Characterization and remediation of a controlled DNAPL release

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Characterization and remediation of a controlled DNAPL release field study and uncertainty analysis
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xiii, 147 leaves : ill. ; 29 cm.
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Brooks, Michael Carson, 1965-
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Groundwater -- Pollution   ( lcsh )
Groundwater -- Purification   ( lcsh )
Environmental Engineering Sciences thesis, Ph. D   ( lcsh )
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Thesis:
Thesis (Ph. D.)--University of Florida, 2000.
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Includes bibliographical references (leaves 140-146).
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by Michael Carson Brooks.
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Printout.
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Vita.

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CHARACTERIZATION AND REMEDIATION OF A CONTROLLED DNAPL
RELEASE: FIELD STUDY AND UNCERTAINTY ANALYSIS













By

MICHAEL CARSON BROOKS


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA














ACKNOWLEDGEMENTS


I would like to thank my committee members: Drs. Paul Chadik, Wendy D.

Graham, P. Suresh C. Rao, and Michael D. Annable; and my committee chair: William

R. Wise for their professional dedication. They have continually been an inspirational

source of guidance and assistance. I have also benefited from discussions with Drs. Kirk

Hatfield, A. Lynn Wood and Carl G. Enfield, and I thank them for their assistance. I

would also like to recognize and thank my fellow graduate students, for they too have

served as an invaluable resource in my education. This study involved numerous people,

and this dissertation would not be possible without their work. I wish to specifically

thank Dr. Wise for his guidance with the material presented in Chapters 2 and 3, and Dr.

Annable for his work and assistance with Chapters 4 and 5 (including the tracer

degradation correction work he completed). Chapter 5 has benefited from several

reviews by Drs. Annable, Rao, Wise, Wood, and Enfield, as well as reviews by Dr. James

Jawitz, and I thank them all for their helpful comments. I would also like to specifically

thank Irene Poyer and Jaehyun Cho for their work in the laboratory, and Dr. Andrew

James for producing the graphical display of the MLS data in Chapter 5. Finally, most of

all, I would like to thank my family for their love and support.














TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ................................ ................................ ii

LIST OF TABLES ....................... .............. ............................ vi

LIST OF FIGURES ......................................................... ....................... viii

A B STRA CT ............................................. ........................ ................................. xii

CHAPTERS

1 INTRODUCTION ....................... ....................................... 1

2 GENERAL METHODS FOR ESTIMATING UNCERTAINTY
IN TRAPEZOIDAL RULE-BASED MOMENTS ............................... 5

Introduction ...................... ............................................. 5
T theory ............................................... ................... .... 8
General Expressions ........................................................... 8
Systematic Errors .............................. ........................... 11
Random Errors .......................................... ....................... 11
Validation and Analysis Using a Synthetic Data Set ............................ 18
Results and Discussion .................................. ............................ 19
System atic Errors ................................... ........................... 19
Random Errors ............................... .... .... .................... 22
Conclusions .................................... ............. ....................... 27

3 UNCERTAINTY IN NAPL VOLUME ESTIMATES BASED
ON PARTITIONING TRACERS .......................... ..................... 29

Introduction ..................................................................... ... ......... 29
A Review of Partitioning Tracer Tests ..................................... 29
Sources of Uncertainty and Errors ........................................... 30
Uncertainty-Estimation Method ......................... ...................... 37
General Equations ................................... ........................ 37
Systematic Errors ................................... ........................... 38









R andom Errors .......................................... ............................ 38
Results and Discussion .......................................... 42
Systematic Errors ................................... ........................... 42
Random Errors ................................... ............................ 45
Applications .............................................. 46
Conclusions .................................. ................................. 50

4 PRE- AND POST-FLUSHING PARTITIONING TRACER TESTS
ASSOCIATED WITH A CONTROLLED
RELEASE EXPERIMENT ............................................ 52

Introduction ................................. ............. ......... 52
Site Description ................................... .......................... 52
Background Sorption Tracer Test .......................................... ... 55
Controlled Release Conducted by EPA ................................... 55
Partitioning Tracer Tests ....................... ..................... 59
Results and Discussion ............................. ...... ....................... 61
Extraction W ells ......................................... ...... ..................... 61
Comparison to Release Locations and Volumes ...................... 68
Summary of Post-Flushing Partitioning Tracer Test ................ 69
Discussion .................................. ............................... 71
Conclusions .................................. .. ............................. 75

5 FIELD-SCALE COSOLVENT FLUSHING OF DNAPL FROM
A CONTROLLED RELEASE ....................................................... 77

Introduction .................................. ............................... 77
M methods ............................................ ................... .. .................... .. 80
PCE Volume Initially Present......................... ................. 80
System Description ....................................... .. ...... 81
Performance Monitoring ......................... ..................... 83
Results and Discussion ............................... .......... 84
System Hydraulics................................. ................... 84
Mass Recovery .................................. ...................... 87
Ethanol Recovery .................................. ................ 92
PCE Recovery ............................... ... ... ................... 93
Treatment Efficiency ......... ................. .. ............ 97
Changes in Aqueous PCE Concentrations ................................ 100
Recycling Treatment ................................. .... ........... 100
Conclusions .................................... ............... 102

6 CONCLUSIONS ................. ........................................................ 103

APPENDICES

A SYSTEMATIC ERRORS ............................... ....... ......... 108










B RANDOM ERRORS IN MOMENT CALCULATIONS ............................ 116

C DELTA METHOD FORMULAS ....................................................... 126

REFERENCES ................................................ 140

BIOGRAPHICAL SKETCH ................................................. .. 147















LIST OF TABLES


Tables page

1-1. Sequence of activities completed in the cell ......................................... 4

2-1. Comparison of mass and swept volume CV (%) based on Monte
Carlo (M.C.) simulations and semi-analytical calculations (S.A) ...... 25

3-1. Summary of errors and their impact on partitioning tracer test
predictions ................................ ................ ..................................... 32

3-2. Comparison of the CV (%) estimated from Monte Carlo (M.C.)
simulations and semi-analytical procedure (S.A) for three cases ...... 46

4-1. Summary of results from the background sorption tracer test ............. 56

4-2. Volume of PCE (L) added and removed from the cell ......................... 58

4-3. Partitioning coefficients for tracers used in the pre- and post-
flushing partitioning tracer tests ............................ .................. 62

4-4. Summary of results for common non-reactive lower and upper
zone tracers from the pre-flushing test............................................ 64

4-5. Pre-flushing partitioning tracer test, common lower zone
partitioning tracer results.......................... ...... ................. 64

4-6. Pre-flushing partitioning tracer test, upper-zone reactive tracer (n-
heptanol) results. The corrected mass recovery is based on a
first-order degradation model..................................... ............. 65

4-7. Pre-flushing partitioning tracer test, summary of unique tracer
pairs injected into wells 45 and 55 ...................................... ....... 69

4-8. Post-flushing partitioning tracer test summary ..................................... 72

4-9. Comparison in NAPL volume (L) estimates based on four schemes
of log-linear BTC extrapolation .......................... .................. 74









5-1. Phases of the flushing demonstration ................................................... 83

5-2. Summary of PCE volumes predicted from pre- and post-flushing
PITTs....................................................................... ......... 97














LIST OF FIGURES


Figures page

2-1. Relative error between trapezoidal and true values, expressed as a
function of the number of intervals used in the numerical
integration. The normal probability density function was used
in the comparison (average = 1, standard deviation = 1, and
integrated from -4 to 6). Shown on the graph are the absolute
first moment by equation (2-5) (0) and equation (2-4a) (0), and
the absolute second moment by equation (2-5) (A) and equation
(2-4a) (x) ......................... ...... .......... ... ..................... 10

2-2. Relative errors in the zeroth moment (solid line) and the
normalized first moment (dashed line) for a) constant
systematic volume errors, and b) proportional systematic
volume errors. The volume errors are benchmarked to the
swept volume .................................................. ..................... 20

2-3. Relative error in zeroth moment (solid line) and normalized first
moment (dashed line) as a function of the ratio of constant
systematic concentration errors to injection concentration ................ 23

2-4. BTCs for the synthetic non-reactive and reactive tracers, as well as
"measured" non-reactive (crosses) and reactive (circles) BTCs
generated from one Monte Carlo realization. Both volume
standard deviation and concentration CV were equal to 0.15 ........... 25

2-5. Coefficient of variation (%) of the a) zeroth and b) normalized first
moments as a function of the ratio of volume standard deviation
to swept volume. Each line represents concentration CV of 0.0
(0), 0.5 (o), 0.10 (0), 0.15 (A), 0.20 (*), 0.25 (x) and 0.30 (+),
respectfully ................................... ..... .......... ................... .... 26

2-6. Coefficient of variation for the zeroth moment (closed symbols)
and the normalized first moment (open symbols) for a range in
concentration detection-limit coefficient of variation (CVDL)
values. Results are shown for maximum-concentration









coefficient of variation (CVmx) values of 5% (0), 10% (o), and
15% (A). Volume error was neglected ........................................ .... 28

3-1. The effects of systematic errors on retardation (solid line),
saturation (short-dashed line), and NAPL volume (long-dashed
line) are illustrated for the case of a) constant systematic
volume errors, b) proportional systematic volume errors, and c)
constant systematic concentration errors. The retardation factor
was 1.5 in each case, and the BTCs were composed of 100 data
points ....................................... ........... ........................ 43

3-2. NAPL volume CV as a function of retardation factor for volume
and concentration measurement errors of 0.05 (diamonds), 0.15
(squares), and 0.30 (triangles). BTCs with 100 data points were
used to generate the figure ......................... .................... 47

3-3. NAPL volume coefficient of variation as a function of
dimensionless volume errors for BTCs of 50 (diamonds), 100
(squares), and 350 (triangles) volume-concentration data points.
The figure is based on a retardation factor of 1.5 ........................... 47

3-4. Retardation (triangles), NAPL saturation (squares), and NAPL
volume (circles) CV as a function of the concentration detection
limit CV. The CV of the maximum concentrations were 5%
(open symbols) and 15% (closed symbols). The figure is based
on 100 volume-concentration data points, and a retardation
factor of 1.5 .......................................................... ........... ... .. 49

3-5. Impacts of background-retardation uncertainty. The NAPL
volume CV is presented as a function of retardation for
background retardation CVs of 5% (circles), 15% (triangles),
and 30% (squares). The curves with the open symbols are
based on a partitioning coefficient of 8, and the curves with the
closed symbols are based on a partitioning coefficient of 200 .......... 49

4-1. Cell instrumentation layout ............................................ 54

4-2. a) Double five-spot pumping pattern used in the background
sorption tracer test and the ethanol flushing demonstration
(discussed in Chapter 5), and b) inverted, double five-spot
pumping pattern used in the pre- and post-flushing tracer test .......... 56

4-3. PCE injection locations and volumes (plan view). The number
inside the circles indicates the release volume (L) per location ......... 58








4-4. Selected EW 51 BTCs from the pre-flushing partitioning-tracer
test. a) Common lower zone tracers: methanol (closed
diamonds) and 2-octanol (open diamonds), b) unique lower
zone tracers: isobutanol (closed circles) and 3-heptanol (open
circles), and c) upper zone tracers: isopropanol (closed squares)
and n-heptanol (open squares) ........................................................ 63

4-5. Pre-flushing PITT estimate of a) upper zone and b) lower zone
spatial distribution of NAPL based on extraction well data .............. 70

4-6. DNAPL volume estimated from the pre- and post-partitioning
tracer tests as a function of the tracer partitioning coefficient ........... 73

4-7. Average and standard deviation in NAPL volume from four
different extrapolation schemes ......................... ....... ........... 74

5-1. Cumulative volume injected into a) the lower zone, and b) the
upper zone. Injected fluid consists of new ethanol (triangles),
recycled ethanol (squares), and water (circles) for the lower
zone; and re-cycled water (squares) and water (circles) for the
upper zone.................................. .... ..................... 85

5-2. PCE concentrations (squares) and ethanol percentages (triangles)
from a) upper zone extraction well 45A, and b) lower zone
extraction well 45B. ............................. .......................... 88

5-2. continued. PCE concentrations (squares) and ethanol percentages
(triangles) from c) upper zone extraction well 55A, and d) lower
zone extraction well 55B............................ ...................... 89

5-3. Ratio of PCE concentration to PCE solubility limit for upper zone
(plus signs) and lower zone (circles) samples from extraction
wells a) 45 and b) 55. The PCE solubility limits are a function
of ethanol content, and were based on values reported by
VanValkenburg (1999)......................... ........................ 90

5-4. Aqueous PCE distribution based on MLS samples from the end of
the flushing demonstration. The concentration contours were
created using an inverse distance contouring method in the
TechPlot software package. .................................. ................ ...... 95

5-5. Removal efficiency for a) upper zone: 45A (plus symbols) and
55A (triangles); and b) lower zone: 45B (minus symbol), 55B
(circles), and 51B (x)............................ ........................... 99








5-6. DNAPL removal effectiveness versus reduction in PCE
concentrations ................................................ .......... 101














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

CHARACTERIZATION AND REMEDIATION OF A CONTROLLED DNAPL
RELEASE: FIELD STUDY AND UNCERTAINTY ANALYSIS

By

Michael Carson Brooks

December, 2000


Chair: William R. Wise
Major Department: Environmental Engineering Sciences

A dense non-aqueous phase liquid (DNAPL) source zone was established within

an isolated test cell through the controlled release of 92 L of perchloroethylene (PCE) by

EPA researchers. The purpose of the release was to evaluate innovative DNAPL

characterization and remediation techniques under field conditions. Following the

release, a partitioning-tracer test to characterize the DNAPL, a cosolvent flood to

remediate the DNAPL, and a second partitioning tracer test to characterize the remaining

DNAPL were conducted by University of Florida researchers who had no knowledge of

the volume, the method of release, nor the resulting spatial distribution.

The pre-flushing, partitioning tracer test predicted 60 L of PCE, or 70% of the 86

L of PCE estimated in the cell at the start of the tracer test. The estimate of 86 L was

based on the release information and the amount of PCE removed by activities conducted

between the PCE release and the tracer test. The partitioning tracer test estimate was








complicated by tracer degradation problems. During the cosolvent flood, the cell was

flushed with an ethanol-water solution for approximately 40 days. Alcohol solution

extracted from the cell was recycled after treatment using activated-carbon and air-

stripping. Based on the release information and the amount of PCE removed by all prior

activities, it was estimated that 83 L of PCE was in the cell at the start of the flood. The

amount of PCE removed during the alcohol flushing demonstration was 53 L, which

represents a flushing effectiveness, defined as the percent mass of PCE removed, of 64%.

The mass balance from the cosolvent flood indicated that 30 L of PCE remained in the

test cell prior to the final tracer test, but the results from this test only predicted 5 L.

The majority of the data from these tests was analyzed using moments calculated

from breakthrough curves. General stochastic methods were investigated whereby the

uncertainty in volume and concentration measurements were used to estimate the

uncertainty of the zeroth and normalized first moments. These methods were based on

the assumption that moments are calculated from the breakthrough curves by numerical

integration using the trapezoidal rule. The uncertainty associated with the NAPL volume

estimates using partitioning tracers was then quantified by propagating uncertainty in

moments to NAPL volume estimates.














CHAPTER 1
INTRODUCTION


Groundwater contaminants originate from a number of sources in modem society,

including: fuels for transportation and heating, solvents and metals from commercial and

industrial activities, herbicides and pesticides from fanning activities, and spent nuclear

material from nuclear power and weapons production. While an awareness for the need

to preserve and protect natural resources can be traced back to the late 1800s, it is only

within the last 30 years that society has taken steps, in the form of federal laws, to protect

groundwater resources, and correct adverse impacts on ground-water resources. Most

environmental protection regulations in the United States (US) were not established until

the 1970s, starting with the basic environmental policy act, the National Environmental

Policy Act (NEPA), in 1969. Specific water protection and restoration regulations were

established by the Federal Water Pollution Control Act of 1972, which was later amended

to become the Clean Water Act in 1977, the Safe Drinking Water Act in 1974, the

Resource Conservation and Recovery Act (RCRA) in 1976, and the Comprehensive

Environmental Response, Compensation, and Liability Act in 1980.

