EPA/600/A-92/223
Paper for ASTM meeting on modeling IAQ April 1992.
Modeling Individual Exposure from Indoor Sources
by
Leslie E, Sparks, B. A. Tichenor, and J. B. White
Air and Energy Engineering Research Laboratory
United States Environmental Protection Agency
Research Triangle Park, NC 27711
Author's phone; (919) 541-2458 Fax (919) 541-2157
Abstract
Individual exposure to air pollutants is determined by the behavior of indoor sources and sinks
and activity patterns. This paper discusses a model that allows analysis of individual exposure for
a wide range of sources and sinks. Emphasis of the discussion is on exposures to VOCs from
commonly used sources. The effects of source and sink behavior on exposure are complex.
Important factors include source strength, source decay rate, rates to the sink, re-emissions from
the sink, and building operation parameters such as ventilation rate. Sources provide the primary
exposure and dominate exposure while the source strength is strong. Sinks modify exposure by
reducing peak concentrations and, because of re-emissions from sinks, by increasing the time of
relatively high concentrations. Exposures from several different sources are analyzed both with
and without sinks and under a range of different building operation scenarios. The need for
standard scenarios in evaluating the effects of sources on individual exposure is discussed. Model
concentration predictions are compared with data from an IAQ test house.
Key Words
Indoor Air Quality model, exposure, sources, sinks, activity patterns

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Introduction
Indoor air quality (IAQ) is determined by the interactions of sources, sinks, and air movement
between rooms and between the building and the outdoors. Sources may be located in rooms, in
the heating, ventilation, and air-conditioning (HVAC) system, or outdoors. There may be sinks
(i.e., materials that adsorb indoor pollutants) in the same locations. Sinks may also act as sources
by re-emitting the pollutants collected in them. Individual exposure to pollutants from indoor
sources is determined by the combination of indoor pollutant concentrations and individual
activity patterns.
A personal computer model, EXPOSURE, to predict in-room pollutant concentrations and
individual exposure to the pollutants is being developed as part of EPA's IAQ program. The
model is intended as a tool to allow analysis of IAQ situations. The analyses provided by the
model can assist in providing guidance on ways to reduce exposure to indoor air pollutants.
General mathematical framework of the model
EXPOSURE is a multi-room model based on an earlier model called INDOOR[l], EXPOSURE
allows calculation of pollutant concentrations based on source emission rates, room-to-room air
movement, air exchange with the outdoors, and indoor sink behavior.
Each room is considered to be well mixed. The validity of the well mixed assumption was verified
in several experiments in the EPA IAQ test house [1] and by data reported by Maldonado [2].
2

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A mass balance for each room gives:
V,^- = CmQ^ - CiOUTQiOUT +S, -R,
(I)
where Vj is the volume of the room, Q is the pollutant concentration in the room, Cjjjsj is the
concentration entering the room, Qjj^j is the air flow into the room, Cjqut ls the concentration
leaving the room, QjoUT's ^ie a'r flow leaving the room, Sj is the source term, Rj is the removal
term, and the subscript i refers to room i for a room in a set of multiple rooms, i = 1,2,., N where
N is the number of rooms. The removal term, Rj, includes pollutant removal by air cleaners and
sinks.
The well mixed assumption requires that Cjguj equals Cj. Equation (1) can be rewritten as;
Equation (2) is one of a set of similar equations that must be solved simultaneously in a multiple
room model.
EXPOSURE uses a fast discrete time step algorithm developed by Yamamato et al. [3] to solve
the series of equations. The algorithm is based on the assumption that, for sufficiently small time
steps, dt, the source and sink terms and all neighboring concentrations are constant. Under this
assumption, there is an exact solution to the set of equations. The algorithm uses this exact
solution to calculate the concentration under varying conditions at the end of each time step. The
method is stable for all time steps and is accurate for sufficiently small time steps. (The size of the
time step depends on how rapidly concentrations are changing. In general a time step of 1 minute
Vi —J- = CwQw ~ C,Q,ovt + S, - Ri
(2)
3

