Ann. occup. Hyg., Vol. 41, No. 6, pp. 625-641, 1997
© 1997 British Occupational Hygiene Society
Published by Elsevier Science Ltd. AU rights reserved
Printed in Great Britain
0003-4878/97 SI7.00+ 0.00
PII: S0003-4878(97)00032-X
EVALUATION OF EVAPORATION AND CONCENTRATION
DISTRIBUTION M O D E L S ^ TEST CHAMBER STUDY
Anne Lennert, Frands Nielsen and Niels Oluf Breum
1 Department of Occupational Hygiene, National Institute of Occupational Health! Lerso Park Alle 105,
DK-2100\Copenhagen 0 , Denmark""!
(Received in final form 2 June 1997)
Abstract^—Occupational exposure to airborne volatile organic compounds is governed by the
source strength and dispersion of the pollutant into workroom air. The purpose of the present test
chamber study was to validate suggested models for the prediction of evaporation rates and
concentration distributions. The study design was organized into different scenarios to simulate
workplace conditions. Evaporation rates of organic compounds of different volatilities were
recorded gravimetrically and the corresponding concentrations in air were measured at various
locations equally distributed in the test chamber. The evaporation models generally showed a fair
agreement with experiments but tended to underestimate the evaporation rate especially at low air
velocity. Based on factorial experiments a new simple evaporation model was suggested. The
performances of the concentration distribution models were of different quality. The model
developed by Roach (Annals of Occupational Hygiene 24, 105-132, 1981) cannot be used in
predicting the concentration distribution in case of a convective air flow. If knowledge of the
evaporation rate and pollutant concentration at some distances from the source were available, the
model suggested by Scheff et al. (Applied Occupational and Environmental Hygiene 7, 127-134,
1992) generated a concentration distribution in reasonable agreement with the observed data. The
box-model (Sinden, Building and Environment 13, 21-28, 1978) generally offered a fair performance
but tended to underestimate the pollutant concentration in a region close to the source in the
direction of the main air flow.i© 1997 British Occupational Hygiene Society. Published by Elsevier
Science Ltd.
^
NOMENCLATURE
D, Air
diffusion coefficient of substance i in air (m2 s~')
L
surface length (m)
LD
pool equivalent diameter (m)
/-o
starting length (m)
5
source strength (mg s~')
M
molar mass (g m o l " 1 )
P
total pressure (Pa)
P\{
v a p o u r pressure of substance i (Pa)
Q
v o l u m e flow rate ( m 3 s ~ ' )
r
radius distance between the source and sampling location (m)
R
gas constant (Pa m 3 mol"' K."')
Rs
hollow sphere with radiud R,
R{[
specific e v a p o r a t i o n rate of p u r e liquid i (mol m ~ 2 s ~ ' )
S
steady-state emission rate (g min~')
T
temperature (K)
V
centre axis o r m a i n stream air velocity (m s ~ ' )
x
downwind component distance of r (m)
Greek symbols
v
kinematic viscosity of air (m2 s~')
Subscripts
i
volatile organic compound
w
water
625
626
A. Lennert el al.
Superscripts
s
oo
conditions at evaporation surface
conditions in workroom air
INTRODUCTION
For an occupational hygienist, data on the source strengths and dispersion of
pollutants are important for the prevention of workers exposure to air pollutants.
Measurements of personal exposure to air pollutants are expensive and time
consuming and therefore modelling is attractive. A model based on the laminar
boundary layer theory (Table 1; the NIOH-1 model) for prediction of isothermal
evaporation rates for volatile organic compounds was recently suggested for
occupational environments (Nielsen et al., 1995). The model was validated by
comparing model predictions with experimental data obtained in a test duct under
laminar air flow conditions. The model was found to have a high performance
compared to previous semi-empirical evaporation models (Table 1) (Mackay and
Matsugu, 1973; Gray, 1974; Weidlich and Gmehling, 1986; Gmehling et al., 1989;
Olsen et al., 1992; U. S. EPA, 1987) also suggested for occupational hygiene.
Based on knowledge of the source strength, three simple models have been
proposed for estimating the concentration distribution of air pollutants at work
places (Table 2). Two of the models (Roach, 1981; Scheff et al., 1992) estimate the
pollutant concentration in air at different distances from the source. The third
model, the box-model, (Sinden, 1978) estimates the average pollutant concentration
in air assuming air and pollutant to be instantaneously perfectly mixed.
