EPA/600/R-94/039b
April 1995
The Hydrocarbon Spill Screening Model (HSSM)
Volume 2: Theoretical Background and Source Codes
by
Randall J. Charbeneau
Center for Research in Water Resources
The University of Texas at Austin
Austin, Texas 78712
James W. Weaver and Bob K. Lien
Robert S. Kerr Environmental Research Laboratory
United States Environmental Protection Agency
Ada, Oklahoma 74820
Robert S. Kerr Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Ada, Oklahoma 74820
Printed on Recycled Paper
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Disclaimer
The research described in this report has been supported by the United States Environmental
Protection Agency under cooperative agreement CR-813080 to The University of Texas at Austin, and by
direct support of the EPA authors, it has been subjected to Agency 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.
All research projects funded by the U.S. Environmental Protection Agency that make conclusions
or recommendations based on environmentally related measurements are required to participate in the
Agency Quality Assurance Program. The experimental work described in section 2.7 was conducted under
an approved Quality Assurance Project Plan and the procedures, specified therein were used. Information
on the plan and documentation of the quality assurance activities are available from the second author.
The computer program described within this report simulates the behavior of water-immiscible
contaminants (LNAPLs: Non-Aqueous Phase Liquids) in idealized subsurface systems. The approaches
described are not suited for application to heterogeneous geological formations nor are they applicable to
any other scenario other than that described herein. The model is intended to provide order-of-magnitude
estimates of contamination levels only. The full model has not been verified by comparison with either lab
or field studies. Therefore the EPA does not endorse the use of this computer program for any specific
purpose. As in the case of any subsurface investigation, the scientific and engineering judgement of the
model user is of paramount importance. Any model results should be subjected to thorough analysis. In
this user's guide, typical values are given for various parameters. These are provided for illustrative
purposes only.
When available, the software described in this document is supplied on an "as-is" basis without
guarantee or warranty of any kind, expressed or implied. Neither the United States Government (United
States Environmental Protection Agency, Robert S. Kerr Environmental Research Laboratory), The
University of Texas at Austin, nor any of the authors accept any liability resulting from the use of this
software.
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Foreword
EPA is charged by Congress to protect the Nation's land, air and water systems. Under a mandate
of national environmental laws focused on air and water quality, solid waste management and the control
of toxic substances, pesticides, noise and radiation, the Agency strives to formulate and implement actions
which lead to a compatible balance between human activities and the ability of natural systems to support
and nurture life.
The Robert S. Kerr Environmental Research Laboratory is the Agency's center of expertise for
investigation of the soil and subsurface environment. Personnel at the Laboratory are responsible for
management of research programs to: (a) determine the fate, transport and transformation rates of
pollutants in the soil, the unsaturated and the saturated zones of the subsurface environment; (b) define
the processes to be used in characterizing the soil and subsurface environments as a receptor of pollutants;
(c) develop techniques for predicting the effect of pollutants on ground water, soil, and indigenous
organisms; and (d) define and demonstrate the applicability of using natural processes, indigenous to the
soil and subsurface environment, for the protection of this resource.
One of the most common, yet complex, class of subsurface contaminants is the light nonaqueous
phase liquids (LNAPLs). Although the LNAPL itself remains distinct from the subsurface water, chemical
constituents of the LNAPL can cause serious ground-water contamination. Since a number of phenomena
and parameters interact to determine contaminant concentrations at the receptor points, models are needed
to estimate the impacts'of LNAPL releases on ground water. This volume describes the theoretical basis
for the Hydrocarbon Spill Screening Model (HSSM) which is intended to simulate release of an LNAPL. The
intent of the model is to provide a practical tool which is easy to apply and runs rapidly on personal
computers.
Clinton W. Hall, Director
Robert S. Kerr Environmental
Research Laboratory
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Abstract
A screening model for subsurface release of a nonaqueous phase liquid which is less dense than
water (LNAPL) is presented. The model conceptualizes the release as consisting of 1) vertical transport
from near the surface to the capillary fringe, 2) radial spreading of an LNAPL lens through the capillary
fringe and dissolution of LNAPL constituents into a water table aquifer, and 3) transport in the flowing
ground water to a potential exposure location. Each component of the conceptual model is treated as a
distinct process by separate models. This report describes the modules for the vadose zone, lateral
spreading at the water table and dissolution of constituents into the aquifer, and aquifer transport of the
dissolved constituents to receptor points. Spreading of the hydrocarbon lens and dissolution of
hydrocarbon constituents are transient phenomena, and the aquifer transport model must be capable of
addressing a time-variable source term. This is incorporated through application of Duhamel's principle to
a gaussian-source plume model. The resulting screening model is computationally efficient and has only
moderate parameterization requirements.
IV
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CONTENTS
Disclaimer .,..:.. . : ii
Foreword iii
Abstract ...... iv
List of Figures '. .... -......... . vii
List of Symbols . . ix
List of Abbreviations and Acronyms . :..... xii
Acknowledgement xiii
Section 1 Introduction " 1
1.1 Model Overview 1
1.2 Obtaining a Copy of HSSM '. 3
1.3 Volume 2 Organization . 4
Section 2 Flow and Transport in the Vadose Zone 5
2.1 KOPT Model Framework 6
2.2 Derivation of the Vadose Zone NAPL Flow Model 7
2.3 Derivation of the Vadose Zone Transport Model 15
2.4 Summary of Approximate Governing Equations for the KOPT Module 17
2.5 Model Implementation 17
2.6 General Features of the KOPT Solution 18
2.7 Experimental Results and Simulation 18
2.8 Closure on the KOPT model _•....'. 27
Section 3 NAPL Lens Formation at the Capillary Fringe and Source Term Characterization 28
3.1, OILENS Model Development 31
Section 4 Gaussian-Source Plume Model • 39
Section 5 The Response of HSSM to Parameter Variation . 47
5.1 Base Scenario 47
5.2 Usage of Parameters in HSSM 51
5.3 Sensitivity Results 53
5.4 HSSM Response: Increasing Peak Concentration, Constant Arrival Time 54
5.4.1 Initial Constituent Concentration in the NAPL . 54
5.5 HSSM Response: Increasing Peak Concentration, Increasing Arrival Time 55
5.5.1 Source Radius 55
5.6 HSSM Response: Decreasing Peak Concentration, Increasing Arrival Time 56
5.6.1 Depth to water . 56
5.6.2 Porosity and bulk density 57
5.6.3 NAPL viscosity 57
5.6.4 Vadose zone residual NAPL saturation 58
5.6.5 Soil/water partition coefficient for the constituent 60
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5.6.6 NAPL/water partition coefficient for the constituent 60
5.6.7 Smear zone thickness 61
5.7 HSSM Response: Decreasing Peak Concentration, Constant Arrival Time 63
5.7.1 Aquifer thickness (less than penetration thickness) . . . 63
5.7.2 Transverse horizontal dispersivity 63
5.8 HSSM Response: Decreasing Peak Concentration , Decreasing Arrival Time 65
5.8.1 Ratio of horizontal to vertical conductivity 65
5.8.2 Gradient ' 65
5.8.3 Transverse vertical dispersivity 67
5.8.4 All dispersivity 67
5.8.5 Percent maximum radius 68
5.8.6 Constituent half-life '.'.'.'.'.'.'.'.'.'. 68
5.9 HSSM Response: Constant Peak Concentration, Decreasing Arrival Time 71
5.9.1 Saturated vertical conductivity 71
5.10 HSSM Response: Increasing Peak Concentration, Decreasing Arrival Time 72
5.10.1 Recharge 72
5.10.2 Longitudinal dispersivity 72
5.10.3 Residual water saturation 74
5.10.4 van Genuchten's n 74
5.10.5 Source flux 75
5.10.6 NAPL saturation in the lens 75
5.11 HSSM Response: Constant Peak Concentration, Constant Arrival Time -. 77
5.11.1 van Genuchten's a 77
5.11.2 Water surface tension 77
5.11.3 Maximum water phase relative permeability during infiltration 78
5.11.4 NAPL surface tension 78
5.11.5 NAPL density '.'.'.'.'.'.'.'.'. 7Q
5.11.6 Aquifer residual NAPL saturation 78
5.11.7 NAPL/water interfacial tension 78
5.11.8 Capillary thickness parameter 78
Section 6 Discussion 83
References 84
Appendix 1 Evaluation of the Volume Integral 88
Appendix 2 Summary of KOPT and OILENS Sensitivity Results 91
Appendix 3 FORTRAN Source Codes for HSSM and the Utility Programs 99
3.1 Source Code for HSSM-KO 99
3.2 Source Code for HSSM-T 197
3.3 Source Code for NTHICK '.'.'.'.'.'.'.'..'.'.'.'. 227
3.4 Source Code for RAOULT 234
3.5 Source Code for REBUILD 240
3.6 Source Code for SOPROP 255
3.7 Compilation with Microsoft FORTRAN '.'.'.'.'.'. 259
vi
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List of Figures
Figure 1 Schematic view of the Hydrocarbon Spill Screening Model (HSSM) scenario 2
Figure 2 Schematic comparison of sharp and diffuse fronts 6
Figure 3 Base characteristic plane 7
Figure 4 Total liquid profiles . . -8
Figure 5 KOPT model release scenarios 14
Figure 6 Upstream characteristic and front speeds 19
Figure 7 Glass column used for the laboratory evaluation of KOPT 20
Figure 8 Measured NAPL position at right-hand edge, center and left-hand edge of column 20
Figure 9 Measured NAPL ponding depth at the surface of the sand 21
Figure 10 Measured distribution of hydraulic conductivity in the sand pack 23
Figure 11 Data from two measured capillary pressure curves for the c109 sand and the fitted
Brooks and Corey model (solid line) 24
Figure 12 Nondimensional sensitivity coefficients for the Green-Ampt portion of the simulation
B parameter set 25
Figure 13 Nondimensional sensitivity coefficients for the kinematic portion of the simulation B
parameter set 26
Figure 14 Calculation of LNAPL thickness in an oil lens 30
Figure 15 Effective saturation of a hydrocarbon in a sand 31
Figure 16 Volume balance for the source cylinder 32
Figure 17 Plan view of the oil lens . 35
Figure 18 Residual volume for decaying mound . • 38
Figure 19 Basic setup of the gaussian-source plume model 40
Figure 20 Development of mixing zone beneath the facility 40
Figure 21 Gaussian distribution which is taken as the boundary condition at the downstream
extent of the area beneath the facility 42
Figure 22 Concentration histories for the X2BT.DAT data set 49
Figure 23 Plan view of HSSM model scenario 49
Figure 24 Concentration Histories at 50 meters for benzene, toluene and the xylenes . 50
Figure 25 Possible HSSM responses to parameter variation 50
Figure 26 NAPL lens radius and aqueous concentration for the example 2 data set 51
Figure 27 Pie chart showing frequency of parameter variation responses 53
Figure 28 Peak concentration vs arrival time for variation in the initial contaminant
concentration 55
Figure 29 Peak concentration vs arrival time for variation in the source radius 56
Figure 30 Peak concentration vs arrival time for variation of depth to water 58
Figure 31 Peak concentration vs,arrival time for variation of porosity and bulk density 59
Figure 32 Peak concentration vs arrival time for variation of the NAPL viscosity 59
Figure 33 Peak concentration vs arrival time for variation of the vadose zone residual NAPL
saturation • 60
Figure 34 Peak concentration vs arrival time for variation of the soil water partition coefficient
for the constituent • • • • • 61
Figure 35 Peak concentration vs arrival time for variation of the NAPL/water partition coefficient ... 62
Figure 36 Peak concentration vs arrival time for variation of the smear zone thickness 62
Figure 37 Peak concentration vs arrival time for variation of the aquifer thickness 64
Figure 38 Peak concentration vs arrival time for variation of transverse dispersivity 64
Figure 39 Peak concentration vs arrival time for variation of the ratio of horizontal to vertical
conductivity • 66
Figure 40 Peak concentration vs arrival time for variation of the hydraulic gradient 66
Figure 41 Peak concentration vs arrival time for variation of transverse vertical dispersivity 67
vii
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Figure 42 Peak concentration vs arrival time for variation of all dispersivities (longitudinal,
transverse and vertical) 68
Figure 43 Transverse horizontal concentration profiles for the variation in all the dispersivities 68
Figure 44 Peak concentration vs arrival time for variation of the percent maximum radius 69
Figure 45 Peak concentration vs arrival time for variation of the constituent decay rate 70
Figure 46 Concentration history for a degrading constituent 70
Figure 47 Peak concentration vs arrival time for variation of the saturated hydraulic conductivity ... 71
Figure 48 Peak concentration vs arrival time for variation of recharge 73
Figure 49 Peak concentration vs arrival time for variation of the longitudinal dispersivity 73
Figure 50 Peak concentration vs arrival time for variation of the residual water saturation 74
Figure 51 Peak concentration vs arrival time for variation of van Genuchten's n 75
Figure 52 Peak concentration vs arrival time for variation of source flux 76
Figure 53 Peak concentration vs arrival time for variation of the NAPL saturation in the lens 76
Figure 54 Peak concentration vs arrival time for variation of van Genuchten's a 79
Figure 55 Peak concentration vs arrival time for variation of the water surface tension 79
Figure 56 Peak concentration vs arrival time for variation of the maximum water phase relative
permeability during infiltration 80
Figure 57 Peak concentration vs arrival time for variation of the NAPL surface tension 80
Figure 58 Peak concentration vs arrival time for variation of the NAPL density 81
Figure 59 Peak concentration vs arrival time for variation of the aquifer residual NAPL
saturation 82
Figure 60 Peak concentration vs arrival time for variation of the NAPL/water interfacial tension .... 82
Figure 61 Peak concentration vs arrival time for variation of the capillary thickness parameter 82
Rgure 62 Representation for the lens volume 88
VIII
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List of Symbols
Latin
A
av
B
B(o>)
b
b0
C
c, cw
cm
C0
Co(soll)
Co(surf.)
cs
Cw(initiai)
DL
DT
E
erf()
erfcQ
Ft
G
g
H
Hdis
Hf
h
hcao
hca«
hcij
hcea
hcea
hn
Area
Aquifer vertical dispersivity
Bulk partition coefficient defined by equation (25)
Time varying function of concentration at boundary (equation (86))
Aquifer saturated thickness
Observation well thickness of NAPL
Nondimensional concentration (equation (81))
Concentration of the constituent in the water phase
Maximum concentration
Concentration of the constituent in the NAPL phase
Constituent concentration in the NAPL in equilibrium with the soil
Constituent concentration in the released NAPL
Sorbed phase concentration of the constituent
Initial water phase concentration of the constituent
Equilibrium constituent concentration for water in contact with the NAPL
Nondimensional dispersion coefficient (equation (81))
Formation free-product thickness
Longitudinal dispersion coefficient
transverse horizontal dispersion coefficient
Vertical dispersion coefficient
Depth of the NAPL contaminated zone
Constant defined by equation (93)
Error function
Complementary error function
OILENS NAPL source head function
OILENS lens radius function
nth function to be solved for a general Runge-Kutta scheme
Known constant that relates lens source heads and radii at different times
Acceleration of gravity
Sum of the NAPL head terms in KOPT; Total penetration depth of leachate in TSGPLUME
Penetration depth due to vertical advection of water entering the aquifer
Penetration depth due to vertical dispersion in the aquifer
NAPL head at the NAPL front ,
NAPL head at the surface
Pressure head in KOPT (equation (16))
Air-NAPL capillary pressure head
Air-water capillary pressure head
Capillary pressure head or capillary rise for the i-j fluid pair
Air-NAPL entry head
Air-water entry head
NAPL head at a given location
NAPL head in the lens below the source (Figure 16)
NAPL-water capillary pressure head
Value of the integral in equation (56)
Rate of infiltration outside the facility
Advective flux
IX
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K
L
L(y)
M,
f"c
m
n
Pi
QKOPT
Q
•
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VL
V0
VT
Vvz
'VS2
v
W
w
WR,WRS
X
x
Y
y.,,y2,.
Z
.,yn
Greek
P
AML
AVL
AVR
8m(y)
6
T|
A
A,
X*
Mi
Mo
Pb
Pi
Po
Pw
a
orv
3ors
NAPL volume in the spreading lens
NAPL volume incorporated into the soil in KOPT
Total lens volume (including LNAPL, water and soil)
Total lens volume (including LNAPL, water and soil) in the vadose zone
Total lens volume (including LNAPL, water and soil) in the saturated zone
Seepage velocity in the aquifer
Width (across the direction of ground water flow) of a surface facility
Variable of integration in equations (55) and (95)
Limits of integration in equation (95)
Nondimensional x coordinate (equation (81))
Distance from upgradient edge of NAPL lens
Nondimensional y coordinate (equation (81))
1st through nth independent variable
Nondimensional z coordinate (equation (81))
Depth
Level of the air-NAPL interface
Level of the air-water interface (water table) in the absence of NAPL
Level of the NAPL-water interface
Front depth in KOPT
Density term in equation (36)
Constituent mass loss from NAPL lens during a time step
Volume of free product (LNAPL) that becomes trapped in a time step
Change in total lens volume (LNAPL, water and soil)
Increment of mass flux into the aquifer
Brooks and Corey relative permeability exponent
Porosity
Nondimensional effective decay coefficient in TSGPLUME (equation (81))
Brooks and Corey capillary pressure exponent; Decay coefficient in TSGPLUME
Effective decay coefficient in TSGPLUME
Dynamic viscosity of fluid i
Dynamic viscosity of the NAPL
Bulk density
Density of fluid i
Density of NAPL
Density of water
Standard deviation
Water surface tension
NAPL surface tension
NAPL-water interfacial tension
Volumetric NAPL content
Volumetric residual NAPL content in the vadose zone
Volumetric residual NAPL content in the aquifer
XI
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List of Abbreviations and Acronyms
CSMoS
HSSM
HSSM-KO
HSSM-T
KOPT
LNAPL
NAPL
OILENS
RSKERL
TSGPLUME
USEPA
Center for Subsurface Modeling Support
Hydrocarbon Spill Screening Model
Computer code that implements KOPT and OILENS
Computer code that implements TSGPLUME
Kinematic Oily Pollutant Transport (vadose zone portion of HSSM)
Lighter-that-water nonaqueous phase liquid
Nonaqueous phase liquid
HSSM Module for NAPL lens motion and chemical dissolution into the aquifer
Robert S. Kerr Environmental Research Laboratory
Transient source gaussian plume model (aquifer module of HSSM)
United States Environmental Protection Agency
XII
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Acknowledgement
The authors wish to express their appreciation to Julia Mead and Sarah Hendrickson for the
simulation runs and graphics presented in Section 5 on parameter variation.
XIII
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Section 1 Introduction
The subsurface release of a liquid hydrocarbon from a spill or a leaking tank or pipeline is of
concern because the hydrocarbon phase or its constituents may migrate through the subsurface •
environment to contaminate drinking water supplies or fresh water resources. With a near-surface release,
the hydrocarbon must migrate vertically through the vadose zone before reaching ground water. Capillary
forces play an important role in determining the transport times and rates for constituents reaching the
water table. If the nonaqueous phase accumulates at the water table in sufficient quantities, it will build
sufficient head to cause radial spreading. At the same time, its constituents will dissolve into ground water
flowing beneath the lens and be transported to potential downgradient receptor locations. A detailed
analysis of such a release using site-specific models would require a significant computational expense as
well as vast resources for characterization of required physical and chemical parameters.
For many applications such resources are not available, especially during the initial phases of a
site investigation or in the analysis of impacts from potential releases. In such cases, screening models
provide appropriate tools for investigation. These models are based on a simplified interpretation of the
hydrogeology, including generally the assumption of uniform aquifer flow in a specified direction and
homogeneous conditions for other parameters. These assumptions allow the use of analytic or semi-
analytic solutions to the transport problem. Analytic solutions have the advantage of simplicity and ease
of computation. Screening models may be developed which capture, in an approximate sense, many of
the important factors and processes which control the fate and behavior of subsurface contaminants. Such
models may then be used to evaluate the behavior of large numbers of chemicals in the environment.
The Hydrocarbon Spill Screening Model (HSSM) described herein is such a model. The basic
scenario of the model is shown in Figure 1. A hydrocarbon is released near the ground surface and
transported downward through the vadose zone to the water table. At the water table a hydrocarbon lens
forms and spreads laterally. Constituents from the hydrocarbon lens dissolve into ground water flowing
beneath the lens, creating a plume which may contaminate downgradient wells or other exposure points.
HSSM may be used to estimate the effects of LNAPL loading, partition coefficients, ground water flow
velocities, etc., on pollutant transport. Since numerous approximations are used for developing the model,
the model results must also be viewed as approximations.
1.1 Model Overview
The following paragraphs provide an overview of the HSSM model and discuss some of the model
assumptions and limitations. The spill or release of the LNAPL phase may be simulated in three basic
ways. First is a release of a known LNAPL flux for a specified duration. The release occurs at the ground
surface. Based on an approximate capillary suction relationship, some of the LNAPL may run off at the
surface if the flux exceeds the maximum effective LNAPL infiltration capacity. Second, a constant depth
of ponded LNAPL, for a known duration, may also be specified. This case represents a slowly leaking tank,
or a leaking tank within an embankment. A generalization of this scenario is that a constant depth may
by specified for a given duration, with the subsequent period modeled based on continuity between the
remaining ponded depth and the cumulative infiltration. This scenario, with a short initial constant ponded
depth duration, may be appropriate for modeling an extreme containment failure for a tank within a
contained or bermed area. Lastly, a known volume of LNAPL may be placed over a specified depth of the
soil. This last scenario represents either a land treatment operation or a landfill containing a known amount
of contaminants at the beginning of the simulation.
