EP A/600/A-97/007
MODELING THE VOC EMISSIONS FROM INTERIOR
LATEX PAINT APPLIED TO GYPSUM BOARD
Zhishi Guo, Roy Fortmann, and Steve Marfiak
Acurex Environmental Corp., PO Box 13109, Research Triangle Park, NC 27709, USA
Bruce Tichenor1, Leslie Sparks, John Chang, and Mark Mason
US EPA, National Risk Management Research Laboratory, Indoor Environment
Management Branch, MD-54, Research Triangle Park, NC 27711, USA
ABSTRACT
Small chamber emissions studies have demonstrated that the substrate played an important
role in determining the rate of volatile organic compound (VOC) emissions from interior
latex paint. An empirical source model for a porous substrate was developed that takes both
the wet- and dry-stage emissions into consideration. Tests in the U.S. Environmental
Protection Agency's (EPA) Source Characterization Laboratory showed that common
interior surfaces such as gypsum board and carpet could adsorb significant amounts of latex
paint VOCs from the air, and that they were re-emitted very slowly. An IAQ model
incorporating the source model, an irreversible sink model, and the air movement data
obtained from tracer gas tests made satisfactory predictions for the VOC levels in a test
house.
INTRODUCTION
Over 1 billion gallons (-3.8 x 109 liters) of paint is sold in the United States each year. Of
this paint, more than 50% is interior paint which, in recent years, has followed the trend
towards water-based paint. Since the use of this paint can cause elevated concentrations of
volatile organic compounds (VOCs) in indoor environments, exposure of building occupants
to paint VOCs is of concern. It is generally believed that solvent evaporation from indoor
coatings involves two physical processes: evaporation and internal diffusion, and that
evaporation is the predominant mechanism early in the drying process (1, 2). A number of
source models have been developed to represent the emission rate based on either or both
mechanisms. Some examples are given in Table 1 with the symbols explained below: R=
emission factor; Mq = initial total VOC (TVOC) mass in the source; Ro, R„ and R2=
initial emission factors; k, k,, and k2 = decay rate constants; t = time; = gas-phase
mass transfer coefficient; Cv = initial total vapor pressure; M = TVOC mass remaining in
the source; C = TVOC concentration in indoor air; X = film thickness or thickness of
diffusion layer; MD = VOC mass remaining in the source available for diffusion; Mm =
initial VOC mass in the source available for diffusion; and D = solid- or liquid-phase
diffusion constant.
In the recent evaluation of VOC emissions from latex paint (3), we observed that the
substrate played a significant role in determining the emission rates, and that some common
interior surfaces such as carpet and gypsum board could strongly adsorb latex paint VOCs
1 Current address: Rt 1, Box 302C, Macon, NC 27551, USA

