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Multi-orifice plate distributors in gas fluidised beds — a model for design of distributors
Powder Technology, 24 (1979) 215 223 © Elsevier Sequoia S.A., Lausanne - - Printed in the Netherlands -
215
Multi-Orifice Plate Distributors in Gas Fluidised Beds -- A Model for Design of Distributors
D. SATHIYAMOORTHY and Ch. SRIDHAR RAO Metallurgy Division, Bhabha A t o m i c Research Centre, Trombay, B o m b a y - 4 0 0 0 8 5 (India) (Received May 5, 1978; in revised form July 3, 1979)
SUIVIMARY
T h e u s e o f a s u i t a b l e g a s d i s t r i b u t o r is essential for satisfactory performance of gas-solid fiuidised beds. Multi-orifice plate type gas distributors in fluidised beds are frequently used in industrial practice. This paper analyses the factors governing the operating characteristics of the multi-orifice p l a t e t y p e o f gas d i s t r i b u t o r . R e s u l t s o f the experiments carried out in a 100 mm d i a m . glass t u b e a s s e m b l y w i t h a d i s t r i b u t o r plate having 20 orifices are presented. Rutile and zircon sands and alumina powder (70 1 5 0 / ~ m ) w e r e u s e d as t h e b e d m a t e r i a l , w h i l e air --up to ten times the minimum fluidising v e l o c i t y ( U m f ) - - w a s u s e d as t h e f l u i d i s i n g medium. It has been observed that all the orifices bec o m e o p e r a t i v e a t a g a s v e l o c i t y UM a n d t h e r a t i o U M / ( U M ~ Umf) is r e l a t e d t o t h e p r e s s u r e drop (distributor/bed) ratio (APd/APb)
by a constant K o which is independent of syst e m parameters. A theoretical m o d e l for the estimation of K o and the experimental values are presented. INTRODUCTION T h e f l u l d i s e d b e d t e c h n i q u e is a d o p t e d i n a number of metallurgical and chemical process industries. The performance of the fluidised bed system largely depends on the satisfactor y d e s i g n a n d s e l e c t i o n o f gas d i s t r i b u t o r s . B a s i c a l l y a gas d i s t r i b u t o r h a s t o h a v e t h e f o l l o w i n g c h a r a c t e r i s t i c s . (i) I t s h o u l d d i s t r i b u t e t h e g a s u n i f o r m l y i n t h e b e d . (ii) I t s h o u l d have a definite and non-changing (with time) p r e s s u r e d r o p f o r t h e gas. ( i i i ) I t s h o u l d n o t permit the drain of solids. Though a variety
of distributors have been reported in the patent l i t e r a t u r e , t h e p u b l i s h e d w o r k o n t h e s u b j e c t is v e r y l i m i t e d . Whitehead [1] has studied the operation of gas d i s t r i b u t o r s c o n t a i n i n g m u l t i - t u y e r e s in rectangular assemblies. Detailed investigations have been carried out to determine the minim u m gas v e l o c i t y a t w h i c h all t h e t u y e r e s become operative. Fakhimi and Harrison [2] have studied the behaviour of multi-orifice distributors and derived a relationship between t h e n u m b e r o f o p e r a t i n g o r i f i c e s a n d t h e gas superficial velocity. Kassim [3] has reported certain discrepancies between his observations and the calculated values using Fakhimi's relationship, when working with materials which had a low minimum fluidising velocity. I t is o b s e r v e d t h a t f o r s t a b l e o p e r a t i o n o f the bed, a certain magnitude of pressure drop at the distributor should exist [4]. This could be of the order of 10 - 15% of that in the bed. H o w e v e r , t h e r e is s t i l l a c e r t a i n a m o u n t o f u n c e r t a i n t y o n t h i s a s p e c t as a s y s t e m w o r k i n g on such low pressure drop ratio has not always given good performance of the bed [1]. Hiby [5] indicates that the required pressure drop r a t i o (APdistr~utor/APbed) f o r a p e r f o r a t e d o r nozzle type distributor should be 0.15 when U/Um~ ~- 1 - 2 a n d a b o u t 0 . 0 1 5 w h e n u / u = , f 1.The effect of distributor to bed resistance ratio on the onset of fluidised bed channelling was analysed by Siegel [6]. Based on observations on the bed expansion ratio, it was determined that the ratio of distributor to bed resistance required for stability was 0.14 0 . 2 2 o v e r a w i d e r a n g e o f G a l i l e o n u m b e r (1 10,000). The authors of the present paper have shown [9] that the fractional n,,mber of o p e r a t i n g o r i f i c e s i n a m u l t i - o r i f i c e t y p e o f gas d i s t r i b u t o r is a f u n c t i o n o f o p e r a t i n g g a s ve~
216
|.0
---
0
U-Urnf
UM
Umf
Fig. 2. Relat;onship b e t w e e n fractional n u m b e r o f
orifices o p e r a t i n g and gas flow. Fig.
I. O r i f i c e s
in a circular
distributor.
I o c i t y U , m i n i m u m f l u i d i s a t i o n v e l o c i t y Umf a n d a c o n s t a n t K (i.e. K = K o ( A P d ] A P b ) ~ ) w h i c h i n i t s e I f is d e p e n d e n t o n s y s t e m p a r a meters. In the present paper, the behaviour of the multi-orifice plate distributor has been anal y s e d a n d a n a t t e m p t is m a d e t o e s t a b l i s h K o as an independent constant. A method has also been suggested to predict this constant. The experimental observation and the proposed model are confined to a gas velocity range varying from the first orifice to the last one becoming operative. Results of the experimental studies carried out in a 100 mm diam. glass tube assembly are presented.
THEORY
W h e n a f l u i d i s i n g g a s is p a s s e d t h r o u g h a bed of particles held on an orifice plate or a gas distributor, a drop in the pressure of the gas occurs and the velocity of gas increases. O n c e t h e m i n i m u m f l u i d i s a t i o n v e l o c i t y is reached, with subsequent increase in the gas flow rate the pressure drop across the distributor increases while that in the bed remains rather steady at a value equivalent to the weight of bed material per unit cross-sectional a r e a o f t h e b e d . I t is k n o w n t h a t t h e f l o w o f g a s t h r o u g h a l l t h e o r i f i c e s is n o t u n i f o r m f o r various reasons. Depending on the size and shape of particles, shape and size of container (bed) and also the c~]ming section, the gas selects an easy path and an orifice offering such a path becomes operative. The characteristic flow of gas in the calming section with a
velocity gradient across the section also contributes to the preferential operation of certain orifices. It may be expected, say in an orifice plate of circular section, in which the orifices are arranged in concentric circles as shown in Fig. 1, that the resistance to flow of gas increases as the distance of an orifice from the centre of the distributor increases, As a result o f t h i s , a t a c e r t a i n g a s v e l o c i t y w h i c h is U m f o r uif ( m e a s u r e d o n t h e b a s i s o f e m p t y b e d diameter), the orifices in the first circle (assumed to be offering equal resistance) may operate first, and with a subsequent increase in the gas flow rata, orifices in the other circles operate. The picture on the number of orifices operating with respect to gas flow rate may be like that shown in Fig. 2. An orifice m a y b e s a i d t a b e O l : . e r a t i n g w h e n i t is a d m i t ting the gas sufficiently to develop bubbles and a periodic fluctuation of the pressure at the orifice occurs (unlike steady pressure at a non-operating orifice). In the development of the proposed theor y , a d i s t i n c t i o n is m a d e b e t w e e n t h e t w o g a s flow rate ranges; nameIy one of 'unstable or apparent" bubble formation range (between U m t o r u-it a n d Urn) a n d t h e o t h e r o f ' s t a b l e o r real" bubble formation and their growth range ( a b o v e Um )- T h e t h e o r y h o w e v e r c o n c e r n s t h e 'apparent' bubble formation range. In this range all the orifices are not operating (not u n t i l Um i s r e a c h e d ) a n d h e n c e t h e b e d i s n o t u n i f o r m l y f l u i d i s e d . H o w e v e r , a t Um a l l t h e o r i f i c e s b e c o m e o p e r a t i v e , t h e b e d is u n i f o r m ly fluidised and any excess gas flow over U M will result in stable bubble formation. The b e d i s t h e n t e r m e d a b u b b l i n g b e d . I n t h e "ap-