These regulations ultimately provided the driving force for the work in the area of

groundwater contaminant characterization and remediation within the US since the late

1970s. In turn, from this work emerged a better understanding of the complexity of

groundwater contamination characterization and remediation issues. It became apparent

that new methods would be necessary to economically characterize and remedy source-








zone contamination. Persistent organic contaminant plumes have a source, which

typically consists of non-aqueous phase liquid (NAPL). Dense, non-aqueous phase

liquids (DNAPLs) have densities greater than water and are particularly difficult to

characterize and remove because of their subsurface behavior in complex geology.

Within the last 5 years, efforts have focused on new and innovative techniques to deal

with source-zone contamination.

Partitioning tracers are among the new characterization techniques for source-

zone contamination. The technique originated in the petroleum industry as a means to

estimate oil saturations in reservoirs, and has been applied to groundwater

characterization to estimate the amount of NAPL present. Likewise, cosolvent flushing is

among the new source-zone remediation techniques, and it too has roots in the petroleum

industry (Rao et al., 1997). These techniques have been successfully demonstrated in

laboratory experiments and pilot studies, and partitioning tracers have been used in full-

scale operations.

Due to the challenges associated with DNAPL characterization and remediation,

the performance of innovative techniques is still uncertain. A jointly sponsored

demonstration was undertaken to investigate the ability of six different techniques to

remediate DNAPLs. The demonstration discussed herein was the first of these

techniques. The tests were conducted at the Dover National Test Site (DNTS), located at

Dover Air Force Base (AFB) in Dover, Delaware. The DNTS is a field-scale laboratory,

designed as a national test site for evaluating remediation technologies (Thomas, 1996).

Each demonstration is to follow a similar test protocol. Researchers from the

Environmental Protection Agency (EPA) begin each test by releasing a known quantity








of PCE into an isolated test cell. However, the amount and spatial distribution of the

release are not revealed to the researchers conducting the demonstration until they have

completed the characterization and remediation components of their test protocol. After

a release, a partitioning tracer test is completed to characterize the volume and

distribution of PCE, followed by the remedial process, and finally, a post-remediation

partitioning tracer test is conducted to evaluate the remedial performance. Since multiple

technologies were planned for each test cell, DNAPL characterization using soil cores

was not feasible. The University of Florida was involved in two of the demonstrations.

The first demonstration, enhanced dissolution by ethanol flushing, was

completed between July 1998 and June 1999. The sequence of activities for this

demonstration is summarized in Table 1-1.

In the course of analyzing the data from the demonstration, it became of interest

to estimate the uncertainty associated with the results. This was of particular interest due

to the unique feature of this demonstration: a controlled contaminant release into a native

medium. However, it is easily understood that the uncertainty of a result is of

fundamental importance to the proper use of that result, and many introductory texts on

measurement uncertainty or error propagation provide illustrative examples of this point.

There are limited references to quantifying the uncertainty of NAPL estimates from

partitioning tracer tests. For that matter, there are limited references to the more general

problem of estimating uncertainty for moments based on breakthrough curves (BTCs).

Consequently, procedures to estimate the uncertainty of the demonstration results were

investigated.









Table 1-1. Sequence of activities completed in the cell.


Activity


Purpose


Hydraulic Test September 5 8, 1997 Estimate cell-average
hydraulic conductivity.
Pre-Release Partitioning May 28 June 4, 1998 Investigate cell hydraulics
Tracer Test (PITT) and background retardation.
Controlled PCE Release June 10- 12, 1998 Release known PCE
volume at specified
locations.
Conservative Interwell June 18 25, 1998 Investigate PCE dissolution
Tracer Test (CITT) characteristics.
Pre-Demonstration PITT July 1 12, 1998 Estimate PCE distribution.
Ethanol Flushing February 2 March 19, DNAPL remediation by
Demonstration 1999 ethanol flushing.


Post-Demonstration PITT


May 7 19, 1999


Estimate remaining PCE
distribution.


Chapter 2 presents the methods investigated to estimate the uncertainty in

moments calculated from BTCs, and Chapter 3 presents the method used to estimate

uncertainty in NAPL volume estimates. Chapter 4 presents the results from the pre- and

post-flushing partitioning tracer tests, and Chapter 5 presents the results from the ethanol-

flushing test. Chapter 6 is the conclusion.














CHAPTER 2
GENERAL METHODS FOR ESTIMATING UNCERTAINTY
IN TRAPEZOIDAL RULE-BASED MOMENTS


Introduction


There are many instances in hydrology and engineering where tracers are used to

characterize system hydrodynamics. This typically involves measuring the system

response to an injected tracer in the form of a breakthrough curve (BTC). Subsequent

BTC analysis has varied, but has generally followed one of two methods: moment

analysis or model analysis. Model analysis typically consists of a procedure whereby

model parameters are determined such that the mathematical model prediction matches

the tracer response (curve fitting), and hydrodynamic properties of the system are

characterized by the model parameters. It has been reported that curve-fitting techniques

produce more accurate results compared to the use of moments (Fahim and Wakao, 1982;

Haas et al., 1997). The mathematical model must be based on the physical and chemical

nature of the hydrodynamic system. The inability of mathematical models to accurately

describe the physical and chemical nature of complex hydrodynamic systems is a

disadvantage of this approach. In moment analysis, hydrodynamic properties of the

system are investigated using moments calculated from the BTCs. For example, the

zeroth moment of the BTC is a measure of the tracer mass recovered from the system, the

first moment is a measure of the travel time through the system, and the second moment

is a measure of the mixing in the system. Moments can be estimated from the BTCs








either by direct numerical integration, or by fitting a curve to the BTC and then

subsequent analysis is based on moments estimated from the mathematical curve (Jin et

al., 2000, Haas et al., 1997, Helms, 1997). In the latter case, it is not necessary for the

model to be an accurate representation of the physical system, all that is necessary is for

the curve to accurately describe the shape of the breakthrough curve. Helms (1997)

showed that nonlinear regression methods were more reliable for estimating BTC

moments than direct integration for imperfect BTCs. However, assuming an adequate

number of data points are available to define a BTC, direct numerical integration of the

BTC has been found to satisfactorily predict moments (Helms, 1997; Jin et al., 1995).

With this qualification, direct integration using the trapezoidal rule to estimate moments

from BTCs is advantageous due to its simplicity.

Skopp (1984) stated that the accurate estimation of moments is prevented for

two reasons. "First, the data obtained is invariably noisy; second, at some point the data

must be truncated." Noisy data is the result of measurement error, and is inherent in any

experimental procedure. The uncertainty associated with each measurement can be

divided into what has traditionally been referred to as systematic and random errors.

Systematic errors are generally defined as errors that affect the measurement in a

consistent manner, and if identified can be corrected by applying an appropriate

correction factor (Massey, p. 67, 1986). Systematic errors can be further classified as

constant or proportional errors (Funk et al., 1995). Constant systematic errors have a

magnitude that is independent of the measurement magnitude, while proportional

systematic errors are scaled to the measurement magnitude. Random errors result from

unidentifiable sources, and must be handled using stochastic methods. The accuracy of a









measurement is therefore a function of both systematic and random errors, and the

precision of multiple measurements is a function of random errors.

The uncertainty in an experimental result due to random measurement error can

best be estimated by conducting statistical analysis on results from multiple trials of the

same experiment. However, in many cases, it is not practical to conduct multiple trials of

the same experiment, as in the case of large field-scale experiments. In such situations, it

is necessary to estimate experimental uncertainty by other means, such as error-

propagation techniques. This basically consists of measuring or estimating uncertainty

for fundamental variables, and then propagating the uncertainties through to the final

experimental result. For moments based on direct numerical integration of the BTCs,

fundamental variables consist of time or volume, and concentration. Eikens and Carr

(1989) used error-propagation methods to estimate the uncertainty in statistical moments

of chromatographic peaks. Their method was based on several simplifying assumptions,

which limited application to temporal moments based on evenly spaced data and constant

concentration uncertainty. Specifically, they presented formulas for the absolute zeroth,

first normalized, and second normalized moments under the stated conditions.

This chapter presents analytical and semi-analytical equations to estimate the

uncertainty in moments resulting from systematic and random measurement errors. The

method is based on the assumption that moments are estimated from experimentally

measured BTCs by numerical integration using the trapezoidal rule. It is also assumed

that a finite tracer pulse is used in the tracer test. However, the same methods could be

used to develop uncertainty equations if tracer is introduced into the system by a step

change in concentration. A synthetic data set is used to demonstrate uncertainty









estimates with the equations. Uncertainly predictions resulting from random

measurement errors are compared to results from a Monte Carlo analysis for validation.

Finally, the equations are used to investigate general relationships between uncertainty in

measurements and estimated moments.


Theory


General Expressions

An experimentally measured BTC can be represented by a series of volume and

concentration measurements:

V1, ..., Vi-V, V,, Vi+l, ..., Vn, and cid, ..., Ci.d, Cid, ci+1d ... cnd (2-1)

where Vi = i' cumulative volume measurement [L3], and cid = ith dimensioned

concentration measurement [ML3]. Each dimensioned concentration, cid, is converted to

a dimensionless concentration, c,, by dividing by the tracer injection concentration (co):


ci = (2-2)
co

The absolute kth moment, mk [L30'+1)], of the BTC based on volume measurements is

defined as


mk = cVkdV (2-3)


and can be approximated using the trapezoidal rule by

n- V (2-4a)
mk C cVikAVi (2-4a)
itl









where AVi = (Vi+l Vi), and cVi = (ciVik + Ci+lVi+lk)/2. Note that the numerical

approximation methods used herein employ a forward difference scheme starting with i=

1. The absolute zeroth moment of the breakthrough curve, mo [L3] is


mO = cdV IE,AV, (2-4b)
0 i=W

where ci = (Ci + ci+,)/2. The zeroth moment is a measure of the mass associated with the

breakthrough curve, and is typically used to measure the tracer mass recovered, or to

measure contaminant mass removed during treatment processes. The absolute first

moment of the breakthrough curve, mi [L6], can be approximated by


m, = cVdV cViAVi (2-4c)
0 =1-1

where cV, = (ciVi+ ci+iVi+t)/2.

Haas (1996) discussed the difference between approximating moments using

equation (2-4a) and


m, = cVkdV a Y AV, (2-5)
0 il

where ik = (Vik + Vi+1k)/2. He concluded that equation (2-4a) produced a less biased

estimate of the moments, and therefore should be used in preference to equation (2-5).

As an illustration of this point, Figure 2-1 shows the percent difference between the first

and second absolute moments of the normal probability density function estimated using

equations (2-4a) and (2-5), as a function of the number of intervals used in the trapezoidal

rule. The percent difference between the first absolute moments is practically










15%



g 10%



S5%



0%
10 100 1000
Number of Intervals


Figure 2-1. Relative error between trapezoidal and true values, expressed as a function
of the number of intervals used in the numerical integration. The normal probability
density function was used in the comparison (average = 1, standard deviation = 1, and
limits of integration = -4 to 6). Shown on the graph are the absolute first moment by
equation (2-5) (0) and equation (2-4a) (o), and the absolute second moment by equation
(2-5) (A) and equation (2-4a) (x).


insignificant for 10 or more intervals. However, significant differences are observed for

the higher moment. At least 80 intervals are needed to ensure the percent difference

between the second absolute moments is less than 1%. Equation (2-5) is considered

accurate enough for use herein because this work is limited to the zeroth and first

absolute moments, and the BTCs typically consist of 50 or more volume-concentration

pairs.

The pulse-corrected, normalized first moment, iI' [L3] is defined as


V, (2-6)
m, 2








where Vp = tracer pulse volume [L3]. The normalized first moment for a non-reactive

tracer is a measure of the volume through which the tracer was carried. This is generally

referred to as the mean residence volume, or for groundwater tracer tests, the swept pore

volume.


Systematic Errors

The effect of systematic errors can be estimated in a deterministic manner by

deriving the moment equations using equation (2-1), modified to include systematic

errors in volume and concentration measurements. The resulting equations accounting

for constant and proportional systematic errors in volume and concentration

measurements are presented in Appendix A.


Random Errors

Absolute moments. The effects of random errors in volume and concentration

measurements on equations (2-1) through (2-6) were estimated by the application of

conventional stochastic formulas for variance propagation. The procedure is presented

below for the zeroth moment, and in Appendix B for the first absolute moment.

Each measurement is assumed to have a zero-meaned, random error such that

a=a' +e. (2-7)

where a = measured value, at = true value, and ea = zero-meaned, random measurement

error. The expectation, or mean, ix, of a random variable x is defined as


px =E[x]= jxp,(x)dx (2-8a)








where x = random variable, and px(x) = probability density function of x. The variance

of x, referred to as either var[x] or Ox2, is defined as


a = var[x]-= {(x-)2 p(x)dx =E[x2-p (2-8b)


Applying equations (2-8a) and (2-8b) to equation (2-7) results in

E[a]= a' ,and (2-9a)

var[a]= var[e~ ], (2-9b)

respectively. Each dimensioned concentration is converted to a dimensionless

concentration as shown in equation (2-2). Generally, the value of co has less uncertainty

than cid because co is a controlled concentration produced at the start of tracer tests, and

because multiple samples from the injection volume are generally collected and analyzed.

Therefore, the error associated with co is neglected, and the error associated with ci is

assumed equal to the error associated with cid, scaled by co. The variance of AVi can be

expressed in terms of the variance in the ith and (i+l)t volume measurements by

A(il = (i] + ai+1. (2-10)

Note that equation (2-10) reflects that the volume measurements are independent of one

another. To avoid double subscripts, the notation V[i] is used to represent Vi. Likewise,

the variance in the average concentration over the ith interval in terms of the variance in

the it and (i+l)' dimensionless concentration is given by

2 12 12
rae- = Ioii + I ,l (2-11)








Equation (2-11) reflects that concentration measurements (for a given tracer) are also

independent from one another. Formally, the expected value of a function, g(x,y), with

two random variables x and y is

E[g(x, y)]= g(x,y)p,(x,y)dxdy (2-12a)

where px,y(x,y) is the joint probability density function. If x and y are independent, then

the expected value of the function is


E[g(x,y)]= Jg(x,y)p,(x)p,(y)dxdy (2-12b)

where p,(x) and py(y) are the probability density functions for random variables x and y,

respectively. The variance ofg(x,y) is defined as

var[g(x, y)]= E[g(x, y)}2]- ~_ ,y,y2 (2-13)

Assuming volume and concentration measurements are independent, equations (2-12b)

and (2-13) can be used to derive the following variance equation for the ith product AVE:

(,i = (AL,)2 t + OiCl + vrli] i (2-14)

The variance of the sum of the i'h and (i+1)'h products of differential volumes and average

concentrations is given by

var[AV;c, + AVj.,ii ] = var[AVc,]+ var[A,c,,,] J+ 2cov[AV,c,AV],c,,,] (2-15)

The i* and (i+l)th products of differential volumes and average concentrations are not

independent since they both use the (i+l)th measure of cumulative volume and

concentration. The general definition ofcovariance is

y = cov[x,y]= E[(x- u)(y -u) )]= E[xy]- Puuy (2-16)








Applying equation (2-16) to the ith and (i+l)"' products of differential volumes and

average concentrations yields

cov[AcVi ,AV,,J, ]= E[AVicAVic,,,]-AV ,'E;'AV ,+ (2-17)

which results in the following equation after expansion and subsequent simplification

using the fact that the expected value of a zero-meaned random variable is zero (see

Appendix B):

cov[AV,,Av,,, = AVi'AV cil c ci'v+1 Ci+I],Vi+I (2-18)

The variance of the absolute zeroth moment estimate using the trapezoidal rule is then

given by the sum of all n-1 products of differential volume and average concentration:


va[mr[m[,, AV,car[ ]+ 2 cov[AV,c,,AV,.,i,] (2-19)
i-l i-l

The derivation for the variance of the first absolute moment is complicated by the

addition of the average-volume term (see equation (2-5) with k = 1), but follows the same

basic outline completed for the zeroth moment. The final equation for the absolute first

moment variance is similar to equation (2-19), but the covariance expression (analogous

to equation (2-18) for the zeroth moment) contains 15 terms, and each variance of the

product AVJBc must account for the corresponding covariance between the differential

and average volumes. The complete derivations are presented in Appendix B.

