REMFuel
Remediation Evaluation Model for Fuel Hydrocarbons
User's Manual
Version 1.0
by
Ronald W. Falta, Ph.D.
Clemson University
Clemson, South Carolina
Abu N. M. Ahsanuzzaman, Ph.D, P.E.,
Superfund Support Branch
Superfund Division
US EPA Region 4
Atlanta, Georgia
Mark B. Stacy and Robert C. Earle
Center for Subsurface Modeling Support
R. S. Kerr Environmental Research Center
Ada, Oklahoma
EPA Project Officer
John T. Wilson, Ph.D.
Subsurface Remediation Branch
Ground Water and Ecosystems Restoration Division
National Risk Management Research Laboratory
US EPA Office of Research and Development
Robert S. Kerr Environmental Research Center
Ada, Oklahoma
February, 2012
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This work was supported in part by the US EPA under Cooperative Agreement CR-
830829 between the National Risk Management Research Laboratory, Ada, OK, and
Ciemson University. It was supported in part through a Technical Services
Agreement between Shaw E&l, Inc. and Falta Environmental, LLC. It was supported
in part by funds provided by the Strategic Environmental Research and Development
Program (Department of Defense) to Ciemson University.
Shaw E&l, Inc. (On-site contractor)
Center for Subsurface Modeling Support
Ground Water and Ecosystems Restoration Division
Ada, OK
U.S. Environmental Protection Agency
-o
EPA/600/R-12/028
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Contents
Overview 4
Abstract 4
REMFuel Software Installation and Computer Requirements 6
Analytical Mathematical Model 7
Background 7
LNAPL Source Model in REMFuel 8
Coupled Plume Model with Biodegradation 13
Additional Plume Biodegradation Models 21
Input Values for Gasoline Components 23
Graphical User Interface 27
Projects Tab 27
Parameter Entry 27
Options for Viewing Model Output 27
View File Output 27
View Graphical Output 27
Basic Operation 28
Model Input Variables 33
LNAPL Source Parameters in REMFuel 33
Basic Source Parameters 33
Source Parameters Related to the Chemical of Concern 34
Flow Parameters 36
Source Remediation 36
Transport Parameters 37
Component Setup and Reaction 38
Simulation Output Parameters 40
REMFuel Tutorials 41
Tutorial 1 41
Reactive Transport of BTEX and MTBE with Remediation 41
Tutorial 2 49
Reactive Transport of MTBE from a Gasoline Spill Site 49
References 55
Manual for REMFuel
Contents • iii
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Overview
Abstract
An analytical solution, called REMFuel (for Remediation Evaluation Model for
Fuel hydrocarbons) has been developed for simulating the transient effects of
groundwater source and plume remediation for fuel hydrocarbons. In the
analytical method, the contaminant source model is based on a power function
relationship between source mass and source discharge for multiple fuel
constituents, and it can consider partial source remediation at any time after the
initial release. The source model serves as a time-dependent mass flux
boundary condition to the analytical plume model, where flow is assumed to be
one-dimensional. The plume model for each fuel component simulates first
order sequential decay and production of one daughter species. REMFuel can
also simulate zero order or Monod's kinetics for decay of fuel components in the
plume. The decay rates and other reaction coefficients are variable functions of
time and distance in the plume. This approach allows for flexible simulation of
enhanced plume remediation that may be temporary in time, limited in space,
and which may have different effects on different contaminant species in the
plume.
The Center for Subsurface Modeling Support (CSMoS) at EPA has developed a
Graphical User Interface (GUI), for REMFuel that will allow the user to
quickly and easily evaluate the balance of LNAPL source remediation, plume
remediation, and natural attenuation. The GUI consists of a user-friendly,
visually intuitive model parameter data entry screen, and a variety of quick and
powerful ways of displaying the resulting model output.
The primary objective of the REMFuel GUI is to simplify model data input, and
viewing/interpreting model data output. The GUI is written in Visual Basic. It
will compile the model input file, run the input file through the FORTRAN
model code, and provide a seamless way of working with the resulting output
data files.
REMFuel provides a suite of powerful tools for building and interpreting
models.
Manual for REMFuel
Overview • 4
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DISCLAIMER OF LIABILITY
With respect to REMFuel software and documentation, neither the United
States Government, Clemson University, 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.
Manual for REMFuel
Overview • 5
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REMFuel Software Installation
and Computer Requirements
1. To install the software, ran the file 'REMFuelsetup.exe'. The software will guide the user through the
installation process. Upon first running this beta version of REMFuel from the desktop icon, the user will be
asked to run it again. This serves to initialize the application after which REMFuel will ran properly in
Windows.
2. REMFuel v 1.0 requires a standard PC running Windows 98 or greater. The .Net framework that is required
comes with the setup.exe and will be loaded with the application. Minimum requirements for the .Net
framework are a Pentium 90 MHz or faster processor and 32 MB of RAM or higher (96 MB or higher
recommended).
Manual for REMFuel
REMFuel Software Installation and Computer Requirements • 6
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Analytical Mathematical Model
Background
Groundwater has been contaminated with fuel hydrocarbons (BTEX and other gasoline additives)
at thousands of sites from gasoline spills. Many of these sites contain light nonaqueous phase liquids
(LNAPLs) that serve as a concentrated source of groundwater contamination, and most dissolved plumes
of volatile organic chemicals (VOCs) can be traced back to concentrated source zones. The VOCs often
are suspected carcinogens, and they have low maximum contaminant levels (MCLs) in drinking water.
Considering that source concentrations can be four or five orders of magnitude greater than MCLs,
restoration of source zones to pristine conditions seems unlikely; however, reduction of VOC plumes is a
realistic goal that can be achieved through various combinations of source and plume remediation.
The Center for Subsurface Modeling Support (CSMoS), a unit of EPA's Ground Water and
Ecosystem Restoration Division (GWERD), distributes a modeling software package called REMChlor
(Remediation Evaluation Model for Chlorinated solvents that simulates the transient effect of
groundwater source and plume remediation for chlorinated solvents [Falta, 2008], In this project, similar
modeling software, named REMFuel (Remediation Evaluation Model for Fuel hydrocarbons) has been
developed for gasoline and other fuel components. Similar to REMChlor, REMFuel assumes a power
function relationship between source mass and source discharge, and it can consider partial source
remediation at any time after initial release. The contaminant source is composed of multiple fuel
constituents, and can be depleted naturally by the processes of dissolution and first order aqueous phase
decay, and the effects of a delayed removal or destruction of part or all of the source is considered. The
contaminant source is analytically coupled to a plume model that considers 1-D advection, retardation,
and 3-D dispersion. Also similar to REMChlor, the plume model in REMFuel simulates first order
sequential decay and the production of daughter species; however, it only considers production and decay
of one daughter product from sequential decay. Allowing only one daughter product seems sufficient for
gasoline and other fuel components. Additional features in REMFuel include zero order decay and
Monod's kinetics options in the plume model. The plume model considers all of the contaminant reaction
rates and yield coefficients to be independent functions of distance from the source and time since the
contaminant release, and they are independent for each fuel species in the plume. This approach allows
for flexible simulation of enhanced plume degradation that may be temporary in time and limited in
space.
Manual for REMFuel
Analytical Mathematical Model • 7
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LNAPL Source Model in REMFuel
The LNAPL source model in REMFuel is similar to that in REMChlor except that it considers
biodecay in the aqueous phase only [Parker and Falta, 2008], and it considers multiple source zone
contaminants. The contaminant discharge for each component from a source zone is the product of the
flow rate of water passing through the source zone and the average concentration of contaminant in the
water (Figure 1). Source discharge has units of mass per time, and should not be confused with mass
flux, which is discharge divided by area. If water flows through the source at a rate of 0(t), and if the
mass in the source zone is also subjected to first order aqueous phase decay, then a mass balance on the
source gives:
dM(t)
dt
= -Q(t)Cs(t)-0VAsCs(t)
(l)
where M(t) is the mass remaining in the source zone with time, Cs(t) is the time-dependent source
dissolved concentration (flow averaged), Xs is the source zone aqueous phase decay rate by processes
other than dissolution, (j> is the porosity, and V is the volume of the source zone. Water flow through the
source may be due to infiltration (above the water table) or groundwater flow (below the water table).
LNAPL source
Groundwater flow, Vd zone
Dissolved plume
cin=o
Source
MASS, M(t)
^OUt~^s(0
Figure 1. Conceptual model of source zone with time-dependent contaminant mass and discharge.
The source mass/source discharge relationship is shown in Figure 2, and it is modeled by a simple
power function (Rao et al., 2001; Rao and Jawitz, 2003; Parker and Park, 2004; Zhu and Sykes, 2004;
Falta et al., 2005a):
Manual for REMFuel
Analytical Mathematical Model • 8
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cm
cn
f M(t)^
vM,
(2)
where Co is the flow-averaged source concentration corresponding to the initial source mass, M0.
The exponent, r, determines the shape of the source discharge response to changing source mass
(Figure 2).