In the present study the performance of the evaporation and the concentration
distribution models are evaluated in a test chamber. In the test chamber, conditions
at workplaces, where laminar air flow condition can not be expected to prevail, are
simulated.
Table 1. Evaporation models suggested for occupational hygiene
GRAY:
RU = 2\.l D}%^\WDfrV?W'r^r
BAU:
/?„ = 1.11 - 1 0 - 2 D ^ ? v - 0 1 5 ^ 9 6 L - 0 0 4 ^
Mackay:
Ru = 4.82 • 10- 3 Z)?j?v-°- 67 V°- n Li°"
SUBTEC:
Ru = 1.6 • 102D° fir V
EPA(USA):
Ru = 2.5 • lO"3
NIOH-1:
*,,
NIOH-2:
Ru = 1.1 •
V°78(^
L-U
$
L
Evaporation and concentration distribution models
627
Table 2. Concentration models suggested for occupational hygiene
Roach:
Cu =
s+_j_{i_±)
Scheff:
CM = 4 j ^
Box-model:
C,, = |
EXPERIMENTAL
The test chamber, with dimensions, is shown in Fig. la. Laminated plastic was
used for the walls and the ceiling while the floor was made out of stainless steel. The
chamber had a balanced air supply and exhaust and an adjustable air exchange rate.
The air exchange rate, N, was set at 9.2±0.8 h~'. N was measured using tracer gas
techniques (Breum, 1993). The air flow rate, Q, at the exhaust duct was then
calculated as Q = Nx V, where V is the volume of the chamber. Throughout all
experiments the air velocity at the exhaust duct was measured with a
thermoanemometer (Alnor 175) to a keep record of the ventilation process. An
open cylindrical vessel (i.d. 0.20 m, volume 0.00050 m3) containing the organic
solvent was used as the pollutant source.
Experiments were carried out at three different air velocities above the vessel in
the range usually met in occupational environments. The air velocity was measured
at the begining of an experiment and every 150 s throughout the experiment using
an omnidirectional probe (DANTEC 54N50). The probe was placed 0.04 m above
the surface of the vessel to measure the free stream air velocity.
For the first velocity, forced convective air flow at high velocity (0.70 m s~') at
the source was used. Medium air velocity (0.38 m s~') was used for the second case
and low air velocity (< 0.08 m s~') for the third. The high and medium air velocities
were generated with a fan running at an adjustable speed. For low air velocity the
fan was not used. The fan was placed close to the wall between the two air inlets.
Smoke testing showed that the air flow direction at the source was towards the
exhaust duct for the medium and high air velocity cases and towards the air supply
with low air velocity.
For each air volicity, the thickness of the air velocity boundary layer above the
liquid was varied by placing flat disks of different sizes on top of the vessel. All disks
had an aperture of diameter D equal to the diameter of the vessel (see detail A, Fig.
la). Three different flat disks were used with diameters equal to D, £> + 0.1 m, and
D + Q.2 m.
For each combination of air velocity and disk diameter, experiments were
performed for three different organic compounds. The compounds were of different
volatility: methyl-isobutyl-ketone (MIBK), toluene (To) and butanone (MEK),
with vapour pressures ranging from 2.0 to 9.7 kPa at 20°C. All chemicals were of
high purity [>99.5% (w/w)].
Each experiment lasted for 35 min and was carried out in triplicate. The 81
experiments were performed in random order.
The vessel filled to the top with the organic compound under testing was placed
on a balance (Mettler PM4800). The mass of solvent in the vessel was recorded every
A. Lennert el al.
628
Test
Tubes
Exhaust
2.30 m
ft
Detail A
Measuring
point
'2.58 m
3.48 m
Detail A front view.
Disk
Vessel containing the organic solvent
Balance
Detail A seen from above.
The flat disk with an aperture of diameter D and a
diameter of D + 0.1 m seen from above. The disk
is placed on top of the vessel containing the
solvent.
Fig. 1. (a) The experimental chamber with the pollutant source placed on top of the balance at the centre
of the chamber. The air supply is on the right and the exhaust opening on the left of the chamber, (b)
Location of the measuring points with the source (S) placed at the origin. A measuring point is indicated
by a number. (No. 2-13). The axes are scaled to equal the dimensions of the test chamber.
150 s throughout the experiment. The evaporation rate was obtained from
regression analysis of the recorded loss of mass from the vessel against time. The
evaporation rate was also obtained from measured steady-state concentrations at
the exhaust duct (see below) multiplied by the exhausted air flow rate.
