EPA/600/A-92/209
ON VALIDATION OF SOURCE AND SINK MODELS:
PROBLEMS AND POSSIBLE SOLUTIONS
by
Zhishi Guo
Acurex Environmental Corporation
P. O. Box 13109
Research Triangle Park, NC 27709

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ABSTRACT:
While model validation remains the weakest part of the entire
process of indoor air quality (IAQ) model development, special
problems have made the validation of indoor source and sink models
even more difficult. Many source and sink models have been
developed, but few have been properly validated. Major problems
with current procedures include: elusive model parameters;
confusion in parameter estimation methods; uncertainty in scale-up
and misleading scaling factors; unspecified validity ranges; and
weakness in quantitative comparisons between models and
experimental observation.
To improve validation procedures, we have identified a number
of potential areas including: proper definition of validation
scope, proper use of statistical comparison methods, development of
mass transfer indices to bridge the gap between test chambers and
real buildings, and development of a cooperative effort to build a
source and sink database to facilitate validation.
KEY WORDS: model validation, source, sink, indoor air quality
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Introduction
Model validation is the process of evaluating the usefulness,
accuracy and limitation of a model under various application
conditions. While validation remains the weakest part in the
entire process of IAQ model development, validating of source and
sink models has its special difficulties. In fact, although many
source and sink models have been developed, few have been properly
validated.
General discussions on model validation can be found in the
literature [1-4], but the special problems associated with source
and sink models remain untouched. This paper identifies the major
problems with current practice in validating source and sink
models, and discusses some possible solutions. Most of the
problems raised came from examining the author's own practice in
model validation, and some came from reviewing other researchers'
work. Although this paper is focused on validation, the author has
found it difficult to completely separate model validation from
model building. Some discussions here may be applicable to both
steps.
Purposes of Validating Source and Sink Models
Why must we validate source and sink models? Before
answering this question, we need to briefly discuss how they are
developed and how they are used. It is generally agreed that,
before any satisfactory verification scheme is adopted, it is
necessary to determine the primary purpose or purposes to be served
by the verification [4].
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The development of source and sink models relies heavily on
experimental observations and understanding of the mechanisms.
From chamber data, one can often calculate the emission rate based
on mass balance equations. For example, if we assume that the
adsorption of pollutants on chamber walls is negligible, the mass
balance for an area source in a chamber in an infinitesimal time
period dt is:
Mass increased in chamber = Mass emitted - Mass exfiltrated
dC
or V 	 = S R(t) - Q C	(1)
dt
where V = chamber volume;
C = chamber concentration;
S = area of the source;
R(t) = emission rate at time t; and
Q = inlet/outlet air flow rate.
Let L = S/V be the loading factor, and N = Q/V be the air exchange
rate, we then have:
dc/dt + N C
R(t> = 		(2)
L
When the concentration data have reasonable time resolution, the
term dC/dt can be well represented by &C/At. The data represented
by empty squares in Figure 1 is an example of using Equation 2 to
calculate the emission rates from the chamber concentration data.
The source tested was an indoor coating product. A total of 1.82
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g of the product was applied to a 0.021 m2 oak board, and tested
for total organic emissions in a 53 L stainless steel chamber; the
chamber was kept at 23° C and 45% relative humidity; and the air
exchange rate was 0.514 h"1.
Direct calculation of the adsorption and desorption rate is
impossible because the two processes occur simultaneously, but it
is possible to calculate the net mass transfer rate for the
pollutant to or from the sink surface.
Based on experimental observations, a model can be developed
in different ways. For the convenience of discussion, we can
roughly divide all source and sink models into two categories:
statistical models and fundamentally based models.
To find a statistical model suitable to the data in Figure 1,
basic knowledge of analytic geometry will convince us that the
emission pattern in Figure 1 can be approximated by a first order
decay model[5]:
R(t) = R,, e"kt	(3)
where R0 = initial emission rate; and
k = first order decay constant.
The next step is to estimate the model parameters — the constants
(or coefficients) in a model's expression. In this case, we need
to determine the values for Rq and k that could give the best
agreement between the model prediction and observation. The solid
line in Figure 1 was obtained by log-linear regression imposed on
the emission rate data.
