9 A Two-Bubble Class Model for Churn Turbulent Bubble Column Slurry Reactor
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S. JOSEPH and Y. T. SHAH Chemical and Petroleum Engineering Department, University of Pittsburgh, Pittsburgh, PA 15261
A two-bubble-class model for the churn turbulent bubble column reactor is proposed. The model parameters include both small and large bubble holdups, liquid side mass transfer coefficients for small and large bubbles, and the small and large bubble diameters. All of these parameters, except the large bubble diameter, are either measured or estimated. The model is used to correlate and explain the experimental data of Schumpe et al. (7) for the absorption of CO2 in NaOH. The model is believed to be more realistic than the conventional single-bubble-class model. It, however, requires independent measurements of large bubble diameters under a wide range of operating conditions. Further verification of the model requires additional experimental data at superficial gas velocities greater than 0.2 m/s and in large diameter columns. The data for slow reaction systems (e.g., absorption of CO2 in NaCO3) would also be desirable for the further critical evaluation of the model. A bubble column is a contactor which involves the passage of a discontinuous gas phase in the form of bubbles, through a continuous phase, which can either be a liquid or a homogeneous slurry. The various flow regimes that can occur in a bubble column have been characterized by Shah et al. (1). The bubbly flow regime occurs for low superficial gas velocities (< 0.05 m/s), and is distinguished by bubbles of uniform size. At higher gas velocities, the homogeneous gas-in-liquid dispersion cannot be maintained and two bubble classes develop: large bubbles moving with high rise velocities in the presence of small dispersed bubbles. This has been classified as the heterogeneous or churn turbulent regime. 0097-6156/84/0237-0149$06.00/0 © 1984 American Chemical Society In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
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CHEMICAL AND CATALYTIC REACTOR MODELING
Bach and P i l h o f e r (2) have suggested that the churn turbulent regime i s the most commonly encountered flow regime i n the i n d u s t r i a l bubble columns. Vermeer and Krishna (3_) have concluded from t h e i r s t u d i e s on a bubble column operating i n the churn turbulent regime that gas transport i n t h i s regime occurred exclusively due to l a r g e bubbles. The bimodal d i s t r i b u t i o n of bubble s i z e s i n the churn turbulent regime has been reported by s e v e r a l i n v e s t i g a t o r s (3-6). The churn turbulent regime has been modeled by a s i n g l e c l a s s of bubbles moving i n a plug flow manner (_7)« T h concept of a mean gas phase residence time i n t h i s regime i s somewhat meaningless. The two bubble c l a s s e s behave d i f f e r e n t l y as they move up the column. The l a r g e bubbles t r a v e l i n a plug flow manner due to t h e i r h i g h bubble r i s e v e l o c i t i e s , while the s m a l l bubbles tend towards complete backmixing due to l i q u i d circulations. Hence the mean r e s i d e n c e time of the l a r g e bubbles i s smaller than that of the small bubbles. A r e a l i s t i c model f o r the churn t u r b u l e n t regime should thus c o n s i d e r the c o n t r i b u t i o n of both bubble c l a s s e s . The a p p l i c a t i o n of the two bubble c l a s s model i s important f o r r e a c t i o n s which are mass t r a n s f e r c o n t r o l l e d . The scale-up of a mass t r a n s f e r c o n t r o l l e d o p e r a t i o n based on a f i x e d gas phase residence time assumes i n c o r r e c t and higher a c t u a l gas velocities. Thus, when the flow regime changes from homogeneous to churn t u r b u l e n t , an apparent drop i n conversion could be encountered due to decreased mass t r a n s f e r r a t e s . G e n e r a l l y , the scale-up of a bubble column i s accompanied by the change i n flow regime and under t h i s s i t u a t i o n , the two bubble c l a s s model w i l l give a more r e l i a b l e scale-up than the conventional s i n g l e bubble c l a s s model. In t h i s paper, we f i r s t develop the two bubble c l a s s model f o r a bubble column r e a c t o r which c a r r i e s out a simple r a p i d f i r s t order r e a c t i o n i n the l i q u i d phase. The model i s a p p l i e d to the a b s o r p t i o n of CO2 i n NaOH i n the churn t u r b u l e n t regime. The a p p l i c a t i o n of the model to a s l u r r y r e a c t o r i s a l s o b r i e f l y discussed.
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e
Development of Model Consider a gas A which i s being absorbed i n t o a l i q u i d containing a reactive species B. The reaction d i s s o l v e d A and Β i s g i v e n by A + ZB
•>
solution between
products
(1)
For s i m p l i c i t y , we assume the c o n c e n t r a t i o n of Β i n the l i q u i d phase to be i n excess and the r a t e of r e a c t i o n to be pseudof i r s t order with respect to A. Thus r
A
"
k
l
C
AL
In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
(2)
9. The
151
Column
r e a c t i o n i s i n the f a s t r e a c t i o n regime, i f Ha =
D
The f o l l o w i n g model. 1.