The air temperature was measured at the centre of the chamber, and throughout
all the experiments the temperature ranged from 21 to 23°C. Evaporation from a
surface causes not only a mass transfer but also a heat transfer (evaporative
cooling). During the evaporation a temperature gradient is created in the solvent
close to the surface. All evaporation models include vapour pressure as an
important parameter, and vapour pressure is sensitive to temperature. Therefore the
Evaporation and concentration distribution models
629
S
Fig. 1. (b) See full caption on facing page.
surface temperature of the solvent and the temperature 0.01 m below the surface
were measured. The measurements were performed every 150 s throughout the
experiment. All temperature measurements were performed with transducers
calibrated at the supplier.
The location of the source defined the origin of a three-dimensional coordinate
system with the positive Z-axis as the height above the vessel (Fig. lb). The pollutant
concentration in air was measured at 12 positions located symmetrically around the
source along the three axes. The concentration was also measured at the air supply
duct, at the exhaust duct and outside the chamber. Air samples from all positions were
collected by 15 Teflon tubes (i.d. 3 mm) of equal length (7 m). Using a channel selector
air samples were continuously flushed through all the tubes and were sequentially
delivered to a photoionization detector (PID) model AID 580. Air samples from all
tubes not currently being analysed were directed to the exhaust duct. Air samples from
a tube were delivered to the analyser for a period of 10 s. Testing of the experimental
set-up indicated that concentrations obtained for the first 5 s of a sampling period
were influenced by the previous air sample. Therefore, only air samples obtained
from the last 5 s of the sampling period were used for quantification of the
concentration. No correction for adsorption to tube surfaces was necessary, as
experiments with or without channel selector and tubes did not indicate a difference in
concentration measurements. Prior to an experiment the concentration of the air
pollutants in the chamber was measured to ensure that the level was negligible.
630
A. Lennert el al.
The PID was calibrated on a daily basis using a standard series of known
concentrations. Regression analysis was performed on the calibration data; the
calibration was accepted if the slope and the intercept were not significantly
(a = 0.05) different from unity and zero, respectively. From the PID the
concentration, as an analogue signal, was passed on to a PC where it was converted
to a digital signal. To reduce the effects of noise and bias current this conversion was
done in differential mode. The data collection was monitored on the PC.
STATISTICAL METHODS
Hypotheses on differences between groups of data were tested parametrically
using analysis of variance. MINITAB statistical software (version lOxtra;
MINITAB Inc., PA) was used for the calculations.
ERROR EVALUATION
Calculated from propagation of the errors in measuring the mass loss and the
temperature of the organic solvent the a priori uncertainty of measuring evaporation
rates was 10%. The error of the balance was estimated to be less than 1%. The
temperature of the solvent varied within ±1°C corresponding to an error in
evaporation rate of approximately 10%. For all the measured evaporation rates, the
a posteriori uncertainty was on average 7%, that is, the experiments were in
statistical control.
The uncertainty of a predicted evaporation rate depends on the evaporation
model applied. As an example the uncertainty for the NIOH-2 model (Table 1) was
found to be less than 8% based on propagation of the following errors: 5% in
measuring the air velocity, 5% in estimating the vapour pressure assuming an error
of 1 % in measuring the solvent temperature and an error of 5% in the diffusivity
coefficient from Lugg (1968). For the models of Mackay and Matsugu (1973), Gray
(1974), and BAU (Bundesanstalt fur Arbeitsschutz) (Weidlich and Gmehling, 1986;
Gmehling et al., 1989) the estimated uncertainty of predicting the evaporation rates
was 12%. The uncertainty for the EPA (USA) (1987) and the SUBTEC-model
(Olsen et al., 1992) was less than 8%.
The a priori uncertainty in measuring the concentration of air contaminants
equals the uncertainty in calibrating the PID. The uncertainty was approximately
10%. As an average the a posteriori uncertainty was 9%.
The a priori uncertainty for evaporation rates calculated from the exhausted air
flow rate (uncertainty 12%) and concentration measurements (uncertainty 10%) at
the exhaust duct was approximately 16%. As an average the a posteriori uncertainty
was 10%.
RESULTS
A typical result of the measured loss of mass of solvent from the vessel (low air
velocity, MEK, and no disk) is given in Fig. 2. Data at steady-state (liquid
temperature constant within ±1°C) were used to estimate the evaporation rate.