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In most cases, however, model parameters are estimated by
fitting the model to concentration data. This is especially true
for sink models. No matter what data are used, such model
development depends heavily on statistical estimations.
To develop fundamentally based models, or mass transfer
models, one needs to understand the physical-chemical phenomena
involved such as evaporation, adsorption, molecular diffusion in
the air-surface interface, and molecular diffusion within the
source. The parameters of a mass transfer model often have well
defined physical meanings such as vapor pressure, molecular weight,
mole fraction, adsorption energy, diffusivity, and boundary layer
thickness. Most parameters are obtained either directly from the
literature or from well-established models. Therefore parameter
estimation for mass transfer models does not rely heavily on curve-
fitting. In some cases, however, one or two of the parameters may
have to be estimated empirically. It should be pointed out that,
among existing source and sink models, many are neither pure
statistical models nor pure mass transfer models.
Like any other model, a source or sink model is at best a
simplification and approximation of a real source or sink.
Therefore, no one should expect the model to represent reality
perfectly. There is a definite need, however, to know how good the
agreement would be under certain conditions between the model and
reality. In other words, we need some estimation of the model's
predictive error.
A model may give satisfactory prediction in one case but fail
in another. Then we must know the conditions under which the model
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gives acceptable prediction, and those under which the model fails.
We also need to know the sensitivity of the model to its
parameters.
Source and sink models are seldom used alone. In most cases,
they are part of an IAQ model. Since both source and sink models
serve the IAQ model, any predictive errors they generate can be
propagated during an IAQ simulation. We need to know how the
inaccuracy of a source or sink model could affect the IAQ
simulation output.
In summary, the purposes of validating source and sink models
may include:
—	estimating the model's predictive error by comparing the
predicted values to observed ones;
—	defining validity range and validity conditions;
—	defining conditions of failure;
—	defining the applicability of the model (good for a
single product or for a type of product, or for several
types of products);
—	estimating the model's sensitivity to its parameters; and
—	if possible, estimating the model's propagated error in IAQ
simulation.
For those who want to use source and sink models, proper
validation will provide them with a clear view of the conditions
for reliable model application, and the uncertainty they may expect
under certain conditions. Such information may prevent the user
from misusing the models. For those who develop source and sink
models, proper validation may enable them to learn how to improve
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their models, and how to develop more advanced models.
Major Problems with Current Validation Procedures
Variable Model Parameters
Most statistical models have at least one variable parameter
— the parameter that is determined through statistical estimation
and whose value changes as the environmental conditions change.
Parameters Rq and k in Equation 3 are such variable parameters.
Unlike physical parameters (such as boiling point, vapor pressure,
diffusivity, and air velocity), these parameters are sensitive to
any change of the environment. The modelers often find it
difficult to choose proper values under certain given conditions.
The following example illustrates how those parameters may vary
with test conditions.
A wood stain product was tested for its organic emissions in
small environmental chambers [5]. The concentration data were fit
by the first-order source model. Test conditions and estimated
emission factors are summarized in Table 1. As one can see, both
R(j and k vary over a wide range. Unless correlations are found
between these parameters and the environmental conditions (such as
air exchange rate, loading factor, application rate, and degree of
air turbulence), there is no way to tell what values to choose for
Rfl and k under certain given conditions.
(N/L) - a Misleading Scaling Factor
The ratio of air exchange rate (N) over chamber loading factor
(L) has been one of the most commonly used scaling factors in
chamber experimental design and model validation. The concept
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behind this factor is that, if we double the chamber loading and
the air exchange rate simultaneously, the two effects will be
canceled out, and the resulting chamber concentration should be the
same [6], This assumption is correct if, and only if, we are
dealing with a constant source at steady state. The problem is
that it has been used far beyond the above limitations. It is
theoretically incorrect to apply such a scaling factor to either
non-steady state situations and/or non-constant sources. To
illustrate this problem, let's look at two theoretical
concentration models; Equation 4 is the expression for a constant
source and Equation 5 for the first-order decay source [5],
Xj r
C(t) = 	 (1 - e*Nt)	(4)
N
L R0
C(t) = 	 (e"kt - e"Nt)	(5)
N - k
where C(t) is the chamber concentration;
R = emission rate for constant source;
L = chamber loading;
N = air exchange rate; and
t = time.
