EPA/600/R-08/058
June 2008
FOOTPRINT
(A Screening Model for Estimating the Area of a Plume Produced from Gasoline Containing Ethanol)
Version 1.0
A. Noman M. Ahsanuzzaman, Ph. D.1
John T. Wilson, Ph. D.2
Mingyu Wang, Ph. D.1, and Robert C. Earle1
1Shaw Environmental & Infrastructure Inc.
2 U.S. EPA, Office of Research and Development, National Risk Management Research Laboratory
EPA Project Officer
Mary S. McNeil
U.S. EPA, Office of Research and Development, National Risk Management Research Laboratory
Center for Subsurface Modeling and Support
Ground Water and Ecosystem Restoration Division
Ada, OK
U.S. Environmental Protection Agency
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NOTICE
Preparation of this document and the FOOTPRINT software application has been funded in part
by the United States Environmental Protection Agency through its Office of Research and
Development under Contract # 68-C-03-097 to Shaw Environmental & Infrastructure Inc. It has
been subjected to the Agency's peer and administrative review, and it has been approved for
publication as an EPA document. Mention of trade names or commercial products does not
constitute endorsement or recommendation for use.
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Contents
Overview 4
Purpose 4
Software Installation 5
How to Install? 5
Software Requirements 5
Disclaimer of Liability 5
Disclaimer of Endorsement 5
Theory 6
Conceptual Model 6
Simulation Steps 7
Potential Limitations of FOOTPRINT 8
Input 9
Input Options 9
Single Dataset 9
Multiple Datasets 9
Advection 10
Dispersion 10
General Inputs 11
Source Thickness 11
Source Width 11
Approximate Domain Length 11
Grid Spacing 12
Ethanol/Oxygenate Alcohol Source 12
Ethanol Concentration at Source 12
Biodegradation Rate 12
Threshold Ethanol Concentration 12
Retardation Factor 12
Benzene or Other Chemical of Concern (COC) 13
Concentration at Source 13
Biodegradation Rate 13
Maximum Contaminant Level (MCL) 13
Source Decay Rate 13
Retardation Factor 15
Run Options 16
Steady State 16
Transient 16
COC Only [No Ethanol] 16
Output 17
Numeric 17
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Single Dataset 17
Multiple Datasets 17
Graphic 17
Plume 17
Cone. vs. Distance 18
Additional Menu Options 19
Print Screen 19
Exit 19
Help 19
Help Topics 19
About 19
Tutorials 20
Single Dataset 20
Steady State 20
Transient 20
Multiple Datasets 20
Using the Sample Input File 20
Modifying the Sample Input File 20
Typical Values of Biodegradation Rates for Benzene and Ethanol 22
Biodegradation Rates for Ethanol 22
Biodegradation Rates for Benzene 23
References 25
Appendices 27
Appendix A : Background Theory of FOOTPRINT 28
Appendix B : Analytical Model for Zero-Order Decay 39
Appendix C: Expression for Zero-Order Decay in both Aqueous and Solid Phases 42
Appendix D: Expression for First-Order Decay in both Aqueous and Solid Phases 44
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Overview
Purpose
Many grades of gasoline contain both ethanol and petroleum hydrocarbons
such as benzene and the other BTEX compounds. Ethanol can inhibit the
natural biodegradation of BTEX compounds in ground water (Deeb et al.,
2002), causing the plume of BTEX compounds to be larger than they would
be if the ethanol were not present in the gasoline. FOOTPRINT is a simple
and user-friendly screening model that can be used to estimate the effect of
ethanol in gasoline on the surface area of the plume of benzene or any of the
other BTEX compounds in groundwater. FOOTPRINT estimates the
overall surface area of a plume that is contained within two biodegradation
zones, one zone where ethanol is present and there is no biodegradation of
BTEX compounds, surrounded by a second zone where the ethanol has
been removed by natural biodegradation and the BTEX compounds are
biologically degraded. In the second zone, the rate constant for
biodegradation of the BTEX compound does not change as water moves
along the flow path.
The software uses a modified version of the Domenico (1987) model that
was published by Martin-Hay den and Robbins (1997). The model of
Martin-Hayden and Robbins (1997) is an approximate analytical solution of
the advective-dispersive solute transport equation with first-order decay.
Natural degradation of ethanol at concentrations expected from a gasoline
spill is likely to be a zero-order process. The Domenico model as used in
FOOTPRINT is further modified to allow the option of zero-order decay for
either ethanol or the BTEX compounds (see Appendix B for details).
FOOTPRINT can be used to estimate the surface area of the plume or the
concentration at any given point down-gradient from the source. It can also
be used to estimate the behavior of any chemical of concern (COC) in the
absence of ethanol.
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Software Installation
How to Install?
To install the software, run 'FOOTPRINTsetup.exe'. The software will
guide the user through the installation process.
Software Requirements
Microsoft Excel software must be installed on the computer. FOOTPRINT
displays the model outputs in Excel Chart format.
Disclaimer of Liability
With respect to FOOTPRINT software and associated documentation,
neither the United States Government nor any of their employees, assumes
any legal liability or responsibility for the accuracy, completeness, or
usefulness of any information, apparatus, product, or process disclosed.
Furthermore, software and documentation are supplied "as-is" without
guarantee or warranty, expressed or implied, including without limitation,
any warranty of merchantability or fitness for a specific purpose.
Disclaimer of Endorsement
Reference herein to any specific commercial products, process, or service
by trade name, trademark, manufacturer, or otherwise, does not necessarily
constitute or imply its endorsement, recommendation, or favoring by the
United Sates Government. The views and opinions of authors expressed
herein do not necessarily state or reflect those of the United States
Government, and shall not be used for advertising or product endorsement
purposes.
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Theory
Conceptual Model
The conceptual model used in FOOTPRINT is an extension of the model
proposed by Deeb et al. (2002). Figure 1 shows the conceptual model used
in FOOTPRINT. The following are the assumptions in the FOOTPRINT
conceptual model.
1. The release of gasoline containing ethanol and BTEX
compounds is located at the water table (or at the top of the
aquifer).
2. Ethanol dissolves in ground water and disperses as the ground
water moves away from the release of gasoline. The rate
constant for biodegradation of ethanol does not change as
water moves along the flow path.
3. Biodegradation of the BTEX compounds in ground water is
negligible until the concentration of ethanol drops to a
threshold concentration. The threshold concentration is an
input to FOOTPRINT. Following Deeb et al. (2002), the
default value of the threshold is 3 mg/L. When concentrations
of ethanol are above the threshold, the only processes that
reduce the concentration of BTEX compounds are dispersion
and sorption.
4. Biodegradation of the BTEX compound that is addressed in a
particular model run is only allowed when the concentration of
ethanol is below the threshold concentration. Biodegradation
of the BTEX compound begins along a flow path in the
aquifer when the concentration of ethanol falls below the
threshold. The rate constant for biodegradation of the BTEX
compound does not change as water moves further along the
flow path.
5. FOOTPRINT estimates plume length at the water surface of
the aquifer and it assumes an infinite depth for the aquifer.
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Figure 1: Conceptual Model of FOOTPRINT
Ethanol concentration at the source
Virtual concentration of the COG
g
a
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2. Run the modified Domenico model for the chemical of concern (COC)
with no biodegradation to get the concentration at Le (Q).
3. Simulate the inverse solution to the modified Domenico model to
determine a virtual concentration of the COC (Cv) that would be
expected at the source for Q, assuming that the COC was biodegrading
at a given rate from the source to Le, i.e., Zone-1 (see Figure 1).
4. Run the modified Domenico model for the virtual concentration of the
COC at the source (Cv) to get the distance Lc (i.e., Zone-2), where the
steady-state (or transient) concentration of the COC drops to the MCL
(maximum contaminant level) or any target ground water
concentration.
5. Calculate the area of the plume. In order to calculate the area, the
model domain is divided into a finite number of cells. Concentrations
of the COC are calculated at every cell in the model domain. The
number of cells that exceed the MCL (or the target concentration) in
both zones (Le and Lc) are counted and used to estimate the plume area.
Potential Limitations of FOOTPRINT
FOOTPRINT uses a modified version (Martin-Hayden and Robbins, 1997)
of the Domenico model (1987). Potential limitations of fate and transport
models based on the Domenico analytical solutions have been identified in
recent journal articles (Guyonnet and Neville, 2004; Srinivasan et al., 2007;
and West et al., 2007). CSMoS (Center for Subsurface Modeling Support)
acknowledges that fate and transport models based on the Domenico
analytical solutions are approximate solutions of the advective-dispersive
solute transport equation; therefore they could generate error for a given set
of input parameters when compared with the exact solutions to the
advective-dispersive solute transport equation as provided by Wexler
(1992).