From a balanced analysis of variance on the obtained data the air velocity, the
Evaporation and concentration distribution models
488
486
^484
-482
$480 ^478 476 474
10
631
= -0.75+/-0.01g/min
R-squared=100%
H
12
1
1
16 18 20
Time (min)
1
1
22
1
h
24
26
Fig. 2. The recorded loss of mass during the experiment with MEK. as the pollutant source at low air
velocity and with no disk. The absolute value of the slope a of the line is the reported source strength.
compound under testing, and the diameter of the disk appeared to be significant
(a = 0.05) parameters for the evaporation rate (a = 0.05).
In Fig. 3 the evaporation rate derived from the recorded loss of mass from the
vessel is compared to the evaporation rate derived from data obtained at the exhaust
duct. For clarification only the averages of triplicate experiments are given. The
results of orthogonal regression analysis (Mandel, 1984) with the estimated standard
deviations are also shown; for the analysis it was taken into account that the
evaporation rates on the two axes were subject to different uncertainties. The
evaporation rate calculated from data obtained at the exhaust was in general biased
towards high values with no indication of one air velocity being more biased than
another. The evaporation rate derived from the measured loss of mass from the
vessel was superior in terms of accuracy compared to the evaporation rate derived
from data obtained at the exhaust duct. Therefore, data from the exhaust duct are
not discussed further.
In Fig. 4a-f evaporation rates predicted using the tested models (Table 1) are
compared to experimental evaporation rates obtained from the recorded loss of
mass from the vessel. Data from all three air velocities were used for the
comparison. For each model the results of the orthogonal regression analysis are
given (Mandel, 1984). Linear regression analysis was performed on predicted versus
measured evaporation rates for the three air velocities (Table 3).
For the NIOH-1 (Fig. 4a) model the best agreement between measured and
predicted evaporation rates was observed for the experiments with low air velocity.
However, in general the model underestimated the evaporation rate and the bias
increased significantly (a = 0.05) as the air velocity increased. The diameter of the
disk was also a significant (a = 0.05) parameter for the bias but with no systematic
pattern. The expression in square brackets in the NIOH-1 model (Table 1) is termed
the configuration factor (Edwards and Furber, 1956). This factor was varied by
using three different values for the starting length, LQ, each corresponding to one of
the three disks. The starting length is, by definition, the distance from where a
possible air velocity boundary layer begins to develop to the border of the liquid in
632
A. Lennert el al.
18
15
y = -0.11+/-0.11+(1.14+/-0.02)x
R-squared = 0.99
u
3
j
(0
2
9
CO
o
6 Ul
3 -
6
9
12
Evaporation rate (Balance)
18
Fig. 3. The evaporation rate (mmol s 1 m 2) calculated from loss of mass from the vessel vs. the
evaporation rate calculated from concentration measurements in the exhaust duct. D , H , and • denote
low (0.17 m s~'), medium (0.43 m s" 1 ), and high air velocity (0.70 m s~') respectively. The identity line
is dotted and the line of linear regression is solid.
the direction of the air flow. The configuration factor was found by numerical
quadrature as the length of Lo was not afixedvalue due to the disks. The numerical
quadrature was performed by a Romberg algorithm (Software: Mathcad 6.0). The
configuration factor ranged from 2.55 (no disk) to 1.95 (large disk). Within a given
scenario and for a given compound (nine cases) 91% of the variation in the
evaporation rates was explained by the configuration factor.
For the GRAY-model (Fig. 4b) and the BAU-model (Fig. 4c) predicted and
experimental evaporation rates were generally in close agreement. However, at low
air velocity the models underestimated the evaporation rates (Table 3). The
Mackay-model (Fig. 4d) and the SUBEC-model (Fig. 4e) generally underestimated
the evaporation rates. The bias was found to be negatively correlated with the air
velocity (Table 3). As observed from Fig. 4f (and Table 3) the EPA (USA) model
strongly underestimated the evaporation rates for all three levels of air velocity. For
all the models the air velocity influenced the bias more than the vapour pressure or
diameter of the disk.
