RESEARCH FOR ABATEMENT OF
LEAKS FROM UNDERGROUND STORAGE TANKS
CONTAINING HAZARDOUS SUBSTANCES
U.S. E.P.A. CONTRACT NO. 68-03-3409
DRAFT
FINAL REPORT
PHASE 1 OF
MODELING VAPOR PHASE MOVEMENT
IN RELATION TO
UST LEAK DETECTION
EPA WORK ASSIGNMENT NO. 1-4
25 FEBRUARY 1988
CAMP DRESSER & McKEE, INC.
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DISCLAIMER
This report is an external draft for review purposes only and does not
constitute Agency policy. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
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CDM
environmental engineers, scientists,
planners, &'management consultants
February 25, 1988
CAMP DRESSER & McKEE INC.
One Center Plaza
Boston.'Massachusetts 02108
'6-17 742-5151
Mr. Philip Durgin
Technical Project Monitor
US EPA/EMSL
944 East Harmon
Las Vegas, Nevada 89109
Subject: "Modeling Vapor Phase Movement in Relation to
UST Leak Detection."
Work Assignment No.: 1-4
EPA Contract No.: 68-03-3409
Dear Mr. Durgin:
We are pleased to submit this Draft Final Report on Phase 1 of
"Modeling Vapor Phase Movement in Relation to UST Leak Detection." We
look forward to meeting with you to discuss the findings in the
report.
Very truly yours,
CAMP DRESSER & McKEE INC.
APPROVED:
CAMP DRESSER & McKEE INC.
7
Myro^ S/. Rosenberg , j
Deputy 'Project Director
Robert P. Schreiber, P.E.
Work Assignment Manager
Enclosure
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RESEARCH FOR ABATEMENT OF
LEAKS FROM UNDERGROUND STORAGE TANKS
CONTAINING HAZARDOUS SUBSTANCES
U.S. E.P.A CONTRACT NO. 68-03-3409
DRAFT
FINAL REPORT
ON PHASE 1 OF
MODELING VAPOR PHASE MOVEMENT
IN RELATION TO
UST LEAK DETECTION
EPA WORK ASSIGNMENT NO. 1-4
Prepared by: ^^^T j*^^
Robert P. Schreiber, P.E.
Date
Work Assignment Manager
Camp Dresser & McKee Inc.
approved by:
«
:s»J P.E.
Deputy Pr6ject Director
/ {
Approved bv: M
/
Project Directo
Date
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ABSTRACT
Diffusive transport of hydrocarbon vapors in the soil from a leaking
underground storage tank (UST) was simulated with a three-dimensional
groundwater flow model. This modeling was performed by analogy between
Pick's Second Law of diffusion and the confined groundwater flow equation.
A model of a cylindrical UST, emplaced in backfill and surrounded by native
soils, was designed. The tank was 6 feet in diameter by 12 feet in length
and was surrounded on all sides by backfill to a thickness of 2 feet. The
ground surface was assumed to be paved and impervious to vapors.
A synthetic gasoline blend, incorporating commonly occurring chemical
constituents of commercial gasolines, was devised for the vapor transport
simulations. Physicochemical properties, such as air diffusion
coefficients and equilibrium vapor concentrations, were taken from the
literature. Soil-air diffusion coefficients for the gasoline blend
incorporated a formulation for porous medium tortuosity given by Millington
and Quirk (1961).
Simulations were designed to examine the importance of moisture content and
total porosity in the native soils and backfill. These properties were
varied from "average" conditions in gravel backfill and sandy soil to "wet"
or "very wet" conditions in low porosity materials.
The model results indicated that decreasing the soil-air diffusion in the
native soil would be expected to have an insignificant influence on
diffusion, under the same backfill conditions. Similar changes in the
backfill, however, strongly influenced diffusive transport. These results,
while hardly surprising, underscore the importance of understanding the
physical properties of the backfill.
Additional simulations were performed to test the effects of an unpaved
surface. They showed that an unpaved surface is expected to have an
insignificant influence on sensor response.
Results of the simulations also indicated that low molecular weight alkanes
(e.g., isobutane, n-butane, isopentane, n-pentane) are predicted to be
detected much earlier by external, passive vapor sensors at the same
threshold vapor concentration than would aromatic compounds (e.g., benzene,
toluene, xylene) or heavy molecular weight compounds (C.-C aliphatics).
This result argues for the development of sensors specific to those
compounds in gasoline having high vapor concentrations and diffusion
coefficients. Furthermore, analysis with an expression based on Henry's
Law indicated that those compounds such as the C4-C5 alkanes are expected
to suffer little attenuation due to water-air phase partitioning.
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Simulation results were presented as time histories of vapor concentrations
in the backfill, and as time histories of the vaporized gasoline. It was
found that, even under the most conservative simulation conditions, total
gasoline hydrocarbon concentrations of 500 parts per million were predicted
to reach halfway across the backfill by one month. Under "average"
conditions, this threshold concentration was reached at all points within
the backfill by less than one month.
The modeling also predicted that vaporization rates of about 10"4 gallons
per hour would be detected by vapor sensors in the backfill within one
month. This compares favorably to in-tank detection methods that may
achieve detection at rates of 0.2 gallons per hour, with allowable sampling
intervals of several months. The early detection time afforded by
external, passive vapor sensors translates into low liquid gasoline volumes
lost to vaporization, providing a high degree of "protection" about an UST.
Recommendations on sensor network design were made, considering the effects
of soil conditions and temperatures. For the simulated hypothetical UST, a
plot of sensor distance from the leak versus volume of vaporized gasoline
before detection occurs showed an "optimum" sensor spacing of about 10
feet.
Further investigations should include an improved characterization of the
leakage source of vapors, and the quantification of the effects of
density-driven vapor transport.
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ACKNOWLEDGEMENTS
This report was prepared by Camp Dresser and McKee Inc./ and submitted
in partial fulfillment of Contract No. 68-03-3409 with the U.S.
Environmental Protection Agency.
The principal authors are Robert Schreiber and Benjamin Levy, who
prepared the report under the direction of Myron S. Rosenberg, Deputy
Project Director. Significant contributors to this report were Warren
Lyman, Richard Kossik, Dale Schmidt, Ricardo Lezama, and Richard
Schroeder. Linda O'Brien, Patricia Sharkey, and Corrie Dostaler
performed the word processing.
Additional inviduals who lent their expertise on various aspects of
this project include Peter Riordan, Bernadette Kolb, Jonathan French,
William Glynn, and Lynn Gelhar.
Also to be acknowledged for their insight and influence on the
direction of this report are: from the Environmental Monitoring
Systems Laboratory of the U.S. Environmental Protection Agency, Philip
Durgin, Technical Project Monitor, and John Worlund; and, from the
Environmental Research Center of the University of Nevada at Las
Vegas, Dennis Weber, and Klaus Stetzenbach.
iii
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CONTENTS
DISCLAIMER
LETTER OF SUBMITTAL
APPROVAL/SIGN-OFF FORM
ABSTRACT
ACKNOWLEDGEMENTS
TABLE OF CONTENTS
LIST OF APPENDICES. '. ............ ........................... vi
LIST OF FIGURES ............................................ vii
LIST OF TABLES ............................................. ix
Section
1.0 OBJECTIVES
1 . 1 Overview ......................................... 1-1
1.2 Conceptual Approach .............................. 1-1
1.3 Phase 1 Report Objectives ---- . ................... 1-4
2.0 TECHNICAL APPROACH ..................................... 2-1
2.1 System Conceptualization ......................... 2-1
2.1.1 Fate and Transport Processes . . . ........... 2-1
2.1.2 Major Assumptions ..... . ................... 2-2
2.2 Description of Simulated UST ..................... 2-5
2.2.1 Product Characteristics ................... 2-5
2.2.2 UST System Geometry and Hydrogeologic
Characteristics ........................... 2-6
2.3 Simulation Methodology ........................... 2-7
2.3.1 "Base Case" Volatilization Scenario ....... 2-7
2.3.2 Selection of Simulation Model ............. 2-8
2.3.3 Description of Model Geometry and
Boundary Conditions ........................ 2-8
2.3.4 Definition of Simulation Matrix ........... 2-9
2.3.5 Transforming Results for Different Product
Characteristics ........................... 2-10
2.3.6 Creating and Performing the Simulations... 2-11
IV-
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TABLE OF CONTENTS (continued)
Section -2SSS
3.0 NUMERICAL SIMULATION RESULTS 3-1
3.1 "Base Case" Volatilization over Time 3-1
3.2 Vapor Spreading Throughout Backfill _
and Native Soil 3~3
3.3 Sensor Location Vapor Concentrations 3-3
3.4 Detection Time Versus Sensor Location 3-4
3.5 Volume of Leakage at Detection Time 3-5
3.6 Effects df Open Surface 3-5
4.0 DISCUSSION AND CONCLUSIONS *~l
4.1 Vapor Sensors as Early Warning Devices 4-1
4.2 Implications for Monitoring Network Design 4-2
4.3 Implications for Vapor Detector Regulations 4-4
4.4 Vapor Transport Analysis and Modeling
Recqmmendations
5.0 REFERENCES 5~1
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LIST OF APPENDICES
Appendix A
Appendix B
Appendix C
Appendix D
Appendix E
Appendix F
Appendix G
Appendix H
Appendix I
Appendix J
Appendix K
Appendix L
Appendix M
Appendix N
Glossary
Dictionary of Variables and Parameters
Chemical Property Estimation Equations
Physicochemical Properties of Representative
Gasoline Blends
Evaluation of Air-Water Phase Exchange on Diffusion
of Hydrocarbon Vapors
Calculation of Equilibrium Gasoline Vapor-Air Mixture Density
Calculation of the Liquid Volume of Leaked Gasoline
Analogy of Diffusion and Confined Ground Water Flow
Analytical Verification of the DYNFLOW-Based
Diffusion Model
Vapor Diffusion Tortuosity and Effective Soil Diffusion
Equations
^Simulation Matrix
Comparison of UST Vapor Diffusion Simulation Models:
MODFLOW and DYNFLOW
DYNFLOW Command Files
Tabular DYNFLOW Results
VI
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LIST OF FIGURES .
Figure
2-1 Geometry of the "Generic" UST.
2-2 Cut-Away Isometric View of the Vapor Diffusion Model.
2-3 Plan View of the Vapor Diffusion Model.
2-4 Longitudinal Cross-Section of the Vapor Diffusion Model.
2-5 Lateral Cross-Section of the Vapor Diffusion Model.
2-6 UST Leak and Vapor Sensor Locations in the Vapor Diffusion Model.
3-1 Time History of Simulated Gasoline Volatilization Rate for Different
Soil Conditions at 10°C.
3-2 Time History of Simulated Gasoline Volatilized Volume for Different
Soil Conditions at 10°C.
3-3 Time History of Simulated Gasoline Volatilized Volume for Average
Soil Conditions at Different Temperatures.
3-4 Time History of Simulated Volatilized Volume for Different Gasoline
Components for Average Soil Conditions at 10°C.
3-5 Contour Plot of Simulated Vapor Concentrations at 8 Foot Depth for
Average Soil Conditions at 10°C and 14 Days Since Leak Started.
3-6 Contour Plot of Simulated Vapor Concentrations at 8 Foot Depth for
Dry Gravel Backfill, Dry Silty Sand Native Soil Conditions at 10°C
and 14 Days Since Leak Started.
3-7 Contour Plot of Simulated Vapor Concentrations at 2 Foot Depth for
Average Soil Conditions at 10°C and 14 Days Since Leak Started.
3-8 Time History of Simulated Vapor Concentrations at Various Sensor
Locations for Average Soil Conditions at 10°C.
3-9 Time History of Simulated Vapor Concentrations at a Deep,
"Intermediate" Sensor for Different Soil Conditions at 10°C.
NOTE: All figures are found at the end of their corresponding section,
following the text and preceding the tables.
vii
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LIST OF FIGURES (continued)
Figure
3-10 "Sensor Distance" Definition
3-11 Alarm Time Versus "Sensor Distance" for Deep Sensors and Different
Soil Conditions at 10°C.
3-12' Alarm Time Versus "Sensor Distance" for Shallow Sensors and Different
Soil Conditions at 10°C.
3-13 Alann Time Versus "Sensor Distance" for Deep Sensors and Average Soil
Conditions at Various Temperatures.
3-14 Alarm Time Versus "Sensor Distance" for Deep Sensors with Different
Alann Levels -Under Average Soil Conditions at 10°C.
3-15 Volatilized Liquid Volume at Detection Time Versus "Sensor Distance"
for Deep Sensors and Different Soil Conditions at 10 C.
3-16 Open Versus Closed Surface: Time Histories of Vapor Concentrations at
an "intermediate" Deep Sensor.
NOTE: All figures are found at the end of their corresponding section,
following the text and preceding the tables.
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LIST OF TABLES
Table
2-1 Components of the Simulated Gasoline Blend.
2-2 Average Physicochemical Properties of the Simulated
Gasoline Blend at Different Temperatures.
2-3 Physicochemical Properties of Individual
Chemicals Versus the Simulated Gasoline Blend, at 10°C.
2-4 Vapor Transport Properties of Excavation Zone Backfill
and Native Soils.
2-5 Sensor Locations in the Vapor Diffusion Model.
2-6 Summary of Simulation Matrix.
2-7 Equilibrium Vapor Concentrations Used in Transforming
Simulation Results.
Note: All tables are found at the end of their corresponding section,
following the figures.
ix
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1.0 OBJECTIVES
1.1 OVERVIEW
The objectives of this work assignment are to use modeling of vapor
phase contaminants emanating from a leaking Underground Storage Tank
(UST) to improve the understanding of vapor transport in the vicinity
of a leaking UST. Modeling is used to simulate and analyze the
sensitivity of contaminant vapor concentrations, measured at sensor
sampling points, to variations in the parameters governing vapor
transport.
The processes that govern vapor transport in- the excavation zone
underlie the selection of simulation modeling and analysis tools.
Using information from other portions of EPA's UST research program,
(e.g., the testing of sensor detection capabilities), the modeling of
vapor transport helps identify the parameters of vapor transport roost
critical to network design. Also, this work yields results that can
be used to guide the design of field programs for the testing of vapor
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sensors.
1.2 CONCEPTUAL APPROACH
This research.effort provides technical information on the transport
of vapors in the UST excavation zone from a leak source to an external
vapor sensor. The findings aid in understanding external leak
detection methods and network design. In its proposed UST
regulations, EPA's Office of Underground Storage Tanks (OUST) has
expressed a preference for adopting method-specific performance
requirements, partly because soil vapor sensing and subsurface vapor
transport were considered to be poorly-understood. Since vapor
sensors may act, however, as "early warning" devices, EPA/OUST did not
want external detection to be excluded from consideration prior to
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more study. This report is directed at this need.
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This project was designed to produce technical information consistent
with EPA's "four-parameter" approach to setting regulations for leak
detection systems. The four parameters are:
- release rate;
- probability of detection (PD);
i- probability of false alarms (PrA);
- and frequency of testing.
Each of these is discussed separately below.
Release Rate
The release rate was addressed in this research effort through the
development of a methodology, called "base" volatilization, in which
the UST leak was treated as a point source at the bottom of the tank.
By assuming that there is sufficient leaking product to maintain a
constant concentration source of vapor which diffuses into the
excavation zone, the simulation model yielded estimates of
instantaneous, time-varying leak rates based on the ability of the
excavation zone and native soil to transport the diffusing vapors.
When integrated over time, the vaporization rates provided estimates
of the minimum volume of leaked product lost to vaporization from
initiation of the leak until detection. These estimates were made for
different combinations of soil conditions, temperatures, and leaked
products.
Probability of Detection
The probability of detection, PD, is comprised of a sensor-related
component, and for vapor monitors, another component that is
determined by network design and vapor transport processes and
parameters. The component related to the sensor performance is being
investigated by Radian Corporation under a separate work assignment.
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The P component determined by network design and vapor transport
phenomena was addressed by the vapor transport modeling described
herein. For example, spacing vapor sensors 5 feet apart rather than
10 feet has been shown to yield a higher PD as expected. The effects
of varying the location and density of vapor sensors were analyzed
with the modeling techniques. Plots of concentration versus time at
potential sensor locations were produced by the simulation model, and
were used as the basis for comparing sensor performance under
different conditions of soil moisture, soil properties, and
temperature.
Probability of False Alarm
The probability of false alarm (PrA) is assumed to be primarily a
function of the detector hardware, although background vapor
concentrations in the subsurface can also contribute to PFA. The
probability of false alarm, however, was not included in this study at
this time.
Sampling Frequency
The fourth regulatory parameter, sampling frequency, is a key variable
in designing a leak detection network. Vapor transport modeling has
provided estimates of vapor movement rates, from which diffusive rates
from a leak to a sensor were estimated directly. Other types of
modeling results presented herein illustrate vapor concentration
versus time at a given point in space. These results, in conjunction
with the network design work at the Environmental Research Center of
the University of Nevada at Las Vegas (UNLV/ERC) and the device
testing by Radian Corporation, are intended to provide EPA with the
basis for selecting suggested sampling frequencies for vapor sensors.
In summary, the overall objective of this work assignment is to build
the technical foundation, based on modeling, for understanding the
aspects of subsurface vapor transport that are important to vapor
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monitoring network design. From this foundation, EPA will be in a
better position to promulgate method-specific performance requirements
for vapor detection systems, and ultimately general performance
standards for all leak detection methods, including vapor sensors.
1.3 PHRSE 1 REPORT OBJECTIVES
This report was intended to provide an initial understanding and
estimation of possible vapors sensor performance, assuming
diffusion-dominated transport of vapors from a single leaking UST.
Recommendations for further work, by including investigations of leak
characterization and modeling of leaking pipeline systems are made,
including simulation of "sandbox" vapor experiments now being
conducted by the Oregon Graduate Center.
The purpose of this Phase I Final Report is to present and discuss the
results of the UST vapor transport simulations performed under this
work assignment. Section 2 of this report describes the development
of a typical, or "generic" UST, which was used as the basis for the
modeling, presenting the simulation methodology and analytical
techniques that were developed and used. Section 3 includes graphical
depictions of the modeling results, emphasizing the changes in vapor
transport due to variations in soil conditions and temperature.
Discussions of the implications of the simulation results appear in
Section 4 with recommendations for Phase.2 activities.
The appendices to this report provide the technical foundation for
this study, and they can serve as a valuable source of information for
investigators. The appendices provide other researchers sufficient
information to reproduce the results presented in this report. The
appendices include: a glossary; a variable dictionary; a presentation
of the governing equations used in the vapor transport modeling; a
discussion of how CDM's DYNFLOW model was used for vapor transport
simulations; estimation of physicochemical properties of gasolines;
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development and presentation of equations used to estimate the
modeling parameters; an analysis of the potential effects of
vapor-water partitioning; verification of the DYNFLCW model versus an
analytical solution; a comparison of DYNFLCW and the U.S. Geological
Survey's MODFLOW program; a listing of the simulated UST conditions;
and listings of the simulation model command files and simulated time
histories of vapor concentrations and volatilized volumes.
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2.0 TECHNICAL APPROACH
2.1 SYSTEM CONCEPTUALIZATION
Development of a conceptual model was the first step in modeling vapor
transport from a leaking UST. This system conceptualization formed the
basis for the mathematical model of the system.
In formulating the system conceptualization, important processes to vapor
transport were included, whereas unimportant ones were neglected. The
conceptualization addressed such issues as tank and sensor configuration,
source characterization, hydrological conditions, and fate and transport
processes. This system conceptualization represents an abstraction of a
hypothetical leaking UST, including important features of the system, from
which a generic model of the UST system and surrounding excavation zone was
developed. The generic UST model was then used to perform vapor transport
simulations.
2.1.1 FATE AND TRANSPORT PROCESSES
t
The various processes which govern the fate and transport of contaminant
vapors in the vicinity of a leaking UST are described in detail in reports
by EPA (1987) and COM (1986). In summary, the migration of contaminants
released from underground storage tanks is governed by a complex
combination of processes involving multi-phase transport. That is, the
contaminant can be transported as a dissolved component in water, as a
volatile component in air, or as a separate immiscible liquid.
When a leak starts, an immiscible fluid phase consisting of one or more
petroleum constituents leaks from the tank and migrates downward through
the excavation zone due to gravity. Capillary forces cause the downward
migrating liquid to spread laterally. Due to volatilization of the lighter
constituents, a gaseous envelope of contaminant vapor will surround the
immiscible fluid phase.
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This contaminant vapor may diffuse or be advected and dispersed into the
porous media. In addition, if the vapor is denser than the surrounding
air, it will sink due to gravity.
Several natural processes retard the migration of the contaminant vapors,
including biodegradation and adsorption of chemical constituents to the
soil matrix. In addition, chemicals may partition between the vapor phase
and the residual soil moisture.
If the leak is of sufficient size, the immiscible fluid will eventually
reach the water table. If the fluid is lighter than water, it will travel
under its own pressure gradients in the capillary fringe zone above the
water table and may depress the water table to some extent. If the fluid
is heavier than water, it will tend to sink through the saturated
groundwatei: zone.
It is important to realize that a large percentage of the immiscible fluid
can be trapped by capillary forces in the pores of the unsaturated zone.
This trapped fluid, filling as much as 30% of the soil pore volume (J.T.
Wilson, 1987), can serve as a source of contaminant vapor, in addition, it
may serve as a source for dissolved contaminants for infiltrating rain
water or a rising water table.
2.1.2 MAJOR ASSUMPTIONS
The primary purpose of the system conceptualization was to reduce the
complexity of the processes summarized above by making assumptions allowing
analysis and simulation of vapor transport while still preserving the
essential aspects of the processes. The following paragraphs list these
assumptions, and provide further explanations as appropriate.
- Only a single UST was investigated. Although most UST's are found
in groups of 2 or 3 or more, with piping and fill systems that may
also leak, the assumption of using only one tank was made to keep
the simulations simple and straightforward. More complex
arrangements can be analyzed in FY88, although the results presented
here will not vary with multiple tanks.
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The UST was assumed to be cylindrical, and located in a homogeneous
and isotropic backfill, with the geometry and vapor transport
properties as defined in Section 2.2.2.
Conceivably, it is possible to consider the influence of interfering
sources (e.g., adjacent UST systems, surface spills), existing
background contamination, and the presence of man-made or natural
obstacles to measurement. It was decided, however, that these
factors would not be considered; only a "clean" system was assumed.
Gasoline and its chemical components were selected for simulation.
A discussion of the physiocochemical properties of the simulated
blend is found in Section 2.1.2, with a more complete presentation
of properties for different blends in Appendix D. This assumption
was made because of the prevalence of gasoline in UST's. Other
fuels and chemicals, however, can be considered and simulated in the
future; results may also be inferred from information presented
here.
The ground surface was assumed to be paved and therefore impermeable
to vapors. This is a valid assumption because most UST's, in
general, are located below paved areas. One simulation of an open,
unpaved surface was performed.
The water table was assumed to be below the excavation zone. This
is generally the case at most UST's where vapor sensors would be
used.
Although the presence of the water table below the excavation zone
indicates unsaturated conditions, moisture content of the excavation
zone ancl surrounding native soils was varied to examine the effects
of reduced air-filled porosity or vapor transport. The moisture
content was assumed to be homogeneous throughout the backfill and
native soils, with different values possible for the backfill versus
the native soil.