In steady state simulations, the approximation error is most sensitive to high
values of longitudinal dispersivity (Srinivasan et al., 2007; and West et al.,
2007). West et al. (2007) conducted a sensitivity analysis and reported in
Figure 2 of that article that the approximation error is 16% when
longitudinal dispersivity is 10% of the plume length. Approximation errors
in FOOTPRINT may be significant at values of longitudinal dispersivity
greater than 10% of the plume length. In real-world modeling applications,
longitudinal dispersivity is most often a calibration parameter, not a
parameter that is measured in the field. If longitudinal dispersivity is varied
to calibrate FOOTPRINT to a particular plume, use values of longitudinal
dispersivity that are less than 10% of the plume length to minimize the
approximation error.
In transient simulations, in addition to the approximation error that is
associated with large values of dispersivity, there is also approximation
error associated with early values of simulation time. The early values of
simulation time where approximation error is a possibility can be
indentified by comparing increasing values of simulation time until the
predictions of plume behavior stabilize.
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Input
Input Options
Single Dataset
This option uses a single set of data as input. The input data are entered
from the screen. The user can change any data in the input screen and run
the model.
Simulation far Multiple Datasets
Multiple Datasets
This option determines plume area for more than one dataset. The data are
input from a 'comma delimited' text file (*.csv). The user can create a new
input file with multiple sets of data and get the output quickly. Under this
option, the only input from the screen is the approximate domain length.
Please see the Input File Format for details. The following pop-up screen
will appear once the 'Multiple Datasets' option is selected.
Multiple datasets are used to simulate more than one dataset at once. The Input file format must be identical to the default file . Users can
add rows, if more datasets are needed for the simulation; however, the 1st cell in the input file MUST BE UPDATED to show the number of simulations
(rows) to be run.
OK
The 'input.csv'file can be
found in the same directory
where the software is
installed.
Input File Format
The Input File is in 'comma delimited' (*.cvs) format. An example of
the required format for the Input File is provided in the file titled
input.csv. The example file is stored in the same directory where
FOOTPRINT was installed. Double-Click the icon above the 'Open'
label next to the 'Browse' button in FOOTPRINT to view and modify
the example file in MS Excel. After modifications are made, save the
file under a new name as *.cvs. The first cell in the modified Input
File should represent the number of rows or datasets in the Input
File. The other data fields are explained by their column headings. The
decay rates (first or zero order) for ethanol and the COC should be
input in respective cells. The user will be asked to define the decay rate
law (first or zero order) of both the COC and ethanol from a pop-up
screen (see below) as soon as the 'Multiple Datasets' option is selected.
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Decay Conditions for Mutiple Simulations
Decay Condition for Ethanol:
1st Order f" Zero Order
Decay Condition for Benzene/COC: f» 1st Order f~ Zero Order
The user must input the grid spacing in the longitudinal direction to
ground water flow (called, column spacing) and in the transverse
direction (called, row spacing) for each simulation. This is important to
speed up the simulation. For smaller values of the biodegradation rate,
the domain size can become very large, and the simulation time will
increase. To reduce the simulation time in such cases, increase the
column and row spacing. To minimize run time, run a single dataset
case for the slowest biodegradation rate to obtain the smallest usable
value for approximate domain length, and then use that length in the
multiple datasets option. Otherwise, the simulation might terminate
before completion. Note that input of an excessively large approximate
domain length will not increase the simulation time, as FOOTPRINT
optimizes the domain length during the simulation.
Advection
Where the velocity is
shown in 'blue color'.
Calculate the groundwater seepage velocity from the input of hydraulic
conductivity, hydraulic gradient, and effective porosity. To calculate
the velocity, press the 'Calculate' button. You can also directly input
the velocity by changing the value in the velocity input box. The model
uses the value shown in the velocity input box. Note that clicking the
'Calculate' button will overwrite the manually entered value.
Dispersion
Longitudinal, transverse, and vertical dispersivity are input in this section.
In the absence of a value for longitudinal dispersivity (ax) that is extracted
from site specific field data, there are two common approaches to estimate a
value that can be used to calibrate a transport and fate model.
Following Pickens and Grisak (1981):
ax = 10% L
where L is the longitudinal distance to the reference point from the source
of the chemical of concern.
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General Inputs
Following Xu and Eckstein (1995):
ax = 3.28*0.83*[log10 (L/3.28)]2'414
where L is the length of the plume in feet.
It is a common practice to calibrate groundwater flow models with a value
of transverse dispersivity that is 10% of longitudinal dispersivity.
By choosing a very small vertical dispersivity (the default value), the user
can limit the model to two-dimensional dispersion. Note that FOOTPRINT
estimates the effect of ethanol on the plume length of the BTEX compound
or COC at the water surface of the aquifer.
FOOTPRINT assumes an infinite depth for the aquifer. When the COC [No
Ethanol] Run Option is selected, and a value is assigned to Z such that the
observation point is specified to be below the source thickness, be aware
that the predicted concentration may be very low, giving the impression that
the plume has not reached that far in the longitudinal direction, when in
actuality, the plume may be above the observation point.
It is good practice to conduct a sensitivity analysis of plume length and area
for the model outputs over the range of expected values of the calibration
parameters.
Source Thickness
This is the dimension of the source along the vertical direction in the
aquifer. FOOTPRINT assumes an infinite aquifer dimension in the vertical
direction.
Source Width
This is the dimension of the source along the transverse (lateral) direction,
perpendicular to the direction of ground water flow.
Approximate Domain Length
This is the domain length along the direction of ground water flow. The
user is required to input a large value in this field. FOOTPRINT itself
optimizes the longitudinal domain length. This input is required to start the
simulation. If the user inputs a value that is too small, a message box will
pop-up (see below), asking them to increase the input value. This input is
also used to scale the longitudinal dimension of the concentration vs.
distance output (see the output section).
Plume has reached the end or the domain. Increase the Domain Length and Run Again
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Grid Spacing
Longitudinal spacing is the Concentration is calculated at the center of each grid cell. Therefore,
grid spacing along the smaller grid spacing will provide better accuracy in estimating the
direction of flow. plume area. However, smaller grid spacing will require more
computation time.
Transverse spacing is the The user is required to input the grid spacing along the longitudinal and
grid spacing along the transverse directions to the ground water flow.
direction perpendicular to
flow.
Ethanol/Oxygenate Alcohol Source
Ethanol Concentration at Source
This is the concentration in ground water at the source of the plume of
ethanol or another alcohol used as an oxygenate such as methanol, or of
biofuels, such as, butanol or propanol.
Biodegradation Rate
The user has the choice to assume either a first order or zero order rate
constant in the model run. This is the rate of biodegradation in the aqueous
phase. If the user assumes that the chemical is decaying at a constant
rate in both the aqueous and adsorbed phases, you need to multiply the
decay constant in the aqueous phase by the retardation factor.
If the user wants to use different decay rates for the aqueous phase and
sorbed phase, you can input a lumped decay rate. Appendix C provides
equations to estimate the lumped decay rate for zero order rates and
appendix D provides equations for first order rates (see Equation 5 in both
appendices C and D for detail).
To facilitate a sensitivity analysis for rates of biodegradation of ethanol in
ground water, a synopsis of rates of ethanol biodegradation available from
the literature are provided in Table 1 (see page 22).
Threshold Ethanol Concentration
This is the concentration of ethanol below which biodegradation of the
COC is allowed in FOOTPRINT. The default value is 3 mg/L (Deeb et al.,
2002).
Retardation Factor
This is the retardation factor for ethanol or other alcohol (R). In most
aquifer sediment, R for ethanol is near 1.0.
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Benzene or Other Chemical of Concern (COC)
The chemical of concern (COC) is the chemical for which the simulation is
conducted. COC could be any of the BTEX compounds. The output
represents the simulation for the COC.
Concentration at Source
This is the actual concentration of the COC in ground water at the source.
The user has the option to assume either a constant concentration at the
source or a source concentration that decays exponentially with time. The
original Domenico model assumes a constant concentration at the source. If
the source is decaying over time, the user can estimate a first-order decay
constant for the source concentration by fitting an exponential decay model
to the long term monitoring data for concentrations of the COC at the
source (see Aziz et al., 2002, BIOCHLOR Version 2.2 manual for detail).
Note that the decaying source is only applicable for the COC.