Figures 2 and 3 were plotted based on Equations 4 and 5,
respectively, assuming that chamber volume = 1 m3 and R = Rg = 400
mg/m2/h. Figure 2 shows that, for the same constant source, the
same N/L may not yield the same concentration curve if steady state
is not approached; and Figure 5 shows that, for a given finite
source, very different concentration curves are obtained with the
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same N/L.
Confusion in Parameter Estimation
Estimating the parameters for a given model from a given set
of data can be confusing, too, because there are many ways to fit
a model to data. For example, to fit the first-order model to the
indoor coating data described above, we have many ways of
estimating Rg and k. For illustration purposes, four different
regression methods are discussed here: (A) Using nonlinear
regression to fit Equation 5 to the concentration data without any
data transformation; (B) Using nonlinear regression to fit Equation
5 to the concentration data with logarithmic transformation; (C)
Using nonlinear regression to fit Equation 3 to directly calculated
emission rate data (as shown in Figure 1); and (D) Using linear
regression to fit Equation 3 to directly calculated emission rate
with logarithmic transformation. The different results are given
in Table 2. Parameters obtained from method C appeared the best in
catching the peak (Figure 4) and also the worst in tracing the tail
as illustrated in the semi-log plot (Figure 5) . Just the opposite,
curve D looked the worst in the high concentration region but gave
the best prediction in the tail. The other two curves fell between
the two extremes. The questions then become: Which estimation
method should we choose? and which set of parameters should we
report?
The Effect of Data Range
Many indoor sources last for a long period of time, and the
effect of indoor sinks lasts even longer. Tracking such long term
effects can be very costly and time-consuming. People usually
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have to develop and validate their models by using chamber data
within a limited time period. It is clear that, unless the
validity range is defined, the statement of "validated" can be very
confusing.
The following is an example of this problem. We tested the
emission of ethylbenzene from a piece of 0.113 m2 duct liner in a
53-L chamber (0.54 air change per hour, 23° C, and 45% relative
humidity). The sample was taken from the air handling system in a
test house, and was previously exposed to ethylbenzene polluted
indoor air. Using the first 10 hours of chamber data, we found
that the simple first order model (Equation 3) fit the data
adequately (Figure 6). The model prediction failed after 10 hours,
and the double exponential model R(t) = R, exp(-k,t) + R2 exp(-k2t)
seemed more suitable to the wider data range (Figure 7) . After 120
hours, however, it failed too. A second-order model, R(t) =
R0/ (1+ktRjj) , fit the data almost perfectly within 400 hours (Figure
8). It is difficult to tell if or when the second order model
fails beyond 400 hours.
Obviously, selection of data range plays an important role in
both model building and validation. Without specifying the
validity range of a model, the whole validation becomes
meaningless. Information on conditions of model failure is
especially important to IAQ modelers for IAQ simulation programs do
not turn off a source or a sink automatically.
The Effect of Air Velocity and Turbulence
The degree of air turbulence above the source or sink surface
can alter the rate of mass transfer in both directions. This means
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that a model validated in one chamber may not work at all in
another if the air turbulence conditions are significantly
different.
To show how the degree of air turbulence affects the model
parameters, we did a set of preliminary sink tests in a two-chamber
experimental system [7]. A piece of wallboard was placed in the
test chamber and insulted by a first-order decay ethylbenzene
source. To alter the air circulation conditions, a small biscuit
fan was placed inside the test chamber (fan speed could be adjusted
by varying the voltage) . Tests were conducted with the fan at 50
V, 70 V, and 110 V, respectively, and all other conditions were
kept the same. Figure 9 shows one of the test results and the
fitting of the dynamic Langmuir sink model [7,8] to the data. The
estimated model parameters — adsorption rate constant ka and
desorption rate constant kd — are given in Table 3. It seems that
both adsorption and desorption were accelerated by the increased
air circulation. During these tests, we did not measure the fan
speed and air velocity in the chamber; therefore, the results
presented below should be considered as a qualitative illustration.