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from the air. This paper presents source and sink models for use in predicting the indoor
concentrations when latex paint is applied to gypsum board.
Table 1. Selected Models for VOC Emissions from Indoor Coatings and Other Materials
Name
Expression
Type
Mainly Used For
Ref.
First-Order Model
R = Moke*
Empirical
Evaporation
(4)
Second-Order Model
R = R0/[l+(k/A)tR0]
Empirical
Both mechanisms
(5)
Double Expon. Model
R = R,eklt + R2ek2t
Empirical
Both mechanisms
(6)
VBa Model
R = k^ (Cv M/M0 - C)
Mass Transfer
Evaporation
(2)
Diffusion Model (Dl)
R = 0.632/A Md (D/t)*
Mass Transfer
Source Diffusion
(7)
Diffusion Model (D2)
R = ir'AIX Mm (D/tf
Mass Transfer
Source Diffusion
(8)
a VB: vapor pressure and boundary layer controlled emissions.
EXPERIMENTAL OBSERVATIONS
The test latex paint was purchased from a local store. According to the manufacturer's
Environmental Data Sheet, the paint contained 3.7% of VOCs by weight. Our formulation
analysis yielded a 4.5 % VOC content, in which ethylene glycol was the dominant
component (53%) followed by Texanol (30%), 2-(2-butoxyethoxy)ethanol (11%),
propylene glycol (5%), and diethylene glycol (1 %). In preparing the test specimens, the
manufacturer's recommended method of application and film thickness were used.
A strong influence by substrate was observed in emissions testing conducted in 53-liter
stainless steel environmental chambers: the peak concentration was much lower when the
paint was applied to gypsum board than to stainless steel plates (Figure 1). Long-term tests
[at 23°C, 50% relative humidity (RH), 0.5 air change per hour (ACH), and a 0.5 loading
factor] showed that the emission factor for ethylene glycol from painted gypsum board was
still 40 ng/m2/h at an elapsed time of 1 year. For individual VOCs, the gypsum board
seemed to have a stronger effect on ethylene glycol and propylene glycol (Table 2).
The loss of latex paint VOCs to common interior surface materials (i.e., the sink effect)
was studied in the same type of small chambers by first injecting the test compounds into
the chamber at a constant rate for 7 days and then purging the chamber with clean air.
Very strong adsorption was observed for every latex paint VOC tested (see Figure 2 as an
example). Results from mass balance calculations showed that, after purging with clean air
for 2 weeks, only 11 % of ethylene glycol adsorbed by the gypsum board was re-emitted.
The deposition velocity (i.e., first-order adsorption rate constant) was estimated from:
Adsorption Rate = Wa / (At S) = ka C	...(1)
where W4 = total mass adsorbed by the sink material; At = duration of dosing period; S =
area of the sink material; ka = deposition velocity; and C = average chamber concentration
(i.e., average outlet concentration). For the loss of ethylene glycol onto gypsum board and
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carpet, the estimated deposition velocities were 1.5 and 2.4 m/h, respectively.
Table 2. Amounts of VOCs Emitted from Different Substrates in a 2-Week Testing Period
Compound
On Stainless Steel Plate
On Gypsum Board
Applied
(mg/m2)
Emitted
(mg/m2)
Fraction
Emitted
Applied
(mg/m2)
Emitted
(mg/m2)
Fraction
Emitted
Ethylene Glycol
3906
4023
103%
3855
582
15%
Propylene Glycol
378
337
89%
372
59
16%
Butoxyethoxyethanol
813
758
93%
801
194
24%
Texanol
2191
1961
90%
2160
1305
60%
MODEL DEVELOPMENT
The goal was to develop a source model that could predict the VOC emissions for both
short- and long-term emissions from latex paint applied to porous materials such as gypsum
board. The proposed model is a combination of the first-order decay model and a diffusion
model (model D1 in Table 1) with an additional adjusting factor (or weighing factor);
R = Mv k exp(-kt) +a 0.632IX MD (D/t)*	...(2)
where Mv = VOC mass available for evaporation; MD = VOC mass available for
diffusion; and a = adjusting factor. The adjusting factor we chose was a = (1- e"kt)2. As
illustrated in Figure 3, adding a to the model is necessary because the original diffusion
model gives unrealistically high emission rates early on but, in reality, the diffusion-
controlled emissions can not become dominant until the paint film is dried. Since both X
and D in the diffusion model are unknown, we combined them to give a single parameter,
fD = 0.632 D* / X (diffusion constant), which bears the unit of h'A. Equation 2 can then be
simplified to:
R = Mv k exp(-kt) +a fD MD / t*	...(3)
where MD is a variable and is governed by:
dMD/dt = -a fD Md /t*	...(4)
The chamber concentration, C, can then be computed from:
dC/dt = L R - N C	...(5)
where L=the loading factor and N=air exchange rate. Equations 3 to 5 can be used in
indoor air quality (IAQ) simulations but they must be solved simultaneously. Further
simplification can be made to eliminate Equation 4. Since a only has an effect in a short
period of time and will quickly approach 1 afterwards, we can set o = 1 to obtain an
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approximate solution to Equation 4 given that MD = MD0 when t = 0:
