)
Aquifer volume for porous media with regional gradient is estimated by
V =LWH, (69)

and aquifer volume for porous media under forced-gradient conditions is estimated by

H 2
Venl (4) : (70)
Average flow velocity v for a surface stream or solution conduit may be estimated from
Q
== 71
v=< (71)

or, for a natural gradient tracer test in porous media, by application of Darcy’s law. Initial
average flow velocity for a natural gradient tracer test will conform to the basic form of
Equation (71) when n, is included

Q

°= WHn.’

(72)

although width W may be difficult to estimate. If W cannot reasonably be estimated, then
velocity is estimated from

Q

= TRHn.’

(73)

which is not theoretically correct but may result in an acceptable approximation.

For a forced gradient tracer test in porous media in which the gradient is influenced by
either a single extraction well or by a combination of an injection well and a withdrawal
well, velocity may be estimated from (Ka8, 1998, p. 377)

v= @ :
aLHne

(74)

and for an injection-withdrawal tracer test with recirculation from (Webster et al., 1970)

_ 32
us TLH Ne

(75)

49



Section 7. contains a detailed examination of how well EHTD functions under a variety
of conditions. It will be noted from Section 7. that EHTD appears to work extremely well
for any the environmental condition or design consideration.

6.3. EFFECT OF INITIAL CONCENTRATION AND EXPONENTIAL PRO-
DUCTION

The inclusion of an initial (background) concentration and exponential (growth) production
can greatly influence the shape of the BTC and two final estimated parameters: average
concentration and peak concentration. However, the EHTD-suggested tracer mass is not
affected.

These two additional conditions will generally be most beneficial when used in conjunc-
tion with a user-supplied solute mass (see Section 4.4., page 72) and EHTD is used as a
counterterrorism tool (see Section 8.). This may be especially true for exponential produc-

tion for the release of a bacteria if adequate nutrients and respiratory conditions exist.

6.3.1. Effect of an Initial Concentration

An initial concentration will cause the BTC to begin at a concentration that is equal to
the value entered by the user. This effect may or may not be evident depending upon the
initial concentration entered relative to the final peak concentration (see Lines 10 and 11 of
Table 25 and explanation on page 93).

6.3.2. Effect of Exponential Production

Exponential growth will cause the entire BTC to continue rising even as concentration is
decreasing because of the growth factors included. This effect may or may not be evident, de-
pending on the dimensionless exponential production constants (GAMMA1, GAMMA2) entered
relative to the final peak concentration (see Lines 10 and 11 of Table 25 and explanation on

page 93).
6.3.3. Breakthrough Curve Shape

The influence of an initial concentration (C; = 0.3 pg L~!) and exponential production
("1 = 2 = 0.5) (Figure 17) is reflected in Figure 18. A comparison of the data listed
in Figure 18 with the data listed in Figure 14 (pages 100-104) shows that BTC time data
and sample time data (columns 1 and 3 of Figures 14 and 18) are identical, but that BTC

118



17.
17.
17.
17.
18.
18.
18.
18.
19.
19.
19.
19.
19.
20.
20.
20.
20.
21.
21.
21.
21.
22.
22.
22.
22.
23.
23.
23.
23.
24.
24.
25.
25.
26.
26.
27.
27.
28.
28.

Figure 14. Data file generated by EHTD used to produce Figure 13 continued.

134
368
603
838
072
307
542
777
O11
246
481
715
950
185
419
654
889
124
358
593
828
062
297
532
767
001
236
471
940
409
879
348
818
287
757
226
695
165
634

-8157
+3463
. 9350
-5803
+2795
-0284
-8214
-6518
~5115
-3916
- 282
.173
-054
-913
-T4L
-527
+262
+936
-543
-075
-528
-897
-180
-376
-484
.505
+443
-300
-790
-018
-033
-891
-643
341
-028
9.7425
8.5131
7.3621
6.3044

ODNDADHNRWWH

Pe
RO

PREP BP PPP BBE BRB RRP RP BR Be Pe epee
PNHNWAANNDAWADWDBDAANNNAATKWNND

102



46.
47.
47.
48.
48.
49.
49.
50.
50.
$1.
51.
52.
52.
53.
53.
53.
54.
54.
55.
55.
56.
56.
57.
57.
58.
58.
59.
59.
60.
60.
61.
61.
61.
62.
62.
63.
63.
64.
64.

Figure 14. Data file generated by EHTD used to produce Figure 13 continued.

