WALL PAINT EXPOSURE MODEL (WPEM):
Version 3.2
USER'S GUIDE
Wall Paint Exposure Model (WPEM)
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Designing Wall Paint for the Indoor Environment
introduction j| Painting Scenario | Paint a Chemical | Occupancy & Exposure Execution |
Wall Paint Exposure Model
(WPEM)
This model has been developed as a MS Windows Application. It estimates an individual's inhalation
exposure to a chemical in latex or alkyd wall paint, during and after the time when a building is painted.
Various default values are provided, as well as help through ? buttons, to assist the user in providing
model inputs.
IMPORTANT INFORMATION ON MODEL LIMITATIONS I
Developed for:
The Designing Wall Paint for the Indoor Environment Project
Under EPA's Office of Pollution Prevention and Toxics (OPPT)
In Partnership With
National Paint and Coatings Associations (NPCfl)
By:
GEOMET Technologies, Inc. (A Division ofVersar, Inc.)
Office of Pollution Prevention and Toxics
Economics, Exposure and Technology Division
www.epa .gov/oppti ntr/exposure/docsAvpem .hitm
Developed by
GEOMET Technologies, Inc. (a Division ofVersar, Inc.)
Germantown, MD
for
USEPA Office of Pollution Prevention and Toxics
Washington, DC
and
National Paint and Coatings Association
Washington, DC
March 2001
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DISCLAIMER
This document has been reviewed in accordance with U.S. Environmental Protection
Agency policy and approved for publication. Mention of trade names or commercial products
does not constitute endorsement or recommendation for use.
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ACKNOWLEDGMENTS
This report was prepared by GEOMET Technologies, Inc. (a division of Versar, Inc.) for the
Economics, Exposure and Technology Division of EPA's Office of Pollution Prevention and Toxics
under EPA Contract No. 68-W6-0023 (Work Assignment Nos. 1-22, 2-15, and 3-4) and EPA
Contract No. 68-W-99-041 (Work Assignment Nos. 1-3 and 2-9). The EPA Work Assignment
Manager was Christina Cinalli. Her support and guidance are gratefully acknowledged.
The primary author of the report is Michael Koontz of GEOMET, who also developed the
overall design for the WPEM software. The following Versar and GEOMET personnel have
contributed to this project over the period of performance:
Work Assignment Management - Greg Schweer, Versar
Software Development - Gene Cole, GEOMET
Keith Drewes, Versar
Charles Wilkes, Wilkes Technologies, Inc.
Analysis/Graphics Support -
Laura Niang, GEOMET
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TABLE OF CONTENTS
Section Page
1. BACKGROUND AND OVERVIEW 1 -1
1.1 Proj ect Background 1-1
1.2 Model Overview 1-2
1.3 Model Purpose and Limitations 1-4
2. INPUT SCREENS 2-1
2.1 Painting Scenario Screen 2-1
2.2 Paint & Chemical Screen 2-7
2.3 Occupancy & Exposure Screen 2-16
2.4 Execution Screen 2-24
2.5 Summary of Model Inputs 2-28
3. MODEL RESULTS AND OUTPUTS 3-1
3.1 Exposure Estimates 3-1
3.2 Report 3-3
3.3 Concentration Time Series 3-3
4. DEFAULT SCENARIOS AND APPLICATION TIPS 4-1
4.1 Default Scenarios 4-1
4.2 Exposure Descriptors 4-3
4.3 Some Application Tips 4-9
5. REFERENCES 5-1
Appendix A — Alkyd Paint Chamber Tests
Appendix B — Paper on Emissions Model for Alkyd Paints
Appendix C — Latex Paint Chamber Tests
Appendix D — Paper on Emissions Model for Latex Paint
Appendix E — Model Evaluation Using Data from EPA Research House
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1.
BACKGROUND AND OVERVIEW
1.1 Project Background
The U.S. Environmental Protection Agency's Office of Pollution Prevention and Toxics
(OPPT) has initiated a Design for the Environment (DfE) Project intended to develop a wall paint
exposure assessment model for interior latex and alkyd paints. The EPA is working with the
National Paints and Coatings Association (NPCA), in addition to paint manufacturers and
chemical suppliers, to develop this model. The purpose of the planned model is to allow industry
product developers and health and safety officials to more easily and accurately identify chemicals
in paint formulations that may pose potential exposure problems. It is envisioned that
identification and/or evaluation of potentially problematic chemicals will be done by individual
paint manufacturers and chemical suppliers during the design stage of paint development and/or
during a product-stewardship effort to fully assess a current line of products.
The EPA has selected latex and alkyd wall paints to evaluate as sources of chemicals
emitted into indoor air because of the relatively large number of people exposed and the fact that,
as a wet product, paint emissions (and thereby exposures) could be relatively high when compared
to dry products. The EPA believes that data generated from small-chamber testing translates
well, when an appropriate indoor-air model is used, into exposure estimates. If a suitable
exposure model were to be made available, then it would be relatively easy (compared to a field
study) to quantitatively assess exposures to one or more chemicals in paint.
Under the DfE project, EPA established a working group to guide additional data
collection and development of a wall paint exposure assessment model. The joint
government/industry working group identified the data and capabilities needed for the exposure
model. Although fairly extensive testing has been done in recent years by the EPA Office of
Research and Development's Air Pollution and Prevention Control Division (APPCD) to
characterize emissions from latex and alkyd paints through chamber tests, additional data were
deemed necessary to (1) cover a broader sample of paints and associated chemicals, and (2) better
characterize the behavior of potential indoor sinks such as carpeting and wallboard. In addition,
experiments were carried out at EPA's research house in North Carolina to obtain concentration
data from "real-world" painting events under carefully controlled and well-documented
conditions, for purposes of model evaluation. The data described above were collected by
ARCADIS Geraghty & Miller, Inc. Methods for and results of the data collection have been
documented in a recent report (ARCADIS 1998).
This document summarizes the model, called the Wall Paint Exposure Model (WPEM),
that has been developed under the Wall Paint DfE project. The remainder of this section provides
an overview of the model's general features and input requirements, and the model's purpose and
limitations. Subsequent sections provide further details on input screens, model outputs, and
default scenarios provided with the model, along with a summary of the emission models used in
WPEM. The appendices describe procedures and results for chamber emission and sink tests,
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development of emission models that are used in WPEM, and procedures for and results of model
evaluation.
1.2 Model Overview
WPEM has been developed as a Windows 95/98 application. As noted in the Introduction
Screen for the model (Figure 1-1), it estimates an individual's inhalation exposure to airborne
concentrations of a chemical released from latex or alkyd primer/paint, during and after the time
when a building (residence, office, or standard box) is painted. The model requires certain
information from the user in order to provide these estimates. User inputs are gathered in an
organized manner through a series of input screens called Painting Scenario, Paint & Chemical,
and Occupancy & Exposure (see the tabs in Figure 1-1). Once these inputs have been provided,
model calculations can be invoked through the Execution screen.
The following are the major types of information to be provided on each screen:
Painting Scenario screen
- building volume and airflow rates
- percent of building painted
- whether walls, ceilings, or both are painted
- amount of paint used, painting rate, and resultant painting duration
Paint & Chemical screen
- type of paint and primer/paint density
- properties of the chemical to be modeled, weight fraction in the primer/paint
- chemical emissions model for primer and paint
- indoor sink model (optional)
Occupancy & Exposure screen
- type/gender of exposed individual
- individual's location and breathing rate during the painting event
- weekday and weekend activity patterns (locations, breathing rates)
- number of painting events in lifetime
- length of lifetime and body weight
• Execution screen
- title of run and length of model run
- results (exposure estimates) after execution
- option to view/print a report summarizing inputs and outputs
The user is advised to proceed through these screens sequentially. Efforts have been made
to provide model defaults wherever possible, and to make certain calculations on behalf of the
user. Within each screen, areas where user inputs are required are shown in white. For example,
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on the Painting Scenario screen the user must choose a residence, office building, or "standard
box," and must indicate the number of coats applied for the primer and/or paint. Areas where
user inputs are optional are shown in gray. For such areas, edit buttons enable the user to
override default values that have been provided or calculated by the model. For example, on the
Painting Scenario screen there is a default coverage of 400 square feet per gallon (equating to a
wet film thickness of 4 mil) for paint, but the user can override this value. Six default scenarios
are provided with the WPEM software and can be accessed from the "File" "Open" toolbar in
WPEM.
I Wall Paint Exposure Model (WPEM)
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Designing Wall Paint for the Indoor Environment
Introduction \ Painting Scenario Paint & Chemical [ Occupancy & Exposure Execution )
Wall Paint Exposure Model
(WPEM)
This model has been developed as a MS Windows Application. It estimates an individual's inhalation
exposure to a chemical in latex or alkyd wall paint, during arid after the time when a building is painted.
Various default values are provided, as well as help through ? buttons, to assist the user in providing
model inputs.
IMPORTANT INFORMATION ON MODEL L IMITATIONS I
Developed for:
The Designing Wall Paint for the Indoor Environment Project
Under EPA's Office of Pollution Prevention and Toxics (OPPT)
In Partnership With
National Paint and Coatings Associations (NPCA)
By:
GEOMET Technologies, Inc. (A Division of Versar, Inc.)
Office of Pollution Prevention and Toxics
Economics, Exposure and Technology Division
www.epa .gov/oppti ntr/exposure/docsAvpern .htrn
Figure 1-1. WPEM Introduction Screen.
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Context-sensitive help for WPEM is provided through ? buttons. Each ? button is located
near the input area to which it pertains. These buttons generally provide guidance for editing
default selections or values provided with the model. In some cases, they also describe the basis
for a default value or the algorithm used by WPEM to calculate the value.
In addition, the following buttons provide background information on specific topic areas:
IMPORTANT INFORMATION ON MODEL LIMITATIONS, located on the
Introduction screen;
DESCRIPTION OF DEFAULT SCENARIOS, located on the Painting Scenario
screen;
DISPLAY CHEMICALS USED TO DEVELOP EMISSION MODELS, located
on the Paint & Chemical screen; and
• MODEL LIMITATIONS, located on the Execution screen.
1.3 Model Purpose and Limitations
As noted in Section 1.1, the primary purpose of the model is to allow industry product
developers and health and safety officials to more easily and accurately identify chemicals in paint
formulations that may pose potential exposure problems. Once the user has provided model
inputs as summarized in Section 1.2 and has executed the model, the resulting outputs can be
used to assess inhalation exposure and associated risk for a chemical that is currently formulated,
or is being considered for formulation, in primer and/or paint. The model provides both short-
term and long-term exposure measures. Short-term measures include the highest instantaneous,
15-minute-average, and 8-hour-average airborne concentration to which an individual is exposed,
under the conditions represented by model inputs. Long-term measures include lifetime average
daily dose (LADD) and lifetime average daily concentration (LADC).
The IMPORTANT INFORMATION ON MODEL LIMITATIONS button on the
Introduction screen (see Figure 1-1) describes some cautions to be considered when using the
model. For example, the model is designed to estimate indoor-air concentrations and associated
inhalation exposures for interior applications involving alkyd or latex primer/paint. The emission
algorithms used in the model, and their relationship to chemical properties, are based on chamber
tests specific to interior paints. At present there is no basis for applying these algorithms to other
types of products.
The model calculations are intended to represent the time series of indoor concentrations
for a chemical, and exposure measures derived from those concentrations, that can be expected
when primer or paint is applied in an indoor environment. Although these calculations are based
on fundamental principles such as the conservation of chemical mass indoors, there are certain
assumptions and/or limitations inherent in the model:
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The emission and sink models used in WPEM are derived from a limited number of
small-chamber tests, conducted at a fixed air exchange rate, a fixed loading of
wallboard, and a fixed product application rate for one type of application (roller).
A single-chamber model is used when an entire building is painted; when part of a
building is painted, a two-chamber model (painted and unpainted parts) is used.
Within the modeled compartment(s), uniform mixing is assumed; no distinction is
made between airborne chemical concentrations in the applicator's breathing zone
versus elsewhere in the compartment where paint is applied.
Only one chemical can be modeled at a time; within a model run, it is not possible
to combine different primer/paint types (e.g., alkyd primer and latex paint), but
such a combination can be modeled through separate model runs (see Section 4).
The indoor-outdoor air exchange rate is treated as a constant (i.e., it cannot vary
over time). Model defaults for the air exchange rate assume a closed-building
condition, as supporting data for other conditions (e.g., windows open or exhaust
fans on) are limited.
Dose estimates provided by the model are measures of potential inhaled dose (i.e.,
100 percent uptake is assumed).
The model has no capability for Monte Carlo simulation as a means of addressing
uncertainty, but another model (MCCEM) developed for OPPT has this capability.
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2. INPUT SCREENS
2.1 Painting Scenario Screen
This screen (Figure 2-1) is designed to obtain user inputs on (1) the type of building and
the percent of building painted, (2) the building volume and airflow rates, and (3) the painted
surface area, amount of paint used, and painting duration.
HI Wall Paint Exposure Model (WPEM)
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Designing Wall Paint for the Indoor Environment
9
Introduction j Painting Scenario j Paint & Chemical | Occupancy & Exposure | Execution |
DESCRIPTIONS OF DEFAULT SCENARIOS (To access a default scenario, go to "File", "Open", and then select a .wem file from the list)
Painted Building (choose 1)
Residence: (* House C Apartment
Office Building: C High-rise C Low-rise
Other: c Standard Box
i—BUILDING VOLUME—
15,583.0 | K"
f" Entire Building (* One Bedroom
AIR EXCHANGE RATE
(Between Indoors and Outdoors)
[ ' Q 451 air changes^hr
Edit Volume
?|
Edit % Painted |
1
?|
Edit Airflows
Jj
Painted Surface and Number of Coats-
(* Walls only
C Ceilings only
C Walls and ceiling
Edit Painted Surface Area |
?|
Apply
1 coats of primer
Painted Surface Area
Edit Amount of Paint j
jJ
Apply
1 coats of pai nt
] 451.91 | ftI
Edit Painting Duration |
Figure 2-1. Painting Scenario Screen.
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Required and optional user inputs for this screen are summarized in Table 2-1. As noted
in Section 1, required inputs are indicated in white whereas optional inputs are indicated in gray.
Although defaults are provided for the required inputs, these may not be appropriate for the
scenario that the user wishes to model. For the optional inputs, the model always provides or
calculates values, but the user is free to override these values through edit buttons that typically
are located to the right of corresponding input areas.
Table 2-1. Required and Optional Inputs for Painting Scenario Screen
Required Inputs
Optional Inputs
Building Type/Volume
Choose residence (house or
apartment), office building (high-
rise or low-rise), or standard box
Edit building volume
Painted Space
Choose entire building/floor or
part of building/floor
Edit percent painted
Airflow Rates
—
Edit air exchange rate and
interzonal airflow rate
Painted Surface
Choose walls, ceilings, or both
Edit wall/ceiling loading ratio
Amount of Paint
Specify number of coats for
primer and paint
Edit primer/paint coverage
Painting Duration
—
Edit number of painters,
primer/paint application rate,
daily work hours, and start day
2.1.1 Input Sequence and Options
A button near the top of the Painting Scenario screen, labeled DEFAULT SCENARIOS,
lists default scenarios that can be accessed by the user. Descriptions of these scenarios and how
to access them are provided in Section 4 of this guide.
If a default scenario is not chosen, then the first step on this screen is to select the type of
building to be painted. For a residence, the user can select a house or apartment. For an office
building, the user can select a high-rise or low-rise. The first available selection (residence/house)
is checked by default when the user enters the model. The model displays the default volume for
the selected building to the right. This value cannot be changed where it is displayed in gray
color; rather, the user must press the Edit Volume button to change the value. The revised value
then will be displayed in the gray area. Within the Edit Volume dialog box, the volume can be
edited in cubic feet or in cubic meters (the model automatically converts from one unit to the
other), but the volume value displayed on the main screen is in cubic feet.
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Another option for the type of painted building is a "standard box." This choice allows
the user to customize the scenario by supplying dimensions (length, width, and height) for the
building to be painted. When a standard box is selected, the building volume cannot be changed
with the Edit Volume button, but rather by editing the building dimensions.
The second step is to choose the building space to be painted. If residence/house is
selected, for example, then the choices are entire building (100 percent) or one bedroom (10
percent). Similar choices are provided for office building, (e.g., entire building or floor) and
standard box (entire building or part of building). The choice results in a model default value for
percent painted, which is displayed to the right in gray color. This value can be changed using the
Edit % Painted button (unless entire building is selected for residence or standard box).
The third step (optional) is to specify an air exchange rate and interzonal airflow rate
for the selected building. The model provides default values keyed to the building types, and the
default air exchange rate is displayed in gray color. The user can change this default value, as
well as the default value for the interzonal airflow rate, through the Edit Airflows button. There
is one cautionary note here - changing the air exchange rate will cause the model to automatically
use a preset algorithm for the interzonal airflow rate; thus, if the user wishes to customize both
the air exchange rate and the interzonal airflow rate, then the air exchange rate should be changed
first.
The fourth step is to choose the painted surface — walls, ceilings, or both. The choice
leads to a model default value for the loading ratio (i.e., the ratio of surface area to volume). This
value is not displayed on the main screen, but can be changed using the Edit Painted Surface Area
button. The model uses the loading ratio to calculate the painted surface area, and displays this
value in gray color near the bottom-right portion of the main screen. The loading ratio can be
edited either in ft2/fit3 or in m2/m3 (the model automatically converts from one unit to the other).
The fifth step is to choose the number of coats to be applied for primer and/or paint
(one coat for each is shown by default). The user can elect to do painting only, for example, by
entering zero coats for primer. Further details relating to the amount of primer/paint used are
provided through the Edit Amount of Paint button, where the coverage (ft2 or m2 per gallon) and
associated wet film thickness (mil, or 1/1000 inch) are displayed. For paint, the model provides a
default coverage of 400 ft2 per gallon (37.2 m2/gallon or 4.01 mil film thickness); the default
coverage for primer is half that of paint. These default values can be edited using any of the units
provided; the model calculates and displays the resultant amount of paint used (in gallons) within
the dialog box. The amount of paint is not displayed on the main screen.
The final step for this screen is to determine the duration of the painting event, using
the Edit Painting Duration button (see Figure 2-2). Within the associated dialog box, the user can
choose a default application rate for a do-it-yourself (DIY) or a professional painter and can edit
the number of painters as well as the primer/paint application rates (gallons per hour) and the
maximum priming/painting duration per day (hours). The maximum input value for priming or
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painting hours per day is 12. Within the dialog box, the model calculates and displays the total
duration for priming and painting.
By default, painting starts immediately after priming is finished, but the user can change
this default by entering a value in the input area for hours between priming and painting.
Optionally, the user can specify that priming starts the next day, or the second day, after painting
is finished. The model assumes that each day of painting starts at 9:00 a.m., and the user cannot
change that time. The user can select the day of the week when painting starts. The start day can
have some effect on the estimated exposure, through interaction with weekday/weekend activity
patterns (see Occupancy and Exposure Screen, Section 2.3). The model calculates and displays
the total number of days for priming and painting.
Painting Duration
(* Use Default for DIY Painter
C Use Default for Professional Painter
2.26 Gallons Primer and
Number of Painters = I
Primer Application Rate = [
Paint Application Rate = [
Calculated Duration
6.85 hours for primer
3.42 hours for paint
10.27 hours total
Primer/Paint Interval
(* Paint Same Day
C Paint Next Day
C Paint Second Day
1.13 Gallons Paint to be Used
1
0.33
0.33
Gallons/Hour per Painter
Gallons/Hour per Painter
Maximum Hours per Day for Priming
n
8.00
Hours per day
Hours Between Priming and Painting
if He
lours
Maximum Hours per Day for Painting =
Calculated Days to Apply Primer = 1 days
Calculated Days to Apply Paint = 1 days
Start Day:
8.00 Hours per day
(* Mon C Tue C Wed C Thu C Fri C Sat C Sun
OK
Cancel
Figure 2-2. Dialog Box for Edit Painting Duration.
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2.1.2 Basis for Default Values
The basis for default values assigned on the Painting Scenario screen is summarized in
Table 2-2. Some of the values, such as painting hours per day and start day for painting, are
arbitrary selections intended to serve simply as "place holders" that the user can change. Several
of the values come from the Exposure Factors Handbook (USEPA 1997), Volume III, Chapter
17 (Residence Characteristics). These include the default house volume (15,583 ft3 or 441.3 m3)
and apartment volume (7,350 ft3 or 208.1m3), as well as the default residential air exchange rate of
0.45 air changes per hour (ACH).
The default value for the interzonal airflow rate (IAR) for residences, in cubic meters per
hour, is calculated by the model from the air exchange rate and house volume according to the
following equation:
IAR = (0.046 + 0.39*A)*V (2-1)
where A is the air exchange rate (inverse hours), and V is the building volume (cubic meters).
The equation is an empirical relationship developed by Koontz and Rector (1995) from an analysis
of residential volumes, air exchange rates and interzonal airflow rates. As described in the
referenced document, the relationship was developed through regression analysis, using air
exchange rates and interzonal airflow rates (between the bedroom and the remainder of the house)
that were measured in various field studies for using perfluorocarbon tracers (PFTs).
Table 2-2. Basis for Default Values on Painting Scenario Screen
Variable
Basis for Default
Building Volume
Exposure Factors Handbook for residences
Professional judgment for office buildings
Percent Building Painted
Arbitrary selection
Air Exchange Rate
Exposure Factors Handbook for residences
Persily (1989) for office buildings
Interzonal Airflow Rate
Koontz and Rector (1995) for residences
Professional judgment for office buildings
Wall/Ceiling Loading Ratios
Exposure Factors Handbook for residences
Professional judgment for office buildings
Paint Coverage
Label on paint containers
Paint Application Rate
Household Solvent Products: A National Usage Survey
(WESTAT 1987) for DIY painters
Estimating Guide, 19th Edition (PDCA 1998) for
professional painters
Painting Hours Per Day
Arbitrary selection
Start Day for Painting
Arbitrary selection
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Because available data are relatively scarce for office buildings, professional judgment was
used in developing certain defaults. For example, for the office-building interzonal airflow rate, it
was assumed that air communication between the painted and unpainted spaces occurs only
through the heating, ventilating, and air-conditioning (HVAC) system for the building. It was
further assumed that the internal recirculation of air through the HVAC system is equivalent to
one air change per hour; that is, a volume of air equivalent to the total building volume is
circulated each hour. Given these assumptions, the interzonal airflow rate (IAR, in m3/hour) can
be calculated as follows:
IAR = building volume * % volume in painted area * % volume in unpainted area (2-2)
For example, if the building volume is 100,000 ft3 and the painted area is 10 percent of that
volume, then the interzonal airflow rate is 100,000 * 0.1 * 0.9, or 9,000 ft3/hour.
In determining a default loading ratio for ceilings in office buildings, a ceiling height of 10
feet was assumed. Because the volume is the product of the floor area times the ceiling height,
the loading ratio for the ceiling (ceiling area/building volume) can be stated as:
ceiling area / (ceiling area * 10 ft) = 0.10 fit2/fit3, or 0.33 m2/m3 (2-3)
By comparison, the default ceiling loading ratio for residences (from the Exposure Factors
Handbook) is 0.13 fit2/fit3 (0.43 m2/m3).
To estimate a default loading ratio for walls in office buildings, a floor plan was laid out
for a building with a ceiling height of 10 feet. This floor plan was split equally into two spaces,
one with 10 ft by 10 fit offices and associated hallways, and one with several larger areas that
would contain cubicles. The resultant loading ratio for walls was estimated to be 0.25 fit2/fit3 (0.82
m2/m3), as compared to the default value of 0.29 fit2/fit3 (0.95 m2/m3) for residences.
For a standard box, the default air exchange rate, interzonal airflow rate, and loading
ratios for walls and ceilings are the same as those for office buildings.
The default value for DIY paint application rate derives from an EPA-sponsored national
usage survey of household solvent products. From that survey, the median amount of latex paint
used is one gallon and the median duration of use is three hours, corresponding to an application
rate of 0.33 gallons/hour. The default application rate for a professional painter derives from an
estimating guide developed by the Painting and Decorating Contractors of America (PDCA).
According to the guide, the labor production rate for painting is 337.5 ft2/hour (range of 325 to
350 ft2/hour) for roller application. Given a paint coverage of 400 fit2/gallon, the labor production
rate equates to an application rate of 0.85 gallons/hour.
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2.2 Paint & Chemical Screen
This screen (Figure 2-3) is designed to obtain user inputs on (1) the type of paint used and
the primer/paint density, (2) properties of the chemical under assessment, (3) the weight fraction
of the chemical in primer and paint, (4) parameters of an emissions model for primer and paint,
and (5) parameters for a sink model (or assumption of no indoor sinks).
I Wall Paint EKposure Model (WPEM)
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Designing Wall Paint for the Indoor Environment
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Introduction | Painting Scenario j Paint & Chemical j| Occupancy & Exposure | Execution |
"Chemical
-Type of Paint (Choose 1)
Latex: Flat C Semi-Gloss
Alkyd: (" Semi-gloss
jJ
-Paint Density-
r
9rams/gal
Paint: | 4,6011.1)1 grams/gal
Edit Density
DISPLAY CHEMICALS USED TO DEVELOP EMISSION MODELS
Select Chemical |TMPD-MIB
1]
Molecular Weighrt |_
V^por Pressure
Primer Emissions
Paint Emissions
0.0019000 ton-
Weight Fraction: In Primer
I 0.011 lnPaint
jj
Current Model
| Empirical
| Empirical
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216.31 aAmole jJ
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Figure 2-3. Paint & Chemical Screen.
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Required and optional user inputs for this screen are summarized in Table 2-3. Unlike the
previous (Painting Scenario) screen, for which numerous elements have both required and
optional inputs, the inputs for this screen are either required or optional. In the case of weight
fraction in primer and paint, default values are provided simply to serve as "place holders" to be
edited by the user.
Table 2-3. Required and Optional Inputs for Paint & Chemical Screen
Required Inputs
Optional Inputs
Type of Paint
Choose latex or alkyd
—
Paint Density
—
Edit paint density for primer
and/or paint
Chemical Name
Select a chemical from the
list, or add to the list
—
Chemical Properties
Use/edit molecular weight
and vapor pressure from the
list
—
Weight Fraction
Edit weight fraction of
chemical in primer/paint
—
Primer/Paint Emissions
Model
—
Override default model, edit
default parameter estimates
Indoor Sink Model
—
Override default model (no
indoor sinks), supply
parameter estimates
2.2.1 Input Sequence and Options
The first step on this screen is to select the type of paint (latex or alkyd) to be applied.
There are two choices (flat and semi-gloss) for type of latex paint. Default values for primer and
paint density are assigned by the model for each type of paint. These values can be changed by
the user using the Edit Density button. Within the Edit Density dialog box, the density can be
edited in units of pounds/gallon, grams/gallon, or grams/cm2; the software automatically makes
conversions across the units, and displays the current values on the main screen in grams/gallon.
The second step is to select a chemical. A button labeled DISPLAY CHEMICALS
USED TO DEVELOP EMISSION MODELS lists all chemicals that were measured in small-
chamber emission tests under the DfE project, and further highlights the subset of chemicals on
which empirical emission models (described below) were based. The range of molecular weights
and vapor pressures covered by these chemicals also is described. Figure 2-4 shows the
information provided through this button.
2-8
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ill
CHEMICALS USED TO DEVELOP EMISSION MODELS
HI ^i°se
Print
CHEMICALS IN ALKYD PAINT
An empirical emissions model has been developed for chemicals in alkyd paint
based on chamber tests involving selected paint formulations. The chemicals listed
below were present in one or more of the tested formulations. The emissions model
was based on a further subset of chemicals (indicated below with an*) that met
additional criteria as described in Appendix A of the WPEM User's Guide. The
chemicals below represent a range of molecular weights from 87 to 170 g/mole
(120-170 g/mole for the subset on which the model was based) and a range of vapor
pressures from 0.4 to 18.7 torr (0.4-7.1 torr for the subset on which the model was
based).