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is small enough when concentrations are changing rapidly, and time steps of several minutes are
adequate when concentrations are near steady state.)
Source terms
The ability of any model to predict indoor air pollutant concentrations depends on the accuracy of
the source models incorporated into the model. EXPOSURE uses source models developed as a
part of EPA's source characterization research program and source models provided in the
literature. The model incorporates a wide range of emission characteristics to allow simulation of
the range of sources encountered in indoor spaces. Several sources are allowed in each room.
The model includes a data base of source emission rates for these various sources based on
research conducted by the Indoor Air Branch, Air and Energy Engineering Research Laboratory,
of EPA. The user can add to the data base and can override the data base emission rates.
Generally sources can be divided into three categories:
Long term steady state sources such as moth cakes,
On/off sources such as heaters, and
Decaying sources such as painted surfaces.
Some sources also have short term emissions associated with using the source. For example, a
painted surface has a long term decaying emission and a short term emission associated with the
act of painting. This short term emission is defined as the application emission.
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The most common source model used in EXPOSURE is given by:
R = R0e_lt +RA for t &A
and	(3)
R — for i >r4
where R is the emission rate (mass/unit source/time), Rq is the initial emission rate, k is a decay
constant(l/time), t is the elapsed time, R^ is the application emission rate (mass per unit source
size), and t^ is the application time. This type of source term allows simulation of a wide range
of source types. For a steady state source, k is zero. For sources without an application phase,
R^ and t^ are zero.
Ro and k can be determined from chamber studies[4,5]. In many cases all of the emissions are
accounted for by Rq and k as determined by chamber studies. However, there are sources, such
as wood stain, paint, and floor wax, where significant emissions may not be accounted for by the
chamber studies. These emissions occur while the source is being used (for example while a floor
is being waxed) and during the time it takes to place the source in the chamber. The emissions
during the time the source is being used are termed application emissions. The values of R^ can
be estimated or at least bounded from large chamber studies, test house studies, mass balance
analysis of small chamber studies, or other experiments.
A series of experiments to estimate the emissions during application have been completed. The
data for these experiments have not been folly analyzed. Preliminary data analysis Indicates that
the application emissions for wood stain and varnish are less than 5% of the total emissions.
5

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Estimates of source terms for several sources are given in Table I. These data are based on
experiments conducted in EPA's small chambers and in EPA's IAQ test house.
Table I. Emission rates for selected indoor pollutant sources.
Source
Ro mg/m2-h
k 1/h
Ra mg/m^-h
Wood stain
17,000
0.4
1,000
Polyurethane
20,000
0.25
1,000
Wood floor wax
20,000
6.0
10,000
Moth crystals
14,000
0
0
Dry cleaned clothing
1.6
0.03
0
Liquid nails
10,000
1
0
Sink terms
Research in the EPA test house [1,6,7] and in the small chamber laboratory [7] has shown that
sinks (i.e., surfaces that remove pollutants from indoor air) play a major role in determining
indoor pollutant concentrations. These sinks may be reversible or irreversible, A reversible sink
re-emits the material collected in it, and an irreversible sink does not. Sink behavior depends on
the pollutant, on the nature of the sink, and on environmental factors such as temperature, air
velocity, and humidity. A sink may appear to be irreversible when the pollutant concentration is
high and then become reversible when the pollutant concentration is low. Considerable research
is necessary to define the behavior of sinks. Sink models have been published by Tichenor et al.
[7] and Axley [8],
6

