The Water Gas Shift Reaction in a Fluidized Bed Catalytic Reactor
by WILLIAM THOMAS ALUMKAL
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY in Chemical Engineering
Montana State University
© Copyright by WILLIAM THOMAS ALUMKAL (1966)
Abstract:
Increased uses of fluidized bed reactors have brought about intensive interest in the behavior of
fluidized beds. Several physical models of fluidized bed reactors are available in the literature many of
them with little or no experimental backing. This research project was designed to investigate these
models and determine how well they predict the actual behavior, and if necessary, modify them.
Conversions of carbon monoxide were calculated using the physical models and were compared with
the observed values. The two basic models were modified first by introducing one undetermined
parameter in each case; namely, cloud size in Rowe's model and the number of transfer units in the
models of Davidson and Harrison. In both of these models the emulsion phase was considered under
the conditions of plug flow and back-mixing. These two models were further modified by introducing a
longitudinal diffusion coefficient in the emulsion phase.
The study involved a 3-inch diameter fluidized bed reactor. Water gas shift /reaction on chromia
promoted iron oxide catalyst was used as the reaction system. A pseudo first order reaction was
obtained by keeping the concentration of carbon monoxide low in the feed stream.
The results show that considering no undetermined parameters, Rowe's model with plug flow in the
emulsion phase yielded a better agreement with the observed values than the models of Davidson and
Harrison. Some improvement was obtained by introducing the undetermined parameters into these
models.
THE WATER GAS SHIFT REACTION IN A FLUIDIZED BED
CATALYTIC REACTOR
by
WILLIAM THOMAS
ALUMKAL
A t h e s i s s u b m itte d t o t h e G ra d u a te F a c u l t y i n p a r t i a l
f u l f i l l m e n t o f th e r e q u i r e m e n ts f o r t h e d e g re e
of
DOCTOR OF PHILOSOPHY
in
C h e m ic a l E n g in e e r in g
A ppro v ed :
(L
H e a d , M ajor D e p a rtm e n t
C h a irm a n , E x a m in in g C om m ittee
''2 2
Gfadi
a d u a t e Dean
MONTANA STATE UNIVERSITY
B ozem an, M ontana
A u g u s t, 1966
ill
ACraowpiDGMENjT
The a u t h o r .w ish es t o th a n k t h e e n t i r e s t a f f o f .t h e C h e m ic a l
E n g i n e e r in g .D e p a rtm en t o f M ontana S t a t e . .U n i v e r s i ty an d i n p a r t i c u l a r . .
D r. E 0 iAoj B if k h im e r who d i r e c t e d . t h f s r e s e a r c h , .f o r t h e i r s u g g e s t i o n s
-Which, l e d t o t h e . . c o m p le tio n - o f t h e p r o j e c t .
. T hanks a r e a l s o due. t o
. M r. .Jam es T i l i d r y an,d .to M r. AriI p n ,Huso who he,I p e d j i n t h e b u i l d i n g ,and
r e p a i r of. th e . e q u ip m e n t.
. The a u t h o r a l s o w is h e s t o a c k n o w le d g e t h e ,- N a t io n a l S c ie n c e E o y n d a t.iqn, a n d .th e E n g i n e e r in g E x p e rim e n t S t a t i o n , of. M ontana ,S ta te . U n i v e r s i t y
f o r t h e i r f i n a n c i a l s u p p o r t a n d C h em etro n C h em icals, who. f u r n i s h e d t h e
c a t a l y s t u se d i n t h i s s tu d y .
The a u t h o r .,a l s o w is h e s t o t h a n k t h e g r a d u a t e S t u d e n ts o f t h e
C h e m ic a l E n g in eerin g D e p a r tm e n t, , e s p e c i a l l y . M r. .R alph .H u n ts in g e r f o r
h i s h e lp w i t h th e c o m p u te r o p e r a t io n s .
. iv .
TABLE OF CONTENTS
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TABLE .GF CONTENTS ( c o n tin u e d )
A p p en d ices.
. N o m e n c la tu re .