Transport of the NAPL through the unsaturated zone is assumed to be one-dimensional. Capillary
. 1
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VADOSE ZONE
YDROCA
GROUNDWATER
FLOW
RECEPTOR
WELL
Figure 1 Schematic view of the Hydrocarbon Spili Screening Model (HSSM) scenario
pressure gradients are neglected except as they influence the infiltration of NAPL into the soil. The
resulting equations for NAPL flow are hyperbolic and are solved by the generalized method of
characteristics. When relatively large amounts of LNAPL are released, downward transport of the LNAPL
(say gasoline) is the primary mechanism for downward transport of hydrophobic chemicals (e.g., benzene,
toluene, and xylene). Assumptions concerning aquifer recharge are relatively unimportant in this case. If
a large enough volume is supplied, the LNAPL reaches the water table. If sufficient head is available, the
water table is displaced downward, lateral spreading begins, and the oil lens part of the model is triggered.
Spreading is assumed to be radial, and, the thickness of the lens is determined by buoyancy only (Ghyben-
Herzberg relations). The shape of the lens is given by the Dupuit assumptions, where the flow is assumed
horizontal and the gradient is independent of depth.
The LNAPL is treated as a two-component mixture. The LNAPL itself is assumed to be soluble
[Section 1 Introduction] 2
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in water and sorbing. Due to the effects of the recharge water and contact with the ground water, the
LNAPL may be dissolved. The LNAPL's transport properties (density, viscosity, capillary pressure, .relative
permeability), however, are assumed to be unchanging. The second component is a chemical constituent
which can partition between the LNAPL phase, water phase and the soil. This constituent of the LNAPL
is considered the primary contaminant of interest. The mass flux of the second constituent into the aquifer
comes from recharge water being contaminated by contact with the lens and from dissolution occurring as
ground water flows under the lens. The concentration of the chemical in the aquifer is limited by its
effective solubility in water.
The aquifer transport of the dissolved contaminant is simulated by using a two-dimensional,
vertically averaged analytic solution of the advection-dispersion equation. The vertical extent of the
contaminant is estimated from the recharge rate, ground water seepage velocity and vertical dispersivity,
rather than assuming the contaminant is distributed over the entire aquifer thickness. The boundary
conditions are placed at the downgradient edge of the lens and take the form of a gaussian distribution with
the peak directly downgradient of the center of the lens. The peak concentration of the gaussian
distribution adjusts through time so that the simulated mass flux from the lens equals that into the aquifer.
Although the size of the lens varies with time, a constant representative lens size is used for the aquifer
source condition. In many cases, the lens reaches its maximum size rather rapidly compared with the
transport in the aquifer, so that the use of the maximum lens size will not introduce large errors. The model
contains an option for choosing the effective size of the lens based on its size at the time when the mass
flux to the aquifer is greatest. This option may be appropriate for. releases of viscous hydrocarbon liquids.
The required input parameters include parameters specifying the type, extent and magnitude of the
LNAPL release, the residual oil contents for the unsaturated and saturated zones, the residual water
content of the oil lens, the transport properties of the water and LNAPL (density, viscosity, surface tension),
the aquifer and soil water retention characteristics (vertical and horizontal hydraulic conductivities, porosity,
irreducible water content, pore size distribution index, and air entry head), the dissolved constituent
characteristics (initial concentration within the LNAPL, aqueous solubility, and the soil-water and oil-water
partition coefficients), and the aquifer transport characteristics (vertical, longitudinal and transverse
dispersivities, hydraulic gradient, half-life of the constituent within the aquifer). Other parameters control
the simulation and locations where the LNAPL chemical constituent concentrations are calculated. Specific
information on running the model is presented in The Hydrocarbon Spill Screening Model (HSSM) Volume
1: User's Guide (Weaver et al., 1994).
1.2 Obtaining a Copy of HSSM
HSSM is available from the Center for Subsurface Modeling Support (CSMoS) at the Robert S. Kerr
Environmental Research Laboratory (RSKERL) at Ada, Oklahoma. CSMoS distributes software and
documentation free-of-charge through a diskette exchange program and provides technical support for the
codes they distribute. To obtain the HSSM software and user documentation send a letter of request along
with one high density 3.5" formatted diskette to the following address:
Center for Subsurface Modeling Support
Robert S. Kerr Environmental Research Laboratory
United States Environmental Protection Agency
P.O. Box 1198
Ada, Oklahoma 74820
Voice: 405-436-8586
FAX: 405-436-8529
[Section 1 Introduction]
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Please indicate if the DOS or Windows version is needed. If both interfaces are needed, enclose two
formatted diskettes.
The complete HSSM package consists of the documents
n The Hydrocarbon Spill Screening Model (HSSM) Volume 1: User's Guide,
a The Hydrocarbon Spill Screening Model (HSSM) Volume 2: Theoretical Background and Source
Codes,
and the two high density 3.5" diskettes. The diskettes contain:
For Windows:
n diskette HSSM-1-w The Windows Interface, HSSM-WIN
For DOS:
a diskette HSSM-1-d The DOS Interface, HSSM-DOS
HSSM and the user documentation are in the public domain. They may be freely distributed or copied by
anyone.
1.3 Volume 2 Organization
The remainder of the report describes the three modules which compose HSSM. These modules
each implement one part of the release scenario discussed above. First, in Section 2, the vadose zone
module is presented. The approach taken in the vadose zone is to combine Green-Ampt and kinematic
wave theory to simulate the flow and transport of the LNAPL. This module is called Kinematic Oily
Pollutant Transport (KOPT). The second module, described in Section 3 implements the capillary fringe
and dissolution scenarios and is called OILENS. OILENS uses the density difference between water and
the LNAPL and the Dupuit assumptions to simulate the growth and decay of the lens at the capillary fringe.
The third module is called the Transient Source Gaussian Plume model (TSGPLUME) and is described
in Section 4. An example simulation is presented in Section 5 that illustrates the effects of distance to the
receptor point and chemical properties on the estimated aquifer concentrations. Section 6 summarizes the
document. The complete FORTRAN source codes for HSSM and the HSSM utilities are presented in
Appendix 3.
[Section 1 Introduction]
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Section 2 Flow and Transport in the Vadose Zone
The method of characteristics has been applied to simplified versions of multiphase,
multicomponent transport problems by neglecting diffusion-like terms. By applying fractional flow theory
the problem can be written as a system of hyperbolic conservation laws. Helfferich (1981,1986) developed
a comprehensive theory for problems with uniform initial conditions and constant boundary conditions. The
theory includes as special cases the Buckley-Leverett model of two-phase flow (Buckley and Leverett,
1942) and the three-phase models of Dougherty and Sheldon (1964) and Pope et al. (1978). Corapcioglu
and Hossain (1990) applied the Buckley-Leverett approach to the flow of DNAPLs in two-dimensional
aquifer systems. In mathematical terms, systems of hyperbolic conservation equations with these boundary
and initial conditions are called Riemann problems (Smoller, 1983). As noted by Weaver (1991), such
solutions potentially have direct application to vadose zone transport only where the release of the fluids
is unending.
Several solutions of simplified, multiphase governing equations have been developed for one-
dimensional NAPL infiltration, based upon the following restrictive assumptions. Richards' (1931)
approach to soil moisture was to formulate only a mass conservation equation for the water phase. For
this to be a valid approximation, the flow of the air must not impede the flow of the water. One accounts
for the presence of the air phase by the usage of an appropriate relative permeability function. Further,
if the saturation of water is uniform and remains so, the continuity equation for the water phase is
eliminated. From these assumptions, Mull (1971, 1978), Raisbeck and Mohtadi (1974), Dracos (1978),
Reible et al (1990) and El-Kadi (1992) developed models for NAPL flow assuming that the NAPL fills a
fixed portion'of the available pore space in a homogeneous medium. The models developed by Raisbeck
and Mohtadi (1974) and Dracos (1978) share the limitation that they cannot simulate unsteady NAPL
drainage in the soil after the release ends. The models of Mull (1971, 1978) and Reible et al. (1990)
simulate drainage with arbitrary assumptions concerning the profile shape. Mull's model uses a series of
rectangular profiles while Reible et al. (1990) assume a zone of residual NAPL saturation behind a NAPL
body moving within the profile. El-Kadi (1992) extended the approach of Mull to multiple dimensions.
Durinq the redistribution period, however, the NAPL saturation may be non-uniform. Also, these models
have not included transport of soluble constituents of the NAPL phase. Ryan and Cohen (1991) developed
a one-dimensional, finite difference, front tracking model which can simulate non-uniform saturation profiles
and chemical transport.
The model presented herein extends the simple one-dimensional model approach as it allows
nonuniform saturations to be modeled after infiltration ceases and includes advective transport, of a
partitionable constituent of the NAPL phase. The resulting model is named KOPT for,kinematic oily
pollutant transport to emphasize its reliance on kinematic wave theory. The objective of this development
is to provide a computationally efficient screening model for NAPL infiltration and redistribution. In general, -
screening models allow comparisons of the effects of various parameters (e.g., hydraulic conductivity,
partition coefficients, etc.) on the flow and transport of NAPLs in an idealized setting. By utilizing a semi-
analytic method of characteristics approach, a numerical solution technique is avoided. The resulting
efficiency in running the model is achieved primarily because the capillary pressure gradient is neglected.
This assumption leads to approximate hyperbolic governing equations which can be solved by the
generalized method of characteristics (Smoller, 1983). One major effect of this assumption on the
simulation results is that the leading edge of the L-NAPL moving into the soil is idealized as a sharp front
(Fiqure 2) Method of characteristics solutions have been developed for one-dimensional water flow in
the vadose zone by Sisson et al. (1980), Smith (1983), and Charbeneau (1984, 1991). Where the front
spreads Charbeneau (1984), for example, presented a theoretical proof that the mean displacement speed
of the sharp and true fronts is the same. Smith (1983) presented a numerical result for water flow showing
that a numerical solution of Richards' equation was tracked by a sharp-front solution. The flow visualization
experiment presented below demonstrates the ability of the KOPT model to match experimental results to
c [Section 2 Vadose Zone]
-------
Saturation
I
Q
Sharp Front
Spreading Front
Figure 2 Schematic comparison of sharp and diffuse fronts
a certain degree of accuracy. '" " ' '
The theory of kinematic waves was presented by Lighthil! and Whitham (1 955)"for flood waves
in rivers. They note that whenever an approximate functional relation exists at each point between the flux
M^rn" ft!'011 (ana'°gously in mul«Phase flow, flux and saturation), then the wave motion follows
directly from the continuity equation. For most cases of interest, the functional relationship is nonlinear
and the kinematic waves are either regions of constant state, self-spreading, or self-sharpening In the
multiphase flow problem, the region of constant state corresponds to a uniform saturation profile 'The self-
fhPrSM?D,9 T6 GOIlesPonds to a re9jon of internal drainage and redistribution occurring after the end of
the NAPL release. The self-sharpening wave corresponds to a wetting front moving into the profile. Each
1£ lel °f the SOlUti°n Wi" be illustrated by the model results presented in Figure 3 and Figure 4
Although the shape of the wetting front is determined by the capillary gradient, the kinematic model is able
to move the sharp-front representation of the wetting front downward at the correct speed so that mass is
S> kinemati° m°dels are able to rePresent the essential features of nonlinear
2.1 KOPT Model Framework
deformabhp- d°CUmen!' the Ik1uids are assumed incompressible and the medium non-
deformable. The NAPL is assumed to be composed of two components. The first is the water immiscible
(Section 2 Vadose Zone]
-------
0
50 100
Time (Minutes)
Figure 3 Base characteristic plane
phase which acts as a carrier for the second component. The second component is a chemical of
environmental concern. The concentration of dissolved constituents is assumed to have no effect upon
the fluid transport properties including densities, dynamic viscosities, and surface tensions.
Although actual flow in the vadose zone is three-dimensional, the model treats transport through
the unsaturated zone as being one-dimensional downward. Gravity, which is the only driving force for
kinematic model, acts downward, though lateral spreading of the NAPL may occur because of capillary
forces. Spreading may also be caused by heterogeneity, as layering may impede flow. For situations
where the NAPL is applied over relatively large areas, the flow becomes nearly one-dimensional in the
center. For contaminant sources that are of small areal extent, the lateral transport of contaminants may
be significant, and the assumption of one-dimensional flow is less applicable. From the point of view of
ground-water contamination, however, one-dimensional modeling leads to a conservative model as all of
the NAPL is assumed to move downward and potentially reach the water table.
2.2 Derivation of the Vadose Zone NAPL Flow Model
Kinematic models are unit gradient models where drainage occurs due to the force of gravity and
capillary pressure gradients are neglected. The downward Darcy volume flux of phase i is
if tf if (1)
r7, — /\_r = r\-j Ji-j \ /
where Kei is called effective hydraulic conductivity of the medium to fluid i, Ksl is the fully saturated
7 [Section 2 Vadose Zone]
-------
_
(D
Q
0
0.2
0.4
0.6
9.0 Minutes
— 12.0 Minutes
— 24.0 Minutes
— 48.0 Minutes
--- 96.0 Minutes
0
Figure 4 Total liquid profiles
0.2 0.4 0.6 0.8 1
Total Liquid Saturation
conductivity of i, and krl is the relative permeability of the medium to fluid
is related to properties of the fluids and the porous medium through
The fully saturated conductivity
(2)
where k is the intrinsic permeability of the medium, p, is the density of the fluid, g is the acceleration due
to gravity, and u, is the dynamic viscosity of fluid i.
In order to estimate the Darcy fluxes in equation (1), expressions for the relative permeabilities are
needed. One way to develop these relationships is to begin with conceptual models of the porous medium,
presumed distributions of fluids within the medium, and a solution of laminar flow through the medium
(Bear, 1972). The Burdine (Burdine, 1953, Wylie and Gardner, 1958) equations form one such model.
Using the Brooks and Corey (1964) model of the capillary pressure to evaluate the Burdine equations yields
the following model of drainage relative permeability for water and NAPL:
[Section 2 Vadose Zone]
-------
/L
1 -S,
wr
(3)
1 -
'or
1 -S,
wr
kro = 0
\e-2
\e-2
1 -s.
wr
s0>sor
(4)
(5)
(2 + 3A)
(6)
where X is called the pore size distribution index, S, is the saturation (saturation is defined as the percent
of the pore space filled by a given fluid) of phase i, and Sir is the residual saturation of phase i. The pore
size index and residual water saturation are obtained through measurement of the capillary pressure curve.
The scaling of the NAPL saturation in equation (4) is used so that the NAPL relative permeability is equal
to one only when the NAPL entirely fills the pore space (i.e., Swr = 0) and so that the NAPL relative
permeability is zero when the NAPL saturation is less than or equal to its residual. Implicit in the use of
equation (4) is the assumption that NAPL has previously displaced air; and that during subsequent
drainage, some NAPL is retained as a trapped phase. Sor is introduced as ah empirical parameter to
represent the retention of NAPL in the vadose zone after the passage of a NAPL infiltration event. If no
NAPL is retained, then Sor can be set equal to zero. Wilson et al. (1990) present a method for measuring
vadose zone residual NAPL saturations in the presence of a residual water saturation. These authors
further suggest that residual NAPL saturations are dependent upon the saturation history of the system and
would be reduced in the presence of higher water saturations. The usage of equation (4) for imbibition at
the NAPL front is discussed below. Further refinement of the relative permeability function is not proposed
for the KOPT model, because the model is intended for screening calculations where large uncertainty is
expected in all the model parameters.
Water is assumed to occupy a fixed, uniform portion of the pore space. This assumption eliminates
the mass conservation equation for water from the model. This approach is taken because the temporal
distribution of rainfall is required to simulate the time varying moisture profile. This requirement goes
beyond the anticipated data available for screening purposes. Richards' assumption is then used to
eliminate the mass conservation equation .for the air phase in accordance with common soil science
practice. This approximation is acceptable as long as pressure does not build up in the air phase (Youngs
and Peck, 1964).
The water saturation is calculated from the average annual recharge rate by assuming that
maximum effective conductivity of the soil is greater than the recharge rate. A kinematic model is then
appropriate; and the recharge rate and water saturation are related through the relative permeability
function for the water. If qwi is the average annual recharge flux, then equations (1) and (3) give the
resulting water saturation as
[Section 2 Vadose Zone]
-------
w(avg)
(7)
The calculated Sw(avg) is used as the water saturation for the entire profile and is maintained by the assumed
recharge through the system. Equation (7) replaces the phase conservation equation for water.
The presence of air in the vadose zone is accounted for via the usage of a three-phase relative
permeability function and by assuming that there is a trapped air saturation, which limits the maximum
effective conductivity, Kao, of the NAPL phase. Bouwer (1966) reported that the maximum effective
hydraulic conductivity to water is 40% to 60% of the saturated hydraulic conductivity, Ksw. In the present
work, 50% Ksw is used to determine the trapped air saturation. In equation (3) the relative permeability
to water, km, is set equal to 0.5. Sar is then taken as the air saturation which would occur with that amount
of soil water and is calculated by
- (1 -S^) (0.5)*
(8)
In equation (8), air and water are assumed to fill the pore space; when the NAPL enters the soil, Swr and
S,r are assumed to be unchanged.
With equation (7) and Richards' assumption, the only phase equation to be solved is that for
the NAPL. For gravity driven flow, the NAPL flux q0 from equation (1) becomes
*w(avg) i
(9)
Since Sw=Sw(avg) is constant, Keo is a function of S0, and Sw(avg) serves as a parameter. Using a single-
valued, relative permeability function with known Sw(avg) , the continuity equation for NAPL can be written
in terms of its unknown saturation
8S.
at
dS
dz
= 0
(10)
where TI is the porosity and z is directed positive downward. The relative permeability function (equation
(4)) is used in equation (10).
The solution then may proceed as follows. Where the NAPL saturation distribution varies
continuously, the classical method of characteristics (MOG) solution of equation (10) is
dS,
dt
= 0
(11)
[Section 2 Vadose Zone]
10
_
-------
along, characteristics given by
dz
dt
(12)
The solution is valid only where the derivatives appearing in equation (10) exist at each point of the solution
domain (e.g., Rozdestvenskii and Janenko, 1980). For most cases, S0is fixed along the length of the
characteristic line, since there is no source term in the governing equation (10). Conservation of mass
results in straight characteristics, as the slope dz/dt is constant.
When the saturation derivatives fail to exist in the solution, integral equations are used to find
solutions that are called generalized or weak solutions. An integral form of the continuity equation applied
to a control volume around the front can be integrated to give (e.g., Charbeneau, 1984),
at
s01 -
- AC
s01 -
(13)
where the subscripts 1 and 2 refer to values at locations on either side of the front as indicated in Figure 2.
The form of equation (13) which uses the effective conductivities (Keo) is applicable for kinematic flows.
When the NAPL invades a pristine medium, as assumed in KOPT, S02 and thus Keo(2) are equal to zero.
Equation (13) is the solution of equation (10) in the weak or integral sense. This is the well-known
jump condition. Discontinuities form in the solution domain because either characteristics cross, which is
a physically impossible situation, or because the boundary data are discontinuous and the 3K/3S function
does not cause smoothing of the front (Weaver, 1991). In KOPT, the latter condition is applicable as the
NAPL flux (or ponding depth) is assumed to increase discontinuously from zero to the initial level. 3K/9S
is of greater magnitude for the high saturations that occur behind the front, than for those ahead of the front
so the front is not smoothed.
So-called entropy conditions are used to pick out a physically realistic solution from a set of multiple
possible solutions of equation (13). For fluxes, q, such that q" = (32z/3tE) > 0 and saturations S, > £ > S2,
then the appropriate entropy inequality is given by Smoller (1983) as
dt
(14)
since q'(^) = dz/dt which is given by equation (14). • .
During infiltration, the capillary pressure gradient may play a role in determining the NAPL flux into
the soil. If NAPL flux exceeds the kinematic capacity of the media (q0> Keo) or if ponding occurs at the
surface, then the kinematic model must be augmented by a dynamic model, because the NAPL flux cannot
be solely attributed to gravity. During loadings of either type, the Green and Ampt (1911) model is used
as an approximate dynamic supplement to the kinematic model to determine the NAPL flux. With ponding
head of Hs, the flux equation is integrated from the surface to the position of the NAPL front, z,, to give
(Neuman, 1976) . '.
