THREE PHASE SPARGED REACTORS SOME DESIGN ASPECTS
A.B. PANDIT and J.B. JOSHI*
Department of Chemical Technology
University of Bombay
Matunga Road, Bombay - 400 019, India
CONTENTS
1.
2.
3.
Abstract
Introduction
Fractional Gas Hold-up
2.1. No Liquid Flow
2.7.7. Effect of Superficial Gas Velocity
27.2. Effect of Average Particle Size
2.7.3. Effect of Solid Phase Hold-up
2.1.4. Comparison with Previous Work
2.2. Presence of Liquid Flow
2.2.7. Effect of Superficial Gas and Liquid Velocities
2.2.2. Effect of Particle Size
2.2.3. Effect of Solid Phase Hold-up
Critical Gas Velocity for the Suspension of Solid Particles
3.1. Introduction and Previous Work
3.2. Mathematical Model
3.3. Effect of Terminal Settling Velocity of a Particle
3.4. Effect of He/T Ratio
3.5. Effect of Solid Phase Hold-up
3.6. Effect of Column Diameter
3.7. Comparison Between Predicted and Experimental Values
3.7.1. Suspension of a Single Particle
3.7.2. Suspension of Multiple Particles
3.8. Effect of Superficial Liquid Velocity on VGC
3
3
5
5
5
8
19
20
22
22
24
24
24
24
25
27
28
29
29
31
31
33
34
To whom correspondence should be sent
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
4.
Concentration Profiles of Solid Particles
4.1. Axial Concentration Profiles
4.1.1. Previous Work
4.1.2. Mathematical Model
4.1.3. Settling Velocity of a Particle
4.1.4. Solid Phase Axial Dispersion Coefficient
4.2. Radial Concentration Profiles
5. Mixing
5.1. Introduction
5.2. Mathematical Model
5.3. Effect of Superficial Gas Velocity
5.4. Effect of HC/T Ratio
5.5. Effect of Column Diameter
5.6. Effect of Terminal Settling Velocity of a Particle
5.7. Effect of Solid Phase Hold-up
5.8. Comparison Between Predicted and Experimental Values of
Mixing Time
5.9. Axial Mixing in the Liquid Phase
6. Heat Transfer
6.1. Introduction and Previous Work
6.2. Mathematical Model
6.3. Discussion
6.4. Model Predictions
7. Worked Examples
8. Conclusions
9. Recommendations for Future Work
10. Nomenclature
11. References
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
36
36
36
38
39
41
43
50
SO
SO
SI
54
54
54
58
58
60
61
61
61
63
65
66
77
78
79
82
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
Abstract
This review evaluates the present state-of-the-art on the estimations
of parameters necessary for the design of three phase sparged reactors.
The published information has been scrutinised and the apparent anomalies
in the reported data have been brought out with plausible explanations.
In order to understand the missing links in the reported literature, experimental investigation was undertaken. Fractional phase hold-ups, solid
phase concentration profiles, critical superficial gas velocity for the suspension of solid particles and mixing time have been measured using 100,
200 and 385 mm i.d. three phase sparged reactors. The particle size was varied in the range of 40-2000 microns and the superficial gas velocity was
varied in the range of 1 to 720 mm/s.
The hydrodynamic behavior of three phase sparged reactors has been
analysed. The complex relationship between the gas hold-up and the particle
size has been explained. A criterion has been developed for the prediction
of critical superficial gas velocity for the suspension of single as well as
multiple particles. Axial and radial concentration profiles of the solid phase
have been measured. A new rational correlation for the solid phase dispersion
coefficient has been presented.
A mathematical model has been developed for the prediction of liquid
phase mixing time. The model has been verified. On the basis of liquid
circulating velocity a rational correlation has been developed for the wall
heat transfer coefficient. The occurrence of maximum in the value of heat
transfer coefficient has been explained.
Specific recommendations have been suggested for the future work.
Worked examples are given which illustrate the design procedure.
1. Introduction
Three phase sparged reactors are widely used in industry with solid particles as a catalyst or a reacting species. These units are simple in construction
and operation, provide fairly high values of heat and mass transfer coefficients and offer flexibility for the liquid phase residence time. Three phase
sparged reactors are particularly suited when a precise temperature control
is desired.
Three phase sparged reactors have received considerable attention (in
the past and substantial amount of data are available in the published literature on the individual phase hold-ups, mass and heat transfer coefficients
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2. No. 1, 1984
Three Phase Sparged Reactors
and the extent of mixing). 0stergaard /34/, Shah /43/, Epstein /12/ have
presented excellent state of the art reviews.
A careful examination of the published information reveals the following:
(i) Empirical correlations have been developed for the estimation of
individual design parameters. It is well known that the bubble diameter
and the terminal velocities of bubbles and particles are the most important
parameters which govern the phase hold-ups, mass and heat transfer coefficients and mixing in the liquid as well as in the gas phases. There is a
need to evolve a coherent theme to explain the performance of three phase
sparged reactors.
(ii) The variation of fractional gas-hold-up with respect to the particle
diameter is peculiar. A clear understanding of this relationship is desired.
(iii) For the prediction of minimum superficial gas velocity for complete suspension of solid particles, a rational approach is needed which
will hold over a wide range of column diameter, particle diameter, density
and concentration.
(iv) It appears that the settling velocity of solid particle is substantially
different from the terminal settling velocity. While explaining the axial
concentration profiles for solids there has been considerable discrepancy
in selecting the values of settling velocities. The radial concentration profiles
of solids also have not been satisfactorily explained.
(v) It is known that the bed-wall heat transfer coefficient (hw) has
optimum values with respect to the particle size and the superficial gas
velocity. This behavior needs to be understood. Further, the equation for
hw should have general applicability and should hold for bubble columns
(no solids).
(vi) The presence of solid particles may enhance or reduce the value
of liquid phase axial dispersion coefficient. It would be desirable to evolve
a rational criterion for the above behavior.
In order to explain the above observations and to develop rational correlations for the estimations of design parameters, better understanding
of the bubble-liquid and the particle-liquid interactions is needed. In this
review, the published information has been critically analysed to seek answers
to the above points. Measurements were also undertaken to bridge some of
the missing links in the available data.
Some specific suggestions have been made for future investigations.
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
2. Fractional Gas Hold-Up
2.1. No Liquid Flow
In the absence of liquid flow, Imafuku etal\\ 5/, Efremov and Vakhrushev
/10/, Kato et al /22/, Abou Al Hassan /!/, Kito and Shimada /26/, Ying
et al /47/ and Patwari /40/ have measured the fractional gas hold-up in
three phase sparged reactors. The range of variables covered in these studies
are summarised in Table 1. It can be seen from this Table that the maximum
column diameter used was 0.214 m and the maximum particle size employed
was 6000 microns. In order to cover a wider range of variables experiments
were performed using 0.1, 0.2 and 0.385m i.d. columns. Solid particles
of different sizes and densities were used (Table 2). A typical experimental
set-up is shown in Figure 1. Predetermined quantities of the desired particle
and water were added to the column. Fractional gas hold-up was measured
by noting the liquid height in the presence and absence of gas.
2.1.1. Effect of Superficial Gas Velocity
Figure 2 shows the values of fractional gas hold-up (eG) with respect
to superficial gas velocity (VG). Solid particles having different terminal
settling velocities (Vg^„) were used and the fractional solid phase hold-up
was also varied. For comparison, the fractional gas hold-up values for airwater system under otherwise identical conditions are also shown.
A very peculiar behaviour was observed in the case of all solid particles.
As the superficial gas velocity was increased from zero, the fractional gas
hold-up values compare well with that of air-water system till the solid
particles start getting suspended [Point A in Figure 2, 22 and 23], the slope
of the plot of eG versus VQ suddenly changes (reduces) and an increase
in the values of VG increase eG values marginally [eG o VG2S~°·05] till
all the solids are suspended [Point B in Figure 2, 22 and 23], At this stage
further increase in VG increases eG with a rate comparable to that of airwater system [eG α VG-4S±°·03 ].
Visual observations indicated that, when VG is in the vicinity of point
A, the fixed bed of particles starts moving in the form of lumps and get
shifted from one place to another at the bottom. Under these conditions
very large gas bubbles are formed which reduce the dependency of fractional
gas hold-up on VG. Qstergaard and Theisen /36/ have shown that the rate of
coalescence is very large near the point of incipient fluidisation.
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. 1,1984
Tliree Phase Sparged Reactors
^<u<y>
1
^H
SM/
*
0
/-N
_^
J
·»-
0
<a. «a.
W
ο
Μ
Ο
s
tt
II
ο
0.°
CO
Q>
Η-
(U
||
"o
(U
c
.9
"+*
CD
cn
%j
S
"b
1
1
1
CO
*
Ε
ίο
§"
m
M
^
-
<*.
s
S ™
Ό ία
0
^
c
c
o.
Io
«N
0
1
o
CO
0)
*
J
«(
1
o
l
2
σ
S
c
0
oo
C 3 O O O O O O
« Ο Ό * Λ * Ο Ο Ο Ο
«ovi»o»n«NOoo
<NCN<N<Mt-lt-OO
O
Ο
«o
O
<N
"0
0
1^
l>
l-H
«N
CD
E
"·α ^tI
,3
α
T5
m «N
ίο ο
Ο^τί^ίο«»?^·
oo^^c^^o^^r-*vO
<—t
<—t
Ό
~H
"
v-l
O
IO
ot
oo
1
χ
W
_
E
Ο
ID
H
00
c
o
Ο
VO «S ^i·
VO «M
rt
O t-H 0»
O
ts
2
u_
o'
I—1
•s
3
k.
0
4J
l
-^
2
—^
^
'S
ii
>
**
Qj
^L
C
CO
_^^
es
es
•^
5
|
^
c3
(*TJ
3
.Ξc3
εβ>
o
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Reviews in Chemical Engineering
A.B. Pandit and J.B. Joshi
<o
+
2
S
„
·*
2
-
f~
^
S?
<*
S"
Η
u <»'S
υ
°~
'
o s j. ^
J? -M ^ J,
^»
=ί χ,
«
Correlation
S
«
w
Q-
S
u
«
"ί
σ<
·*
+
^
υ
Ι?
S
rl
,°
*
.elie
>l>
5
«ί.
n^
Ξ>
^U
<i
«T «
ο
J. H
^
^
Ο
·
« T o
·—
n
1
10
^£-
ία
2«o
^
0
1
o
l
<u
m
= 1
I ««
o o o
o o o
•0
10
10
es r< 10
o" o
o ex
O
-H
10
o
o
10
es
sc
'C
0)
Q.
X
uj
P
^
^
0.
-σ
Ε
Η
10
T|-f~-H
^•rSi-l
^*~H
Ο
•-H
O O O
Ο Ό Ι —
O O O
O O O
Ο
oΌ ·-;
ΙΟ Ο
o
»H
C5 C3
O
*-i\ooo
-H «N rs
i-i\om
1
VO
rj^
*4
I
d>
3
Investigator
l—1
l
1
'S
^
—
Ό
β
0
0
2
5
ί
a
a
I
t
5
»
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1,1984
Three Pliase Sparged Reactors
TABLE 2
Survey of Particles Used in the Present Investigation
Size range
microns
Average particle
size (microns)
Density
(kg/m3)
Shape factor
53-«3
105-150
177-250
250-420
70
110
210
340
500
850
2000
2260
2260
2500
2500
2500
2500
2500
0.762
0.727
(0.5-1.0) x l O 3
(1.68-2.2) χ 103
Φ·ν
—
—
0.623
0.752
Terminal settling
velocity (mm/s)
8.5
12.5
50.0
76.0
104.0
134.0
164.0
With an increase in particle settling velocity, it can be seen from Figure 2A-F
that the point Ά' gets shifted to a higher value of superficial gas velocity.
Similarly, with an increase in the solid phase hold-up (es) the flatter portion
ΆΒ' gets extended over larger range (point 'B' gets shifted to higher values
of VG ) of superficial gas velocity.
2.1.2. Effect of Average Particle Size
Figures 3 and 4 show the variation of fractional gas hold-up with respect
to average particle size (dp). From Figures 3 and 4 it can be seen that the
variation in fractional gas hold-up with average particle size is somewhat
complex. For very small particles (Rep < 2) an increase in the average particle size was found to increase the fractional gas hold-up though somewhat
marginally. For the particles having intermediate range of Reynold's number
(2 < Rep < 300) an increase in the average particle size decreases the fractional gas hold-up. For larger particles (Rep > 500) again, an increase in
the fractional gas hold-up was observed with an increase in the average
particle size.
Kato et al /22/ have shown that the values of fractional gas hold-up
decreased with an increase in d p . It may be noted that the authors operated
in the intermediate range of particle size (100 to 180 //m) mentioned above.
Michelson and 0stergaard /32/ and Patwari /40/ observed an increase in
the value of eG with an increase in the average particle size in the range
1 to 8 mm. In this case the Rep value varies in the range of 325 to 7650
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
COLUMN
SAMPELING PORTS
R E T A I N E R CLOTH
c*
SIEVE PLATE
DISTRIBUTOR
PACKING FOR U N I F O R M
GAS D I S T R I B U T I O N
GAS INLET
DRAIN
ROTAMETER
BLOWER
(ίο)
TUBE FOR R A D I A L
MEASUREMENT OF SOLID
HOLD-UP
ΛΣ®
C O N D U C T I V I T Y PROBE -==!
Fig. 1. Experimental set-up
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
z;5
o ?»l °?n °9n 9
on
'jj p
*(*9)'dn-aioH
J Ssvo SIVMOIIDVUJ
! J
n
S
10
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
'dfl-tnOH SYO 1VNOI13VHJ
11
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1,1984
v»
<M
in
in
o
ία
o
•Μ
IM
Jliree Phase Sparged Reactors
ο
-*
C4
m
·IM
in
m
C4
ο
n
IM
ui
IM
IM
ο in ο
IM r- »IM
IM
M
m
o
in
IM
ο ι η ο ι η ο η ο ι η ο
S 8 S 5 " - - t » :
o
l
I
in
in
q
d
α
3l
o
S
S
·*·
c
o
u
t
ri
.9
O
O
O
O
O
O
O
O
O
o
dn-ΟΙΟΗ SV9 1VNOI13VMJ
12
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
ρ
Ο
S
.2
S
«·c
o
o
'tr
S
'S
in
C4
A
O
M
·
o
«·
*
O
«M
·
o
N
*
O
( * 3 ) ' dn-ΟΊΟΗ SV9 tVNOliDYHJ
13
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
and the observations are consistent with the behaviour shown in Figures
3 and 4.
In order to explain this complex behaviour, the knowledge of the effect
of particle size on the average bubble diameter and the bubble rise velocity
is essential. The published information on this subject is very limited. Kim
et al /23/ have indirectly shown that the bubble break-up by solid particles
can occur when the particle size is larger than half the bubble diameter
(dp > 2 mm). Henrikson and 0stergaard /14/ have reported with the measurement of V b „ in 2 dimensional column that increasing particle size from
0.2 to 1 mm increased Vboo by about 20 per cent which is likely to reduce
the fractional gas hold-up (eG ).