An alternative method to estimating BTC moment uncertainty is the delta method

(Kendall and Stuart, pg. 246, 1977; Papoulis, 1991; Lynch and Walsh, Appendix A,

1998). This method uses Taylor series expansions to estimate the statistical moments of

random variables. Higher accuracy is obtained by including higher-order terms in the








Taylor series. The first-order approximation to the variance of the kh absolute moment

based on numerical integration using the trapezoidal rule is

2n
2 ] (2-20a)


and the second-order approximation is

2" 28m 2n\ 2n ( a2 2
_2 1Y2 2 20b
a^.[k] .( 0 Ia[ja l XiXj (2-20b)
i-= 1 i l ax WM ~ J>

Equations (2-20a) and (2-20b) are based on the assumption that all xi random variables

are independent, and equation (2-20b) is based on the additional assumption that the

random variables have symmetric probability distributions. An overview of the delta

method is presented in Appendix C, and the method is applied to estimate the uncertainty

in the absolute zeroth and first moments. As shown in Appendix C, the second-order

expression for the zeroth-moment variance is an exact expression, and is therefore

equivalent to the variance given by equation (2-19). A second-order expression for the

first absolute moment is also given in Appendix C. However, this is an approximation to

the true variance since it ignores third-order mixed derivative terms.

Normalized moment. To estimate the uncertainty associated with the kth

normalized moment, it is necessary to estimate the variance of the ratio of the kth absolute

moment to the zeroth moment. The exact analytical solution is obtained by the

evaluation of equation (2-12a) and (2-13), with g(x,y) defined as mk/mo. The difficulty in

evaluating the resulting integrals, however, makes approximation methods more

practical. The delta method is often used to estimate the uncertainty of a ratio of two








random variables. Winzer (2000) discussed the accuracy of error propagation related to

the ratio of two numbers using the delta method, which in general can be expressed as

2 b )2 + 2.b
cb/. a 2 b2 ab- (2-21)

For the ratio of the absolute kth to the zeroth moment,
2 2 2
a2 mk m 0] f m [k] 20mI0mll[k (2-22)
"k] l m0 m W mk mom

Equations (2-21) and (2-22) are first-order approximations because all terms in the Taylor

series expansion with second- and higher-order derivatives are neglected (See Appendix

C). The zeroth and kth absolute moments are not independent since they are based on the

same measurements of volume and concentration. Therefore, the covariance between the

two is needed to apply equation (2-22). Due to the complexity of an analytical solution, a

delta method approximation to the covariance is also used. For two random variables a

and b, which are functions of random variables xl to xm, the first-order approximation to

a(a,b) is (see Appendix C)


,(a,b)= o (x,,x, )(l b- (2-23)
,.i j- x, j (axi

For the covariance between the zeroth and kit absolute moments, equation (2-23)

becomes


a(mo,m,)= t (xx (2-24a)
iMI j-1 \ x \ e j)

The second-order approximation to o(mo,mk) is (see Appendix C)

~2 2 +mo 2. 2.(' 2 2 a'mO a'mk
a(mo,mk,)=~a o- A,,,im +2- P)l j] (2-24b)
Wii x axi i- ij >i xi xj ax ixi








Equation (2-24b) is based on the assumptions that all x, random variables are independent

and that they have symmetric probability distributions. Since the zeroth and first-

absolute moments are calculated using the trapezoidal rule, the variables x, through x2n in

equation (2-24) are the measured volume and concentration values:

{x, x... x,, } ..., x = {V,. ..., V, and (2-25a)

(x,,,,..., x,- ... x = {c,,..., c,,...,c.} (2-25b)

Appendix C also presents the derivation of the first-normalized moment uncertainty. The

uncertainty of the pulse-corrected, first-normalized moment is

2 ,r=0 + p (2-26)
AP Opj)] VIP]+

where o v[p] is the variance of one-half the tracer-pulse volume, which is estimated from

the field methods employed in the tracer test.

Special case: constant flow rate. For the case where the flow rate is constant

over the duration of the test, moments can be calculated on a temporal basis rather than a

volumetric basis. From a practical standpoint, random errors in measuring time can be

neglected, and the equations for estimating moment uncertainty can be simplified. In this

case, the uncertainty for the kth temporal moment (mk,t) can be written as
a F-2 1 A

m [kt"l t +k-I (Atl2 +Atjt2+ [i+]) + 2AttnCt (2-27a)

Under the additional condition of constant At, equation (2-27a) becomes

1 -2
a,2 4 i2,t 2 .-+ 2k2 12 +]t2i k cn] (2-27b)

and under the further condition of constant rc, equation (2-27b) reduces to









2 t2k k k
O2kt = At'- tk + 2 + t21 (2-27c)
2] 4 i2

For the zeroth moment, equation (2-27c) becomes


Cmot = (n-1)At' (2-28)

(The equation for the zeroth-temporal moment reported by Eikens and Carr (1989) under

the same conditions (constant At and ac) was nAct2~2. The difference between their

equation and that reported in equation (2-28) results from a difference in the formulation

of the numerical approximation to the moment integral). The uncertainty in the flow rate

is then used to estimate the uncertainty in the kth volumetric moment:

o (Qm. )= Qlot + 2 m2 + o2a2 (2-29)

where Q = the volumetric flow rate [L'T-'], and a [L6T 2] is the variance of the flow

rate. Equation (2-29) is based on the assumption of independence between measurement

errors in the flow rate and temporal moments.


Validation and Analysis Using a Synthetic Data Set

A synthetic data set was generated to validate the method for estimating moment

uncertainty and to investigate the impact of measurement uncertainty on moment

calculations. The synthetic data set was generated using the solution to the one-

dimensional advective-dispersive transport equation, subject to the initial condition of

c(x,0) = 0 for x > 0, and the boundary conditions of c(0,t) = co for t > 0, and c(oo,t) = 0 for

t > 0 (Lapidus and Amundson, 1952; Ogata and Banks, 1961). The nondimensional form

of the solution, accounting for retardation, is









c(r,RP)= Lek (R-r) +exp(Perfc R+r) (2-30)
2) 4R[ 4Rr (2-30)

where c is the dimensionless concentration (cd/co), t is the dimensionless pore volume (r

= vt/L, where v = pore velocity [LT'], t = time [T], and L = linear extent of the flow

domain [L]), R = retardation factor (R = l+(SKNw)/(1-S), where S = NAPL saturation

and KNW = NAPL partitioning coefficient), and Pe = Peclet number (Pe = vL/D, where D

= dispersion coefficient [L2T']). Note that for the nonreactive tracer, R = 1. This

solution is for a step input of tracer, and was used to generate a pulse-input solution by

superposition, lagging one step-input solution by the tracer pulse-input length and

subtracting it from another. The nondimensional pulse length (defined as Tp = vtp/L,

where tp is the pulse duration [T]) was 0.1, and the Peclet number was 10. The

nonreactive and reactive breakthrough curves represented the known, or true data set.

The synthetic data set was chosen such that the zeroth moment of the tracers was 1, and

the normalized first moment of the non-reactive tracer was 10. Unless noted otherwise, a

total of 100 volume-concentration data points were used to represent the BTCs, and a

retardation factor of 1.5 was used to generate the reactive breakthrough curve.

Results and Discussion


Systematic Errors

Constant systematic volume errors. The impact of constant systematic errors in

volume measurements on the absolute zeroth moment and the normalized first moment

are illustrated in Figure 2-2a. The volume error shown on the abscissa in Figure 2-2a is

expressed as a fraction of the pore volume, as predicted by the non-reactive normalized





































-5% "


Constant Systematic Volume Error


Proportional Systematic Volume Error





Figure 2-2. Relative errors in the zeroth moment (solid line) and the normalized first
moment (dashed line) for a) constant systematic volume errors, and b) proportional
systematic volume errors. The volume errors are benchmarked to the swept volume.


i


C)


r


(C

r
c
z


...r









first moment. Constant systematic errors in volume measurements have no impact on the

zeroth moment because this moment is based on a volume differential, and consequently

the error is eliminated. However, higher-order moments, like the first-normalized

moment (see Figure 2-2a), will be affected because of the volume dependency in the

numerator of the moment calculation (see equation (2-4a) or (2-5)). As shown in Figure

2-2a, the normalized first moment is directly proportional to the constant systematic

volume error.

Proportional systematic volume errors. The impact of proportional systematic

errors in volume measurements on the absolute zeroth moment and normalized first

moment are illustrated in Figure 2-2b. The error shown on the abscissa in Figure 2-2b is

defined in the same manner above for the constant systematic volume error. Proportional

systematic errors in volume measurements directly impact both the absolute zeroth

moment and the normalized first moment. As shown in Figure 2-2b, the zeroth moment

is directly proportional to the proportional systematic volume error. The normalized first

moment is also directly proportional to the proportional systematic volume error, and the

difference between the lines in Figure 2-2b is due to the correction of one-half the pulse

volume. Errors in pulse volume were neglected in this analysis.

Constant systematic concentration errors. For this analysis, constant

systematic errors are limited to magnitudes equal to or less than method detection limits,

based on the assumption that larger values would be readily identified by typical quality

assurance procedures used in the laboratory. Assuming typical values for alcohol tracers,

i.e., injection concentrations on the order of 1000 mg/L and method detection limits on

the order of 1 mg/L, dimensionless concentration errors could range from -0.001 to








+0.001. The impacts of errors in this range on the absolute zeroth moment and

normalized first moment are shown in Figure 2-3. It is noted that the effects of these

types of errors will be more pronounced for smaller injection concentrations, but they

would also be easier to identify. For example, dimensionless errors ranging from -0.001

to +0.001 produce errors in the zeroth moment ranging from -7% to +7%. Mass

recoveries ranging from 93% to 107% are not unrealistic, and do not necessarily indicate

analytical problems. However, dimensionless concentration errors ranging from -0.01 to

+0.01 (1 mgL)' /100 mgL') produce errors in the zeroth moment ranging from -70% to

+70%. Mass recoveries less than 90% or greater than 110% should be used with caution,

and certainly, mass recoveries as low as 30% or as large as 170% would clearly reflect a

serious problem with the tracer data.

Proportional systematic concentration errors. As shown by equations (A-20a)

through (A-20c) in Appendix A, the impact of proportional systematic errors in

concentration measurements is eliminated by using dimensionless concentrations.

Therefore, proportional systematic concentration errors do not impact moments.


Random Errors

Method validation. The variance of the zeroth and absolute first moments

calculated by the analytical expressions were compared to variances estimated by the

delta method. The zeroth-moment variance calculated by the two methods is the same

since both expressions are exact. The first-absolute moment variance calculated by the

two methods were similar, and the slight differences between the two were attributed to

the delta-method approximation.












30%

20%

10%

0% i

S-10% ,-

-20% -

-30% -- -,--
-0.0010 -0.0005 0.0000 0.0005 0.0010
Constant Systematic Concentration Error



Figure 2-3. Relative error in zeroth moment (solid line) and first-normalized moment
(dashed line) as a function of the ratio of constant systematic concentration errors to
injection concentration.


Monte Carlo analysis (see, for example, Gelhar, 1993) was used to verify

normalized moment uncertainty estimates. Measurement uncertainty was assumed to be

a normally distributed random variable with a zero mean. Concentration-measurement

uncertainty was assigned using a coefficient of variation (CV), defined as the ratio of

standard deviation to true measurement, between 0 and 0.15. Volume-measurement

uncertainty was assigned by equating volume standard deviation to a value less than or

equal to one-half the interval between volume measurements (a constant interval was

used). A unique measurement error was applied to each volume and concentration value

in the synthetic data set. Moment calculations were then completed on the "measured"

BTC. This process was repeated 10,000 times, and the averages and standard deviations








of the moments were computed. Convergence of Monte Carlo results was tested by

completing three identical simulations, each with 10,000 iterations; the CV for the

moments differed by no more than 0.02%. Figure 2-4 shows BTCs for the synthetic non-

reactive and reactive tracers, as well as "measured" BTCs generated from one Monte

Carlo realization with the volume standard deviation and concentration CV defined as

0.15.

Table 2-1 compares the absolute zeroth and normalized first moment CVs using

the semi-analytical equations to those estimated from the Monte Carlo simulation. Three

cases are presented: the first with volume uncertainty (standard deviation) equal to 0.35

and no concentration uncertainty, the second with no volume uncertainty and

concentration uncertainty equal to 0.15, and the third case with volume uncertainty equal

to 0.35 and the concentration uncertainty equal to 0.15. The second-order covariance

expression between the zeroth and absolute first moments (equation (2-24b)) provided

much better agreement with the Monte Carlo results, and was therefore used in the semi-

analytical method rather than the first-order covariance expression (equation (2-24a)).

As shown in Table 2-1, the agreement between the two methods demonstrates that the

semi-analytical method correctly accounts for the uncertainly in volume and

concentration measurements.

Application. Based on the CV of the moments, concentration errors have a

greater impact on the results than volume errors. This is illustrated in Figure 2-5, which

shows the CV for the zeroth and normalized first moments as a function of volume and

concentration errors. Concentration errors are expressed as CV, and volume errors are

expressed as the ratio of the volume measurement standard deviation to the swept























0 1 2 3 4
Pore Volume

Figure 2-4. BTCs for the synthetic non-reactive and reactive tracers, as well as
"measured" non-reactive (crosses) and reactive (circles) BTCs generated from one Monte
Carlo realization. Both volume standard deviation and concentration CV were equal to
0.15.




Table 2-1. Comparison of mass and swept volume CV (%) based on Monte Carlo
(M.C.) simulations and semi-analytical calculations (S.A).


S. A. M. C.
Case A
Mass 1.8 1.8
Swept Volume 0.9 0.9
Case B
Mass 3.4 3.5
Swept Volume 1.1 1.0
Case C
Mass 4.1 4.1
Swept Volume 1.4 1.4


Case A: volume error = 0.35 and concentration CV = 0; Case B: volume error = 0 and
concentration CV = 0.15; and Case C: volume error = 0.35 and concentration CV = 0.15.










a)
8% ---------- ---
7% ------. -t ..
5% 6

4% .- ------- -- ----- -----------

--- <--- -----<--- ---1-^----
2% o
1% -
0%
0 0.005 0.01 0.015 0.02 0.025 0.03
Normalized Volume Error

b)
b) 2.5%
U 2.5% ... ----- --- -- ------- .--- -- ------.. -

1 ------------
S2.0% ,



1.0% ---
0.5%




Z 0.0%
0 0.005 0.01 0.015 0.02 0.025 0.03
Normalzed Vohume Error



Figure 2-5. Coefficient of variation (%) of the a) zeroth and b) normalized first moments
as a function of the ratio of volume standard deviation to swept volume. Each line
represents concentration CVs of 0.0 (0), 0.05 (o), 0.10 (0), 0.15 (A), 0.20 (*), 0.25 (x)
and 0.30 (+), respectfully.








volume. The robust nature of moment calculations is exemplified by the fact that relative

uncertainty in moments is less than the relative uncertainty in volume and concentration

measurements. In addition, measurement uncertainty has less impact on the first-

normalized moment than the zeroth moment, which results from the fact that normalized

moments are a function of the ratio of absolute moments.