MD = MD0exp(-2fDt%)	,.,(6)
Substituting Equation 6 into 3, we obtain the following expression for emission factor:
R = Mv k exp(-kt) +afD Mm exp(-2 fD t*) / t44	.,.(7)
This source model can be inserted directly into Equation 5 to compute concentrations.
Numerical examinations showed that the error caused by this approximation of Equation 6
was insignificant.
MODEL EVALUATION AND PRELIMINARY VALIDATION
There are four parameters in this model: Mv, k, and fD. Since the sum of Mv and
Moo is the amount of VOC applied to the substrate, only one of them needs to be
determined if the formulation of the product is known. Table 3 presents the estimated
parameters for one chamber test. The model fits the data very well in the whole data range
(Figure 4).
Table 3. Estimated Model Parameters for a Chamber Test
Compound
Mv (mg/m2)
k (h"1)
Md (mg/m2)
fix, (h-*)
Ethylene Glycol
19.1
1.05
3304
0.00235
Propylene Glycol
21.8
0.0814
299
0.00374
Butoxyethoxyethanol
47.5
0.165
643
0.00203
Texanol
404
0.0635
1465
0.00173
Preliminary validation of the source model was made by painting the gypsum board walls of
one bedroom in a test house with the latex paint tested in the small chambers and
monitoring the VOC concentrations in three rooms for 1 month. The air exchange rate was
determined by the tracer gas decay method (four tracer releases a day). The air flows
through the air handling system were measured in the return grille and each register. The
IAQ mass balance model used was:
Vs dC/dt = Sj R(t) + XQjj q - EQy Q - A; k. C;	...(8)
where V; = volume of zone i; Q = concentration in zone i; Cj = concentration in zone j;
Sj = area of newly painted wall; R = emission factor calculated from Equation 7 (for
source room only); Qj; = air flow from zone j to zone i; Qy = air flow from zone i to zone
j; Aj = area of the sink in zone i; and k, = deposition velocity for wall loss (assumed to be
same for all zones).
Using the model parameters obtained from small chamber testing and an average deposition
velocity of 2.0 m/h for ethylene glycol, this IAQ model made reasonable predictions for the
VOC concentrations in different zones (Figure 5).
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DISCUSSION
One of the desirable features of the proposed model is that it uses actual VOC mass applied
to the surface, which can be calculated from formulation analysis and the amount of paint
applied. None of the existing empirical models gives realistic amounts of VOC available
for emissions. For instance, the amount of ethylene glycol applied in a chamber test was
2332 mg/m2, but the double exponential model gave an emittable mass of 429 mg/m2; on
the other hand, the second-order model would allow an infinite amount of VOC to be
emitted. The other desirable feature of this model is that the parameters obtained from
short-term testing can be used to predict the long-term emissions (Figure 6). The drawback
of this model is that the first-order decay model used for the evaporation-controlled
emissions is empirical. We are currently trying to replace it with a mass transfer model.
ACKNOWLEDGEMENT
The research described in this paper was funded by the U.S. EPA under Contract No. 68-
D4-0005. The authors also wish to acknowledge the work of Mark Bero, Huei-chen Lao,
Kenneth Krebs, and Nancy Roache of Acurex Environmental Corp. on this project.
REFERENCES
1.	Sullivan, D.A. 1975. "Water and solvent evaporation from latex and latex paint films."
Journal of Paint Technology. Vol. 47, pp. 60-67.
2.	Tichenor, B.A.; Guo, Z.; and Sparks, L.E. 1993. "Fundamental mass transfer model for
indoor air emissions from surface coatings." Indoor Air. Vol. 3, pp. 263-268.
3.	Krebs, K.; Lao, H.C.; Fortmann, R.; and Tichenor, B. 1995. "Test methods for
determining short and long term VOC emissions from latex paint." Engineering solutions to
indoor air quality problems. Air & Waste Management Association, Pittsburgh, pp. 71-75.
4.	Clausen, P. A. 1993. "Emission of volatile and semivolatile organic compounds from
waterborne paints - the effect of the film thickness," Indoor Air '93. Vol. 2, pp. 567-572.
5.	Clausen, P. A.; Laursen, B.; Wolkoff, P.; Rasmusen, E.; and Nielsen, P. A. 1993.
"Emission of volatile organic compounds from a vinyl floor covering," Modeling of Indoor
Air Quality and Exposure, ASTM STP 1205. pp. 3-13.
6.	Colombo, A.; De Bortoli, M.; Knoppel, H.; Schauenburg, H.; and Vissers, H. 1990.
"Determination of volatile organic compounds from household products in small test
chambers and comparison with headspace analysis." Indoor Air '90. Vol. 3, pp. 599-604.
7.	Hanna, S. R. and Drivas, P. J. 1993. "Modeling VOC emissions and air concentrations
from the Exxon Valdes oil spill." J. Air and Waste Manage. Assoc., Vol. 43, pp. 298-309.
8.	Christianson, J.; Yu, J. W.; and Neretnieks, I. 1993. "Emission of VOC's from PVC-
flooring - models for predicting the time dependent emission rates and resulting
concentrations in the indoor air." Indoor Air '93. Vol. 2, pp. 389-394.
5