Since air movement and turbulence conditions in a building can be
significantly different from that in a chamber, the applicability
of chamber results to real buildings has been challenged. This so-
called "scale-up" problem has been the most troublesome in
validating source and sink models.
Oversimplified Illustration of the Goodness of Fit
Checking the agreement between model prediction and
observation can be misleading, too. So far, most modelers,
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including the author [9], have tried to show the validity of their
models by presenting the model prediction and observation together
in a diagram. Then the authors would claim that the presented
model had been "validated" (or sometimes more cautiously,
"preliminarily validated"). While there is nothing wrong with
graphical comparison, something is missing here: What does
"validated" or "preliminarily validated" mean? There have to be
some criteria so that the model developer and, more importantly,
the user can make an objective and quantitative judgement.
Statistical methods for verification comparisons are available;
unfortunately, many of us often neglect those useful tools.
Special Problems with Fundamentally Based Models
Mass transfer models are preferred to statistical models
because the former emphasize the physical understanding of the real
mechanisms and because their parameters are usually well defined.
But these types of models have their own problems.
To model very complex reality with relatively simple models,
the modelers have to exclude whatever they consider "unnecessary"
details and focus on one or two mechanisms. Due to the omission of
the remaining mechanisms, the resulting models are often unusable
unless some fuzzing factors are introduced. These variables often
make the mass transfer models less attractive because they have
made the mass transfer models undistinguishable from empirical
models.
Mass transfer models are often much more complicated than
their corresponding statistical models. It is commonly true that
a mass transfer model has better "validity" than a statistical
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model, but is more difficult to use than the latter due to its
complexity.
Recommendations
Three Levels of Validation
As just discussed, the primary purpose of validating source or
sink models is to make sure they represent reality close enough
under certain conditions so that they can be used in IAQ simulation
without bringing in excessive propagation errors. Keeping this in
mind, we can divide the validation process into three steps: (1)
Checking the agreement between the model and a single set of
observations; (2) Checking the agreement between the model and
multiple sets of observations; and (3) Verification of scale-up.
After a model is formulated, it is usually compared to a
single set of observations to determine if the model represents the
real pattern in that particular case reasonably well. If there are
variable parameters in the model, they can be estimated by this
step. If the model concept is poor, the model may not "survive"
this step at all.
Since many, if not all, source and sink models contain
variable parameters, one set of parameters which give satisfactory
prediction in one event may not work in others. By comparing the
model with a few sets of data, one can either fine-tune the
parameters or find correlations between the values of parameters
and test conditions. The author believes that not all existing
source and sink models can survive this validation step.
The last step — scale-up verification — requires data from
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either real buildings or large test chambers. Without this step,
the usefulness of a model cannot be justified.
Some Aspects in Validation Procedures
When comparing a model with observation, the modeler should
clearly specify the conditions under which the observation was
obtained. This will allow the modeler and the potential users to
distinguish the conceptual errors of the model from those of the
data. The list of conditions should include, but not be limited
to, the following information:
—	Chamber specification (type, material, volume, shape,
temperature, humidity, pressure, etc.);
—	Sample specification (material, size, sample preparation,
and position in the chamber);
—	Air exchange rate;
—	Description of air movement in the chamber (qualitative
description such as inlet/outlet pipeline design, with or
without forced mixing; and quantitative description such as
surface velocity, Reynold's number, or other fluid dynamic
parameters);
—	Sampling and analytical methods;
—	Data quality; and
—	Data range.
If some or all the model parameters are estimated using
statistical means, a detailed description of the approach used
should be given:
—	The equation used in the regression (it may or may not be
the source or sink model itself);
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—	Independent and dependent variables;
—	Statistical method (linear regression, nonlinear
regression, or other methods); and
—	Data Transformation (no transformation, logarithmic
transformation or, in more general terms, Box-Cox power
transformation).
When comparing a model to multiple sets of observations, the
chamber data should include:
—	Observations under at least two air exchange rates; and
—	Observations under at least two loading factors.
If a model is statistically based, the sensitivity of a model
to its parameters, and the dependence of model parameters on
environmental conditions (such as air exchange rate, loading
factor, and degree of air turbulence) should be described.