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The sink model used in EXPOSURE is based on research of Tichenor et al.[7j:
R. =k.CA*	(4)
where Rs is the rate to the sink (mass per unit time), ka is the sink rate constant (length per time),
C is the in-room pollutant concentration (mass per length cubed),	is the area of the sink
(length squared), kj is the re-emission or desorption rate constant (1/time if n =1), Ms is the mass
collected in the sink per unit area (mass per length squared), and n is some exponent (generally n
= 1).
Experimental data in the EPA test house and small chambers show that, for typical gaseous
organic pollutants of interest in indoor air, ka ranges from about 0.1 to 0,5 m/h, the sink re-
emission rate, kj, is about 0.001/h, and n is 1. Experiments are under way to provide better
estimates of ka and kj for a wide range of pollutants and sink materials.
The impact of sinks on individual exposure depends on the activity patterns, Sinks slightly reduce
the peak exposure of individuals spending 24 h/day in a building and have no impact on their
cumulative exposure. Sinks can have major impacts on the exposure of individuals with other
activity patterns. These impacts are discussed in detail in the example calculations later in the
paper.
Exposure
The types of exposure of interest are the instantaneous exposure and the cumulative exposure.
The instantaneous exposure is the exposure at any time, t, and the cumulative exposure is the total
or integrated exposure over the time of interest. The nature of the pollutant and the effects of the
pollutant determine which type of exposure is more important.
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Because the most common route for exposure to indoor air pollutants is via inhalation, it is
convenient to define inhalation exposure, Ej, as:
E, = C(t)bv	(5)
where C is the pollutant concentration, b is the breathing rate, and v is the volume per breath. The
exposure defined by equation (5) is instantaneous; i.e., the exposure at any instant in time, t, The
peak exposure is the maximum of the instantaneous exposure versus time curve. The cumulative
inhalation exposure, Ejc> is given by:
Ek =J"c(()6vA	(6)
The advantage of defining inhalation exposure is that the exposures calculated by the computer
can be used without requiring the user to manually calculate the amount breathed. Note that no
assumptions are made about the amount of material actually retained by the lungs.
For exposure by mechanisms other than inhalation, the instantaneous exposure, E, to a pollutant
at time t is the concentration, C(t), the person is exposed at time, t:
E = C(t)	(7)
The cumulative exposure from tl to t2 is given by:
Ec =f<'l2cWrf'	(8>
Calculation of exposure requires the pollutant concentration, the time exposed to the
concentration, and (for inhalation exposure) the breathing rate and the volume per breath. The
time exposed to the concentration depends on the individual activity pattern.
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An activity pattern, in the context of the model, is defined by providing the time a person enters
and leaves the various rooms of the building, or leaves the building for the outdoors. The model
allows up to 10 room changes per day. The model is based on a 24-hour day. The activity
patterns (and most source usage patterns) in the model repeat from day to day.
The model provides instantaneous exposure time plots and cumulative exposure time plots for
individual activity patterns. The instantaneous exposure allows identification of high exposure
situations and of the peak exposure.
While the model was designed to allow assessment of impact of indoor air pollution sources and
sinks and IAQ control options on individual exposure from specific activities, it can also be used
to help estimate population exposures if data on population activity patterns are available. The
model can be run for each activity pattern and then the results can be weighted according to the
population statistics.
Model verification
The model predictions of concentration versus time have been compared to experimental data
from the EPA IAQ test house. In all cases the agreement between predictions and experiment has
been good. Predicted versus measured concentrations for many of these experiments are plotted
in Figure 1. Details of the comparisons between model predictions and indoor pollutant
concentration are given by Sparks et al. [9,10],
Exposure predictions
The examples in this section demonstrate some of the model's capabilities. The first example is
calculation of the exposure to an aerosol spray product. The activity patterns are for a person
9

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who uses the product in a bathroom for 10 minutes, moves to the living room, and then leaves the
building after 1 hour; and for a person who does not enter the bathroom where the source was
used, but stays in the building for 24 hours. The instantaneous and cumulative inhalation
exposures for the two individuals are given in Figures 2 and 3, respectively. Note that, while the
initial instantaneous exposure for the person using the product is much higher than for the other
person, the cumulative exposure for the person using the product is less. However, the exposure
for the person using the product is probably underestimated in this example. The local
concentration near the person is somewhat higher for several minutes than the average room
concentration. EXPOSURE can deal with this situation if a pseudo room with a volume of about
5 m3 and an air flow rate between of 30 m^/h with the rest of the room is defined. (This
recommendation is based on preliminary experiments and modeling.) For the case shown in
Figure 2, the difference in exposures is not great because the volume of the bathroom is relatively
small (20 m^).
The second example shows the exposure due to wood stain, a "typical wet source." Because of
adsorption and re-emission from sinks, the exposure lasts for a considerable time. The cumulative
exposures for a person spending 24 hours in the building and for a person spending 16 hours in
the building (starting 8 hours after the stain is applied) are shown in Figure 4 both with and
without a sink. Note the major effect of the sink on the exposure of the person spending part time
in the building. The source term is given by Table I.
The two examples model experiments conducted in the EPA test house. All model input is based
on the conditions in the test house at the time of the experiments. The model predictions of
concentration versus time for both cases are in excellent agreement with the test house data.
10

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Importance of scenario
The importance of the scenario used to evaluate the impact of a given source on exposure can be
demonstrated by looking at the impact of three sources on exposure. The source characteristics
of the three sources are given in Table II . The emission rate as a function of time for the three
sources are shown in Figure 5. Two activity patterns are analyzed—a person who spends 24
hours/day in the building and a person who spends 9 hours/day (from 8:00 am to 5:00 pm) in the
building.
Table II. Emission rate factors for three sources.
Source
Rf) mg/m^-h
k 1/h
Total emission mg/m^-h
A
25
0.05
500
B
100
0.J
1,000
C
8,000
4.0
2,000
The first scenario is for a ventilation rate of 1 air change per hour (ACH) and no sinks. The
concentration time profiles for the three sources are given in Figure 6, and the cumulative
exposures as a function of time are given in Figure 7. Note that source C has no impact on the
building after about 48 hours.
The second scenario is for a ventilation rate of 1 ACH and typical sinks. The concentration time
profiles for the three sources are given in Figure 8, and the cumulative exposures as a function of
time are given in Figure 9. Note that the sinks have greatly extended the time that the sources
impact on the IAQ in the building.
II