Decane*
Dodecane*
Ethylbenzene
o-Ethyltoluene*
p-Ethyltoluene*
Isopropylbenzene*
MEKO
CHEMICALS IN LATEX PAINT
2-M ethyl decane*
Nonane*
Octane
n-Propyl benzene*
Pro pyl-cy cl o h exan e*
Toluene
Trans-decalin*
1.2.3-T rimethylbenzene
1.2.4-Tri m ethylbenzene*
1.3.5-T rimethylbenzene*
Undecane*
o-Xylene
p-Xylene
An empirical model also has been developed for a limited set of chemicals in latex
paint again based on chamber tests involving selected paint formulations. The
chemicals listed below were present in one or more of the tested formulations arid
were used as a basis for developing the emissions model. These chemicals
represent a range of molecular weights from 62 to 216 g/mole and a range of vapor-
pressures from 0.002 to 0.2 torr.
B utoxy eth oxy eth an o I
Ethylene Glycol
Propylene Glycol
TMPD-MIB
d
Figure 2-4. Information Shown for Display Chemicals Button.
2-9
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A chemical can be selected from the drop-down list of the chemicals used in the DfE
testing program. Once a chemical has been selected, its name, molecular weight, and vapor
pressure are displayed on the main screen. Chemicals on the list can be edited (name and
properties), or the user can add chemicals to the list, using the Edit/Add button. Within the dialog
box (Figure 2-5), a chemical can be edited by clicking on its name and pressing the Edit button -
the name, molecular weight, or vapor pressure can then be modified. Edits are not retained,
however, until the Save button is pressed.
Similarly, within the dialog box a chemical can be added to the list by pressing add,
entering the name and chemical properties, and then pressing Save. Pressing the OK button
closes the dialog box. The lowest value allowed for vapor pressure is 0.0000001 torr; if a value
below this limit is entered, then the program will issue a warning and reset the value to the
minimum. The lowest value allowed for molecular weight is O.Olg/mole. The values for
molecular weight and vapor pressure are used by the model in calculating certain default values
pertaining to chemical emissions from primer and paint. However, the emission models developed
for WPEM are based on a limited set of chemicals and an associated range of molecular weights
and vapor pressures (see Figure 2-4). The models may not be valid for chemicals outside these
ranges, unless the user has appropriate model inputs from chamber tests.
1 Edit/Add Chemicals
XJ
Chemical Name
—
Name
Add
1,2,4-trimethyibenzene
A.
|1,2,3-trimethylbenzene
1,3..5-trimethylbenzene
2-methyldecane
Edit
butoxyethoxyethanol
decane
Molecular Weight
Delete
dodecane
ethylbenzene
ethylene glycol
isopropylbenzene
120.20
g/mole
Save
methyl ethyl ketoxinne
nonane
n-propylbenzene
Vapor Pressure
d
j 1.5700000
torr
Cancel
OK
Figure 2-5. Dialog Box for Edit/Add Chemicals.
The third step on this screen is to provide values for the weight fraction of the
chemical in primer and paint. A default weight fraction of 0.01 is provided simply as a "place
holder" that the user should override based on knowledge of the primer/paint formulations to be
modeled. The lowest value currently allowed is 0.000001; if a value below this limit is entered,
then the software will issue a warning and reset the value to the minimum.
2-10
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The final entries on this screen relate to emission models for primer and paint, and to
models for indoor sinks. For alkyd primer or paint, there is a choice of two types of models -
empirical model and semi-empirical model - through the Primer Emissions or Paint Emissions
button. The algorithms and basis for these models are described in Appendices A and B for alkyd
paint and in Appendices C and D for latex paint. In brief, the empirical single-exponential model
for chemical emissions from alkyd paint, developed under this project, was derived from a
nonlinear regression relating the first-order rate constant for emission decay to wet film thickness
and the chemical's molecular weight and vapor pressure. A semi-empirical model developed
under a separate project also has an algorithm for the emission decay rate, derived largely from
first principles but still requiring use of the chamber testing results from this project to estimate
one of its parameters. For chemical emissions from latex paint there is an empirical double-
exponential model with one emission rate constant dependent on a chemical's vapor pressure and
the other dependent on its molecular weight.
The input array for the empirical model is shown in Figure 2-6. The total mass is
determined as the product of the applied primer/paint mass times the chemical weight fraction (for
chemicals in latex paint, 25 percent of the applied chemical mass is assumed to be emitted; see
Appendix C). For the single-exponential model for alkyd primer/paint, all mass is associated with
the first exponential, whereas for the double-exponential model for latex primer/paint 10 percent
of the mass is associated with the first exponential (90 percent with the second) by default.
Default values for the rate constants are based on algorithms described generally above and in
detail in the appendices.
Empirical Model
Total M ass of Chemical:
Zof M ass Associated with 1st Exponential:
First-order Rate Constant* for 1st Exponential:
First-order Rate Constant* for 2nd Exponential:
25.98
10.00
0.44317
0.012G3
grams
percent
1/hr
1/hr
'The first-order rate constant for both exponentials must be greater
than zero, unless all mass is associated with the first exponential.
\/ OK
X Cancel
Figure 2-6. Dialog Box for Empirical Emissions Model.
2-11
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Default values for all parameters needed for the empirical model are supplied by the
WPEM software. It is recommended that the user retain these defaults unless there are chemical-
specific data (e.g., from small-chamber emission tests) that suggest more appropriate values.
Two types of indoor-sink models — one-way sink and reversible sink - are available
through the Indoor Sinks button (the default is no indoor sinks). With a one-way sink, chemical
mass in the indoor air can move into the sink but can never exit it, whereas for a reversible sink
chemical mass can enter and leave the sink. The rate of mass entering the sink is governed in
WPEM by an adsorption rate constant, and the rate of mass leaving the sink by a desorption rate
constant. Thus, for the one-way sink model, inputs are required for the area and adsorption rate
for each sink; for the reversible-sink model, inputs are required for a desorption rate as well. The
one-way sink model can be viewed as a special case of the reversible-sink model whereby all
desorption rates are zero.
The input array for the reversible-sink (Langmuir) model is illustrated in Figure 2-7. The
WPEM software calculates areas for selected indoor sinks (carpeting and wallboard) but does not
provide any default values for adsorption or desorption rate constants, because the basis for such
values is limited at this time. In the absence of appropriate information on the rate constants, it is
suggested that the user assume no indoor sinks. This approach will tend to produce conservative
(higher) exposure estimates, at least in comparison to estimates from a one-way sink model. A
reversible-sink model will tend to lower the peak concentration and to "stretch out" the period of
chemical emissions (or re-emissions) indoors. Although the peak concentration will be lower, the
time-integrated exposure could be higher in some cases than for the no-sink case. The difference
will depend in part on how activity patterns intersect the indoor-air concentration profile over
time. In the case of a professional painter who permanently leaves the building once it is painted,
the reversible-sink model will lower the overall exposure because its net impact is to effectively
delay the chemical emissions.
Table 2-4 list values for adsorption (Ka) and desorption (Kd) rates for selected chemicals
and sink materials, based on small-chamber tests conducted under this project (see Appendix A,
Section A5) or reported in the published literature. As noted by Tichenor et al. (1991), the ratio
Ka/Kdis indicative of the sink strength, or the capability of a sink material to adsorb indoor air
pollutants. For the work under this project (ARCADIS 1998), for example, of the four VOCs
tested only MEKO had a notable sink strength. The rate constants summarized in the table
indicate a considerable range of sink strengths for different chemical-material combinations. It is
noteworthy, however, that the investigators used substantially different loading ratios in their
respective tests, ranging from 0.4 to 5.0 m2/m3. By comparison, loading ratios in residential
environments typically are close to 0.95 m2/m3 for wall materials such as gypsum board and 0.43
m2/m3 for floor/ceiling materials such as carpeting or ceiling tiles. Thus, considerable care must
be taken in estimating an input value based on the previous experimental work. Chang et al.
(1998) reported strong sink effects for four chemicals in latex paint; the authors indicated that the
Langmuir model was adequate for the adsorption phase but failed to predict the relatively slow re-
emission process (desorption phase), and suspected that physical/chemical properties of the
oxygenated polar compounds that were tested may have significant effects on the sink behavior.
2-12
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Reversible Sink Values
Adsorption Rate
Desorotion Rate
Jb.
Zone1
Sink"
Area
Constantfmftr)
Constants Jhrt
1
Garnet
0.00000
0.00000
1
Wallboard
18.96
0.00000
0.00000
1
Other
0.00
0.00000
0.00000
2
CarDet
136.53
0.00000
0.00000
2
Wallboard
547.72
0.00000
0.00000
d
7
Othpr
o.on
n.onnoo
o.ooonn
Zone 1 is the painted area, zone 2 is the remainder of the building. Zone
2 is not applicable if the entire building is painted
Carpet is always assumed to be a sink. The wallboard sink area is a
combination of:
(1) any within the painted area that is not painted (e.g., ceilings if walls are
painted], and
(2) All wallboard in the unpainted area, if applicable.
The category "Other" allows the user to specify some other type of
sink, such as furniture or draperies.
\y ok ]
Figure 2-7. Dialog Box for Reversible-Sink Model.
X Cancel
2.2.2 Basis for Default Values
The basis for default values assigned on the Paint & Chemical screen is summarized in
Table 2-5. Default values are limited to paint density and certain parameters for emission and sink
models. Values for paint density (4,600 grams/gal for latex primer, latex paint and alkyd paint;
5,800 grams/gal for alkyd primer) are based on material safety data sheets accompanying all
primer/paint formulations that have been studied (i.e., used in small-chamber tests) under the DfE
project.
Default values for primer/paint emissions models are based on an analysis of data from
small-chamber emission tests conducted under the DfE project. In brief, nonlinear regression
analysis was used to fit a single-exponential emissions model for chemicals in alkyd paint (see
Appendix A) and a double-exponential emissions model for latex paint (see Appendix C). The
chemical-specific values for rate constants governing the exponential decline in emission rates
have been analyzed in relation to molecular weight and vapor pressure, to develop a predictive
equation for determination of default values. The fraction of applied chemical mass that one can
expect to be emitted also has been analyzed for alkyd and latex paints.
2-13
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Table 2-4. Parameter Estimates for Langmuir Sink Model from Four Chamber Studies
Chemical
Sink Material
K,
Kd
Juruensen el ;il. < I'WJ) \oliime <> <>5 in . Inadiim ralm 4 4<> in in .
aire\ehaime r;ile 1 <• ACM. lempeniliire 2' C. KM 5(>"„
Toluene
Wool carpet
0.73
1.03
Nylon Carpet
0.25
0.41
PVC floor covering
0.07
0.26
Cotton curtain
0.02
0.31
a-pinene
Wool carpet
0.41
0.21
Nylon Carpet
0.29
0.17
PVC floor covering
0.05
0.06
Cotton curtain
0.03
0.09
\kC \I)IS (I'WNi uilnnie t) n5i in', loading ratio 1.^15 in in',
aire\eliaime rale <> 5 \( II. lemperaliire 2' C. KM 5<>"„
MEKO
Carpet
0.25
0.04
Gypsum board
1.10
0.03
1,2,4-trimethylbenzene
Carpet
0.10
6.00
Gypsum board
0.25
0.25
2-methyldecane
Carpet
0.04
0.03
Gypsum board
0.90
1.20
Undecane
Carpet
0.06
0.50
Gypsum board
0.40
0.25
kirelinerel al. < l'W5i \olunie 1 <) in'. loading ratio o 4 in in .
air exchange rale <>5 \('ll. lemperaliire 2' ('.KM 45"..
2-butoxyethanol
Carpet (6 mm thick)
0.49
0.41
Carpet (10 mm thick)
0.56
0.77
PVC wall covering
0.50
0.22
Gypsum board
1.08
0.36
Acoustic tile
1.32
0.56
Tidiennrel al. (I'Wl) \olunie d <>5' in . loading ratio 2 <4 in in n <)2 in in lor pillow ).
air esehaime rale In \CII. lemperaliire 2' C.kll 45"..
T etrachloroethy lene
Carpet
0.13
0.13
Gypsum board
0.21
1.50
Ceiling tile
0.10
0.61
Pillow
0.03
0.10
Ethylbenzene
Carpet
0.08
0.08
Gypsum board
0.45
1.50
Ceiling tile
0.24
0.59
Pillow
0.004
0.016
2-14
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Table 2-5. Basis for Default Values on Paint & Chemical Screen
Variable
Basis for Default
Paint Density
Material safety data sheets for paint formulations studied
under the DfE project
Primer/Paint Emissions Model
Fit of empirical (exponential decay of emissions) models to
small-chamber concentration data for latex and alkyd paint,
relationship of rate constants for emissions decay to vapor
pressure and molecular weight (both types of paint) and to
wet film thickness of applied product (alkyd paint only)
Development of semi-empirical model (alkyd paint only)
relating rate constant for exponential emissions decay to
paint formulation and wet film thickness of applied product
Indoor Sinks Model
Areas of potential one-way or reversible sinks (carpeting,,
wallboard) estimated from floor/wall loading ratios, per
Exposure Factors Handbook (user must supply values for
assumed adsorption/desorption rate constants)
As noted above, currently there are no default values available in the model for
adsorption/desorption rate constants for indoor sinks. Default values are provided for the areas of
two types of potential sinks - carpeting and wallboard - based on the default wall/ceiling loading
ratios provided in WPEM. For carpeting, it is assumed that the floor loading ratio is the same as
the ceiling loading ratio, and that 80 percent of the floor area is covered by carpeting. It is
assumed that wallboard is present on both walls and ceilings in residences, and on walls only in
office buildings or a standard box. In the portion of the building that is not painted, it is assumed
that all wallboard will act as a sink. In the portion of the building that is painted, only the
unpainted wallboard is assumed to act as a sink. Thus, for example, if walls are painted in a
residence, then within the painted portion of the building the sink area is computed as the volume
of that space times the ceiling loading ratio.
2-15
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2.3 Occupancy & Exposure Screen
This screen (Figure 2-8) is designed to obtain user inputs on (1) the type of exposed
individual and his/her location during the painting event, (2) weekday/weekend activity patterns
(locations and associated breathing rates) for the exposed individual, and (3) parameters needed
to develop lifetime exposure measures, such as lifetime average daily dose (LADD).
HWall Paint Exposure Model (WPEM)
-|fl| X
File
Help
B
L
b
"S
si
Designing Wall Paint for the Indoor Environment
Introduction | Painting Scenario | Paint £ Chemical ; Occupancy S Exposure j| Execution
Exposed Individual (choose 1)
(* Professional painter
( Adult occupant
f-* DIY Painter (residence only)
r Child occupant (residence only)
Activity Patterns
Weekday Pattern
jJ
Weekend Pattern
Pattern During Painting
Exposure Parameters ^
Number of Exposure Events in Lifetime: J"
Number of Years in Lifetime: p
events
5,000 I
JJl ^ars
Edit Exposure Events
Edit Years in Lifetime
Average Body Weight during Lifetime: ^
71.8
Edit Body Weight
jJ
Individual's Location during the Painting Event (choose 1)
(* In painted area
C In building, not in painted area (This choice does not apply if "Entire Building" is selected) ^ |
l Not in building
jJ
jJ
jJ
jJ
Gender (choose 1)-
(* Non-Specific
C Male
C Female
jJ
Figure 2-8. Occupancy & Exposure Screen.
2-16
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Required and optional user inputs for this screen are summarized in Table 2-6. Most of
the inputs are optional, as the model provides many default choices or values here. The only
choice required of the user is the type of exposed individual (professional painter by default).
Once the exposed individual is selected, the model provides a default location during the painting
event, which the user can override. Similarly, default values are provided for activity patterns,
number of exposure events, years in lifetime, and body weight.
Table 2-6. Required and Optional Inputs for Occupancy & Exposure Screen
Required Inputs
Optional Inputs
Exposed Individual
Choose a type of exposed
individual
—
Gender
—
Override default choice
(non-specific gender)
Location during the Paint
Event
Choose a location (default
value is linked to type of
exposed individual)
—
Activity Patterns
Override default values for
time, location, or breathing
rate for weekday/weekend
patterns (breathing rate only
for pattern during painting)
Number of Exposure Events
in Lifetime
—
Override default values for
events per year and years of
exposure
Number of Years in Lifetime
—
Override default value
Body Weight
—
Override default value
2.3.1 Input Sequence and Options
The first step on this screen is to select the type of exposed individual. Different
default activity patterns and lifetime exposure events or years of life are provided in the model for
each of four types of exposed individuals - professional painter, do-it-yourself (DIY) painter,
adult occupant, and child occupant. Two of these choices - DIY painter and child occupant - are
not valid if the user has specified on the Painting Scenario screen that an office building or
standard box is being painted.
2-17
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The second step is to choose the gender of the exposed individual. The choice of gender
(non-specific is the default) affects the default values supplied by WPEM for breathing rate, years
in lifetime, and body weight.
The third step is to choose the individual's location during the painting event, for
which the model always provides a default that is tied to the type of exposed individual. For
example, by default an adult or child occupant is assumed to be in the building, but not in the
painted area, during the painting event. The model will issue a warning if a professional or DIY
painter is not placed in the painted area, but will allow the user to make that choice.
The fourth step (optional) is to edit the weekday/weekend activity patterns, or
activity patterns during the painting event, that already are provided by the model. The
weekday and weekend patterns (see Figure 2-9 for an example) have been developed to match the
typical amounts of daily time spent at home (in bedrooms and in the remainder of the house), at
work, and outdoors by the different types of individuals listed above, as reported in the Exposure
Factors Handbook. The defaults should suffice for most applications.
| Weekday Pattern
~
Zone
Enter Time
Min |
Breathing Rate
Hr
m3/day
jJ
1
0
0
9.60
2 |
2
7
0
24.00
3j
0
8
0
13.30
sJ
2
16
0
18.00
1
22
0
12.00
6
8
9
10 I
11
12
Note: Zone 1 is the painted area, zone 2 is the
remainder of the building, and zone 0 is
outside the building. Zone 2 is not applicable
if the entire building is painted (the model
will reset zone values of 2 to 1 in that case).
\y ok ]
X Cancel
Figure 2-9. Example Default Weekday Activity Pattern.
2-18
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Items that can be edited for weekday/weekend patterns are the time of day when each
environment is entered (enter time), location (zone) at that time, and breathing rate. The enter
time is input in separate cells for hour of the day (Hr) and minute with the hour (Min). The entry
for hour must be between 0 (midnight, or beginning of the day) and 23 (11 p.m.), and the entry
for minute must be between 0 and 59. The first enter time must be 0 Hr, 0 Min, and the user
cannot edit that value. Another constraint is that the enter time for any given line must be later
than the time for the line that precedes it. Exit times do not need to be entered, as the enter time
for the current line equates to the exit time for the previous line. The final entry is in effect until
the end of the 24-hour day. For the example in Figure 2-9, the individual enters zone 1 (the
painted potion of the building) at midnight, enters zone 2 (the unpainted portion) at 7 a.m., leaves
the building (zone 0) at 8 a.m., returns to the building (zone 2) at 4 p.m. (hour 16), and enters
zone 1 at 10 p.m. (hour 22).
For the pattern during painting (Figure 2-10), only the breathing rate can be edited; all
other inputs are determined by the model based on the user's description of the priming/painting
event on the Painting Scenario screen. This restriction prevents the user from entering a pattern
that is inconsistent with the previously described painting event. Following the painting event, the
individual is placed in the location (zone) indicated by the weekday or weekend activity pattern
(whichever applies) at the time when painting is finished.
Pattern During Painting
_
Zone
Enter Time
_
_J
Exit Time
_
-J
Breathing Rate
day
hr
min
day
hr
min
m3/day
_
1
Mon
9
0
Mon
15
51
27.50
2j
1
Mon
15
51
Mon
17
0
27.50
3
1
Tue
9
0
Tue
11
16
27.50
Note: Only Breathing Rates can be changed!
X Cancel
\y ok ]
Figure 2-10. Example Activity Pattern During Painting Determined by WPEM.
2-19
-------
The final step (also optional) is to edit the exposure parameters - number of exposure
events in lifetime, number of years in lifetime, and body weight - through their associated edit
buttons. A change to the default number of lifetime exposure events is accomplished by supplying
two values - exposure events per year and years of exposure. The default value for lifetime
exposure events is keyed to the type of exposed individual and to the type of building and percent
painted, from the Painting Scenario screen. For example, for a DIY painter, if the entire residence
is painted then one exposure event every 10 years is assumed by default. By comparison, if only a
bedroom is painted then one event per year is assumed. Further details on rules used by WPEM
to calculate the default value for lifetime exposure events are provided in Section 2.3.2.
2.3.2 Basis for Default Values
The basis for default values assigned on the Occupancy & Exposure screen is summarized
in Table 2-7. Many of the defaults for this screen are based on data contained in the Exposure
Factors Handbook. In selected cases, such as the location or breathing rate during the painting
event, professional judgment has been exercised in developing the defaults.
Table 2-7. Basis for Default Values on Occupancy & Exposure Screen
Variable
Basis for Default
Exposed Individual
Arbitrary selection
Location during Painting Event
Professional Judgment
Weekday/Weekend Activity
Patterns
National Human Activity Pattern Survey, as reported in the
Exposure Factors Handbook
Pattern during Painting
Professional judgment
Exposure Factors Handbook
Number of Exposure Events per
Lifetime
Professional judgment
Household Solvent Products: A National Usage Survey
(WEST AT 1987)
Number of Years in Lifetime
Professional judgment for professional painters, children
Exposure Factors Handbook for DIY painters, adults
Body Weight
Exposure Factors Handbook
2-20
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Default weekday/weekend activity patterns for residence provided with WPEM assume
that zone 1 (the painted portion) is a bedroom area and zone 2 is the remainder of the residence
(if the entire building is painted, the model collapses zones 1 and 2 to a single zone). The
collective times spent by adult/child occupants in zone 1, zone 2, and zone 0 (outside or away
from the residence) over a 24-hour period are summarized in Table 2-8 for the default activity
patterns.
Table 2-8. Hours Spent in Different Residential Zones,
per Default Activity Patterns in WPEM
Zone
Weekday
Weekend
Adult
Child
Adult
Child
1 (painted area)
9
11
9.5
11
2 (remainder)
7
7
8
7
0 (outside/away)
8
6
6.5
6
The default breathing rates for these patterns correspond to values for resting, sedentary,
or light activities, as given in the Exposure Factors Handbook (gender-specific rates for adults
were estimated using the method described in the handbook; insufficient data were provided to
permit estimation of gender-specific rates for children). Default breathing rates associated with
different activity levels are summarized for adults and children in Table 2-9. For the first line of
the activity pattern (bedroom, asleep), the rate for resting was assigned. For the second line, a
rate corresponding to light activities was assigned. For the third line (away from the residence), a
daily-average rate was assigned; this value has no impact on the estimated inhalation exposure,
which is zero during times when the individual is outside the residence. For the fourth line, a rate
corresponding to the average for sedentary/light activities was assigned. For the fifth line, a rate
corresponding to sedentary activities was assigned. For the breathing rate during painting, for a
professional or DIY painter the rate was estimated as a combination of light (75 %) and moderate
(25 %) activity. For an adult or child occupant (not involved in the painting), the rate during
painting was estimated as a combination of sedentary (50 %) and light (50 %) activity.
2-21
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Table 2-9. Default Breathing Rates for Different Activities,
per Exposure Factors Handbook
Activity Level
Adult (average)
Adult Male
Adult Female
Child
Resting
9.6
9.6
7.2
7.2
Sedentary
12.0
14.4
12.0
9.6
Light
24.0
26.4
21.6
24.0
Moderate
38.4
43.2
38.4
28.8
Heavy
76.8
86.4
72.0
45.6
Daily average
13.3
15.2
11.3
10.0
The number of lifetime exposure events is calculated by WPEM as the product of number
of exposure events per year times the number of years of exposure. The default values for years
of exposure, based on professional judgment, are 25 years for a professional painter, 50 years for
a DIY painter or an adult occupant, and 10 years for a child occupant. The following rules or
algorithms have been developed for exposure events per year, to result in default numbers of
lifetime exposure events that are reasonable:
If a residence is painted and the exposed individual is a DIY painter, then the
default number of exposure events per year is equal to 7.5 divided by the percent
of building painted (e.g., if percent painted = 10, then events/year = 0.75; if
percent painted = 20, then events/year = 0.375). An EPA-sponsored national
survey (WESTAT 1987) indicates a median time-since-last-painting of 8 months.
Assuming that respondents, on the average, were queried at the halfway point
between successive painting events, the median duration between painting events
would be 16 months, equating to 0.75 events per year. The median amount of
paint per event from that survey would be sufficient to cover about 10 percent of
the wall area of a house.
If a residence is painted and the exposed individual is an adult or child occupant,
then the default number of exposure events per year is equal to 10 divided by the
percent of building painted (e.g., if percent painted = 10, then events/year =1.0; if
percent painted = 20, then events/year = 0.5). This approach is equivalent to the
assumption that, when occupants hire professional painters, the entire residence
typically is painted in full once every 10 years.
2-22
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If an office or a standard box is painted and the exposed individual is an adult
occupant, then the number of exposure events per year is equal to 0.2, regardless
of the percent painted. This approach is equivalent to the assumption that the
office building is painted once every five years.
Regardless of type of building painted, if the exposed individual is a professional
painter then the number of exposure events per year is equal to 1500 divided by
the total priming/painting duration (in hours), as determined on the Painting
Scenario screen. With this approach, the painter spends 1500 hours per year
painting (e.g., 50 weeks per year times 30 hours per week).
Gender-specific defaults taken from the Exposure Factors Handbook are provided for
years in lifetime. The default values for adults are 79 years for female, 72 years for male, and 75
years for non-specific. For children the default is 10 years, regardless of gender. The default for
a child does not correspond to length of lifetime per se, but rather to length of time as a child.
Gender-specific defaults taken from the Exposure Factors Handbook also are provided for
body weight. The default values for adults are 65.4 kg for female, 78.1 kg for male, and 71.8 kg
for non-specific. For children the default is 20.3 kg, regardless of gender. The body weight can
be edited in pounds or kg; the model automatically converts from one unit to the other, and
displays the edited value in kg on the main screen.
2-23
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2.4 Execution Screen
This screen (Figure 2-11) is designed primarily for executing the model and reviewing
results of that execution. It also provides the user with selected options related to documenting
the run and choosing a length of model run and reporting interval.
UWall Paint Exposure Model (WPEM)
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Designing Wall Paint for the Indoor Environment
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Figure 2-11. Execution Screen (Results before Execution).
2-24
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2.4.1 Input Sequence and Options
The first step on this screen is to provide optional entries for Title of Run and Notes.
These entries enable the user to provide a general description of the run that is being made, along
with some useful reminders such as input choices for one or more key parameters. If it is likely
that the full set of inputs for the run may need to be reviewed or perhaps updated at some future
point in time, then it is strongly recommended that the user save the inputs (see below).
The second step is to provide inputs for length of model run and reporting interval.
Although the model provides a default value of 5 days for length of model run, this default is
intended only as a "place holder," to be edited by the user. The following are some useful tips for
determining the length of model run:
It takes a longer time for emissions from latex paint to decay than for emissions
from alkyd paint. The emissions from alkyd paint typically are "gone" within 24
hours after painting is completed, unless a reversible-sink model is being used.
A reversible-sink model for either latex or alkyd paint will tend to extend the time
duration during which chemical emissions (or re-emissions from the sink) are
present.
A professional painter leaves the building once it is painted and does not return.
Thus, when a professional painter has been selected as the exposed individual, the
length of model run can be set equal to the total number of primer/painting days
(or the total number of days plus one), as determined on the Painting Scenario
screen.
A model run that is too short can result in underestimaton of outputs such as single
event dose or lifetime average daily dose. To ensure that a model run is
sufficiently long, initially select a number of days that is somewhat greater than the
total number of priming/painting days, and note the resultant value for single event
dose. Next, select a length of model run that is a few days greater than the number
previously selected, rerun the model, and compare the value for single-event dose
with the previous result. When the dose value is no longer changing, or is
changing by a very small amount, the model run is sufficiently long.