Figure 2. Power function representation of source mass/source discharge relationship (Equation 2)
Field, laboratory, and theoretical evaluations of the source mass/source discharge response
suggest that r may vary between about 0.5 and 2 at real sites [Rao and Jawitz, 2003; Falta et al.,
2005a; Newell and Adamson, 2005; Fure et al., 2005; Jawitz et al., 2005; McGuire et al., 2006;
Newell et al., 2006], Simulation studies suggest that sites with DNAPL located predominantly in
low permeability zones exhibit r >1 and sites with DNAPL in high permeability zones exhibit
r< 1 [Falta et al., 2005 a, b]. Park and Parker [2005] suggest /"values greater than 1 for finger-
dominated residual DNAPL and less than 1 for DNAPL pools. Essentially, r should be
considered as an uncertain parameter, whose mean value can be roughly estimated, but whose
actual value may never be precisely known at a site.
Manual for REMFuel
Analytical Mathematical Model • 9
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Equations (1) and (2) may be combined, and written as:
There (3)
dt Ml0
Separating and integrating from zero to t with M=Ma at l 0 gives a general solution for the
source mass. For the special case of constant Q and Xs, the source mass function becomes
[Parker and Falta, 2008]
(r-i)(g+^)C0
1
I i-r
M = \^ °t+Ml0T\ (4)
40
Using Equation 2, this leads to the time-dependent source discharge function:
(5)
K K
Similar expressions can be derived for the case of Xs=0 (Parker and Park, 2004; Zhu and Sykes, 2004).
A very important special case of Equation 3 occurs when T =1 and As =0. In that case, the
differential equation is linear and may be integrated to get a simple exponential decay solution (Newell et
al., 1996; Parker and Park, 2004; Zhu and Sykes, 2004):
QCpt
M(t)=M0eM° (6)
and
QCpt
Cs(t) = C0eM° (?)
Therefore, when T =1, both the source mass and the source discharge will decline exponentially with
time. If 2V =0, then the apparent source decay rate due to dissolution is QCJMa, giving a source half-life
of ,693MJ(QC0) (Newell and Adamson, 2005). This type of source behavior has been observed in the
field at many chlorinated solvent sites (Newell and Adamson, 2005; McGuire et al., 2006; Newell et al.,
2006), as well as at sites contaminated by petroleum hydrocarbons (Chen et al., 2002). The widely used
EPA BIOCHLOR (Aziz et al., 2002) and BIOSCREEN (Newell et al., 1996) analytic models for natural
attenuation include exponentially decaying source terms.
An important characteristic of source zones with Y greater than or equal to one, is that the source
is never completely depleted, and the source discharge is always greater than zero, even at large times. In
simple terms, this happens because the rate of discharge from the source drops as fast as or faster than the
rate of mass depletion of the source. When T <1, the source has a finite life, and the source discharge
eventually is equal to zero.
Manual for REMFuel
Analytical Mathematical Model *10
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Another useful special case occurs when T =0.5 and /.v=0. This leads to a source concentration
that declines as a linear function of time (Falta et al., 2005a; Newell and Adamson, 2005):
c (t) = C -®c° t
' 0 2M0
and the source completely disappears at a time of
2Mn
(8)
t = ¦
QC0
(9)
The simplest model of source behavior is one in which T =0, and Xs =0, which leads to a constant source
discharge (concentration) until the source is fully depleted. This is also known as a "step function"
model, and the source mass declines at a constant rate with respect to time.
The source model (Equations 4 and 5) represent source depletion by the natural process of
dissolution and aqueous phase biodecay. This model can easily be modified to account for aggressive
source remediation activities that remove a substantial fraction of the source mass over a short period of
time (Falta et al., 2005a). If a source remediation effort (such as alcohol or surfactant flooding, chemical
oxidation, thermal treatment, air sparging or excavation) begins at a time of ti, and ends at a time of t2,
during which a fraction, X of the source mass is removed, the functions can be simply rescaled. Then the
source mass and concentration following remediation are given by:
M =
(T-l )(g + ^)C2
Ml
(t-t2)+M.
(10)
c,(/) = c2
f M(t)^
V ^2 J
M1=(l-X)Ml
c =c
^2 ^0
f (1 -X)M^r
V ^ J
(11)
(12)
(13)
where A/, is the source mass at th and M2 is the source mass at t2. The change in source discharge
following remediation varies as the fraction of mass remaining (1 -X) raised to the power T . Therefore if
r =1, a linear reduction of source discharge is expected; if T =2, the discharge will drop as the square of
the mass fraction remaining, while if T =0.5, the discharge will drop as the square root of the mass
fraction remaining. Examples of this type of source behavior with and without remediation are shown in
Figures 3 and 4, for a case where the initial source mass is 1620 kg, with an initial source concentration of
100 mg/1, and a water flow rate of 600 m3/yr with no aqueous phase biodecay.
Manual for REMFuel
Analytical Mathematical Model *11
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100000
O)
3
c
o
TO
c
0)
o
c
o
o
0)
£
3
o
(/)
10000
1000
100
no remediation,
gamma = 0.5
remove 90%
after 20 years,
gamma = 0.5
remove 90% at
time zero,
gamma = 0.5
-r
20 40 60 80
Time since LNAPL release, years
100
Figure 3. Source zone dissolved concentrations with and without source remediation for T =0.5
(from Falta et al., 2005a)
100000
O)
3
C
o
?
ra
i.
c
0)
o
c
o
O
0)
e
3
O
(0
10000
1000
100
¦ no remediation,
gamma = 2.0
¦ remove 90%
after 20 years,
gamma = 2.0
¦ remove 90% at
time zero,
gamma = 2.0
20 40 60 80 100
Time since LNAPL release, years
Figure 4. Source zone dissolved concentrations with and without source remediation for T =2.0
(from Falta et al., 2005a)
Manual for REMFuel
Analytical Mathematical Model
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Coupled Plume Model with Biodegradation
The plume model for REMFuel is similar to REMChlor, except it allows zero order decay and
Monod's kinetics in addition to the first order decay option in REMChlor. Falta et al. (2005b) used
Equations (5) and (11) to form a mass flux boundary condition used in an advection-dispersion equation
with decay reactions. A significant limitation of that solution was that it required the solute decay rates in
the plume to be constant in both space and time. There are many cases in which the decay rates of the
compounds are spatially variable, or where they are manipulated in space and time through the addition of
electron donors, electron acceptors, oxygen or nutrients.
The current analytical approach, from Falta (2008) assumes a constant groundwater pore velocity
of v in the x-direction, with longitudinal, transverse, and vertical dispersion. The solute can be retarded
by adsorption, but the different solutes involved in coupled reactions must have the same retardation
factor. These assumptions are similar to those used in previous natural attenuation plume models such as
BIOCHLOR (Aziz et al., 2000; 2002), BIOSCREEN (Newell et al., 1996), LNAST (Huntley and Beckett,
2002), and the model by Falta et al. (2005b).
The BIOCHLOR natural attenuation model allows for two spatial zones to be defined in which
the solute decay rates are different, but this is only valid if the solute concentrations in the upstream zone
are at steady-state, which implies a constant source concentration in time. The solute decay rates in
BIOCHLOR are constant in time. The other analytical models assume that the reaction rates are constant
in both space and time. The key difference in the REMChlor and REMFuel models and these earlier
models, is that the chemical reaction parameters (rates, yield coefficients) can now be arbitrary functions
of both time and distance from the source.
The governing equation for the dissolved concentration of each contaminant species in the plume,
C, is:
„ DC DC d2C d2C d2C , ,
K = -v + CCV—— + avv—— + azv—— + rxn(x,t)
dt dx dx2 y dy2 dz2 (14)
where ax, ay. and a _ are the longitudinal, transverse, and vertical dispersivities, respectively; R is the
retardation coefficient, and rxn(x,t) represents the rate of generation (+) or destruction (-) of the species
due to chemical or biological reactions that are spatially and temporally variable. This plume model is
coupled with the source zone mass balance given by Equation (1), using the power function relationship
for the Cs vs M relationship (Equation 2). A specified flux boundary condition at x=0 ensures that the
rate of discharge from the source zone is exactly equal to the rate at which contaminants enter the plume
(see van Genuchten and Alves (1982)). The mass flux entering the plume is specified as:
Q(QCs(t)
A
tf>vC(t)-(f>axv
dC(t)
dx
(15)
where A is the area over which the contaminant flux enters the groundwater flow system, and is the
porosity. Outside of this area, the mass flux is zero. For sources that are located below the water table, A
would be the cross-sectional area of the source zone perpendicular to the groundwater flow. For sources
located above the water table, A would be the cross-sectional area at the top of the water table
perpendicular to flow that was required to accommodate the infiltration rate from the source. Falta et al.
(2005b) solved Equations (14) and (15) analytically for the case of first order decay reactions with
Manual for REMFuel
Analytical Mathematical Model *13
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constant and uniform decay rates, using a Laplace transform method, combined with Domcnico's (1987)
approximation for transverse and vertical dispersion. Analytical solution of Equation (14) with variable
plume reaction rates by this method would be much more difficult. Instead, a different approach is taken
where the solute advection and reactions are decoupled from the longitudinal dispersion using a simple
streamtube technique (Falta, 2008). Scale-dependent longitudinal dispersion is accounted for by
considering a collection of streamtubes with a normally distributed pore velocity. Transverse and vertical
dispersion are then simulated using Domenico's (1987) approximation.
