U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2007–5280

Prepared in cooperation with the

U.S. Department of Energy,

under Interagency Agreements

DE-AI08-92NV10874 and DE-AI08-97NV12033

Analysis of Conservative Tracer Tests in the Bullfrog, Tram, 

and Prow Pass Tuffs, 1996 to 1998, Yucca Mountain, 

Nye County, Nevada

TIME SINCE TRACER INJECTION (DAYS)

Actual field 

dimensionless

breakthrough

curve

Moench dual-porosity analytical solution

using optimized parameter values

from PEST analysis 

DIMENSIONLESS CONCENTRATIO

N
Analysis of Conservative Tracer Tests in 

the Bullfrog, Tram, and Prow Pass Tuffs, 

1996 to 1998, Yucca Mountain, Nye County, 

Nevada

By Amjad Umari, Michael F. Fahy, John D. Earle, and Patrick Tucci

Prepared in cooperation with the 

U.S. Department of Energy, 

under Interagency Agreements

DE-AI08-92NV10874 and DE-AI08-97NV12033

Scientific Investigations Report 2007–5280

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

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Manuscript approved for publication, September 2007

Edited by Mary A. Kidd and Pamela B. Daddow

Layout by Sharon Powers

Suggested citation:

Umari, Amjad, Fahy, Michael F., Earle, John D., and Tucci, Patrick, 2008, Analysis of conservative tracer tests in the 

Bullfrog, Tram, and Prow Pass Tuffs, 1996 to 1998, Yucca Mountain, Nye County, Nevada: U.S. Geological Survey 

Scientific Investigations Report 2007–5280, 40 p.

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.
iii

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Purpose and Scope ..............................................................................................................................3

Previous Work .......................................................................................................................................3

Acknowledgments................................................................................................................................3

Hydrogeologic Setting at the C-hole Complex..........................................................................................3

Tracer Tests at the C-hole Complex............................................................................................................3

Field and Laboratory Methods............................................................................................................6

Analytical Solution Methods...............................................................................................................6

Tracer Tests in the Bullfrog and Tram Tuffs.............................................................................................11

Iodide Tracer Test in the Lower Bullfrog–Upper Tram Interval...................................................11

2,6 Difluorobenzoic Acid Tracer Test in the Lower Bullfrog Interval..........................................13

Pyridone Tracer Test in the Lower Bullfrog Interval .....................................................................16

Tracer Tests in the Prow Pass Tuff............................................................................................................17

2,4,5 Trifluorobenzoic Acid and Iodide Test from Borehole UE-25 c#3 to UE-25 c#2 ...............17

Single-Porosity, Radially Convergent Solution .....................................................................19

Single-Porosity, Partially Recirculating Solution..................................................................21

Dual-Porosity, Partially Recirculating Solution.....................................................................23

2,3,4,5 Tetrafluorobenzoic Acid Test from Borehole UE-25 c#1 to UE-25 c#2 ...........................26

Summary of Transport Parameter Values and Presentation of Conceptual Models of 

Solute Transport in the Bullfrog, Tram, and Prow Pass Tuffs .................................................26

Uncertainties and Limitations....................................................................................................................27

Summary........................................................................................................................................................29

References....................................................................................................................................................30

Glossary.........................................................................................................................................................32
iv

Figures

1. Map showing location of the C-hole Complex, boreholes UE-25 c#1, UE-25 c#2, 

and UE-25 c#3, and nearby boreholes.......................................................................................2

2. Generalized geologic map showing the location of the C-hole Complex and 

nearby boreholes..........................................................................................................................4

3. Hydrogeologic intervals in the C-holes.....................................................................................5

4. Conceptual diagram of the flowing and immobile water components of an 

equivalent porous medium (EPM) in a fractured rock mass .................................................7

5. Visual match of the actual field breakthrough curve to the Moench (1989) 

single-porosity analytical solution type curve for the iodide tracer test 

in the Bullfrog-Tram interval (Matching Method 1) ................................................................9

6. Visual match of the actual field breakthrough curve to the Moench (1995) 

dual-porosity analytical solution for the iodide tracer test in the 

Bullfrog-Tram interval (Matching Method 3) .........................................................................10

7. PEST-optimized match of the actual field breakthrough curve to the Moench 

(1995) dual-porosity analytical solution for the iodide tracer test in the 

Bullfrog-Tram interval (Matching Method 4) .........................................................................12

8. Visual match of the actual field breakthrough curve to the Moench (1995) 

dual-porosity analytical solution type curve for the 2,6 difluorobenzoic 

acid (DFBA) tracer test in the Lower Bullfrog interval (Matching Method 3) ..................14

9. Visual match of the actual field breakthrough curve to the Moench (1995) 

dual-porosity analytical solution for the 2,6 difluorobenzoic acid

(DFBA) tracer test in the Lower Bullfrog interval (Matching Method 3)...........................14

10. Visual match of the actual field breakthrough curve to the Moench (1995) 

dual-porosity analytical solution for the 2,6 difluorobenzoic acid

(DFBA) tracer test in the Lower Bullfrog interval (Matching Method 4)...........................15

11. PEST-optimized match of the actual field breakthrough curve to the Moench 

(1995) dual-porosity analytical solution for the 2,6 difluorobenzoic 

acid (DFBA) tracer test in the Lower Bullfrog interval (Matching Method 4) ..................16

12. Breakthrough curve for the pyridone tracer test in the Lower Bullfrog interval 

from January 9 to July 10, 1997 ................................................................................................17

13. Actual field breakthrough curves for the partially recirculating 

2,4,5 trifluorobenzoic acid (TFBA) and iodide tracer test in the 

Prow Pass interval......................................................................................................................18

14. Visual match of the actual field breakthrough curves to the Moench (1989) 

single-porosity analytical solution for radially convergent flow for the 

2,4,5 trifluorobenzoic acid (TFBA) and iodide tracer test in the Prow Pass 

interval (Matching Method 2)...................................................................................................19

15. Visual match of the actual field breakthrough curves to the modified 

Moench (1989) single-porosity analytical solution, modified for partially 

recirculating flow, for the 2,4,5 trifluorobenzoic acid (TFBA) and iodide 

tracer test in the Prow Pass interval (Matching Method 2)................................................20

16. Comparison of ground-water streamlines around UE-25 c#2 (production well) 

 and UE-25 c#3 (injection well) for (A) partially recirculating flow field, and 

 (B) radially convergent flow field.............................................................................................22
v

17. Visual match of the actual field breakthrough curves to the modified 

Moench (1995) dual-porosity analytical solution, modified for partially 

recirculating flow, for the 2,4,5 trifluorobenzoic acid (TFBA) and iodide 

tracer test in the Prow Pass interval showing effects of changing 

GAMMA, with a storage porosity of 0.001 (Matching Method 4).......................................24

18. Visual match of the actual field breakthrough curves to the modified 

Moench (1995) dual-porosity analytical solution, modified for partially 

recirculating flow, for the 2,4,5 trifluorobenzoic acid (TFBA) and iodide 

tracer test in the Prow Pass interval showing effects of changing 

GAMMA, with a storage porosity of 0.01 (Matching Method 4).........................................25

19. Actual field breakthrough curve for the 2,3,4,5 tetrafluorobenzoic acid 

(TeFBA) tracer test in the Prow Pass interval........................................................................26

20. Conceptual diagram comparing the proportions of the flowing and immobile 

water components of the fractured rock equivalent porous mediums (EPMs) 

in the Bullfrog-Tram and Prow Pass intervals at the C-hole Complex...............................28

Tables

1. Stratigraphy of Miocene tuffaceous rocks in the C-hole area. ............................................5

2. Selected breakthrough results and estimated transport properties from 

radially convergent tracer tests conducted in the Bullfrog and Tram Tuffs 

at the C-hole Complex, 1996 to 1997 ........................................................................................13

3. Selected breakthrough results and estimated transport properties 

from partially recirculating tracer tests conducted in the Prow Pass 

Tuff at the C-hole Complex, 1998 ..............................................................................................18
vi

Conversion Factors and Datum

Multiply By To obtain

centimeter (cm) 0.3937 inch

gram (g) 2.205×10–3 pound

kilogram (kg) 2.205 pound

kilometer (km) 0.62139 mile

liter (L) 0.26417 gallon

liter per minute (L/min) 0.26417 gallon per minute

liter per second (L/s) 15.85 gallon per minute

meter (m) 3.2808 foot

microgram per liter (mg/L) 1 part per billion

micrometer (mm) 3.937×10–5 inch

milligram (mg) 2.205×10–6 pound

milligram per liter (mg/L) 1 part per million

nanogram per liter (ng/L) 1 part per trillion

square meter 10.76 square foot

The following abbreviations are for basic dimensions:

Length: [L]

Time: [T]

Mass: [M]

Concentration given variably as mg/L, mg/L, or ng/L as appropriate for the range of concentration being discussed or graphically displayed.

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

Sea level: Altitudes in this report are referenced to the National Geodetic Vertical Datum of 1929 

(NGVD of 1929), a geodetic datum derived from a general adjustment of the first-order level nets 

of the United States and Canada, formerly called “the Sea Level Datum of 1929” or “mean sea 

level.”
Analysis of Conservative Tracer Tests in the Bullfrog, 

Tram, and Prow Pass Tuffs, 1996 to 1998, Yucca Mountain, 

Nye County, Nevada

By Amjad Umari, Michael F. Fahy, John D. Earle, and Patrick Tucci

Abstract

To evaluate the potential for transport of radionuclides 

in ground water from the proposed high-level nuclear-waste 

repository at Yucca Mountain, Nevada, conservative (nonsorbing) tracer tests were conducted among three boreholes, 

known as the C-hole Complex, and values for transport (or 

flow) porosity, storage (or matrix) porosity, longitudinal dispersivity, and the extent of matrix diffusion were obtained. The 

C-holes are completed in a sequence of Miocene tuffaceous 

rock, consisting of nonwelded to densely welded ash-flow tuff 

with intervals of ash-fall tuff and volcaniclastic rocks, covered 

by Quaternary alluvium. The lower part of the tuffaceous-rock 

sequence includes the Prow Pass, Bullfrog, and Tram Tuffs of 

the Crater Flat Group. The rocks are pervaded by tectonic and 

cooling fractures. Paleozoic limestone and dolomite underlie 

the tuffaceous rocks.

Four radially convergent and one partially recirculating conservative (nonsorbing) tracer tests were conducted at 

the C-hole Complex from 1996 to 1998 to establish values 

for flow porosity, storage porosity, longitudinal dispersivity, 

and extent of matrix diffusion in the Bullfrog and Tram Tuffs 

and the Prow Pass Tuff. Tracer tests included (1) injection of 

iodide into the combined Bullfrog-Tram interval; (2) injection 

of 2,6 difluorobenzoic acid into the Lower Bullfrog interval; 

(3) injection of 3-carbamoyl-2-pyridone into the Lower Bullfrog interval; and (4) injection of iodide and 2,4,5 trifluorobenzoic acid, followed by 2,3,4,5 tetrafluorobenzoic acid, into the 

Prow Pass Tuff. All tracer tests were analyzed by the Moench 

single- and dual-porosity analytical solutions to the advectiondispersion equation or by superposition of these solutions. 

Nonlinear regression techniques were used to corroborate 

tracer solution results, to obtain optimal parameter values from 

the solutions, and to quantify parameter uncertainty resulting 

from analyzing two of the three radially convergent conservative tracer tests conducted in the Bullfrog and Tram intervals.

Longitudinal dispersivity values in the Bullfrog and Tram 

Tuffs ranged from 1.83 to 2.6 meters, flow-porosity values 

from 0.072 to 0.099, and matrix-porosity values from 0.088 

to 0.19. The flow-porosity values indicate that the pathways 

between boreholes UE-25 c#2 and UE-25 c#3 in the Bullfrog 

and Tram intervals are not connected well. 

Tracer testing in the Prow Pass interval indicates different transport characteristics than those obtained in the Bullfrog 

and Tram intervals. In the Prow Pass Tuff, longitudinal dispersivity was 0.27 meter, flow porosity was 4.5 × 10–4, and matrix 

porosity was 0.01. This indicates that the flow network in the 

Prow Pass is dominated by interconnected fractures, whereas 

in the Bullfrog and Tram, the flow network is dominated by 

discontinuous fractures with connecting segments of matrix.

Introduction

Yucca Mountain, located about 145 kilometers (km) 

northwest of Las Vegas in southern Nevada (fig. 1), is the 

site designated by the U.S. Department of Energy (DOE) to 

store high-level nuclear waste in a proposed mined, underground repository. To evaluate the potential for transport of 

radionuclides in ground water from the proposed repository 

area, conservative (nonsorbing) tracer tests were conducted 

among three boreholes known as the C-hole Complex (fig. 1), 

and estimates of transport porosity (or flow porosity), storage 

porosity (or matrix porosity), longitudinal dispersivity, and 

the extent of matrix diffusion (the dimensionless diffusion 

coefficient) were obtained. The C-hole Complex has been 

extensively described in Geldon (1993, 1996) and Geldon 

and others (1998, 2002). A range of transport parameters was 

sought by conducting tracer tests in the high-transmissivity 

Bullfrog Tuff and Tram Tuff and in the low-transmissivity 

Prow Pass Tuff, all of Miocene age. The results of these tracer 

tests are presented as part of a series of investigations by the 

U.S. Geological Survey (USGS) regarding the hydrologic and 

geologic characteristics of Yucca Mountain. This investigation was conducted in cooperation with the U.S. Department 

of Energy (DOE), under Interagency Agreements DE-AI08-

92NV10874 and DE-AI08-97NV12033.
2 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Amargosa Desert

116o30’

36o

52’

36o

40’

116o25’ 116o20’

USW H-4

UE-25 p#1

ONC-1

WT #14

UE-25 c#1

UE-25 c#2

UE-25 c#3

95

Proposed repository

Bedrock

EXPLANATION

NEVADA TEST SITE BOUNDARY

Fortymile Wash

0 5 10 KILOMETERS

0 5

0 25 50 METERS

0 50 100 FEET

10 MILES

Crater Flat

Solitario

Canyon

Windy Wash

Yucca Wash

Prow

Pass

Fran Ridge

Yucca Mountain

Jackass

Flats

Borehole

UE-25 c#2

Borehole

UE-25 c#1

76.5 meters

68.3 meters

30.4 meters

N

E173,590

E173,610E173,630E173,650E173,670

94°

63°

23°

N230,700

N230,720

N230,740

N230,760

N230,780

Borehole

UE-25 c#3

N230,680

N230,660

Surface location 

 of borehole

Projected trace 

 of borehole location

NEVADA

Carson City

Area of 

map

Las Vegas

Yucca Mountain

Bow 

Ridge

Busted 

Butte

20-meter grid based on Nevada State coordinate system, central zone

(Modified from Frizzell and Shulters, 1990)

Figure 1. Location of the C-hole Complex, boreholes UE-25 c#1, UE-25 c#2, and UE-25 c#3, and nearby boreholes.
Tracer Tests at the C-hole Complex 3

Purpose and Scope

This report presents the results of four convergent tracer 

tests and one partially recirculating tracer test in 

Miocene tuffaceous rocks in three boreholes at the C-hole 

Complex at Yucca Mountain, Nevada. The tests were conducted with conservative tracers from February 1996 to 

September 1998 to determine the transport porosity (or flow 

porosity), matrix porosity (or storage porosity), and longitudinal dispersivity of the Bullfrog, Tram, and Prow Pass Tuffs. 

