DSHW-2018-007101 - 0901a0688088cab1

20183051.001A/SLC18L77340 Page 1 of 3 April 26, 2018
© 2018 Kleinfelder www.kleinfelder.com
849 West Levoy Drive, Suite 200 Salt Lake City, UT 84123 p | 801.261.3336 f | 801.261.3306
April 26, 2018
Kleinfelder Project No.: 20183051.001A
Mr. Kory Larsen
Larsen Family Trust
3548 North 2375
Layton, Utah 84040
SUBJECT: CONCENTRATION VS TIME ATTENUATION RATE CALCULATION
FORMER PEPSI BOTTLING & DISTRIBUTION FACILITY
1715 WASHINGTON BOULEVARD
OGDEN, UTAH
Dear Mr. Nelson:
Kleinfelder has prepared this letter report for the Larsen Family Trust to summarize our calculation
of the natural attenuation rate constant for groundwater contaminants at the former Pepsi Bottling
and Distributing facility (Site). Our scope of services included analysis of data and calculations
to derive a concentration vs. time rate constant and preparation of this letter report.
BACKGROUND
The former Pepsi Bottling and Distribution facility was located at 1715 Washington Street in
Ogden, Utah (Site) (Figure 1). The Site was owned by the Larsen Family until 1990, at which time
Admiral Beverage purchased the property. A 300-gallon waste oil underground storage tank
(UST) was removed from the Site in 1990 prior to the property purchase. A release of volatile
organic compounds (VOCs) was identified in groundwater associated with the UST. Larsen
Family Trust retained responsibility for the waste oil UST and the associated environmental
impacts.
Upon UST removal, a Site characterization was conducted to assess the nature and extent of
VOCs in groundwater, and in 1992 a 100-gallon per minute groundwater pump-and-treat system
was installed at the Site to address the VOC impacts. The treatment system was operated until
1996, when it was shut down after treating 80 million gallons of groundwater and removing 345
pounds of tetrachloroethene (PCE). The system was shut down because contaminant
concentrations had decreased significantly, and the resulting recoveries were negligible. In 2001
Kleinfelder submitted a Human Health Risk Assessment evaluating land use conditions and
contaminant exposure pathways. Based on the risk assessment, no significant risk to human
health was identified. Utah Division of Solid and Hazardous Waste (DSHW), approved the
calculated health risk analysis. In 2003 Kleinfelder prepared a Site Management Plan, which was
accepted by the DSHW. Groundwater at the Site has continued to be monitored periodically
throughout this period and was most recently monitored in January 2018.
The highest concentrations of PCE have historically been detected in well KMW-22, located near
the former UST in the southwest corner of the Site. In the most recent sampling event
(January 2018) PCE was detected above the U.S. EPA Maximum Contaminant Level (MCL) of

20183051.001A/SLC18L77340 Page 2 of 3 April 26, 2018
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849 West Levoy Drive, Suite 200 Salt Lake City, UT 84123 p | 801.261.3336 f | 801.261.3306
.005 milligrams per liter (mg/L) in well KMW-22 at 0.0207 mg/L. The January 2018 PCE
concentrations have decreased by two orders of magnitude compared to the historical maximum
Site PCE concentrations. Concentrations of trichloroethylene (TCE), cis-1,2-dichloroethene, and
toluene were not detected above their respective U.S. EPA drinking water MCLs.

PURPOSE FOR ATTENUATION RATE CALCUATION

Based on the corrective actions performed, significant reduction in contaminant concentrations,
lack of exposure pathways, and good faith efforts at the Site over the last 28 years, the Larsen
Family Trust has requested the current regulatory agency, Utah Division of Waste Management
and Radiation Control (DWMRC) to consider a path to formal regulatory closure of the Site. The
closure criteria for groundwater quality at the Site is the MCL for PCE, which is 0.005 mg/L.

At the request of DWMRC, Kleinfelder calculated the Site’s PCE concentration attenuation rate
to estimate the time remaining until PCE concentrations in groundwater at the Site reach the MCL.
The methodology used for the calculation is presented in Environmental Protection Agency (EPA)
Ground Water Issue “Calculation and Use of First-Order Rate Constants for Monitored Natural
Attenuation Studies” dated November 2002. The calculation and results are presented below and
on the attached graph.

NATURAL ATTENUATION CALCULATION

Kleinfelder analyzed data from the apparent plume source (monitoring well KMW-22) to determine
a concentration versus time (C vs. T) point decay rate constant, which was then used to estimate
when the remediation goals will be reached at the Site. The C vs. T point decay rate constant can
be used to estimate the time required to reach a remediation goal at a given location. Long term
groundwater monitoring data for well KMW-22, collected from January 1997 through January
2018, was used in the calculation. The groundwater data prior to 1997 was collected during
operation of the treatment system and does not reflect natural attenuation concentrations.

The following input was used in the attenuation calculation: The initial date of monitoring was
January 1997. The remediation goal is 0.005 mg/L of PCE. A point decay rate constant of 0.079
was determined from the exponential best fit line of the measured concentrations (see Graph 1).
Using the calculation below, provided by the EPA Groundwater Issue as guidance, the estimated
time to remediation is no greater than 40.5 years from 1997, or the year 2037.

Time in years: Ln [(target concentration)/(starting concentration)]/K constant

Ln (0.005 mg/L)/0.1215/0.079= approximately 40.38 years

Where 0.005 mg/L is the target concentration; 0.1215 is the y-intercept of the best fit line of the
PCE concentration in mg/L vs elapsed time; and 0.079 is the degradation constant derived from
the slope of the best fit line.

CONCLUSIONS

Based on the results of our calculations, the estimated time to remediation is no longer than 40.5
years from the calculation start date of January 1997, or approximately 19 years from now in the
year 2037.

20183051.001A/SLC18L77340 Page 3 of 3 April 26, 2018
© 2018 Kleinfelder www.kleinfelder.com

849 West Levoy Drive, Suite 200 Salt Lake City, UT 84123 p | 801.261.3336 f | 801.261.3306
LIMITATIONS

This work was performed in a manner consistent with that level of care and skill ordinarily
exercised by other members of Kleinfelder’s profession practicing in the same locality, under
similar conditions and at the date the services are provided. Our conclusions, opinions and
recommendations are based on a limited number of observations and data. It is possible that
conditions could vary between or beyond the data evaluated. Kleinfelder makes no other
representation, guarantee or warranty, express or implied, regarding the services, communication
(oral or written), report, opinion, or instrument of service provided.

Kleinfelder offers various levels of investigative and engineering services to suit the varying needs
of different clients. It should be recognized that definition and evaluation of geologic and
environmental conditions are a difficult and inexact science. Judgments leading to conclusions
and recommendations are generally made with incomplete knowledge of the subsurface
conditions present due to the limitations of data from field studies. Although risk can never be
eliminated, more-detailed and extensive studies yield more information, which may help
understand and manage the level of risk. Since detailed study and analysis involves greater
expense, our clients participate in determining levels of service that provide adequate information
for their purposes at acceptable levels of risk. More extensive studies, including subsurface
studies or field tests, should be performed to reduce uncertainties.

CLOSURE

If you have any questions or comments concerning this letter or the project, please contact us at
801.261.3336.

Sincerely,

KLEINFELDER

Jennifer Micovic Corinne Hillard
Staff Geologist Senior Project Manager, PG UT

Attachments: Graph 1 - PCE Concentration vs Time Atténuation Rate
Table 1 - Summary of PCE Concentrations in Groundwater
y = 0.1215e-0.079x
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 5 10 15 20 25 30 35 40 45
Co
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(
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C
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P
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i
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/
L
Elapsed Time (years from 1997 start date)
PCE Concentration Vs Time Attenuation Rate
Former Pepsi Bottling and Distribution Facility
January 1997 -January 2018
PCE Concentrations
Target Concentration
MW-4 MW-5 MW-6 MW-7 MW-8 MW-9 MW-12 KMW-13 KMW-14 MW-16 KMW-18 KMW-19 KMW-24 KMW-15 KMW-17 KMW-20 KMW-21 KMW-22 KMW-23
Sep-91 470 640 63 460
Jan-92 <2.0 <2.0 <2.0 110 28 31 350
Aug-92 13 560 9 400 <2.0 12 <2.0 79 24 99 13 <2.0 620 <2.0
Jan-93 59 45 5.1 70 <2.0 290 <2.0 63 2.2 7.9 <2.0 <2.0 180 <2.0
Apr-93 14 16 3.7 200 <2.0 20 <2.0 15 65 6 <2.0 <2.0 410 <2.0
Jul-93 31 15 21 410 <2.0 7 <2.0 8.7 130 4.6 <2.0 <2.0 740 5.4 <2.0 <2.0 790
Oct-93 19 26 47 12 100 16 610 <2.0 <2.0 2.1 190
Jan-94 11 440 23 4.5 330 5.4 1200 <2.0 2.8 3 810
Apr-94 32 320 <2.0 25 130 5.1 1700 <2.0 <2.0 2.7 4500
Jul-94 54 300 2 12 75 9.9 2100 <2.0 5.9 2.3 2400
Jan-95 5.8 7.1 24 580 17
Jul-95 66 15 8 260 <2.0
Jan-961 36 43 9.2 310 12
Jul-96 2.7 83 2.7 17 3.2 <2.0 56 28 <2.0 10 120
Aug-96 <2.0 71 170
Jan-97 2.4 52 <2.0 34 <2.0 26 3.6 2.2 10 47 <2.0 16 80 11
Jul-97 <2.0 26 2.7 15 <2.0 17 3.1 <2.0 52 20 5 78 50
Oct-99 <2.0 16 2.7 24 <2.0 91 4.4 46 10 38 50 120 12
Jan-03 <2.0 9.7 <2.0 29 <2.0 <2.0 <2.0 14 2.1 8.8 <2.0 <2.0 4.4 40 <2.0 <2.0 9.7 100 15
May-05 *19 *****7.5 ****11 ***4.0 31/312 65
Dec-08 4.0/4.22 6.0 2.3/3.02 3.6 160 1.4
Jun-15 6/6 Destroyed 1.3/1.22 1.1 18 <1.0
Jan-18 Destroyed Destroyed Destroyed <1.0 20.7/ 20.72 Destroyed
MCL
Notes:
1 The groundwater treatment system was shut off on April 3, 1996.
2 When two concentrations are listed separated by a slash, the duplicate sample concentration is listed after the slash.
* Monitoring well was decommissioned in 2004.
µg/L - micrograms per liter
<1.0 - Analyte was not detected at or above the laboratory detection limit indicated.
MCL - U.S. EPA Maximum Contaminant Level
PCE - tetrachloroethene
Concentrations of PCE were analyzed by U.S. Environmental Protection Agency (U.S. EPA) Method 8260B.
Concentrations shown in bold exceed U.S. EPA MCL for PCE in drinking water of 5 µg/L.
5 µg/L
Shallow Wells Deep Wells
Table 1
Summary of PCE Concentrations in Groundwater
Larsen Family Trust
Former Pepsi Bottling and Distribution Facility
PCE Concentration (µg/L)
Sampling Date
September 1991 - January 2018
20183051.001
© 2018 Kleinfelder April 26, 2018
Ground Water Issue