11
[Section 2 Vadose Zone]
-------
<7i
H
(15)
with
Hf =
y$*dh
(16)
where q, is the flux in the NAPL-filled pore space with NAPL saturation S,, K1 is the corresponding NAPL
effective conductivity, h is the pressure head, subscripts 1 and 2 refer to locations behind and ahead of the
front, respectively. The head as a function of NAPL saturation is determined by scaling the Brooks and
Corey (1964) capillary pressure model from air/water drainage to air/NAPL drainage by the ratio of surface
tensions and densities. The pore geometry is assumed to be the same in the NAPL/air system, so that
Brooks and Corey's X is the same for both curves. The air/water entry head, hceaw is scaled by
'caao
'coaw
ao
Po °aw
(17)
to estimate the air/NAPL entry head, hceao. The definition of the effective saturation is modified to reflect
that the total liquid saturation St, which is the sum of the water and NAPL saturations, is controlled by the
air/NAPL capillary pressure (Leverett, 1941). The resulting expression for the air/NAPL capillary head at
the front is
h = h
'oaao
1 -
(18)
'wr
After transforming the independent variable to S0, the integral appearing in equation (16) becomes
K h
Aso "caao
f U to o \
I Kro (*<>>*>*)
J
(19)
'wr
The scaling of the air/NAPL capillary pressure curve in equations (18) and (19) does not include the
residual NAPL saturation, because no NAPL is present in the profile before the passage of the front. In
this situation, the relative permeability equation for the NAPL is also assumed to have no residual NAPL
saturation. Equation (19) is evaluated numerically, because the complexity of the relative permeability
function precludes a closed form solution. The capillary head behind the front, r^ , is calculated using
equation (18).
[Section 2 Vadose Zone]
12
-------
The jump condition (Equation (13)) is used to determine the speed of the invading front with the
effective conductivity, Keo, replaced by the flux determined from equation (15), giving
dz
~dt
1 +
H\
(20)
where H is the sum of the head terms in the numerator of equation (15). Although this function could be
left as a differential equation and solved numerically, an analytic solution for the position of the front is
given by .
t-
\zf-Hlfl(zt+.H)\
(21)
Equation (21) is preferred over equation (20), because the high initial pressure gradient causes problems
in the numerical solution of equation (20). The contribution of the suction head to the driving force causes
increased NAPL flux and is included to assure that the proper amount of fluid is drawn into the soil during
the loading period. Even though there is a NAPL head at the surface, the amount of water in the soil is
assumed unchanged; thus this boundary condition strictly applies only to situations where the water
saturation is residual. The water saturation in the profile, however, remains uniform as it is assumed to
result from the continuous supply of recharge at the surface. . , ,
When the supply of the NAPL is finite, the kinematic approach is used to determine the flux during
redistribution. Like the beginning of the NAPL event, the end of the event is treated as an abrupt change
in ponding depth or flux from a specified value to zero. This change in boundary data triggers a wave
which displays a smooth transition from low saturation near the surface to higher saturation at depth and
the classical method of characteristics solution applies. The behavior is caused by the shape of the relative
permeability function for the NAPL phase. Because the derivative of equation (4) is a monotonically
increasing function of NAPL saturation, the characteristic speeds increase with saturation. Thus the high
saturations deeper in .the profile move faster than the low saturations near the surface, and the
redistribution profile appears smooth.
Several surface conditions can be included in the model. Four options have been included in
KOPT to correspond to spill or release scenarios (Figure 5). The first condition is a flux condition. NAPL
fluxes less than the maximum NAPL effective conductivity produce no runoff, and all the NAPL enters the
soil. Thus, a constant flux for a specified duration is used as a boundary condition. Conditions where the
specified flux exceeds the effective conductivity are treated by the Green-Ampt approach discussed above.
Excess flux is assumed to run off the surface of the soil. The second condition corresponds to a land
treatment scenario where a certain volume of NAPL is incorporated uniformly over a specified depth at time
zero. The third option is the constant head ponding scenario. Here, NAPL is ponded at the surface at a
constant head. This scenario corresponds to an impoundment which is maintained at a certain depth for
a specified duration. A ruptured tank contained within a berm is envisioned here. This boundary condition
requires use of the Green-Ampt model. The fourth boundary condition implemented in the model allows
constant head ponding for a specified duration, followed by variably decreasing ponding. This boundary'
condition is primarily useful for laboratory experiments, where ponding depths cannot instantly be reduced
to zero. The falling head condition is implemented by considering that Hsis a function of time, and that the
reduction in NAPL ponding height is equal to the NAPL infiltrated over a time increment, thus '
13
[Section 2 Vadose Zone]
-------
JTTTTTm
1. Flux Source Representation
2. Volume Source Representation
Tnj
.
3. Constant Head Source Representation
Figure 5 KOPT model release scenarios
H
/7+1
n 8, (zf
(22)
where H,n is the ponding depth at time n and z," is the front depth at time n. Equation (22) is used with
equation (21) to incorporate the time varying ponding depth into the Green-Ampt model.
Although the primary contaminant of interest is a dissolved constituent of the NAPL, in some cases
it is important to consider the dissolution of the NAPL itself. Examples are when NAPL is a pure chemical
such as trichloroethene or carbon tetrachloride, or for consistency with models for transport at the water
table (Weaver and Charbeneau, 1990). The water solubility of the NAPL presents a loss of mass of the
NAPL phase, thus the loss to the pore water of NAPL reduces NAPL saturations in the profile. The amount
of mass lost to the water phase is subtracted uniformly from the NAPL saturation profile at the end of each
simulation time step. The result of this operation is that the characteristics curve toward the land surface
because of the changing saturations. For this situation, the location of the characteristics must be found
by integrating the characteristic speeds (equation (12)). Obviously, the additional computational burden
for this case is significant.
[Section 2 Vadose Zone]
14
_
-------
2.3 Derivation of the Vadose Zone Transport Model
The kinematic model is also applied to the dissolved constituent. This is justified in part from the
fact that advection, multiphase partitioning, volatilization, and degradation are the major controls on
transport and fate for many organic contaminants. Hydrophobic constituents of NAPLs are largely
transported by advection of the NAPL, because of their preferential partitioning into the NAPL phase.
Chemicals like xylene dissolved in gasoline move primarily with the NAPL due to this reason. As noted
previously, the kinematic models move the concentration fronts at the correct speed for mass conservation.
The dissolved constituent solution proceeds as follows. For the nondispersive migration of a
constituent initially dissolved in the NAPL, the mass of constituent per unit volume, mc, is
mo =
(23)
where c0 and cw are the constituent concentrations in oil and water, pb is the soil's bulk density, and cs is
the sorbed concentration expressed as mass of constituent/mass of soil. The mass advection flux is given
by
(24)
substituting these into the general mass conservation equation gives
!<•«
= 0
(25)
where B = B(S0,SJ = (Sw+ S0k0) + pbkd/r|, which may be called a bulk water partition coefficient. The
individual partition coefficients are given by
(26)
k,., = 1
The partition coefficient, kd, is the usual soil water distribution coefficient. The NAPL/water partition
coefficient, k0, is estimated from the NAPL composition by using Raoult's law (e.g., Cline et al., 1991). For
consistency, with the assumption that the flux of air is neglected, partitioning into the air phase is not used
in the mass balance equation for the constituent. Neglect of volatilization and air phase partitioning is
conservative since KOPT is one module of a screening model for predicting water phase concentrations
in downgradient ground-water wells. In addition, for many constituents, the total percent of mass within the
air phase is small compared to that within the NAPL and sorbed to the soil. Expanding the derivatives and
using equations (9) and (10) while applying the linear partitioning relationships gives
15
[Section 2 Vadose Zone]
-------
at
dz
(27)
After the saturations of water and the NAPL are known, cw is the only unknown in equation (27).
Applying the MOC results in
dc.
dt
y- = 0
(28)
along
dt
(29)
Equation (27) is a semi-linear equation, as it is linear in the unknown cw. For such equations, characteristic
speeds match jump speeds as the jumps are co-located with characteristics. The jumps are contact
discontinuities by definition (Smoller, 1983). Another feature of both linear and semi-linear equations is that
the characteristic speed given by equation (29) is independent of the dependent variable, cw.
The concentration at the beginning of simulation is determined as follows. The constituent
concentration in the released NAPL, c0(sur(), changes instantly upon placement in the soil, because of the
local equilibrium assumed for the constituent. For situations where the NAPL flux is specified, the
constituent concentration in water in the soil can be determined by balancing mass fluxes across the
surface of the soil
Co(surf.)
~ C
w(initial)
(30)
This relation supplies the initial concentration, cw(lnitial), for each constituent characteristic. Equation (30)
shows that only if the water flux is zero will the initial concentration in the NAPL be the same as that in the
NAPL phase in the soil; otherwise, c0(soil) < c0(surf,. When a specified volume of NAPL is applied to a zone
of thickness, dpz (i.e., the plow zone thickness for a land treatment system), the initial concentration is
calculated via equation (31) where V0is the volume of applied oil per unit surface area.
co(surf.)
- C
w(initigl)
B(S0,SW)
Ql'-'Wl "pz
(31)
The initial concentration in a land treatment waste, cw(inlUal) is used to calculate the initial constituent
concentration in the oil phase.
[Section 2 Vadose Zone]
16
-------
2.4 Summary of Approximate Governing Equations for the KOPT Module
The flow of the NAPL is governed by the two parts of the generalized method of characteristics
solution. Equations (11) and (12), the classical solution, are used where the NAPL saturation varies
continuously, in which case both partial derivatives appearing in the continuity equation (10) exist in the
solution domain. Equation (13), the generalized solution, is used to determine the speed and position of
the front at the leading edge of the NAPL. In KOPT, these equations are solved first and determine the
distribution of the NAPL in the profile. Equations (28) and (29) are the approximate governing equations
for the dissolved constituent. Since .transport of the dissolved constituent is governed by a semi-linear
equation, a characteristic is co-located with the leading-edge front and no generalized solution is needed.
The solution for the dissolved constituent is determined from the governing equations and the NAPL
distribution and flux. By simplifying the governing equations and applying the method of characteristics,
the original nonlinear system of coupled partial differential equations has been reduced to a system of
nonlinear ordinary differential equations. An analytic solution is not known for this case, so a numerical
method is used to solve the ordinary differential equations.
2.5 Model Implementation
The solution of the model equations is obtained by the use of an ordinary differential equation
solver^ With such a technique, the solution of a system of n equations of the form
dt
(32)
may be obtained, if appropriate boundary conditions are specified. The functions, fn, may be coupled
arid/or nonlinear functions of the y,. In this case the y, represent the NAPL front position, cumulative NAPL
mass applied at the boundary, position of the dissolved chemical characteristics and, if required for the
simulation performed, the position and saturation of the NAPL characteristics, the NAPL ponding depth at
the surface and cumulative NAPL runoff from the surface. For KOPT, a Runge-Kutta-Fehlberg, RKF,
method (Fehlberg, 1969) was selected in order to allow automatic time step variation to control truncation
error.
There are several advantages to using a differential equation solver instead of finite difference or
finite element techniques for this problem. Use of the differential equation solver leads to simplified
programming in the sense that the programmer supplies the functions on the right-hand side of equation
(32) to the solver in a subroutine. Second, the RKF methods maintain the truncation error below a
specified tolerance by reducing the time step. This feature operates automatically during the program
execution, resulting in a variable time step routine. The method used here, RKF1(2), uses a first-order
scheme to get the solution and an embedded second-order scheme to check the truncation error. Third,
under certain conditions, only a few of the equations need to be solved. For example, the characteristics
for non-dissolving NAPLs are straight lines; and only the equations for the discontinuities need be solved.
A final advantage is that the location of the fronts is determined directly as a function of time.
In addition to the truncation error control of the method, a fairly complicated and specialized system
of ad hoc controls is needed to assure the accuracy of the solution. For example, the following features
of the solution must occur at times the solver picks for the solution:
-the beginning and end of the NAPL release
-the end of the maximum NAPL saturation region
17
[Section 2 Vadose Zone]
-------
-the origin of any characteristic
The checks are implemented in a controller routine that is called by the RKF solver. A beneficial side
effect of using the controller is that the number of steps rejected for truncation error violations is reduced,
since the solver is guided to critical times in the solution by the controller (Charbeneau et al., 1989).
2.6 General Features of the KOPT Solution
Figure 3 shows the base characteristic plane and the projection of a few displacement paths in
z-t space. The input parameters for this example are presented in Table 1, Simulation A and are discussed
in further detail below. The NAPL leaks into a sand with water at residual saturation. During infiltration,
the NAPL fills 76.8% of the pore space and moves at its maximum speed, which is determined by the
Green-Ampt model with variable surface ponding. Once the supply of NAPL ends at 6.2 minutes (point
B), drainage begins. There is in the profile a region of constant oil saturation (triangle ABC), associated
with the NAPL release, that will now be replaced by a region of variable saturation, associated with the
MOC solution for NAPL drainage. The displacement path (called a characteristic) of the residual saturation,
S0(, remains at the surface, because its speed is zero by definition. Bounding the region of maximum
saturation, ABC, is the characteristic corresponding to S0= S0(max)= 0.768. In between are characteristics
for all intermediate values of S0, as labeled in Figure 3. As noted above, the highest NAPL saturations
are found the deepest in the profile, because the derivative of the kro function is such that the highest NAPL
saturations have the highest speeds.
Figure 4 shows oil profiles for 9.0 to 96.0 minutes. In the profiles, water and the total liquid
saturations are plotted; the NAPL saturation is read as the difference between the two. By 9 minutes after
the beginning of the release, drainage is occurring from the surface down to a depth of 12.4 cm. The
region from 12.4 to 24.2 cm still has the original saturation of 0.768. Once the NAPL saturations that are
less than S0(max) reach the oil front as has occurred in the profiles for 24, 48 and 96 minutes, then its speed
begins to be reduced in accordance with equation (13). As time goes on, the speed of the front slows as
it intersects slower and slower characteristics (Figure 3). By 96 minutes, which corresponds to the end
of the experiment described below, the NAPL front has reached 59.0 cm and its saturation has dropped
to 0.367.
The entropy condition is such that the characteristic speeds should decrease across the front, and
that the front speed should be intermediate to these two. With a pristine initial condition, the characteristic
speed ahead of the front is zero. Figure 6 shows the characteristic speeds and the front speed,
demonstrating compliance with the entropy condition (equation (14)). The abrupt drop in both speeds
occurs when the surface ponding ends and the Green-Ampt model solution is switched to the kinematic
model solution. At this time, the contribution to the speed from the capillary suction at the front is dropped
from the model. The subsequent short plateau occurs because the front speed remains constant since the
NAPL saturation at the front remains at 0,768 until the drainage wave reaches the front (Figure 3 and
Figure 4). Once the latter occurs, the front and characteristic speeds decrease as shown in Figure 6.
2.7 Experimental Results and Simulation
A simple laboratory experiment was conducted in order to evaluate the NAPL phase flow portion
of the KOPT model. The ponding depth and front position were observed visually by tracking the flow of
a dyed oil in a laboratory column described in the following. A 1.0 m long, 0.05 m diameter glass column
with a coarse, porous glass frit at the bottom was modified by adding seven air release vents oppositely
(Figure 7). The vents were packed with glass wool before packing the column with a uniform sand (Gilson
[Section 2 Vadose Zone]
18
-------
Upstream (Z,) Characteristic Speed
10C
'••...^fc-^- ^ont Speed
.Downstream (Z2) Characteristic Speed
0 0.02 0.04 0.06 0.08
Time (days)
0.1
Figure 6 Upstream characteristic and front speeds
ASTM c109). With the vents closed, the column was purged with CO2, and followed by an applied vacuum
of 20 cm of mercury. De-aired water was allowed to enter from the bottom of the column, gradually
saturating the sand pack. The saturated sand pack was used as a permeameter for determining the
hydraulic conductivity under steady state flow conditions. Manometers attached to the vents on one side
of the column were used to determine the head drop over each 10 cm long section of the column. After
measuring hydraulic conductivity, the column was drained by lowering the water table to the top of the frit.
The c109 sand is coarse enough to have a low capillary fringe, and the water saturation above the fringe
was assumed to be near residual after several hours of drainage.
Approximately 100 g of dyed Soitrol 220 was then released at the surface and allowed to enter the
column (with vents opened ahead of the Soitrol front) to simulate a NAPL spill. The ponding depth and
location of the NAPL front were recorded with time. The NAPL front was measured at three locations (left
edge, center, and right edge) to capture variability in the front; as even in nearly uniform packings, the front
does not remain absolutely uniform. In a test case, a core was taken from the column to verify that the
NAPL flowed through the sand pack and not preferentially along the walls. The core confirmed that the
oil was found at the same depth inside the column and along the walls. Figure 8 shows the NAPL front
position at the left edge, center and right edge of the column. Figure 9 shows the measured depths of
ponded Soitrol at the surface. Both of these figures also show simulation results which are described
below.
19
[Section 2 Vadose Zone]
-------
Figure 7 Glass column used for the laboratory evaluation of KOPT
0 20 40 60 80 100
Time (Minutes)
A Left Edge
a Center
o Right Edge
— Simulation D
- - Simulation A
; — Simulation B
--- Simulation C
Figure 8 Measured NAPL position at right-hand edge, center and left-hand edge of
column.
[Section 2 Vadose Zone]
20
-------
0.06
0.05
0.04
•B 0.03
CL
(U
Q 0.02
0.01
0
a Measured Ponding
— Simulation D
Simulation A
— Simulation B
--- Simulation C
Time in Minutes
Figure 9 Measured NAPL ponding depth at the surface of the sand
The model parameters, K, T\, hceao, X,, Swr, p0, u0, and a0 were determined independently of the
transient flow experiment, so that the ability of the model to match the outcome of the experiment could
be seen without fitting or other adjustment of the parameters. The values of the parameters used in
simulation A are listed in Table 1, along with the technique used for their measurement. Figure 10 shows
the variation of hydraulic conductivity along the length of the column. The average hydraulic conductivity
of the sand is 78.0 m/d. The air/water capillary pressure curve for the c109 sand was measured by the
technique developed by Su and Brooks (1980). The measurements were made on a 5.0 cm long, 5.0 cm
diameter column, packed using the same procedure as was used for the long column. The Brooks and
Corey parameters of the air/water capillary pressure curve were fitted by using the RETC program
developed by van Genuchten et al. (1991). RETC returns average values of the parameters along with
95% confidence limits for the values. Two sets of water-air capillary pressure data and the fitted model are
shown in Figure 11. This figure shows only a few measured points at low water saturations, so the fitted
residual water saturation has greater uncertainty than the other parameters. The water saturation in the
column, Sw(avg)l was taken as either the residual, Swr, or as a value determined by the NAPL penetration into
the column as discussed below. The porosity was estimated from the bulk density of the sand pack in the
long column. The NAPL phase properties, p0, u0, and o-0, were averaged from replicate measurements.
The residual NAPL and air saturation were estimated; the trapped NAPL saturation is estimated to be 5%
of the pore space, while the trapped air saturation is estimated as the air saturation at kw = 0.5 (equation
(8)), which is 0.1757 for this example.
21
[Section 2 Vadose Zone]
-------
Table 1 Simulation Parameters and the Techniques Used for Their Measurement
Parameter
K8 (m/d)
11
hcoaw(cm)
X
SWf
sor
Po (CP)
PO (g/c°)
cr0 (dyne/cm)
initial ponding depth
(cm)
maxk™
Simulation
A
78.0
0.41 1
-24.8
4.84
0.0588
0.05
4.76
0.79
25.0
6.5
0.5
0.0588
B
78.0
0.411
-24.8
4.84
0.0588
0.05
4.76
0.79
25.0
6.5
0.5
0.1129
C
83.0
0.411
-24.8
4.84
0.0588
0.05
4.76
0.79
25.0
6.5
0.5
0.1129
D
78.0
0.372
-24.8
4.84
0.0588
0.05
4.76
0.79
25.0
6.5
0.5
0.0588
Measurement Technique
Column Permeameter
1 Column Permeameter
2 Su and Brooks Cell
Su and Brooks/RETC
Su and Brooks/RETC
Su and Brooks/RETC
Estimated
Cannon-Fenske Viscometer
Gravimetric
DuNuoy Ring Tensiometer
Estimated from NAPL Volume
Estimated
Estimated as discussed in the text
Figure 8 and Figure 9 show that the KOPT simulation, using the average parameter values
(simulation A, Table 1), captures the qualitative behavior of the front and ponding depth. The simulation
matches the initial rapid influx of NAPL during ponded infiltration, followed by a slowing of the front speed
as the NAPL redistributes. This simulation, however, fails to match exactly either the ponding depths or
the front positions. The model overpredicts the infiltration rate, resulting in a shorter period of ponding than
actually observed. This behavior suggests that the model's estimates of effective conductivity or capillary
suction may be too high. Also note that in the experiment, the NAPL was poured onto the sand surface;
thus the ponding began at zero, increased to a maximum, then declined. In Figure 9 it can be noted that
the simulated ponding depths are achieved instantaneously and do not go through the first experimental
point. This behavior is likely to result from the way the NAPL is poured'into the column.
Simulation B uses modified water and NAPL saturations in the profile that are determined as
follows. In KOPT, the NAPL is assumed to fill a fixed portion of the pore space during infiltration, so at
the end of the ponding period, the entire infiltrated volume of NAPL is between the surface and the NAPL
front. From the column geometry, porosity, measured depth of the front, and the NAPL volume applied to
the surface, the NAPL saturation is estimated by mass balance to be 0.7141, which is lower than the
value generated by KOPT for simulation A (0.7682). The water saturation to fill the remaining pore space
is 0.1129, if the trapped air saturation is unaltered. KOPT was then rerun with the water saturation set
to 0.1129, which forces the model to give precisely the measured front position when the surface ponding
first equals zero. Figure 8 indicates that simulation B lies closer to the experimental data after 25 minutes
Into the experiment. In effect, the maximum effective NAPL conductivity was reduced by lowering the
[Section 2 VadoseZone]
22
-------
NAPL saturation (Table 2,)- Simulation B has a longer ponding period, reflecting the lower average NAPL
flux. The results from simulation A suggest that lowering the NAPL flux during infiltration should bring the
simulated and measured results closer together.