The choice of reporting interval has no impact on the results displayed on this screen, as
the model uses an internal time step of 30 seconds for calculations in all cases. The reporting
2-25
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interval does, however, affect the level of detail in a file generated by the model (see Section 3)
that contains the time series of concentrations for each zone in the residence and for the
concentration to which the individual is exposed. The file can be easily imported into Excel, for
example, and plotted using the chart wizard. If the user wishes to examine this file and also
wishes to see greater time resolution than for the default reporting interval of 60 minutes, then a
shorter interval such as 15 minutes or 5 minutes (as short as one minute) can be selected. A
shorter interval will result in greater time-related detail with a corresponding increase in the size
of the file.
The third step is to execute the model. The user has the option of just executing the
model (Execute button) or first saving the inputs and then executing (Save & Execute button).
The latter option is recommended as a general practice. Once inputs has been developed,
documented and saved for a given run, they can readily be edited, for example, to make certain
perturbations for examining various "what if' scenarios. Saving can be accomplished without
executing through a Save button on the toolbar near the top of the screen. Standard Windows
options such as "Save" and "Save As" are available under File at the upper left of the screen.
When a file is saved, WPEM always prompt for a name (with the current name displayed) so that
existing files are not inadvertently overwritten.
Once the user has pressed Execute or Save & Execute, the Execute button changes to a
Stop button that can be used to abort the run. Such an action will save significant time only in the
event that the user has selected a relatively long length of model run (e.g., 15-20 days or greater).
Before executing the model, it may be useful to perform a quick review of inputs by
pressing the View/Print Report button. As described in Section 3, the report both summarizes
model inputs and presents model results. A button below the Save & Execute button, with a title
of MODEL LIMITATIONS, lists the limitations that were previously indicated in Section 1.3 of
this guide. Following execution, the model results can be reset to zero if desired using the Clear
button to the right of the % completion bar in the lower half of the screen.
2.4.2 Modeling Approach and Calculations
Indoor-air concentrations in one or two zones are predicted in WPEM by implementing a
deterministic, mass-balance equation. The modeled concentration in each zone is a function of the
time-varying emission rate in one or more zone, the zone volumes, the airflow rates among zones
and between each zone and outdoors, losses to indoor sinks, and (if a reversible sink model is
used) re-emissions from indoor sinks.
2-26
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Consumer products such as paints that are applied to surfaces are best represented by an
incremental source model. This model assumes a constant application rate over time, coupled
with an emission rate for each instantaneously applied segment that declines exponentially. The
mathematical expression for the total emission rate resulting from the combination of constant
application rate and exponential emission rate for each applied segment has been developed by
Evans (1994).
The model requires the conservation of pollutant mass as well as the conservation of air
mass. WPEM uses a set of differential equations whereby the time-varying concentration in each
zone is a function of the rate of pollutant loss and gain for that zone. These relationships can be
expressed as follows:
Pollutant Mass Balance
(Change in Pollutant Mass) / (Change in Time) = Production ± Transport - Removal ± Reactions
Neglecting reactions:
(d Mass) / (dt) = £ Sources + £ Mass in - X Mass out ± £ Sinks (2-4)
Or:
(Vi dCi) / (dt) = X Sources + £ Cj*Qji - £ Ci*Qij ± £ Sinks (2-5)
where C refers to an air concentration, Q refers to a flow rate, i and j refer to zones (there are up
to two indoor zones plus outdoors), and the ± for sinks accounts for the possibility that they may
be reversible.
Air Mass Balance
Flows into a zone = Flows out of a zone
Or:
I Qji = I Qij (2-6)
where Q, i and j are defined as above. The flow rates are input as constants. The pollutant mass
balance is used in conjunction with the flow rates to predict the time-varying pollutant
concentration in each indoor zone.
2-27
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The differential equations can be solved by a variety of numerical solution techniques.
The fourth-order Runge-Kutta method (also referred to as the Kutta-Simpson formula) is used for
temporal integration (Matthews, 1992). Although this method is not as computationally efficient
as some others, it is very stable, self-starting, and accurate. The formula takes the following form:
C (t + delta t) = C (t) + 1/6 [K1 + 2*K2 + 2*K3 + K4] (2-7)
where: K1 = dC/dt * (delta t), evaluated at time = t, C = C (t)
K2 = dC/dt * (delta t), evaluated at time = t + (delta t)/2, C = C (t) + Kl/2
K3 = dC/dt * (delta t), evaluated at time = t + (delta t)/2, C = C (t) + K2/2
K4 = dC/dt * (delta t), evaluated at time = t + (delta t), C = C (t) + K3.
The Runge-Kutta technique has been evaluated for stability over a wide range of values for time
step, zone volumes, and flow rates.
Model calculations relating specifically to outputs (e.g., exposure measures) are described
in Section 3.
2.5 Summary of Model Inputs
Table 2-10 provides a summary of model inputs by screen, with a distinction between
inputs for which the user should make a deliberate decision (indicated by an asterisk) versus those
for which model defaults may suffice. The summary for each screen follows the general flow of
inputs for that screen. One choice that is not linked to a particular screen, but should be made at
the outset, is whether to open a file containing inputs for a default scenario. The available default
scenarios are described in Section 4. Even when a default scenario is chosen, the user should
review the inputs with an asterisk in the table below, as certain edits or changes still may be
warranted (e.g., selection of a chemical and entry of its weight fraction in primer and paint).
2-28
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Table 2-10. Summary of Model Inputs
Screen
Inputs
General
*Open a file containing inputs for a default scenario
Painting Scenario
*Choose type of building and portion painted
Edit building volume
Edit % painted
Edit air exchange rate and/or interzonal airflow rate
*Choose to paint walls, ceilings, or both
Edit loading ratio
*Choose number of coats for primer/paint
Edit type/number of painters, primer/paint application rates,
maximum priming/painting hours per day, start day
Paint & Chemical
* Choose type of paint
Edit primer/paint density
*Choose/add/edit a chemical
*Edit chemical weight fraction in primer/paint
Choose/edit primer/paint emission models
Choose/edit indoor sink model
Occupancy & Exposure
*Choose type of exposed individual
* Choose gender for exposed individual
Change default location during painting event for exposed
individual
Edit weekday/weekend patterns, pattern during painting
Edit exposure events, years in lifetime, body weight
Execution
Enter title of run and notes
* Choose length of model run and reporting interval
View/print report before/after execution
* Choose to execute or to save inputs and then execute
indicates inputs for which user should make a deliberate decision/choice; model defaults may
suffice for other inputs.
2-29
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3. MODEL RESULTS AND OUTPUTS
3.1 Exposure Estimates
An example of the exposure estimates provided by WPEM after executing the model is
shown in Figure 3-1. The particular results shown here are obtained when all values in WPEM
have been reset to defaults by selecting File at the top left of the screen, then New.
| Wall Paint Exposure Model (WPEM)
File Help
Hi £) ¦!
JnJ-Xj
Designing Wall Paint for the Indoor Environment
Introduction j Painting Scenario | Paint & Chemical | Occupancy & Exposure Execution |
Title of Run:
Notes:
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Length of Model Run: Days
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[M| Execute
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k-q Save & Execute
View/Print Report
MODEL LIMITATIONS
% Compl et[on
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LADD
ADD
APDR
APDR Time
Single Event Dose
mg>kg-days
LADC
mg/kg-days
ADC
mg/kg-days
C
peak
days
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mg
C
8-hr
7.72E-002 mgAn1
2.31 E-001 mgrtnx -or-
e.26E-K)00 m9/m' .or.
6.23E-W00 m9Al>" _ or _
4.98E+000 . or _
8.72E-003 ppm
2.62E-002 PPm
7.08 E-001 ppm
7.04E-001 ppm
5.63 E-001 ppm
Figure 3-1. Execution Screen (Results after Execution).
3-1
-------
Four exposure estimates based on inhalation dose are reported by WPEM: Lifetime
Average Daily Dose (LADD); Average Daily Dose (ADD); Acute Potential Dose Rate (APDR);
and single event dose. In general, each uses a form of the following equation:
where: C = average air concentration (mg/m3)
IR = inhalation rate (m3/hr)
FQ = frequency (events/year)
D = duration of an event (hours/event)
Y = years of exposure (years)
BW = body weight (kg)
AT = averaging time (years).
The algorithm used in WPEM actually multiplies the air concentration every 30 seconds
by the corresponding inhalation rate at that time, rather than using an average concentration as
indicated in the simplified expression given above. These products © * IR) for each time interval
are summed over the entire length of the model run, to obtain a single event dose that is used in
place of C * IR in the equation given above. For the LADD calculation, the averaging time is the
lifetime of the exposed individual. For the ADD calculation, the averaging time is the same as the
number of years of exposure. For the APDR calculation, an averaging time of one day is used.
That is, the APDR is the highest dose over a 24-hour period throughout the model run. The
reported APDR time, in days, marks the beginning of the 24-hour period with the highest dose.
Two different long-term measures of inhalation concentration are calculated in WPEM -
Lifetime Average Daily Concentration (LADC) and Average Daily Concentration (ADC) - based
on the following equation:
where: TC = time-integrated air concentration per event (mg/m3-days/event)
FQ = frequency (events/year)
Y = years of exposure (years)
AT = averaging time (years).
The model also provides several short-term concentration measures:
Cpeak ~ the highest instantaneous concentration to which the individual is exposed.
Cl5.min - the highest 15-minute-average concentration to which the individual is
exposed.
C8-hour ~ the highest 8-hour-average concentration to which the individual is
exposed.
Dose = (C * IR * FQ * D * Y) / (BW * AT * 365 days/yr)
(3-1)
Concentration = (TC * FQ * Y) / (AT * 365 days/yr)
(3-2)
3-2
-------
The calculation engine for WPEM currently has no constraint relating to the saturation
concentration in air for the chemical that is modeled.
3.2 Report
The report provided by WPEM summarizes the model inputs and presents the model
results. If the View/Print button is pressed before the model is executed, then all results show as
zeroes but the summary of inputs still is useful for review purposes. The report has two pages
(see Figures 3-2 and 3-3) that can be viewed in any sequence. The first page of the report
summarizes user inputs for the Painting Scenario screen and the Paint & Chemical screen. The
second page summarizes user inputs for the Occupancy & Exposure screen and the Execution
screen, and provides the summary model outputs (exposure estimates) as well. Either or both
pages of the report can be printed using the Printer command that can be accessed at the top of
the report.
3.3 Concentration Time Series
An additional output from the model is a comma-separated (.csv) file that contains details
on time-varying concentrations within the modeled building as well as concentrations to which the
individual is exposed. This file format can be read directly into spreadsheet software (e.g., Excel)
for developing concentration plots or calculating additional summary statistics. The .csv file
includes as its first line column headers that are read in along with the model outputs. If the user
does not save the inputs, then the file will be named wpem.csv. If the user does save the inputs,
then the .csv file will have the same prefix as that associated with the inputs.
Figure 3-4 is an example of the type of plot that can be developed rapidly with the aid of
the Excel chart wizard, for example. The time series of modeled concentrations over the length of
the model run (5 days) is shown for the painted space (zone 1), the remainder of the building
(zone 2), and outdoors. The modeled outdoor concentrations in WPEM are always zero or very
small. Figure 3-5 shows a plot of the concentrations to which the individual is exposed, a mixture
of those shown by zone in the previous plot and thereby providing an indication of the exposed
individual's location by zone over time. In this case the exposed individual is a professional
painter who leaves the building permanently when painting is finished on the first day and, thus,
has zero exposure thereafter.
3-3
-------
WPEM Model Report
Printer Page 1 Page 2 Exit
WPEM MODEL INPUTS
File with Concentration Details: C:\Program FilesVupemVmpem.CSV
Title of Run:
Notes:
Length of Model Run: 5 Days Reporting Interval: 60 minutes
3/13/2001
Type of Building: House
Wume: 15583 ft1
Percent Painted: 100.0 %
Painted Surface A"ea: 4519.07 ft1
,£
-------
1 WPEM Model Report
Printer Page 1 Page 2 Exit
WPEM MODEL INPUTS (cont'd)
3/13/2001
Exposed Individual: Professional Painter
Location During Painting: In painted area
Weekday Pattern
Line: 1 Zone: 0 Enter Hr: 0 Enter Min: 0
Gender: Non-Specific
Breathing Rate: 13.3 m'/day
Weekend Pattern
Line: 1 Zone: 0 Enter Hr: 0 Enter Min: 0
Breathing Rate: 13.3 m'/day
Breathing Rate During Painting: 27.5 mVday
Years in Lifetime: 75
WPEM MODEL RESULTS
Lifetime Exposure Events: 365
Avg. Body Weight: 71.8 kg
LADD: 2.96E-QQ2 mgfcg-days LADC: 7.72E-002 mg/rn1
ADD: 8.86E-002 mgAig-days ADC: 2.31E-001 rng/m1
APDR: 6.37E-G01 nng/kg-days Cpeak: 6.26E+000 mg/hi1
APDR Time: 4.71E+000 days 015-nnin: 6.23E+000 rng/rn1
Single Event Dose: 1.59E+002 mg C8-hour: 4.98E+000 rngAm*
-or- 8.72E-003 ppm
-or- 2.62E-0Q2 ppm
-or- 7.08E-0Q1 pprn
-or- 7.04E-001 pprn
-or- 5.63E-0Q1 ppm
LADD = Lifetime average daily dose
ADD = Average daily dose
APDR = Acute Potential Dose Rate [highest 24-hour dose rate for exposed individual)
LADC = Lifetime average daily concentration
ADC = Average daily concentration
Cpeak = highest instantaneous concentration to which individual is exposed
C15-min = highest 15-minute average concentration to which an individual is exposed
CS-hour = highest 8-hour average concentration to which individual is exposed
Figure 3-3. Page 2 of WPEM Report.
3-5
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0
Elapsed Time, days
• Cone Outdoors
(mg/m3)
n Cone Zone 1
(mg/m3)
* Cone Zone 2
(mg/m3)
Figure 3-4. Plot of Modeled Concentrations by Zone, from wpem.csv File.
10
8
6
4
2
0
o
o
o
o
o
o
o
o
o
o
o Conc@Person
0 2 4
Elapsed Time, days
Figure 3-5. Plot of Concentration to Which Individual is Exposed, from wpem.csv File.
3-6
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4.
DEFAULT SCENARIOS AND APPLICATION TIPS
4.1 Default Scenarios
A button near the top of the Painting Scenario screen, labeled DEFAULT SCENARIOS,
lists six default scenarios that can be accessed by the user:
RESDIY - A do-it-yourself (DIY) painter is exposed to a chemical in paint while
painting the bedroom of a house.
RESADULT - An adult located in the non-painted part of the house is exposed to
a chemical in paint while a bedroom is painted by a professional painter.
RESCHILD - A child located in the non-painted part of the house is exposed to a
chemical in paint while a bedroom is painted by a professional painter.
RESPROF - Two professional painters are exposed to a chemical in paint while
painting an entire apartment.
• OFF ADULT - An office worker is exposed to a chemical in paint after an entire
floor of a low-rise office building is painted by ten professionals over a weekend.
OFFPROF - Ten professional painters are exposed to a chemical in paint while
painting an entire floor of a low-rise office building over a weekend.
The name associated with each scenario refers to a file that can be loaded to access that
scenario. Such files, provided with the model, are located in the directory from which WPEM is
executed and have an extension of .wem. For example, to access the scenario called RESDIY,
the user can open the file named resdiy.wem, using the "Open a File" button on the toolbar near
the top of the screen. Alternatively, one can click on File at the top left of the screen, then Open,
to access the files with default scenarios.
Each file contains defaults for entries such as the type and percent of building painted, the
amount of primer and paint applied, the application rate and painting duration, the type of
exposed individual and location during the painting event, and the number of lifetime exposure
events. There are certain selections that are common across the default scenarios, such as
painting of walls only, selection of latex flat paint, selection of TMPD-MIB (texanol) as the
chemical, and selection of non-specific gender for the exposed individual. These and other default
entries should be reviewed by the user, and changed as needed using appropriate edit buttons,
before executing the model.
Table 4-1 summarizes input values used for each of the default scenarios. Exposure
descriptors for each scenario follow the table (see Section 4.2). Some application tips are
provided in Section 4.3.
4-1
-------
Table 4-1. Summary of Inputs for Default Scenarios
Input
Default Scenario
RESDIY
RESADULT
RESCHILD
RESPROF
OFFADULT
OFFPROF
Type of
Building
House
House
House
Apartment
Low-rise
office
Low-rise
office
Percent Painted
One bedroom
(10 %)
One bedroom
(10 %)
One bedroom
(10 %)
Entire building
(100 %)
Entire floor
(50 %)
Entire floor
(50 %)
Painted Surface
Walls only
Walls only
Walls only
Walls only
Walls only
Walls only
Painted Area
452 ft2
452 ft2
452 ft2
2,131.5 ft2
20,000 ft2
20,000 ft2
Number of
Coats
0 primer
1 paint
1 primer
1 paint
1 primer
1 paint
1 primer
1 paint
1 primer
1 paint
1 primer
1 paint
Paint Coverage
200/400 ft2/gal
(primer/paint)
200/400 ft2/gal
(primer/paint)
200/400 ft2/gal
(primer/paint)
200/400 ft2/gal
(primer/paint)
200/400 ft2/gal
(primer/paint)
200/400 ft2/gal
(primer/paint)
Number of
Painters
1 DIY
1 professional
1 professional
2 professional
10
professional
10
professional
Application
Rate per
Painter
0.33 gal/hr
0.85 gal/hr
0.85 gal/hr
0.85 gal/hr
0.85 gal/hr
0.85 gal/hr
Priming vs.
Painting
N/A
Paint same day
Paint same day
Paint same day
Paint same day
Paint same day
Total Duration
3.42 hours
3.99 hours
3.99 hours
9.4 hours
17.65 hours
17.65 hours
Type of Paint
Latex flat
Latex flat
Latex flat
Latex flat
Latex flat
Latex flat
Chemical
TMPD-MIB
TMPD-MIB
TMPD-MIB
TMPD-MIB
TMPD-MIB
TMPD-MIB
Weight
Fractions
0.01 primer
0.01 paint
0.01 primer
0.01 paint
0.01 primer
0.01 paint
0.01 primer
0.01 paint
0.01 primer
0.01 paint
0.01 primer
0.01 paint
Exposed
Individual
DIY
painter
Adult
occupant
Child
occupant
Professional
painter
Adult
occupant
Professional
painter
Gender
Non-specific
Non-specific
Non-specific
Non-specific
Non-specific
Non-specific
Location
during Painting
In painted area
In building,
not in painted
area
In building,
not in painted
area
In painted area
Not in
building
In painted area
Total Exposure
Events
37.5
50
10
3988
10
2125
Years in
Lifetime
75
75
10
75
75
75
Body Weight
71.8 kg
71.8 kg
20.3 kg
71.8 kg
71.8 kg
71.8 kg
Length of
Model Run
20 days
20 days
20 days
2 days
20 days
3 days
4-2
-------
4.2 Exposure Descriptors
RESDIY (Residential Do-It-Yourself, environment = house, exposed individual = non-professional
painter, e.g., homeowner)
The mean house volume (15,583 ft3 or 441 m3) and median air exchange rate (0.45 air changes per hour,
or ACH) used for this scenario are recommended values from the Exposure Factors Handbook (USEPA
1997). The value for the air exchange rate is indicative of a closed-house condition. A closed-house
situation was selected to be conservative. Data on residential air exchange rates under open-window
conditions are quite limited. An appropriate value for an open-window situation is probably on the order
of 1 to 2 air changes per hour (the 90th percentile for the distribution given in the Exposure Factors
Handbook is 1.26 ACH).
Values for the amount of paint, painting duration, and lifetime number of painting events are intended to
match closely those from an EPA-sponsored national usage survey of household solvent products
(WESTAT 1987). From that survey, for do-it-yourself (DIY) painters the median amount of latex paint
used is one gallon and the median duration of use is three hours, for an application rate of 0.33 gallons/hour.
The WPEM default house volume is 15,583 ft3 and the default wall loading ratio is 0.29 ft2/ft3 (see Section
2.1.2 of User's Guide), for a total wall area of 4,519 ft2. Assuming a paint coverage of 400 ft2/gallon
(container label, PDCA 1998) and that only walls are painted, about 9 percent (400 / 4,519) of the wall area
would be painted with one gallon. Therefore, for the RESDIY scenario, it is assumed that 10 percent (452
ft2) of the wall area is painted; this percentage results in 1.13 gallons of paint applied (i.e., 452 ft2/ 400 ft2
per gallon) and apainting duration of 3.42 hours (i.e., 1.13 gallons / 0.33 gallons per hour). This duration
is close to the median value (3 hours) from the above-cited national survey.
The national survey also indicates a median time-since-last-painting of 8 months. Assuming that
respondents, on the average, were queried at the halfway point between successive painting events, the
median duration between painting events would be 16 months, equating to 0.75 events per year. The
RESDIY scenario has 0.75 events per year over 50 years, or 37.5 painting events per lifetime. It is assumed
that for 25 years (i.e., the years of infancy, child, senior), a DIY painter would not paint at all.
The amount of time spent in different locations and the breathing rates for weekday/weekend activity
patterns in WPEM are derived from recommended values in the Exposure Factors Handbook. By
definition, the DIY painter is in the painted space during the painting event. Breathing rates while painting
are a weighted average of recommended values for light and moderate activities, with light receiving a
weight of 25 % and moderate a weight of 75 %. The values used for years in lifetime (75) and body weight
(71.8 kg for non-specific gender) also are recommended values from the Exposure Factors Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint
(Chang et al. 1998), again using four target compounds, indicated a substantial sink effect for all four
VOCs that were tested.
Figure 4-1. Exposure Descriptor for RESDIY Scenario.
4-3
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RESADULT (Residential Adult, environment = house, exposed individual = adult occupant)
The mean house volume (15,583 ft3 or 441 m3) and median air exchange rate (0.45 air changes per hour,
or ACH) used for this scenario are recommended values from the Exposure Factors Handbook (USEPA
1997). The value for the air exchange rate is indicative of a closed-house condition. A closed-house
situation was selected to be conservative. Data on residential air exchange rates under open-window
conditions are quite limited. An appropriate value for an open-window situation is probably on the order
of 1 to 2 air changes per hour (the 90th percentile for the distribution given in the Exposure Factors
Handbook is 1.26 ACH).
For this scenario 10 percent of the house is painted each year, based on the assumption that residential
occupants who use professional painters have their entire house painted once every 10 years. One coat of
primer and one coat of paint are applied to walls by a professional, with WPEM default coverages of 200
ft2/gallon for primer and 400 ft2/gallon for paint (per container labels, PDCA 1998). The WPEM default
house volume is 15,583 ft3 and the default wall loading ratio is 0.29 ft2/ft3 (see Section 2.1.2 of User's
Guide), for a total wall area of 4,519 ft2. For 10 percent of the wall area (452 ft2), as used in this scenario,
the default coverages result in 2.26 gallons of primer and 1.13 gallons of paint applied. The default
primer/paint application rate of 0.85 gallons/hour for a professional painter gives a total painting duration
of 3.99 hours. The default application rate is derived from the Estimating Guide developed by the Painting
and Decorating Contractors of America (PDCA 1998) - a labor production rate of 337.5 ft2/hour for
painting with a roller (range of 325-350 ft2/hour given in the guide), with a paint coverage of400 ft2/gallon,
equates to an application rate of 0.85 gallons/hour (i.e., 337.5 ft2/hour / 400 ft2/gallon).
As noted above, for this scenario it is assumed that a house is repainted in its entirety once every 10 years.
Since 10 percent of the house is being painted for the specific scenario, the painting event is assumed to
occur once a year. Over a period of 50 years of exposure (the WPEM default for an adult), this scenario
equates to 50 painting events per lifetime.
The amount of time spent in different locations and the breathing rates for weekday/weekend activity
patterns in WPEM are derived from recommended values in the Exposure Factors Handbook. An exposed
adult for this scenario is assumed to be in the house, but not in the painted area, during the painting event.
The values used for years in lifetime (75) and body weight (71.8 kg for non-specific gender) also are
recommended values from the Exposure Factors Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint
(Chang et al. 1998), again using four target compounds, indicated a substantial sink effect for all four
Figure 4-2. Exposure Descriptor for RESADULT Scenario.
4-4
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RESCHILD (Residential Child, environment = house, exposed individual = child occupant)
The mean house volume (15,583 ft3 or 441 m3) and median air exchange rate (0.45 air changes per hour,
or ACH) used for this scenario are recommended values from the Exposure Factors Handbook (USEPA
1997). The value for the air exchange rate is indicative of a closed-house condition. A closed-house
situation was selected to be conservative. Data on residential air exchange rates under open-window
conditions are quite limited. An appropriate value for an open-window situation is probably on the order
of 1 to 2 air changes per hour (the 90th percentile for the distribution given in the Exposure Factors
Handbook is 1.26 ACH).
For this scenario 10 percent of the house is painted each year, based on the assumption that residential
occupants who use professional painters have their entire house painted once every 10 years. One coat of
primer and one coat of paint are applied to walls by a professional, with WPEM default coverages of 200
ft2/gallon for primer and 400 ft2/gallon for paint (per container labels, PDCA 1998). The WPEM default
house volume is 15,583 ft3 and the default wall loading ratio is 0.29 ft2/ft3 (see Section 2.1.2 of User's
Guide), for a total wall area of 4,519 ft2. For 10 percent of the wall area (452 ft2), as used in this scenario,
the default coverages result in 2.26 gallons of primer and 1.13 gallons of paint applied. The default
primer/paint application rate of 0.85 gallons/hour for a professional painter gives a total painting duration
of 3.99 hours. The default application rate is derived from the Estimating Guide developed by the Painting
and Decorating Contractors of America (PDCA 1998) - a labor production rate of 337.5 ft2/hour for
painting with a roller (range of 325-350 ft2/hour given in the guide), with a paint coverage of400 ft2/gallon,
equates to an application rate of 0.85 gallons/hour (i.e., 337.5 ft2/hour / 400 ft2/gallon).
As noted above, for this scenario it is assumed that a house is repainted in its entirety once every 10 years.
Since 10 percent of the house is being painted for the specific scenario, the painting event is assumed to
occur once a year. Over a period of 10 years of exposure (the WPEM default for a child), this scenario
equates to 10 painting events per "lifetime."
The amount of time spent in different locations and the breathing rates for weekday/weekend activity
patterns in WPEM are derived from recommended values in the Exposure Factors Handbook. An exposed
child for this scenario is assumed to be in the house, but not in the painted area, during the painting event.
The value used for body weight (20.3 kg for non-specific gender) also is a recommended value from the
Exposure Factors Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint
(Chang et al. 1998), again using four target compounds, indicated a substantial sink effect for all four
Figure 4-3. Exposure Descriptor for RESCHILD Scenario.
4-5
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RESPROF (Residential Professional, environment = apartment, exposed individual = professional
painter)
The mean apartment volume (7,350 ft3 or 208 m3) and median air exchange rate (0.45 air changes per hour,
or ACH) used for this scenario are recommended values from the Exposure Factors Handbook (USEPA
1997). The handbook does not list air exchange rates for apartments, as all or most measured values have
been for attached/detached houses. The chosen value, indicative of a closed-house condition, is intended to
be conservative. Data on residential air exchange rates under open-window conditions are quite limited. An
appropriate value for an open-window situation is probably on the order of 1 to 2 air changes per hour (the
90th percentile for the distribution given in the Exposure Factors Handbook is 1.26 ACH).
For this scenario it is assumed that two professionals paint an apartment in its entirety. One coat of primer
and one coat of paint are applied to walls by the professionals, with WPEM default coverages of 200
ft2/gallon for primer and 400 ft2/gallon for paint (per container labels, PDCA 1998). The WPEM default
apartment volume is 7,350 ft3 and the default wall loading ratio is 0.29 ft2/ft3 (see Section 2.1.2 of User's
Guide), for a total wall area of 2,131.5 ft2. The default coverages result in 10.66 gallons of primer and 5.33
gallons of paint applied, for a total of 16 gallons. The default application rate by each of the two
professionals (0.85 gallons/hour for both primer and paint) results in a total painting duration of 9.4 hours.