The report describes the tests that were conducted, breakthrough curves (BTCs) for injected tracers, and analyses performed on the test data; presents values of transport properties 

determined from test analyses; summarizes conceptual models 

of solute transport in the Bullfrog and Tram Tuffs compared to 

the Prow Pass Tuff; and evaluates uncertainties and limitations 

associated with the test data, analyses, and quantitative results.

Previous Work

Hydrogeologic intervals at the C-hole Complex were 

identified initially by Geldon (1996) on the basis of borehole 

geophysical logs, borehole flow surveys, cross-hole seismic 

tomography, and aquifer tests that were conducted in 1983–84. 

Hydraulic tests and associated flow surveys conducted in 

1995–97 are documented in Geldon and others (1998, 2002). 

Hydraulic properties of the hydrogeologic intervals in the 

C-holes, such as matrix porosity, matrix permeability, hydraulic conductivity, transmissivity, and storativity, were determined by Geldon (1993, 1996) from geophysical logs, laboratory analyses, and aquifer tests. The barometric efficiency and 

effective porosity of the C-holes were established (Geldon 

and others, 1997). An open-hole hydraulic test, conducted in 

borehole UE-25 c#3 from May 22 to June 12, 1995 (Geldon 

and others, 1998), was designed to determine the transmissivity, hydraulic conductivity, and storativity of the composite 

saturated thickness of Miocene tuffaceous rocks at the C-hole 

Complex, lateral variations in hydraulic properties within a 

2-mile radius of the C-hole Complex, and possible hydraulic 

connection between the Miocene tuffaceous rocks and an 

underlying regional aquifer composed of Paleozoic carbonate 

rocks (Geldon and others, 2002). 

A series of hydraulic tests was conducted at the C-hole 

Complex from June 1995 through November 1997, prior to 

and in conjunction with the tracer tests discussed in this report. 

Water levels in several wells near the C-hole Complex were 

monitored during the hydraulic tests and were used in the 

analyses of the tests. Geldon and others (2002) describe those 

tests and analyses, present the hydraulic properties (transmissivity and storativity) obtained, and describe changes in water 

chemistry during the tests.

Acknowledgments

The authors wish to thank Drs. Jake Turin and Amr 

Abdel-Fattah of Los Alamos National Laboratory for their 

excellent technical reviews. This report reflects the improvement from their input.

Hydrogeologic Setting at the C-hole 

Complex

The C-hole Complex was constructed in 1983–84 in 

the channel of an ephemeral stream that cuts through Bow 

Ridge, a spur of Yucca Mountain (fig. 2). The C-holes are 

30.4 to 76.5 meters (m) apart at land surface (fig. 1); however, 

because of borehole deviation during drilling, interborehole 

distances at depth range from 28.6 to 86.3 m (Geldon and 

others, 1997, p. 2). The C-holes are completed in Miocene tuffaceous rocks (table 1 and fig. 3) that are covered by 0 to 24 m 

of Quaternary alluvium. The tuffaceous rocks are estimated to 

be 1,040 to 1,590 m thick in the vicinity of the C-holes, where 

they consist of nonwelded to densely welded ash-flow tuff 

with intervals of ash-fall tuff and volcaniclastic rocks (Geldon, 

1993; Geldon and others, 1998). The lower part of the tuffaceous rock sequence includes the Prow Pass, Bullfrog, and 

Tram Tuffs of the Crater Flat Group. The tuffaceous rocks are 

pervaded by tectonic and cooling fractures that strike predominantly north-northeast to north-northwest and dip westward 

at angles of 50 to 87 degrees (Geldon, 1996, p. 4). Paleozoic 

limestone and dolomite (Carr and others, 1986) penetrated by 

borehole UE-25 p#1, which is about 600 m southeast of the 

C-hole Complex (fig. 2), underlie the tuffaceous rocks and are 

estimated to be about 455 m below the bottom of the C-holes. 

For more detail on the hydrogeologic setting of the C-holes, 

see Geldon and others (2002, p. 4).

Tracer Tests at the C-hole Complex

Four tracer tests were conducted by the USGS at the 

C-hole Complex using tracers that are conservative with 

respect to the tuffaceous rocks at the complex: (1) injection of 

iodide into the combined Lower Bullfrog–Upper Tram interval 

(called the Bullfrog-Tram interval); (2) injection of 2,6 difluorobenzoic acid (2,6 DFBA) into the Lower Bullfrog interval; 

(3) injection of 3-carbamoyl-2-pyridone (pyridone) into the 

Lower Bullfrog interval; and (4) injection of iodide and 2,4,5 

trifluorobenzoic acid (2,4,5 TFBA), followed by 2,3,4,5 tetrafluorobenzoic acid (2,3,4,5 TeFBA), in the Prow Pass Tuff. 

Los Alamos National Laboratory also conducted tracer tests 

at the C-hole Complex using tracers that are both conservative 

and nonconservative (“reactive” or sorbing) with respect to 

the tuffaceous rocks at the complex (Bechtel-SAIC Company, 

2003). These tests are not discussed in this report.
4 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

0

0

500 1,000

2,000 4,000 6,000 FEET

1,500 2,000 METERS

36°

50'

36°

48'

116°26' 116°24'

PA

NI TBRUSH CANYON

FAULT

PA

NI TBRUSH

CA

NYON

FAULT

SPUR

MIDWAY

VALLEY FAULT

EXILE HILL FAULT

BO

W

RIDGE

FAULT

DUNE

WASH

FAULT

MIDWAY

VALLEY

FRAN RIDGE

BOW RIDGE

BOUNDARY RIDGE

ANTLER WASH

JACKASS FLATS

DUNE WASH

WT#17

WT#3

WT#13

p#1

WT#14

J-13

H-4

C-HOLE

COMPLEX

ONC-1

WT#1

EXPLANATION

ALLUVIUM

MIOCENE TUFFACEOUS ROCKS

BOREHOLE

GEOLOGIC CONTACT

FAULT TRACE—Fault may be partly or entirely

 concealed by alluvium; ball on downthrown side

 of normal fault; teeth on upthrown side of reverse

 fault

BOREHOLE ABBREVIATIONS

FORTYMILE

WASH

Geology modifed from Day and others (1998)

H-4 

p#1 

WT#1 USW WT#1

WT#3 UE-25 WT#3

WT#13 UE-25 WT#13

WT#14 UE-25 WT#14

WT#17 

ONC-1 UE-25 ONC-1

USW H-4

UE-25 WT#17

UE-25 p#1

Figure 2. Generalized geologic map showing the location of the C-hole Complex and nearby boreholes.
Tracer Tests at the C-hole Complex 5

Table 1. Stratigraphy of Miocene tuffaceous rocks in the C-hole area. 

[Modified from table 1, p. 6, Geldon and others, 1998]

Geologic unit Depth below land surface, in meters

UE-25 c#1 UE-25 c#2 UE-25 c#3

Paintbrush Group

 Tiva Canyon Tuff 

 Topopah Spring Tuff

0–96

96–406

21–88

88–401

24–88

88–396

Calico Hills Formation 406–516 401–510 396–496

Crater Flat Group

Prow Pass Tuff

 Bullfrog Tuff

 Tram Tuff

516–656

656–828

 828–914+

510–652

652–829

 829–914+

496–644

644–814

 814–914+

0

50 100 FEET

25 50 METERS

0

UE-25 c#3 UE-25 c#1 UE-25 c#2

BEND IN SECTION

Pt

Pt

Ch

Ch

Cp

Cp

Cb

Cb

Ct

Ct

HYDROGEOLOGIC INTERVALS

METERS BELOW

LAND SURFACE

CALICO HILLS

PROW PASS

UPPER BULLFROG

EXPLANATION

TOPOPAH SPRING TUFF

CALICO HILLS FORMATION

PROW PASS TUFF

BULLFROG TUFF

TRAM TUFF

TRANSMISSIVE INTERVAL

NONTRANSMISSIVE ROCK

TUFF BRECCIA

GEOLOGIC CONTACT

GEOLOGIC CONTACT WITH

 AN OPEN PARTING OR, IN

 BRECCIA ZONES, AN UNEVEN

 SURFACE

BOUNDARY OF TRANSMISSIVE

 INTERVAL

FAULT—Arrows indicate direction

 of movement

WATER TABLE IN 1993 (Geldon and

 others, 1997, their table 4)

LOWER TRAM

UPPER TRAM

BULLFROG-TRAM

LOWER

BULLFROG

400

500

600

700

800

900

Figure 3. Hydrogeologic intervals in the C-holes.
6 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Field and Laboratory Methods

The purpose of the field testing was to establish flow 

porosity, storage porosity, and longitudinal dispersivity of 

the Bullfrog-Tram interval, the Lower Bullfrog Tuff, and the 

Prow Pass Tuff by using conservative tracers. The approach to 

developing the parameters was to conduct multiple cross-hole 

tests and to use multiple analytical solution methods to interpret the results. The results were in the form of BTCs (concentrations plotted against time) of the various tracers. In these 

cross-hole tracer tests, a known mass of tracer is injected into 

the interval being tested at one well, the injection well, while 

another well, the production well, is pumped at some rate. In 

the Prow Pass tracer tests, the test interval fluid was mixed by 

pumping it to the surface, where it could be sampled, and then 

back to the test interval. If some, or all, of the water pumped 

from the production well is reinjected into the injection well, 

the test is called a partially or fully recirculating tracer test; 

otherwise it is called a radially convergent tracer test. For 

either case, prior to tracer injection, pumping from the production well and, if applicable, reinjection of the pumped water 

into the injection well, is conducted until a quasi-steady-state 

flow field is established as determined from pressure sensors 

in the wells (this was done whether it is explicitly stated in 

the description of each test or not). The tracer travels from the 

injection to the production well where it is gradually pumped 

from the tested interval. At the surface, some of the pumped 

water is diverted to an automated sampler that collects specified amounts of water (samples) at specified time intervals. 

The automated sampler is controlled by a personal-computer 

(PC)-based program described in Geldon and others (2002, 

p. 14).

The concentrations of iodide, benzoic acids (2,6 DFBA; 

2,4,5 TFBA; and 2,3,4,5 TeFBA), and pyridone in a water 

sample can be obtained by reverse-phase high-pressure liquid 

chromatography (HPLC) in conjunction with an ultraviolet 

(UV)-absorption detector (Stetzenbach and Thompson, 1983). 

This method was selected not only because it is precise and 

sensitive, but also because the instruments are portable and the 

ground-water samples can be injected directly into the instrument. These features allow preliminary analyses to be conducted in the field for immediate test results. Tracer concentrations were confirmed later in the laboratory. Field-determined 

tracer detection limits, and field-determined accuracy and 

precision of the HPLC analytical technique were obtained only 

for the tracer tests in the Bullfrog-Tram and Lower Bullfrog 

intervals. The field-determined detection limit was 3 micrograms per liter (mg/L) for iodide; 40 mg/L for 2,6 DFBA; and 

0.1 mg/L for pyridone.

The accuracy of the HPLC analytical technique was calculated as the difference between the nominal and measured 

concentrations of standards divided by the nominal concentration. These calculated accuracy values were as follows: iodide, 

±3.47 percent for field analyses and ±2.67 percent for laboratory analyses; 2,6 DFBA, 2,4,5 TFBA, and 2,3,4,5 TeFBA, 

±10 percent for laboratory analyses; and pyridone, ±7 percent 

for laboratory analyses. HPLC runs of tracer “standards” prepared at specific concentrations, used to create the calibration 

curves to convert from HPLC raw readings to tracer concentrations, are done against a blank fluid stream moving through 

the HPLC system, whereas the runs of standards used for this 

accuracy calculation are interspersed among runs of different 

water samples.

The precision of the HPLC analytical technique, as 

determined by comparing replicate analyses, was as follows: 

iodide, ±2.30 percent for field-determined concentrations 

and ±1.61 percent for laboratory-determined concentrations; 

2,6 DFBA, 2,4,5 TFBA, and 2,3,4,5 TeFBA, ±10 percent for 

laboratory-determined concentrations; and pyridone, ±10 

percent for laboratory-determined concentrations greater than 

100 nanograms per liter (ng/L) and exceeding ±10 percent for 

laboratory-determined concentrations less than 100 ng/L.

Analytical Solution Methods

All tracer tests were analyzed with the Moench singleporosity (Moench, 1989) or dual-porosity (Moench, 1995) 

analytical solution to the advection-dispersion equation for 

radially convergent, areal flow for a single- or dual-porosity, 

homogeneous, isotropic medium, or by superposition of these 

solutions. Multiple solutions were used to ensure that the 

appropriate solution method was used in matching a particular 

set of data and to determine whether the aquifer behaves as 

a single- or dual-porosity aquifer. The fractured tuff at the 

C-hole Complex has been conceptualized for this report as 

an equivalent porous medium (EPM) that is either a singleporosity medium or dual-porosity medium. A single-porosity 

medium is conceptualized as consisting of only a flowingwater component, made up of interconnected fractures and 

discontinuous fractures that have connecting segments of 

matrix (fig. 4). The porosity of the flowing-water component 

is referred to as the “flow porosity.” A dual-porosity medium 

is conceptualized as consisting of both a flowing-water 

component and an immobile-water component. The immobilewater component (or storage component) is made up of 

dead-end fractures and the part of the matrix not contributing 

to the flow network. The porosity of the immobile-water 

component is referred to as the “storage porosity” or “matrix 

porosity.” The flowing-water component of an EPM is 

represented by a longitudinal dispersivity and a flow porosity, 

and the immobile-water component is represented by a storage 

porosity and a dimensionless matrix-diffusion coefficient. A 

PC-based graphical user interface was developed by the USGS 

to perform pre- and postprocessing for the Moench analytical 

solutions (Umari, 1996). The input parameters required by the 

Moench single-porosity or dual-porosity solution are:

•	 production rate, qo [ L3/T ]

•	 distance from the production well to the injection well, 

rL [L]

•	 aquifer thickness, h [L]
Tracer Tests at the C-hole Complex 7

Figure 4. Conceptual diagram of the flowing and immobile water components of an 

equivalent porous medium (EPM) in a fractured rock mass.