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Sam ple C a l c u l a t i o n s
T a b le s ..«
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LIST OF TABLES
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Tafyle-. I.
E x p e r im e n ta l, C o n d itio n s .
T a b l e .11
.C a ta ly s t S iz e
T a b le I I I
F i x e d Bed D a ta
T a b le IV'
E f f e c t o f B u b b le S i z e on C o n v e rs io n
U s in g R o w e's M odel
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T a b le .V
T a b le VI.
T a b le V II
T a b le V I I I
T a b le IS.
T a b le S
T a b le S I
T a b le S I I
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E f f e c t . o f C loud .S iz e on C o n v e rs io n
U s in g R o w e's ,M o d e l,.w ith P lu g F low i n
t h e E m u lsio n P h a s e
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. O b s e rv e d and. C a l c u l a t e d .C arbon
M onoxide C o n v e rs io n s . . . .
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E f f e c t o f C lo u d S i z e on C o n v e rs io n
U s in g R o w e's M odel . w i t h .B ack m ix in g
in . t h e E m u lsio n P h a s e
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Sum o f t h e S q u a r e s ,o f E r r o r s . f o r t h e
B e s t . F i t D a ta U s in g .t h e M odels o f Rowe
H a v in g None#. One.# a n d Two U n d e te rm in e d
P a r a m e te r s
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C l o u d .t o B a b b le D ia m e te r R a t i o and.
D i f f u s i o n . - C o e f f i c i e n t V a lu e s . f o r . th e .
.B e s t .F .it. D a ta .U sin g t h e M odels
. . o f . Rowe .
E f f e c t ,o f Number o f T r a n s f e r U n i t s . o n
C o n v e r s io n U s in g t h e M odel o f D a v id so n
a n d H a r r i s o n w i t h B ackm ix i n t h e
E m u ls io n P h a s e .
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E f f e c t o f t h e Num ber o f T r a n s f e r U n its
• o n C o n v e r s io n U s in g t h e M odel o f D a v id s o n
a n d .H a r r i s o n w i t h P lu g F low .i n t h e
E m u ls io n P h a s e
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Sum o f . t h e S q u a r e s ,o f E r r o r s f o r t h e B e s t
F i t D a ta .U sin g M o d e ls .o f D a v id s o n add
H a r r i s o n w i t h None.#,.One# an d Two Un­
d e te r m in e d P a ra m e te rs .
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.L IST OF. TABLES ( c o n tin u e d )
. PageT a b le X l I l
T a b le XIV.
T a b le . XV
T a b le XVI
T a b le X V Il
T a b le X V lII
T a b le XIX
. Number- o f T r a n s f e r . U n i t s a n d .D i f f u s i o n ■
- C o e f f i c i e n t s , V a lu e s . f o r t h e .B esb F i t
. D a ta U s i n g ,t h e .M odels o f D a y ld e o n and.
.H a rris o n . = •
• » •• - ' •’
F o r t r a n P rogram , f o r . Rowe.1s .M odel C a l­
c u l a t i o n , w ith . P lu g F lo w .in . -th e .E m ulsion.
P hase
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F o r t r a n P ro g ra m f o r Row e 1s ..M odel C alr
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.-C-Uiations w ith . P lu g ,Flow , and, - .L o n g itu d in a l
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t h e ,M o d el o f D a r id s o n a n d . H a r r i s o n w ith
P lu g ,Flow i n .th e - E m u ls io n P h a s e '
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F o r t r a n , P ro g ra m f o r th e . L l a c u l a t i o n s . o f
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-th e . B a c k m ix in g i i i th e Em ulsion P h a s e '
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F o r t r a n -Program .f o r . C a l e u l a t i o n s o f ■I h e
•Model .o f D i v i d s o h -and ..H a rriso n , w i t h P lu g
F low a n d ..L o n g i t M i h a i D i f f u s i o n i n ' t h e
E m u lsio n . P h a s e
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LIST OF FIGURES
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Row e1S Models C o n s i d e r i n g .t h e E m u ls io n P h a s e
a s P lu g ,Flow a n d B ackm ix ,
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-Rowe!-s M odels C ohsi d e r i u g .t h e .E m ulsion ' P h a s e
a s P lu g Flow and .B a c k itix .