217 parent' bubble formation range the bed may still be considered to behave like a static bed f o r h-lterstitial gas f l o w a n d like a l i q u i d colurnn for bubble flow -- the bed being in the t r a n s i t i o n r e g i o n . T h e p r o p e r t i e s o f "real" b u b bles differ from the "apparent" bubbles as the 'real' bubbles grow in size due to excess flow and coalescence while the 'apparent' bubbles s h r i n k i n size a n d d i s s o c i a t e d u e t o l i m i t e d gas flow and decreasing bed pressure along the bed height. The basic assumptions made in arriving at a mathematical expression are stated as follows: (i) T h e n u m b e r o f " a p p a r e n t " b u b b l e s f o r m e d a t a n o r i f i c e , a o , is a f u n c t i o n o f t h e fractional number of operating omfices and t h e gas v e l o c i t y r a t i o v/-6o, i.e. ao = K 1
(1)
w h e r e K 1 is a c o n s t a n t ( f r e q u e n c y o f b u b b l e f o r m a t i o n ) , v is t h e a c t u a l g a s v e l o c i t y t h r o u g h a n o p e r a t i v e o r i f i c e a n d v0 is t h e a v e r a g e gas v e l o c i t y t h r o u g h a l l t h e o r i f i c e s , n is t h e n u m ber of operating orifices and N the total number of orifices in the distrib~,tor. At a particular n / N , i f a s m a l l i n c r e a s e i n t h e g a s f l o w r a t e is made, v increases, though the magnitude of t h i s i n c r e a s e is v e r y s m a l l . W i t h f u r t h e r i n c r e a s e o f gas f l o w n / N a l s o i n c r e a s e s a n d t h e p r o c e s s continues until all orifices become operative. W h e n n = N w h e r e v b e c o m e s e q u a l t o To, a 0 will then attain a constant value equal to Kx. T h e a s s u m p t i o n is i n a c c o r d a n c e w i t h t h e o b s e r v a t i o n o n t h e n u m b e r o f gas b u b b l e s f o r m e d a t a n o r i f i c e i n a l i q u i d c o l u m n i n t h e l o w gas flow range and that of a constant bubble frequency in the fluidised bed [11]. (ii) O n l y a l i m i t e d n u m b e r o f " a p p a r e n t " bubbles are formed at an operating orifice subsequent to which other orifices become operative. (iii) T h e n u m b e r o f " a p p a r e n t ' b u b b l e s diss o c i a t i n g p e r s e c o n d is a f u n c t i o n o f v e l o c i t y r a t i o u b / u , i.e. --
f o r m e d r e s u l t i n g i n a l a r g e (UM - - Um~)/Um~ v a l u e t o a t t a i n s t a b l e f l u i d i s a t i o n , as a g a i n s t a coarse size particle bed forming larger size bubbles -- larger ub -- which require a smaller ( V M - - Umf)/Umf t o a t t a i n s t a b l e f l u i d i s a t i o n . This would imply that the dissociation rate o f s m a l l e r b u b b l e s is l o w e r t h a n t h e l a r g e r b u b b l e s . T h e a s s u m p t i o n is t h u s c o n s i s t e n t with observation on the fluidisation behaviour of fine and coarse size particles. However, no information on the formation and velocity of ' a p p a r e n t " b u b b l e s is a v a i l a b l e t h o u g h u b o f "real" b u b b l e s c o u l d b e e x t e n d e d t o " a p p a r e n t ' b u b b l e s a t t h e UM c o n d i t i o n . (iv) S t a b l e f l u i d i s a t i o n is i n i t i a t e d as a r e sult of two successive irreversible isothermal processes, one of formation of "apparent" bubbles at the orifice plate and the other of their dissociation in the bed. For unit volume of the reactor, we may write
( U - - U m f ) A t K 1 -- F V b K 2
w h e r e ( U - - Um~) is s u p e r f i c i a l g a s v e l o c i t y o v e r Umf. A t is t h e b e d c r o s s - s e c t i o n a l a r e a , F is t h e b u b b l e f r e q u e n c y a n d Y b t h e " a p p a r ent' bubble volume. I f ( 1 - - n / N ) is t h e f r a c t i o n a l n u m b e r o f n o n - o p e r a t i n g o r i f i c e s a n d u / U m f is t h e f r a c t i o n a l gas v e l o c i t y , t h e d e c r e a s e i n t h e (fractional) number of non-operating orifices with i n c r e a s i n g ( f r a c t i o n a l ) gas v e l o c i t y m a y b e given by the equation D
d(1 -- n/N)
(4)
0
Umf
i°e.
K = In (i -- n/N)U~d(~
-- U~f)
(5)
For small values of u, eqn. (5) may be given as n K
=
--
N
Umfl(~
--
U,~)
(6)
Substituting the value of (u- Umf) from eqn. (3) in eqn_ (6) and further substituting the values of K 1 and K2 from eqns. (1) and (2) a n d p u t t i n g a 0 = f0, w e h a v e
UmfAtUb) w h e r e K z is a c o n s t a n t , Ub is t h e " a p p a r e n t ' b u b b l e v e l o c i t y a n d u is t h e a v e r a g e g a s v e l o c ity in the bed. In the case of a fine size partic l e b e d , s m a l l e r s i z e b u b b l e s - - l o w e r Ub - - a r e
(3)
(7)
The average velocities through the orifices, To, a n d t h e b e d , u , m a y b e p r e s e n t e d i n t e r m s
218
I
p
-i:'-'~",
P
t I CA-- COMPRESSED
I I AIR
t J t-~
R--REGULATOR
U - - U TUBE
F - - FLUIDISATION
ST-- SURGE TANK
N--NEEDLE
OM--0RIFICE METER
DT-DISTRIBUTION TANK
P~
RM-ROTAMETER
PRESSURE G A U G E
Fig. 3. Experimental
set-up
VALVE
BP--BACK PRESSURE
for distributor
studies
(
ebe3g°
[ 2APdgc
)"
We have
K
FV b v
D-DISTRIBUTOR
in fluidisation.
of the pressure drops corresponding to the flow through the orifices [7] and a static bed [ 8 ] . T h a t is, or
COLUMN
creases, a corresponding increase in the terms of the denominator occurs, resulting in a cons t a n t K 0 w h i c h is i n d e p e n d e n t o f s y s t e m p a r a . meters. Equation (10) provides a method for predicting Ko- (The value of K o was determined by direct measurements of U M and APd/AP b using eqn. (9) as well by substituting the required values in eqn. (10).)
EXPERIMENTAL
] ~,
2fLe 3
"'--~'~b !
(8) or
(APd ~Z/2
K = K0 x X~J
(9)
Since K does not change with gas velocity for a given bed height we can also express K o a t t h e U M o r Um~ c o n d i t i o n s . N o w
Ko=(UmfAtUb. IFvbv/~{D[-IS~J2~(1--
e)
)112
(10)
The right-hand side of eqn. (10) comprises terms which are interdependent, Ub i n c r e a s ing with Vb, and u with H [7] and ~ decreasing. Thus when the term in the numerator in-
The experimental set-up (Fig. 3) consisted of (1) fluidi~ed bed column with orifice plate distributor, (2) orifice meters, (3) surge tank, (4) rotameter, (5) manometers, and (6) control valves. A 100 mm i.d. thick-walled glass column was used to hold the material on a 20 mm thick gas distributor. The distributor was provided with twenty-five 3-mm-diam. orifices having 8 mm spacing. All these twentyfive orifices were arranged as in Fig. (4) in the form of a cross, with six orifices on each arm of the distributor. Five orifices on each arm were used for gas distribution while the sixti one on each arm and a central one were use to measure the bed pressure drop. All the twenty orifices were connected to an air dist r i b u t i o n tank through twenty orifice meters each designed to give equal flow rate. Each orifice in the di~tEibutor was provided with a side pressure tapping to note the pressure
219 20~3~HOLES
_ ~ \
4--3-5
~ D M A T E R h - ~ L - - ZIRCON O~D FEIGHT ~ I D Umf 4~-'i C M / ~ C
@ HOLES
"
i
/,,
20
!1
I'1 i l l l l l i l ' l
13
~;~ll.,~--
6~%7
12
8~
9
~ A .,. J. J.J.
(~iFICE
LOCATION
-
<
<.
/ I00
"Plus'
D
D¢------¢'-----
A
A
-"
, o
- - -
~Ol
i-
r~i// I---~---
~
ALL OIMENSIONS ARE IN MM
Fig. 4.
' "---
.
type distributor.
variation at that point. Three-mm
~----.-
~
| ~5
C--0-8 D__ I O - U ~ UM E'T--- I O-(J~U~ . II 0 I 16 = = 6
20
, 14 tg
~ 13 I8
, 12 17
"
~.~-,.,<,.,,,-, , 2 T
= 3 8
, 4 9
~0-o io
(a) BED M A T E R I A L - U m f ~
D
I[
ZIRCON 4<) i
4-61Clrd#~Ec
D ~---~---30
E
# V r
D'I
!