The default application rate is derived from the Estimating Guide developed by the Painting and Decorating
Contractors of America (PDCA 1998) - a labor production rate of 337.5 ft2/hour for painting with a roller
(range of 325-350 ft2/hour given in the guide), with a paint coverage of 400 ft2/gallon, equates to an
application rate of 0.85 gallons/hour (i.e., 337.5 ft2/hour / 400 ft2/gallon).
For this scenario it is assumed that professional painters spend 1,500 hours per year painting (i.e., 30
hours/week times 50 weeks/year). Since the event described above takes 9.4 hours, there would be 159.5 such
events in a year of painting. Assuming that a professional painter works for 25 years on average, there would
be 3,988 such events over a painting "lifetime."
By definition, the professionals are located in the painted area throughout the entire application, and they are
assumed to leave the apartment as soon as painting is finished. Breathing rates while painting are a weighted
average of recommended values from the Exposure Factors Handbook for light and moderate activities, with
light receiving a weight of 25 % and moderate a weight of 75 %. The values used for years in lifetime (75)
and body weight (71.8 kg for non-specific gender) also are recommended values from the Exposure Factors
Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint (Chang
et al. 1998), again using four target compounds, indicated a substantial sink effect for all four VOCs that were
Figure 4-4. Exposure Descriptor for RESPROF Scenario.
4-6
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OFFADULT (Office Adult, environment = office building, exposed individual = adult office worker)
For this scenario an entire floor (50 percent) of a low-rise office building is painted by a team of ten
professional painters. The building volume (160,000 ft3 or 4,531 m3) was chosen using professional
judgment, and equates to a two-story office building with nominal length of 100 feet, width of 80 feet, and
height of 10 feet per story. The air exchange rate (1 air change per hour, or ACH) is close to the average (0.9
ACH) reported by Persily (1989), based on measurements in a number of office buildings.
One coat of primer and one coat of paint are applied to walls by the professionals, with WPEM default
coverages of200 ft2/gallon for primer and 400 ft2/gallon for paint (per container labels, PDCA 1998). Based
on the WPEM default volume of 80,000 ft3 for half of the building and the default wall loading ratio of 0.25
ft2/ft3 (see Section 2.1.2 of User's Guide), the painted wall area is 20,000 ft2. The default coverages result
in 100 gallons of primer and 50 gallons of paint applied, for a total of 150 gallons. With a team of ten
professional painters and an application rate of 0.85 gallons/hour for each painter, the total painting duration
is 17.65 hours. The default application rate is derived from the Estimating Guide developed by the Painting
and Decorating Contractors of America (PDCA 1998) - a labor production rate of337.5 ft2/hour for painting
with a roller (range of 325-350 ft2/hour given in the guide), with a paint coverage of 400 ft2/gallon, equates
to an application rate of 0.85 gallons/hour (i.e., 337.5 ft2/hour / 400 ft2/gallon).
For this scenario it is assumed, based on professional judgement, that office buildings are painted in entirety
once every 5 years, corresponding to 0.2 exposure events per year. Over a period of 50 years of exposure
(the WPEM default for an adult), this scenario equates to 10 painting events per lifetime.
The amount of time spent in different locations and the breathing rates for weekday/weekend activity patterns
in WPEM are derived from recommended values in the Exposure Factors Handbook. An exposed adult for
this scenario is assumed to be out of the office during the painting event. Following the event, the adult is the
office according to the default weekday/weekend activity patterns in WPEM. The values used for years in
lifetime (75) and body weight (71.8 kg for non-specific gender) also are recommended values from the
Exposure Factors Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint (Chang
et al. 1998), again using four target compounds, indicated a substantial sink effect for all four VOCs that
Figure 4-5. Exposure Descriptor for OFFADULT Scenario.
4-7
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OFFPROF (Office Professional, environment = office building, exposed individual = professional
painter)
For this scenario an entire floor (50 percent) of a low-rise office building is painted by a team of ten
professional painters. The building volume (160,000 ft3 or 4,531 m3) was chosen using professional
judgment, and equates to a two-story office building with nominal length of 100 feet, width of 80 feet, and
height of 10 feet per story. The air exchange rate (1 air change per hour, or ACH) is close to the average (0.9
ACH) reported by Persily (1989), based on measurements in a number of office buildings.
One coat of primer and one coat of paint are applied to walls by the professionals, with WPEM default
coverages of200 ft2/gallon for primer and 400 ft2/gallon for paint (per container labels, PDCA 1998). Based
on the WPEM default volume of 80,000 ft3 for half of the building and the default wall loading ratio of 0.25
ft2/ft3 (see Section 2.1.2 of User's Guide), the painted wall area is 20,000 ft2. The default coverages result
in 100 gallons of primer and 50 gallons of paint applied, for a total of 150 gallons. With a team of ten
professional painters and an application rate of 0.85 gallons/hour for each painter, the total painting duration
is 17.65 hours. The default application rate is derived from the Estimating Guide developed by the Painting
and Decorating Contractors of America (PDCA 1998) - a labor production rate of337.5 ft2/hour for painting
with a roller (range of 325-350 ft2/hour given in the guide), with a paint coverage of 400 ft2/gallon, equates
to an application rate of 0.85 gallons/hour (i.e., 337.5 ft2/hour / 400 ft2/gallon).
For this scenario it is assumed that professional painters spend 1,500 hours per year painting (i.e., 30
hours/week times 50 weeks/year). Since the event described above takes 17.65 hours, there would be 85 such
events in a year of painting. Assuming that a professional painter works for 25 years on average, there would
be 2,125 such events over a painting "lifetime."
By definition, the professionals are located in the painted area throughout the entire application, and they are
assumed to leave the building as soon as painting is finished. Breathing rates while painting are a weighted
average of recommended values from the Exposure Factors Handbook for light and moderate activities, with
light receiving a weight of 25 % and moderate a weight of 75 %. The values used for years in lifetime (75)
and body weight (71.8 kg for non-specific gender) also are recommended values from the Exposure Factors
Handbook.
Default emission rates determined by the WPEM software are based on chamber tests of latex and alkyd
paints (ARCADIS 1998) conducted under EPA's Designing Wall Paint for the Environment Project. The
default WPEM assumption of no indoor sinks may be conservative, depending on the specific chemical of
concern. Chamber sink tests for constituents of alkyd paint, under EPA's Designing Wall Paint for the
Environment Project, indicated a significant sink effect for MEKO but little or no effect for 1,2,4-
trimethylbenzene, 2-methyldecane, and undecane. Prior EPA sink tests for constituents of latex paint (Chang
et al. 1998), again using four target compounds, indicated a substantial sink effect for all four VOCs that
Figure 4-6. Exposure Descriptor for OFFPROF Scenario.
4-8
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4.3
Some Application Tips
Once inputs have been supplied and saved as needed, and the model has been executed, the
user may wish to model some other scenario that is different from the one just modeled. To reset
all model input parameters to their initial default values, it is not necessary to close WPEM and then
reopen the software. The same effect can be achieved by clicking on File at the top left of the
screen, then New. Alternatively, a file for a default scenario can be selected to insert the default
values for that scenario.
If the user selects a file for one of the default scenarios and then edits the file, it is advisable
to save the edits under a new file name, rather than overwriting the file that contains the default
scenario. The user is further advised to make copies of the default scenario files (the six sets of files
provided with the model that have extensions of .wem and .wel) in a directory that is different from
the one from which WPEM is executed (by default, the install package for WPEM places all files in
c:\program filesYwpem). With this safeguard, a default-scenario file can be restored to its original
values in the event that it is inadvertently overwritten, without the need to re-install the software.
The user also may wish to have a customized list of default values for his/her own use. The
simplest way of accomplishing this is to first reset all values to their initial defaults (as occurs when
first opening WPEM or when clicking on File, then New). Next, the appropriate inputs can be
edited to the values that the user would like to keep as a basic set of defaults. Once all edits have
been completed, they can be saved to a file with a name of the user's choice by clicking on File,
then Save As.
The WPEM software is sufficiently flexible to model a wide variety of situations. For
example, even a chamber test can be simulated using the software. The volume of the chamber can
be input by selecting residence, for example, and then editing the building volume. The user also
should make the choice that the entire building is painted, so that WPEM will use calculations for a
single-zone model. Next, the air exchange rate should be edited to match the conditions for the
chamber test. The value for the interzonal airflow rate does not matter because a single-zone model
will be used. Then one of the painted-surface choices (e.g., walls only) can be selected and the
value edited to match the loading in the chamber. The coverage or film thickness also should be
edited to match the modeled application. For small-chamber tests, the paint usually is applied
nearly instantaneously outside the chamber, after which the painted specimen is inserted. To match
this condition closely, the number of painters or the application rate can be edited so that the
calculated priming or painting duration (whichever applies) is a small value such as 0.01 hours. The
remaining edits would pertain to the type of paint and chemical to be modeled.
4-9
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5. REFERENCES
ARCADIS, 1998. Testing to Determine Chemical Emissions from Paint in Support of the EPA
Designing Wall Paint for the Indoor Environment Project - Description of the Testing Program
and Results. Final report prepared by ARCADIS Geraghty & Miller, Inc., for USEPA Office of
Pollution Prevention and Toxics under EPA Contract No. 68-W6-0023.
Chang, JCS, Sparks, LE, Guo, Z, and Fortmann, R, 1998. "Evaluation of Sinks Effects on VOCs
from a Latex Paint," J. Air & Waste Manage. Assoc. 48:953-958.
Evans, WC, 1994. "Development of Continuous-Application Source Terms and Analytical
Solutions for One- and Two-Compartment Systems." In Characterizing Sources of Indoor Air
Pollution and Related Sink Effects, ASTM STP 1287, American Society for Testing and
Materials, pp 279-293.
Koontz, MD, and Rector, HR, 1995. Estimation of Distributions for Residential Air Exchange
Rates. Final report prepared by GEOMET Technologies, Inc., for USEPA Office of Pollution
Prevention and Toxics.
PDCA, 1998. Estimating Guide, Nineteenth Edition. Published by the Painting and Decorating
Contractors of America, Fairfax, VA.
Matthews, JH, 1992. Numerical Methods for Mathematics, Science, and Engineering, Second
Edition, Prentice Hall, Englewood Cliffs, NJ.
Persily, AK, 1989. "Ventilation Rates in Office Buildings," In I AO 1989, American Society of
Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE), pp 128-136.
USEPA, 1992. Guidelines for Exposure Assessment. EPA/600/Z-92/001, U.S. Environmental
Protection Agency, Office of Research and Development, Office of Health and Environmental
Assessment.
USEPA, 1997. Exposure Factors Handbook, Volumes I-III. EPA/600/P-95/002Fa, b, c, U.S.
Environmental Protection Agency, Office of Research and Development, National Center for
Environmental Assessment.
WESTAT, 1987. Household Solvent Products: A National Usage Survey. Final report prepared
for USEPA Office of Pollution Prevention and Toxics under EPA Contract No. 68-02-4243.
5-1
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APPENDIX A
ALKYD PAINT CHAMBER TESTS
-------
Al. INTRODUCTION
A series of small-chamber tests was conducted by ARCADIS Geraghty and Miller, Inc., to
(1) characterize concentrations of various volatile organic compounds (VOCs) emitted from
different formulations of alkyd primer and paint, and (2) to explore the interactions of some of
these compounds with selected indoor sinks. In addition to the broad objectives of improving the
understanding of emission and sink behavior for these chemicals in alkyd primer and paint, a more
specific objective was to provide a quantitative basis for development of emission/sink models or
for estimating parameters for such models. In addition to the small-chamber tests, ARCADIS
Geraghty and Miller, Inc., conducted painting events at EPA's research house in North Carolina
for the primary purpose of gathering data to be used for model evaluation.
The sections that follow describe methods and results for bulk analysis of the alkyd
primer/paint formulations prior to chamber testing, small-chamber emission tests of these
formulations, development of predictive models for VOC emissions from alkyd primer and paint,
and sink behavior of selected chemicals in alkyd primer or paint.
A2. BULK ANALYSIS
Prior to conduct of small-chamber emission tests, each formulation of alkyd primer or
paint was analyzed to determine its chemical composition by weight. In brief, the procedure for
analysis of the bulk product that was followed by ARCADIS Geraghty and Miller, Inc.,
(ARCADIS 1998) involved (1) extracting alkyd primer and paints with methylene chloride, (2)
centrifuging the sample to remove solids, and (3) analyzing the supernatant by GC/MS.
Results of the bulk analysis are shown as chemical weight fractions (mg/g) in Table A-l.
The primary constituents of both the primer (formulation AP-F) and one of the paints
(formulation ASG-G) were propyl-cyclohexane, decane, and undecane. The second paint
(formulation ASG-H) was dominated by 2-methyldecane and various branched undecanes.
A-l
-------
Table A-l. Results of Bulk Analysis (mg/g) for Alkyd Primer and Paints
Chemical
AP-F
ASG-G
ASG-H
(primer)
(paint)
(paint)
Toluene
0.40
1.43
0.02
Octane
0.24
0.87
0.004
MEKO
2.63
1.95
2.56
Ethylbenzene
1.27
1.85
0.91
p-Xylene
3.98
5.47
2.93
Nonane
3.88
4.36
0.40
o-Xylene
1.71
2.02
1.28
Propyl-cyclohexane
13.30
16.50
0.59
Isopropylbenzene
0.20
0.17
0.01
n-Propylbenzene
0.90
0.73
0.10
p-Ethyltoluene
3.96
4.07
0.55
1,3,5 -T rimethy lbenzene
2.07
1.75
0.23
Decane
11.80
21.40
-
n-Decane
-
-
5.71
Branched Decane A
-
-
16.90
Branched Decane B
-
-
6.09
o-Ethyltoluene
1.52
1.20
0.15
1,2,4-Trimethy lbenzene
4.78
3.98
0.81
1,2,3 -Trimethy lbenzene
1.19
1.05
0.16
2-Methyldecane
1.97
3.47
51.50
Trans-decalin
2.41
3.16
1.17
Undecane
8.76
16.50
-
n-Undecane
-
-
5.48
Branched Undecane A
-
-
27.10
Branched Undecane B
-
-
13.40
Branched Undecane C
-
-
49.30
Branched Undecane D
-
-
7.41
Branched Undecane E
-
-
24.90
Branched Undecane F
-
-
21.30
Dodecane
1.85
2.40
0.22
A-2
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A3. SMALL-CHAMBER EMISSION TESTS
The small-chamber emission tests were conducted by ARCADIS Geraghty and Miller,
Inc., in the EPA APPCD Source Characterization Laboratories located in the EPA Environmental
Research Center in Research Triangle Park, NC. The tests were conducted using 53-liter,
stainless-steel chambers housed in a temperature-controlled incubator. These chambers have been
fitted with inlet and outlet manifolds for the air supply, temperature and relative humidity sensors,
and a small fan to ensure mixing within the chamber. During each test, clean (VOC- and particle-
free) air was supplied to the chamber at a controlled relative humidity. A glass sampling manifold
has been connected to the chamber outlet for collection of air samples.
The substrate used in the tests was 0.5-inch gypsum wallboard that was purchased from a
local retail outlet in North Carolina. For each test, the substrate was cut to a size of 16 by 16 cm
(total area of 256 cm2 or 0.0256 m2), resulting in a surface-to-volume loading ratio of about 0.5
m2/m3 in the chamber. The edges were sealed and the test specimen was placed on the floor of
the chamber during the test. The cut and sealed substrate was conditioned in the chamber for at
least 24 hours prior to application of primer/paint.
Primer and paint were applied to the wallboard with a roller purchased at a local retail
outlet. The rate of primer/paint application in the tests, and resulting wet film thickness, were
based on recommendations from the manufacturers. The mass of paint applied was determined
gravimetrically by two methods. Wet film thickness was not measured with a gage during the
tests because the gage affects surface film characteristics and the specimen was to be inserted into
the chamber as quickly as possible after priming or painting. Based on the measured mass of paint
applied and the known specific gravity of the coating, the average calculated wet film thickness
was 415 jim (16.4 mil) for the alkyd primer and 105 //m (4.1 mil) for the alkyd paint.
As noted above, the wallboard specimen was conditioned in the chamber at least 24 hours
before the test. Background concentrations were measured prior to removing the specimen.
Primer then was applied, the specimen was re-inserted in the chamber, and air samples were
collected for the next 48 hours. Then the specimen was removed, paint was applied, the
wallboard again was inserted in the chamber, and air samples were collected during the next 12
days. Thus, the total monitoring period for each test was 14 days in duration.
Two tests were conducted for alkyd primer and paint. The primer AP-F, for which the
A-3
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contents (as determined through bulk analysis) were previously described in Table A-l, was used
for both tests. Paint formulation ASG-G was used in the first chamber emission test (test Al),
and formulation ASG-H was used in the second test (test A2).
It has been observed in previous chamber tests that emission rates for various compounds
in paint tend to decline exponentially over time as the reservoir of material that can be emitted is
gradually depleted, and as the drying paint forms a barrier that retards emissions. Two types of
empirical models for estimating the time-varying emission profile can be used: (1) a single-
exponential model governed by an initial emission rate and a rate of decline from the initial rate,
and (2) a double-exponential model with two sets of initial emission rates and rates of decline, one
to account for an early ("fast") phase of evaporation-dominated emissions and one to account for
a later ("slow") phase of diffusion-dominated emissions.
Because chemicals in alkyd paint tend to volatilize quite rapidly, a single-exponential
model should be sufficient to describe the emissions behavior. The time-varying emission rate for
the single-exponential model is given by the following equation:
S(t) = £0e"b (A"1)
where: S(l) = Source strength as a function of time (mass/time)
E0 = Initial emission rate (mass/time)
k = First-order rate constant (time"1)
t = Time.
The mass-balance equation for an environmental test chamber with a constant airflow rate and a
single source is as follows:
dC
V — = S{t)~ QC (A-2)
at
where: C = Concentration in the chamber (mass/volume)
V = Volume of the chamber
Q = Airflow rate into and out of the chamber (volume/time).
Integrating Equation A-2 with the source term defined by Equation A-l and assuming an initial
concentration of zero gives the following equation:
A-4
-------
c(0 =
En
V
VV J
—kt
7 V
J
(A-3)
For each chamber test, equation A-3 was fit to chamber data for each of the chemicals in
alkyd primer and paint using non-linear regression analysis. The measured chamber volume and
airflow rate were taken as "knowns," and the initial emission rate and the first-order rate constant
for emissions decline were estimated through the regression technique. In each case, the fits were
done separately for the priming and painting portions of the test.
Examples fits of the single-exponential emissions model to the chamber concentration data
are shown in Figures A-l, A-2, and A-3, for MEKO, decane, and undecane, respectively. All data
shown in the figures are from in test Al, involving primer formulation AP-F and paint formulation
ASG-G. All three fits are quite good, both for primer and paint, with departure only at the peak
value for paint. In some cases the modeled concentrations decrease somewhat more rapidly than
indicated by the data, but the overall trend in the data still is followed quite closely by the model.
MEKO -- Alkyd Test A1
5.00E+01
4.00E+01
E
ui
E
c
¦x 3.00E + 01
2.00E+01
-Line of Best Fit
0.00E+00
——~—~ + i ~
150 200
Time, hours
Figure A-l. Fit of Single-Exponential Emissions Model to Alkyd Chamber Data for MEKO.
A-5
-------
Decane--Alykyd Test A1
1.20E+03
1.00E+03
, 8.00E+02
E
E
c
¦| 6.00E+02
c
~ Data
Line of Best Fit
Q)
C
o
o
4.00E+02
2.00E+02
0.00E+00
0
50
100
150
200
250
300
350
400
Time, hours
Figure A-2. Fit of Single-exponential Emissions Model to Alkyd Chamber Data for Decane.
Undecane -- Alkyd Test A1
.00E+02
5.00E+02
4.00E+02
~ Data
Line of Best Fit
c
O
3.00E+02
CO
c
0)
o
< ,
c
o
° 2.00E+02
1.00E+02
0.00E+00
0
50
100
150
200
250
300
350
400
Time, hours
Figure A-3. Fit of Single-exponential Emissions Model to Alkyd Chamber Data for Undecane.
A-6
-------
Estimates of the parameters (Eo and k) for the single-exponential emissions model
described above are summarized for chemicals in the primer and paint for test A1 in Table A-2
and for test A2 in Table A-3. The R2 values shown in the table provide a general indication of
how well the empirical emissions model fits the data for each chemical, with values of 0.9 or
higher indicating particularly good fits. Adequate fits ( R2 value > 0.7) were obtained in test A1
for 18 of the 20 chemicals in primer and for all 20 of the chemicals in paint (same chemicals in
paint as in primer for this test), and in test A2 for 20 of 28 chemicals in primer and for 20 of 22
chemicals in paint.
One notable difference in the test results is that very good fits were obtained for MEKO,
both for primer and paint, in test Al, whereas for test A2 the fits were quite poor. Most of the
cases of poorer fits for test A2 were for branched undecanes, for which there may be greater
measurement uncertainty due to inability to obtain clear separation in the GC analysis. There also
were a few estimates for the decay rate (k) in emissions that appeared to be unduly high, possibly
as an artifact of measurement uncertainty, for chemicals in paint for test A2. These potential
outlier cases include ethylbenzene, p-xylene, propyl-cyclohexane, and one of the branched
undecanes, each with an estimated k value between 45 and 75, or about an order of magnitude
higher than most other estimated k values.
Another notable pattern apparent in both Table A-2 and Table A-3 is that, for virtually all
chemicals, the estimated decay rate constant is higher (i.e., faster rate of decline) for paint than for
primer. This faster rate of decline for chemicals in paint is believed to be related to its lower wet
film thickness. That is, a "thinner" film could be expected to result in a more rapid rate of off-
gassing or volatilization. This apparent relationship between volatilization rate and wet film
thickness is discussed further below under the topic of an empirical emissions model that has been
developed for chemicals released from alkyd primer and paint.
The emitted mass for each chemical can be estimated as the integral of equation A-l, or
E0/k (values for E0 and k are shown for each chemical in Tables A-2 and A-3). The applied mass
for each chemical is the total applied paint mass multiplied by the chemical weight fraction from
bulk analysis (shown for each chemical in Table A-l). The recovery for each chemical, shown in
Table A-4, is defined as ratio of emitted mass to applied mass; ideally, the recovery value would
be close to unity, or 100 percent. Considering measurement uncertainty, recovery values in the
range of 70 to 130 percent are reasonably close to the ideal value. Cases meeting this criterion,
and the criterion of adequate fit for the single-exponential emissions model (i.e., R2 value of at
A-7
-------
least 0.7 in Table A-2 or Table A-3), were used for development of a predictive model for
emissions as described below.
Table A-2. Alkyd Parameter Estimates (Single-exponential Emissions Model) for Test A1
Chemical
Primer
Paint
Eo (mg/h)
k (h-1)
R2
Eo (mg/h)
k (h-1)
R2
Toluene
5.4
5.8
0.99
3.5
7.9
0.87
Octane
3.6
4.6
0.96
8.9
9.4
0.89
MEKO
16.1
4.0
0.98
9.8
5.6
0.95
Ethylbenzene
18.7
5.0
0.97
15.6
8.0
0.89
p-Xylene
68.5
4.9
0.97
60.4
8.5
0.94
Nonane
84.4
3.5
0.95
82.3
7.8
0.94
o-Xylene
26.5
4.3
0.95
22.1
8.0
0.94
Propyl-cyclohexane
254.8
3.0
0.95
300.6
7.4
0.94
Isopropylbenzene
3.1
3.7
0.91
1.9
5.9
0.90
n-Propylbenzene
14.5
3.1
0.91
10.5
6.9
0.94
p-Ethyltoluene
76.9
3.7
0.85
64.5
8.3
0.94
1,3,5 -T rimethy lbenzene
21.4
0.8
0.87
65.1
8.6
0.93
Decane
97.1
1.3
0.87
261.2
5.0
0.94
o-Ethyltoluene
12.8
2.2
0.69
14.3
7.4
0.90
1,2,4-Trimethy lbenzene
42.8
1.8
0.84
43.5
5.4
0.94
1,2,3 -Trimethy lbenzene
5.4
1.4
0.78
6.2
4.8
0.93
2-Methyldecane
10.8
1.1
0.87
22.7
3.1
0.90
Trans-decalin
11.0
1.0
0.84
21.7
4.0
0.93
Undecane
21.4
0.4
0.81
67.6
2.1
0.91
Dodecane
0.9
0.1
0.37
1.4
0.3
0.81
A-8
-------
Table A-3. Alkyd Parameter Estimates (Single-exponential Emissions Model) for Test A2
Chemical
Primer
Paint
Eo (mg/h)
k (h-1)
R2
Eo (mg/h)
k (h-1)
R2
Toluene
6.3
6.4
0.99
--
--
--
Octane
5.5
6.1
0.99
-
-
-
MEKO
6.5
4.1
0.19
0.1
0.0
0.43
Ethylbenzene
19.9
4.6
0.98
43.6
74.5
0.97
p-Xylene
74.0
4.8
0.98
197.7
75.5
0.98
Nonane
82.4
3.1
0.97
9.5
16.9
0.96
o-Xylene
27.8
4.0
0.97
16.9
13.3
0.97
Propyl-cyclohexane
256.1
2.6
0.96
50.9
63.5
0.92
Isopropylbenzene
3.1
3.3
0.93
-
-
-
n-Propylbenzene
15.4
3.1
0.89
-
-
-
p-Ethyltoluene
98.0
4.1
0.89
5.7
7.2
0.91
1,3,5 -T rimethy lbenzene
42.1
3.7
0.69
2.0
5.2
0.90
Decane
119.3
1.7
0.82
58.5
4.6
0.96
Branched Decane A
42.0
2.4
0.84
209.5
5.5
0.97
Branched Decane B
15.6
2.2
0.78
64.0
4.6
0.97
o-Ethyltoluene
23.4
3.9
0.84
-
-
-
1,2,4-Trimethy lbenzene
55.6
2.4
0.78
3.9
4.1
0.91
1,2,3 -Trimethy lbenzene
5.9
1.5
0.78
-
-
-
2-Methyldecane
6.9
1.0
0.58
265.2
2.2
0.96
Trans-decalin
13.7
1.4
0.69
3.4
1.8
0.87
Undecane
21.6
0.5
0.64
13.2
1.4
0.93
Branched Undecane A
32.0
1.4
0.71
176.1
2.7
0.94
Branched Undecane B
4.1
0.7
0.72
85.2
2.7
0.93
Branched Undecane C
11.6
1.3
0.65
326.9
2.8
0.95
Branched Undecane D
11.2
1.2
0.60
1487.4
45.2
0.68
Branched Undecane E
6.3
0.9
0.33
200.6
3.8
0.81
Branched Undecane F
1.4
0.7
0.85
82.1
1.8
0.90
Dodecane
1.1
0.1
0.71
0.1
0.1
0.93
A-9
-------
Table A-4. Recoveries for Chemical in Alkyd Primer and Paints
Test A1-Primer
Test A1-Paint
Test A2-Primer
Test A2-Paint
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
Chemical
PlipmifQl
Applied
Emitted
Recovery
Applied
Emitted
Recovery
Applied
Emitted
Recovery
Applied
Emitted
Recovery
(mg)
(Eo/k)
(%)
(mg)
(Eo/k)
(%)
(mg)
(Eo/k)
(%)
(mg)
(Eo/k)
(%)
Toluene
2.69
0.93
34.58
3.09
0.44
14.38
2.80
0.98
34.97
Octane
1.61
0.77
47.87
1.88
0.95
50.79
1.68
0.89
53.11
—
--
—
MEKO
17.67
4.02
22.73
4.21
1.74
41.41
18.44
1.60
8.67
5.71
3.82
66.99
Ethylbenzene
8.53
3.76
44.01
4.00
1.96
48.93
8.90
4.30
48.32
2.03
0.59
28.88
p-Xylene
26.75
13.98
52.26
11.82
7.12
60.22
27.90
15.43
55.32
6.53
2.62
40.07
Nonane
26.07
23.99
92.00
9.42
10.58
112.29
27.20
26.67
98.04
0.89
0.56
62.76
o-Xylene
11.49
6.15
53.55
4.36
2.77
63.45
11.99
6.99
58.30
2.85
1.27
44.36
Propyl-cyclohexane
89.38
85.76
95.96
35.64
40.57
113.83
93.23
97.07
104.12
1.32
0.80
60.87
Isopropylbenzene
1.34
0.84
62.19
0.37
0.33
89.27
1.40
0.95
68.11
--
--
--
n-Propylbenzene
6.05
4.69
77.51
1.58
1.52
96.39
6.31
5.02
79.55
--
--
--
p-Ethyltoluene
26.61
20.73
77.90
8.79
7.78
88.50
27.76
24.03
86.57
1.23
0.79
64.33
1,3,5 -T rimethy lbenzene
13.91
25.91
186.29
3.78
7.60
200.95
14.51
11.43
78.74
0.51
0.38
74.85
Decane
79.30
76.81
96.86
46.22
52.72
114.06
82.72
70.70
85.47
12.73
12.78
100.37
Branched Decane A
--
--
--
--
--
--
--
--
--
37.69
37.91
100.60
Branched Decane B
--
--
--
--
--
--
--
--
--
13.58
13.89
102.29
o-Ethyltoluene
10.21
5.86
57.38
2.59
1.93
74.37
10.66
5.99
56.19
--
--
--
1,2,4-Trimethy lbenzene
32.12
24.19
75.31
8.60
8.05
93.63
33.51
23.28
69.49
1.81
0.95
52.34
1,2,3 -Trimethy lbenzene
8.00
3.77
47.13
2.27
1.30
57.15
8.34
4.00
47.92
--
--
--
2-Methyldecane
13.24
9.95
75.14
7.50
7.26
96.86
13.81
7.02
50.81
114.85
118.61
103.27
Trans-decalin
16.20
11.28
69.67
6.83
5.43
79.51
16.89
9.72
57.53
2.61
1.85
71.07
Undecane
58.87
55.07
93.55
35.64
32.20
90.34
61.41
46.03
74.95
12.22
9.55
78.11
Branched Undecane A
--
--
--
--
--
--
--
--
--
60.43
65.58
108.51
Branched Undecane B
--
--
--
--
--
--
--
--
--
29.88
31.53
105.50
Branched Undecane C
--
--
--
--
--
--
--
--
--
109.94
115.22
104.80
Branched Undecane D
--
--
~
~
--
~
--
--
~
16.52
32.89
199.07
Branched Undecane E
--
--
~
~
~
~
~
~
~
55.53
53.16
95.74
Branched Undecane F
--
--
--
~
~
~
~
~
~
47.50
46.88
98.69
Dodecane
12.43
14.63
117.71
5.18
4.30
82.90
12.97
7.06
54.44
0.49
1.09
223.09
A-10
-------
As stated earlier, a single-exponential model should be sufficient to describe the emissions
behavior of chemicals in alkyd paint, because they tend to volatilize quite rapidly. To verify this
assertion, a double-exponential model was fit for selected chemicals in alkyd paint, representing a range
of volatilities. The assessment was limited to the painting portion of the test, to have a sufficiently long
"tail" to enable a reliable fit to the data (chamber measurements for the priming portion of the test lasted
only 48 hours). As described in greater detail for latex paint in Appendix C, the initial emission rate and
rate constant for emissions decline were estimated first for the "slow" phase of emissions decline, using
concentration data after the first 24 hours following paint application. Next, the entire time series was
used to estimate parameters for the "fast" phase, treating the estimates for the slow phase as "knowns."