941
411
880
350
819
288
758
227
697
166
635
105
574
044
513
983
452
921
391
860
330
799
268
738
207
677
146
615
085
554
024
493
963
432
901
371
840
310
779

. 16362E-03
.11658E-03
-82901E-04
- 58834E-04
-41675E-04
- 29465E-04
- 20796E-04
-14652E-04
- 10305E-04
- 72362E-05
.50731E-05
-35511E-05
- 24820E-05
- 17322E-05
-12071E-05
- 84008E-06
. 58385E-06
-40523E-06
- 28089E-06
-19447E-06
-13447E-06
- 92868E-07
-64064E-07
-44144E-07
-30384E-07
- 20891E-07
.14349E-07
- 98452E-08
-67484E-08
-46212E-08
-31615E-08
- 21608E-08
.14756E-08
. 10067E-08
-68627E-09
-46742E-09
-31809E-09
-21630E-09
. 14696E-09

104



7. TRACER TEST DESIGN EXAMINATION DATA SETS
7.1. FLOWING STREAMS

7.1.1. Small Creek . .

7.1.2. Large River . .

7.1.3. Solution Conduit

7.1.4. Meltwater Channel

. POROUS MEDIA

7.2.1. Natural-Gradient Tracer Test

7.2.2. Forced-Gradient Tracer Test

7.2.3. Injection-Withdrawal Tracer Test

7.2.4, Recirculation

. TRACER-TEST DESIGN RESULTS

7.3.1. Flowing Streams Results
7.3.1.1. Uvas Creek Tracer Test.
7.3.1.2. Missouri River Tracer Test... 2... eee ee eee
7.3.1.3. Dyers Spring Tracer Test.
7.3.1.4. Variegated Glacier Tracer Test.
Porous Media Results
7.3.2.1. Test Site Wilerwald Tracer Test.
7.3.2.2. Kirchdorf-Unteropfingen Tracer Test.
7.3.2.3. Mobile Site Tracer Test.
7.3.2.4. Chalk River Site Tracer Test.

IV. ADDITIONAL APPLICATION OF EHTD

8. APPLICATION OF EHTD TO SUPPORT RISK ASSESSMENTS
8.1. EXPOSURE ASSESSMENT OVERVIEW
8.2. FORECASTING POLLUTION FOR RISK ASSESSMENTS
8.2.1. Dimensionless Dye-Recovery Curve
8.2.2. EHTD for Forecasting pollution Effects tae
8.2.2.1. Using EHTD Directly to Forecast Pollution. .........-
8.2.2.2. Using the LHS-Routine in EHTD to Forecast Pollution.

9. SUMMARY AND CONCLUSIONS
NOTATIONS

REFERENCES



4.6.1.1. File. Items listed under this heading in Table 24 are described as follows.

Print... A screen dump to the local printer attached to the respective PC.
Save... Save the screen as a bitmapped (*.BMP) file.

Exit Ctrl+C Exit the program.

4.6.1.2. Edit. Items listed under this heading in Table 24 are described as follows.

Select Text Select text for pasting to the clipboard.

Select Graphics Select graphics for pasting to the clipboard.
Select All Select both tert and graphics for pasting to the clipboard.
Copy Ctrl+Ins Copy selected items to the clipboard.

Paste Paste selected items to the screen.

4.6.1.3. View. Items listed under this heading in Table 24 are described as follows.

Size To Fit Fit the graphics screen to the view surface without scroll bars.

Full Screen Alt+Enter Fit the entire graphics screen to the view surface without the menu
items displayed (a left-mouse click returns to the original screen).

4.6.1.4. State. Items listed under this heading in Table 24 are described as follows.
Pause Ctrl+S Pause the graphic display.

Resume Ctrl+Q Resume graphic display.

Pause and Resume appear only as alternates of each other, so that only the one that is not
currently functioning is accessible. The one that is currently in operation is not displayed
in the pull-down menu.

81



2.3.1. Examination of Tracer-Mass Estimation Equations

The tracer-test design examination parameters originally listed in Parriaux et al. (1988)—
and reprinted in Table 11 with additional parameters—were applied to 32 of the 33
equations in Table 3. Liquid Na-fluorescein, which is considered to be the tracer material
used, is conventionally available as a 30% solution (T, = 0.3) and has a density of
1.2 gcm~*. Equation (33) was not evaluated because it was designed for conditions other
than those listed in Table 11. Tracer mass estimates using the tracer test design examination
parameters and Equations (1)-(32) resulted in tracer mass estimates that ranged from a
fraction of a gram of tracer to tens of thousands of grams of tracer (Table 12). Large tracer
mass ranges are probable using the same equation when variable hydrologic conditions
and/or tracer-dependent coefficients Tc, are applied. Equation (25) is expected to produce
greater tracer mass estimates than the other equations because it is based on a long-pulse
release (tz > t), which will also cause a much later real value for tp than the one listed in
Table 11.

