Comparison of Different Collection Efficiency Models For Venturi Scrubbers
Comparison of Different Collection Efficiency Models For Venturi Scrubbers
Comparison of Different Collection Efficiency Models For Venturi Scrubbers
(2)
,
1.5
16, 400
1.45
d
t
d R
V
+
(3
)
( )
d d o
M
(4)
2.1.2 Calverts model
As in many of the available models for the design of venturi scrubbers, the Calvert et al
(1972) model, is based on the prediction of the penetration (Pt
d
) for a given particle diameter.
Penetration is defined as the fraction of particles (in the exhaust stream) that passes through the
scrubber uncollected. Penetration is the opposite of the fraction of particles collected (i.e. collection
efficiency,
d
), and is expressed as shown in Equation 5. The total penetration can be calculated as
shown in Equation 6.
1
d d
Pt
(5)
,
( )
o d d
Pt Pt M
(6)
According to Calvert et al (1972), the penetration can be calculated by the following Equation:
0.7
0.49 1
exp 0.7 1.4ln
55 0.7 0.7
p
L G L d
d p
G G p p
K f
Q V d
Pt K f
Q K f K
1 + _
+ +
1 ' ;
+
1 , ]
(7
)
where Q
L
and Q
G
are the liquid and gas volumetric flow rates respectively (dimensionless), V
G
is the
gas velocity at the throat (cm/s),
L
is the liquid density (g/cm
3
),
G
the gas viscosity (poise), and f is
a correlative parameter that ranges from 0.2 to 0.7. It should be noted that that for the correlation
parameter (f), Cooper and Alley (2004), suggest that the value 0.25 should be used for hydrophobic
particles, while 0.5 should be used for hydrophilic particles. The inertial impaction parameter (K
p
) is
given by the following Equation (please note that the first part in Equation 8 is identical to Equation
2 presented above):
2 2
, ,
9 9
p p p d w a p d
p
G d G d
C d V d V
K
d d
(8)
with d
p
in cm,
p
in g/cm
3
, V
p,d
the particle velocity relative to the droplet velocity, in cm/s (thus in
effect it equals V
t
),
G
in poise,
w
the density of water (in g/cm
3
) and d
a
the particles aerodynamic
diameter (in cm). The mean droplet diameter (d
d
) for standard air and water in a venturi scrubber, is
given by another form of the NukiyamaTanasawa relationship (in m) as follows:
( )
0.45
1.5 0.5
0.5
58, 600
597 1000
L L
d
G L G
L
Q
d
V Q
_
_ _
+
, ,
,
(9)
where the liquid surface tension (dynes/cm), and
L
the liquid viscocity (poise).
2.2 Pressure drop
The pressure drop in venturi scrubbers can be calculated by the model developed by Young
et. al. (1977) by the following equation:
( )
2 4 2 2
1 2 X X X
Q
Q
V P
G
L
G L
+
,
_
(10
)
where P the pressure drop (dyne/cm
2
), and the dimensionless throat length, which can be
calculated by Equation 11 (where l
t
the venturi throat length, in cm). The drag coefficient, C
D
for
droplets with Reynolds numbers, Re, from 10 to 500 can be obtained by Equation 12 (Cooper and
Alley, 2004). The Reynolds number can be calculated using Equation 13 (where
G
the gas density,
in g/cm
3
).
3
1
16
t D G
d L
l C
X
d
+
(11)
,
( )
1/3
24 4
Re
Re
D
C +
(12)
,
Re
d G g
G
d V
(13
)
3. RESULTS AND DISCUSSION
As has been mentioned above, some of the best educational textbooks for air pollution
abatement technologies (e.g., Cooper and Alley, 2004; Wang et al 2004; Theodore, 2008), consider
the models chosen for the development of the software presented herein, useful in the training of
future engineers in the design of venturi scrubbers. Naturally, these models are not without flaws.
Further, of the numerous models developed in the past 30 years, some were bound to give more
accurate predictions. Thus, a short discussion, comparing the models used in this paper, with other
models reported in the literature is warranted.
Calvert et al (1970) presented the first model for pressure drop in venturi scrubbers,
however, they neglected wall friction and momentum recovery in the divergent section, so other
researchers tried to improve this model. Boll (1973) solved simultaneous equations of drop motion
and momentum exchange for variable cross section ducts with acceptable results, except for very
high and low liquid to gas ratios, where it did not show agreement with the experimental data.
Azzopardi and Govan (1984) considered momentum losses due to accelerating droplets entrained
from the film and the interfacial drag between the fast moving core and the slower moving liquid
film. However, they had little successes with this procedure (Nasseh et al, 2006). Pulley (1997)
carried out various experiments and suggested more effective variables such as drop size,
entrainment at liquid injection and entrainment and deposition along the venturi length. He also
compared pressure drop predictions from various models (amongst these were the models
developed by Young, Boll and Azzopardi) and concluded that the corrected proposed model of
Azzopardi et al. (1991) gave a better prediction of pressure drop for a wider variety of data.
Goncalves et al (2001) studied a large number of models for the prediction of pressure drop in
venturi scrubbers and concluded that all of them must be used with caution.