Equivalent

porous

medium (EPM)

Flowing

water

component

Immobile

water

component

(storage)

Fracture

network Matrix

Matrix

allows flow

between close

discontinuous

fractures

carrying

moving

water

Matrix

No close

fractures with

moving water

for the matrix

to connect

Discontinuous

fractures

(dead-end

fractures):

stagnant water

Discontinuous

fractures

carrying 

moving

water

Interconnected

fractures

Single porosity

Dual porosity

•	 radius of the production well, rw [L]; and the injection 

well, ri [L]

•	 mixing length in the production well, hw [L]; and the 

injection well, hi [L]. The length within the borehole 

through which the tracer is assumed to enter or exit the 

surrounding aquifer. For this report, the mixing length 

is assumed to be equal to the length of the transmissive 

intervals (based on previously conducted geophysical 

logs and (or) hydraulic tests) within the packed-off 

interval during a tracer test

•	 mass of tracer injected, M ́ [M]

•	 volume of water in which the tracer is dissolved prior 

to entering the aquifer, V ́ [L3]

•	 length of time for the tracer slug to enter the aquifer, 

t

inj [T], which is assumed to be equal to the duration 

of tracer injection into the borehole of the injection 

well. It is used for calculating a Moench type curve for 

analyzing radially convergent tracer tests except when 

the tracer injection is assumed to be instantaneous as 
8 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

is explained later for analyzing the recirculating tracer 

tests in this report

•	 flow porosity, ff , and matrix porosity, f ́ [dimensionless]. Matrix porosity is referred to interchangeably as 

“storage porosity” in this report

•	 longitudinal dispersivity, aL [L], in the form of the 

dimensionless Peclet number, PE = rL/aL. Longitudinal dispersivity is a measure of the ability of a porous 

medium to disperse a solute along streamlines (groundwater flow lines)

•	 retardation coefficient representing linear, reversible 

adsorption, R, in the fractures; R ́ , in the matrix 

[dimensionless]. Because all the tracers used were 

conservative (nonsorbing), a retardation coefficient of 

1.0 was used for all solutions

•	 dimensionless diffusion coefficient, GAMMA (g), 

diffusion of a solute into the matrix (immobile-water 

component of the EPM). GAMMA (g) is a function of 

the effective coefficient of diffusion from the fractures 

into the matrix, D ́ , and of h, ff , R, qo, and the radius, 

b ́ , of the theoretical sphere-shaped matrix blocks of 

the dual-porosity medium. It also is a function of rL

and rw (Moench, 1995, table 1, p. 1826)

•	 dimensionless storage coefficient, SIGMA (s), which 

is a function of ff , f ́ , R, and R ́ 

•	 dimensionless skin parameter, SK, which is a function of D ́, b ́, and the mass transfer coefficient (ks), 

the latter representing the continuity of diffusive flux 

across the “skin” (such as mineral coatings on fracture 

surfaces separating fractures from matrix blocks) 

In a radially convergent flow field, the volume of interest 

is a cylinder centered at the pumping borehole and extending 

to the injection borehole. The volume of water in the pores 

of this cylinder is phff (rL

2

 – rw

2

). The time that it would take 

to pump this amount of water at the rate of qo is referred to 

as the advection traveltime, t

a

 , and is given by the equation 

(Moench, 1989, table 1, p. 441):

 t

a

 = phff(rL

2

 – rw

2

) / qo (1)

The advection traveltime, t

a

, represents the length of time for 

a tracer slug to travel from the injection well to the production 

well by plug flow (pure advection: no dispersion, aL= 0).

To approximate the effects of mixing in the injection 

well, Moench (1989) used the hypothesis that the average 

value of the tracer concentration over this large cylindrical 

surface area equals the tracer concentration of the well-mixed 

fluid in the injection borehole multiplied by a constant (epsilon, e, eq. 8, p. 441). Epsilon represents the fraction of the 

water withdrawn by the production well that passes through 

the injection well.

To perform the Moench analysis, curves of theoretical 

tracer concentrations versus time at the production well are 

compared to curves of actual field tracer concentrations as 

a function of time at the production well. Specifically, type 

curves for the Moench analytical solution methods for radially 

convergent flow were generated for a range of Peclet numbers. 

These single-porosity and dual-porosity type curves are in the 

form of log-log plots of theoretical dimensionless concentration, CD, versus theoretical dimensionless time, t

D = t/ta

, where 

t is the dimensional time since injection. CD = C/Ci for the 

case of a finite-duration pulse considered in this report, where 

C [M/L3] is the dimensional concentration, and Ci [M/L3] is a 

reference concentration defined as (Moench, 1989, table 1, 

p. 441): 

 Ci = M ́ / [phff(rL

2 – rw2

)] (2)

The actual field tracer breakthrough concentrations plotted as a function of elapsed dimensional time since injection 

(or actual field dimensional BTCs) are converted to log-log 

plots of normalized concentration, c/cmax (where the concentration is normalized by the maximum observed concentration) 

versus dimensional time since injection, hereinafter referred 

to as actual field dimensionless BTCs. By overlaying the type 

curve and actual field dimensionless BTC and matching the 

rising portions of the two curves, estimates of t

a

 (and through 

equation 1, ff) and PE (Peclet number) are obtained. The 

estimate of t

a

 is obtained when the match point (t

D = 1, CD = 1) 

is projected onto the log-time axis of the actual field dimensionless BTC (shown in fig. 5 for the tracer test described in 

the following section). Because dimensionless time is defined 

as the ratio of time since injection to t

a

, the value of ta is equal 

to the time since injection, indicated on the time axis of the 

actual field dimensionless BTC, corresponding to t

D=1. The 

PE value generating the type curve that best matches the rising 

limb is considered the estimated PE. If the medium is conceptualized as a single-porosity medium and the Moench singleporosity type curve was used to match the rising limb, the 

matching is complete (Matching Method 1). This method of 

obtaining t

a

 and PE from matching the rising limb with a type 

curve also can be performed by matching the rising limb of the 

single-porosity theoretical BTC to the rising limb of the actual 

BTC. t

a

 is varied to move the theoretical BTC horizontally 

along the dimensional time axis, and PE is varied to change 

the shape of the rising limb until a good match with the rising 

limb of the actual BTC is obtained. Even for a medium that 

is well represented by the Moench single-porosity analytical 

solution, Matching Method 1 may result in a close match of 

the rising limb but not of the falling limb. The falling limb 

match may not be very good but may be good enough to assert 

that the medium is a single-porosity medium. 

If the falling limb match is not very good, it may be 

possible to improve the match by using Matching Method 

2. In this method, t

a

 and PE are varied until a loose match is 

obtained of the whole BTC. To obtain a better overall match 

of the rising and falling limbs to the whole actual BTC, t

a

 and 
Tracer Tests at the C-hole Complex 9

Figure 5. Visual match of the actual field breakthrough curve to the Moench (1989) single-porosity 

analytical solution type curve for the iodide tracer test in the Bullfrog-Tram interval (Matching Method 1).

PE can be varied such that the single-porosity type curve or 

theoretical BTC loosely matches the whole actual BTC (for 

the type-curve match, type curves of different PE values are 

overlain loosely until one with a corresponding match point 

and associated ta is chosen). This will be referred to as Matching Method 2. 

If Matching Method 2 cannot match the falling limb 

of the actual BTC, then the aquifer may be a dual-porosity 

medium and the Moench dual-porosity solution should be 

used. For a dual-porosity medium, PE also is estimated first by 

matching the rising-limb part of the type curve for either the 

single- or dual-porosity solution. The PE value generating the 

type curve that best matches the rising-limb part of the actual 

field dimensionless BTC is considered the “estimated” PE. In 

this process of estimating the PE from the rising-limb typecurve match, the assumption is made that in a dual-porosity 

aquifer, and therefore in the dual-porosity solution, diffusion 

is minimal on the rising limb of the BTC and, therefore, PE is 

the main influence on the shape of the rising limb (Moench, 

1995, p. 1831) and the single- and dual-porosity solutions are 

essentially the same. 

This process of estimating t

a

 and PE also can be performed by matching the rising limbs of either the single- or 

dual-porosity theoretical BTC to the rising limb of the actual 

BTC, such as in figure 6 for the analysis of the tracer test 

described in the following section. ta is varied to move the 

theoretical BTC horizontally along the dimensional time axis, 

and PE is varied to change the shape of the rising limb until a 

good match with the actual BTC is obtained. The falling limb 

of the actual BTC in figure 5 can be matched to a theoretical 

dual-porosity BTC with diffusion processes in which the controlling parameters include the dimensionless diffusion coefficient, GAMMA, and the SIGMA term, which is a function of 

the matrix porosity, f ́ (fig. 6). To match the falling limb, the 

optimal values of t

a

 and PE obtained from matching the rising 

limb are used, then GAMMA and SIGMA are varied and their 

values estimated from a match of the falling limb. This visual 

graphical matching process is referred to as Matching 

Method 3. 

In cases where the assumption that “in a dual-porosity 

aquifer, diffusion is minimal on the rising limb of a BTC” is 

not valid for the tracer test being analyzed, Matching Method 

3 may result in a close match for only the rising limb, and 

the tail may diverge substantially. In these cases, t

a

 and (or) 

PE may be varied from their rising-limb match values, along 

with SIGMA and GAMMA, when matching the falling limb 

(Matching Method 4). This may result in a “loose” match, but 

it generally leads to improved overall matches of the whole 

BTC, and estimates of all four parameters (t

a

, PE, SIGMA, 

GAMMA) are obtained. This match, referred to as a global 

DIMENSIONLESS CONCENTRATION 

(CONCENTRATION/MAXIMUM 

CONCENTRATION OF 98 MICROGRAMS PER LITER)

THEORETICAL DIMENSIONLESS CONCENTRATION, 

CD

THEORETICAL DIMENSIONLESS TIME, t

D

TIME SINCE TRACER INJECTION (DAYS)

Moench 

single-porosity analytical 

solution type curve

dimensionless 

breakthrough

curve

Longitudinal dispersivity (L)

Peclet number (PE)

Flow porosity (f )

2.6 meters

11

0.086 

Match Point (t

D = 1, CD = 1) Actual field

Estimated parameters
10 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Figure 6. Visual match of the actual field breakthrough curve to the Moench (1995) dual-porosity analytical 

solution for the iodide tracer test in the Bullfrog-Tram interval (Matching Method 3).

match because it does not favor matching the rising limb or the 

falling limb, can be performed visually by graphical matching 

or mathematically by the nonlinear regression technique, 

PEST, explained below. 

In summary, four methods were used to obtain matches. 

In Matching Method 1 for a single-porosity medium, t

a

 and 

PE are first obtained from a close match of the rising limb 

by using the Moench single-porosity analytical solution. The 

falling limb match may not be very good, but good enough to 

assert that the medium is a single-porosity medium. If the falling limb match is not very good, it may be possible to improve 

it by using Matching Method 2. In this method, t

a

 and PE are 

varied until a loose match is obtained of the whole BTC.

If Matching Method 2 cannot match the falling limb, then 

the Moench dual-porosity solution can be used as Matching 

Method 3 where t

a

 and PE, again, are first obtained from a 

close match of the rising limb. With these values of ta and 

PE fixed, the parameters SIGMA and GAMMA are then 

varied and their values estimated from a match of the falling 

limb. In this method, parts of the match, notably the rising 

limb, are very close and others, notably the tail, may diverge 

significantly. Only visual graphical matching (as opposed to 

PEST matching) is used in Matching Method 3.

In Matching Method 4, t

a

 and PE are first obtained from a 

close match of the rising limb with the Moench dual-porosity 

solution, as in Matching Method 3. With these values of t

a

 and 

PE used as starting values, SIGMA and GAMMA, along with 

t

a

 and (or) PE, are varied and estimates of all four parameters 

are obtained from matching the whole BTC (both rising and 

falling limbs). Even though in this method some parts of the 

match may be loose compared to Matching Method 3, the 

overall match for the whole BTC is generally better. Both 

visual graphical matching and (or) PEST matching (explained 

below) are used in Matching Method 4.

Some of the analyses of conservative tracer tests in this 

report used the single-porosity Moench solution, some used 

the dual-porosity Moench solution, and some used a combination of both, depending on the type of test. The purpose of this 

multiple-analysis approach was to ensure that the appropriate 

solution method is used in matching a particular set of data 

Actual field 

 breakthrough curve

Estimated parameters

Longitudinal dispersivity (L)

Flow porosity (f)

Moench dual-porosity

analytical solution 

(calculated at 

the solid circles)

CONCENTRATION, IN MICROGRAMS PER LITER

TIME SINCE TRACER INJECTION (DAYS)

2.6 meters

11

0.086 

0.19

Peclet number (PE)

Matrix (storage) porosity (’)
Tracer Tests in the Bullfrog and Tram Tuffs 11

and to determine whether the aquifer behaves as a single- or 

dual-porosity aquifer.

In addition to graphical matching techniques, nonlinear 

regression techniques were used in this report to match 

theoretical BTCs to actual BTCs. Nonlinear regression 

techniques have been used for many years to determine 

optimal transport parameters (for example, Umari, 1977; 

Umari and others, 1979; Wagner and Gorelick, 1986; Medina 

and Carrera, 1996; and Anderman and Hill, 1999). In this 

report, nonlinear regression techniques, in the form of a 

parameter-estimation software program (PEST; Watermark 

Computing, 1994), were used to supplement the analyses 

conducted with graphical matching techniques using the 

Moench single- and dual-porosity solutions. PEST was used 

to corroborate tracer-test solution results, to obtain optimal 

parameter values from the solutions, and to quantify parameter 

uncertainty resulting from analyzing two of the three radially 

convergent conservative tracer tests in the Bullfrog and Tram 

Tuffs. The third test had only a rising limb of the BTC and was 

not suitable for optimization by PEST. PEST was implemented 

so that it executes the Moench analytical solution. Initial 

estimates of PE, SIGMA, and GAMMA were provided to 

PEST from a visual match, and PEST was instructed to keep 

one of the three parameters constant while varying the other 

two. PEST repeatedly executed the Moench solution until 

it obtained optimal parameters that minimized the sum of 

the squares of the differences between actual and theoretical 

concentrations. PEST was always run with the ff obtained 

from the visual graphical match. The above process is referred 

to as PEST matching.

Tracer Tests in the Bullfrog and Tram 

Tuffs

Tracer tests conducted in the Bullfrog and Tram Tuffs 

at the C-holes consisted of: (1) injection of iodide into the 

combined Lower Bullfrog–Upper Tram interval, (2) injection 

of 2,6 DFBA into the Lower Bullfrog interval, and (3) injection of pyridone into the Lower Bullfrog interval. The iodide 

test was conducted while the production well, UE-25 c#3, was 

pumped continuously from February 8, 1996, to March 31, 

1996. The other two tests were conducted starting in January 

1997, and well UE-25 c#3 was pumped continuously from 

May 8, 1996, to November 12, 1997.

Iodide Tracer Test in the Lower Bullfrog–Upper 

Tram Interval

The most transmissive interval in the C-holes (the 

Bullfrog-Tram interval), the shortest interborehole distance 

(from borehole UE-25 c#2 to borehole UE-25 c#3), and the 

simplest flow field (a radially convergent flow field) were 

selected for the first tracer test at the C-holes to enhance the 

possibility of successful tracer recovery (see fig. 1). Following 

establishment of a quasi-steady-state hydraulic gradient by 

pumping the production well (UE-25 c#3) for about 7,000 

minutes (4.86 days), the first tracer test at the C-hole Complex 

was initiated in the Bullfrog-Tram interval on February 13, 

1996, under convergent flow field conditions (also discussed 

in Fahy, 1997). Tracer solution was injected into the packedoff Bullfrog-Tram interval (about 170 m thick, fig. 3) of 

borehole UE-25 c#2 for 28 minutes at an average rate of 0.41 

liter per second (L/s). 