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A final scenario is for a 4 hour period of ventilation at 6 ACH followed by ventilation at 1 ACH
and typical sinks. The results are shown in Figures 10 and 11. Note that under this scenario,
source C has minimal impact on the exposure of the individual spending 9 hours in the building.
Conclusions
The impact of indoor pollutant sources on individual exposure is determined by the interactions of
sources, sinks, building operation, and individual activity patterns. Failure to consider all of these
factors can lead to wrong conclusions. A series of standard scenarios should be developed to
allow comparison of the impact of various sources on IAQ.
12

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REFERENCES
1.	L. E. Sparks, Indoor Air Quality Model Version 1.0. EPA-600/8-88-097a (NTIS PB89-
133607), U. S, Environmental Protection Agency, Research Triangle Park, NC (1988).
2.	E. A. Maldonado, A Method to Characterize Air Exchange in Residences for Evaluation of
Indoor Air Quality. Ph. D. Dissertation in Mechanical Engineering, Iowa State University, Ames,
IA (1982).
3.	T. Yamamato, D. S. Ensor, P. A. Lawless, et al., "Fast Direct Solution Method for Multizone
Indoor Air Model," Building Systems: Room Air and Air Contaminant Distribution Ed. L. L.
Christiansen, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.,
Atlanta, GA, pp 147-148 (1989).
4.	ASTM, Standard Guide for Small-Scale Environmental Chamber Determination of Organic
Emissions from Indoor Materials/Products. ASTM D5116-90, In Press (1991).
5.	B. A. Tichenor, Indoor Air Sources. Using Small Environmental Test Chambers to
Characterize Organic Emissions from Indoor Materials and Products. EPA-600/8-89-074 (NTIS
PB90-110131), U. S. Environmental Protection Agency, Research Triangle Park, NC (1989).
6.	B. A. Tichenor, L. E. Sparks, J. B. White, and M. D. Jackson, "Evaluating Sources of Indoor
Air Pollution," J. Air & Waste Management Assoc. 40 (4): pp 487-492 (1990).
7.	B. A. Tichenor, Z. Guo, J. E. Dunn, et al., "The Interaction of Vapour Phase Organic
Compounds with Indoor Sinks," Indoor Air 1: pp 23-35 (1991).
13

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8.	J. W. Axley, "Adsorption Modeling for Building Contaminant Dispersal Analysis," Indoor Air
1: ppl47-171 (1991).
9.	L. E. Sparks, B. A, Tichenor, J. B, White, and M. D. Jackson, "Comparison of data from an
IAQ test house with predictions of an IAQ computer model," Indoor Air. In Press (1991).
10.	L. E. Sparks, EXPOSURE Version 2 A Computer Model for Analyzing the Effects of Indoor
Air Pollutant Sources on Individual Exposure, EPA-600/8-91-013 (NTIS PB91-201095), U. S.
Environmental Protection Agency, Research Triangle Park, NC (1991).
14

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Predicted = 1.6 + 0.99 x measured r = 0.96
100	150	200
Measured value
300
Figure 1. Predicted versus measured concentrations for test house
experiments.
15

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10
Person uses products, leaves after 1 hr and returns at 14 hours
OS
SB
O
Ck
V
e
©
JS,
c
§
I
0.1 |
0.01 -r
0.001
Exposure to VOC from aerosol product.
Product release 280 mg VOC i it 2 sec
Air exchange with outdoors 0,25 ACH
All factors based on IAQ test house data
Includes effects of sinks
Person does not use product stays in building 24 hours
0	5	10	15	20
Time (hrs)
Figure 2. Instantaneous inhalation exposure to VOC from use of aerosol spray product.
25

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3
Person not using product in house 24 hrs
/
Person uses product, leaves alter 1 hr, returns at 14 hrs
Aerosol spray releases 280 mg of spot remover in 2 sec
Air exchange with outdoors 0.25 ACH
Includes sink effects
10
15
20
25
Time (hrs)
Figure 3. Cumulative inhalation exposure to VOC from use of aerosol spray product.

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4000
24 hrs in building with no sink
3500
a
a
w
3000
24 hrs in building with sink
6 sq m of floor stained with 311 g
RO = 17,000 mg/sq m, k = 0.4/h
Application emission 3,200 mg/sq m
Volume 300 cu m
Air exchange 0.3 ACH
2500
a
©
2000
«
¦a
xs
16 hrs in building with sink
a
.g 1500
£
"3
| 1000
16 hrs in building with no sink
500
0	50	100	150	200	250	300 350	400 450	500
Time (hrs)
Figure 4. Cumulative exposure to VOC from wood stain.