Biodegradation Rate
The user has the choice to assume either a first order or zero order rate
constant in the model run. This is the rate of biodegradation in the aqueous
phase. If you assume that the chemical is decaying at a constant rate in
both the aqueous and adsorbed phases, you need to multiply the decay
constant in the aqueous phase by the retardation factor. If you want to
use different decay rates for the aqueous phase and sorbed phase, you can
input a lumped decay rate. Appendix C provides equations to estimate the
lumped decay rate for zero order rates and appendix D provides equations
for first order rates (see Equation 5 in both appendices C and D for detail).
To facilitate a sensitivity analysis for rates of biodegradation of the BTEX
compound or other COC in ground water, a synopsis of rates of
biodegradation available from the literature are provided in Tables 2, 3,4,
and 5 (see pages 23-24).
Maximum Contaminant Level (MCL)
This is the concentration below which concentrations of the COC are
considered acceptable. The plume area from the simulation sums the areas
of the cells in the grid where the concentration of the COC is above this
value.
Source Decay Rate
This is the decay rate for the COC at the source. If the COC concentration is
decreasing at the source with time, the user can use this option by selecting
the 'Decaying Source' box. Appendices A and B provide the modified
Domenico model for decaying source where the plume is decaying at first
and zero order, respectively. The mathematics imposes an upper limit on
the rate of source decay, depending on other input data. The upper limit of
the source decay rate for the first and zero order models are provided in
the appendices (see Equation 7 in Appendix A and Equation 14 in
Appendix B). FOOTPRINT uses an additional 20% factor of safety on the
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g
ffl
o
O
limiting values obtained from these equations in order to ensure that the
model will run properly.
In addition to the limiting conditions in the modified Domenico model for
decaying source, FOOTPRINT imposes a further constraint on the
source decay rate. The model does not allow the COC concentration to
drop below the target concentration or the MCL inside Zone-1, where the
ethanol concentration is higher than the threshold limit. FOOTPRINT
estimates the limiting value of the source decay rate (see Figure 2). It
simulates the inverse model to estimate a virtual concentration of COC at
the source for 10% more than the MCL (or target concentration) at Le.
The following equation provides the limiting value of first-order source
decay rate used in FOOTPRINT (note that an additional 10% factor of
safety is assumed).
Ks<0.9x-ln|
Cr
(1)
where, Ks is the decay rate of COC at the source (1/yr), t is the simulation
time in years, C0 is the initial concentration of COC at the source, and C0p is
the virtual concentration of the COC necessary to produce a concentration
of the COC at the end of zone-1 (Le) that is equal to 1.1 times the MCL,
when there is no decay or degradation of the COC in the source and the
plume.
Typical values for the rate of decay of concentrations of benzene and xylene
in ground water in the LNAPL source area of gasoline spill sites are 0.135
and 0.073 per year respectively for sites that have not been remediated and
0.80 and 1.1 per year respectively for sites where some source remediation
has been attempted (Peargin, 2000).
Figure 2: Technique to Estimate the Limiting Source
Decay Rate
COC with decay in source and plume (Inverse Model)
COC with decay in source, but not in plume (Forward Model)
COC with no decay in source and plume (Inverse Model)
Virtual concentration of the COC (Cv)
Actual concentration of the COC at the source at t=0 (C0)
Virtual concentration of the COC at the source at time t (C0p)
Concentration of the COC at Le (C,)
1.10 times MCL of the COC
- - -. _ MCL of the COC
Le
Distance from the source
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Retardation Factor
This is the retardation factor (R) for the individual BTEX compound or
COC. R is a function of the partitioning coefficient of the compound
between soil organic matter and water (Koc), the organic matter content of
the soil (foc), the soil bulk density (pb), and the soil porosity (ri).
(2)
The unit for pb is typically Kg/L, n is dimensionless, and the unit for Kp is
L/Kg. Kp is usually estimated as the product of Koc (L/Kg) and foc (Kg/Kg).
Typical value forpb ranges from 1.37 to 1.81 Kg/L for fine to coarse sand,
and from 1.36 to 2.19 Kg/L for fine to coarse gravel (Domenico and
Schwartz, 1990). Typical value for n ranges from 0.1 to 0.35 for sand, 0.1
to 0.25 for gravel, and from 0.01 to 0.3 for silt (Domenico and Schwartz,
1990). Note thatpb and n are correlated through the following equation.
ph = SG(l-n)pw (3)
where, SG = soil specific gravity (typically range from 2.65 to 2.70), and
pw = density of water (typically, 1 Kg/L).
Typical values for Koc for benzene, toluene, ethylbenzene, and the xylenes
are 38, 95, 135, and 240 L/Kg respectively (ASTM, 2002). Typical values
for foc range from 0.0002 to 0.2. When site-specific data are not available,
use a default value of 0.001 for foc (ASTM, 2002). The corresponding value
of R is 1.2 for benzene, 1.6 for toluene, 1.8 for ethylbenzene, and 2.4 for the
xylenes.
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Run Options
Click the 'Run' button to execute the model.
Steady State
This option runs the model under steady-state conditions. The model uses a
simulation time equal to 100 years to ensure a steady state condition. If you
want to run the model for any other time interval, change the value of
'Simulation Time' in the Run Options input box.
Transient
This option runs the model under transient conditions. If this option is
selected, you are required to input the time interval (years) you desire in the
'Simulation Time' input box.
COG Only [No Ethanol]
This option runs the simulation for the COC without the presence of
ethanol. There is one decay zone for the COC instead of two. Once the
'COC Only [No Ethanol]' option is checked, the following message will
pop-up on the screen.
Simulation Options for the COC without Ethanol
This is an option to simulate the Domenico model when ethanol is NOT present that is when only
the COC/Benzene is present in the plume. To get the plume area click 'AREA'. Otherwise, click
'CONCENTRATION' to estimate concentration at the observation point (x.y,z).
AREA
CONCENTRATION
To obtain the plume area click on the 'AREA' button, otherwise click the
'CONCENTRATION' button to obtain the concentration at any given
observation point in the aquifer. Input the coordinates of the observation
point, and then click the 'Run' button to view the concentration in a pop-up
window. This option can be run under either steady-state or transient
conditions.
The 'COC Only [No Ethanol]' option can be run for both single and
multiple dataset options. Under the single dataset option, when the 'AREA'
button is clicked, the simulation will use the input data from the screen for
the COC to estimate the plume area. Under the multiple datasets option, the
'AREA' button will use the input file for the multiple datasets option to
estimate the plume areas. The 'CONCENTRATION' button is inactive
under the 'COC Only" option for multiple datasets run.
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Output
Numeric
Graphic
This option shows the numeric output from FOOTPRINT.
Single Dataset
This option shows the output for the 'single dataset' run from the screen.
The outputs shown are the area of the plume along with four other values
(Le, Le+Lc, Ci, Cv) from the conceptual model. The figure depicting the
conceptual model is also shown in the window. The user can print the
output window by clicking the 'Print' button.
Multiple Datasets
This option shows the outputs for the multiple datasets simulation. The
outputs shown are simulation name, plume area in square feet, and plume
area in acres. The user can open the output file (OutMult.xls) in MS Excel
by 'double clicking' on the window.
This option shows the graphical output from FOOTPRINT.
Plume
This option provides a figure that shows the plume in an aerial view. The
figure shows the distribution of concentrations of the COC that are above
the target concentration (MCL). This option can only be viewed for the
single dataset option. Note that the grid spacing used in the figure is
different from that used in determining plume area.
The color in the middle portion of the figure represents the area where the
concentration of the COC exceeds the target concentration. The other color
along the boundary of the plume represents the area where the concentration
of the COC is less than the target level (MCL). The figure was created
using the surface option for 'chart type' in Excel. The user can view the
figure in MS Excel by 'double clicking' on the figure (OutArea-l.xls). By
double clicking the upper margin of the grid (within Excel), you select the
chart and can modify the chart using options from the "Chart" drop down
menu in Excel. You can also view the output data by selecting the "sheetl"
tab of the spreadsheet in Excel. Any data in the "sheetl" tab is the target
concentration (MCL), not the actual computed concentration for that cell.
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FOOTPRINT records only the target concentration (MCL) for all cells
exceeding that value.
Cone. vs. Distance
This option shows the concentration vs. distance along the centerline of the
plume. This option is only available for the single dataset input option. You
can also view the figure for the 'COC Only [No Ethanol]' option by
checking that box and then selecting the menu option 'Cone. vs. Distance'
under the 'Graphic' option from the 'Output' options (OutputlGraphiclConc.
vs. Distance). By 'double clicking' on the figure, the user can open the
output file (CvsX-l.xls) in Excel.
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Additional Menu Options
Print Screen
This option prints the input screen window.
Exit
This option will close FOOTPRINT.
