United States
Environmental Protection
Agency
Air and Energy Engineering
Research Laboratory
Research Triangle Park NC 27711
Research and Development
EPA/600/S8-91/013 July 1991
v>EPA Project Summary
EXPOSURE Version 2,
A Computer Model for
Analyzing the Effects of Indoor
Air Pollutant Sources on
Individual Exposure
Leslie E. Sparks
A model for calculating individual ex-
posure to indoor air pollutants from
sources is presented. The model is de-
signed to calculate exposure due to indi-
vidual, as opposed to population, activity
patterns and source use. The model uses
data on source emissions, room-to-room
airflows, air exchange with the outdoors,
and indoor sinks to predict concentra-
tion/time profiles for all rooms. The con-
centration/time profiles are then
combined with individual activity pat-
terns to estimate exposure. The model
allows analysis of the effects of air clean-
ers located in either/or both the central air
circulating system or individual rooms
on indoor air quality (IAQ) and exposure.
The model allows simulation of a wide
range of sources including long term
steady state sources, on/off sources, and
decaying sources. Several sources are
allowed in each room. The model allows
the analysis of the effects of sinks and
sink re-emissions on IAQ. The results of
test house experiments are compared
with model predictions. The agreement
between predicted concentration/time
profiles and experimental data is good.
The average deviation of the predicted
value from the experimental value is less
than 30% for all experiments, and the
maximum deviation is less than 60%.
This Project Summary was developed
by EPA's Air and Energy Engineering Re-
search Laboratory, Research Triangle
Park, NC, to announce key findings of the
research project that Is fully documented
In a separate report of the same title (see
Project Report ordering Information at
back).
Introduction
An indoor air quality (IAQ) computer
model, INDOOR, was developed to use
emission characteristics of sources to pre-
dict in-room pollutant concentrations.
INDOOR's predictions for several sources
have been verified by experiments con-
ducted in an IAQ test house, and emission
characteristics have been determined using
small environmental test chambers.
INDOOR, however, does not allow calcu-
lation of individual exposure due to a given
source and personal activity pattern. The
ability to estimate individual exposure is nec-
essary before guidance on exposure reduc-
tion can be given. Therefore, a new model,
EXPOSURE, that allows analysis of expo-
sure due to indoor sources (given pollutant
source characteristics and individual activity
patterns) was developed.
General Mathematical
Framework
EXPOSURE is a multiroom model based
on INDOOR. EXPOSURE allows calcula-
tion of pollutant concentrations based on
source emission rates, room-to-room air
movement, air exchange with the outdoors,
and indoor sink behavior.
Printed on Recycled Paper
-------
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 and by other data.
A mass balance for each room gives:
dCj
Vj - CJIN QJIN -
QOUT QJOUT + Sj - RJ
0)
where Vj is the volume of the room, Cj is the
concentration of room i, CHN is the concen-
tration entering the room, QMN is the air flow
into the room, CJOUT is the concentration
leaving the room, QJOUT is the air flow leaving
the room, Si is the source term, and RJ is the
removal term. RJ includes pollutant removal
by air cleaners and sinks.
The well mixed assumption requires that
CJOUT equal Cj. Equation (1) can be rewrit-
ten as:
*r *-N
dCj ^
Vj 77- Ca Qa,i +
dt -i-
H.i-'
j-N
2 (CjQjj) + Sj - RJ
H,l-i
- CjQi,a -
(2)
where Ca is the concentration outdoors, Qa,i
is the air flow from the outdoors into room i,
Cj is the concentration in room j, QJ,J is the air
flow from room j into room i, Qj,ais the airflow
from room i to the outdoors, and QJ,J is the air
flow from room i into room j. Equation (2) is
one of a set of identical equations that must
be solved simultaneously in a multiple room
model.
EXPOSURE uses afastdiscrete time step
algorithm 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. The exact so-
lution to equation (2) can then be used to
calculate the concentration at the end of the
time step. The exact solution is:
Lit P:
Ci-Ci(to)e- ^~\
Li
(3)
where Cj(to) is the concentration at time to, t
is some time greater than to, U is:
N
Qi,a + Qi,h + J Qi,j
Vj
and Pj is given by:
Qa,jCa
(5)
where Qj,h is the air flow from room i into the
HVAC system, Qh.i is the air flow from the
HVAC into room i, Cj(t) is the concentration
in room j at time t, and Ch is the concentration
in the HVAC system.
Equation (3) 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 gen-
eral a time step of 1 minute is small enough
for situations when concentrations are
changing rapidly, and time steps of several
minutes are adequate when concentrations
are near steady state. The model automat-
ically adjusts the time step to maintain a
balance between speed and accuracy.)
Source Terms
The model incorporates a wide range of
emission characteristics to allow simulation
of the range of sources encountered in in-
door 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 Re-
search Laboratory, of EPA. The user can
add to the data base and can override the
data base emission rates.
Sink Terms
Research in the EPA test house and small
chamber laboratory has shown that sinks
(i.e., surfaces that remove pollutants from
the indoor air) play a major role in determin-
ing indoor pollutant concentrations. These
sinks may be reversible or irreversible. A
reversible sink re-emits the material col-
lected in it, and an irreversible sink does not.
Sink behavior depends on the pollutant and
the nature of the sink. Considerable re-
search is necessary to define the behavior
of sinks.
The sink model used in EXPOSURE is:
Rs
(6)
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 concen-
tration (mass per length cubed), Asink is the
area of the sink (length squared), kd is the
re-emission or desorption rate constant, Ms
is the mass collected in the sink per unit area
(mass per length squared), and n is some
power between 1 and 2. For typical gaseous
organic pollutants of interest in indoor air: ka
ranges from about 0.1 to 0.5 m/h; kd ranges
from about 0 003 to 0.009; and n ranges from
1 to 1.5. Experiments are under way to
provide estimates of ka and kd for a range of
pollutants and sink materials.