When performing scale-up verification, data from large test
chambers are preferred to those from buildings because the
conditions in a building are difficult to control. The most
important uncontrolled factors include: varying air exchange rate,
multiple air zones, and strong adsorption on many different surface
materials. If the model parameters established from previous
validation steps need further adjustment in scale-up, such
adjustment should be justified.
Finally, validity range and validity conditions should be
specified.
Making Comparisons More Objectively
Graphic comparison of model performance is absolutely
necessary, but using it alone isn't enough. Statistical tools
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should be used to complement graphical comparison.
Quite a few statistical methods are available in making
comparisons [10,11]. At least one statistical verification method
should be used along with graphical comparisons. The modeler
should make careful selection among those methods because different
validation purposes require different statistical techniques. The
danger of using any goodness-of-fit index in model verification is
illustrated by Benarie [4], Besides, some methods may not be
suitable to our particular situation. We should emphasize the
importance of physically understanding the model during validation.
Some statistical comparison techniques do not help very much in
this aspect.
Dealing with Scale-up Problems
Source and sink models based on basic mass transfer theories
have received ever-increasing attention by the indoor air community
in recent years [12-14]. Many of us, who have been frustrated by
elusive statistical models, believe that fundamentally based models
are the final solution to our problems, especially to the scale-up
problem. Mass transfer models for emission and adsorption are not
new: they can be found in many mass transfer monographs. The
problem is that people can rarely find a proper model from the
existing engineering literature that can be used by IAQ modelers on
an "as is" basis because the processes being modeled are too
complicated for those models.
To develop relatively simple mass transfer models, we need to
select proper expressions for mass transfer coefficients (or mass
transfer resistance). Criteria for selecting good expressions may
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include:
—	They should separate the properties of the environment from
those of the source or sink;
—	They should be simple enough to be used in source or sink
models;
—	They can be measured independent of source and sink models;
and
—	They can be correlated to more complicated boundary layer
models.
Making a Cooperative Effort bv Building a Source and Sink Database
Generating quality data to validate a model can be very costly
and time-consuming. A modeler may have the talent to develop
scientifically sound models but may not have the ability or
resources to generate good quality data. This has left little
choice to the modelers: they often have to accept whatever data
they can get, regardless of the suitability of the data to serve
their validation purposes.
All modelers would benefit if some organization (a
professional society or university, for example) would assume the
responsibility for collecting source and sink data from volunteer
research organizations and build an indoor source and sink
database. Such a cooperative effort could make a great difference
in easing the shortage of quality data.
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Ending Remarks
As stated earlier, the major purpose of this paper has been to
raise issues regarding the validation of source and sink models.
We have identified a number of potential problem areas in IAQ
modeling. Due to the great difficulty in validating indoor source
and sink models, we cannot expect all the problems to be solved
overnight. Improvement can only be made gradually. Besides, as
long as a new model is built on a sound scientific basis, the model
can be published without complete validation. The model developer
should be allowed to leave part of the validation work to other
researchers. Validating a model is as important as creating one,
and can be an original contribution to science.
Acknowledgement
Research was supported by U.S. Environmental Protection Agency
Contract 68-DO-0141. This work has been subject to the Agency's
peer and administrative review, and has been approved for
publication. However, it does not necessarily reflect the views of
the Agency and no official endorsement should be inferred.
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References
[1]	Ingles, D. M., What Every Engineer Should Know About. Volume
15: Computer Modeling and Simulation, Marcel Dekker, Inc., New
York, 1985.
[2]	Knox, J. B., "Model Validation: Purpose and Expectations,"
Lawrence Livermore National Laboratory Report UCRL-91664,
October 1984.
[3]	Morrison, F., The Art of Modeling Dynamic Systems. John Wiley
& Son, Inc., New York, 1991.
[4]	Benarie, M. M., Urban Air Pollution Modeling. The MIT Press,
Cambridge, 1980.
[5]	Tichenor, B. A. and Guo, Z., "The Effect of Ventilation on
Emission Rates of Wood Finishing Materials," Environment
International. Vol. 17, 1991, pp. 317-323.
[6]	Matthews, T.G., Wilson, D.L., and Thompson A.J.,
"Interlaboratory Comparison of Formaldehyde Emissions from
Particleboard Underlayment in Small-Scale Environmental
Chambers, Journal of Air Pollution Control Association. Vol.