Several factors influencing vapor transport were assumed to be
insignificant, based on-literature -reviews, simple calculations,- and
consideration of the influence of the paved surface (COM, 1986).
These factors are:
- wind over a ground surface
- barometric pressure fluctuations
- water table fluctuations
- rainfall infiltration
- temperature gradients
Although it was assumed that there were no horizontal or vertical
temperature gradients across the UST site, temperature was a factor
in the vapor simulations. Temperature strongly affects the
equilibrium vapor pressure (i.e., maximum vapor concentration) of
gasoline vapors in the air-filled pores. . Consequently, variation in
the equilibrium vapor pressure of gasoline due to temperature
changes, (presented in Appendix D), was used as a key model
variable.
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Vapor density will most likely have a significant effect on gasoline
vapor transport because gasoline vapors are roughly 50% heavier than
air (See Appendix F). For this study, however, gravity-driven
advection was neglected. This means that the modeling results
presented herein may overestimate the time-to-detection for sensors
placed deep in an UST excavation zone, and conversely underestimate
the time-to-detection for shallow sensors. The future research
should include Investigations into the quantitative effects of
gravity-driven vapor advection.
Diffusion was assumed to be the dominant vapor transport process.
Also, it was determined that simulation of diffusion in three
dimensions were required to estimate realistically the movement of
vapors. Two-dimensional radial simulation of diffusion, it was
determined, could significantly underestimate the time for vapors to
reach a sensor. Capturing the geometries of the UST and its
excavation zone, and their influence on three-dimensional aspects of
vapor movement, was essential.
Advection due to artificially-induced pressure gradients was not
considered. This is a conservative approach, because suction wells
or active (pumping) sensors will draw in vapors sooner, in general,
that would occur under static air pressure.
It was assumed that biological and chemical degradation were slow
when compared to the time scale of interest, which is hours to days
(Corapcioglu and Baehr, 1987). Also, given that pea gravel
backfill, for example, is unlikely to possess a high organic matter
content, the degree of sorption was assumed to be insignificant.
Spurious pathways for vapor movement were not considered, because
they are highly dependent on individual UST site conditions and thus
difficult to assign in a generic representation.
For purposes of presenting estimated times for sensors to reach
alarm or detection levels, sensor response to total vapor
hydrocarbons at 500 ppm levels-were*investigated. These numbers can
be easily modified to reflect the results of on-going sensor
testing. Also, sensor specificity to chemicals can be incorporated
because the simulation models can produce estimates for not only a
gasoline blend, but for individual chemical components as well.
Partitioning 'between the vapor phase and water in the subsurface was
assumed to have a negligible effect on diffusion. The validity of
this assumption is examined in Appendix E.
Changes in diffusion of gasoline vapors due to temperature
variations are small compared to the effects of soil moisture
content and porosity. Also, vapor diffusion rates do not vary
significantly between the constituitive chemicals of gasoline. The
small variability of vapor diffusion with temperature or
constituents justified using a single vapor diffusion coefficient
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for gasoline for the vapor transport simulations. Appendix D
tabulates the average and individual vapor diffusion coefficients
for selected gasoline blends and their constituents.
By making the assumptions listed above, the problem of simulating vapor
transport from an UST leak was made tractable. The key parameters that
were then varied, in performing the vapor simulations, were:
- Vapor diffusion coefficients of the backfill and surrounding native
soils, as affected and determined by the moisture content,
air-filled porosity, and total porosity of the soils;
- Temperature, which effects the equilibrium vapor pressure of the
leaked gasoline according to the chemical properties of the
constituents of the gasoline blend;
- Ground surface conditions, with one simulation performed with an
open, unpaved surface, and all the others a paved, impervious
surface.
2.2 DESCRIPTION OF SIMULATED UST
Based on the system conceptualization, a generic model of an UST excavation
zone and surrounding native soil was developed. It incorporates all of the
key parameters and considerations that were identified, and it is based on
the assumptions described above that make the problem tractable.
*
The following text describes the typical gasoline blend and the
physicochemical properties of it and its components (Section 2.2.1), and
the geometry and hydrogeologic properties of the excavation zone and native
soil (Section 2.2.2). This conceptualization of the UST and the leaking
product was then transformed into a numerical model-, as described in
Section 2.3.
2.2.1 PRODUCT CHARACTERISTICS
A typical gasoline blend (Table 2-1) was developed to represent an average
mixture of the various chemical constituents of gasoline. This synthetic
gasoline was used for all of the simulations in this report and is similar
to one of the gasoline blends suggested by K. Stetzenbach (1987). See
Appendix D for further information on synthetic gasoline blends.
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The physiocochemical properties of this blend and its component chemicals
were estimated based on literature values, chemical estimation techniques,
or literature-reported estimation equations, as discussed in Appendix C. A
summary of the average properties for the typical gasoline blend, as
affected by temperature variations, appears in Table 2-2. A comparison of
the properties for individual components to the average properties for the
blend is shown in Table 2-3. Similar tables for other synthetic blends are
listed in Appendix D.
Tables 2-2 and 2-3 show how vaporization varies significantly with
temperature. Vapor transport simulations therefore included vapor
pressures at temperatures of 0°, 10°, and 20°C for the synthetic gasoline
blend. This wide temperature range, from freezing to 68°F, is intended to
bracket the more typical range of about 45°F to 60°F. The constituitive
chemicals of the gasoline blend also exhibit a wide variation in vapor
pressure; thus, simulations were produced for a compounds with a low vapor
pressure,, (e.g., benzene, toluene, and xylene), and for two with high
vapor pressures, (i.e., isopentane and isobutane).
The estimate diffusion coefficients do not vary significantly with
component or with temperature. Therefore, a diffusion coefficient equal
to the average diffusion coefficient for the synthetic gasoline blend at
10°C was used in performing the simulations.
2.2.2 UST SYSTEM GEOMETRY AND HYDROGEOLOGIC CHARACTERISTICS
The geometry of the single UST used for the simulations is depicted in
Figure 2-1. The tank and excavation zone have the following dimensions:
- The tank is cylindrical, 12 feet long, and 6 feet in diameter;
- The top of tank is 2 feet deep below ground surface;
- The excavation zone is rectangular in plan view and in
cross-section, surrounding the tank with at least 2 feet of
backfill. Further simulations in Phase 2 will include 1:1 or 2:1
side-slopes, as required for safely excavating the native soils.
2-6
-------
The excavation zone.is assumed to be backfilled with coarse.sand or pea
gravel, while the native soil ranged from clay to coarse sand. The ranges
of hydraulic and hydrogeologic properties for the backfill and native soil
used to bracket the different simulation conditions are listed in Table
2-4.
2.3 SIMULATION METHODOLOGY
2.3.1 "BASE CASE" VOLATILIZATION SCENARIO
The representation of the UST leak itself was based on the assumption that
diffusion alone transports vapors away from the leak, and that the loss of
the diffused mass is exactly balanced by the vaporization of liquid
product. The leak was assumed to be a "point" at the far bottom end of the
tank. Based on the mathematics of the simulation model, the leak source
at "time zero" of the simulations was approximated as a cube of vapors,
varying linearly from 100 percent saturation at the center (leak) to zero
concentration at the edge, 1 foot from the leak. It is recognized that the
liquid-vapor interface location is a difficult and complex problem to
describe and solve; this source geometry approximation, however, was
necessary at this time. Further analysis of the source representation
should be performed in future work.
This volatilization scenario is called "base case," because the
volatilizing leak is confined to a point source, instead of a line or plane
source, which produces the minimum volume of vapors that can be detected.
The vapor transport model can do this because it simulates the spreading of
vapors from the point source, and thus time-varying concentrations at
sensor locations are predicted. When the vapor concentration at a sensor
point reaches the detection level, there is a distributed amount of vapor
around the leak and the total mass can be computed. The "base case"
volatilized volume can be estimated for any potential sensor location
within the excavation zone.
2-7
-------
2.3.2 SELECTION OF SIMULATION MODEL
Because diffusion was to be the only vapor transport process to be
simulated, it was determined that the most accurate representation of the
three-dimensional nature of that process would be attained by using a
simulation model. The most suitable was the DYNFLOW ground water flow
simulation mode, which solves the diffusion equation by analogy. Appendix
H provides a description of the diffusion-groundwater flow analogy, as well
as background information on DYNFLOW. The work assignment team has had
extensive experience with DYNFLOW, and the work assignment manager was a
co-developer of the program.
Although several three-dimensional confined ground water flow or heat
conduction models could have been used in the assignment, the advantages of
DYNFLOW to the work assignment team were familiarity, and the availability
of powerful software for grid generation and multi-color graphics display.
A test simulation of a preliminary UST scenario was also performed using
MODFLOW from the U.S. Geological Survey, as described in Appendix L.
Reasonable agreement between MODFLOW and DYNFLOW was shown, demonstrating
that any threes-dimensional groundwater flow model could be used to address
this problem.
2.3.3 DESCRIPTION OF MODEL GEOMETRY AND BOUNDARY CONDITIONS
The generic UST was transformed into a three-dimensional numerical model as
shown in Figures 2-2 through 2-5. Because the simulation results are
symmetrical about the longitudinal centerline of the tank, only half of the
tank, surrounding backfill, and native soils was simulated. Simulating
only half the volume of the site reduces computer computation and storage
charges that would be necessary for a full representation.
The sides and bottom of the native soil portion of the model were placed
far enough from the tank so that significant vapor concentrations would not
reach the edges of the model before concentrations at sensors in the
excavation zone would reach detection limits. The bottom of the model can
be likened to a water table that is 24 feet from the ground surface.
2-8
-------
The leak was represented as a fixed concentration at 100 percent of
equilibrium vapor concentration. The tank leak was simulated as a constant
100 percent concentration in the model, at the node point located at the
bottom left end of the tank. The model elements at this location are 1
foot in width. The DYNFLOW model interpolates concentrations linearly
across each element. Thus, the concentration gradient at the leak source
point at the beginning of the first simulation time step was an abrupt
linear drop from 100 percent to 0 percent across the surrounding elements.
The bottom and top of the model were no-flow boundaries, except in one
simulation with an open top surface which had concentrations fixed at zero
to simulate diffusion through the top surface. The lateral sides were held
at a fixed concentration of zero so that vapors would not build up and
cause concentrations in the backfill zone to be overestimated.
The sensor locations depicted in Figure 2-6 and listed in Table 2-5 are the
points at which model results were tabulated for the time history plots
presented in Section 3. These locations were selected to represent
"nearby," "intermediate," and "distant" locations from the source. In
actuality, simulation results for any point in the model can be tabulated
and plotted.
2.3.4 DEFINITION OF SIMULATION MATRIX
A set of seven simulation runs was defined, with the input parameters for
each run selected to represent various soil moisture and porosity values.
Table 2-6 is a summary of the simulation matrix; Appendix K contains a
complete listing of the conditions simulated. Run number 1 is considered
the "average soil conditions" run because it represents what may be
considered the most typical situation. This is a dry sand native soil
surrounding a dry gravel backfill.
2-9
-------
The simulation matrix contains "pairs" of backfill/soil conditions. The
first run in each pair has the same backfill as the native soil; the second
run in each pair has a contrast, testing the effects of decreased diffusion
in the native soil. Run number 7 is not in a "pair," but was rather
designed to test the effects of an open surface.
The only parameter that varied from run to run was the effect diffusion
coefficient. This term incorporates the influences of porosity and
moisture content. Therefore, a single simulation run can represent more
than just the single combination of properties listed in the simulation
matrix, as long as the combination of properties results in the same
effective diffusion coefficient.
2.3.5 TRANSFORMING RESULTS FOR DIFFERENT PRODUCT CHARACTERISTICS
To interpret the output from the simulation runs, in which all concentra-
tions are expressed as "percent of equilibrium vapor concentration," the
concentrations and vapor flux (or minimum volatilization rate) predictions
were multiplied by the equilibrium vapor concentration (in ppm) and divided
by 100 (correction for percentage). The vapor fluxes were also transformed
into the equivalent liquid volume of the volatilized and diffused vapors
through a similar transformation process, described in Appendix G, that is
also based on the equilibrium vapor concentration. In this way, the
results from a single run were used to tabulate and plot predicted results
for different volatilized products and temperatures.
Table 2-7 is a listing of the equilibrium vapor concentrations for selected
gasoline components, and for the synthetic gasoline blend, that were used
for transforming model results into more meaningful concentration units.
This listing gives a good indication of how sensor response may be expected
to vary according to temperature, and how predicted vapor diffusion would
be expected to vary by gasoline component.
2-10
-------
2.3.6 CREATING AND PERFORMING THE SIMULATIONS
A set of seven simulation runs, defined in Table 2-6 and Appendix K, was
formulated as DYNFLOW command files, which are listed in Appendix M. Each
command file was run against DYNFLOW Version 4B, with output from the
program stored on computer files for later display and analysis of results.
The simulation time^frame was from time zero, when the volatilization
started, to 28 days afterwards. Simulation results were saved every
three-and-a-half days.
Time histories of simulated concentrations at the sensor point locations
are listed in Appendix N, as well as time histories of simulated vapor
influx at the leak. Transformed versions of these time histories appear in
some of the graphs contained in Section 3.
Additional simulation results, besides the output listed in Appendix N,
were sued to prepare the contour plots and some of the "sensor response,"
or "alarm time" plots shown in Section 3. The results were extracted from
the computer output files, which were too extensive to list in this report.
2-11
-------
-------
Plan View
- 12 ft.
Tank
6 ft.
Longitudinal
Cross Section
Leak
Pavement
Tank
, I2JU
.!!!.!!!!»!
Pavement
Lateral
Cross Section
Figure 2-1. Geometry of the "Generic" UST
-------
Lslail Blinnst (B) _.24
(ml M Kill)
Longimml DhllnM (>) \-
Figure 2-2. Cut-Away Isometric View of the Vapor Diffusion Model.
-------
SOILS
BACKFILL
TANK
4J
4-1
30s-
25
20
3 15
4J
to
H
Q
-------
SOILS
TAMK
Longitudinal Distance (ft)
i i i ii
20
30
40
Figure 2-4. Longitudinal Cross-Section of the Vapor Diffusion Model.
-------
SOILS
BACKFILL
TANK
Lateral Distance (ft)
Figure 2-5. Lateral Cross-Section of the Vapor Diffusion Model.
-------
SOILS
BACKFILL
TANK
sa
25
4-1
U-J
to
H
Q
20
10
- 5
-10
I I
Sensors 1 & 2
Sensors
Sensors 5 & 6
Longitudinal Distance (ft)
10
20
30
40
Figure 2-6. UST Leak and Vapor Sensor Locations in the Vapor Diffusion Model.
-------
TABLE 2-1
COMPONENTS OF THE SIMULATED GASOLINE BLEND
COMPONENT OF BLEND PERCENTAGE
Isopentane 14
C12 -aliphatic 10
n-Hexane 9
2 , 4-Dimethylhexane 8
2-Methylpentane 8
m-Xylene 7
Toluene 5
2-Methylhexane 5
1 , 4-Diethylbenzene 5
1,3, 5-Trimethylbenzene " 5
Cyclohexane 3
Benzene 3
n-Pentane 3
Isobutane 2
Ethylbenzene 2
2,2, 4-Trimethylhexane 2
2, 2, 5, 5-Tetramethylhexane 1.5
n-Heptane 1.5
1-Pentene 1 . 5
1-Hexene 1.5
n-Butane 1
n-Octane 1
Methylcyclohexane 1
Total 100%
-------
TABLE 2-2
AVERAGE PHYSICOCHEMIGAL PROPERTIES OF THE SIMULATED
GASOLINE BLEND AT DIFFERENT TEMPERATURES
Temperature
0°C 10°C 20°C
Average Gram Molecular 68.34 68.92 69.48
Weight of Gasoline
Vapors(g /tool)
Average Liquid Density 0.7358 0.7271 0.7182
of Gasoline Components
(g /cm3 )
Equilibrium Vapor Concentration 165,976 248,191 360,661
of Pure Gasoline Vapor in
Air (ppm)
Average Air Diffusion 0.0642 0.0684 0.0726
Coefficient of Gasoline
Components (cm /sec)
-------
Table 2-3. Physicochemical Properties of Individual Chemicals
versus the Simulated Gasoline Blend ,at 10° Centigrade,
REPRESENTATIVE PERCENT
CHENICM. CWIP08IIIM
liriutini
n-Butini
lioptfltini
n-Pmtini
n-Octint
' Binnni
Toluini
lyltnt III
n-Hiiiiii
2-lhUiylp9flttni
Cyclohnnt
n-Htptuii
2-Htthylliluin
Kethylcyclohiiint
2,4-DiHthylltcuni
EthylbHiini
I-Pent«fli
2,2,4-TrlMthylhmni
2,2,5,3-litriMthylhinni
l,4-Dl(thylbcn»ne
1-Hticni
Ii3,5-Trlitt(i)ilb«n:ini
C12-iliphitic
Total
Ttiptritirt * 293.13 ttq.
Pruiuri 740 II H(
C» CansUnt
2
1
14
3
1
3
9
7
9
8
1
I.S
3
1
1
2
1.3
2
1.3
3
1.3
9
10
100
It
8RMI HOI. LIB. PHASE
KIBHT ML FRACT.
I6N/NOU
98.12 0.0321
98.12 0.0113
72.19 0.1840
72.19 0.0394
114.23 0.0083
79.11 0.0314
12.14 0.0915
101.17 0.0629
81.18 M990
06.18 S/flB80
84.11 ' i.0338/
100.20 0.0142
100.20 0.0473
18.19 0.0017
114.21 0.0664
106.17 0.0171
70.14 0.0201
128.21 0.0149
142.21 0.0100
114.22 0.0333
94.16 0.0161
120.20 0.0114
170.00 0.0559
102.20 1.0000
Vipor Oenilty
of Giiollni-fllr
KUttirt
MR DIFFUSION
COEFFICIENT
-------
-------
TABLE 2-4
VAPOR TRANSPORT PROPERTIES OF
EXCAVATION ZONE BACKFILL AND NATIVE SOILS
BACKFILL
Material: Gravel or Sand
Total Porosity: 20% to 40%
Saturation: 30% to 75%
NATIVE SOILS
Material: Sand, Silty Sand, or Clay
Total Porosity: 20% to 45%
Saturation: 30% to 84%
-------
-------
TRBLE 2-5
SENSOR LOCATIONS IN THE VAPOR DIFFUSION MODEL
Sensor
Number
1
2
3
4
5
6
Depth
(ft)
8
2
8
2
8
2
Vertical
Distance
From Source
(ft)
0
6
0
6
0
6
Longitudinal
Distance From
Source (ft)
1
1
5
5
13
13
Lateral
Distance
From Source
(ft)
2
2
4
4
2
2
Direct
Horizontal
Distance from
Source (ft)
2.2
2.2
6.4
6.4
13.1
13.1
Approximate
Travel
Distance (ft)
2.2
6.4
6.4
12.0
13.1
19.1 ...
-------
TABLE 2-6
SUMMARY OF SIMULATION MATRIX
Effective
Simulation
Run Number
1
2
3
4
5
6
7
Surface
Condition
Paved
Paved
Paved
Paved
Paved
Paved
Open
Backfill
Material
Dry Gravel
Dry Gravel
Moist Sand
Moist Sand
Wet Sand
Wet Sand
Dry Gravel
Native
Soil
Dry
Silty Sand
Moist
Silty Sand
Moist Sand
Wet
Silty Sand
Wet Sand
Wet Clay
Dry
Silty Sand
Diffusion
Backfill
0.017
0.017
0.005
0.005
0.002
0.002
0.017
Coefficient (on /sec)
Native Soil
0.017
0.008
0.005
0.001
0.002
0.0008
0.017
-------
TABLE 2-7
EQUILIBRIUM VAPOR CONCENTRATIONS
USED IN TRANSFORMING SIMULATION RESULTS
Temperature
Component
Equilibrium
Vapor
Concentration
(ppm)
0° Celsius
Benzene
Isopentane
Isobutane
Gasoline Blend
1262
62785
50423
165976
10° Celsius
Benzene
Isopentane
Isobutane
Gasoline Blend
2182
95030
70756
248191
20° Celsuis
Benzene
Isopentance
Isobutane
Gasoline Blend
3604
139200
96734
360661
-------
-------
3.0 NUMERICAL SIMULATION RESULTS
3.1 "BASE CASE" VOLATILIZATION OVER TIME
The vapor diffusion model predicts minimum liquid gasoline volatilization
rates (see Figure 3-1). Figure 3-1 shows a decline with time of the rate
of volatilized liquid gasoline entering the UST model. This decline in the
influx rate of volatilized liquid gasoline occurs as a consequence of the
reduced vapor concentration gradient away from the leak with time.
Figure 3-1 also shows the effect of increasing moisture content in the
backfill on the influx rate of volatilized liquid gasoline. The rate of
volatilization of liquid gasoline declines with increasing water content of
the backfill from Run 1 (water saturation percent = 30%) to Run 3 (water
saturation percent = 63%) to Run 5 (water saturation percent = 75%). See
Appendix K for a tabulation of the total porosity, air-filled porosity, and
moisture content values used in the numerical simulations. The increased
moisture content of the backfill reduces the air-filled porosity through
which volatilized liquid gasoline may diffuse, thereby reducing the "base
case" volatilization rate of the leaking gasoline.
Figure 3-2 depicts the cumulative volume of liquid gasoline lost to
volatilization. Increasing the moisture content from Run 1 to Run 3 to Run
5 reduces the volume of leaked gasoline that may enter the excavation zone
in a volatile state.
Simulations were performed to examine the effect of increasing moisture
content in the surrounding native soils. In each of the simulation pairs
(i.e., Run 1 and 2, Run 3 and 4, and Run 5 and 6), the moisture content of
the native soils within each simulation pair was increased, holding the
backfill properties constant. The simulations demonstrated that increasing
moisture content in the native soils had little effect on "base case"
volatilization. Figure 3-1 and 3-2 show the effects of variation in
backfill properties only for Runs 1, 3, and 5.
3-1
-------
Another interesting and related aspect of these plots is that the rate of
"base case" volatilization reached a steady value soon after volatilization
had started, because the excavation zone was still filling with vapors.
The rate of "filling" was apparently balancing the volatilization. Because
sensors would have responded well before the excavation zone was filled
with enough vapors to slow down diffusion at the leak, none of the
simulations were extended long enough to demonstrate this effect.
Figure 3-3 demonstrates the strong effect of temperature on the "base case"
volatilization. Results of Run 1, plotted in Figure 3-3 at 0°, 10°, and
20°C, show an increase in volatilization rate with temperature. The effect
of temperature on the pure chemical vapor pressure and vapor concentration
of gasoline can be seen in equation C-6 of Appendix C and in Table 2-7 and
Tables D-l, D-7, and D-3 of Appendix D.
The cumulative volumes of vaporized product for three constituents of
gasoline (i.e., isopentane, isobutane, and benzene) are plotted versus time
in Figure 3-4. The differences in the results for isopentane, isobutane,
and benzene are due to differences in equilibrium vapor concentration
between the three compounds (see Table 2-7). The equilibrium vapor
concentrations of isopentane and isobutane are about ten times higher than
that of benzene, for the synthetic gasoline used in these simulations.