It could be argued that the uncertainties in concentrations near the detection limit

are higher than the uncertainties in concentrations near the largest concentration

measurements on the BTC. To investigate the impact of variable concentration

uncertainty, it was assumed that the concentration CV varied linearly between the CV of

the maximum concentration (CV,) and the CV of the detection-limit concentration

(CVDL). A detection limit of 0.001 (1 mg/L in 1,000 mg/L) was assumed for this

analysis, and all concentrations equal to, or less than this value were assigned CVDL.

Figure 2-6 shows the CV for the zeroth and normalized first moments for 50% < CVDL <

200%, and for CV.m = 5%, 10% and 15%. Volume errors were neglected in this

analysis. The zeroth moment CV varies from 4 to 15%, and the normalized first moment

CV varies from 2% to 7%. These results provide further support for the conclusion that

the relative uncertainty in moments is less than the relative uncertainty in concentration

measurements.

Conclusions

This chapter presented a generalized method for estimating the uncertainty of

BTC moments calculated by numerical integration using the trapezoidal rule. The

method can be applied to either temporal or volumetric moments, and in the latter case,

explicitly accounts for errors in volume measurements. The complexity of the















16%
14%
12%
0 10%


0 6%


S2%
0%
50% 100% 150% 200%

Detection-Limit Coefficient of Variation, CVDL



Figure 2-6. Coefficient of variation for the zeroth moment (closed symbols) and the
normalized first moment (open symbols) for a range in concentration detection-limit
coefficient of variation (CVDL) values. Results are shown for maximum concentration
coefficient of variation (CVma) values of 5% (0), 10% (n), and 15% (A). Volume error
was neglected.


calculations for the zeroth moment is comparable to that associated with the typical

propagation-of-errors formula. However, the formulae for higher moments, as

exemplified by the first-absolute moment formulae, are substantially more complex than

the typical propagation of errors formula. The results have shown that the relative

moment uncertainty is less than the relative volume and concentration measurement

uncertainties, and that the normalized first moment is impacted less than the zeroth

moment. Moment uncertainties are more sensitive to concentration uncertainties as

opposed to volume uncertainties.














CHAPTER 3
UNCERTAINTY IN NAPL VOLUME ESTIMATES
BASED ON PARTITIONING TRACERS


Introduction


This chapter begins with a review of partitioning tracer tests and the errors and

uncertainties that can affect their results. A method is then presented for estimating the

uncertainty in NAPL volume estimates using partitioning tracers. It is based on the

assumption that moments are calculated from the experimentally measured BTCs using

the trapezoidal rule for numerical integration. The method for estimating uncertainty

from random errors is based on standard stochastic methods for error propagation, and is

verified through a comparison of uncertainty predictions to those made by Monte Carlo

simulations using a synthetic data set. Systematic errors are also addressed. Finally, the

methods are used to develop some general conclusions about NAPL volume

measurement and uncertainty.


A Review of Partitioning Tracer Tests

Partitioning tracers were first used in the petroleum industry to estimate oil

saturation. The first patents related to partitioning tracers were issued in 1971 (Cooke,

1971; Dean, 1971). Tang (1995) reviewed the application of partitioning tracers in the

petroleum industry, and reported that over 200 partitioning tracer tests had been

conducted in the petroleum industry since 1971. The first publication discussing the









application of the method to groundwater contaminant, source-zone characterization

occurred in 1995 (Jin et al., 1995), in which the theory of partitioning tracers for source-

zone contamination characterization was described and supported by experiments and

model simulations. The first field application to a NAPL-contaminated aquifer took

place at Hill AFB in 1994 (Annable et al., 1998). Other field applications have been

described by Cain et. al. (2000), Sillan et al. (1999), Hayden and Linnemeyer (1999), and

Nelson and Brusseau (1996). Dwarakanath et al. (1999) report that over 40 field

demonstrations of the technique had been completed at that time. Rao et al. (2000) and

Brusseau et al. (1999a) review partitioning tracer test methods, applications and

reliability. Patents for source-zone characterization using partitioning tracers were issued

in 1999 (Pope and Jackson, 1999a and 1999b).


Sources of Uncertainty and Errors

General sources of errors. Uncertainty in partitioning tracer predictions can

result from two major sources: uncertainty in meeting underlying assumptions (modeling

uncertainty), and uncertainty in measured values used in the partitioning tracer technique

(measurement uncertainty). As discussed in Chapter 2, measurement uncertainty can be

divided into systematic and random errors.

In general, a partitioning tracer is retarded relative to a non-partitioning tracer due

to its interaction with NAPL, and the NAPL saturation can be estimated based on the

extent of retardation. NAPL saturation can also be estimated using two partitioning

tracers, provided the partitioning coefficients differ enough to ensure the retardation of

one relative to the other can be sufficiently measured. Partitioning-tracer tests are based

on several assumptions, and they can be summarized broadly as: retardation of the








partitioning tracer results solely from the NAPL, partitioning tracers are in equilibrium

contact with all the NAPL within the swept zone, and the partitioning relationship

between the NAPL and the tracer can be accurately described by a linear equilibrium

relationship (Jin et al., 1995). Uncertainty in tracer predictions can result when these

assumptions are not sufficiently satisfied. Table 3-1 summarizes the different types of

errors that can occur in partitioning tracer tests.

Dwarakanath et al. (1999) discussed errors caused by the background retardation

of tracers due to tracer adsorption onto porous media. This will cause a systematically

larger prediction in NAPL saturation due to the increase in tracer retardation. This error

can be corrected by subtracting the background retardation factor from the partitioning

tracer retardation factor, assuming that the total retardation of the partitioning tracer is the

sum of background retardation and NAPL retardation. However, it should be recognized

that in certain circumstances the total retardation may not be the sum of background

retardation and NAPL retardation. Nelson et al. (1999) investigated the effect of

permeability heterogeneity, variable NAPL distribution, and sampling methods on

partitioning tracer predictions. Observations in laboratory experiments indicated that

flow by-passing, resulting from both low conductivity regions and relative permeability

reductions due to NAPL saturation, resulted in lower predictions of NAPL saturation.

They also noted that the mixing in sampling devices of streamlines that have passed

through a heterogeneous NAPL distribution resulted in under-predictions of NAPL

saturation. Errors from these processes (flow by-passing, and streamline mixing) could

result in a systematically lower prediction of NAPL saturation by partitioning tracers.









Table 3-1. Summary of errors and their impact on partitioning tracer test predictions.


Error


Type of Error


References


Nonlinear partitioning Systematically larger Wise et al. (1999), Wise
(1999)
Rate-limited mass transfer Systematically lower Willson et al. (2000),
Nelson and Brusseau
(1996)
Non-reversible partitioning Systematically lower or Brusseau et al. (1999a)
larger
Background retardation Systematically larger Dwarakanath et al.
(1999)
Flow by-passing Systematically lower Nelson et al. (1999),
Dwarakanath et al.
(1999), Brusseau et al.
(1999a), Jin et al. (1995)
Nonequilibrium Systematically lower Dwarakanath et al.
partitioning (1999), Brusseau et al.
(1999a)
Tracer mass loss Systematically lower or Brusseau et al. (1999a),
larger Brusseau et al. (1999b)
Measurement Error Systematically lower or Dwarakanath et al.
larger, and random (1999)
Variable NAPL Systematically lower or Dwarakanath et al.
characteristics larger, and random (1999), Brusseau et al.
(1999a)
Effects from remedial Systematically lower or Lee et al. (1998)
flushing solution larger


A linear, reversible equilibrium relationship is usually used to describe the

partitioning relationship between the tracer and the NAPL. Brusseau et al. (1999a)

qualitatively discuss errors due to mass-transfer limitations and non-reversible

partitioning. Dwarakanath et al. (1999) suggested results from laboratory column

experiments could be used to select tracer residence times large enough to ensure

partitioning is adequately described by equilibrium relationships. Lee et al. (1998)

reported differences in partitioning coefficients measured from batch and column

experiments, and suggested that the discrepancy in measurements could have resulted








from diffusion limitations of the tracer in the NAPL. Willson et al. (2000) investigated

the effect of mass-transfer rate limitations on partitioning tracer tests. They conducted

column laboratory experiments using TCE as the NAPL, isopropanol as the non-

partitioning tracer, and 1-pentanol and 1-hexanol as the partitioning tracers.

Experimental results were modeled using an advective-dispersive model, where mass

transfer between the NAPL and aqueous phase were estimated using terms to describe

boundary layer mass transfer resistance and intemal-NAPL diffusion resistance.

Modeling results successfully matched the experimental results. However, it was noted

that the method-of-moments analysis also reasonably agreed with the experimental

results. Valocchi (1985) showed that nonequilibrium does not effect the normalized first

moment for diffusion physical, first-order physical, and linear chemical nonequilibrium

models. If nonequilibrium partitioning of the tracer into the NAPL is adequately

described by one of these models, then it could be concluded that nonequilibrium will not

effect NAPL volume estimates. If nonequilibrium partitioning does occur, it should

result in less tracer retardation, and therefore produce a systematically lower prediction of

NAPL saturation and volume.

Wise et al. (1999) reported that partitioning between tracers and NAPL was

inherently nonlinear, and showed that an unfavorable form of the Langmuir partitioning

relationship effectively predicts the partitioning behavior. Error associated with using a

linear equilibrium model in place of a nonlinear equilibrium model, as well as steps to

minimize this error were discussed by Wise (1999). It was reported that this type of error

produced systematically larger predictions of the NAPL saturation, and could be

minimized by avoiding large injection concentrations for partitioning tracers.








Additional uncertainty in partitioning tracer tests can result from the interaction of

tracers to resident remediation flushing solutions (such as cosolvent or surfactant

solutions) if the partitioning tracer test is conducted after remediation efforts. Lee et al.

(1998) investigated the impact of changes in NAPL characteristics from cosolvent

flushing on tracer partitioning coefficients. They found that preferential dissolution of

more soluble NAPL components during cosolvent flushing to enhance NAPL dissolution

decreased the tracer-partitioning coefficient. This resulted in NAPL-volume estimates

lower than the actual NAPL volume. Spatially variable NAPL characteristics could also

impact partitioning-tracer behavior, and Dwarakanath et al. (1999) discussed the resulting

uncertainty in partitioning coefficients using a model relating partitioning coefficients to

NAPL composition.

The loss of tracer mass, and its affect on partitioning tracer tests was qualitatively

discussed by Brusseau et al. (1999a). Brusseau et al. (1999b) investigated the effect of

linear and non-linear degradation on the moments of a pulse-input of contaminant, the

results of which can be applied to tracers as well. It was reported that the first moment

for the case of linear degradation is reduced relative to the first moment for the case

without degradation. Nonlinear degradation was investigated using a Monod equation. It

was reported that the first moment with non-linear degradation was at first less than, and

then greater than the first moment without degradation.

Previous uncertainty estimations. Helms (1997) compared techniques for

estimating moments associated with imperfect data sets of tracer BTCs. Nonlinear least-

squares regression was found to be an effective method for working with imperfect data;

methods to estimate standard deviations and confidence intervals of temporal moments









based on a nonlinear regression technique were presented. However, the uncertainty

analysis was not extended to NAPL-volume estimates.

Jin et al. (1997), Dwarakanath et al. (1999) and Jin et al. (2000) discussed errors

and uncertainty related to partitioning tracer tests. The method discussed in the latter two

papers is based on the propagation of random errors in the retardation factor and the

partitioning coefficient through to NAPL saturation. Dwarakanath et al. (1999) also

investigated the impact of systematic measurement errors in volume and concentration

measurements on NAPL volume predictions. Systematic errors in volume measurements

were reported to have limited impact on NAPL volume estimates, and systematic errors

in concentration measurements were shown to inversely effect NAPL volume estimates.

Random errors in retardation factors were characterized using nonlinear regression

analysis to estimate the variance between collected BTC data and a theoretical model.

Random errors in the measurement of the partitioning coefficient were assessed using the

standard deviation of the isotherm slope from batch partitioning experiments, or by

calculating the standard deviation of results from multiple experiments when the

partitioning coefficient was estimated from column experiments. It was concluded that

random errors in the retardation factor and in the partitioning coefficient result in an error

of approximately 10% in the NAPL saturation when tests yield retardation factors greater

than 1.2. Jin et al. (2000) made a similar presentation regarding the uncertainty in NAPL

saturation as a function of retardation factor and partitioning coefficient uncertainty.

However, they also include a formula for the uncertainty in the retardation factor as a

function of the non-partitioning and partitioning first moments. However, no discussion

of estimating these uncertainties is presented. As a further point of interest, Jin et al.









(2000) also present a formula for the normalized temporal moment, as a function of BTC

extrapolation. Specific application of this formula for uncertainty analysis was not

presented.

The technique used by Dwarakanath et al. (1999) and Jin et al. (2000) is based on

the first-order Taylor series expansion for error propagation (delta method), and assumes

that errors in the retardation factor and the partitioning coefficient are independent. The

error in the retardation factor and normalized moments is based on the residual error

between the measured data and the curve used to fit the data. The limitation in the

method presented by Dwarakanath et al. (1999) is that the uncertainty in retardation and

partitioning coefficient can only be propagated through to NAPL saturation. The

uncertainty in NAPL volume cannot be estimated without the uncertainty in the swept

volume (provided by the normalized first moment), and the correlation between the swept

volume and saturation. Jin et al. (2000) provide an estimate of the non-partitioning

normalized first moment uncertainty, which is based on the residual error between data

points and the curve fit. However, the uncertainty in NAPL volume still requires the

correlation between the swept volume and NAPL saturation. Furthermore, the

uncertainty in the normalized moments and retardation does not explicitly account for

measurement uncertainty, but is more accurately a measure of how well the curve fits the

measured data. Curve-fitting techniques that explicitly include measurement uncertainty

could be used with the procedure outlined by Dwarakanath et al. (1999) and Jin et al.

(2000) to better estimate partitioning tracer test uncertainty.








Uncertainty-Estimation Method


General Equations

An outline of the equations used to estimate NAPL saturations and volumes from

tracer information is presented as an introduction into the uncertainty equations. The

retardation factor, R is defined as


R= (3-la)


where gNR' [L3] and tLR' [L3] are pulse-corrected, normalized first moments for the non-

partitioning and partitioning tracers, respectively. The partitioning tracer may be retarded

relative to the non-partitioning tracer due to adsorption onto the aquifer matrix

(background retardation). If background retardation (RB) has been measured, it can be

accounted for using


R = -'(R -1), (3-lb)


where RB is defined as the ratio of the pulse-corrected normalized first moment of the

partitioning tracer in the absence of NAPL to the pulse-corrected normalized first

moment of the non-partitioning tracer. Assuming a linear equilibrium partitioning

coefficient (KNw), and pore space occupied by water (or air) and NAPL only, the

saturation (S) can be calculated from

R-1
S = (3-2)
R-l+K,

and the volume of NAPL, VN, is given by

VN= 'S (3-3)









Systematic Errors

The effect of systematic errors can be estimated in a deterministic manner by

developing equations (3-1) through (3-3) with systematic errors in volume and

concentration measurements. This was done for both constant and proportional

systematic errors in volume and concentration measurements; those derivations and

resulting formulae are presented in Appendix A.