Help
Help Topics
This option opens the help file. The help file is created from this user's
manual.
About
This option identifies the software developers and provides a disclaimer.
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Tutorials
Single Dataset
Steady State
To run FOOTPRINT for the default values, select the 'Single Dataset' and
the 'Steady-State' input options, then click the 'Run' button. FOOTPRINT
will run for the input values in the screen. To view the output, select the
desired options from the Output menu.
Transient
To run FOOTPRINT for the default values, select the 'Single Dataset' and
the 'Transient' input options, then click the 'Run' button. The model will
run for the input values in the screen, for the particular time selected in the
Simulation Time option. To view the output, select the desired options from
the output menu.
Multiple Datasets
Using the Sample Input File
Select the 'Multiple Dataset' and click the 'Run' button. The model will run
for the input values in the sample input file 'input.csv'. To view the sample
input file, double-click on the icon above the 'Open' label next to the
'Browse' button. To view the output, select the desired options from the
output menu.
Modifying the Sample Input File
To practice modifying the input file and run the model, do the following:
1. Open the sample input file (input.csv) by double-clicking on
the icon above the 'Open' label next to the 'Browse' button.
2. Add two rows of data and change the first cell value to 5.
Please note that the first cell in the data file should represent
the number of rows/datasets in the input data file.
Footprint User's Manual
20
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3. Save the file as inputl.csv (or any other name in *.cvs format).
As a default, the saved file is put in the same directory as the
FOOTPRINT application. This is usually the 'Program Files'
file under the local disk. It may be more convenient to backup
your input files, and to transfer files to another computer, if
they are saved in a separate directory. Please remember to
save the file in *.csv (comma delimited) format.
4. Exit from MS Excel.
5. Update the 'Input File Name' to inputl.csv (or whatever name
you selected for the modified file). You must input the entire
path of the file correctly. Alternatively, you can click the
Browse button and navigate through your directories to find
the input file in the directory where you saved it, and then
press the 'open' button to open it into FOOTPRINT.
6. Run the model.
7. To view the output, select the respective menu option.
Footprint User's Manual 21
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Typical Values of
Biodegradation Rates for
Benzene and Ethanol
Biodegradation Rates for Ethanol
FOOTPRINT has the option to run the model using either a first-order or a
zero-order rate for biodegradation of ethanol. Since a spill of ethanol-
blended gasoline typically results in a very high concentration of ethanol in
ground water, the biodegradation process tends to follow zero-order rate
law instead of first-order rate law. Table 1 provides some values of zero-
order decay rates for ethanol that were extracted from field studies and
laboratory studies. Note that the two highest values of decay rates were
resulted from continuous injection of ethanol at the source, while ethanol
was released as a slug in the other studies.
Table 1. Zero-order decay rates for ethanol.
Study Type
Field
Field
Field
Field
Field
Field
Field, Continuous Ethanol
Injection
Lab
Lab
Lab
Lab
Lab, Column, Continuous Ethanol
Injection
Redox Process
Methanogenesis
Methanogenesis
Sulfate Reduction
Methanogenesis
Methanogenesis
Iron Reduction
Decay Rate
mg/L/day
55
2.3
9
14
18
1.4
500
8
14
34
11
13,000
mg/L/yr
20075
839.5
3285
5110
6570
511
182500
2920
5110
12410
4015
4745000
Reference
Buscheck et al. (2001)
Corseuil et al. (2000)
Mravik et al. (2003)
Zhang et al. (2006)
Mocanu et al. (2006)
Mocanu et al. (2006)
Mackay et al. (2006)
Corseuil et al. (1998)
Corseuil et al. (1998)
Suflita and Mormile (1993)
Corseuil et al. (1998)
Da Silva and Alvarez (2002)
Footprint User's Manual
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Biodegradation Rates for Benzene
FOOTPRINT has the option to run the model with either first-order or zero-
order rate constants for biodegradation of benzene or any other COC. Table
2 presents the mean, the 90th-percentile, and the range of first-order decay
rates for BTEX compounds summarized from different field/in-situ studies
under anaerobic conditions. Table 3 presents the mean, the median, the 25th-
percentile, the 75th percentile, the 90th percentile, and the range for first-
order decay rate constants for benzene under different anaerobic conditions.
Table 4 provides first-order decay rate constants for benzene at different
sites across the United States. Finally, Table 5 provides zero-order decay
rate constants for BTEX compounds from field/in-situ studies under
anaerobic conditions. Suarez and Rifai (1997) and Aronson and Howard
(1997) provide further detail about the decay rates of benzene and the
BTEX compounds.
Table 2. First-order decay rate constants for BTEX compounds from field/in-situ studies^
Compounds
Benzene
Toluene
Ethylbenzene
m-Xylene
o-Xylene
p-Xylene
Unit
(1/day)
d/yr)
(1/day)
d/yr)
(1/day)
d/yr)
(1/day)
d/yr)
(1/day)
d/yr)
(1/day)
d/yr)
Mean
0.003
1.10
0.24
87
0.22
80
0.031
11
0.019
7.0
0.013
4.8
90th-percentile
0.009
3.29
0.27
97
0.034
12
0.066
24
0.042
15.3
0.035
12.8
Minimum
0
0
0
0
0
0
0
0
0
0
0
0
Maximum
0.023
8.40
4.3
1600
6.0
2200
0.32
116
0.21
78
0.081
30
Number of data
45
43
33
30
27
25
' Source: Suarez and Rifai (1997)
Table 3. First-order decay rate constants for benzene at different redox conditions ^
Redox Process
Unit
Mean
Median
25th-percentile
75th-percentile
90th-percentile
Minimum
Maximum
Number of data
Sulfate Reduction
(1/day)
0.008
0.003
0
0.006
0.023
0
0.049
(1/yr)
3.0
1.10
0
2.2
8.4
0
17.9
16
Methanogenesis
(1/day)
0.01
0
0
0.006
0.033
0
0.077
(1/yr)
3.7
0
0
2.2
12.1
0
28
15
Iron Reduction
(1/day)
0.009
0.005
0
0.011
0.024
0
0.034
d/yr)
3.3
1.8
0
4.0
8.8
0
12.4
20
' Source: Suarez and Rifai (1997)
Footprint User's Manual
23
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Table 4. First-order decay rate constants for benzene from field studies summarized by Aronson and Howard
(1997)
Site Name
Rocky Point, NC
Tibbett's Road Site,
Barrington, NH
Tibbett's Road Site,
Barrington, NH
Bemidji, MN
Patrick AFB, FL
Traverse City, Ml
Sleeping Bear Dunes,
Natl. Lakeshore, Ml
Sleeping Bear Dunes,
Natl. Lakeshore, Ml
Hill AFB, Utah
Hill AFB, Utah
Hill AFB, Utah
Redox Process
Iron reduction
Iron reduction
Iron reduction
Methanogenesis
Iron and Manganese reduction
Methanogenesis
Methanogenesis
Methanogenesis
Nitrate/Sulfate reduction
Methanogenesis
Nitrate/Sulfate reduction
Sulfate reduction
Sulfate reduction
Sulfate reduction
Rate
Constant
(1/day)
0.0002
0.00011
0.0022
0.017
0.01
0.0071
0.00043
0.002-0.004
0.0072-0.046
0.028
0.038
d/yr)
0.073
0.040
0.80
6.2
3.7
2.6
0.157
0.73-1.46
2.6-16.8
10.2
13.9
Table 5. Zero-order anaerobic decay rates for BTEX compounds from field/in-situ studies^
Benzene
Toluene
Ethyl-
benzene
m-Xylene
o-Xylene
(mg/L/day)
(mg/L/yr)
(mg/L/day)
(mg/L/yr)
(mg/L/day)
(mg/L/yr)
(mg/L/day)
(mg/L/yr)
(mg/L/day)
(mg/L/yr)
Mean
0
0
0.15
55
0.087
32
0.23
85
0.127
46
Median
0
0
0.09
33
0.05
18
0.1
37
0.007
2.6
25th-
percentile
0
0
0.007
2.6
0.005
1.83
0.006
2.2
0.002
0.73
75th-
percentile
0
0
0.108
39
0.067
24
0.108
39
0.007
2.6
90th-
percentile
0
0
0.37
134
0.21
78
0.61
220
0.38
136
Range
0-0.001
0-0.37
0.007-
0.54
2.6-197
0.003-
0.31
1.1-113
0.005-
0.95
1 .83-350
0-0.62
0-230
Number
of data
5
5
5
5
5
' Source: Suarez and Rifai (1997)
Footprint User's Manual
24
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References
American Society for Testing and Materials. ASTM E1739-95; "Standard Guide for Risk-Based Corrective
Action Applied at Petroleum Release Sites" (2002). Available at http://webstore.ansi.org/default.aspx
Aronson, D., and P. H. Howard. Anaerobic Biodegradation of Organic Chemicals in Groundwater: A
Summary of Field and Laboratory Studies. Final Report. Prepared by Environmental Science Center, Syracuse
Research Corporation, North Syracuse, NY, 268 pp., 1997.