A new simple evaporation model denoted NIOH-2 (Table 1) was generated by a
multiple linear regression analysis on measured evaporation rate against the
configuration factor, air velocity, and vapour pressure. This new model explained
most of the variation in the measured evaporation rates (R2 = 0.99). The parameters
GRAY'S MODEL
(a)
BAU MODEL
NIOH-1 MODEL
R-squared o 0.98
0
2
4
6
8
10
12
Experimental evaporation rate
14
16
0
2
4
6
8
10
12
14
16
0
2
Experimental evaporation rate
4
6
8
10
12
Experimental evaporation rate
14
16
MACKAY'O M O D E L
(8)
y-0.40W-0.18+(0.64*M>.03)x
R-squared a 0.9S
SUBTEC MODEL
EPA ( U S A ) M O D E L
y . 1 4 W - 0 . 7 * ( 0 . 2 4 W - 0 . 0 1 )x
R-squared o 0.95
y-O.44*/-O.32*(0.71 W-0.06)x
R-squared o 0.96
3.
|
12
0
2
4
6
8
10
12
14
Experimental evaporation rate
16
0
2
4
6
8
10
12
14
Experimental evaporation rate
16
0
2
4
6
8
10
12
Experimental evaporation rate
14
16
Fig. 4. (a-f) Performance of six different evaporation models tested under three different air velocities. • air velocity 0.70 m s '; 12) 0.38 m s '; •
The evaporation rates are listed in mmol s" 1 m~ 2 . The identity line is dotted and the line of linear regression is solid.
<0.08 m s"
634
A. Lennert et al.
Table 3. Regression analysis on experimental vs. predicted evaporation rates for six different evaporation
models
Air velocity
(ms-1)
0.08
0.38
0.70
GRAY
BAU
O.75±O.O5
0.96±0.08
1.00±0.09
0.42±0.03
0.82±0.06
1.00±0.09
Evaporation model
Mackay
SUBTEC
0.42±0.03
O.59±O.O5
O.65±O.O6
0.66±0.05
0.77±0.06
0.74±0.07
EPA (USA)
NIOH-1
0.16±0.01
0.23±0.01
0.25±0.02
0.85±0.02
0.77±0.02
0.71 ±0.02
The slopes±SD for the regression lines are listed against the level of air velocity used for the
experiments. All regression lines have an intercept not significantly different from zero (a = 0.05).
estimated from the regression analysis are listed in Table 1. The correlation between
the measured and predicted evaporation rates is given in Fig. 5 together with the
orthogonal regression analysis (Mandel, 1984) and the line indicating a perfect
match. Figure 5 shows that the discrepancies between experiments with low vapour
pressure and low air velocity, and experiments with high vapour pressure and high
air velocity fit equally well in the correlation. This indicates that the temperature
sensors were placed sufficiently close to the surface of the liquid. That is the
temperature used in the models must have been close to the actual surface
temperature. The NIOH-2 model was also compared to evaporation rates obtained
under laminar air flow conditions in a test duct (Nielsen et al., 1995). The result of
the orthogonal regression analysis (Mandel, 1984) on the measured evaporation
rates against predicted values (NIOH-2) is given in Fig. 6 together with the perfect
agreement line. The performance of the NIOH-2 model was compared to all the
evaporation models tested by linear regression analysis on data obtained under
laminar and turbulent air flow conditions (Table 4).
In general the spatial distribution of air pollutants in the test chamber did not
depend on the type of solvent. However, the distribution was sensitive to the
different air flow patterns. In the low air velocity case, the highest steady-state
concentrations were observed in the negative x-direction and the lowest
concentrations were in the positive x-direction. For the medium and high air
velocity cases, the distribution shifted towards high concentrations in the positive xdirection and low concentrations in the negative ^-direction.
To illustrate the performance of the contentration distribution model suggested
by Scheff et al. (1992) (Table 2) a contour plot for estimated concentrations are
given in Fig. 7. Also given in the plot are experimental data obtained from the
experiments with MEK as the solvent at medium air velocity and no disk. For the
model, data are required on the source strength, the coefficient of turbulent
diffusion, and the air velocity. In this study measured source strength (evaporation
rate times area of evaporation surface) was used directly, while data on the turbulent
coefficient of diffusion and the air velocity were obtained from nonlinear regression
analysis (SYSTAT software, 1800 Sherman Ave, Evanston, IL 60201-3793). As
input for this analysis, steady-state concentrations were used, measured at four
positions (measuring points Nos 4, 5, 8, and 9) located on the line determined by
y = 0 and Z = 0.07 m. The convergence criterion used for the analysis was a
minimum of the squared residual. The experimental data on the air velocity were not
used in the nonlinear regression analysis although data were available. This
Evaporation and concentration distribution models
635
Turbulent air flow
ID
a//
14 - .y=(1.04+/-0.01)x
R-squared = 0.99
/''
//
//
/
12
CD
//
J
//
/'
/'
//
//
La.
g 10
2?