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10000
1000
100
E
cr
tn
"S
E
10
6
0.01
0,001
0	20	40	60	80	100	120	140	160	180	200
Time (hrs)
Figure 5. Emission rates for three products.

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1000
100
10
0.1
0,01
20
40
60	80
Time (hrs)
100
120
140
Figure 6. In-building concentrations of three products with no sinks.

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250
— 200
24 hr C
24 hr B
24 hr A
9 hr B
9 hr A
9 hr C
10 20 30 40 50 60
Time (hrs)
70
80
90
100
Figure 7. Cumulative exposure to three products with no sinks.

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100

to
to
10
a
1
E
W
e
©
s
a
©
U
f
0.1
0.01

* *.,
20
40
60
80
100 120
Time (hrs)
Figure 8. In-building concentrations of three products with sinks.
140
160
180
200

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250
to
co
WD
9
n
e
a.
N
«

*mrn
3
E
s
U
200
150
100
50
0
24 hr C
24 hr B
24 hr A
9 hr B
9 hr C
9 hr A
50
100
150
200
250
Time (hrs)
Figure 9. Cumulative exposure to three products with sinks.

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100
10
3
u
"ell
E
v—'
a
o
a
u
u
a
o
U
0.1
0,01
20
40
60
80
Time (hrs)
100
120
140
160
Figure 10. In-building concentrations of three products with 4 hours of high ventilation followed
by normal ventilation, with sinks.

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120
100
80
w 60
40
20
0
24 hr B
24 hr A
9 hr B
9 hr A
24 hr C
20 40 60 80 100 120 140 160 180 200
Time (hrs)
Figure 11. Cumulative exposure to three products with 4 hours of high ventilation
followed by normal ventilation, with sinks.

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A UPD T _ T3_ n o 7 TECHNICAL REPORT DATA
-rt-tl.il. I V i. r 3 0 l (Phase mad Instructions on the reverse before cample
1. REPORT NO. 2.
EPA/600/A-92/223
3.
4, TITLE AND SUBTITLE
Modeling Individual Exposure from Indoor Sources
5. REPORT OATE
6. PERFORMING ORGANIZATION CODE
7. AUTHORiSl
L. E. Sparks, B. A. Tichenor, and J. B. White
8. PERFORMING ORGANIZATION REPORT NO.
9, PERFORMING ORGANIZATION NAME AND ADDRESS
See Block 12
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
NA (Inhouse)
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Air and Energy Engineering Research Laboratory
Research Triangle Park, North Carolina 27711
13, type of report and period covered
Published paper;7/91-1/92
14. SPONSORING AGENCY CODE
EPA/600/13
is.supplementary notes ^EERL project officer is Leslie E. Sparks, Mail Drop 54, 919/
541-2458. Presented at ASTM meeting on modeling IAQ, Pittsburgh, PA, 4/27-28/92
16. abstract paper discusses a model that allows analysis of individual exposure for
a wide range of sources and sinks. (NOTE*. Individual exposure to air pollutants is
determined by the behavior of indoor sources and sinks and activity patterns.) The
discussion emphasizes exposures to volatile organic compounds (VCCs) from com-
monly used sources. The effects of source and sink behavior on exposure are com-
plex, Important factors include source strength, source decay rate, rates to the
sink, re-emissions from the sink, and such building operation parameters as venti-
lation rate. Sources provide the primary exposure and dominate exposure while the
source strength is strong. Sinks modify exposure by reducing peak concentrations
and, because of re-emissions from sinks, by increasing the time of relatively high
concentrations. Exposures from several sources are analyzed both with and without
sinks and under a range of building operation scenarios. The need for standard sce-
narios in evaluating the effects of sources on individual exposure is discussed.
Model concentration predictions are compared with data from an indoor air quality
test house.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.identifiers/open ended terms
c. cosati Field/Group
Pollution
Mathematical Models
Exposure
Sources
Volatility
Organic Compounds
Residential Buildines
Pollution Control
Stationary Sources
Indoor Air Quality
Sinks
Activity Patterns
Volatile Organic Com-
pounds
13 B
12	A
06S
14G
20 M
07C
13	M
18. DISTRIBUTION STATEMENT
Release to Public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
26
20 SECURITY CLASS (This page)
Unclassified
22, PRICE
EPA Form 2220-1 (9-73)

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