Hydraulic Conductivity c!09. Sand
9 OH 1 1 1 1 1 1 1 1 1
85--
80- •
Hydraulic
Conductivity 75- -
-------
C109 Sand water/air curve
-60 -
-40
\[/(cm.)
-20
0.1
0.2
0.3
0.4
0 (cms/cm3)
Figure 11 Data from two measured capillary pressure curves for the c109 sand and
the fitted Brooks and Corey model (solid line)
KOPT requires single values for each input parameter. As shown in Figure 10, the hydraulic
conductivity varies along the length of the column. Simulation C uses the value of the hydraulic
conductivity found nearest the surface (83.0 m/d, Figure 10) and the NAPL and water saturations from
simulation B. The NAPL enters sand with higher than average conductivity and initially has generally higher
fluxes than given by the average of 78.0 m/d. The duration of ponding is reduced and the simulated front
position is closer to the experimental data. Table 2 indicates that the variation in H, is relatively low so
that the Green-Ampt flux is mostly affected by the maximum effective conductivity, rather than variation in
«,
In order to assess the sensitivity of the model to the parameters, Figure 12 shows first order,
nondimensional, sensitivity coefficients, SC,, for the first 7.5 minutes of the simulation. Throughout this
time, there is some NAPL ponded at the surface; and the Green-Ampt model is used to determine the
NAPL flux. The SQ values are calculated from
SC, -
zf dp,
(33)
[Section 2 Vadose Zone]
24
-------
1
I
-1 — 1
c
•8 °-5
-------
•£
(D
'O
o—o HWE
•-• XLAMB
x—x SWR
A—A SOR
D—D POR
o-o SWMAX
v-v XMKRW
20 40 60 80
Time (Minutes)
100
Figure 13 Nondimensional sensitivity coefficients for the kinematic portion of the
simulation B parameter set
Simulation D is presented to illustrate the sensitivity of the model to the estimate of the porosity.
The sensitivity analyses indicate the high sensitivity of the model to the porosity. The value of 0.41 used
in simulations A-C is obtained from the 1.0-meter long column. The value used in simulation D is 0.37,
which was obtained from the measurement of the air/water capillary pressure curve. The lower value of
porosity causes the front to lie deeper in the profile. The density of the sand in the column is likely to vary,
as evidenced by the variation in hydraulic conductivity; the porosity is likewise expected to vary. So it is
possible that lower porosities are encountered in the column than given by the average of 0.41. This
simulation also illustrates that parameters may be adjusted to fit a set of experimental data. In this case,
only one parameter of the simulation A data set was adjusted, and the model result closely matches the
experimental data. Other sets of parameter values can be found to match the experimental data closely,
if fitting the model to data is desired.
Since equation (10) expresses mass conservation, a correct solution demonstrates conservation
of mass. For simulation A, the model allowed 0.1008 kg of NAPL to infiltrate during ponded infiltration.
The NAPL mass in the profile matches nearly exactly the mass applied in the experiment, because the
boundary condition allows the amount of mass applied to the column to be precisely specified. The model
integrates the NAPL mass flux at the boundary and compares it to the NAPL mass found within the profile.
These mass balances performed during simulation A show a maximum error of 0.050%.
[Section 2 VadoseZone],
26
-------
2.8 Closure on the KOPT model
Use of Green-Ampt theory for ponded infiltration and kinematic wave theory for redistribution allows
the construction of an approximate model of NAPL releases into the vadose zone. The generalized method
of characteristics can be applied to both of these approaches; and so allows either model to be used for
the NAPL flux as necessary. Use of kinematic wave theory for redistribution of the NAPL yields transient
NAPL profiles which are not based on arbitrary assumptions and represent the profiles better than previous
simplified models. Transport of a dissolved constituent of the NAPL can also be formulated as kinematic
model. The partitioning between the phases can be represented by equilibrium linear partition coefficients,
which yields an approximate equation for the water phase concentration of the constituent. The flow and
transport model can then be entirely stated in terms of ordinary differential equations, which are solved in
the KOPT code by a Runge-Kutta technique. The computational efficiency of the model results from the
direct use of the characteristic directions and front speeds, which eliminates the need to discretize the
domain and solve the equations by a differencing method.
The laboratory evaluation of the model demonstrates the ability of the model to capture the
essential qualitative features of NAPL infiltration and redistribution for the experimental conditions. The
quantitative evaluation of the model is limited by the estimation of some of the model parameters in this
work, the variability of the sand pack, and the inability to measure the transient saturations and capillary
pressure curves in situ. The quantitative agreement of KOPT with the experimental results is still
considered acceptable, as in a screening model, exact simulation of heterogeneous conditions is not
intended. The simulation of the experiment illustrates that the treatment of the flow processes in KOPT
is approximately correct and there are not large errors in the gross behavior of the model.
27
[Section 2 Vadose Zone]
-------
Section 3 NAPL Lens Formation at the Capillary Fringe and Source
Term Characterization
When an LNAPL reaches the water table after a spill or release from a leaking tank or pipeline, it
will pond in an oil lens which grows in thickness and spreads. After the source is cut off, the lens will
spread until it reaches a thin layer within the capillary fringe. Much of the hydrocarbon will remain isolated
both above and below the water table at residual saturations. The constituents from the LNAPL release
can dissolve into groundwater which flows beneath the lens, thereby contaminating downgradient drinking
water through miscible phase transport. The OILENS model discussed in this section was developed to
provide a groundwater transport model source term resulting from dissolution of constituents from a floating
free product lens. The OILENS model is based on a number of simplifying assumptions which are listed
below:
1) The hydrocarbon and its constituents enter the lens within a circular area of radius Rs
centered beneath the surface source area. The hydrocarbon enters at a time-variable rate
calculated by the KOPT model.
2) As the oil lens grows and spreads, residual hydrocarbon is trapped within the vadose zone
and the saturated zone beneath the lens. Part of this trapping is associated with the dynamics
of the source term (from the KOPT model) and lateral spreading capacity of the lens. Release
of a more viscous hydrocarbon will result in a lens which achieves a greater thickness before it
spreads, and will result in a greater amount of the hydrocarbon being trapped within the porous
medium. OILENS calculates dynamic trapping through the simulation model itself, as described
below. An additional source of trapping is associated with fluctuations of the water table. Water
table fluctuations result in an apparent thickness of hydrocarbon which is independent of that
required to drive lateral spreading. Capillary trapping due to fluctuations in the water table is
included through a parameter that specifies the thickness of the hydrocarbon layer which must
develop before the lens starts to spread. This residual fluctuation thickness is taken into account
through the continuity equations.
3) A condition of vertical equilibrium holds for the fluids present at any given location. In
particular, for the fluid levels in an observation well, this implies that the levels of the air-oil
interface, zao, the oil-water interface, zow, the air-water interface (water table) in the absence of
hydrocarbon, zaw, and the observation well hydrocarbon thickness, b0, are related through
(34)
(35)
'w
[Section 3 NAPL Lens Formation ...]
28
-------
Pw
Pw ~ PC
(36)
where h0 is the head in the hydrocarbon layer at the given location (h0 = zao if the elevation of the
water table, zaw, is chosen as the datum). These are essentially the relationships presented by
van Dam (1967) and they are the same as the Ghyben-Herzberg approximations used for
modeling fresh water floating on top of saline water in a porous medium (Bear, 1972). It should
be noted that equation (36) states that the head within the hydrocarbon layer is directly
proportional to the oil layer thickness as observed in a well. These relations are helpful in
development of a computational model in that they provide the fluid energy distribution in a
fashion which is not confounded by capillary pressure effects. The OILENS model is based on
the observation well thickness of the lens and an effective volumetric oil content for the lens
which comes from mass balance considerations.
4) Spreading of the hydrocarbon is purely radial, which implies that the slope of the regional
water table is small enough to be unimportant for the lens motion.
5) In calculating the movement of the lens, both the hydrocarbon and water phase are assumed
to be incompressible. Since the flow is assumed to be incompressible, the steady state solution
can be applied at each instant in the unsteady motion of the oil lens (Muskat, 1946). The rate
of lateral spreading is also assumed to be slow enough to confirm and justify use of a lens shape
corresponding to steady-state flow. With the assumption of vertical equilibrium, this implies that
a profile based on the Dupuit assumptions is appropriate.
6) An average effective volumetric oil content may be assigned to the lens, 90, along with
retention oil contents for the vadose zone and the saturated zone beneath the lens, 0orv and 0ors,
respectively. The meaning of the term "effective" is that it represents the ratio of the average lens
thickness b0 (as seen in an observation well) to the actual free product thickness D0. That is, D0
= 90 b0. The actual distribution of an LNAPL near the water table is a function of the capillary
pressure curve for the soil and the fluid densities and interfacial tensions. The capillary pressure
curve for the soil (air-water system) may be scaled for the air-LNAPL and LNAPL-water systems
following Leverett (1941), Schiegg (1984) and others who suggest that the capillary pressure
heads are related by
'cow
(37)
'cao
Po°aw
'caw
(38)
where hdj is the capillary pressure head or capillary rise for the ij-fluid pair, hcaw is the capillary
head for the water-air system, p is the fluid density, 0 is the interfacial tension, and Apow is the
density difference between the hydrocarbon and water. For the oil-water system, its capillary rise
is measured from zao. These allow the LNAPL thickness D0 to be calculated from its thickness
as seen in an observation well, as shown in Figure 14.
29
[Section 3 NAPL Lens Formation ...]
-------
Figure 15 shows representative values of the effective LNAPL saturation as a function of average
lens thickness for 35 API petroleum and for a gasoline in a sand soil.
7) The constituent mass is transported from the lens to groundwater by infiltrating water moving
through the lens and by groundwater flowing beneath the lens and coming into contact with it.
Equilibrium partitioning occurs between the hydrocarbon and water when they are in direct contact.
U
WATER
Saturation
o
z.
ow
Figure 14 Calculation of LNAPL thickness in an oil lens
[Section 3 NAPL Lens Formation ...]
30
.
-------
c
JO
I
is
V)
o
*&
8
5
1 2 3 4 56 7
Observation Well Thickness (ft)
Figure 15 Effective saturation of a hydrocarbon in a sand
3.1 OILENS Model Development
The assumptions of vertical equilibrium, radial flow, and a steady-state hydrocarbon distribution lead
to a simplified representation of the lens. At any given time the free product distribution is specified by
three variables: the effective lens oil volumetric content, 90, the lens head beneath the source, hos, and
the radius of the lens, Rt. The lens oil content is specified as a constant input parameter and must be
estimated from the conditions of the release. The remaining two variables, hos and Rt, vary with time and
must be calculated as part of the model. Their calculation is based on continuity principles, as described
below.
From the Dupuit equation, the oil layer head at any radius r > Rs is given by
h0(r) = h.
OS ,
ln(/?f/rf
(39)
In this last equation Rs is the source radius and R, is the radius of the oil lens. Application of the continuity
principle to the vertical circular cylinder of the lens beneath the source zone, as shown in Figure 16, gives
31 [Section 3 NAPL Lens Formation ...]
-------
loss
Figure 16 Volume balance for the source cylinder
''KOPT
"radial
- a
loss
(40)
In equation (40), QKOPT is the inflow to the lens from the vadose zone as calculated by the KOPT model,
Qf«di«i is tne lateral flow from the circular cylinder, Q,oss includes the volume of oil dissolved from the central
cylinder plus the oil which remains trapped at residual saturation above and below the lens as the lens
thickness decreases after the source has been cut-off. The right-hand-side in equation (40) gives the
change In hydrocarbon volume within the cylinder. The radial flow component may be calculated from
'os
''radial
drlr:
(41)
a
Equations (40) and (41), when combined with the discussion below for calculation of Q!oss, provide an
ordinary differential equation for solving for the lens source head as a function of time:
[Section 3 NAPL Lens Formation ...]
32
_
-------
dh.
OS
dt
(^os' "fJ QKOPT)
(42)
In equation (42), hos and Rt are functions which must be calculated and QKOPT is a function of time which
is provided by the KOPT model.
The second equation for calculation of R, comes from application of continuity to the lens as a whole.
The continuity for the lens volume, Vu may be written
dt
Q
KOPT
(43)
where Qout represents the hydrocarbon losses from the lens due to dissolution as well as that left as
residual during mound decay following source control. VL includes only the actively spreading LNAPL.
Since VL is a function of hos and Rt, we may use to chain rule to write
dVL _ dVL
~dt ~ "6/7
dt
BVL dRt
~ ~dT
(44)
When combined with equation (43), this equation gives
BVL dht
OS
dRt
~dt
dhos dt
dV,
dRt
(45)
The lens volume, VL, is given by (see Appendix 1)
-5- erf
4"
, r
h — -
(*•
, ( Rt}
In —
(46)
In equation (46), erf() is the error function. With this equation the partial derivatives with respect to hos and
R, may be evaluated analytically. The resulting equation is
dRt
~dt
(hos' RP QKOPT)
(47)
33
[Section 3 NAPL Lens Formation ...]
-------
Thus the lens model (equations (42) and (47)) gives a system of ordinary differential equations which are
integrated with an ordinary differential equation solver. Since the KOPT model is also expressed as a
system of ordinary differential equations, the two models are combined together in a single computer code.
That code is called HSSM-KO, and is described in Volume 1 of the User's Guide (Weaver et. al., 1993).
Mass transfer of both the hydrocarbon and the chemical constituent from the oil lens to the aquifer
occurs from infiltrating rainfall and dissolution caused by flowing groundwater. As the infiltrating rainfall
moves through the lens it comes into chemical equilibrium with both the oil and the constituent, and the
mass loss rate to the aquifer is
'infil
Rt
'wo
(48)
where q^ is the volume flux (Darcy velocity) of infiltrating rainfall and cw
for water in contact with the hydrocarbon (see discussion below).
is the equilibrium concentration
For dissolution it is assumed that the concentration of the contaminant at the base of the lens is equal
to its equilibrium value in water. As the migrating groundwater within the aquifer approaches the lens it
has no contaminant within it, and as the groundwater moves beneath the lens, the contaminant diffuses
into th,e groundwater at a rate determined by continuity and vertical dispersion. This is essentially the
model presented by Hunt et al. (1988). Let point x = 0 correspond to the upgradient edge of the lens with
z being measured downward from the lens, and consider a column of groundwater which moves with
velocity v beneath the lens. Then the continuity equation and boundary conditions for this moving column
takes the form
dct
w
dx
(49)
or with Dv = av v where av is the vertical dispersivity,
dx
= a,,
w
with
cw(z,Q) = 0
cw(0,x) = cwo
(50)
(51)
where c^, is the contaminant concentration within the water immediately beneath the lens. The solution
is
cw(z,x) = cwo eric
(52)
[Section 3 NAPL Lens Formation ...]
34
-------
The plan view of the lens is shown in Figure 17. The total flux into the aquifer from the strip of width dy
and of length L(y) is given by
L(y)
•'tvV ^ J / >
"^ ' dx
dz
\
(53)
The length, L(y), of the chord of the circle is
(54)
V
Figure 17 Plan view of the oil lens
35 [Section 3 NAPL Lens Formation ...]
-------
so the total flux is given by
md[ss = 2fdm(y)dy
0
A
(55)
p/(1 _
The Integral in equation (55) may be evaluated numerically to give
1
/<
0
0.87402
(56)
Thus the mass loss due to dissolution within the aquifer is
vRtld\
2Rtav
(57)
The groundwater source term is given by the sum of the minfil and mdiss terms. Thus
m.
source
2Rtav
(58)
It is apparent that the aquifer source term is dependent on the size of the lens, the infiltration rate and
groundwater velocity, the constituent concentration within the lens, and the partitioning characteristics of
the constituent between the oil and water.
The groundwater source term given by equation (58) requires an estimate of the equilibrium concentration
in water in direct contact with the hydrocarbon, cwo. This source term is derived from leaching of trapped
hydrocarbon both above and below the lens, and from the spreading lens itself. The constituent mass
continuity equations give the total mass, Mt, within the lens plus that trapped within the vadose and
saturated zones. This total mass is related to the water equilibrium concentration through the partitioning
relationships as follows:
[Section 3 NAPL Lens Formation ...]
36
-------
M,
cwo
(59)
In equation (59), VVE and Vsz are the total volumes (including LNAPL, water, and soil) containing residual
hydrocarbon in the vadose and saturated zones, and VL is the hydrocarbon volume in the spreading lens.
These volumes are calculated as shown below. With M, and the volumes known at any time, equation (59)
provides the effective water phase concentration of the constituent.
It remains to determine the mass which remains behind with the hydrocarbon at residual saturation
for a decaying lens after source control. The situation is shown in Figure 18. The lens continues to spread
even if dhos/dt < 0. The hydrocarbon and contaminant within the shaded region of Figure 18 becomes
isolated from the lens with the hydrocarbon at residual saturation and the contaminant dissolved within the
hydrocarbon and sorbed on the soil. Since the lens heights are the same at r = R for both times, equation
(39) gives
In
Rt(t+ Af)
In^i
In
Rt(t+ Af)
= G
(60)
In
where G is a constant and this equation is written for the lens radius and source height at times t and t+At.
Since these are calculated from the model and are considered known at the end of time t+At, G is a known
constant. We then have
/ _ , x. \ G
= RM\ (6D
or
R =
G-1
(62)
With the radius R known from (62), the change in total volume occupied by residual hydrocarbon (LNAPL,
w.ater, and soil) may be found from equation (100) of Appendix 1:
(63)
where it is understood that this is used only if dhos/dt< 0. The fraction of the residual volume above the
lens is 1/P and the fraction below the lens is (P-1)/P- Thus the volume of free product which becomes
37
[Section 3 NAPL Lens Formation ...]
-------
t+At
Figure 18 Residual volume for decaying mound
trapped during the time step is
AV,
P P
(64)
The corresponding mass loss is
(65)
The lens concentration is calculated from the ratio ML/VU where ML is the total constituent mass within the
spreading lens.
[Section 3 NAPL Lens Formation ...]
33
-------
Section 4 Gaussian-Source Plume Model
The OILENS model discussed in the last section provides the size of the LNAPL lens and the mass
flux to the aquifer as a function of time. Since the contaminant release to the aquifer may occur over a
long period of time, aquifer transport leads to the development of a contaminant plume. In order to predict
potential exposure concentrations at downgradient receptor locations, a plume model must be coupled with
the OILENS model.
The simplest models for predicting plume concentrations from localized sources are point-source plume
model.. These models consider that the release occurs from a single point, and they are useful for
predicting the time development of a plume from a continuous source, though they have the disadvantage
of predicting infinite concentrations at the source. The concentrations at the source must be infinite in order
to introduce a finite mass flux to the aquifer through a single point. If one is interested in predicting
concentrations near the source as well as in the far field, then a source of finite size must be considered.
As an alternative, we consider the gaussian-source plume model which provides a useful representation
for this purpose. The model presented in this section is very similar to EPACML, the composite landfill
model developed for the U. S. Environmental Protection Agency. The basis for EPACML was presented
by Huyakorn et al. (1982).
In the gaussian-source plume model, the leachate from a surface facility is assumed to migrate
through the unsaturated zone and mix with groundwater flowing beneath the facility. This is shown
schematically in Figure 19. The groundwater model is set up with a gaussian source placed at the
downgradient end of the facility as a boundary condition. Questions of interest concern the depth of
penetration of the leachate into the aquifer, and the coupling of the facility release with the aquifer source
so that mass balance is achieved.
Figure 20 shows a rectangular facility of length L and width W. The total penetration depth of leachate
at the downgradient end of the facility is H. Penetration is caused both by the vertical advection of water
as it moves from the vadose zone into the aquifer, and by vertical dispersion:
H =
H.
dls
(66)
Both Hadv and Hdjs are estimated using the formulation of EPACML.
For Hdis it is assumed that the vertical
component of the velocity decreases linearly from its inflow value at the water table to zero at the base of
the aquifer. Considering the transport of a fluid particle in the resulting flow field leads to
H.
'adv
= bn - exp -
(67)
where b is the aquifer saturated thickness,
velocity in the aquifer beneath the facility.
is the infiltration rate through the facility and q is the Darcy
39
[Section 4 Gaussian-Source Plume Model]
-------
Facility
t
J T VADOSEZONE
AQUIFER
Figure 19 Basic setup of the gaussian-source plume model
\
Figure 20 Development of mixing zone beneath the facility
[Section 4 Gaussian-Source Plume Model] 40
-------
For the dispersive contribution, the width of the dispersive front is proportional to the standard
deviation of the concentration distribution. The concentration distribution variance is given by
Var = 2Dt
(68)
which is Einstein's relation. With Dv = av v where av is the vertical dispersivity, and with t = L/v, then
= ,/Var =
(69)
Using these results in equation (66) we find
H =
- exp -
(70)
Equation (70) gives the depth of penetration of the contaminant into the aquifer beneath the facility. If the
value of H calculated with equation (70) exceeds b, H > b, then in the plume calculations we take H = b.