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M odels o f D a v id so n a n d H a V riso n C o n s id e r in g
Pl.ug Flow and B a c k m ix in g i n 'th e E m u ls io n P h a s e
,
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99
-M odels o f D a v id so n a n d - H a r r i s o n C o n s id e r in g
P lu g ,Flow- a n d . B a c k m ix ln g i n •t h e E m u ls io n P h a s e
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.B e s t F i t D a ta o f. Row e 1S -Model .C a l c u l a t i o n s
W ith One U n d e te rm in e d P a r a m e te r • .• - ' •
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B e s t F i t D a ta o f t h e M odel - C a lc u l a t i o n s o f
D a v id s o n d n d - H a r r i s o n W ith Ohe U n d e te rm in e d
P a r a m e te r . . . . . . . . . . . . .
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B e s t F i t D a ta fro m t h e M odel C a l c u l a t i o n s o f
D a v id s o n a n d H a r r i s o n W ith One U n d e te rm in e d
P a r a m e te r
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F ig u re
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P r e s s u r e Drop i n .F lu id iz e d , Bed
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2
D ia g ra m .o f A p p a ra tu s
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F ig u re
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- F i t t e d L in e f o r R e a c t i o n V e l o c i t y C o n s ta n t
F ig u re
4
A c t i v a t i o n E n e rg y
F ig u re
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E n t i r e . R e a c to r a s .P lu g .F lo w , a n d Backm ix
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E n t i r e .R e a c to r a s .P lu g .F lo w . a n d .Backm ix
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F ig u re
7
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F i g u r e .11
F i g u r e 12
F i g u r e 13
F i g u r e 14-
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W ith One. U n d e te rm in e d P a r a m e te r • « .
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ix
LIST.OF' FIGURES ( c o n tin u e d )
Page
F i g u r e 15
. F ig u r e . 1 6
.F i g u r e .17
'B e s t. F i t D a ta ...fo r. M odel C a l c u l a t i o n s , o f
.Ro1-We and. . t h a t o f D av id so n , an d H a r r i s o n
C o n ta in in g '.T w o U n d e te rm in e d - .P a ra m e te r's
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.Rowe .and. , t h a t o f D a v id s o n a n d ,.H a r r is o n
C o n t a in i n g ,Tvjo 'U n d e te rm in e d ; P a r a m e te r s . •
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,M odel o f Mamuro ,and, M uohi
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. . . . .
- F ig u r e 18
E f f e c t . o f. T e m p e r a tu r e o n C onversion
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■ F ig u re 19
E f f e c t o f Bed. H e ig h t ,o n Conversion.
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F i g u r e 20.
E f f e c t o f P a r t i c l e S iz e on C o n v e r s io n
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ABSTRACT
In c re a s e d u se s o f f lu i d iz e d bed r e a c to r s have, b ro u g h t a b o u t i n ­
t e n s i v e i n t e r e s t i n t h e b e h a v io r o f . f l u i d i z e d b e d s .
S e v e ra l p h y s ic a l
.m odels o f f l u i d i z e d b e d r e a c t o r s a r e a v a i l a b l e i n t h e l i t e r a t u r e , many
o f them w i t h l i t t l e o r .n o e x p e r i m e n t a l .b a c k in g .
T h is r e s e a r c h p r o j e c t
was d e s ig n e d t o . i n v e s t i g a t e t h e s e m o d e ls a n d d e te r m i n e how w e l l t h e y
p r e d i c t t h e a c t u a l b e h a v i o r , a n d i f n e c e s s a r y , . m o d ify th e m .
