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

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  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

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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.

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                  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

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 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

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