Aziz, C. E., C. J. Newell, and J. R. Gonzales. BIOCHLOR Natural Attenuation Decision Support System;
User's Manual, Version 2.2. Robert S. Kerr Environmental Research Center, National Risk Management
Research Laboratory, Ada, OK, 2002. Available at http://epa.gov/ada/csmos/models.htnil
Buscheck, T. E., K.O'Reilly, G. Koschal, and G. O'Regan. "Ethanol in groundwater at a Pacific Northwest
Terminal." In Ground Water: Prevention, Detection, and Remediation; 2001 Conference and Exposition,
Proceedings of the Petroleum Hydrocarbons and Organic Chemicals Conference, Houston, TX, November 14-
16, 2001, 55-66.
Corseuil, H. X., M. Fernandes, M. Do Rosario, and P. N. Seabra. "Results of a Natural Attenuation Field
Experiment for an Ethanol-Blended Gasoline Spill." In Proceedings of the 2000 Petroleum Hydrocarbons and
Organic Chemicals in Ground Water: Prevention, Detection, and Remediation, Anaheim, CA, November 14,
2000,24-31.
Corseuil, H. X., C. S. Hunt, R. C. F. Dos Santos, and P. J. J. Alvarez. The Influence of the Gasoline Oxygenate
Ethanol on Aerobic and Anaerobic BTX Biodegradation. Water Research 32 (7): 2065-2072 (1998).
Da Silva, M. L. B., and P. J. J. Alvarez. Effects of Ethanol versus MTBE on Benzene, Toluene, Ethylbenzene,
and Xylene Natural Attenuation in Aquifer Columns. Journal Environmental Engineering 128 (9): 862-867
(2002).
Deeb, R. A., J. O. Sharp, A. Stocking, S. McDonald, K. A. West, M. Laugier, P. J. J. Alvarez, M. C.
Kavanaugh, and L. Alvarez-Cohen. Impact of Ethanol on Benzene Plume, Lengths: Microbial and Modeling
Studies. Journal of Environmental Engineering 128 (9): 868-875 (2002).
Domenico, P. A. An analytical method for multidimensional transport of a decaying contaminant species.
Journal of Hydrology 91: 49-58 (1987).
Domenico, P. A., and G. A. Robbins. A new method of contaminant plume analysis. Ground Water 23 (4):
476-485 (1985).
Domenico, P. A., and F. A. Schwartz., 1990. Physical and Chemical Hydrogeology. Wiley, New York, 824
pp.
Guyonnet, D., and C. Neville. Dimensionless analysis of two analytical solutions for 3-D solute transport in
groundwater. Journal of Contaminant Hydrology 75: 141-153(2004).
Footprint User's Manual 25
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Mackay, D. M., N. R. de Sieyes, M. D. Einarson, K. P. Feris, A. A. Pappas, I. A. Wood, L. Jacobson, L. G.
Justice, M. N. Noske, K. M. Scow, and J. T. Wilson. Impact of Ethanol on the Natural Attenuation of Benzene,
Toluene, and o-Xylene in a Normally Sulfate-Reducing Aquifer. Environmental Science & Technology 40 (19):
6123-6130 (2006).
Martin-Hayden, J., and G. A. Robbins. Plume distortion and apparent attenuation due to concentration
averaging in monitoring wells. Ground Water 35 (2): 339-346 (1997).
Mocanu, M., J. L. Zoby, J. Barker, and J. Molson. "The Fate of Oxygenates and BTEX from Gasolines
containing MTBE, TEA, and Ethanol: Is Ethanol more Persistent than MTBE?" Keynote Presentation: NGWA
Petroleum Hydrocarbons and Organic Chemicals in Ground Water: Prevention, Assessment, and Remediation
Conference, Houston, TX, November 6-7, 2006.
Mravik, S. C., G. W. Sewell, R. K. Sillan, and A. L. Wood. Field Evaluation of the Solvent Extraction Residual
Treatment (SERB) Technology. Environmental Science & Technology 37 (21): 5040-5049 (2003).
Peargin, T. R. "Relative Depletion Rates of MTBE, Benzene, Xylene from Smear Zone NAPL." In Proceeding
of the 2000 Petroleum Hydrocarbons and Organic Chemicals in Ground Water: Prevention, Detection, and
Remediation. Special Focus: Natural Attenuation and Gasoline Oxygenates. API, NGWA, STEP Conference
and Exposition, Anaheim, CA, November 15-17, 2000, 207-212.
Pickens, J., and G. Grisak. Scale-dependent dispersion in a stratified granular aquifer. Water Resources
Research 17 (4): 1191-1211 (1981).
Srinivasan, V., T. P. Clement, and K. K. Lee. Domenico solution - is it valid? Ground Water 45 (2): 136-146
(2007).
Suarez, M. P., and H. S. Rifai. Biodegradation rates for fuel hydrocarbons and chlorinated solvents in
groundwater. Bioremediation Journal 3 (4): 337-362 (1997).
Suflita, J., and M. Mormile. Anaerobic biodegradation of known and potential gasoline oxygenates in the
terrestrial subsurface. Environmental Science & Technology 27 (5): 976-78 (1993).
West, M. R., B. H. Kueper, and M. J. Ungs. On the use and error of approximation in the Domenico (1987)
solution. Ground Water 45(2): 126-135(2007).
Wexler, E. "Analytical solutions for one -, two -, and three-dimensional solute transport in groundwater
systems with uniform flow." Techniques of Water Resources Investigations of the United States Geological
Survey, Chapter B7, Book 3, 1992, 79 pp.
Xu, M., and Y. Eckstein. Use of weighted least-squares method in evaluation of the relationship between
dispersivity and field scale. Ground Water 33 (6): 905-908 (1995).
Zhang, Yi, I. A. Khan, X-H Chen, and R. F. Spalding. Transport and Degradation of Ethanol in Groundwater.
Journal of Contaminant Hydrology 82: 83-194 (2006).
Footprint User's Manual 26
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Appendices
Footprint User's Manual 27
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Appendix A : Background Theory of FOOTPRINT
Reprinted with permission of the National Ground Water Association. Copyright 2005.
Ahsanuzzaman, A. N. M., and Wilson, J. T., FOOTPRINT: A Computer Application for
Estimating Plume Areas of BTEX Compounds in Ground Water Impacted by a Spill of
Gasoline Containing Ethanol, 2005 NGWA Conference on MTBE and Perchlorate:
Assessment, Remediation, and Public Policy, National Ground Water Association, San
Francisco, CA, 2005.
FOOTPRINT: A Computer Application for Estimating Plume Areas of BTEX Compounds in
Ground Water Impacted by a Spill of Gasoline Containing Ethanol
Abstract
Ethanol has a potential negative impact on the natural biodegradation of other gasoline
constituents, including BTEX compounds, in ground water. The impact of ethanol on the
size of the BTEX plume should be considered in the risk evaluation of spills of gasoline
containing ethanol. FOOTPRINT was developed as a simple and user-friendly computer
application that can be used as a screening model to estimate the extent of the BTEX plume
when the gasoline that is spilled contains ethanol. FOOTPRINT estimates the overall area of
a plume of BTEX compounds that are contained within two biodegradation zones, one zone
where ethanol is present and there is no biodegradation of BTEX compounds, surrounded by
a second zone where the ethanol has been removed by natural biodegradation and the rate of
biodegradation of BTEX compounds is constant. Existing simple models for BTEX
compounds (such as BIOSCREEN) can not model this interaction between ethanol and
BTEX compounds because these models are limited to a single biodegradation rate uniformly
applied across the flow path. FOOTPRINT applies a 3-dimensional analytical solute
transport model to estimate solute concentration at any location downgradient from a
constant concentration source for a fixed first-order decay rate. It first uses an estimate of the
rate of ethanol biodegradation to estimate the zone downgradient from the source where
ethanol inhibits BTEX biodegradation. Within this zone, concentrations of BTEX
compounds can only attenuate through dilution and dispersion. Downgradient from this
zone, FOOTPRINT models BTEX biodegradation at a constant rate. FOOTPRINT assumes
that the concentration of BTEX at the source is constant. It allows either a constant
concentration or exponentially decaying source for ethanol. FOOTPRINT could also be
applied to estimate the plume area of any single chemical compound downgradient from a
constant concentration source for a constant decay rate. Finally, results obtained from
simulating FOOTPRINT for a synthetic case study were verified by comparing with the
results from a conceptually identical numerical model.