The reactive plume model is based on a simple one-dimensional streamtube that is characterized
by a constant pore velocity and solute retardation factor. Since there is only advection taking place in the
streamtube, the flux boundary condition at the edge of the source zone simplifies to
aol
*>A (16)
If the source is located below the water table, and Q= (f)vA, then the flux boundary condition is just the
time-dependent source concentration,
c(o|„0=c,(o (17)
where Cs(t) could be calculated, for example, by Equations (5) and (11).
One-dimensional advective transport of a solute can be represented graphically on a distance-time
plot (Figure 5). Here, the time axis corresponds to the time since the contaminant was first released to the
groundwater system, while the distance axis is the distance downstream from the source.
time
Distance from source, m
location x,t
C=0 ahead of
the advective
front
time when
contaminant
was released
from source
for location
Advective front
Located at
t=Rx/v
Figure 5. Distance-time plot for advective transport with a single set of plume reaction rates
Manual for REMFuel
Analytical Mathematical Model *14
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The advective front moves at a constant velocity of v/R, so that at any location, x, the front passes
by at a time of t=Rx/v. At any time, the front is located at x=vt/R, and the solute concentration is always
zero below this line (ahead of the front). In the absence of any plume degradation process, the
concentration at any location behind the advective front can be determined from the time of solute release
from the source, treiease. For a distance from the source, x, the travel time is t,ravei Rx v. Therefore, if the
total time is t. the parcel of water found at that location (x, t) was released from the source at a time of
Release = t ~ Rx ./ V ( | g)
and the concentration at that (x, t) point would be
C(x,t) = C(trelease) |x=o
(19)
Plume reactions can easily be included in this advective streamtube model. As a parcel of solute is
translated downstream, it is not subject to any mixing processes, so it is conceptually equivalent to a batch
reaction that starts at time T =0 with an initial condition of C (trelease) | x=0 and reacts for a period of time
equal to the travel time to position x, r =Rx/v. As an example, if the solute reaction was first order decay
in the aqueous phase with a decay rate coefficient of k, then the equivalent batch reaction is
R^- = -kC with C|r_0=Cfc„.,,)L_„
dv lr-° lx-° (20)
Then at location (x,t) behind the front, the solute concentration would be
( -kx\
C(x,t) = C(t-Rxlv)\ exp —
\x-0 ^ v J
(21)
This result is exactly the same as the Laplace transform solution to Equations (14) and (15) with zero
dispersion (Falta et al., 2005a). More complicated coupled reactions can be considered using this same
method, but a fundamental limitation is that the parent and daughter compounds from the decay reaction
must move at the same velocity.
The analysis can be extended to the case of time and distance dependent reaction rates by
dividing the time-distance domain into distinct zones (Figure 6). Here, nine zones have been chosen to
approximately represent conditions downgradient from a contaminant source over the life of a plume.
The first time zone after the spill, tt2, could be used to represent long term conditions in the plume after
manipulation of the plume ended (another period of natural attenuation).
Manual for REMFuel
Analytical Mathematical Model *15
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time
VIII
VII
location x,t
time when
contaminant
was released
from source
C=0 ahead of
the advective
front
Advective front
Located at
t= Rx/v
Distance from source, m
Figure 6. Distance-time plot for advective transport with multiple sets of plume reaction rates.
Distance from the source is similarly divided into zones so that near the source, for x
-------
The analytical solution for multiple reaction zones is developed using the residence time in each
zone to develop the batch reaction solution for that zone. The initial conditions for the batch reaction are
the final conditions from the previously encountered reaction zone. The residence times in each reaction
zone are calculated using straightforward logic. For the example shown in Figure 6, the solutes that are
present at location fx, t) left the source at a time, treiease that was before tu so they initially encounter
reaction zone (I). The residence time in zone (I) is then t(I)=trtreiease. The solutes next enter zone (II),
where they remain until they cross xi, at a time of treiease+Rxi/v. Therefore, the residence time in zone (II)
is t(jj)=treiease+Rxi/v-ti. The solutes next enter zone (V), where they remain until t2, so the residence time
in zone (V) is ifVl i3-ireiaKe-Itxrv. In this way, the residence times for each reaction zone are tabulated.
In general, solutes can pass through any of the nine reaction zones, so a total of nine reaction zone
residence times are computed. For any given value of (x,t), the advective path leading to that location
will cross at most five zones, so several of the zone residence times are zero. The analytical solution is
constructed by sequentially performing the batch reactions in each zone that is encountered, starting with
a concentration of C(trelease )| ,. 0 . With the zone numbering scheme used in Figure 7, the numerical value
of the reaction zone always increases with increasing travel distance.
Going back to the example of a single solute undergoing first order decay in the aqueous phase, a
set of nine reaction rates are defined (k^-k^x)). The solute concentration at fx, t) is then:
C(x,t) = C(t-Rx / v)|x=Q exp j-£
L „=/ J (22)
A problem of significant practical interest involves simultaneous first order parent-daughter
decay/production reactions. Considering a two component system, the relevant batch reaction equations
for species A and B in zones (n) are:
R^r=-KMcMn) i.e. ->c,(„,(o)=
dt (23)
R = yBA(n)kA(nfA(n) ~ kB(nfB(n) 1-C¦ CB(n) (0) = CB(n_x)
dt (24)
where y, is the yield coefficient for the parent-daughter reaction. The yield coefficient is defined as
milligrams per liter of daughter produced divided by milligrams per liter of parent consumed. Equations
(23-24) are written for reaction zone (n), and the reactions proceed for a period equal to the residence
time, t(„), with initial conditions that are the concentrations from end of the previous reaction zone. The
starting conditions for the first reaction zone are C.(0) =Ci(t — Rx/v)| x=0 .
Following methods used in chemical reactor design (see, for example, Chen (1983)), the coupled
reaction equations can be solved by Laplace transform methods to yield:
^A(n) = ^'A(n-l)f{^'A(n)^(n)) (25)
^B(n) ~ ^A{n-l)f2 (^A(n) > ^B(n) > }'BA(n) > \n) ) + ^'B(n-\)f\ (^B(n) > \n) ) (2g)
Manual for REMFuel
Analytical Mathematical Model *17
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where the Ai(n) =ki(n/R, and
ft(A,r) = ^v
f2 , ^2, y2\,t) — y 21^
(e-^ -e-^\
(27)
(28)
Longitudinal dispersion is included by considering a bundle of streamtubes that have a normally
distributed velocity field, with a mean velocity of v , and a velocity standard deviation of crv. This
approach is similar to that used by Small (2003) in his streamtube transport model, except that he
assumed a lognormal distribution of velocity.
For a given location, x, and time, i. a velocity of v* is needed for the advective front to exactly
reach that location. Assuming a normally distributed velocity field, the probability that a streamtube's
velocity is less than v is (Abramowitz and Stegun, 1972)
exp
f~(T-V)2^
V 2^v ,
dr = —
2
f
l + erf
f * -W
v -v
V°"v
r2
J J
(29)
This expression can be written in terms of travel distances at some time t by multiplying the
relevant quantities in Equation (29) by L and by using x=v t. If the inlet concentration is fixed at a value
of C0, then the concentration at (x,t) would be one minus the probability that the streamtube's advective
front had not passed that location yet:
C = 1 - P(yt < vt) = 1 - —
C,
1 + erf
f * -A
1 vt-vt^
K0-vtyfl
= —erfc
2
f
x-vt
Kavty/2
(30)
Equation (30) has the same form as the analytical solution to the one-dimensional advection
dispersion equation in an infinite system where the initial concentration is C0 for x 0. and C=0 for x>0
(Charbeneau, 2000):
C 1 .
— = —eric
cn 2
x-vt
2 ^ajt j
(31)
These two expressions are equivalent if the dispersivity in Equation (31) is
t2 ^-2
CT CT _ _
ar = -^-t = —Vx =ax
2v 2v (32)
where x is average front location, v t. Therefore, the normally distributed velocity streamtube model
produces a scale dependent dispersion solution, whose dispersivity is a linear function of the mean front
location. One small drawback of this solution is that it does not exactly guarantee that the concentration
Manual for REMFuel
Analytical Mathematical Model *18
-------
at x=0 is C0, due to the infinite domain. This is generally a minor effect except at very large dispersivity
values (Charbeneau, 2000). The same problem arises in the streamtube model, because with a normally
distributed velocity distribution, some of the velocities would theoretically be negative. This effect would
be more pronounced as the ratio of the standard deviation of velocity to the mean velocity becomes large.
The computational procedure for the streamtube dispersion model requires the specification of the
number of streamtubes, n,uhcs, mean and standard deviation of velocity, and the minimum and maximum
velocities, vmin and vmax. The advective system is then divided into ntubes with a velocity range for each
tube calculated by
v —v ¦
max min
ntubes (33)
The probability that a streamtube,/ has a velocity within the range of (vr Av 2) v; (vj Av/2)
is calculated from the probability function:
P(v, < (v, + Av/2))- P(v, < (v, - Av/2)) (34)
Beginning at vr Av/2=vmin, each streamtube is assigned a weight, w; equal to this probability.