The tracer solution consisted of 5.9 kilograms (kg) of 

sodium iodide (of which 5.0 kg was iodide) dissolved in 500 

L of water from borehole UE-25 c#3. Chemical analysis 

indicated that the tracer solution had an iodide concentration 

of 10,200 milligrams per liter (mg/L). The tracer solution 

was chased with 182 L of water from UE-25 c#3, which was 

pumped into borehole UE-25 c#2 to enhance the evacuation 

of the tracer slug out of the borehole and into the aquifer. The 

tracer was detected in samples from borehole UE-25 c#3 5.07 

days after injection, and the average peak concentration of 

approximately 98 mg/L occurred 17.8 days after injection. The 

test was terminated on March 29, 1996, 45.1 days after injection. The mass recovered was estimated as 2.35 kg, about 47 

percent of the injected mass.

The tracer test was complicated by progressively decreasing discharge from the recovery well, which was caused by 

a mechanically failing pump. The pump discharge decreased 

from 8.5 L/s on February 13, 1996, to 6.2 L/s on March 29, 

1996 (Bechtel-SAIC Company, 2003, section 6.3.5.1). For 

analysis, the average value of 7.4 L/s was used as the discharge rate. Despite this problem, a recovery curve, with 

breakthrough and peak arrival times readily discernible, was 

established clearly by March 29, 1996 (figs. 5, 6, 7).

Both the single- and dual-porosity Moench solutions 

(Moench, 1989, 1995) were used to interpret this test. The rising limb was first analyzed using the single-porosity solution 

and Matching Method 1 to obtain t

a

 (and, through equation 

1, ff ) and the Peclet number (fig. 5). The falling limb did 

not match well, so the dual-porosity solution and Matching 

Method 3 then were used with these estimated parameter 

values to match the falling limb (fig. 6) to obtain GAMMA 

and SIGMA, the latter a function of the matrix porosity. Input 

parameters and results are:

•	 discharge rate of 7.4 L/s

•	 aquifer thickness 51.2 m, equal to the transmissive 

thickness of the Bullfrog-Tram interval between boreholes UE-25 c#2 and UE-25 c#3 (Geldon and others, 

2002, table 8, p. 35)

•	 Peclet number of 11, which corresponds to a longitudinal dispersivity (αL

) of about 2.6 m (figs. 5 and 6)

•	 advection traveltime, t

a

, of 18.5 days
12 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

•	 flow porosity, ff , estimated as 0.086. This flow porosity estimate is high if fractures are considered as the 

only pathway. Typical fracture porosities range from 

10–2 to 10–5 (see, for example, Freeze and Cherry, 1979, 

p. 408). The high flow-porosity value indicates that a 

composite pathway occurs for the iodide; that is, the 

fracture network is not connected well at the scale 

of the test. The solute travels through a connectedfracture-network segment, then through a segment of 

matrix until it reaches the next connected-fracturenetwork segment

•	 using Matching Method 3 and matching the falling 

limb (fig. 6) results in an estimate of GAMMA = 

0.04, and SIGMA = 2.0, the latter resulting in an 

estimate of 0.19 for the matrix (storage) porosity (φ ́) 

This estimated matrix porosity is reasonable based on 

geophysical logging conducted at the C-hole Complex 

that resulted in a range of total porosity (sum of matrix 

and flow porosity) from 0.12 to 0.43 (Geldon, 1993, 

p. 60–62)

In addition to the best visual graphical matches of figures 

5 and 6 presented above, the parameter-estimation program 

PEST (Watermark Computing, 1994) was used to obtain a 

match by minimizing the sum of squares of the differences 

between actual and theoretical concentrations. The PEST 

analysis, consisting of several runs, started with the values 

resulting from the visual graphical match presented in figure 

6, which are: PE = 11, SIGMA = 2.0, and GAMMA = 0.04. 

Each run varied one of these parameters while the others were 

held constant. In the first run, PEST was given the values 

Figure 7. PEST-optimized match of the actual field breakthrough curve to the Moench (1995) 

dual-porosity analytical solution for the iodide tracer test in the Bullfrog-Tram interval (Matching 

Method 4).

TIME SINCE TRACER INJECTION (DAYS)

Actual field 

dimensionless

breakthrough

curve

Moench dual-porosity analytical solution

using optimized parameter values

from PEST analysis (calculated at the solid circles)

Initial parameter estimates from the visual match of these data (fig. 6)

Other estimated parameters

PEST-optimized parameter results (with 95-percent confidence intervals)

Longitudinal dispersivity (L)

Flow porosity (f ) 

Matrix (storage) porosity (’) 

Peclet number (PE)

Dimensionless storage coefficient (SIGMA)

2.52 meters

11.478 (11.228–11.728)

1.717 (1.435–2.000)

Dimensionless diffusion 

 coefficient (GAMMA)

0.03565 (0–0.1274)

EXPLANATION

0.086 

0.16

DIMENSIONLESS CONCENTRATION

(CONCENTRATION/MAXIMUM CONCENTRATION OF 98 

MICROGRAMS PER LITER) AND 

THEORETICAL DIMENSIONLESS CONCENTRATION
Tracer Tests in the Bullfrog and Tram Tuffs 13

PE = 11, SIGMA = 1.0 (changed from its best-visual-match 

value of 2.0), and GAMMA = 0.04, and only SIGMA could 

be changed. PEST values for PE, SIGMA, and GAMMA are 

more accurate than visual match values and are, therefore, 

given to 5 significant figures for PE and 4 for SIGMA and 

GAMMA, as opposed to 2 for visual match values. PEST 

converged on an optimal value of SIGMA = 1.717. In the 

second run, PEST was given the values PE = 8 (changed 

from its best-visual-match value of 11), SIGMA = 1.717, and 

GAMMA = 0.04, and only PE could be changed. PEST converged on an optimal value of PE = 11.478. In the third run, 

PEST was given the values PE = 11.478, SIGMA = 1.717, and 

GAMMA = 1.0 (changed from its best-visual-match value of 

0.04), and only GAMMA could be changed. PEST converged 

on an optimal value of GAMMA = 0.03565. The PEST match 

of the Moench dual-porosity solution using the above optimal 

values to the actual BTC and the associated confidence intervals of the optimal values are shown in figure 7.

The estimated parameters resulting from the visual 

graphical match of figure 6 and the PEST match of figure 7 

are quite close. The Peclet number and dispersivity estimates 

vary by approximately 4 percent. The visual-graphical-match 

matrix porosity estimate is 0.19, and the PEST match estimate 

is 0.16. The difference in values is attributed to the different emphasis given to fitting portions of the BTC. Matching 

method 3 was used for the visual graphical match of figure 6, 

where the rising limb is used exclusively to estimate the Peclet 

number and the advection traveltime, and then the advection 

traveltime is used to estimate the flow porosity. Matching 

Method 4 was used for the PEST match of figure 7, where the 

match is optimized to both rising- and falling-limb data. This 

results in slightly different matches. The transport properties 

obtained from the conservative tracer testing in the BullfrogTram interval for the iodide test from borehole UE-25 c#2 to 

UE-25 c#3 with radially convergent flow are summarized in 

table 2. 

2,6 Difluorobenzoic Acid Tracer Test in the 

Lower Bullfrog Interval

On January 10, 1997, a radially convergent conservative 

tracer test was initiated between the same boreholes as the 

iodide tracer test, UE-25 c#2 to UE-25 c#3, but only in the 

97-m-thick Lower Bullfrog interval. Approximately 11.4 kg of 

2,6 DFBA, dissolved in 795 L of water from borehole UE-25 

c#3, was injected for 28 minutes at an average rate of 0.52 

L/s into the Lower Bullfrog interval in borehole UE-25 c#2, 

followed by 238 L of rinsate (from rinsing the tracer-solution 

tank) and chase water from a tank of water previously pumped 

from UE-25 c#3. Chemical analysis indicated that the 2,6 

DFBA injectate solution had a concentration of 15,560 mg/L.

Breakthrough of the tracer occurred at borehole 

UE-25 c#3 on January 15, 1997, 5.07 days after injection, and 

the peak concentration of approximately 251 mg/L occurred 

13.5 days after injection. The average discharge rate was 9.47 

L/s. The mass recovered was estimated as 7.6 kg, which is 

approximately 67 percent of the injected mass.

Interpretation of the 2,6 DFBA test using the Moench 

(1995) dual-porosity analytical solution for radially convergent 

Table 2. Selected breakthrough results and estimated transport properties from radially convergent tracer tests conducted in the 

Bullfrog and Tram Tuffs at the C-hole Complex, 1996 to 1997.

[DFBA, difluorobenzoic acid; μg/L, micrograms per liter; m, meter; PEST, parameter-estimation software program, Watermark Computing (1994); na, not 

available]

Parameter

Iodide test from 

UE-25 c#2 to 

UE-25 c#3 in 

Lower BullfrogUpper Tram interval

2,6 DFBA test from 

UE-25 c#2 to 

UE-25 c#3 in 

Lower Bullfrog 

interval

Pyridone test from 

UE-25 c#1 to 

UE-25 c#3 in 

Lower Bullfrog 

interval

Breakthrough (days) 5.07 5.07 77.0

Peak concentration (μg/L) 98 251 0.252

Visual 

match

PEST 

match

Visual 

match

PEST 

match

Longitudinal dispersivity (m) 2.6 2.52 1.9–2.4 1.83 na

Peclet number 11 11.478 12–15 15.795 na

Flow porosity, φf 0.086 0.086a 0.072–0.099 0.072a na

GAMMA (dimensionless 

 matrix-diffusion coefficient) 0.04 3.565×10–2 0.12 0.1179 na

Storage or matrix porosity, φ’ 0.19 0.16 0.088–0.13 0.15 na

a

Flow porosity fixed in PEST runs to visual match values.
14 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Figure 8. Visual match of the actual field breakthrough curve to the Moench (1995) dual-porosity 

analytical solution type curve for the 2,6 difluorobenzoic acid (DFBA) tracer test in the Lower 

Bullfrog interval (Matching Method 3). CONCENTRATION, IN MICROGRAMS PER LITER

TIME SINCE TRACER INJECTION (DAYS)

Actual field breakthrough curve

Moench dual-porosity analytical solution

(calculated at the solid circles)

Estimated parameters

Longitudinal dispersivity (L) 

Peclet number (PE)

Flow porosity (f) 

Matrix (storage) porosity (’)

12

0.088

2.4 meters

 0.099

Figure 9. Visual match of the actual field breakthrough curve to the Moench (1995) dual-porosity 

analytical solution for the 2,6 difluorobenzoic acid (DFBA) tracer test in the Lower Bullfrog interval 

(Matching Method 3).

DIMENSIONLESS TIME, t

D

TIME SINCE TRACER INJECTION (DAYS)

THEORETICAL DIMENSIONLESS 

CONCENTRATION, 

CD

Actual field 

dimensionless

breakthrough 

curve

Moench dualporosity

analytical 

solution

type curve

Estimated parameters

Longitudinal dispersivity (L)

Peclet number (PE)

Flow porosity (f)

Matrix (storage) porosity (’)

2.4 meters

12

0.099 (9.9x10-2)

0.088 (8.8x10-2)

DIMENSIONLESS CONCENTRATION 

(CONCENTRATION/MAXIMUM 

CONCENTRATION OF 98 

MICROGRAMS PER LITER)
Tracer Tests in the Bullfrog and Tram Tuffs 15

Figure 10. Visual match of the actual field breakthrough curve to the Moench (1995) dual-porosity 

analytical solution for the 2,6 difluorobenzoic acid (DFBA) tracer test in the Lower Bullfrog interval 

(Matching Method 4).

flow produced the following input parameters and results 

(figs. 8 and 9 use Matching Method 3 and fig. 10 uses 

Matching Method 4):

•	 discharge rate of 9.47 L/s

•	 aquifer thickness of 51.2 m, approximately equal to the 

average transmissive thickness of the Lower Bullfrog 

interval between boreholes UE-25 c#2 and UE-25 c#3 

(fig. 3)

•	 Peclet number between 12 and 15 (figs. 8, 9, 10)

•	 advection traveltime between 12 and 16.5 days

•	 flow porosity between 0.072 and 0.099 (figs. 8, 9, 10) 

•	 matrix porosity between 0.088 and 0.13 (figs. 8, 9, 10) 

•	 longitudinal dispersivity between 1.9 and 2.4 m (figs. 

8, 9, 10) 

The range of values shown in figures 9 and 10 reflects 

two approaches for the matching process. The Peclet number 

of 12, flow porosity of 0.099, matrix porosity of 0.088, and 

a dispersivity of 2.4 m, obtained using Matching Method 3, 

reflect matching the rising limb of the BTC and honoring the 

initial decline closely (figs. 8 and 9). At longer times, the data 

and the match diverge, possibly indicating secondary arrivals 

from longer residence-time flow pathways. The approach 

in figure 10 is to match the rising limb of the BTC and 

reasonably match the complete declining portion of the curve 

using Matching Method 4.

The program PEST was applied to the 2,6 DFBA test 

results by starting with the visual graphical fit to the BTC 

presented in figure 10, for which PE = 15, SIGMA = 1.7, and 

GAMMA = 0.12. Three PEST runs were made, each with 

one of these parameters changed from the above values while 

the others were held constant. In the first run, PEST was 

given PE = 15, SIGMA = 3.0 (intentionally changed from its 

best-visual-match value of 1.7), and GAMMA = 0.12, and it 

was allowed to change only SIGMA. At the end of this run, 

PEST converged on an optimal value of SIGMA = 1.878 and 

an associated confidence interval for SIGMA. In the second 

run, PEST was given the values PE = 8 (intentionally changed 

from its best-visual-match value of 15), SIGMA = 1.878 and 

GAMMA = 0.12, and it was allowed to change only PE. At 

the end of this run, PEST converged on an optimal value of 

PE = 15.795 and an associated confidence interval for PE. 

In the third run, PEST was given the values PE = 15.795, 

SIGMA = 1.878, and GAMMA = 1.0 (intentionally changed 

Actual field 

breakthrough curve

Moench dual-porosity

analytical solution

(calculated at the solid circles)

TIME SINCE TRACER INJECTION (DAYS)

CONCENTRATION, IN MICROGRAMS PER LITER

Estimated parameters

Longitudinal dispersivity (L

)

Peclet number (PE)

Flow porosity (f )

Matrix (storage) porosity (’)

1.9 meters

15

0.072

0.13
16 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

from its best-visual-match value of 0.12), and it was allowed 

to change only GAMMA. At the end of this run, PEST 

converged on an optimal value of GAMMA = 0.1179 and an 

associated confidence interval for GAMMA. These optimal 

values, their associated confidence intervals, and the fit to the 

actual BTC that they produce, are presented in figure 11.

The visual graphical match parameters and the PEST 

match parameters are quite close. The Peclet number and 

dispersivity estimates vary by approximately 5 percent as can 

be seen by comparing figures 10 and 11. The visual graphical 

match matrix-porosity estimate is between 0.088 and 0.13, 

and the PEST match estimate is 0.15.

Pyridone Tracer Test in the Lower Bullfrog 

Interval

On January 9, 1997, approximately 3.02 kg of pyridone, 

mixed with about 795 L of water from borehole UE-25 c#3, 

was injected into borehole UE-25 c#1, followed by 252 L of 

rinsate and chase water from UE-25 c#3 to test the Lower 

Bullfrog interval. This injection was made while UE-25 c#3, 

the production well, was being pumped at an average rate 

of 9.53 L/s. A total of about 2,080 L of fluid was injected, 

the first part of which was the fluid in the injection string 

Figure 11. PEST-optimized match of the actual field breakthrough curve to the Moench (1995) dual-porosity 

analytical solution for the 2,6 difluorobenzoic acid (DFBA) tracer test in the Lower Bullfrog interval (Matching 

Method 4).