A
/
>3
assumptions
(3) are made i n the development
of
the
The large bubbles are assumed t o t r a v e l i n a plug flow manner. The small bubbles a r e e i t h e r p a r t i a l l y o r completely backmixed. The v a r i a t i o n i n gas molar flow r a t e caused by absorption and r e a c t i o n i s n e g l i g i b l e . When the gas phase r e a c t a n t i s d i l u t e d with an i n e r t (as i n t h i s case), this i s a reasonable assumption. There a r e no a x i a l v a r i a t i o n s i n gas holdup. The pressure v a r i e s l i n e a r l y along the a x i s o f the column and i s given as
2. Downloaded by UNIV OF CINCINNATI on February 18, 2015 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch009
Churn Turbulent Bubble
JOSEPH AND SHAH
3.
4. 5.
Ρ =P
T
Pg L
where
[1 + α (1-z)]
(4)
L (1-ε ) 0
α = *T
6.
The e q u i l i b r i u m ±iquid phase concentration of A i s given by Henry's law f o r both small and l a r g e bubbles. Thus,
7. 8.
There i s no i n t e r a c t i o n between the two bubble c l a s s e s . The gas phase r e s i s t a n c e i s n e g l i g i b l e .
The mass balance assumptions i s U
-fc( GÎ lx> G
f o r A i n large
L
L
bubbles
based
on these
C
= ( - AL>*
6
where φ i s the enhancement f a c t o r due to chemical r e a c t i o n and f o r Ha > 3, φ = Ha. The mass balance f o r A i n small bubbles is U
S
In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
152
CHEMICAL AND CATALYTIC REACTOR MODELING
If the small bubbles are assumed to be p a r t i a l l y backmixed, then t h e f o l l o w i n g mass balance equation can be w r i t t e n , d2
d
4
ι
4
L
s
< v > Is U
di dz
r
t (
Y Downloaded by UNIV OF CINCINNATI on February 18, 2015 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch009
t
z
=
X
>
*
)
S
c
)
-
c
φ
_
0
(
8
)
k i ? * - °
„ d Y
L =L,o
d a
c
r ^ k O Ρ
G
w i t h t h e boundary c o n d i t i o n s
a t z = 0,
(
Y
Y
'
G
+
f e d T ^
0 °*
di
The s o l u t i o n o f t h i s equation i s
Y
g AG
=
A
e
l
x
p
m
z
^ l ^
+
A
2
e
x
p
m
z
( 2 ^
(9)
where -1 ± VI + 4 St /Pe G
m
i,2
—
Pe
St, = a" / D ^
(«) G Y
2 A
1
s
AG,0 1 + (m /Pe-m /m ) exp (n^-mj) - m /Pe 2
2
1
2
= - ( A n^/mp exp (n^-nij) 2
In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
(
8
)
Churn Turbulent Bubble
9. JOSEPH AND SHAH
153
Column
The c o n c e n t r a t i o n of A i n the bulk l i q u i d i s zero and hence i t s l i q u i d phase balance can be n e g l e c t e d . The f l u x o f A through l a r g e and small bubbles i s given by
(10) G br G Equation 6 can be i n t e g r a t e d to give
Downloaded by UNIV OF CINCINNATI on February 18, 2015 | http://pubs.acs.org Publication Date: December 9, 1984 | doi: 10.1021/bk-1984-0237.ch009
τ Y
τ
AG,1 =
τ
4G,0
(
1
+
«>
E X
P
{
"
L
a H
0
R
T
L
/
D
A
1 br
The mass balance f o r A i n small bubbles, s i m p l i f i e d t o give
C C
where
U
=
equation
7, can be
K
i
}
2
e
br G
= C
» = a RT /D k, A 1 A
P
C
n
^ > G
Y 1 AG,0 1+ c
L
and
i
}
S
C
S _ "AG.l
k
P
0 pm
l — 0
Note the s o l u t i o n given i n both equations 11 and 12 do not depend on k-^, but on the i n t r i n s i c r a t e parameter k^ and on " a " f o r l a r g e and small bubbles. The gas phase conversion f o r A i s c a l c u l a t e d from the o v e r a l l mass balance f o r the gas phase a s ,
U
£
br G
4,1
+
U
£
br G
Y a
n
d
A
4,1
U
Y
" G AG,1
(
1
3
)
Y
AG,Q- AG,1
(
1
4
)
AG,0
Hence, the gas phase conversion f o r a pseudo-first order r e a c t i o n i n the churn t u r b u l e n t regime can be c a l c u l a t e d i f the f r a c t i o n a l gas holdups, r i s e v e l o c i t i e s , and i n t e r f a c i a l areas f o r the two bubble c l a s s e s as w e l l as the p h y s i c o chemical data are known.
In Chemical and Catalytic Reactor Modeling; Dudukovi, M., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1984.
154
CHEMICAL AND CATALYTIC REACTOR MODELING
The assumption of a plug flow model f o r the e n t i r e gas phase leads to the f o l l o w i n g expression f o r the gas phase conversion, ( 7 ) Y
where
X
AG,0 A
-
( 1
Y
- AG,0>
St
L N
"V
( 1
= a
Q
"
S t
G
( 1 5 )