The longitudinal dispersion solution is constructed for each value of (x, t) by calculating the individual
streamtube analytical solutions using the distributed velocities. All of the streamtubes are fed from the
same source function that was described earlier. After all of the individual streamtube solutions have
been calculated, they are weighted by the function defined by Equation (34), and summed to get the
solution for advection with longitudinal dispersion.
The streamtube model is compared to Equation (31) in Figure 8 for a highly dispersive case, with
a=l/l0, and for an advection dominated case with a=l/200. The streamtube solution perfectly matches
the analytical solution when a large number of streamtubes (as many as 10,000) are used, and it provides
a reasonable approximation of the solution with as few as ten streamtubes. This method produces
concentration profiles that are exactly symmetrical around the mean advective front. The profiles do not
change with distance scales if the x-axis is normalized to the mean front location, due to the linear scale
dependency of dispersivity.
As mentioned earlier, these solutions can produce a relative concentration at x 0 that is slightly
less than one. For the highly dispersive case shown here, the relative concentration at x=0 was 0.987, so
the magnitude of this effect is small for practical values of dispersivity. An attractive feature of the
approach is that for small values of x, the dispersive flux approaches zero, so the flux boundary condition,
Equation (10), can be satisfied by just using the advective flux term.
The total mass discharge of the dissolved species crossing a downgradient control plane can be
computed directly from the streamtube solution by simply summing the individual streamtube discharges,
using the weighting function, Equation (34).
Manual for REMFuel
Analytical Mathematical Model *19
-------
0.8 -
F 0.6 -
9 0.5 -
0)
> 0.3 -
d) 0.2 -
— analytical, a=1/10
O a=1/10, 500 tubes
—¦— a=1/10,10 tubes
— analytical, a=1/200
O a=1/200, 500 tubes
—*-a=1/200,10 tubes
0.5 1 1.5 2
Normalized Distance, Rx/vt
2.5
Figure 8. Comparison of REMFuel streamtube dispersion model to error function analytical
solution using a scale dependent dispersivity equal to ax=ax .
The effects of transverse and vertical dispersion are included using Domenico's (1987)
approximation. With this method, the solution with three-dimensional dispersion is constructed from the
one-dimensional solution:
C(x,y,z,t)=C(x,t)fy(y)f2(z) (35)
where the transverse and vertical functions are
fv(y) =
fM =
y + Y/2
2 Ja^x
-erf
-erf <
y-Y/2
2yja~c
and
z-Z
2-y/i
a,x
(36)
This formulation assumes a source zone with dimensions of Y by Z, with dispersion occurring in
the positive and negative y directions, but only in the positive z direction. Equation (36) can be altered to
allow vertical dispersion in both directions (Domenico and Schwartz, 1990).
Manual for REMFuel
Analytical Mathematical Model • 20
-------
Because this dispersion method is approximate, the solutions may differ from exact solutions for
transverse dispersion. Cleary and Ungs (1978) and Wexler (1992) give exact integral solutions for two-
dimensional and three-dimensional dispersion problems, respectively. Comparisons of the Domenico
(1987) approximation with the Cleary and Ungs (1978) solution for several examples tabulated in
Javandel et al. (1984) show that the error that results from using the Domenico approximation is relatively
small. Falta (2008) shows a comparison of REMChlor simulation results with the exact solution for two-
dimensional advection-dispersion, and again the differences are small except for when large dispersivities
are used. West et al. (2007) and Srinivasan et al (2007) provide additional analysis of possible errors
resulting from the use of the Domenico approximation.
Additional Plume Biodegradation Models
REMFuel can be used to model biodegradation in the plume through first order, zero order or
Monod's kinetics. The first order parent-daughter decay option has been discussed in the previous section
(see Equations 20 through 28). If the solute reaction was zero order decay in the aqueous phase with a
decay rate coefficient of y, then the equivalent batch reaction is
R^=~y with CL <3')
Then at location (x, t) behind the front, for constant y the solute concentration would be
C{xj)=C{t-Rxlv)\x__Q-{^ (38)
In REMFuel, the zero order decay rate may be different in each of the nine space/time zones, and it is
different for each solute in the plume. No daughter products are produced from this reaction in the model.
Monod's kinetics can also be assumed for plume biodegradation model. The rate of change in
contaminant concentration according to Monod's kinetics can be given by
ndC C
R = — u (39)
j, r*max ^ v '
at Kc+C
where, unwx is maximum contaminant utilization rate (mg/L/d) and K, (mg/L) is the half-saturation
constant or the contaminant concentration when the utilization rate is half of the maximum rate (i.e.,
max) •
Monod's kinetics contains three regions depending on the concentration and the coefficients:
first-order, zero-order, and mixed-order behavior. When C«Kc, Equation 39 becomes a first-order
equation with decay rate equal to umax Kc. Similarly, when C»Kc, Monod's equation becomes a zero-
order equation with decay rate equal to umax. The intermediate region in Monod's kinetics remains as a
mixed-order zone between the first and zero-order regions.
The solution of the Monod's kinetics at a location in the plume behind the advective front, with
constant parameters is given by
Manual for REMFuel
Analytical Mathematical Model • 21
-------
C(x t) , C(t-Rx/v)I ^max[ v /
In C(x, t) + -Ll2 = ]nC(t-Rx/ v)\x_Q + AlZ (40)
Kc Kc
where C(t-Rx/v)\x=0 is the contaminant concentration in the source at the time of release (i.e., treiease)- The
REMFuel model does not consider daughter production in this model, but the reaction parameters are
variable functions of space and time in the plume, and are independent for each plume species.
Evaluation of Equation (40) in REMFuel is done by a Newton Raphson iterative nonlinear root finding
method.
Important Limitations of REMFuel
The user should be particularly mindful of two important limitations of REMFuel.
Because REMFuel is not a distributed parameter model, it may provide misleading projections of
plumes in landscapes where the hydrogeological parameters change along the extent of a potential plume
of contamination. The possibility that the parameters will change increases with the size of the release
and the size of the plume that would be produced from the release. The user is cautioned to compare any
plume that is modeled using REMFuel to the geological context at the site to determine whether the
assumptions in the model are justified over the extent of the modeled plume. As part of the peer review
of REMFuel, calibration was attempted on a large spill of gasoline at a site in the intermountain west. The
actual plume extended approximately 1700 feet from the point of release to the banks of a nearby river.
The modeled plume was much longer, and extended across the river.
REMFuel does not account for natural attenuation of the source due to volatilization of petroleum
hydrocarbons into soil gas and subsequent loss to the hydrocarbons from soil gas due to diffusion to the
land surface or aerobic biodegradation in the unsaturated zone. The losses can be substantial. Ostendorf
and Kampbell (1991) characterized aerobic biodegradation of aviation gasoline in the unsaturated zone
above a spill and estimated that over the 20 years since the release, 39% of the original amount of
gasoline that was spilled was lost by evaporation and subsequent biodegradation in the unsaturated zone.
As the elevation of the water table varies up and down, more or less of the LNAPL source area
will be inundated and contribute to ground water contamination. At any point in time, that portion of the
LNAPL source area that is above the water table will be subject to losses due to volatilization and
biodegradation. The importance of this interaction will depend on the depth interval occupied by the
LNAPL and the depth intervals occupied by excursions of the water table over time.
Loss by volatilization and subsequent biodegradation is a complex and dynamic process. At best
the-state-of-science can describe the rate of overall weathering of the LNAPL source area, but cannot
describe the rate of weathering of any particular constituent in the LNAPL (compare Lundegard and
Johnson (2006a, 2006b)).
Because REMFuel does not consider losses to the unsaturated zone, it will overestimate the
persistence of the contamination in the source area of the plume. The bias will be related to the depth of
the source area used to calibrate the model (which corresponds to the depth from the water table to the
bottom of the LNAPL source area) and the fraction of that depth interval that is water saturated over time.
Manual for REMFuel
Analytical Mathematical Model • 22
-------
Input Values for Gasoline Components
Default values for 1st and zero-order plume decay rates and Monod's constants (i.e., umaxand Kc)
for different gasoline components are included in the REMFuel software. These values are obtained from
literature survey on studies presenting field scale values and from using professional judgment. The
following tables show the default values in REMFuel for all the decay constants and the range of values
of the first-order decay rates, which is the most commonly used degradation kinetic model for gasoline
compounds.
Gasoline
Compounds
Solubility
(fl/L)
Molecular
wt. (g/mol)
Koc
(L/Kfl)
1 st Order
Rate (per
year)
Zero Order
Rate (mg/L/d)
Half Saturation
Constant
(mg/L)
Maximum
Utilization Rate
(mg/L/d)
Benzene
1.8
88
83
1.1
0.004
7
0.004
Toluene
0.53
92
300
20.8
0.54
10
0.54
Ethyl Benzene
0.15
106
1100
1.1
0.31
10
0.31
o-Xylene
0.13
106
830
19.7
0.62
6
0.62
m-Xylene
0.175
106
982
11
0.95
13
0.95
p-Xylene
0.198
106
870
13.5
1.58
16
1.58
MTBE
48
88*
11
1.2
0.2
30
0.2
TBA
780
74
15
7
2
50
2
TAME
20
102
102
1.2
0.2
30
0.2
DIPE
9
102
102
0
0
Not Applicable
Not Applicable
ETBE
26
102
102
0
0
Not Applicable
Not Applicable
Naphthalene
0.03
128
1300
1
Not Applicable
Not Applicable
Not Applicable
EDB
4.3
188
44
0.63
Not Applicable
Not Applicable
Not Applicable
1,2-DCA
8.7
98.9
14
0.71
Not Applicable
Not Applicable
Not Applicable
* REMFuel has 78 for MTBE. The user can change this in the program.