:Sl
i r -'o ., i
.11
#1
;
f
~
"
-
-
o
~N
4
~t
,
o,---,
a~
\% 1
I
~o~
W-
tO F ~ G - -
~F-/CE 15 20
LOCATION
14
I
,
•
19
18
17
iG
O'85 I-oo
AS
SHOWN ~1 FtG. {_~} OO
= ~
G
7
8
9
10
(b)
Fig. 5 (a, b). Typical flow distribution pattern for zircon sand bed. the orifices at the centre discharge more flow t h a n a n y o t h e r o r i f i c e s , in c e r t a i n cases o r | rices n e a r t h e n o n - o p e r a t i n g o n e d e l i v e r relat i v e l y m o r e f l o w . W h e n all t h e o r i f i c e s b e c o m e o p e r a t i v e , t h e f l o w in e a c h o r i f i c e is a l m o s t t h e s a m e . A g i t a t i o n in t h e b e d m a t e r i a l and the appearance of bubbles on the surface d o n o t o c c u r u n t i l all t h e o r i f i c e s b e c o m e
220 BED M A T E R I A L - - R U T I L E
IOC~
,-
Ume
NO OF KEY
4 8! CMTBEC
ORIFICES-- 2 0
TO SYMEOL AS
IN T A B L E ( A }
28C o
8OO
BED MATERIAL-Umf
24~
:o
,o, ~
-
ALUMINA I CM/SEC
-
o
NO. O F 0 R I F [ C E S - - 2 0
Jk
KEY TO SYMBOL AS
2OO
TABLE
IN
•
(A)
t
4(--
¢ Q~
40¢
x
•
TABt,.E (A) ~D
TABLE 4~ %"
20¢
SYMBOL
~D
80
.f~IG H T
2o ~ ~
0"O 00
1
I
I
1
I
100
:ZOO
300
400
.500
I
600
I
I
BOO
900
I
1000
NO OF
9O(
KEY
ZIRCON
IN T A B L E
o
(A)
70(
i x
A
g s°'~ x ~1~
TABLE (A) SYMECI~ _BE.D HEIGHT
~2OC
-3D
:--~
o
o
I
I
200
I
300
l
400
I
500
I
~'~-00
°o
- - 6 0
~
IO0
I00
2: D
x
3 o
;
4
D
; •
•
12o
•
•
*so
,
zoo
,
6 D 7, Do
;~4o
•
2eo
,
,
~ao
c~/sEc
between
(n/N)u
a n d D0 f o r a l u -
BAND
a,
•00
~
eo
~. ~
o
t ~
|
Fig. 8. Relationship mina powder.
0R~-'ICES-- Z0
TO SYMBOL A S
s
4o
CM/SEC
4-~I C M / B E G
Umr
°o
MATERIAL
Io
50 ~¢"
7D
700
Fig. 6. Relationship between (n/N)u and DO for futile bed. BED M A T E R I A L - -
,~
6D
. t~
~; ~
'~*~
4~
4D BD
~100
.-
(A}
"I'D ~00
I 800
I 900
!
1000
Fig. 7. Relationship between (n/N)u and DO for zircon sand bed. operative. The incremehtal flow in the case of alumina powder, from one set of orifices bec o m i n g o p e r a t i v e t o a n o t h e r , w a s a l s o Iarger. Experimental observations on the pattern of the orifices becoming operative at different air v e l o c i t i e s a t t w o b e d h e i g h t s a r e s h o w n i n Figs. 5(a, b). These observations support the discussions on the progressive increase in the number o£ operating orifices with increasing gas v e l o c i t y a n d a l s o t h e a b s e n c e o f "real' b u b b l e f o r m a t i o n i n Ume o r uif t o U ~ g a s v e l o c ity range.
T h e e x p e r i m e n t a l r e s u l t s o n t h e air v e l o c i t y To, v a n d n / N f o r t h e t h r e e b e d m a t e r i a l s a n d f o r d i f f e r e n t b e d h e i g h t s are s h o w n in F i g s . 6 - 8. I t is o b s e r v e d t h a t t h e r a t i o nv/N-Uo = a~ K1, the slope of the line varying from 0.8 to 1, 0.75 to 1 and 0.17 to 1 for zircon, futile and alumina powder respectively at the bed height of 4D t. This indicates an increase of a w i t h t h e gas v e l o c i t y r a t i o . S i m i l a r o b s e r v a t i o n s c a n b e n o t e d f o r all b e d h e i g h t s e x c e p t for 1Dr. The results thus prove the validity of assumption (i). The point where the line [ ( n / N ) u vs. Vo] c u t s t h e x - a x i s r e p r e s e n t s t h e air v e l o c i t y ui a t w h i c h t h e o p e r a t i o n o f t h e orif i c e s w o u l d j u s t s t a r t . T o a c c o u n t f o r t h i s obo s e r v a t i o n , e q n . ( 1 ) m a y b e r e w r i t t e n as
a0 = K 1
To
--
Ui
A c c o r d i n g l y e q n . ( 2 ) m a y b e e x p r e s s e d as ui,
)
and eqn. (7) now becomes
Since
(12)
221
...,
,o.-oo,,
240
x,@ u
200
9
cn
s
=E ¢J
7
160
J>
u~
,_.
//
280
I0
{.
120 / /
80 3
D
.
2 !
~'*
i ~ 0
~/~
•
RUTILE
/ /
BED
40
/ //
.25;''
~T
0
/ /
1
i
r
,
v
2
3
4
5
~
6
,
i
i
v
,
,
T
I
7
8
9
I0
II
12
13
14
f
0
X I05
(a)
f
; 3
t 4
T 5
I 6 X 10 5
p-.-
(b)
Fig. 9. ( a ) R e l a t i o n s h i p b e t w e e n u ( a t U M c o n d i t i o n ) a n d ,~. ( b ) R e l a t i o n s h i p b e t w e e n v ( a t U~.I c o n d i t i o n ) for alumina bed.
and
centage variation o f the individual values o f
we have
Ko f r o m t h e a v e r a g e v a l u e is w i t h i n a b o u t K
Vo (Um~AtUb~ =--~FVbv )
(7)
F i g u r e 9 ( a , b ) s h o w s a p l o t o f v versus [J a t t h e UM c o n d i t i o n . I t is s e e n t h a t t h e e x p e r i m e n t a l results indicate a linear relationship, t h u s s a t i s f y i n g e q n . (8). F r o m t h e s e p l o t s t h e slope Ub/FV b was determined and found to be 0.000625, 0.00092 and 0.000509 for r u t i l e , z i r c o n a n d a l u m i n a r e s p e c t i v e l y . Ass u m p t i o n (iii) c o u l d n o t b e p r o v e d d i r e c t l y b e c a u s e o f d i f f i c u l t y in m e a s u r i n g Ub f o r ' a p p a r e n t " b u b b l e s . H o w e v e r , Ub v a l u e s f o r "real" b u b b l e s h a v e b e e n e x t r a p o l a t e d t o t h e UM c o n d i t i o n t o c a l c u l a t e t h e v a l u e o f Ub/ F V b (see A p p e n d i x ) . I t is o b s e r v e d t h a t t h e c a l c u l a t e d a n d t h e o b s e r v e d v a l u e s are o f t h e same order of magnitude. T h e t e r m Ub/FVb m a y b e c o n s i d e r e d as a n index of fluidisation character of the bed material. A higher value generally indicates t h a t t h e f i u i d i s e d b e d will b e s t a b l e a t l o w e r UM/Umf r a t i o . U s i n g t h e e x p e r i m e n t a l v a l u e s Of Ub/FVb and U at U M conditions and those available in t h e l i t e r a t t w e f o r o t h e r t e r m s , K o has been determined from eqn. (10). Ko thus d e t e r m i n e d is f o u n d t o b e 0 . 6 5 3 , 0 . 6 3 1 2 a n d 0.692 for futile, zircon, and al-m~na powder respectively. The values of Ko calculated from e q n . (9) a r e p r e s e n t e d i n T a b l e 1 . T h e p e r -
15%. A l o g - l o g p l o t (Fig. 1 0 ) f o r t h e e x p e r i m e n t a l v a l u e s o f K a n d A P d / A P b a t t h e UM c o n d i t i o n ( f o r all t h e e x p e r i m e n t a l c o n d i t i o n s ) establishes the relationship K-
0.65(APd/APb)°'43
(14)
Since K o and the exponent for APd/AP b are i n d e p e n d e n t constants, eqn. (14) m a y n o w b e given as
A P b /UM
__ Umf
(15)
w h e r e C is a c o n s t a n t . T h o u g h t h e s i m p l i c i t y of eqn. (15) for determining the desired APd/ A P b is re~li.~ed, it involves, h o w e v e r , t h e u n k n o w n t e r m UM- I t is p r o p o s e d t o l o o k i n t o the possibility o f arriving at an e q u a t i o n f o r d e t e r m i n i x , g U M in t e r m s o f U t a n d Umf-
CONCLUSION In order to facilitate the design of the m u l t i - o r i f i c e t y p e o f gas d i s t r i b u t o r in f l u i d i s e d beds a theoretical model, based on the kinetics o f b u b b l e f o r m a t i o n a t t h e d i s t r i b u t o r a n d t h e i r d i s s i p a t i o n in t h e b e d , h a s b e e n p r o p o s e d . F r o m this m o d e l i t h a s b e e n f o u n d
222 TABLE 1 Ub/FV b (cm -2)
Least-squares l i n e
Bed material
Bed height
(cm) Y
Rutile Umf = 4.8 cm/sec
=
1.083x--I05.4
Zircon sand Uraf = 4 - 6 1 c m / s e c
Y
Alumina powder Um~ = 1 . 0 c m f s e c
Y= 1.235x--61.53
=
1.126x--124.7
Calculated
Experimental
Mean
0.97 0,597 0,586 0,589 0.617 0.305 0.609 0,653
0,68 0.527 0.579 0.5938 0.64 0.6175 0.618 0.6079
10 20 30 40 50 60 70 Mean
0.60 0.565 0.62 0.67 0,675 0.649 0.64 0.6312
0.5418 0.496 0.553 0.6756 0.558 0.554 0.6008 0.56845
10 20 30 40 50 60 70 Mean
0.72 0,70 0.685 0.650 0.69 0.706 0.695 0.692
0.714 0.674 0.690 0.6308 0.693 0.733 0.718 0.693257
10 20 30 40 50 60 70
0.000625
0.00092
0.000509
Values of g 0
N . B . Y = ( r z / N ) v , x = Vo"
also b e e n f o u n d t h a t ub/FVb m a y b e u s e d as a n i n d e x f o r c h a r a c t e r i s i n g t h e f l u i d i s a t i o n behaviour of any bed material.