Results of the assessment are summarized in Table A-5 for the seven chemicals used for this
exercise. Although there are parameter estimates for both the fast and the slow phases for the double-
exponential model, only the estimates for the fast phase are shown in the table, for direct comparison with
those for the single-exponential model. As shown in the table, there is virtually no difference in the two
sets of parameter estimates, supporting the assertion that a single-exponential model is adequate for
chemicals in alkyd paint. The R2 values (fraction of variance explained by the model) in the table also are
practically identical for the two sets of estimates, indicating that addition of a second exponential makes
no significant improvement to the fit. The only chemical for which the R2 value changed noticeably (from
0.81 to 0.83) was undecane, the least volatile of the chemicals used in this assessment.
Table A-5. Alkyd Parameter Estimates (Single- vs. Double-exponential Emissions Model) for Painting Portion of Test A1
Chemical
Single-exponential Model
Double-exponential Model*
Eo (mg/h)
k (h-1)
R2
Eo (mg/h)
k (h-1)
R2
p-Xylene
60.4
8.5
0.94
60.4
8.5
0.94
o-Xylene
22.1
8.0
0.94
22.1
8.0
0.94
n-Propylbenzene
10.5
6.9
0.94
10.5
6.9
0.94
1,2,4-Trimethylbenzene
43.5
5.4
0.94
43.7
5.4
0.94
2-Methyldecane
22.7
3.1
0.90
22.8
3.2
0.90
Undecane
67.6
2.1
0.91
68.1
2.1
0.91
Dodecane
1.4
0.3
0.81
1.4
0.4
0.83
*Estimates shown for Eo and k are for the first ("fast") exponential of the double-exponential model, for direct
comparison with the estimates for the single-exponential model; the R2 value is for both exponentials combined.
A-ll
-------
A4. DEVELOPMENT OF A PREDICTIVE MODEL
Table A-6 lists the estimated emission decay rates for chemicals in primer and paint from the two
chamber tests that were conducted (tests A1 and A2). Chemical properties (molecular weight and vapor
pressure) also are listed in the table. Perhaps the most noteworthy relationship apparent from the table is
that, for nearly every chemical, the decay rate for the chemical in paint was consistently higher (by about
a factor of two) than that for the same chemical in primer. The primary difference between the primer
and paint application in these tests was the much greater wet film thickness (by about a factor of four) for
primer than paint. Thus, there is an apparent inverse relationship between film thickness and the decay
rate - the greater the film thickness (as with primer), the slower the decay rate.
Table A-6. Emission Decay Rates and Chemical Properties for Chemicals in Alkyd Primer and Paints
Chemical
Emission Decay Rates (h1)
Molecular
Weight
(g/mole)
Vapor
Pressure
(mm Hg)
Test Al-
Primer
Test Al-
Paint
Test A2-
Primer
Test A2-
Paint
Toluene
5.82
7.93
6.45
92.2
12.10
Octane
4.62
9.38
6.12
—
114.3
18.90
MEKO
4.00
5.64
4.09
0.02
87.1
0.90
Ethylbenzene
4.98
7.98
4.62
74.46
106.2
4.34
p-Xylene
4.90
8.49
4.80
75.53
106.2
4.34
Nonane
3.52
7.79
3.09
16.90
128.3
7.08
o-Xylene
4.30
7.99
3.97
13.32
106.2
4.34
Propyl-cyclohexane
2.97
7.41
2.64
63.50
126.3
4.59
Isopropylbenzene
3.74
5.92
3.28
-
120.2
2.89
n-Propylbenzene
3.09
6.89
3.07
-
120.2
1.56
p-Ethyltoluene
3.71
8.28
4.08
7.21
120.2
1.56
1,3,5 -T rimethy lbenzene
0.83
8.57
3.69
5.18
120.2
1.57
Decane
1.26
4.96
1.69
4.58
142.3
2.67
Branched Decane A
--
--
2.36
5.53
142.3
2.67
Branched Decane B
--
--
2.15
4.61
142.3
2.67
o-Ethyltoluene
2.19
7.40
3.91
--
120.2
1.56
1,2,4-Trimethy lbenzene
1.77
5.41
2.39
4.11
120.2
1.57
1,2,3 -Trimethy lbenzene
1.43
4.78
1.47
-
120.2
1.57
2-Methyldecane
1.09
3.13
0.99
2.24
156.4
1.82
Trans-decalin
0.97
3.99
1.41
1.84
138.3
1.35
Undecane
0.39
2.10
0.47
1.38
156.4
1.02
Branched Undecane A
--
--
1.45
2.69
156.4
1.82
Branched Undecane B
--
--
0.74
2.70
156.4
1.82
Branched Undecane C
--
--
1.30
2.84
156.4
1.82
Branched Undecane D
--
--
1.18
45.22
156.4
1.82
Branched Undecane E
-
-
0.90
3.77
156.4
1.82
A-12
-------
For paint in test A-2, there are six chemicals with estimated emission decay rates greater than ten.
Such outcomes are believed to be an artifact, probably due to insufficient values for the rising part of the
concentration curve.
Empirical Model
Relationships between the emission decay rate and chemical properties, if any, cannot be deduced
readily from Table A-6. The scatter plots in Figures A-4 and A-5 indicate an inverse relationship between
the decay rate and molecular weight (R2 = 0.45) and a direct relationship between the decay rate and
vapor pressure (R2 = 0.12). That is, higher values of molecular weight are associated with slower
emission decay rates, like the relationship between film thickness and decay rate, whereas higher values of
vapor pressure are associated with higher emission rates.
The above relationships indicate that the following empirical model may be useful as a tool for
predicting the emission decay rate from chemical properties and wet film thickness:
Parameter estimates for the constants were obtained through nonlinear regression analysis. As noted
previously, the subset of chemicals from tests A-l and A-2 that met certain conditions was used in the
estimation procedure. The model with parameter estimates can be expressed as follows:
This model provides a reasonably good fit to the data, with an R2 value of 0.86. The relatively strong
relationship between emission decay rates estimated from the chamber data and those predicted by the
empirical model is illustrated in Figure A-6.
k = a * VPb / (MW * FT1)
(A-4)
where k = emission decay rate (inverse hours);
VP = vapor pressure (torr);
MW = molecular weight (g/mole);
FT = film thickness (mil); and
a, b, c, and d are constants to be estimated.
E = 2.95 * 109 * VP0'27/ (MW4-02 *FT-58)
(A-5)
A-13
-------
Pri me r
Paint
80 100
Molec u lar We ight
Figure A-4. Relationship between Emission Decay Rate and Molecular Weight.
~
A
~
~
~
~
~
~ Primer
~ Pai nt
~ ~
~
~
~ A
~ ~
~
~
~
~ ~
~
~ ~
* •
012345678
Vapor Pressure (mm h g )
Figure A-5. Relationship between Emission Decay Rate and Vapor Pressure.
A-14
-------
0123456789
Estimated kfrom Chamber Data
Figure A-6. Comparison of Predicted Emission Decay Rates from Empirical Model
with Estimated Decay Rates from Chamber Data.
Table A-7 provides a comparison between predicted emission decay rates, based on the empirical
model (see Equation A-5), and decay rates that were estimated from the chamber concentration data. As
noted above, not all chemicals were used in developing the empirical model. Most of the chemicals with
the largest discrepancy between predicted and estimated rates have larger k values and were not used in
development of the predictive model. The majority of the errors have a positive sign, meaning that the
predicted decay rate typically is larger then estimated rate. As a result, the empirical model will tend to
provide a conservative prediction - that is, a larger k value will result in a higher modeled peak
concentration, other things being equal.
The empirical model tends to have a larger prediction error for chemicals with a lower molecular
weight (see Figure A-7). Although the relationship is not as pronounced, the model also tends to have a
greater prediction error for chemicals with higher vapor pressure (see Figure A-8), with the notable
exception of MEKO (which has a relatively low vapor pressure of 0.9 torr but relatively high prediction
errors, on the order of 5 and 15 for primer and paint, respectively). As noted above, the greatest
prediction errors generally are for chemicals with higher k values; most of these chemicals have a
comparatively low molecular weight and high vapor pressure.
A-15
-------
Table A-7. Predicted Versus Estimated Emission Decay Rates for Chemicals in Test A1
Chemical
Primer
Paint
Predicted
k
Estimated
k
Error*
Percent
Error**
Predicted
k
Estimated
k
Error
Percent
Error
Toluene
14.4
5.8
8.6
147
32.2
7.9
24.3
307
Octane
6.8
4.6
2.2
48
15.3
9.4
5.9
63
MEKO
9.1
4.0
5.1
126
20.3
5.6
14.6
259
Ethylbenzene
6.2
5.0
1.2
25
13.9
8.0
5.9
74
p-Xylene
6.2
4.9
1.3
27
13.9
8.5
5.4
64
Nonane
3.3
3.5
-0.2
6
7.4
7.8
-0.4
5
o-Xylene
6.2
4.3
1.9
44
13.9
8.0
5.9
74
Propyl-cyclohexane
3.1
3.0
0.2
6
7.0
7.4
-0.4
5
Isopropylbenzene
3.4
3.7
-0.4
9
7.6
5.9
1.7
28
n-Propylbenzene
2.9
3.1
-0.2
7
6.4
6.9
-0.5
7
p-Ethyltoluene
2.9
3.7
-0.8
23
6.4
8.3
-1.9
22
1,3,5 -T rimethy lbenzene
2.9
0.8
2.1
247
6.4
8.6
-2.1
25
Decane
1.7
1.3
0.4
33
3.8
5.0
-1.2
24
o-Ethyltoluene
2.9
2.2
0.7
31
6.4
7.4
-1.0
13
1,2,4-Trimethy lbenzene
2.9
1.8
1.1
63
6.4
5.4
1.0
19
1,2,3 -Trimethy lbenzene
2.9
1.4
1.5
101
6.4
4.8
1.7
35
2-Methyldecane
1.0
1.1
-0.04
4
2.3
3.1
-0.8
26
Trans-decalin
1.6
1.0
0.6
60
3.5
4.0
-0.5
12
Undecane
0.9
0.4
0.5
129
2.0
2.1
-0.1
5
Dodecane
0.5
0.1
0.4
716
1.1
0.3
0.8
247
* Error = (predicted k - estimated k).
**Percent Error = (absolute value of error / estimated k) * 100.
Summary statistics on prediction errors for the empirical model are provided in Table A-8 for three
sets of chemicals - (1) chemicals used to develop the model, (2) all chemicals used in test Al, and (3) the
subset of chemicals in test Al that were not used in developing the model. Not unexpectedly, the smallest
errors were for the set of chemicals used to develop the model, and the largest errors were for the test-Al
subset not used in developing the model. The medians in the table are more indicative of the central
tendency for prediction error, as the mean can be heavily influenced by relatively large prediction errors at
the upper tail of the distribution. The median errors are 0.5 (22 percent) for chemicals used to develop the
empirical model, 1.1 (30 percent) for all test-Al chemicals, and 2.1 (63 percent) for the subset of test-Al
chemicals that were not used in developing the model. There generally is a larger prediction error for
chemicals in paint than for chemicals in primer.
A-16
-------
+
~ Primer
+
+ Paint
~
1
~
-H-
+
B D f
i i i B
a fi A ±
80 90 100 110 120 130 140
Molecular Weight, g/mole
150 160
170
180
Figure A-7. Relationship between Empirical Model Prediction Error and Molecular Weight.
~ Primer
+ Paint
1*1 ijmjfi So
a
! 10 12
Vapor Pressure, torr
14
16
20
Figure A-8. Relationship between Empirical Model Prediction Error and Vapor Pressure.
A-17
-------
Table A-8. Summary Statistics on Errors in Emission Decay Rates Predicted by Empirical Model
Sets of Chemicals
Error
Percent Error
(number of chemicals per set)
Mean
Median
Range
Mean
Median
Range
All chemicals used for model (35)
0.7
0.5
0.004-1.9
59
22
0.2 - 716
- chemicals in primer (19)
0.5
0.4
0.004-1.2
77
22
0.2 - 716
- chemicals in paint (16)
0.9
0.8
0.1 - 1.9
37
21
4-247
All chemicals in test 1 (40)
2.6
1.1
0.05-24.3
79
30
4 - 716
- chemicals in primer (20)
1.5
0.8
0.05 -
93
39
4 - 716
- chemicals in paint (20)
3.8
1.4
8.6
n i
66
25
5 - 37
24.3
Chemicals in test 1 not used
for the model (19)
4.8
2.1
0.4 -
90
63
5 - 307
- chemicals in primer (10)
2.5
1.7
24.3
81
46
9-246
- chemicals in paint (9)
7.4
5.9
0.4 - 8.6
101
64
5 - 307
0.4 -
24.3
The prediction errors for the empirical model are not severe, especially when considered in light of
the evidence provided below in Table A-9. Once the emission decay rate becomes arbitrarily large (e.g.,
greater than 5 h"1), doubling the rate has little effect on the peak concentration. Similarly, once the painting
duration becomes arbitrarily long (e.g., longer than 3 hours), the decay rate has little effect on the peak
concentration except at very low values (e.g., below 1 h"1). As shown in the lower part of the table, the
effect of the emission decay rate on single-event dose is even less pronounced, regardless of the painting
duration.
For the data shown in Table A-9, a single-zone scenario was modeled whereby the walls of a
"standard box" with a volume of 1,000 ft3 were painted with one coat of paint. The default loading ratio of
0.25 ft2/fit3 was used, resulting in a painted surface area of 250 ft2. The default film thickness for paint was
used, and the application rate was varied in sequential model runs to achieve the durations listed in the table.
The default density for alkyd paint was used along with an arbitrarily chosen chemical weight fraction of
0.01. For each run of the model, the default emission decay rate was replaced by one of the values listed in
the table. The model was run for two days; for purposes of estimating a time-integrated dose over this
duration, the exposed individual was placed in the painted box throughout the two-day modeling period.
A-18
-------
Table A-9. Effect of Emission Decay Rate and Painting Duration on
Modeled Peak Concentration and Single Event Dose
Emission
Decay Rate
Painting Duration, hours
0.1
1
3
5
10
Peak Concentration, mg/m3
0.1
79
79
76
72
61
1
377
361
275
195
102
5
683
576
317
201
102
10
790
613
319
202
102
20
868
630
320
202
102
Single Event Dose, mg
0.1
562
568
601
645
740
1
568
628
811
929
1040
5
571
721
934
1020
1090
10
574
751
952
1030
1100
20
579
768
962
1040
1100
A final look at the predictive capability of the empirical model was taken by modeling chamber
concentrations of selected chemicals for test Al, applying Equation A-3 and using the known conditions of
the test (i.e., chamber volume, air exchange rate, and applied mass of primer/paint) along with the chemical
weight fraction from the bulk analysis (reported previously in Table A-l). The values for the emission
decay rates (k) for primer and paint were taken from the empirical model, and values for the initial emission
rates (Eo) were determined from the relationship that applied chemical mass is equal to Eo/k. Modeled
chamber concentrations are shown in Figures A-9 to A-11 for nonane, o-xylene, and MEKO, respectively.
Nonane is one of the chemicals used in developing the empirical model, and its modeled concentrations
match the chamber data very well. The predicted k for o-xylene was 44 percent higher than measured for
primer and 74 percent higher for paint; however, this over-estimation appears to have little impact as the
modeled data again match measurements very well. For MEKO the predicted k values were substantially
higher than estimated, and the modeled chamber concentrations are much higher than measured. However,
the discrepancy also is due to the low recovery for MEKO (that is, integrated mass based on chamber
concentrations was much lower than applied mass; see Table A-4).
A-19
-------
Nonane -- Alkyd Test A1
4. 00 E + 02
3. 00 E + 02
2. 50 E + 02
5 1.50 E + 02
-Using Predicted K
L
150 200
Time, hours
Figure A-9. Modeled Chamber Concentrations for Nonane Using Predicted Emission Decay Rates.
O-Xylene -- Alkyd Test A1
2. 00 E + 02
1.80E + 02
~ Data
Using Predicted K
1.60E + 02
1 40E+02
£
|> 1.20 E + 02
c
¦¦§ 1 . 00 E + 02
c
Q)
. 00 E + 01
c
o
o
6.00E + 01
4.00E + 01
2.00E + 01
0. 00 E + 00
0
50
100
150
200
250
300
350
400
Time, hours
Figure A-10. Modeled Chamber Concentrations for O-xylene Using Predicted Emission Decay Rates.
A-20
-------
MEKO -
- Alkyd Test A1
2.50E + 02
„E 2.00E + 02
D)
E
c
~ 1.50E+02
° 1.00E+02
-Using Predicted K
0.00E + 00
150 200 250
Time, hours
Figure A-l 1. Modeled Chamber Concentrations for MEKO Using Predicted Emission Decay Rates.
Semi-empirical Model
A potential alternative to the purely empirical model described above is a semi-empirical model
suggested by Guo et. al (see Appendix B). The model is termed "semi-empirical" because it is based on
chemical/physical principles and has some embedded constants derived from those principles, but it also has
one or more parameter to be estimated from the chamber data. As noted earlier, the integral of a single-
exponential emissions model is defined as E0/k, where E0 is the initial emission rate and k is the emission
decay rate. Since the integral, by definition, is the total emitted mass (equal to applied mass by assumption),
the relationship alternatively can be expressed as:
k /•; ,1.1/
(A-6)
where AM is the applied mass, which is the product of the wet film thickness times the paint density times
the chemical weight fraction. Per Appendix B, E0 can be estimated as follows:
= 1.32 * MTC * VP * MW/VM *y,/y0
(A-7)
A-21
-------
where
1.32 is a constant (see Appendix B for details);
MTC = mass transfer coefficient for the chemical;
VP = vapor pressure for the chemical;
MW = average molecular weight of VOCs in the formulation;
VM = volume of 1 mole gas under 1 atm (0.0243 m3 at 23 °C);
y; = weight fraction for the chemical; and
y0 = total weight fraction for all VOCs in the formulation.
Because the chemical weight fraction (y;) appears in the equations for both E0 and AM, equation (A-7) can
be simplified slightly as follows:
where FT is film thickness and PD is paint density. The mass transfer coefficient, in turn, is dependent on
the diffusion coefficient (DC) and several other terms, most of which are constants (see Appendix B for
details). The one term that is not a constant is the characteristic length of the emission source (equal to the
square root of the source area). However, while this term is of use for applications relating to the chamber
where tests were done, it may not apply directly to full-scale settings such as those for which the model is
intended to be used. Thus, it can be ignored for this application. Since MTC then depends only on DC and
a set of constants, and since MW/VM in the above equation also can be viewed as a constant (for the alkyd
primer/paint formulations tested under this project, the average molecular weight was always close to 140
g/mole, the above equation can be reduced further to:
k = (1.32 * MTC * VP * MW/VM) / (FT * PD *yQ)
(A-8)
k = (A* DC* VP)/ (FT * PD * yQ * 0.000623)
(A-9)
where
A
DC
VP
FT
PD
is a constant to be estimated;
is the diffusion coefficient for the chemical of interest (m2/hr);
is the vapor pressure for the chemical (mm Hg);
is the film thickness (mil);
is the paint density (grams per gallon);
is the total VOC weight fraction; and
is a factor to convert FT and PD from units in the user interface (mil and
g/gal, respectively) to units consistent with the equations in Appendix B.
y0
0.000623
A-22
-------
The diffusion coefficient (DC) for a chemical in the above equation can be estimated from its molecular
weight (MW) using the following equation that is provided in EPA's CEB Engineering Manual:
where 0.36 is a conversion factor from cm2/sec (the units for equation A-10) to m2/hr (the units needed for
equation A-9).
The above model (equation A-9) for the emission decay rate, although based almost in entirety on
chemical/physical principles, still must be termed semi-empirical because of the need to estimate one term
(the constant A) using the set of emission decay rates derived from the chamber data. The best-fit value for
A, based on linear regression analysis, was determined to be 240. Comparisons of the values for k
predicted from the above equation with the values estimated from the chamber data are shown in Figure A-
12. Although the fit is relatively modest (R2 = 0.49), the semi-empirical model may have broader
applicability (e.g., outside this project) than the empirical model because it is less dependent on the chamber
data.
DC = (1/29 + 1 MW/" * MW'0'33 * 0.36
(A-10)
Reference Line
+ Primer Data
O Paint Data
0.0
0.0
2.0
4.0
6.0
8.0
10.0
Estimated kfrom Chamber Data
Figure A-12. Comparison of Predicted Emission Decay Rates from Semi-empirical Model
with Estimated Decay Rates from Chamber Data.
A-23
-------
A5.
SMALL-CHAMBER SINK TESTS
Three small-chamber tests were conducted by ARCADIS Geraghty and Miller, Inc., to evaluate sink
effects for four VOCs - methyl ethyl ketoxime (MEKO), 1,2,4-trimethylbenzene, 2-methyldecane, and
undecane. Two sink tests involved placing either aged carpet or gypsum wallboard in the chamber as a sink
material. For the third test, used as a baseline for comparison, there was no sink material in the chamber.
The chamber was "dosed" with known input concentrations of the VOCs for 48 hours, after which clean air
was supplied to the chamber. The VOCs were generated by passing clean air through diffusion vials that
were held at a constant temperature. VOC concentrations in the chamber were measured periodically both
in the chamber inlet and outlet streams during the 48-hour dosing period, and then in the chamber outlet
stream for 12 days after dosing was terminated.
The chamber used for the sink tests has a volume of 53 liters (0.053 m3). For both carpet and
wallboard the sink area for the tests was 696.8 cm2 (0.0697), resulting in a loading ratio of 1.315 m2/m3.
During both tests the air exchange rate averaged 0.51 air changes per hour (ACH). The average
temperature was 22.9 °C for the carpet test and 21.9 °C for the wallboard test. The average relative
humidity was 51.5 % for the carpet test and 49.9 % for the wallboard test.
Figure A-13 shows the concentrations in the outlet stream for MEKO during the three tests (no
sink, carpet, and wallboard). With no sinks, the chamber concentration approached a steady-state value of
about 11 mg/m3, equivalent to the concentration in the input stream. Once dosing was terminated, the
concentration rapidly approached zero due to the supply of clean air to the chamber. With carpet as the
sink, the peak concentration was reduced to about 9 mg/m3 and the return toward zero concentration was
delayed, indicating a modest sink effect. For wallboard the sink effect was more pronounced - the peak
concentration reached only about 4-5 mg/m3.
Figure A-14 shows the concentrations for undecane during the same three tests. In this case the
sink effect was minimal - the rise to the peak chamber concentration with carpet or wallboard was delayed
slightly, but the peak still reached 11-12 mg/m3 (equivalent to that in the input stream) within the 48-hour
dosing period. Similarly, after clean air was introduced, the return toward zero concentration was delayed
slightly but zero concentration still was reached. By comparison, for MEKO there still were measurable
concentrations days after the dosing was terminated. The behaviors for 1,2,4-trimethylbenzene and 2-
methyldecane were quite similar to that of undecane.
A-24
-------
Chamber Sink Tests for MEKO
No sinks
Carpet
Wallboard
0
20
40
60
80
100
120
140
160
180
Elapsed Time, hours
Figure A-13. Chamber Concentrations for MEKO during Sink Tests.
Chamber Sink Tests for Undecane
B— No sinks
-I—Carpet
-0—Wallboard
0
20
40
60
80
100
120
140
160
180
Elapsed Time, hours
Figure A-14. Chamber Concentrations for Undecane during Sink Tests.
A-25
-------
The reversible-sink model used in the calculation engine for WPEM describes adsorptive and
desorptive sink behavior based on the Langmuir isotherm, which assumes a monolayer of molecules on a
homogeneous surface. The reversible-sink model has both a removal rate and a re-emission rate. The
removal rate (rate to the sink) is a product of the sink rate times the indoor-air concentration. The sink rate,
in turn, is the product of the deposition velocity (in m/hr) times the sink area (m2), with resultant units of
m3/hr. Thus, the removal rate has units of mg/hr. The re-emission rate (rate from the sink) is the product of
the desorption rate (in inverse hours), the sink area (m2), and the mass accumulated in the sink (mg/m2),
with resultant units of mg/hr.
The following equations (after Tichenor et al., 1991) describe rates to and from a reversible sink:
This sink model assumes that a very small fraction of the potential adsorption sites on the sink are occupied.
For this reason, the limitation on saturation of the indoor sink (not to be confused with a pollutant's
saturation concentration in air) is neglected in the model.
For each of the four VOCs used in the chamber sink tests, values for Ka and Kd were estimated
through an iterative technique, implemented in an Excel spreadsheet, that was designed to find the best fit of
the reversible-sink model to the chamber concentration data. The estimated values are listed in Table A-10.
For MEKO the estimated value for Kais considerably larger than that for Kd. For the other VOCs the
estimated Kd value generally is close to, or even larger than, the estimated Ka value. In fact, for the VOCs
other than MEKO, values of zero for both Ka and Kd fit the data virtually as well as any other combination;
this outcome is indicative of a negligible sink effect for those chemicals.