Figure 3-4 shows the effect of the larger vapor pressure values on the
volume of volatilized gasoline. More pure product of isopentane and
isobutane will be lost to volatilization and diffusion than benzene under
the same physical conditions, and at the same time. The implication of
Figure 3-4 is that if a benzene-specific external sensor is placed within
the backfill, a longer time-to-detection of vapors will result than if the
sensor was sensitive to a more volatile compound such as isopentane. The
result of the increased detection time from a benzene-specific sensor is to
increase the volume of liquid gasoline lost to leakage and volatilization
prior to detection.
3-2
-------
As a final point concerning Figure 3-4, the volume of volatilized gasoline
is greater than any of the volumes for isopentane, isobutane, or benzene.
This is because each of these three compounds are constituitive compounds
of gasoline, and so their individual volumes are all less than the total
volume of gasoline .
3.2 VAPOR SPREADING THROUGHOUT BACKFILL AND NATIVE SOIL
Contours of gasoline vapor concentrations have been plotted to demonstrate
the spreading of vapors away from the'leak. The "pair" of simulation runs
1 and 2, representing "average conditions" and "dry backfill with moist
native soil," were used to show the effect of a contrast between the
backfill and native'soil. As shown in Figures 3-5 and 3-6, an increased
moisture content in,the native soil caused the vapors to diffuse
preferentially into the backfill materials.
Another contour plot (Figure 3-7) shows the vapor spreading at a depth of
two feet for Run 1. Comparison of the gasoline vapor concentration
contours at depth of 8 feet (Figure 3-5) and 2 feet (Figure 3-7) show the
reduced vapor concentration at the shallower depth. This is primarily due
*
to the increased vertical distance from the source. The presence of the
UST as a no-flow boundary also impedes the vertical diffusion of vapors,
thereby reducing vapor concentrations in Figure 3-7.
3.3 SENSOR LOCATION VAPOR CONCENTRATIONS , "..
The simulation results were tabulated as time histories at six sensor
locations (see Figure 2-6 and Table 2-5), and then plotted with respect to
time.
Figure 3-8 shows vapor concentrations at each of the six sensors for the
"average conditions" simulation. The effects of sensor distance and depth
are apparent, with the "nearby" and "intermediate" sensors responding
within 8 days. This analysis assumes that a sensor can respond to total
gasoline hydrocarbons at about 500 parts per million. Even the most
distant, shallow sensor is predicted to respond within about one month.
3-3
-------
Figure 3-9 shows predicted vapor concentrations at the deep, "intermediate"
sensor. As in the plots of leakage rates and volumes (Figures 3-1 and
3-2), the effects of decreasing air-filled porosity outweigh the effects of
contrasting backfill/soil conditions. Figure 3-9 does, however,
demonstrate how decreased porosity in the surrounding soils enables the
vapors to spread more quickly in the backfill.
3.4 DETECTION TIME VERSUS SENSOR LOCATION
Assuming that a sensor can detect 500 parts per million of total gasoline
hydrocarbons, plots of detection time versus potential sensor locations
were developed. These plots were based on the definition of "sensor
distance," as depicted in Figure 3-10. "Sensor distance" was defined based
on the assumption that sensors driven into an existing backfill zone would
have to be placed at least one foot from the edge of the tank in plan view.
"Sensor distance" is thus the distance from the leak along the line defined
by this one-foot spacing.
Figure 3-11 depicts the variation in "sensor distance" with alarm time at a
500 ppm total hydrocarbon vapor concentration threshold. Figure 3-11
indicates the closest "sensor distance" at which an external sensor must be
placed to detect the leak at a given alarm time.
The effects of increasing the water content in the backfill on the "alarm
sensor distance" is also depicted in Figure 3-11. An increase in moisture
content in the backfill reduces the distance at which a sensor are
predicted to detect 500 ppm of total hydrocarbon vapor at a given alarm
time. In other words, as the moisture content of the backfill increases,
sensors must be placed more closely to the leak in order to detect the leak
at the same required alarm time.
Figure 3-11 indicates that increasing moisture content of the native soils
(e.g., from Run 1 to Run 2) has little effect. The same general
observation may be made for Figure 3-12, except, that the shallow sensors of
Figure 3-12 require closer placement to the leak to enable detection at the
same alarm time.
3-4
-------
Increasing temperature increases -the "sensor distance" at which external
sensors are predicted to detect vapors at the 500 ppm level by a given
alarm time (see Figure 3-13). The increased vapor concentrations at higher
temperatures indicates that sensors may be placed further from the leak for
a required alarm time.
Figure 3-14 shows the effect of sensor threshold on the sensor distance at
a required alarm time. Increasing the sensor threshold, from 250 to 500 to
750 ppm of total hydrocarbon vapors, reduces the distance at which external
sensors are predicted to detect vapors at a given alarm time. At sites
where background vapor concentrations are high or sensor thresholds are
high, Figure 3-14 indicates that the sensors must be placed more closely
to the leak to detect the leak at a required alarm time.
Figures 3-12, 3-13, and 3-14 exhibit a slope break at about 17 feet of
"sensor distance," becoming near-vertical. This is because those sensors
placed beyond 17 feet of "sensor distance" (see Figure 3-10) from the vapor
source are not increasing in radial distance from the source.
Consequently,.there is little change in alarm time in the portion of the
curves beyond 17 feet of "sensor distance."
3.5 VOLUME OF LEAKAGE AT DETECTION TIME
Combining the time histories of "base case" volatilized liquid volume and
the simulated detection times versus "sensor distance" yielded the plot
shown in Figure 3-15. This plot shows how much gasoline is simulated to
have vaporized by the time a sensor responds, as a function of the distance
a sensor is placed away from the leak.
3.6 EFFECTS OF OPEN SURFACE
Opening the ground surface and allowing the free escape of vapors had
little effect on the simulated leakage or spread of gasoline vapors. This
is shown in Figure 3-16, which is a plot of vapor concentrations from the
"average condition" simulation at the deep, "intermediate" sensor. The
3-5
-------
time history of "base case" volatilization, when plotted, showed no
discernible differences over the time scale of the simulation. Differences:
in "base case" volatilization under conditions of open and closed top
surface are predicted to become more evident as the leak continues beyond
one month.
Having an open top surface with a zero vapor concentration at the top
surface is physically equivalent to an unpaved land surface with a stiff
wind blowing across it. The wind removes any diffusing contaminant vapors
from the land-air interface. The wind keeps the vapor concentration at the
interface at zero throughout time. The effect of this zero concentration
at the land-air interface is to maximize the flux of contaminant vapors
diffusing through the top of the model to the atmosphere. As a result, the
volume of vapors lost through the open top surface (i.e., Run 7), and
plotted in Figure 3-14, represents a maximum volume loss. A non-zero vapor
concentration at the air-land interface, such as might occur under
conditions of intermittent wind removal, would reduce the loss of vapors
through the open top surface.
3-6
-------
0.00012'
0.00010
I
"5
3
o
er
if
w
CD
CD
8
CO
(3
S
0)
o
oc
0.00008 -
0.00006 -
0.00004 -
0.00002 -
-0.00000
t PL
o- run 1
-* run 3
HB- runs
dry gravel backfill
moist sand backfill
wet sand backfill
10
20
30
TIME (Days)
Figure 3-1. Time History of Simulated Gasoline Volatilization Rate
for Different Soil Conditions at 10 deg. C.
-------
0.06
0.05-
m
.0
I
o
s
a
2
tr
to
I"
05
CO
ffi
"o
0)
a
O
a
I
"o
6)
3
I
0.04-
0.03-
0.02-
0.01
0.00
dry gravel backfill
O- Run 1
-- Run3
« Run5
moist sand backfill
wet sand backfill
TIME (days)
Figure 3-2. Time History of Simulated Gasoline Volatilized Volume
for Different Soil Conditions at 10 C.
-------
S
I
g
CD
(3
.1
s
-------
0.05
§
"a
I
s
05
if
o =
So
_N 3£
:>
s
Component Total = Gasoline
All Others
BTX
Isobutane
Isopentane
0.00
Time (days)
Figure 3-4. Time History of Simulated Volatilized Volume of Different
Gasoline Components for Average Soil Conditions at 10. deg. C.
-------
SOILS
BACKFILL
TANK
Lateral
Distance
(ft.)
23
15
10
-5
O 00 O
m om o
o
o o oo
o o oo
o o oo
in o
oo
mo
Values are Gasoline Vapor Concentrations in parts per million.
10
15
20
25
30
35
Longitudinal Distance (ft.)
+5
Figure 3-5. Contour Plot of Simulated Vapor Concentrations at 8 Foot Depth for
Average Soil Conditions at 10°C and 14 Days Since Leak Started.
-------
SOILS
ill BACKFILL
TANK
Lateral
Distance
(ft.)
20
15
10
-5
o ooo oo oo
in omo oo oo
rg mr-o oo oo
mo
r-l
oo
Values are Gasoline Vapor Concentrations in parts per million._
10
15
20
25
30
35
40
Longitudinal Distance (ft.)
Figure 3-6. Contour Plot of Simulated Vapor Concentrations at 8 Foot Depth for
Dry Gravel Backfill, Dry Silty Sand Native Soil Conditions at 10°C
and 14 Days Since Leak Started.
-------
I I SOILS
BACKFILL
TANK
Lateral
Distance
(ft.)
25
20
15
to
-to
Values are Gasoline Vapor Concentrations in parts per million.
to
15
Longlrhidinaf^istancl (ft.)'
Figure 3-7. Contour Plot of Simulated Vapor Concentrations at 2 Foot Depth for
Average Soil Conditions at 10°C and 14 Days since Leak Started.
-------
c
I
i
i
o
CO
m
C3
8000
7000-
6000 -i
5000
4000
3000
2000
1000
shallow, near
deep, intermediate
» SENSOR 1
-*- SENSOR2
B- SENSOR 3
-» SENSOR 4
* SENSORS
o- SENSOR6
shallow, intermediate
deep, distant
shallow, distant
TIME (DAYS)
Figure 3-8. Time History of Simulated Vapor Concentrations at Various Sensor Locations
for Average Soil Conditions at 10 deg. C.
-------
8000-
6000-
o.
0)
o
a.
CO
0
to
C5
4000-
2000-
Run#2
Dry Gravel Backfil
Moist Silly Sand Native Soil
Run#1
'Dry Gravel Backfill
Dry Siky Sand Native Soil
Run #4
Moist Sand Backfill
Wet Silty Sand Native Soil
Run #3
Moist Sand Backfill
Moist Sand Native Soil
Run #6
Wet Sand Backfill
Wet Sand Native Soil
Of
Run #5
Wet Sand Baddiil
Wet Clay Native Soil
Time (days)
Figure 3-9. Time History of Simulated Vapor Concentrations at a Deep, "Intermediate"
Sensor for Different Soil Conditions at 10 deg. C.
-------
SOILS
BACKFILL
TANK
Lateral
Distance
(ft.)
10 -
15
2O 25
Longitudinal Distance (ft.)
Figure 3-10. "Sensor Distance" Definition.
-------
« 10-
I
I
5
8
I
20-
15-
Run #2 Dry Gravel Backfill
Motet Sity Sand Native Soil
Run #1 Dry Gravel Backfill
Dry Silty Sand Native Soil
Run *4 Moist Sand Backfill
Wet Silly Sand Native Soil
Run #3 Moist Sand Backfill
Moist Sand Native Soil
Run #5 Wet Sand Backfill
Wet Clay Native Soil
Run *6 Wet Sand Backfill
Wet Sand Native Soil
500 ppm Alarm Time (days)
Figure 3-11. Alarm Time Versus "Sensor Distance" for Deep Sensors
and different Soil Conditions at 10 deg. C.
-------
£
~o
ta
<*~
i
8
Run #2 Gravel Backfill
Moist Snty Sand Native Soil
Run #1 Dry Gravel Backfill
Dry Sitty Sand Native Soil
Run #4 Moist Sand Backfill
Wet Sitty Sand Native Soil
Run #3 Moist Sand Backfill
Moist Sand Native Soil
Run #5 Wet Sand Backfill
Wet day Nalive Soil
Run #6 Wet Sand Backfill
Wet Sand Native Soil
500 ppm Alarm Time (days)
Figure 3-12. Alarm Time Versus "Sensor Distance" for Shallow Sensors
and Different Soil Conditions at 10 deg. C.
-------
1
o
500 ppm Alarm Time (days)
Figure 3-13. Alarm Time Versus "Sensor Distance" for Deep Sensors
and Average Soil Conditions at Various Temperatures
-------
1
CO
o
in
Alarm Time (days)
Figure 3-14. Alarm Time Versus "Sensor Distance" for Deep Sensors with Different Alarm Levels
Under Average Soil Conditions at 10 Deg. C.
-------
20-
£
o
§
o
m
0)
CO
Run1
Run 3
Run5
0.00 0.01 0.02 0.03 0.04 0.05
Volume of Volatilized Gasoline (gallons)
Figure 3-15. Volatilized Liquid Volume at Detection Time Versus "Sensor Distance"
for Deep Sensors and Different Soil Conditions at 10 deg. C.
-------
6000
o
f
5000-
4000-
Q.
O.
& 3000 -
E
1
§
5
2000-
1000
0- Run1
-*- Run?
TIME (Days)
Figure 3-16. Open Versus Closed Surface: Time Histories of Vapor Concentrations
at an "Intermediate" Deep Sensor.
-------
4.0 DISCUSSION AND CONCLUSIONS
4.1 VAPOR SENSORS AS EARLY-WARNING DEVICES :
The most significant finding of the vapor transport modeling is that, under
a variety of soil and temperature conditions, external vapor detectors,
responding to total hydrocarbons in the 500 parts per million range, are
predicted to act as well as in-tank sensors as good early warning devices.
The vapor transport simulations predicted that, for average conditions, a
shallow vapor sensor on the opposite side of the tank from the leak will
detect the volatilized product within approximately 30 days. Sensors
halfway across the excavation zone were predicted to respond within about 8
days. :
Moreover, the minimum amount of volatilized product that can be detected
with external sensors is far lower than the minimum volume of leak that
would be detectable with in-tank methods. For example, if regulations
allow 12 months between in-tank tests and they stipulate the ability to
detect 0.2 gallons per hour, then as much as 1,752 gallons could leak
before detection. For the simulated case with the lowest air-filled
*
porosity, in which the native soil was a clay at 50 percent of saturation,
and the backfill was a wet sand, vapors from the leak were predicted to be
at detectable (500 parts per million) concentrations at a sensor halfway
across the excavation zone before 0.004 gallons had vaporized. For the
"average" conditions, with dry gravel backfill and dry sand native soil,
the "base case" volatilized volume at detection, by a shallow sensor on the
opposite end of the excavation zone, was estimated to be about 0.05
gallons.
The high volatility and high diffusion rate of the gasoline hydrocarbons
produces early detection times, and therefore a low volume of vaporized
gasoline escapes before detection.
4-1
-------
4.2 IMPLICATIONS FOR MONITORING NETWORK DESIGN
The vapor transport simulations provide information that can guide the
conceptualization of sensor network design. Primarily, the simulations
predict that a single sensor, in an excavation zone in which diffusion of
vapors is the most important transport mechanism, can out-perform in-tank
leak detection methods. Sensible network designs for multi-tank systems
could then be based on predicted "zones of detection," a concept analogous
to the "zones of influence" of ground water pumping wells in an aquifer.
Commonsense would also lead the designer to strive to place the vapor
sensors as close to the leak as possible. Not knowing in advance where
this is, the designer should anticipate where leaks are likely to occur and
where they would be most difficult to detect. Leaks are more likely to
occur from the tank bottom, since that area of the tank is in contact with
pure product more often than the tank's top or sides. Thus, if leaks can
be expected to be at the tank bottom, this would indicate that sensors
should be placed lower in the excavation zone, and preferably at or around
the depth of the tank or excavation zone bottom. This is the most
difficult and^expensive monitoring depth, but according to the vapor
transport simulations, a shallower sensor at the same plan view location,
will respond substantially later. Even shallow sensors, however, perform
quite well as evidenced in Section 3.
Although density effects were not simulated, they would have produced an
even greater differential between deeper vapor monitors and shallow ones.
This is because most of the gasoline components are denser then air. But,
again, such consideration even for sensors placed near the surface would
not imply "poor" performance overall.
Advection effects, or the movement of vapors due to pressure gradients,
could influence the design of a sensor network. Gradients caused by active
pumping sensors should enhance the ability to detect vapors, and so a
continuous, powerful air suction device would be anticipated to serve one
or more tanks. On the other hand, pressure gradients could cause a single
passive sensor to miss sensing the vapors. For example, warm basements in
4-2
-------
the winter induce a subsurface "wind" that moves vaporized product away
from the sensor. In anticipation of this possibility, a four point
network, as an example, would provide good coverage against predominating
advection currents. The sensors would be placed with two on opposite
(longitudinal) ends of the tank, and two straddling the middle (laterally).
With regard to sensor spacing, the vapor modeling has predicted that under
static air pressure conditions (i.e., negligible pressure gradients), total
hydrocarbon sensors will respond within days of each other whether 12 feet
or 4 feet from the leak. Thus, the issues of density and pressure-induced
flow would be the only ones that would indicate the need for multiple
sensors at an individual tank.
The modeling investigation also illustrated how sensor specificity plays a
role in the network design process; the characterization of the leakage
source included the calculation of saturation concentrations of typical
gasoline components for several representative blends. In particular, it
was determined that components such as isopentane and isobutane typically
comprise the highest percentage or most volatile portion of the blends and
will therefore have the highest hydrocarbon concentration at the sensors.
Sensors that are specific or sensitive to these compounds, and to the other
chemicals that have similar saturation concentrations as shown in Appendix
D, will be the most successful at detecting gasoline UST leaks. Sensors
that are specific to benzene, toluene, and xylenes (BTX) will be less suc-
cessful, unless such sensors.are capable of achieving detection at much
lower thresholds.
Network design issues such as sensor location, spacing, and specificity
will be affected if typical background vapor concentrations are found to
approach the concentrations that the vapor modeling showed would be
reaching the sensors. In this case, false alarms could be avoided, in
theory, by raising the detection concentration threshold above the expected
background interference and spacing the detectors more closely together.
The vapor transport modeling results can be re-interpreted easily for
higher detection limits, to investigate how high background concentrations
could affect the timing of sensor response.
4-3
-------
4.3 IMPLICATIONS FOR VAPOR DETECTOR REGULATIONS
Vapor transport modeling has demonstrated that external vapor 'sensors in
the tank excavation zone can be expected to act as good early warning
devices. Vapor sensors in a properly designed network are predicted to be
capable of detecting vaporizing leaks on the order of 10" 4 gallons per hour
within days or weeks, based on the speed with which vapors from leaks are
expected to diffuse throughout the backfill and soils surrounding the UST.
This promising evaluation of vapor sensors should be tempered by recalling
that the modeling results were based on a generic, single UST, assuming
diffusion-dominated transport. Actual conditions vary from site to site.
The modeling results, however, are a good first step in the assessment of
the expected performance of vapor detectors.
4.4 VAPOR TRANSPORT ANALYSIS AND MODELING RECOMMENDATIONS
The next round of vapor transport analysis and modeling should be designed
to focus on the most pressing issues raised by the results reported herein.
Several aspects of the generic UST representation could be modified or
refined, including:
o Leaking product - other fuels and chemical components could be
evaluated;
o Number of tanks - multiple tanks, including the piping network,
could be simulated;
o Tank geometry - a different tank size or geometric shape could be
defined;
o Excavation zone - its shape and size could be modified;
o Pressure gradients - ambient gradients and sensor-induced suction
could be simulated;
o Density effects - this could be investigated further by analysis and
modeling;
o Validation of the diffusion model could be accomplished, using
laboratory or field data;
4-4
-------
o Background interference - current work on determining background
levels could be incorporated as boundary conditions in the model to
investigate false alarms versus detection limits;
o Sensor Performance - the work on defining sensor characteristics
could be incorporated;
o Leak Representation - the complex dynamics of the leak "source" term
in the model could be investigated; and
o Hydrogeologic Conditions - other soil .and temperature conditions
could be simulated.
Future research should concentrate on refining the leak representation, in
advance of performing additional simulations with the diffusion-based UST
model. This would be accomplished through a combination of analytical and
numerical model-based investigations.
Also to be included in future research on the UST vapor modeling and
analysis should be simulation of leakage from pipeline systems. It is
anticipated that a simple geometric configuration, similar to the single
UST simulated in this report could be used. The bulk of the efforts could
be comprised of sensitivity analyses, testing the effects of leak
characterizatio'n, temperature, soil conditions, or other phenomena, as
appropriate.
Future research should also include validation of the diffusion model using
data from "sandbox" experiments being conducted by the Oregon Graduate
Center. This would involve simulation of the experimental apparatus, in a
three-dimensional model grid similar to the UST model described herein.
The comparison of computer model results to laboratory data is expected to
yield information on the effects of gravity, the significance of
vapor-water partitioning, and the importance of diffusion with respect to
other fate and transport processes. Further research of the significance
of gravity-driven advection through the use of modeling is recommended.
4-5
-------
-------
5.0 REFERENCES
Alberton, M., 1979.
"Carbon Dioxide Balancing the Gas-Filled Part of the Soil, Demonstrated
at a Podzol" (in German), Zeitschrift Pflanzenernaeher.
Bodenkd., 147, 39-56.
Allan, R.E., 1986.
"Modeling and Sensitivity Analysis of Vapour Migration in Soil from
Spilled Volatile Liquids", M.S. Thesis, University of Waterloo.
Arthur D. Little, Inc., 1987.
"The Installation Restoration Program Toxicology Guide," V.3, Prepared
for the Aerospace Medical Division Air Force Systems Command, Wright
Patterson Air Force Base, OR, Available from NTIS, ch. 65, 6/87.
Bruell, C., 1987.
University of Lowell, Personal Communications.
Buckingham, E., 1904.
"Contribution to Our Knowledge of the Aeration of Soils," Bull. 25,
52 pp., USDA Bur. of Soils, Washington, DC.
Camp, Dresser & McKee Inc., 1984.
"DYNFLOW: A Three-Dimensional Finite Element Groundwater Flow Model,
Description and User's Manual."
Camp, Dresser & MpKee Inc., 1986.
"Interim Report: Fate and Transport of Substances Leaking from
Underground Storage Tanks." Boston: Camp Dresser & McKee, prepared for
the Office of Underground Storage Tanks, U.S. Environmental Protection
Agency.
Camp, Dresser & McKee Inc., 1986.
"Fate and Transport of Substances Leaking from Underground Storage
Tanks,; Volume II - Appendices," Interim Report on Contract No.
68-01-6939 Submitted to U.S. Environmental Protection Agency, Office of
Underground Storage Tanks.
CHEMEST is a Computerized Chemical Property Estimation System Developed by
W. Lyman and R. Potts at Arthur D. Little, Inc., Details are available
from W. Lyman, Camp Dresser & McKee, Inc., One Center Plaza, Boston, MA
02108.
Corapcioglu, M.Y. and A.L. Baehr, 1987.
"A Composition Multiphase Model for Groundwater Contamination by
Petroleum Products, I. Theoretical Considerations," Water Resources
Research, 23(1), 191-200.