Actual field dimensionless 

breakthrough curve

Moench dual-porosity

analytical solution

using optimized parameter

values from PEST analysis 

(calculated at the solid circles)

TIME SINCE TRACER INJECTION (DAYS)

Initial parameter estimates from the visual match of these data (fig. 10)

Other estimated parameters

PEST-optimized parameter results (with 95-percent confidence intervals)

Longitudinal dispersivity (L )

Flow porosity (f )

Matrix (storage) porosity (’)

Peclet number (PE)

Dimensionless storage 

 coefficient (SIGMA)

1.83 meters

15.795 (15.500–16.091)

1.878 (1.655–2.101)

Dimensionless diffusion 

 coefficient (GAMMA)

0.1179 (0.01741–0.2185)

0.072 

0.15

EXPLANATION

DIMENSIONLESS CONCENTRATION 

(CONCENTRATION/MAXIMUM CONCENTRATION OF 251

MICROGRAMS PER LITER) AND THEORETICAL 

DIMENSIONLESS CONCENTRATION
Tracer Tests in the Prow Pass Tuff 17

preceding the injectate solution. The average injection rate 

was 0.38 L/s. Chemical analysis using the HPLC method 

indicated that the pyridone injectate solution had an average 

concentration of about 3,000 mg/L (or 3×106 mg/L). 

Breakthrough of the tracer at UE-25 c#3 occurred on 

March 27, 1997, 77.0 days after injection (fig. 12). The concentration of pyridone in samples continued to increase, but 

at a decreasing rate, and the test was terminated on November 

12, 1997, before a clear peak in concentration was observed. 

Except for very high concentrations at the time of breakthrough (up to about 0.8 mg/L), the maximum concentration 

of pyridone was 0.252 mg/L, as of July 10, 1997, which was 

determined by analyses in the laboratory where detection limits were much lower (0.01 mg/L) than the field detection limit 

of 0.1 mg/L. Because the pyridone test was terminated before 

a peak concentration was reached, no definitive analysis of the 

test could be made.

Tracer Tests in the Prow Pass Tuff

Tracer tests conducted in the Prow Pass Tuff at 

the C-holes Complex consisted of injection of 2,4,5 

trifluorobenzoic acid (TFBA) and iodide in the first test, and 

2,3,4,5 tetrafluorobenzoic acid (TeFBA) in the second test. 

The tracers were injected into borehole UE-25 c#3 in the first 

test and into borehole UE-25 c#1 in the second, with borehole 

UE-25 c#2 as the production well for both. Parameter values 

obtained from the conservative tracer testing in the Prow Pass 

Tuff are discussed in this section (table 3).

2,4,5 Trifluorobenzoic Acid and Iodide Test from 

Borehole UE-25 c#3 to UE-25 c#2

On June 17, 1998, a partially recirculating conservative 

tracer test was initiated from borehole UE-25 c#3 to UE-25 

c#2 by injecting approximately 14.8 kg of 2,4,5 trifluorobenzoic acid (2,4,5 TFBA) and 12.3 kg of iodide (in the form 

of 14.6 kg of sodium iodide) into the Prow Pass interval of 

UE-25 c#3, while UE-25 c#2 was pumped at an average rate 

of approximately 0.33 L/s. The concentration of 2,4,5 TFBA, 

as determined from HPLC analyses, was about 14,200 mg/L 

in the injected slug and that of sodium iodide about 14,300 

mg/L. About 0.095 L/s of the approximately 0.33 L/s pumped 

from UE-25 c#2 was piped and continuously reinjected into 

the Prow Pass interval of UE-25 c#3.

0 20 40 60 80 100 120 140 160 180 200

0

0.1

–0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CONCENTRATION, IN MICROGRAMS PER LITER

TIME SINCE TRACER INJECTION (DAYS)

Figure 12. Breakthrough curve for the pyridone tracer test in the Lower Bullfrog interval from January 9 to July 10, 1997.
18 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Figure 13. Actual field breakthrough curves for the partially recirculating 2,4,5 trifluorobenzoic 

acid (TFBA) and iodide tracer test in the Prow Pass interval.

Table 3. Selected breakthrough results and estimated transport properties from partially recirculating tracer tests conducted in 

the Prow Pass Tuff at the C-hole Complex, 1998.

[TFBA, trifluorobenzoic acid; TeFBA, tetrafluorobenzoic acid; m, meter; mg/L, milligrams per liter; na, not available; --, not applicable for singleporosity solution]

Parameter

2,4,5 TFBA & iodide test from 

UE-25 c#3 to UE-25 c#21 2,3,4,5 TeFBA 

test from 

UE-25 c#1 to 

UE-25 c#22

Single-porosity, 

radially convergent 

solution (Matching 

Method 2)

Single-porosity, partially recirculating 

solution (Matching 

Method 2)

Dual-porosity, partially 

recirculating solution 

(Matching Method 4)

Longitudinal dispersivity (m) 1.4 0.27 0.27 na

Peclet number 20 107 107 na

Flow porosity, φf

7×10–4 4.5×10–4 4.5×10–4 na

GAMMA (dimensionless 

matrix-diffusion 

 coefficient)

-- -- 4.4×10–4 to 0.001 na

Storage or matrix porosity, φ’ -- -- 0.01 na

1Breakthrough 1.67 days; peak concentration for TFBA, 3.81 mg/L and for iodide, 2.55 mg/L.

2Breakthrough 17 days; peak concentration for TeFBA, 0.10 mg/L.

2,4,5 TFBA

Iodide

TIME SINCE TRACER INJECTION (DAYS)

CONCENTRATION, IN MILLIGRAMS PER LITER
Tracer Tests in the Prow Pass Tuff 19

Approximately 40 hours (1.67 days) after the injection, 

breakthrough of both tracers occurred in UE-25 c#2. The peak 

for the 2,4,5 TFBA occurred 6.74 days after injection, and the 

peak for iodide about 7 days after injection (fig. 13).

The 2,4,5 TFBA and iodide BTCs were analyzed using 

the single- and (or) dual-porosity analytical solutions of the 

advection-dispersion equation for a hypothetical radially 

convergent flow field as given in Moench (1989, 1995). These 

solutions also were modified by lagging and superposing to 

obtain the solution for the actual partially recirculating flow 

field. The curves were first analyzed assuming Moench’s 

single-porosity solution for both the radially convergent 

and the partially recirculating flow field assumptions, using 

the entire curves for the fits, to obtain estimates of the flow 

porosity and longitudinal dispersivity for a single-porosity 

medium (figs. 14, 15). The curves then were analyzed 

assuming a dual-porosity medium and a partially recirculating 

flow field, also using the entire curves for the match to obtain 

estimates of longitudinal dispersivity, flow porosity, GAMMA, 

and storage porosity. 

The flow porosity and longitudinal dispersivity are different for each of the solutions presented. All the solutions used 

the following input test-configuration parameters:

•	 average discharge rate of about 0.33 L/s

•	 recirculation rate of about 0.095 L/s

•	 aquifer thickness of about 61 m, the average Prow Pass 

thickness in UE-25 c#1 and UE-25 c#3 (calculated 

from Geldon and others, 2002, table 1)

•	 distance of about 29 m in the Prow Pass between injection and pumping wells (Geldon and others, 2002, 

table 1) based on borehole location at depth, not the 

surface

•	 radii of 14.0 cm for injection and pumping wells 

(Geldon, 1993, p. 7 and 10)

•	 borehole mixing length of 30.5 m (assumption discussed in the following section)

Single-Porosity, Radially Convergent Solution

The single-porosity, radially convergent solution is 

obtained directly from the Moench (1989) solution to the 

advection-dispersion equation. A best visual graphical match 

using the Moench single-porosity solution corresponding to 

flow porosity and longitudinal dispersivity values of about 

7×10–4 and 1.4 m, respectively, is presented in figure 14, along 

Figure 14. Visual match of the actual field breakthrough curves to the Moench (1989) single-porosity 

analytical solution for radially convergent flow for the 2,4,5 trifluorobenzoic acid (TFBA) and iodide 

tracer test in the Prow Pass interval (Matching Method 2).

2,4,5 TFBA

actual field 

dimensionless 

breakthrough 

curve

(cmax = 3.81 milligrams

per liter) Moench single-porosity analytical

solution (calculated at the

open diamonds)

Iodide actual field 

dimensionless breakthrough 

curve (cmax = 2.55 milligrams

per liter)

TIME SINCE TRACER INJECTION (days)

Estimated parameters

Peclet number (PE)

1.4 meters

20

Longitudinal dispersivity (L)

7x10 Flow porosity ( –4 f

)

DIMENSIONLESS CONCENTRATION

(CONCENTRATION/MAXIMUM CONCENTRATION) AND 

THEORETICAL DIMENSIONLESS CONCENTRATION
20 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

with the normalized 2,4,5 TFBA and iodide BTCs. This longitudinal dispersivity value and flow length of about 29 m (flow 

length is equal to the distance between injection and pumping wells in a radially convergent tracer test) corresponds to a 

Peclet number of about 20.

The estimated longitudinal dispersivity and flow porosity 

values obtained from the best visual graphical match of figure 

14 may be sensitive to the mixing lengths assumed for the 

injection and production wells. The 30.5-m mixing length 

assumed for all Prow Pass solutions equals the thickness of 

the transmissive interval within the packed-off Prow Pass 

interval and, as such, is consistent with the hydrogeology of 

the interval (Geldon and others, 2002, table 8). 

The residence time of the tracer slug within the injection 

borehole is directly proportional to the mixing length. The 

concentration measured in water samples from the injection 

interval (obtained from an injection-interval mixing system 

that brought interval water to the surface and then back to the 

interval) rose from below detection limit to 2,721 mg/L and 

then back to below detection limit in 8.5 hours (Bechtel-SAIC

Company, 2003, section 6.3.1.2.1.1). When the mixing length 

is reduced to 0.3 m and only the rising limb of the actual BTC 

is matched to the theoretical BTC from the single-porosity 

solution of Moench (1989), a longitudinal dispersivity value of 

about 4.3 m and a flow porosity value of 0.0016 are obtained 

as estimated parameters. Changing the mixing length from 

30.5 m to 0.3 m constitutes a two-orders-of-magnitude change 

Figure 15. Visual match of the actual field breakthrough curves to the modified Moench (1989) singleporosity analytical solution, modified for partially recirculating flow, for the 2,4,5 trifluorobenzoic acid 

(TFBA) and iodide tracer test in the Prow Pass interval (Matching Method 2).

Iodide (cmax = 2.55 milligrams per liter)

actual field dimensionless 

breakthrough curve

Modified Moench single-porosity

analytical solution, modified for partially

recirculating flow

actual field dimensionless 

breakthrough curve

TIME SINCE TRACER INJECTION (DAYS)

DIMENSIONLESS CONCENTRATION

(CONCENTRATION/MAXIMUM CONCENTRATION) AND 

THEORETICAL DIMENSIONLESS CONCENTRATION

2,4,5 TFBA (cmax = 3.81 milligrams per liter)

Estimated parameters

Three interstreamline pathways were 

 assumed with delay factors of 2.01, 2.99, 

 and 3.11 days

Peclet number (PE)

0.27 meter

107

Longitudinal dispersivity (L)

4.5x10–4

30.5 meters

Initial flow porosity (f ) (assumed for 

 all three pathways)

Borehole mixing length

EXPLANATION
Tracer Tests in the Prow Pass Tuff 21

in this parameter. Corresponding to this change in the assumed 

mixing length, the estimates of longitudinal dispersivity 

and flow porosity change from about 1.4 m and 7×10–4 (for 

a 30.5-m mixing length) to 4.3 m and 0.0016 (for a 0.3-m 

mixing length). This is a threefold change in longitudinal 

dispersivity and a twofold change in flow porosity, both less 

than one order of magnitude. These two estimated parameters, 

therefore, are not very sensitive to the mixing length.

The flow porosity value of 7×10–4 is within the range of 

10–2 to 10–5 cited in the literature to represent fracture porosity (see, for example, Freeze and Cherry, 1979, p. 408). This 

implies that the flow network for this test in the Prow Pass 

Tuff is composed predominately of fractures.

Single-Porosity, Partially Recirculating Solution

When the radially convergent flow-field assumption of 

figure 14 is replaced by a partially recirculating flow field, the 

resulting solution to the advection-dispersion equation changes 

from the curve labeled “Moench single-porosity analytical 

solution” in figure 14 to the curve labeled “Modified Moench 

single-porosity analytical solution” shown in figure 15. The 

difference between the two solutions reflects the difference 

in flow-field representation and in the estimated values of 

longitudinal dispersivity and flow porosity used for each 

solution. 

Two elements of partially recirculating flow are represented in this solution: the flow field and the reinjected tracer 

concentration. Rather than the straight streamlines converging 

into the pumped well for the radially convergent flow field, the 

partially recirculating flow-field streamlines that are within 

the capture zone of the pumped well emanate in all directions from the injection well but then curve around toward the 

pumped well (fig. 16A). The streamlines shown in figure 16A

are lines of equal stream function values, where the stream 

function of the partially recirculating field is calculated as the 

sum of the stream functions of a 0.33 L/s sink (the approximate production rate) and a 0.095 L/s source (the approximate 

recirculation rate), about 29 m apart. The rock mass between 

pairs of these curved streamlines emanating from the injection well and curving toward the production well constitute 

distinct pathways for the tracer to take from the injection to 

the pumped well. 

Three such interstreamline pathways emanating from 

the injection well and curving toward the production well 

(fig. 16A) are assumed for the partially recirculating flow 

analysis in this report. These pathways, labeled Interstreamline 

pathways 1, 2, and 3 in figure 16A, and the three nonlabeled 

pathways that are mirror images of them around the horizontal 

line of symmetry (Interstreamline pathway 1 and its mirror 

image are combined in fig. 16A), carry most of the tracer 

mass from injection to production well (in figure 16A mass 

leaving c#3 directly to the left [in the negative x direction] 

is eventually captured in c#2 after being deflected at the 

stagnation point [not shown] and is ignored). Symmetry 

allows that the analysis be restricted to only three of the 

six interstreamline pathways emanating from the injection 

well and curving toward the production well, namely 

Interstreamline pathways 1, 2, and 3; and that half of the mass 

of the tracer and half the reinjection flow rate be carried by 

these three pathways. 

The Moench (1989) single-porosity, radially convergent 

solution is viewed as the solution of the advection-dispersion 

equation along a single straight pathway (fig. 16B). This solution for a particular longitudinal dispersivity value, and for a 

single flow porosity value that initially is assumed to apply to 

all three pathways (as opposed to the interpretation of three 

different porosity values presented later) is applied to each 

of the above three distinct pathways. Because the Moench 

solution is for a strictly convergent flow field, its application 

to the first-diverging-then-converging flow pattern (partially 

recirculating) within Interstreamline pathways 1, 2, and 3 

in figure 16A is an approximation and will introduce some 

error. A delay factor (the advection traveltime calculated from 

the volume of rock of each pathway, the flow rate within the 

pathway, and the assumed porosity) is used to account for the 

differences in lengths, or swept volumes, of these pathways 

relative to the straight radially convergent pathway, and half of 

the injected mass is distributed among the three pathways in 

proportion to the flow in each of them. 