Rate to the Sink = Ka* A * C
Rate from the Sink = Kd* A * M
(A-ll)
(A-12)
where: Ka = adsorption rate constant (m/hr)
A = sink area (m2)
C = concentration in air in contact with the sink (mg/m3)
Kd = desorption rate constant (inverse hours)
M = mass accumulated in the sink (mg/m2).
A-26
-------
Table A-10. Sink Parameter Estimates for Four Chemicals
Chemical
Chamber Input
Concentration, mg/m3
Peak Concentration in
Chamber, mg/m3
Sink Parameters
Ka
Kd
Carpet as a Sink
MEKO
11.9
9.6
0.25
0.04
1,2,4-trimethylbenzene
10.3
10.0
0.10
6.00
2-methyldecane
10.2
10.5
0.04
0.03
Undecane
12.1
12.7
0.06
0.50
Wallboard as a Sink
MEKO
10.5
5.0
1.10
0.03
1,2,4-trimethylbenzene
9.9
9.7
0.25
0.25
2-methyldecane
8.0
8.2
0.90
1.20
Undecane
11.1
11.6
0.40
0.25
A-27
-------
APPENDIX B
PAPER ON EMISSIONS MODEL FOR ALKYD PAINTS
(published in Atmospheric Environment, Vol. 33, No. 8, pp. 1205-1215)
-------
Estimation of the Rate of VOC Emissions
From Solvent-Based Indoor Coating Materials
Based on Product Formulation
Zhishi Guo, John C. S. Chang, and Leslie E. Sparks
U.S. Environmental Protection Agency
National Risk Management Research Laboratory
Indoor Environment Management Branch, MD-54
Research Triangle Park, NC 27711, U.S.A.
Roy C. Fortmann
ARCADIS Geraghty & Miller Company
P. O. Box 13109
Research Triangle Park, NC 27709, U.S.A.
Published in
Atmospheric Environment
Vol. 33, No. 8, pp 1205-1215
B-l
-------
ABSTRACT
Two computational methods are proposed for estimation of the emission rate of volatile
organic compounds (VOCs) from solvent-based indoor coating materials based on the knowledge of
product formulation. The first method utilizes two previously developed mass transfer models with
two key parameters — the total vapor pressure and the average molecular weight for total volatile
organic compounds (TVOCs) — being estimated based on the VOC contents in the product. The
second method is based on a simple, first-order decay model with its parameters being estimated
from the properties of both the source and the environment. All the model parameters can be readily
obtained. Detailed procedures for computing the key parameters are described by using examples.
The predictive errors were evaluated with small chamber data, and the results were satisfactory.
Thus, the proposed methods provide a way to predict the VOC emissions in the indoor environment
without having to conduct costly chamber testing. The two proposed methods work for both
TVOCs and individual VOCs. Pros and cons for each method are discussed.
Key Words
indoor air, emissions, volatile organic compounds, model, coating materials
B-2
-------
1. INTRODUCTION
Solvent-based interior coating materials have long been recognized as a major source of
volatile organic compounds (VOCs) in the indoor environment (Sterling, 1984). They usually
contain more than 25 percent of the solvent that will be released into the air during the drying period.
The most commonly used solvent in these products is mineral spirits — a type of petroleum distillate
consisting of aliphatic hydrocarbons with a trace amount of aromatics (Howe-Grant, 1996). Other
VOCs are sometimes added to the formulation to enhance its performance, including oxygenated
hydrocarbons (such as alcohols), nitrogenated hydrocarbons (such as methyl ethyl ketoxime), and
other solvents (such as toluene). Some of the solvent components are identified as hazardous air
pollutants (HAPs) in the Clean Air Act Amendments of 1990 (U. S. Public Law 101-549, 1990).
The increased exposure to those HAPs and the subsequent health risk are of special concern when
solvent-based coatings are used in the indoor environment.
Small environmental chambers have been used to determine the VOC emissions from interior
coatings (ASTM, 1995a). The cost of chamber testing could be very high because characterization
of emission patterns requires multiple samples over time and this is especially true when the
emissions of individual VOCs are to be quantified. A tremendous amount of time and resources can
be saved if the emission rates can be predicted based on the properties of the source and those of the
environment.
This paper presents two methods that can be used to predict the emissions of TVOCs and
individual VOCs from solvent-based indoor coatings. They are both based on gas-phase mass
transfer theories but differ in complexity.
The proposed methods should be useful in exposure estimation and risk assessment for they
can predict indoor VOC emissions with reasonable accuracy without having to rely on costly
chamber testing. These methods should also be useful to manufacturers in developing low-emission
products for, once the concentrations of predominant VOCs in a product are known, all the
information needed to predict the VOC emission rates is known.
B-3
-------
2. LITERATURE REVIEW
Among all available source models for emissions from indoor coating materials, the first-
order decay model is the simplest and most widely used (ASTM, 1995a):
E
dM
(1)
dt
where E = emission factor, mg m"2 h"1;
M = amount of VOCs remaining in the source, mg m"2;
E0 = initial emission factor, mg m"2 h"1;
k = first-order decay rate constant, h"1; and
t = time, h.
This model has several variations, one of which (Clausen, 1993) is:
where M0 = E0/k is the amount of VOCs applied, mg m"2.
The major advantage of this family of models is their simplicity. If the air exchange flow
rates remain constant, there are analytical solutions to indoor concentrations (Tichenor and Guo,
1991; Evans, 1996). For a single air zone, the solution is:
E
dM
M0ke-kt
(2)
dt
(3)
and
C
e
V
(if N = k)
(4)
B-4
-------
where C = indoor concentration, mg m"3;
S = source area, m2;
V = room volume, m3; and
N = air exchange rate, h"1.
The first-order decay model has two major drawbacks, however. First, estimation of
parameters E0 and k often relies on costly chamber tests. Second, as an empirical model, it is
difficult to scale-up.
Efforts have been made to overcome these problems. Clausen (1993) found that, for a given
product, the decay rate constant k is inversely proportional to the wet film thickness:
k--k-iL (5)
e
where e = wet film thickness, |im; and
kE1 = decay rate constant for an evaporative source with wet film thickness of 1 |im, |am h"\
This equation provides a way to adjust k when the wet film thickness changes.
Chang and Guo (1994) reported that, for individual VOCs in a given product, the decay rate
constant k can be related to their vapor pressure P:
k, P
— = — (6)
k2 P2
Such correlation allows estimation of k for one compound relative to another.
Another development allows estimation of k based on the drying time of the solvent (Evans,
1996). Integrating Equation 2 yields:
M = M0e -kt (7)
B-5
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If the drying time, tD, is defined as the time needed for 90 percent of the solvent to evaporate, then
Equation 7 becomes:
0.1 M0 = M0e~kt° (8)
or
A = _ In^Ol) (9)
Two mass transfer models were introduced to solve the scale-up problem. One, known as
the VB model, is for TVOC (Tichenor, et al., 1993) and the other, known as the VBX model, for
individual VOCs (Guo, et al., 1998). These two models are discussed further in the following
section.
The gas-phase mass transfer coefficient, which appears in both the VB and VBX models,
plays an important role in controlling the rate of VOC emissions from wet sources (Guo, et al.,
1996). Two theoretical models have been developed to estimate this parameter in indoor
environments (Sparks et al., 1996; Zhang, et al., 1996). Sparks et al. proposed a simple formula
based on correlation of the Nusselt and Reynolds. Zhang, et al. reported a slightly more complex
formula, which takes into consideration such additional factors as the boundary layer flow condition
and the wall shear stress.
To date, no reported methods allow estimation of emission rates for either TVOCs or
individual VOCs based on information about the product formulation. The two methods proposed in
this paper attempt to fill this gap.
3. DESCRIPTION OF I II I METHODS
3.1 Method 1
Method 1 utilizes the VB model (Tichenor, et al., 1993) for TVOCs (Equation 10) and a
modified VBX model for individual VOCs (Equation 11):
B-6
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E = k» (C^ IT " ° (10)
TO
where 1^= gas-phase mass transfer coefficient for TVOCs, m h"1;
Cv0 = initial airborne TVOC concentration at air/source interface, mg m"3, based on the total
vapor pressure of the TVOCs;
Mx = amount of TVOCs remaining in the source, mg m"2;
Mxo = amount of TVOCs applied, mg m"2; and
C = TVOC concentration in the bulk air, mg m"3.
M m
E = k (C — — - C) (11)
miV VI Mt mt '
where E; = emission factor for component i, mg m"2 h"1;
kmi = gas-phase mass transfer coefficient for component i, m h"1;
Cvi = airborne concentration of component i at air/source interface, mg m"3, based on the
vapor pressure of component i;
Mj = amount of component i remaining in the source, mg m"2;
m = average molecular weight for the organic solvent, g mole"1;
ir^ = molecular weight for component i, g mole"1; and
Q = concentration of component i in the bulk air, mg m"3.
M
The term —- is the approximate molar fraction of component i in the solvent mixture.
Mt mi
Equation 11 is equivalent to the original VBX model (Guo, et al., 1998) but easier to use because it
does not require any unit conversion between (mg m"3) and (mole m"3) for the concentration.
When the emission factor is estimated from the VOC contents in the formulation, it is more
convenient to convert Cv0 and Cvi to commonly used pressure units such as (mm Hg):
B-7
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c„» = 103 ^7 — <12)
760 v
„ P m.
C = 103 — - (13)
760 v
where P0 = total vapor pressure for TVOCs, mm Hg;
P; = vapor pressure for the pure component i, mm Hg; and
vm = volume of 1 mole gas under 1 atm, m3 (vm = 0.0243 m3 at 23°C).
Substituting Equation 12 into 10 and Equation 13 into 11:
jfi Mt
E = km (1.32 P0 -~f-C) (14)
v MTn
m TO
~m M
E = k (1.32 P — — - C) (15)
m 1 v Mt K J
m 1
The room concentration model consists of two differential equations for TVOCs (Equations
16 and 17) and an additional two for each individual VOC (Equations 18 and 19):
= M - nc (16)
dt V
dMT
= -E (17)
dt
dC SE
' - NCt (18)
dt V
dM
dt
= -E, (19)
B-8
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where E and E; are from Equations 14 and 15, respectively. The most common initial conditions for
Equations 16-19 are: C = 0, C; = 0, Mx = Mxo, and Mj = when t = 0. The amount of TVOCs and
individual VOCs initially applied, Mxo and Mi(h can be calculated from:
Mw = edy0
(20)
Mw = e dyj
(21)
where e = wet film thickness, m;
d = product density, g m"3;
y0 = TVOC content in the product, mg g"1; and
y; = content of component i in the product, mg g"1.
Equations 20 and 21 are also valid when e is in |im and d in kg L"1.
This method requires knowledge of total vapor pressure (P0) and average molecular weight
(m) for TVOCs, and mass transfer coefficients (km and kmi). Methods to estimate these parameters
are described in Sections 4.2-4.4.
3.2 Method 2
In the second proposed method, the first-order decay model (Equation 1) — the simplest
possible source model for decaying sources — is adopted, with the two model parameters, E0 and k,
being estimated from the two mass transfer models described in the previous section by making
certain approximations. At t = 0, Equations 14 and 15 become:
E, = k (1.32 A, — — - 0) = 1.32 k P,
0 0 Mrn J
m TO
V
m
m
(22)
m M.n
En. = k (1.32P —
01 mA 1 v Mrn
m TO
0) = 1.32 k P ¦
7 mi i
(23)
B-9
-------
Mw yi
Since = —, Equation 23 can be changed to:
Mto yo
= 1 32kMP, H- y-L (24)
vm yQ
From Equations 1 and 2, the first-order decay rate constant for TVOCs can be calculated from;
k = — (25)
Mto
Substituting Equation 20 into 25:
Eo
k = —(26)
edy
For an individual VOC, the decay rate constant (kj can be derived in a similar manner:
kt = (27)
e dy
Once E0 and k or Eoi and kj are obtained, Equations 3 and 4 can be used to calculate room
concentrations.
B-10
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4. PARAMETER ESTIMATION
4.1 Overview
The source models used in the two methods are summarized in Table 1. Table 2 is a list of all
parameters required to compute indoor VOC concentrations with the two proposed methods: the
first three parameters are properties of the environment, and the rest are properties of the source. It
is fair to say that all the parameters can be readily obtained except P0, m, km and kmi. Methods for
estimating these parameters are discussed below.
4.2 Estimation of Total Vapor Pressure for TVOC from VOC Contents in the Product
To date, parameter P0 can only be determined by experiment (an example is described
below). An alternative method proposed here is to estimate P0 based on the contents of major VOCs
in the solvent. If we assume that the behavior of the solvent is close to an ideal solution, the total
vapor pressure can then be estimated from Raoult's law. If the number of VOCs in the mixture is n,
then:
E (pr y, /m,)
P0 = iiL¦ (28)
E (y, /m)
i = 1
Although it is difficult to account for all the constituent VOCs in a petroleum-based solvent,
routine chromatographic analysis of the coating material can easily identify one to two dozen major
VOC peaks, which provides a good estimate of P0 by using Equation 28.
To estimate the accuracy of Equation 28, the computed total vapor pressures were compared
against those determined by headspace analysis for three test specimens: an alkyd primer, an alkyd
paint, and a synthetic wood stain (Tichenor, et al., 1993). About 120 ml of a paint sample was
quickly poured into a 250 ml amber bottle, which was then sealed with a Teflon coated septum and
placed in an incubator overnight at 23°C. A magnetic stirrer in the bottle helped mix the test
specimen. For the synthetic wood stain, a 60 ml bottle was used and the volume of the test specimen
B-ll
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was 20 ml. Samples (200 to 500 |il) were drawn from the headspace the next morning with a syringe
which was heated to 60°C and rinsed once with the headspace air. The samples were then injected
directly into a gas chromatograph/flame ionization detector (GC/FID) for quantitative analysis. The
TVOC mass was computed by using the response factor for toluene and the sum of area counts
between toluene and tetradecane, inclusive. In Table 3, the "measured" value was from the
headspace analysis and the "computed" value from equation 28. The results showed that the
difference between these two methods was no greater than 16 percent. We are uncertain, however,
why the computed values are systematically greater than those from the headspace analysis.
Table 4 is an example demonstrating how P0 can be calculated in an electronic spreadsheet.
After entering VOC contents in the product, molecular weights and vapor pressures, the two sums in
Equation 28 are obtained. The total vapor pressure can then be calculated:
4.3 Estimation of Average Molecular Weight for TVOC (m) from VOC Contents in the Product
We previously recommended that m be represented by the molecular weight for the most
predominant constituent in the solvent mixture (Guo, et al., 1998). In the majority of oil-based
indoor coating materials we have tested, the most predominant VOC is either decane or undecane.
An alternative method is to estimate m based on the contents of major VOCs in the product:
3.946 (mmHg)
(29)
n
m
(30)
i=i mi
B-12
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The calculations can be performed in the same spreadsheet for P0. No additional information
is needed. In the example shown in Table 4, the calculated average molecular weight is:
m
^ ^ = 132 gmole
0.595
(31)
Parameter m estimated from Equation 30 is slightly smaller (less than 10 percent difference)
than that represented by the most predominant VOC, which is decane in this example. We believe
Equation 30 is more accurate because more than half of the VOC constituents have smaller
molecular weights than the most predominant constituent (see data in Table 4 for example).
4.4 Estimation of Gas-Phase Mass Transfer Coefficients (km and km)
Parameters km and kmi can be either determined by experiment or estimated based on gas-
phase mass transfer theories. For experimental determination, the />dichlorobenzene method (Guo,
et al., 1996) is commonly used.
Two theoretical models have been proposed to estimate gas-phase mass transfer coefficients
in indoor environments (Sparks, et al., 1996; Zhang, et al., 1996). The model proposed by Sparks,
et al. — the simpler one of the two — is derived by finding the correlation between the Nusselt
number (Nu) and the Reynolds number (Re) from experimental data:
N = 0.33 R
U I
2
3
(r2 = 0.98; n = 24)
(32)
e
and the equation used to compute the mass transfer coefficient is:
2
k =0.33 DLr3(^-)3
m C \ /
(33)
where D = diffusivity of the VOC in air, m2 h"1;
B-13
-------
Lc = characteristic length of the source (equal to the square root of the source area), m;
v = air velocity over the source, m h"1;
Q = density of the air, g m"3; and
|i = viscosity of the air, g h"1 m"1.
In general, all the parameters in Equation 33 can be obtained readily. The density and viscosity of
the air can be found from the literature. Parameters Lc and v vary from case to case. Figure 1 shows
the mass transfer coefficient as a function of air velocity and characteristic length for decane (D =
0.0207 m2 h"1). An air velocity range of 5 to 10 cm s"1 is considered typical in indoor environments
(Mathews, et, al., 1987).
The following is an example of how the mass transfer coefficient is estimated for decane
emissions from a surface with an area of 12 m2 when the indoor temperature is 23°C and air velocity
10 cm s"1. The values needed to compute km are:
Lc = yf\2 = 3.464 m (34)
i = 10 cm s"1 = 360 m h"1 (35)
D = 0.0576 cm2 s"1 = 0.0207 m2 h"1 (36)
q = 1193 g m"3 (37)
|i = 184.4 |ipoises = 66.52 g h"1 m"1 (38)
where q and |i were found from the literature (Weast, 1972) and D was calculated by using the FSG
method (Layman, et al., 1982). Substituting the above values into Equation 33 yields:
-- t \-
km = 0.33 x 0.0207 x (3.464) 3 x ( 3 = 157 mhl (39)
Practically, the mass transfer coefficient for TVOC is represented by that for the most abundant
component (Tichenor, etal., 1993).
B-14
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5. EVALUATION OF MODEL PERFORMANCES
5.1 Chamber Data
Small chamber data for three types of indoor coating materials were used to evaluate the
performance of the proposed methods: an alkyd primer, an alkyd paint, and a conversion varnish that
cures at room temperature. The solvents used in the first two products were typical petroleum
distillate solvents. The conversion varnish contains large amount of aromatic compounds. Table 5
summarizes the properties of the test specimens and the test conditions. Detailed information about
these products and test procedures are reported elsewhere (Fortmann, et al., 1998; Howard, et al.,
1998). Not all concentration data were used in this evaluation. Data for some VOCs were
disqualified for one or more of the following reasons: (1) most data points were below the practical
method quantification limit; (2) the chamber recovery was either less than 75 percent or greater than
125 percent; and (3) the vapor pressure for a given VOC was not available at room temperature
range. Thus, only 23 sets of concentration data were qualified for the evaluation.
5.2 Results
The performance of the two methods was evaluated by using two indicators: the error in the
predicted peak concentration and the normalized mean square error (NMSE) for a given data set. As
shown in Table 6, the average percent difference between observed and predicted peak
concentrations is 16.6 percent for method 1 and 22.9 percent for method 2. The observed peak
concentrations cover a wide range (from 3.79 to 9770 mg/m3) and, thus, the two methods work for
both major and minor components of the solvent mixture. It should be pointed out, however, that
the predicted peak concentrations are often (but not always) higher than the observed ones.
Possible causes of such overestimation are discussed in the following section.
The NMSE, one of the standard indices for statistical evaluation of indoor air quality models
(ASTM, 1995b), is calculated from
B-15
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£ (C„ - CJ (40)
nmse = ——=—
n C C
O p
where Cpi = predicted concentrations;
Coi = observed concentrations;
Yl
Co = Y. Cqi / n ;
i=1
n
CP = ^ Cpi / n ; and
2 = 1
n = total number of data points.
As shown in Table 7, the average NMSE value was 0.159 for method 1 and 0.253 for method 2.
According to the ASTM standard guide, an NMSE value of 0.25 or less is generally considered
indicative of adequate model performance.
Both indicators suggest that the performances of the two methods are adequate and that, in
general, method 1 is more accurate than method 2. Examples of predicted chamber concentrations
with good and poor accuracy are shown in Figures 2 and 3, respectively.
6. DISCUSSION
6.1 Comparison of the Two Methods
Each of the two proposed methods has its advantages and disadvantages. The first method
provides more accurate predictions and is less sensitive to errors in the input. On the other hand, this
method requires solving a system of differential equations numerically and, therefore, is relatively
computation intensive.
The second method is less accurate but easier to use. All the calculations can be performed
in an electronic spreadsheet. Thus, it is more suitable for product screening purposes. It is also of
choice if a large number of calculations are needed (such as in Monte Carlo analysis).
B-16
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In terms of computational intensity, the difference between these two methods is more
significant for individual VOCs than for TVOCs. The reader is reminded that, in a single-zone
situation, the VB model has an explicit solution to indoor concentration (Tichenor, el al., 1993).
With slightly more computational steps, this mass transfer model offers better accuracy than the first-
order decay model.
6.2 Validity of Estimating Total Vapor Pressure for TVOCs from the VOC Contents in the Product
Because of the many constituent VOCs contained in the petroleum-based solvent, the
predominant VOCs that can be quantified by routine GC analysis account for only a small portion of
the total mass. In the example shown in Table 4, the 15 quantified major VOCs account for about 24
percent of the total weight of the solvent (the TVOC content was 333 mg/g). It is doubtful that 24
percent of predominant VOCs can represent the properties of the solvent if there is no similarity
between those components and the remaining 76 percent of the VOCs. As stated in Introduction,
above, petroleum-based solvents consist mainly of aliphatic hydrocarbons. Although many less
abundant constituents are not the targets in routine GC analysis, their properties are similar to some
of the quantified VOCs. For instance, n-decane is the most abundant component in many solvent-
based coating products. This compound also has many isomers (e.g., branched decanes), which are
not quantified but have molecular weights and diffusivities identical to n-decane and vapor pressures
close to n-decane. Thus, n-decane represents a group of VOCs with similar physical properties. The
usefulness of Equation 28 is that it makes the headspace analysis unnecessary.
6.3 Overestimation of Peak Concentrations
As shown in Table 6, both methods tend to overestimate the peak concentrations. There are
several explanations for the causes. First of all, the test specimen was prepared outside the chamber
and it typically took several minutes to apply the coating and to determine the total amount of
material applied. Such a delay may cause significant VOC loss before the test specimen is placed in
the chamber, especially for more volatile components (Guo, et al., 1996).
The second cause is the substrate effect. When a petroleum-based coating material is applied
B-17
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to a substrate such as wood or gypsum boards, a small amount of solvent will penetrate the
substrate. This fraction of solvent will be emitted in a delayed time. Limited data analysis suggests
that this fraction accounts for 5 to 10 percent of the total solvent applied.
The third cause applies only to the second method. It is due to the omission of the back
pressure effect. As shown in Equations 10 and 11, the driving force for solvent evaporation is the
concentration difference between the surface of the source and the indoor air. As a result, the high
chamber concentration in the early hours slows the evaporation process. Method 2 does not take
this factor into consideration and, consequently, its predicted peak concentrations are generally
higher than those predicted by method 1.
6.4 Making Use of Information in Material Safety Data Sheets and Product Data Sheets
Predicting the emission rate of an individual VOC with the first-order decay model does not
require knowledge of the total vapor pressure for TVOCs (Equations 24 and 27). This feature
makes it possible to estimate the emission rate based on the information in the Material Safety Data
Sheets (MSDSs) and the Product Data Sheets. The United States laws require that the
manufacturer provide MSDSs with their products. For indoor coating products, the contents of total
volatile matter (TVM) and some hazardous VOCs (if greater than 1 percent by weight) are reported
in MSDSs. If the VOC of interest appears in the MSDS, one can use Equations 24 and 27 to
roughly estimate its emission rate. The TVOC content can be represented by TVM. The only
information lacking about the TVOCs is their average molecular weight. In most indoor coating
products we have tested, including wood stain, polyurethane wood finish, floor wax and alkyd paint
(Tichenor et al., 1991, 1993; Fortmann, et al., 1998), the most predominant VOC in the solvent is
either decane (m; = 142) or undecane (m; = 156). The only exception was conversion varnish, in
which xylene (m; = 106) is often the most abundant component in the solvent (Howard, et al.,
1998). For screening purposes, we recommend that the average molecular weight of 142 be used
when the most abundant component is unknown. The density of the product is always reported in
the related Product Data Sheet.
B-18
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7. CONCLUSIONS
Two methods have been developed to predict the emissions of TVOCs and individual VOCs
from solvent-based indoor coating materials based on the product formulation. The first method is
based on two mass transfer models with the key parameters being estimated from the contents of
major VOCs in the product. The second method utilizes the first-order decay model with its
parameters being estimated based on the properties of the source and the environment. Model
evaluation using small chamber data indicates that both methods provide reasonable accuracy in
predicting emissions to indoor environments, with the average normalized mean square error being
0.159 and 0.253, respectively. Further evaluation with data collected from real rooms, where VOC
adsorption and desorption from interior surface are often significant, is desirable.
The first method is more accurate than the second but is more computation intensive. The
second method is simple enough to be implemented in an electronic spreadsheet and is more suitable
for product screening. These two methods provide a way to obtain exposure information on the
indoor use of petroleum-based indoor coating materials without having to perform costly chamber
testing.
ACKNOWLEDGMENT
The authors would like to thank the following personnel for generating the experimental data
used in this paper: Kenneth Krebs of the U.S. EPA; and Mark Bero, Hueichen Lao, Scott Moore,
and Nancy Roache of ARCADIS Geraghty & Miller Company. Robert McCrillis and Betsy Howard
of the U.S. EPA are thanked for managing the conversion varnish evaluation project.
REFERENCES
ASTM (1995a), "Standard guide for small scale environmental chamber determination of organic
emissions from indoor materials/products," Philadelphia, PA, American Society for Testing and
Materials (ASTM Standard D-5116-90).
ASTM (1995b) "Standard guide for statistical evaluation of indoor air quality models,"
Philadelphia, PA, American Society for Testing and Materials (ASTM Standard D-5157-91).
B-19
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Chang, J. C . S. and Z. Guo (1994), "Modeling of alkane emissions from a wood stain," Indoor Air,
Vol. 4, pp 35-39.
Clausen, P. A. (1993), "Emission of volatile and semivolatile organic compounds from water-borne
paints — the effect of the film thickness," Indoor Air, Vol. 3, pp 269-275.
Evans, W. C. (1996), "Development of continuous-application source terms and analytical solutions
for one- and two-compartment systems," Characterizing Sources of Indoor Air Pollution and
Related Sink Effects, ASTM STP 1287, B. A. Tichenor, Ed., American Society for Testing and
Materials, pp 279-293.
Fortmann, R., N. Roache, Z. Guo, and J. C. S. Chang (1998), "Characterization of emissions of
volatile organic compounds from interior alkyd paint," accepted for publication by J. Air Waste
Manage. Assoc.
Guo, Z., B. A. Tichenor, K. A. Krebs, and N. F. Roache (1996), "Considerations on revision of
emissions testing protocols," Characterizing Sources of Indoor Air Pollution and Related Sink
Effects, ASTM STP 1287, B.A. Tichenor, Ed., American Society for Testing and Materials, pp 225-
236.
Guo, Z., L. E. Sparks, B. A. Tichenor, and J. C. S. Chang (1998), "Predicting the emissions of
individual VOCs from petroleum-based indoor coatings," Atmospheric Environment, Vol. 32, No. 2,
pp 231-237.
Howard, E. M., R. C. McCrillis, K. A. Krebs, R. C. Fortmann, H. Chen-Lao, and Z. Guo (1998),
"Indoor emissions from conversion varnishes," accepted for publication by J. Air Waste Manage.
Assoc.
Howe-Grant, M., Ed. (1996), Encyclopedia of Chemical Technology, Vol. 17, p 1052, John Wiley
& Sons, New York.
Layman, W. J., W. F. Reehl, and D. H. Rosenblatt (1982), Handbook of Chemical Property
Estimation Methods, McGraw-Hill, New York.
Mathews, T. J., C.V. Thompson, D. L. Wilson, A. R. Hawthorne, and D.T. Mage. "Air velocities
inside domestic environments: an important parameter for passive monitoring," Indoor Air '87,
B-20
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Proceedings of the 4th International Conference on Indoor Air Quality and Climate, Institute for
Water, Soil and Air Hygiene, West Berlin, Vol. 1, August 1987. pp. 154-158.