5-1
-------
Environmental Protection Agency, 1987.
"Processes Affecting Subsurface Transport of Leaking Undergound Tank
Fluids." EPA Report No. 600/6-87/005. Las Vegas: Environmental
Monitoring {Systems Laboratory.
"Handbook of Chemistry and Physics," 1980.
R.C. Weast, ed., CRC Press.
Huyakorn, F.S. and G.F. Finder, 1983.
"Computational Methods in Subsurface Flow," Academic Press, London,
473 pp.
Kirk-Othmer, 1973.
"Encyclopedia and Chemical Technology", 2nd ed., J. Wiley and Sons.
Lugg, G.A., 1968.
"Diffusion Coefficients of Some Organic and Other Vapors in Air,"
Analytical Chemistry, 40(7): 1072-1077, 1968.
Lyman, W. J., W.F. Reehl, and D.H. Rosenblatt, 1982.
"Handbook of Chemical Property Estimation Methods," McGraw-Hill Book Co.
MacKay, p. and W.Y. Shiu, 1981.
"A Critical Review of Henry's Law Constants for Chemicals of
Environmental interest", Journal of Physical Chemistry Ref. Data, 10(4):
1175-99.
McDonald, M.G. and A.W. Harbaugh, 1984.
"A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model",
U.S. Geological Survey Open File Report 83-875, 528 pages.
Metcalfe, D.E., 1982.
"Modeling Gas Transport from Waste Disposal Sites," M.S. Thesis,
University of Waterloo.
Millington, R.J., 1959.
"Gas Diffusion in Porous Media," Science, 130, 100-102.
Millington, R.J. and J.M. Quirk, 1961.
"Permeability of Porous Solids," Transactions of the Faraday Society,
57: 1200-7.
Penman, H.L, 1940.
"Gas and Vapour Movements .in the Soil, 1. The Diffusion of Vapours
through Porous Solids," Journal of Agricultural Science, 30, 347-462.
Perry, R.H. and C.H. Chilton, 1973.
"Chemical Engineer's Handbook," 5th ed., McGraw-Hill Book Co.
Reid, R.C., J.M. Prausnitz, and T.K. Sherwood, 1977.
"The Properties of Gases and Liquids," 3rd ed., McGraw-Hill Book Co.
5-2
-------
"Influence of Pore Air/Water Exchange on the Diffusion of Volatile
Organic Vapors in Soil," Presented at NWWA Conference, Petroleum
Hydrocarbons and Organic Chemicals in Groundwater, November 17-19,
Houston, TX.
soecomstion," and "Memorandum on Standard
aoe Mixture," University of Nevada at Las Vegas^nvironmental
Research Center. Written to P. Durgin, U.S. Environmental Protection
Agency/Environmental Monitoring Systems Laboratory-
U.S. Environmental Protection Agency, May, 1986. ,,^1,-,. i
"Underground Moter Fuel Storage Tanks: A National Survey, Volume 1,
Technical Report," EPA 560/5-86-03, Office of Pesticides and Toxic
Substances, Washington, D.C.
* Baking Underground Tank
Fluids." EPA Report No. 600/6-87/005. Las Vegas: Environmental
Monitoring Systems Laboratory.
"S^ryVsomphysics and Chemistry of Movement of ^ Organic s in the
Vadose and Saturated Zone," Presented at B.P.A. Seminar on the
Evaluation of Corrective Action Technologies for Leaking underground
Storage Tanks, 10/7/87.
5-3
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APPENDIX A
GLOSSARY
This appendix is a glossary of terms used in this document. The
definitions are related to the problem of vapor transport as presented in
this report, and in many cases are not generalized definitions. A
consistent set of Systeme Internationale (S.I.) units is used in the
definition of physical and chemical parameters and variables. Related
terms are cross-referenced.
Defined Terms
Advection
Anisotropy
Backfill
Background Concentration
Capillary Fringe
Density
Diffusion
Dynamic Viscosity
Effective Diffusion Coefficient
Excavation Zone
Pick's First Daw
Pick's Second Law
Henry's Law
Heterogeneity
Moisture Content
Organic Matter Content
Partial Pressure
Pea Gravel
Phreatic Surface
Porosity
Raoult's Law
Residual Oil Saturation
Saturated Zone
Solubility
Specific Yield
Surface Tension
Tortuosity
Unsaturated Zone
Vadose Zone
Vapor Pressure
Volatilization
Water Table
Wettability
A-l
-------
Definitions .
Advection
The process of transfer of vapors through a geologic formation in response
to a pressure gradient which may be caused by changes in barometric
pressure, water table levels, wind fluctuations, or rainfall percolation.
Advection can result from a thermal gradient caused by a heat source.
Anisotropy
Hie variation of a property- of a porous medium according to the direction
of measurement. For example, hydraulic conductivity in a stratified
deposit will be higher in the horizontal plan than in the vertical
direction.
Backfill
The material emplaced around an UST in an excavation zone for support.
Clean, well-sorted sand or gravel is the backfill material recommended by
the American Petroleum Institute. See pea gravel.
Concentration
The initial level of contamination existing in the subsurface at a site
preceding a leak of contaminants at the site.
Capillary Fringe
*
The zone above the water table characterized by saturated voids within
which water pressure is less than atmospheric. The capillary fringe is
thicker in fine-grained materials than in coarse materials and depends on
the size distribution of grains.
Density
The amount of mass of a substance per unit volume of the substance, having
units of mass per volume (g/cm3).
Diffusion
The process whereby the molecules of a compound in a single phase
equilibrate to a zero concentration gradient by random molecular motion.
The flux of molecules is from regions of high concentration to low
concentration and is governed by Fick's First Law. See Fick's First Law,
effective diffusion coefficient.
Dynamic Viscosity
The measure of internal friction of a fluid that resists shear within the
fluid; the constant of proportionality between a shear stress applied to a
liquid and the rate of angular deformation within the liquid, having units
of mass per length per time (g/cm sec).
A-2
-------
Effective Diffusion Coefficient
Hie constant of proportionality in Pick's Second Law which is-dependent on
tortuosity, porosity, and moisture content and properties of the diffusing
compound, having units of squared length per time (cm /sec): See
tortuosity, porosity, moisture content, Fick's Second Law.
Excavation Zone
The zone excavated of native materials into which the UST is emplaced and
then filled with backfill material. Depth of the excavation zone is
between 10 and 15 feet and is covered by a concrete pad in areas of heavy
traffic.
Fick's First Law
An equation relating the flux of molecules to the concentration gradient,
with the proportionality constant being the diffusion coefficient. See
Fick's Second Law, diffusion, effective diffusion coefficient.
Fick's Second Law
An equation relating the rate of change of concentration with time due to
diffusion to the rate of change in concentration gradient with distance
from the source of concentration. See Fick's first Law, diffusion,
effective diffusion coefficient.
Henry's Law
*
The relationship between the partial pressure of a compound in the vapor
phase over a liquid and the compound's equilibrium concentration in the
liquid, through a constant of proportionality known as Henry's Law
Constant. Generally used for low solution concentrations. See partial
pressure.
Heterogeneity
The variation in a property of a porous medium as a function of location.
Heterogeneity may be due to grain size trends, stratigraphic contacts,
faults, and vertical bedding.
Moisture Content
The amount of water lost from the soil upon drying to a constant weight,
expressed as the volume of water per unit bulk volume of the soil. For a
fully saturated medium, moisture content equals the porosity; in the vadose
zone, moisture content ranges between zero and the porosity value for the
medium. See porosity, vadose zone, saturated zone.
A-3
-------
Organic Hatter Content
The fraction of soil, sediment, or porous medium composed of organic
matter. In natural systems, this material consists primarily of the decay
products of plants and animals.
Partial Pressure
The equilibrium vapor pressure exerted on the atmosphere by a component of
a liquid mixture. See Henry's Law.
Pea Gravel
A well-sorted, clean, and well-rounded sediment (gravel) of diameter
between 3/8 and 1/2 inch which is commonly used as backfill material. See
backfill.
Phreatic Surface
The surface of water in an unconfined aquifer on which the fluid pressure
in the voids is at atmospheric pressure, also termed the water table.
Piezometric Surface
The hydraulic head of water in a confined aquifer as defined by the
elevation head and the pressure head at a particular location.
Porosity
The void fraction of a porous medium of rock or sediment, usually occupied
by water and/or air. See also moisture content.
Pressure Head
The component of hydraulic head resulting from the weight of overlying
water at the point of measurement, and any other forces, such as water well
injection, that may be inducing pressures.
Raoult's Law
The relationship between the partial pressure of a component in a liquid to
the product of the mole fraction of the component in the liquid and the
vapor pressure of the pure component.
Residual Oil Saturation
The amount of oil remaining in the voids of a porous medium below which oil
is retained in an immobile state.
Respiration
The biological consumption of oxygen during the oxidation of organic
compounds or material by aerobic bacteria.
A-4
-------
Saturated Zone , :
The zone of a porous medium below the water table in which the voids are
fully saturated with fluid and the pressure is greater than atmospheric.
See water table.
Solubility
The amount of mass of a compound that will dissolve into a unit volume or
mass of the solvent (usually water), or final solution, having units of
mass per volume (g/cm ).
Specific Yield
The volume of water released from storage per unit area of aquifer in
response to a unit.decline of water table in an unconfined aquifer, having
units of volume per.unit area per unit thickness (cm3/cm2/cm).
Surface Tension
The measure of interfacial tension due to molecular attractions between two
fluids in contact or between a liquid in contact with a solid. Surface
tension is measured in units of dyn/cm and varies with temperature.
Tortuosity
The ratio of the average length of pore passages to the length of the
column of the porous medium. This is the definition commonly used for the
flow of water in a porous medium. "Vapor diffusion tortuosity" is a
similar property of a porous medium, expressions for which have been
derived empirically. See Appendix J.
Unsaturated Zone
See vadose zone.
Vadose Zone
The zone of a porous medium where the voids are partially filled with
water.
Vapor Pressure
The equilibrium pressure exerted on the atmosphere by the vapors of a pure
liquid at a given temperature.
Viscosity
See dynamic viscosity.
A-5
-------
Volatilization .
The process of transfer of a chemical from the aqueous or oth6r liquid
phase to the air phase. Solubility, molecular weight, and vapor pressure
of the liquid and the nature of the air-liquid/water interface affect the
rate of volatilization. See solubility, vapor pressure.
Water Table
See phreatic surface.
Wettability
The tendency of a liquid to spread over a solid surface, which depends on
the surface tension of the liquid.
A-6
-------
APPENDIX B
DICTIONARY OF VARIABLES AND PARAMETERS
This appendix defines the physical and chemical panneters and variables
used in this report. Dimensions of each parameter or variable are
provided. Values of constant parameters (i.e., atmospheric pressure,
Pa - 760 mm Hg) are provided where appropriate. All dimensions are given
in consistent S.I. units. In the report, other units are used for
convenience and for ease of understanding the results. A table of units
conversion factors is therefore provided at the end of this appendix.
Definitions
A,B,C Antoine equation coefficients (dimensionless).
C Gas-phase concentration of kth constituent of gasoline
(cm /cm ).
C Water-phase concentration of kth constituent of gasoline
(cm3 /cm3).
t
Co Equilibrium gasoline vapor concentration (cm3/cm3).
De Effective diffusion coefficient (cm2/sec).
DO Air diffusion coefficient (cm2/sec).
r
Do Reference air diffusion coefficient measure for a specific
compound (cm /sec).
D25 Air diffusion coefficient meausured at 25°C (cm2/sec).
Di. Dispersion tensor element (cm2/sec).
erfc(z) Complementary error function on variable z (dimensionless).
Fk Retardation coefficient of kth gasoline constituent
(dimensionless).
h Piezometric head (cm).
B-l
-------
^ Henry's Law constant for kth gasoline constituent
(dimensionless). Non-dimensional units obtained from ratio .
of weight, per volume of air to weight of water (e.g., g/cm ).
j- Volume flux per unit area entering system at source
(ftVhr/ft2).
K Hydraulic conductivity (cm/sec).
Mv Average molecular weight of gasoline vapors (g/mol).
M^ Average molecular weight of air, Ma - 28.96 g/mol.
M Average molecular weight of gasoline-air mixture (g/taol).
VL Molecular weight of kth gasoline vapor constituent (g/mol).
Pa Atmospheric pressure, Pa - 760 mm Hg.
Pk Partial pressure of kth gasoline constituent (mm Hg).
p* Pure chemical vapor pressure of kth gasoline constituent
(mm Hg).
Pt Total sum of partial pressures of gasoline constituents
(mm Hg).
Q Influx rate of gasoline-air mixture entering system
(cm /sec).
t
R Universal gas constant, R - 62,360 mm Hg«cm3/mol«deg K.
Rk Heterogenous reaction term for kth gasoline constituent
(dimensionless).
s Volumetric gas concentration (cm3/cm3).
sw Volumetric water concentration (cm3/cm3).
S Scalar quantity used to scale gasoline liquid volumes.
S8 Specific storativity (cm"1).
t Time (seconds or hours).
T Temperature (deg. C or deg. K).
Tb Boiling point temperature (deg. K).
Vb Molar volume of kth gasoline vapor constituent at its boiling
point (cm /g mol).
B-2
-------
V1 Volume of liquid gasoline (cm3). ;
V Volume of gasoline-air vapor entering system (cm3).
Wv Mass of gasoline vapors (g).
x Distance (cm).
x. Mole fraction of kth gasoline vapor constituent
(dimensionless).
/a Dynamic gas viscosity of kth gasoline vapor constituent
*'k (g/cm sec).
it Dynamic gas viscosity calculated at a reference temperature
°'k (g/cm sec).
Dynamic gas viscosity at 20° C (gm/cm sec).
'20
, th
p Liquid density of kth gasoline constituent at its boiling
b point (g/cm ).
p Gas-phase density (g/cm3).
PI Liquid-phase density (g/cm3).
p Vapor density of gasoline-air mixture (g/cm ).
T .Tortuosity coefficient (dimensionless).
6 Air-filled porosity (cm3/cm3).
0w Water-filled porosity (cm3/cm3).
9t Total porosity (cm3/cm3).
units Conversion Table
1 foot - 30.48 centimeters
1 ft/hr - 8.4667 x 10~3 cm/sec
1 ft2/hr - 0.258 cm2/sec
B-3
-------
-------
APPENDIX C
CHEMICAL PROPERTY ESTIMATION EQUATIONS
This appendix lists the equations used to estimate values of
physicochemical properties of the constitutive chemicals of the gasoline
blends presented in this appendix. Equations used to calculate leaked
liquid gasoline volume from hydrocarbon vapor concentrations appear as well
in this appendix. Physicochemical terms appearing in this appendix are
defined in Appendices A and B. References used in estimating the chemical
properties are listed in Section 5 of this report.
Average Molecular Weight of Gasoline Vapors, My (g/mol):
_ N N
Mv - -Z x ML = Z (P /P ) M. (Equation C-l)
k = l ^ ^ k-l k t -k ~»
N
where:
xk mole fraction of kth gasoline vapor constituent [dim.].
Mk molecular weight of kth gasoline vapor constituent (g/mol).
Pk partial pressure of kth gasoline vapor constituent (mm Hg).
Pt total pressure of gasoline vapors (mm Hg).
N number of gasoline vapor constituents.
Volume Influx of Gasoline Vapors, Vv (cm ):
Vv = Co Q t (Equation C-2a)
where:
Cc equilibrium vapor concentration in air of gasoline
vapors (cm /cm ).
C-l
-------
Pa atmospheric pressure, Pa - 760 mm Hg at sea level..
Q average influx of gasoline-air mixture into system (cm3 /sec).
t duration of leak (seconds).
Mass of Gasoline Vapors, Wv (g):
Wv - M Vv Pa/(T-R) (Equation C-3a)
where:
T system temperature (°K)
R universal gas constant, R - 62,360 mm Hg*cm3/mol'°K.
Liquid Gasoline Volume, V1 (cm3):
vi " WV/PI (Equation C-3b)
PX gasoline liquid density, (g/cm3)
Gasoline-Air Vapor Density, pv (g/cm3 ) at equilibrium concentration:
*
a. Average molecular weight of gasoline, My , see Equation C-l
above .
b. Average molecular weight of air, Ma :
Molecular
Element _ % Composition _ Weight (g/mol)
N2
°2
Ar
C02
Total
78.084
20.946
0.934
0.033
100.000
28.0134
31.9988
39.9480
44.0100
M - 28.9641 g/mol
C-2
-------
c. , Average molecular weight of gasoline-air mixture, M (g/tool):
M - (Pt/P. ) Mv + (Pa -, Pt) Ma/Pa ( Equation -C-4a)
d. Vapor density of gasoline-air mixture, pv (g/cm3):
Pv - P. ' V(T R) (Equation C-4b)
Air Diffusion Coefficient, DO [cm2/secj:
a. Correction of air diffusion coefficient to any temperature from
25°C.
1 .75
Do - D25 (T/298.15°K) (Equation C-5a)
T temperature (°K)
Do air diffusion coefficient at temperature T (cm2 /sec).
D25 air diffusion coefficient at 25°C (cm2 /sec).
b. Calculation of air diffusion coefficient from a measured
reference air diffusion coefficient for a structurally similar
compound.
r 1/2
DO Do. * (Mr/M) (Equation C-5b)
where :
r
Do air diffusion coefficient measured for a reference compound
(cm /sec).
M molecular weight of compound of interest (g/tnol).
Mr molecular weight of the reference compound (g/mol).
Pure Chemical Vapor Pressure, Pk*(mm Hg):
Pk -= exp(A - (B/(T + C))) (Equation C-6)
where:
T temperature (°K)
A,B,C Antoine equation coefficients for a compound of interest.
C-3
-------
Partial Pressure Over Gasoline Liquid, Pk (mm Hg):
*
where:
(Equation 'C-7)
P. partial pressure of a compound over gasoline liquid (mm Hg)
x. mole fraction of kth gasoline vapor constituent (dimensionless).
Henry's Law Constant, H^:
Temperature dependence of Henry's Law Constants.
Note: following equation1assumes no significant change in solubility over
temperature range of interest.
H, _ - H. , (?,/!> ) (Equation C-8)
where:
H. Henry's Law Constant for a compound at a given temperature
(dimensionless).
Pure Chemical Vapor Density, pVfl (g/ta ):
(Equation C-9)
Estimation of Liquid Density, p± (g/cm ):
P, - H, PL {3 - 2 [T/(T. + 273.15"K)]}
0 .29
(Equation C-10)
where:
Tfc boiling point temperature (°C).
pb liquid density at the boiling point (mol/cm3)
C-4
-------
Liquid Mole Fraction, xjt [dimensionless]:
x - (%w/Jl) [I/?! (%wk/W|c)] (Equation C-ll)
where:
%w percentage composition of gasoline mixture of the kth constituent
Vapor Concentration of a Gasoline Constituent over Pure Gasoline Liquid,
C . (parts per million):
9 / K K
C . - (P../P..) x 106 (Equation C-12)
91 K k t
Gas Vapor Viscosity, //g k (g/cm sec): (Equation C-13)
1/2 3/2 2/3
// « (27.0 f T )/((T+ 1.47 Tfc ) Vfc
where: ,
f/ . gas vapor dynamic viscosity (g/cm sec).
9 i ^
i.th
Vb molar volume at boiling point of k constituent
(cm/g mol).
Temperature-dependence of gas viscosity:
H - u20 (T/293.15eK) (Equation C-14)
//20 gas vapor dynamic viscosity at 20°C (g/cm sec).
C-5
-------
-------
APPENDIX D , .
PHYSIOCOCHEMICAL PROPERTIES OF REPRESENTATIVE GASOLINE BLENDS
Tables of Properties
This appendix contains tables of the physiocochemical properties of the
chemical constituents of four gasoline blends. The first blend is a
representative gasoline devised by Warren Lyman of COM for this project.
The other three blends were proposed by K. Stetzenbach of the Environmental
Research Center at the University of Nevada at Las Vegas in a recent memo
(1987), a copy of which is included at the end this appendix.
Values of physicochemical properties of the constitutive chemicals of each
blend are provided for 20°, 10°, and 0° C. The physiocochemical properties
reported for each blend are:
Property Reference
- Percent composition Arthur D. Little, Inc., 1987.
- Liquid phase mole fraction Equation C-ll.
- Pure chemical vapor density Equation C-9.
- Concentration over liquid gasoline Equation C-12
- Henry's Law constants Mackay and Shiu, 1981.
- Gram molecular weight Reid, Prausnitz, and Sherwood, 1977.
-Air diffusion coefficient Lugg, 1968.; COM, 1986.
- Partial pressure over gasoline Equation C-7.
- Boiling point Reid, Prausnitz, and Sherwood, 1977,
- Gas viscosity Perry and Chilton, 1973.
Average gasoline blend properties are reported for:
- Average molecular weight of gasoline vapors (Equation C-l).
- Average molecular weight of gasoline vapor-air mixture
- Vapor density of gasoline vapor-air mixture (Equation C-4).
- Average air diffusion coefficient
- Average liquid density
- Average gas density
D-l
-------
References that appear in Section 5 of this report were used to prepare the
tables .in this appendix.
LIST OF TABLES FOR APPENDIX D
Table
Gasoline Blend Temperature Page
D-l aw Synthetic 20°C D-4
D-2 cm Synthetic K>°C D-5
D-3 COM Synthetic °°c D~6
D-4 Stetzenbach Low Reid Vapor Pressure 20°C D-7
D-5 Stetzenbach Low Reid Vapor Pressure 10°C D-8
D-6 Stetzenbach Low Reid Vapor Pressure 0°C D-9
D-7 Stetzenbach High Reid Vapor Pressure 20°C D-10
D-8 Stetzenbach High Reid Vapor Pressure 10 °C D-ll
D-9 Stetzenbach High Reid Vapor Pressure 0°C D-12
D-10 Stetzenbach High Octane 20°C D-13
D-ll Stetzenbach High Octane 10°C D-14
D-12 Stetaenbach High Octane 0°C D-15
Comparison to "Standard Gasoline Vapor Mixture"
The vapor mixture of the COM synthetic gasoline blend was compared against
the gasoline vapor mixture suggested by K. Stetzenbach (1987) of this
appendix. Assuming the vapor mixture given by Stetzenbach is for 10° C,
the percentages of the vapor mixture on a constituent basis are:
D-2
-------
CDM Gasoline , Stetzenbach
Vapor Mixture Vapor Mixture
isopentane 39% 30%
isobutane 27% 19%
n-pentane 6% 19%
n-butane 9% 30%
toluene 0.4% 1%
m-xylene 0.1% 1%
others 18.5% 0%
sum 100% 100%
This comparison shows that the Stetzenbach gasoline vapor mixture contains
more n-pentane and n-butane and less isopentane and isobutane than the CDM
gasoline vapor mixture. If the vapor rercentages are grouped into the C4
and C5 alkanes and aromatic compounds, the comparison becomes:
CDM Gasoline Stetzenbach
Vapor Mixture Vapor Mixture
C4 alkanes 36% 49%
Cs alkanes 45% 49%
aromatics 0.5% 2%
others 18.5% 0%
sum 100% 100%
This comparison indicates that the CDM gasoline vapor mixture and the
Stetzenbach vapor mixture are similar.