C o n v e rs io n s o f c a rb o n m o n o x id e w ere c a l c u l a t e d u s i n g 't h e ^ - p h y s l e a l
m o d els a n d w e re co m p ared w i t h the- .o b s e rv e d . v a l u e s . The two b a s i c m o d e ls
w e re m o d if ie d . f i r s t by', i n t r o d u c i n g .o n e u n d e te r m in e d p a r a m e t e r i n e a c h
c a s e j. ,n a m e ly ,,,,c lo u d s i z e i n R o w e 's m odel a n d t h e num ber o f t r a n s f e r u n i t s
i n t h e m o d els o f D a v id s o n a n d H a r r i s o n '. I n b o th o f t h e s e m o d e ls t h e
e m u lsio n , p h a s e w a s ..c o n s id e r e d u n d e r t h e . c o n d i t i o n s o f p l u g f lo w a n d b a c k m ix in g . T h e se tw o m o d els w e re f u r t h e r m o d if ie d by i n t r o d u c i n g a l o n g i ­
t u d i n a l d i f f u s i o n c o e f f i c i e n t . i n t h e . e m u l s i o n ; p h a s e .■
The s t u d y i n v o l v e d a 3 - i n c h d i a m e t e r f l u i d i z e d b e d , r e a c t o r . W a te r
g a s s h i f t , r e a c t i q n on chromia p ro m o te d i r o n o x i d e . c a t a l y s t w a s .u s e d
a s t h e r e a c t i o n s y s te m . A p s e u d o f i r s t . o r d e r r e a c t i o n was o b t a i n e d by
k e e p in g ,th e .'c o n c e n t r a t io n o f c a r b o n m onoxide lo w ..in , t h e f e e d s tr e a m .
The r e s u l t s show . t h a t - . c o n s i d e r i n g no .u n d e te r m in e d .p a r a m e t e r s 4
P o w e ' s m o d el w i t h p l u g flo w i n t h e e m u ls io n p h a s e y i e l d e d a . b e t t e r a g re e .m erit w i t h t h e o b s e rv e d , v a lu e s t h a n - th e m o d els ,o f D a v id s o n a n d H a r r i s o n .
Some im p ro v em en t was o b t a i n e d . b y , i n t r o d u c i n g the- u n d e te r m in e d p a r a m e t e r s
i n t o t h e s e m o d e ls .
INTRODUCTION
When, g a s i s f o r c e d t o f l o w , u pw ards t h r o u g h a . b e d . o f s o l i d p a r t i c l e s
s u p p o r t e d .by a p o r o u s p l a t e , , t h i s .c a u se s, a .p r e s s u r e d ro p . a c r o s s t h e b e d .
When t h i s p r e s s u r e d ro p becom es e q u i v a l e n t . t o ■t h e w e ig h t .o f t h e bed.,, t h i s
colum n o f s o l i d . p a r t i c l e s r e s e m b le s .a l i q u i d .o f h i g h . v i s c o s i t y . ,
At t h i s
p o i n t g, t h e i n d i v i d u a l . p a r t i c l e s a r e d is e n g a g e d , .som ew hat .fro m e a c h o t h e r .
Any f u r t h e r i n c r e a s e in . g a s f l o w , r a t e w i l l .c a u se , t h e b e d t o e x p a n d t o
accom m odate t h i s . i n c r e a s e .
T h is t y p e o f a b e d . o f p a r t i c l e s i s . c a l l e d a
" F lu id iz e d B ed".
■H is tp y y
The f i r s t - f l u i d i z e d u n i t t o b e o p e r a t e d on a c o m m e r c i a l - s c a le was
t h e W in k le r Gas G e n e r a t o r ( I ) . f o r t h e m a n u f a c t u r e . o f w a t e r a n d p r o d u c e r
gas.
. I t was d e v e lo p e d i n Germany in . 1 9 2 1 .
T he f i r s t - l a r g e s p a t e f l u i d i ­
z a t i o n a p p l i c a t i o n i n t h e U n ite d . S t a t e s d a t e s t o a b o u t 1940 a n d p e r t a i n s
to th e c a t a l y t i c c ra c k in g o f o i l v a p o rs .