2~
,<
l,,c
t
x "
W A
a.
ACKNOWLEDGEMENTS
x
x
x
A
S'¢MBOU -
-
1
~
,~. -
-
~
BED ID
O" O']
eEo AT. ~ .~.~Xj~J~.~ ZI~,~ON -
RUTILE
AL~,m"dA
SAND
POWI~R
HEIGHTS TOTD
FOR EACH
I 1~
MATERIAL
T h e a u t h o r s are greatly i n d e b t e d to Shri C. V. S u n d a r a m , H e a d , M e t a l l u r g y D i v i s i o n a n d t o D r . C. K . G u p t a , H e a d , E x t r a c t i v e Metallurgy Section for their constant encoura g e m e n t a n d s u p p o r t in c a r r y i n g o u t t h e s e studies.
] 2:0
(" *d/~'Ou,, ex~ Fig. 10. Relationship between experimental values of K and (~Dd/~b)~/~.
possible to estimate the value of a constant relating the gas velocity (ratio) and the ratio of the pressure drops across the distributor and the bed. T h e m o d e l has been s h o w n to agree well with the ~_xperimental observations. F r o m t h e e x p e r i m e n t a l observations it has
LIST O F SYM_BOLS
At ao
D Dt fo F
cross-sectional area for fluidised
bed
(L 2)
r a t e o f b u b b l e f o r m a t i o n (T -x) d i a m e t e r o f t h e old_lice ( L ) d i a m e t e r o f t h e b e d (L) bubble d i s s o c i a t i o n r a t e ( T - x ) frequency of bubble formation
(T -x)
223
f gc
H K, K0, K~ K1, K2
L N n
APd
friction factor Newton's law conversion factor bed height (L) dimensionless constants
rate c o n s t a n t s (T-1) tube length or orifice length (L) total number of orifices number of operating orifices pressure drop across the distributor (ML -1 T -2)
pressure d r o p across t h e bed S
(ML-i T -2) surface area per unit volume of bed (L-1 ) average superficial gas velocity in bed ( L T - 1 )
Ub
b u b b l e rise v e l o c i t y ( L T - i )
U
average gas velocity at the operating orifices (LT -1) average gas v e l o c i t y f o r all t h e orifices (LT -1) velocity at which ~rst orifice just operates (LT -1) velocity in the bed corresponding to (LT -1) s u p e r f i c i a l gas v e l o c i t y i n t h e b e d for n/N = 1 (LT -1) s u p e r f i c i a l gas v e l o c i t y i n t h e b e d at minimum fluidisation condition (LT -1) bubble volume at the distributor ( L a) bed friction factor
UM Umf
Vb Pf P~
d e n s i t y o f fluid (ML-3) d e n s i t y o f solid (ML-3)
P
as s h o w n i n Fig. (9) ( L a T - i ) bed porosity
APPENDIX T h e f u n c t i o n Ub/FVb m a y b e e v a l u a t e d from the genera|i.~ed reported values of the i n d i v i d u a l t e r m s . I t is k n o w n t h a t t h e b u b b l e v e l o c i t y is Ub ~ 2 2 - 2 ~ / d b 0 ( c m / s e c ) w h e r e d b o is t h e i n i t i a l b u b b l e d i a m e t e r ( c m ) . M a k i n g u s e o f M i w a e t a l . "s e q u a t i o n [ 1 0 ] f o r d b o ----0 . 0 0 3 7 6 ( U M - - Umf) z ( c m ) a t g a s v e l o c i t y U M , w e h a v e t h e b u b b l e v e l o c i t y Ub
[ 0 . 0 0 3 7 6 ( U M - - U m f ) ] 0.s × 2 2 . 2 ( c m / s e c ) . T h e b u b b l e v o l u m e Vb is a f u n c t i o n o f v o l u metric flow rate Q (Q = AUM, where A = area o f c r o s s - s e c t i o n o f t h e b e d , c m 2) o f t h e gas. H e n c e Vb = 1.138(AUM)SlS/g 315 ( e r a 3 ) - T h e frequency of the bubbles at the distributor has not yet been well established. However, one could extend the lines shown in ref. [4], Fig. (20) on p. 129, to a reasonable value. A value of 20 bubbles per second for each orifice has been selected. On substituting the a p p r o p r i a t e v a l u e s i n t h e f u n c t i o n Ub/FVb, we have Ub
2 2 - 2 ( 0 - 0 0 3 7 6 ) °'5 (UM - - U m f ) g 3/5
FVb
2 0 × 2 0 × 1 . 1 3 8 ( A U M ) GI5
S e l e c t i n g UM = 1 9 . 2 c m / s e c a n d U m f = 4 . 8 cm/sec (for futile bed material) and cross-sect i o n a l a r e a o f t h e b e d A = 7 8 . 5 4 c m 2, w e g e t Ub
FVb
- 4.12
X 10 -4
w h i c h is o f t h e s a m e o r d e r o f m a g n i t u d e as the experimental results. REFERENCES 1 A. B. Whitehead, in Davidson and Harrison (Eds.), FluldLcation, Academic Press, L o n d o n , 1971, p. 781. 2 S. F a k h i m i a n d D. Harrison, Chemica, 70, Butterworths and Inst. o f Chem. Engrs., L o n d o n , 1971, Session 1, p. 29. 3 W. M. S. Kassim, Ph.D. Thesis, Univ. o f A s t o n in Birmingham, 1972. 4 D . K u n i i and O. Levenspiel, Fluidisation Engineering, Wiley, New York, 1969, p. 89. 5 J . W . Hiby, Chem. Ing. Tech., 36 (1964) 228. 6 R. Siegel, AIChE J., 22 (1976) 590. 7 W. L. McCabe and J. C. Smith, U n i t Operations o f Chemical Engineex-;ng, McGraw-Hill, New York, 1956, p. 67. 8 J. F. Richardson, in Davidson a n d Harrison(Eds.), Fluidisation, Academic Press, L o n d o n , 1971, p. 25. 9 ]D. S a t h l y a m o o r t h y a n d Ch_ Sridhar Rao, Powder Technol., 20 (1978) 47 - 52. 10 K. S. Miwa, S. Mori, T. Kato and Io Mochi, Int. Chem. Eng., 12 (1972) 181. 11 T . P . Hsiung and J. R. Grace, i n Davidson (Eds.), Fluidisation, Cambridge Univ. Press, L o n d o n , 1978, pp. 19 - 24.