United States
Environmental Protection
Agency
Calculation and Use of First-Order Rate
Constants for Monitored Natural Attenuation
Studies
Charles J. Newell1, Hanadi S. Rifai2, John T. Wilson3, John A. Connor1,
Julia A. Aziz1, and Monica P. Suarez2
Introduction
This issue paper explains when and how to apply first-order
attenuation rate constant calculations in monitored natural
attenuation (MNA) studies. First-order attenuation rate constant
calculations can be an important tool for evaluating natural
attenuation processes at ground-water contamination sites.
Specific applications identified in U.S. EPA guidelines (U.S. EPA,
1999) include use in characterization of plume trends (shrinking,
expanding, or showing relatively little change), as well as
estimation of the time required for achieving remediation goals.
However, the use of the attenuation rate data for these purposes
is complicated as different types of first-order rate constants
represent very different attenuation processes:
Concentration vs. time rate constants ( kpoint ) are used for
estimating how quickly remediation goals will be met at a site.
Concentration vs. distance bulk attenuation rate constants
( k ) are used for estimating if a plume is expanding, showing
relatively little change, or shrinking due to the combined
effects of dispersion, biodegradation, and other attenuation
processes.
Biodegradation rate constants ( λ ) are used in solute
transport models to characterize the effect of biodegradation
on contaminant migration.
Correct use of attenuation rate constants requires an
understanding of the different attenuation processes that different
first-order rate constants represent.
For further information contact John T. Wilson [phone] at
the Subsurface Protection and Remediation Division of the National
Risk Management Research Laboratory, Office of Research and
Development, U.S. Environmental Protection Agency, Ada,
Oklahoma.
Why Are Attenuation Rate Constants Important?
Monitored natural attenuation (MNA) refers to the reliance on
natural attenuation processes to achieve site-specific remediation
objectives within a reasonable time frame. Natural attenuation
processes include a variety of physical, chemical, and/or biological
processes that act without human intervention to reduce the mass
1Groundwater Services, Inc., Houston, Texas
2University of Houston, Texas
3U.S. Environmental Protection Agency, Office of Research and
Development, National Risk Management Research Laboratory,
Subsurface Protection and Remediation Division, Ada, Oklahoma
or concentration of contaminants in soil and ground water. These
in-situ processes include biodegradation, dispersion, dilution,
sorption, volatilization; radioactive decay; and chemical or
biological stabilization, transformation, or destruction of
contaminants (U.S. EPA, 1999).
The overall impact of natural attenuation processes at a given
site can be assessed by evaluating the rate at which contaminant
concentrations are decreasing either spatially or temporally.
Recent guidelines issued by the U.S. EPA (U.S. EPA, 1999) and
the American Society for Testing and Materials (ASTM, 1998) have
endorsed the use of site-specific attenuation rate constants for
evaluating natural attenuation processes in ground water. The
U.S. EPA directive on the use of Monitored Natural Attenuation
(MNA) at Superfund, RCRA, and UST sites (U.S. EPA, 1999)
includes several references to the application of attenuation rates:
Once site characterization data have been collected and
a conceptual model developed, the next step is to evaluate
the potential efficacy of MNA as a remedial alternative.
This involves collection of site-specific data sufficient to
estimate with an acceptable level of confidence both the
rate of attenuation processes and the anticipated time
required to achieve remediation objectives.
At a minimum, the monitoring program should be sufficient
to enable a determination of the rate(s) of attenuation and
how that rate is changing with time.
Site characterization (and monitoring) data are typically
used for estimating attenuation rates.
The ASTM Standard Guide for Remediation of Groundwater by
Natural Attenuation at Petroleum Release Sites (ASTM, 1998)
also identifies site-specific attenuation rates as a secondary line
of evidence of the occurrence and rate of natural attenuation. In
addition, technical guidelines issued by various state
environmental regulatory agencies recommend estimation of rate
constants to evaluate contaminant plume trends and duration (New
Jersey DEP, 1998; Wisconsin DNR, 1999). For example, the
New Jersey Department of Environmental Protection (DEP) now
requires such calculations for establishing “Classification
Exception Areas (CEAs)” at sites where ground-water quality
standards are or will be exceeded for an extended time period.
The technical literature contains numerous guidelines regarding
methods for derivation of site-specific attenuation rate constants
based upon observed plume concentration trends (e.g., ASTM,
1998; U.S. EPA, 1998a; 1998b; Wiedemeier et al. 1995; 1999;
Wilson and Kolhatkar, 2002). Other resources, such as the
1

BIOSCREEN and BIOCHLOR natural attenuation models (Newell
et al., 1996; Aziz et al., 2000), include use of first-order rate
constants for simulating the attenuation of dissolved contaminants
once they leave the source and the attenuation of the source
itself. However, many of these references do not clearly distinguish
between the different types of rate constants and their appropriate
application in evaluation of natural attenuation processes. The
objective of this paper is to address this gap by briefly describing
the derivation, significance, and appropriate use of three key types
of attenuation rate constants commonly employed in natural
attenuation studies.
Key Point:
Rate calculations can help those performing MNA studies evaluate
the contribution of attenuation processes and the anticipated time
required to achieve remediation objectives. There are different
types of rate calculations, however, and it is important to use the
right kind of rate constant for the right application.
Types of First-Order Attenuation Rate Constants
In general, there are three different types of first-order attenuation
rate constants that are in common use:
Concentration vs. Time Attenuation Rate Constant, where
a rate constant, in units of inverse time (e.g., per day), is
derived as the slope of the natural log concentration vs. time
curve measured at a selected monitoring location (Figure 1).
Time
Na
t
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L
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k point =
Slope
Figure 1. Determining concentration vs. time rate constant
(kpoint).
Concentration vs. Distance Attenuation Rate Constant,
where a rate constant, in units of inverse time (e.g., per day),
is derived by plotting the natural log of the concentration vs.
distance and (if determined to match a first-order pattern)
calculating the rate as the product of the slope of the
transformed data plot and the ground-water seepage velocity
(Figure 2).
Distance from Source
SLOPE =
k/ Vgw Na
t
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Figure 2. Determining concentration vs. distance rate
constant (k).
Biodegradation Rate Constant. The “biodegradation rate
constant” ( λ ) in units of inverse time (e.g., per day) can be
derived by a variety of methods, such as comparison of
contaminant transport vs. transport of a tracer, or more
commonly, calibration of solute transport model to field data
(Figure 3).
Figure 3. Determining biodegradation rate constant ( λ ).
Distinctions Between Rate Constants
To interpret the past behavior of plumes, and to forecast their
future behavior, it is necessary to describe the behavior of the
plume in both space and time. It is necessary to collect long-term
monitoring data from wells that are distributed throughout the
plume. Concentration vs. Time Rate Constants describe the
behavior of the plume at one point in space; while Concentration
vs. Distance Rate Constants describe the behavior of the entire
plume at one point in time. The Biodegradation Rate Constant is
usually applied over both time and space, but only applies to one
attenuation mechanism. Standard practice for the environmental
industry finds applications for each of these rate constants. Under
appropriate conditions, each of the three constants can be
employed to assist in site-specific evaluation and quantification
of natural attenuation processes. Each of these terms is identified
as an “attenuation rate.” Because they differ in their significance
and appropriate application, it is important to understand the
potential for misapplication of each type of rate as summarized
below:
Concentration vs. Time Rate Constants: A rate constant
derived from a concentration vs. time (C vs. T) plot at a single
monitoring location provides information regarding the
potential plume lifetime at that location, but cannot be used to
evaluate the distribution of contaminant mass within the
ground-water system. The C vs. T rate constant at a location
within the source zone represents the persistence in source
strength over time and can be used to estimate the time
required to reach a remediation goal at that particular location.
To adequately assess an entire plume, monitoring wells must
be available that adequately delineate the entire plume, and
an adequate record of monitoring data must be available to
calculate a C vs. T plot for each well. At most sites, the rate
of attenuation in the source area (due to weathering of
residual source materials such as NAPLs) is slower than the
rate of attenuation of materials in ground water, and
concentration profiles in plumes tend to retreat back toward
the source over time. In this circumstance, the lifecycle of the
plume is controlled by the rate of attenuation of the source,
and can be predicted by the C vs. T plots in the most
contaminated wells. At some sites, the rate of attenuation of
the source is rapid compared to the rate of attenuation in
ground water. This pattern is most common when
contaminants are readily soluble in ground water and when
contaminants are not biodegraded in ground water. In this
case, the rate of attenuation of the source as predicted by a
C vs. T plot will underestimate the lifetime of the plume.
Concentration vs. Distance Rate Constants: Attenuation rate
constants derived from concentration vs. distance (C vs. D)
Contam
.
Tracer λ
Find λ
λ = 0
2