D-3
-------
Table D-l
G
CHDIICM. mnm mmim m inmeuc
MSM.K AM CWmniEIITI AT 20 K8HEH C.
KErttlEKTATIVt tOCOT
lioiutine !
n-Mm 1
liofKiUne t<
i-Octini
tettitne
Toluene
lyltne III
i-ftnane
2-IMhylpentini
Cyclohnane
-Hettane 1
i-ftethylkeuni
Htthylcyclohe«ant
2,4-DlKtfiylheune
Etkflontiiu
1-Ptnlene 1
2,2,4-Trleethylhettne
2,2,5,9-Tetriiethylhenine 1
1,4-Biithylbiwetie
t-fleieni I
1,3,3-Trluthylbenieni
C12-allpliitic 1
MMIM.
ION KIEHT
38.12
31.12
72.19
72.19
114.23
78.11
12.14
101.17
81.18
81.19'
84.11
100.20
100.20
18.11
114.23
101.17
70.14
128.21
142.21
134.22
84.11
9 120.20
0 170.00
III. PHASE
DOLFKACT.
0.0321
0.0113
0.1840
0.0314
0.0083
0.0314 .
0.0913
1,0123
WHO
.1.0880
0.0338
0.0142
0.0473
0.0017
0.0114
0.0171
0.0203
0.0148
0.0100
0.0393
0.0111
0.0314
0.0938
Ait BiFFWiw
COEFFICIHt
(Cfl'2/IEC)
0.0111
0.0111
0.0917
0.0817
0.0319
0.0109
0.0924
0.01(8
0.0711
0.0711
0.0711
0.0(31
0.0(51
0.0444
0.0117
0.0733
0.0921
0.0109
0.0977
0.0914
0.0711
0.0129
0.0924
LINII
KKSIir
(CN/CH'3)
0.9370
0.3710
0.1200
0.1210
0.7030
0.9830
0.9170
0.9140
0.1310
0.1930
0.7710
0.1940
0.1710
0.7707
0.7000
0.9170
0.1400
0.7173
0.7200
0.9120
0.1730
0.9190
0.8100
FUAE CtCniCAL
VAPOA FUESSWE
|H Hi)
2292.75
T999.33
974.81
424.38
10.41
79.20
21.84
1.11
121.24
171.90
77.99
33.39
91.10
31.21
23.32
7.08
930.80
11.30
1.47
0.70
141.17
1.73
0.08
PAIIIAl WEttUK
OVER tASOLIKE
(MK|I
...__...-
73.9178
25.3788
109.7129
11.73(4
t.0811
2.7310
1.1237
0.3892
12.0080
15.0183
2.1219
0.5047
2.45(3
0.3417
1.3412
0.1214
10.7134
0.1171
0.0447
0.0241
2.5349
0.0181
0.0042
run CHEHICAI
VAfM KKSUV
iiWol
.....-
7112.14
4144.83
2219.17
1174.12
19.37
321.31
110.09
39.79
971.97
808.91
397.04
114.81
284.30
114.30
145.75
41.01
2031.97
71.30
90.33
9.11
110.40
11.31
0.70
CMCEIIT'.ATION OVER
LIDIIIt GASDUIE
......... . . « 11 - -
11733.1
33313.1
131200.7
22011.2
114.3
3104.0
1478.1
901.9
13800.0
119(1.4
. 3441.7
114.1
3232.0
410.2
2039.4
IU.3
14113.0
211.1
85.1
32.4
3335.3
81.7
3.3
KILIIrt
POINT
(d:;. K!
'"""
272.19
300.19
301.19
318.79
333.29
383.79
411.29
341.89
333.39
393.99
371.59
313.19
374.03
392.39
401.29
303.09
311.19
410.55
491.89
331.55
437.89
481.19
HEMriLf*
CQMTANT
3104.37
4712.13
42H.17
1330.24
18.07
21.31
21.10
9113.19
9724.28
514.42
7412.11
11212.8!
1300.11
1931.15
24.71
1314.40
10111.52
31373.43
40.43
1401.19
17.84
11822.79
MM.M?
MI vitcotin
(nfOlHI
70 fit
70.10
19.11
13.85
11.04
72.22
74.01
33.72
58.50
51.40
70.52
54.20
55.00
51.00
52.20
54.00
U.90
41.78
48.11
47.10
10.50
50.20
41.40
t,t,|
100
102.20
Tttferituri ' 213.15 deg. K
Fteswri « 710 n Hg
Its Ctuistint
0.01231 H Hji«"3/Ml«K
IMeculir Height
of Air 28.11 giful
Artrige Italiculir
Height of Bisolint
Vipors * 11.48 gi/ul
Kolecilir Might
of Buoline-Air
Kin tire * 43.98 gi/ul
1.0000
Vipir Den
-------
Table D~2
CHtmCN. PROPERTY EMIHATIM FOR imHETIC
MBOUIIE m CONSTITUENTS AT It DECREES C.
a
i
Ui
REPRESENTATIVE PERCENT
CHEN1CAL COHPG9ITIOK
Iiotitint
«-tulint
IiopHitini
n-PinUnt
n-Octint
ttflltflt
TolMfll
lyltnt dl
n-Hnint
2-Ntthylftfitiitt
Cyclohnint
n-Htptint
2-Htthylliiimi
Ktthylcyclohttui
2,4-Dinthylhnint
Ethylbtflitnt
l-Ptntmi
2,2,4-TrlHthyIhnint
2,2,9,9-TttriitUiylhMint
1,4-Oiitkylbtnitnt
1-HtlMI
l,3,9-TrinthytbM»ni
C12-iliphitic
Totil
THpfflturt 293.19 dtg.
Prniurt * 710 n Kg
Git Conitint *
0.01231 H Hjii'Sfin
Koltculir.VtliM
of Air 29.fi 11/inl
Avtrigt Ibltculir
tight of Oiiotlm
Vipuri 19.72 gi/tol
tfoltculir Night
of 9nollnt-Alr
Kiituri * 39.89 gi/iol
8RAN HOU ' ~tID. PHASE AIR 91FFU810N LIWIO
KISHT KOIFRACT. COEFFICIENT 0£II8IT»
(EH/imi (CIC2/SECI tat/ciMi
2
1
14
3
1
3
9
7
7
8
3
1.9
9
1
8
2
1.9
2
1.9
9
1.9
9
to
100
K
UK
98.12 0.0321
99.12 0.0113
72.19 0.1840
72.19 0.0374
114.23 0.0083
79.11 0.0314 -
72.14 0.0919
101.17 0.0129
81.19 0.0770
84'. 18 0.0980
84.11 0.0338
100.20 . 0.0142
100.20 0.0473
78.17 0.0077
114.23 0.0114
101.17 0.0177
70.14 0.0203
128.21 0.0148
142.27 0.0100
134.22 0.0333
84.11 0.0149
120.20 0.0374
170.00 0.0958
102.20 1.0000
Vipor Oeniity
of Gitolirti-fllr
Mixture *
Vtlghtid inriji
air diffmlon
cotfflcittit
Vtlghttd ivH-ijt
liquid dimity
Ktlghttd tvtrigt
gn dcniity
0.0837
0.0837
0.0717
0.0717
0.0913
0.0831
0.0771
0.0127
0.0117
0.0117
0.0177
0.0120
0.0120
0.0427
0.0981
0.0170
0.0790
0.0972
0.0943
0.0997
0.0177
0.0971
0.0473
1173.38 51/1*3
0.9729
0.5931
0.1311
0.1314
0.70ft
0.9937
0.8738
0.8701
0.1171
0.1120
0.7B84
0.4914
0.1817
0.77B9
0.7071
0.9749
0.1313
0.7240
0.7214
0.1(93
O.U2I
0.9719
0,9651
0.7497
PURECNENICAL
VAPOR PRESSURE
(uHgl
. 1147.77
1112.79
372.47
283.84
9.13
43.93
12.43
3.21
79.70
107.99
47.91
20.11
30.74
21.43
13.30
3.77
397.48
1.18
3.40
0.32
74.87
0.84
0.03
PARTIAL PRESSURE PURE CHEN1CAI
OVER SA90LINE VAPOR OEKSITV
(HHjl
93.7743
18.1371
72.2231
11.1729
0.0418
1.1983
0.1377
0.2037
7.4771
7.1441
1.6060
0.2733
1.4142
0.2071
0.9933
0.0173
7.2707
0.0719
0.0340
0.0113
1.1031
0.0333
0.0014
188.1232
(SH/N-31
3423.71
3(12.17
1103.70
1137.80
31.43 ..
201.40
14.81
17.11
317.48
334.70
221.44
117.23
173.97
117.21
81.03
22.U
1427.77
44.72
27.37
2.43
492.20
3.74
0.27
CONCENTRATim OVER MILlffl
UCtllO 8ASOUNE POINT
Ippil
70799.7
53990.9
79030.4
14727.0
11.9
2182.0
841.7
268.3
7019.2
12170.2
2113.2
389.7
1721.9
272.1
1112.2
88.1
7973.3
120.3
44.7
14.7
2110.1
41.8
2.1
248191.2
(dq. Kl
211.29
272.19
300.79
307.19
378.79
393.29
383.73
4(1.29
341.89
333.39
393.89
371.99
313.19
374.09
382.99
407.29
303.09
377.19
410.99
491.89
331.99
437.89
487.19
HENRri LA*
CONSTANT
Mil.)
3297.14
2921.19
3307.13
2777.27
9200.01
11.32
12.10
11.83
3111.34
3799.17
371.77
4497.78
1712.73
777.24
9808.19
13.13
777.71
1214.17
21409.79
17.24
717.79
7.02
7742.94
3202.173
8A8 VISC8HT7
luPOISEI
17.12
M.4t
11.91
11.17
98.78
17.71
71.47
91.87
91.90
97.37
19.11
S2.J3
93.12
94.07
90.41
92.11
(4.23
40.08
41.47
49.71
98.44
48.47
3f,77
0.0194 ci«2/ttc
0.7271 Ji/ci"3
731.29 gi/iA3
-
-------
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illBNM 80i»A
TOU3W3WW mum Tnim
UM'O
SSSO'O
KtO'O
EZSO'O
OIEO'O
USO'O
UU'O
ItSO'O
MEO'O
OOOO'I
BSSO-0
H£0'0
:s£0'o
btio'o
BklO'O
tOZO'O
tllO'O
1990'0
Z400-0
zttro
9849-0
SUt'O
UU'O
4U9-0
IMB'O
ttftB-0
IH4-0
IIU'O
ntro
aitro
tNI'O
9/B'O
£850-0
taco'o
9190 '0
8Z90-0
az90*o
0450-0
azu'o
OOBO-0
ItSO'O
ZtU'O
ZZtt'O
SOH'O
SOH'O
tlH'O
ZHO-0
etco'o
OBSO'O
0440-0
5290-0
siso-o
tKO'O
£600-0
tUO'O
018J-0
£910-0
fZH'O
(Oi/ii 0!'S£ * 'Jnl«m
[OJ/lb t£'B9 «
I"
icn/ii 94'BZ « >!« (0
M&1»»
9£Z90'0
OZ'ZOI
6H II091 * SJMHJJ
j -tap 5|'£/Z > am)iJ>i)»l
l'l»l
vO
P
1333/ZvlOI IWiai
1B13U3S3 '1WW Tffll 1HS12S a!l!SM83 TW!H2a
iinaii wiiiujii»t» 3HHJ -an 'ten vm uasat mmwmt
3 1131331 0 a iU3fUUM03 W *lWVi
3I13MUUI WJ WI1WI1U tl»M THIUM
-------
Table D-4
cmicM. mretn EttimTtM rat mrraniwi UN nil
mm pffiiMtc MtoiiK MO coisiinioiti AUO KIREI c.
o
KEPRElBlTATIVE PERCEKT
CHEHICAL COWOSITIM
IfOfaHttltt
n~Butinc
IfOplfltlfll
-Pintini,
1-Octiflt
llflltflC
Tallinn
lylene d)
i-HM«fli
2-ltalhytdftim
2,2,4-TriiitliylfiSfltin!
-Hiptint
t-NtUiyl-Z-titiot
2,3-Dlnlhyl-l-lntMi
l,l-Jl«thyl-2-ph(Byl«thini
Totil
Tufuritart 213.l5deg
3
3
3
14
2'
15
10
5
9
9
S
S
3
8
9
100
. K
Prtuurt * 7(0 n Kg
IM Conitint
SRWt ROL. U». PHME AM IIFFUB1M LI9UII
K1EHT flQlFRACT. COEFFICIENT HKSlIf
(BN/MJll (W2/SECI (SN/nni
38.12 0.0403
38.12 0.0405
72.13 0.0631
72.13 0.0691
114.23 0.1151
78.11 0.0240
92.14 0.1528
106.17 ' 0.0804
86. IB 0.0543
191.31 0.0300
114.23 0.0411
100.20 0.0468
70.14 .0.06(1
84.11 0.0330
120.20 0.0125
134.22 0.0390
91.30 1.0000
Vapor tensity
df Biiollne-Atr
Itlxturi *
0.0911
0.0911
0.0817
0.0817
0.0398
0.0903
0.0024
0.0(18
0.0711
0.0104
0.0707
0.0639
0.0787
0.0719
0.0601
0.0691
1004.06 91/1*3
0.3370
0.5190
0.6200
0.6210
0.7030
0.8830
0.8170
0.0140
0.6310
0.7(00
0.6120
0.6940
0.1120
0.6741
0.0770
O.OS30
0.7473
PURE CHEHICAL PARI1AI PRESSURE PURE CHEHICAl
VAPOR PRESSURE OVER EASOUKE VAPOR DEKS1IV
In Kg) (H Hgl IStl/H'S)
.2292.75
1535.33
374.89
424.38
10.41
75.20
21. H
6.16
121.24
0.21
30.72
33.33
384.13
203.21
1.43
1.32
109.1671
73.3702
37.4029
27.6103
1.2030
1.8076
3.3372
0.3447
6.1040
0.0070
1.3911
1.1155
23.7076
11.4450
0.0904
0.04(3
303.6022
7162.14
4944.03
2260.17
1674.92
65.37 .
321.31
110.09
35.78
571.57
2.22
241.93
114.86
1473.82
144.73
1.51
1.72
CMCEnilATIM OVER MIIINB
L1QUII BASOltK rOIK!
Ippil (dig. Kl
143640.1
91171.3
41214.3
31321.4
1383.1
2378.3
4311.0
716.7
8189.9
10.3
2013.9
2111.4
33825.1
19010.3
1)9.0
60.9
391476.6
261.23
272.63
300.19
301.13
318.79
393.29
383.79
466.29
341.89
462.30
572.40
371.33
304.30
328.00
442.30
443.90
HENRrt LAN
CMSTAKT
4304.31
3404.37
4792.13
4299.67
1333.36
18.07
21.31
21.60
3663.95
9131.23
12421.93
7412.91
1147.76
1119.01
17.77
97.45
3333.339
BAS VIKNITT
(uPDISEI
70.01
70.90
61.11
63.13
61.06
72.22
74.01
93.72
98.90
43.70
33.10
34.20
66.40
61.40
96.00
40.40
0.06231 H Hg«i"3/§ol«
Boleeulir ftight
({ Air > 20.11 gi/tol
Averige HoUculir
'fclgtit of BiMlini
Viport * 13.09 giflol
Ibleculir wight
«f Bunline-Air
ffiituri 43.37 91/10!
righted ivtrigi
ilr dlHmlon
CMlliclent
Melghttd tvirigt
liquid dcnilty
Kelghttd ivtrigt
gii demity
0.0746 ci'2/iec
0.7323 |i/uA3
1081.03 gi/i*3
-------
Table D-5
OBKCM. nrapEMt EiiiMitoK Fn rEntm*w iw KII
WWnEt»IIE MSDUKE SB CffltttlTOM M 1
00
KMEEIimtVE PEttEKT MM IB..
oeicM. coiraium netful
tHtitini 3
-tutine 3
luftotint 3
-fcttni " l<
9MIMI 2
IltUKIt 19
lyltni III 10
i-tfeiini
2-ltathyUicini
1,2,4-TrliiUiylpiflUni
Mhthyl-2-tatiM
2,3-DlMthyl-l-titMi
1,2,4-TrlHthrlbHiiiiii
lil-DlMthyl'2-phniylithini
Wri" 1M
tHftrrtart « 293.13 deg. K
Friiion 7(0 n Kg
III ConiUot *
Mmlir vilgM
if Mr < 28.94 gi/nl
torigt Koliculir
lilglit of GitoliM
Vqiori (4.95 gital
IWeculir night
if tiioIliw-Mr
Hlxturt * 39.90 gi/ial
99.12
99.12
72.19
72.19
114.23-
79.11
72.14
104.17
J4.I8
154,31
114.23
100.20
70.14
94. 14
120.20
134.22
»».--
71.39
LIB. PHME Mil IIFTtSlW UWI9
Bi. FRSCT. CiiwFiCiEKT ncmll?
fCH'2/tEC) (BMBI43I
0.0499
0.0495
0.0(51
0.0(91
0,1151
0.0240
0.1929
O.OBB4
0.0949
0.0300
0.0411
0.04(9
O.OU1
0.0959
0.0(29
0.0330
l.OMO
Vipw Dtnilty
of Giullnt-Alr
Kliturt
hlghtri mirigi
ilr dlffuitm
cnlltclint *
Hilghtnl ivirigi
liquid dMilty
Ktlghtcd wtrtge
gu dtniity
0.0857
O.H57
0.07(7
0.07(7
0.09(3
0.0931
0.077(
0.0(27
0.0449
0.09(9
0.0443
0.0(20
0.0741
0.0(77
0.0(47
0.0413
1(74.39 gi/i«3
.9729 *
0.9131
0.4311
0.4344
0.7094
0.9997
0.9799
0.9701
0.4474
0.7453
O.M99
0.19M
0.4735
0.4837
0.9939
0.9519
0.7597
ME CHEHtCKl
VSfffl FKESSWIE
In Kg)
1(47.77
1112.79
392.47
293.94
3,43
45.93
12.43
3.24
73.70
0.11
23.02
20.44
294.79
132.47
0.70
0.44
PMIIM. FDESEWE
ova EmiRE
IN H|l
71.9902
93.9232
25.5344
18.4643
O.MBO
1.0944
1.9997
0.2993
4.1234
0.0032
0.14(1
0.1(79
17.0493
7.3S95
0.0439
0.0223
212.2411
PURE CHEH1CM.
Virat KKSllt
9423.7(
3642.49
1(03.70
1151.90
3M3--
201.40
44.84
19.41
3(1.49
0.94
149.74
117.23
1011.94
(31.39
4.77
4.94
CWCtlttUTlM OVER ' HlltM
Liiui9 usaiie nin
Ipfl) 1*1. tl
IMC44.0
70931.4
33317.1
242T9.0
992.7
1440.1
2497.3
377.4
9429.9
4.3
1244.7
1273.4
22433.3
7721.7
97.(
27.3
271279.2
2(1.29
272.43
300.19
301.19
311.79
393.29
393.79
444.23
341.99
4(2.30
372.40
371.99
304.30
329.90
442.90
449.70
HEMfllW MIVIKM1TT
CMITMT (iMIKI
Uli.)
3239.44
2521.44
3317.43
2777.27
9201.77
11.32
12.40
11.93
3441.33
22M.43
129(0.22
4497.93
791.09
1277.14
1.71
49.33
2429.477
47.42
(9.49
44,54
41.47
99.79
49.7(
71.47
91.17
94.50
42.21
91.27
92.39
(4.13
97.31
94.07
4(.79 -;
0.0702 ci*2/l«
0.7413 gi/ci*3
773.77 gi/i*3
.-4
-------
l
P
i
Q
0)
rt
H
= I
sssssacsssiesKSSs
i SI K S S S r S S K K 5: K S S
se _ :
s=l iiiiillliliilllil
«s«s^'i°°«;<=;';cS" *> 9 ^ O ^ O ^
iiiiiiiiiiiiip.
»«>eo«4»«>oooooo
i
<» o ^ » *
s
1
.,..
S If". T5 =
- -
l llf.
isflf!
I " "I~I '
S
-I-J
"«.*
Ill
S S £
Ifv
fit
3i-S
.£
f =
ss
I
r i
Its
s .
HfHi3£f£3f£i&l2 lla ll
&
f.r
u -S s - s
i!
; s s =
S s <3 ^
£C%£
-------
Table D-7
WHICH, mum EsiiMtiw FM itEHEWwi HUH Kit
Wffl PKBSWE tmilE Ml CWSIIIUEItT! H 20 ICWEE8 C.
I
I'
o
(KWE5ENIHIVE PERCEKI OHM Ml. LH. PHASE AH ItFFMIM 110011
BBHCH. corosnm KIEHT MLFMCT. CQEFFICIEKI KBITT
Iiotitini'
n-lutini
Iinotntine
i-Penttne
i-Octine
hniene
TdlUHt
lylene III
i-Hinne
2-Ktthylf>cini
2,2,4-Triitthylptntine
i-Hfitini
2-Kethyl-2-tutmi
2,3-DlHthyl-l-tutent
1,2,4-TriiiUiylbMimt
l,l-DlHthyl-2-phenylethine
Totil
fitotriturt « 293.15 dig
Pressure 760
hi Conitint
IGIWHOU
3
10
3
5
5
2
15
to
5
3
5
3
3
3
8
3
100
. K
Kg
38.12 0.0734
58,12 0.1300
72.15 0.0607
72.15 0.0607
114.23 D.03BI
78.11 0.0224
92.14 0.1426
106.17 0.0823
86.18 0.0508
156.31 0.0280
114.23 0.0384
100.20 0.0437
70.14 0.0623
84.16 0.0521
120.20 0.0583
134.22 0.0326
94.53 1.0000
Vipgr Oeniity
of Eisoline-Air
Nintiire «
(Gm/SEC) (G«/CI1"3I
0.0911
0.0911
0.0817
0.0817
0.0598
0.0905
0.0924
0.0668
0.0711
0.0604
0.0707
0.0659
0.0787
0.0711
0.0681
0.0651
2130.88 gi/iA3
0.3570
0.5790
0.6200
0.6260
0.7030
0.8830
0.8670
0.8640
0.6590
0.7400
0.6120
0.6840
0.6620
0.6741
0.8770
0.8530
0.7357
PWE CHEMICAL
vim ptESsntE
diHgl
. 2232.73
1333.33
574.81
424.38
10.46
73.20
21.84
6.16
121.24
0.26
38.72
35.55
384.13
205.21
1.45
1.32
mm PRESSME HUE CHEHICH
OVER 6ASOUKE VITOI KffilTV
(H Hj) '"
161.8184
234.4812
34.1091
25.7701
0.4013
1.6872
3.1148
0.5084
6.1638
0.0073
I.4B50
1.5545
23.1141
10.6830
0.0844
0.0432
514.7144
iwtnrMi
7142.14
4144.83
2268.17
1674.12
45.37 .