In the gaussian-source plume model the source is specified by a boundary condition along the
x = 0 axis which takes the shape of a gaussian distribution and is specified by :
c(0,y,t) = cmexp
2 a2
(71)
where cm is the maximum concentration and the standard deviation, a, is a measure of the width of the
source. This is shown in Figure 21. The boundary condition is coupled with the facility by requiring that
the mass flux from the facility equal the advection and dispersion flux from the boundary.
In order to couple the surface release of contaminants with the aquifer boundary condition we use
a condition of mass balance. Considering just the advective flux and with reference to Figure 18 we have
/
= JA = qwicwA = qH f cmexp
-------
m =
\
where X* is the effective decay constant that is defined by
1 +
(73)
A* = A
(74)
with lf equal to the diffuse recharge rate outside of the facility.
Figure 21 Gaussian distribution which is taken as the boundary condition at the
downstream extent of the area beneath the facility
[Section 4 Gaussian-Source Plume Model] 42
-------
For the implementation of TSGPLUME that is used with HSSM, the diffuse recharge rate outside
the facility is taken as being equal to the diffuse recharge rate inside the facility, qwi. The retardation factor,
Rd, is defined by
Rd = 1 +
(75)
where pb is the bulk density, kd the soil water partition coefficient and r| is the porosity. With equation (73)
we see that the peak concentration beneath the facility is related to the mass rate of flow through
m
•"m
71 Han
2 nqa
/
1 +
\
\
WDLRd
V2
(76)
A similar relation may be written from equation (72).
Within the aquifer, transport is assumed to occur in two dimensions. In addition, we now want to
have the possibility of adding on the effects of dilution from infiltration of surface recharge into the plume,
at least in an approximate manner. We assume that recharge serves to dilute the plume and acts as an
equivalent decay term. In this case the transport equation is
D dC .,dC
rtj — T v — —
dt
dX
62c
dy2
c = 0
(77)
In equation (77) the flow is assumed steady and the velocity remains uniform in the x-direction. To simplify
notation we use the effective decay coefficient, X*, so that the transport equation is
dt
dx
= 0
(78)
43
[Section 4 Gaussian-Source Plume Model]
-------
subject to
c(x,y,0) = 0
c(0,y,t) =
c(~,y,f) = c(x,-oo,f)
(79)
= 0
In order to simplify the development which follows, it is useful to place the problem in dimensionless form.
Introduce the following variables:
vzt
A =
DLD7
(80)
Then equations (78) and (79) become
8C
- + -
BT 8X
BY2
+ AC = 0
and
(81)
C(0,Y,T) = exp
(82)
where the other boundary conditions remain the same. To proceed, it is easiest to first solve the steady-
state problem.
[Section 4 Gaussian-Source Plume Model] 44
-------
For the steady-state problem the transport equation takes the form
dc
dx
dY2
c(Q,Y) = exj
A~ n
+ A C = 0
(83)
The solution to this equation follows through application of Fourier transforms, and is found to be
C(X, V) -
-/H
71 J \
The mathematical statement of the transient problem is given in equations (81) and (82).
Application of the Laplace transform reduces the equation to the steady state form whose solution is
given above. Using a few well known theorems the general solution is then found to be
C(X,Y,T)
X 1 +4A
4t 2+4Df 2
dt
(85)
2DO
This is the general solution for a constant boundary condition.
The solution given by equation (85) is the transient solution for the case with a fixed boundary
condition along X=0. If one wishes to model the case with a time-variable source strength, then one
needs the solution for the case with a variable concentration along this boundary. If we assume that
the width of the gaussian-source remains constant and that the concentrations change uniformly, then
one may find the desired solution directly through use of Duhamel's theorem. Paraphrasing Carslaw
and Jaeger (1959, pg. 31), Duhamel's theorem may be stated as follows:
If C = F(X,Y,T) represents the concentration at point (X,Y) at the time T in an aquifer in which
the initial concentration is zero, while its "surface" concentration is the constant function
(|)(X,Y), then the solution of the problem in which the initial concentration is zero, and the
surface concentration is B(T) <|)(X,Y) is given by
45 -
[Section 4 Gaussian-Source Plume Model]
-------
C(X,Y,T)
0
r
9 /
(86)
Since the transient solution of equation (85) is an integral with T appearing only in the upper limit, the
partial derivative with respect to T is simply the integrand. Recognizing this and using equation (86),
the solution may be written
r S(7-(o)ex
C(X, Y, T)
X2
K-
Y2
1 +4A
2+4Dw
(87)
2Do>)
Equation (87) forms the basis of the Transient Source Gaussian Plume (TSGPLUME) model. The
integral is evaluated using Romberg integration to achieve the desired level of accuracy.
[Section 4 Gaussian-Source Plume Model]
-------
Section 5 The Response of HSSM to Parameter Variation
The HSSM model results are sensitive in varying degrees to all of the input parameters. To give the
user a feel for some important parameters of the model, sensitivity analyses are presented in this section.
Model parameters are varied individually over arbitrary ranges to demonstrate the behavior of the model.
In some cases, the ranges selected are most likely to cover the entire range of variation of the parameter.
The results illustrate the variation in chemical concentrations at receptor points that are caused by the
variations in input parameter values, This output was chosen to demonstrate the sensitivities of the model
because it is a principle output of the model. Other outputs such as the arrival time at the water table
(Section 5.1 of Volume 1) or lens radius could also be used to demonstrate the model sensitivities.
Depending on the results of interest, the sensitivities may follow different patterns than shown below for
the receptor concentration. For example, the lens radius is not greatly affected by variation in the
NAPL/water partition coefficient, but the receptor concentration is affected significantly. So for the lens
radius, the conclusion is that the NAPL/water partition coefficient is not an important parameter, while it is
important for the receptor concentrations. To provide information on other sensitivity measures,
Table 10, Table 12 contains the NAPL arrival time at the water table and the lens radius that occurs when
the mass flux to the aquifer is at its peak. These tabular results compliment the concentration data and
can be used to assess the impact of the parameters on these other outputs.
5.1 Base Scenario
The base scenario for the sensitivity analyses is given in Problem 2, entitled "Transport of Gasoline
Constituents in Ground Water to Receptor Locations," presented in Section 5.2 of Volume 1 of the HSSM
user's guide (Weaver et al., 1994). The problem statement reads:
"During a one-day period, 1500 gallons of gasoline leak from a tank surrounded by a circular berm
of 2.0 meter radius. Benzene is believed to compose 1.15% by mass of the gasoline. The benzene
concentration in the ground water at locations 25, 50, 75, 100, 125 and 150 meters away are needed
to assess the impact of the spill. The soil is believed to be predominantly sand in the vicinity of the
spill. The aquifer is 10 meters below the ground surface, and its saturated thickness is 15 meters.
"Complete information for the site is not available so many of the HSSM parameters must be
estimated. In the absence of better information, parameter values will be estimated from tabulations
from the literature. The data set for this example will be organized according to the four dialog boxes
for entering data in HSSM-WIN. The parameters for this example are found in the file X2BT.DAT,
which is found on the HSSM-WIN distribution diskette.
The complete set of results from this problem is found on pages 59 to 62 of Volume 1. Concentration
histories at four receptor locations are shown by solid lines in Figure 22. Each receptor location lies along
the centerline of the flow system, as shown in Figure 23. To extend the effects demonstrated by this
example, simulations results for the 50 meter receptor are shown for toluene and the xylenes (lumped
para-, meta- and ortho-xylene) in Figure 24. The peak concentration and arrival time of the peak are
influenced by the initial concentration of the constituent in the NAPL and the NAPL/water partition
coefficient. These parameter values are shown in Table 3. Comparing the toluene result with the benzene
result shows that increasing the initial constituent concentration in the NAPL increases the peak
concentration. Comparing the result for xylenes against benzene shows that even with higher initial
concentration in the NAPL, the receptor peak concentration is lower for the xylenes because of the
increased partition coefficient. Increasing the partition coefficient tends to lower receptor concentrations
because the constituent remains in the NAPL thus decreasing the peak mass flux to the aquifer.
47
[Section 5 Parameter Variation]
-------
Table 3 Constituent Parameters for benzene, toluene and the xylenes
Constituent
benzene
toluene
xylenes
Initial Concentration in the
NAPL
(mg/L)
8,208
43,600
71,800
NAPL/water partition
coefficient
311
1,200
4,440
The centerline locations are used below to show the effects of parameter variation. To simplify
presentation of the results, only the peak concentration is plotted against the arrival time. The peak
concentration for each receptor is indicated by an open square in Figure 22.
The response of HSSM to parameter variation can follow nine patterns that are illustrated in Figure 25.
Squares indicate the peak concentrations and arrival times from the X2BT.DAT data set for receptors at
25 m, 50 m, 100 m and 150 m down gradient from the source. By varying input parameters, this curve
may shift in various directions as indicated by the labeled arrows. Thus the curve may shift vertically
upward if the peak concentration increases and the arrival time remains the same (arrow labeled A), or
increased concentrations may occur with earlier (arrow labeled H) or later (arrow labeled B) arrival times.
If variation of the parameter has a negligible impact on the peak concentration and the arrival time, then
it is classified as "I."
As will be seen to be obvious below, this classification system only approximately captures the
variation in the results. Some results would be better described by a rotation of the curve, as the impacts
change character with the distance to the receptor (e.g., Figure 49). Also some effects which are dominant
near the source tend to die out further away (e.g., Figure 50). Deviations such as these are noted in the
following text.
[Section 5 Parameter Variation]
48
_
-------
0 500 1000 :1500 2000 2500
Time (days)
Figure 22 Concentration histories for the X2BT.DAT data set
y
-e e-
source
25 50
lens
100
receptors
150
Figure 23 Plan view of HSSM model scenario
49
[Section 5 Parameter Variation]
-------
o>
c=
g
"sa
(D
O
8
20
15
10
0
A—A Benzene
o—D Toluene
o—o Xylene
0 1000 2000 3000 4000
Time (d)
Figure 24 Concentration Histories at 50 meters for benzene, toluene and the xylenes.
20
o
'
'§
o
o
8.
15 -
10
i.... i
100 200 300 400 500 600
arrival time (days)
Figure 25 Possible HSSM responses to parameter variation
[Section 5 Parameter Variation]
50
-------
5.2 Usage of Parameters in HSSM
To determine the concentration history at each receptor point, the aquifer model, TSGPLUME, uses
a portion of the HSSM input parameter set, and the mass flux that is determined by HSSM-KO as a
boundary condition. Thus, some portion of the TSGPLUME results directly from the effects of HSSM
parameter variation on solute transport in the aquifer. A significant portion also depends on the boundary
condition. The mass flux to the aquifer is determined by HSSM-KO and depends on the parameters of
KOPT and OILENS. Some of these parameters are not used by TSGPLUME, but their effect is felt
through the boundary condition.
Generally, the arrival time of the peak concentration at a given receptor depends on the arrival time
of the NAPL at the water table, and the time at which the mass flux to the aquifer is a maximum. The
arrival time at the water table depends on the KOPT model results and thus represents the effects of
vadose zone flow and transport. The time of maximum mass flux depends upon the rate of spreading of
the NAPL lens, since the mass flux is a function of the radius of the lens (equation (58)). Further, equation
(58) shows that the mass flux increases with radius because of the terms that include R,2 and R,3/2. Also
appearing in that equation is the aqueous phase concentration that is in equilibrium with the lens, Cwo.
As can be noted from equation (59), this concentration depends on the lens volume, which in turn depends
upon the lens radius. So for a given set of parameters, the lens radius, Rt, and concentration Cwo (plotted
for X2BT.DAT in Figure 26) determine the variation in mass flux. This figure shows that the aqueous
concentration reaches a maximum at a relatively low radius, and declines while the radius continues to
increase. Notice that because of the contribution of the lens radius, the peak mass flux occurs later than
does the peak concentration in this example.
25
20
O)
|S,5
.3
8
o
Aqueous Concentration
Mass Flux
0 200 400 600 800 1000
Time (days)
0.1
0.08
0.06,
0.04
0.02
0
X
J3
LL
Figure 26 NAPL lens radius and aqueous concentration for the example 2 data set
51
[Section 5 Parameter Variation]
-------
Equation (76) is used in TSGPLUME to determine the centerline concentration at the boundary (the
leading edge of the lens). Combining equations (58) and (76), and noting the definition of the penetration
thickness (equation (70)) gives
2Rtav
(88)
^
1 +
1 +
The length of the facility, L, is taken as twice the lens radius, and the standard deviation of the gaussian
distribution, 0, is taken as one quarter of the lens radius. In equation (88), the radius R, refers to the single
value that is used in TSGPLUME. As noted in Volume 1, a value is selected from the radius history
(Figure 26). Normally the radius that occurs when the mass flux is at its peak is chosen. The
concentrations determined from equation (88), thus reflect the balance between mass flux and dilution, both
of which increase with the radius of the lens. Peak concentrations from equation (76) are used below to
assess the impact of increasing lens radius on the receptor concentrations, because higher receptor
concentrations are expected if the concentration at the source increases.
Before beginning the presentation of the results, two features of HSSM must be noted. First, because
the procedure used for finding the peak concentration in HSSM-T is an approximation (see discussion on
page 14 of Volume 1 of the user's guide), the arrival time is precise only to within a few days (typically 2
to 5). The peak concentrations determined by HSSM-T can vary, depending primarily upon the time step
taken in the program. Thus the values reported in this section may not be exactly reproduced if the cases
were rerun with a slightly different time interval in HSSM-T. The trends are valid, however, and care was
taken to determine that variations in the peak concentration and arrival times were significant, rather than
artifacts of the procedures used.
Second, for each parameter that affects the size of the NAPL lens, the appropriate value of the
maximum NAPL saturation in the lens, S0(max), must be found. The NTHICK utility (Appendices 3.3 and 7
of Volume 1 of the User's Guide) or an automated version, NTHICK2, was used for these calculations. The
sotm«x) values can be found in the data sets on the distribution diskette. Generally four or five runs of
HSSM-KO were required to converge to a value of S0(max) within a tolerance of 0.0001.
[Section 5 Parameter Variation]
52
-------
5.3 Sensitivity Results
Each physical and chemical parameter of HSSM was used in the analysis. The parameters were
varied over a plausible, but arbitrary, range. The data sets are found in the EXAMPLES \SENS directory
on the distribution diskette. Table 12 in Appendix 2 lists the file names for each parameter. The results
are classified according to the possible impacts on the peak concentration vs. time-to-peak curve
(Figure 25). A total of 34 sets of parameter variation trials are reported below. Of these, three are
repetitions of some other parameter (smear zone repeats the capillary thickness parameter, "all
dispersivities" repeats the individual dispersivities, and aquifer thickness has two response types) and two
are not independent physical parameters (percent maximum radius and NAPL saturation in the lens).
Figure 27 shows the frequency of response types from the 29 remaining sets of parameter variation trials.
The smallest slices (A, B, and G) each represent one parameter and compose 3.45% of the pie. The
largest slice (I) has is the null response and contains eight parameters. Of the remaining slices, the largest
are those of the parameters where both the peak concentration and its arrival time are affected (D six
parameters, F four parameters, and H six parameter). There are relatively few parameters that impact only
the concentration or the arrival time (A one parameter, C no parameters, E two parameters, G one
parameter).
E 6.90%
D 20.69%
F 13.79%
H 20.69%
I 27.59%
Figure 27 Pie chart showing frequency of parameter variation responses
For each response type, A through I, the parameters are listed in tables followed by a discussion of
the results. The following tables (e.g., Table 4) list the parameter names (column 1), the classification or
type at the 150 m receptor (column 2), the minimum and maximum parameter values used (columns 3 and
5), the value from the base case (column 4), and the HSSM modules that are affected by the parameter
(column 6). The classification at the 150 m receptor is included, because for a number of the parameters
the impact changes with distance from the receptor. In cases where the impact is great enough to change
the classification, the type listed in column 2 differs from the type of the table. Sometimes a type is
indicated with an arrow (->) which means that the results tend toward the indicated type. The 6th column
53
[Section 5 Parameter Variation]
-------
is included because the impacts of certain parameters are similar. Often these parameters are related,
both in the HSSM modules that use them and in their physical or chemical significance. Codes are listed
for each module of HSSM in the order: KOPT, OILENS, and TSGPLUME. A "Y" or "N" in this column
indicates direct use or nonuse of the parameter, respectively. The "I" indicates an indirect impact, meaning
that the parameter only impacts the input to the module and not the equations solved in the module itself.
Note, for example, that porosity has a direct impact on KOPT, OILENS and TSGPLUME and the code in
column 6 is YYY. NAPL viscosity, however, directly impacts KOPT and OILENS; its impact on
TSGPLUME is indirect because the NAPL viscosity is not used in the aquifer model, but affects the model
results through the boundary condition. Table 13 in Appendix 2 summarizes the fraction of parameters
which impact each module, classified by response type.
Table 4 Parameter with Type A Response
(Increasing Peak Concentration, Constant Arrival Time)
Parameter
Initial constituent
concentration in the NAPL,
Colni
Type
at
150
m
A
Minimum
Value
820 mg/l
(0.0115 %)
Po = 0.71
g/cm3
K0 = 307
Value used in
Problem 2
Section 5.2 of
Volume 1
8208 mg/l
(0.115 %)
Po = 0.72
g/cm3
K0 = 311
Maximum
Value
12300 mg/l
(0.172%)
Po = 0.72
g/cm3
K0 = 314
Module
Impacts
(K,0,T)
Yll
5.4 HSSM Response: Increasing Peak Concentration, Constant Arrival Time
5.4.1 Initial Constituent Concentration in the NAPL
The only parameter that causes the peak concentration to increase with constant arrival time is the
initial constituent concentration in the NAPL, Colni (Table 4). When Coini changes so, do the NAPL density,
and the NAPL/water partition coefficient. The values shown in Table 4 were determined by using the
RAOULT utility (Appendices 3.2 and 6 of Volume 1 of the User's Guide). Figure 28 shows that the peak
concentrations increase with the initial constituent concentrations and that the arrival times are unaffected.
CM is used directly only by KOPT, but determines the magnitude of the mass flux into the NAPL lens and
the aquifer. As Colnl increases from 820 mg/L to 12300 mg/L the peak mass flux to the aquifer increases
from 0.0070 kg/d to 0.10 kd/d. The resulting source concentration (equation (88)) in the aquifer increases
from 3.905 mg/L to 55.73 mg/L. At the same time the water table arrival times, and time to peak mass flux
remain relatively constant (+/- 4 days).
[Section 5 Parameter Variation]
54
_
-------
Table 5 Parameter with Type B Response
(Increasing Peak Concentration, Increasing Arrival Time)
Parameter
Source radius, Rs
Type
at
150
m
B
Minimum
Value
0.2m
Value used in
Problem 2,
Section 5.2 of
Volume 1
2.0m
Maximum
Value
4.0 m
Module
Impacts
(K,0,T)
Yll
5.5 HSSM Response: Increasing Peak Concentration, Increasing Arrival Time
5.5.1 Source Radius
The source radius (defined in Figure 23) is the only parameter to cause the both the peak
concentration and the arrival time to increase (Table 5). The low peak concentration at low radii are
generally related to the reduced amount of contaminant introduced into the aquifer with a low source radius.
The arrival time increases with source radius, because the peak mass flux (as input to TSGPLUME) occurs
later as the source radius increases. As the radius increases from 0.2 meters to 4.0 meters, the time for
the peak mass flux increases from 31.9 days to 142.0 days after the NAPL arrives at the water table. This
time lag accounts for the difference in the peak concentration arrival times. The peak mass fluxes to the
aquifer and the effective source concentrations also increase with the radius of the source.
20
E 15
1
CD
O
cd
8.
10
25m
O 820 mg/L
D 8208 mg/L
A 12300 mg/L
D
50m
O
A 100m
D
O. . . . ,
150m
A
D
. O .
200 300 400 500, 600
arrival time (days)
Figure 28 Peak concentration vs arrival time for variation in the initial contaminant
concentration
55
[Section 5 Parameter Variation]
-------
£U
^ ^
_J
I5 15
c
.0
1 10
CD
O
0
O
\^ p~
8.
n
O 0.2 meters
~ D 1.0 meters
A 2.0 meters
O 4.0 meters
O
A
0
A
D C
A
D A
0 D D
\J /-^.
• • -V ' O . . , 1 . , , (7M , , ......
100 200 300 400 500
arrival time (days)
600
Figure 29 Peak concentration vs arrival time for variation in the source radius
5.6 HSSM Response: Decreasing Peak Concentration, Increasing Arrival Time
5.6.1 Depth to water
In HSSM, the NAPL travels through the vadose zone to reach the aquifer. Thus the depth to water
determines the distance from the surface to the water table. This distance affects the travel time through
the vadose zone and its ability to retain NAPL. The first effect is that as the depth to the water table
increases, so does the arrival time of the NAPL at the water table (Table 12). Thus, the times for the peak
mass flux to the aquifer increase with the depth to water. Since some of the NAPL is retained within the
vadose zone (because of the residual NAPL saturation of 0.10), the amount of NAPL reaching the water
table also decreases with depth to water. This is reflected in reduction in lens radius for the peak mass
flux, and resulting reductions in peak mass flux and effective concentration. These lead to reduction in
peak receptor concentration with depth to water (Figure 30).