plots serve to characterize the distribution of contaminant
mass within space at a given point in time. A single C vs. D
plot provides no information with regard to the variation of
dissolved contaminant mass over time and, therefore, cannot
be employed to estimate the time required for the dissolved
plume concentrations to be reduced to a specified remediation
goal. This rate constant incorporates all attenuation
parameters (sorption, dispersion, biodegradation) for
dissolved constituents after they leave the source. Use of the
rate constant derived from a C vs. D plot (i.e., characterization
of contaminant mass over space) for this purpose (i.e., to
characterize contaminant mass over time) will provide
erroneous results. The C vs. D-based rate constant indicates
how quickly dissolved contaminants are attenuated once
they leave the source but provides no information on how
quickly a residual source zone is being attenuated. Note that
most sites with organic contamination will have some type of
continuing residual source zone, even after active remediation
(Wiedemeier et al., 1999), making the C vs. D rate constant
inappropriate for estimating plume lifetimes for most sites.
Biodegradation Rate Constant: Another type of error occurs
if a C vs. D rate constant is used as the biodegradation rate
term ( λ ) in a solute transport model. The attenuation rate
constant derived from the C vs. D plot already reflects the
combined effects of contaminant sorption, dispersion, and
biodegradation. Consequently, use of a C vs. D rate constant
as the biodegradation rate within a model that separately
accounts for sorption and dispersion effects will significantly
overestimate attenuation effects during ground-water flow.
These examples serve to illustrate the need to ensure an
appropriate match between the significance and use of each rate
constant. Further guidelines regarding derivation and use of
attenuation rate constants are provided below.
Key Point:
There are three general types of first-order rate constants that
are commonly used for MNA studies: (1) Concentration vs.Time,
(2) Concentration vs. Distance, and (3) Biodegradation.
Rate Constants vs. Half-Lives
Both first-order rate constants and attenuation half-lives represent
the same process, first-order decay. Some environmental
professionals prefer to use rate constants (in units of per time) to
describe the first-order decay process, while others prefer
half-lives. These two terms are linearly related by:
Rate constant = 0.693 / [ half-life ] and
Half-life = 0.693 / [ rate constant ]
For example, a 2 year half-life is equivalent to a first-order rate
constant of 0.35 per year. This document describes the first-
order decay process in terms of rate constants instead of half-
lives.
Key Point:
Rate constants and half-lives represent the same first-order decay
process, and are inversely related.
Appropriate Use of Attenuation Rate Constants in
Natural Attenuation Studies
Attenuation rate constants may be used for the following three
purposes in natural attenuation studies:
Plume Attenuation: Demonstrate that contaminants are
being attenuated within the ground-water flow system;
Plume Trends: Determine if the affected ground-water plume
is expanding, showing relatively little change, or shrinking;
and
Plume Duration: Estimate the time required to reach ground-
water remediation goals by natural attenuation alone.
Appropriate use of the various attenuation rate constants for
evaluation of plume attenuation, trends, and duration is shown in
Table 1.
As described in the U.S. EPA MNA Directive (U.S. EPA, 1999):
Site characterization (and monitoring) data are typically
used for estimating attenuation rates. These calculated
rates may be expressed with respect to either time or
distance from the source.Time-based estimates are used
to predict the time required for MNA to achieve remediation
objectives and distance-based estimates provide an
evaluation of whether a plume will expand, remain stable,
or shrink.
To clarify the applicability of the various first-order decay rate
constants, appropriate nomenclature is useful to indicate the
significance of each term. For example, point decay rates (defined
Table 1. Summary of First-Order Rate Constants for Natural Attenuation Studies
Rate Constant Method of Analysis Significance
Use of Rate Constant
Plume
Attenuation
Plume
Trends?
Plume
Duration?
Point Attenuation
Rate (Fig. 1)
(kpoint, time per year)
C vs. T Plot
Reduction in contaminant
concentration over time at a
single point
NO* NO* YES
Bulk Attenuation Rate
(Fig. 2)
(k; time per year)
C vs. D Plot
Reduction in dissolved
contaminant concentration with
distance from source
YES NO* NO
Biodegradation Rate
(Fig. 3)
(λ, time per year)
Model Calibration,
Tracer Studies,
Calculations
Biodegradation rate for
dissolved contaminants after
leaving source, exclusive of
advection, dispersion, etc.
YES NO NO
* Note: Although assessment of an attenuation rate constant at a single location does not yield plume attenuation information, or plume
trend information, an assessment of general trends of multiple wells over the entire plume is useful to assess overall plume attenuation
and plume trends.
3
as kpoint) , derived from single well concentration vs. time plot, may
be used to determine how long a plume will persist (Plume
Duration). While concentration vs. time data at a single point in
the plume are useful for determining trends at that location (i.e.,
are concentrations increasing, showing relatively little change, or
declining), a rate constant calculated from concentration vs. time
data at a single location cannot be used to estimate the trend of
an entire plume.
Bulk attenuation rates (defined as k), derived from concentration
vs. distance plots, can be used to indicate if a plume is expanding,
showing relatively little change, or shrinking (Plume Trends).
Biodegradation rates ( λ ), modeling parameters which are
specific to biodegradation effects and exclusive of dispersion, etc.,
can be used in appropriate solute transport models to indicate if
a plume is expanding, showing relatively little change, or shrinking
(Plume Trends).
For each of these first-order decay rate parameters, Table 2
summarizes information on the derivation and appropriate use
as well as providing representative values. In summary, different
types of first-order attenuation rate calculations are available to
help evaluate natural attenuation processes at contaminated
ground-water sites. These different types of rate constants
represent different types of attenuation processes, therefore, the
right type of rate constant should be used for the right purpose.
Examples 1-3 illustrate how the three types of rate constants are
calculated and applied.
Key Point:
In general, all three types of rate constants are useful indicators
that attenuation is occurring. Concentration vs. time rate constants
( kpoint ) can be used to estimate the duration of contamination at a
particular location. Concentration vs. time rate constants for wells
encompassing the entire plume can be used to identify overall
trends and predict the duration of the plume. Concentration vs.
distance rate constants ( k ) and biodegradation rate constants
( λ ) can be used to project the rate of attenuation of contaminants
along the flow path in ground water, and predict the spatial extent
of the plume.
Tables 1 and 2 provide more detail on use, calculations, and
analysis of the three types of rate constants. Examples 1-3
illustrate the use and application of the three types of rate
constants.
Other Types of Rate Constants
Mass-Based Rate Constants. The previous discussion focused
on concentration-based rates. It is also possible to calculate mass
vs. time rate constants and mass vs. distance rate constants. In
practice, these rates would be very similar to the concentration-
based rates.
Mass vs.Time Rate Constant. This constant compares changes
in the total mass of contaminants in the plume over time. A
Thiessen polygon network can be used to weight the concentration
data from all the available wells at a site to derive a comprehensive
estimate of the mass of contaminants in the plume at any particular
round of sampling. Mass vs. time decay rates (in units of inverse
time) are estimated by plotting the natural log of total dissolved
mass as a function of time and estimating the slope of the line.
This rate is similar to the concentration vs. time rate and since it
accounts for the entire plume, it is a good indicator of how long a
plume will persist. Many plumes change flow direction over time,
making it difficult to identify a stable centerline. Estimates based
on the entire plume are less subject to errors caused by changes
in flow direction. See Hyman and DuPont, 2001 and DuPont et
al.,1998 for discussion and details of the methods.
Mass Flux vs. Distance Rate Constant. A mass vs. distance
decay rate (in units of inverse time) can be calculated by plotting
the natural log of mass flux through different transects
perpendicular to the flow as a function of distance from the source
and multiplying the slope of the best-fit line by the seepage velocity.
Comparable to the bulk attenuation rate, this type of rate can be
used to indicate if a plume is expanding, showing relatively little
change, or shrinking. See Einarson and Mackay, 2001 for
examples of mass flux calculations. Another method for calculating
mass loss rates is described by the Remediation Technologies
Development Forum (RTDF, 1997).
Mass Flux-Based Biodegradation Rate Constant. Mass fluxes
across plume transects can be further analyzed to determine
whether the observed mass loss spatially and temporally can be
attributed to biodegradation and/or source decay. For this purpose,
the mass flux across the source area is compared to the mass
flux through the next downgradient section. Theoretically, mass
fluxes at the downgradient transect should mimic the trends
observed in the source transect if source decay, sorption, and
dispersion were the only mass reduction attenuation mechanisms.
If there is additional mass loss, it can only be attributed to
biodegradation since the other processes are already accounted
for in the mass flux calculation. Once the actual mass loss
attributable to biodegradation has been determined, it is plotted
as a function of time and a biodegradation rate is estimated using
linear regression or a first-order decay model fit to the data. See
Borden et al. (1997) and Semprini et al. (1995) for examples of
biodegradation rates calculated from mass flux across transects.
Mass-based rate constants are not often used in practice due to
the data needs for mass estimates including a dense well network
as well as localized gradients, conductivity measurements, and
aquifer thickness at monitoring points.
Average-Plume Concentration Rate Constants. Some researchers
and practitioners have calculated rate constants for the change
in average plume concentration. This rate constant reflects
primarily the change in source strength over time.
Effect of Residual NAPL on Point Decay Rate
Constant
When a monitoring well is screened across an interval that
contains residual NAPL, and when the rate of weathering of the
NAPL is slow, the well water may sustain high concentrations of
contaminants over long periods of time.
Effect of NA Processes on Rate Constants
Natural attenuation processes include a variety of physical,
chemical, or biological processes that act without human
intervention to reduce the mass or concentration of contaminants
in soil and ground water. These in-situ processes include
biodegradation, dispersion, dilution, sorption, volatilization,
radioactive decay, and chemical or biological stabilization,
transformation, or destruction of contaminants (U.S. EPA, 1999).
Each of these processes influences contaminant concentrations
in soil and ground water both spatially and temporally at a site.
Contaminant concentrations in ground water are reduced as they
travel downgradient from the source. Subject to source
degradation, contaminant concentrations will also be reduced with
time at any given distance downgradient from the source. These
concepts are illustrated in Appendices II and III. The data in
Appendix II illustrate the change in contaminant concentrations
downgradient from the source at a hypothetical site in response
4

to the different attenuation processes. It can be clearly seen from
Appendix II that contaminant concentrations downgradient from
source areas are attenuated due to dispersion, sorption,
biodegradation and source decay.The data in Appendix III illustrate
the change in contaminant concentrations with time at two points
downgradient from the source at the hypothetical site (one point
near the source and the other point at the leading edge of the
plume). As can be seen from Appendix III, contaminant
concentrations near the source will attenuate with time only if
source decay is occurring. While source decay is also important
for the leading edge of the plume, maximum contaminant
concentrations in that zone are significantly attenuated from their
source concentration counterparts due to biodegradation,
sorption, and dispersion.
Uncertainty in Rate Calculations
Rate calculations can be affected by uncertainty from a number
of sources, such as the design of the monitoring network, seasonal
variations, uncertainty in sampling methods and lab analyses,
and the heterogeneity in most ground-water plumes. Appendix I
discusses uncertainty in rate calculations and provides methods
for managing this uncertainty.
ORD has developed software (RaCES) to extract rate constants
from field data. This software is intended to facilitate an evaluation
of the uncertainty associated with the projections made by
computer models of the future behavior of plumes of contamination
in ground water. The software is available from The Ecosystem
Research Division of the National Exposure Research Laboratory
in Athens, Georgia (Budge et al., 2003).
Notice
The U.S. Environmental Protection Agency through its Office of
Research and Development funded and managed the research
described here under Contract No. 68-C-99-256 to Dynamac
Corporation. It has been subjected to the Agency’s peer and
administrative review and has been approved for publication as
an EPA document. Mention of trade names or commercial
products does not constitute endorsement or recommendation
for use.
Quality Assurance Statement
All research projects making conclusions or recommendations
based on environmental data and funded by the U.S.
Environmental Protection Agency are required to participate in
the Agency Quality Assurance Program. This project did not
involve the collection or use of environmental data and, as such,
did not require a Quality Assurance Project Plan.
5

Table 2. Quick Reference Summary of Three Types of Attenuation Rate Constants
Point Decay Rate Constant (k point) Bulk Attenuation Rate Constant (k ) Biodegradation Rate Constant ( λ )
USED FOR: Plume Duration Estimate. Used to
estimate time required to meet a
remediation goal at a particular point
within the plume.
zone are used to derive k point, then this
rate can be used to estimate the time
required to meet remediation goals for
the entire site. k point should not be
used for representing biodegradation of
dissolved constituents in ground-water
models (use λ as described in the right
hand column).
Plume Trend Evaluation. Can be used
to project how far along a flow path a
plume will expand.
be used to select the sites for monitoring
wells and plan long-term monitoring
strategies. k should not be
used to estimate how long the plume will
persist except in the unusual case where
the source has been completely
removed, as the source will keep
replenishing dissolved contaminants in
the plume.
Plume Trend Can be
used to indicate if a plume is still
expanding, or if the plume has reached
a dynamic steady state. First calculate λ,
then enter λ into a fate and transport
model and run the model to match
existing data.
simulation time in the model and see if
the plume grows larger than the plume
simulated in the previous step.
that λ should not be used to estimate
how long the plume will persist except in
the unusual case where the source has
been completely removed.
REPRESENTS: Mostly the change in source strength
over time with contributions from other
attenuation processes such as
dispersion and biodegradation. k point is
not a biodegradation rate as it
represents how quickly the source is
depleting.
source has been completely removed
(for a discussion of source zones, see
Wiedemeier et al., 1999), k point will
approximate k .
Attenuation of dissolved constituents due
to all attenuation processes (primarily
sorption, dispersion, and biodegradation).
The biodegradation rate of dissolved
constituents once they have left the
source.
attenuation due to dispersion or
sorption.
Plot natural log of concentration vs.
time for a single monitoring point and
calculate k point = slope of the best-fit
line (ASTM, 1998).
can be repeated for multiple sampling
points and for average plume
concentration to indicate spatial trends
in k point as well.
Note this calculation does not account
for any changes in attenuation
processes, particularly Dual-Equilibrium
Desorption (availability) which can
reduce the apparent attenuation rate at
lower concentrations (e.g., see Kan et
al., 1998).
HOW TO
CALCULATE:
Plot natural log of conc. vs. distance.
the data appear to be first-order,
determine the slope of the natural log-
transformed data by:
1.
natural logs and performing a linear
regression on the transformed data, or
2.
taking the natural log of the y intercept
minus the natural log of the x intercept
and dividing by the distance between the
two points.
Multiply this slope by the contaminant
velocity (seepage velocity divided by the
retardation factor R) to get k .
Adjust contaminant concentration by
comparison to existing tracer (e.g.,
chloride, tri-methyl benzenes) and then
use method for bulk attenuation rate
(see Wiedemeier et al., 1999); or
Calibrate a ground-water solute
transport computer model that includes
dispersion and retardation (e.g.,
BIOSCREEN, BIOCHLOR, BIOPLUME
III, MT3D) by adjusting λ; or
Use the method of Buscheck and
Alcantar (1995) (plume must be at
steady-state to apply this method).
this method is a hybrid between k and λ
as the Buscheck and Alcantar method
removes the effects of longitudinal
dispersion, but does not remove the
effects of transverse dispersion from
their λ.
Find λ
λ = 0
Contam
.
Tracer λ
Distance from Source
SLOPE =
k/ Vgw Na
t
.

L
o
g

Co
n
c
e
n
t
r
a
t
i
o
n

Time
Na
t
.