321.31 '
110.05
35.78
371.57
2.22
241.1]
114.86
1471.82
144.7]
1.51
1.72
OMCEKTMTIM OVEft
LtlUlt HSOUKE
Iff*'
223445.3
30H38.4
43134.1
33108.0
328.0
2220.0
4098.4
661.0
1110.3
9.4
1134.0
2043.3
31371.2
14036.3
111.0
36.1
477255.1
NIUM
raiin
.if. -
241.29
272.49
300.19
301.13
3TI.79
353.25
383.73
446.23
341.13
442.30
172.40
371.33
304.30
321.80
442.30
445.10
HcmriiM MtviKitin
CJffiTNtr ItPdlEEl
JJI. 1
\mimtl
4304.11
3404.37
4712.1]
4291.47
1333.36
11.07
21.31
21.40
3443.93
9131.23
12421.33
7412.91
1147.74
1113.01
17.77
17.45
3161.221
70.01
71.10
48.11
43.83
41.04
72.22
74.01
33.72
38.30
43.70
33.10
34.20
46.40
41.40
36.00
48.40
0.06236 H Hl*i*3/iol'K
Koltculir Height
if Air ' 28.96 gi/io!
ftverigt KolicuUr
' Height of Siioline
»ipon 61.88 gi/iol
Hol«c»t»r wight
of BHolim-Mr
Hintort * 51.26 gi/«l
Heignteo avenge
lir diffusion
coefficient *
Helghted ivenge
liquid density
Heighted iverige
gts density
0.0778 u*2/»c
0.7121 gi/ct'3
1742.30 gih'3
-------
Table D~8
CKNICM. PROPER!? EST1IHTIW FOfl STETZENIACH HIGH REID
HMR PRESSURE MSOllffi AKD CBHSTITUENTS flT 10 DEGREES C.
REPRESENTATIVE
CHEN1CAI
liobttute
n-tutine '
Itopentine
O'Ptfltint
O'Octini
Benzine
Toluene
lylene dl
M'HfXiflt
2-Hithyli'Kine
2,2|4-Trltethylpentine
H'Htptitie
2-lhthyl-2-butene
2,3-DiMthyl-l-buttnt
1,2,4-TrlNlhylbenzene
Totil
Teioeriture * 293.
PERCENT
coitrnsmoN
3
to
3
3
2
13
10
S
3
3
5
5
8
me 5
too
13 dtg. K
Prtiiurt * 710 u Kg
Sii Conltint *
BRAN KOL. UO. PHASE MR OIFFU8KM UWII
VEI8HT HOIFRACT. COEFFICIENT KffilTi
(ENfltOll
39.12 0.0734
39.12 0.1308
72.13 0.0407
72.13 0.0107
114.23 0.0384
78.11 ,0.0224
12.14 0.1421
104.17 0.0923
81.18 0.0508
131.31 0.0280
114.23 0.0394
100.20 0.0437
70.14 0.0123
84.11 0.0321
120.20 0.0383
134.22 0.0321
94.53 1.0000
Vipor Density
of Bisolire-Air
Ninturt *
(CIT2/6ECI (8«/CHA3l
0.0937
0.0837
0,071?
0.071?
0.0313
0.0951
0.0771
O.M27
0.8449
0.05(8
0.0113
0.0120
0.0741
0.0177
0.014?
0.0111
1119.93 ii/l*3
0.5728,
0.3131
0.1311
0.13(4
0.7071
0.8957
0.9758
0.9701
0.4576
0.7433
0.1993
0.1114
0.1735
0.1937
0.8838
0.1595
0.7448
PURE CHEKICAL
VAPOR PRESSURE
(MHgl
1447.77
1112.75
312.47
283.84
3.13
43.53
12.43
3.21
75.70
0.11
23.02
20.44
234.73
132.47
0.70
0,64
PARTIAL PRESSURE
OVffl MSOLINE
(Httgl
124.2135
1(7.7(40
23.8325
17.2357
0.21(0
1.0215
1.7730
0.2691
3.8481
0.0030
0.6830
0.9033
13.9130
(.8711
0.040?
0.0208
314.833?
PUK CHEN1CM. COKCEKTRAT1MI OVEII
VAPOR tENBITT LIOUID M&OUNE
I6fl/«"3l
5423.71
3442.19
1403.70
1137.80
31.43.
201.40
(4.81
17.11
311.48
0.11
148.74
117.23
1011.11
131.38
4.77
4.84
Ippil
113438.8
220742.0
31359.4
22178.3
284.2
1344.1
2333.0
334.1
30(3.1
4.0
1188.3
20938.1
1073.8
33.8
27.3
480044.7
tOILIM
POINT
Ideg. Kl
2(1.23
272.15
300.15
309.13
398.73
333.29
383.73
411.23
341.83
412.30
172.40
371.53
304.30
328.80
442.50
445.70
HENRY'S UK Ml VIKNin
CIMtTMT (uPOlKI
(dii.)
3257.14
2521.11
33)7.13
2177.J?
5201.7?
11.32
12.10
11.83
3141.33
22M.I3
12810.22
4457.93
788.08
1271.84
8.71
48.53
2211.121
I7.lt
(8.41
(1.51
(1.47
38.78
(1.71
71.4?
31.8?
31.50
42.21
31.2?
52.33
(4.13
37.31
34.0? '
41.73 .
0.04234 M Hg
-------
Table D-9
CKHICR mum HIIMTIM FOR IIETIQIMCH HIM Kit
VAH» pffissttiE etsBUK m coxsumms AT o KMU c.
KWESEKTATIVE PEKCENT MM KOI. 119. PHASE All BIFFUI1M UKIII
OatCAL CMPOSITIOK KIEHT HOL FRACT. COEFFICIEKT KM1T»
IGH/Kflll (BI*2«ECI (8)1/01*31
iMblttnt
i-ktint
Impintini
n-Pentint
i-Octint
Beutfit
Toluint
lylene dl
i-Htiint
MMhyldtctnt
2|2|4-TriMthyIpftitine
Hfcptini
2-fcthyl-2-butini
2,3-Dloethyl-l-titMt
1,2,4-TrlMthylbMHM
l,l-JiMthyl-2-pktnylethin«
Tltil
Twperrtitri * 273.19 dig.
Prnsurc 710 it t
hi Conitint
9
10
9
9
9
2'
19
to
9
9
9
9
9
9
9
9
100
K
ig
99.12 0.0794
99.12 0.1908
72.19 0.0107
72.19 0.0107
114.23 n.0394
79.11 6.0224
12.14 0.1421
104.17 0.0829
91.18 0.0909
191.31 0.0280
114.23 0.0394
100.20 0.0437
70.14 0.0129
84,14 0.0921
120.20 0.0983
134.22 0.0321
94.93 1.0000
Vipor Dtniity
ol SiuUm-Air
Hitture
0.0109
0.0809
0.0722
0.0722
0.0928
0.08H
0.0728
0.0310
0.0428
0.0934
0.0129
0.0983
0.0191
0.0131
O.M09
0.0971
1711.09 U/l'3
0.9171
O.M14
0.1418
0.1419
0.7141
0.9041
0.8844
0.8711
0.1791
0.7909
0.7017
0.1981
0.1841
0.1930
0.8103
0.8199
0.7931
WK CHEHICAl
(MHgl
. 1174.21
774.01
291.30
183.40
2.81
21.34
1.72
1.13
43.32
0.04
13.08
11.42
113.10
82.31
0.32
0.28
PMTIN. HEKtlK PK CHEMICAL
ova 8«soLiK VAPID KHSITT
(H Kg) ICH/V3I
M.9I87
111.7093
19.7431
11.1319
0.1011
0.3110
0.1988
0.1343
2.3042
0.0011
0.9011
0.4112
10.1877
4.2949
0.01B9
0.0093
291.7070
4001.19
2441.24
1018.34
771.84
19.11 -.
120.79
31.31
10.14
229.31
0.37
87.71
17.17
171.99
401.17
2.23
2.29
CMCEinMTlW OKI KHUN
LIKJ1I MtOllNE NIHT
Ippil ('«! Ki
111471.9
193991.9
20718.3
14193.7
144.2
777.1
1211.9
171.7
3031.8
1.3
110. 1
. 191.9
13404.9
9138.0
24.3
12.2
331193.1
211.29
272.19
300.99
309.19
318.79
393.29
383.79
411.29
341.89
412.30
372.40
371.99
304.30
328.BO
442.90
443.90
HEMTIIM
CM1IWT
Uii.l
2407.97
1819.42
2320.11
1194.20
2731.13
1.79
7.04
1.12
2272.33
813.72
13331.03
2999.01
923.01
824.34
4.17
22.92
1443.579
MS VIKBITT
(aPOICEl
19.23
U.M
14.21
39.49
M.91
17.29
18.91
50.03
94.91
40.72
49.48
90.30
11.87
97.21
92.18
49.10 -
0.01231 H HjU'3/wHi;
Itolunlir Height
t) Air 29.11 gtVial
Avtrigt Itoleculir
flight ol Biioline
Vifors 11.23 gi/tol
Ihleculir might
tt BtioIlneAir
Iliittri » 39.69 gi/iol
Kiightid ivirigt
ilr ditfuilM
CMlficient >
Ktighttd wiriji
liquid dcniity
Htlghted ivtrige
gu deniity
0.0188 ct*2/»c
0.7323 gi/u*3
904.97 |i/i*3
-------
Table D-10
CHEHICAL rRDPEnv BTIIMTIOX FOR STETIENMCU mm
OCTANE BASOLINE NTO CONSTITUENTS AT 20 DEGREES C.
b
I1
LO.
REPRESENTATIVE PERCENT BRAN DDL.
CKEKICM. COMPOSITION KISHT
If otutini 3
fl-Butini 3
liopmtini 3
n-Pintini 3
n-Octini 5
Binttfli 2
Tolutflt 25
lyltflt (I) 10
2-Ntthyldicini
2,2,4-Trluthylpintini
-Htitini
Mtfthyl-2-buttnt
2,3-OlMthyl-l-tutMi
1,2,4-Trlnthytbtittiin
ltl-Dl«ithyl-2-pkinyti«iini 5
Totil 100
Tnptriturt 273.13 dtg. It
PTMWM 7(0 M Hg
t» Comtmt «
0.01231 M Hgit*3/K>I
-------
Table D-ll
HBIIUL MDKUTT ElttMTIM FOR IJETIDIMCH mtfl
ICTUS MKUIK m cowTtniEKti AT to KB«EII c.
KMtEEEXTMIVf PERCENT
efiEBICM. CW05ITI8S
Iiotntuti'
lioptnUnt
Hfctini
lyltni dl
i-flMini
MkUiylfccwi
2,2,4-Trlnthylpntme
iHhptiiw
Mhthrl-2-tttMi
2,3-DiMthyl-l-titmi
1,2,4-TrtnthyltimitM
l,l-0inlhyl-2-phinylithini
3
J
3
5
5
2
25
10
3
9
5
0
9
5
9
Wfln WuL»
KI8HT
(GN/noti
31.12
38.12
72.13
72.13
114.23
78.11
12.14
104.17
04.19
134.31
114.23
100.20
70.14
04.14
120.20
134.22
LIB. tmi
sa FBJST.
0.0772
0.0772
0.0422
0.0422
0.0393
0.0230
0.2434
0.0944
0.0321
0.0297
0.0393
0.0000
0.0440
0.0533
0.0598
0.0334
Alt HFFUlim L1WI1
KCTflCIESI K)!!!IJ
(CN'2/SECI
0.0957
0.0937
0.0749
0.0749
0.0343
0.0931
0.0774
0.0429
0.0441
0.03(9
0.0443
0.0420
0.0741
0.0477
0.0441
0.0413
-------
Table D-12
. mum ESTIMTIIM FOR BTETZEKMCH mm
«nm MEOllHE MID CtmSTITUEIITS AT 0 KBflEEB C.
t)
ii
Ui
ffiPREEfflT'TIVE
CHEH1CM.
liobuttm
i-Butini
Iinpntint
n-Ptfitini
n-Ctlint
BIIUMI
ToUMi
lyltni III
B-KlIIIH
Mhtdrliicwi
2,2,4-TrlHthylpmtMi
ii-flifUni
2-Nthyl-2-tit(M
2,3-tlHthyl-Huttiii
I|2|4-Trlnthylbintiai
FtffiEITT
C01OTSITIOK
S
3
S
3
3
2
23
to
3
3
3
0
3
5
8
l,l-DlMthy!-2-phMyl(tliini S
totil
100
MM KM..
HEIGHT
(ffl/inil
39.12
SB. 12
72.13
72.13
114.23
JB.II
92.14
104.17
BUB
136.31
114.2]
100.20
70.14
B4.lt
120.20
134.22
93.B3
LIO. FUME
not. ma.
0.0772
0.0772
0.0(22
0.0(22
0,0393
0.0230
0.2434
0.0941
0.0321
0.0287
0.0393
0.0000
0.0(40
0.0333
0.0379
0.0334
1.0000
I1R OIFFIBIOK IIOUII
COEFFICIENT tEKSIU
(Ctl*2/GEC) (611/01*31
0.0103 0.3474
0.0(03 0.1014
0.0722 0.4(11
0.0722 0.4(43
0.032B 0.7141
O.OBOO 0.9041
0.072B O.BI44
0.0390 O.B7II
0.0i28 0.4739
0.0334 0.7303
O.M23 0.7047
O.OSB3 0.4914
0.0494 0.48(4
0.0634 0.4930
0.040? 0.8905
0.0374 O.B439
0.77(9
FWE CHEKtCM.
VdPM FUKSURE
laiH?)
, 1174.24
774.09
239.30
183.40
2.86
24.34
4.72
1.43
43.32
0.04
13.09
11.42
It). 10
82.31
0.32
0.28
MRT1N. PHESSUK
OVEI BKOUNE
(HHgl
M.49H
59.7BS2
14.1332
11.4108
0.1123
0.4033
1.4373
0,1374
2.3408
0.0012
0.3140
0.0000
10.4383
4.3903
0.018?
0.0093
178.233?
PURE CHENICM.
VtfOS KKSITf
(En/mi
4004.43
2441.24
1078.34
774.84
19.14 .
120.7?
34.34
10.14
227.31
0.37
97.71
47.17
471.3?
404.47
2.23
2.23
COWEKTMT10K OVER
UBUII MSOUNE
<;)>
117337.0
71441.4
21227.7
13014.2
147.8
774.7
2134.3 .
181.0
3104.4
1.3
474.3
0.0
13734.7
3774.7
24.7
12.3
2408(0.3
NILIK8
POINT
(di«. Kl
241.23
272.43
300.73
307.13
378.73
333.23
383.73
444.23
341.83
442.30
372.40
371.33
304.30
329.90
442.30
443.70
HEMriUW
comrrMT
Kit.)
2407.77
1111.42
2320.11
1774.20
2734.13
4.7?
7.04
4.12
2272.33
843.72
13331.03
2333.01
323.01
824.34
4.17
22.32
1430.274
BM VlBCMIt
(rftlBEl
19.23
44.14
44.21
57.4?
34.87
4T.27
41.74
M.«3
34.91
41.72
47.48
3t.3»
41.17
37.21
32.18
49.18
TnperiUrt 273.13 dtg. K
Prmun 7(0 n Kg
8« CmitMt
0.04231 M HgA3
Heljhtfd iverigt
confident 0.0(97 crt/itc
(flighted mUge
llqild density 0.7393 (I/CIA3
Ktlglittd iverige
gn density 723.M gi/iA3
-------
Ihe vapor mixture of the CDM synthotic gasoline blend was compared against
the gasoline vapor mixture suggested by K. Stetzenbach (1987) of this
appendix. Assuming the vapor mixture given by Stetzenbach is for 10° C,
the percentages of the vapor mixture on a constituent basis are:
CDM Gasoline Stetzenback
Vapor Mixture Vapor Mixture
isopentane 39% 30%
isobutane 27% 19%
n-pentane 6% 19%
n-butane ' 9% 30%
toluene 0.4% 1%
m-xylene 0.1% 1%
others 18.5% 0%
sum 100% 100%
i
This comparison shows that the Stetzenbach gasoline vapor mixture contains
more n-pentane and n-butane and less isopentane and isobutane than the CDM
gasoline vapor mixture. If the vapor rercentages are grouped into the C4
and C5 alkanes and aromatic compounds, the comparison becomes:
CDM Gasoline Stetzenbach
Vapor Mixture Vapor Mixture
C4 alkanes 36% 49%
C5 alkanes 45% 49%
aromatics 0.5% 2%
others 18.5% 0%
sum 100% 100%
This comparison indicates that the CDM gasoline vapor mixture and the
Stetzenbach vapor mixture are similar.
D-16
-------
ENVIRONMENTAL RESEARCH CENTER
UNIVERSITY OF NEVADA, LAS VEGAS
4505 MARYLAND PARKWAY LAS VEGAS, NEVADA 89154 (702) 739-3382
MEMORANDUM
TO: Philip Durgin
FROM: Klaus Stetzenbach
DATE: September 24, 1987
SUBJECT: Standard Gasoline
In my memorandum to you. on September 10, 1987, I presented components and
concentrations for consideration of several standard gasolines. Subsequently,
I have discussed this with Rick Johnson, Dave Kreamer, Gwen Eklund, Henry
Kerfoot and Jim Stuart. From these discussions it was decided that:
1) There is a need for at least three types of standard gasolines; a
low Reid vapor pressure (RVP), a high RVP, and a high octane.
2) Small volumes of calibration standards should be made at a central
location, but larger volumes for experimental use should be mixed
by the user.
3) If a re'searcher wishes to add extra components, the hexane,
heptane, or octane concentrations should be reduced. All other
components should remain at their original concentrations.
4) For instrumental standardization purposes, it will be acceptable
to use a standard mixture of fewer components provided that the
standardization mixture has been calibrated against one of the
standard gasolines.
A table containing components and their concentrations for three standard
gasolines is attached.
KS/
Attachment
Divisions: Anthropological Studies Earth Sciences Environmental Resources Limnological Research Quality Assurance Laboratory
-------
-------
STANDARD GASOLINE MIXTURES
COMPONENT
2-methylpropane
butane
2-methylbutane
pentane
hexane
heptane
2,2,4 trimethylpentane
octane
2-methyldecane
2-methyl-2-butene
2,3-dimethyl-l-butene
benzene
toluene
xylene(s) *
1,2,4-tri methyl benzene
1,1-dimethyl-2-phenylethane
LOW RVP
3
3
5
5
5
5
5
14
5
5
5
2
15
10
8
5
CONCENTRATION (%)
HIGH RVP HIGH OCTANE
5
10
5
5
5
5
5
5
5
5
5
2
15
10
8
5
5
5
5
5
5
5
5
5
5
5
2
25
10
8
5
% aliphatics
% olefins
% aromatics
% C4 & C5
50
10
40
16
50
10
40
25
40
10
50
20
can be any mixture of xylenes, but concentration
of each isomer must be specified.
-------
-------
ENVIRONMENTAL RESEARCH CENTER
UNIVERSITY OF NEVADA. LAS VEGAS
4505 MARYLAND PARKWAY » LAS VEGAS. NEVADA 89154 (702) 739-3382
MEMORANDUM
TO: Philip Durgin
FROM: Kl aus Stetzenbach
DATE: September 29, 1987
SUBJECT: Standard Gasoline Vapor Mixture
Based on the data from the references listed in my memo to you of September
10, 1987, I recommend that a standard gasoline vapor contain the compounds
listed below. These are the same set of compounds that will be used by Radian
in their testing of the gasoline vapor monitors.
STANDARD GASOLINE VAPOR MIXTURE
COMPONENT
2-methyl propane
butane
2-methylbutane
pentane
toluene
xylene(s) *
CONCENTRATION (%)
19
30
30
19
1
1
can be any mixture of xylenes, but the concentration of each
isomer must be specified.
Divisions: Anthropological Studies Earth Sciences Environmental Resources Limnological Research Quality Assurance Laboratory
-------
-------
APPENDIX E
EVALUATION OF AIR-WATER PHASE EXCHANGE ON DIFFUSION
OF HYDROCARBON VAPORS
Development
The potential for loss of hydrocarbon vapors to vadose zone water was
evaluated with a consideration of a retardation factor, F, which is based
on Henry's Law. This retardation factor has the effect of linearly scaling
the effective diffusion coefficient, reducing diffusive transport because
of losses to the water phase. Aromatic hydrocarbons with high Henry's Law
constant values (e.g., benzene, toluene, xylene) would be expected to
experience higher losses to exchange with water than the low-molecular
weight alkanes (e.g., isopentane, isobutane, n-butane) which have lower
Henry's Law constant values. As a result, it would be expected that the
aromatic hydrocarbons would be retarded relative to the alkanes in a
diffusive transport simulation. The effect on diffusive transport of
exchange between air and water as governed by Henry's Law was investigated
by formulating an expression to include Henry's Law into the diffusion
equation.
The governing equation for vapor diffusion is given in Equation H-l of
Appendix H. Dividing each term by the air-filled porosity produces:
sc/at - a/3x± ID. .... (ac/axj)] + os/at)/ea (Equation E-D
where:
C vapor concentration (cm3 /cm3 )
t time (seconds)
XA distance in ith direction (cm)
D . . effective diffusion coefficient (cm2/sec)
f * D
3s/3t vapor source/sink term (cm3 /cm3 /sec)
ea air-filled porosity (on3 /cm3 )
E-l
-------
source/sink term can be expanded to: .
8s/at - 3S/3C 3C/3t (Equation E-2)
To describe the partitioning term, 3s/3C, Henry's Law can be introduced:
; r m H c (Equation E-3)
u ^c w
where: H. Henry's Law constant (dimensionless)
3 3
C concentration in water (cm /cm )
Using Henry's Law, an expression for the rate of partitioning into the
water phase can be obtained by defining the "sink" (water) concentration,
according to volume, and then differentiating with respect to vapor
concentration:
_ e C/a (Equation E-4)
W W ' K
3SW/3G - 6w/Hk = -3S/3C (Equation E-5)
where:
s volumetric water concentration (cm /cm )
33
6W water-filled porosity (cm /cm )
Equation E-5 is based on the assumptions that partitioning is
instantaneous, linear, and reversible.
Substituting Equation E-5 into Equation E-l, and defining a retardation
coefficient, Fk, for vapor-water partitioning, produces:
Fk - 3C/3t - 3/3x.[D.r.j(3C/3xj)] (Equation E-6)
Fk - l+Ov/ej/H* (Equation E-7)
E-2
-------
this is the same equation solved by the DYNFLOW UST model (see Appendix H)
except that the effective diffusion coefficient should be scaled by the
retardation factor to account for gas-liquid phase exchange. The
expression for the retardation factor (Equation E-7) is corroborated by G.
Robbins (1987).
Discussion
The effect of low Henry's Law constant values (e.g., benzene, toluene,
xylene) in equation 9 is to make the value of F greater than 1, thereby
reducing the effective diffusion coefficients for these hydrocarbons. By
contrast, large values of H for compounds such as isopentane will result in
F values close to 1, indicating little or no effect on diffusive transport
by the loss of these compounds to the water phase by exchange governed by
Henry's Law.
Calculations performed with Equation E-7 show that, except in the case of
benzene (i.e., H - 11), the effect of gas-liquid phase exchange on the
effective diffusion coefficient is negligible. These calculations were
i
made for the native soils of simulation run number 6 to maximize the effect
of gas-liquid phase exchange since this simulation modeled the largest
moisture content of any of the simulations performed. For the purposes of
the DYNFLOW UST simulation, this analysis shows that the effect of losses
of hydrocarbon vapors to the water phase in the vadose zone on diffusive
transport can be safely neglected.