In regards to collection efficiency, Rudnick et al (1986), vigorously compared the models
developed by Calvert et al (1972), Boll (1973) Young et al (1978) and concluded that the model of
Yung et al (1978) is probably best for most applications because it is an explicit algebraic
expression and gave the best results of the models tested. The model of Calvert et al. (1972), while
also an explicit algebraic expression (and thus easy to use), is very dependent on the choice of the
correlative parameter, f, and thus should be used with caution. One of the latest attempts at
modeling the collection efficiency was undertaken by Concalves et al (2004) who studied the
atomization of the liquid jets injected transversally to a gas stream in a venturi scrubber. A
mathematical model was developed to predict the trajectory, breakup and penetration of the liquid
jets. With this model for liquid jet dynamics, Concalves et al (2004) calculated the spatial
distribution of droplets for the case where liquid was injected through a single orifice in a
rectangular venturi scrubber.
The software presented herein (Figure 3) enables the calculation of a venturi scrubbers
efficiency and pressure drop for the theoretical models described in section 2. The parameters that
are necessary in order to carry out the design are the following: (i) Gas and liquid characteristics
(temperature and pressure - viscosity and density are calculated by the software), (ii) Particle
characteristics (particle distribution and density) and (iii) Process characteristics (volumetric flow
rate and particle loading). Further, when using the Johnstone et al (1954) model the user must
choose a value for the correlation coefficient k (ranges between 0.10.2 acf/gal), while for the
Calvert et al (1972) model the user must know/decide whether the particles that need removing are
hydrophobic or hydrophilic, as this determines the value of the correlation parameter, f (0.25 and
0.5 respectively).
Figure 3: Graphic interface of the software developed Calvert et al (1972) model
FIGURE 4: Efficiency as a function of the
liquid-to-gas ratio
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm,
V
G
=32.68m/s, d
aj
=2.5, 7.5, 15, 35, 60,
80m, m
j
=8, 18, 23, 23, 20, 8%
f=0.5 (Calvert model)
k=0.2acf/gal (Johnstone model)
FIGURE 5: Efficiency as a function of the
gas velocity at the Venturi throat
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm, f=0.5,
Q
L
/Q
G
=1L/m
3
,
d
a
=2.5, 7.5, 15, 35, 60, 80m,
m
j
=8, 18, 23, 23, 20, 8%
f=0.5 (Calvert model)
k=0.2acf/gal (Johnstone model)
Figure 4 presents the predicted efficiency as a function of the the liquid-to-gas ratio for the
models included in the software that was developed in the present work. It can be observed that the
Johnstone model predicts much higher efficiencies even at low ratio values. Moreover, the
difference between the lowest and highest ration values is small, compared to the predictions
obtained using Calverts model. Figure 5, presents the predicted efficiency as a function of the gas
velocity at the venturi throat, In essence, the Johnstone et al (1954) model fails to make any
predictions (predictions close to 100%) regardless of the changes in the throat velocity. This may be
attributed to the large particle diameters chosen for these diagrams. This is better demonstrated in
Figure 6, which shows a curvature in the Johnstone model for particles up to 2m, while Calverts
model reaches peak values at 7m. It should be noted that in all three Figures, Calvert et al (1972)
model predictions are a lot closer to the curve one would normally expect. Figure 7 shows the
predicted efficiency as a function of the the liquid-to-gas ratio, Figure 8, presents the predicted
efficiency as a function of the gas velocity at the venturi throat, and Figure 9 the efficiency as a
function of particle diameter, in Calverts model, for different correlative parameter (f) values,
demonstrating the models dependence on it. This is in accordance to the available literature (see
above) and emphasises the need for caution when using the model.
FIGURE 6: Efficiency as a function of
particle diameter
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm,
V
G
=32.68m/s
f=0.5 (Calvert model)
k=0.2acf/gal (Johnstone model)
FIGURE 7: Efficiency as a function of the
liquid-to-gas ratio Calverts model
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm,
V
G
=32.68m/s
d
a
=2.5, 7.5, 15, 35, 60, 80m,
m
j
=8, 18, 23, 23, 20, 8%
4. CONCLUSIONS
In concluding, the software presented herein offers an easy way to calculate the efficiency
and pressure drop of a venturi scrubber. Some of the most widely used theoretical models for
venturi design have been incorporated in this software. Thus, a comparison of the results predicted
by the models with experimental results, will allow the user to either determine which model
provides the most accurate predictions or to choose the configuration most adapted to an operating
condition. However, in its current state, the software will prove more useful to educators and/or
students of air pollution abatement devices.
A number of improvements could be done in the future to make the software more efficient
by:
(i) Allowing the user to enter the desired collection efficiency or pressure drop in order to
obtain the proposed liquid to gas ratio and/or gas entrance velocity,
(ii) Introducing additional models for the calculation of collection efficiency (e.g. those
developed by Boll (1973), Young et al (1977), Concalves et al (2004)),
(iii) Introducing additional models for the calculation of pressure drop (e.g. those developed by
Boll (1973), Pulley (1997)).
Furthermore, one may also try to incorporate additional wet scrubbing configurations (e.g.
spray towers).
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FIGURE 8: Efficiency as a function of the
gas velocity at the Venturi throat
Calverts model
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm,
Q
L
/Q
G
=1L/m
3
, d
aj
=2m
FIGURE 9: Efficiency as a function of
particle diameter Calverts model
P=1atm, T=80
o
F,
L
=62.22lb/ft
3
,
L
=0.86cp, =71.7dynes/cm,
Q
L
/Q
G
=1L/m
3
, V
G
=50m/s
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