[Section 5 Parameter Variation]
56
-------
Table 6 Parameters with Type D Response
(Decreasing Peak Concentration, Increasing Time-to-Peak)
Parameter
Depth to water
Porosity and bulk density,
TI and pb
NAPL viscosity, u0
Vadose zone residual NAPL
saturation, Sorv
Soil/water partition
coefficient for the constituent
NAPL/water partition
coefficient for the constituent
Smear zone thickness
Type
at
150
m
D
D
->C
D
->C
D
->C
Minimum
Value
7.5 m
0.35
1 .72 g/cm3
0.30 cP
0.0
0.0415 L/kg
250
0.065 m
Value used in
Problem 2
Section 5.2 of
Volume 1
10.0 m
0.43
1.51 g/cm3
0.45 cP
0.05
0.083 L/kg
311
0.065
Maximum
Value
12.5m
0.50
1 .32 g/cm3
0.60 cP
0.075
0.1660 L/kg
375
1.0m
Module
Impacts
(K,0,T)
Yll
YYY
YYI
YYI
YYY
YYI
NYI
5.6.2 Porosity and bulk density
Porosity, TI, and bulk density, pb, both play a role in determining receptor concentrations and are
related by
= Ps(1 - l
(89)
where ps is the solid density. Increasing the porosity delays the NAPL's arrival at the water table, because
with higher porosity, more of the NAPL is needed to fill a given volume of the vadose zone. The same
effect causes the resulting lenses to be smaller. The lens radius at peak mass flux to the aquifer thus
declines, resulting in lowered mass flux and effective concentrations at the.source. These effects tend to
decrease the receptor concentrations. Sorption of the constituent, however, declines as the porosity
increases, because of equation (89). This effect would tend to increase the receptor concentrations, but
is not dominant in this example.
5.6.3 NAPL viscosity
The NAPL viscosity in part determines the effective conductivity to the NAPL. Equation (2) shows
that increasing the NAPL viscosity decreases the effective conductivity. This behavior impacts the receptor
concentrations indirectly, as it increases the arrival time at the water table; and slows the rate of expansion
of the NAPL lens. With increasing viscosity, NAPL lenses tend to be thicker and thus have lower radii.
57
[Section 5 Parameter Variation]
-------
These characteristics of the lens cause the peak mass flux to the aquifer to occur somewhat later with the
range of viscosity used here. Much higher viscosities are encountered with other types of oils, these would
accentuate these effects. As the lens radius at peak mass flux declines, so does the peak mass flux and
to some extent the effective source concentration. The result is that increasing the NAPL viscosity delays
the arrival and reduces the peak concentration (Figure 32).
5.6.4 Vadose zone residual NAPL saturation
In the vadose zone, increasing the residual NAPL saturation increases the amount of NAPL retained
per unit volume of soil. The effect is similar to that caused by increasing the depth to water (Figure 30),
with the exception that the OILENS results are also affected by the vadose zone residual NAPL saturation.
As the vadose zone residual NAPL saturation increases, the arrival time at the water table increases. This
is due largely to the impact on the NAPL relative permeability function, because as the residual NAPL
saturation increases, the amount of NAPL needed to achieve a certain relative permeability also increases
(equation (4)). The phase flow speeds in vadose zone (equations (12) and (13)) both depend on the
relative permeability and thus both decline with increase vadose zone residual NAPL saturation. In OILENS
as the input flux declines, the lens collapses (Figure 18) and some NAPL is retained in the vadose zone
at the residual vadose zone saturation. The constituent that is held in the residual NAPL is gradually
leached into the aquifer by the aquifer recharge. This leaching contributes a relatively small amount to the
peak mass flux. In this example, the mass flux to the aquifer is more highly dependent upon the size of
the lens at the water table. The result is the type D response shown in Figure 33.
13
^ ^
_J
"5)
e
c 10
o
1?
"c
8
8 *
"ro
Q_
n
*"* \^ O 7.5 meters
^^^^ D 10 meters
^ 25m A 12,5 meters
I — I •^*^'
0 1
A
D
50m
~~ A O — ioOm
°X \ o
AD 150m
A
, . . . t . . . . 1 , „ ; , ,
100 200 300 400 500 600 700
arrival time (days)
Figure 30 Peak concentration vs arrival time for variation of depth to water
[Section 5 Parameter Variation]
58
-------
15
c 10 -
o
'•g
§'
| 5h
CO
-------
20
15
10
8
8
o
D
25m
O
D
50m
100m
O
D
A
O o.o
D 0.025
A 0.05
O 0.075
150m
A
0
100 200 300 400 500 600 700
arrival time (days)
Figure 33 Peak concentration vs arrival time for variation of the vadose zone residual
NAPL saturation
5.6.5 Soil/water partition coefficient for the constituent
Although the partition coefficient, kd, is used by all three modules of HSSM, the KOPT and OILENS
results are only slightly affected by changing kd. This result occurs because the NAPL constituents are
usually hydrophobic and tend to remain mostly in the NAPL phase. Flow of the NAPL itself, largely
determines the distribution of the constituent within KOPT and OILENS. The main impact of kd occurs in
the aquifer (Figure 34) where increased partitioning leads to lower peak concentrations (because sorbed
constituent does not add to aqueous concentration) and to later arrival times (because sorbed mass is
immobile and the overall rate of transport is reduced). For this example, the partition coefficient was
changed by assuming varying amounts of organic carbon in the aquifer. The kd values of 0.0415 L/kg,
0.083 L/kg, and 0.166 L/kg correspond to organic carbon fractions of 0.0005, 0.001 and 0.002, respectively
and an organic carbon/water partition coefficient, Koc, of 83 L/kg for benzene.
5.6.6 NAPL/water partition coefficient for the constituent
The NAPL/water partition coefficient is defined as the ratio between the water phase and the NAPL
phase concentrations of the constituent (equation (26)). As K0 increases, the time of the peak mass flux
increases. This behavior is due to higher retention of the constituent in the NAPL phase, and more time
required to remove the constituent from the lens. The peak fluxes to the aquifer decline, because on
average the concentrations in the water phase are reduced. In most of the cases examined for this Section
increasing lens radius resulted in increased mass flux to the aquifer. The NAPL/water partition coefficient
is one example where the radius increases with the parameter value, but the mass flux declines (due to
the decreased concentrations).
[Section 5 Parameter Variation]
60
-------
5.6.7 Smear zone thickness
The smear zone that can be built into HSSM data sets represents water table fluctuation that can
spread the NAPL over a certain thickness. When the thickness of the smear zone increases, the size of
the lens is reduced. The effect is to reduce the mass flux to the aquifer, thus delaying and reducing the
magnitude of the peak (Figure 36). The effective source concentrations are highest, however, for the
thicker smear zones.
I
o
8
8
cd
CD
CL
15
10
O 0.0415 Ukg
D 0.083 Ukg
A 0.1660 Ukg
A
50m
A
100m
°D
A 150m
0 D
0
100 200 300 400 500 600 700
arrival time (days)
Figure 34 Peak concentration vs arrival time for variation of the soil water partition
coefficient for the constituent
61
[Section 5 Parameter Variation]
-------
_J
w
c:
o
1
§
c
o
o
!
14
12
10
8
6
4
2
n
O O 250
25m 0 311
D A 375
- A
O
D 50m
• A
_ 100m
n^ 150m
CftA
1 ..,.,....,.,.,
200 300 400 500
arrival time (days)
600
Figure 35 Peak concentration vs arrival time for variation of the NAPL/water partition
coefficient
BJ
E.
*4_J
03
•*=;
I
CD
O
§
CO
8.
\C-
10
g
6
4
Q O 0.065 meters
D 0.25 meters
D A 0.50 meters
A 25 m O 0.75 meters
O V 1,0 meters
V
O 50m
n
A>
100m
150m
A
-------
5.7 HSSM Response: Decreasing Peak Concentration, Constant Arrival Time
Parameters with Type E Response
(Decreasing Peak Concentration, Constant Time-to-Peak)
Parameter
Aquifer thickness
(less than penetration
thickness)
Transverse horizontal
dispersivity, aT
Type
at
150
m
E
E
Minimum
Value
0.5 m
0.5 m
Value used in
Problem 2
Section 5.2 of
Volume 1
15 m
1.0m
Maximum
Value
20 m
1.5 m
Module
Impacts
(K,0,T)
NNY
NNY
5.7.1 Aquifer thickness (less than penetration thickness)
In TSGPLUME, the penetration thickness represents the thickness of the aquifer that is contaminated
with the NAPL constituent. In this way the model does not assume that the constituent is mixed over the
entire aquifer thickness, but is confined to a region near the water table. For this example, the calculated
penetration thickness is 1.966 m (equation (70)) and the aquifer thickness is 15 m. For the purposes of
this study, simulations were run with the aquifer thickness set to values that are less than the calculated
penetration thickness (0.5 m, 1.0 m and 1.5 m). In such cases, the concentration increases because the
chemical is introduced into a volume that is smaller than that determined from the penetration thickness.
The concentrations here indeed increase, with no change in arrival time (Figure 37). When the aquifer
thickness exceeds the penetration thickness (1.966 m, 15 m, and 20 m), the concentrations become
independent of the aquifer thickness.
5.7.2 Transverse horizontal dispersivity
The transverse horizontal dispersivity, aT, is only used in the aquifer model and determines the
amount of lateral spreading of the contaminant plume. The concentrations decline along the centerline of
the flow system (Figure 38), because there is increased horizontal spreading of the plume as the transverse
dispersivity increases.
63
[Section 5 Parameter Variation]
-------
^3"
.£,
c
.g
Is
i *
CD
O
|
CD
Q.
uu
40
30
20
10
n
o
o n
A
o
V
X
-
o
25m
: n
-
50m _
- A D °
& . 100m
& n
r .... i .... i ....
0.5m
1.0m
1.5m
1.966m
15m
20m
150m
0
n
200 300 400 500
arrival time (days)
600
Figure 37 Peak concentration vs arrival time for variation of the aquifer thickness
ID
1
1
?
"cT 10
o
"E
H — •
c.
8
c
8 5
•s
CD
Q.
1C
O 0.5 melers
Q D 1.0 melers
A 1 .5 mete:rs
25m
D
A
O
50m
n
A 100m
O
150m
2
)0 200 300 400 500 60
arrival time (days)
Figure 38 Peak concentration vs arrival time for variation of transverse dispersivity
[Section 5 Parameter Variation]
64
-------
5.8 HSSM Response: Decreasing Peak Concentration , Decreasing Arrival Time
Table 8 Parameters with Type F Response
(Decreasing Peak Concentration, Decreasing Time-to-Peak)
Parameter
Ratio of horizontal to vertical
conductivity, RKS
Gradient
Transverse vertical
dispersivity, av
Dispersivities
% maximum radius
Constituent half-life
Type
at
150
m
->G
->G
F
F
F
F
Minimum
Value
1.0
0.005
0.05 m
aL = 5 m
aT = 0.5 m
av = 0.05 m
25 %
247.5 d
Value used in
Problem 2
Section 5.2 of
Volume 1
2.5
0.01
0.1 m
aL = 1 0 m
aT = 1 .0 m
av = 0.1 m
49.15 %
Infinite
Maximum
Value
10.0
0.02
0.15m
aL = 1 5 m
aT = 1 .5 m
av = 0.15 m
100%
Infinite
Module
Impacts
(K,0,T)
NYY
NYY
NYY
NNY
NNY
NYY
NNY
NNY
5.8.1 Ratio of horizontal to vertical conductivity
In HSSM, the ratio of the conductivities is used to specify the horizontal conductivity of the aquifer.
Thus when the ratio of horizontal to vertical conductivity, RKS, increases, the horizontal hydraulic
conductivity increases while the vertical conductivity remains unchanged. KOPT uses only the vertical
conductivity, while OILENS and TSGPLUME both use only the horizontal conductivity. Thus the KOPT
result, the NAPL arrival at the water table, is independent of horizontal conductivity variation. The extent
of the lens, however, is greater with increasing horizontal conductivity, because with higher conductivity the
lens can spread more readily. The peak mass flux, though, occurs at a lower radius, leading to a decline
in the magnitude of the peak mass flux and the effective concentration. The result is earlier peak arrival
times due to the increased conductivity of the aquifer and lower peak concentrations (Figure 39) due to the
variation in the mass flux distribution.
5.8.2 Gradient
Along with the hydraulic conductivity, the hydraulic gradient in the aquifer determines the ground water
velocity. The effect of increasing the gradient is similar to that of increasing the horizontal hydraulic
conductivity (Figure 39), except that in HSSM the gradient does not affect the NAPL lens. Obviously, the
NAPL arrival time at the water table is independent of the ground water gradient. The lens radius at peak
mass flux to the aquifer and the effective source concentration decrease with the gradient, so the receptor
concentrations decline with increasing gradient (Figure 40).
65
[Section 5 Parameter Variation]
-------
15
S
1z
8
8
8.
O 1.0
n 2.5
D
50m
D
o
100m
A
A
D
150m
0
500 1000 1500
arrival time (days)
Figure 39 Peak concentration vs arrival time for variation of the ratio of horizontal
to vertical conductivity
ID
^
?
c 10
.g
"&
c
0)
o
§ 5
o
•s
CD
Q.
n
O 0.005
D 0.01
o 25m A 0.02
D
'A
50m
O
D
A
100m
D O
A A D 150mO
200 400 600 800 1000
arrival time (days)
Figure 40 Peak concentration vs arrival time for variation of the hydraulic gradient
[Section 5 Parameter Variation] QQ
-------
5.8.3 Transverse vertical dispersivity
The vertical dispersivity, av is used in calculating the mass flux to the aquifer (equation (58)), the
effective source concentration (equation 76), and the penetration thickness (equation (70)). Increasing
the vertical dispersivity causes both the mass flux and the penetration thickness to increase. These are
competing effects as the first tends to increase peak receptor concentrations and the second to decrease
them. Here the net effect is a decrease in the effective source and receptor concentrations (Figure 41).
The peak arrival times at the receptors decrease, because the increased mass flux causes the chemical
to be leached more rapidly with high av than with low.
5.8.4 All dispersivity
When all the dispersivities vary, with the proportions of longitudinal to horizontal transverse and
longitudinal to vertical transverse dispersivity maintained at rations of 10:1 and 100:1, respectively; the
peak receptor concentrations and their arrival times vary as shown in Figure 42. Of the effects of
dispersivity seen so far (horizontal transverse, Figure 38; and vertical transverse, Figure 41), the behavior
of variation in all the dispersivities is similar to that of the vertical transverse (Figure 41). The pattern also
matches the longitudinal dispersivity effect at the more distant receptors (Figure 49). So the combined
effects of proportional variation in all of the dispersivities is to decrease both the arrival time and the peak
concentration at the receptor points. Figure 43 shows the horizontal spread of the concentrations at the
50 m receptor (illustrated in Figure 23). These profiles were drawn at the arrival time for each set of
dispersivities. With the high-valued set of dispersivities, the center line concentration is reduced because
the mass has been transported outward from the centerline of the plume. The opposite effect is evident
for the low-value set of dispersivities. This behavior matches that shown on Figure 42.
15
CD
cT 10
o
1 5
03
o
25m
O .05 meters
D .10 meters
A .15 meters
D
A
50m
O
D
A
100m
.D
150m
O
A°
100 200 300 400 500 600 700
arrival time (days)
Figure 41 Peak concentration vs arrival time for variation of transverse vertical
dispersivity
67
[Section 5 Parameter Variation]
-------
DJ
15
10
CD
O
1 5
cd
CD
Q.
O
25m
O low
D average
A high
°
50m
100m
O
150m
D
n
A
0
100 200 300 400 500 600 700
arrival time (days)
Figure 42 Peak concentration vs arrival time for variation of all dispersivities
(longitudinal, transverse and vertical)
5 10 15 20 25 30
distance (m)
Figure 43 Transverse horizontal concentration profiles for the variation in all the
dispersivities
(Section 5 Parameter Variation]
68
-------
5.8.5 Percent maximum radius
The TSGPLUME input parameter, percent maximum radius, is described in Volume 1 of the Users
Guide (page 49 or 142). The recommended value of the parameter is 101. When this value is used, the
radius of the boundary condition used in TSGPLUME is taken as the radius that occurs when the mass flux
to the aquifer is a maximum. For the base scenario (X2BT.DAT), this occurs at a radius of 8.41 m which
is 49.15% of the maximum radius. The effect of using other values for the radius is shown in Figure 44.
The peak concentrations are inversely related to this parameter value, because when the peak mass flux
is introduced into a smaller area, the resulting concentrations increase. The arrival times decrease with
increasing percent maximum radius used in TSGPLUME, because in any case the initial input of mass to
the aquifer occurs at a smaller radius than is used in TSGPLUME. This mass would have to travel all the
way to the receptor, but the travel distance is shortened by selecting a radius (which is necessary). The
larger the radius that is selected, the greater the shortening of the travel distance and hence the earlier
arrival time.
5.8.6 Constituent half-life
The half-life of the constituent affects only the TSGPLUME results. With increasing decay rate, the
peak concentrations decline due to loss of the constituent. At the near receptors, the arrival time remains
nearly constant. Further away, the arrival time for the peak concentration decreases. The rising limb of
the concentration history is truncated before the no-degradation peak is reached, as shown in Figure 46.
In that figure, the concentration histories for the 100 m receptor begin at the same point in time and begin
to rise at the same rate. For the smaller half-life (greater degradation rate) curve, the concentrations
increase to a lower peak that occurs slightly earlier, because more time is required for the concentration
to reach its maximum in the lower degradation rate case.
£U
c=? •
1 15
c
o
"ctf
^ 10
0)
o
L —
o
O
V K
cd °
CD
Q_
n
^ % Max. Radius
A 25%
, O 40%
D 49.15%
O O 55%
' V 75%
. a A o 100%
O A
•v °
: 5
P V
O $ A
c*7 ^p
200 300 400 500
Arrival Time (days)
600
Figure 44
radius
Peak concentration vs arrival time for variation of the percent maximum
69
[Section 5 Parameter Variation]
-------
o
ts
15
10
CD
I "
5
CD
CL
A
O 0.0
D 0.0014 1/d
A 0.0028 1/d
O
50m
100m
150m
D
200 300 400 ,500 600
arrival time (days)
Figure 45 Peak concentration vs arrival time for variation of the constituent decay
rate
2.5
D)
E 2
g
'
1.5
§ 1
O
° 0.5
t1/2 = 495 d
t1/2 = 248 d
500 • 1000 1500 2000
Time (days)
Figure 46 Concentration history for a degrading constituent
[Section 5 Parameter Variation] 70
_
-------
5.9 HSSM Response: Constant Peak Concentration, Decreasing Arrival Time
5.9.1 Saturated vertical conductivity
Increasing the saturated vertical conductivity, Ks, also increases the horizontal conductivity, because
in HSSM the horizontal conductivity is taken as RKS x Ks. As expected, the NAPL arrives sooner at the
water table with increasing conductivity. More rapid flow in the ground water causes the time for the peak
mass flux to decrease with increasing horizontal conductivity. Lastly, the increased conductivity causes the
constituent to be more rapidly transported within the aquifer. These three effects are reflected in the
TSGPLUME results which show the arrival time of the peak receptor concentration decreasing with
increasing conductivity (Figure 47). The peak concentrations remain very similar as the source zone
concentrations remain relatively similar (Table 12) despite the variation in conductivity.
Parameters with Type G Response
(Constant Peak Concentration, Decreasing Arrival Time)
Parameter
Saturated vertical
conductivity, Ks
Type
at
150
m
G
Minimum
Value
1 .75 m/d
Value used in
Problem 2
Section 5.2 of
Volume 1
7.1 m/d
Maximum
Value
28.4 m/d
Module
Impacts
(K,0,T)
YYY
CD
C.
.o
05
£
CD
a.
15
10
0
n 0 25m
IH
O
50m
100m
vo A n
VOA n
o
O 1.75 m/d
D 3.5 m/d
A 7.1 m/d
O 14.2 m/d
V 28.4 m/d
150m
O
0' 500 1000 1500 2000 2500
arrival time (days)
Figure 47 Peak concentration vs arrival time for variation of the saturated hydraulic
conductivity
71
[Section 5 Parameter Variation]
-------
5.10 HSSM Response: Increasing Peak Concentration, Decreasing Arrival Time
Table 1 0 Parameters with Type H Response
(Increasing Peak Concentration, Decreasing Arrival Time)
Parameter
Recharge, qwl
Longitudinal dispersivity, aL
Residual water saturation,
SWr
van Genuchten's n
Source flux, q0
Source duration
NAPL Saturation in the Lens
Type
at
150
m
->G
D
I
H
H
H
G
Minimum
Value
0.0 in/yr
5 m
0.05
2.0 m'1
0.3392 m/d
0.75 d
0.2000
Value used in
Problem 2,
Section 5.2 of
Volume 1
20 in/yr
10 m
0.10
2.68 rrf1
0.4255 m/d
1.0 d
0.3236
Maximum
Value
30 in/yr
30 m
0.15
3.4 nY1
0.9044 m/d
2.0 d
0.4500
Module
Impacts
(K,0,T)
YYY
NNY
YYI
YYI
Yll
Yll
NYI
5.10,1 Recharge
The effect of increasing recharge is to increase one component of mass flux to the aquifer (equation
(48)). With higher recharge the NAPL reaches the water table sooner (Table 12) and the time to the peak
mass flux decreases, because the increased mass flux causes the constituent to more rapidly leave the
fens. The peak receptor concentrations are higher because of the higher flux to the aquifer throughout the
leaching period (Figure 48).