215
Multi-Orifice Plate Distributors in Gas Fluidised Beds -- A Model for Design of Distributors
D. SATHIYAMOORTHY and Ch. SRIDHAR RAO Metallurgy Division, Bhabha A t o m i c Research Centre, Trombay, B o m b a y - 4 0 0 0 8 5 (India) (Received May 5, 1978; in revised form July 3, 1979)
SUIVIMARY
T h e u s e o f a s u i t a b l e g a s d i s t r i b u t o r is essential for satisfactory performance of gas-solid fiuidised beds. Multi-orifice plate type gas distributors in fluidised beds are frequently used in industrial practice. This paper analyses the factors governing the operating characteristics of the multi-orifice p l a t e t y p e o f gas d i s t r i b u t o r . R e s u l t s o f the experiments carried out in a 100 mm d i a m . glass t u b e a s s e m b l y w i t h a d i s t r i b u t o r plate having 20 orifices are presented. Rutile and zircon sands and alumina powder (70 1 5 0 / ~ m ) w e r e u s e d as t h e b e d m a t e r i a l , w h i l e air --up to ten times the minimum fluidising v e l o c i t y ( U m f ) - - w a s u s e d as t h e f l u i d i s i n g medium. It has been observed that all the orifices bec o m e o p e r a t i v e a t a g a s v e l o c i t y UM a n d t h e r a t i o U M / ( U M ~ Umf) is r e l a t e d t o t h e p r e s s u r e drop (distributor/bed) ratio (APd/APb)
by a constant K o which is independent of syst e m parameters. A theoretical m o d e l for the estimation of K o and the experimental values are presented. INTRODUCTION T h e f l u l d i s e d b e d t e c h n i q u e is a d o p t e d i n a number of metallurgical and chemical process industries. The performance of the fluidised bed system largely depends on the satisfactor y d e s i g n a n d s e l e c t i o n o f gas d i s t r i b u t o r s . B a s i c a l l y a gas d i s t r i b u t o r h a s t o h a v e t h e f o l l o w i n g c h a r a c t e r i s t i c s . (i) I t s h o u l d d i s t r i b u t e t h e g a s u n i f o r m l y i n t h e b e d . (ii) I t s h o u l d have a definite and non-changing (with time) p r e s s u r e d r o p f o r t h e gas. ( i i i ) I t s h o u l d n o t permit the drain of solids. Though a variety
of distributors have been reported in the patent l i t e r a t u r e , t h e p u b l i s h e d w o r k o n t h e s u b j e c t is v e r y l i m i t e d . Whitehead [1] has studied the operation of gas d i s t r i b u t o r s c o n t a i n i n g m u l t i - t u y e r e s in rectangular assemblies. Detailed investigations have been carried out to determine the minim u m gas v e l o c i t y a t w h i c h all t h e t u y e r e s become operative. Fakhimi and Harrison [2] have studied the behaviour of multi-orifice distributors and derived a relationship between t h e n u m b e r o f o p e r a t i n g o r i f i c e s a n d t h e gas superficial velocity. Kassim [3] has reported certain discrepancies between his observations and the calculated values using Fakhimi's relationship, when working with materials which had a low minimum fluidising velocity. I t is o b s e r v e d t h a t f o r s t a b l e o p e r a t i o n o f the bed, a certain magnitude of pressure drop at the distributor should exist [4]. This could be of the order of 10 - 15% of that in the bed. H o w e v e r , t h e r e is s t i l l a c e r t a i n a m o u n t o f u n c e r t a i n t y o n t h i s a s p e c t as a s y s t e m w o r k i n g on such low pressure drop ratio has not always given good performance of the bed [1]. Hiby [5] indicates that the required pressure drop r a t i o (APdistr~utor/APbed) f o r a p e r f o r a t e d o r nozzle type distributor should be 0.15 when U/Um~ ~- 1 - 2 a n d a b o u t 0 . 0 1 5 w h e n u / u = , f 1.The effect of distributor to bed resistance ratio on the onset of fluidised bed channelling was analysed by Siegel [6]. Based on observations on the bed expansion ratio, it was determined that the ratio of distributor to bed resistance required for stability was 0.14 0 . 2 2 o v e r a w i d e r a n g e o f G a l i l e o n u m b e r (1 10,000). The authors of the present paper have shown [9] that the fractional n,,mber of o p e r a t i n g o r i f i c e s i n a m u l t i - o r i f i c e t y p e o f gas d i s t r i b u t o r is a f u n c t i o n o f o p e r a t i n g g a s ve~
216
|.0
---
0
U-Urnf
UM
Umf
Fig. 2. Relat;onship b e t w e e n fractional n u m b e r o f
orifices o p e r a t i n g and gas flow. Fig.
I. O r i f i c e s
in a circular
distributor.
I o c i t y U , m i n i m u m f l u i d i s a t i o n v e l o c i t y Umf a n d a c o n s t a n t K (i.e. K = K o ( A P d ] A P b ) ~ ) w h i c h i n i t s e I f is d e p e n d e n t o n s y s t e m p a r a meters. In the present paper, the behaviour of the multi-orifice plate distributor has been anal y s e d a n d a n a t t e m p t is m a d e t o e s t a b l i s h K o as an independent constant. A method has also been suggested to predict this constant. The experimental observation and the proposed model are confined to a gas velocity range varying from the first orifice to the last one becoming operative. Results of the experimental studies carried out in a 100 mm diam. glass tube assembly are presented.
THEORY
W h e n a f l u i d i s i n g g a s is p a s s e d t h r o u g h a bed of particles held on an orifice plate or a gas distributor, a drop in the pressure of the gas occurs and the velocity of gas increases. O n c e t h e m i n i m u m f l u i d i s a t i o n v e l o c i t y is reached, with subsequent increase in the gas flow rate the pressure drop across the distributor increases while that in the bed remains rather steady at a value equivalent to the weight of bed material per unit cross-sectional a r e a o f t h e b e d . I t is k n o w n t h a t t h e f l o w o f g a s t h r o u g h a l l t h e o r i f i c e s is n o t u n i f o r m f o r various reasons. Depending on the size and shape of particles, shape and size of container (bed) and also the c~]ming section, the gas selects an easy path and an orifice offering such a path becomes operative. The characteristic flow of gas in the calming section with a
velocity gradient across the section also contributes to the preferential operation of certain orifices. It may be expected, say in an orifice plate of circular section, in which the orifices are arranged in concentric circles as shown in Fig. 1, that the resistance to flow of gas increases as the distance of an orifice from the centre of the distributor increases, As a result o f t h i s , a t a c e r t a i n g a s v e l o c i t y w h i c h is U m f o r uif ( m e a s u r e d o n t h e b a s i s o f e m p t y b e d diameter), the orifices in the first circle (assumed to be offering equal resistance) may operate first, and with a subsequent increase in the gas flow rata, orifices in the other circles operate. The picture on the number of orifices operating with respect to gas flow rate may be like that shown in Fig. 2. An orifice m a y b e s a i d t a b e O l : . e r a t i n g w h e n i t is a d m i t ting the gas sufficiently to develop bubbles and a periodic fluctuation of the pressure at the orifice occurs (unlike steady pressure at a non-operating orifice). In the development of the proposed theor y , a d i s t i n c t i o n is m a d e b e t w e e n t h e t w o g a s flow rate ranges; nameIy one of 'unstable or apparent" bubble formation range (between U m t o r u-it a n d Urn) a n d t h e o t h e r o f ' s t a b l e o r real" bubble formation and their growth range ( a b o v e Um )- T h e t h e o r y h o w e v e r c o n c e r n s t h e 'apparent' bubble formation range. In this range all the orifices are not operating (not u n t i l Um i s r e a c h e d ) a n d h e n c e t h e b e d i s n o t u n i f o r m l y f l u i d i s e d . H o w e v e r , a t Um a l l t h e o r i f i c e s b e c o m e o p e r a t i v e , t h e b e d is u n i f o r m ly fluidised and any excess gas flow over U M will result in stable bubble formation. The b e d i s t h e n t e r m e d a b u b b l i n g b e d . I n t h e "ap-