Random Errors

To estimate the random uncertainty in R, it is necessary to estimate the covariance

between the partitioning and non-partitioning normalized first moments, since they are

based on the same volume measurements. Furthermore, it is possible for correlation to

exist between the non-partitioning and partitioning tracer concentrations. The covariance

is estimated using a first-order delta method approximation (see equation (2-23) in

Chapter 2), which can be expressed as


U]" /4,") a [ dr: xL )] + ,^ c (3-4a)
i.1, j-, i Iaxi V av, e v,

The last term on the right-hand side on equation (3-4a) describes the covariance resulting

from a common tracer-pulse volume. It is assumed that the tracer-pulse volume

uncertainty is negligible due to the controlled conditions generally used in its

measurement, and this term will be ignored in subsequent analysis. Since errors in

volume and concentration measurements are assumed independent, equation (3-4a) can

be written as


I. ~f (Vi a (ccf NR P) c, (3-4b)
i= (av, Adi ila~ ~








or expressing the derivatives of the normalized first moments in terms of the zeroth and

absolute first moments:



_mNR m mR inFm R[m m O R -
Sav av, av, av|+--


aNR 8m NR R R aURn
m 0 macNR m, NR mR O,
(m N (m. R



where a(cNR, CR) is the covariance between the non-partitioning and partitioning

concentrations. One possible approach to approximating the covariance is to assume a

linear correlation between the non-partitioning and partitioning concentrations, in which

case,

(Ci,CR)= K[var( )j (3-5)

where K is estimated as the ratio of the ith partitioning and non-partitioning

concentrations. If it is assumed that there is no correlation between the non- partitioning

and partitioning concentrations, then the second terms on the right-hand side of equations

(3-4b) and (3-4c) are zero. The derivatives of the zeroth and absolute first moments with

respect to volume and concentration measurements are the same as those used to estimate

the covariance between the zeroth and absolute first moments from Chapter 2 (see

Appendix C for a listing of those derivative expressions). Using a first-order delta

method approximation to the uncertainty of the ratio of two random variable (see

equation (2-21) in Chapter 2) the retardation variance, oR is approximated as









C2 2 2 ), 2 .R)
(= -1 + (3-6)


Likewise, equation (2-21) is used to estimate the uncertainty in saturation. The

variance of the numerator in equation (3-2) is

a I =-R (3-7a)

and the variance of the denominator in equation (3-2) is
2 2 +2 (3a2)
R-I+KINW] = (R + '[NW] (-)

Note that equation (3-7b) reflects the assumption that the retardation factor and the

partitioning coefficient are independent, which is the same assumption made by

Dwarakanath et al. (1999) and Jin et al. (2000) in their analysis of NAPL saturation

uncertainty. It could be argued that R and KNW are correlated since the partitioning

coefficient controls the degree of retardation. For this analysis, however, it is assumed

that R and KNW are independent because the random errors incurred in measuring either

R or KNW are independent. Accounting for the fact that R occurs in the numerator and

denominator, the variance of the saturation, as2 becomes

+U 2c +' (3-7c)
_2 (R-1l)2 (a (+aNW^ ) 2cr
S (R-l+K, [ (R-l)2 0-1+^,) (R-1XR-- +KN- )J (37

which reduces to

2 K2WR +(R-1) 2a IKn
s= (R-i+Kw)' (3-7d)
(R-1+K )4

Equation (3-7d) is equivalent to that presented by Dwarakanath et al. (1999) and Jin et al.

(2000).








The uncertainty of the NAPL volume must account for the correlation between

the normalized first moment of the non-partitioning tracer and the saturation, since they

are both based on the same volume and non-partitioning concentration measurements.

Likewise, it must account for the correlation in non-partitioning and partitioning

concentrations if present. The covariance between the two is estimated using the delta-

method approximation (equation (2-23)):


a(SNR) (,,x S X (3-8)
i-i .i- iA. ax
1=1 j=1 OS )(P vi!

The x values in equation (3-8) are the same as those stated in equations (2-25a) and (2-

25b). The derivative of g NR' with respect to x, in terms of the zeroth and absolute first

moments is given in equation (3-4c). The derivative of S with respect to measurement xi

in terms of the zeroth and absolute first moments is

OS KNW
axi (R-1+ Kw)2(Y u-1N)2

M a Aaf M MNR 8amNR-M NR "ONR
[ -M 0 m 1 (3-9)
NMA f x, __x,_ 8x,
PW i ax; kxi &i



The derivatives of the zeroth and first absolute moments are listed in Appendix C. The

covariance terms o(xi,xj) in equation (3-8) include the covariance between the volume

and concentration measurements used in S and gNR'. The volume and non-partitioning

concentrations measurements are the same, consequently, the covariance is simply the

volume variance and the non-partitioning concentration variance. The covariance

between the non-partitioning and partitioning concentrations can be estimated using

equation (3-5), but is assumed negligible for this analysis. With the covariance between








the NAPL saturation and the non-partitioning normalized first moment known, the

variance in the volume estimate of NAPL is given by

2
V[N] -
+[N] [(3-10)
'-"'NRY2^ +s (-R*) 32,&.. Wy S)r YFroN,sNR (72


Results and Discussion


Systematic Errors

Constant systematic volume errors. The impact of constant systematic errors in

volume measurements on retardation, saturation, and NAPL volume are illustrated in

Figure 3-la. The error shown on the abscissa in Figure 3-la is expressed as a percent of

the pore volume, as predicted by the non-partitioning normalized first moment. Constant

systematic errors in volume measurements impact the retardation estimate to a lesser

extent because the volume error occurs in both the numerator and denominator, and the

saturation estimate to a greater extent because the magnitude of the partitioning

coefficient relative to the error reduces the effect of the error in the denominator of

equation (3-2). Interestingly, the final error in NAPL volume is relatively small due to

the offsetting errors in saturation and the normalized first moment. This result agrees

with that presented by Dwarakanath et al. (1999).

Proportional systematic volume errors. The impact of proportional systematic

errors in volume measurements on retardation, saturation, and NAPL volume are

illustrated in Figure 3-1b. The error shown on the abscissa in Figure 3-1b is the percent

volume error. Proportional systematic errors in volume measurements have minimal









a)
30%

15% ....


S-15%

-30%- -
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
Constant Systematic Vohlme Error
b)
30%

S15% -

o 0% -

-15% -

-30% -- -
-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15
Proportional Systematic Volume Error

c)
30%

15%

0% ----

& -15% I

-30%
-0.0010 -0.0005 0.0000 0.0005 0.0010
Constant Systematic Concentration Error



Figure 3-1. The effects of systematic errors on retardation (solid line), saturation (short-
dashed line), and NAPL volume (long-dashed line) are illustrated for the case of a)
constant systematic volume errors, b) proportional systematic volume errors, and c)
constant systematic concentration errors. The retardation factor was 1.5 in each case, and
the BTCs were composed of 100 data points.








impact on retardation and saturation estimates, because the error occurs in both the

numerator and denominator of these terms. However, this type of systematic error has a

larger impact on the NAPL volume estimate because of its impact on the swept volume

(see Figure 2-2b).

Constant systematic concentration errors. The range of constant systematic

errors is limited to magnitudes equal to or less than method detection limits, based on the

assumption that larger errors would be more readily identified by typical quality

assurance procedures used in the laboratory. Assuming typical values for alcohol tracers,

i.e., injection concentrations on the order of 1000 mg/L and method detection limits on

the order of 1 mg/L, dimensionless concentration errors could range from -0.001 to

+0.001. The impact of errors in this range on the retardation, saturation, and NAPL

volume are shown in Figure 3-1c. It was assumed that the systematic error was the same

for both non-partitioning and partitioning concentrations. As shown in Figure 3-1c, these

types of errors have the largest impact on NAPL volume estimates, and smaller, but

similar impacts on retardation and NAPL saturation estimates. Comparable estimates

were obtained when the results from Figure 3-1c for NAPL volume errors were compared

to NAPL volume errors estimated by the formula presented by Dwarakanath et al. (1999).

Proportional systematic concentration errors. As shown by equations (A-20a)

through (A-20c) in Appendix A, the impact of proportional systematic errors in

concentration measurements on the moment calculations is eliminated by using

dimensionless concentrations. Therefore, proportional systematic concentration errors do

not impact retardation, NAPL saturations, or NAPL volume estimates.









Random Errors

A Monte Carlo analysis was used as a means to verify uncertainty estimates from

the error-propagation equations. For the Monte Carlo analysis in this work, measurement

uncertainty was estimated as a normally distributed random variable with a zero-mean,

and an assumed standard deviation. Concentration measurement uncertainty was

estimated using a coefficient of variation (CV), ranging from 0 to 0.15. Volume

measurement uncertainty was estimated by assuming the volume standard deviation

ranged from 0 to one-half the interval between volume measurements. A unique

measurement error was applied to each volume and concentration value in the synthetic

data set. Moment calculations were then completed on the "measured" BTC. This

process was repeated 10,000 times, and the averages and standard deviations of the

retardation, NAPL saturation, and NAPL volume were computed. Convergence of

Monte Carlo results was tested by completing three identical simulations, each with

10,000 iterations; the coefficient of variation for the moments, retardation, NAPL

saturation, and NAPL volume differed by no more than 0.0002.

Table 3-2 compares the coefficient of variation for retardations, NAPL

saturations, and NAPL volumes estimated using the semi-analytical approach to those

estimated from the Monte Carlo simulation. Three cases are presented: the first with the

volume standard deviation equal to 0.35 and no concentration CV, the second with no

volume standard deviation and concentration CV equal to 0.15, and the third with volume

standard deviation equal to 0.35 and the concentration CV equal to 0.15.

The agreement shown in Table 3-2 demonstrates that the semi-analytical method

correctly accounts for the uncertainly in volume and concentration measurements, based













Table 3-2. Comparison of the CV (%) estimated from Monte Carlo (M.C.)
simulations and the semi-analytical procedure (S.A) for three cases.

Case A Case B Case C
S.A. M.C. S.A. M.C. S. A. M.C.
Retardation 0.8 0.8 1.4 1.4 1.6 1.6
Saturation 2.2 2.2 4.0 4.0 4.8 4.8
NAPL Volume 1.4 1.5 3.1 3.2 3.8 3.8

Case A: volume standard deviation = 0.35, and concentration CV = 0; Case
B: volume standard deviation = 0, and concentration CV =0.15; and Case C:
volume standard deviation = 0.35, and concentration CV = 0.15.


on the assumption of independence between all measurements. Based on the coefficient

of variation of the retardation, NAPL saturation, and NAPL volume, concentration errors

have a greater impact on PITT results than volume errors.


Applications

The NAPL volume CV is shown in Figure 3-2 as a function of retardation for

several combinations of volume errors (standard deviation) and concentration errors

(CV). As indicated by Figure 3-2, the uncertainty in NAPL volume estimates is high for

low retardation values, and the uncertainty decreases as retardation increases. This result

agrees with that presented by Jin et al. (1995). For reliability, estimates of saturation and

NAPL volume should be based on retardation values of 1.2 or greater. In contrast, there

is a high degree of uncertainty associated with the conclusion that little or no NAPL is

present based on small retardation values. Figure 3-3 shows the NAPL volume

coefficient of variation as a function of the dimensionless volume error for breakthrough

curve resolutions of 50, 100, and 350 volume-concentration data points. The intent of
























0.0
I


1.2 1.4 1.6 1.8 2
Retardation


Figure 3-2. NAPL volume CV as a function of retardation factor for volume or
concentration measurement errors of 0.05 (diamonds), 0.15 (squares), and 0.30
(triangles). BTCs with 100 data points were used to generate the figure.


0.08


0.04

0.02


Dimensionless Volume Error


Figure 3-3. NAPL volume coefficient of variation as a function of dimensionless
volume error for BTCs of 50 (diamonds), 100 (squares), and 350 (triangles) volume-
concentration data points. The figure is based on a retardation factor of 1.5.










this figure is to quantify NAPL volume uncertainty as a function of BTC resolution. The

data used in the figure is based on a concentration CV of 0.15, and a retardation factor of

1.5. The dimensionless volume error used on the abscissa in Figure 3-3 is the ratio of

volume standard deviation to the normalized first moment. It is apparent from the figure

that the uncertainty decreases as the resolution increases, which is a reasonable result

since more points should serve to better define the BTCs.

Figure 3-4 shows the impact of variable concentration uncertainty on retardation,

NAPL saturation, and NAPL volume. The analysis was based on the same conditions

used in Chapter 2: uncertainty in volume measurements was neglected, concentration

uncertainty varied linearly from the uncertainty of the detection limit concentration to the

uncertainty of the peak concentration, and a dimensionless detection limit of 0.001 was

assumed. The uncertainty of the peak concentration, defined using concentration CV,

was 0.05 and 0.15. The uncertainty of the detection limit concentration was varied using

CV values ranging from 0.5 to 2.0. As illustrated in Figure 3-4, the uncertainty in the

peak concentration has less impact than uncertainty in the detection limit concentration.

However, even with the detection limit uncertainty set as high as CVDL = 2.00, the

uncertainties (expressed as CVs) in NAPL volume are only approximately 20%.

The impact of uncertainty in background retardation on NAPL volume

uncertainty is shown in Figure 3-5. This figure was based on equations (3-1b), (3-7d),

and (3-10) with all variances equal to zero except the variance of the background

retardation. Partitioning coefficients of 8 and 200, and background uncertainties (defined

as CV) of 0.05, 0.15 and 0.30 were used to produce the figure. By comparison to Figure








Saturation


20%

0 15%

S10%

U 5%

0%.
50%


Retardation


100% 150%

Detection-Limit Coefficient ofVariation, CVDL


200%


Figure 3-4. Retardation (triangles), NAPL saturation (squares), and NAPL volume
(circles) CV as a function of the concentration detection limit CV. The CV of the
maximum concentrations were 5% (open symbols) and 15% (closed symbols). The
figure is based on 100 volume-concentration data points, and a retardation factor of 1.5.


1000%


100%


10%


1 1.5 2 2.5 3 3.5 4
Retardation
Figure 3-5. Impacts of background-retardation uncertainty. The NAPL volume CV is
presented as a function of retardation, for background retardation CVs of 5% (circles),
15% (triangles), and 30% (squares). The curves with the open symbols are based on a
partitioning coefficient of 8, and the curves with the closed symbols are based on a
partitioning coefficient of 200.









3-2, it is evident that NAPL volume uncertainty is more sensitive to background

retardation uncertainty compared to its uncertainty from volume- and concentration-

measurement uncertainty.


Conclusions


This chapter presented a method of estimating uncertainties associated with

partitioning tracer tests. The method differs from previous work on measurement

uncertainty in that retardation, saturation, and NAPL volume uncertainty are based on the

uncertainty in volume and concentration measurements, rather than uncertainty based on

the difference between measurements and model predictions. Uncertainty in the NAPL

volume estimate has also been presented, which was not discussed in previous work. The

method is equally applicable to volumetric and temporal moments, and in the case of the

former, accounts for volume-measurement uncertainty. Results from this chapter

quantitatively indicate how the uncertainty in NAPL volume grows as the retardation

factor decreases. In other words, the conclusion that NAPL is not present based on

partitioning tracer test results has a high degree of uncertainty, simply because of

measurement uncertainty. This suggests that using partitioning tracers as a means to

detect small volumes of NAPL is not a reliable technique, or at least, if used as such,

should be done so with great care.

It should be clearly stated that the methods presented in this chapter, as well as

those presented by Dwarakanath et al. (1999) and Jin et al. (2000) provide estimates of

the uncertainty associated with partitioning tracer tests arising from measurement error.

These errors have been found to be relatively small; less than 10% for retardation factors






51


greater than approximately 1.2. As discussed in the next chapter, however, caution is still

advised when qualifying the uncertainty (and reliability) of partitioning tracer results.














CHAPTER 4
PRE- AND POST-FLUSHING PARTITIONING TRACER TESTS ASSOCIATED
WITH A CONTROLLED RELEASE EXPERIMENT


Introduction


This chapter describes the partitioning tracer tests conducted in the cell at the

DNTS before and after the ethanol-flushing demonstration. A tracer test was conducted

prior to the release of PCE in order to characterize the background retardation of the

tracers, and results from that test, as well as a description of the controlled PCE release,

are included. The chapter begins with a description of the site geology and cell

instrumentation, and this is followed by a description of the background sorption test,

controlled PCE release, and pre- and post-partitioning tracer tests. Results based on

extraction well BTCs are presented, and a comparison is made between the volume of

PCE predicted by the partitioning-tracers and the volume released into the cell. The

uncertainty of the tracer-test results is quantified using the methods presented in Chapters

2 and 3. However, for the sake of clarity, uncertainty quantifications are limited to PCE-

volume estimates since this is the measure used to compare tracer-test results to release

information.