Michelson and 0stergaard /32/ observed two regimes of bubble behaviour:
the coalescence regime and the dispersion regime. They have studied the
effect of 1, 3 and 6mm dia spherical particles (e§ = 0.10) on fractional
gas hold-up. They have shown that the dispersion regime prevails at lower
VG and the coalescence regime at higher VG. The transition occurs at a
certain VGt. They also observed that the value of VGt decreases with a decrease in the particle diameter. Deckwer et al /8/ studied fractional gas
hold-up in paraffin wax/air system. The solid phase used was A12O3 of
size 5 |zm. The maximum superficial gas velocity used was 40 mm/s. The
fractional gas hold-up in the presence of such fine particles is marginally
less than that for two phase systems (in the absence of particles) at low
values of VG. He also has reported that the bubble size is reduced in the
presence of such a small particle and hence at high superficial gas velocities
(VG > 100 mm/s) the fractional gas hold-up values are likely to be higher
than those for gas-liquid systems. These observations confirm the behaviour
shown in Figures 3 and 4.
From the foregoing it appears that, at any given values of VG and eg,
when the particle size is increased, initially the average bubble diameter
slightly decreases (over a small range) and then increases. When the average
particle size exceeds a certain critical value (perhaps dB/2), the bubble diameter again decreases.
The above discussion is very qualitative in nature. In order to understand
the hydrodynamics of the three phase systems, it is very important that
the effect of particle diameter on the bubble diameter and rise velocity
is known. Since practically no information is available in the published
literature, a systematic investigation was undertaken. The average bubble size
was measured using chemical method. The details of the chemical method
have been discussed elsewhere [Sharma and Danckwerts /44/, Doraiswamy
14
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Cliemical Engineering
and Sharma /45/]. It essentially consists of measuring the effective interfacial
area and the fractional gas hold-up. The average bubble diameter is given by
the following equation:
6er
d B = -2
(2.1)
It may be noted that, in the chemical method, the liquid phase is an
aqueous alkaline solution of sodium hydroxide ( = 2 kgmole/m2). The
average bubble diameter in aqueous alkaline solutions is somewhat different
from that of air-water system under otherwise identical conditions. However,
as far as the effect of particle diameter on the bubble diameter is concerned,
the chemical method gives the desired information.
Figure 5 shows the effect of superficial gas velocity, average particle
size and the fractional solid hold-up on the average bubble diameter. It
can be seen from this Figure that, in the presence of fine particles (dp <
100 μιτι), the average bubble diameter is smaller than that obtained in the
absence of solids (bubble columns). Similarly, when the particle size is
relatively large (dp > 850 μηι), again the average bubble diameter is smaller
than that in the case of bubble column. However, in the intermediate range
of particle size, krger bubbles are produced as compared to those in the
absence of solid particles.
Figure SB clearly shows the effect of particle diameter at different superficial gas velocities. It can be seen from Figure SB that the average bubble
diameter (d ) decreases with an increase in dp (upto 100 μηι). A further
increase in d p increases d and a maximum value of d is attained at a
certain value of d p . It may be noted that, at all the three superficial gas
velocities, a maximum average bubble diameter was observed when the
particle size was about SOO μιη. When the average particle size is increased
beyond this critical value, d decreases gradually. It may be emphasized
that the effect of d p on d becomes less and less pronounced with an increase in the superficial gas velocity. This particular fact is consistent with
the experimental observation that the values of CG in the presence of particles tend towards the values of bubble column as the superficial gas velocity
is increased.
The second important parameter is the terminal rise velocity of a bubble
(Vb„). Darton and Harrison /?/ have measured Vb„ of bubbles (in the range
of 5-25 mm equivalent diameter) in the presence of 0.5 and 1.0 mm diameter
particles. The fractional solid hold-up was varied from 0.43 to 0.526. A
dramatic effect on V],«, was found in the presence of solids. For instance,
15
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1,1984
Three Phase Sparged Reactors
IΕ
.D
φ
E E
?
Ε Ε
s;
S ϊ£§ §
r»
ID
C
Ο
α>
II η π
>β >β >β
»
u
a
•s
s
Ο · Θ
r~
D
o 4J +*·-'
ο
η Ε »
Ε i
οο
5χ
•π
ο
>·
ΜM *- s
G ί
υ
>β
.3 §
Οm
10 ,
ι«t
*
Ο ~
σ
«*;
mK
III
a.
m
0
S
aneena ·«—
ο
3ΊββΠ9
•δ
Ι
«#UI
<
10
.5>
16
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
Vt,_ of 10 mm diameter bubbles decreased by a factor of 10 in the presence
of 0.5 mm particles and 47 per cent solid phase hold-up. Further, at the
same value of solid hold-up (50 per cent) V^» of 10mm bubble is about
50 per cent lower, in the presence of 1 mm particles as compared with
that in the presence of 0.5 mm particles. It may be emphasized that the
extent of the effect of solid particles on Vb„ strongly depends upon the
fractional solid phase hold-up. Darton and Harrison /?/ have pointed out
that when the value of es is below 0.35, there is no appreciable effect of
es on the values of Vt,«,. In the present work, the fractional solid hold-up
was always less than 15 per cent and it is reasonable to assume that the
value of Vb_ is unaffected by es. Nevertheless, the average bubble diameter
depends upon es and d p . Figure 6 shows the values of Vb„ with respect
to particle size and superficial gas velocity. The procedure for the calculation
of Vb„ is discussed below:
In the case of sparged reactors two regimes prevail. At relatively low
superficial gas velocities (approximately less than 50 mm/s) the bubbles
generated at the sparger, rise without coalescence and dispersion. The rise
velocity of bubbles almost equals the terminal rise velocity and the bulk
liquid flow is feable. In the heterogeneous regime, intense liquid flow is
developed which is upward near the centre and downward near the column
wall. The gas hold-up profile is parabolic with a maxima at the centre.
In this case, because of the liquid flow, the average rise velocity of a bubble
(with respect to the wall, V0) is much higher than the terminal rise velocity
(with respect to surrounding liquid, Vj,,») and is given by the following
equation:
V0 = f(V c ) + Vb_
(2.2)
where, VQ is the average liquid circulation velocity. Fractional gas hold-up
is given by the following equation:
VG
VG
f(v c )
(23)
The value of V^. depends upon the superficial gas velocity and for airwater system, equation (2.3) takes the following form:
17
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2. No. 1,1984
TJirce Phase Sparged Reactors
(S/uiui) ( plx°°V 3ΊβθΠβ JO AilD013A 3SIM 1VNIWM31
18
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
In view of equation (2.4), the fractional gas hold-up data for any gas-liquid
system can be correlated by the following equation:
(2 5)
·
Comparison of equations (2.3) and (2.5) indicates that the constant
'a' corresponds to the terminal rise velocity of a bubble. Though it may
not be strictly true, the value of 'a' gives fairly good approximation for
Vb„. The values of fractional gas hold-up in the presence of different particles and at different loadings were correlated by equation (2.5) and the
values of 'a' and 'b' are reported in Table 3.
TABLE 3
Correlating Parameters for Fractional Gas Hold-up
e
dp. μηι
70
110
210
340
500
850
2000
s=
0.01
a
b
0.22
0.23
0.29
0.28
0.24
0.29
0.31
2.55
2.40
2.50
2.69
2.82
2.40
2.00
Average 0.266
2.48
0.02
a
0.28
0.03
b
a
b
a
b
0.3
0.26
2.2
2.47
0.446
0.38
0.40
—
2.68
2.69
2.02
-
0.41
0.28
—
0.55
0.49
1.97
2.50
_
2.52
2.60
_
—
-
-
0.43
2.40
2.69
0.36
2.23
0.32
2.46
0.050
0.357
2.41
2.1.3. Effect of Solid Phase hold-up
It is obvious from Figures 2A-2F that, an increase in the average fractional
hold-up of solids reduces the fractional gas hold-up substantially. The
reduction (as compared with air-water system) in the fractional gas hold-up
is -maximum in the vicinity of critical superficial gas velocity needed for
suspension (point B in Figure 2) and the difference gradually decreases as
the superficial gas velocity is increased.
With an increase in the value of es the flatter portion (portion between
points A and B in Figures 2 (A-F) of the eG versus VG plot gets extended
19
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1, 1984
Three Phase Sparged Reactors
to a higher value of VG (point B gets shifted to higher VG). This is consistent with the observation that an increase in es increases the value of
critical superficial gas velocity for suspension.
It can be seen from Figure 5A that an increase in e§ increases the bubble
diameter. The maxima in d B also gets shifted to somewhat higher value
of superficial gas velocity and the rate of decrease in dB with an increase
in VG also reduces, which corresponds to the extension in the portion AB
of Figure 2. From equation (2.3), an increase in Vj,,, (with an increase in
d B ) decreases eG. Kalo et al /22/ also observed an increase in d B with an
increase in es.
2.1.4. Comparison with Previous Work
Table 1 gives the details of the experimental conditions employed by the
various investigators.
Imafuku et al /15/ have reported fractional gas hold-up data in the bubbly
flow regime (Figure 2B). The values of eG compare well with our data for
dolomite particles (125 μ) and at low superficial gas velocities.
Kalo et al /22/ have reported fractional gas hold-up data for 3 phase
systems from 0.066, 0.122 and 0.214 m i.d. columns. They also have reported the existence of flatter portion AB. Similarly, they also observed
a decrease in eG with an increase in the particle size.
Efremov and Vakhrushev /10/ have reported the following correlation:
(eG)s
=e
G(P L /Pc)°· 4
(2-6)
where eG and (eG)s are the values of fractional gas hold-up in two and
three phase systems. pc is given by the following equation:
PC = 6S"S
+
"LeL
For particles in the size range of 0.01 to 0.5 mm, Figure 2C shows the
plot of (eG)s versus VG at es = 0.05. Equation (2.6) does not show any
effect of particle size and predicted values are about 35 to 40 per cent higher
than those observed in the present work. Moreover, eG values are less than
that of air-water system by a constant factor which is contrary to usual
observations.
Figure 7 shows the plot of eG versus VG obtained from the correlation
proposed by Abou Al Hassan /!/. The values of gas hold-up obtained by
20
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
(*3)'dn-<nOH SV9 1VNOI1DVMJ
21
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. 1,1984
Three Phase Sparged Reactors
them are about 10 to IS per cent higher than those observed in the present
work for dolomite (dp = 110 μ, ps = 2260 kg/m3). The solids used by
Abou Al Hassan /I/ are glass particles of size 127 μπι and density 2500
kg/m3. The difference in these two investigations may be due to the use of
small column (T = 0.10 m) by Abou Al Hassan.
Ying et al /47/ have measured eG values in 0.05 and 0.10 m i.d. column
with two size ranges of solid particles. The fractional gas hold-up behaviour
with respect to solid size or eg is similar to observed in this work.
2.2. Presence of Liquid Flow
2.2.7. Effect of Superficial Gas and Liquid Velocities
Michelson and stergaard /32/, Efremovand Vakhrushev/10/, 0stergaard
and Michelson /35/ and Patwari /40/ have studied the effect of superficial
liquid velocity on the fractional gas hold-up at a given superficial gas velocity.
The details of the experimental set up and the range of variables are summarised in Table 4. The effect of liquid velocity cannot be separated from
the effect of particle size. When the particles are larger than 3 mm, Michelson
and 0stergaard /32/ observed that a two-fold increase in superficial liquid
velocity decreased the fractional gas phase hold-up only by about 8 to
10 per cent. Begovich and Watson /4/ have proposed an empirical correlation
which reads as:
eG = (0.048 ± 0.010)V£720±0-028(dp)ai68±0·061 (T)-0.125 ±0.088
(28)
With the help of this correlation the data of Kim et al /24/, Bhatia and Epstein
/5/, Michelson and 0stergaard /32/, Efremov and Vakhrushev /10/, 0stergaard and Michelson /35/ could be correlated. Patwari /40/ observed that
equation (2.8) predicts low values of eG than observed. Equation (2.8)
predicts fractional gas hold-up to be independent of liquid velocity. This
approximation may be valid till the superficial liquid velocities does not
exceed 0.20 m/s.
From Table 4, it can be seen that the column diameter and the average
particle size have been varied in the range of 50 to 150 mm and 10 to 6200
jum respectively. The superficial gas and liquid velocities were varied in the
range of 0 to 0.3 and 0 to 0.26 m/s, respectively.
22
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Reviews in Chemical Engineering
A.B. Pandit and J.B. Joslii
2
5°
O
l-H
Λ· j
g
1°
V*
CD
"1_J
(Λ
χ— ν
,3
*υ
^^
C
+" -H
^
11
? p
Μ
'S
*ί
^e*
^
CO
o
+°
ΐ
S "
i·^
^3
t~i
II
II
Λ
^j^°
3
§
°p
S-^^a r?,
f__?
"^
«υ
β>
M
«D
o g
° §
O
1
'
1
<u
ιΟ
t-H
S
D
ο
νο
Μ
0
W
I'S
. C*i
E
>
t
"(3
10
E
0 0
<i
u n
U >J
*ΪΓ *^
II
c
CM
?
»-H
M
•1
•o
*3
σ
4_i
.—
^
s
Ϊ.
0.
(D
II
II
O *^^
j-l
*^r
^H
~H
2 I
II
II
1-1
O
*^*
*^l·
OO
« «f
*~* ίο
2§
H
II
O
*^r
*^!-)
S
es
*?es•n
OO
v-H
1
(O
~
W
C
0>
II
P <s
'S
s _E
<l
2 S
i 0
(U
J —·
III "j
1
§ 5*
Οϊ
S.
«·
X
ο
0
o
ΓΜ
es
es
1
Ο
§
o
VO
0
o
<-H
1980-5
.
O
Ξ
U i^^
>J
*ί*
in C3
^^^
CO
^L·
°1
<*> ι
OO
0
•n
0
UJ
E
3.*
ο
•η
α
•o
Q.
?
Έ
o
in
0
o
o
VO
OO
m
es
o
0 OO
o
§ o
0 0
m in oo
0
0
VO
·*
X
1
fA
ω
U
E
K
1
0
•n
«—1
•n
O
0
S
o
0
0
w-t
es <s
vo in
5
VO
0
G
S
U.
ο"
>
•S3
^3
Μ
i.
o
•α
α
c
ο
ο
W
.1
rs
ΓΟ
•a
&
I
oi
^.
34
^_
c
cd
'Sca
1s
a>
S
S*
·§
1
Q
c
s
•g
M
•S
1
c?
CQ
o
!
£
23
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1, 1984
Tliree Pliase Sparged Reactors
2.2.2. Effect of Particle Size
Michelson and Ostergaard /32/ observed that for particles larger than
3 mm, one hundred per cent increase in the superficial liquid velocity (from
0.1 to 0.2 m/s) decreased the fractional gas hold-up values only by about
8 to 10 per cent. For particles which are about 1 mm or less in diameter,
the fractional gas hold-up was found to be independent of the superficial
liquid velocity. Observations by Dhanuka and Stepanek /9/ are also similar,
even in the lower range of superficial liquid velocity. From the available
information, it is very difficult to predict the effect of particle diameter
on the fractional gas hold-up in presence of liquid flow. This is also obvious
from the variation in the exponent of d p in equation (2.8).