For perspective, the results of Equations (1)-(32) may be compared to similar results
produced by

_ TQ10

M=—S®

(39)

for an impulse release and

M =T,Qt210° (40)

for a pulse release. Although Equations (39) and (40) were not found in any of the references
listed in Table 3, it is likely that they are commonly used because they exhibit mass balance.
However, there appears to be no reason to believe that either would yield reasonable results
because Q is the only included flow system parameter.

2.3.1.1. Porous Media. Application of Equations (1)-(32) to the porous media ex-
amination parameters listed in Table 11 resulted in tracer mass estimates that ranged from
2.5 x 10-8 g to 4.75 x 10° g, or a difference of >16 orders of magnitude (Table 12). If
Equations (5b), (9), and (20) are removed from consideration, the difference is 3 orders of
magnitude. Equations (5b) and (9) may legitimately be removed from consideration on the
assumption that Tc, was misprinted in Milanovié (1981, p. 276). Equation (20) may also
include a misprint (volume rather than discharge). A range of 3 orders of magnitude for

tracer mass is difficult to resolve without additional information or site-specific experience.

26



to Darcy’s law, estimated tracer travel times (Table 31) could not be improved, but an
improvement in calculated tracer mass to release (Table 32) could be improved by providing
an estimate for tracer decay. Evident from Figure 27 and Table 31 is that the estimated
times of travel ~ and t, were underestimated by EHTD, which is a direct result of the
application of Darcy’s law.

The actual tracer mass released was 24x more than the EHTD-nonreactive recommended

estimate. Setting y to 0.0044 h7! raised the tracer mass estimate to the actual amount

released, but a consequent and significant decrease in estimated C, was required (Table 30).
The tracer used for the Test Site Wilerwald tracer test was fluorescein, which is generally
regarded as being slightly retarded in granular aquifers and not very sensitive to degradation
in the subsurface. For this test, fluorescein appears not to have been significantly retarded,
but it may have been severely degraded according to EHTD. This contention is supported by
the actual tracer test, which indicates that only about 77 g of fluorescein were recovered [85
g when evaluated using QTRACER2 and a straight-line projection for data extrapolation
(Field, 2002b, pp. 57-58)].

Figure 27 shows that EHTD inadequately predicted the measured BTC for both the
nonreactive and the reactive cases but that most of the BTC, including the long, relatively
gently sloping BTC tail, would be identified during the sampling process even though
EHTD failed to accurately predict the BTC when Darcy’s law is applied. For the Test
Site Wilerwald tracer test, tracer was added as a small, short-duration pulse, the effect of
which was a relatively insignificant amount so Dy = V for both of the EHT! 'D-predicted
results (Table 32). The EHTD-predicted volumes only slightly exceeded the measured value
for V, suggesting that the EHTD-predicted volumes are reasonable.

7.3.2.2. Kirchdorf-Unteropfingen Tracer Test. In porous media systems, forced-
gradient tracer tests are prefered because the length of time for the test is greatly reduced
and the transport parameters necessary for designing the tracer test are more easily
estimated. However, errors in estimated parameters may still result in a poor tracer test
design. The Kirchdorf-Unteropfingen tracer test was designed using parameters that were
determined from a pumping test.

The EHTD-predicted BT'Cs poorly match the measured BTC, and initial tracer break-
through was not adequately predicted (Figure 28). Peak concentration for the measured
BTC was missed by both EHTD-predicted cases by more than 17 days (Table 31). The
poor EHTD predictions for the Kirchdorf-Unteropfingen tracer test are directly related to

146



21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59

Figure 15. Standard-form example output file generated by EHTD from a typical input file

(see Figure 12) continued.