CO
8
CD
T3
CD
O
TO
6-
/
am
42
0 -/ \
f
I
I
I I I I I I I I I i I i
4
6
8
10
12
14
16
Experimental evaporation rate
Fig. 5. The correlation between the NIOH-2 predictions and the measured evaporation rates in the test
chamber. • , |3 , and • denote low (0.17 m s~'), medium (0.43 m s~'), and high (0.70 m s~') air
velocity respectively. The evaporation rates are listed in mmol s ' m 2 . The identity line is dotted and
the line of linear regression is solid.
approach was made because the predited air velocity was used for validating the
physical basis of the model. For futher details see below (Discussion). The results of
the nonlinear regression analysis and the experimental source strength were used as
input for the model under test. The concentration distribution generated was
validated against the concentrations measured at the four poits mentioned
previously (on the line y=0, Z = 0.07 m) and the other eight points in the test
chamber. It is recognized that it may be difficult to evaluate the performance of the
model from the data presented in Fig. 7 (??). Therefore, maximum, minimum, and
average deviation (as a percentage of absolute values) between the experimental and
the estimated concentration are given in Table 5. Also listed in Table 5 are data on
A. Lennert el al.
636
Laminar air flow
20
•
y=-0.45+/-0.37+(1.22+/-0.05)x
R-squared = 0.83
n
16
&
CO
o
co 1 2 ••
o
Q.
to
CD
f
Q.
4 -•
8
12
16
Experimental evaporation rate
20
Fig. 6. The performance of the NIOH-2 model for data obtained in a test duct under laminar air flow
conditions. D, [3 , and • denote low (0.17 m s~'), medium (0.43 m s~'), and high (0.70 m s~') air
velocity respectively. The evaporation rates are listed in mmol s~' m~2. The identity line is dotted and
the line of linear regression is solid.
estimated turbulent coefficients of diffusion and air velocity. Neither the type of
solvent nor the size of the disk had a significant influence on the estimated coefficient
of diffusion or the estimated air velocity (a = 0.05). However, the coefficient of
diffusion was sensitive to the level of air velocity (a = 0.05).
The concentration model suggested by Roach (1981) requires data on the source
strength, the coefficient of diffusion, and the air flow rate to estimate concentrations
in air. The data on air flow rate, and coefficient of diffusion were obtained from
nonlinear regression analysis (SYSTAT software). The convergence criterion used
for the analysis was a minimum of the squared residual. The experimental data on
the air flow rate were not used in the nonlinear regression analysis although they
Evaporation and concentration distribution models
637
Table 4. Results from an analysis of linear regression on predicted evaporation rates against measured
evaporation rates in laminar or turbulent air flow
GRAY
Laminar air flow
Slope 1.82±0.03*
R2
0.86
Turbulent air flow
Slope
1.01 ±0.04
R2
0.96
Evaporation models
Mackay
SUBTEC EPA (USA)
NIOH-1
NIOH-2
1.75±0.03
0.77
1.11 ±0.07
0.85
1.39±0.03
0.85
0.38±0.13
0.80
1.04±0.02
0.97
1.21 ±0.05
0.83
1.01 ±0.06
0.92
0.64±0.03
0.95
0.71 ±0.06
0.96
0.24±0.01
0.95
0.70±0.02 1.04±0.01**
0.98
0.99
BAU
All regression lines had intercepts not significantly different from zero (a = 0.05).
* Uncertainty for the slope (Mandel, 1984).
** Note that these values were obtained from regression on data used for generating the NIOH-2
model.
were available. This approach was chosen because the predicted air flow rate was
used to validate the physical basis of the model. From the validation, the typical
estimated values of Q exceeded 105 m 3 s~' compared to the actual value of
5 x l O ~ 2 m 3 s ~ ' . For the coefficient of diffusion estimated values exceeded
10 4 nT2 s „-! compared to 1 m 2 s ' reported for typical occupational settings
(Scheff et al., 1992).
2-0
Fig. 7. The concentration distribution given as a contour plot was calculated from the model suggested by
Schen~<?(a/. (1992) using 5=1.42 gm" 1 , 0 = 0.22 m2 s , u = 0.18 m s" 1 andZ = 0.07 m. * indicates an
experimental value. The X- and K-axes are scaled to equal the size of the test chamber.
638
A. Lennert et al.
Table 5. Estimated parameters of the model suggested by Scheff el al. (1992) for a source of known
strength
Experimental air
velocity (m s" 1 )
0.08
0.38
0.70
Model performance in terms
of concentration in air
Average of
Range in
deviation (%)
deviation (%)
52±2
56±2
54±2
- 8 7 to 62
- 2 8 6 to 79
- 2 0 7 to 37
Model predictions in terms
of D and U
Air velocity
Coeff. of. diff.