Site Description

Site geology. The permit application for the demonstration (Noll et al., 1998)

provided detailed information on the site geology and the cell installation and

instrumentation. The following summary provides information relevant to tests discussed








herein. The site geology consists of the Columbia Formation, characterized by silty,

poorly sorted sands. This is underlain by the Calvert Formation, the upper portion of

which is characterized by silty clay with thin layers of silt and fine sand. This layer

forms the aquitard for the surficial aquifer. Noll et al. (1998) reported that the average

hydraulic conductivity of the surficial aquifer ranges from 2.4 m/day to 10.4 m/day based

on pump tests. The hydraulic conductivity ranged from 2.4 m/day to 3.0 m/day based on

the hydraulic gradient measured under steady flow during initial hydraulic tests in the

cell. Ball et al. (1997) and Liu and Ball (1999) provide additional descriptions of the

geology at the Dover AFB. Boring logs from the wells installed in the cell generally

indicated alternating layers of silty sand, poorly sorted sand, and well sorted sand. The

average depth to clay was approximately 12 m below grade based on the well boring

logs. The grade elevation varied by 0.2 m across the cell; consequently all references to

grade are based on an average grade elevation. The minimum observed clay depth was

11.8 m below grade at well 52 (Figure 4-1), and the maximum observed clay depth was

12.5 m below grade at well 56.

Cell instrumentation. The 3-m by 5-m by 12-m cell was constructed by driving

Waterloo sheet piling with interlocking joints (Starr et al., 1992, 1993) through the

surficial aquifer into the confining unit. A second enclosure of sheet piling was also

installed to act as a secondary containment barrier. Hydraulic tests were performed after

the installation of the cell to ensure containment integrity. In addition, an inward

hydraulic gradient was maintained during the tests, and DNTS personnel conducted

frequent groundwater compliance sampling to safeguard against contaminant migration.

The cell was instrumented with 12 wells, 18 release points, and 18 multi-level sampling











< 4.6 m

4 56, 5



43( t!? "536)1
mo 4 o* 5
45 55


I o o*b o o
3.0 *
4 2(D 0" 052



41 046 6 51e



Well o MLS Release point


Figure 4-1. Cell instrumentation layout.

(MLS) locations (Figure 4-1). Each well was approximately 5 cm in diameter, and

screened from 6.1 m to 12.5 m below grade. A 0.3 m section of casing was installed

below each screen and served as a sump for collecting DNAPL in the event it entered the

wells. The release points terminated at 10.7 m below grade. Each release point had a

sampler installed above it at approximately 9.9 m. Each MLS had 5 vertical sampling

points spaced 0.3 m apart, distributed over the bottom 1.5 m of the cell. MLSs were

distributed within the cell on a tetrahedral grid.











Background Sorption Tracer Test

Prior to release of PCE into the cell, a partitioning tracer test was conducted to

assess background sorption of tracers onto aquifer materials. Alcohol tracers, methanol,

2,4-dimethyl-3-pentanol (DMP), and n-octanol, along with bromide were injected into six

wells at the corners and sides of the cell and extracted from the two wells in the center of

the cell (double five-spot pumping pattern, as shown in Figure 4-2a). Background

sorption was quantified by moment analysis of the extrapolated tracer breakthrough

responses, and the results are summarized in Table 4-1. Retardation of DMP (KNW = 30)

in both wells was approximately 1.13, which is equivalent to a background PCE

saturation of 0.004, or a total volume of PCE in the cell of approximately 50 L.

However, retardation of the most hydrophobic tracer, n-octanol (KNW = 170) was less

than 1. The tail of the BTC for this tracer declined significantly relative to the other

tracers, suggesting n-octanol may have degraded during the test. The effective porosity

in the cell was estimated at approximately 0.2 based on moment analysis of the methanol

non-reactive tracer. Bromide was retarded relative to methanol by a factor of 1.3.

Brooks et al. (1998) showed that bromide-mineral interaction could retard bromide when

used as a groundwater tracer, which may explain its retardation in this test.


Controlled Release Conducted by EPA

The release of PCE into the cell was designed to produce a DNAPL distribution

within the target-flow zone between 10.7 and 12.2 m below ground surface (bgs). The

approach used was intended to minimize pooling of the DNAPL on the clay confining










a) b)

X444 56 ?/44 /-56

A5 5 1 5 X45 5 55

C 046 4 51


X Injection Well

/0)Extraction Well

Figure 4-2. a) Double five-spot pumping pattern used in the background sorption tracer
test and the ethanol-flushing demonstration (discussed in Chapter 5), and b) inverted,
double five-spot pumping pattern used in the pre- and post-flushing tracer test.





Table 4-1. Summary of results from the background sorption tracer test.
Tracer Mass Recovery Swept Volume (L) Retardation
EW 45 EW 55 EW 45 EW 55 EW 45 EW 55
Methanol 107% 94% 6440 5340
Bromide 124% 106% 8700 6740 1.35 1.26
2,4-DM-3-P 115% 101% 7300 5980 1.13 1.12
n-Octanol 96% 88% 4500 4420 0.70 0.83
1Retardation relative to methanol.
22,4-DM-3-P = 2,4-Dimethyl-3-pentanol








unit, which was undesirable because of the increased potential for downward migration

of PCE through natural fractures in the clay or openings produced during sheet-pile

installation. The water table was lowered 0.3 m below the release elevations (11.0 m

below grade) prior to PCE injection. EPA researchers conducted the release by pumping

selected volumes of PCE down the release tubes at a typical flow rate of 0.6 L/min.

Immediately following the release, the water table was lowered further to facilitate

vertical spreading of the DNAPL between the release points and the clay confining unit.

When the water table reached approximately 11.9 m below grade, groundwater extraction

was terminated and water injection was initiated to raise the water table back to the pre-

release elevation (8.5 m below grade).

The target release volume was 92 L. The uncertainty associated with the release

volume was estimated assuming the tolerance of a one-liter graduated cylinder (5 mL)

was equivalent to the standard deviation of a 1-L measurement. The target release

volume was 92 L, therefore the uncertainty was 0.5 L. EPA researchers estimated that

between 0 and 0.5 L of PCE remained in the containers used during the release as

residual fluid. Therefore, it was assumed that 0.3 L of PCE remained in the containers,

and the uncertainty of this number was 0.2 L. Therefore, the best estimate of the volume

of PCE in the cell and its uncertainty was 91.7 0.5 L. Figure 4-3 shows the volume of

PCE released at specific release locations. As indicated in Chapter 1, this information

was withheld until after the remedial demonstration. Table 4-2 summarizes the estimated

volume of PCE in the cell over the entire demonstration based on the release information

and the volume of PCE removed by each subsequent activity.










44 (D0




.41 0


*41 0 00


0


0


Well
Figure 4-3. PCE injection locations and volumes (plan view). The number inside the
circles indicates the release volume (L) per location.


Table 4-2. Volume of PCE (L) added and removed from the cell.


PCE Addition or Removal


Volume in
Cell


Change


Error
Estimate


DNAPL released into the cell 91.7 0.5
Amount at the start of the CITT 91.7 0.5
Removed by dissolution from EWs 3 0.1
Removed by dissolution from MLSs 0.1 0.03
DNAPL removed from EW 56 2.8 0.2
Amount at the start of the first PITT 85.8 0.5
Removed by dissolution from EWs 2.5 0.1
Removed by dissolution from MLSs 0.1 0.03
DNAPL removed by MLSs prior to flood 2 0.2 0.05
Amount at the start of the ethanol flood 83.0 0.6
Total removed during flood through EWs 52.6 0.7
Total removed during flood through MLSs 1.2 0.1
DNAPL removed through MLSs 0.08 0.04
PCE injected through recycling -0.5 0.04
Net PCE removed 53.4 0.7
Amount at the start of the second PITT 29.6 0.9

'This volume was removed from the well before the first PITT.
2This includes the DNAPL removed during the CITT and the first PITT








Partitioning Tracer Tests

Following the release of PCE into the cell, two tracer tests were conducted. The

first tracer test took place two weeks after the release. The goal of this test was to

investigate non-reactive transport characteristics in a line drive flow pattern (injection

through wells 51, 53, and 54, and extraction from wells 41, 42, 43,and 44) using bromide

as a tracer. The transition from a static system to steady flow was studied including the

changes in PCE concentration in extraction wells (EWs) and multilevel samplers. EPA

researchers conducted this test and the results were not used by UF in the design or

interpretation of the partitioning tracer test. Approximately 5 pore volumes of water were

flushed through the cell, and 3.0 L of PCE were removed through dissolution. The EPA

provided this estimate and an uncertainty analysis was not completed. However,

assuming relative uncertainties of 0.15 for volume and concentration measurements,

Figure 2-4a indicates the uncertainty of this mass removal estimate is probably on the

order of 5%. Further results of the line-drive tracer test are not discussed here.

Two weeks after the line-drive tracer test, UF researchers conducted the post-

release partitioning tracer test. The test was designed to estimate the volume and

distribution of PCE released in the cell by monitoring the tracer breakthrough at the

extraction wells and multilevel samplers. Each monitoring well was checked for free-

phase PCE using an interface probe prior to conducting the test. Well 56 had the only

PCE present. A peristaltic pump was used to remove 2.8 0.2 L of PCE from the well.

This may indicate that PCE was pooled on the clay confining unit; however, the PCE

may also have entered the well by migrating on a layer present in the target flow zone.









An inverted, double five-spot pattern was employed for the tracer test (Figure 4-

2b), which consisted of six extraction wells (41, 44, 46, 51, 54, and 56) located around

the perimeter of the cell and two injection wells (45 and 55) located in the center. This

pattern was used because it provided the highest spatial resolution of PCE distribution

from the extraction well breakthrough responses. Of the 108 potential multilevel

sampling locations, approximately 35 yielded breakthrough responses adequate for

moment analysis to determine partitioning tracer retardation. Approximately 60 samplers

failed due to faulty valves and system leaks. These problems were later corrected such

that all 108 samplers worked for the post-flushing partitioning-tracer test.

In an effort to increase the measured partitioning tracer retardation at the

extraction wells, the flow domain was segregated into upper and lower zones. Inflatable

packers were used in the injection wells to segregate fluid into the upper and lower

portions of the wells. The average saturated thickness of the flow domain was 4.3 m so

the center of the packers were placed at 1.8 m above the clay dividing the flow domains

approximately in half. The average flow rate injected into the upper and lower zones was

3.7 L/min and 3.0 L/min, respectively. This approach was intended to deliver a suite of

tracers into the lower zone in order to focus tracer flow though the NAPL contaminated

zone. This would then produce higher retardation for the lower zone tracers than if a

single tracer suite was employed. In the upper zone, very low retardation was expected.

In an effort to provide further spatial resolution of the PCE distribution, unique tracer

pairs were employed in the lower zones of the two injection wells (45 and 55). The

unique non-partitioning and partitioning tracers allowed the flow domain to be segregated








into eight zones based on the extraction well data. The tracers used as common or unique

to the upper and lower zones for both pre- and post-tests are listed in Table 4-3.

The tracer test was conducted over an 11-day period maintaining a steady total

flow of 6.7 L/min based on injection rate measurements. A tracer pulse of 8 hours was

applied in the lower zone and 9.4 hours in the upper zone. Samples were collected from

the six extraction wells and all functioning multilevel samplers to measure tracer BTCs.

The water level in the cell was maintained at 7.9 m bgs producing a saturated zone of

approximately 4.3 m. Up-coning and drawdown in the injection and extraction wells

were approximately one meter but this was assumed to be local to each well. The wells

were installed by direct push using a 30-ton cone penetrometer truck and therefore had no

sand pack that would reduce head loss at the well.


Results and Discussion


Extraction Wells

Each of the six extraction wells yielded 11 BTCs from the suite of tracers

used. Figure 4-4 shows selected non-reactive and reactive BTCs at EW 51. Moments

were calculated and the results for the non-reactive tracer are summarized in Table 4-4

and the partitioning tracers in Table 4-5. All BTCs were extrapolated to provide best

estimates of the true moments (Jin et al., 1995), and background sorption was neglected.

Iodide results (not listed in Table 4-4) showed similar trends in mass recovery and swept

volume per extraction well as those shown by methanol, however the total mass

recovered was 95%, and the total swept volume estimate was 3,920 L. Compared to the

swept volume estimated from methanol, the iodide was retarded by a factor of 1.02. The








Table 4-3. Partitioning coefficients for tracers used in the pre- and
post-flushing partitioning tracer tests.

Tracer Pre-Flushing Post-Flushing
PITT PITT
Lower Zone Common
Iodide 0 0
Methanol 0 0
n-Hexanol 6 6
2,4-Dimethyl-3-pentanol 30 30
2-Octanol 120 120
3,5,5-Trimethyl-1-Hexanol 265
Lower Zone Unique Well 45
Tert-butyl Alcohol 0
n-Octanol 170
Lower Zone Unique Well 55
Isobutyl Alcohol 0
3-Heptanol 31
Upper Zone Common


Isobutyl Alcohol 0
2-Ethyl-l-Hexanol 140


iodide may have been retarded due to mineral interaction, analogously to bromide

retardation discussed by Brooks et al. (1998). Due to the possible retardation and smaller

mass recovery of iodide relative to methanol, results from the latter were used in NAPL

volume calculations. Wells 51 and 56 had the highest average NAPL saturation at 1%.

This is a very low average saturation and produced a retardation over 2 for 2-octanol,

which provided a reasonable measure of the saturation (Jin et al., 1995). The BTCs are

shown on a log scale and indicate that the retardation was primarily in the tailing portion

of the BTC. This indicated that the NAPL was non-uniformly distributed since a uniform

distribution would produce a simple offset of the non-reactive and partitioning tracer

BTCs (Jawitz et al., 1998). The total volume of NAPL estimated in the lower swept zone










1E+00
a)


1E-02 oo oo
a&* 00E-*0000
1E-03 ** ooooooo
1E > **#***.. ooo o o o

1E-04

1E-05
0 2 4 6 8 10 12

1E+00

1E-01 b)

1E-02

1E-03 o 000000oo
S1E04 ge 0 oo o

S1E-05

1E-06 --
0 2 4 6 8 10 12
1E+00

1E-01 c)

1E-02 g B

IE-03 ^aB Sg

1E-04

1E-05
0 2 4 6 8 10 12
Elasped Time (Days)



Figure 4-4. Selected EW 51 BTCs from the pre-flushing tracer test. a) Common lower
zone tracers: methanol (closed diamonds) and 2-octanol (open diamonds), b) unique
lower zone tracers: isobutanol (closed circles) and 3-heptanol (open circles), and c) upper
zone tracers: isopropanol (closed squares) and n-heptanol (open squares).
















Table 4-4. Summary of results for common non-reactive lower and upper zone tracers
from the pre-flushing test.


Mass Recovery

Lower Upper
Zone Zone


Mean Arrival Time (d)

Lower Upper
Zone Zone


Swept Volume (L)

Lower Upper
Zone Zone


41 23% 9% 0.48 2.25 740 3470
44 8% 6% 1.17 2.13 810 1470
46 34% 18% 0.25 0.86 550 1850
51 11% 18% 0.43 1.03 660 1570
54 11% 20% 0.29 0.75 520 1330
56 10% 15% 0.35 0.90 550 1430
Total 97% 87% 3830 11120


Table 4-5. Pre-flushing partitioning tracer test, common lower zone partitioning tracer results.


n-Hexanol


2,4-Dimethyl-3-Pentanol


2-Octanol


M R SN VN M R SN VN M R SN VN
41 22% 1.01 0.0008 0.6 24% 1.15 0.0051 3.7 24% 1.42 0.0035 2.6
44 8% 0.98 9% 1.05 0.0015 1.2 9% 1.10 0.0008 0.7
46 33% 1.15 0.0190 10.5 34% 1.30 0.0010 5.5 37% 1.90 0.0074 4.1
51 11% 1.23 0.0280 18.5 11% 1.42 0.0138 9.2 12% 2.08 0.0089 5.9
54 11% 1.14 0.0171 8.9 11% 1.19 0.0062 3.2 11% 1.16 0.0013 0.7
56 10% 1.34 0.0406 22.3 10% 1.48 0.0157 8.6 11% 2.20 0.0099 5.4
Total 95% 60.8 100% 31.4 104%- 19.4
M = mass recovery (%), R Retardation factor, SN = NAPL saturation, and VN = NAPL
volume (L).