The. s u c c e s s f u l o p e r a t i o n o f f l u i d
c r a c k i n g , u n i t s .c a u s e d a w id e s p r e a d i n t e r e s t i n t h e t e c h n i q u e a n d p r e ­
c i p i t a t e d a . l a r g e num ber o f f u n d a m e n ta l a n d a p p l i e d ..s tu d ie s . i n t h e f i e l d
.o f ,f l u i d i z a t i o n .
. A g r e a t d e a l o f w o rk s t i l l . r e m a i n s t o . b e d o n e .
■I f a g a s . i s f o r c e d .t o flo w , u pw ards th r o u g h a b e d o f s o l i d p a r t i c l e s j,
■t h e p r e s s u r e d ro p a c r o s s t h e b e d . i n c r e a s e s a lo n g th e . l i n e AB (S e e F i g . . I ) ,
, u n t i l , t h e flo w r a t e ..re a c h e s No.
-2 “
Any f u r t h e r i n c r e a s e i n f lo w r a t e w i l l . c a u s e a d i p 4 n t h e p r e s s u r e
d ro p
(B C ).
. A t .h ig h flo w r a t e s t h e p r e s s u r e d ro p a c r o s s t h e b e d w i l l
v e r y n e a r l y b e e q u a l t o t h e . v a l u e a t .B=
z in g v e lo c i ty and a t
U% i s c a l l e d t h e minimum f l u i d i ­
th e b e d .is s a i d .t o be .in c ip ie n tly f lu i d iz e d .
A f l u i d i z e d bed.., when o p e r a t e d a b o v e t h e minimum f l u i d i z i n g v e l o c i t y ,
c o n s i s t s o f two p h a s e s — a d e n s e (.em u lsio n ) p h a s e a n d a . d i l u t e
phase,
(b u b b le )
-The e m u lsio n , p h a s e i s a l s o c a l l e d . c o n t i n u o u s o r p a r t i c u l a t e p h a s e
a n d t h e .b u b b l e , p h a s e i s c a l l e d , a .d i s c o n t in u o u s p h a s e s i n c e t h e b u b b le s
ape d is c re te .
I n t h e e m u ls io n p h a s e , , t h e g a s t r a v e l s a t t h e . r a t e o f
th e .m in im u m f l u i d i z i n g v e l o c i t y .
T he r e m a in in g g a s p a s s e s th r o u g h t h e
bed a t . a h ig h e r v e lo c ity as b u b b le s »
T h e re i s g a s i n t e r c h a n g e b e tw e e n
t h e e m u ls io n p h a s e a n d t h e b u b b le pha.se,.
■T h e .b e h a v i o r . o f t h e f l u i d i z e d b e d . i s . d e s c r i b e d by p h y s i c a l . m o d e l s .
T he e a r l y m o d els o f f l u i d i z e d b e d s c o n s i d e r e d t h e b e d as. a s i n g l e p h a s e .
•The r e l a t i o n s h i p s d e v e lo p e d on t h i s b a s i s w e re n o t a d e q u a t e .
A ll th e
r e c e n t m odels c o n s i d e r t h e f l u i d i z e d b ed a s com posed .o f two p h a s e s t h e
e m u ls io n p h a s e a n d .th e b u b b le p h a s e .
Shen a n d J o h n s to n e (2) w e re t h e . f i r s t o n e s t o s tu d y t h e k i n e t i c s i n
a .f l u i d iz e d bed r e a c to r .
n i t r o u s ,o x i d e .
They s t u d i e d t h e c a t a l y t i c d e c o m p o s itio n o f
■They c o n s i d e r e d b o t h p e r f e c t m i x i n g .a n d .p l u g .flo w i n t h e
e m u ls io n p h a s e a n d e s t a b l i s h e d r a t q e q u a ti o n s f o r b o th c a s e s .
.A p p ro x im a te
a g re e m e n t w a s .f o u n d b e tw e e n c a l c u l a t e d a n d .o b s e rv e d , v a lu e s i n t h e , c a s e o f
b o t h t h e m o d e ls .
The m ass t r a n s f e r c o e f f i c i e n t b e tw e e n t h e p h a s e s was
c a l c u l a t e d ..from -two s im u lta n e o u s f i r s t o r d e r l i n e a r d i f f e r e n t i a l e q u a ti o n s
. o b t a i n e d from , a m a t e r i a l b a l a n c e i n e a c h p h a s e .