37, 1987, pp. 1320-1326.
[7]	Krebs, K. A. and Guo, Z. , "A Two-chamber Design for Testing
the Sink Effect with Dynamic Concentration Profiles,"
presented at EPA/A&WMA International Symposium on Measurement
of Toxic and Related Air Pollutants, Durham, May 3-8, 1991.
[8]	Tichenor, B. A., Guo, Z., Dunn, J. E., Sparks, L. E., and
Mason, M.A., "The Interaction of Vapour Phase Organic Compounds
with Indoor Sinks," Indoor Air. Vol. 1, 1991, pp. 23-35.
[9]	Guo, Z. , Dunn, J. E., Tichenor, B. A., Mason, M. A., and Krebs,
20

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K. A. , "On representing reversible sinks in indoor air quality-
models ," Proceedings of the 5th International Conference on
Indoor Air Quality and Climate, Vol. 4, 1990, pp. 177-182.
[10]	Panofsky, H. A. and Brier, G. W., Some Applications of
Statistics to Meteorology. Pennsylvania Publication,
University	Park, 1968.
[11]	Hanna, A. R. , "Air Quality Model Evaluation and Uncertainty,"
Journal of Air Pollution Control Association. Vol. 38, 1988,
pp. 406-412.
[12]	Nazaroff, W. W. and Cass, R. G., "Mass Transfer Aspects of
Pollutant Removal at Indoor Surfaces," Proceedings of the 4th
International Conference on Indoor Air Quality and Climate.
Berlin, 1987, pp. 244-248.
[13]	Gunnarsen, L., "Air Velocities and Indoor Emissions,"
presented at CIB-W77 Symposium, New Haven, 1991.
[14]	Axley, J.W., "Adsorption Modeling for Building Contaminant
Dispersal Analysis," Indoor Air, No. 2, 1991, pp. 147-171.
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Table 1 — Total Organic Emissions from Wood Stain
Chamber Type
Air Exchange Rate Range
Application Rate Range
Chamber Loading Range
Range of Estimated R0
RSD (mean)
RSD (range)
Range of Estimated k
RSD (mean)
RSD (range)
166 L with a slow stirrer
0.35 to 4.6 [h"1]
23 to 26 [g m"2]
0.1 to 1.3 [m"1 ]
2.2 to 27 [g m~2 h"1]
7%
3% to 12%
0.24 to 2.41 [h"1]
11%
4% to 16%
Table 2 — Estimated Emission Factors with Four Regression Methods
Method A	Method B	Method C	Method D
Model
Eq. 5
Eq. 5
Eq. 3
Eq. 3
Data Type3
Cone.
Cone.
Rate
Rate
Data Scale
Normal
Log
Normal
Log
Regression
Nonlinear
Nonlinear
Nonlinear
Linear
R0 (g m"2 h"1)
10.1
6.68
14.0
4.96
RSD
4.2%
5.8%
4.3%
2.3%
k (h"1)
0.356
0.208
0.599
0.186
RSD
5.1%
2.5%
6.1%
2.0%
a Cone. = concentration data; rate = emission rate data.
Table 3 — The Estimated Adsorption Rate Constant (ka) and
Desorption Rate Constant (kd) at Three Fan Speeds
Fan Voltage (V)
50
70
110
ka ± RSD (m h"1)
kd ± RSD (h"1)
0.64±5.9%
1.48±6.4%
0.91±6.0%
1.44±7.0%
1.23±12%
2 . 54±6.7%
Sink material: 0.14 m2 wallboard; pollutant: ethylbenzene;
air exchange rate = 1.2 h"1; temperature = 2 3 °C; and relative
humidity = 45%.
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100000:
E*
DC
Calculated Emission Rate
(~
10000; dp
l/
1000=
First-Order Model
100=
10
0
10 15
Elapsed Time, h
20
25
Figure 1. Calculated VOC emission rate for an indoor coating product
based on chamber concentrations and first-order model
prediction.