Public Law 101-549, The Clean Air Act Amendments, Title III - Hazardous Air Pollutants, United
States 101st Congress, November 15, 1990.
Sparks, L. E., B. A. Tichenor, J. Chang, and Z. Guo (1996), "Gas-phase mass transfer model for
predicting volatile organic compound (VOC) emission rates from indoor pollutant sources, Indoor
Air,Vol. 6, pp 31-40.
Sterling, D. A. (1984), "Volatile organic compounds in indoor air: an overview of sources,
concentrations, and health effects," Indoor Air and Human Health: Proceedings of the Seventh Life
Sciences Symposium, Knoxville, TN, October 29-31, 1984, pp 387-402.
Tichenor, B. A. and Z. Guo (1991), "The effect of ventilation on emission rates of wood finishing
materials " Environment International, Vol. 17, pp 317-323.
Tichenor, B. A., Z. Guo, and L. E. Sparks (1993), "Fundamental mass transfer model for indoor air
emissions from surface coatings," Indoor Air, Vol. 3, pp 263-268.
Weast, R. C., Ed., CRC Handbook of Chemistry and Physics, The Chemical Rubber Co., Cleveland,
OH, 1972.
Zhang, Y., F. Haghighat, and P. Fazio, (1996) "Modeling of material emission process," Proceedings
of the Seventh International Conference on Indoor Air Quality and Climate, Vol. 1, pp 937-942.
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Table 1. Summary of Source Models Used in the Proposed Methods
Method
Category
Representation of Solvent Volatility
Vapor Pressure
(mm Hg)
Concentration at Air-Source
Interface (mg m"3)
1
TVOCs
m Mt
E=km(\32Po C)
Vm MfO
Mt
E=km (Cv - C)
v Mto J
VOCs
m Mi
Et= km(\2>2Pi C)
Vm A/[t
Mi
Ei-km(Cvi ~ Ci)
V Mt J
2
TVOCs
m
Eo = 1.32 km Po —
Vm
E 0 — km Cv
k = E°
0 a yo
VOCs
m yt
Eoi = 1.32 lam Pi —
Vm y 0
y,
I01 = knn C \ v
yo
Eoi
h-
6 a yt
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Table 2. List of Parameters Required by the Concentration Models
Parameter
Symbol
Method 1
Method 2
TVOC
VOC
TVOC
VOC
room volume
V
X
X
X
X
air exchange rate
N
X
X
X
X
mass transfer coefficient
X
X
X
X
source area
s
X
X
X
X
wet film thickness
e
X
X
X
X
product density
d
X
X
X
X
content of TVOC in product
y0
X
X
X
X
total vapor pressure for TVOC
p0,cv
X
X
X
average molecular weight for TVOC
m
X
X
content of individual VOC in product
Yi
X
X
vapor pressure for individual VOC
P C
rv ^V1
X
X
molecular weight for individual VOC
mi
X
Table 3. Comparison of Headspace TVOC Concentrations with
Theoretically Calculated Cv0 for Three Wet Sources
Product
Measured Cv0 a
(g m"3)
Com
)uted
Percent
Difference
P0 (mm Hg)
Cv0 (g m"3)
Alkyd Primer
Alkyd Paint A
Synthetic Stain
27.2 ± 1.77
12.3 ± 1.66
16.6 ± 1.91
3.49
1.44
2.86
31.9
14.3
18.4
15.9
15.0
10.3
mean ± standard c
eviation; n = 6 for alkyd primer and alkyd paint; and n = 7
for synthetic stain.
B-23
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Table 4. An Exemplary Worksheet for Estimation of the Total Vapor Pressure P0 and
Average Molecular Weight ( m) for TVOCs
Compound
Yi
mi
P;a
y/m,
P;
yilmi
decane
30.7
142
1.575
0
2165
0
3410
nonane
18.4
128
4.144
0
1436
0
5949
octane
15.6
114
7.894
0
1372
1
0831
undecane
6.68
156
0.616
0
0428
0
0264
/ra/7.s-decalin
2.28
138
3.296
0
0165
0
0543
2-methyldecane
2.19
170
0.616
0
0129
0
0079
/^-xylene
1.39
106
7.710
0
0132
0
1014
toluene
0.35
92
24.47
0
0038
0
0921
ethylbenzene
0.29
106
8.850
0
0028
0
0246
o-xylene
0.23
106
5.897
0
0022
0
0129
/?-ethyltoluene
0.21
120
2.864
0
0017
0
0050
1,2,4-trimethylbenzene
0.14
120
2.028
0
0012
0
0024
dodecane
0.063
170
0.253
0
0004
0
0001
//-propylbenzene
0.034
120
3.126
0
0003
0
0009
1,3,5 -trimethylb enzene
0.023
120
2.526
0
0002
0
0005
sum
78.6
0.595
2.348
a at 23 °C.
B-24
-------
Table 5. Summary of Test Specimens and Chamber Conditions®
Alkyd
Alkyd
Conversion
Test specimen
Primer
Paint B
Varnish
Product density (kg L"1)
1.33
1.10
0.97
TVOC content (mg g"1)
333
350
516
Most abundant VOC
decane
decane
xylene
No. of VOCs quantified in liquid product
20
20
10
No. of VOCs quantified in air samples
20
20
4
Total vapor pressure (mm Hg)b
3.94
2.58
8.39
Average molecular weight0
131
133
101
Substrate type
white pine board
white pine board
red oak board
Substrate area (cm2)
256
256
272
Recommended wet film thickness (|im)
102
102
76-102
Actual wet film thickness (|im )
82.5
74.6
123
Air exchange rate (h"1)
0.543
0.543
0.538
Mass transfer coefficient (m h"' )d
4.36
4.36
4.36
a All three tests were conducted in 53-L stainless steel chambers at 23 °C and 50% relative humidity.
b Estimated from Equation 28.
c Estimated from Equation 30.
d For decane; estimated from Equation 33.
B-25
-------
Table 6. Comparison of Observed and Predicted Peak Concentrations
Concentration Units: mg/m3
Test
Specimen
Compound
Observed
Method 1
Predicted % Diffa
Method 2
Predicted % Diffa
TVOCs
9.77xl03
8.91xl03
-9.3
1.23xl04
+22
decane
l.lOxlO3
8.76xl02
-23
8.92xl02
-21
nonane
6.63xl02
6.71xl02
+1.2
7.01xl02
+5.6
Alkyd
//vms-decalin
6.76X101
7.93X101
+16
8.19X101
+19
/^-xylene
4.26X101
5.65X101
+28
5.94X101
+33
Primer
ethylbenzene
1.17X101
1.21X101
+3.4
1.28X101
+9.0
o-xylene
8.31x10°
9.12x10°
+9.3
9.89x10°
+17
p-ethyltoluene
6.19x10°
7.06x10°
+13
7.29x10°
+16
TVOCs
6.55xl03
6.36xl03
-2.9
9.32x10s
+35
decane
4.62xl02
4.87xl02
+5.3
5.45xl02
+16
undecane
4.01xl02
4.60xl02
+14
5.28xl02
+27
nonane
1.92xl02
2.05xl02
+6.5
2.23xl02
+15
Alkyd
/ra/7.s-decalin
7.37X101
1.16xl02
+45
1.29xl02
+55
methylethylketoxime
7.01X101
5.97X101
-16
6.69X101
-4.7
Paint B
p-ethyltoluene
3.45X101
3.82X101
+10
4.19X101
+19
o-xylene
3.01X101
4.09X101
+30
5.48X101
+58
1,2,4-trimethylbenzene
1.55X101
2.55X101
+49
2.54X101
+48
//-propylbenzene
7.72x10°
1.07X101
+32
1.18X101
+42
isopropylbenzene
3.79x10°
4.86x10°
+25
5.31x10°
+33
Conversion
/^-xylene
isobutanol
9.78xl03
3.48xl03
9.11xl03
3.85x10s
-7.0
+9.9
l.OOxlO4
3.65x10s
+2.3
+4.7
Varnish
o-xylene
ethylbenzene
2.79xl03
2.31xl03
2.26x10s
2.18x10s
-21
-5.9
2.41x10s
2.49x10s
-15
+7.3
Average Percent Difference11
16.6
22.9
a Percent difference.
b Average of absolute values.
B-26
-------
Table 7. Normalized Mean Square Error (NMSE) as an Indicator of Model Accuracy
Test Specimen
Compound
Method 1
Method 2
TVOC
0.067
0.044
decane
0.097
0.106
nonane
0.024
0.045
Alkyd
/ra/7s-decalin
0.229
0.212
/^-xylene
0.236
0.293
Primer
ethylbenzene
o-xylene
0.032
0.036
0.056
0.057
p-ethyltoluene
0.459
0.633
TVOC
0.116
0.389
decane
0.111
0.147
undecane
0.125
0.169
nonane
0.160
0.218
/ra/7.s-decalin
0.542
0.687
Alkyd
methylethylketoxime
0.204
0.240
Paint B
/>ethyltoluene
o-xylene
0.117
0.377
0.168
0.547
1,2,4-trimethylbenzene
0.508
0.470
//-propylbenzene
0.384
0.522
isopropylbenzene
0.375
0.498
Conversion
ethylbenzene
o-xylene
0.059
0.116
0.064
0.111
Varnish
isobutanol
p-xylene
0.054
0.048
0.068
0.070
Average NMSE
0.195
0.253
B-27
-------
Figure Captions
Figure 1. Gas-phase mass transfer coefficient (km ) as a function of air velocity and source area (S)
Figure 2. An example of model predictions with good accuracy. NMSE = 0.024 for method 1 and
0.045 for method 2. Data are for nonane in the alkyd primer test.
Figure 3. An example of model predictions with poor accuracy. NMSE = 0.542 for method 1 and
0.687 for method 2. Data are for trans-decalin in the alkyd paint test.
B-28
-------
Air Velocity (cm/s)
B-29
-------
800
~ Data
Method 1
• • • Method 2
600
E
B)
E
c
£ 400
CO
c
(D
O
c
O 200
SB
0
5
10
15
Elapsed Time (h)
B-30
-------
140
120
Data
Method 1
Method 2
0
10
15
Elapsed Time (h)
B-31
-------
APPENDIX C
LATEX PAINT CHAMBER TESTS
-------
CI. INTRODUCTION
A series of small-chamber tests was conducted by ARCADIS Geraghty and Miller, Inc., to
characterize concentrations of various volatile organic compounds (VOCs) emitted from different
formulations of latex primer and paint. In addition to the broad objective of improving the
understanding of emission behavior for these chemicals in latex primer and paint, a more specific
objective was to provide a quantitative basis for development of emission models or for estimating
parameters for such models. In addition to the small-chamber tests, ARCADIS Geraghty and
Miller, Inc., conducted painting events at EPA's research house in North Carolina for the primary
purpose of gathering data to be used for model evaluation.
The sections that follow describe methods and results for bulk analysis of the latex
primer/paint formulations prior to chamber testing, small-chamber emission tests of these
formulations, and development of predictive models for VOC emissions from latex primer and
paint.
C2. BULK ANALYSIS
Prior to conduct of small-chamber emission tests, each formulation of latex primer or paint
was analyzed to determine its chemical composition by weight. In brief, the procedure for
analysis of the bulk product that was followed by ARCADIS Geraghty and Miller, Inc.,
(ARCADIS 1998) involved (1) extracting latex primer and paints with acetone, (2) centrifuging
the sample to remove solids, and (3) analyzing the supernatant by GC/MS. Aliquots of the
supernatant were diluted as necessary to yield sample concentrations that fell within the
calibration range.
Results of the bulk analysis are shown as chemical weight fractions (mg/g) in Table C-l.
One primer (designated as formulation LP-A) was used for the chamber tests together with four
formulations of paint (LF-B, LF-C, LSG-D, and LSG-E). In the designations for formulation, P
indicates primer, F indicates flat paint, and SG indicates semi-gloss paint. Only five VOCs were
found in measurable quantities in any of the formulations that were tested. The primer contained
ethylene glycol and TMPD-MIB, the flat paints primarily contained propylene glycol and TMPD-
MIB, and the semi-gloss paints primarily contained propylene glycol and TMPD-MIB. Thus,
TMPD-MIB was the only VOC common to all formulations. One semi-gloss formulation had a
measurable, but relatively small, quantity of 2-(2-butoxyethoxy) ethanol (BEE), and one of the
flat paints and one of the semi-gloss paints had relatively small quantities of dipropylene glycol.
C-l
-------
Table C-l. Results of Bulk Analysis (mg/g) for Latex Primer and Paints
Chemical
LP-A
(Primer)
LF-B
(Paint)
LF-C
(Paint)
LSG-D
(Paint)
LSG-E
(Paint)
Propylene Glycol
ND*
23.50
0.05
55.20
24.20
Ethylene Glycol
19.60
ND
20.20
0.02
ND
2-(2-Butoxyethoxy)
Ethanol
ND
ND
ND
0.16
ND
TMPD-MIB
12.20
16.80
7.05
25.70
7.00
Dipropylene Glycol
ND
0.28
ND
ND
0.12
* Not detected.
C-2
-------
C3. SMALL-CHAMBER EMISSION TESTS
The small-chamber emission tests were conducted by ARCADIS Geraghty and Miller,
Inc., in the EPA APPCD Source Characterization Laboratories located in the EPA Environmental
Research Center in Research Triangle Park, NC. The tests were conducted using 53-liter,
stainless-steel chambers housed in a temperature-controlled incubator. These chambers have been
fitted with inlet and outlet manifolds for the air supply, temperature and relative humidity sensors,
and a small fan to ensure mixing within the chamber. During each test, clean (VOC- and particle-
free) air was supplied to the chamber at a controlled relative humidity. A glass sampling manifold
has been connected to the chamber outlet for collection of air samples.
The substrate used in the tests was 0.5-inch gypsum wallboard that was purchased from a
local retail outlet in North Carolina. For each test, the substrate was cut to a size of 16 by 16 cm
(total area of 256 cm2 or 0.0256 m2), resulting in a surface-to-volume loading ratio of about 0.5
m2/m3 in the chamber. The edges were sealed and the test specimen was placed on the floor of
the chamber during the test. The cut and sealed substrate was conditioned in the chamber for at
least 24 hours prior to application of primer/paint.
Primer and paint were applied to the wallboard with a roller purchased at a local retail
outlet. The rate of primer/paint application in the tests, and resulting wet film thickness, were
based on recommendations from the manufacturers. The mass of paint applied was determined
gravimetrically by two methods. Wet film thickness was not measured with a gage during the
tests because the gage affects surface film characteristics and the specimen was to be inserted into
the chamber as quickly as possible after priming or painting. Based on the measured mass of paint
applied and the known specific gravity of the coating, the average calculated wet film thickness
was 415 jim (16.4 mil) for the alkyd primer and 105 //m (4.1 mil) for the alkyd paint.
As noted above, the wallboard specimen was conditioned in the chamber at least 24 hours
before the test. Background concentrations were measured prior to removing the specimen.
Primer was then applied, the specimen was re-inserted in the chamber, and air samples were
collected for the next 48 hours. Then the specimen was removed, paint was applied, the
wallboard was again inserted in the chamber, and air samples were collected during the next 12
days. Thus, the total monitoring period for each test was 14 days in duration.
C-3
-------
Four tests were conducted for latex primer and paint. The primer LP-B was used for all
tests. Paint formulation LSG-E was used in the first chamber emission test (test L3), paint
formulation LSG-D for the second test (test L4), paint formulation LF-B for the third test (test
L5), and paint formulation LF-C for the fourth test (test L6).
It has been observed in previous chamber tests that emission rates for various compounds
in paint tend to decline exponentially over time as the reservoir of material that can be emitted is
gradually depleted, and as the drying paint forms a barrier that retards emissions. Two types of
empirical models for estimating the time-varying emission profile can be used: (1) a single-
exponential model governed by an initial emission rate and a rate of decline from the initial rate,
and (2) a double-exponential model with two sets of initial emission rates and rates of decline, one
to account for an early ("fast") phase of evaporation-dominated emissions and one to account for
a later ("slow") phase of diffusion-dominated emissions.
Previous work by Wilkes et al. (see Appendix D), for example, has demonstrated that a
double-exponential model is needed to properly represent the emission behavior of VOCs released
from latex paint. The time-varying emission rate for the double-exponential model is given by the
following equation:
, -kit i 77 ^ -k2t
where:
S(t)=Eole~k" + Eo2e^ (C-l)
S(t) = Source strength as a function of time (mass/time);
E01 = Initial emission rate (mass/time) for the first exponential;
k| = First-order rate constant (time"1) for the first exponential;
E02 = Initial emission rate (mass/time) for the second exponential;
k2 = First-order rate constant (time"1) for the second exponential; and
t = Time.
For each chamber test, an equation for the chamber concentration reflecting the double-
exponential model in equation (C-l) was fit to chamber data for each of the chemicals in latex
primer and paint using non-linear regression analysis. The measured chamber volume and airflow
rate were taken as "knowns." First, the initial emission rate and the first-order rate constant for
the "slow" phase of emissions decline were estimated through the regression technique, using data
after the first 24 hours following primer or paint application. Next, these parameter estimates
C-4
-------
were taken as "known," along with the chamber volume and airflow, to estimate the initial
emission rate and the first-order rate constant for the "fast" phase, using the entire concentration
time series after priming or painting. In each case, the fits were done separately for the priming
and painting portions of the test, where permitted by the data. (In some cases, examples of which
are shown later, the concentrations had not declined sufficiently after priming to enable reliable
estimation of these parameters for the priming and/or painting portion of the test.)
Example fits of the double-exponential emissions model to the chamber concentration data
are shown in Figures C-l through C-4. Figure C-l depicts ethylene glycol concentrations during
test L4 (semi-gloss formulation LSG-D). In this case, the concentrations had not declined
sufficiently by the time paint was applied to enable reliable estimation of model parameters for
emissions from the primer. Although the residual concentrations from priming could influence the
parameter estimates for the painting portion of the test, a fit was attempted nonetheless. The
double-exponential model appears to fit this portion of the data quite well, both during the rapid
and slow phases of concentration decline.
For TMPD-MIB during test L4 (Figure C-2), there were no measurable quantities during
the priming portion of the test, even though the bulk analysis indicated presence of TMPD-MIB in
the primer. As a result, a reliable fit could be attempted to the concentrations during and after
painting. As shown in the figure, the double-exponential model appears to capture the emissions
behavior quite well, following the concentration profile closely throughout the test, with the
possible exception of slight underestimation near the end of the test.
For test L6, involving flat formulation LF-C, propylene glycol concentrations receded
sufficiently before paint application to enable estimation of the emission profile during both the
priming and the painting potions of the test (Figure C-3). For both portions of the test, the
double-exponential model appears to have represented the emissions behavior quite well, again
with the possible exception of underestimation toward the end of the test. For the same test,
ethylene glycol concentrations (Figure C-4) similarly had declined sufficiently after priming to
permit estimation of model parameters for both portions of the test. In this case, the double-
exponential model appears to provide an excellent fit to the concentration data throughout the
test.
C-5
-------
Ethylene Glycol -- Latex Test L4
Double Exponential
6.00E + 00
5.00E + 00
4.00E + 00
c
o
2
"E 3.00E + 00
-------
Propylene Glycol -- Latex Test L6
Double Exponential
3. OOE-O 1
2.50E-01
2. OOE-O 1
5.00E-02
0
50
100
150
200
250
300
350
400
Elapsed Time
Figure C-3. Propylene Glycol Concentrations and Model Fit for Test L6 (Latex Paint LF-C).
Ethylene Glycol-- Latex Test L6
Double Exponential
3.50E + 01
3.00E + 01
2.50E + 01
2.00E + 01
1.50E + 01
1.00E + 01
5.00E + 00
0.00E + 00
0
50
100
150
200
250
300
350
400
Elapsed Time
Figure C-4. Ethylene Glycol Concentrations and Model Fit for Test L6 (Latex Paint LF-C).
C-7
-------
Estimates of the parameters (E0 and k) for each of the exponentials in the double-
exponential emissions model described above are summarized for chemicals in each paint
formulation and the primer in Table C-2. The R2 value shown for the first exponential is actually
the value that results when applying the entire model (first plus second exponentials) to the entire
data set for a given chemical during a chamber test. Excellent overall fits to the data were
obtained in virtually every case, with the R2 value at or above 0.85 in all cases and above 0.95 in
many cases.
The estimated k values for the emission decay rate for any given chemical were not
entirely consistent across paint formulations. The range of the estimates can be summarized as
follows:
K value for first exponential
- for propylene glycol, varied from 0.9 to 2.7 across five formulations
- for ethylene glycol, varied from 0.3 to 3.0 across five formulations
- for TMPD-MIB, varied from 0.5 to 0.9 across three formulations (fourth was 6.5)
- for dipropylene glycol, varied from 0.2 to 0.8 across two formulations.
K value for second exponential
- for propylene glycol, varied from 0.005 to 0.03 across five formulations
- for ethylene glycol, varied from 0.002 to 0.03 across five formulations
- for TMPD-MIB, varied from 0.007 to 0.05 across four formulations
- for dipropylene glycol, varied from 0.007 to 0.03 across two formulations.
The emitted mass for each chemical can be estimated as the integral of equation (C-l), or
EoA + E02/k2. The recovery for each chemical, obtained by expressing this integral as a
percentage of the applied mass, is shown in Table C-3. There is one case (ethylene glycol for
paint LSG-D) for which the recovery value clearly is an outlier. Otherwise, the recovery values
generally range from 10 to 50 percent, averaging about 25-30 percent. This outcome is consistent
with results from Wilkes et al.(see Appendix D), who reported a range of recovery values from 20
to 35 percent for chemicals in interior latex paints.
The previous work by Wilkes et al. also indicated that the second exponential accounts for
about 90 percent of the emitted mass. Corresponding estimates can be obtained from Table C-3
by expressing the emitted mass associated with the second exponential (E02/k2) as a percentage of
C-8
-------
the total emitted mass (E01/kj + E02/k2). Neglecting the outlier case, the estimated percentage
ranges from 64 to 96 percent, averaging 80 percent.
Table C-2. Latex Parameter Estimates (Double-exponential Emissions Model)
Chemical
1st Exponential
2nd Exponential
Eoi
K:
R2
Eq2
K2
R2
PAINT LSG-E
Propylene Glycol
3.106
1.429
0.978
0.021
0.005
0.774
Ethylene Glycol
0.152
0.282
0.851
0.013
0.002
0.380
TMPD-MIB
0.549
0.867
0.947
0.025
0.007
0.924
Dipropylene Glycol
0.004
0.177
0.995
0.001
0.007
0.810
PAINT LF-B
Propylene Glycol
7.156
2.115
0.983
0.043
0.006
0.902
Ethylene Glycol
0.456
1.129
0.958
0.035
0.004
0.936
TMPD-MIB
2.450
1.368
0.930
0.152
0.011
0.978
Dipropylene Glycol
0.006
0.755
0.857
0.002
0.025
0.999
PAINT LSG-D
Propylene Glycol
6.370
0.908
0.987
0.098
0.006
0.894
Ethylene Glycol
0.166
0.702
0.940
0.025
0.003
0.675
TMPD-MIB
1.005
0.519
0.985
0.140
0.010
0.953
PAINT LF-C
Propylene Glycol
0.054
2.752
0.995
0.001
0.019
0.854
Ethylene Glycol
6.815
3.044
0.988
0.104
0.012
0.988
TMPD-MIB
11.535
6.481
0.960
0.340
0.049
0.920
PRIMER LF-C
Propylene Glycol
0.013
1.606
0.892
0.001
0.030
0.976
Ethylene Glycol
1.276
1.699
0.964
0.106
0.029
0.917
C-9
-------
Table C-3. Recoveries for Chemicals in Latex Primer and Paints
Chemical
Paint/Chemical Applied
Chemical Emitted
Recovery
(%)
Paint (g)
Chemical
(mg)
Eqi/Kj
E02/K2
PAINT LSG-E
Propylene Glycol
2.29
55.42
2.17
3.78
10.8
Ethylene Glycol
2.29
N/A
0.54
7.53
N/A
TMPD-MIB
2.29
16.03
0.63
3.57
26.2
Dipropylene Glycol
2.29
0.27
0.02
0.12
52.2
PAINT LF-B
Propylene Glycol
2.56
60.16
3.38
7.63
18.3
Ethylene Glycol
2.56
N/A
0.40
8.95
N/A
TMPD-MIB
2.56
43.01
1.79
13.54
35.6
Dipropylene Glycol
2.56
0.72
0.01
0.08
11.8
PAINT LSG-D
Propylene Glycol
2.82
157.32
7.02
16.92
15.2
Ethylene Glycol
2.82
0.05
0.24
7.50
14437.4
TMPD-MIB
2.82
72.47
1.94
14.65
22.9
PAINT LF-C
Propylene Glycol
2.23
0.12
0.02
0.04
50.4
Ethylene Glycol
2.23
45.05
2.24
9.05
25.1
TMPD-MIB
2.23
15.72
1.78
6.93
55.4
PRIMER LF-C
Propylene Glycol
2.85
N/A
0.01
0.02
N/A
Ethylene Glycol
2.85
55.86
0.75
3.68
7.9
C-10
-------
C4. DEVELOPMENT OF A PREDICTIVE MODEL
The number of cases for which emission decay rates could be estimated for the first or the
second exponential was insufficient for reliable development of an empirical model to predict such
rates. Instead, reliance was placed on an empirical model developed by Wilkes et al. (see
Appendix D). In that model, the emission decay rate associated with the first ("fast") exponential
is predicted by vapor pressure and the emission decay rate associated with the second ("slow")
exponential is predicted by molecular weight, as follows:
• Predicted kx = 233.25 * VP (C-2)
• Predicted k2 = 0.0000584 * MW (C-3)
where VP is vapor pressure (in torr) and MW is molecular weight (in g/mole).
Table C-4 indicates the degree of correspondence between the predicted kx/k2 values from
the empirical model and those estimated from the chamber emission tests conducted under this
project. For k, the model substantially over-predicts the measured k, values for propylene glycol
and ethylene glycol and slightly under-predicts the value for TMPD-MIB, which has the lowest
vapor pressure. For k2the model is quite close in all cases, toward the lower end of the range of
estimated values for propylene glycol and ethylene glycol, and toward the upper end for TMPD-
MIB. The fact that the predictions are quite close for k2 values is encouraging, since the second
exponential is believed to account for 80 to 90 percent of the emitted mass.
Table C-4. Comparison of Estimated and Predicted Emission Decay Rates for Chemicals in Latex
Paint
Chemical Properties* and K
Propylene Glycol
Ethylene Glycol
TMPD-MIB
Values
Molecular Weight (g/mole)
76.1
62.1
216
Vapor Pressure (torr)
0.2
0.05
0.0019
Range of Estimated k Values
0.9-2.7
0.3 -3.0
0.5 - 1.4**
Predicted k Value
46.7
11.7
0.44
Range of Estimated k2 Values
0.005 - 0.002
0.002 - 0.03
0.007 -0.011
Predicted k2 Value
0.004
0.004
0.013
* As reported by Wilkes et al. (see Appendix D).
** Suspected outlier of 6.5 excluded from range of estimated values.
C-ll
-------
APPENDIX D
PAPER ON EMISSIONS MODEL FOR LATEX PAINT
(presented at Indoor Air '96 Conference)
-------
ESTIMATION OF EMISSION PROFILES
FOR INTERIOR LATEX PAINTS
C.Wilkes1, M.Koontz1, M.Ryan2 and C.Cinalli2
' GEOMET Technologies, Inc., Germantown, MD, USA
2Office of Pollution Prevention and Toxics, US Environmental Protection Agency, Washington DC, USA
ABSTRACT
Methods were developed for estimating emission profiles for VOCs released from interior latex
paints, for two situations: time-series data are available from small-chamber experiments; and
only the weight fractions and physical/chemical properties of the paint constituents are known.