2.2.3. Effect of Solid-phase Hold-up
Michelson and ßstergaard /32/, Dhanuka and Stepanek /9/ observed a
decrease in fractional gas hold-up with an increase in solid phase hold-up
(es). About 10 to 15 per cent decrease in eG was observed with an increase
in es from 0.18 to 0.28. Efremov and Vakhrushev /10/ predict much stronger
effect of es on eG than for the system having no liquid flow. The fractional
gas hold-up values were further lowered by about 10 to 15 per cent in the
presence of liquid flow. Patwari /40/ has observed similar behaviour. Our
observations are consistent with the above findings.
3. Critical Gas Velocity for the Suspension of Solid Particles
3.1. Introduction and Previous Work
The knowledge of minimum (or critical) gas velocity (VGC) for the suspension of solid particles is important. The operating superficial gas velocity
should be more than VGC and hence it is desirable (for a given set of conditions) that the value of VG(-. could be predicted.
Roy et al /42/ have proposed a correlation for the critical solid hold-up
(the weight of solids/weight of slurry) that can remain suspended at a given
superficial gas velocity. They have used a column of 50.8 mm i.d. and a wide
range of particle sizes.
Narayanan et al /33/ have studied the solid suspension in 0.114 and
0.141 m i.d. columns with HC/T equal to one. The particle size was varied
24
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
in the range of 125 to 600 microns and which correspond to the terminal
settling velocities in the range of 12.5 to 110 rnm/s.
Recently Koide et al /27/ have critically analysed the above investigations. They have pointed out that the correlations of Roy et al /42/ and
Narayanan et al /33/ predict unusually low values of VQC. It may be noted
that Roy et al /42/ used a column of 50.8 mm i.d. and Narayanan et al
/33/ used columns with height to diameter ratio equal to unity. The liquid
flow patterns in these columns will be totally different from those observed
in relatively large columns (column diameter larger than 150 mm and height
to diameter ratio greater than three). Therefore, the correlations of Roy
et al /42/ and Narayanan et al /33/ will give only preliminary estimates
ofV GC .
Koide et al 127/ have studied the suspension of solid particles in 100,
140 and 200 mm i.d. columns. The particle size and liquid viscosity were
varied so as to give the range of terminal settling velocities of 4 to 74-9
mm/s. For small columns (100 and 140 mm), lower values of VGC were
observed when the bottom was conical as compared with flat bottom. However, for the large column (200 mm i.d.) the value of VQQ was practically
independent of the bottom design. Koide et al /27/ have proposed the following correlation:
V
SN-
= 0.801 (
n.
V
PS
SN-
S78
x [l + 807(-^4-)°]x
pa3
χ [l - 1.20 (l - — ) °-0301<l ] where, q = (Τ^^/σ)0·559
T
(3.1)
It was thought desirable to study the solid suspension in a large size
column and over a wide range of particle size. Further, an attempt has also
been made to develop some rational basis for the prediction of VQ^..
3.2. Mathematical Model
In the case of sparged contactors, it is known that two regimes prevail
which are determined by the column diameter, superficial gas velocity and
the physical properties of the liquid phase. Homogeneous regime prevails
at relatively low superficial gas velocities ( < 50 mm/s) and in relatively
25
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1, 1984
Three Phase Sparged Reactors
small columns. Further details pertaining to these regimes have been discussed by Joshi and Lali /19/. In the homogeneous regime, the behavior
of bubbles is determined by the sparger design. Bubbles are generated near
the sparger, which rise practically without coalescence and dispersion. Liquid
is entrained upward with wakes behind the rising bubbles. The liquid flows
downwards in the bubble-free cross-section. The average downward velocity
is given by the following equation [Joshi /17/] :
V
=(
CL
-C
- eG -
For the suspension of a solid particle the average liquid velocity in the vicinity of solid particle should be equal to the settling velocity of a particle.
Therefore, the value of VGC in the homogeneous regime can be calculated
on the basis of equation (3.2).
In the heterogeneous regime, the bubble size is determined by the bulk
liquid flow which is highly turbulent in nature. The bubbles constantly
undergo coalescence and dispersion. The sparger design has influence only
in the bottom section (HC/T = 1 to 2). However, for the major section
of the sparged contactor, the sparger design has practically no influence.
Joshi /18/ has given the following equation for the liquid phase turbulence
intensity:
If = 0.3275 < ^ _ ^
}
[(VG + VL )(PC - PG)(1 - eG) -
- (PC - PG )ec M,- - es VSN (ps - pc) - VLpL ] >
3
(3.3)
where,
In the case of semi-batch mode of operation, the liquid phase is stationary (VL = 0) and equation (3.3) takes the following form (pc ^P G ):
U' = 0.3275 <gT[V G -e G V b o o - es VgN (ps- PC)/PC]>'/3 (3.5)
In the heterogeneous regime, a particle gets suspended when the value
26
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
of U' equals the settling velocity of the particle. For the calculation of
U' the following two procedures can be used:
(i) When the terminal rise velocity of a bubble (Vb„) and the settling
velocity of a particle are known then equation (3.5) can be used with Cs= e sb
(ii) Pandit and Joshi /38/ have given procedures for the calculation of
average liquid circulation velocity and U'.
The knowledge of U' can give the basis for the prediction of minimum
gas velocity for the suspension of solid particles. However, the following
points should be noted:
(a) The above two procedures for the calculation of U' assume that
the scale of turbulence is 0.08 T which is uniform throughout the contactor.
Experimental measurements are still needed to confirm the validity of this
assumption.
(b) The values of U* calculated by the above procedures hold for the
main section of the column and perhaps not applicable in the bottom, it
is likely that, some regions exist where the liquid flow is relatively less turbulent. If the particles are present in this region then the value of VG required
for the suspension will be higher than at which U' (in the bulk region) equals
3.3. Effect of Terminal Settling Velocity (VSN J of Particle
In order to determine VQQ, superficial gas velocity (VG) was increased
from zero. The value of VG at which the particles do not remain on the
bottom for more than 1-2 s was noted as VQQ. Alternatively, at very high
value of VG (> VQ^) all the particles are completely suspended. From
this value, VG was continuously reduced to get VQQ. The values of VQQ
obtained by these two methods agree within ± 5 per cent. However, in
the case of large particles (> 1000 microns), the measurement of VQQ
was somewhat difficult. In this case, particle aggregates were formed near
the wall. The aggregates were changing the position frequently. The value
of VG at which the aggregates did not remain at a single position for more
than 4 to 5 s was termed as VQQ .
All the particles listed in Table 2 were used. Fractional solid hold-up
( e«,) was varied in the range of 0 to 0.1. Columns of 100,200 and 385 mm
i.d. were employed and the height to diameter ratio was varied in the range
of 2 to 8.
Figure 8 shows the variation of VQQ with respect to VSN-. It can be
seen from the figu-»- that three distinct regimes prevail. In the homogeneous
regime, VGC is almost linearly proportional to VSN... In the heterogeneous
27
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Three Phase Sparged Reactors
VoL 2, No. 1,1984
z
ο
«S
tu
α.
η
νι
BOO
ac
o
100
so
υ
ο
ω
2
Κ
υ
1.6
'ec°MV SNoe ),' € , ' = 7 - 9 , m m
l/l
Ul
η o
(D
9,mm
100-
β
20
7·θ rrim
α.
10
6
10
20
(0
100
200
600
1000
T E R M I N A L SETTLINO VELOCITY OF A PARTICLE ,V SMe> (mm/s)
Fig. 8. Effect of particle settling velocity on the critical gas velocity for the suspension of
particles
regime, VGC was found to be proportional to (VSNee)2'7. In the intermediate
regime, the value of exponent varies and the value of VQ^-. was found to
be approximately proportional to (V«^..)1·7. Koide et al /27/ have found
VGC to ν3Γ^ as (^SN-)°8· This indicates that the data collected by Koide
etal 121 1 lie in the homogeneous regime.
For the case of large particles, the suspension by only sparging is perhaps
uneconomical because the value of V^ increases markedly with an increase
3.4. Effect of HC/T Ratio
For a given particle (size and density) and ej (volume of solids per unit
cross sectional area) there was apparently no effect of HC/T ratio on VQ£.
For a given amount of solids, an increase in HC/T reduces ?„ but does not
affect e's which only depends upon the column diameter. The independence
of VGC with respect to HC/T indicates that the turbulence intensity or
the average circulation velocity is independent of the HC/T ratio. Pandit
28
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
and Joshi /37/ have shown that the liquid circulation velocities do not depend
upon the HC/T ratio, which is consistent with the experimental observations.
It may be pointed out that the same value of VGC does not mean the
same amount of energy requirement. The energy input rate increase linearly
with the HC/T ratio. The energy dissipation rate per unit liquid volume
remains constant.
3.5. Effect of Solid Phase Hold-up
It was discussed in the previous section that the total liquid volume
has no effect on VGC as long as ej is constant. It was thought desirable
to investigate the dependence of VGC on ej. It was found that the dependence of VGCon es was a stron§ function °f VSN«·
Figure 9 shows the variation in VGC as a function of solid concentration
ej, (T = 0.2 m, HC/T = 4 and T = 0.385 m, HC/T = 2.0). It can be seen that
three distinct ranges of e's are present, which have different dependence
on VGC.
For lower range of VSNoe ( < 0.03 m/s), VGC was roughly proportional
to (e's)0'2 over the entire range of e<, (8.0 < e's < 40 mm). For the intermediate range of Vgj^ 30 < Vgjj,., < 134 mm/s) VGC was proportional
to (eo)0·33 in the lower range of ej (0 < e' < 8). In the intermediate range
of e„ (8 < e' < 40 mm) VGC was proportional to (e's)°'s. Again in the
higher range of ej, ( > 40 mm) the dependence of VGC on es decreases
and VGC was found to be proportional to (e* )°·35· For example, for particles
having VSNoo value of 104 mm/s, an increase in ?s value from 0.05 to 0.4
(40 < €'„ < 320 mm) increases VGC ^ a factor of 2.1 as against 3 times
increase in VGC when ?„ was increased from 0.01 to 0.05 (8 <e„ <40 mm).
For particles having VSNoo value greater than 134 mm/s, VGC aßain is a
strong function of ej. In the lower range of e's (0.8 < e's < 8 mm) VGC
was proportional to (ej)0'45. In the range of e^ above 8 mm VGC varies almost linearly proportional to e's.
3.6. Effect of Column Diameter
Experiments were performed in the 100, 200 and 385 mm i.d. columns.
It was found that the value of VGC decreases with an increase in the column
diameter at the same e's value (Figure 10). From equation (3.5) it can be
seen that, for a given value of U' at which particle gets suspended, an increase
in T will decrease VG. The extent of decrease in VG (VGC) depends upon
29
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. 1,1984
Three Pliase Sparged Reactors
T = 386 , mm
20
dp 12 2000 μηπ
dp Si 850 /*m
•ΙΛ
10
7
bl
κ
Ο
U. «
^
E
3
2
r, ε ο-οοι
0-003
0·00β 0-01
0-03
0-06 0-1
001
0-1
0-2
FRACTIONAL SOLID H O L D - U P , 6,
Fig. 9. Effect of fractional solid phase hold-up teg) on the critical superficial gas velocity
for the suspension
the corresponding changes in eG and Vb„. A detailed comparison with the
theory will be explained later. Figure 10 shows the effect of column diameter
on VGC at the same value of ej.
30
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Reviews in Clicinical Engineering
A.B. Pandit and J.B. Joshi
1000
800
800
VI
19
t
500
- ε
til Χ 300
α
3
OT
^
>-
s s;
---Δ
d
100
100
200
-4-
I
300
400
COLUMN DIAMETER , Τ ( m m ) —
Fig 10. Effect of column diameter on the critical superficial gas velocity for the suspension
of particles
3.7. Comparison Between Predicted and Experimental Values
3.7. L Suspension of a Single Particle
In order to determine the critical gas velocity for the suspension of a
single particle, the values of VQC were measured in the es range of 0.001
to 0.01 (0.79 < e's < 7.9 mm). Four to six measurements were made in
this range and the value of VQC as e's tends to zero was obtained by extrapolation. Table 5A shows the experimental values of VQQ for different
particles.
For the prediction of VGC, equation (3.2) was used for the homogeneous
regime and equation (3.5) was used for the heterogeneous regime. The
values of VCL in the homogeneous regime (VG < 50 mm/s) and the values
of U' in the heterogeneous regime are given in Table 5A. It can be seen
from this table that, in the heterogeneous regime, a particle gets suspended
when U' equals the terminal settling velocity (VSNJ. Similarly, in the homo31
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Tlircc Phase Sparged Reactors
VoL 2, No. 1, 1984
m
υ
tu
σι
c
CO
CO
a^
Ο
Q
o
t
^n
1υ
I
Ο
M
c
01
Q.
u>
01
o
·*-
*-·
υ
0
αϊ
E"
10
™o"
•
l·"2
OO
OO
—<
r^
·*
«
·*
^
r-
ΓΜ
0
CD
^^
M
E
co
^
8
Z
ta
>
—
v>
m
O
0
\
"^
"* ~
C5
V>
«N
m
ο τ ί ν ο
t
rrs
o o o
oos^i
r^
01
O « O * N
o·^·^·
ΓΛ
^-t
oo
ornr-;
Ο Γ Ί Ο Ο
M
' " ' ( O
"EE
to
en
.
* ~
t
f
" ^ « >
οι
vo
H
2 t ^
^^
o o o o o
- " O V O O l
^
°
o
o o o i
>
4
t-
o
2
o
""
S
—
^-co
:=
C
2
i
_..
N
S
^^
2
u
-1
^
o
Z
S
vo
L
-H
oo
O
V O
o o r ~
0 0 > V O
p.
^ o · * «
^-«*i
^
M
^H*-cl
"EΕ
^ • • - H ( ~ -
'
CN
t*l
00
o r
t
"εP
Z
o7
§
VO
o o i
t
~
C > » o v o
^
m
S
" j
*O
i«—
o>
Q.
o
t
ίί
"i
oi
rsi
o c n
t
·*!
r-^
TT
vo
τ»· ΙΛ
O T f r f i
t
oo ·*
ο « Λ ν ό
t
*-H
(O
O O O O
^H
-^
O * O O O
»-H
O » O ^ ·
ot^-fn
o*-ic*5
οοίι^-
«O
O
»O
O
«O
O
J ^
5$
l- o
i?
_3
CD
>
^H
V)
O
O
01
V)
0
O
*-H
1—1
1
CD
•0
0
E
O
c>
OO
01
0
O\
p^-^i·
ο ν ό ο ΐ
OS
·<»
oi
OO
<JS
o
O
ro
o
ο«όι-ί
p
o
«0
p o l «
i—1
*—I
«0
«0
«-H
o r - - H
o
m
1—4
1—1
p p o \
e
itt^
f-H
*—1
t—*
LU
01
tD
o
O
'S
S
01
p
01
o
o
so
o
Ο
r-^cn
«-«
1
01
vo
ρ ι ο ^ Η
o
·—t
Ο
1—t
so
c--
*—<
Q.
g
s1 k:u
c
o
<O
i
I
E
0
p
•O
E
E
co
^
i
2
1-
?