Gasoline
Compounds
1 st Order
Rate (per
year)
Range
References
Benzene
1.1
0.1 -28
Suarez and Rifai (1999)
Re in hard et al. (2005)
Toluene
20.8
0.1 -68
Suarez and Rifai (1999)
Reinhard et al. (2005)
Ethyl Benzene
1.1
0.1 -20
Suarez and Rifai (1999)
Reinhard et al. (2005)
o-Xylene
19.7
0.1 -78
Suarez and Rifai (1999)
Reinhard et al. (2005)
m-Xylene
11
0.1 -38
Suarez and Rifai (1999)
Reinhard et al. (2005)
p-Xylene
13.5
0.1 -29
Suarez and Rifai (1999)
Reinhard et al. (2005)
MTBE
1.2
0-2
Wilson et al. (2005); Mormile et al. (1994)
TBA
7
1 -9
Wilson and Adair (2007)
TAME
1.2
0-2
Mormile et al. (1994); Somsamaket al. (2005); Professional Judgment5
DIPE
0
-
Mormile et al. (1994)
ETBE
0
-
Mormile et al. (1994)
Naphthalene
1
0.1 -19
Lewandowski and Mortimer (2003); Greve (2007)
EDB
0.63
0.22-1.3
Wilson et al. (2008)
1,2-DCA
0.71
0.22-0.9
Wilson et al. (2008)
Assumed same as MTBE according to John T. Wilson, Senior Microbiologist, GWERD, NRMRL, USEPA, Ada, Oklahoma.
Manual for REMFuel
Analytical Mathematical Model
-------
Gasoline composition data are collected from Weaver et al. (2005) and Potter and Simmons
(1998). A nationwide gasoline study was conducted by Weaver et al. (2005). Samples were collected
from active gas stations in U.S. states that used conventional and reformulated gasoline. Until 2006
reformulated gasoline was required to contain oxygen at 2% by weight and benzene was required to be
less than 1% by volume. Conventional gasoline had limits on benzene content that were set by producer
baselines. These gasoline products sometimes contain oxygenated additives, because they serve to boost
the octane rating of the fuel (Weaver et al., 2010). The following table shows the mass fraction of some
key gasoline components for different types of gasoline and oil products.
Manual for REMFuel
Analytical Mathematical Model • 24
-------
Compound mass
fraction
Benzene
Toluene
Ethyl
Benzene
0-
Xylene
m-
Xylene
P-
Xylene
MTBE
TBA
TAME
DIPE
ETBE
Napthalene
EDB
1,2-DCA
NAPL
density
(kg/L)
NAPL
mol. wt.
(g/mol)
Gasoline
(unleaded with
high MTBE)
0.006
0.059
0.01
0.051
0.051
0.051
0.12
NAA?
0
0
NAA
0.0003
NAA
NAA
0.72
105
Gasoline
(unleaded with
low MTBE)
0.0075
0.08
0.013
0.07
0.07
0.07
0.013
NAA
0
0
NAA
0.0003
NAA
NAA
0.72
105
Reformulated
Regular Grade
Gasoline
0.0066
0.0506
0.0162
0.0147
0.0267
0.0109
0.097
NAA
0.003
0
NAA
0.0053
NAA
NAA
0.72
105
Reformulated
Premium Grade
Gasoline
0.0043
0.057
0.0118
0.0167
0.0274
0.0121
0.01
NAA
0.004
0
NAA
0.0038
NAA
NAA
0.72
105
Reformulated
Regular Grade
Gasoline (MTBE
ban States)
0.0076
0.0497
0.0103
0.0147
0.0273
0.011
0.002
NAA
0
0
NAA
0.0028
NAA
NAA
0.72
105
Reformulated
Premium Grade
Gasoline (MTBE
ban States)
0.0073
0.0102
0.0179
0.0247
0.0432
0.019
0.002
NAA
0.01
0
NAA
0.0028
NAA
NAA
0.72
105
Conventional
Regular Grade
Gasoline
(Elevation <1000
ft MSL)
0.0145
0.1037
0.0224
0.0237
0.0433
0.019
0.005
NAA
4E-04
0
NAA
0.004
NAA
NAA
0.72
105
Conventional
Premium Grade
Gasoline
(Elevation <1000
ft MSL)
0.0082
0.1423
0.0153
0.0184
0.0325
0.015
0.033
NAA
0.005
0
NAA
0.0043
NAA
NAA
0.72
105
?NAA means No Analysis Available. REMFuel inputs zero as default value in place of NAA. The users have the option to change the default values.
Manual for REMFuel
Analytical Mathematical Model • 25
-------
Compound
mass fraction
Benzene
Toluene
Ethyl
Benzene
0-
Xylene
m-
Xylene
P-
Xylene
MTBE
TBA
TAME
DIPE
ETBE
Napthalene
EDB
1,2-
DCA
NAPL
density
(kg/L)
NAPL
mol. wt.
(g/mol)
Conventional
Regular
Grade
Gasoline
(Elevation
>3000 ft
MSL)
0.0166
0.0676
0.0144
0.0203
0.0385
0.0168
0.001
NAA?
0
0
NAA
0.0038
NAA
NAA
0.72
105
Conventional
Premium
Grade
Gasoline
(Elevation
>3000 ft
MSL)
0.0159
0.0644
0.0118
0.017
0.0321
0.014
5E-04
NAA
0
0
NAA
0.0028
NAA
NAA
0.72
105
Diesel
0.00026
0.0003
0.00017
0.00302
0.00302
0.00302
NAA
NAA
NAA
NAA
NAA
0.0006
NAA
NAA
0.84
230
Diesel #2
0.00029
0.0018
0.00068
0.00043
0.0011
0.0011
NAA
NAA
NAA
NAA
NAA
0.0026
NAA
NAA
0.84
230
Jet fuel JP-4
0.0047
0.016
0.0066
0.01
0.0096
0.0035
NAA
NAA
NAA
NAA
NAA
0.0025
NAA
NAA
0.85
165
Jet fuel JP-5
0
0
0
0.0009
0.0013
0
NAA
NAA
NAA
NAA
NAA
0.0057
NAA
NAA
0.85
165
Jet fuel JP-7
0
0
0
0
0
0
NAA
NAA
NAA
NAA
NAA
0.0072
NAA
NAA
0.85
165
Jet fuel JP-8
0
0
0
0.0006
0.0006
0
NAA
NAA
NAA
NAA
NAA
0.011
NAA
NAA
0.85
165
Kerosene
0
0
0
0
0
0
NAA
NAA
NAA
NAA
NAA
0.0031
NAA
NAA
0.85
170
Fuel oil #2
0
0.0006
0.00034
0.0008
0.0008
0.0008
NAA
NAA
NAA
NAA
NAA
0.0022
NAA
NAA
0.94
250
Fuel oil #6
0
0
0
0
0
0
NAA
NAA
NAA
NAA
NAA
0.000042
NAA
NAA
0.94
250
Lubricating
and Motor Oil
0.00096
0.0022
0.0011
0.0011
0.0011
0
NAA
NAA
NAA
NAA
NAA
0.00059
NAA
NAA
0.94
250
Crude oil
0.0016
0.0067
0.0017
0.0026
0.0066
0.0026
NAA
NAA
NAA
NAA
NAA
0.00069
NAA
NAA
0.88
250
Gasoline Fuel
Oil
0.019
0.081
0.017
0.025
0.046
0.019
0.003
NAA
NAA
NAA
NAA
0.0025
NAA
NAA
0.72
105
?NAA means No Analysis Available. REMFuel inputs zero as default value in place of NAA. The users have the option to change the default values.
Manual for REMFuel
Analytical Mathematical Model • 26
-------
Graphical User Interface
Projects Tab
When REMFuel is started (by double clicking on the application icon), the
default project, "REMFuel", is seen in the title window. Here is where the user
may define the project name and file location.
Once the project name is double-clicked, the tab becomes "REMFuel Project"
and the parameter entry screen is shown.
Parameter Entry
This section allows parameter entry for setting up the entire model run. The
various model input variables are described in the next section
Options for Viewing Model Output
View File Output
The text files created by the model may be viewed in either Notepad (the .inp
and .out files) or Excel (the .csv files).
View Graphical Output
Concentration or mass discharge versus distance in the x-direction for any value
of time, t can be viewed graphically by clicking on "Output vs Distance" under
"View Graphical Output". The users can view the output along any later section
and any vertical layer by selecting the Y and Z tabs in the output window.
Model output can also be viewed in a spreadsheet format that shows the
concentration or mass discharge output at any instant and space i.e., (x,y,z,t) by
clicking the 'Output Data' tab.