Sinks reduce the peak exposure to pollu-
tants slightly but increase the cumulative
exposure because of re-emissions.
Exposure
Because the most common route for ex-
posure to indoor air pollutants is via inhala-
tion, it is convenient to define inhalation
exposure, Ej as:
Ej = C(t)bv (7)
where C is the pollutant concentration, b is
the breathing rate, and v is the volume per
breath. The exposure defined by equation
(7) 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 inhala-
tion exposure, EJC, is given by:
C(t)bvdt
(8)
The advantage of defining inhalation ex-
posure is that the exposures calculated by
the computer can be used without requiring
the user to manually calculate the amount
breathed.
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) (9)
The cumulative exposure from t1 to \2 is
given by:
-/
Ml
C(t)dt
(10)
Calculation of exposure requires the pol-
lutant concentration, the time exposed to the
concentration, and (for inhalation exposure)
the breathing rate and the volume per
breath. The time exposed to the concentra-
tion depends on the individual activity pat-
tern.
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 expo-
sure time plots and cumulative exposure
time plots for individual activity patterns.
The instantaneous exposure allows identifi-
cation of high exposure situations and of the
peak exposure.
While the model was designed to allow
assessment of the impact of indoor air pollu-
tion sources and sinks and IAQ control op-
tions 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 experi-
mental data from the EPA IAQ test house.
In all cases the agreement between predic-
tions and experiment has been excellent.
An example from a recent experiment is
shown in Figure 1.
Exposure Predictions
The examples below demonstrate some
of the model's capabilities. The first exam-
ple is calculation of the exposure to an aero-
woo
100
10 .
0.1
6 sq m of floor stained with 311 g
Sink term ka = 0.09 m/hr, kd = 0.003
Source term Ro = 17,000 mg/rrf-hr, k = 0.4/hr
Air exchange with outdoors = 0.3 ACH
Data from EPA IAQ test house
Background total hydrocarbon = 0.3 mg/cu m
0 50 100 150 200 250 300 350 400 450
Time (hrs)
Figure 1. Total hydrocarbon concentration in living room from wood stain.
10 :r
1 :
0.1 :
0.01-
0.001
Person uses product, leaves after 1 hr, and
returns at 10 hrs
Inhalation rate 1200 breaths/hr
Inhalation volume 0.6 I/breath
Person, not using product, stays in house 24 hrs
Aerosol release 280 mg VOC in 2 sec
Air exchange with outdoors 0.25 ACH
All factors based on test house data
sol spray product. The activity patterns are
for a person who (1) uses the product in a
bathroom for 10 minutes, moves to the living
room, and then leaves the building after 1
hour; and (2) stays in the building for 24
hours. The instantaneous and cumulative
inhalation exposures for the two individuals
are given in Figures 2 and 3. 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 underesti-
mated irt this example. The local concentra-
tion near the person is somewhat higher for
several minutes than the average room con-
centration. EXPOSURE can deal with this
situation if a pseudo room with a volume of
about 5 m3 and an air exchange of 30 m3/h
with the rest of the room is defined. For
Figure 2, the difference in exposures is not
great because 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 per-
son 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 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 examples are in excellent
agreement with the test house data.
Conclusions
EXPOSURE is a tool to estimate individual
exposure to air pollution from a wide range
of indoor sources. The model allows analy-
sis of a wide range of activity scenarios in a
single model calculation. The effect of miti-
gation options on individual exposure can be
evaluated by simulating the mitigation option
in the model.
10 15 20 25
Time (hrs)
Figure 2. Instantaneous inhalation exposure to VOC from aerosol spray product.
-------
2.5
c
-§
4!
7.5-
1
0.5-
Person, not using product, stays in house 24 hrs
Person uses product, leaves after 1 hr, and
returns at 10 hrs
Air exchange with outdoors 0.25 ACH
Aerosol spray releases 280 mg of VOC in 2 sec
Inhalation rate 1200 breaths/hr
inhalation volume 0.6 I/breath
0 5 10 15 20
Time (hrs)
Figure 3. Cumulative inhalation exposure to VOC from use of aerosol product.
25
4000
3500-
3000-
24 hr/day in building with no sink
6 sq m of floor stained with 311 g
Long term emission factor:
Ro = 17,000 mg/sq m, k = 0.4/hr
Initial emission 3,200 mg/sq m
Air exchange with outdoors 0.3 ACH
24 hr/day in building with sink
16 hr/day in building with
no sink
16 hr/day in building with sink
1
I
I
I
-S
o
0 50 100 150 200 250 300 350 400 450
Time (hrs)
Figure 4. Cumulative exposure to VOC emissions from wood stain.
&U.S. GOVERNMENT PRINTING OFFICE: 1991 - 548-028/40044
-------
-------
-------
-------
The EPA author, Leslie E. Sparks (also the EPA Project Officer, see below), is with Air
and Energy Engineering Research Laboratory, Research Triangle Park, NC 27711.
The complete report, entitled "EXPOSURE Version 2, A Computer Model for Analyzing
the Effects of Indoor Air Pollutant Sources on Individual Exposure:"
Paper Copy (Order No. PB 91-201 095; Cost $23.00, subject to change)
Diskette (Order No. PB 91-507 764; Cost $130.00, subject to change)
(Cost of diskette includes paper copy)
The above items will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA 22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Air and Energy Engineering Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
United States
Environmental Protection
Agency
Center for Environmental Research
Information
Cincinnati, OH 45268
BULK RATE
POSTAGE & FEES PAID
EPA PERMIT NO. G-35
Official Business
Penalty for Private Use $300
EPA/600/S8-91/013
------- |