L
o
g

Co
n
c
e
n
t
r
a
t
i
o
n

k point =
Slope
If wells in the source
This information can
Note that
Evaluation.
Then increase the
Note
In the rare case where the
It does not account for
This calculation
If
Transforming the data by taking
Plotting the data on a semi-log plot,
Note
6

Table 2. Continued...
Point Decay Rate Constant (kpoint) Bulk Attenuation Rate Constant (k) Biodegradation Rate Constant ( λ )
HOW TO USE: To estimate plume lifetime:
The time (t) to reach the remediation
goal at the point where K point was
calculated is:
Ln goal
start
point
C
C t k
 −    =
To estimate if a plume is showing
relatively little change:
Pick a point in the plume but
downgradient of any source zones.
Estimate the time needed to decay these
dissolved contaminants to meet a
remediation goal as these contaminants
move downgradient:
Calculate the distance L that the
dissolved constituents will travel as they
are decaying using Vs as the seepage
velocity and R is the retardation factor for
the contaminant:
If the plume currently has not traveled
this distance L then this rate analysis
suggests the plume may expand to that
point. If the plume has extended beyond
point L, then this rate analysis suggests
the plume may shrink in the future. Note
that an alternative (and probably easier
method) is to merely extrapolate the
regression line to determine the distance
where the regression line reaches the
remediation goal.
Ln goal
start
C
C t k
 −    =
sVL t R = ⋅
To estimate if a plume is showing
relatively little change:
Enter λ in a solute transport model that
is calibrated to existing plume
conditions. Increase the simulation time
(e.g. by 100 years, or perhaps to the
year 2525), and determine if the model
shows that the plume is expanding,
showing relatively little change, or
shrinking.
TYPICAL
VALUES:
Reid and Reisinger (1999) indicated that
the mean point decay rate constant for
benzene from 49 gas station sites was
0.46 per year (half-life of 1.5 years). For
MTBE they reported point decay rate
constants of 0.44 per year (half-life of 1.6
years). In contrast, Peargin (2002)
calculated rates from wells that were
screened in areas with residual NAPL;
the mean decay rate for MTBE was 0.04
per year (half life of 17 years) the rate for
benzene was 0.14 per year (half life of 5
years).
Newell (personal communication)
calculated the following median point
decay rate constants: 0.33 per year (2.1
year half-life) for 159 benzene plumes at
service station sites in Texas; and 0.15
per year (4.7 year half-life) for 37 TCE
plumes around the U.S.
For many BTEX plumes, k will be similar
to biodegradation rates λ (on the order of
0.001 to 0.01 per day; see Figure 4) as
the effects of dispersion and sorption will
be small compared to biodegradation.
For BTEX compounds, 0.1 - 1 %/day
(half-lives of 700 to 70 days)(Suarez and
Rifai, 1999). Chlorinated solvent
biodegradation rates may be lower than
BTEX biodegradation rates at some
sites (Figures 4 and 5).
For more information about
biodegradation rates for a variety of
compounds, see Wiedemeier et al.,
1999 and Suarez and Rifai, 1999.
7

Typical Decay Rate
Range:
0.1% to 1% per day
25 percent.: 0
Min:
Type Rate Const:
Source:
Number:
Field or Lab:
Constituents:
Maximum
Minimum
Median
LEGEND
75 Percentile
25 Percentile
RA
T
E

C
O
N
S
T
A
N
T

(
P
e
r

D
a
y
)

AP
P
R
O
X
I
M
A
T
E

H
A
L
F

L
I
F
E

(
D
A
Y
S
)

λ
Suarez & Rifai, 1999
35-50 studies
Field Only
B, T, E, X
λ
Wied. et al, 1999
23 Air Force sites
Field Only
BTEX
k and λ
Rifai et al, 1995
14 sites
Field Only
Benzene
λ
Rifai & Newell, 2002
66 Florida Gas Stations
Field
Benzene and BTEX
0.7
0.07
70
7
7,000
700
Be
n
z
e
n
e

To
l
u
e
n
e

Et
h
y
l
B
e
n
z
e
n
e

m-
X
y
l
e
n
e

BT
E
X

Be
n
z
e
n
e
,

B
T
E
X

Be
n
z
e
n
e

Be
n
z
e
n
e

-
Ae
r
o
b
i
c

Be
n
z
e
n
e

-
An
a
e
r
o
b
i
c

λ
Suarez & Rifai, 1999
23-61 studies
Lab Only
Benzene
25 percent.: 0
Min:
1
10
0.01
0.1
0.0001
0.001
Figure 4. Biodegradation Rate Constants ( λ ) and Bulk Attenuation Rate Constants (k) for BTEX compounds from the literature.
Source: Rifai and Newell, 2001.
0.0001
Bio
d
e
g
r
a
d
a
t
i
o
n

R
a
t
e

C
o
n
s
t
a
n
t

λ
(
p
e
r

d
a
y
)

0.001
0.01
0.1
Ap
p
r
o
x
i
m
a
t
e

H
a
l
f
-
L
i
f
e

7000 days
700 days
(~1.9 yrs)
70 days
(~0.2 yrs)
7 days
Maximum
Minimum
75 Percentile
Median
25 Percentile
LEGEND
0 0
(~19yrs)
Constituent
Number of Sites
VC
VC
cDCE
cDCE
7
TCE
TCE
10 9
Figure 5. Biodegradation Rate Constants ( λ ) for Trichloroethene (TCE), cis-Dichloroethene (cDCE), and Vinyl Chloride (VC)
compounds from BIOCHLOR modeling studies. Source: Aziz et al., 2000.
8
y = 1.9568e-0.7676x
0.001
0.01
0.1
1
10
0 1 2 3 6 8
Time (years since 1/1/86)
Be
nz
e
n
e C
o
n
c
e
n
t
r
a
t
i
o
n
(m
g
/
L
)

Benzene MCL (0.005 mg/L)
Calculation Tip:
If you calculate the
slope of the line
with a calculator or
with a spreadsheet,
you need to change
the sign to get a
degradation rate
constant.
KEY POINT: The kpoint degradation rate constant is +0.77 per year.
QUESTION: Why is the sign positive?
ANSWER: The rate constant is defined as a rate of degradation. The
slope of the line is the rate of change. If the slope is negative, then
concentrations are attenuating, and the rate of degradation is positive.
EXAMPLE 1. Use of Concentration vs.Time Rate Constants (kpoint)
INTRODUCTION: A leaking underground storage tank site in Elbert, Anystate, has a maximum source concentration of
1.800 mg/L of benzene at well MW-3. A remediation goal of 0.005 mg/L ene has been established. How long will it take
for this site to reach the remediation goal using MNA with no active remediation? Mace et al. 1997)
DATA:
The following are data from well MW-3
for the period 1986 to 1991.
Years MW-3
Since Benzene
DATE 1/1/86 (mg/L)
8/19/86 0.63 1.800
7/17/87 1.54 0.440
9/29/87 1.74 0.370
12/19/87 1.96 0.320
6/25/88 2.48 0.270
9/30/88 2.75 0.260
12/21/88 2.97 0.260
4/25/89 3.31 0.220
10/23/89 3.81 0.110
7/4/91 5.50 0.030
11/20/91 5.88 0.018
CALCULATION: Construct a plot of concentration vs. time. Although the plot can be developed in many ways, the clearest
way is to convert the time data to years using an arbitrary starting point (for this example we chose 1/1/86). By transforming the
concentrations to natural log concentration, and using a spreadsheet or calculator to get the slope (-0.77) and intercept (0.67),
the following equation of the line was generated:
Ln ( Conc. Benzene) = exp (0.67-0.77x) which resulted in the following rate equation:
Benzene concentration (mg/L) = 1.96 mg/L* exp (- 0.77 yrs since 1/1/86) where kpoint = +0.77 per year.
Rearranging the equation:
Time (years since 1/1/86) Benzene (mg/L) / 1.96 ] / 0.77
For the case where the remediation goal is 0.005 mg/L benzene,
Time (years since 1/1/86) ears =
A statistical analysis of the uncertainty involved in the calculation can be performed by determining the “one tailed” 90%
confidence interval using the methods outlined in Appendix I. The “one tailed” 90% confidence limit on the time to remediation
is a time that is no longer than 8.6 years from 1/1/86, or late 1994.
Key Point:
A concentration vs. time rate constant is one of the best ways to estimate how long MNA (or any type of remediation system)
might take to reach a clean-up goal. A second method is to perform a mass-based approach (i.e., see DuPont et al., 1998;
Hyman and DuPont, 2001; Newell et al., 1996 or Chapter 2 of Wiedemeier et al., 1999).
Plume Attenuation?
The concentration vs. time rate
constant is positive, indicating that
attenuation at this location (the source
zone in this example) is occurring. The
attenuation is probably due to
weathering of the source caused by
dissolution of benzene from a residual
NAPL into flowing ground water.
Raoult’s Law predicts that weathering
from dissolution will be a first-order
process.
Plume Trends?
The concentration vs. time rate
constant is positive, indicating that
concentrations in this portion of the
plume are going down and that at
least a portion of the plume may be
shrinking. However, from the
information obtained at a single
location, no conclusion can be drawn
regarding the overall plume trend.
Plume Duration?
The concentration vs. time rate
constant was used to show that if
current trends hold then the plume will
reach the clean-up goal in 1994. Note
this assessment does not consider any
other processes which could reduce
the observed attenuation rate (i.e.,
changes in water levels, availability
effects at low concentration as
described by Kan et al., 1998, etc.).
5 4 7 9
of benz
(Data source:
= - Ln [ Conc.
= 7.7 y= - Ln [ 0.005 / 1.96 ] / 0.77 late 1993
9

EXAMPLE 2. Use of Concentration vs. Distance Rate Constants (k)
INTRODUCTION: This constant is estimated between wells along the inferred centerline of the plume. An MTBE plume at a
former fuel farm located at a U.S. Coast Guard Base has a maximum source zone concentration of 1.740 mg/L of MTBE. The
average calculated seepage velocity at the site was calculated to be 82 meters per year and the retardation factor, R, is
assumed to be equal to one. For the purpose of this example, a clean-up goal of 0.030 mg/L was assumed. Most importantly,
the site is strongly anaerobic, indicating that relatively high rates of MTBE biodegradation are possible. Is the MTBE plume
attenuating? w far should it extend?
(source: Wilson et al., 2000).
DATA:
The following is data from wells
along the plume centerline:
Well Distance from MTBE
Source(m) Conc.(mg/L)
CPT-1 0 1.74
CPT-3 40 0.823
CPT-5 70 0.672
ESM-14 104 0.383
ESM-3 134 0.319
ESM-9 180 0.001
ESM-10 195 0.0097
GP-1 250 0.001
CALCULATION: First, plot the natural log of concentration vs. distance at a point in time and calculate the slope of the best-fit
line using linear regression analysis, as shown above. The slope of the C vs. D plot is -0.033 per meter of travel.
Next, calculate the bulk attenuation rate constant, k, by multiplying the negative of the slope of the regression by the contaminant
velocity. The contaminant velocity equals the seepage velocity divided by the retardation factor. In this case the retardation
factor is 1, and the contaminant velocity is 82 meters per year. The bulk attenuation rate is (+0.033 per meter) * (82 meter per
year) = . This corresponds to a dissolved-phase half-life of 0.26 yrs (0.26 yrs = 0.69 / 2.7 per yr) after the MTBE
leaves the source zone.
To estimate the travel time required for the concentration of MTBE to attenuate to the cleanup goal, use the equation in Table 2.
The travel time to reach the remediation goal at the down gradient margin of the plume is 1.5 years (1.5 yr = - Ln [0.030 mg/L/
1.74 mg/L] / 2.7 per y). Based on the calculated attenuation rate, an MTBE source concentration of 1.74 mg/L, and a cleanup
goal of 0.030 mg/L, the MTBE plume should extend 123 meters from the source (123 meters = 82 meters per yr * 1.5 yr travel
time).
A sensitivity analysis can be performed on the rate estimates. See Appendix I for a discussion of confidence intervals. The
one-tailed 95% confidence interval on the slope is -0.021 per foot. At a seepage velocity of 82 meters per year, this is
equivalent to a concentration vs. distance rate constant (k) of 1.7 per year. The plume would require 2.4 years of travel in the
aquifer to attenuate to the cleanup goal. At 95% confidence, the plume boundary would be no more than 200 meters from the
source. The estimate of seepage velocity is also subject to uncertainty. A reasonable upper boundary on the seepage velocity
at this site is 150 meters per year (Wilson et al., 2000). At the upper bound on seepage velocity, and at the 95% confidence
interval on the slope, the MTBE plume would extend no more than 360 meters.
Key Point:
Concentration vs. distance rate constants cannot be used for estimating remediation time frames, and are only marginally
useful for estimating plume trends. This type of rate constant is most useful to predict the boundaries of a plume. It can be used
to plan the location of monitoring wells or sentinel wells. This rate constant is also used with other information to calculate the
rate of biodegradation.
Plume Attenuation?
The calculated concentration vs. distance
rate constant is positive, indicating that
attenuation of dissolved MTBE is
occurring after the MTBE leaves the
source zone. The rate constant of 2.7 per
year indicates that dissolved MTBE
concentrations will be reduced by 50%
every 0.25 yrs after the MTBE leaves the
source zone. It does not indicate the
entire plume will be reduced in
concentration by 50% in 0.25 yrs.
Plume Trends?
In theor y, the concentration vs.
distance rate constant can provide
supporting evidence that the plume
may be showing relatively little change
or shrinking in the future. However, an
analysis of concentration vs. time data
for all locations within an adequately
delineated plume is a much more direct
and robust method for estimating
plume trends.
Plume Duration?
A concentration vs. distance rate
constant is not useful for
estimating plume duration (i.e.,
the time to reach a clean-up goal).
A mass-based analysis by Wilson
et al., 2000 indicated that
60 years might be required to
reach the clean-up goal.
y = 4.3561e -0.0333x
R2 = 0.828
0.001
0.01
0.1
1
10
0 50 100 150 200 250 300
Distance from Source (meters)
MT
B
E
C
on
c
e
n
t
r
a
t
i
o
n