The solutions from Moench (1989) for a particular longitudinal dispersivity value, an initial value of flow porosity 

(assumed to be the same for all three pathways), and assuming 

an instantaneous-slug injection are then superimposed with 

delay factors (previously defined) to calculate what is considered to be the system’s unit response function. The summed 

curve represents what is seen at the pumped well in response 

to an instantaneous input function at the injection well in a 

partially recirculating flow field.

The second element of partial recirculation is that the 

reinjected water contains a concentration of the tracer; so, 

the tracer is continuously reintroduced into the aquifer. For 

the calculations presented here, it was estimated that this lag 

duration is approximately 1 hour—the estimated time of travel 

of the recirculated fluid in the 2.54 cm (1-inch) coil-tubing 

return line from the production well, c#2, to the injection well, 

c#3 (536 m at 5.7 L/min in Bechtel-SAIC Company, 2003, 

section 6.3.1.2.1.2). The injection concentration curve is then 

convolved (Levenspiel, 1972) with the unit response function 

to produce the calculated BTC for the partially recirculating 

flow field at the pumped well. This calculated BTC is then 

compared visually to the actual BTC to evaluate the goodness of the flow porosity and longitudinal dispersivity values 

assumed. Different values of flow porosity and longitudinal 

dispersivity are tried until the visual difference between calculated and actual BTCs is minimized. The values resulting 

in the minimum difference between the two curves are called 

the “optimal” values of this qualitative, visual, trial-and-error 

parameter-estimation process.

Using this process, a longitudinal dispersivity of 0.27 m 

(PE about 107) and an initial flow porosity of 4.5×10–4

assumed to be the same for all three pathways, which result 
22 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

DISTANCE, IN FEET

DISTANCE, IN FEET

DISTANCE, IN FEET DISTANCE, IN FEET 

A

B

Figure 16. Comparison of ground-water streamlines around UE-25 c#2 (production well) and 

UE-25 c#3 (injection well) for: (A) partially recirculating flow field; (B) radially convergent flow 

field.
Tracer Tests in the Prow Pass Tuff 23

in the calculated partially recirculating BTC presented in 

figure 15, were obtained as the “optimal” parameters for the 

single-porosity, partially recirculating case (as opposed to 

the 1.4 m and 7×10–4 optimal values estimated for the singleporosity, radially convergent solution).

The delay factors for the three interstreamline pathways 

inherent in the calculation of the BTC of figure 15 were 

initially assumed to be 1.83 days for the first pathway, 3.5 days 

for the second, and about 7.5 days for the third. (These are 

the advection traveltimes calculated from the volume of rock 

of each pathway, the assumed same initial porosity value for 

all three pathways, and the flow rate within each pathway.) 

However, use of these delay factors produced a calculated 

BTC that did not fit the actual BTC. The fit was substantially 

improved by changing the delay factors to 2.01 days, 

2.99 days, and 3.11 days, which resulted in the calculated 

BTC of figure 15. Because these three delay factors are not the 

ones indicated by the volumes of rock calculated for the three 

interstreamline pathways, they are interpreted to represent 

the uncertainty in either the same initial flow-porosity value 

assumed for all three pathways or in the assumed streamline 

pattern and resulting rock volumes. If the streamline pattern 

with associated rock volumes is assumed correct, then the 

delay factors of 2.01, 2.99, and 3.11 days correspond to flow 

porosities of about 0.0005, 0.0004, and 0.0002 for the three 

interstreamline pathways, respectively. However, because 

different porosities for the three pathways is not compatible 

with the underlying homogeneity assumption, the three 

porosities provide a range of uncertainty for the single porosity 

estimate of 4.5×10–4 used for all partially recirculating cases.

The results shown in figures 14 and 15 indicate that if the 

BTCs of 2,4,5 TFBA and iodide are analyzed as if they result 

from a radially convergent flow field, ignoring that the real 

flow field is partially recirculating, some error in the estimated 

parameters occurs. A longitudinal dispersivity of about 1.4 m 

is obtained when radially convergent conditions are assumed, 

approximately 5 times the 0.27 m obtained when the partially 

recirculating flow field is recognized. The flow porosity of 

about 7×10–4 obtained for radially convergent conditions is 

about 1.6 times the initial flow porosity of 4.5×10–4 obtained 

for partially recirculating conditions. 

The partially recirculating solution shown in figure 15 

(and other tests in the Prow Pass Tuff section) does not match 

the actual BTCs as well as the radially convergent solution of 

figure 14, even though the latter ignores the flow field created by partial recirculation. This could mean either that the 

explicit representation of the partially recirculating flow field 

is not important and that the test can be analyzed successfully 

as a radially convergent tracer test, or that the homogeneous 

and isotropic representation of the partially recirculating flow 

field presented here does not represent the actual partially 

recirculating flow field very well. Perhaps increasing the 

number of the interstreamline pathways beyond three to, in 

effect, “discretize” the flow field more finely would improve 

the matches. A fourth interstreamline pathway capturing the 

ignored mass between interstreamline pathway 3 and the stagnation point may improve the matches. 

Dual-Porosity, Partially Recirculating Solution

The calculated dual-porosity, partially recirculating solution uses the same parameter values as the single-porosity, 

partially recirculating solution presented: a longitudinal dispersivity of 0.27 m and the same initial flow porosity value of 

4.5×10–4 for all three pathways. Two calculated BTCs obtained 

for a matrix (storage) porosity of 0.001 and two dimensionless matrix-diffusion coefficients (GAMMA) of 4.4×10–4 and 

0.001, are presented in figure 17, along with the actual BTCs 

of 2,4,5 TFBA and iodide. 

The effect of changing GAMMA on the shape of the falling limb of the theoretical BTC depends on the matrix (storage) porosity. For two tracers traveling in the same medium 

under the same testing configuration, the ratio of the dimensionless matrix-diffusion coefficient, GAMMA, for the two 

tracers is the same as the ratio of their free-water molecular 

diffusion coefficients (Moench, 1995, table 1). The free-water 

molecular diffusion coefficients of 2,4,5 TFBA and iodide 

are 8.0×10–6 cm2/s and 18×10–6 cm2/s, respectively (Bowman, 

1984, table 2; Skagius and Neretnieks, 1986, tables 2 and 3), 

which corresponds to a ratio of 8/18 or 1:2.25 (TFBA: iodide). 

GAMMA values of about 4.4×10–4 and 0.001 were chosen for 

figure 17 because they provide the best visual match for the 

BTCs in the figure and have the 1:2.25 ratio. 

Figure 17 shows the effects on matrix diffusion, as represented by the two calculated BTCs, of changing GAMMA by 

a factor of 2.25 for a fixed matrix (storage) porosity of 0.001

and the fixed flow rate of the test. The effect of increasing the 

free-water molecular diffusion coefficient, which increases 

GAMMA, causes a delay of the calculated BTC for higher 

GAMMA relative to the BTC for lower GAMMA. This “differential matrix-diffusion delay” is seen as a horizontal offset 

between the two calculated BTCs in figure 17. The larger the 

difference in GAMMA between the two curves, the larger the 

differential matrix-diffusion delay.

Furthermore, the differential matrix-diffusion delay 

for a particular pair of free-water molecular diffusion coefficients (or GAMMA values) increases with increasing matrix 

(storage) porosity. Figure 18, which uses the same pair of 

GAMMA values used in figure 17, shows that when the storage porosity is increased from the 0.001 value of figure 17 to 

0.01, the differential matrix-diffusion delay is markedly larger. 

The differential matrix-diffusion delay between calculated BTCs in figure 18 is similar to that between the actual 

BTCs for 2,4,5 TFBA and iodide, and this indicates a storage 

porosity value of approximately 0.01. This result is combined 

with earlier ones to indicate a dual-porosity medium with an 
24 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Figure 17. Visual match of the actual field breakthrough curves to the modified Moench (1995) dualporosity analytical solution, modified for partially recirculating flow, for the 2,4,5 trifluorobenzoic acid (TFBA) 

and iodide tracer test in the Prow Pass interval showing effects of changing GAMMA, with a storage 

porosity of 0.001 (Matching Method 4).

DIMENSIONLESS CONCENTRATION 

(CONCENTRATION/MAXIMUM CONCENTRATION)

AND THEORETICAL DIMENSIONLESS CONCENTRATION 

TIME SINCE TRACER INJECTION (DAYS)

Actual field 

dimensionless breakthrough 

curves for iodide and 2,4,5 TFBA

Modified Moench 

dual-porosity analytical solution, modified 

for partially recirculating flow

GAMMA = 4.4x10–4

GAMMA = 0.001

2,4,5 TFBA

(cmax = 3.81 milligrams per liter)

Estimated parameters

Three interstreamline pathways were assumed with 

 delay factors of 2.01, 2.99, and 3.11 days

Other estimated parameters

Initial flow porosity (f) (assumed

 for all three pathways)

0.27 meter

 4.5 x 10–4

Longitudinal dispersivity (L)

Peclet number (PE)

Borehole mixing length 30.5 meters

 Storage porosity

 Dimensionless diffusion coefficient (GAMMA) 

0.001

Iodide

(cmax = 2.55 milligrams 

per liter)

EXPLANATION

4.4 x 10–4 and 0.001

107
Tracer Tests in the Prow Pass Tuff 25

Figure 18. Visual match of the actual field breakthrough curves to the modified Moench (1995) dual-porosity 

analytical solution, modified for partially recirculating flow, for the 2,4,5 trifluorobenzoic acid (TFBA) and iodide 

tracer test in the Prow Pass interval showing effects of changing GAMMA, with a storage porosity of 0.01 

(Matching Method 4).

TIME SINCE TRACER INJECTION (DAYS)

Actual field 

dimensionless breakthrough 

curves for iodide and 2,4,5 TFBA

Modified Moench 

dual-porosity 

analytical solution, 

modified for partially 

recirculating flow GAMMA = 4.4x10–4

2,4,5 TFBA

(cmax = 3.81 milligrams per liter)

Iodide

(cmax = 2.55 milligrams 

per liter)

GAMMA = 0.001

Estimated parameters

Three interstreamline pathways were assumed with 

 delay factors of 2.01, 2.99, and 3.11 days

Other estimated parameters

Initial flow porosity (f) (assumed

 for all three pathways)

0.27 meter

 4.5 x 10–4

Longitudinal dispersivity (L)

Borehole mixing length 30.5 meters

 Storage porosity

 Dimensionless diffusion coefficient (GAMMA) 

0.01

EXPLANATION

4.4 x 10–4 and 0.001

Peclet number (PE) 107

DIMENSIONLESS CONCENTRATION

(CONCENTRATION/MAXIMUM CONCENTRATION)

AND THEORETICAL DIMENSIONLESS CONCENTRATION
26 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Figure 19. Actual field breakthrough curve for the 2,3,4,5 tetrafluorobenzoic acid (TeFBA) tracer test in 

the Prow Pass interval.

initial flow porosity of 4.5×10–4 (which may represent three 

interstreamline pathways of flow porosities ranging from 

0.0002 to 0.0005), a storage porosity of 0.01, and a 

longitudinal dispersivity of 0.27 m. 

2,3,4,5 Tetrafluorobenzoic Acid Test from 

Borehole UE-25 c#1 to UE-25 c#2

On July 31, 1998, the conservative tracer 2,3,4,5 tetrafluorobenzoic acid (2,3,4,5 TeFBA) was injected in the 

Prow Pass interval of borehole UE-25 c#1 while UE-25 c#2 

continued to be pumped at the average rate of approximately 

0.33 L/s with no recirculation. Breakthrough of this tracer 

at UE-25 c#2 occurred on August 14, 1998, 13.2 days after 

injection, and the concentration eventually rose to a maximum 

of about 0.10 mg/L approximately 65 days after tracer 

injection (fig. 19). The accentuated peak shown in figure 19 is 

a result of a disturbance in borehole UE-25 c#2 in which the 

pump stopped and had to be restarted on September 22, 1998, 

approximately 53 days after injection. The results of this tracer 

test were used to qualitatively assess flow heterogeneity at the 

C-wells (see Bechtel-SAIC Company, 2003, table 6.3–1).

Summary of Transport Parameter 

Values and Presentation of Conceptual 

Models of Solute Transport in the 

Bullfrog, Tram, and Prow Pass Tuffs

Estimated transport parameter values varied among 

the tracer tests in the Bullfrog, Tram, and Prow Pass Tuffs. 

Conceptual models of solute transport consistent with 

these parameter estimates are different for the BullfrogTram and Lower Bullfrog intervals than they are for the 

Prow Pass interval. Variations in the values of longitudinal 

dispersivity, flow porosity, and matrix (storage) porosity 

result from physical processes, such as the scale-dependence 

of dispersivity (when comparing tracer tests conducted from 

borehole UE-25 c#1 to those conducted between boreholes 

UE-25 c#2 and UE-25 c#3), as well as from variability in the 

0

0.02

0.04

0.06

0.08

0.10

0.12

0 20 40 60 80 100 120 140 160

Disturbance when

pump stopped and

was restarted

CONCENTRATION, IN MILLIGRAMS PER LITER

TIME SINCE TRACER INJECTION (DAYS)
Uncertainties and Limitations 27

transport characteristics of the tracer materials. However, there 

is good agreement in dispersivity values obtained from tracer 

tests conducted between boreholes UE-25 c#2 and UE-25 c#3 

in the Bullfrog and Tram intervals. Peclet numbers derived 

from the tests are similar, ranging from approximately 11 to 

15.8; therefore, the longitudinal dispersivities also are similar, 

ranging from about 2.6 m to 1.83 m, respectively (table 2).

The breakthrough times of 5.07 days are identical for 

the iodide and the 2,6 DFBA tracer tests (table 2), and the 

advection traveltimes are within 12 percent. The inferred flow 

porosities are similar, which implies that similar flow pathways are used by the tracers in those tests. 

The parameter estimates are robust (not sensitive to the 

matching method) because the visual graphical match is similar to the PEST match. The differences are less than 5 percent 

for all parameters except matrix porosity, and matrix porosity 

estimates vary by 0.02 (13 percent) for the Lower Bullfrog 

tracer test and 0.03 (16 percent) for the Bullfrog-Tram tracer 

test.

The higher-than-expected estimated flow porosities for 

the Bullfrog and Tram Tuffs of 0.086 and 0.072 to 0.099 

(table 2) indicate that the pathways between boreholes 

UE-25 c#2 and UE-25 c#3 in these intervals are not connected well. Test results using microspheres (Bechtel-SAIC 

Company, 2003, sections D3 and D4) are consistent with this 

interpretation. The arrival of the microspheres at the recovery 

borehole demonstrates the existence of a connected pathway, 

with an aperture at least 0.36 micrometer wide. The small 

recovery percentage of the microspheres, however, also suggests poorly connected/tortuous pathways, dead-ended flow 

pathways, or some attachment mechanism.