~m
~
O
«0
·—·
"o
»-π η
X
|<u
o
>
*—t
O\
O
«—1
O\
O
p o o l
p " o r ~
"i
f
i
0 - 3 ·
0 - 3 ·
3 - s ·
E
^
o
«—1
E
*~
"g·^-,*"
w
R
•7
°
-W
x
b
_
i—
E
O
^
"&·!?*"
8
y
^ ^ ,
O ^
^ " o , «
M
l^u
1^
?
i^
-
i~
U
f
OT&?
|tu
^*
^
«^
O ^ ^
>
° >
i^
"&'3'
8
z
_
-—
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
"x^
M
l^u
0 ?
i^
^^
A.B. Pandit and J.B. Joslii
Reviews in Qiemical Engineering
geneous regime, a particle gets suspended when VCL equals VSNoe. These
are very useful results.
3.7.2. Suspension of Multiple Particles
It was discussed earlier that the value of VQQ increases with an increase
in e's (Figure 9). In this case also, equation 3.5 can be used for the calculation
of U'. The settling velocity of a particle gets hindered in the presence of
other particles. However, the hindered settling velocity (VSN) at e- values
upto 0.05 almost equals the terminal settling velocity. It was found that
when VSN„ is less than 100 mm/s and eg is less than 5 per cent, the value
of U' was found to be equal to VSNno within 10 per cent. It may be emphasized that the above range of VSN-, and ?s perhaps covers the range of practical interest. For three phase catalytic slurry reactors, relatively small particles at low loading are employed.
Equation (3.5) satisfactorily explains the effect of column diameter
and the HC/T ratio. For a given U', the term on the right hand side of equation (3.5) should remain constant. With an increase in T, the value of VG
will decrease accordingly after keeping allowance for the corresponding
changes in e„ and Vj,„.
When the particle loading or VSNae was high, some of the particles get
into the slow moving region which exist on the bottom near the wall. Under
these conditions, very high values of V^ are required to remove/lift the
particles from the region.
It may be noted that the value of CG and Vb<. should be available for
using equation (3.5). It is known that eG and Vb„ strongly depend upon
the system properties. Therefore, it is recommended that the values of
eG and Vb_ be determined for a given system in a small scale aparatus (say
150 mm i.d.) and can be used for large columns.
As an alternative to equation (3.5), the value of U' can also be calculated
according to the procedure of Pandit and Joshi /37/. In this case also the
scale of turbulence was assumed to be 0.08 T and the value of U' works
out to be 25 per cent of the average liquid circulation velocity. Using this
procedure, the value of U' was found to be equal to VSNo<1 over a es range
of 0.001 to 0.05 and VSN_ range of 50 to 134 mm/s. Table 5B gives the
values of VCL and U' calculated from equations (3.2) and (3.5) against
V
SN- v31"65 over the entire range. In this Table (VCL)p and (U')p are the
values calculated by equations (3.2) and (3.5) respectively. The observed
values of V£L and U' are obtained from the mixing time data [Pandit and
Joshi /37/].
33
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol.2, No. 1,1984
Three Phase Sparged Reactors
TABLE SB
Comparison between Predicted and Experimental Values of Critical Superficial
Gas Velocity for the Suspension of Multiple Particles
a) LAMINAR RANGE
€„ = 0.0027 to 0.10
T = 0.20m
VSN-· mm/s
< V CL> P
mm/s
1) 8.5
2) 14.0
< v CL»obs
mm/s
7.4
8.9
16.7
15.2
Τ = 0.385m
mm/s
< V CL> P
< v CL>obs
mm/s
_
_
13.1
14.6
b) INTERMEDIATE RANGE
VSN—
T = 0.20m
mm/s
(U-)p
mm/s
62.7
92.2
120.2
1) 50
2) 76
3) 100.4
«U')0bs
mm/s
54.9
78.7
101.0
Τ = 0.385m
(U')p
<u-)obs
mm/s
mm/s
_
_
88.2
106.3
74.4
90.8
c) TURBULENT RANGE
T = 0.20 m
^SN<» * f*"*^*
(U')p
mm/s
1) 134
2) 164
128.7
193.2
«U') obs
mm/s
117.7
153.0
T = 0.385m
(U')p
mm/s
137.5
173.7
«U'lobs
mm/s
124.0
168.0
3.8. Effect of Superficial Liquid Velocity on VGC
When the terminal settling velocity of a particle is greater than 100 mm/s,
it was discussed in the earlier section that very high values of V^ are required. Therefore, it was thought desirable to study the effect of superficial liquid velocity with a view of reducing VGC. Particles having VSN<>>
values of 134 and 164 mm/s were employed at a loading of 1 per cent in
the 200 mm i.d. column. From Figure 11 it can be seen that the value of
34
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Ο
10
20
Reviews in Chemical Engineering
30
40
60
00
SUPERFICIAL LIQUID VELOCITY, VL ( mm/s )
».
Fig. 11. Effect of superficial liquid velocity on the critical superficial gas velocity for the
suspension of particles
VQ£ substantially decreases with an increase in VL. At the extreme situation
of no gas sparging, the particles are suspended by only liquid as in the solidliquid fluidized bed. In this case the value of V^ obtained in this work
were found to agree with those reported by Barnea and Mizrahi /3/ for
solid-liquid fluidized beds.
One more important observation was that, in the presence of liquid flow,
the dependence of VGC on e§ was considerably weakened. (VGC a (e· )»·«-<»·«»)
35
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1,1984
Three Phase Sparged Reactors
Under extreme conditions of VG = 0, the value of VLC is known to be
independent of e^.
4. Concentration Profiles of Solid Particles
4.1. Axial Concentration Profiles
4.1.1. Previous Work
The knowledge of solid phase concentration profiles is very important
in deciding the performance of sparged three phase reactors. As the terminal
settling velocity of the particle increases, the axial concentration profile
becomes steeper and the predicted conversion increasingly deviate from
the situation where uniform particle concentration is assumed. The principle
difference between the three phase sparged reactors and the solid-liquid
fluidized beds is the existence of particle concentration profiles in the
former.
Cova 161, Imafuku et αϊ /15/, Kalo et al /22/ and Abou Al Hassan /!/
have studied the axial concentration profiles. The range of variables used
in these studies is summarized in Table 6. A careful examination of these
investigations indicate that the particle size and density have been varied
over a limited range. The largest particle had a terminal settling velocity
of 27.2 mm/s. It may be emphasized that the particle settling velocities
need to be very high (at least > 50 mm/s) for a clear understanding of concentration profiles. The range of column diameter and the superficial gas
velocity covered by previous investigators is also limited. In most of these
cases homogeneous regime prevailed (mainly because of the small diameter
columns and fine particles which increase the apparent viscosity). It may
be pointed out that the concentration profiles are markedly different in
homogeneous and heterogeneous regimes and the latter regime prevails
in the commercial size equipment. Further, there is very limited information
in the published literature regarding the effect of superficial gas velocity
on the concentration profiles. Therefore, it was thought desirable to undertake some measurements. Ports were constructed at height to diameter
ratios of 1, 2, 3, 4 ... etc. A horizontal tube (with a stopper at the end)
could be inserted and a dispersion (solid-liquid) sample could be taken at
several radial positions.
36
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Α. Β. Pandit and J.B, Joshi
Reviews in Chemical Engineering
σ>
n
o
M
^
j
>
m
1-H
S
§
O
p
^*
1
1
o
o
<M
VO
-H
P
l
<O
0
r—t
o
0
CN
VO
o
S
CN
0
1
<N
VO
I
p
M
E
M
«
3
O
m
o
00
|
^^
v*4
C3
0
O
C3
^
L.
'S>»
CD
δ
"E
»S
O)
O
υ
Io
| o
«ucn
co
i
i~
o
?
«D
^
S
υ
t
α
o±
at TJ
~
co
'S
S
I
_
o
1
*··
i
^^
fl>
m
^^
O>
co
**·
cd
«>
2
g
«5
o
O
"0
§
o o o
0 O 0
CN O OO
Ot
C*
r^
<s m o o
-H
ν Ο Γ ^ Ή Ο Ο
-H
§
«0
<N
t- OO
VO
CN
l i
N
«-H
m
C
u
Έ
α
Ό
δ
"x
£
c
l—1
l—t
vo o
-Ht^VO
«—1
VO
«Λ
t—
*-H
^H
1-1
oo ο
OO
»n
^· t—
m oo <n o\
vo oo es ·*
«-!*-(
t— τf
es τ h
^H
" i
ΙΛ
«
*-H
*-H
1O
VO
1-H
E
1-'
vo
S
O
O
O
0 0
-H <M
O O
VO CS Tf
VO CN i-i
O ·-< <N
O
O
O
rt
^·
—^
H.A
o
a
2
^ 5
% > a
1 δ Μ
"^CN
Λ
t
^^
1z;
Ies
§
A
W
<
So
1
oo
Ό
n
1
JU
37
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1,1984
Three Phase Sparged Reactors
4.1.2. Mathematical Model
The following assumptions are made:
(i) All the particles are identical as regards to their terminal settling
velocity.
(ii) There is no radial variation in the fractional solid phase hold-up.
This assumption is somewhat stringent. The subject of radial concentration
variation of solids will be discussed later.
(iii) The fractional gas hold-up is uniform throughout the contactor.
(iv) The solid phase axial dispersion coefficient is uniform throughout
the contactor.
The solids move upwards because of the dispersion and move downwards
because of the settling velocity. In addition, in the case of continuous slurry
phase, solids also move because of the bulk flow. A differential mass balance
with respect to the solid phase gives the following equation:
(4.1)
The solution of the above equation is:
es = A + Bexp[
(VSN
SN -VSL
SI )
D
-x]
(4.2)
S
The boundary conditions are:
at χ = 0 ,
(4.3)
es = esb
and
de«; ι
VoM —V«;,
V«
(4 4)
-
where ei is the volumetric concentration of solids in the feed stream.
The values of A and B in equation (4.2) can be obtained using equation
(4.3) and (4.4)
(4 5)
·
38
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
and
V
SL -
V
SN
Substitution of equations (4.5) and (4.6) in (4.2) gives:
(4.7)
For semi-batch operation (gas: continuous, liquid: batch), VSL = 0 and
equation (4.7) takes the following form:
-!s_=exp(
Sb
|p)
(4.8)
S
Cova /6/ has suggested the following equation for the axial concentration
profile:
(4.9)
Cova (6) assumed that the concentration of solids in the feed and at
the bottom to be the same (εί = e~ at χ = 0), which is not appropriate.
A jump in the concentration [equation (4.4)] is perhaps more appropriate
boundary condition [Imafuku et al /IS/]. Also, equation (4.9) can not
explain the observed concentration profiles of Kato et al /22/.
4.1.3. Settling Velocity of a Particle
The settling velocity of a particle depends upon dp, Δρ and the shape
factor (0V). In the case of solid-liquid fluidisation the settling velocity
of a particle (VSN) is less than the terminal settling velocity (VSNoJ. In
the turbulent regime (Rep > 500). The reduction in settling velocity in
the presence of other particles occurs because of the increased turbulence
39
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
in the liquid phase, generated by the other particles. In the laminar regime
(Re p < 0.2) however, the neighbouring particles provide additional viscous
drag. When the gas is introduced in the solid-liquid fluid ised bed, the situation becomes more complex. In the presence of gas some of the energy
from the gas phase is dissipated in the liquid phase or some energy from
the liquid phase might get extracted. As a result, the liquid phase turbulence
might increase or decrease depending upon the net energy dissipated in
the liquid phase. If the liquid phase turbulence increases then the effective
settling velocity of the particle (VjN) might decrease and vice-versa. There
is another factor by which VjN might get affected. When the particle diameter is relatively big, it might pass through the bubble. Observations by
Kim et al /23/ and our own observation support this hypothesis. Since the
terminal settling velocity of a particle in the gas phase is greater by an order
of magnitude than in the liquid, the resultant settling velocity of a particle
(Vgfj) will be more than Vg^. Epstein /12/ have also pointed out a criteria
for the bubble breakage by a falling particle which states that PcVgNoridp/a
should be > 3 and is applicable in our case beyond d p equal to 850 microns.
Fractional gas hold-up measurements also support this observation. There are
very few data available in the published literature on the settling velocity
of a particle in the presence of other particles as well as gas bubbles.
Imafuku et al /15/ have estimated the effective settling velocity, of a
particle (V£ N ) experimentally. In the range of particle sizes covered in
their work (1.3 < VSN_ < 27.2 mm/s), the value of VjN was found to be
always greater than VSN (the hindered settling velocity because of the presence of other particles only). The increase in settling velocity in the presence of gas was attributed to the formation of aggregates. The ratio (VjN/
V SN ) was found to decrease with an increase in VSN=II and independent
of the superficial gas velocity. They have reported the following correlation
for the estimation of VjN :
N
=1.45V-S
(4.10)
Kato et al /22/ have reported the following correlation for VgN (63 <
dp < 177 microns and 4.8 < VSNet, < 16.9 mm/s):
V^N = l-33V SN _(-^-)°- 2S (e L ) 2 · 5
V
(4.11)
SN-
From this correlation it can be seen that the value of VgN increases with
40
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
an increase in VSN_. This observation is in contrast to that of Imafuku
et αϊ /15/. Kalo et al /22/ have also found VSN to depend upon the superficial gas velocity and the fractional liquid phase hold-up (CL).
Parulekar and Shah /41/ assumed that the effective settling velocity
of a particle in the presence of gas ( V^N ) increases with an increase in fractional gas hold-up. They have proposed the following correlation:
-
SN~ ' L
From the above equations, it can be seen that, some of the observations
are contrary to each other. In fact the value of Vj^ is expected to depend
upon several factors including bubble diameter (dg), bubble rise velocity
(Vb-). column diameter, the solid and gas phase hold-ups. It appears that
the prediction of VgN is very difficult. It is appropriate, as a first approximation, to select the value for VgN to be equal to Vg^.
4. 1.4. Solid Phase Axial Dispersion Coefficient
(Ds)
Cova /6/ and Imafuku et al /15/ have assumed that the solid and liquid
phase dispersion coefficients are identical. Kalo et al /22/ estimated the
values of D§, on the basis of measurements of axial solid concentration
profiles for batch and continuous operation. In this measurement technique
it was assumed that the DS value remains the same for batch and continuous
operations or it is independent of the superficial liquid or slurry velocity.
They found that the assumption of Ds = DL is valid upto a certain value
of VSN- and above which the following correlation has been proposed for
the estimation of solid phase axial dispersion coefficient (Ds):
VGT
VG
[i + 0.009 (
- - = 13-0 ( - ) --- - (4.13)
VgT
Kato et al /22/ varied the particle size in the range of 63-177 microns
which correspond to VSN„ range of 4.8-16.9 mm/s. From the correlation
given by equation (4.13), the value of DS works out to be linearly varying
with VG- It appears that, Kato et al /22/ worked mostly in the homogeneous
regime.