E-3
-------
TABLE E-l
Example Calculation of Retardation Coefficient
Gasoline Component
or Blend
H F
Henry's
Law Retardation
Coefficient Coefficient
(dimensionless) (dimensionless)
CDM Synthetic Gasoline Blend
Isopentane
Isobutane
Benzene
3,203
3,388
3,260
11
1.00
1.00
1.00
1.49
Note:
All values in this table are for 10° C
Assumptions: 6t - Total Porosity - 45%
Air Filled Porosity - 7%
Represents "Wet Clay" native soil as in Simulation Run
Number 6 (See Appendix K)
E-4
-------
APPENDIX F
CALCULATION OF EQUILIBRIUM GASOLINE VAPOR-AIR MIXTURE DENSITY
This appendix presents the equations used for calculation of the
equilibrium vapor density of the gasoline vapor-air mixture. A sample
calculation for equilibrium vapor density is presented also in this
Appendix.
Vapor density of «gasoline vapor-air mixture, pv:
pv >* M Pa/(T- R) (Equation F-l)
where:
M average molecular weight of gasoline vapor-air mixture (g/mol)
R universal gas constant (62,630 mm Hg cm3/tool- °K)
T temperature (°K)
Pa atmospheric pressure (mm Hg)
2. Average molecular weight of gasoline vapor-air mixture, M:
M = (Pt/Pa)« Mv + ((Pa - Pt)/Pah Ma (Equation F-2)
where:
Pt equilibrium vapor pressure of gasoline vapor (mm Hg)
Ma average molecular weight of air, Ma -= 28.96 (g/mol)
M average molecular weight of gasoline vapors (g/mol)
V
F-l
-------
The following is an example calculation of the density of a gasoline
vapor-air mixture. From Table D-l of Appendix D, and using Equation F-2s
Mv - 69.48 g/mol
T « 293.15 °K
R « 62,360 mm Hg cm3/(mol °K)
Ma - 28.96 g/mol
Pt - 274 mm Hg
M - (274/760) 69.48 + ((760-274)/760) 28.96
M - 43.57 g/taol
Ptr m (43.57 760/(293.15 62,360)
g/cm3
- 1.811 x 10"3 -'3
The calculated gasoline vapor-air mixture vapor density from this sample
calculation indicates that the gasoline vapor-air mixture is about 50%
denser than air (e.g., air density = 1.2 x 10~ g/m ).
F-2
-------
APPENDIX G .
CALCULATION OF
THE LIQUID VOLUME OF LEAKED GASOLINE
This appendix presents the methodology for calculating the liquid volume of
leaked gasoline, using the simulation results from the DYNFLOW
diffusion-based model of vapor transport from an UST leak. A sample
calculation is also provided.
At the end of each simulation time step, DYNFLOW prints a "mass balance"
table that includes all inflows and outflows from the model for the UST
leak simulations. The only gasoline vapor inflow was at the simulated
leak, which was represented as a fixed concentration. Thus, for each
simulation run, DYNFLOW produced a time history of inflow rate versus
simulation time. An example of this, for simulation run number 1 ("average
conditions"), is listed in Table G-l. Note that the inflow rates are those
printed directly by DYNFLOW, corresponding to a leak concentration of "100"
representing 1QO percent of equilibrium concentration.
To compute the volume of gasoline that has leaked, incremental and
cumulative volumes of diffused gasoline vapors at the end of each time step
were computed, as shown in Table G-l. The incremental leaked volume was
calculated as follows:
v - KQo +9i-iioo>/2J Ati (Equation G-l)
i,ioo i.ioo i-i,ioo
where: V± 100 incremental leak volume of gasoline vapors (ft3);
Qi 100 simulated influx rate for time step i (ft3/hr);
At. length of time step i (hours);
100 subscript referring to "100 per cent" concentration.
G-l
-------
The cumulative volume was computed at each simulation time by adding all
previous incremental volumes:
N
.. _ r v (Equation G-2)
vv,ioo *ml vi,ioo ^
where: N number of simulation time steps
The cumulative volumes were then converted from "100 percent" of
equilibrium concentration equivalents to estimated gasoline vapor volumes
by multiplying by the equilibrium vapor concentration and air-filled
porosity:
V - V C 6 / 100 (Equation G-3)
vv v100 o »
C equilibrium vapor concentration in air of gasoline
vapors (ft3/ft3)
6^ air filled porosity (ft3/ft3)
A
The air-filled porosity is included because the DYNFLCW simulations were
performed with a unit storage coefficient. The concentrations predicted by
DYNFLOW are correct, and they are based on reasonably-estimated effective
diffusion coefficients that incorporate porosity; but, the inflows need to
be corrected for the available space for vapors to occupy.
For the example in Table G-l, the total volume of leaked vapors at the end
of two days was estimated as follows:
V (at 2 days) - 656 0.284 0.20/100 ft3
0.37 ft3 - 10,551 cm3
G-2
-------
The next step was to compute the .mass of these gasoline vapors:
W - M V Pa/(T-R) (Equation G-4)
where: Wv mass of gasoline vapors (g)
M average gram molecular weight
of gasoline-air mixture (g/mol)
R universal gas constant
(62,360 mm Hg cm3/tnol °K)
T 'temperature (°K)
p atmospheric pressure (mm Hg)
From the example:
Wv - 38.88 10,551 760/{283.15 62,360) - 17.7 g
Knowing the mass of gasoline vapors, the corresponding volume of liquid
gasoline was calculated using:
V -* W /p (Equation G-5)
where: Vi leaked volume of liquid gasoline (cm )
PI gasoline liquid density (g/cm3)
Completing the example, and converting cubic centimeters to gallons:
Vi - 17.7/0.7271 - 24.3 cm3 - 0.01 gallons
This is the estimated minimum volume of leaked gasoline after a simulated
leak duration of two days> using the conditions from simulation run number
1 ("average conditions").
G-3
-------
The cumulative volume of leaked gasoline, V1, can be calculated from the
cumulative volume of gasoline vapor, Vv 100, through a scalar ijuantity,
air-filled porosity, and saturation vapor concentration.
v! -vv,ioo ' c0 ea s
where:
S scalar quantity
at 0° C, S - 1.61 x 10~4
at 10° C, S - 1.72 x 10~4
at 20° C, S = 1.89 x 10~4
G-4
-------
TABLE G-l
Example Time History of DYNFLCW-Simulated
Vapor Volatilization Flux Bates and Volumes
Simulation Time
at End
of Time Step
(hours)
Time
Step
Length
DYNFLOW
Inflow
Rate
Volatilization
Volume Cumulative
During Volatilization
Time Step Volume
(hours) (ft3/hr)
(ft3)
(ft3)
1
2
3
4
5
6
9
12
18
24
30
36
42
48
1
1
1
: 1
1
1
3
3
6
6
6
6
6
6
17.594
16.229
15.630
15.237
14.952
14.750
14.313
14.033
13.689
13.473
13.320
13.205
13.174
13.081
8.797
16.912
15.930
15.434
15.095
14.851
43.595
42.520
83.166
81.486
80.379
79.575
79.137
78.765
8.797
25.709
41.639
57.073
72.168
87.019
130.614
173.134
256.300
337.786
418.165
497.740
576.877
655.642
Note: All rates and volumes in this table correspond to simulation of the
volatilization as 100 percent of equilibrium vapor concentration.
The volatilization rates are from Simulation Run Number 1 ("average
conditions")/ as listed in Table N-8.
G-5
-------
-------
APPENDIX H
ANALOGY OF DIFFUSION AND CONFINED GROUND WATER FLOW
This appendix presents the mathematical justification for using DYNFLOW to
perform diffusion simulations with a computer model which solves the
confined ground water flow equation. A description of DYNFLOW, its
development, usage, validation, and availability also is presented in the
appendix.
GOVERNING EQUATIONS
The governing differential equation for vapor diffusion in three dimensions
can be expressed as:
ea ac/at - em a/axi[D)ifij(8c/axj)] + as/at, i - 1,2,3
(Equation H-l)
where:
C vapor concentration (ft3/ft3 of gas)
t time (hours)
D effective diffusion coefficient tensor (ft2/hr)
» i j
x± distance in direction i (ft)
6a air-filled porosity (ft3/ft3)
as/8t vapor source term (ft3/ft3/hr)
Similarly, the equation for confined ground water flow is:
S8 ah/at - a/3x.[Ki:J Oh/ax.)] + Q, i - 1,2,3 (Equation H-2)
where:
h aquifer piezometric head (ft)
S aquifer specific storativity (ft~ )
K±. hydraulic conductivity tensor (ft/hr)
Q hydraulic source term (ft3/hr/ft3)
H-l
-------
By analogy, the two equations can be made identical by letting:
D ,< «K.,/SB (Equation H-3)
»* 3 * 3 °
c m h (Equation H-4)
(3s/3t)/ea « Q/S8 (Equation H-5)
in fact, Ki;|/S8 is referred to as the "aquifer diffusivity" in ground water
hydrology.
This analogy means that any computer program that simulates
three-dimensional confined ground water flow can be used to solve the vapor
diffusion equation. In this work assignment, CDM's three-dimensional
program called DYNFLOW was used.
For sake of convenience, the term SB was set equal to unity. This meant
that the hydraulic conductivity values in all simulation runs were equal to
the effective diffusion coefficients.
To interpret the fluxes computed by DYNFLOW at source or sink boundary
condition locations (such as the point used to simulate the UST leak as a
constant concentration), the air-filled porosity was multiplied by the
computed "water" flux, giving a simulated flux of vapor product (ft /hr).
This was cross-checked by taking the simulated concentration distribution
and computing the volume of vapor product occupying the pore spaces, and
comparing it to the integral of the fluxes over time.
DYNFLOW SIMULATION MODEL
DYNFLOW is a three-dimensional, finite element groundwater flow code,
developed and applied at COM. DYNFLOW uses the finite element formulation
and allows the user to mix 3-D, 2-D, 1-D, planar, and pond elements. The
code also has flexible capabilities for changing boundary conditions,
geometries in all three dimensions, and model time-stepping during the
course of a simulation run.
H-2
-------
The present version of DYNFLCW evolved from work performed over the last
decade. The original research for the model was conducted at .the
Massachusetts Institute of Technology in the mid 1970's. Many of the
personnel involved in this original development work subsequently joined
COM as full-time employees, including the work assignment manager, who is a
co-author of DYNFLCW. These people, while at COM,- were involved in
numerous groundwater flow and groundwater contamination studies (including
many related to RCRA and CERCLA) and continued to make refinements and
improvements on the original models to enhance both their usefulness and
their ability to accurately represent real-world behavior.
The current versions of DYNFLCW and DYNTPACK have been applied by COM at
numerous sites under our current OERR contract; they have been used in
performing RI/FS work at many sites. In addition, DYNFLCW and DYNTRACK
have formed the basis of CDM's involvement in enforcement-related efforts.
For one of these projects, OWPE commissioned the International Ground Water
Modeling Center (IGWMC) of the Holcomb Research Institute at Butler
University to review the DYNFLCW and DYNTRACK simulation codes. IGWMCfs
Report of Findings (May 3, 1985) provides a formal acknowledgment of the
code's theoretical and scientific appropriateness.
»
COM will license an executable version of DYNFLCW to any interested party,
for a licensing fee that is commensurate with the extensive research and
development time that COM has invested in the progranu (For public sector
entities, this fee is often waived.) The availability of licensing
arrangements puts DYNFLCW in the public sector. This, in addition to the
code verification performed by the International Ground Water Modeling
Center, makes DYNFLCW a robust and publicly-defensible numerical simulation
program.
A complete Users Manual is available for DYNFLCW (COM, 1984). It contains
sections on theory, program structure, command language, computer
implementation, and code verification. Details on the verification
simulation runs can be provided.
H-3
-------
-------
APPENDIX I
ANALYTICAL VERIFICATION OF THE DYNFLOW-BASED DIFFUSION MODEL
This appendix presents an analytical verification of the DYNFLOW diffusion
model. The analytical verification describes theory, methodology,
simulation input, simulation results, and conclusions.
A simple, one-dimensional diffusion problem was constructed to verify the
performance of the DYNFLOW diffusion model. The diffusion equation solved
in this.exercise was:
8C/8t = De-82C/3x2 (Equation 1-1)
where:
C vapor concentration (ft3/ft3)
De effective soil diffusion coefficient (ft2/hr)
t time (hr)
x , horizontal distance from source (ft)
The grid was constructed as two parallel rows of elements, each row 2 feet
wide, for a total lateral width of 4 feet. The vertical thickness was 2
feet, giving a cross-section area of 8 square feet. The longitudinal
length of the grid was 18 feet, and so the volume was 144 cubic feet.
Boundary conditions were no-flow boundaries on the sides, top, and bottom
of the numerical grid used to solve this differential equation. It was
assumed that no vapors were present within the system prior to initiation
of simulation. With the initiation of simulation, the nodes on one end of
the numerical grid were set at constant concentration values with time.
The numerical simulations were made with an effective soil diffusion
coefficient of De « 0.1348 ft2/hr, which was assumed to be constant and
isotropic.
1-1
-------
Two grid densities for the numerical model were selected to examine the
effect of spatial discretization on the numerical results. The fine
numerical grid utilized 6 levels separated by a 0.4 foot of vertical
distance; nodes along the longitudinal horizontal axis were separated by a
0.4 foot of horizontal distance, The coarse numerical grid utilized 2
levels separated by 2 feet of vertical distance; nodes along the
longitudinal horizontal axis were separated by 2 feet of horizontal
distance.
Hie analytical solution to the diffusion equation used the same diffusion
coefficient value and is solved with:
C/C0 - erfc(x/(4 D, t)1/2 ) (Equation 1-2)
where:
C vapor concentration at distance x from the source (ft3 /ft3)
Co source vapor concentration (ft3 /ft3)
erfc(z) complementary error function, with argument z.
i
A good fit between the numerical solution results for the fine grid and the
analytical solution at time t - 6 hours was found (Figure 1-1). A poorer
fit, however, between the coarse grid numerical results and the analytical
solution resulted at time t « 6 hours (Figure 1-2).
At time t - 96 hours, results from the fine and coarse numerical grid
simulations showed good agreement with the analytical solution (Figures 1-3
and 1-4).
As a second verification measure, the influxes calculated by the DYNFLOW
diffusion model were compared to fluxes computed for the analytical
solution. The analytical fluxes were computed from:
Jx * ~D. ' 3tc/col/8x (Equation 1-3)
1-2
-------
where:
Jx volume flux per unit area entering system at source
(ft3/hr/ft2)
To determine the gradient, ac/Bx, near the source, Equation 1-2 was
evaluated at progressively smaller values of x. In the limit as x
approached zero, the calculated gradient approached the gradient at the
source. This estimate of the gradient very near the source was multiplied
by Da - 0.1348 ft2/hr to evaluate Jx. This analytical value for Jx was
compared against the flux values generated by DYNFLOW, as shown in Table
1-1.
This analysis shows that the flux computed by DYNFLOW for the fine grid
agrees with the analytical calculation of flux at both simulation times.
The coarse grid flux at 96 hrs also corresponds to the analytical flux at
96 hrs. Some discrepancy, due to the discretization of the coarse grid, is
apparent at the earlier time.
i
The grid used for the UST simulations described in this report had a
spacing of 1 foot in the backfill zone. This spacing falls between the
fine and coarse grids used in this appendix.
Based on the results of the verification test, it was determined that the
DYNFLOW diffusion model produces results that accurately match analytic
solutions. More importantly, it was determined that a 1-foot spacing is
adequate for the simulation of vapor diffusion from an UST leak.
1-3
-------
Addendum
Further proof of verification for the use of DYNFLOW, and for the method of
calculating liquid leaked volume, was obtained by simulating the
one-dimensional case to steady-state and computing the cumulative influx
volume. This volume should equal the available storage space in the
DYNFLOW grid, or 144 cubic feet. Multiplication by the air-filled
porosity, as described in Appendix G, would give the volume of vapors in
the system.
The simulation to steady-state produced good agreement between simulated
results and the grid volume: DYNFLOW simulated about 152 cubic feet of
total inflow, using' the coarse test grid. These results further enhance
the verification of DYNFLCW and they support the methods outlined in
Appendix G and Appendix H for computing liquid volume equivalents based on
DYNFLCW simulation results.
1-4
-------
: TABLE 1-1
COMPARISON OF DYNFLOW AND ANALYTIC SOLUTION OF VAPOR INFLUX
One-Dimensional
Vapor Influx (ft3/hr/ft2)
Simulation DYNFLOW RESULTS
Time Analytic
(hour) Solution Fine Grid Coarse Grid
6 0.085 0.083 0.060
96 0.021 0.021 0.020
-------
-------
100
x
i
o- Analytical
*- Fine Grid
Lateral Distance (ft.)
FIGURE 1-1. Analytic vs. DYNFIOW (fine grid) at 6 hours.
-------
100
I
X
20
a- Analytical
-* Coarse Grid
Lateral Distance (ft.)
FIGURE I-2. Analytic vs. DYNFLOW (coarse grid) at 6 hours.
-------
100
I
x
40-
20-
HS- Analytical
*- Fine Grid
0 2 4 6 8 10 12 14 16
Lateral Distance (ft.)
FIGURE I-3. Analytic vs. DYNFLOW (fine grid) at 96 hours.
-------
100
x
5
0 24 6 8 10 12 14 16
40-
20-
0- Analytical
+ Coarse Grid
Lateral Distance (ft.)
FIGURE I - 4. Analytic vs. DYNFLOW (coarse grid) at 96 hours.
-------
APPENDIX J
VAPOR DIFFUSION TORTUOSITY AND EFFECTIVE SOIL DIFFUSION EQUATIONS
This appendix describes how air diffusion coefficients from Appendix D were
scaled by values of vapor diffusion tortuosity. The result is an effective
soil diffusion coefficient. Values of air diffusion coefficients,
effective soil diffusion coefficients, and the vapor diffusion tortuosity
coefficients used in making the UST vapor transport in simulations are
presented in Appendix K.
Values for the vapor diffusion tortuosity factor were derived using an
expression presented in Millington (1959):
1/3
T - 6a . (6a/eT)2 (Equation J-l)
where:
T vapor diffusion tortuosity coefficient (dimensionless),
0 < T < 1
6a air-filled porosity (cm3/cm3), 0 < 0a < 0t
6 total porosity (cm3/cm3),
e. < et < i
Although there exist many other expressions for vapor diffusion tortuosity
(Buckingham, 1904; Penman, 1940; Alberton, 1979), recent research suggests
that the Millington formulation is physically realistic (C. Bruell, U.
Lowell, personal communication, 1987). Because of this, the Millington
expression was used to calculate vapor diffusion tortuosity coefficients
used in the DYNFLOW diffusion simulations.
J-l
-------
Mr diffusion coefficients, Do, for the hydrocarbon vapors (see Appendix D)
were scaled with the vapor diffusion tortuosity coefficient to obtain a
diffusion coefficient suitable for modeling diffusion in a porous medium:
D (Equation J-2)
O
where:
D effective soil diffusion coefficient (cm /sec)
D air diffusion coefficient (cm2/sec)
o
Care should, be taken in referring to the "effective diffusion coefficient,"
because when this coefficient is placed in the governing equation (see
Equation H-l in Appendix H), it is multiplied by the air-filled porosity,
9 . For this reason, Equation J-2 does not include the air-filled
porosity.
References for the equations presented above appear in Section 5 of this
report.
J-2
-------
It
APPENDIX K
SIMULATION MATRIX
This appendix presents tables of simulation parameters used in the modeling
of diffusive transport of hydrocarbon vapors. Table K-l contains
parameters for the excavation zone/backfill, and Table K-2 is for the
native soils.
The parameters required to calculate the effective soil diffusion
coefficients (see Appendix J) are presented for both excavation zone
backfill and native soils. Values of total porosity and moisture content
were varied to simulate and assess the sensitivity of diffusion results to
these properties.
Each of the six reported simulations were performed with a paved,
impervious ground surface. Simulation Run Number 7 was the same as Number
1, except an open surface was simulated, with concentrations there fixed at
zero, to represent free discharge of vapors at the surface.
Run Number 1 was taken to be the "average" situation that was used for
plotting and analyzing "average" condition results in Sections 3 and 4 of
this report. Runs 2 through 6 represent increasing moisture contents and
decreasing air-filled porosities. These are hypothetical conditions which
may be considered worse than average and were used solely to simulate the
sensitivity of results to those conditions.
K-l
-------
-------
TABLE K-l
Simulation Properties of Backfill Materials
Simulation Run Number
Backfill
Material
Total
Porosity
Air-Filled
Porosity
Water Filled
Porosity
Saturation
Water
Content
Vapor Diffusion
Tortuosity
I
Dry
Gravel
0.20
0.14
.0.06
0.30
3%
0.25
Dry
Gravel
0,20
0.14
0.06
0.30
3%
0.25
3
Moist Sand
*
0.30
0.11
0.19
0.63
8%
0.07
1
Moist Sand
0.30
0.11
0.19
0.63
8%
0.07
5
Wet Sand
0.40
-
0.10
0.30
0.75
12%
0.03
6
Wet Sand
0.40
0.10
0.30
0.75
12%
0.03
7
Dry
Gravel-
0.20
0.14
0.06
, 0.30
3%
0.25
Effective Diffusion
Coefficient
(cm2 /sec)
0.017
0.017
0.005
0.005
0.002
0.002
0.017
Effective Diffusion
Coefficient
(ft2/hr)
Surface
Condi ton
0.065
Paved
0.065
Paved
0.020
Paved
0.020
Paved
0.008
Paved
0.008
Paved
0.065
Onpn
-------
TABLE K-2
Simulated Native Soil Conditions
Simulation Number
1
Native Soil Dry
Material Silty Sand
Total Porosity
Air-Filled
Porosity
Water-Filled
Porosity
Saturation
Water Content
Vapor Diffusion
Tortuosity
0.20
0.14
0.06
0.30
3%
0.25
2
Moist
Silty Sand
0.20
0.10
0.10
0.50
4%
0.12
3
Hoist
Sand
0.30
0.11
0.19
0.63
8%
0.07
4
Wet
Silty Sand
0.20
0.05
0.15
0.75
6%
0.02
5
Wet
Sand
0.40
0.10
0.30
0.75
12%
0.03
6
Wet
Clay
0.45
0.07
0.38
0.84
15%
0.01
7
Dry
Silty Sand
0.20
0.14
0.06
0.30
3%
0.25
Effective Diffusion
Coeficient
(on2 /Sec)
0.017
0.008
0.005
0.0015
0.002
0.0008
0.017
Effective Diffusion
Coefficient
Surface
Condition
0.065
PAVED
0.031
PAVED
0.020
PAVED
0.006
PAVED
0.008
PAVED
0.003
PAVED
0.065
OPEN
-------
APPENDIX L
MODFLQW VERIFICATION
This appendix presents the results of a simulation performed with MODFLOW,
a computer program from the U.S. Geological Survey (McDonald and Harbaugh,
1984) that simulates three-dimensional groundwater flow. The purpose of
this exercise was to reproduce simulation results produced by DYNFLOW with
a groundwater flow program that is widely used throughout this country.