The estimates of flow porosity cannot be separated from 

the parameter h, which represents a uniform thickness. In 

conducting tracer tests in isolated, permeable intervals in fractured rock, identification of a meaningful thickness is difficult 

because transport occurs through an interconnected network of 

fractures. For this report, the appropriate thickness was based 

either on the interval thickness or the transmissive thickness 

according to Geldon and others (2002, tables 1 and 8, respectively). For the 56-m- to 73-m-thick Prow Pass interval, the 

appropriate thickness was assumed to be the interval thickness 

and for the 94-m- to 116-m-thick Lower Bullfrog interval 

and the 168-m- to 180-m-thick Bullfrog-Tram interval, it was 

assumed to be the transmissive thickness.

If the ratio of advection traveltimes is equal to the ratio of 

first arrivals (which is strictly correct only for purely advection 

flow without dispersion), then equation 1 shows that, for the 

same pumping rate, qo; aquifer thickness, h; and flow porosity, φf

; and ignoring rw relative to rL, the ratio of first arrivals 

is equal to the ratio of squares of the interborehole distances. 

For the pyridone and 2,6 DFBA tests, the ratio of first arrivals, 

15.2 (77.0 d/5.07 d), is within one order of magnitude of 8.54, 

the ratio of the squares of the interborehole distances of UE-25 

c#1 to UE-25 c#3 and UE-25 c#2 to UE-25 c#3, (85.6 m)2/

(29.3 m)2 (Geldon and others, 2002, table 1).

Tracer testing in the Prow Pass interval (table 3) shows 

different transport characteristics than those obtained in the 

Bullfrog and Tram intervals. The flow porosity was found to 

be 0.00045 in the Prow Pass as opposed to 0.072 to 0.099 in 

the Bullfrog and Tram intervals (tables 3 and 2, respectively). 

This difference indicates that the flow network in the Prow 

Pass is dominated by interconnected fractures (fracture porosity is in the range from 10–2 to 10–5), whereas in the Bullfrog 

and Tram intervals, the flow network is dominated by discontinuous fractures with interconnecting segments of matrix 

(figs. 4 and 20).

Longitudinal dispersivity in the Prow Pass Tuff testing at 

the scale of the distance between UE-25 c#2 and UE-25 c#3 

is calculated as 0.27 m, whereas it is 1.9 to 2.6 m in the 

Bullfrog and Tram intervals at the same scale. A relatively 

small dispersivity is consistent with a flow network dominated 

by interconnected fractures (Prow Pass), and a relatively large 

dispersivity is consistent with a flow network dominated by 

discontinuous fractures with interconnecting segments of 

matrix (Bullfrog and Tram). The more the actual microscopic 

flow pathways are different from the macroscopic, averaged, 

flow pathway, the larger the longitudinal dispersivity. A 

flow network dominated by discontinuous fractures with 

interconnecting segments of matrix (Bullfrog and Tram) will 

have more microscopic flow pathways than a flow network 

dominated by interconnected fractures (Prow Pass).

The storage (or matrix) porosity calculated for the Prow 

Pass Tuff is 0.01 (table 3), whereas it is 0.088 to 0.19 for the 

Bullfrog and Tram (table 2). A small storage porosity is consistent with a dual-porosity medium dominated by interconnected fractures (Prow Pass). In such a medium, the storage 

component, which is assumed to consist of dead-end fractures 

and the part of the matrix not contributing to the flow network, 

would be dominated by fractures that have very small porosities. Similarly, a large storage porosity is consistent with a 

dual-porosity medium dominated by discontinuous fractures 

with interconnecting segments of matrix (Bullfrog and Tram). 

In such a medium, the porosity of the storage component 

(dead-end fractures and the part of the matrix not contributing 

to the flow network) would be dominated by the large porosity 

of the matrix component of storage.

Uncertainties and Limitations

Several factors contributed to uncertainty in, and limitations of, tracer-test results and interpretations. During the 

iodide tracer test in the Bullfrog-Tram interval (February to 

March 1996), the pump gradually failed, leading to a decreasing flow rate during the test, which changed from 8.5 L/s 

at the beginning of the test to 6.2 L/s at the end of the test 

(Bechtel-SAIC Company, 2003, section 6.3.5.1). This violated 

the assumption of a steady-state flow field in the Moench 

(1989, 1995) analytical methods used to analyze tracer test 

results, which would introduce some error into estimates of 
28 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Equivalent

porous

medium (EPM)

Bullfrog-Tram

and Lower

Bullfrog

intervals

Prow Pass interval

Flowing

water

component

Immobile

water

component

(storage)

Discontinuous

fractures

(dead-end fractures): 

stagnant water

Matrix allows flow

between close

discontinuous fractures

carrying moving

water

Interconnected

fractures

Interconnected

fractures

Discontinuous fractures

carrying moving

water

Single porosity

Dual porosity

High 

' 

High matrix porosity, 

' Low 

' 

Low matrix porosity, 

' High 

f

High flow porosity, 

f Low 

Low flow porosity, 

f

f

Matrix

allows flow

between close

discontinuous

fractures

carrying

moving

water

Matrix

No close

fractures with

moving water

for the matrix

to connect Matrix

No close fractures with

moving water for the 

matrix to connect

Discontinuous

fractures

(dead-end

fractures):

stagnant water

Discontinuous fractures

carrying moving

water

Figure 20. Conceptual diagram comparing the proportions of the flowing and immobile water components of 

the fractured rock equivalent porous mediums (EPMs) in the Bullfrog-Tram and Prow Pass intervals at the C-hole 

Complex.
Summary 29

flow porosity. This source of uncertainty was eliminated for 

subsequent tests by replacing the pump. 

There was uncertainty regarding the extent to which 

the tracer was evacuated from the borehole to the aquifer in 

the injection interval during the Bullfrog-Tram and Lower 

Bullfrog tests. This problem was due to the thickness of the 

injection intervals (97 m for the Lower Bullfrog, and about 

170 m for the Bullfrog-Tram interval) and to the lack of downhole mixing. Attempts were made to reduce this source of 

uncertainty in the Prow Pass testing by reducing the injectioninterval thickness and by designing and deploying a downhole 

system capable of mixing the tracer after its injection into the 

borehole. Even though the downhole mixing system worked 

only marginally, it is believed that the above two combined 

measures did minimize stratification of tracer concentration in 

the borehole and led to better evacuation of the tracer into the 

aquifer.

The influence of the natural potentiometric head gradient 

to the southeast that exists at the C-holes (Luckey and others, 

1996, figs. 8 and 9) on tracer recovery at the pumped well is 

a source of uncertainty. Determination of the capture zone of 

the pumped well and how it is altered by the existence of a 

natural gradient depend on the assumptions made regarding 

heterogeneity and anisotropy of hydrogeologic parameters. 

Tracer mass that was not recovered by the pumped well is 

evidence that pathways other than the postulated radially 

convergent or partially recirculating streamlines toward the 

pumped well (fig. 16) contribute to the transport of tracers.

When analyzing tracer test results using an analytical 

solution to the advection-dispersion equation, such as the 

Moench (1989, 1995) solutions used in this study, several 

assumptions are made, as mentioned previously. The medium 

is assumed to be homogeneous and isotropic, and the flow 

regime is assumed to be strictly areal (that is, no vertical component). On the basis of these assumptions, transport parameters are determined by matching type curves to the BTCs. To 

the extent that any of these assumptions are not correct for the 

tracer tests presented in this report, some uncertainty in the 

estimated parameters is introduced.

When assuming a dual-porosity medium, as was done in 

this study, the number of transport parameters that would have 

to be determined is large, and nonuniqueness of the solution 

becomes an issue. The uncertainty was reduced by using the 

PEST quantitative parameter-estimation software (Watermark 

Computing, 1994). PEST quantifies uncertainties in parameter 

determinations by providing confidence intervals on optimal 

parameter values that it produces. PEST was used to quantify 

parameter uncertainty for two of the three radially convergent 

conservative tracer tests conducted in the Bullfrog and Tram 

intervals.

A limitation of all tracer tests conducted so far is that 

they produce estimates of only longitudinal dispersivity, not 

transverse dispersivity. Transverse dispersivity represents 

the medium’s ability to disperse a solute in a direction 

perpendicular to streamlines. In addition, in all tracer tests, the 

estimation of flow porosity has the uncertainty of an unknown 

travel distance between the tracer injection and production 

wells. The probability that the travel distance is a straight line 

distance is remote. The unknown travel distance can affect the 

flow porosity calculation.

Uncertainty in the chemistry data is presented in terms of 

the error bounds that bracket the data. For the tracer concentrations, the maximum error is plus or minus 10 percent of the 

value as was discussed under “Field and Laboratory Methods.” 

These limitations are a function of the HPLC analytical technique used to obtain tracer concentrations.

Summary

Tracer tests were conducted among three boreholes 

(UE-25 c#1, UE-25 c#2, UE-25 c#3) known as the C-hole 

Complex to determine the hydraulic and chemical-transport 

characteristics of the underlying rocks in order to evaluate the 

potential for transport of radionuclides from a proposed highlevel nuclear-waste repository at Yucca Mountain, Nevada.

The C-holes are completed in a sequence of Miocene 

tuffaceous rocks that are covered by Quaternary alluvium. The 

tuffaceous rocks are estimated to be 1,040 to 1,590 m thick in 

the vicinity of the C-holes, where they consist of nonwelded 

to densely welded ash-flow tuff with intervals of ash-fall tuff 

and volcaniclastic rock. The lower part of the tuffaceous-rock 

sequence includes the Prow Pass, Bullfrog, and Tram Tuffs 

of the Crater Flat Group. The rocks are pervaded by tectonic 

and cooling fractures that strike predominantly north-northeast 

to north-northwest and dip westward at angles of 50 to 87 

degrees. Paleozoic limestone and dolomite that underlie the 

tuffaceous rocks are estimated to be about 455 m below the 

bottom of the C-holes.

Conservative tracer tests (four radially convergent and 

one partially recirculating) were conducted at the C-hole 

Complex from February 1996 to September 1998 to establish 

flow porosity, storage porosity, longitudinal dispersivity, and 

extent of matrix diffusion in the Bullfrog and Tram Tuffs and 

the Prow Pass Tuff. Multiple cross-hole tests were conducted, 

and multiple solutions were used to interpret the results.

All tracer tests were analyzed by applying the Moench 

single- or dual-porosity analytical solutions to the advectiondispersion equation or by superposition of these solutions. 

This multiple-analysis approach was done to ensure that the 

appropriate solution method is used in matching a particular 

set of data. 

Nonlinear regression techniques in the form of a parameter-estimation software program (PEST) were used to supplement the analyses conducted using the Moench single- and 

dual-porosity solutions. PEST was used to corroborate tracer 

solution results, to obtain optimal parameter values from the 

solutions, and to quantify parameter uncertainty resulting from 

analyzing two of the three radially convergent conservative 

tracer tests conducted in the Bullfrog and Tram intervals.
30 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Analysis of the tracer-test data in the Bullfrog Tuff and 

Tram Tuff resulted in longitudinal dispersivity values ranging 

from 1.83 to 2.6 m, flow-porosity values ranging from 0.072 to 

0.099 and matrix-porosity values ranging from 0.088 to 0.19. 

The parameter estimates are robust (not sensitive to the matching method) because the visual graphical match is similar to 

the PEST match, both of which are based on the dual-porosity 

analytical solution. 

The higher-than-expected flow-porosity values obtained 

for the Bullfrog and Tram Tuffs indicate that the pathways 

between boreholes UE-25 c#2 and UE-25 c#3 in these intervals are not connected well. Independent test results using 

microspheres are consistent with this interpretation.

 Analysis of the tracer-test data in the Prow Pass Tuff 

resulted in a longitudinal dispersivity of 0.27 m, a flow 

porosity of 4.5 × 10–4, and a matrix porosity of 0.01. Tracer 

testing in the Prow Pass interval indicates different transport 

characteristics than those obtained in the Bullfrog and Tram 

intervals. This difference indicates that the flow network in the 

Prow Pass is dominated by interconnected fractures, whereas 

in the Bullfrog and Tram, the flow network is dominated by 

discontinuous fractures with interconnecting segments of 

matrix. 

Several factors contributed to uncertainty in, and limitations of, tracer-test results. These factors include equipment 

failure during testing, possible incomplete tracer evacuation from the injection interval, the influence of the natural 

potentiometric gradient, assumptions inherent in the analytical 

methods, and potential errors in chemical analyses. 

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32 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Glossary

Selected terminology used in this report, arranged alphabetically, with Greek symbols at end. Bold terms in the second column 

are defined in the first column.

TERMINOLOGY MEANING

actual dimensional time (t) Time since tracer injection. Same notation, t, as used for theoretical 

dimensional time.

actual field dimensional breakthrough 

 curve

Arithmetic or log-log plot of actual field dimensional concentration of 

tracer measured at the production well plotted against actual dimensional time since injection. 

actual field dimensional concentration

 (c)

Actual field concentration of tracer measured in ground water at the 

production well. 

actual field dimensionless 

 breakthrough curve

Arithmetic or log-log plot of actual field dimensionless concentration

plotted against actual dimensional time since injection.

actual field dimensionless 

 concentration (c/cmax)

Actual field dimensional concentration of tracer measured in ground 

water at the production well normalized by the maximum actual field 

dimensional concentration of tracer for a particular test.

advection traveltime (t

a

)

Length of time for a tracer slug to travel from the injection well to the 

production well by plug flow (pure advection: no dispersion). Equation 1 in text is used to calculate t

a

. One of the input aquifer-property 

parameters for the Moench single- or dual-porosity analytical solution.

advection-dispersion transport 

 equation

Well-known differential equation for describing ground-water solute transport, that is, the movement and spreading of solutes with 

ground-water flow.

analytical solution method

Analytical, as opposed to numerical, method to solve the advection-dispersion transport equation. Specifically, for this report, the Moench 

single-porosity analytical solution (Moench, 1989) and the Moench 

dual-porosity analytical solution (Moench, 1995).

aquifer 

Geologic material through which ground-water flow and solute transport occur. An aquifer can consist of either:

(1) loose material above bedrock and called a porous medium or,

(2) fractured bedrock and called an equivalent porous medium.

areal flow Ground-water flow field that is contained in the horizontal plane, without a vertical component.

best visual graphical match

A match of BTC(s) subjectively deemed by the analyst to be the “best” 

match by overlaying a type curve or theoretical (dimensional or 

dimensionless) BTC on the actual field (dimensional or dimensionless) BTC. The input aquifer-property parameters used for this 

“best” match are the estimated parameters. Compare to PEST match.

borehole A hole drilled into geologic formations.
Glossary 33

breakthrough curve (BTC)

Arithmetic or log-log plot of concentration of tracer at the production 

well plotted against actual dimensional time since injection at the 

injection well. Can be actual field (dimensional or dimensionless)

BTC (if actual field measurements) or theoretical (dimensional or 

dimensionless) BTC (if calculated by either the Moench single- or 

dual-porosity analytical solution). Consists of rising limb and falling 

limb.

BTC Breakthrough curve.

c Actual field dimensional concentration.

C Theoretical dimensional concentration.

CD Theoretical dimensionless concentration.