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100
m
O)
c
o
¦Jk
2
4-i
c
(D
O
c
o
o
N=1.0, L=0.2, and N/L=5
N=0,2, L=0.04, and N/L=5
3 4 5 6 7
Elapsed Time, h
Figure 2. Improper use of (N/L) - constant source at non-steady state.
24

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50
N=1.0, L=0.2f and N/L=5
40-
m
D)
N=0,5, L=0.1, arid N/L=5
N=0.2, L=0.04, and N/L=5
o 20-
10-
3
5
6
7
8
9
10
0
1
2
4
Elapsed Time, h
Figure 3. Improper use of (N / L) - finite source.
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4000
3000-
m
E
D>
EE
!»•
c
o
2000-
"5
¦#-*
©
o
o
O
1000
5
10
15
0
20
25
Elapsed Time, h
Figure 4. The effects of parameter estimation methods on model performance -
normal scale.
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10H	1	1	1	1
0	5	10 15 20	25
Elapsed Time, h
Figure 5. The effects of parameter estimation methods on model
performance - log scale.
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500
400-
First-Order Model
: 300-
8 200
100
0
1
2
3
4
5
6
7
Elapsed Time, h
Figure 6. Modeling the re-emission of ethylbenzene from polluted duct liner
10 hour data.
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1000
£
D) 1 00:
£ :
c
o
Double Exponential Model
1
Lb*
c
Q>
O
c
o
o
10:
First-Order Model
20
40
0
60
80
100
120
Elapsed Time, h
Figure 7. Modeling the re-emission of ethylbenzene from polluted
duct liner - 120 hour data.
29

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1000q
10=
Second-Order Model
First-Order Model
Double Exponential Model
0.1
0
50
100
150
200 250 300
400
350
Elapsed Time, h
Figure 8. Modeling the re-emission of ethylbenzene from polluted duct liner -
400 hour data.
30

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25
Without Sink
20-
E
ro
E- 15-
c
o
Sink Mode
c
8 io-
C
O
Q
Sink Data
0
1
3
4
6
7
2
5
8
9
10
Elapsed Time, h
Figure 9. Dynamic sink test and model prediction.
31

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qnr TECHNICAL REPORT DATA
-tLi iL X\ i-/ J. ~^oj (Please read Instructions on the reverse before complet
1. REPORT NO. 2.
EPA/600/A-92/209
3. PJ93 - 10 b 7 81)
4. TITLE AND SUBTITLE
On Validation of Source and Sink Models: Problems
and Possible Solutions
5. REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Zhishi Guo
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
A cur ex Environmental Corporation
P. O. Box 13109
Research Triangle Park, North Carolina 27709
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-DO-0141
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; 9/91-4/92
14. SPONSORING AGENCY CODE
EPA/600/13
is.supplementary notes AEERL project officer is Bruce A. Tichenor, Mail Drop 54, 919/
541-2991. Presented at Symposium on Modeling of Indoor Air Quality and Exposure,
Pittsburgh, PA, 4/27-28/92.
i6. abstract paper discusses solutions for problems relating to validating indoor
air quality (IAQ) source and sink models. While model validation remains the weak-
est part of the entire process of IAQ model development, special problems have made
the validation of indoor source and sink models even more difficult. Many source and
sink models have been developed, but few have been properly validated. Major pro-
blems include: elusive model parameters, confusion in parameter estimation meth-
ods, uncertainty in scale-up and misleading scaling factors, unspecified validity ran-
ges, and weakness in quantitative comparisons between models and experimental ob-
servation. Possible solutions include: proper definition of validation scope, proper
use of statistical comparison methods, development of mass transfer indices to
bridge the gap between test chambers and real buildings, and development of a co-
operative effort to build a source and sink database to facilitate validation.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. COSATI Field/Group
Pollution
Mathematical Models
Proving
Sources
Pollution Control
Stationary Sources
Indoor Air Quality
Sinks
13	B
12 A
14	G
18. DISTRIBUTION STATEMEN REPRODUCED BY
Rplpacp fo PnhllV US. DEPARTMENT OF COMMERCE
NATIONAL TECHNICAL INFORMATION SFRVICc
SPRINGFIELD. VA 22161
19. SECURITY CLASS (This Report)
Unclassified
21. M^OF PAGES
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (9-73)
t

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