TAHAAKHHKHKHTHHPHP AAA AAR AL AR WWWHWWWWWWWWNNNN

- T085E+01
« T942E+01
- 8799E+01
- 9655E+01
-0512E+01
. 1369E+01
+ 2225E+01
-3082E+01
-3939E+01
-4795E+01
-5652E+01
- 6509E+01
. T365E+01
-8222E+01
.9079E+01
-9935E+01
-O792E+01
-1649E+01
-2505E+01
-3362E+01
-4219E+01
-5075E+01
-5932E+01
-6789E+01
- T645E+ 01
-8502E+01
-9359E+01
-O215E+01
- 1072E+01
.1929E+01
« 2786E+01
- 3642E+01
-4499E+01
- 5356E+01
-6212E+01
- 7TO69E+01
. 7926E+01
-8782E+01
-9639E+01

113

27.
27.
28.
29.
30.
31.
32.
33.
33.
34.
35.
36.
37.
38.
39.
39.
40.
At.
42.
43.
44.
45.
45.
46.
47.
48.
49.
50.
51.
51.
52.
53.
54.
55.
56.
57.
57.
58.
59.

5.
57.
48.
39.
31.
22.
14.

5.
56.
48.
39.
31.
22.
13.

5.
56.
48.
39.
30.
22.
13.

5.
56.
47.
39.
30.
22.
13.

4.
56.
47.
39.
30.
21.
13.

4.
56.
47.
38.



Table 22. Description of the input file components (continued).

Line Type Identifier Description
10 ote oo Comment line.

11 Real INIT. CONC. (ug/L) Initial (background) tracer concentration
(2 0.0) (ug LTM).

Real GAMMA1 First exponential production (growth) constant
(> 0.0).

Real Second exponential production (growth) constant
(> 0.0).

Comment line.

RETARDATION Factor to account for possible tracer retardation
(> 1.0).

Factor to account for possible tracer decay (> 0.0).

Global program optimization data code:
0 No optimization.
1 Optimization.

AVE. CONC. (ug/L) Desired average concentration at the sampling
station (ug L-1).

Optimization for tracer retardation.
it) No optimization.
1 Optimization.

Optimization for tracer decay.
0 No optimization.
1 Optimization.

Minimum bound on tracer retardation optimization.

Minimum bound on tracer decay optimization.

16 Real tee Maximum bound on tracer retardation optimization.
16 Real tee Maximum bound on tracer decay optimization.

17 ee te Comment line.

18 = oe Comment line.

continued on next page

88



For comparison purposes, Equations (39) and (40) would yield 2.16 x 107 g and 3.37 x
10"° g for the impulse and pulse releases, respectively. The results of Equation (39) appear
to be the greatest of all except for those of Equation (20) and the results of Equation (40) are
greater than those of all 32 examined equations (Table 12). Equations (20), (39), and (40)
likely represent an absolute upper range of tracer mass to release, and releases in this range
would probably be excessive and possibly harmful (Field et al., 1995; Behrens et al., 2001).

2.3.1.2. Karstic Media. Results of the karstic media examination parameters listed
in Table 11 in Equations (1)~(29) produced tracer mass estimates that ranged from
7.50 x 10-7 g to 8.55 x 10° g, a difference also of >16 orders of magnitude. Removing
Equations (5b), (9), and (20) results in a difference of 5 orders of magnitude. As in the case
with porous media, such a large range is difficult to resolve without additional information
or site-specific experience.

Equations (39) and (40) resulted in 1.08x 108 g and 1.0110" g for the impulse and pulse
releases, respectively. Equation (39) resulted in an estimated mass greater than all but that
of Equation (20) (Table 12) and the results of Equation (40) are greater than those of all 32
examined equations (Table 12). As with the porous media estimates, Equations (20), (39),
and (40) likely represent an upper limit for tracer mass to release, and such a release would
probably be excessive and possibly harmful (Field et al., 1995; Behrens et al., 2001).

2.4. EHTD ANALYSIS OF THE TWO TRACER TESTS

As with the 33 equations listed in Table 3, use of the EHTD methodology requires
that specific flow-system parameters be measured or reasonably estimated. A subset of
parameters from Table 11 that represent the required parameters necessary for evaluation
by EHTD are shown in Table 13. From Table 13 it is apparent that only measurable
parameters related to the hydraulics of the flow system are required for EHTD analysis.
However, the two tracer-specific parameters, retardation and decay, and the sinuosity factor
are not required. The sinuosity factor is an adjustable multiplier <1.5 that is similar
to the one used in Equation (26) except that Equation (26) requires the inclusion of
Sn = 1.5, It is also used by EHTD to increase the measured straight-line distance by
an appropriate distance, because natural solution conduits are not constrained to perfectly
straight channels.

‘Although not presented in Table 13, EHTD also requires identification of the type of

flow system tracer test, the type of release, and the time for tracer injection, in an attempt

29