Ci

Reference concentration that relates theoretical dimensional concentration and theoretical dimensionless concentration. Equation 2 in 

text is used to calculate Ci.

conservative tracer Tracer that is nonsorbing; it does not sorb onto rock material that is 

being tested.

dead-end fractures

Discontinuous fractures opening into a portion of the matrix where 

there are no nearby fractures carrying water to be connected to by the 

matrix. This results in stagnant water, a part of the immobile-water 

component (storage) of an EPM.

differential matrix-diffusion delay

Delay of the actual field dimensionless BTC and the theoretical 

dimensionless BTC for higher values of GAMMA (more diffusion 

into the matrix) relative to the actual field dimensionless BTC and 

theoretical dimensionless BTC for lower GAMMA.

dimensional time (t) Either actual dimensional time or theoretical dimensional time.

dimensionless concentration Either actual field dimensionless concentration or theoretical dimensionless concentration.

dimensionless matrix-diffusion 

 coefficient (GAMMA, γ)

Dimensionless parameter in Moench dual-porosity analytical solution that represents the diffusion of a solute into the immobile-water 

component of an EPM. One of the input aquifer-property parameters for the Moench dual-porosity analytical solution.

dimensionless storage coefficient 

 (SIGMA, σ)

Dimensionless parameter in Moench dual-porosity analytical solution that represents the storage of a solute in the immobile-water 

component of an EPM. One of the input aquifer-property parameters for the Moench dual-porosity analytical solution.
34 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

dimensionless time (t

D)

Actual dimensional time since tracer injection divided by the advection traveltime (t

D = t ÷ ta

). Same notation, t

D, as used for theoretical 

dimensionless time.

discontinuous fractures 

Fractures that are not continuous from injection well to pumping well. 

They can be either part of the flowing-water component of an EPM

if the discontinuous fractures carry moving water and are connected 

by matrix, which allows flow between the fractures; or they can be 

part of the immobile-water component of an EPM if they open into 

a portion of the matrix where there are no nearby fractures carrying 

water to be connected to by the matrix. This results in dead-end 

fractures and stagnant water.

dual-porosity medium An EPM with a flowing-water component and an immobile-water 

component.

dual-porosity partially recirculating

 solution

Solution developed in this report in which the Moench dual-porosity 

analytical solution (Moench, 1995), derived for a radially convergent flow field, is modified to represent solute transport in a 

partially recirculating flow field. The modification involves superposition of three Moench dual-porosity analytical solution(s) to 

represent the cumulative effects of three separate interstreamline 

pathways of the tracer between injection well and production well in a 

dual-porosity medium.

EPM Equivalent porous medium.

equivalent porous medium (EPM) An aquifer consisting of fractured bedrock that is assumed to behave 

like a porous medium at some appropriate scale.

flow field

The pattern of ground-water flow as depicted graphically by the pattern 

of a collection of streamlines, either radially convergent, or fully or 

partially recirculating. In a fully or partially recirculating flow field, 

the streamlines first diverge when they emmanate from the injection 

well, then converge toward the production well. See also radially 

convergent flow field.

flowing-water component of an EPM

Component of an EPM that allows ground-water flow in it. Consists, in 

varying proportions, of (1) interconnected fractures and (2) adjacent 

discontinuous fractures carrying moving water and connected by 

matrix, which allows flow between the fractures. See also immobilewater component of an EPM.

flow porosity (φf)

Porosity of the flowing-water component of an EPM. One of the 

transport properties and input aquifer-property parameters for the 

Moench single- or dual-porosity analytical solution.

fully recirculating tracer test See tracer test.

GAMMA (γ) See dimensionless matrix-diffusion coefficient. 
Glossary 35

immobile-water component of an

 EPM

Component of an EPM that does not allow ground-water flow in it, but 

stores the water (and the solute dissolved in it). A solute gets into this 

portion of an EPM from the flowing-water component of an EPM

and back out in response to concentration differences between the two 

components. Consists, in varying proportions, of distant discontinuous fractures (dead-end fractures) and the matrix between them 

(portion of matrix not contributing to flow). 

input aquifer-property parameters

Aquifer-property parameters required as input for the Moench single- or 

dual-porosity analytical solution: advection traveltime, t

a

; dimensionless storage coefficient, SIGMA (σ); dimensionless matrixdiffusion coefficient, GAMMA (γ); longitudinal dispersivity, αL

, in 

the form of the Peclet number (PE); transverse dispersivity; flow 

porosity, φf; and matrix (storage) porosity, φ′.

input test-configuration parameters

Tracer test information about the wells, pumping, and tracer required for 

the Moench single- or dual-porosity analytical solution: production rate, distance between injection well and production well, aquifer

thickness and mixing lengths, and mass of tracer injected and volume 

of water. 

interstreamline pathway

One of the paths taken by water and tracer from the injection well to the 

production well in a partially recirculating flow field. It is defined by 

two curved bounding streamlines (ground-water flow lines) (see fig. 

16A).

longitudinal dispersivity (αL)

A transport parameter that is a measure of the ability of a porous 

medium to disperse a solute along streamlines (ground-water flow 

lines). One of the input aquifer-property parameters for the 

Moench single- or dual porosity analytical solutions.

match

To make a portion of a Moench type curve or a theoretical dimensional or dimensionless BTC overlie a portion of an actual field dimensional or dimensionless BTC to some extent. Various matches are 

obtained when the analyst varies the input aquifer-property parameters. The match can be a best visual graphical match or a PEST 

match by the PEST parameter-estimation program. The match can be 

of the rising limb, of the falling limb, or of the whole BTC.

Matching Method 1

In this process, estimates of t

a

 and PE are obtained from closely matching the rising limbs of the actual field dimensional or dimensionless 

BTC with the type curve or theoretical dimensional or dimensionless BTC using the Moench single-porosity analytical solution. The 

resulting falling limb match may not be very good but good enough to 

assert that the medium is a single-porosity medium.

Matching Method 2

In this process, estimates of t

a

 and PE are obtained from loosely matching the whole actual field dimensional or dimensionless BTC to the 

type curve or theoretical dimensional or dimensionless BTC using 

the Moench single-porosity analytical solution, or the Modified 

Moench single-porosity analytical solution.
36 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

Matching Method 3

In this process, estimates of t

a

 and PE are first obtained from closely 

matching the rising limbs of the actual field dimensional or dimensionless BTC with the type curve or theoretical dimensional or 

dimensionless BTC using the Moench dual-porosity analytical 

solution. These values then are fixed and SIGMA and GAMMA are 

varied and their values estimated from matching the falling limbs, 

which may not match well. Only a best visual graphical match is 

used for this method.

Matching Method 4

In this process, estimates of t

a

 and PE are first obtained from closely 

matching the rising limbs of the actual field dimensional or dimensionless BTC with the type curve or theoretical dimensional or 

dimensionless BTC using the Moench dual-porosity analytical 

solution or the Modified Moench dual-porosity analytical solution. 

With these values of t

a

 and PE used as starting values, the match of 

the falling limb may be improved by varying SIGMA and GAMMA, 

along with t

a

 and PE, and estimating values for all four from matching 

the whole BTC. A best visual graphical match or a PEST match

(nonlinear regression technique) can be used for this method. This 

method may produce a loose match of the rising limb but may lead to 

improved matches of the falling limb relative to Matching Method 3.

matrix

The part of a fractured tuff rock mass that is not the fractures (fig. 4). 

For a single-porosity medium, the matrix is part of the flowing-water 

component of an EPM because it allows flow through it. For a dualporosity medium, part of the matrix contributes to the flowing-water 

component of an EPM, but part of the matrix does not contribute to 

flow and is part of the immobile-water component of an EPM. 

matrix porosity (φ′)

Porosity of the immobile-water component of an EPM. Same as storage porosity. One of the input aquifer-property parameters for the 

Moench dual-porosity analytical solution.

medium See aquifer. 

Moench dual-porosity analytical 

 solution

Solution to the advection-dispersion transport equation governing 

solute transport in a dual-porosity medium for specific values of 

input test-configuration parameters and input aquifer-property 

parameters, such as PE, GAMMA, and SIGMA, as given in Moench 

(1995). The solution is represented graphically by a dual-porosity type 

curve, dual-porosity theoretical dimensional BTC, or a dual-porosity

theoretical dimensionless BTC.

Moench input parameters

Parameters required as input for the Moench single- or dual-porosity 

analytical solution: input test-configuration parameters and input 

aquifer-property parameters. 
Glossary 37

Moench single-porosity analytical

 solution

Solution to the advection-dispersion transport equation governing 

solute transport in a single-porosity medium for specific values of 

input test-configuration parameters and input aquifer-property 

parameters as given in Moench (1989). The solution is represented 

graphically by a single-porosity type curve, single-porosity theoretical dimensional BTC, or a single-porosity theoretical dimensionless

BTC.

Moench type curve

Log-log plot of theoretical dimensionless concentration at the production well against theoretical dimensionless time since injection, 

obtained from either the Moench single- or dual-porosity analytical 

solution.

normalize To make the actual field concentration dimensionless, by dividing by 

the maximum actual field concentration, which has the same units.

optimal PEST parameters or results Optimal PE, GAMMA, and SIGMA parameter values resulting from a 

PEST match.

parameter One of the input test-configuration parameters or input aquiferproperty parameters.

partially recirculating flow field

The pattern of ground-water flow as depicted graphically by the pattern 

of a collection of streamlines resulting from partial recirculation in a 

tracer test (reinjecting some of the water pumped from the production 

well back into the injection well). See also flow field.

partially recirculating solution See single- or dual-porosity partially recirculating solution.

partially recirculating tracer test See tracer test.

PE Peclet number.

Peclet number (PE)

Parameter equal to rL, the distance from the production well to the 

injection well, divided by αL, the longitudinal dispersivity, the ability 

of the aquifer to disperse a solute along streamlines (ground-water 

flow lines). One of the input aquifer-property parameters for the 

Moench single- or dual-porosity analytical solution.

PEST match

The result from making a portion of a theoretical (dimensional or 

dimensionless) BTC calculated from the Moench single- or dualporosity analytical solution (Moench, 1989, 1995) executed by the 

parameter-estimation program, PEST (Watermark Computing, 1994), 

overlie a portion of an actual field (dimensional or dimensionless)

BTC to some extent. The first PEST run starts with the PE, SIGMA, 

and GAMMA values from a best visual graphical match. These 

initial estimates of PE, SIGMA, and GAMMA are varied in a series 

of PEST runs until the sum of squares of differences between actual 

concentrations on an actual field (dimensional or dimensionless)

BTC and theoretical concentrations on a theoretical (dimensional or 

dimensionless) BTC is minimized. This PEST theoretical BTC is the 

PEST match that determines the associated PE, SIGMA, and GAMMA parameter values that are the optimal PEST parameters.
38 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

PEST theoretical BTC

Theoretical (dimensional or dimensionless) BTC in a PEST match

using the optimal PEST parameters, as explained under PEST 

match.

porosity See flow porosity, matrix porosity, and storage porosity.

radially convergent flow field Ground-water flow pattern resulting from pumping one well in which the 

streamlines converge radially to the well. See also flow field.

radially convergent tracer test See tracer test.

recirculation Process of reinjecting some or all of the water pumped from the production well into the injection well.

robust Parameter estimate not sensitive to the matching method.

SIGMA (σ) Dimensionless storage coefficient.

single-porosity medium An EPM with only a flowing-water component of an EPM (no 

immobile-water component of an EPM).

single-porosity partially recirculating 

 solution

Solution developed in this report in which the Moench single-porosity 

analytical solution (Moench, 1989), derived for a radially convergent flow field, is modified to represent solute transport in a partially recirculating flow field. The modification involves superposition of 

three Moench single-porosity analytical solution(s) to represent the 

cumulative effects of three separate interstreamline pathways of the 

tracer between injection well and production well in a single-porosity 

medium.

solute transport Movement and spreading of solutes with ground-water flow.

storage Process of storing immobile water and solute in a portion of an EPM

(immobile-water component of an EPM), as opposed to flow.

storage component of an EPM Same as immobile-water component of an EPM.

storage porosity (φ′) Same as matrix porosity.

streamline(s) Curvilinear or straight line along which ground water flows.

swept volume

Volume of water in an interstreamline pathway. Because water is continously moving through the interstreamline pathway, this volume 

represents the volume of pore space that water will pass through, or 

sweep, on its way from the injection well to the production well.

t Actual dimensional time or theoretical dimensional time.
Glossary 39

t

a Advection traveltime.

t

D Dimensionless time or theoretical dimensionless time.

theoretical dimensional BTC

Arithmetic or log-log plot of theoretical dimensional concentration

at the production well against theoretical dimensional time since 

injection obtained from either the Moench single- or dual-porosity 

analytical solution.

theoretical dimensional concentration

 (C)

Theoretical breakthrough concentration at the production well (calculated by either the Moench single- or dual-porosity analytical solution). C = CD×Ci

theoretical dimensional time (t)

Obtained from multiplying the theoretical dimensionless time, t

D, 

obtained from either the Moench single- or dual-porosity analytical 

solution, by the advection traveltime (t = t

D× ta

). Same notation, t, as 

used for actual dimensional time.

theoretical dimensionless BTC

Arithmetic or log-log plot of theoretical dimensionless concentration

at the production well against theoretical dimensional time since 

injection obtained from either the Moench single- or dual-porosity 

analytical solution.

theoretical dimensionless 

 concentration (CD)

Theoretical breakthrough concentration at the production well, equal to 

the theoretical dimensional concentration, C, (calculated by either 

the Moench single- or dual-porosity analytical solution), and normalized by Ci

, a reference concentration (defined by equation 2 in the 

text). CD = C/Ci

theoretical dimensionless time (t

D)

Obtained from either the Moench single- or dual-porosity analytical 

solution and multiplied by the advection traveltime to give the theoretical dimensional time (t = t

D× ta

).

tracer test 

Test conducted in an aquifer to estimate its transport properties. A 

tracer solution is injected into an injection well while a production 

well is pumped. If the water pumped from the production well is not 

reintroduced into the aquifer, the flow field tested is a radially convergent flow field and the tracer test is called a radially convergent tracer 

test. If part of the water pumped from the production well is reintroduced into the aquifer (reinjected into the injection well), the flow 

field tested is a partially recirculating flow field and the tracer test 

is called a partially recirculating tracer test. If all of the water pumped 

from the production well is reintroduced into the aquifer (reinjected 

into the injection well), the tracer test is called a fully recirculating 

tracer test. When the tracer arrives at the production well, an actual 

field (dimensional or dimensionless) BTC is plotted and analyzed for 

transport properties of the aquifer. 

transport See solute transport.

transport parameter(s) Same as transport property(ies).
40 Analysis of Conservative Tracer Tests, Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada

transport porosity See flow porosity.

transport property(ies)

One of the aquifer properties that govern solute transport in groundwater flow. Same as transport parameters. See input aquifer-property 

parameters for the Moench single- or dual-porosity analytical solution.

transverse dispersivity

One of the transport properties representing the ability of the medium

to disperse a solute in a direction perpendicular to streamlines. One 

of the input aquifer-property parameters for the Moench single- or 

dual-porosity analytical solution.

type curve See Moench type curve.

well Borehole with equipment installed that is used to perform a 

function; for example, injection well or production well.

Greek Symbols

αL Longitudinal dispersivity.

γ (GAMMA) Dimensionless matrix-diffusion coefficient.

σ (SIGMA) Dimensionless storage coefficient.

φf Flow porosity.

φ′ Matrix (storage) porosity. 
Umari and others—Analysis of Conservative Tracer Tests in the Bullfrog, Tram, and Prow Pass Tuffs, 1996–98, Yucca Mountain, Nevada—SIR 2007–5280

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