217 parent' bubble formation range the bed may still be considered to behave like a static bed f o r h-lterstitial gas f l o w a n d like a l i q u i d colurnn for bubble flow -- the bed being in the t r a n s i t i o n r e g i o n . T h e p r o p e r t i e s o f "real" b u b bles differ from the "apparent" bubbles as the 'real' bubbles grow in size due to excess flow and coalescence while the 'apparent' bubbles s h r i n k i n size a n d d i s s o c i a t e d u e t o l i m i t e d gas flow and decreasing bed pressure along the bed height. The basic assumptions made in arriving at a mathematical expression are stated as follows: (i) T h e n u m b e r o f " a p p a r e n t " b u b b l e s f o r m e d a t a n o r i f i c e , a o , is a f u n c t i o n o f t h e fractional number of operating omfices and t h e gas v e l o c i t y r a t i o v/-6o, i.e. ao = K 1
(1)
w h e r e K 1 is a c o n s t a n t ( f r e q u e n c y o f b u b b l e f o r m a t i o n ) , v is t h e a c t u a l g a s v e l o c i t y t h r o u g h a n o p e r a t i v e o r i f i c e a n d v0 is t h e a v e r a g e gas v e l o c i t y t h r o u g h a l l t h e o r i f i c e s , n is t h e n u m ber of operating orifices and N the total number of orifices in the distrib~,tor. At a particular n / N , i f a s m a l l i n c r e a s e i n t h e g a s f l o w r a t e is made, v increases, though the magnitude of t h i s i n c r e a s e is v e r y s m a l l . W i t h f u r t h e r i n c r e a s e o f gas f l o w n / N a l s o i n c r e a s e s a n d t h e p r o c e s s continues until all orifices become operative. W h e n n = N w h e r e v b e c o m e s e q u a l t o To, a 0 will then attain a constant value equal to Kx. T h e a s s u m p t i o n is i n a c c o r d a n c e w i t h t h e o b s e r v a t i o n o n t h e n u m b e r o f gas b u b b l e s f o r m e d a t a n o r i f i c e i n a l i q u i d c o l u m n i n t h e l o w gas flow range and that of a constant bubble frequency in the fluidised bed [11]. (ii) O n l y a l i m i t e d n u m b e r o f " a p p a r e n t " bubbles are formed at an operating orifice subsequent to which other orifices become operative. (iii) T h e n u m b e r o f " a p p a r e n t ' b u b b l e s diss o c i a t i n g p e r s e c o n d is a f u n c t i o n o f v e l o c i t y r a t i o u b / u , i.e. --
f o r m e d r e s u l t i n g i n a l a r g e (UM - - Um~)/Um~ v a l u e t o a t t a i n s t a b l e f l u i d i s a t i o n , as a g a i n s t a coarse size particle bed forming larger size bubbles -- larger ub -- which require a smaller ( V M - - Umf)/Umf t o a t t a i n s t a b l e f l u i d i s a t i o n . This would imply that the dissociation rate o f s m a l l e r b u b b l e s is l o w e r t h a n t h e l a r g e r b u b b l e s . T h e a s s u m p t i o n is t h u s c o n s i s t e n t with observation on the fluidisation behaviour of fine and coarse size particles. However, no information on the formation and velocity of ' a p p a r e n t " b u b b l e s is a v a i l a b l e t h o u g h u b o f "real" b u b b l e s c o u l d b e e x t e n d e d t o " a p p a r e n t ' b u b b l e s a t t h e UM c o n d i t i o n . (iv) S t a b l e f l u i d i s a t i o n is i n i t i a t e d as a r e sult of two successive irreversible isothermal processes, one of formation of "apparent" bubbles at the orifice plate and the other of their dissociation in the bed. For unit volume of the reactor, we may write
( U - - U m f ) A t K 1 -- F V b K 2
w h e r e ( U - - Um~) is s u p e r f i c i a l g a s v e l o c i t y o v e r Umf. A t is t h e b e d c r o s s - s e c t i o n a l a r e a , F is t h e b u b b l e f r e q u e n c y a n d Y b t h e " a p p a r ent' bubble volume. I f ( 1 - - n / N ) is t h e f r a c t i o n a l n u m b e r o f n o n - o p e r a t i n g o r i f i c e s a n d u / U m f is t h e f r a c t i o n a l gas v e l o c i t y , t h e d e c r e a s e i n t h e (fractional) number of non-operating orifices with i n c r e a s i n g ( f r a c t i o n a l ) gas v e l o c i t y m a y b e given by the equation D
d(1 -- n/N)
(4)
0
Umf
i°e.
K = In (i -- n/N)U~d(~
-- U~f)
(5)
For small values of u, eqn. (5) may be given as n K
=
--
N
Umfl(~
--
U,~)
(6)
Substituting the value of (u- Umf) from eqn. (3) in eqn_ (6) and further substituting the values of K 1 and K2 from eqns. (1) and (2) a n d p u t t i n g a 0 = f0, w e h a v e
UmfAtUb) w h e r e K z is a c o n s t a n t , Ub is t h e " a p p a r e n t ' b u b b l e v e l o c i t y a n d u is t h e a v e r a g e g a s v e l o c ity in the bed. In the case of a fine size partic l e b e d , s m a l l e r s i z e b u b b l e s - - l o w e r Ub - - a r e
(3)
(7)
The average velocities through the orifices, To, a n d t h e b e d , u , m a y b e p r e s e n t e d i n t e r m s
218
I
p
-i:'-'~",
P
t I CA-- COMPRESSED
I I AIR
t J t-~
R--REGULATOR
U - - U TUBE
F - - FLUIDISATION
ST-- SURGE TANK
N--NEEDLE
OM--0RIFICE METER
DT-DISTRIBUTION TANK
P~
RM-ROTAMETER
PRESSURE G A U G E
Fig. 3. Experimental
set-up
VALVE
BP--BACK PRESSURE
for distributor
studies
(
ebe3g°
[ 2APdgc
)"
We have
K
FV b v
D-DISTRIBUTOR
in fluidisation.
of the pressure drops corresponding to the flow through the orifices [7] and a static bed [ 8 ] . T h a t is, or
COLUMN
creases, a corresponding increase in the terms of the denominator occurs, resulting in a cons t a n t K 0 w h i c h is i n d e p e n d e n t o f s y s t e m p a r a . meters. Equation (10) provides a method for predicting Ko- (The value of K o was determined by direct measurements of U M and APd/AP b using eqn. (9) as well by substituting the required values in eqn. (10).)
EXPERIMENTAL
] ~,
2fLe 3
"'--~'~b !
(8) or
(APd ~Z/2
K = K0 x X~J
(9)
Since K does not change with gas velocity for a given bed height we can also express K o a t t h e U M o r Um~ c o n d i t i o n s . N o w
Ko=(UmfAtUb. IFvbv/~{D[-IS~J2~(1--
e)
)112
(10)
The right-hand side of eqn. (10) comprises terms which are interdependent, Ub i n c r e a s ing with Vb, and u with H [7] and ~ decreasing. Thus when the term in the numerator in-
The experimental set-up (Fig. 3) consisted of (1) fluidi~ed bed column with orifice plate distributor, (2) orifice meters, (3) surge tank, (4) rotameter, (5) manometers, and (6) control valves. A 100 mm i.d. thick-walled glass column was used to hold the material on a 20 mm thick gas distributor. The distributor was provided with twenty-five 3-mm-diam. orifices having 8 mm spacing. All these twentyfive orifices were arranged as in Fig. (4) in the form of a cross, with six orifices on each arm of the distributor. Five orifices on each arm were used for gas distribution while the sixti one on each arm and a central one were use to measure the bed pressure drop. All the twenty orifices were connected to an air dist r i b u t i o n tank through twenty orifice meters each designed to give equal flow rate. Each orifice in the di~tEibutor was provided with a side pressure tapping to note the pressure
219 20~3~HOLES
_ ~ \
4--3-5
~ D M A T E R h - ~ L - - ZIRCON O~D FEIGHT ~ I D Umf 4~-'i C M / ~ C
@ HOLES
"
i
/,,
20
!1
I'1 i l l l l l i l ' l
13
~;~ll.,~--
6~%7
12
8~
9
~ A .,. J. J.J.
(~iFICE
LOCATION
-
<
<.
/ I00
"Plus'
D
D¢------¢'-----
A
A
-"
, o
- - -
~Ol
i-
r~i// I---~---
~
ALL OIMENSIONS ARE IN MM
Fig. 4.
' "---
.
type distributor.
variation at that point. Three-mm
~----.-
~
| ~5
C--0-8 D__ I O - U ~ UM E'T--- I O-(J~U~ . II 0 I 16 = = 6
20
, 14 tg
~ 13 I8
, 12 17
"
~.~-,.,<,.,,,-, , 2 T
= 3 8
, 4 9
~0-o io
(a) BED M A T E R I A L - U m f ~
D
I[
ZIRCON 4<) i
4-61Clrd#~Ec
D ~---~---30
E
# V r
D'I
!