41
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
It was thought desirable to develop a correlation over a wide range of
particle size and column diameter. For this purpose, the particle size was
varied in the range of 70-2000 microns (Table 2) and the column diameter
was varied in the range of 100-385 mm. Axial concentration profiles of
the particles were measured by taking samples. In all the cases, it was found
that in the region close to the sparger (height = diameter) the concentration
profile was found to be flatter than that in the bulk of the vessel. Joshi
and Shah /21/ have shown that the flow patterns near the sparger and in
the bulk liquid are entirely different. In the bulk of the liquid (which occupies most of the column volume), the slope of the concentration profiles
was found to be practically constant for all the particles at different loading
(Figure 12). Equation (4.8) was used to evaluate Dg.
0 -20 -40 -60 -BO 1-0
0-2
I
' OP·/· n '
A110
0-ΟΙ,Χκ-
α 40 ο·οι,νκ
III
- 0-01
0-1
0-007
-0-005
0-06
fj-0-ιο, v.c
dp« 340, microns
? 0-02
Ο
Ο
Χ
ο
ο
in
o.oi
β,-0-01 , He
dp = 340, microns
00-006
Ρ
υ
•xX if* ο·οι
0-002
0-001
V e «0-ZOm/s
dp-340 ,
microns
dp· 340. microns
ι Ι ι I I
0-2 0-4 0-0 04 1-0 1-2
0 ^=0-01,dp= 600 microns ,\{,c
• 63=0-01, dp-500 microns,^ =0-2*m/s
€,=0-01,dp = 850 microns,^
• €,=0-01,d p =850 microns, Ve =0-2m s
1
I
0 0-2
I
1
I
0-6
I
I
1
AXIAL DISTANCE FROM THE BOTTOM ,m
Fig. 12. Axial concentration profiles
42
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
I
A.B. Pandit and J.B. Joslii
Rericws in Clicmical Engineering
For the liquid phase, Joshi /16/ has proposed the following equation
for the estimation of liquid phase axial dispersion coefficient:
DL = 0.3 T Vc
(4.14)
A similar equation was developed for the solid phase. The following correlation holds (70 < dp < 2000 microns, 100 < T < 385 mm, 0.001 <
es < 0.15, 7.6 < VSN„ < 164 mm/s and 50 < VG < 600 mm/s) (standard
deviation = 11.0 per cent, Figure 13):
Ds = 0.33 T(Vc - 1.785VSN. )
(4.15)
It can be seen from equation (4.15) that, in the absence of solid particles
(VSN- = 0), equation (4.15) practically boils down to equation (4.14).
The particles used in this work were non-spherical. The values of shape
factor (0V) for these particles were obtained by Pandit and Joshi /39/ by
finding velocity-hold-up relationships in solid-liquid fluidized beds. The
values of 0V are reported in Table 2. On the basis of 0V values the terminal
settling velocity of the equivalent spherical particle (Vs») was estimated.
Equation (4.15) takes the following form (standard deviation = 17 per
cent):
Ds =0.33T(V C - VSo.)
(4.16)
Table 7 lists some of the values of DS . For comparison it was thought
desirable to calculate the values of Ds in the bottom section (DSb) and
are given in Table 7. It can be seen that the values of Dj^, are higher than
Dg and the difference increases with an increase in VSN„. Table 7 also shows
that the values of Ds predicted by the correlation of Kato et al /22/ are
much lower than those obtained in the present work. This is because of
the wider range of variables covered in this work.
4.2. Radial Concentration Profiles
4.2.1. Introduction
No previous study is available on the measurement of radial concentration
profiles of solids.
The value of liquid phase radial dispersion coefficient is found to be
much less than that of axial dispersion coefficient in packed columns. The
43
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Three Phase Sparged Reactors
Vol. 2. No. 1.1984
0-09
(Vc-1-788
E, 0-08
v>
Ο
Ζ 0·07
ω
u. ο·οβ
ω
ο
υ
1 «OS
«η
κ
ω
ft 0-ΟΑ
ω
ν> 0*03
ο.
2 0-02
ο
VI
0-01
0-02
ΟΌβ
0-1
0-14
0-18
0-22
0*26
0-28
Τ ( Vc - 1·7βΒ VS
Fig. 13. Correlation for the solid phase axial dispersion coefficient (D_)
e
e
Symbol
Symbol dpW
Τ (m)
s
s
<y/d
Φ
β
θ
χ
θ
α
0
S
Δ
V
850
850
850
340
340
500
500
500
110
110
0.05
0.0027
0.01
0.0027
0.01
0.01
0.05
0.1
0.01
0.05
θ
2000
0.2
•
*
0.385
A
0.2
0.2
0.2
0.2
0.2
0.2
5l
β
340
340
110
850
850
110
340
340
0.2
0.385
T
+
Ο
T (m)
0.01
0.05
0.027
0.2
0.2
0.1
0.2
0.027
0.0135
0.0027
0.0135
0.385
0.385
0.385
0.385
0.1
0.2
44
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
0.385
Reviews in Chemical Engineering
A.B. Pandit and J.B. Josh i
TABLE 7
A) T = 0.20 m
S- No. VSN„
1
2
V
G
m /s
Ds χ 104
m2/s
Ds χ 104 m2/s
Predicted by
Equation (4.1?
Dsb x10
2
e
s
4
3
4
5
6
7
1
0.85
0.75
15.00
1.75
2.50
0.01
0.01
0.05
0.10
188.0
368.0
142.2
144.0
124.0
382.0
110.5
144.0
35.6
202.0
52.0
63.36
2
1.25
2.50
5.00
3.50
3.75
0.01
0.01
0.05
0.10
182.0
326.0
226.0
275.0
212.5
300.00
212.00
290.0
61.30
90.29
71.30
74.60
3
7.60
5.75
20.00
14.50
24.50
0.01
0.01
0.05
0.10
349.0
494.0
335.0
358.0
304.0
470.0
302.0
372.0
69.30
229.90
167.40
238.40
4
10.05
7.00
28.0
20.0
60.5
37.5
0.01
0.01
0.05
0.05
0.10
392.0
540.0
414.0
675.0
447.0
302.0
525.0
250.0
692.0
288.0
48.60
214.70
148.20
503.30
108.90
5
13.4
10.0
20.0
25.0
0.01
0.01
0.05
510.0
368.0
542.0
268.0
379.0
368.0
34.40
77.00
100.90
6
16.4
19.5
60.0
0.01
0.01
551.0
580.0
229.0
533.0
30.10
130.28
B) T = 0.385m
1
2
3
4
5
6
7
7
7.6
2.5
10.0
4.4
5.4
0.00271
0.00271
0.01355
0.0271
304.0
756-0
324.0
318.0
253.0
704.0
318.0
309.0
65.90
230.00
108.56
130.51
8
13.4
4.81
10.00
9.5
14.5
0.00271
0.00271
0.01355
0.0271
442.0
706.0
572.0
579.0
285.0
690.0
536.0
568.0
28.11
64.07
60.67
96.58
45
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. 1. 1984
Three Phase Sparged Reactors
difference may not be so drastic in the case of bubble columns operating
in churn turbulent regime. But this may not be true when solid phase dispersion coefficient is considered.
In the case of catalyst particles, presence of radial concentration profile
may give rise to liquid phase reactant profile affecting selectivity and hence
the knowledge of solid phase radial concentration profile is a very important
parameter.
Experiments were carried out in a 0.2 m and 0.385 m i.d. columns. The
radial variation of es was studied using a 1 cm i.d. perspex tube, having one
end fitted with cork which could be opened and closed from outside to
collect a sample. Figure 1 shows the sketch.
4.2.2. Effect of Superficial Gas Velocity
The effect of superficial gas velocity on the radial concentration profile
was different at different axial locations. At the sparger or Hp = 0, increase
in gas superficial velocity decreased the concentration near the centre and
the profile became steeper. At a location of 0.20 m above the sparger the
wall and centre concentration increased proportionately affecting the radial
concentration profile only slightly. Further increase in axial distance from
the bottom decreased the difference between the concentrations at the
centre and at the wall making the profile flatter.
Figures 14a, 14b and 14c show the variation in fractional solid hold-up
(es) as a function of radial distance. The radial concentration profile was
found to be exactly opposite to that of fractional gas hold-up profile for
particles in the intermediate/turbulent range. The extent of variation reduced
as the axial distance from the bottom increased and the concentration of
solids become more or less uniform throughout the cross section of the
column. es values near the wall were about 1.5 to 1.7 times higher than
those at the centre. The maximum variation was observed at some distance
from the bottom. This variation is expected if the velocity pattern in the
bubble column is studied. The flow pattern shows liquid velocity in a downward direction near the wall and upward direction at the centre. The maximum solid phase concentration was at 0.015m from the wall for 0.2m
column diameter where the maximum component of the downward liquid
velocity is located. In the case of very small particles (dp = 70 microns)
and when operating in homogeneous regime (VG < 0.03 m/s) it was observed that the radial concentration profile was similar to that of radial
fractional gas hold-up profile. This may be due to the fact that such a fine
46
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
0-10
dp=340yumt(e s ) = 0 - 0 5 » Ο
0.08
(Υ«,,.) -0-135 m/s
V, = 0-20
H„ =-80
dp = 360yum ,(€,)
= 0-01
0-002
AT (V ee ) = 0-0575
m/s
AT (V a ) = 0-20 m/s
0-001
0-1
0-2
0-3
0-4
0-5
0-8
0-7
DIMENSIONLESS RADIAL DISTANCE, r/R -
0-8
0-9
1-0
Fig. 14A Radial concentration profiles
47
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2. No. 1, 1984
Three Phase Sparged Reactors
0-08
H0=0
0-06
(
0-0*
O.QB
—Ο H0 =-20
0-02
HO =-40
0.01
dp = 850 μ m ,(6 S )
= 0.02
0-008
HO =-60
HO ( i n meters)
0
0-2
0-4
0-6
0-8
1-0
D I M E N S I O N L E S S R A D I A L 01 S T A N C E , r / R
Fig. 148 Radial concentration profiles
48
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Qiemical Engineering
V6 = 26
c
Θ x B 5-0
0.3
= 100 mm/s
s
0.137
Δ
x =38-5
• χ =79-5
d
H
=110
0-2
M
W
0.1
0-07
Ο
υ
ο
0-05
ι
0-03
0-2
Ο
ζ
Ο 4
0*6
r/R
\^ = 20.1
ο
Μ
_ι 0-010
<
Ζ
Ο
0-007
Ο χ » 5*0
• χ = 38*5
Ο Χ = 79-5
0-8
*
*S
0-0027
.
-*-
dp
Η = 110 yum
1.0
1-2
1^ = 100 mm/s
Δ χ β 5-0
• χ = 38-5
Ο χ = 79-5
Η
υ 0-005
<r
u.
0-003
0-002
0-001
Ο
Ι
Ι
Ι
Ι
0-2
0-4
0-6
0-8
1-0
1-2
DIMENSIONLESS R A D I A L DISTANCE , r / R - >
Fig. 14C Radial concentration profiles
49
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Ttiree Phase Sparged Reactors
particles move in the liquid mainly in the wakes of the bubbles and hence
it is most likely that they follow the gas phase com
ation profiles.
4.2,3. Effect of Average Solid Phase Hold-up
Figures 14a and 14b show that an increase in the e„ decreases the difference and makes radial concentration profile flatter. This may be due
to the fact that higher superficial gas velocities are needed for suspension
of particle and no appreciable (within 10 per cent) change in the mixing
time was found, indicating there is only slightly increase in circulation velocity. This alteration in circulation velocity is not enough to alter the radial
concentration profile and hence no appreciable change in the radial concentration profile is observed.
5. Mixing
5.1. Introduction
Residence time distribution (RTD) and micromixing in all the phases
are very important parameters which govern the performance of multiphase
reactors. Measurements of mixing time is a useful tool for assessing the
extent of axial mixing and the degree of segregation in the continuous phase.
Further, mixing time gives an estimate of average continuous phase circulation velocity (Vc). It appears that Vc is a powerful parameter for correlating
axial dispersion coefficient, bed-wall heat transfer coefficient, particle
concentration profile and the critical superficial gas velocity for the suspension of solid particles.
In the published literature there are practically no data on mixing time
for gas-liquid-solid sparged reactors. In the first part of this section, new
mixing time data will be reported over a wide range of column diameter,
particle size and density and superficial gas velocity. Towards the end of
this section, a critical review will be presented on RTD studies carried out
in the past.
5.2. Mathematical Model
Mixing time measurements were made using 100, 200 and 385 mm i.d.
sparged reactors. Solid particles of different size and density were employed
(Table 2). Superficial gas velocity was varied over the range of'7.5 to 250
50
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
mm/s. The details pertaining to the experimental procedure have been reported by Pandit and Joshi /37/.
Mixing characteristics of the liquid phase under semibatch operation
can be expressed in terms of 'stirred tanks in series with interstage circulation
model'. Each stirred tank is assumed to have a height equivalent to 0.8
times the column diameter and the number of tanks in series depends upon
the dispersion height. The following equation was obtained by Pandit and
Joshi Ι3ΊΙ:
U„Β · 0
Λ
"tt
—n
_
a«
re
-r i*
b,..
β
(c 1
t\
ι
V· '
;:— J
where, UB is the interstage recirculation velocity. HD is the dispersion
height and 'S' is the number of tanks in series. The values of aa, b« and
ca vary depending upon the extent of mixing and are given by Pandit and
Joshi /37/. They have shown that the experimental values of mixing time
agree with the predicted values which correspond to 95 per cent mixing.
Joshi /16/ has given the following equation for the interstage recirculation velocity:
UB=0.4<gT[VG-es.VSN(
ep
Ο
+
d
*
(5.2)
From this equation, it can be seen that the value of UB can change with
a change in eG or Vb«, and also with VSN and es, when VG is kept constant.
The values of eG were observed experimentally, whereas the values of VJ,»
were estimated according to the procedure discussed in Section 2. The
values of VSN are reported in Table 2, which were experimentally measured.
5.3. Effect of Superficial Gas Velocity
The effect of superficial gas velocity was studied at and above the critical
superficial gas velocity needed for the suspension of solid particles (VgN- =
7.5 to 164 mm/s) in the 100, 200 and 385 mm i.d. columns. It can be seen
from Figure 15 that the mixing time (0mix) decreases with an increase
in VQ. In some cases 0mix attains a minimum value and with a further increase in VG the mixing time also increases, though the rate of increase
is nominal.
51
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Three Pliase Sparged Reactors
Vol. 2. No. 1, 1984
-ι
Superficial gas velocity , Va x 1 0 ( m m / s )
14
1
I
2
I
3
I
4
I
5
6
7
Β
9
10
».