A double-exponential model fit the data quite well in most cases. The rate constant for the
"fast" (evaporation-dominated) exponential is related to vapor pressure, and the rate constant
for the "slow" (diffusion-dominated) exponential is related to molecular weight. Although the
fast component dominates the early phase of the emission profile, it generally accounts for 10
percent or less of the released VOC mass. The mass released, in turn, generally was between
20 and 35 percent of the applied VOC mass.
INTRODUCTION
Estimation of human inhalation exposure in residential settings, due to use of consumer
products or installation of building materials or furnishings, requires integration of time-varying
pollutant concentrations with information on individuals' locations and breathing rates. Often
the concentration component is estimated using an indoor air quality (IAQ) model. The
accuracy of the exposure estimate is enhanced by providing a faithful depiction of the time-
varying airborne concentration which, in turn, relies on reasonable characterization of the
emission profile for the chemical(s) of concern.
The main objective of the effort described in this paper was to develop methods for estimating
emission profiles for chemicals released from interior latex paints, for two situations: data are
available from small-chamber experiments whereby airborne concentrations are measured in
the chamber at selected points in time after the paint has been instantaneously applied to a
substrate; and only the weight fractions and physical/chemical properties (molecular weight
and vapor pressure) of the paint constituents are known. Small-chamber data used for this
analysis have been recently collected for latex paint applied to gypsum board (1).
METHODS
The experimental data were collected under sponsorship of the EPA Air and Energy
Engineering Research Laboratory (AEERL) in Research Triangle Park, NC. These
experiments involved application of two different formulations, called A and B in this paper, of
latex paint to a small piece of pre-painted gypsum board. Following the paint application,
D-l
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the specimen was immediately inserted in a small stainless-steel chamber, and concentrations of
four individual VOCs were measured at selected points in time over a period of several
hundred hours. Multiple samples were collected during each experiment on Tenax®TA sorbent
and analyzed by a gas chromatograph with a flame ionization detector (GC/FID). The sample
durations were variable, ranging from an hour or less at the start of the experiment to much
longer durations toward the end, when the chamber air concentrations were lower.
Bulk analysis of the paint sample was performed to determine which volatile organic
compounds (VOCs) are present in each paint, and to estimate the weight fraction of each
VOC. Four individual VOCs were found to comprise the majority of the VOCs present in
each paint. The molecular weight (MW) and vapor pressure (VP) of these four compounds
were estimated (2) to be:
• Propylene Glycol: MW = 76.1 g/mol VP = 0.2 torr
• Ethylene Glycol: MW = 62.1 g/mol VP = 0.05 torr
• Butoxyethoxyethanol: MW = 162.2 g/mol VP = 0.02 torr
• Texanol: MW = 216 g/mol VP = 0.0019 torr
Various representations of the emission profile were considered, including a mass-transfer
representation based on physical and chemical properties, an empirically fit single-exponential
model to account for the (assumed) general decline in the emission rate over time, and an
empirically fit double-exponential model (the sum of two exponentials) that assumes two
components of emissions decline — a "fast" (evaporation-dominated) component that primarily
governs the early stage of emissions and a "slow" (diffusion-dominated) component that
governs the later stage. The exponential model is given by the following equation:
S(t)=E0ekt (1)
where: S(l) = Source strength as a function of time (mass/time)
E0 = Initial emission rate (mass/time)
k = First-order rate constant (time"1)
t = Time.
For estimation of the single- and double-exponential model parameters (an initial emission rate
and a first-order rate of decline in the rate), nonlinear regression analysis was applied to the
chamber concentration data, taking advantage of the known chamber volume and the
experimentally controlled air exchange rate for the chamber.
RESULTS
The mass-transfer model was found by other researchers (1) to provide a good fit to measured
air concentrations. However, because of the large number of parameters that are difficult to
estimate or must be measured, it was not possible to use this model for this study. Based on
the results of the nonlinear estimation process, the single-exponential model did not fit the data
well, most likely because it is insufficient to provide an empirical representation of the physical
process as the paint dries. The double-exponential model fit the data quite well in most cases.
D-2
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Chamber data for painted gypsum board currently are limited to two formulations of latex
paint. Methods were sought by which to estimate parameters of the double-exponential
emission model for brands of latex paint for which only the weight fraction, molecular weight
and vapor pressure of a VOC constituent are known, so that the emissions of untested
formulations can be estimated. Therefore, the data from experiments with formulation A of
latex paint were used to develop relationships between the parameters of the fitted double
exponential and the chemical properties of each VOC, and the data from the experiments with
formulation B were used to evaluate the predictive ability of these relationships.
It was hypothesized that the "fast" decline would be evaporation-dominated and, hence, the
rate term for this decline would be related to a chemical's vapor pressure. Similarly, it was
hypothesized that the rate term for the diffusion-dominated "slow" decline would be related to
a chemical's molecular weight. These hypotheses were indeed supported by the data.
Regression through the origin indicated strong linear relationships between the "fast" decline
rate constant (k,) and vapor pressure (R2 = 0.92), and between the "slow" decline rate (k2) and
molecular weight (R2 = 0.96). Regression not constrained to go through the origin was also
examined, but was discarded because of the possibility of predicting a negative rate constant.
These relationships are shown in Figure 1.
The parameters of the fitted double exponentials are presented in Table 1. The mass released
by each exponential is also given in the table, along with the estimate of the total mass released
based on the fitted double exponentials. The fraction of the total applied VOC mass that was
released is between 20% and 35%, as estimated by the fitted double exponentials and shown in
the table. In addition, the "fast" exponential generally accounts for less than 10% of the
released mass, leaving the remaining 90% for long-term emissions. Based on these
observations, along with the relationships presented in Figure 1, a method for estimating the
parameters to a double-exponential representation of the emissions has been developed. The
method assumes that 25% of the total available mass (determined based on the bulk analysis of
the paint) is ultimately released. Of this 25% total emissions, 10% is assumed to be released as
described by the first ("fast") exponential, and the remaining 90% is assumed to be released as
described by the second ("slow") exponential. Therefore, the parameters of the two
exponentials can be estimated by using the relationships presented in Figure 1 to approximate
k| and k2. Then E01 and E02 can be determined by assigning the appropriate mass to each,
recognizing that the released mass associated with each exponential is the ratio of the initial
emission rate to the rate constant (E0/k).
This method was applied to the emissions from the latex paint described as formulation A, as
well as a different latex paint (formulation B). The double exponential fits to the chamber
data, as well as double exponentials based on the parameter-estimation method described
above, are shown for one VOC (butoxyethoxyethanol) in Figure 2 (formulation A) and in
Figure 3 (formulation B). In each case, the double exponentials based on the parameter-
estimation procedure are not drastically different from those fit directly to the chamber data.
The estimated double exponential for formulation B provides some evidence that the
estimation method performs reasonably well. This process also was applied with similar
success for the other three VOCs. In most cases, the peak chamber concentration predicted by
the estimation method was within a factor of two of the measured peak concentration.
D-3
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0.014
0.012
Tb = (5.839E-5)*MW
0.01
s- 0.008
0.006
0.004
~k-2 = (7.08E-5)*MW -0.002
R2 = 0.995
0.002
0
50
100
150
200
60
-kj = (233.25)* VP
R2 = 0.92
50
40
30
20
k, = (264.7)*VP-4.961
10
0
0
0.05
0.1
0.15
0.2
Vapor Pressure (torr) Molecular Weight (g/mol)
Figure 1 Correlation between chemical properties and parameters of the double exponential.
Table 1 Summary of Parameters of the Double-Exponential Fit for 4 VOCs, Formulation A.
Fraction of
Mass of
Total Mass
Applied
voc
of VOC
Mass
Compound Exponential
E0,
k,
Released,
Applied,
Released,
mg/hr
1/hr
mg
mg
mg/mg
Propylene Glycol
1st
0.815
49.68
0.02
—
0.002
2nd
0.0058
0.0030
1.95
—
0.220
Total
—
—
1.97
8.86
0.222
Ethylene Glycol
1st
2.812
1.344
2.09
—
0.023
2nd
0.055
0.0026
20.75
—
0.226
Total
—
—
22.84
91.68
0.249
Butoxyethoxyethanol
1st
0.253
0.158
1.60
—
0.084
2nd
0.022
0.0099
2.27
—
0.119
Total
—
—
3.87
19.02
0.203
Texanol
1st
1.46
0.944
1.55
—
0.030
2nd
0.22
0.013
16.65
—
0.323
Total
—
—
18.21
51.57
0.353
D-4
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8
A Butoxyethoxyethanol
Double Exponential; Parameters Predicted Based on Vapor Pressure and Molecular Weight
~ Fitted Double Exponential
TIME (HOURS)
A Butoxyethoxyethanol
Double Exponential; Parameters Predicted Based on Vapor Pressure and Molecular Weight
~ Fitted Double Exponential
Figure 2 Comparison of Butoxyethoxyethanol Chamber Concentrations to the Fitted Double
Exponential and the Predicted Double Exponential for Latex Paint, Formulation A.
Figure 3 Comparison of Butoxyethoxyethanol Chamber Concentrations to the Fitted Double
Exponential and the Predicted Double Exponential for Latex Paint, Formulation B.
TIME (HOURS)
D-5
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CONCLUSIONS
The double-exponential model was found to fit the data quite well in most cases, provided that
the second ("slow") exponential was estimated first, by fitting a single-exponential model to
the data after the first 48 hours in the chamber. The first ("fast") exponential could then be
estimated using all the chamber data, by specifying a double-exponential model with the second
exponential's parameters input as "knowns."
Integration of the fitted double-exponential model to infinity provided an estimate of the total
emitted mass of each VOC. Comparison of this emitted mass with the applied mass, as
estimated from the bulk analysis, indicated that the emitted mass ranged from 20 to 35 percent
of the applied mass for those compounds, averaging about 25 percent. Integration of the
respective exponentials indicated that the amount of emitted mass attributable to the first
("fast") exponential was generally less than 10 percent. Thus, although this exponential
dominates the early emission phase, the later phase of "slow" emissions accounts for most of
the total VOC emissions.
A relationship between the parameters of the double exponential and the chemical properties of
the VOC was identified. Because the VOCs are leaving the paint primarily through
evaporation in the initial phases of the paint-drying process, it is reasonable for the rate
constant to be correlated with the VOC's vapor pressure. Similarly, the VOCs are leaving
later in the paint-drying process primarily through diffusion, and in this case it is reasonable for
the rate constant to the be correlated with the VOC's molecular weight. The number of data
points is small, and therefore these relationships cannot be used with great confidence,
especially for VOCs with vapor pressures and molecular weights outside the range of those
examined in this study. With data from additional chamber tests, the confidence in these
relationships could be improved, and a physically/chemically based mass-transfer model could
be developed.
Several areas where improved information or theoretical developments would aid any future
iterations of estimation procedures for interior latex paints are apparent. More small-chamber
experimental data for paint applied to gypsum board are needed so that differences across flat,
semi-gloss and gloss paints can be evaluated, and so that a broader array of individual VOCs is
available to support development of regression estimates. Ideally, a physically and chemically
based model could be developed that accounts for the mass-transfer process yet requires only
minimum parameter estimates such as VOC weight faction, vapor pressure and molecular
weight, with possible addition of selected parameters specific to the painting event (e.g., paint
application rate, indoor volume).
ACKNOWLEDGMENTS
This work was funded by the US Environmental Protection Agency under contract number
68-D3-0013.
D-6
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REFERENCES
(1) Acurex Environmental Corporation. 1995. "Data Summary for the Latex Paint
Assessment Program. II. Dynamic and Static Chamber Testing and Model
Development", Report Prepared for the US Environmental Protection Agency Under
Contract Number 68-D4-0005, June 9, 1995.
(2) Environmental Fate Database, Syracuse Research Corporation, Syracuse, NY, USA.
D-7
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APPENDIX E
MODEL EVALUATION USING DATA FROM EPA RESEARCH HOUSE
-------
El. INTRODUCTION
A series of two related experiments was conducted by ARCADIS Geraghty and Miller,
Inc., at the EPA test house, for the primary purpose of gathering data to be used for model
evaluation. One of the experiments involved alkyd primer and paint and the other latex primer
and paint. Each of the experiments followed the same general protocol — one coat of primer was
applied to the walls of the front corner bedroom, and approximately 48 hours later one coat of
paint was applied to the same walls. For each experiment, new gypsum board was primed and
painted. The new wallboard was mounted on furring strips that were temporarily applied to
existing walls, so that the source could be removed after each experiment.
The sections that follow describe (1) the EPA test house, (2) certain specifics of the
experiment for alkyd primer and paint together with model inputs and modeling results in
comparison with measurements, and (3) experiment specifics, model inputs and modeling results
for latex primer and paint.
E2. TEST HOUSE DESCRIPTION AND GENERAL TEST CONDITIONS
The EPA test house, located in North Carolina, is a single-family residence of wood frame
construction. As shown in Figure E-l, the floor plan consists of three bedrooms, two bathrooms,
a combination living/dining room, a small kitchen, and a den. The home is heated with a gas
furnace and cooled by a central air conditioning system. All floor areas are carpeted except the
kitchen and bathrooms, which have linoleum flooring. All windows have either curtains or
shades. The attached garage contains all monitoring and test support instrumentation and is
equipped with a heat pump for climate control.
The house has an interior volume of 319 cubic meters, or 11,272 cubic feet. The volume
of the front corner bedroom that was painted is 30.25 cubic meters, or 1,069 cubic feet, which
accounts for about 9.5 percent of the total house volume. The wall area that was painted in the
front corner bedroom totals about 29.5 square meters, or 317.5 square feet. Thus, the loading
ratio for the painted space (i.e., ratio of the painted surface area to room volume) was 0.297 ft2/ft3
for these experiments, similar to the WPEM default of 0.29 ft2/ft3 when only walls are painted.
E-l
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Master
bedroom
Master
' bath
Instruments
Comer
bedroom
Middle
bedroom
uv»ig
Room
s Registers
Figure E-l. Floor Plan for the EPA Test House.
Throughout each experiment the air handler fan for the central air conditioner was placed
in the constant-operation mode, and ceiling fans were operated and all supply registers were kept
open, to ensure good mixing throughout the house. With this configuration, air exchange rates
prevailing during the experiments could be measured more accurately (using a tracer-decay
method) and air sampling could be restricted to two locations — the painted bedroom and the den
at the opposite end of the house. Exterior doors and windows were closed during each
experiment, interior doors were open, and the indoor temperature setting was 72 °F (22.2 °C).
The measured air exchange rate averaged 0.48 air changes per hour (ACH) for the alkyd test and
0.47 ACH for the latex test. Based on previous measurements in the supply registers for the
painted bedroom, the airflow rate between that room and the remainder of the house was assumed
to be 325 m3 per hour, or 11,484 ft3 per hour.
E-2
-------
Background air samples were collected both outdoors and in the house prior to each of
the two experiments. Paint was applied approximately 48 hours after primer application, and air
samples were collected over a 14-day period (48 hours after priming and 12 days after painting),
at a progressively lower rate as indoor concentrations receded following the priming/painting
event. The latex test was conducted first (August 1997). Following the 14-day measurement
period, the painted wallboard was removed, the house was aired out, and then new wallboard was
installed for the alkyd test (September 1997).
E3. MODEL EVALUATION FOR ALKYD PRIMER AND PAINT
The report of the experiments by ARCADIS Geraghty and Miller, Inc., indicates that,
for the alkyd experiment, 6.96 kilograms of primer AP-F were applied to the walls in the front
corner bedroom over a period of 43.4 minutes, beginning at 11:13 a.m. on September 9, 1997.
Approximately two days later, 4.93 kilograms of paint ASG-G were applied over a period of 33.7
minutes, beginning at 10:41 a.m. on September 11, 1997. The reported wet film thickness was
14.4 mil for primer and 8.05 mil for paint. The measured air exchange rate prevailing during the
test averaged 0.48 ACH, as noted previously.
Corresponding WPEM inputs for the painting scenario described above are summarized in
Table E-l. The input for house volume matched the actual value listed above. The percent
painted was set to 9.5 percent, resulting in a painted volume of 1071 ft3 (the actual painted
volume was 1069 ft3). The inputs for air exchange and interzonal airflow rates matched the actual
values listed above. Based on a loading ratio of 0.30 ft2/ft3 for walls, the painted surface area
input was 321 ft2 (the actual area was 317.5 ft2).
The wet film thickness values reported by ARCADIS Geraghty and Miller, Inc. — 6 mil
for primer and 5.375 mil for paint — correspond to primer/paint coverages of 267 and 298
ft2/gallon, respectively. The application rates input for WPEM — 1.66 gallons/hour for primer and
1.92 gallons/hour for paint — were chosen to result in priming/painting durations that matched
those reported for the experiment at the EPA test house.
E-3
-------
Table E-l. WPEM Inputs for Alkyd Painting Scenario at EPA Test House
Input Parameter
Input Value
House volume
11,272 ft3
Percent of house painted
9.5 %
Air exchange rate
0.48 ACH
Interzonal airflow rate
11,484 ft3/hour
Painted wall surface area
321 ft2 (using loading ratio of 0.30; actual = 317.5 ft2)
Wet film thickness
6 mil for primer, 5.375 mil for paint
Calculated amount of paint
1.20 gallons for primer, 1.08 gallons for paint
Application rate
1.66 gallons/hour for primer, 1.92 gallons/hour for paint
Calculated application time
0.72 hours for primer, 0.56 hours for paint
Primer/paint interval
Paint second day after priming
WPEM inputs pertaining specifically to the modeled paint and chemical are listed in Table
E-2. The paint density values were chosen such that the product of gallons applied times paint
density yielded the applied-mass values reported by ARCADIS Geraghty and Miller, Inc. — 6.96
kg for primer and 4.93 kg for paint. The first chemical modeled was undecane, one of the primary
constituents by weight in both alkyd primer and paint, with physical/chemical properties as listed
in the table. The input values for weight fraction were based on the results of bulk analysis for
primer and paint (see Appendix A, Section A2). The default emission decay rate calculated by the
empirical emissions model in WPEM was used; the basis for the WPEM algorithm to calculate
this default value is described in Appendix A, Section A4. Based on results of sink tests
conducted by ARCADIS Geraghty and Miller, Inc. (see Appendix A, Section A5), indoor sinks
were assumed to be negligible.
A DIY painter was arbitrarily chosen as the exposed individual. WPEM inputs for
occupancy and exposure affect exposure/dose calculations, but the interest here was in a
comparison of modeled versus measured indoor concentrations (there were no exposure/dose
measurements). The model was run for 4 days with a 5-minute reporting interval.
E-4
-------
Table E-2. WPEM Inputs for Alkyd Paint and Chemical
Input parameter
Input Value
Paint density
5800 grams/gallon for primer, 4565 grams/gallon for paint
Chemical name
Undecane
Molecular weight
156.4 g/mole
Vapor pressure
1.02 torr
Weight fraction
0.00875 for primer, 0.0165 for paint
Chemical mass emitted
60.98 grams for primer, 81.08 grams for paint
Emission decay rate
1,60/hr for primer, 1,70/hr for paint
Sink model
No sinks
Model results (concentrations in the painted bedroom and in the den) are compared with
measurement results in Figure E-2. The actual priming and painting were done around 11 a.m.,
whereas in WPEM priming and painting begin at 9 a.m. Thus, for direct comparison, both model
and measurement time scales were normalized to elapsed time after priming was started. Another
minor difference is that in WPEM the painting starts exactly 48 hours after priming is started,
whereas at the test house the interval was somewhat less (about 47.5 hours). As a result, the
measured values for the painting event rise slightly ahead of the modeled values.
There generally is a high degree of correspondence between modeled and measured
values, particularly in the painted bedroom. For example, the peak modeled concentrations in the
bedroom were about 210 and 300 mg/m3, respectively, corresponding to peak measured values of
about 140 and 210 mg/m3. The modeled peak values for the den exceeded measured values by a
greater amount, on the order of 100 versus 25 mg/m3 for priming and 150 versus 50 mg/m3 for
painting. Based on paired values at corresponding points in time, the average modeled
concentration in the bedroom was 66.5 mg/m3 (versus 63.9 mg/m3 measured) and the average
modeled value in the den was 38.2 mg/m3 (versus 20.7 mg/m3 measured).
E-5
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350
300
E
250
0
0
^***
Model - Bedroom
— Model - Den
O Data - Bedroom
A Data - Den
0.5
1.5
2
Elapsed Time, days
2.5
3
3.5
4
Figure E-2. Modeled and Measured Undecane Concentrations for the EPA Test House.
A second chemical chosen for model evaluation with alkyd primer/paint was p-xylene.
Two reasons for this selection were that (1) its molecular weight (106.2) was about 50 percent
lower than undecane's and its vapor pressure (4.34 torr) was about a factor of four higher, and
(2) unlike undecane, p-xylene was not among the chemicals used in the nonlinear regression to
develop an empirical emissions model for VOCs in alkyd primer/paint. Other than molecular
weight and vapor pressure, the only differences in inputs for p-xylene were its weight fractions —
0.00398 for primer and 0.00547 for paint, both lower than for undecane. The emission decay
rates for p-xylene calculated by the empirical emissions model in WPEM were considerably higher
than for undecane —11.1/hour for primer and 11,9/hour for paint.
As with undecane, the concentrations predicted by WPEM for p-xylene were higher than,
but generally consistent with, measured values. For example, the peak modeled concentrations in
the painted bedroom were 155 and 180 mg/m3 for priming and painting, respectively, versus
measured values of about 80 mg/m3. The peak modeled concentrations in the den were around 65
mg/m3 for both priming and painting, compared to measured peaks of about 20 mg/m3. Based on
paired values at corresponding points in time, the average modeled concentration in the bedroom
was 30.6 mg/m3 (versus 20.6 mg/m3 measured) and the average modeled value in the den was
17.9 mg/m3 (versus 7.6 mg/m3 measured).
E-6
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E3.
MODEL EVALUATION FOR LATEX PRIMER AND PAINT
The report of the experiments by ARCADIS Geraghty and Miller, Inc., indicates that,
for the latex experiment, 5.26 kilograms of primer LP-A were applied to the walls in the front
corner bedroom over a period of 36.4 minutes, beginning at 11:18 a.m. on August 20, 1997.
Approximately two days later, 4.65 kilograms of paint LSG-E were applied over a period of 35.4
minutes, beginning at 10:02 a.m. on August 22, 1997. The reported wet film thickness was 7.72
mil for primer and 5.17 mil for paint. The measured air exchange rate prevailing during the test
averaged 0.47 ACH.
Corresponding WPEM inputs for the painting scenario described above are summarized in
Table E-3. Inputs for house volume, percent painted, interzonal airflow rate and painted surface
area were the same as for the alkyd test.
The wet film thickness values reported by ARCADIS Geraghty and Miller, Inc. — 6.88 mil
for primer and 5.17 mil for paint — correspond to primer/paint coverage rates of 233 and 310
ft2/gallon, respectively. The input painting rates of 2.27 gallons per hour for primer and 1.76
gallons per hour for paint are higher than typical values that have been reported for do-it-yourself
painters (on the order of 0.5 to 1 gallon/hour), but were were chosen to result in priming/painting
durations that matched those reported for the experiment at the EPA test house.
Table E-3. WPEM Inputs for Latex Painting Scenario at EPA Test House
Input Parameter
Input Value
House volume
11,272 ft3
Percent of house painted
9.5 %
Air exchange rate
0.47 ACH
Interzonal airflow rate
11,484 ft3/hour
Painted wall surface area
321 ft2 (using loading ratio of 0.30; actual = 317.5 ft2)
Wet film thickness
6.882 mil for primer, 5.171 mil for paint
Calculated amount of paint
1.38 gallons for primer, 1.04 gallons for paint
Application rate
2.27 gallons/hour for primer, 1.76 gallons/hour for paint
Calculated application time
0.61 hours for primer, 0.59 hours for paint
Primer/paint interval
Paint second day after priming
E-7
-------
WPEM inputs pertaining specifically to the paint and chemical are listed in Table E-4. The
paint density values were chosen such that the product of gallons applied times paint density
yielded the applied-mass values reported by ARCADIS Geraghty and Miller, Inc. — 5.26 kg for
primer and 4.65 kg for paint. The first chemical modeled was TMPD-MIB, one of the primary
constituents by weight in both latex primer and paint, with physical/chemical properties as listed in
the table. The input values for weight fraction were based on the results of bulk analysis for
primer and paint (see Appendix C, Section C2). The default emission decay rate calculated by the
empirical emissions model in WPEM was used; the basis for the WPEM algorithm to calculate
this default value is described in Appendix C (Section C4). Indoor sinks were assumed to be
negligible.
Table E-4. WPEM Inputs for Latex Paint and Chemical
Input parameter
Input Value
Paint density
3812 grams/gallon for primer, 4471 grams/gallon for paint
Chemical name
TMPD-MIB
Molecular weight
216 g/mole
Vapor pressure
0.0019 torr
Weight fraction
0.0122 for primer, 0.007 for paint
Chemical mass emitted*
16.02 grams for primer, 8.10 grams for paint
Emission decay rate
- first exponential
- second exponential
0.44/hr for primer and paint
0.01/hr for primer and paint
Sink model
No sinks
*For the empirical emissions model for latex primer/paint, 25 % of the applied chemical mass
is assumed to be emitted.
A DIY painter was arbitrarily chosen as the exposed individual. WPEM inputs for
occupancy and exposure affect exposure/dose calculations, but the interest here was in a
comparison modeled versus measured indoor concentrations (there were no exposure/dose
measurements). The model was run for 7 days with a 5-minute reporting interval.
E-8
-------
Model results (concentrations in the painted bedroom and in the den) are compared with
measurement results in Figure E-3. The actual priming and painting were done around 10-11
a.m., whereas in WPEM priming and painting begin at 9 a.m. Thus, for direct comparison, both
model and measurement time scales were normalized to elapsed time after priming was started.
Another minor difference is that in WPEM the painting starts exactly 48 hours after priming is
started, whereas at the test house the interval was somewhat less (about 47 hours). As a result,
the measured values for the painting event rise slightly ahead of the modeled values.
10
9
8
7
6
Model - Bedroom
Model - Den
5
O Data - Bedroom
4
A Data - Den
3
2
•AA
o
o
2
3
4
5
6
7
Elapsed Time, days
Figure E-3. Modeled and Measured TMPD-MIB Concentrations for the EPA Test House.
The modeled peak concentration for TMPD-MIB in the bedroom was lower than the
measured peak by about a factor of two (3-4 mg/m3 vs. 6-7 mg/m3), whereas the modeled peak in
the den was somewhat higher than measured (2-3 mg/m3 vs. about 1 mg/m3). Thus, the modeled
values generally bracket the measurements. The higher measured-than-modeled values in the
painted bedroom could be related to the model assumption that 25 percent of the applied
primer/paint mass is emitted (i.e., the percentage could be somewhat higher for TMPD-MIB), and
the lower measured-than-modeled values in the den could be related to sink behavior. Based on
paired values at corresponding points in time, the average modeled concentration in the bedroom
was 1.96 mg/m3 (versus 3.15 mg/m3 measured) and the average modeled value in the den was
1.39 mg/m3 (versus 0.59 mg/m3 measured).
E-9
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The second chemical modeled was propylene glycol. The bulk analysis indicated that this
chemical was not detected in primer and had a weight fraction of 0.0242 in the paint. The value
entered for the primer weight fraction in WPEM was 0.000001, the lowest value allowed. The
modeled peak concentrations in the bedroom and den were about 19 and 7 mg/m3, as compared
with measured values of 8 and 1 mg/m3. The relatively high modeled peaks are driven primarily
by the emission rate decay constant for the first exponential of the empirical (double-exponential)
emissions model.
As noted in Appendix C (see Table C-4), the predicted rate value for the decay constant of
the first exponential for propylene glycol (46.7/hour) was considerably higher than values
estimated from small-chamber emission tests (range from 0.9 to 2.7/hour). With a rate constant
of 1.8/hour, the modeled peak concentrations dropped to about 11 mg/m3 in the bedroom and 5
mg/m3 in the den. With this rate constant, the average modeled concentration in the bedroom was
1.37 mg/m3 (versus 1.41 mg/m3 measured) and the average modeled value in the den was 0.74
mg/m3 (versus 0.20 mg/m3 measured).
E-10
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