Footprint User's Manual 28
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Introduction
Ethanol could be used as an oxygenate in gasoline as opposed to MTBE. A potential impact
from using ethanol in gasoline is that in case of a spill, ethanol might inhibit natural
attenuation of the other gasoline constituents (e.g., BTEX compounds) by depleting the
electron acceptors and nutrients in the subsurface. As a result, the plumes of BTEX
compounds could persist for an extended period of time. Inhibition of biodegradation of
BTEX compounds along with the effect of increased solubility of the BTEX compounds and
other gasoline constituents (cosolvency) due to the presence of ethanol might cause the
BTEX plume to be longer than otherwise would be the case. It would be useful to have a
simple approach to evaluate the potential impact of ethanol in gasoline on the size of the
BTEX plume.
Deeb et al. (2002) conducted a study to estimate the effect of ethanol on the size of the
benzene plume from a spill of ethanol-blended gasoline. They presented a conceptual
approach to estimate the impact of ethanol on the length of the benzene plume. As long as
ethanol was present in ground water above a critical concentration, natural biodegradation of
benzene or any BTEX compound, was inhibited. In the presence of ethanol, the only
processes that contributed to the attenuation of benzene were non-biological processes such
as dispersion or sorption. When the ethanol degraded to the critical concentration, then
biodegradation of benzene and the other BTEX compounds could begin.
In this study, we developed a simple computer application, named FOOTPRINT, to estimate
the length of any two contaminants in ground water, when the contaminants behaved like
ethanol and benzene in the approach of Deeb et al. (2002). We expanded the approach of
Deeb et al. (2002) to estimate the total area of the plume, instead of the plume length. The
probability that a spill will impact a receptor is more closely related to the area of a plume
than to its length.
Analytical Model for Solute Transport Through Saturated Zone
The governing equation for solute transport through a saturated soil, called the Advection-
Dispersion-Equation (ADE) is derived from conservation of mass in an elementary volume
of porous media. The ADE is based on the assumptions that the porous media is
homogeneous and isotropic, and that the flow condition follows Darcy's law. The general
form of the 3-dimensional ADE for a miscible and degradable solute in a homogeneous
medium with uniform groundwater velocity in the horizontal direction (X-axis) and with
equilibrium partitioning between the solid and liquid phase (equilibrium sorption) is given
by:
„ ac ( ac^
R—= - VY— +
X
D
+—C0-—C-^C (1)
y
n n
Footprint User's Manual 29
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where C is the solute concentration (mg/L), vx is the average fluid velocities in the X
directions, respectively (m/d), and Dx, Dy, Dz are the hydrodynamic dispersion coefficients in
the X, Y, and Z directions (m2/d), respectively, n is the porosity of the medium (m3/m3), W
and Q are volume of water injected and extracted per unit volume of aquifer per unit time (d~
!), respectively, A, is the first order decay constant in the aqueous phase(d"!), and R is the
retardation factor for sorption. For linear sorption, R is expressed as
n p
where, pb is soil bulk density (Kg/L) and Kp is the linear sorption coefficient (L/Kg).
Domenico (1987) provided a solution of Equation (1) for a finite and constant concentration
source at the top of the aquifer (see Equation 3)
(3)
where, Co is the constant concentration at the source, and
= exP
X
la.
1-1 +
•erfc
x-v.t 1 +
/v =
-erf
y-
fz =
-erf
Z-Zc
where, a* is the longitudinal dispersivity (m), vc is the contaminant velocity (= vx/R), Ys, and
Zs represent source dimensions along the y and z directions (m), respectively, and erf and
erfc represent the error function and complementary error function, respectively.
Figure 1 shows the schematic of the Domenico (1987) model (Equation 3). The source in the
model is assumed to be rectangular in the vertical plane and is oriented perpendicular to
groundwater flow. The model is applicable in a uniform flow field with advection in the x-
direction and dispersion in all three directions. Also, the source is assumed to be at the top of
a semi-infinite aquifer, i.e., the aquifer is infinite in only one side of the vertical dimension.
Equation 3 is used in the BIOSCREEN Natural Attenuation Decision Support System
(Newell et al., 1996), which is a public domain screening tool for simulating natural
attenuation of dissolved hydrocarbons at petroleum fuel release sites. BIOSCREEN was
developed by Air Force Center for Environmental Excellence (AFCEE) and is distributed by
the U.S. EPA's Robert S. Kerr Environmental Research Center (RSKERC).
Footprint User's Manual
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Martin-Hayden and Robbins (1997) modified the Domenico (1987) model by using the full
Ogata and Banks (1961) terms instead of the truncated version used by Domenico. Martin-
Hayden and Robbins (1997) replaced the/x term in Equation 3 with/x, which is given by
Equation 4.
= exP
+ exp
(4)
X
Ground Water Flow Direction
Monitoring Well (x, y, z)
Aquifer Bottom at Infinite Distance
Figure 1. Schematic of Domenico model used in BIOSCREEN
Equation 4 is used in the BIOCHLOR Natural Attenuation Model (Aziz et al, 1999).
BIOCHLOR simulates natural attenuation of chlorinated solvents subjected to sequential
chain reactions, where the parent solvent biodegrades to a daughter product and that daughter
biodegrades to another daughter product, and so on. BIOCHLOR was developed in
collaboration with the AFCEE and RSKERC and is also distributed by the RSKERC.
Footprint User's Manual
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Conceptual Model Used in FOOTPRINT
The model for predicting the plume area of any gasoline constituents or other chemicals of
concern (COC) as a result of accidental spill of ethanol-blended gasoline is conceptualized in
FOOTPRINT according to Figure 2. Following a spill, ethanol and the gasoline constituents
(or the COCs) reach the water table. Ethanol transports through the groundwater by
advection and dispersion and biodegrades downgradient from the source. Biodegradation of
the gasoline constituents (or the COCs) is negligible from the source to the distance where
the ethanol concentration drops to a threshold concentration, i.e., no biodegradation for the
COC within the distance Le from the source (see Figure 2). According to Deeb et al. (2002),
this threshold concentration of ethanol is approximately 3 mg/L for benzene. At the zone
between the source and the location where the ethanol concentration reaches the threshold
limit (i.e., within Le), the decrease in COC concentration is only due to advection, dispersion
and sorption. Biodegradation of the gasoline constituent (or the COC) starts downgradient
from the zone where the ethanol concentration is over the threshold concentration. First order
decay is assumed for both ethanol and the COC.
Ethanol concentration at the source
Virtual concentration of the COC (Cv)
o
ro
0)
o
o
O
Actual concentration of the COC at the source
Ethanol
• COC with biodegradation
COC without biodegradation
Concentration of the COC at Le (Q)
Threshold concentration of ethanol
---.._ MCL of the COC
\i
COC not Biodegrading
COC Biodegrading
Distance from the source
Figure 2. Conceptual model for FOOTPRINT
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Methodologies to Estimate Plume Area
Methodology Used in FOOTPRINT
FOOTPRINT uses Equation 4, which is the modified version of the Domenico (1987) model
by Martin-Hayden and Robbins (1997), to estimate solute concentration at any downgradient
location from the source. However, Equation 4 could not be applied directly to the COC for
the condition explained in the conceptual model shown in Figure 2. Equation 4 is limited to
only one biodegradation rate, while the COC has two biodegradation zones: no decay from
the source to where the ethanol concentration drops to the threshold concentration (i.e., Le),
and at any given decay rate downgradient from Le. Therefore, a modified approach has been
taken to apply Equation 4 to obtain the COC concentration downgradient from the source.
Following are the steps of the modified approach taken in FOOTPRINT:
1. Simulate Equation 4 for ethanol at steady-state conditions (i.e., for a large time
period, t) to compute the distance Le (see Figure 2), which is the distance along the
centerline of the plume and at zero vertical distance from the water table.
2. Simulate Equation 4 for the COC with zero decay rate to compute the steady-state
concentration at Le, which is Q in Figure 2.
3. Simulate the Inverse of Equation 4 to compute the concentration of the COC at the
source (Cv) from Q for the given decay rate for the COC (see Figure 2). Cv is named
as the virtual concentration of the COC at the source.
4. Finally, simulate Equation 4 with the virtual concentration of the COC at the source
(Cv) to compute the distance Lc (see Figure 2), where the steady-state concentration of
the COC drops to the maximum contaminant level (MCL).