5.10.2 Longitudinal dispersivity
The longitudinal dispersivity only affects the aquifer module of HSSM. The NAPL arrival time at the
water table and the mass input to the aquifer are all unaffected by this parameter. Thus the results shown
In Figure 40, Figure 49 depend only on transport in the aquifer. For all of the receptors, increasing the
dispersivity decreases the arrival time. This is caused by the positive contribution of dispersion to the
mass flux. Although increased dispersivity is associated with increased apparent dilution of concentration,
at the nearest receptors the peak concentrations increase with increasing dispersivity. At the most distant
receptors, the peak concentrations decline with increasing longitudinal dispersivity. This example
contrasts with that of the horizontal transverse dispersivity where there is increased lateral movement of
the constituent. Here, however, the lateral transport remains the same for each value of longitudinal
dispersivity and so the width of the plume is constrained. The only effects of dispersion that vary in this
example are longitudinal. Apparently there is a trade off between the more rapid arrival time and dilution
of the concentrations, which always causes the peak to occur sooner with increasing longitudinal
dispersivity. At the near receptors, the more rapid arrival time dominates over the increased dilution effect,
which is dominant further downgradient.
[Section 5 Parameter Variation]
72
-------
Q"
"03
c 10
.0
1
CD
O
| 5
03
CD
0_
0
1(
. O Oin/yr
D 2in/yr
A 1 0in/yr
O 20in/yr
^ 25m y 30in/yr
O
*% 50m
O
100m
^D 150m
O
O
)0 200 300 400 500 600 700
arrival time (days)
Figure 48 Peak concentratic
14
O- 12
•£ 10
c.
O
"_jn; o
O3 °
CD fi
0 °
1 <
03
S. 2
n
n vs arrival time for variation of recharge
O 5.0 meters
O 25m D 10.0 meters
A A 15.0 meters
t§> O 30.0 meters
-
50m
0
100m
O AD° 150m .
O Ad
100 200 300 400 500 600
arrival time (days)
Figure 49 Peak concentration vs arrival time for variation of the longitudinal
dispersivity
73
[Section 5 Parameter Variation]
-------
5.10.3 Residual water saturation
The residual water saturation affects the vadose zone modules (KOPT and OILENS). Variation of the
residual water saturation, Swr, has a small effect on the receptor concentrations (Figure 50), and this
parameter could reasonably be listed in group "I". Increasing the residual water saturation casues the
NAPL to arrive at the water table somewhat more rapildy. The peak mass flux to the aquifer occurs more
rapildly as Sw increases and the peak mass flux and source concentrations increase. This parameter has
no direct effect on the aquifer model, so the impacts are limited to KOPT and OILENS.
5.10.4 van Genuchten's n
van Genuchten's n is a parameter of the capillary pressure curve that describes the steepness of the
curve. In Figure 51 the values range from 2.0 to 4.5; the latter is the value from X2BT.DAT. Generally,
high values of n indicate uniformity in the pore size distribution. For such media, the effective conductivity
to the NAPL stays relatively higher as the NAPL saturation decreases. In the vadose zone, the result is
that the NAPL moves more nearly as a pulse if n is high. In HSSM, as the value of n increases, the NAPL
arrival time at the water table decreases, as does the time for. the peak mass flux. In these cases, the
NAPL arrives at the water table in a relatively short pulse, that generates sufficient head to drive the lens
radially. Thus the lens radius at peak mass flux increases with n; giving high peak mass fluxes and source
concentrations.
CD
C
o
to
CD
O
8
^.
05
CD
CL
15
10
25m
O o.os
D 0.10
A 0.15
50m
100m
150m
100 200 300 400 5.00
arrival time (days)
600
Figure 50 Peak concentration vs arrival time for variation of the residual water
saturation
[Section 5 Parameter Variation]
74
-------
O)
C
o
"
CD
O
CD
CL
15
10
5 -
o
25m
40
O
O
50m
O
100m
°^0
O 2
D 2.68
A 3.0
O 4.5
150m
O
0
100 200 300 400 500 600 700
arrival time (days)
Figure 51 Peak concentration vs arrival time for variation of van Genuchten's n
5.10.5 Source flux
The source flux and duration determine the amount of contaminant mass introduced into the
subsurface. With higher flux, the NAPL arrives at the water table sooner (Table 12), and the lenses that
form are larger because of the increased mass of NAPL present. Bigger lenses tend to generate higher
peak mass fluxes because of their large radii. In this case the larger peak mass flux corresponds to higher
peak source concentrations. The result is that the receptor arrival times decrease and the peak
concentrations increase with increasing source flux (Figure 52).
5.10.6 NAPL saturation in the lens
The NAPL saturation in the lens, Somax, is an integrated measure of the vertical distribution of NAPL
through the lens. Each HSSM input data set has an appropriate value of Somax that can be determined
by using the NTHICK or NTHICK2 utilities. The X2BT.DAT data set contains the correct value of 0.3236;
the two other values used here were selected to illustrate the sensitivity of the results to this parameter.
Generally, lenses with higher NAPL saturations are smaller because more NAPL is contained in a unit
volume of the lens. The time to the peak mass flux decreases with Somax; the radius increases and the
peak mass flux increases. The reduction in time to peak mass flux occurs because higher NAPL
saturations give higher NAPL lens effective conductivities and thus lenses which develop quicker. Hence
the peak mass flux and transport to the receptor occur more rapidly (Figure 53).
75
[Section 5 Parameter Variation]
-------
20
15
10
8
0
O 0.3392 m/d
D 0.4522 m/d
A 0.9044 m/d
D
50m
100m A
O D
O
100 200 300 400 500 600 700
arrival time (days)
Figure 52 Peak concentration vs arrival time for variation of source flux
O)
8
8
^
cc
8.
15
10
25m
50m
O 0.2000
D 0.3236
A 0.1500
100m
150m
0
100 200 300 400 500 600 700
arrival time (days)
Figure 53 Peak concentration vs arrival time for variation of the NAPL saturation in
the lens
[Section 5 Parameter Variation]
76
-------
5.11 HSSM Response: Constant Peak Concentration, Constant Arrival Time
Table 1 1 Parameters with Type I Response
(Constant Peak Concentration, Constant Arrival Time)
Parameter
Aquifer thickness
(greater than the penetration
thickness)
van Genuchten's oc
Water surface tension, aaw
Max. water phase relative
permeability during
infiltration, kwmax
NAPL surface tension, aao
NAPL density, p0
Aquifer residual NAPL
saturation, Sors
NAPL/water interfacial
tension
Capillary thickness
parameter
Type
at
150
m
I
I
I
I
I
I
I
I
->C
Minimum
Value
1.966
2.0
58 dyne/cm
0.4
25 dyne/cm
0.64 g/cm3
0.075
30 dyne/cm
0.001 m
Value used in
Problem 2
Section 5.2 of
Volume 1
15.0
4.5
65 dyne/cm
0.5
35 dyne/cm
0.72 g/cm3
0.15
45 dyne/cm
0.01 m
Maximum
Value
20.0
4.5
72 dyne/cm
0.6
45 dyne/cm
0.80 g/cm3
0.50
60 dyne/cm
0.02m
Module
Impacts
(K,0,T)
NNY
YYI
YYI
Yll
YYI
YYI
NYI
NYI
NYI
5.11.1 van Genuchten's a
van Genuchten's a, is one of the parameters that describes the capillary pressure curve. The values
used here are: 2.0 rrf1, 2.68 m'1, and 3.4 rrf1. These values correspond to entry pressures of 37 cm, 28
cm and 22 cm respectively. These are the heights for fully saturated capillary rise of water. Figure 54
shows that this range of values has a negligible impact on the receptor concentrations.
5.11.2 Water surface tension
The surface tension of water is used by HSSM only in the KOPT module and for determining the
NAPL saturation in the lens by NTHICK. Figure 55 shows its minimal impact on the receptors.
77
[Section 5 Parameter Variation]
-------
5.11.3 Maximum water phase relative permeability during infiltration
During infiltration, a certain amount of the pore space is occupied by trapped air. The trapped air
saturation is included in HSSM by setting a maximum water phase relative permeability during infiltration
(<„,„. This parameter has little impact on receptor concentration histories when the vadose zone is relatively
permeable as in this example (Figure 56).
5.11.4 NAPL surface tension
The NAPL surface tension impacts vadose zone flow and transport and the NAPL saturation in the
lens in much the same was as does the water surface tension. The NAPL surface tension has little impact
on the receptor concentration histories (Figure 57).
5.11.5 NAPL density
The NAPL density affects vadose zone flow and the development of the lens. For LNAPLs, the typical
range of density variation is limited; the maximum is 1.0 g/cm3, and 0.50 g/cm3 or 0.06 g/cm3 would be the
lower bound. As seen in Figure 58, this parameter has little impact on the receptors.
5.11.6 Aquifer residual NAPL saturation
In HSSM, the residual NAPL saturation in the aquifer, Sors, is used in the development of the NAPL
lens. Over the range used in the analysis, 0.075 to 0.50, there is essentially no impact on the receptor
concentrations (Figure 59).
5.11.7 NAPL/water interfacial tension
The NAPL/water interfacial tension, CTOW, is used only in the NTHICK utility. aow plays a role in
determining the maximum NAPL saturation in the lens, Somax. By increasing oow from 30 dyne/cm to 60
dyne/cm, there is negligible impact on the peak concentrations and arrival times (Figure 60). The range
of a^ used in this example covers the expected range.
5.11.8 Capillary thickness parameter
The capillary thickness parameter is used to establish a smear zone. The values for the capillary
thickness parameter (0.001 m, 0.01 m and 0.02 m) used in Figure 61 represent nominal smear zone
thicknesses of 0.64 cm, 6.5 cm, and 13 cm respectively. This range of variation causes little change in the
receptor concentration history, in contrast to the larger smear zones used in Figure 36, Figure 53.
[Section 5 Parameter Variation]
78
-------
o
"
8
_*:
05
CD
Q.
15
10
25m
50m
O 2.0 1/m
D 2.68 1/m
A 3.4 1/m
100m
150m
100 200 300 400 500 600
arrival time (days)
Figure 54 Peak concentration vs arrival time for variation of van Genuchten's a
i ;j
IIT
E
c 10
0
§
8 5
03
CD
0.
n
O 58 dyne/cm
D 55 dyne/cm
pc m A 72 dyne/cm
1
-
50m
®
100m
H 150m
100 200 300 400 500 600
arrival time (days)
Figure 55 Peak concentration vs arrival time for variation of the water surface
tension
79
[Section 5 Parameter Variation]
-------
15
D)
"c. 10
o
8
co
8.
25m
O 0.4
n 0.5
A 0.6
50m
100m
150m
100 200 300 400 500 600
arrival time (days)
Figure 56 Peak concentration vs arrival time for variation of the maximum water
phase relative permeability during infiltration
03
15
10
I 5
Cv3
CD
CL
25m
O 25 dyne/cm
D 35 dyne/cm
A 45 dyne/cm
50m
100m
150m
KS
100 200 300 400 500 600
arrival times (days)
Figure 57 Peak concentration vs arrival time for variation of the NAPL surface
tension
[Section 5 Parameter Variation]
80
-------
'15
CD
,£
a 10
o
'•&
CD
O
8 *
CD
Q_
25m
O 0.64 g/cm3
D 0.72 g/cm3
A 0.80 g/cm3
50m
100m
150m
_J—i—,—,—,—L_
100 200 300 400 500 600
arrival time (days)
Figure 58 Peak concentration vs arrival time for variation of the NAPL density
05
15
10
8 5
j£
05
CD
CL
25m
O 0.075
D 0.15
A 0.30
. O 0.50
50m
100m
150m
0 i i i , , ,
100 200 300 400 500 600 700
arrival time (days)
Figure 59 Peak concentration vs arrival time for variation of the aquifer residual NAPL
saturation .
81
[Section 5 Parameter Variation]
-------
15
c 10
o
"•s
8
8
•S
8.
25 m
O 30.0 dyne/cm
D 45.0 dyne/cm
A 60.0 dyne/cm
50m
oa
100m
i . . . . i . . . . i . . . . i
150m
dZL
100 200 300 400 500 600
arrival time (days)
Figure 60 Peak concentration vs arrival time for variation of the NAPL/water interfacial
tension
IO
"~T
15)
"c 10
_o
B
§
1 5
CO
8.
n
O 0.001 meters
D 0.01 meters
A 0.02 meters
25m
50m
-------
Sections Discussion
The HSSM model is a screening model for exposure assessment from spills or other releases of
LNAPLs to the subsurface. The model decomposes the transport problem to three independent
components which are simulated by three separate models. KOPT models the transport of a NAPL from
the release location to the water table. This model incorporates the effects of capillarity and multiphase
partitioning, though volatilization and degradation processes are neglected. KOPT provides the LNAPL and
constituent flux to the water table. OILENS models the spreading of an LNAPL along the capillary fringe
taking into account the time variable source strength and buoyancy. This model computes the size of the
lens as a function of time and the constituent mass transfer to the water table aquifer due to infiltration
through the lens and groundwater flowing beneath the lens. Transport in the water table aquifer is modeled
using TSGPLUME. This model uses the time variable source strength provided by OILENS to calculate
downgradient concentrations at potential exposure locations. TSGPLUME estimates the depth of
penetration of the contaminant into the aquifer and uses this depth in a two-dimensional model. The
processes of advection, dispersion, sorption, and degradation (including dilution) are included in the model.
HSSM is a model which uses many approximations, and at the present time it is not possible to
evaluate the adequacy of each of them. Nevertheless, it is hoped that the model has captured the
essential behavior of the underlying processes. The model is computationally efficient and may be used
to estimate the potential impacts of a large number of chemicals in an economical fashion.
83
[Section 6 Discussion]
-------
References
Abriola, L. M. and G. F. Finder, A multiphase approach to the modeling of porous media contamination
by organic compounds, 1 Equation development, Water Resources Research. 21, 11-18, 1985a.
Abriola, L. M. and G. F. Finder, A multiphase approach to the modeling of porous media contamination
by organic compounds, 2 Numerical simulation, Water Resources Research, 21, 19-26, 1985b.
Allen, M.B., Numerical modelling of multiphase flow in porous media, Advances in Water Resources. 8,
162-187, 1985.
Bear, J., Dynamics of Fluids in Porous Media. American Elsevier, New York, 1972.
Bouwer, H., Rapid field measurements of air entry value and hydraulic conductivity of soil as significant
parameter in flow system analysis, Water Resources Research. 2, 729-738, 1966.
Brooks, R. H. and A. T. Corey, Hydraulic Properties of Porous Media. Colorado State University
Hydrology Paper No. 3, Ft. Collins, Colorado, 1964.
Buckley, S. E. and M. C. Leverett, Mechanism of fluid displacement in sands, Transactions American
Institute of Mining Engineers. 146, 107-116, 1942.
Burdine, N. T., Relative permeability calculations from pore size distribution data, Transactions
American Institute of Mining Engineers. 198, 71-78, 1953.
Carslaw, H.W. and J.C. Jaeger, Conduction of Heat in Solids. 2nd ed., Oxford Univ. Press (Clarendon),
London, 1959.
Charbeneau, R. J., Kinematic models for soil moisture and solute transport, Water Resources
Research. 20, 699-706, 1984.
Charbeneau, R. J. , Simulation of the transient soil water content profile for a homogeneous bare soil,
Water Resources Research. 17, 1271-1279, 1991.
Charbeneau, R. J., J. W. Weaver, and V. J. Smith, Kinematic Modeling of Multiphase Solute Transport
in the Vadose Zone. U.S. EPA/600/2-89/045, 1989.
Cline, P.V., J. J Delfino, and P. S. C. Rao, Partitioning of aromatic constituents into water from
gasoline and other complex solvent mixtures, Environmental Science and Technology. 25, 914-920,
1991.
Corapcioglu, M. Y., and A. Baehr, A compositional multiphase model for groundwater contamination by
petroleum products, I. Theoretical considerations, Water Resources Research. 23, 201-243, 1987
Corapcioglu, M. Y., and M. A. Hossain, Ground-water contamination by high-density immiscible
hydrocarbon slugs in gravity-driven gravel aquifers, Ground Water. 28, 403-412, 1990.
Dougherty, E. L. and J. W. Sheldon, The use of fluid interfaces to predict the behavior of oil recovery
process, Society of Petroleum Engineers Journal. 4, 171-182, 1964.
[References]
84
-------
Dracos, T., Theoretical considerations and practical implications on the infiltration of hydrocarbons in
aquifers, Proceedings International Symposium on Groundwater Pollution by Oil Hydrocarbons,
International Association of Hydrologists, Prague, June 5-9, 1978.
El-Kadi, A. I., Applicability of sharp-interface models for NAPL transport: 1. Infiltration, Ground Water.
30, 849-856, 1992.
Faust, C. R., Transport of immiscible fluids within and below the unsaturated zone--a numerical model,
Water Resources Research. 21, 587-596, 1985.
Faust, C. R., J. H. Guswa, and J. W. Mercer, Simulation of three-dimensional flow of immiscible fluids
within and below the unsaturated zone, Water Resources Research. 25(12), 2449-2464, 1989.
Fehlberg, E., Low-order Classical Runge-Kutta Formulas With Stepsize Control and Their Application to
Some Heat Transfer Problems. NASA TR R-315, 1969.
Green, W. H. and G. A. Ampt, Studies on Soil Physics, Journal of Agricultural Science. 4, 1-24, 1911.
Helfferich, F. G., Theory of multicomponent, multiphase displacement in porous media, Society of
Petroleum Engineers Journal. 21. 51-62. 1981.
Helfferich, F.G., Multicomponent wave propagation: Attainment of coherence from arbitrary starting
conditions, Chemical Engineering Communications. 44, 275-285, 1986.
Hochmuth, D. P. and D. K. Sunada, Ground-water model of two-phase immiscible flow in coarse
materials, Groundwater. 23, 617-626, 1985.
Hunt, J.R., N. Sitar and K.S. Udell, "Nonaqueous phase liquid transport and cleanup 1. Analysis of
Mechanisms," Water Resour. Res., 24(8), 1247-1258, 1988.
Huyakorn, P.S., M.J. Ungs, L.A. Mulkey and E.A. Sudicky, "A three-dimensional analytical model for
predicting leachate migration," Ground Water, 25(5), 588-598, 1982.
Kessler, A. and H. Rubin, Relationships between water infiltration and oil spill migration in sandy soils,
Journal of Hydrology. 91, 187-204, 1987.
Kueper, B. H. and E. O. Frind, Two-phase flow in heterogeneous porous media, 1. Model
development, Water Resources Research. 27(6), 1049-1057, 1991.
Leverett, M.C., Capillary behavior in porous solids, Transactions American Institute of Mining
Engineers. 142, 152-169, 1941
Lighthill, M.J. and G.B. .Whitham, On kinematic waves |. flood movement in long rivers, Proceedings of
the Royal Society A. 229, 281-316, 1955.
Mull, R., The migration of oil-products in the subsoil with regard to ground-water pollution by oil,
Proceedings of the Fifth International Conference on Advances in Water Pollution Research. San
Francisco and Hawaii, S. A. Jenkins, ed., Pergammon, Oxford, Vol. 2, HA 7(A)/1-8, 1971.
Mull, R., Calculations and experimental investigations of the migration of oil products in natural soils,
Proceedings International Symposium on Groundwater Pollution by Oil Hydrocarbons. International
Association of Hydrologists, 167-181, Prague, June 5-9, 1978.
85 [References]
-------
Muskat, M., The Flow of Homogeneous Fluids Through Porous Media. J.W. Edwards, Inc., Ann Arbor,
1946.
Neuman, S.P., Wetting front pressure head in the infiltration model of Green and Ampt, Water
Resources Research. 12, 564-566, 1976.
Osborne, M. and J. Sykes, Numerical modelling of immiscible organic transport at the Hyde Park
landfill, Water Resources Research. 22, 25-33, 1986.
Finder, G. F. and L. M. Abriola, On the simulation of nonaqueous phase organic compounds in the
subsurface, Water Resources Research. 22, 109s-119s, 1986.
Pope, G.A., L.W. Lake, and F.G. Helfferich, Cation exchange in chemical flooding: Part 1- Basic theory
without dispersion, Society of Petroleum Engineers Journal. 18, 418-434, 1978.
Raisbeck, J. M. and M. F. Mohtadi, The environmental impacts of oil spills on land in the arctic regions,
Water. Air and Soil Pollution. 3, 195-208, 1974.
Reibie, D.D., T.H. Illangasekare, D.V. Doshi, and M.E. Malhiet, Infiltration of immiscible contaminants in
the unsaturated zone, Groundwater. 28(5), 685-692, 1990.
Richards, L. A., Capillary conduction of liquids through porous mediums, Physics. 1, 318-333, 1931.