11 12 13 14 16 18
Ι Γ
microns
13
12
S "
κ 10
E
^D
A
.. 9
I·
P
7
14
Dolomite - dp Ά 110 microns 13
-o- e s = o.oi
—·- e e = o-05
11
0-10
10
12
01
IS
o>
c
1 κ
14
13
«
Ion exchange resin-d p «340 microns
-o- es = o-o5
en
c
"3
i
Ό
2 4 β 8 10 12 U 16 18 20 22
Superficial gas velocity,V e x10(mm/s)
Fig. ISA Effect of superficial gas velocity on mixing time
52
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
6 i
A.B. Pandit and J.B. Joshi
Reviews in Oiemical Engineering
15
Quartz dp — 500, microns
U
-o- e s ± 0-01
-·- es = D-OS
13
Quartz dp - 650 , microns
0-01
0-02
x 11
E
β 10
ο. β
c
χ 7
5
6
Ζ
IS
4
6
8
10 12 U
16 18 20 22 24 26 28 30 32
Quartz-dp ~ 340 microns
U
Gs = 0-01
13
0-03
12
ee
0-05
χ
1 10
a>
E
£ 8
cn
c 7
χ
ϊ β
l '
' 2 4 6 8 10 12 14 16 18 20 20 24 26 28 30 32
Superficial gas velocity,^ xl (mm/s)
»>
Fig. 158 Effect of superficial gas velocity on mixing time
53
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2. No. I. 1984
Three ttiase Sparged Reactors
It can be seen from equations (5.1) and (5.2) that UB increases with
an increase in VG. Higher values of UB will reduce mixing time, but at the
same time an increase in VG increases the fractional gas hold-up (eG) and
hence the dispersion height. Therefore the number of circulation cells also
increase. The combined effect of the above two factors result in a minima
of mixing time at a certain value of VG.
5.4. Effect of Ης/Τ Ratio
The effect of HC/T was studied in the range of 2 to 6. It was observed
that the mixing time increases with an increase in HC/T under otherwise
identical conditions (Figure 16).
It is indicated by equation (5.1) that, the increase in HC/T increases
HD and the number of circulation cells (S). Therefore more time is taken
for the pulse to get homogenised in more number of cells with the same
UB, which in turn increases the mixing time. It has been shown by Gopal
and Sharma /13/ that beyond HC/T equal to two, the fractional gas hold-up
does not depend upon HC/T and hence the interstage recirculation velocities
are not likely to change.
5.5. Effect of Column Diameter
Columns having diameters 0.10, 0.2 and 0.385 m i.d. were studied. The
values of mixing time (0mix) were found to increase with an increase in
column diameter (Figure 17). The effect of column diameter on mixing
time was not as pronounced as the HC/T ratio. With an increase in the column
diameter (at the same HC/T ratio) the actual liquid height is more but at
the same time, the average liquid circulation velocity increases with an
increase in the column diameter (equation (5.2)). The opposite effects
of the above two parameters result in a marginal increase in the values
ofomixEquations (5.1) and (5.2) can successfully explain the effects of superficial gas velocity, HC/T ratio and the column diameter on mixing time,
when appropriate values of Vj,,», (section 2) were used to predict the interstage circulation velocities.
5.6. Effect of Terminal Settling Velocity of a Particle
Particles having terminal settling velocities of 8.5, 12.9, 76, 100.5, 134
and 164 mm/s were studied. Figure 18 shows the effect of terminal settling
54
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Josl
Reviews in Chemical Engineering
Ο DOLOMITE-dp 1ϋ70 MICRONS,V e = SO ^^
mm
es=o-oi
pOLOMITE-dp «S 70 MICRONS Ve = 100 ~
s ,
mm
QUARTZ-dpGiSOO MICRONS, Ve = 70 -~
mm
= 0-01
QUARTZ - dp QJ 500 MICRONS ,V e = 100-5-
26
24
22
20
12
16
M
U
E
φ 12
•t
ω 10
Σ
Ο
Ζ
8
6
χ
χ
A
Hc /T
10
Fig. 16. Effect of HC/T ratio on mixing time
55
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
ο
ο
at
ιω
ο
ο
CO
ι
Ε
χ
1
II β
C
ο
II φ
>·» >η
ο
ο Ε
Ε
U
0
r-
ο
"
α:
ω
ο. α
•ο -σ
Ι
ω
UJ
2
Ι
ω
ο ο
ο
§ο §ο
ο
t*
*·*
Ο
01
-ι,
ο
υ
α
Η
€0
r-
.3
•ο
ι
φ
v
ι
t
τ-
ι
ι
M O O
«·
*~
ω
O
t
O
^
M
O
(δ)*1 θ * 3ΗΙ1 9 Ν Ι Χ Ι Η
56
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joslii
Reviews in Chemical Engineering
200
400
600
800
1000
Particle diameter ,d p ( microns ) —
8-25
1200
Fig. 18. Effect of particle diameter on mixing time
velocity on mixing time. It was observed that for smaller particles (dp <
340 μ) an increase in the average particle size decreased the mixing time.
In the higher range of particle sizes (dp > 500 μιτι), an increase in the average particle size increases the mixing time.
At the same superficial gas velocity Figures 3 and 4 show the values
of fractional gas hold-up as a function of terminal settling velocity of part-
57
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
icles (VSN-)· Similarly Figure 6 shows the extent of variation in Vb_ with
respect to VSN- (or particle size, dp). Figure 18 shows a trend in mixing
time, which is exactly similar to that observed for fractional gas hold-up
(«Ο*
The procedure of predicting mixing time in bubble columns proposed
by Pandit and Joshi /37/ also holds for three phase sparged reactors. A
detailed comparison will be presented in Section 5.8.
5.7. Effect of Solid Phase Hold-up
Solid phase hold-up was varied from 1 to 10 per cent by volume. For
particles in the lower range of sizes ( < 120 μπι) the value of mixing time
was independent of solid concentration (within ± 10 per cent). Here,
very little variation in the fractional gas hold-up and Vi,» is observed. For
the particles in the higher range ( > 500 /urn), at superficial gas velocities
which are considerably higher than VGC, the mixing time was independent
of solid phase hold-up (0.01 < es < 0.05). Near the critical superficial
gas velocity, the mixing time increased with an increase in the solid phase
hold-up. About 30 per cent increase in 0 m j X was observed, when es was
increased from 0.01 to 0.05. Visual observations indicated that, with an
increase in e«, near VGC, *ne bubble size was considerably larger. This in
turn reduces the average liquid circulation velocity, resulting in larger values
of mixing time.
5.8. Comparison Between Predicted and Experimental Values of
Mixing Time
Figure 19 shows the comparison between predicted and experimental
values of 0mjx for air-water-solid system. For the prediction of 0mix equations (5.1) and (5.2) were used with constants aa, ba and ca corresponding
to the 95 per cent homogeniely [Pandit and Joshi /37/ ] . It can be seen
from Figure 19, that the predicted and experimental values of mixing time
are comparable. The standard deviation for Figure 19 is 16 per cent.
It may be emphasized that appropriate values of e_ and Vt« need to
be used while estimating UB with equation (5.2). In the present case, experimentally observed values of eG were used.
In order to estimate \^„ the procedure discussed in Section 2 was used.
The value of constant 'a' in equation (2.5) was assumed to represent Vb„.
58
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
2
Reviews in Chemical Engineering
ί
6
8
1Z
14
16
M I X I N G T I M E P R E D I C T E D , θρ ( s )
Fig. 19. Comparison between the predicted and observed values of mixing time
A) T = 0.385 m
Symbol d (microns)
H
850
<$>
850
β
500
*
340
Φ
2000
Β) Τ = 0.20 m
®
500
χ
2000
Ο
340
Δ
850
•
110
π
110
•β.
110
e
Symbol
d (microns)
e
0.0054
0.027
0.027
0.027
0.0027
S.
70
70
340
340
340
500
850
500
340
340
0.01
0.10
0.01
0.03
0.05
0.03
0.02
0.05
0.03
0.05
s
V
β
-θVI
φ
0.01
0.01
0.01
0.01
0.01
0.05
0.1
'S"
•
οο
+
s
59
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1,1984
Ttirce Phase Sparged Reactors
5.9. Axial Mixing in Liquid Phase
The effect of solid phase on the liquid phase axial dispersion coefficient
is very complex. Joshi /16/ has critically reviewed all the published literature and has proposed the following correlation:
(5.3)
DL = 0.3 T (VC + V L )
where \Q is the average liquid circulation velocity and can be calculated
using the following equation:
VC = 1.31<gT[VG + V L - —
(^s
T
*I»L>
• 0 - eGVb~ 1 > Vs
(5-4)
El Temtamy and Epstein /I I/ have reported some DL data using 0.45,
0.96, 2 and 3 mm particles and 50 mm i.d. column diameter. They have
proposed the following equation:
VL dp
'
= 0.0012 ( V L P L d P)'-'56 T -i.i56
(5.5)
Recently Kim and Kim /25/ have studied liquid phase axial mixing in a
0.145 m i.d. column using 1.7, 3 and 6 mm particles. They have suggested
the following correlation:
(5.6,
Equations (5.5) and (5.6) do not consider the existence of different
regimes in three phase sparged reactors. Further the effect of particle size
on DL is not unidirectional as indicated by these equations. The value of
DL passes through a maxima with respect to particle size. Equation (5.6)
does not hold for semibatch operation ( VL = 0).
60
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
6. Heat Transfer
6.1. Introduction and Previous Work
There are several industrially important gas-liquid-solid reactions which
are accompanied by large heat effects. For the removal of heat, the column
wall or coils are often employed as heat transfer elements. Kolbel et al /28/,
1291, 1301, Viswanathan et al /46/, Armstrong et al /2/ and Deckwer et al
l&l have experimentally studied this aspect under variety of operating conditions. The details of the parameters are given in Table 8. The analysis of
the data indicate the following:
(i) For the case of relatively small particles (less than 100 jum) the
difference between heat transfer coefficient for gas-liquid and gas-liquidsolid system is nominal. The difference increases with an increase in the
solid phase hold-up (es).
(ii) The heat transfer coefficient initially increases with the particle
size and levels off when the particle diameter exceeds 3 mm.
(iii) A maximum value of heat transfer coefficient is obtained at a certain
value of e„. This value of eg depends upon the particle diameter (dp ).
(iv) The value of heat transfer coefficient increases with an increase
in the superficial gas velocity (VG). However, for a given VG, a maxima
in heat transfer coefficient occurs with respect to the superficial liquid
velocity.
(v) The value of heat transfer coefficient is practically independent
of the column diameter. Further, the values of heat transfer coefficient
at the column wall and at the surface of the centrally located heating rod
were found to be practically the same.
It was thought desirable to analyse all the available data on a rational
basis and explain the above mentioned points.
6.2. Mathematical Model
For the case of gas liquid bubble columns Joshi et al /20/ have analysed
the problem of heat transfer on the basis of liquid phase velocity profile
and the analogy with the single phase pipe flow. The following equation
was proposed (For VL = 0):
- 0.087 t^'Vo-^b-^j
Cp/z
k
73
X
/
61
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
77ι w Pliasc Sparged Reactors
Vol 2. No. 1. 1984
00
<N
v
h-
<
<*·»·
Cl
«v
tu
.D
Q
£ s„
1
"o
>^M
·_
Q
*-·
01
c
1
i>
£
cm c
.5 8
υ
φ
«m
I
£0> £ E
S 2
CD
Q.
^^
(A
E
£
m
Χ
«·-
ο
ν»
5i
C
ES
S
ε -S
•
^^
>Ή
00
0
o
c»»
•o
1
•g
<M
·*
1
o
«N
«N
ar- i
«M
ri-
1^
5
(O
^5
OO
•o
*—1
»O
«0
«0
O
t-^ o\ c>
01
t-H
S
*·»
M
I-«
o
^J
i
4
C
"8 B
0
Λ
o
o
•™<
i-H
Q
«->
CD
concent
9»- ΪΗ
1
4>
1
«N
1>
s
g
1
c
s
">
•i,
1
o
M
1
o
L^
c
-J
i
"3
•5
ss
E
_J
T3
"
TJ
'3
.?
1—1
(A
J5 Ϊ3
a
10
tV_
to
δ
!
8
+*
o
.o
Φ
""O
e φ Εa.
5 .uβ» —~
«O «N
f^
..
ι ι? S
1
IH
(D
tr~
oo
Γ-Ι
σν
Ov
rjvo
v*^
o
rs
1
oo
·*
§1
§
§
*n m
O
f-H
V)
,^5
>0
3
If
s s
I
S
c
Experime
o> ^
*a
.Si
3^-g
U
•g -s !
s
t
§
'S
Έ
S* Ee
S 5
O
s
φ
t;
£
444
's
S 'S
•o^ ^^ ^»^
l_
«n
«M «-·
m vo tf
«—t
O
C
X
tc 2
E3
ii
=0 Ι-
<Λ 00
z
<N
O\ O\ O\
O —< M
IN C<
<N
O\
O
0
0 O
0 OO
€M
—'
N
σ·
έ
<N
Ov
-H
»N
O\
<N
S3
4-J
1 •i
0
cn
o
<M
εs
g,
d
es
τΤ
«0
*-H
^H
1
o
't
<s
••H
ro
·*
«o
•-I
•—1
Ο
(
~H
vo r» «o
01
glass bead
δ
C
•S Φ
(%wt)
Sc
oo
0-b
<X>
S S*·
••s35 Hc
«*i
•S 8
Λ
£
ο
4-ι
«N
c
s
«.
*>
•3
Φ
·£
C
σ\
M.«
^1
«»
W
s
^^^fc
»N
^·
«a
8
c
VO
<5
<*ϊ
«0
62
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Cliemical Engineering
X(-^-)°· 1 4
When VL Φ Ο
VT_ =
k
(6.1)
0.087
08
(1.31) ·
TVfcp
μ
C^ ,/3 ^
k
/i w
Joshi /16/ has given the procedure for the calculation of liquid circulation
velocity for the case of gas-liquid-solid sparged reactors.
The following equation is proposed:
VC = 1 . 3 1 ( g T [ V G + V L - ^ ^ ^
-V L -
'3
(6-3)
Substitution of equation (6.3) in (6.2) and simplification gives:
hw = 0.087g0'266 c£3V°-33k0·67 Ρςα·Τβ·β6μ;,αΐ4 χ
χ [(VG
6.3. Discussion
For the prediction of heat transfer coefficient by equation (6.4), it is
necessary to know the hydrodynamic and physical properties such as Vj,,.,
PC' ^SN> Cp' k and μ of the three phase systems.
6.3.1. Estimation of Parameters: Rise Velocity of a Bubble ( V^)
Darton and Harrison / 7 / have measured the terminal rise velocities
of bubbles (Vboc) for 500 and 1000 μηι glass particles fluidised by water.
The data can not be applied directly for the cases of different particle sizes
and solid density. The procedure discussed in Section 2 has been adopted.
The value of constant 'a' in Table 3 can be used as Vboo in equation (6.4).
63
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1. 1984
Time Phase Sparged Reactors
Settling velocity of a particle ( VSN)
The terminal settling velocity (VSN„) of particles was obtained from
McCabe and Smith /31 /. The hindered settling velocity (VgN ) was obtained
by following the procedure of Joshi /18/.
Deckwer et al /8/ has used the following physical/thermal properties
for the liquid solid slurry.
(i) Density pc = pse^ + pLeL
(6.5)
(ii) Heat capacity,
(6.6)
Cp = Ws · CpS + WLCpL
(iii) Thermal conductivity, k = ki
(iv) Viscosity,
2kL + k s -2e" s (k L -k s )
r—
2kL+ks+2e-s(kL-ks)
μ = /i/ L (l + 4.5e"s )
(6.7)
(6.8)
The empirical correlation proposed by Deckwer et al /8/ is as follows:
hw = 0.1 VG°-25 g°-2S pc°-7S C°-s μ-0'25 k °·5
(6.9)
Equation (6.4) when applied for the case of small particles and in absence
of liquid flow reduced to:
hw = 0.087(VG-eGVbJ°-266g0-26^0-8Cp0-34M-°-33k0·66 X
χ
J0.06
χ
μ-0.14
(6 j0)
iV
It can be seen that the exponents and constants over most of the parameters in equations (6.9) and (6.10) compare well. The very low exponent
over T in equation (6.10) also explains the independence of heat transfer
coefficient with respect to the column diameter.