(
m
g
/
L
)

Key Point: The degradation rate
constant k is + 0.0033 per year.
Ho
2.7 per yr
10

Example 3. Use of Biodegradation Rate Constants (λλλλλ).
IINTRODUCTION: A chlorinated solvent plume at the Cape Canaveral Air Force Base, Florida, has maximum source
concentrations of 0.056 mg/L Tetrachloroethene (PCE), 15.8 mg/L Trichloroethene (TCE), 98.5 mg/L cis-Dichloroethene (DCE),
and 3.08 mg/L Vinyl Chloride (VC), 33 years after the spill originally occurred. The calculated seepage velocity at the site is
111.7 ft per year. Based on the existing distribution of chlorinated solvents and degradation products, how far down the flow
path will the plume extend when it eventually comes to a steady state? This example is based on the example in Appendix A.6
of the User’s Manual for the BIOCHLOR natural attenuation decision support system (Aziz et This model and the
user’s guide can be downloaded at no cost from the EPA Center for Subsurface Modeling Support (CSMoS) at http://www.epa.gov/
ada/csmos/models.html.
Well Distance from Source (feet) PCE TCE cis-DCE (mg/L) VC
CCFTA2-9S 0 0.056 15.8 98.5 3.08
MP-3 560 <0.001 0.220 3.48 3.08
CPT-4 650 ND 0.0165 0.776 0.797
MP-6 930 <0.001 0.0243 1.2 2.52
MP-4s 1085 <0.001 <0.001 0.556 5.02
Key Point:
Biodegradation rate constants cannot be used for estimating remediation time frames, but are useful for identifying possible
trends in the behavior of plumes using mathematical models.
Plume Attenuation?
The calculated biodegradation
rate constant is positive,
indicating that biodegradation of
dissolved chlorinated solvents
is occurring after the solvents
leave the source zone. PCE
and TCE had the highest rates,
while VC had the lowest rate at
this site.
Plume Trends?
The screening model used biodegradation rate
constants to project the future distribution of PCE,
TCE, cis-DCE, and VC. The model projects relatively
little change in the PCE, and TCE plumes, but the
model predicts that the cis-DCE and VC plumes are
expanding. To confirm the true behavior of the
cis-DCE and VC plume, it may be necessary to install
more monitoring wells to adequately delineate the
plume, and collect data on concentration vs. time in
all the wells in the plume.
Plume Duration?
A biodegradation rate
constant is not useful for
estimating the duration of
the plume (i.e., the time to
reach a clean-up goal).
CALCULATION: The following
approach was used to determine
biodegradation rate constants for
each of the chlorinated solvents
using a solute transport model:
Step 1: Perform parameter estima­
tion and enter data into model.
Step 2: By trial-and-error, adjust the
first-order biodegradation rate
constants ( λ) to match the
observed site data. The resulting
first-order biodegradation rate
constant for PCE was 2.0 per year
(half-life of 0.34 years), for TCE was
1.0 per year (half-life was 0.7 years),
for cis-DCE was 0.7 per year (half-
life 1.0 years) and for VC was 0.4
per year (half- life of 1.7 years).
Step 3: Run the simulation forward
in time until it comes to an apparent
steady state.
Step 4: Compare the simulated distribution of contaminants to the existing data used to calibrate the model. As discussed
in Example 1, attenuation rates for declining concentration are positive values. When compared to values in the literature
(see Figures 4 and 5), the values appear to be reasonable. All plume lengths were projected to the boundary defined by the
MCL for Vinyl Chloride. Available data to calibrate the model extended 1085 ft from the source. The model was calibrated
to the first 33 years of the plume. When the simulation was extended to 100 years the projections reached a steady state.
At steady-state, there was no significant increase in the length of the TCE plume, but the cis-DCE plume was approximately
twice as long at the time data available for calibration were collected, and the VC plume was approximately three times as
long.
0
0.001
0.01
0.1
1
10
100
0 1000 2000 3000 4000
Distance From Source (ft)
Con
c
e
n
t
ra
t
i
on

(
mg
/
L
) TCE Prediction
DCE Prediction
VC Prediction
TCE Field Data
DCE Field Data
VC Field Data
Data
Available
Projections of
Model into Future
al., 2000).
(mg/L) (mg/L) (mg/L)
11

Appendix I. Uncertainty in Rate Calculations
Using Statistics to Estimate the Time Frame to
Achieve Remediation Objectives
As with any remediation method, one of the fundamental questions
that arises is “How much time will be required before remediation
objectives are achieved?” At the current state of practice, the
only practical approach available uses a statistical analysis of
long-term monitoring data from wells in the source area of the
contaminant plume. Many practitioners will calculate the Pearson
product moment correlation coefficient (R2) for the regression used
to extract the Point Decay Rate constant (kpoint). If the coefficient
is near one (e.g., greater than 0.9 or 0.95), the regression is
accepted as being useful in a qualitative way. There are two
problems with this approach; it does not allow the user to select a
level of confidence for the comparison, and it does not give more
validity to regressions with many points compared to regressions
with only a few points.
Table I-1. Sources of Uncertainty in Calculated Rate Constants
The slope of the regression is the rate constant. A better approach
is to calculate a confidence interval on the slope of the regression.
The following data from Kolhatkar et al., 2000 will be used to
illustrate this approach. They collected long-term ground-water
monitoring data from three wells at a gasoline release site in New
Jersey. Their original data displayed extreme oscillations with
concentrations bouncing from a high value down to the analytical
detection limit of 1µg/L, and then back to a high value over
sequential sampling intervals. Although the scatter in the data
set is typical of the variation seen at many other sites, the influence
of these outliers on the statistical estimate of the rate of attenuation
was removed by editing the data set to remove those points where
the concentration of MTBE was less than the detection limit.
Type of Uncertainty Applies to Type of Effect Ways to Manage
Monitoring Well
Location
(horizontal and
vertical location)
Point Decay Rate (k point)
Bulk Attenuation Rate
Constant (k )
Biodegradation Rate
Constant (λ)
Wells not in strongest source area may
not give repres entative indication of how
long entire plume will persist.
Wells not on centerline of plume can give
mis leading indications about
concentration profile in plume.
A poorly des igned monitoring well
network may give misleading information
about source s trength, source size, and
centerline plume concentrations used for
calibration.
Characterize source with several wells.
Estimate and report uncertainty in final result
(estimated time to reach clean-up s tandards ).
Us e a well-designed monitoring well network
with transects of wells in rows across the
plume rather than one set of wells down the
inferred centerline. Estimate and report
unc ertainty in final res ult (es timated plume
length).
The source and plume need to be well
c haracterized to ensure representative
modeling res ults . Perform sensitivity analysis
on model.
Seasonal Effects
Point Decay Rate (k point)
Bulk Attenuation Rate
Constant (k )
Biodegradation Rate
Constant (λ)
Can introduce additional s catter in data
us ed to develop k point rate c ons tant.
Ty pically not a problem as all data are
collected at the same time.
Can be a problem if seas onal effects are
significant and the data used for
calibration are not c ollec ted
(concentration vs. distance) at the same
time.
Addres s as part of an uncertainty calculation
(s ee below). For s trong seasonal effects, use
of data from the same season c an be
c onsidered.
Not applicable.
For strong seasonal effects, use data from
s ame s eas on to help ensure representativ e
modeling res ults . Perform sensitivity analysis
on model.
Seepage Velocity
Estimate
Bulk Attenuation Rate
Constant (k )
Increases ov erall uncertainty in
calculation.
Average results from multiple seepage
estimates along plume centerline. Improv e
seepage velocity estimate. Estimate and
report uncertainty in final result (estimated
plume length).
Plume
Heterogeneity
All rate constant
c alc ulations
Increases apparent uncertainty. Use worst-case data. Use transects to
c apture plume heterogeneity. For regression-
bas ed rate cons tants (k and k point), estimate
and report uncertainty in final result. For
modeling studies designed to determine λ,
perform sensitivity analy sis on model by
c hanging k ey variables to their upper and
lower expected range and evaluate how
modeling res ults c hange.
12

Because there is natural scatter in the long-term monitoring data,
there is uncertainty in the estimate of the Point Decay Rate (kpoint),
and in the projected time frame to achieve cleanup in that
monitoring well. To account for this uncertainty, a confidence
interval was calculated for each estimate of the Point Decay Rate
(kpoint) at a pre-determined level of confidence of 90% and 95%.
The level of confidence is simply the probability that the true rate
is contained within the calculated confidence interval. A
confidence level of 90% is reasonable for many sites. At other
sites, a more stringent confidence level (e.g., 95%) may be more
appropriate, depending upon the level of risk that is acceptable.
In most applications of regression, the user wishes to calculate
both an upper boundary and lower boundary on the confidence
interval that will contain the true rate at the pre-determined level
of confidence. This is termed a “two tailed” confidence interval
because the possibility of error (the tail of the probability frequency
distribution) is distributed between rates above the upper boundary
and below the lower boundary of the confidence interval. As a
consequence, tables of critical values in statistical reference books
and computer applications provide a “two-tailed” confidence
interval. At a level of confidence of 80%, the estimate will be in
error 20% of the time. The true rate will be contained within the
calculated confidence interval 80% of the time, 10% of the time
the true rate will be faster than the upper boundary of the
confidence interval, and 10% of the time the true rate will be slower
than the lower boundary of the confidence interval. Using the
data provided above from MW-5, the slope of a regression of the
natural logarithm of concentration of MTBE on time is -0.188 per
year. The Point Decay Rate (kpoint) is +0.188 per year. The
boundaries of the “two tailed” confidence interval on the rate at
80% confidence are 0.248 per year and 0.127 per year. This
means that 80% of the time the true rate will be between 0.248
and 0.127 per year, that 10% of the time the true rate is greater
than 0.248 per year, and 10% of the time the true rate is less than
0.127 per year. The true rate will be greater than 0.127 per year
90% of the time.
There is little value in estimating the shortest possible time that
would be required to reach the goals for cleanup; remedial options
are compared and evaluated based on the greatest time required
to reach goals. At the selected level of confidence, all the
possibility of error should be assigned to rates that are slower
than the lower boundary of the confidence interval. This is a “one-
tailed” confidence level; it includes all true rates that are faster
than the lower boundary of the confidence interval. A “one tailed”
Table I-2. MTBE Concentrations in the Three Most Contaminated Monitoring Wells at a Gasoline Spill Site
MW-5 MW-6 MW-11
Date Concentration
(µg/liter)
Concentration
(µg/liter)
Concentration
(µg/liter)
9/17/93 1,900 270
9/23/94 1,800 200 2200
5/17/96 1,300 120 880
8/10/96 980 120
11/7/96 620 66 660
12/8/97 500 339
3/27/98 635 71.2 426
7/23/98 470 419
9/18/98 1,210 44
12/16/98 379 144
3/1/99 700 42.2 123
6/21/99 574 464
9/7/99 792 43.2 195
9/7/99 1,050 155
12/30/99 525 220
3/20/00 501 36 173
6/22/00 420 51.2 146
13