Table 4-6. Pre-flushing partitioning tracer test, upper-zone reactive tracer (n-
heptanol) results. The corrected mass recovery is based on a first-order
degradation model.

Well Mass R Corrected Corrected SN VN
Recovery Mass R
Recovery
41 5% 0.89 10% 1.03 0.0010 3.9
44 3% 0.74 5% 0.78
46 17% 1.04 23% 1.29 0.0095 16.2
51 16% 0.91 22% 1.31 0.0101 19.2
54 17% 0.82 21% 0.95
56 14% 0.88 19% 1.02 0.0005 0.8
Total 72% 100% 40.2


is 19.4 L. This is based on using the tracer with the largest measured retardation

(2-Octanol). Using individual tracers showed high variability ranging form 31.4 L for

DMP to 60.8 L for n-hexanol.

The upper zone tracers showed a retardation of less than one in all extraction

wells except EW 46 (Table 4-6). However, the non-reactive tracer, isopropanol (IPA),

and the partitioning tracer, n-heptanol, showed poor recovery (87% and 72%,

respectively). This is likely due to tracer degradation since straight-chain alcohols tend

to degrade more rapidly in the environment. These tracers were not in the original suite

of tracers designed for this test but were substituted for pentaflourobenzoic acid and 2,6-

dimethyl-4-heptanol when regulatory approval for those tracers was denied. In order to

provide an estimate of the volume of PCE in the upper swept zone, some correction for

tracer degradation was required. The simplest approach is to assume a first-order

degradation model and estimate the degradation-rate constant by recovering the zeroth









moment using the BTC of the degraded tracer. Each concentration measurement in the

BTC is adjusted using


Cj =~- (4-1)
e

where C is the measured concentration, Cadj is the estimated concentration with no

degradation, k is the decay coefficient, and t is the time that the sample was collected

after the mean of the tracer-pulse injection. Applying this adjustment and recalculating

the zeroth moment of each tracer, the degradation coefficient was adjusted until the mass

recovery matched the mass injected. This approach has several critical assumptions. The

degradation is assumed to be first order and can be described by a single value for the

entire cell. The approach used here ignores the width of the tracer pulse assuming the

width is small and injection occurred at one-half the tracer pulse. This approximation

should have minimal impact on the adjusted moments.

The degradation corrected moments for all wells were tabulated in Table 4-6.

These results were based on a temporal moment analysis in order to simplify the

degradation corrections necessary to obtain 100% mass recovery. The NAPL saturations

in two of the extraction wells remained less than zero, and these values were assumed

zero for estimating the total NAPL volume present in the cell. The total volume of PCE

estimated using the degradation corrected BTCs was 40.2 L. This represents a significant

portion of the total 60 L of PCE estimated to be in the cell. The degradation correction

therefore takes on significant importance. This also indicates that a substantial fraction of

the PCE present in the cell was in the upper swept zone. This may indicate that PCE was

located higher in the cell than anticipated based on the release locations, however,








another explanation is that the upper zone tracers in fact traveled down into the target

zone between 10.7 and 12.2 m bgs.

The issue of uncertainty associated with the current estimate, 60 L, must be

assessed. In general the estimated volume in the lower zone is more reliable than the

upper zone because of the degradation problem and the significant size of the upper

swept zone, 11,000 L compared to 3,800 L for the lower zone. General sources of

measurement uncertainty associated with the NAPL volume estimates include BTC

volumes, BTC concentrations, tracer-pulse volumes, tracer partitioning coefficients, and

the background-retardation estimate. The combined extraction well effluent was

discharged to storage tanks, and cumulative volume measurements were made based on

the volume in the storage tanks. Flow meters were also used on each well, but were

considered less reliable measures of cumulative volume compared to the storage tanks

because flow rates were often near the lower operational limit of the instruments.

Instead, the flow meters were used to estimate the flow distribution between the wells,

and this distribution along with the cumulative volume estimated from the storage tanks

was used to estimate the cumulative volume produced at each well. Uncertainties in BTC

volume measurements were therefore based on one-half of the smallest division of the

tank-volume scale ( 25 L). Uncertainties in BTC concentration measurements were

conservatively assumed to be 0.15 of the measured concentration. Uncertainty in the

tracer-pulse volume was assumed negligible due to the controlled conditions under which

the measurement was made. It was assumed that the uncertainty in partitioning

coefficients was described using a coefficient of variation equal to 0.15. Uncertainty in

the background retardation factor was neglected. The BTCs were extrapolated to








improve estimates of the normalized first moments. The uncertainty of the extrapolated

portion of the BTC should be based on the measurements used in the extrapolation

process. However, as an approximation, it was assumed that each extrapolated volume-

concentration measurement had the same relative uncertainty as the measured points.

Propagation of these uncertainties using the methods from Chapters 2 and 3

produced an uncertainty estimate of 19.4 1.5 L for the lower zone. Those methods,

however, neglect the estimation of uncertainty associated with degradation of the tracers.

This can be partially addressed by looking at the sensitivity of the results to the

degradation parameter and the model assumed. This was done and indicated that

significant errors on the order of 25% can be introduced. Based on this, the estimate of

PCE in the upper zone can be presented as 40 10 L. This gives a revised total estimate

of 60 10 L.

The extraction well results can be used to estimate the spatial distribution of PCE

within the cell. The six extraction wells have unique swept zones and the unique tracers

applied to the two injection wells can further delineate swept zones to eight separate

zones within the lower portion of the cell. The results of the unique tracer suites are

presented in Table 4-7. The results of the spatial analysis based on extraction wells are

presented in Figure 4-5.


Comparison to Release Locations and Volumes

The total release volume, 92 1 L, after reduction to 86 1 L (see Table 4-2)

by mass removed prior to the start of the partitioning tracer test, should be compared with

the estimate of 60 10 L. Approximately 2 L of PCE may have been resident in solution

when the tracer test was initiated and would not be part of the tracer estimate.











Table 4-7. Pre-flushing partitioning tracer test, summary of unique tracer pairs injected
into wells 45 and 55.

Well Non-reactive Tracer Swept Zone (L) NAPL Volume (L)
mass recovery
IW 45 IW 55 IW 45 IW 55 IW 45 IW 55
41 46% 0.02% 798 2.1
44 17% 0.01% 793 1.2
46 24% 39% 971 513 6.5 5.6
51 0.1% 22% 737 7.3
54 0.02% 23% 631 1.6
56 12% 9% 615 605 5.7 12.1
Total 100% 93% 3177 2486 15.5 26.6

The non-reactive and partitioning tracers injected into well 45 were tert-butyl alcohol and
n-octanol, and the non-reactive and partitioning tracers injected into well 55 were
isobutyl alcohol and 3-heptanol.


The spatial injection pattern of the PCE release can be compared to the spatial

resolutions based on the extraction well data (Figures 4-3 and 4-5). The comparison must

be made recognizing that the DNAPL may have migrated to different regions of the cell

based on the geologic structure of the media in the cell. In general, the spatial pattern of

the PCE distribution based on the extraction wells agrees with the release data. Higher

saturation zones are located in the swept zones of wells 51 and 56 where significant mass

was released.


Summary of Post-Flushing Partitioning Tracer Test

Two months after the cosolvent flood, a final post-flushing partitioning tracer test

was conducted. The procedure followed was the same as the pre-flushing test with the

exception that unique tracers were not used in wells 45 and 55. The tracer suite used was

also modified to reduce degradation problems experienced with the first tracer test, since

those tracers planned for use in the first test were given regulatory approval.









a) Upper Zone


S = 0V,=OL.0005 S = 0
S V =0.8 L VN=OL
>................. .. ................ *,*.............


S = 0.0010 = 0.0095
SS, = 0.0101
V,=3.9L VN = 16.2L
V = 19.2 L
:46 51 -


b) Lower Z


one

44 56 54
SN = 0.0008
08 SN= 0.0013
VN=0.7L d
S1 1 II VN = 0.7 L

...................................... ..............


SN = 0.0035 SN0.0089
VN =2.6L II VN=5.9L

4 : 461 51


..** Boundary of area
proportional to
swept volume


--.. Boundary based on
Unique Tracers


Figure 4-5. Pre-flushing PITT estimate of a) upper zone and b) lower zone spatial
distribution of NAPL based on extraction well data.


1


SExtraction
Well








The mass balance from the cosolvent flood (discussed in Chapter 5) indicated that

30 1 L of PCE remained in the cell prior to the final tracer test (see Table 4-2). The

results of the final partitioning tracer test are summarized in Table 4-8. The swept

volume estimated from methanol was approximately 17% larger in the post-flushing

tracer test compared to the pre-flushing tracer test. A total of 4.9 0.4 L of PCE was

estimated based on upper and lower zone tracers.


Discussion


It is apparent that both the pre- and post-flushing tracer tests underestimated the

volume of PCE present in the cell by approximately 25 L. This might suggest that 25 L

of PCE was not accessible to the tracers. This NAPL could have been pooled on the clay

or located in isolated comers or regions of the cell. The fact that the pre-flushing tracer

test has high uncertainties caused by degradation of the upper zone tracers must be

recognized when reaching this conclusion.

The volume of PCE present in the cell represents relatively low average NAPL

saturations. When expressed as NAPL saturation within the lower-swept zone, the pre-

and post-flushing saturations are 0.005 and 0.0008 respectively. If averaged over the

entire swept zone these drop to 0.004 and 0.0003. While these are very low saturations,

tracers with high partitioning coefficients such as 3,5,5 TMH (KNW = 265) would provide

a retardation of 1.2 at the lower saturation. Even though this retardation is within the

range considered acceptable for tracer applications (Jin et al., 1995), it should be

recognized that the tracer technology was generally being tested under conditions that








Table 4-8. Post-flushing partitioning tracer test summary.

Lower Zone Upper Zone
Well
Non-reactive Reactive Non-reactive Reactive
(Methanol) (3,5,5-TM-3-H) (Isobutyl Alcohol) (2-E-1-H)
M AT SV M SN VN M AT SV M SN VN
41 27% 0.51 880 26% 0.0008 0.7 11% 1.94 3320 11% -
44 6% 1.54 710 6% 0.0005 0.3 2% 0.87 1490 2% 0.0004 0.7
46 11% 0.32 650 13% 0.0013 0.9 17% 0.85 1450 18% -
51 14% 0.51 840 20% 0.0008 0.7 18% 0.83 1420 18% 0.0002 0.3
54 20% 0.29 510 22% 0.0010 0.5 17% 0.89 1520 16% 0.0001 0.1
56 11% 0.46 1020 11% 0.0008 0.8 26% 0.70 1200 25% -
Total 89% 4610 97% 3.9 91% 10400 91% 1.1

3,5,5-TM-3-H = 3,5,5-Trimethyl-3-hexanol; 2-E-1-H = 2-Ethyl-l-hexanol; M = Mass
recovery (%); AT = Arrival time (d); SV = swept volume (L).


approached the limits of its application.

The trend in NAPL volume estimates as a function of the tracer partitioning

coefficients is illustrated in Figure 4-6. Tracers with higher partitioning coefficients

predicted less NAPL volume. The tracer with the lowest partitioning coefficient, hexanol

(KNW = 8) predicted the NAPL volume closest to the release volume. However, this

tracer had the lowest retardation factor, and consequently, the corresponding NAPL

volume estimate has a higher uncertainty than estimates from the other tracers.

Furthermore, this tracer overestimated the volume of NAPL in the cell after the ethanol

flood. This trend could be the result of neglecting background retardation estimates.

Another possible explanation for this observation is that the tails of the BTCs from the

higher KNW tracers were not properly characterized. In order to investigate the

uncertainty in BTC extrapolation, three different approaches to log-linear extrapolation

were compared. The first log-linear extrapolation, used to estimate all moments reported










70
60 OPre-flushing test
50 0 Post-flushing test
540
30

20 0
10.
0I
1 10 100 1000
Partitioning Coefficient


Figure 4-6. DNAPL volume estimated from the pre- and post-partitioning tracer tests as
a function of the tracer partitioning coefficient.


thus far, was based on the most "reasonable" fit to the data in the BTC tail. This was a

somewhat subjective approach based on log-linear regression using those data points that

visually produced the best over-all fit to the BTC tails. The second approach was to

extrapolate from that portion of the BTC tail that yielded the largest retardation factor.

The final extrapolation scheme was based on log-linear regression using the last ten data

points above the method detection limit (estimated as 1 mg/L). Results from moment

calculations without extrapolation were also used for comparison. The NAPL volumes

estimated from the pre-flushing, lower zone tracers are shown in Table 4-9. As an

estimate of the uncertainty due to the extrapolation procedure, the average and standard

deviation of the NAPL volume predicted for each tracer is shown in Figure 4-7. While

there is more overlap of the estimates by this approach, the trend of smaller NAPL

volume predictions with increasing partitioning coefficients is still apparent.













Table 4-9. Comparison in NAPL volume (L) estimates based on four
schemes of log-linear BTC extrapolation.


Extrapolation


2-Octanol
(KNW = 120)


2,4-DM-3-P
(KNw = 30)


Hexanol
(KNW = 6)


None 17.4 30.4 55.6
General 19.7 32.1 67.8
Maximum 42.6 57.0 178.6
10 points >lmg/L 24.1 25.2 33.2
Average 26.0 36.2 83.8
Standard Deviation 11.4 14.2 64.8

2,4-DM-3-P = 2,4-Dimethyl-3-pentanol


160
140 -- --
120
100
80
S-----------------
60- -
40
40 -.- -- -- -- -- -- -- -- --
20 -------
0


Partitioing Coefficient


Figure 4-7. Average and standard deviation in NAPL volume from four different
extrapolation schemes.








Conclusions


The best estimate of the volume of DNAPL in the cell prior to the first

partitioning tracer test (pre-ethanol flushing tracer test) was 86 1 L based on the release

information, while the partitioning-tracer test results predicted a NAPL volume of 60

10 L. This represents an error of approximately 30%, which is considered very

encouraging. The post-flushing partitioning-tracer test predicted only 4.9 0.4 L of the

estimated 30 1 L remaining. This represents an error of approximately 83%, which is

certainly less encouraging. However, both the pre- and post-flushing tests

underestimated the DNAPL by approximately 25 L. This discrepancy can most likely be

explained by the possibility that contact between the tracers and this volume of DNAPL

was prevented due to geological conditions.

Partitioning tracer tests are limited by geological considerations. In theory,

partitioning tracers with higher partitioning coefficients could be used to predict smaller

volumes of NAPL. However, this is predicated on the assumption that the tracer will

contact the NAPL. In some situations, it can easily be envisioned that the DNAPL is

distributed in regions of low conductivity, especially following remediation efforts, such

that tracer-NAPL contact is prevented. Partitioning tracer predictions of NAPL volume

should always be qualified with the statement that the NAPL volume is that predicted in

the swept-zone of the tracer. The swept-zone of the tracer and the target area of

investigation are not always the same. These results caution against the use of

partitioning tracer tests as detection methods.

Neither the pre- nor post-partitioning tracer test results agreed with the PCE mass

estimated from mass balance within the calculated limits of uncertainty. This highlights





76

the fact that the calculated uncertainty is based only on measurement uncertainty. It does

not account for uncertainty that may arise from conditions contrary to the assumptions

used in the partitioning tracer test. In this sense, the estimates of uncertainty provide the

minimum level of uncertainty associated with partitioning tracer predictions. As

conditions deviate from those necessary to meet the assumptions, the resulting

uncertainty will grow, however, this will not be reflected in the uncertainty estimates

based on the methods presented in Chapters 2 and 3.