:Sl
i r -'o ., i
.11
#1
;
f
~
"
-
-
o
~N
4
~t
,
o,---,
a~
\% 1
I
~o~
W-
tO F ~ G - -
~F-/CE 15 20
LOCATION
14
I
,
•
19
18
17
iG
O'85 I-oo
AS
SHOWN ~1 FtG. {_~} OO
= ~
G
7
8
9
10
(b)
Fig. 5 (a, b). Typical flow distribution pattern for zircon sand bed. the orifices at the centre discharge more flow t h a n a n y o t h e r o r i f i c e s , in c e r t a i n cases o r | rices n e a r t h e n o n - o p e r a t i n g o n e d e l i v e r relat i v e l y m o r e f l o w . W h e n all t h e o r i f i c e s b e c o m e o p e r a t i v e , t h e f l o w in e a c h o r i f i c e is a l m o s t t h e s a m e . A g i t a t i o n in t h e b e d m a t e r i a l and the appearance of bubbles on the surface d o n o t o c c u r u n t i l all t h e o r i f i c e s b e c o m e
220 BED M A T E R I A L - - R U T I L E
IOC~
,-
Ume
NO OF KEY
4 8! CMTBEC
ORIFICES-- 2 0
TO SYMEOL AS
IN T A B L E ( A }
28C o
8OO
BED MATERIAL-Umf
24~
:o
,o, ~
-
ALUMINA I CM/SEC
-
o
NO. O F 0 R I F [ C E S - - 2 0
Jk
KEY TO SYMBOL AS
2OO
TABLE
IN
•
(A)
t
4(--
¢ Q~
40¢
x
•
TABt,.E (A) ~D
TABLE 4~ %"
20¢
SYMBOL
~D
80
.f~IG H T
2o ~ ~
0"O 00
1
I
I
1
I
100
:ZOO
300
400
.500
I
600
I
I
BOO
900
I
1000
NO OF
9O(
KEY
ZIRCON
IN T A B L E
o
(A)
70(
i x
A
g s°'~ x ~1~
TABLE (A) SYMECI~ _BE.D HEIGHT
~2OC
-3D
:--~
o
o
I
I
200
I
300
l
400
I
500
I
~'~-00
°o
- - 6 0
~
IO0
I00
2: D
x
3 o
;
4
D
; •
•
12o
•
•
*so
,
zoo
,
6 D 7, Do
;~4o
•
2eo
,
,
~ao
c~/sEc
between
(n/N)u
a n d D0 f o r a l u -
BAND
a,
•00
~
eo
~. ~
o
t ~
|
Fig. 8. Relationship mina powder.
0R~-'ICES-- Z0
TO SYMBOL A S
s
4o
CM/SEC
4-~I C M / B E G
Umr
°o
MATERIAL
Io
50 ~¢"
7D
700
Fig. 6. Relationship between (n/N)u and DO for futile bed. BED M A T E R I A L - -
,~
6D
. t~
~; ~
'~*~
4~
4D BD
~100
.-
(A}
"I'D ~00
I 800
I 900
!
1000
Fig. 7. Relationship between (n/N)u and DO for zircon sand bed. operative. The incremehtal flow in the case of alumina powder, from one set of orifices bec o m i n g o p e r a t i v e t o a n o t h e r , w a s a l s o Iarger. Experimental observations on the pattern of the orifices becoming operative at different air v e l o c i t i e s a t t w o b e d h e i g h t s a r e s h o w n i n Figs. 5(a, b). These observations support the discussions on the progressive increase in the number o£ operating orifices with increasing gas v e l o c i t y a n d a l s o t h e a b s e n c e o f "real' b u b b l e f o r m a t i o n i n Ume o r uif t o U ~ g a s v e l o c ity range.
T h e e x p e r i m e n t a l r e s u l t s o n t h e air v e l o c i t y To, v a n d n / N f o r t h e t h r e e b e d m a t e r i a l s a n d f o r d i f f e r e n t b e d h e i g h t s are s h o w n in F i g s . 6 - 8. I t is o b s e r v e d t h a t t h e r a t i o nv/N-Uo = a~ K1, the slope of the line varying from 0.8 to 1, 0.75 to 1 and 0.17 to 1 for zircon, futile and alumina powder respectively at the bed height of 4D t. This indicates an increase of a w i t h t h e gas v e l o c i t y r a t i o . S i m i l a r o b s e r v a t i o n s c a n b e n o t e d f o r all b e d h e i g h t s e x c e p t for 1Dr. The results thus prove the validity of assumption (i). The point where the line [ ( n / N ) u vs. Vo] c u t s t h e x - a x i s r e p r e s e n t s t h e air v e l o c i t y ui a t w h i c h t h e o p e r a t i o n o f t h e orif i c e s w o u l d j u s t s t a r t . T o a c c o u n t f o r t h i s obo s e r v a t i o n , e q n . ( 1 ) m a y b e r e w r i t t e n as
a0 = K 1
To
--
Ui
A c c o r d i n g l y e q n . ( 2 ) m a y b e e x p r e s s e d as ui,
)
and eqn. (7) now becomes
Since
(12)
221
...,
,o.-oo,,
240
x,@ u
200
9
cn
s
=E ¢J
7
160
J>
u~
,_.
//
280
I0
{.
120 / /
80 3
D
.
2 !
~'*
i ~ 0
~/~
•
RUTILE
/ /
BED
40
/ //
.25;''
~T
0
/ /
1
i
r
,
v
2
3
4
5
~
6
,
i
i
v
,
,
T
I
7
8
9
I0
II
12
13
14
f
0
X I05
(a)
f
; 3
t 4
T 5
I 6 X 10 5
p-.-
(b)
Fig. 9. ( a ) R e l a t i o n s h i p b e t w e e n u ( a t U M c o n d i t i o n ) a n d ,~. ( b ) R e l a t i o n s h i p b e t w e e n v ( a t U~.I c o n d i t i o n ) for alumina bed.
and
centage variation o f the individual values o f
we have
Ko f r o m t h e a v e r a g e v a l u e is w i t h i n a b o u t K
Vo (Um~AtUb~ =--~FVbv )
(7)
F i g u r e 9 ( a , b ) s h o w s a p l o t o f v versus [J a t t h e UM c o n d i t i o n . I t is s e e n t h a t t h e e x p e r i m e n t a l results indicate a linear relationship, t h u s s a t i s f y i n g e q n . (8). F r o m t h e s e p l o t s t h e slope Ub/FV b was determined and found to be 0.000625, 0.00092 and 0.000509 for r u t i l e , z i r c o n a n d a l u m i n a r e s p e c t i v e l y . Ass u m p t i o n (iii) c o u l d n o t b e p r o v e d d i r e c t l y b e c a u s e o f d i f f i c u l t y in m e a s u r i n g Ub f o r ' a p p a r e n t " b u b b l e s . H o w e v e r , Ub v a l u e s f o r "real" b u b b l e s h a v e b e e n e x t r a p o l a t e d t o t h e UM c o n d i t i o n t o c a l c u l a t e t h e v a l u e o f Ub/ F V b (see A p p e n d i x ) . I t is o b s e r v e d t h a t t h e c a l c u l a t e d a n d t h e o b s e r v e d v a l u e s are o f t h e same order of magnitude. T h e t e r m Ub/FVb m a y b e c o n s i d e r e d as a n index of fluidisation character of the bed material. A higher value generally indicates t h a t t h e f i u i d i s e d b e d will b e s t a b l e a t l o w e r UM/Umf r a t i o . U s i n g t h e e x p e r i m e n t a l v a l u e s Of Ub/FVb and U at U M conditions and those available in t h e l i t e r a t t w e f o r o t h e r t e r m s , K o has been determined from eqn. (10). Ko thus d e t e r m i n e d is f o u n d t o b e 0 . 6 5 3 , 0 . 6 3 1 2 a n d 0.692 for futile, zircon, and al-m~na powder respectively. The values of Ko calculated from e q n . (9) a r e p r e s e n t e d i n T a b l e 1 . T h e p e r -
15%. A l o g - l o g p l o t (Fig. 1 0 ) f o r t h e e x p e r i m e n t a l v a l u e s o f K a n d A P d / A P b a t t h e UM c o n d i t i o n ( f o r all t h e e x p e r i m e n t a l c o n d i t i o n s ) establishes the relationship K-
0.65(APd/APb)°'43
(14)
Since K o and the exponent for APd/AP b are i n d e p e n d e n t constants, eqn. (14) m a y n o w b e given as
A P b /UM
__ Umf
(15)
w h e r e C is a c o n s t a n t . T h o u g h t h e s i m p l i c i t y of eqn. (15) for determining the desired APd/ A P b is re~li.~ed, it involves, h o w e v e r , t h e u n k n o w n t e r m UM- I t is p r o p o s e d t o l o o k i n t o the possibility o f arriving at an e q u a t i o n f o r d e t e r m i n i x , g U M in t e r m s o f U t a n d Umf-
CONCLUSION In order to facilitate the design of the m u l t i - o r i f i c e t y p e o f gas d i s t r i b u t o r in f l u i d i s e d beds a theoretical model, based on the kinetics o f b u b b l e f o r m a t i o n a t t h e d i s t r i b u t o r a n d t h e i r d i s s i p a t i o n in t h e b e d , h a s b e e n p r o p o s e d . F r o m this m o d e l i t h a s b e e n f o u n d
222 TABLE 1 Ub/FV b (cm -2)
Least-squares l i n e
Bed material
Bed height
(cm) Y
Rutile Umf = 4.8 cm/sec
=
1.083x--I05.4
Zircon sand Uraf = 4 - 6 1 c m / s e c
Y
Alumina powder Um~ = 1 . 0 c m f s e c
Y= 1.235x--61.53
=
1.126x--124.7
Calculated
Experimental
Mean
0.97 0,597 0,586 0,589 0.617 0.305 0.609 0,653
0,68 0.527 0.579 0.5938 0.64 0.6175 0.618 0.6079
10 20 30 40 50 60 70 Mean
0.60 0.565 0.62 0.67 0,675 0.649 0.64 0.6312
0.5418 0.496 0.553 0.6756 0.558 0.554 0.6008 0.56845
10 20 30 40 50 60 70 Mean
0.72 0,70 0.685 0.650 0.69 0.706 0.695 0.692
0.714 0.674 0.690 0.6308 0.693 0.733 0.718 0.693257
10 20 30 40 50 60 70
0.000625
0.00092
0.000509
Values of g 0
N . B . Y = ( r z / N ) v , x = Vo"
also b e e n f o u n d t h a t ub/FVb m a y b e u s e d as a n i n d e x f o r c h a r a c t e r i s i n g t h e f l u i d i s a t i o n behaviour of any bed material.