confidence interval can be calculated as the slower of the two
confidence intervals from a “two-tailed” test that has twice the
uncertainty. In the example above, where “two tailed” confidence
intervals were calculated for a confidence level of 80%, the true
rate will be greater than a rate of 0.127 per year 90% of the time.
The “one tailed” confidence intervals reported in the table below
were calculated in this fashion. Monitoring well MW-5 has the
highest concentration of MTBE and the lowest Point Decay Rate,
and can reasonably be expected to be the last monitoring well to
reach the goal. The other monitoring wells should reach the goal
much sooner; the best estimate of the lifetime of the plume is the
expected lifetime of MTBE in MW-5.
Note that for a given number of observations, as the level of
confidence is increased, the interval that is expected to contain
the real value for the rate constant increases as well. As the level
of confidence increases, the lower boundary on the rate constant
decreases, and the projected time required to meet the clean-up
goal increases. In the examples presented above, the estimated
rate of natural attenuation of MTBE in MW-5 is 0.188 per year,
which requires 16 years to attain a concentration of 20 µg/L. At a
90% confidence level, the lower boundary of the confidence
interval is 0.127 per year, which requires 24 years to meet the
goal. At a 95% confidence level, the lower boundary is 0.109 per
year, which requires 28 years to reach the goal. At the 95%
confidence level the upper bound of the time expected to reach
the clean-up goal has increased by a factor of almost two (from
16 years to 28 years). This does not necessarily mean that the
actual time to achieve cleanup will be 28 years; it simply means
that the length of time that will actually be required is estimated to
be no more than 28 years at a 95% level of confidence.
At many sites, the long-term monitoring data show that the
concentration of MTBE actually increases over time. At other
sites, the general trend in the concentration of MTBE may be
down, but there is a great deal of variation in the data. These
variations in concentrations over time are not necessarily errors
in sampling and analysis of ground water. In many cases they
reflect real changes in the plume caused by seasonal variations
in precipitation. These variations are a natural property of plume.
If the variation is large enough, one boundary of the “two tailed”
confidence interval will be a positive number and the other
boundary will be a negative number. When zero is included in
the confidence interval on the rate, there is no evidence in the
data that the true rate is different from zero. If this is the case, it is
possible that attenuation is occurring in that particular well over
time, but the monitoring data do not present evidence that
attenuation is occurring at the predetermined level of confidence.
At the predetermined level of confidence, it is impossible to predict
how long it will take to reach the clean-up goals.
The ability to extract a rate of attenuation from long-term monitoring
data is related to the number of measurements, and the time
interval over which they are collected. As an example, the rate of
attenuation extracted from the last three years of monitoring data
for well MW-5 (3/27/1998 to 6/22/2000) is 0.106 per year, but the
“one tailed” 90% confidence interval is all rates greater than
-0.125 per year. The confidence interval includes zero. If only
these three years of data were available, there would be no
evidence of natural attenuation of MTBE in well MW-5 at 90%
confidence. The rate extracted from the last four years of data
(5/17/1996 to 6/22/2000) is 0.130 per year. The 90% confidence
interval on the rate (0.0302 per year) would reach the clean-up
goal in 100 years. The rate extracted using all the seven years of
monitoring data is 0.188 per year. The 90% confidence interval
on the rate would reach cleanup in 24 years. A few extra years of
monitoring data have a strong influence on the ability to extract
useful rate constants.
Key Point:
The Point Decay Rate (kpoint) can be used to project the time
required for reaching a clean-up goal. However, there are a
number of points to keep in mind. First, an appreciable record of
long-term monitoring data must be available to make a statistically
valid projection of the rate of natural attenuation. As a practical
matter, it is difficult to extract rate constants that are statistically
significant with fewer than six sampling dates, or with a sampling
interval of less than three years. Second, it is unrealistic to expect
just a few years of monitoring data to accurately predict plume
behavior several decades into the future. Third, it is important to
realize that these estimates are merely estimates and that the
true rate may change over time.
Table I-3. Point Decay Rate (kpoint) of Attenuation of MTBE in Monitoring Wells and the Projected Time Required to Reach a
Clean-Up Goal of 20 mg/L as Calculated from the Long-Term Monitoring Data for the Wells
Well MTBE (µg/L) Estimated rate and time
required
Rate and time significant
at 90% confidence
Rate and time significant
at 95% confidence
First
Sample
1993
Last
Sample
2000
Rate
(per year)
Time
(years)
Rate
(per year)
Time
(years)
Rate
(per year)
Time
(years)
MW-5 1900 420 0.188 16 0.127 24 0.109 28
MW-11 2200 146 0.453 4.4 0.365 5.4 0.337 5.9
MW-6 270 51.2 0.29 3.2 0.246 3.8 0.231 3.8
14

Appendix II. Contaminant Concentration Attenuation Downgradient from Source Areas as a
Function of Dispersion, Sorption, and Biodegradation
INTRODUCTION: The Domenico solution to the advection-dispersion-biodegradation equation along the centerline of a plume was
applied to a hypothetical case to illustrate the impact of the different attenuation parameters on the overall bulk attenuation rate. The
Domenico solution is given by
λαx 41 v +   x  λα + x 41 v
−
Cx,t)= C
2
0 exp 
 2αx 1−


 erfc



xv
2
t
α x tv
 erf 

 2 xα y
Y 
(

where Co is the initial concentration, α x is the longitudinal dispersivity, α y is the transverse dispersivity, λ is the biodegradation rate, t is
time, x is distance from the source, v is the retarded ground-water velocity (i.e., v=vs/R), and Y is source width.
DATA: The following are the parameters assumed for this example:
vs = 100 ft/yr (median value from the HGDB database (Newell et al., 1990))

Y = 40 ft

t = 10 years

α = 0.1 α
y x
b = 10 ft (source thickness used for the Bioscreen runs)

CALCULATION: Four different scenarios were considered to estimate the effect of the different parameters on the overall attenuation
rate: 1) the only process acting at the plume is dispersion (α = 100 ft); 2) previous scenario plus the effect of sorption (R=5);x 3) dispersion, sorption, and biodegradation (λ=0.2 per yr) are acting; and 4) previous scenario plus the effect of source decay
(k = 0.139 per yr).source
For each scenario, the Domenico solution was applied to obtain concentrations along the centerline of the plume. Next, concentrations
vs. distance were plotted and data were fit with an exponential equation (first-order model). The slopes of the C vs. D plots were
0.002, 0.0106, 0.0124, and 0.0237/ft for scenarios 1, 2, 3, and 4, respectively. Finally, the bulk attenuation rate constant, k, for each
scenario was calculated by multiplying the slope by the contaminant velocity (100 ft/yr/retardation factor). This calculation yielded
bulk attenuation rates equal to 0.2, 0.212, 0.248, and 0.474/year for scenarios 1, 2, 3, and 4, respectively. These values correspond
to dissolved-phase half-lives of 3.5, 3.3, 2.8 and 1.5 years after the contaminant leaves the source zone.
0
5
10
0 200 400 600 800 1000 1200
Distance from source (ft)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

Dispersion+Sorption+Biodegradation
k=0.248/year
Dispersion+Sorption+Biodegradation+
Source Decay
k=0.474/year
Dispersion
k=0.2/year
Dispersion+Sorption
k=0.212/year
This example illustrates incremental attenuation impacts of the various attenuation processes and how the overall bulk rates change
as a result (i.e., the more processes present at a given site, the higher the bulk attenuation rate). The effect of individual parameters
on the attenuation rate is discussed below:
15
ααααBulk Attenuation Rate (k) as a Function of Longitudinal Dispersivity (α x)
The figures below show the calculation of k for different dispersivity values as well as a resulting plot of bulk attenuation rate as a
function of longitudinal dispersivity. The transverse dispersivity (α y) was set to 10% of the longitudinal dispersivity (α x), the vertical
dispersivity (α z) was set to 10% of the transverse dispersivity (α y), and t = 30 years. The slopes of the concentration vs. distance plots
were multiplied by the contaminant velocity to obtain bulk attenuation rates. This type of calculation assumes that the plume is at
steady-state. The figures below suggest that the bulk attenuation rate (k) increases as dispersivity increases.
0
5
10
0 200 400 600 800 1000 1200
Distance from Source (ft)
Co
n
c
e
n
t
r
a
t
i
o
n

(mg
/
L
)

�x = 3 ft, y = 10.2 e -0.00058x
�x = 10 ft, y = 8.7 e -0.0011x
�x = 30 ft, y = 6.6 e -0.0014x
�x = 100 ft, y = 4.7 e -0.0020x
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100 120
� x
Bu
l
k

ra
t
e

(
pe
r

ye
a
r
)
k
feet
16

Bulk Attenuation Rate (k) as a Function of Sorption prior to Equilibrium.
When a plume comes to a steady state, sorption no longer removes contaminants from ground water, and there is no effect of
sorption on the bulk attenuation rate (k). Prior to equilibrium, sorption removes contaminants from the ground water and contributes
to the bulk attenuation rate. The effect of sorption on the bulk attenuation rate was evaluated by calculating k for different retardation
factors and plotting the resulting k values as a function of R as illustrated in the figures below. For this analysis a longitudinal
dispersivity of 100 ft was assumed, and t = 10 years. In this case, the slopes of the concentration vs. distance plots were multiplied by
the seepage velocity rather than the contaminant velocity to obtain bulk attenuation rates, since retardation was already included in
the Domenico calculation. It can be concluded that with all the other parameters constant, the bulk attenuation rate is roughly
proportional to the retardation factor.
0
5
10
0 500 1000 1500 2000 2500
Distance from source (ft)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

R=1 y = 12.261e -0.0031x
R=2 y = 43.744e -0.0082x
R=5 y = 150.085e -0.0185x
R=10 y = 120.133e-0.0268x
R=50 y =169.4577e-0.061x
0
1
2
3
4
5
6
7
0 0 20 30 40 50 60
Retardation factor
Bu
l
k

r
at
e

(

pe
r

y
r
)
k
1
17

λλλλBulk Attenuation Rate (k) as a Function of Biodegradation Rate (λ)
Bulk attenuation rates for first-order biodegradation rates within the range 0 to 0.5/year were estimated and a plot of k versus λ was
prepared to illustrate the impact of this parameter on the overall attenuation rate. For this analysis a longitudinal dispersivity of and a
retardation factor equal to 1 (no sorption) were assumed. As shown in the following figures, with all the other parameters being
constant, the bulk attenuation rate increases as the biodegradation rate increases.
0
5
10
0 500 1000 1500 2000 2500 3000
Distance from source (ft)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

l =0 y =12.26e-0.0031x
l =0.1/yr y =11e -0.0035x
l =0.3/yr y =9.1343e-0.0043x
l =1/yr y =6.5575e-0.0071x
l =3/yr y =5.9249e-0.0137x
l =0.5/yr y =7.9563e-0.0051x
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 2 3 4
Biodegradation rate ( � per yr)
Bu
l
k

rat
e

(

pe
r

y
r
)
k
1
18

Bulk Attenuation Rate (k) as a Function of Source Decay Rate (ksource)
The figures below show the calculation of k for source decay rates varying between 0 and 0.69/yr as well as the resulting plot of bulk
attenuation rate as a function of k . The effect of source decay was evaluated using the Bioscreen model (Newell et al., 1996). For source this scenario, a longitudinal dispersivity of 100 ft and no sorption nor biodegradation were assumed. It can be inferred that the bulk
attenuation rate decreases as source decay rate increases.
0
5
10
0 50 100 150 200 250 300 350 400 450
Distance from source (ft)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

k source =0 y =5.9929e-0.0038x
ksource =0.0139/yr y =5.231e-0.0037x
ksource =0.069/yr y =3.038e-0.0031x
ksource =0.139/yr y =1.5404e-0.0024x
k source =0.346/yr y =0.2007e-0.0004x
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 0.1 0.2 0.3 0.4
Source decay rate (k source per yr)
Bu
l
k

r
at
e

(

pe
r

y
r
)
k
k
ksource
19

Appendix III. Effect of Dispersion, Sorption, Biodegradation, and Source Decay on
Concentration vs.Time Profiles
INTRODUCTION: Concentration versus time profiles for a hypothetical case were generated using the Domenico solution to the
advection-dispersion-biodegradation equation along the centerline of a plume to illustrate the impact of the different attenuation
parameters on the point attenuation rate at two different locations, one near the source area and the other 200 ft downgradient from
the source.
DATA: The parameters assumed for this example are as follows:
vs = 100 ft/yr (median value from the HGDB database (Newell et al., 1990)), Y = 40 ft , α y = 0.1 α x , b = 10 ft (source thickness used
for the Bioscreen runs)
CALCULATION: Four different scenarios were considered to estimate the effect of the different parameters on the overall attenuation
rate: 1) the only process acting at the plume is dispersion (α = 100 ft); 2) previous scenario plus the effect of sorption (R=5); 3)x dispersion, sorption, and biodegradation (λ=0.2 per yr) are acting; and 4) previous scenario plus the effect of source decay (k = source 0.139 per yr).
For each scenario, the Domenico solution was applied to obtain concentrations at two locations: one near the source area (X=20 ft)
and the other at a point located 200 ft downgradient from the source as a function of time. As illustrated in the figures below, when
running Concentration vs. Time profiles, a decline in concentration near the source is not observed unless the source is decaying.
Without source decay, the concentrations increase until they reach a steady-state maximum value and thereafter remain constant
even when dispersion, sorption, and biodegradation are present at a site (scenarios 1, 2, and 3). On the other hand, when source
decay is included, concentrations increase up to a maximum and decrease with time. (Note the two graphs have different scales).
Near source location
0
2
4
6
8
10
12
0 5 10 5 0 25 30
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