To calculate the area of the plume, the domain downgradient of the source is divided into a
finite number of cells. Concentrations of the COC at each cell within each zone (i.e., Le and
Lc) are calculated from the model. The number of cells exceeding the MCL within both
zones are counted and used to calculate the total plume area. Note that the area is computed
for the plume at the water table, as the plume concentration should be higher in the water
table compared to any other underneath horizontal planes.
Alternative Approach
An alternative approach to the methodology outlined in the above section could also be
considered. Following the first two steps stated in the above section, the third step could be
skipped and the fourth steps could be applied to compute Lc for the source concentration Q at
Le. This approach follows the assumption that the constant concentration source would shift
to Le. This assumption could be reasonable for estimating the plume length, as the simulation
is conducted at steady-state condition. It seems that Deeb et al. (2002) have followed this
approach to estimate the plume length for benzene from a spill of ethanol-blended gasoline.
However, this approach could not be applied in estimating the plume area, as the source
dimensions at Le would be expanded from the actual source area due to dispersion.
Footprint User's Manual 33
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Therefore, an underestimation of the plume area could result from this approach. A
comparison between the two approaches for a given set of input values is presented in the
following section.
Verification of the Conceptual Model Used in FOOTPRINT
In order to verify the conceptual model used in FOOTPRINT, a numerical model with
boundary conditions and assumptions comparable to the Domenico model was prepared.
Visual MODFLOW (WHI, 1999), a Windows-based pre- and post-processing interface for
groundwater flow and transport models, was used for setting up the numerical model.
MODFLOW (McDonald and Harbaugh, 1988) is a 3-dimensional finite difference model for
groundwater flow, developed by the U.S. Geological Survey. MT3DMS (Zheng and Wang,
1999) is a 3-dimensional multi-species numerical transport model that considers advection,
dispersion, and sorption. MT3DMS (Zheng and Wang, 1999) was used for modeling
transport of ethanol and the COC.
Numerical Model Setup
A 600x300x30 m model domain, encompassing about 10 times the source width and depth,
was considered. The model domain is set up so that the plumes never transport out of the
domain and the transverse and vertical boundaries do not affect the plume. This is necessary
as the Domenico model assumes infinite boundaries in the lateral and vertical directions.
Constant heads at the upgradient and downgradient boundaries, and no-flow boundaries at
the bottom and at the lateral sides of the model domain were selected for the flow model.
Boundaries were set up to ensure a unidirectional flow field, as assumed in the Domenico
model.
A 3x3x1.5 m grid dimension was used in the model. In order to verify the flow model,
distance traveled by a water particle for a given time was predicted by using the particle
tracking code, MODPATH (Pollock, 1994) and then compared with the same obtained from
the seepage velocity. Equation 5 was used to estimate the seepage velocity (Vs).
Ksxl
Vs = — S- (5)
nxR
where, Ks is the saturated hydraulic conductivity (m/d), Ig is the hydraulic gradient (m/m), n
is the porosity (m3/m3), and R is the retardation factor.
Table 1 presents the values of all input parameters used in the model. The hydraulic
conductivity value represents a loamy sand according to Carsel and Parrish (1988). Decay
rates for ethanol and the COC (here, benzene), the threshold concentration limit for ethanol,
and source concentrations for ethanol and benzene were obtained from Deeb et al. (2002).
All other input parameters are typical values for the scale of the model. As the purpose of
simulating the model is to compare the results of the numerical model with that of
Footprint User's Manual 34
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FOOTPRINT and thus verify the latter, use of typical values is reasonable. Note that
although Deeb et al. (2002) used 1 ^ig/L as the maximum contaminant level (MCL) for
benzene (the primary MCL for benzene in California), a higher value for the same was
assumed in this study in order to minimize the computational time required for simulating the
numerical model.
Numerical Model Simulation and Comparison of Modeling Results
The numerical transport model (i.e., MT3DMS) was first simulated for ethanol. An iso-
concentration map for the ethanol plume, outlined by the threshold limit (e.g., 3 mg/L), was
plotted. Then, the decay rate for the COC was set to zero within the zone where the ethanol
concentration is over 3 mg/L, while the decay rate away from that zone was set to the given
value (see Table 1). Simulations of the transport model for both the COC and ethanol were
conducted for a long time (about 15,000 days) so that the downgradient concentration
reaches steady state. Note that the 'no biodegradation zone' for the COC (Le) remains fixed
in size due to the assumptions of constant ethanol source concentration and a steady state
condition. For a decaying ethanol source, the 'no biodegradation zone' would shrink with
time.
Table 1. Input parameters used for model verification.
Parameters Values
Hydraulic conductivities in X and Y directions (m/d) 3.3
Hydraulic conductivities in Z direction (m/d) 0.33
Hydraulic gradient (m/m) 0.005
Effective porosity (m3/m3) 0.20
Longitudinal dispersivity (m) 12
Transverse dispersivity (m) 1.2
Vertical dispersivity (m) 0.0012
Source width (m) 30
Source thickness (m) 3.0
Ethanol/Oxygenate concentration at the source (mg/L) 4000
Decay rate for ethanol (1 /year) 5.11
Threshold concentration of ethanol (mg/L) 3.0
COC concentration at the source (mg/L) 8
COC maximum contamination level (mg/L) 0.08
Decay rate for COC (I/year) 2.26
Retardation Factors for both ethanol and COC 1.0
Simulation results obtained from the numerical model (i.e., Visual MODFLOW),
FOOTPRINT and the alternative technique discussed earlier are presented in Table 2. It is
observed that all three techniques resulted in equivalent values for the plume length (i.e.,
Le+Lc). Also, the plume area estimation from the technique used in FOOTPRINT results in a
less than 4% error for the given input values (Table 1) when compared to the results from the
numerical model. However, the alternative technique produced about 42% error in estimating
the plume area. This discrepancy in the plume area estimation by the alternative technique
resulted from underestimation of lateral spreading of the plume. Even larger error could
Footprint User's Manual 35
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result for a dispersion dominated transport condition. On the contrary, less error is likely for
advection dominated transport.
Table 2. Comparison of modeling results for constant concentration sources.
Parameters
Le(m)
Lc(m)
Le + Lc (m)
Plume Area
(m2)
Numerical
Model
78.3
80.5
155.0
10,740
FOOTPRINT
78.0
80.2
158.2
11,130
Error Alternative Technique Error
(%) (%)
-0.38
-0.37
2.06
3.63
78.0
79.0
157.0
6,200
-0.38
-1.86
1.29
-42.3
Decaying Ethanol Source
Analytical model for an exponentially decaying source is presented in BIOCHLOR version
2.2, which is available from the RSKERC web page (http://www.epa.gov/ada/csmos.html).
The model is an extension of the original Domenico (1987) model. Equation 6 presents the
model for an exponentially decaying source, i.e., at the source, C = Co exp(-kst), where Co is
the initial concentration at the source and ks is the first order decay rate.
(6)
where, fy and fz are same as Equation 3, and
/,*=exp
x
2ar
1-1 +
+ exp
x
2ar
1+1 +
where,
k<
(7)
FOOTPRINT uses Equation 6 for a decaying ethanol source. The simulation procedure for a
decaying ethanol source remains the same as the constant ethanol source, except that the
modeling condition is transient rather than steady state. Since the ethanol concentration at the
source is changing with time for a decaying source, the downgradient concentration can not
Footprint User's Manual
36
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reach steady state. Therefore, the 'no biodegradation zone' for the COC would change with
time, and plume area of the COC would change as well. FOOTPRINT conducts the
simulation for a decaying ethanol source in increasing time steps and computes the COC
plume area at every time step. Therefore, the output from FOOTPRINT shows the change in
COC plume area with time instead of a fixed plume area as obtained for a constant ethanol
source.
Notice
The U.S. Environmental Protection Agency through its Office of Research and Development
partially funded and collaborated in the research described here under an in-house project. It
has not been subjected to Agency review and therefore does not necessarily reflect the views
of the Agency, and no official endorsement should be inferred.
Reference
Aziz, C. E., C. J. Newell, J. R. Gonzales, P. Haas, T. P. Clement, and Y. Sun. BIOCHLOR Natural Attenuation
Decision Support System; User's Manual, Version 1.0. U. S. EPA, EPA/600/R-00/008, Robert S. Ken-
Environmental Research Center, Ada, OK, 1999.
Carsel, F. F., and R. S. Parrish. Developing Joint Probability Distributions of Soil Water Retention
Characteristics. Water Resources Research 24 (5): 755-769 (1988).