It can also be pointed out at this stage that equation (6.4) shows heat
transfer coefficient to be independent of the particle diameter. Equation
(6.9) could not explain the data of Kolbel et al /28/, /29/, as they observed
an increase in heat transfer coefficient with an increase in the particle size
from 40 μ m to 200 μ m. Equation (6.10) can explain the data of Deckwer
et al 18/ and Kolbel et al /28/, /29/ within ± 1 5 per cent when appropriate
values of the fractional gas hold-up (eG) were substituted. The eG behaviour
with respect to the particle size explained in Section 2 shows that a decrease
64
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
in ec will increase the value of the bracketed term in equation (6.10). As
a result the value of heat transfer coefficient increases.
6.3.2. Equivalent Diameter
The experimental measurements of heat transfer coefficient have been
either for the column wall or at the surface of the heating rods. For the
case of rod, it can be considered that the liquid flow is between the annulus
formed by the rod and the column. Usual correlations (for instance SeiderTate) for calculating the inside heat transfer coefficient can be applied
for the outside heat transfer coefficient if suitable definition is used for
the calculation of equivalent diameter (based on the heated perimeter).
It has been shown that the value of heat transfer coefficient is practically
independent of the equivalent diameter of the heat transfer element. This
explains the observation that the values of heat transfer coefficient at the
column wall and at the rod surface are practically the same under otherwise
identical conditions.
6.4. Model Predictions
6.4.1. Effect of Superficial Gas Velocity ( VG)
Equation (6.10) predicts heat transfer coefficient to be proportional
to (VG - eGVbjf>-i66. Deckwer et al /8/ has shown that, in the presence
of small particles, the fractional gas hold-up varies linearly with superficial
gas velocity (Section 2, Figure 2 shows similar observation in the lower
range of VG). As a result of these, the predicted heat transfer coefficient
varies as V^266 which is in close agreement with the experimental findings
of Kolbel et al /28/, /29/ and Deckwer et al /8/ which show heat transfer
coefficient to be proportional to Vi'25.
6.4.2. Maximum Heat Transfer
Coefficient
Armstrong et al /2/ have reported that a maxima in heat transfer coefficient occurs with respect to solid phase hold-up (ε,Λ superficial liquid
velocity (VL) and the particle diameter (dp). Since the predicted heat transfer
coefficient is given by equation (6.4), it is expected that the analytical
equation can be derived for the optimum values of es, VL and d p . However,
the parameters in equation (6.4) are interrelated as eG, V{,„ depend on
VG, es and d p and ?s also depends on VG making the relationship very
65
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. l, 1984
Three Phase Sparged Reactors
complex. Nevertheless, the occurrence of maxima can be discussed qualitatively. From equations (6.5) to (6.8) it can be seen that the values of
the physico-chemical properties such as μ, ρ and k increase and Cp decreases
with an increase in e"s (provided pg > pL and ks > kL). The value of the
liquid circulation velocity also decreases with an increase in e„ mainly due
to the increase in Vj,«, (mixing time readings also support this conclusion).
Figure 21 shows the comparison between the predicted and experimental
values of heat transfer coefficient. It can be seen from Figure 21 that there
is a good agreement between the predicted and experimental values of e„ at
which the maxima in heat transfer coefficient occurs.
6.4.3. Effect of Particle Size
When the particle size is very small ( < 20 μηι) the VSN value is negligible. Further, the physico-chemical properties of the slurry approach to
that of liquid when solid phase hold-up is small and heat transfer coefficient
approaches to that of gas liquid system.
At the same values of VG and VL an increase in particle size results into
an increase in the solid phase hold-up. Therefore, the effect of particle
size follows the same pattern as the effect of solid phase hold-up. The behaviour in mixing time with respect to the particle size also supports this
conclusion (Figure 18, Section 5).
6.4.4. Comparison with the Experimental Data
Figure 21 shows the comparison between the experimental and the predicted values [Equations (6.4) and (6.10)] of heat transfer coefficient.
It can be seen that the agreement is within 25 per cent. It may be emphasised that most of the experimental data have been obtained from relatively
small columns. Further, a systematic information on the effect of particle
size on the heat transfer coefficient is not available in the published literature. A carefully planned experimental investigation needs to be undertaken.
7. Worked Examples
7.1. Example — 1
It is desired to estimate design parameters for a 1.0m i.d. three phase
sparged reactor to be used for the removal of sulphur by oxydesulphurisa-
66
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
•l
ι
o £ .
" l i"
^ £<
o S:
a ·»
-*
o .si
x J
ΙΛ
X
ο. ι
O
CO < O
0
W £
·§
·?
2
ά
u
ει
X
i
Ν
1N3IOIJJ300 H3JSNVM1 1V3H
67
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2. No. 1,1984
Three Pliase Sparged Reactors
2000
1000
4000
P R E D I C T E D , h w ( k cal/hr m* *C )
Fig. 21. Comparison between the predicted and observed values of heat transfer coefficiSymbol
ent:
d (microns)
V-, mm/s
Ο
5000
0
(D
Δ
3000
V
D
1000
60
180
0
60
0
3000
180
θ
60
tion. Some experimental results are available from 150 mm i.d. pilot scale
reactor. The reactor was operated at 150°C and 0.5 M Pa pressure and in
a semi-batch manner (slurry phase was stationary and the gas phase was
continuous). The fractional solid phase hold-up was 10 per cent. The average
coal particle size was 40 microns and the terminal settling velocity (obtained
by sedimentation) was found to be 1 mm/s (ps = 1400 kg/m3).The fractional
gas hold-up and the mixing time results on the pilot scale reactor are as follows:
68
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Superficial
gas vel. VG
mm/s
eQ%
Mixing time
5
"mix·
HC/T = 5
0.42
0.65
0.84
1.3
1.7
2.1
1
2
3
4
5
6
Reviews in Chemical Engineering
4565
2147
1392
6(0
418
200
Superficial
gas vel. VQ
mm/s
10
20
50
120
150
200
€G%
Mixing time
omix.s
H c /T-5
3.2
7.8
12.8
22.0
24.0
26.5
140
28
18
10.2
10.3
9.4
Estimate the ciitical superficial gas velocity for the suspension of solids,
the axial concentration profile of solids, the liquid and solid phase dispersion
coefficients and the wall heat transfer coefficient for the commercial three
phase sparged reactor. The commercial size reactor is also proposed to be
operated in a semi-batch manner.
Solution
7.1. 1. Critical Gas Velocity for the Suspension of Solids
The fractional gas hold-up data was fitted by a correlation of the type
discussed in Section 2. The following correlation was obtained:
VG
G
0.234 + 3.0 VG
'
where VG is expressed in m/s. Equation (7.1) indicates that Vj,,» value is
equal to 0.234 m/s.
The particles lie in the laminar regime (Rep = 0.03). It was discussed
in Section 3 that the particles get suspended when the liquid circulation
velocity (VCL) equals the settling velocity of the particle. The value of
VCL is given by equation (3.2). It was observed in the present investigation
that the fractional gas hold-up is practically independent of the column
diameter under otherwise identical conditions (this observation needs confirmation under the conditions of high temperature and pressure).
For the estimation of design parameters it is necessary to know the hydrodynamic regime prevailing in the column. Joshi and Lali /19/ have given
a criterian for predicting the transition from homogeneous to heterogeneous
regime and for the 150 mm i.d. pilot scale reactor the transition occurs
69
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1 984
Three Phase Sparged Reactors
at about 50 mm/s. For the proposed commercial reactor, the transition
will occur at about 27 mm/s. It may be emphasised that the transition depends upon the system properties and the sparger design and substantial
amount of work is still required for the prediction of regimes.
The fractional gas hold-up data from the pilot scale unit are plotted
versus VG in Figure 22. The point B gives the value of the critical gas velocity
for the suspension of solid particles, which can be seen to be 2.4 mm/s.
Using equations (3.2) and (7.1) the value of V^L works out to be 1.23
mm/s, which favourably agrees with the terminal settling velocity of the
particle (VSN„). It was pointed out in Section 3 that the value of VGC is
independent of column diameter in the homogeneous regime. Let us select
the operating VG to be equal to twice the value of VGC·
7. 1. 2. Liquid Pfiase Dispersion Coefficient (DL )
For the homogeneous regime Joshi /17/ has given the following equation
for the liquid phase dispersion coefficient:
DL = 326(TV CL ) 1 · 7
(7.2)
where VCL is given by the equation (3.2). Substitution of pertinent parameters in equations (3.2) and (7.2) give the value of DL equal to 0.019
m 2 /s.
7. 1.3. Solid Pliase Dispersion Coefficient
(Ο$)
For the homogeneous regime, no correlation is available. As a first approximation it is reasonable to select Dg equal to DL since Vg^- is negligible.
7. 1.4. Solid Pfiase Axial Concentration Profile
Solid phase axial concentration profile is obtained by substituting the
necessary quantities in equation (4.8):
e
S
,
V
SN- · x .
—
= exp( -- zr- )
e
Sb
°S
esb was obtained by integrating the above equation over the total height
of the dispersion. Knowing eg = 0.10, HC/T = 5.0, e^ was found to be
0.1125.
70
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Renews in Cliemical Engineering
0-040
dp = 40 MICRONS
e, = 0-10
A I R WATER
2
4
6
8
1 0 1 2
SUPERFICIAL GAS V E L O C I T Y ( m m / s ) —
Fig. 22. Fractional gas hold-up versus superficial gas velocity for particles of 40 microns
71
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Three Phase Sparged Reactors
VoL 2, No. 1, 1984
The solid phase axial concentration profile obtained is as follows:
χ, m
x, m
0.5
1.5
2.5
3.5
4.5
0.1125
0.106
0.101
0.096
0.0911
0.086
0
1.0
2.0
3.0
4.0
5.0
7.7.5. Bed-wall Heat Transfer
0.109
0.104
0.0986
0.0935
0.088
Coefficient
The wall side heat transfer coefficient is obtained by use of equation
(6.10).
The physical properties are obtained from equations (6.5) to (6.8) and
are as follows:
= 1040 kg/m3
(1)
p
(2)
Cp = 0.853 kca!/kg°C
(3)
k
(4)
μ. = 1.16 χ 10- 3 Pa-s
(5)
f/ w = 8 χ ΙΟ' 4 Pa-s
= 3.58 kcal/hr m °C
Hence,
hw = 0.087(0.005-0.017 χ0.234)°·26(9.81)°·26(1040)08 χ
χ (0.853)0·34(1.16χ10-3Γ0·33(3.58)0·66(1)0-06(8χ10-4)-0·14 =
' = 0.087 χ 0.162 χ 1.81 χ 259.19 χ 0.947 χ 9.30 χ 2.32 χ 2.71
hw = 0.11 kcal/m2 °Cs
7.2. Example-2
Rework the above problem for the case of particle size of 2000 microns.
The value of VSN„„ is 50 mm/s. The pilot scale data are as follows:
72
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
mm/s
20
50
ISO
250
Reviews in Chemical Engineering
eQ
Omjx, s
VQ.mm/s
€G
^mix· 5
0.042
0.07
0.188
0.26
21.0
12.5
9.1
7.1
30
100
200
300
0.0606
0.118
0.23
0.28
17.0
10.8
8.3
6.8
7.2. 1. Critical Superficial Gas Velocity for the Suspension of Solids
The fractional gas hold-up data can be correlated by the following equation:
VG
0.35 + 2.98 VG
'
The plot of eG versus VG gives the value of VGQ equal to 100 mm/s.
As pointed out earlier the value of VQ£ lies in the heterogeneous regime
[Figure 23].
Hence equation (3 .5) is used to evaluate the critical superficial gas velocity
for the suspension:
0.05 = 0.3275 <gT [VGC - eGV - esb - VSN
a
c
p
c
]>
(7.5)
The value of e^ in the pilot scale was 0.184. Substituting all the quantities
in the above equation:
11
0.05 = 0.3275 [9.81 χ 1 (V^ - eGVbi>> - 0.184 χ 0.05 -^)]
or
0.153 = [9.81 (VGC ~ *GVb- ~ 3'54 " 10"3)1 '*
or
V
GC - *GVb~ = 3.90 x l O - 3
(7.6)
Substituting equation (7.4) in (7.6), we get:
73
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1. 1984
VGC - 0.35 + 2.98 VGC
Three Phase Sparged Reactors
xO.35 = 3.90 χ 10'3
or
2.98V£C - 0.0116 V^ - 1.37 χ ΙΟ' 3 = 0
The solution of the quadratic equation gives:
VGC = 0.02 m/s
0.32
dp = 2000 U
~ea - 0-10
AIR-WATER
0
I
I
I
ι
50
100
150
200
250
S U P E R F I C I A L GAS VELOCITY (mm/s )
ι
300
»·
Fig. 23. Fractional gas hold-up versus superficial gas velocity for particles of 2000
microns
74
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
7.2.2. Liquid Phase Dispersion Coefficient
Reviews in Chemical Engineering
(DJ
Let the operating superficial gas velocity be equal to twice the value
The average liquid circulation velocity in the heterogeneous regime is
given by the following equation:
vc = 1.31 [gT(vc - ccv - '«Λ
-^ >J / 3
(7 7)
-
Substituting VG, eQ values in equation (7.7) we get (VG = 0.05 m/s, CG =
0.107, egb = 0.1 84, VSN = 0.05 m/s)
Vc = 0.578 m/s
The liquid phase dispersion coefficient given by (Joshi /18/):
DL = 0.3 T Vc
= 0.3 χ 1 χ 0.578
= 0.1734m2/s
7.2.3. Solid Phase Dispersion Coefficient
(Ds)
From equation (4.15):
Ds = 0.33 T (Vc - 1.785 VSNJ
or
Ds = 0.161 m 2 /s
7. 2. 4. Axial Concentration Profile of Solids
The solid phase axial concentration profile can be obtained (eg = 0.1,
HC/T = 5, e„b = 0.184) from the following equation:
es = 0.
75
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
VoL 2, No. 1,1984
Jliree Phase Sparged Reactors
The values of e with respect to height are tabulated below:
x, m
χ, m
0.184
0.137
0.101
0.074
0.054
0.040
0
1.0
2.0
3.0
4.0
5.0
0.5
1.5
2.5
3.5
4.5
7.2.5. Bed-wall Heat Transfer Coefficient
0.161
0.118
0.086
0.063
0.046
(hw)
The bed wall heat transfer coefficient is obtained by using equation
(6.4):
The physical properties are obtained from equations (6.5) to (6.8) and
are as follows:
(1)
pc = 1040 kg/m3
(2)
Cp = 0.853 kcal/kg °C
(3)
k
= 3.58 kcal/m hr °C
(4) μ
= 1.16χ ΙΟ' 3 Pa-s
(5) i / w = 8 x l O ' 4 P a - s
Hence,
hw = 0.087 gO.