Rozdestvenskii, B. L. and N. N. Janenko. Systems of Quasilinear Equations and Their Applications to
Gas Dynamics. American Mathematical Society, Providence, 1980.
Ryan, P. A., and Y. Cohen, One-dimensional subsurface transport of a nonaqueous phase liquid
containing sparingly water soluble organics: A front tracking model. Water Resources Research. 27(7),
1487-1500, 1991.
Schlegg, H.O., "Consideration on water, oil and air in porous media," Water Science and Technology,
17, 467-476, 1984.
Sisson, J. B., A. H. Ferguson, and M. Th. van Genuchten, Simple method for predicting drainage from
field plots, Soil Science Society of America Journal, 44, 1147-1152, 1980.
Smith, R. E., Approximate soil water movement by kinematic characteristics, Soil Science Society of
America Journal. 47, 3-8, 1983.
Smoller, J., Shock Waves and Reaction-Diffusion Equations. Springer, New York, 1983.
Su, C. and R. H. Brooks, Water retention measurement for soils, Journal of the Irrigation and Drainage
Division of the American Society of Civil Engineers. 106(IR2), 105-112, 1980.
van Dam, J., "The migration of hydrocarbons in a water-bearing stratum." In The Joint Problems of
the Oil and Water Industries. P. Hepple (Ed.), The Institute of Petroleum, London, 1967.
van Genuchten, M. Th., F. J. Leij and S. R. Yates, The RETC Code for Quantifying the Hydraulic
Functions of Unsaturated Soils. U.S. EPA, EPA/600/2-91/065, December, 1991.
[References]
86
-------
Weaver, J.W., R.J. Charbeneau, and B.K. Lien, A screening model for nonaqueous phase liquid
transport in the vadose zone using Green-Ampt and kinematic wave theory, Water Resources
Research. 30(1), 93-105, 1994.
Weaver, J. W., R.J. Charbeneau, J.K. Tauxe, B.K. Lien, and J.B. Provost, The Hydrocarbon Spill
Screening Model (HSSIvn Volume 1: User's Guide. US EPA, EPA/600/R-94/039a, 1994.
Weaver, J. W., Approximate Multiphase Flow Modeling By Characteristic Methods. U.S. Environmental
Protection Agency, EPA/600/2-91/015, NTIS PB91-190959, May, 1991.
Weaver, J.W., and R. J. Charbeneau, Hydrocarbon spill exposure assessment modeling, Proceedings
of the NWWA/API Conference on Petroleum Hydrocarbons and Organic Chemicals. Oct. 31 - Nov. 2,
Houston, Texas, pp.233-247, 1990.
Wilson, J.L., S. H. Conrad, W.R. Mason, W. Peplinski and E. Hagan, 1990, Laboratory Investigation of
Residual Liquid Organics from Spills. Leaks and the Disposal of Hazardous Wastes in Groundwater.
U.S. Environmental Protection Agency, EPA/600/6-90/004, April, 1990.
Wylie, M. R. J. and G. H. F. Gardner, The generalized Kozeny-Carman equation: Its application to
problems of multiphase flow in porous media, World Oil. 146, 210-227, 1958.
Youngs, E. G. and A. J. Peck, Moisture profile development and air compression during water uptake
.by bounded porous bodies: 1. Theoretical introduction, Soil Science. 98(5), 290-294, 1964.
87
[References]
-------
Appendix 1 Evaluation of the Volume Integral
The objective of this appendix is to evaluate the total volume contained within the lens out to a radius
R, as shown in Figure 62. The volume within the source cylinder beneath the surface source is
V
's K "os
(90)
Figure 62 Representation for the lens volume
The volume contained within the outer part of the lens is given by
V
(91)
With equation (38) this gives
R
\
(92)
[Appendix 1 Evaluation of the Volume Integral] QQ
-------
where
E =
'OS
(93)
To evaluate (92) substitute
-.•"?
(94)
to find
V
= ERf f wze wZ dw
(95)
Integrating by parts Judv = uv - Jvdu with
v = e
(96)
equation ((95)) becomes,
= ERf
wa
2 a 2
(97)
noting that
(98)
89 [Appendix 1 Evaluation of the Volume Integral]
-------
With the definition of the error function and equation (93), equation (97) becomes
V0 = 7t p
-
, i
lnk
TC
1'\
Tt .
e/f
In -^
- erf
In -
(99)
The total volume with R > Rs is given by VT = Vc + V0 , or
"3
7t
In -^
- e/f
(100)
As expected, equation (100) reduces to equation (46) when R = Rt.
[Appendix 1 Evaluation of the Volume Integral] go
-------
Appendix 2 Summary of KOPT and OILENS Sensitivity Results
Table 12 contains a summary of results from the HSSM sensitivity analysis that is presented in
Section 5. Further information is provided in that Section.
Table 12 Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
A 1. Initial Contaminant Concentration
820 mg/L
8208 mg/L
12300 mg/L
25.0
24.6
24.6
116.7
121.9
124.1
8.27
8.41
8.49
0.0070
0.0697
0.1040
3.9
37.9
55.7
XIC1.DAT
X2BT.DAT
XIC2.DAT
B1. Source Radius
0.2 m
1.0 m
2.0 m
4.0 m
24.6
24.6
24.6
24.6
56.5
92.9
121.9
166.6
0.80
4.16
8.41
17.0
0.0166
0.0230
0.0697
0.2080
32.3
36.7
37.9
38.2
XSOURCE1.DAT
XSOURCE3.DAT ,
X2BT.DAT
XSOURCE2.DAT
D1. Depth to Water
7.5 m
10.0 m
12.5 m
7.74
24.6
70.5
89.0
121.9
186.4
10.23
8.41
6.60
0.1040
0.0697
0.0411
41.9
37.9
32.4
DEPTH75.DAT
X2BT.DAT
DEPTH125.DAT
D2. Porosity and Bulk Density
0.35
1 .72 g/cm3
0.43
1.51 g/cm3
0.50
1 .32 g/cm3
10.5
24.6
49.2
84.8
121.9
168.0
10.43
8.41
6.94
0.1050
0.0697
0.0475
41.0
37.9
34.66
SP1.DAT
X2BT.DAT
SP2.DAT
[Appendix 2 Sensitivity Results]
91
-------
Table 12 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
D3. NAPL viscosity
0.3 cP
0.45 cP
0.60 cP
16.8
24.6
32.5
97.3
121.9
135.9
9.14
8.41
7.69
0.0828
0.0696
0.0608
39.6
37.9
37.9
XVIS1.DAT
X2BT.DAT
XVIS2.DAT
D4. Vadose Zone Residual NAPL Saturation
0.0
0.025
0.05
0.075
11.9
15.7
24.6
47.5
108.0
113.8
121.9
148.4
11.5
10.1
8.41
6.06
.121
.0976
0.0696 .
0.0363
40.7
39.9
37.9
32.6
SORVO.DAT
SORV025.DAT
X2BT.DAT '
SORV075.DAT
D5. Soil/water Partition Coefficient for the Constituent
0.0415 L/kg
0.083 L/kg
0.166 L/kg
24.6
24.6
24.6
118.7
121.9
125.3
8;37
8.41
8.29
0.0705
0.0696
0.0678
38.6
37.9
37.0
FOC0005.DAT
X2BT.DAT
FOC002.DAT
D6. NAPUwater Partition Coefficient for the Constituent
250
311
375
24.6
24.6
24.6
110.3
121.9
145.9
7.95
8.41
9.18
0.0775
0.0696
0.0635
45.9
37.9
30.2
XPC1.DAT
X2BT.DAT
XPC2.DAT
D7. Smear Zone Thickness
0.065 m
0.25m
0.50m
0.75 m
1.00m
24.6
24.3
24.0
23.6
23.3
121.9
129.7
130.4
124.9
126.6
8.41
7.48
6.41
5.60
5.07
0.0696
0.0594
0.0499
0.0431
0.0382
37.9
38.7
41.1
43.7
45.0
X2BT.DAT
SZ25.DAT
SZ50.DAT
SZ75.DAT
SZ100.DAT
[Appendix 2 Sensitivity Results]
92
-------
Table 12 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
E1. Aquifer Thickness
0.5m
1.0m
1.5 m
1 .966 m
15.0 m
20.0 m
24.6
24.6
24.6
24.6
24.6
24.6
121.3
121.3
121.3
121.9
121.9
121.3
8.39
8.39
8.39
8.39
8.41
8.39
0.0696
0.0696
0.0696
0.0697
0.0696
0.0696
149.2
74.6
49.7
38.0
37.9
38.0
AQU05.DAT
AQU10.DAT
AQU15.DAT
AQU19.DAT
X2BT.DAT
AQU20.DAT
E2. Transverse Horizontal Dispersivity
0.5 m
1.0 m
1.5 m
24.6
24.6
24.6
121.3
121.9
121.3
8.39
8.41
8.39
0.0696
0.0697
0.0696
38.0
37.9
38.0
DlST05.DAT
X2BT.DAT
DIST15.DAT
E3. Constituent Half-Life
Infinite
495.1 d
247.5 d
24.6
24.6
24.6
121.9
121.9
121.9
8.41
8.41
8.41
0.0696
0.0697
0.0697
37.9
26.7
23.8
X2BT.DAT
XHL1.DAT
XHL2.DAT
F1. Ratio of horizontal to vertical conductivity
1.0
2.5
10.0
24.6
24.6
24.6
226.8
121.9
56.4
9.28
8.41
6.81
0.0377
0.0697
0.164
39.9
37.9
32.3
RKS1.DAT
X2BT.DAT
RKS10.DAT
F2. Gradient
0.005
0.01
0.02
24.6
24.6
24.6
177.8
121.9
89.1
9.97
8.41
7.14
0.0494
0.0697
0.0985
38.6
37.9
35.5
GRAD005.DAT
X2BT.DAT
GRAD02.DAT
[Appendix 2 Sensitivity Results]
93
-------
Table 12 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
F3. Transverse vertical dispersivity
0.05m
0.1 m
0.15m
24.6
24.6
24.6
142.1
121.9
117.7
9.04
8.41
8.27
0.0584
0.0697
0.0775
39.1
37.9
35.7
DIS5.DAT
X2BT.DAT
DIS30.DAT
F4. All Dispersivities
at = 5.0 m
ar = 0.5 m
atf = 0.05 m
at = 10.0 m
ar - 0.1 m
atf s 0.01 m
aL = 1 5.0 m
a, 2 1 .5 m
av = 0.15 m
24.6
24.6
24.6
146.9
121.9
111.3
9.18
8.41
8.04
0.0586
0.0696
0.0772
38.3
37.9
37.2
DVL.DAT
X2BT.DAT
DVH.DAT
F5. Percent maximum radius
25
40
49.15
55
75
100
24.6
24.6
24.6
24.6
24.6
24.6
121.3
121.9
121.9
121.9
121.3
121.3
4.28
6.84
8.41
9.41
12.8
17.1
0.0696
0.0697
0.0696
0.0697
0.0696
0.0696
106.4
51.96
37.9
31.9
19.8
12.7
MN25.DAT
MN50.DAT
X2BT.DAT
MN55.DAT
MN75.DAT
MN100.DAT
G1. Hydraulic conductivity
1.75m/d
3.5 m/d
7.1 m/d
14.2 m/d
28.4 m/d
77.9
44.0
24.6
14.1
8.2
429.2
225.3
121.9
63.4
334.2
8.45
8.34
8.41
8.27
8.26
0.0211
0.0377
0.0697
0.131
0.251
38.5
38.9
37.9
37.8
36.9
HC0175.DAT
HC035.DAT
X2BT.DAT
HC142.DAT
HC284.DAT
[Appendix 2 Sensitivity Results]
94
-------
Table 1 2 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
H1. Recharge
0.0 in/yr
2.0 in/yr
10.0 in/yr
20.0 in/yr
30.0 in/yr
60.7
33.0
27.1
24.6
23.2
175.0
141.6
128.6
121.9
117.3
6.98
8.17
8.36
8.41
8.42
0.0442
0.0598
' 0.0657
0.0696
0.0728
34.1
36.1
37.3
37.9
38.2
RECHO.DAT
RECH.DAT
RECH10.DAT
X2BT.DAT
RECH30.DAT
H2. Longitudinal Dispersivity
5.0 m
10.0 m
15.0 m
30.0 m
24.6
24.6
24.6
24.6
' 121.3
121.9
121.3
121.3
8.39
8.41
8.39
8.39
0.0696 •
0.0697
0.0696
0.0696
38.0
37.9
38.0
38.0
DIS5.DAT
X2BT.DAT
DIS15.DAT
DIS30.DAT
H3. Residual water saturation
0.05
0.10
0.15
26.5
24.6
22.8
129.1
121.9
114.3
8.44
8.41
8.37
0.0684
0.0696
0.0709
37.0
37.9
38.8
XWAT1.DAT
X2BT.DAT
XWAT2.DAT
H4. van Genuchten's n
2.0
2.68
3.0
4.5
63.7
42.1
36.7
24.6
174.5
143.3
140.6
121.9
7.28
7.72
8.02
8.41
0.0492
0.0582
0.0614
0.0697
33.4-
36.1
35.9
37.9
VGN20.DAT
VGN26iDAT
VGN30.DAT
X2BT.DAT
H5. Source flux
0.3392 m/d
0.4522 m/d
0.9044 m/d
74.2
24.6
3.6
172.0
121.9
99.6
5.40
8.41
15.87
0.0299
0.0697
0.213
32.0
37.9
43.6
XSF1.DAT
X2BT.DAT
XSF2.DAT
[Appendix 2 Sensitivity Results]
95
-------
Table 12 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d)
Radius ,
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
HS. NAPL saturation in the lens
0.2000
0.3236
0.4500
24.6
24.6
24.6
133.1
121.9
111.4
7.65
8.41
8.47
0.0612
0.0697
0.0724
38.5
37.9
38.9
XSAT25.DAT
X2BT.DAT
XSAT45.DAT
11, Aquifer Thickness (see E1)
12. van Qenuchten's a
2.0 m"
2.68 m'1
3.4 m1'
24.6
24.6
24.6
123.9
121.9
119.6
8.30
8.41
8.46
0.0684
0.0696
0.07Q6
38.0
37.9
38.0
13. Water surface tension
58 dyne/cm
65 dyne/cm
72 dyne/cm
24.6
24.6
24.6
124.8
121.9
125.9
8.44
8.41
8.60
0.0693
0.0696
0.0703
37.5
37.9
36.9
VGA20.DAT
X2BT.DAT
VGA34.DAT
WST1.DAT
X2BT.DAT
WST2.DAT
14. Maximum water phase relative permeability during infiltration
0.4
0.5
0.6
24.6
24.6
24.6
15, NAPL surface tension
25 dyne/cm
35 dyne/cm
45 dyne/cm
24.6
24.6
24.6
118.5
121.9
121.0
8.30
8.41
8.38
0.0694
0.0696
0.0595
38.5
37.9
38.1
MKR1.DAT
X2BT.DAT
MKR2.DAT
118.2
121.9
121.3
8.21
8.41
8.48
0.0687
0.0696
0.0703
38.8
37.9
37.7
NST1.DAT
X2BT.DAT
NST2.DAT
[Appendix 2 Sensitivity Results]
96
-------
Table 12 (Continued) Summary of Sensitivity Results
Parameter
Value
Water table
Arrival Time
(d)
Mass Flux
Time
(d) .
Radius
(m)
Peak Value
(kg/d)
Effective
Source
Concentration
(equation 88)
(mg/L)
Data File Name
16. NAPL density >
0.64 g/cm3
0.72 g/cm3
0.80 g/cm3
27.6
24.6
22.3
119.2
121.9
121.3
8.48
8.41
7.95
0.0705
0.0696
0.0661
37.8
37.9
39.2
XDEN1.DAT
X2BT.DAT
XDEN2.DAT
17. Aquifer residual NAPL saturation
0.075
0.15
0.30
0.50
24,6
24.6
24.6
24.6
125.0
121.9
116.7
118.0
8.58
8.41
8.12
8.01
0.0705
0.0696
0.0682
0.0666
37.2
37.9
39.1
39.0
SORS075.DAT
X2BT.DAT
SORS30.DAT
SORS50.DAT
18. NAPUwater interfacial tension
30 dyne/cm
45 dyne/cm
60 dyne/cm
24.6
24.6
24.6
119.3
121.9
122.5
8.65
8.41
8.18
0.0721
0.0697
0.0676
37.5
37.9
38.4
X2BT1.DAT
X2BT.DAT
X2BT2.DAT
19. Capillary thickness parameter
0.001
0.01
0.02
24.7
24:6
24.5
124.6
121.9
117.5
9.02
8.41
7.82
0.0742
0.0696
0.0652
36.2
37.9
39.6
CAP1.DAT
X2BT.DAT
CAP2.DAT
[Appendix 2 Sensitivity Results]
97
-------
Table 13 Fractions of Y, N, and
Type (Number of
Parameters)
A(1)
B(1)
0(0)
0(7)
E(2)
F(6)'
G(1)
H(7)
I (9)
Responses for Each Type (A-l)
Fraction of Parameters for (KOPT, OILENS, and TSGPLUME)
Y
(1.000, 0.000, 0.000)
(1.000, 0.000, 0.000)
(0.000, 0.000, 0.000)
(0.857, 0.857, 0.286)
(0.000, 0.000, 1.000)
(0.000, 0.500, 1.000)
(1.000, 1.000, 1.000)
(0.714, 0.571, 0.286)
(0.566, 0.778, 0.111)
N
(0.000, 0.000, 0.000)
(0.000, 0.000, 0.000)
(0.000, 0.000, 0.000)
(0.143, 0.000, 0.000)
(1.000, 1.000, 0.000)
(1 .000, 0.500, 0.000)
(0.000, 0.000, 0.000)
(0.286, 0.143, 0.000)
(0.444, 0.111, 0.000)
1
(0.000, 1.000, 1.000)
(0.000, 1.000, 1.000)
(0.000, 0.000, 0.000)
(0.000, 0.143, 0.714)
(0.000, 0.000, 0.000)
(0.000, 0.000, 0.000)
(0.000, 0.000, 0.000)
(0.000, 0.286, 0.714)
(0.000, 0.111, 0.889)
' For Type F, eight is used in the denominator for calculating the fractions, because of the three parameters used for "all dispersivities"
[Appendix 2 Sensitivity Results]
98
-------
Appendix 3 FORTRAN Source Codes for HSSM and the Utility
Programs
3.1 Source Code for HSSM-KO
The source code for HSSM-KO consists of a driver (RNHSSM), 80 subroutines, one function and one
block data subprogram. The following listing is organized roughly according to function as follows. The
heart of the program consists of the four subroutines HSSM, RKF12, EQS, and CHK. These routines are
listed first. The main program RNHSSM and the subroutine HSSM "manage" the simulation calling the
input, initialization, computation, post processing and output subroutines. The computations are performed
in the Runge-Kutta solver (subroutine RKF12) as all of the KOPT and OILENS equations are in the form
of ordinary differential equations. The right hand sides of those equations are contained in the subroutine
EQS and the subroutines which it calls: OEQS, CEQS, OILENS, and GLENS. It is throught EQS that the
equations to be solved are entered into the solver. The solution of the equations is controlled by the
subroutine CHK and the subroutines which is calls. These guide the solver to critical points in the solution
and turn equations on and off as their solutions are needed.
The remaining routines are grouped into the following categories and are listed in sequence.
D KOPT equations (to complete OEQS and CEQS)
D OILENS equations (to complete OILENS and CLENS)
D General parameter calculation used by KOPT and OILENS routines
D Simulation control incorporated into the CHK subroutines
D Mass balance calculation routines
D Numerical methods
D Input routines
D Initialization routines
D Post processing
D Output
D File manipulation
[Appendix 3 FORTRAN Source Codes]
99
[Appendix 3 FORTRAN Source'Codes]
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IRD EVALUAT
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i r \
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NEQ)
YY(I,J) = YI(I,J)
CONTINUE
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o in
•31 -31
a
***THE THIRD EVALUATIO:
b
H
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b
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in
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TEP FROM THE FUNCTION EVALUATIONS
CO
***DETERMINE NEW TIME
IE = 0
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r-
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CONTINUE
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o in us
r- r~ t-~
STEP REJECTION
Sro,NEQ,DM,DTl,DTR,NS,IC,IRR,IE2,IE
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ET = TN
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3.7 Compilation with Microsoft FORTRAN
The HSSM modules and the utilities were compiled with Microsoft FORTRAN version 5.1 compilier.
With one exception, ANSI standard X3.9-1978 FORTRAN was used in writing these routines. Compliance
with the standard was verified by using the /4Ybs compile option on the Microsoft compiler. The full
compilation statement was
fl /4Ybs /Zi /Od /FPi file.FOR
The /FPi option was used so that HSSM would take advantage of a math coprocessor if available, but
not require the coprocessor. The CMD routine was compiled with the /4Yb option which does not enforce
strict ANSI compliance. CMD issues an operating system command to DOS, a feature that is not available
in standard FORTRAN 77. The following routines require the CMD routine:
NSOPEN
PKCON
IOPOST
TSGP2
DIR
«D.S. GOVERNMENT PRINTING OFFICE: 1995-650-006/22026
259
[Appendix 3 FORTRAN Source Codes]
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