Dispersion+Sorption
ts-s =75 yr,
Cmax =9.5 mg/LDispersion+Sorption+Biodegradation
ts-s =12 yr,
Cmax =8.4 mg/L
Dispersion+Sorption+Biodegradation+
Source decay
ts-s =3 yr, C max = 3.9 mg/L
kpoint =0.121/year
Dispersion
ts-s =15 yr,
Cmax=9.5 mg/L
1 2
It should be noted that while concentrations do not
show attenuation as a function of time without source
decay, a decrease in the maximum concentration
occurs as a result of the various attenuation
processes. For instance, the steady-state
concentrations for the well located 20 ft from the
source area were 9.5 mg/L when only dispersion was
present, 9.5 mg/L when both sorption and dispersion
were acting, 8.4 mg/L when dispersion, sorption and
biodegradation were present, and 3.9 when source
decay was included. Similarly, for the point located
200 ft from the source, maximum concentrations were
4.7, 4.7, 1.3, and 0.6 mg/L for scenarios 1, 2, 3, and
4, respectively. In other words, the more processes
acting at a given site, the lower the maximum
concentration observed. In addition, the presence of
different processes impacts the time required to reach
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0 5 10 15 20 25 30
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

Dispersion
ts-s=15 yr,
Cmax=4.7 mg/L Dispersion+Sorption
ts-s=100 yr, C max =4.7
Dispersion+Sorption+Biodegradation
ts-s=12 yr, Cmax =1.3 mg/L
Dispersion+Sorption+Biodegradation+
Source decay
ts-s=10 yr, Cmax=0.6 mg/L
kpoint =0.0629/yr
steady-state. For the source location, the time to
steady-state was 15, 75, 12, and 3 years for
scenarios 1, 2, 3, and 4, respectively; whereas for
the downgradient location, the time to steady-state
was 15, 100, 12, and 10 years for scenarios 1 to 4.
This example illustrates the impacts of the various
attenuation processes on the maximum
concentrations observed at different locations within
a plume. It can be inferred that the more processes
present at a given site, the lower the maximum
concentration observed. The effect of individual
parameters on the Concentration vs.Time profiles is
discussed below.
Downgradient location
20

ααααEffect of Longitudinal Dispersivity (α x) on Concentration vs.Time Profiles
The figures below show concentration vs. time profiles for different dispersivity values for a source location (X=20 ft) and a downgradient
location (X=200 ft). The maximum concentration decreases as the longitudinal dispersivity increases and the time required to reach
steady-state increases as dispersivity increases.
2
3
4
5
6
7
8
9
10
11
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

�=10 ft �=25 ft
�=50 ft
�=100 ft
Near source location
0
1
2
3
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

�=10 ft
�=50 ft
�=25 ft
�=100 ft
Downgradient location
21

Effect of Sorption on Concentration vs.Time Profiles
Changes in Concentration vs.Time profiles as a result of sorption were evaluated by plotting the profiles at the source and downgradient
locations for different retardation factors. For this analysis a longitudinal dispersivity of 100 ft was assumed. As can be seen in the
figures below, the time required to reach steady-state increases as the retardation factor increases. Sorption, however, does not
change the steady-state concentration. (Note the two graphs have different scales.)
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100 120
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

R=1
R=5
R=2
R=10
Near source location
0
1
2
3
4
5
0 20 40 60 80 100 120 140
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

R=1
R=2
R=5
R=10
Downgradient location
22

λλλλEffect of Biodegradation (λ) on Concentration vs.Time Profiles
The figures below show concentration vs. time profiles for different biodegradation rates for both the source and downgradient
locations. For this analysis a longitudinal dispersivity of 100 ft and a retardation factor equal to 1 (no sorption) were assumed. As
shown below, the higher the biodegradation rate, the lower the maximum concentration and the shorter the time required to reach
steady-state. (Note the two graphs have different scales.)
4
5
6
7
8
9
10
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

l=0
l =1 yr -1
l =0.3 yr -1
l =0.5 yr -1
l =3 yr -1
Near source location
0
1
2
3
4
5
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

l =0
l =1 yr -1
l =0.3 yr -1
l =0.5 yr -1
l =3 yr -1
Downgradient location
23

Effect of Source Decay (ksource) on Concentration vs.Time Profiles
The figures below show concentration vs. time profiles for various source decay rates for both the source and downgradient locations.
This scenario was run using the Bioscreen model (Newell et al., 1996) assuming a longitudinal dispersivity of 100 ft, no sorption and
no biodegradation. The maximum concentration is shown to be inversely proportional to the source decay rate. (Note the two graphs
have different scales.)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

8
7
6
5
4
3
2
1
0
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
ksource =0.069 per yr
ksource =0.346 per yr
ksource =0.139 per yr
ksource =0.0139 per yr
ksource =0.693 per yr
ksource =0
Near source location
Downgradient location
0
1
2
3
0 5 10 15 20 25 30 35 40 45 50
Time (yr)
Co
n
c
e
n
t
r
at
i
o
n

(
m
g
/
L
)

ksource =0.139 per yr
k source =0.693 per yr
ksource =0.346 per yr
ksource =0.069 per yr ksource =0.0139 per yr
ksource =0
24

Point Attenuation Rate kpoint as a Function of Source Decay (ksource)
A further analysis of Concentration vs. Time profiles for different source decay rates was conducted to calculate kpoint values. The

effect of source decay on the point attenuation rate was then evaluated by plotting the calculated kpoint
illustrated in the figure below. This example illustrates that the point attenuation rate is proportional to the source decay rate.

as a function of k source as
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
Source decay rate ( per yr)ksource
At
t
e
n
ua
t
i
o
n

r
at
e

(
kpo
i
n
t

pe
r

y
r
)

X=20 ft
X=200 ft
k � k
25

References
American Society for Testing and Materials, 1998. Standard
Guide for Remediation of Ground Water by Natural Attenuation
at Petroleum Release Sites. E 1943-98, West Conshohocken,
PA. www.astm.org
Aziz, C.E., C.J. Newell, J.R. Gonzales, P.E. Haas, T.P. Clement,
and Y. Sun, 2000. BIOCHLOR Natural Attenuation Decision
Support System, User’s Manual Version 1.1, U.S. EPA, Office
of Research and Development, EPA/600/R-00/008, Washington
D.C., www.epa.gov/ada/csmos/models.html
Borden, R.C., R.A. Daniel, L.E. LeBrun IV, and C.W. Davis, 1997.
Intrinsic Biodegradation of MTBE and BTEX in a Gasoline-
Contaminated Aquifer. Water Resour. Res. 33(5):1105-1115.
Budge, T., S. Young, and J. Weaver. 2003. Rate-Constant
Estimation Software (RaCES) for Extracting Biodegradation
Rates from Field Data. Available in 2003 from Jim Weaver at
[e-mail], Later in 2003 the software will be available
at http://www.epa.gov/athens/onsite/index.html, and
http://www.epa.gov/ceampubl/gwater/index.htm
Buscheck, T.E., and C.M. Alcantar, 1995. “Regression Techniques
and Analytical Solutions to Demonstrate Intrinsic
Bioremediation.” In, Proceedings of the 1995 Battelle
International Conference on In-Situ and On Site Bioreclamation,
R. E. Hinchee and R. F. Olfenbuttel eds., Battelle Memorial
Institute, Butterworth-Heinemann, Boston, MA.
Dupont, R.R., C. J. Bruell, D. C. Downey, S. G. Huling, M. C.
Marley, R. D. Norris, B. Pivetz, 1998. Innovative site remediation
technology,design and application. Bioremediation. American
Academy of Environmental Engineers, Annapolis, MD. 450 pp.
Einarson, M.D. and D.M. Mackay, 2001. Predicting Impacts of
Groundwater Contamination. Environ. Sci. Technol.
35(3):66A-73A.
Hyman, M., and R.R. Dupont, 2001. Groundwater and soil
remediation: process design and cost estimating of proven
technologies. American Society of Civil Engineers Press,
Reston, VA. 517 pp.
Kan, A.T., G. Fu, M. Hunter, W. Chen, C.H. Ward, and M.B.
Tomson, 1998. “Irreversible Sorption of Neutral Hydrocarbons
to Sediments: Experimental Observations and Model
Predictions,” Environ. Sci. Technol., 32: 892-902.
Kolhatkar, R., J. Wilson, and L.E. Dunlap. 2000. Evaluating
Natural Biodegradation of MTBE at Multiple UST Sites.
Proceedings of the Petroleum Hydrocarbons and Organic
Chemicals in Ground Water: Prevention, Detection, and
Remediation Conference, API, NGWA, STEP Conference and
Exposition, Anaheim, CA, November 15-17, 2000, pp. 32-49.
Mace, R.E., R.S. Fisher, D.M. Welch, and S.P. Parra, 1997.
Extent, Mass, and Duration of Hydrocarbon Plumes from
Leaking Petroleum Storage Tank Sites in Texas, Bureau of
Economic Geology, University of Texas, Geologic Circular
97-1, Austin, Texas, 1997.
New Jersey Department of Environmental Protection, 1998. Final
Guidance on Designation of Classification Exception Areas,
www.state.nj.us/dep/srp/dl/ceaguid2.pdf
Newell, C.J., and J.A. Connor, 1998. Characteristics of Dissolved
Hydrocarbon Plumes: Results of Four Studies, American
Petroleum Institute, Washington D.C., December, 1998.
www.gsi-net.com
Newell, C.J., S.K. Farhat, P.C. de Blanc, and J.R. Gonzales, 2002.
BIOSOURCE Source Attenuation Decision Support System
and Database,” Air Force Center for Environmental Excellence,
Brooks AFB, TX, in review.
Newell, C.J., R.K. McLeod, and J. Gonzales, 1996. BIOSCREEN
Natural Attenuation Decision Support System, EPA /600/R-96/
087, August, 1996. www.epa.gov/ada/csmos/models.html
Newell, C.J., L.P. Hopkins, and P.B. Bedient, 1990. ”A
Hydrogeologic Database for Ground Water Modeling.” Ground
Water, 28(5): 703-714.
Peargin, T.R. , 2002. Relative Depletion Rates of MTBE, Benzene,
and Xylene from Smear Zone Non-Aqueous Phase Liquid. In
Bioremediation of MTBE, Alcohols, and Ethers. Editors V.S.
Magar, J.T. Gibbs, K.T. O’Reilly, M.R. Hyman, and A. Leeson.
Proceedings of the Sixth International In Situ and On-Site
Bioremediation Symposium. San Diego, California, June 4-7,
2001. Battelle Press. Pages 67 to 74.
Reid, J. B., and Reisinger, H. J. 1999. Comparative MtBE versus
Benzene Plume Length Behavior BP Oil Company Florida
Facilities. Prepared by Integrated Sciences & Technology,
Marietta, Georgia for BP Oil Company, Cleveland, Ohio.
Remediation Technologies Development Forum, 1997. Natural
Attenuation of Chlorinated Solvents in Groundwater Seminar,
RTDF, www.dep.state.pa.us/dep/deputate/airwaste/wm/
remserv/biotreat/P_Pman.pdf.
Rifai, H.S., R. C. Borden, J. T. Wilson and C. H. Ward. (1995).
Intrinsic bioattenuation for subsurface restoration, Intrinsic
Bioremediation, R. E. Hinchee, J.T. Wilson, and D.C. Downey,
eds., Battelle Memorial Institute, Columbus, OH, 1-29.
Rifai, H. S., and C.J. Newell, 2002. Estimating First Order Decay
Constants for Petroleum Hydrocarbon Biodegradation in
Groundwater, American Petroleum Institute, Soil/Groundwater
Technical Task Force, Washington, DC.
Rice, D.W., R.D. Grose, J.C. Michaelsen, B.P. Dooher, D.H.
MacQueen, S.J. Cullen, W.E. Kastenberg, L.G. Everett, and
M.A. Marino, 1995. California Leaking Underground Fuel Tank
(LUFT) Historical Case Analysis, California Environmental
Protection Department, November 16, 1995.
Semprini, L., P.K. Kitanidis, D.H. Kampbell, and J.T. Wilson, 1995.
Anaerobic Transformation of Chlorinated Aliphatic
Hydrocarbons in a Sand Aquifer Based on Spatial Chemical
Distributions. Water Resour. Res. 31(4):1051-1062.
Suarez, M. P. and H. S. Rifai, 1999. Biodegradation Rates for Fuel
Hydrocarbons and Chlorinated Solvents in Groundwater,
Bioremediation J., 3(4):337 - 362, 1999.
U.S. Environmental Protection Agency, 1998a. Technical Protocol
for Evaluating Natural Attenuation of Chlorinated Solvents in
Groundwater, EPA/600/R/128, Washington D.C., Sept. 1998.
www.epa.gov/swerust1/oswermna/mna_epas.htm
U.S. Environmental Protection Agency, 1998b. Seminar Series on
Monitored Natural Attenuation for Ground Water, EPA/625/
K-98/ 001, Washington, D.C., September 1998. www.epa.gov/
swerust1/oswermna/mna_epas.htm
U.S. Environmental Protection Agency, 1999. Use of Monitored
Natural Attenuation at Superfund, RCRA Corrective Action,
and Underground Storage Tank Sites, Office of Solid Waste
and Emergency Response (OSWER), Directive 9200.4-17P,
Final Draft, Washington, D.C., April 21, 1999. www.epa.gov/
swerust1/oswermna/mna_epas.htm
26