Manual for REMFuel
Graphical User Interface • 27
-------
Basic Operation
The following simple tutorial exercise illustrates the most basic functions and capabilities of the graphical user
interface for REMFuel. It uses the "Sample" project file that comes with the model.
1. Double-click the REMFuel icon on your desktop to start the application. You will see the following
screen:
Control
Plane
REMFuel
Remediation Evaluation Model for Fuel Solvents
Version 1.0
©REMFuel LI nil
File Model Help
Projects |
- REMFuel Projects
REMFuel;
T utorial 1
T utorial 2
LNAPL
Source
Zone
Groundwater
Flow B
Compliance I
Plane
Dissolved
Plume
Selected Project:. |REMFuel
Project Folder: | C:\Prograrn Files\REMFuel\Projects\RemFuel\
Manual for REMFuel Graphical User Interface • 28
-------
2.
Double-click on "REMFuel" under REMFuel Projects and you will see the Model Parameters screen:
©REMFuel - [REMFuel Model Parameters]
~00
^ File Model
REMFuel Project I
Help
Project: REMFuel
Model Parameters
a View Model Results
View File Output
a View Graphical Output
Output vs. Distance
Select File to View
Right Click For File Options
discharge, csv
discharge, out
REMFuel. csv
REMFuel. inp
REMFuel.out
Source Zone Parameters
Source Parameters
Gamma |~~
Source Dimensions
Source Width (m) I ~
Source Height (m) | 3
Source Length (m) | To
Flow Parameters
Darcy Velocity (m/yr) j To
Porosity | 0.3333
Source Remediation
Fraction Removed | 0-9
Source Remediation Time
30 (Years) | 31"
Start Time (T1) End Time (T2)
T ransport Parameters
Velocity
0.1
Sigmav
0.5
vMin
vMax
Number of Stream Tubes
0.5 | 0.1
alphay (m) alphaz (m)
Component Name |Benzene
Decay Rate (per year)
0 Time —>
r'enoG
T ime —>
-'eriod 1
CO
Zone 1 |
Zone 2
| Zone 3 |
¦o
o
11.3)
(2.3)
(3.3)
CL
0.0046
0.0046
0.0046
¦o
o
(1.2) |
(2.2)
(3.2)
to
0_
0.0046
0.0046
| 0.0046
-o
o
(1.1)
(2.1)
(3.1)
V
Q-
0.0046
0.0046
| 0.0046
Daughter Name ]Benzene_Daughter
Decay Rate (per year)
cn
*2 50
^ Year
<3>
E
P 30
Year '
Zone 1
Zone 2
Zone 3
o
H-3)
(2.3)
(3-3)
CL
0.0046
0.0046
0.0046
"O
o
(1-2)
(2.2)
(3-2)
0)
Q.
0.0046
0.0046
0.0046
"O
o
(1-1)
(2,1)
(3,1)
0)
CL
0.0046
| 0.0046
| 0.0046
X1 [400 X2 [700
Distance From Source. Meters
Select Component
Add Component | Delete Component j
Component Specific Parameters
Reaction Type
C Zero Order Reaction
(* First Order Reaction
Monod Reaction
Daughter Yield
From Parent
Concentration (g/L) | 0.0145 Calculate
Mass (Kg) | 1GS Calculate
Retardation Factor | T Calculate
Source Decay (1 /yr) j 0
Simulation Parameters
X • Direction
Y - Direction
Z - Direction
Time
Intervals
M in Value
0.1
-100
Max Value I Units I
T
3000.1
[ioo
[Too
[ioo
Meter
Meter
Meter
Year
REMFuel
The parameters are set to run the REMFuel sample problem. As you move the mouse over the input boxes, a
simple explanation of the input is provided in pop-up boxes.
From the Model pull-down menu, click "Run". After completion of the run. you may "View File Output" or
View Graphical Output" simply by clicking on one of these options under "View Model Results".
The "Help" menu has the links to view the user's manual and to open the indexed help window, which was
created from the user's manual.
Manual for REMFuel
Graphical User Interface • 29
-------
This is what you will see if you choose "REMFuel.inp" to view: This is the formatted text file that is used as
the input to the FORTRAN code that computes the analytical solution.
^REMFuel - [Output Files]
£3 File Model Help
REMFuel Project |
i Project: REMFuel
Model Parameters
B View Model Results
View File Output
6 View Graphical Output
Output vs. Distance
Select File to View
Right Click For File Options
discharge, csv
discharge, out
REMFuel. csv
_=lQj2SJ
"""REMFuel global variables ""source zone parameters
gamma, xremove, tl, t2
I. , 0.9, 30., 31.
""""source zone parameters
ysource (m), zsource (m), xsource (m), vd (m/yr)
10., 3., 10., 10.
"'""transport and streamtube velocity parameters
porosity, sigmav, vmin, vmax, ntubes, alphay (m), alphaz (m)
0.3333, 0.1, 0.5, 1.5, 100, 0.5, 0.1
"""distance to end of zone 1 and zone 2 for plume remediation
xl, x2 (m)
400., 700.
"""length of period 1 and period 2 for plume remediation
tplumel, tplume2 (yr)
30., 50.
"""x-directi on locations
, xmin (m), xmax (m)
101, 0.1, 3000.1
"""y-directi on locations
ny, ymin (m), ymax (m)
II, -100., 100.
"""z-direction locations
nz, zmin (m), zmax (m)
10, 0., 100.
"""times
nt, tmin, tmax
50, 0., 100.
"""number OF lnapl compounds 1oop over these
ncompounds
1
+++COMpound specific variables for lnapl component #l(Benzene)source and plume
czero(l),tzeromass(l),rates(1),retard(l),yield21(l),ireact(1)
0.0145,168.,0.,1.,0.79,1
""lnapl component 1 parent plume decay rate constants in zone 1 for 3 time periods
ratepl(l,l,l), ratepl(l,l,2j, ratepl(l,l,3) (1/yr)
0.0046,0.0046,0.0046
""LNAPL COMPONENT 1 parent p'
ratepl(l,2,1), ratepl(l,2,2;
0.0046,0.0046,0.0046
""LNAPL COMPONENT 1 parent p'
ratepl(l,3,1), ratepl(l,3,2)
0.0046,0.0046,0.0046
lnapl component 1 daughter
ratep2(l,l,l), ratepl(l,l,2)
0. 0046, 0. 0046, 0. 0046
""lnapl component 1 daughter
ratep2(l,2,1), ratepl(l,2,2)
0.0046,0.0046,0.0046
""LNAPL COMPONENT 1 daughter
ratep2(l,3,1), ratepl(l,3,2)
0.0046,0.0046,0.0046
ume decay rate constants
ratepl(l,2,3) (1/yr)
ume decay rate constants
ratepl(l,3,3) (1/yr)
in zone 2 for 3 time periods
in zone 3 for 3 time periods
plume decay rate constants in zone 1 for 3 time periods
ratepl(l,l,3) (1/yr)
plume decay rate constants in zone 2 for 3 time periods
ratepl(l,2,3) (1/yr)
plume decay rate constants in zone 3 for 3 time periods
rateplCl,3,3) (1/yr)
Manual for REMFuel
Graphical User Interface • 30
-------
Clicking on "Output vs Distance" under "View Graphical Output", and selecting Time as 44 will bring up the
following screen:
V REMFuel - [REMFuel Graphical Output]
File Model Help
REMFuel Project ]
i Project: REMFuel
; Model Parameters
S View Model Results
View File Output
B View Graphical Output
Output vs. Distance
Select File to View
Right Click For File Options
discharge, csv
discharge, out
REMFuel.csv
Jn|xJ
JSJiSl
Time |y |z |
Select Tin
2.000
4.000
G.OOO
8.000
10.000
12.000
14.000
16.000
18.000
20.000
22.000
24.000
28.000
28.000
30.000
32.000
34.000
38.000
38.000
40.000
42.000
48.000
48.000
50.000
52.000
54.000
56.000
58.000
60.000
62.000
64.000
66.000
68.000
70.000
72.000
74.000
76.000
78.000
80.000
Chart Data Option
[7 Benzene
f~ Benzene_Daughter
Graph | Output Data |
r»
File Copy To Clipboard View Tools
%# te-
i\,i •
Concentration vs. Distance at Time =44.000 Years
Y Direction = 0.000 Meters ; Z Direction = 5.000 Meters
(j 1E+000
(N CN
-------
Clicking on the "Output Data" tab above the graph will display the output in a spreadsheet format.
V REMFuel - [REMFuel Graphical Output]
File Model Help
REMFuel Project ]
^JnjxJ
-la I >1
i Project: REMFuel
; Model Parameters
S View Model Results
View File Output
B View Graphical Output
Output vs. Distance
Select File to View
Right Click For File Options
discharge, csv
discharge, out
REMFuel.csv
Time |y
|Z I
Select Time Intervals
2.000
4.000
6.000
8.000
10.000
12.000
14.000
16.000
18.000
20.000
22.000
24.000
26.000
28.000
30.000
32.000
34.000
36.000
38.000
40.000
42.000
EHH
46.000
48.000
50.000
52.000
54.000
56.000
58.000
60.000
62.000
64.000
66.000
68.000
70.000
72.000
74.000
76.000
78.000
80.000
jd
Chart Data Option
)7 Benzene
r Benzene.