MODFLOW is a modular, three-dimensional, finite difference flow program
developed at the U.S.G.S. It uses a block-centered finite difference
scheme, with solution by a strongly implicit procedure.
Physical dimensions of the MODFLOW diffusion model were the same as those
used for the DYNFLOW diffusion model. The model was 44' wide, 10' long,
and 24' deep. The tank dimensions were 12' by 6', surrounded by 2' of
backfill. Half of the tank, backfill, and surrounding soils were simulated
to reduce computational cost and time. This slicing was performed along
the longitudinal symmetry axis through the tank.
Boundary conditions of the model were no-flow on the top, bottom, and
sides. The tank sides were also treated as no-flow boundaries.
It was assumed that there was no background concentration within the
system. Once the leak was initiated, a constant concentration node
represented a constant source over time of vaporizing product. This point
source was placed at the bottom of one end of the tank.
The diffusion properties of the native soil and backfill used in the
DYNFLOW and MODFLOW simulations were 0.1348 ft2/hr and 0.038 ft2/hr,
respectively. Simulations were performed with 4 time steps of 6 hours
each, for a total simulation period of 24 hours.
L-l
-------
Simulation results from DYNFLOW and MODFLOW were compared by plotting
concentration-distance profiles. ..These concentration profiles were drawn
for the two simulation times: 6 and 24 hours. Figures L-l and L-2 are
horizontal distance-concentration profiles drawn from the point source away
from the tank, along the symmetry boundary, at a depth of 8 feet. A second
profile was taken vertically through the entire thickness of the model, one
foot away from the source, and the results plotted as Figures L-3 and L-4.
These profiles show close agreement between the results produced by DYNFLOW
and MODFLOW. Generally, however, DYNFLOW produced slightly higher
concentration values than MODFLOW, especially near the source. This minor
discrepancy is probably due to differences in the grid set-up, geometric
specification of the leak, and model interpolation procedures.
The rate of mass influx entering the system was simulated by both DYNFLOW
and MODFLOW for each simulation time step. These mass influxes, plotted in
Figure L-5, show fairly close agreement. MODFLOW, however, consistently
produced about 5 percent more mass influx than DYNFLOW. This discrepancy
is probably due to the difference in source geometry. In DYNFLOW, the
point source was at the edge of the simulated tank. In MODFLOW, the leak
4
was at the center of a 1 foot cubic "block" embedded in the tank.
Both models produced similar results, with minor differences due to the
slight differences in numerical approximations. Closer agreement could
have been reached by adjusting the MODFLOW source geometry to put the
simulated leak at the edge of the UST; however, this was determined to be
beyond the objectives of the MODFLOW-DYNFLOW comparison.
Another observation is that representation of the UST and the leakage
source was easier to accomplish, and much smoother geometrically, with
DYNFLOW than with MODFLOW. The leak was placed exactly at the edge of the
UST in the DYNFLOW model; whereas, with MODFLOW, the leak had to be
embedded in the tank. A node point-oriented application of MODFLOW could
have alleviated this problem. With respect to tank geometry, MODFLOW could
only produce a jagged, "blocked" approximation of a circle. The DYNFLOW
L-2
-------
model, even though it was at the same 1 foot spacing, had triangular edges
that simulated the cylinder much more closely, especially at the bottom of
the tank where the leak was simulated.
Finally, note that the time-stepping scheme in MODFLOW uses an implicit
technique with lumped storage, whereas DYNFLOW uses a Crank-Nicholson
(trapezoidal) technique with proportional storage. Given the relatively
small time steps, the differences here are probably small relative to the
differences caused by the source and tank representation, in any event,
these differences cannot be readily separated from the others.
In conclusion, it is clear that either program could be used to address
this problem. For the given application, however, the DYNFLOW results are
considered to be more defensible.
L-3
-------
-------
APPENDIX M
c
DYNFLOW COMMAND FILES
This Appendix contains listings of the command files used to make the
simulation runs described in Appendix K. The simulation runs were made
using the "iterative solver" version of DYNFLOW Release 4.0, called
"DYNFLOW4B."
Not presented herein are the contents of the computer file ("KEEP.SAV")
containing the specifications of grid information and lateral boundary
conditions for the simulations. Sufficient infonnation is provided in the
body of this report. Also, listings of lateral boundary conditions and
grid information are stored and available in CDM's project files.
M-l
-------
-------
I
REST. , KEEP.SAV
TITLE
RUN #1 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY
RUN1.LOG AS OUTPUT; RUNl.CFI, KEEP.SAV AS INPUT
100% SOURCE AT LEVEL7 NODE 61. UNITS ARE IN FEET AND HOURS.
! BACKFILL
PROP
2, 0.065, 0.065, 0.065, 1.0, 0.0, 0.0,
I NATIVE SOIL f
PROP
1, 0.065, 0.065, 0.065, 1.0, 0.0, 0.0,
INIT 0.0
INIT 100. LEVELSING 7 NODE SING 61
FIX LEVELSING 7 NODE SING 61
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168.
24.
252.
24.
336.
24.
420.
24.
504.
24.
588.
24.
672.
R1D01.SAV
R1D03.SAV
R1D07.SAV
R1D10.SAV
R1D14.SAV
R1D17.SAV
R1D21.SAV
R1D24.SAV
R1D28.SAV
-------
c
REST .
TITLE'
RUN #2 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY .
RUN2.LOG AS OUTPUT; RUN2.CFI, KEEP.SAV AS INPUT
100% SOURCE AT LEVEL7 NODE 61. UNITS ARE IN FEET AND HOURS.
1
I BACKFILL
PROP
2, 0.065, 0.065, 0.065, 1.0, 0.0, 0.0,
1 NATIVE SOIL
PROP .
1, 0.031, 0.031, 0.031, 1.0, 0.0, 0.0,
I
INIT 0.0
INIT 100. LEVELSING 7 NODE SING 61
FIX LEVELSING 7 NODE SING 61
KEEP.SAV
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168.
24.
252,
24.
336,
24.
420,
24.
504
24.
588
24.
672
R2D01.SAV
R2D03.SAV
R2D07.SAV
R2D10.SAV
R2D14.SAV
R2D17.SAV
R2D21.SAV
R2D24.SAV
R2D28.SAV
-------
REST KEEP.SAV
TITLE
RUN #3 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY
RUNS.LOG AS OUTPUT; RUN3.CFI, KEEP.SAV AS INPUT
100% SOURCE AT LEVEL? NODE 61. UNITS ARE IN FEET AND HOURS.
1
! BACKFILL
PROP
2, 0.02, 0.02, 0.02,
I NATIVE SOIL
PROP .
1, 0.02, 0.02, 0.02,
1.0, 0.0, 0.0,
1.0, 0.0, 0.0,
INIT
INIT
FIX
1
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
0.0
100.
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168
24.
252
24.
336
24.
420
24.
504
24.
588
24.
672
LEVELSING 7 NODE SING 61
LEVELSING 7 NODE SING 61
R3D01.SAV
R3D03.SAV
R3D07.SAV
R3D10.SAV
R3D14.SAV
R3D17.SAV
R3D21.SAV
R3D24.SAV
R3D28.SAV
-------
C
REST KEEP.SAV
TITLE
RUN #4 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY .-
RUN4.LOG AS OUTPUT; RUN4.CFI, KEEP.SAV AS INPUT
100% SOURCE: AT LEVEL? NODE 61. UNITS ARE IN FEET AND HOURS.
i
! BACKFILL
PROP
2, 0.02, 0.02, 0.02, 1.0, 0.0, 0.0,
I NATIVE: SOIL
PROP-
1, 0.006, 0.006, 0.006, 1.0, 0.0, 0.0,
I
INIT 0.0
INIT 100. LEVELSING 7 NODE SING 61
FIX LEVELSING 7 NODE SING 61
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168.
24.
252.
24.
336,
24.
420.
24.
504.
24.
588.
24.
672.
R4D01.SAV
R4D03.SAV
R4D07.SAV
R4D10.SAV
R4D14.SAV
R4D17.SAV
R4D21.SAV
R4D24.SAV
R4D28.SAV
-------
KEEP.SAV
MV-ANLY
UNITS ARE IN FEET AND HOURS.
REST
TITLE :
RUN #5 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104
RUN5.LOG AS OUTPUT; RUN5.CFI, KEEP.SAV AS INPUT
100% SOURCE AT LEVEL? NODE 61
1
1 BACKFILL
PROP
2, .008, .008, .008, 1.0, 0.0, 0.0,
j NATIVE SOIL
PROP.
1, .008, .008, .008, 1.0, 0.0, 0.0,
I
INIT 0.0
INIT 100.
FIX
1
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168,
24.
252
24.
336
24.
420
24.
504
24.
588
24.
672
LEVELLING
LEVELSING
7
7
NODE SING
NODE SING
61
61
R5D01.SAV
R5D03.SAV
R5D07.SAV
R5D10.SAV
R5D14.SAV
R5D17.SAV
R5D21.SAV
R5D24.SAV
R5D28.SAV
-------
REST
Tl'l'iiF
RUN #6 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY
RUN6.LOG AS OUTPUT; RUN6.CFI, KEEP.SAV AS INPUT
100% SOURCE AT LEVEL7 NODE 61. UNITS ARE IN FEET AND HOURS.
1
1 BACKFILL
PROP
2, 0.008, 0.008, 0.008, 1.0, 0.0, 0.0,
I NATIVE SOIL
PROP.
1, 6.003, 0.003, 0.003, 1.0, 0.0, 0.0,
1
INIT 0.0
INIT 100. LEVELSING 7 NODE SING 61
PIX LEVELSING 7 NODE SING 61
I
ITER 1.
DT 1. :
GOTIL 6.
DT 3.
GOTIL 12.
DT 6.
GOTIL 24.
SAVE
KEEP.SAV
DT 6.
GOTIL 84.
SAVE
DT 6.
GOTIL 168.
SAVE
DT 24.
GOTIL 252.
SAVE
DT 24.
GOTIL 336.
SAVE
DT 24.
GOTIL 420.
SAVE
DT 24.
GOTIL 504.
SAVE
DT 24.
GOTIL 588.
SAVE
DT 24.
GOTIL 672.
SAVE
XCFI
R6D01.SAV
R6D03.SAV
R6D07.SAV
R6D10.SAV
R6D14.SAV
R6D17.SAV
R6D21.SAV
R6D24.SAV
R6D28.SAV
-------
REST KEEP.SAV
TITLE.
RUN #7 FROM FINAL REPORT 2/88, UST W.A. 1-4, 7400-104-MV-ANLY
RUN7.LOG AS OUTPUT; RUN7.CFI, KEEP.SAV AS INPUT :
100% SOURCE AT LEVEL7 NODE 61. UNITS ARE IN FEET AND HOURS.
I
! BACKFILL
PROP
2, 0.065, 0.065, 0.065, 1.0, 0.0, 0.0,
1 NATIVE SOIL
PROP
1, 0.065, 0.065, 0.065, 1.0, 0.0, 0.0,
1
INIT 0.0
INIT 100. LEVELSING 7 NODE SING 61
FIX LEVELSING 7 NODE SING 61
FIX LEVELSING 15 NODE ALL
ITER
DT
GOTIL
DT
GOTIL
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
DT
GOTIL
SAVE
XCFI
1.
1.
6.
3.
12.
6.
24.
6.
84.
6.
168
24.
252
24.
336
24.
420
24.
504
24.
588
24.
672
R7D01.SAV
R7D03.SAV
R7D07.SAV
R7D10.SAV
R7D14.SAV
R7D17.SAV
R7D21.SAV
R7D24.SAV
R7D28.SAV
-------
-------
APPENDIX N
TABULAR DYNFLOW RESULTS :
This Appendix contains tables of DYNFLOW simulation results for the
scenarios that were described in Appendix K. Presented are concentration
time histories and vapor influx time histories. All results are in terms
of "100 per cent" equilibrium vapor concentration at the leakage source,
and they can therefore be transformed into estimated concentrations and
leak volumes according to the methods and equations described in the report
and in Appendix G.
List of Tables
Table Description
N-l Concentration Time Histories, Simulation Run Number 1
N-2 Concentration Time Histories, Simulation Run Number 2
N-3 Concentration Time Histories, Simulation Run Number 3
N-4 Concentration Time Histories, Simulation Run Number 4
N-5 Concentration Time Histories, Simulation Run Number 5
N-6 Concentration Time Histories, Simulation Run Number 6
N-7 Concentration Time histories, Simulation Run Number 7
N-8 Vapor influx Time Histories for All Simulation Runs 8
N-l
-------
-------
TABLE N-l
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 1
DYNFLOW Concentrations Expressed as Percent of Source Concentration
.
: - -
\ - 5.314 0.010 o. o n n
7 iHS °'355 °-372 Si ' '
1^11 <* A J ^ *"* y 0
2.311 2.040 0.801 Q.
?:609 L-M! !:gj :». «:jg
-------
TABLE N-2
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 2
DYNFLOW Concentrations Expressed as Percent of Source Concentration
Simulation Nearby Sensors Intermediate Sensors Distant Sensors
Day peep Shallow Deep Shallow Deep Shallow
jl tt2 13 14 15 t6
1 5.405 0.001 0.002 0. '' 0. . 0.
3 5 10.141 0.364 0.382 0.010 0.001 0.
7 12.557 1.046 1.124 0.133 0.013 0.001
10.5 13.812 1.687 1.747 0.362 0.053 0.009
14 14.623 2.221 2.217 0.588 0.105 0.032
17 5 15.183 2.701 2.603 0.842 0.172 0.072
21* 15.601 3.091 2.922 1.084 0.243 0.121
24.5 15.961 3.485 3.191 1.349 0.322 0.198
28 16.248 3,809 3.425 1.576 . 0.398 0.274
-------
TABLE N-3
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 3
DYNFLOW Concentrations Expressed as Percent of Source Concentration
Simulation Nearby Sensors Intermediate Sensors Distant Sensors
_Deep_ !^ - 15eip- SHJII5*
__ - ep S "Deep-
* ff 3 tt4 |5
SII5*
1 I-7-99 0. o. 0.' o n
3-5 5.550 0.008 0.001 0. o' o
7 7.766 0.121 0.112 0.001 5! 0
10-5 8.935 0.308 0.307 0.008 0. 0
" , 5.J73 0.503 0.508 0.028 0.002 0
J7-5 1J.136 0.671 0.689 0.058 0.004 0
21 10.530 0.841 0.862 0.099 0.009
o '027 °-151 0.018 '0.002
28 H-095 1.181 1.165 0.202 0.029 0 004
-------
TABLE N-4
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 4
DYNFLOW Concentrations Expressed as Percent of Source Concentration
Simulation Nearby Sensors Intermediate Sensors Distant Sensors
Day Deep Shallow - Deep Shallow Deep Shallow
"IT" tt2 ~IT" 14 -=i5c- #6
1 1.804 0. 0. 0. " 0. 0.
3.5 5.708 0.008 0.003 0. 0. 0.
7 8.544 0.105 0.103 0. 0. 0.
10.5 10.308 0.277 0.306 0.009 0. 0.
14 11.558 0.519 0.559 0.030 0.001 0.
17.5 12.492 0.724 0.800 0.059 0.004 0.
21 13.252 0.986 1.078 0.111 0.010 0.001
24.5 13.874 1.231 1.345 0.174 0.019 0.002
28 14.384 1.454 1.575 0.245 0.029 0.004
-------
TABLE N-5
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 5
DYNFLCW Concentrations Expressed as Percent of Source Concentration
SimLation Nearby Sensors Intermediate Sensors Distant Sensors
_peep_IJiXIaf . -peep"sHillo* -pe"
*± ff* #3 p 1
! °-263 o. o. o. o o
3.5 2.677 0. 0. 0. 0 0*
7 4.817 0.001 0. 0. 0 n
10-5 6.161 0.023 0.011 0. 0 0
14 7.081 0.063 0.052 0. 0.° 0
J7-5 7-774 0.124 0.110 0.005 0 0*
21 8-310 0.189 0.187 0.002 0 0*
24.5 8.746 0.267 0.264 0.006 0 0
28 9.110 0.344 0.348 0.011 0 0
-------
TABLE N-6
TIME HISTORY OF SIHULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 6
DYNFLOW Concentrations Expressed as Percent of Source Concentration
Simulation Nearby Sensors Intermediate Sensors Distant Sensors
Dajf Deep Shallow . Deep Shallow ' ~oiip Shallow
*1 *2 ~1T~ tt4 fir- |6
1 0.267 0. 0. 0. 0. 0
3-5 2.682 0. 0.001 0. 0. 0*
7 4.884 0.001 0. 0. 0. 0
10.5 6.387 0.019 0.011 0. 0. 0
14 7.530 0.056 0.047 0. 0 o'
17.5 8.439 0.108 0.104 0. 0. 0*
21 e 9-186 0.177 0.177 0.002 0. 0*
24.5 9.818 0.251 0.259 0.005 0. 0
28 10.358 0.331 0.355 0.010 0. 0*
-------
TABLE N-7
TIME HISTORY OF SIMULATED VAPOR CONCENTRATIONS FOR RUN NUMBER 7
DYNFLOW Concentrations Expressed as Percent of Source Concentration
Nearby Sensors Integrate Sensors Distant Sensors
#6
5.14 0.009 0.001 0.001 o. o
°'335 0-372 0.010 0 o
a-s
I' i I 1 1
-------
TflBLE N-8 '
TUe-Histories of DYNFLOH - Simulated Vapor Fluxes
Siiulation
Days
0.04
O.OB
0.13
0.17
0.21
0.25
0.38
0.50
0.75
1.00
1.25
1.50
1.75
2.00
2.25
2.50
2.75
3.00
3.25
3.50
3.75
4.00
4.25
4.50
4.75
5.00
5.25
5.50
5.75
6.00
6.25
RUN 1
17.594
16.229
15.630
15.237
14.952
14.750
14.313
14.033
13.689
13.473
13.320
13.205
13.174
13.081
13.101
11034
12.982
12.935
12.817
12.961
12.929
12.BB7
12.851
12.691
12.789
12.654
12.751
12.615
12.658
12.655
12.640
Inflow
RUN 2
18.495
16.658
16.100
15.616
15.302
15.008
14.485
14.151
13.756
13.484
13.311
13.168
13.043
12.938
12.883
12.806
12.808
12.744
12.688
12.637
12.590
12.489
12.580
12.551
12.509
12.471
12.437
12.406
12.321
12.281
12.263
at Leak
RUN 3
6.121
5.878
5.705
5.473
5.337
5.229
4.986
4.858
4.643
4.523
4.449
4.386
4.239
4.301
4.266
4.22B
4.204
4.182
4.163
4.159
4.142
4.127
4.103
4.091
4.080
4.084
4.074
4.064
4.055
4.043
4.036
leu. «/hr)
RUN 4 RU
6.119 2
5.862 2
5.687 2
5.473 2
5.339 2
5.232 2
4.981 2
4.841 2
4.640 2
4.518 1
4.444 1
4.378
4.326
4.282
4.241
4.210
4.182
4.157
4.134
4.114
4.095
4.089
4.072
4.056
4.042
4.024
4.013
3.994
3.983
3.972
3.962
N 5
.524
.550
.491
.436
.353
.311
.232
.144
.053
.988
.937
.903
.874
.650
.842
.624
.808
.795
.782
.765
.756
.747
.739
.732
.725
.719
.718
.712
.707
.702
.697
RUN6
2.522
2.545
2.487
2.433
2.352
2.309
2.226
2.156
2.046
1.981
1.936
1.900
1.880
1.859
1.838
1.820
1.805
1.791
1.779
1.76B
1.751
1.742
1.734
1.727
1.720
1.713
1.715
1.70B
1.703
1.697
1.692
RUN 7 (
18.505
16.660
16.123
15.627
15.333
15.061
14.494
14.160
13.620
13.552
13.387
13.286
13.174
13.080
13.101
13.034
12.982
12.935
12.817
12.961
12.928
12.887
12.851
12.691
12.789
12.654
12.751
12.616
12.658
12.655
12.640
Outflow
through
surface
cu. ft/hr)
-0.001
-0.001
-0.001
-0.001
-0.001
-0.001
-0.003
-0.008
-0.007
-0.009
-0.009
-0.016
-0.028
-0.030
-0.053
-0.074
-0.104
-0.137
-0.170
-0.204
-0.235
-0.282
-0.331
-0.380
-0.446
-0.473
-0.547
-0.576
-0.661
-0.736
-0.815
-------
TABLE N-8 (continued)
Tm-Hi stories of DYNFLOH - Simulated Vapor Fluxes
Simulation
Days
6.50
6.75
7.00
8.00
9.00
10.00
10.50
11.50
12.50
13.50
14.00
15.00
16.00
17.00
17.50
18. SO
19.50
20.50
21.00
22.00
23.00
24.00
24.50
25.50
26.50
27.50
28.00
RUN 1
12.636
12.623
12.613
12.548
12.473
12.481
12.633
12.442
12.394
12.385
12.351
12.480
12.337
12.315
12.310
S2.308
12.299
12.302
12.302
12.290
12.280
12.282
12.285
12.272
12.263
12.263
12.266
InfloN
RUN 2
12.243
12.225
12.182
'12.167
12.091
12.048
12.060
11.982
11.955
11.924
12.041
11.881
11.847
11.819
11.829
11.792
11.780
11.756
11.763
11.719
11.694
11.688
11.693
11.668
11.646
11.642
11.647
it Leak
RUN 3
4.038
4.032
4.028
3.999
3.979
3.967
3.975
3.935
3.923
3.962
3.947
3.899
3.894
3.888
3.917
3.879
3.874
3.921
3.902
3.916
3.907
3.899
3.875
3.856
3.854
3.854
3.858
(cu. ft/hr)
RUN 4 Rl
3.952
3.943
3.934
3.917
3.8BB
3.862
3.872
3.829
3.809
3.805
3.794
3.772
3.759
3.745
3.758
3.730
3.752
3.743 1
3.729 1
3.724
3.720
3.710
3.724
3.696
3.689
3.665
3.686 1
JN 5
.693
.688
.684
.672
.661
.646
.647
.643
.636
.629
.623
.614
.609
.605
.613
.609
.606
.602
.621
.591
.595
.586
.607
.589
.588
.583
.600
RUN6
1.687
1.683
1.679
1.656
1.644
1.637
1.632
1.623
1,614
1.607
1.605
1.592
1.586
1.587
1.584
1.579
1.573
1.567
1.568
1.561
1.557
1.553
1.561
1.555
1.552
1.549
1.571
RUN 7
12.636
12.623
12.614
12.549
12.473
12.769
12.462
12.422
12.425
12.413
12.425
12.406
12.383
12.390
12.389
12.376
12.354
12.361
12.361
12.349
12.329
12.336
12.336
12.326
12.307
12.314
12.313
OutfloM
through
surface
(cu. ft/hr)
-0.8B7
-0.958
- .027
- .197
- .347
- .583
- .721
-2.111
-2.299
-2.484
-2.532
-2.660
-2.841
-2.939
-2.984
-3.071
-3.212
-3.293
-3.325
-3.396
-3.508
-3.576
-3.602
-3.659
-3.753
-3.811
-3.833
-------
------- |