D (m 2 min~')
C/(ms"')
O.3O±O.O3
0.26±0.17
0.25±0.03
-0.23±0.04*
0.26±0.11
0.19±0.03
The deviation, as a percentage, was calculated as the difference between the measured and predicted
concentration with respect to the measured concentration. The average deviation was calculated from
absolute values. The range in deviation is given with a sign.
* A negative air velocity indicate air flow in the negative x-direction.
For the box-model (Table 2), experimental data on source strength and air flow
rate in the test chamber were used to predict the air pollutant concentration at
steady-state. The average deviation was 18±3% for the low air velocity, 13±6% for
the medium air velocity, and 4±7% for the high air velocity. The location and
magnitude of the largest deviations were sensitive to the air flow pattern in the test
chamber. In the low air velocity case, the largest deviation was found at measuring
point No. 8, and at medium and high air velocities the largest deviation was found at
measuring point No. 4. In the measuring points with the largest deviation, the boxmodel underestimated the pollutant concentration.
DISCUSSION
For a vessel containing a solvent the size of the boundary layer at the surface is
important for the resistance to evaporation. At least two types of boundary layer
exist: one for the air velocity and one for the concentration. For an increased air
velocity the thicknesses of both boundary layers are reduced and the evaporation
rate increases. As the level of turbulence in the air flow is increased turbulent
diffusion of pollutants becomes more and more important compared to laminar
diffusion (Coulson and Richardson, 1993).
The semi-empirical GRAY-model was developed in a test duct probably with
laminar flow at low air velocities and with turbulent flow at high air velocities
(Nielsen et al., 1995).
The GRAY-model offered the best performance at high and medium air
velocities (Table 3), and model predictions improved (less bias) as air velocity
increased. In the low air velocity case this study indicated an increase in model bias
towards low values. For laminar airflowin a test duct Nielsen et al. (1995) observed
a bias towards high values using the GRAY-model (Table 4). At low air velocity
(less than 0.2 m s~') the bias was moderate, but increased as air velocity increased
to reach values similar to those with medium and high air velocities. This
observation indicates the presence of some turbulence in the test chamber even at
low air velocity.
The BAU-model was developed in a test duct probably with air flow properties
similar to those prevailing in the experiments used to develop the GRAY-model
(Nielsen et al., 1995). The performance offered by the BAU-model was best at high
Evaporation and concentration distribution models
639
air velocity (Table 3). This observation may suggest that the model was probably
generated under air flow conditions similar to those in the high air velocity case but
different from those in medium and low air velocities. At laminar air flow conditions
Nielsen et al. (1995) observed a similar pattern in bias as for the GRAY-model.
These observations support the previously mentioned air flow properties concerning
turbulence in the test chamber even at low air velocity.
The Mackay-model was developed under field conditions in open air for air
velocities up to 6.8 m s~' (Mackay and Matsugu, 1973). In the test chamber the
performance of the Mackay-model was poor for the three air velocities tested
(Table 3), but under laminar air flow conditions a fair agreement between measured
and predicted evaporation rates was observed for all three air velocities (Nielsen,
pers. commun.). Considering the experimental conditions used by Mackay and
Matsugu it seems reasonable to assume that air turbulence was present during the
experiments. Therefore, the observed difference in the behaviour of the model in the
test duct and the test chamber was unexpected.
The SUBTEC-model was developed to predict the evaporation rate from a
surface exposed to an air flow created by an orifice above the surface. In the present
test chamber study, with mainly tangential air flow, model predictions were biased
towards low values (Table 3). For laminar air flow conditions in a test duct Nielsen
et al. (1995) observed the SUBTEC-model to be biased towards high evaporation
rates (Table 4). The experimental data obtained are inconsistent with data reported
from the test duct study and further research is needed.
The origin of the EPA (USA) model is uncertain (Braun and Caplan, 1989). The
EPA (USA) model strongly underestimated the evaporation rates for all three air
velocities (Table 3). For laminar air flow conditions Nielsen et al. (1995) consistently
observed that the EPA (USA) model strongly underestimated the evaporation rates
for all three air velocities (Table 4). In order to discuss the behaviour of this model
further, details of the experimental set-up used for its development are required.