Daughter
! Output
Time
*
y
z
Benzene
Benzene_Da
~
44
0.1
0
5
0
0
44
30.1
0
5
62.9087
0.231757
44
60.1
0
5
63.5558
0.467585
44
90.1
0
5
57.6833
0.636328
44
120.1
0
5
51.8202
0.76212
44
150.1
0
5
46.8532
0.861343
44
180.1
0
5
42.7686
0.943563
44
210.1
0
5
39.4099
1.01448
44
240.1
0
5
36.6345
1.07808
44
270.1
0
5
34.4603
1.14374
44
300.1
0
5
34.0034
1.27463
44
330.1
0
5
40.7577
1.75899
44
360.1
0
5
67.2937
3.26668
44
390.1
0
5
121.151
6.26342
44
420.1
0
5
184.358
9.93826
44
450.1
0
5
227.338
12.8001
44
480.1
0
5
242.068
14.3454
44
510.1
0
5
240.929
15.1026
44
540.1
0
5
235.366
15.6091
44
570.1
0
5
229.557
16.0705
44
600.1
0
5
224.264
16.529
44
630.1
0
5
219.511
16.9907
44
660.1
0
5
215.241
17.4566
44
690.1
0
5
211.401
17.9277
44
720.1
0
5
207.944
18.4046
44
750.1
0
5
204.831
18.8878
44
780.1
0
5
202.028
19.3778
44
810.1
0
5
199.504
19.8748
44
840.1
0
5
197.213
20.3762
44
870.1
0
5
195.14
20.8833
44
900.1
0
5
193.238
21.3921
44
930.1
0
5
191.458
21.8972
44
960.1
0
5
189.506
22.3542
44
990.1
0
5
187.588
22.7972
44
1020.1
0
5
185.429
23.1825
44
1050.1
0
5
181.741
23.3041
44
1080.1
0
5
178.008
23.396
Manual for REMFuel Graphical User Interface • 32
-------
Model Input Variables
LNAPL Source Parameters in REMFuel
Basic Source Parameters
Source Parameters
Gamma 1
Source Dimensions
Source Width (m) 10
Source Height (rn) | 3
Source Length (nn) 10
Gamma = power function exponent T in the source concentration versus mass function. See the 'LNAPL source
model in REMFuel' section for detail on this parameter (also see Figures 2-4). For a constant concentration source.
Gamma = 0 and for an exponentially decaying source Gamma = 1.
Source Width = source zone width perpendicular to flow, Y, m
Source Height = vertical thickness of source zone, Z, m
This is the vertical thickness from the elevation of the mean annual water table to elevation of the bottom of
the source zone contaminated with LNAPL.
Source Length = source zone length in the direction of flow. A", m
Manual for REMFuel
Model Input Variables • 33
-------
Source Parameters Related to the Chemical of Concern
Initial Source
Concentration (g/L) | 0.0145
Mass (Kg) | 168
Calculate
Calculate
Retardation Factor 1
Calculate
Source Decay (1 /yr) | 0
Concentration = initial source zone concentration; C0; flow averaged concentration of LNAPL chemical leaving the
source zone, g/L. Initial source mass can be estimated by clicking the 'Calculate' link next to the concentration input
box. The following screen will pop-up.
Benzene Initial Concentration Calculation
S elect type of N APL
Gasoline - Unleaded with hiqh MTBE
"3
Initial Concentration = Xnapl (Mole Fraction) " Cmax (Pure Solubility) * Dilution Factor
Xnapl (M ole Fraction) =
105 Molecular Wt. NAPL
88 Molecular Wt. Benzene
Xnapl Mass Fraction 0.006
Cmax (Pure Solubility] =
Dilution Factor (0.01 -1.0) =
I nitial Concentration = 0.0129 (g/L)
I? Significant Digits
0K
Cancel
The user needs to select the type of NAPL from the drop-down menu to get an estimate of initial concentration for
the chemical of concern. Also, the user lias the option to change the initial estimate during the calibration process.
Mass = initial source zone contaminant mass, M0, kg. This value can be estimated by clicking the 'Calculate' link
next to the mass input box. The following screen will pop-up.
Manual for REMFuel
Model Input Variables • 34
-------
MTBE Initial Concentration Calculation (- ~ || X |
i ¦
1 Select time of NAPL rf-lMM-Bllil'-l-S
5il'JlHiliTTilili!SHHa
J
Initial Mass = Xnapl (Mass Fraction) 'Volume NAPL * Density of NAPL
Set Volume of NAPL =
0 Unit |LIS Gallon ~
Xnapl (Mass Fraction) =
0.12
Density of NAPL =
0.74
Initial Mass = 0 (kg)
|7 Significant Digits | 3
OK
Cancel
1 1
Retardation Factor = Retardation factor for each dissolved species, R. Different values of retardation can be
assigned to different chemicals of concern. However, it is assumed to be the same for parent-daughter components.
The retardation factor for each chemical of concern can be estimated by clicking the 'Calculate' link next to the
mass input box. The following screen will pop-up.
Calculate Retardation Factor
Retardation Factor
Kgc [L/Kgj iT
Foe (-) | 0.002
Bulk Density (Kg/L) | Ts
Porosity = 0.3333
(11)(0.002](1.6)
Retardation Factor = 1 +
0.3333
Retardation Factor = 1.11
1^ Significant Digits I3
OK
Cancel
Organic carbon partition coefficient (K,„¦). soil fraction of organic carbon (F,„¦). bulk density of soil, and porosity
input are required to get the initial estimate of R. The user lias the option to change the initial estimate during the
calibration process.
Manual for REMFuel
Model Input Variables • 35
-------
Source Decay = First order aqueous phase biodecay of the component in the source zone, Xs, 1/yr
Flow Parameters
Flow Parameters
Darcy Velocity (rn/yr) 10
Porosity | 0.3333
Darcv Velocity = Darcy flux (velocity) in the flow system, Im/yr. The chemical velocity without retardation due
to sorption, (which is also the pore velocity, v) is equal to the Darcy velocity divided by the porosity ((j> ). The total
flow rate through the source zone, O 11Z.
Porosity = effective porosity, (j)
Source Remediation
Source Remediation
Fraction Removed 0.9
Source Remediation Time
30
IV ears) | 31
Start Time (T1) End Time (T2)
Fraction Removed = Fraction A'of source mass at time that is removed by source remediation activities. This
fraction is assumed to be the same for all components in the source zone. 0
-------
Transport Parameters
T ransport Parameters
Velocity
0.1 | 05 | 15
Sigrnav vMin vMax
Number of Stream Tubes
alphay (m) alphaz (m)
100
oT
Sigmav = Coefficient of variation for velocity field, equal to the ratio of the pore velocity standard deviation,
divided by the mean pore velocity, cr, / v . This results in a scale-dependent dispersivity that is equal to
Vi(sigmav)2 x , where X is the average front location at a given time. A sigmav value of 0.1 results in a
longitudinal dispersivity equal to 1/200 of the travel distance; a sigmav value of 0.44721 results in a
longitudinal dispersivity equal to 1/10 of the travel distance. The table below gives Sigmav values
corresponding to different longitudinal dispersivities:
CCX
Sigmav
x/200
0.1
x/100
0.14142
x/50
0.2
x/20
0.31623
x/10
0.44721
vMin = minimum normalized streamtube velocity. Typically set equal to 0, except when very small sigmav is
used. In that case, vmi„ can be somewhat larger (e.g. 0.5), and still effectively capture the full velocity
range. Ideally, vmi„ and vmax would be symmetrical around 1, but this is limited by the restriction that vmjn
must be positive.
vMax = maximum normalized streamtube velocity. Magnitude depends on sigmav. For small sigmav (~0.1),
vmar~1.5. For moderate sigmav (-0.25), vmar~2.0. For large sigmav (-0.447), vmar~3.0.
Number of Stream Tubes = number of streamtubes used to simulate longitudinal dispersion. The more tubes used,
the smoother the solution will look, but the longer it will take to compute; problem execution time is
directly proportional to the number of streamtubes used. A solution calculated with only 10 streamtubes
will still represent the dispersion reasonably well in many cases, but it will not be "smooth". A solution
calculated with 500 streamtubes will usually be smooth but it will take 50 times longer to compute. In
general, the problem run time in seconds is roughly equal to the number of stream tubes times the number
of x locations where the solution is evaluated, times the number of times when the solution is evaluated,
divided by -200,000. A maximum of 10,000 streamtubes can be used.
alphay = Transverse dispersivity, a v, constant value in m. This is generally 1/10 or less of the effective
longitudinal value. If a negative value is used, the transverse dispersivity is scale-dependent, with a value
equal to the travel distance multiplied by the absolute value of alphay.
alphaz = Vertical dispersivity, a _, constant value in m. This is generally 1/100 or less (perhaps much less) of the
effective longitudinal value. If a negative value is used, the vertical dispersivity is scale-dependent, with a
value equal to the travel distance multiplied by the absolute value of alphaz.