= 0.087 χ 1.81 χ 0.947 χ 9.37 χ 2.32 χ 259.19 χ 1 χ 2.71 χ
χ [0.05 - 0.1 χ 0.05 χ
360
- 0.11x0.35] 0.266
1040
hw = 0.184 kcal/s m 2 °C
76
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
8. Conclusions
(i) The effect of particle size on bubble diameter is complex. When
the particle size is less than 100 microns, an increase in particle size decreases the bubble diameter. A further increase in particle size (beyond
100 microns) increases the bubble diameter and attains a maximum value
when the particle size is in the vicinity of 500 microns. The bubble diameter
again decreases when the particle size is increased above 500 microns.
(ii) The critical superficial gas velocity for the suspension of solid particles can be predicted. In the heterogeneous regime, a particle gets suspended
when the settling velocity of a particle equals the liquid phase turbulence
intensity.
(iii) The solid phase and the liquid phase axial dispersion coefficients
are given by the following equations, respectively:
Ds =0.33T(V C - V S „ ) . . . . ( V L = 0)
DL = 0.3T(V C + V L )
(iv) Equation (5.1) together with equation (5.2) predicts the values
of mixing time fairly well. It takes into account the effects of superficial
gas velocity, column diameter, column height, particle size and the solid
phase hold-up.
(v) A reasonably good agreement was found between the predicted
[equation (6.10)] and experimental values of wall heat transfer coefficient.
Also the occurrence of maxima in the wall heat transfer coefficient with
respect to d p , VG and VL can satisfactorily be explained.
(vi) The performance of three phase sparged reactors strongly depend
upon the bubble diameter and its rise velocity. These two parameters strongly
depend upon the physical properties of the liquid, the particle size and
density, superficial gas velocity and the solid phase hold-up. Even the presence of small adventitious impurity can dramatically influence the bubble
diameter. The measurements of fractional gas hold-up and the mixing time
with respect to VQ using a small scale apparatus (say, 150 mm diameter)
and the given system (physical properties of gas and liquid, particle size
and density and solid phase hold-up) are recommended. The gas hold-up
and mixing time data may be analysed according to the procedures discussed in Sections 2 and 5, respectively. These measurements and analysis
will give fairly good idea regarding and the hydrodynamic behaviour of three
phase sparged reactors.
77
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1. 1984
Three Phase Sparged Reactors
9. Recommendations for Future Work
The remarkable feature of the review paper by ^stergaard /34/ lies in
the clear indications regarding the directions for the future research. At
that time, the subject 'three phase reactors' was new. We have come a long
way and all the investigations since 1968 were analysed and summarised
in the previous sections. A substantial amount of work is still needed for increasing the confidence in the design of three phase sparged reactors. Recently,
Epstein /12/ has given the critical account of the present knowledge and has
given valuable suggestions. Some additional suggestions for the future work
are as follows:
(i)
Very limited information is available regarding the effect of physical
properties such as viscosity, surface tension, non-Newtonian behaviour
and the presence of electrolytes on the performance of three phase sparged
reactors. Future investigations should include the effect of physical properties
on the fractional phase hold-ups, critical gas velocity for the suspension
of solid particles, particle concentration profiles, mixing, heat transfer and
mass transfer.
(ii) The major use of three phase sparged reactors is at high temperatures and pressures. The performance of three phase sparged reactors at
elevated temperatures and pressures need to be studied in using reasonable
size equipment (say, 150 mm i.d.).
(iii) The published information on wall heat transfer coefficient is somewhat limited. A systematic investigation needs to be undertaken covering
a wide range of particle sizes and density, superficial gas and liquid velocities
and physical properties. After the accumulation of substantial experimental
data good correlations should be developed. Heat transfer characteristics
across cooling/heating coils should be studied. It is likely that an optimum
location for the coil can be obtained.
(iv) In Section 4, solid phase axial dispersion coefficient was calculated
on the basis of axial concentration profiles. This is a somewhat indirect
method. A systematic investigation needs to be undertaken using radioactive tracer techniques.
(v) The axial and radial solid phase concentration profile needs to be
measured over a wide particle size range, settling velocities and solid phase
hold-up.
(vi) Experimental data on the gas phase axial mixing is practically nonexistent. A systematic investigation needs to be undertaken, over a wide
range of variables. The effect of column diameter and particle diameter
on gas phase axial mixing should be studied.
78
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
(vii) The measurements of flow patterns and turbulence characteristics
will improve our knowledge regarding the particle liquid and gas-liquid
interactions. With the help of Laser-Dopier and Hot-Film anemometers
some progress in this direction can be made.
(viii) Using the modern techniques, the bubble diameter and its terminal
rise velocity need to be measured. The effects of particle size and density,
physical properties, temperature and pressure need to be investigated.
(ix) Mathematical modeling of existing commercial size three phase
sparged reactors needs to be made. For instance, large size equipment are
in operation for catalytic hydrogenation and oxidation, Fischer-Tropsch
reaction, fermentation, waste-water treatment and carbonation. Modeling
will give a clearer picture regarding the interactions between the various
design parameters.
10. Nomenclature
A
a
a
aft
B
b
ba
C
Cp
CpL
Cps
ca
DG
DL
DS
DSÖ
— constant in equation 4.2
— constant in equation 2.5, m/s
— interfacial area (gas-liquid), m 2 /m 3
— constant in equation 5.1
— constant in equation 4.2
— constant in equation 2.5
— constant in equation 5.1
— concentration of solids, wt of solids/wt of slurry
- specific heat ,kcal/kg°C
— specific heat of liquid, kcal/kg°C
- specific heat of solid, kcal/kg °C
— constant in equation 5.1
— diameter of the conical gas distributor, m
— liquid phase axial dispersion coefficient, m 2 /s
— solid phase axial dispersion coefficient, m2/s
— solid phase axial dispersion coefficient at the bottom of the column,
m 2 /s
dg — bubble diameter, mm
dp — particle diameter, microns ( )
g
— acceleration due to gravity, m/s2
hw — wall side heat transfer coefficient, kcal/m2 °C hr
Hc — height of the clear liquid, m
HD — height of the gas-liquid-solid dispersion, m
79
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Tliree Phase Sparged Reactors
k
kL
kg
QG
Rep
S
— thermal conductivity, kcal/m °C s
— thermal conductivity of liquid, kcal/m °C s
— thermal conductivity of solid, kcal/m °C s
— volumetric gas flow rate, m 2 /s
— particle Reynold's number, V SN „d p /Y/μL
— number of cells in series in a bubble column or 3 phase sparged
reactor
T
— column diameter, m
U' — bulk turbulence intensity, m/s
UB — interstage circulation velocity, m/s
YC — average liquid circulation velocity in Churn turbulent regime, m/s
VCL — downward liquid circulation velocity in bubbly flow regime, m/s
^)- — terminal rise velocity of a single bubble, m/s
VG — superficial gas velocity, m/s
VL — superficial liquid velocity, m/s
VLC — critical superficial liquid velocity, m/s
VQ — transition superficial gas velocity from breakage of bubble to coalescence regime, m/s
VGQ — critical superficial gas velocity for the suspension of solid particles,
m/s
V0 - effective rise velocity of the bubble, m/s
superficial slurry velocity, m/s
~ hindered settling velocity of a non-spherical particle, m/s
V' — effective settling velocity of a particle in presence of gas, m/s
VSN- — terminal settling velocity of a non-spherical particle, m/s
Vs_ — terminal settling velocity of a spherical particle, m/s
WL — weight fraction of liquid
w§ — weight fraction of solids
χ
— axial distance from the bottom of the column, m
Greek Symbols
δ
eG
e
GS
CL
es
es
e
— ratio of wake to bubble volume
— fractional gas hold-up
~~ fracti°nal B3s hold-up in presence of solids
— fractional liquid hold-up
— fractional solid hold-up
— average fractional solid hold-up
— fractional solid hold-up at the bottom of the column
80
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joslii
e|
e's
0V
μ
μν
ι»Pf,
pG
pL
ps
Δρ
σ
0mix
0«
Reviews in diemical Engineering
— fractional solid hold-up in the entering slurry
— volume of solids per unit cross sectional area of the column, mm
— volumetric shape factor of a solid particle
— viscosity of a suspension, kg/m s
— viscosity of water, kg/ms
— kinematic viscosity of suspension, m2 /s
— continuous phase density, kg/m3
- gas density, kg/m3
— density of liquid, kg/m3
— density of solid, kg/m3
— density difference between solid and liquid, kg/m3
— surface tension of liquid, Newtons/m
- mixing time, s
- time for certain extent (a) of mixing, s
81
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol. 2, No. 1, 1984
Three Phase Sparged Reactors
References
1. Abou, Al Hassan, Third European Conference on Mixing, April 4th to
6th, 303 (1979).
2. Armstrong, E.R., Baker, C.G.J. and Bergougnou, M.A., "Fluidisation
Technology", Keairns, D.L. (Ed.), Vol. 1, Hemesphere Pub. Co., Washington, 453 (1976).
3. Barnea, E. and Mizrahi, J., Chem. Engng. J., 5, 171 (1973).
4. Begovich, J.M. and Watson, J.S., Fluidisation, Proc. 2nd Eng. Found.
Conf. (J.F. Davidson and D.L Keairns eds.), Cambridge Univ. Press,
190(1978).
5. Bhatia, V.K. and Epstein, N., Proc. Ind. Symp. on Fluidisation and Its
Applications, Toulouse, 380 (1974).
6. Cova, D.R., Ind. and Engng. Chem., Proc. Des. Dev., 5(1), 20-25 (1966).
7. Darton, R.C. and Harrison, D., Trans. Instn. Chem. Engrs., 52, 301
(1974).
8. Deckwer, W.D., Louisi, Y., Zaidi, A. and Ralek, M., Ind. Engng. Chem.,
Proc. Des. Dev., 19, 699 (1980).
9. Dhanuka, V.R. and Stepanek, J.B., Fluidisation, Proc. 2nd Eng. Found.
Conf. (J.F. Davidson and D.L. Keairns eds.), Cambridge Univ. Press,
179(1978).
10. Efremov, G.I. and Vakhrushev, I.A., Int. Chem. Engng., 10(1), 37
(1970).
11. El Temtamy, S.A. and Epstein, N., Can. J. Chem. Engng., 57, 520
(1979).
12. Epstein, N., Can. J. Chem. Engng., 59, 649 (1981).
13. Gopal, J.S. and Sharma, M.M.. Can. J. Chem. Engng., 61(4), 517 (1983).
14. Henrikson, H.K. and (Jstergaard, K., Cliem. Engng. Sei., 29,626 (1974).
15. Imafuku, K., Wang, T.Y., Koide, K. and Kuboto, H.,J. Cftem. Engng.
Japan, 1(2), 153(1968).
16. Joshi, J.B., Trans. Instn. Chem. Engrs., 58, 155 (1980).
17. Joshi, J.B., Trans. Instn. Chem. Engrs., 59, 118 (1981).
18. Jöshi, J.B., Chem. Eng. Res. Des., 61, 143 (1983).
19. Joshi, J.B. and Lali, A.M., in "Frontiers in Chemical Reaction Engineering)'
Doraiswamy, L.K. and Mashelkar, R.A. (eds.) Wily Eastern Ltd., New Delhi, p. 381-407 (1984).
20. Joshi, J.B., Sharma, M.M., Shah, Y.T., Singh, C.P.P., Moanis Ally and
Klinzing, G.E., Chem. Engng. Commn., 6,257 (1980).
21. Joshi, J.B. and Shah, Y.T., Paper presented at ACS Meeting, Las Vegas,
Aug. (1980).
82
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
A.B. Pandit and J.B. Joshi
Reviews in Chemical Engineering
22. Kato, Y., Nishiwaki, A., Fukuda, T. and Tanaka, S., / Chem. Engng.
Japan, 5,112(1972).
23. Kim, S.D., Baker, C.G.J. and Bergougnou, M.A., Can. J. Chem. Engng.,
50,695(1972).
24. Kim, S.D., Baker, C.G.J. and Bergougnou, M.A., Can. J. Chem. Engng.,
53,134(1975).
25. Kim, S.D. and Kim, C.H., /. Chem. Engng. Japan, 16(3), 172 (1983).
26. Kito, M, Shimada, M., Sakai, T., Sugiyama, S. and Wen, C., "Fluidisation
Technology", Vol. I, Hemesphere Publishing Corporation, Washington,
p. 411 (1976).
27. Koide, K., Yasuda, T., Iwamoto, S. and Fukuda, E., J. Chem. Engng.
Japan, 16(1), 7 (1983).
28. Kolbel, H., Siemes, W., Mass, R. and Muller, K., Chemie Ing. Team.,
30,400(1958).
29. Kolbel, H., Borchers, E. and Muller, K., Chemie. Ing. Techn., 30, 729
(1958).
30. Kolbel, H., Borchers, E. and Martins, J., Chemie. Ing. Techn., 32, 84
(1960).
31. McCabe, W.L. and Smith, J.C., "Unit Operations of Chemical Engineering", McGraw Hill, New York, 155 (1976).
32. Michelson, M.L. and 0stergaard, K., Chem. Engng. J., 1, 37 (1970).
33. Narayanan, S., Bhatia, V.K. and Guha, D.K., Can. J. Chem. Engng., 47,
360 (1969).
34. ßstergaard, K., Advances in Chem. Engng. (T.B. Drew et al Eds.), Academic Press, 7,71 (1968).
35. Ostergaard, K. and Michelson, M.L., Symp. Fund. Appl. Fluidisation,
Tampa, Florida, Preprint 31D (1968).
36. 0etergaard, K. and Theisen, P.I., Chem. Engng. Sei, 21, 413 (1966).
37. Pandit, A.B. and Joshi, J.B., Chem. Engng. Sei., 38(8), 1189-1215
(1983).
38. Pandit, A.B. and Joshi, J.B., To be forwarded for publication.
39. Pandit, A.B. and Joshi, J.B., To be forwarded for publication.
40. Patwari, A.N., Ph.D. Thesis, University of Oldenburg (1983).
41. Parulekar, S.J. and Shah, Y.T., Chem. Engng. J., 20, 21 (1980).
42. Roy, N.K., Guha, D.K. and Rao, M.N., Chem. Engng. ScL, 19, 215
(1964).
43. Shah, Y.T., "Gas-liquid-solid Reactor Design", McGraw Hill, Publ.
Co., New York (1979).
44. Sharma, M.M. and Danckwerts, P.V.,Brit. Chem. Eng., 15, 522 (1970).
83
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM
Vol 2, No. 1. 1984
Three Phase Sparged Reactors
45. Doraiswamy, L.K. and Sharma, M.M... "Heterogeneous Reactions —
Analysis, Examples and Reactor Design", John Wiley and Sons, New
York (1984),
46. Vishwanathan, S., Kakar, A.S. and Murti, P.S., diem. Engng. ScL, 20,
903 (1965).
47. Ying, D.H., Givens, E.N. and Weimer, R.F., Ind. Engng. Chem., Proc.
Des. Dev., 19,635-638 (1980).
84
Brought to you by | provisional account
Unauthenticated
Download Date | 1/2/20 11:23 PM