CHAPTER 5
FIELD-SCALE COSOLVENT FLUSHING
OF DNAPL FROM A CONTROLLED RELEASE


Introduction


Nonaqueous phase liquids (NAPLs), such as fuels, oils, and industrial solvents,

may act as long-term sources of groundwater pollution when released into aquifers

because of their low aqueous solubilities. Dense nonaqueous phase liquids (DNAPLs)

are denser than water, and are more difficult to remedy because of their tendency to sink

and pool in the aquifer. Conventional remediation such as pump-and-treat can take many

decades to remove DNAPLs (Mackay and Cherry, 1989). Enhanced source-zone

remediation can expedite the removal of contaminants. One enhanced source-zone

remediation technique is in-situ cosolvent flushing, which involves the addition of

miscible organic solvents to water to increase the solubility or mobility of the NAPL

(Imhoff et al., 1995; Falta et al., 1999; Lunn and Kueper, 1997; Rao et al., 1997;

Augustijn et al., 1997; Lowe et al., 1999). In the case of DNAPLs, increased mobility

can result in greater contaminant risk due to the potential for downward migration, and

density modification of the NAPL has been proposed to prevent this risk (Roeder et al.,

1996; Lunn and Kueper, 1997; Lunn and Kueper, 1999). Alcohols have principally been

used as cosolvents for enhanced source-zone remediation (Lowe et al., 1999).

A limited number of field-scale, cosolvent-flushing demonstrations have been

conducted. Two cosolvent-flushing demonstrations were conducted at Hill AFB, Utah in








isolated test cells installed in a sand and gravel aquifer contaminated with a multi-

component NAPL (Rao et al., 1997; Sillan et al., 1998a; Falta et al., 1999). Rao et al.

(1997) demonstrated NAPL remediation by enhanced dissolution. The test cell was

approximately 4.3 m long by 3.6 m wide, and the clay confining unit was 6 m below

grade. A total of 40,000 L of a ternary cosolvent mixture (70% ethanol, 12% pentanol,

and 18% water) was injected into the cell over a ten-day period. Based on several

remediation performance measures (target contaminant concentrations in soil cores,

target contaminant mass removed at extraction wells, and pre- and post-flushing target

contaminant groundwater concentrations), the cell-averaged reduction in contaminant

mass was reported as >85%. They also reported an approximate 81% reduction in NAPL

saturation based on pre- and post-flushing partitioning interwell tracer tests (PITTs).

Falta et al. (1999) presented results from a second cosolvent-flushing study at Hill AFB

wherein the remedial mechanisms were NAPL mobilization and enhanced dissolution.

Their test cell was approximately 5 m long by 3 m wide, and the clay-confining unit was

9 m below grade. They injected 28,000 L of a ternary cosolvent mixture (80% tert-

butanol, 15% n-hexanol, and 5% water) over a 7-day period. Reductions in target

contaminant concentrations measured from pre- and post-flushing soil cores were

reported to range from 70% to >90%, and an 80% reduction in total NAPL content was

reported based on pre-and post-flushing PITTs.

Jawitz et al. (2000) and Sillan et al. (1999) described a third cosolvent-flushing

field demonstration conducted at a former dry cleaning facility in Jacksonville, Florida

that was contaminated with PCE. It was reported to be the first field-scale demonstration

of DNAPL remediation by cosolvent flushing. Furthermore, no physical barriers were








used. Based on a PITT conducted prior to the demonstration, it was estimated that 68 L

of DNAPL were located in the 17,000 L swept zone of the study. A total of 34,000 L of

alcohol solution (95% ethanol and 5% water) was injected over an 8-day period,

removing 43 L of DNAPL (63% of the PCE initially present). A post-flushing PITT

indicated 26 L of PCE remained. Soil cores were also used to assess remedial

performance, and indicated a 67% reduction in the amount of PCE initially present.

The remedial performance assessments of these three demonstrations were

determined from comparisons between pre- and post-flushing contaminant

characterization techniques (e.g., soil cores, PITTs, and groundwater samples), and from

comparing the amount of contaminant removed during in-situ flushing to the pre-flushing

estimated amount. The accuracy of the remedial performance assessment for these

studies was, thus, hindered by uncertainties in the characterization methods used to

estimate the amount and distribution of the NAPL.

A controlled release experiment, in which a known volume of NAPL is carefully

released into an isolated test cell, provides a unique opportunity to better evaluate

remediation techniques, as well as source-zone characterization techniques. Several

controlled-release experiments have been conducted in the unconfined, sand aquifer at

Canadian Forces Base, Borden, Ontario, but the purpose of these investigations was

characterization, not remediation (Poulsen and Kueper, 1992; Rivett et al., 1992; Kueper

et al., 1993; Broholm et al., 1999). Furthermore, PITTs were not used in these tests to

characterize the NAPL. Poulsen and Kueper (1992) and Kueper et al. (1993) investigated

the distribution of DNAPL resulting from a release, and Rivett et al. (1992) and Broholm








et al. (1999) investigated the aqueous dissolution of DNAPL components resulting from a

release.

The present field-scale test was conducted at the DNTS, located at Dover AFB in

Dover, Delaware. The DNTS is a field-scale laboratory, designed as a national test site

for evaluating remediation technologies (Thomas, 1996). This demonstration was the

first in a series of tests designed to compare the performance of several DNAPL

remediation technologies. Each demonstration will follow a similar test protocol.

Researchers from the Environmental Protection Agency (EPA) begin each test by

releasing a known quantity of PCE into an isolated test cell. However, the amount and

spatial distribution of the release are not revealed to the researchers conducting the

remedial demonstration until they have completed the characterization and remediation

components of their test protocol. After a release, a PITT is completed to characterize

the volume and distribution of PCE, followed by the remedial demonstration, and finally,

a post-demonstration PITT is conducted to evaluate the remedial performance. Since

multiple remedial technologies were planned for each test cell, DNAPL characterization

using soil cores was not feasible. The first demonstration, enhanced dissolution by

ethanol flushing, was completed in the spring of 1999. The purpose of this chapter is to

present the results of the ethanol flushing test.


Methods


PCE Volume Initially Present

The volume of PCE released into the cell by EPA (91.7 0.5 L) was given in

Chapter 4. A total of 5.6 0.1 L of PCE was removed by dissolution during the pre-








flushing tracer tests (Conservative Interwell Tracer Test (CITT) and pre-flushing PITT).

Before the start of the pre-flushing PITT, all of the well sumps were checked for DNAPL

using a Solinst interface probe (model number 122). The only well in which DNAPL

was detected was well 56, from which 2.8 0.2 L of PCE was removed from the well

sump. An additional 0.2 0.05 L of free-phase PCE was produced from the MLSs prior

to the start of the flushing demonstration. Therefore, the volume of PCE in the test cell at

the start of the alcohol flushing test was 83.1 0.6 L. The performance of the alcohol-

flushing test was judged using this value.


System Description

A double five-spot pattern, which consisted of injection wells along the cell

perimeter and extraction wells in the center (Figure 4-2a in Chapter 2), was used to inject

and extract fluids from the cell during alcohol flushing. This pattern was used because of

the flexibility it afforded to target the ethanol to specific regions in the cell. Inflatable

packers were placed in each injection and extraction well to minimize dilution of the

ethanol solution by separating the flow through the cell into upper and lower zones. The

system was designed with flow control on each injection and extraction zone to provide

the flexibility necessary to optimize the alcohol flood.

Alcohol solution and water were pumped into the test cell using Cole Parnner,

Master Flex variable speed peristaltic pumps (I/P series) from holding tanks in a nearby

tank storage area. An air-powered drive was used to pump the alcohol solution to

minimize the explosion hazard associated with potential fugitive ethanol vapors. Water

was injected above the packers into the upper zone and alcohol solution was injected

below the packers into the lower zone. The lower- and upper-zone effluents were








pumped from the cell using Marschalk Corporation air-displacement bladder pumps

(Minnow, Aquarius, and Aquarius II models, with a 99000 Main Logic Controller) to

designated holding tanks in the tank storage area.

The upper-zone fluid was recycled by pumping it through two Advanced

Recovery Technologies activated carbon drums (model number ARTCORP D16) in

series. The lower-zone fluid was recycled by pumping it through either two or three

activated carbon drums in series, or during the latter part of the demonstration, an ORS

Environmental Systems, Lo-ProT II Low Profile air stripper and an activated carbon

drum. Upper-zone recycling started after a sufficient volume of effluent pumped from

the upper zone had been stored (1.0 day), and lower-zone cosolvent recycling started

after the effluent ethanol content was high enough (approximately 70%) to make

recycling feasible (6.9 days). Prior to lower-zone recycling, new 95% ethanol solution

was injected into the lower zone. The recycled alcohol solution was augmented with new

95% ethanol solution as needed to maintain the ethanol content in the influent around

70%. A target ethanol content of 70% was used to maintain a large PCE dissolution

capacity in the solution, yet facilitate cosolvent recycling by minimizing the need to

augment treated effluent with the fresh 95% ethanol solution.

The demonstration was conducted for 38.8 days and consisted of five phases,

which are summarized in Table 5-1. In general, the strategy was to initially target the

alcohol solution to the bottom 0.6 m of the test cell in order to dissolve PCE near the

clay, and to dissolve any PCE mobilized from the higher zones during the test. Packers

were used in both injection and extraction wells to accomplish this. The target zone

thickness was gradually increased by raising the packers until the full flood-zone height













Table 5-1. Phases of the flushing demonstration.

Phase Duration (Days) Purpose
1. Flush Initiation 0 to 0.8 Establish a layer of cosolvent along
the bottom of the cell that would
dissolve PCE near the clay and capture
any PCE mobilized from the higher
zones.
2. Flood Zone Development 0.8 to 6.9 Transition period until the ethanol
content in the lower zone effluent was
sufficient to start lower-zone
recycling.
3. Lower Zone Recycling 6.9 to 27.7 Flush the contaminated portion of the
cell with recycled cosolvent solution.
4. Hot Spot Targeting 27.7 to 34.7 Target cosolvent to specific locations
of elevated PCE concentrations.
5. Water Flood 34.7 to 38.8 Flush out the resident cosolvent
solution with water.


was achieved. The full height corresponded to the bottom of the release points, 10.7 m

below grade.


Performance Monitoring

Samples were collected at regular intervals from the injection wells, extraction

wells, MLSs, and the recycling treatment processes during the demonstration. Samples

were refrigerated onsite, and then shipped overnight in coolers to the University of

Florida for ethanol and PCE analysis. Samples were analyzed for ethanol by gas

chromatography (GC) using a J&W capillary column (DB-624) and a flame ionization

detector (FID). Samples were analyzed for PCE by a similar GC/FID method, as well as

liquid chromatography using a Supelco packed column (PAH C18), UV detection, and a

methanol (70%) and HPLC grade water (30%) mixture as the mobile phase. If free phase









PCE was observed in sample vials in the laboratory, an acetone extract was used to

dissolve the free phase PCE, and the sample was then analyzed by the GC/FID method.

Samples were collected from the extraction wells and MLSs over the entire test

duration. Samples were collected from the injection wells during recycling treatment to

monitor the amount of PCE and ethanol that was re-injected into the cell. Influent and

effluent samples were collected from each carbon drum and from the air stripper to

monitor treatment performance. Selected samples were analyzed in the field using a field

SRI GC (8610B GC with an auto sampler) to provide real-time information for

operational decisions. Density measurements were also taken in the field using Fisher

Scientific specific-gravity hydrometers.

Injection and extraction flow rates, and water levels in the test cell were

monitored throughout the demonstration to maintain a steady flow field to the extent

possible. Injection and extraction rates were monitored using tank-volume data, flow-

meter readings, and volumetric measurements at the wells. Water levels in the cell were

monitored using pressure transducers in selected wells, as well as periodic measurements

from well 42 with a Solinst interface probe. Adjustments to influent flow rates were

made in accordance with these data to minimize water-level fluctuations in the cell.


Results and Discussion


System Hydraulics

The water level in monitoring well 42 during the test averaged 8.2 m below grade,

with a standard deviation of 0.2 m. Figure 5-la shows the cumulative volume of fluid








60
a) Lower Zone
50
5 40 -..---------- ---- -
40

S30 -. .-. ... ... -

o 20 .

10-----


0 10 20 30 40
Elapsed Time (Days)

12
b) Upper Zone .

80 --- -- ----- ---- i 1- --- ---



^--.- 8----- ... ...... ..
i -




0

0 10 20 30 40
Elapsed Time (Days)


Figure 5-1. Cumulative volume injected into a) the lower zone, and b) the upper zone.
Injected fluid consists of new ethanol (triangles), recycled ethanol (squares), and water
(circles) for the lower zone; and re-cycled water (squares) and water (circles) for the
upper zone.








injected into the lower zone during the demonstration. Three different fluids are

indicated: ethanol (new 95% ethanol solution as delivered to the site), recycled ethanol

(ethanol solution extracted from the cell, treated and then re-injected), and water (injected

at the end of the demonstration to flush out the remaining ethanol). Recycled ethanol

accounted for 47% of the fluid injected into the lower zone. The break from 17.5 to 20.9

days represents a flow interrupt that was conducted to investigate mass-transfer

limitations to PCE dissolution. Figure 5-1b shows the cumulative volume of water and

recycled water injected into the upper zone during the test. The recycled water is the

fluid extracted from the upper zone, treated, and then re-injected. Recycling accounted

for 77% of the fluid injected into the upper zone. The total amount of fluid injected into

the lower zone was approximately eight times greater than that injected into the upper

zone. Estimates of the number of pore volumes flushed through the upper and lower

zones separately are not possible because the location of the separation between the two

zones in the cell was not known. However, using the combined upper- and lower-zone

extraction volumes, an average water table position of 4 m above the clay, and an

effective porosity of 0.20, approximately 10 pore volumes were flushed through the test

cell.

In theory, a symmetric double-five spot pattern would have produced a stagnation

point in the center of the test cell, assuming homogeneous hydraulic conductivity and

balanced flow rates in the injection and extraction wells. The center of the cell was

swept, however, by changing the flow system as done during the Hot-Spot Targeting

Phase (Phase 4). During this phase, injection into wells 41, 51, and 54 was stopped and

injection into wells 41, 46, and 56 was increased. In addition, well 51 was converted to








an extraction well from 30.2 to 34.2 days. PCE concentrations in samples collected from

the extraction wells and MLSs during Phase 4 suggested that contaminant was not

trapped in the center of the test cell by the double-five spot pattern.


Mass Recovery

PCE concentrations and the ethanol percentages from extraction well samples are

plotted in Figure 5-2. The ethanol content in the lower zone increased over the first 5

days as the new 95% ethanol solution displaced the resident water in the test cell.

Changes in the ethanol content after approximately 5 days resulted from changes in

flushing operations (i.e., ethanol recycling, ethanol augmentation, and changes in packer

positions). Ethanol content and PCE concentrations from well 51 during the period it

was converted to an extraction well are not shown in Figure 5-2. The ethanol content in

the effluent from this well varied between 58 to 65%, and the PCE concentration varied

from 1300 to 2300 mg/L.

The ratio of aqueous PCE concentration to PCE solubility limit for extraction

wells 45 and 55 are plotted in Figure 5-3 as a function of time. The PCE solubility limit,

which is a function of the ethanol content, was based on PCE solubility limits reported by

Van Valkenburg (1999). The ratio of aqueous PCE concentration to PCE solubility limits

for well 51 (not shown in Figure 5-3) ranged from 0.04 to 0.08. PCE concentrations

above PCE solubility limits are evident in the lower-zone effluent for a short period from

approximately 1 to 2 days, and in the upper-zone effluent from approximately 2 to 13

days. The volume of free-phase PCE represented by a ratio greater than unity is 0.04

0.004 L for the lower zone and 3.2 0.1 L for the upper zone. Gravity separators were




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