Wiedemeier, T. H, H.S. Rifai, C. J. Newell, and J. T. Wilson, 1999.
Natural Attenuation of Fuel Hydrocarbons and Chlorinated
Solvents in the Subsurface, John Wiley and Sons, NY, 1999.
www.gsi-net.com
Wiedemeier, T.H., J.T. Wilson, D.H. Kampbell, R.N. Miller, and
J.E. Hansen, 1995. Technical Protocol for Implementing Intrinsic
Remediation with Long-Term Monitoring for Natural Attenuation
of Fuel Contamination Dissolved in Groundwater (Revision 0),
Air Force Center for Environmental Excellence, Brooks AFB,
TX, November 1995.
Wilson, J.T., J.S. Cho, B.H. Wilson, and J.A.Vardy, 2000, Natural
Attenuation of MTBE in the Subsurface under Methanogenic
Conditions, EPA/600/R-00/006, www.epa.gov/ada/
publications.html.
Wilson, J.T., and R. Kolhatkar. 2002. Role of Natural Attenuation
in Life Cycle of MTBE Plumes. J. Environ. Eng., 128(9):876-
882.
Wisconsin Department of Natural Resources, 1999. Interim
Guidance on Natural Attenuation for Petroleum Releases,
PUBL-RR-614, Wisconsin DNR, Bureau for Remediation and
Redevelopment.
27

Please make all necessary changes on the below label,
detach or copy, and return to the address in the upper
left-hand corner.
If you do not wish to receive these reports CHECK HERE
7/::SU/:.mrn ::;tate ot Utah Mail -1-wd: 1-'epsi ~ottling ::;ite -Natural Attenuation Kate Calculation
Carlee Christoffersen <[e-mail]>
Fwd: Pepsi Bottling Site -Natural Attenuation Rate Calculation
2 messages
Brad Maulding <[e-mail]>
To: Carlee Christoffersen <[e-mail]>
Morning Carlee,
Mon, Jul 30, 2018 at 10:26 AM
I am in the process of reviewing the actions associated with this site and it appears we never got a hard copy of the
attached letter dated April 26, 2018. Would you please have it entered into the system?
Thanks, Brad
---------Forwarded message----------
From: Corinne Hillard <[e-mail]>
Date: Fri, Apr 27, 2018 at 3:36 PM
Subject: Pepsi Bottling Site -Natural Attenuation Rate Calculation
To: "Brad M. Lauchnor" <[e-mail]>, "[e-mail]" <[e-mail]>
Cc: Kevin Murray <[e-mail]>, "Kory Larsen ([e-mail])" <[e-mail]>
Brad and Brad-
Per your request, Kleinfelder has calculated the Natural Attenuation rate for PCE in groundwater at the Pepsi Bottling
Plant site in Ogden, Utah. I have attached our report presenting the data, calculations and results. We performed the
analysis in conformance with the EPA Guidance on MNA (attached).
We appreciate your consideration and support in our efforts to close the release file for Pepsi. Please let me know if you
have questions or comments. ·
Regards,
Corinne Hillard, PG
Sr. Project Manager
849 West Levoy, Suite 200
Salt Lake City, Utah 84123
ol 801-261-3336
di 801-713-2849
ml 801-870-0460
httm::·//m::iil.nnnnlA mm/m::iil/11/0/?11i=?&ik::A1 Firl4fifirl?::i&isvAr=Mmfiw0AtNO n An &r.hl=nm::iil fA 1807?4.14 n4&viAw=nt&sA::irr.h=inhnic&th=1 Fi4Ar.0rl 1 /4
11au1:.ww :state ot Utah Mail -t-wd: 1-'epsi l:3ottling :Site -Natural Attenuation K.ate Galculation
This email may contain confidential information. If you have received this email-including any attachments-in error,
please notify the sender promptly and delete the email and any attachments from all of your systems.
2 attachments
~ Natural Attenuation Calculations • Pepsi Site.pdf
447K
~ EPA Guidance • Groundwater MNA Decay Constant.pdf
751K
Brad Maulding <[e-mail]>
To: Carlee Christoffersen <[e-mail]>
Carlee,
Mon, Jul 30, 2018 at 10:37 AM
Another cleanup item for the Larsen Beverage Co -Pepsi Cola site. Can we please add the email train below to the
record? Thanks, Brad
---------Forwarded message---------
From: Brad Maulding <[e-mail]>
Date: Mon, May 14, 2018 at 6:23 PM
Subject: Re: Pepsi Bottling Site -Natural Attenuation Rate Calculation
To: Kevin Murray <[e-mail]>
Cc: "Brad M. Lauchnor" <[e-mail]>, "Kory Larsen ([e-mail])" <[e-mail]>, Corinne Hillard
<[e-mail]>, Ellie Rudolf <[e-mail]>
Evening Kevin,
Thanks for the response on the path that your client has chosen. I would request that someone on your side undertake
the effort to modify the approved SMP and the EC to reflect the needed changes. The proposed modified documents can
be emailed to us for review. Once we are in agreement on the modifications of the documents, we would ask for them to
be submitted officially.
As to the current owner of the property, do you have any info on who the owner of record is? If I could be provided with
contact information I would be happy to initiate a discussion with the owner. Let me know if this is going to require some
research.
Thanks, Brad
Brad Maulding I Section Manager I Corrective Action Section
Phone: [phone]
'j
WASTE MANAGEMENT
RADIATION CONTROi..
Office Hours: Monday-Friday, 9:00 a.m.-6:30 p.m.
httns·//m::iil nnnnlA r.nm/m::iil/11/0/?11i=?R.ik=A1 flrtd!'lflrt?::iR.isvAr=MmflwOAtNO n.An R.r.hl=nm::iil fP. 1 R07?d 1d ndR.viAw=ntR.sP.::irr.h=inhnxR.th=1 fldP.r.Orl ?Id
7/::SU/:.1018 ::;tate ot Utah Mail -t-wd: Pepsi l::lottling ::;ite -Natural Attenuation Kate c.;a1culat1on
195 North 1950 West, Salt Lake City, Utah 84116
Disclaimer:
Statements made in this e-mail do not constitute the official position of the Director of the Division of Waste Management and Radiation Control. If you desire
a statement of the Director's position, please submit a written request to this office, on paper, including documents relevant to your request.
On Mon, May 14, 2018 at 2:46 PM, Kevin Murray <[e-mail]> wrote:
Brad
. We have now discussed this and would like to move forward with "option one," cease groundwater monitoring,
-modify the SMP, and prepare an EC to reflect these changes. We do not have contact with the existing landowner
for the EC so will need your help getting that in place. Would you like us to make the modifications to the SMP and
_ prepare an EC for your review and comment, or would you like to prepare the first draft?
Kevin
From: Brad M. Lauchnor [mailto:[e-mail]]
Sent: Thursday, May 3, 2018 3:12 PM
To: Corinne Hillard <[e-mail]>
Cc: [e-mail]; Kevin Murray <[e-mail]>; Kory Larsen ([e-mail])
<[e-mail]>
Subject: Re: Pepsi Bottling Site -Natural Attenuation Rate Calculation
Hi Corinne,
-I've had time to review the attenuation rate calculation document you submitted for the former Ogden Pepsi site and I
· concur with the information contained in your letter. The calculations show that the MCL for PCE will be reached by
• approximately 2037.
' There are now 2 options moving forward. One option is to cease groundwater monitoring and to modify the SMP and
EC to reflect these changes. The second option is to cease groundwater monitoring and modify the SMP and EC with
· a provision to monitor groundwater in 2037 and verify that the MCL has been met. When the MCL has been met the
SMP and EC can be terminated.
Please let us know which path your client would like to take.
: Thanks,
• Brad
. Brad Lauchnor P.E., P.G.
Environmental Engineer
Utah Department of Environmental Quality
' Division of Waste Management and Radiation Control
httn~·//mRil.nnnnlA.mm/mRil/11/0/?11i=?R.ik=A1 Arl4fiArl?RR.i~vAr=MmAwOAtNO n.An.R.r.hl=nmRil fA 1807?4.14 n4R.viAw=ntR.~ARrr.h=inhnxR.th=1 A4Ar.0rl ::1/4
7/JU/lU18 :state ot Utah Ma11 -t-wct 1-'epsi l::iottling :Site -Natural Attenuation Kate c.:a1cu1at1on
Disclaimer:
Statements made in this e-mail do not constitute the official position of the Director of the Division of Waste Management
and Radiation Control. If you desire a statement of the Director's position, please submit a written request to this office, on
paper, including documents relevant to your request.
On Fri, Apr 27, 2018 at 3:36 PM, Corinne Hillard <[e-mail]> wrote:
Brad and Brad-
Per your request, Kleinfelder has calculated the Natural Attenuation rate for PCE in groundwater at the Pepsi
Bottling Plant site in Ogden, Utah. I have attached our report presenting the data, calculations and results. We
performed the analysis in conformance with the EPA Guidance on MNA (attached).
We appreciate your consideration and support in our efforts to close the release file for Pepsi. Please let me know if
you have questions or comments.
Regards,
Corinne Hillard, PG
Sr. Project Manager
849 West Levoy, Suite 200
Salt Lake City, Utah 84123
ol 801-261-3336
di 801-713-2849
ml 801-870-0460
This email may contain confidential information. If you have received this email-including any attachments-in
error, please notify the sender promptly and delete the email and any attachments from all of your systems.
httmd/m:iil.nnnnlA r.nm/m:iil/11/0/?11i=?R.ik=A1 fkl4!'ifkl?:iR.isvAr=MmRw0AtNn n.An R.r.hl=nm:iil fA 1 R07?4.14 n4R.viAw=ntR.sA:trr.h=inhmcR.th=1 R4Ar.0rl 4/4