Manual for REMFuel
Model Input Variables • 37
-------
Component Setup and Reaction
For each selected component, the user is allowed to set the initial source parameters (discussed above). The user can
also select from three optional reaction types, zero order, first order or Monod's reaction. Each reaction type lias its
own reaction matrix which allows the user to specify three reaction zones in space as well as three reaction time
periods. Below are example input screens for each reaction type for the component benzene:
Zero Order:
Component Name [Benzene
Select Component
Time —>
' Period 2
a>
.i [30^
I— Time —>
Period 1
Decay Rate (mg/L/day)
Zone 1
| Zone 2
Zone 3 |
"O
o
(1.3)
(2.3)
(3.3)
CL
0.0046
0.0046
0.0046
-o
o
(1.2)
(2.2)
(3,2)
CL
0.0046
0.0046
0.0046
7—
¦a
0
(1.1)
(2.1)
(3.1)
OJ
Q.
0.0046
0.0046
0.0046
X1
[W
X2
[too
Distance From Source, Meters
Component Specific Parameters
Reaction Type
Zero Order Reaction
C First Order Reaction
r Monod Reaction
Initial Source
Concentration (g/L) f
Mass (Kg) |"
Retardation Factor [
Source Decay (1 /yr) |"
0.0145 Calculate
Calculate
1 Calculate
Benzene
Add Component
Delete Component
Manual for REMFuel
Model Input Variables
-------
First Order:
Component Name |Benzene
Select Component
(so-
if}
k_
(U
® Time —>
Period 2
130
Time —>
Period 1
Decay Rate (per year)
ro
Zone 1
Zone 2
Zone 3 |
T5
o
(1,3)
(2,3)
(3,3)
0-
0.0046
0.0046
0.0046
"O
o
(1,2)
(2,2)
(3.2)
v
CL
0.0046
0.0046
0.0046
¦o
o
(1,1)
(2,1)
(3,1)
0)
CL
0.0046
0.0046
0.0046
Daughter Name |Benzene_Daughter
cu
0
>-
£
50
Year
30
Year '
Decay Rate (per year)
CO
Zone 1
Zone 2
Zone 3 |
"o
o
(1,3)
(2,3)
(3.3)
0.
0.0046
0.0046
0.0046
¦o
o
(1,2)
(2,2)
(3,2)
CL
0.0046
0.0046
0.0046
¦o
o
(1,1)
(2,1)
(3,1)
a>
CL
0.0046
0.0046
| 0.0046
XI [400 X2 1700
Distance From Source, Meters
Component Specific Paiametets
Reaction Type
C Zero Order Reaction
(* jFirst Order Reaction
C Monod Reaction
Daughter Yield
From Parent
0.79
Initial Source
Concentration (g/L) | 0.0145 Calculate
Mass (Kg) [*
Retardation Factor |"
Source Decay (1/yr) |
168 Calculate
1 Calculate
Benzene
Add Component
Delete Component
Monod's Reaction:
I Component Name |Benzene I
Select Component
"1 Icn
h/lax Utilization Rate (mg/L/day) |
Period 3
Zone 1
Zone 2
Zone 3 |
(1,3)
(2,3)
(3.3)
to |J,J
fli X ima X
0.0046
0.0046
0.0046
^ I ime
' Period 2
^ Year
a>
E
P v30 ->
rear
Component Specific Parameters
CO
Zone 1 |
Zone 2 |
Zone 3 |
Reaction Type
-O "
o
(1,3)
(2,3)
(3,3)
C Zero Order Reaction
C First Order Reaction
u
CL
0.0046
0.0046
0.0046
(• !Monod Reaction I
CM
•a
o
(1,2)
(2.2)
(3.2)
0)
CL
0.0046
0.0046
0.0046
Initial Source
¦o
o
(1,1)
(2,1)
(3,1)
Concentration fq/'Ll | 0.0145 Calculate
u>
CL
0.0046
0.0046
0.0046
Mass (Kg) | 168 Calculate
A A
Retardation Factor | 1 Calculate
XI |400 X2 |700
Source Decay (1 /yr) | 0
I Distance From Source, Meters
Manual for REMFuel
Model Input Variables
-------
Simulation Output Parameters
A - Direction = Enter the number of x values desired (intervals), and the
minimum and maximum values of x used for plotting. The minimum
x value should be greater than zero (the solution is singular at x=0).
The problem run time is a linear function of the number of x intervals
specified, but this has no effect on solution accuracy. The maximum
number of x values is 200.
Y - Direction = Enter the number of y values desired (intervals), and the
minimum and maximum values of v used for plotting. This is mainly
used for producing x-v contour plots. The maximum number of v
values is 50. If only center-line plots are needed, the number of v
intervals can be set to 1, with the min and max value equal to 0. The
model run time depends somewhat on the number of y-direction values
calculated.
Z - Direction = Enter the number of z values desired (intervals), and the
minimum and maximum values of z used for plotting. This is mainly
used for producing x-v-z or x-z contour plots. If only center-line plots
are needed, the number of z intervals can be set to 1, with the min and
max value equal to 0. Note that z=0 corresponds to the plane of the
horizontal no flow boundary for dispersion; this location gives the
maximum concentration at a given x-y location.
Time = Enter the number of time values desired (intervals), and the minimum
and maximum values of time used for plotting. The problem run time
is a linear function of the number of time intervals specified, but this
has no effect on the concentration solution accuracy.
X - Direction
Y • Direction
2 • Direction
Intervals
Min Value
Max Value |
101
0.1
2000.1
Time |l 00
~[°~~
~|200
Manual for REMFuel
Model Input Variables • 40
-------
REMFuel Tutorials
Tutorial 1
Reactive Transport of BTEX and MTBE with Remediation
This problem involves a hypothetical release of BTEX and MTBE (gasoline spill) from an aqueous source zone
(beneath a lens of product sitting on the water table). The source contains 5 LNAPL components (benzene, toluene,
xylenes, ethylbenzene, and MTBE with TBA produced as a daughter product). The source concentrations reflect
Raoult's law partitioning with typical gasoline compositions, and the source masses reflect a 5,000 gallon gasoline
release. Aqueous phase biodegradation of the LNAPL compounds in the source zone is included for all components
except MTBE. The source parameters are listed in the table below. This example problem makes use of all three
biodegradation reaction mechanisms: Zero Order, First Order, and Monod kinetics.
Component#
chemical
Mole
fraction
in
gasoline
Pure
aqueous
solubility
g/1
Source
zone
aqueous
decay rate
1/yr
Initial
source
mass,
kg
Initial source
concentration,
g/L
Retardation
factor
1
MTBE
.10
50.
1.39
1500
5.00
1.0
2
Benzene
.01
1.8
.693
150
0.018
1.5
3
Toluene
.05
0.5
1.39
750
0.025
2.0
4
Xylenes
.1
.2
1.39
1500
0.020
2.5
5
Ethylbenzene
.02
.2
1.39
300
0.004
2.0
1-daughter
TBA
0
-
-
-
-
1.0
The source volume is 10m by 10m by lm thick with a water flux of 20 m/yr. The components undergo various
plume reactions and MTBE produces TBA as a daughter.
Source remediation occurs at year 10, with 90% removal of the remaining mass of all compounds. Plume
remediation occurs from years 10 to 12, and the reaction rates are increased by a factor of 10 during this time.
Benzene, uses the Monod kinetics reaction, with u„,ax = 0.01 mg/L/d and Kc = 2 mg/L.
Manual for REMFuel
REMFuel Tutorials • 41
-------
Toluene uses the Monod kinetics reaction, with fimax = 0.01 mg/L/d and Kc =.01 mg/L.
Xylenes (represented in tliis tutorial by o-Xylene), uses the Monod kinetics reaction, with = 0.01 mg/L/d and
Kc = 1000 mg/L.
Ethylbenzene uses the zero order reaction with a rate constant of y = 0.01 mg/L/d.
MTBE uses the first order reaction with a rate constant of k = 0.0365/yr, and it produces TEA, which is given the
same reaction rate.
The following are the Model Parameters screens for each component:
Benzene:
© REMFuel - [REMFuel Model Parameters]
Y File Model
REMFuel Project I
Help
Project: T utorial 1
Model Parameters
S View Model Results
View File Output
8 View Graphical Output
Output vs. Distance
Source Zone Parameters
Source Parameters
Gamma [ '
Source Dimensions
Source Width (m) | 7i
Source Height (m) [ 1
Source Length (m) | To
Flow Parameters
Darcy Velocity (m/yr) | 20
Porosity | 0.3333
Source R emediation
Fraction Removed | O S
Source Remediation Time
10 (V ears] | ~
Start Time (T1) End Time (T2)
T ransport Parameters
Velocity
0.1
Sigmav
0.5 | 1.5
vMin vMax
Number of Stream Tubes
r
100
0.5 |~
0.1
alphay (m) alphaz (m)
Component Name (Benzene
Time —>
' Period 2
© ,
,i 10
I— Time— >
Period 1
Man Utilization Rate Img/L/dayl
Zone 1
(1.3)
Zone 2
(2.3)
(1.2)
(1.1)
(2.2)
(2.1)
Zone 3 ~|
(3.3)
(3.2)
(3,1)
en
to
£ 12
Year
|