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*t -
Gypsum Board « Stainless Steel
o 40
O
20	40	60
Elapsed Hours
Figure 1. TVOC emissions from latex
paint applied to different substrates
10
8
E
1> 6
d" 4
s.
Dosing
Purging
•> „ ^ °° o

be o y

	t o— ft
1
/
3
t
L~o
100	200
Elapsed Hours
300
° Inlet (Data) — Inlet (Average) -a- Outlet
Figure 2. Adsorption of ethylene glycol
by gypsum board in a 53-L chamber
50
O<0
t>
£ 30
c
o
co 20
f£>
E
UJ 10

— Not Adjusted — Adjusted
\

2	3	4
Elapsed Hours
° Chamber Data — Model
100	200	300
Elapsed Hours
400
Figure 3. The role of the adjusting factor on
diffusion-controlled emission rate
Figure 4. Modeling ethylene glycol
emissions from painted gypsum board
Source Room ° Other Rooms
o 0.01
0.001
0 100 200 300 400 500 600 700
Elapsed Hours
a Chamber Data — Model
O 0.1
0.01
0 1000 2000 3000 4000 5000
Elapsed Hours
Figure 5. IAQ Simulation for the latex paint
experiment in the test house (Solid lines are
model predictions)
Figure 6. Prediction of long-term ethylene
glycol emissions with model parameters
obtained from short-term test
6

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XTTSTV/TT5T T>T-n T, me TECHNICAL REPORT DATA
i\ KMJtXij- rt I J Jr~ iuu (Please read Instructions on the reverse before completing
1. REPORT NO 2.
EPA/600/A-97/007
3. RE
4. TITLE AND SUBTITLE
Modeling the VOC Emissions from Interior Latex
Paint Applied to Gypsum Board
S. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7 AUTHOR(S)
£.Guo, R. Fortmann, and S. Marfiak (Acurex); and
B. Tichenor, L. Sparks, J. Chang, and M. Mason(EPA)
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Acurex Environmental Corporation
P. 0. Box 13109
Research Triangle Park, North Carolina 27709
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-D4-0005, Task 11
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Air Pollution Prevention and Control Division
Research Triangle Park, NC 27711
13. TYPE OF REPORT ANO PERIOD COVERED
Published paper; 1-4/90
14. SPONSORING AGENCY CODE
EPA/600/13
18.supplementary NOTES APPCD project officer is Leslie E. Sparks, Mail Drop 54, 919/
541-2458. For presentation at 7th Int. Conf. IAQ and Climate. Nagoya, Japan,
7/21-26/1996.
is.abstractpaper discusses modeling volatile organic compound (VOC) emissions
from indoor latex paint applied to gypsum board. Small chamber emissions studies
have demonstrated that the substrate played an important role in determining the
rate of VOC emissions from interior latex paint. An empirical source model for a
porous substrate was developed that takes both the wet- and dry-stage emissions into
consideration. Tests in the U.S. EPA's Source Characterization Laboratory showed
that common interior surfaces such as gypsum board and carpet could adsorb signi-
ficant amounts of latex paint VOCs from the air, and that they were re-emitted very
slowly. An indoor air quality model incorporating the source model, an irreversible
sink model, and the air movement data obtained from tracer gas tests made satis-
factory predictions for the VOC levels in a test house.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. cosati Field/Group
Pollution Volatility
Mathematical Models Substrates
Latex Gypsum
Paints
Emission
Building Boards
Organic Compounds
Pollution Control
Stationary Sources
Latex Paint
Gypsum Board
Volatile Organic Com*-
pounds (VOCs)
Indoor Air Quality
13 B 20 M
12 A 11D
UJ 08G
11C, 13 C
14G
11L
07C
18. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (ThisReport)
Unclassified
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20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)

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