Deeb, R. A., J. 0. Sharp, A. Stocking, S. McDonald, K. A. West, M. Laugier, P. J. J. Alvarez, M. C.
Kavanaugh, and L. Alvarez-Cohen. Impact of Ethanol on Benzene Plume, Lengths: Microbial and Modeling
Studies. Journal of Environmental Engineering, ASCE 128 (9): 868-875 (2002).
Domenico, P. A. An Analytical Model for Multidimensional Transport of a Decaying Contaminant Species.
Journal ofHydrogeology 91: 49-58 (1987).
Martin-Hayden, J. M., and G. A. Robbins. Plume Distortion and Apparent Attenuation Due to Concentration
Averaging in Monitoring Wells. Ground Water 35 (2): 339-346 (1997).
McDonald, M. G., and A. W. Harbaugh. MODFLOW: A Modular Three-Dimensional Finite-Difference
Groundwater Flow Model, U. S. Geological Survey, Reston, VA, 1988.
Newell, C. J., R. K. McLeod, and J. R. Gonzales. BIOSCREEN Natural Attenuation Decision Support System;
User's Manual, Version 1.3. U. S. EPA, EPA/600/R-96/087, Robert S. Kerr Environmental Research Center,
Ada, OK, 1996.
Ogata, A., and R. B. Banks. Solution of the Differential Equation of Longitudinal Dispersion in Porous Media,
U. S. Geological Survey Professional Paper, 411-A, 7 pp, 1961.
Pollock, D. W. User's Guide for MODPATH/MODPATH-PLOT, Version 3: A particle tracking post-
processing package for MODFLOW, the U. S. Geological Survey finite-difference ground-water flow model,U.
S. Geological Survey, Reston, VA, 1994.
WHI. Visual MODFLOW User's Manual, Waterloo Hydrogeologic Inc., Ontario, Canada, 1999.
Footprint User's Manual 37
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Zheng, C., and P. P. Wang. MT3DMS: A Modular Three-Dimensional Multispecies Transport Model for
Simulation ofAdvection, Dispersion, and Chemical Reactions of Contaminants in Groundwater Systems;
Documentation and User's Guide, U. S. Army Engineer Research and Development Center, Vicksburg, MS,
1999.
Footprint User's Manual 38
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Appendix B : Analytical Model for Zero-Order Decay
Analytical Solution for Zero-Order Decay in the Plume
The Advection-Dispersion-Equation (ADE) for zero-order decay in the plume is given by:
ir
dt
a
dx
a2c
-TT
dy
dz
(1)
where C is the solute concentration (mg/L), vx is the average seepage velocities in the X
directions, respectively (m/d), and Dx, Dy, Dz are the hydrodynamic dispersion coefficients in
the X, Y, and Z directions (m2/d), respectively, y is the zero-order decay constant in the
aqueous phase (mg/L/d"1), and R is the retardation factor for sorption. For linear sorption, R
is expressed as
(2)
n
where, phis soil bulk density (Kg/L) and Kp is the linear sorption coefficient (L/Kg).
Solution of Equation (1) for the following boundary and initial conditions (Equations 3 to 5)
is shown in Equation 6.
C (0, t) = Co (i.e., constant source concentration at the top of the aquifer) (3)
C(x, 0) = 0 (i.e., zero initial concentration down gradient from the source) (4)
dx
C(x,y,z,t) = -
(5)
(6)
where, fx is obtained from modifying the solution provided by van Genuchten (1981) (pp.
231), which assumes one-dimensional ADE with zero-order growth in the plume.
f° = C0A(x,t) -5(x,t); where, A(x,t) = -exp —\-erfc
et)
2javt
•-erfc
(x-vet)
2,/aiv t
(7)
+ -
2v
(x-vct)
(8)
Footprint User's Manual
39
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erf
And /. =
-erf
z-Zt
(9)
(10)
where, a* is the longitudinal dispersivity (m), vc is the contaminant velocity (= vx/R), YS, and
Zs represent source dimensions along the y and z directions (m), respectively, and erf and
erfc represent the error function and complementary error function, respectively.
Exponentially Decaying Source with Zero-Order decay in the Plume
The analytical model for a constant concentration source (Equations 6-10) can be modified to
represent a source concentration that is decaying exponentially. Equation 11 presents the
model for an exponentially decaying source, i.e., at the source, C = Co exp(-kst), where Co is
the initial concentration at the source and ks is the first-order decay rate.
C(x,y,z,t)=~ fxd°-fy-fz
(11)
where, fj? is obtained from modifying the solution provided by van Genuchten (1981) (pp.
231), which assumes one-dimensional ADE with exponentially decaying source and zero-
order growth in the plume.
where,
and, c = vr 1-
-nf k t K l
4A KS1K 2
[, 4*,flrl
vc
3Xp
/ 2
~(vc-£)xl
_ 2«xVc
• erfc
[(x-^1
_2V«xvct_
1
2
r(vc+^)xi
. 2(X^c
• erfc
~(x + £)~
2A/axvct_
(12)
(13)
It should be noted that for any exponentially decaying source, the decay rate (ks) should be
limited to the following equation,
k<
(14)
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40
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Reference
Van Genuchten, M. Th. 1981. Analytical Solutions for Chemical Transport with Simultaneous Adsorption,
Zero-Order Production and First Order Decay. Journal of Hydrology. 49:213-233.
Footprint User's Manual 41
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Appendix C: Expression for Zero-Order Decay in
both Aqueous and Solid Phases
Expression for Zero-Order Decay in both Aqueous and Solid Phases
The Advection-Dispersion-Equation (ADE) for zero-order decay occurring in both aqueous
and solid phases in the plume is given by:
(1)
dt
Rac r acy (^^c+D ^c+Dz^cU _A^ Ys (2)
dt v x dx) v ^x2 y ^2 z ^z2 ) o p
/ -^ / o o o \
"^/"l / ^f~^ \ I "^ ^ f~~* ^ £ f~~* ^ £ f~~* \
oL f oL | o L o L o L
3t v x 9x j ^ 3x2 y 3y2 z 3z2 J
where, C is the solute concentration (mg/L); vx is the average seepage velocity in the X
direction (m/d); Dx, Dy, Dz are the hydrodynamic dispersion coefficients in the X, Y, and Z
directions (m2/d), respectively; #, and js are the zero-order decay constants in the aqueous
and solid phases (mg/L/d), respectively; R is the retardation factor for sorption;;^ is soil bulk
density (Kg/L); 0 is volumetric moisture content (L°), which is equal to soil porosity (ri) at
saturated condition; Kp is the linear sorption coefficient (m3/Kg) and ^is lumped zero-order
decay constant for both aqueous and solid phases (mg/L/d). Note that the zero order decay
rates are in term of decay in the aqueous concentration per day.
R is expressed as:
R=I + £>LK (4)
n
where, Kp is the linear sorption coefficient (L/Kg),
Footprint User's Manual 42
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The lumped zero-order decay constant yis given as follows:
—zPrs
— Kv—
n YL
When, JL = ys
Then,
— Kp
n p
(5)
(6)
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Appendix D: Expression for First-Order Decay in
both Aqueous and Solid Phases
Expression for First-Order Decay in both Aqueous and Solid Phases
The Advection-Dispersion-Equation (ADE) for first-order decay occurring in both aqueous
and solid phases in the plume is given by:
~\ f 2)/"~>\ ( 7\^-C^ Tfic* ^)2/"~> \
-AL6C-AspbS (1)
y
dx dy dz
~\t^i /" ~\r~*> ~\ f ~\ 2 r~*> ~\ 2 r~*> ~\ 2 f~\ \ ,-»
R — = -fv — 1 + ID I D I D —}-(AL+As2*-K }C (?)
3t I x 3x J 1 3x2 y 3y2 z 3z2 J 6 p
\^ ^ /
3t v x 3x) ^ 3x2 y 3y2 z 3z2 J
where, C is the solute concentration (mg/L), vx is the average seepage velocity in the X
direction (m/d); Dx, Dy, Dz are the hydrodynamic dispersion coefficients in the X, Y, and Z
directions (m2/d), respectively; AL and AS are the first-order decay constants in the aqueous
and solid phases (1/d), respectively; R is the retardation factor for sorption; pb is soil bulk
density (Kg/L); 0 is volumetric moisture content (L°) ), which is equal to soil porosity (ri) at
saturated condition; A, is lumped first-order decay constant in aqueous and solid phases (1/d).
R is expressed as:
R=I + £>LK (4)
n
where, Kp is the linear sorption coefficient (L/Kg).
The lumped first-order decay constant A, is given as:
n
If AL = As Then
A = ALR (6)
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