The NIOH-1 model was developed for laminar air flow conditions and validated
for air velocities ranging from 0.17 to 0.70 m s~' (Nielsen et al., 1995). No data seem
to be available in the literature on the performance of this model under conditions
similar to those found in workplaces. From the present study data obtained at a low
air velocity were in fair agreement with predictions made using this model. However,
as the air velocity increased the model became more and more biased towards low
values. If the model is to be used in the workplace some modifications are needed.
The NIOH-2 model was developed by a multiple regression analysis performed
on the data obtained. The model had a high validity in terms of the regression
coefficient (/?2 = 0.99). For laminar air flow the NIOH-2 model was superior to the
GRAY-model in predicting the evaporation rates, while the NIOH-1 model was
superior to the NIOH-2 model (Table 4). In the workplace the air flow is usually
turbulent and therefore the evaporation model used should have a high performance
under such conditions. Due to its simplicity and high performance at a wide range of
test conditions the NIOH-2 model is recommended for application at workplaces as
an alternative to the GRAY-model. It has to be remembered that the NIOH-2
model is yet to be validated in the workplace.
The theoretically based model suggested by Scheff et al. (1992) was developed by
solving the differential equation (Seinfeld, 1986) describing the concentration
640
A. Lennert et al.
distribution obtained from a source of strength at the origin in a fluid with a velocity in
the x-direction. In general the contour plots (see example in Fig. 7) reproduced the
measured concentration distribution, with the best agreement being at measuring
points Nos 4, 5, 8, and 9, however, it should be noted that data for the model
parameters were generated from concentrations obtained at these four points. The
average deviation seemed acceptable (approx. 50%, Table 5) for practical
applications. However, for some of the sampling locations deviations were observed
towards low concentrations. This is an uncomfortable situation especially when
concentration prediction is made for chemicals of high health risk. In a field study,
Scheff et al. (1992) applied the model to emissions from open-top vapour degreasers
and reported that, in general, the model reproduced the measured concentrations.
However, from the data given by Scheff et al. (1992) it is difficult to compare the
performance of the model in that study with the performance in this study. The
estimated diffusion coefficients (Table 5) appeared insensitive to the actual air velocity
in the test chamber. The direction of the estimated air velocity reflected correctly the
actual air flow direction but the magnitudes did not agree with the measured local air
velocity. It should be noted that the air velocity estimated by Scheff et al. (1992)
represents an average for the cross-section of theflowregion. The calculated diffusion
coefficients were comparable to data reported previously for workplaces (Scheff et al.,
1992).
The theoretically based model suggested by Roach (1981) was developed by
solving Fick's first law of diffusion for a source at the centre of a hollow sphere
(radius R). Air was supplied and exhausted all over the surface of the sphere. Fick's
law was solved by assuming spherical symmetry. The model predicted a
concentration distribution with high concentrations close to the source; the
concentration decreased as the distance from the source increased. Model
predictions were unrealistic probably because of the asymmetric flow pattern.
The performance of the box-model (Table 2) was expected to improve with
increase in mixing of air and pollutant in the test chamber. Accordingly the best
agreement was observed in the high air velocity case. In general the model had a
high performance but at measuring points close to the source in the air flow
direction the model predictions were biased towards low values. However, the
average deviations were less than for the model by Scheff et al. (1992). The large
deviations found at measuring points close to the source in the direction of the air
flow may, for all air velocities, indicate insufficient time for the pollutant to be
diluted to a level comparable to the other measuring points. The large range in
deviations found at measuring points close to the source may suggest insufficient
time for the pollutant to become mixed with ambient air. The box-model is
commonly used for risk assessment of workers' exposure to air pollutants
(Heinsohn, 1991). This study indicates that caution should be used in applying
the. model due to the observed bias towards low concentrations.
CONCLUSION
From the six different evaporation models investigated in this study the GRAYmodel appeared superior for turbulent air flow and the NIOH-1 model for laminar
flow conditions. For application in occupational environments the new simple
Evaporation and concentration distribution models
641
NIOH-2 model is recomended. This model has a resonable performance for laminar
air flow and a performance comparable to the GRAY-model for turbulent air flow.
From the three models tested in this study for predicting the concentration
distribution of air pollutant the box-model offered a fair performance, but care
should be taken in using the model due to the bias towards low concentrations for
some locations.
Acknowledgements—The authors gratefully acknowledge the financial support given by the Danish
Research Academy and the Danish Working Environment Foundation. Thanks are also given to Ms
Inger Johansen for assistance with the experiments.
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