2~
,<
l,,c
t
x "
W A
a.
ACKNOWLEDGEMENTS
x
x
x
A
S'¢MBOU -
-
1
~
,~. -
-
~
BED ID
O" O']
eEo AT. ~ .~.~Xj~J~.~ ZI~,~ON -
RUTILE
AL~,m"dA
SAND
POWI~R
HEIGHTS TOTD
FOR EACH
I 1~
MATERIAL
T h e a u t h o r s are greatly i n d e b t e d to Shri C. V. S u n d a r a m , H e a d , M e t a l l u r g y D i v i s i o n a n d t o D r . C. K . G u p t a , H e a d , E x t r a c t i v e Metallurgy Section for their constant encoura g e m e n t a n d s u p p o r t in c a r r y i n g o u t t h e s e studies.
] 2:0
(" *d/~'Ou,, ex~ Fig. 10. Relationship between experimental values of K and (~Dd/~b)~/~.
possible to estimate the value of a constant relating the gas velocity (ratio) and the ratio of the pressure drops across the distributor and the bed. T h e m o d e l has been s h o w n to agree well with the ~_xperimental observations. F r o m t h e e x p e r i m e n t a l observations it has
LIST O F SYM_BOLS
At ao
D Dt fo F
cross-sectional area for fluidised
bed
(L 2)
r a t e o f b u b b l e f o r m a t i o n (T -x) d i a m e t e r o f t h e old_lice ( L ) d i a m e t e r o f t h e b e d (L) bubble d i s s o c i a t i o n r a t e ( T - x ) frequency of bubble formation
(T -x)
223
f gc
H K, K0, K~ K1, K2
L N n
APd
friction factor Newton's law conversion factor bed height (L) dimensionless constants
rate c o n s t a n t s (T-1) tube length or orifice length (L) total number of orifices number of operating orifices pressure drop across the distributor (ML -1 T -2)
pressure d r o p across t h e bed S
(ML-i T -2) surface area per unit volume of bed (L-1 ) average superficial gas velocity in bed ( L T - 1 )
Ub
b u b b l e rise v e l o c i t y ( L T - i )
U
average gas velocity at the operating orifices (LT -1) average gas v e l o c i t y f o r all t h e orifices (LT -1) velocity at which ~rst orifice just operates (LT -1) velocity in the bed corresponding to (LT -1) s u p e r f i c i a l gas v e l o c i t y i n t h e b e d for n/N = 1 (LT -1) s u p e r f i c i a l gas v e l o c i t y i n t h e b e d at minimum fluidisation condition (LT -1) bubble volume at the distributor ( L a) bed friction factor
UM Umf
Vb Pf P~
d e n s i t y o f fluid (ML-3) d e n s i t y o f solid (ML-3)
P
as s h o w n i n Fig. (9) ( L a T - i ) bed porosity
APPENDIX T h e f u n c t i o n Ub/FVb m a y b e e v a l u a t e d from the genera|i.~ed reported values of the i n d i v i d u a l t e r m s . I t is k n o w n t h a t t h e b u b b l e v e l o c i t y is Ub ~ 2 2 - 2 ~ / d b 0 ( c m / s e c ) w h e r e d b o is t h e i n i t i a l b u b b l e d i a m e t e r ( c m ) . M a k i n g u s e o f M i w a e t a l . "s e q u a t i o n [ 1 0 ] f o r d b o ----0 . 0 0 3 7 6 ( U M - - Umf) z ( c m ) a t g a s v e l o c i t y U M , w e h a v e t h e b u b b l e v e l o c i t y Ub
[ 0 . 0 0 3 7 6 ( U M - - U m f ) ] 0.s × 2 2 . 2 ( c m / s e c ) . T h e b u b b l e v o l u m e Vb is a f u n c t i o n o f v o l u metric flow rate Q (Q = AUM, where A = area o f c r o s s - s e c t i o n o f t h e b e d , c m 2) o f t h e gas. H e n c e Vb = 1.138(AUM)SlS/g 315 ( e r a 3 ) - T h e frequency of the bubbles at the distributor has not yet been well established. However, one could extend the lines shown in ref. [4], Fig. (20) on p. 129, to a reasonable value. A value of 20 bubbles per second for each orifice has been selected. On substituting the a p p r o p r i a t e v a l u e s i n t h e f u n c t i o n Ub/FVb, we have Ub
2 2 - 2 ( 0 - 0 0 3 7 6 ) °'5 (UM - - U m f ) g 3/5
FVb
2 0 × 2 0 × 1 . 1 3 8 ( A U M ) GI5
S e l e c t i n g UM = 1 9 . 2 c m / s e c a n d U m f = 4 . 8 cm/sec (for futile bed material) and cross-sect i o n a l a r e a o f t h e b e d A = 7 8 . 5 4 c m 2, w e g e t Ub
FVb
- 4.12
X 10 -4
w h i c h is o f t h e s a m e o r d e r o f m a g n i t u d e as the experimental results. REFERENCES 1 A. B. Whitehead, in Davidson and Harrison (Eds.), FluldLcation, Academic Press, L o n d o n , 1971, p. 781. 2 S. F a k h i m i a n d D. Harrison, Chemica, 70, Butterworths and Inst. o f Chem. Engrs., L o n d o n , 1971, Session 1, p. 29. 3 W. M. S. Kassim, Ph.D. Thesis, Univ. o f A s t o n in Birmingham, 1972. 4 D . K u n i i and O. Levenspiel, Fluidisation Engineering, Wiley, New York, 1969, p. 89. 5 J . W . Hiby, Chem. Ing. Tech., 36 (1964) 228. 6 R. Siegel, AIChE J., 22 (1976) 590. 7 W. L. McCabe and J. C. Smith, U n i t Operations o f Chemical Engineex-;ng, McGraw-Hill, New York, 1956, p. 67. 8 J. F. Richardson, in Davidson a n d Harrison(Eds.), Fluidisation, Academic Press, L o n d o n , 1971, p. 25. 9 ]D. S a t h l y a m o o r t h y a n d Ch_ Sridhar Rao, Powder Technol., 20 (1978) 47 - 52. 10 K. S. Miwa, S. Mori, T. Kato and Io Mochi, Int. Chem. Eng., 12 (1972) 181. 11 T . P . Hsiung and J. R. Grace, i n Davidson (Eds.), Fluidisation, Cambridge Univ. Press, L o n d o n , 1978, pp. 19 - 24.