T h is .m a s s t r a n s f e r co­
e f f i c i e n t was. fo u n d ...to b e a f u n c t i o n o f c a t a l y s t .b e d h e i g h t a n d th e . g a s
f lo w r a t e .
■M a th is a n d .W atson .(3) s t u d i e d t h e c r a c k i n g ,o f cum ene .in a . f l u i d i z e d ,
bed.
T h e i r two p h a s e , m o d el assum ed, p l u g ,flo w , i n b o t h t h e p h a s e s .
The
t o t a l . f e e d . . s t r e a m a n d .t h e . t o t a l w e ig h t o f th e , c a t a l y s t .w e r e ., assu m ed to.
be d is trib u te d -b e tw e e n th e . W r p h a se s .
.P s e u d o .m ass-, t r a n s f e r .. c o e f f i c i e n t s
.or- i n t e r a c t i o n c o e f f i O i e n t s a r e . i n t r o d u c e d . t o ..c o m p e n s a te .fo r- t h e i n ^
c r e a s e d c o n v e rs io n , o b s e r v e d i n a n y o f t h e two p h a s e s .
They t r i e d t o
a p p ly t h e i r , d a t a t o o t h e r m o d e ls , b u t w i t h o u t much s u c c e s s .
Lewis.,, e t . a l . s.
(4-) s t u d i e d th e c a t a l y t i c h y d r o g e n a tio n , o f. e t h y l e n e .
-T h e y .a ssu m e d a p l u g , f l o w .i n b o th p h a s e s .
A f r a c tio n o f . th e c a ta ly s t is
c o n t a i n e d I n t h e b u b b le a n d . . t h e r e f o r e r e a c t i o n t a k e s .p l a c e i n b o th
p h a s e s ,.
A pseudo f i r s t . - o r d e r r e a c ti o n w a s ,o b ta in e d .b y ,u s in g a .l a r g e
.e x c e s s o f e t h y l e n e .
Thpy fo u n d th a t th e e f f i c i e n c y . o f t h e ..f l u i d i s e d . b ed
. f o r c a r r y i n g o u t . . . f i r s t . o r d e r . i r r e v e r s i b l e r e a c tio n s .- w a s . in d e p e n d e n t o f t h e
b e d .h e ig h t.
T he gas. i n t e r c h a n g e b e tw e e n t h e .t w o p h a s e s - w a s fo u n d t o be
m o st p ro n o u n c e d a t h ig h , g a s , r a t e s .
They d i d n o t r e a c h a n y c o n c lu s i o n s
on b a e k m ix in g i n th e ,.e m u ls io n p h a s e .
-May (5) p o s t u l a t e d a new m o d e l w h e re a . l o n g i t u d i n a l d i f f u s i o n . c o ­
e f f i c i e n t . -was..i n t r o d u c e d , t o ■a ll o w f o r m ix in g . i n - t h e a x i a l d i r e c t i o n .
-4 T h is d i f f u s i o n c o e f f i c i e n t was c a l c u l a t e d u s i n g r a d i o a c t i v e s o l i d s t r a c e r
in a f lu id iz e d bed.
R a d i o a c t iv e s o l i d s w ere i n j e c t e d .n e a r t h e to p o f th e
b e d and t h e a p p e a r a n c e o f r a d i o a c t i v i t y a t v a r i o u s p o i n t s b e lo w t h e i n ­
j e c t i o n p o i n t was m o n ito r e d . . T h e d i f f u s i o n c o e f f i c i e n t was c a l c u l a t e d
u n d e r t h e a s s u m p tio n t h a t i t i s a c o n s t a n t f o r t h e e n t i r e .c r o s s s e c t i o n
o f th e bed.
The o r o s s ^ f l o w .r a t i o , ,w h ic h i s . t h e t o t a l r a t e ,o f e x c h a n g e .o f g a s
b e tw e e n t h e b u b b le a n d .t h e p a r t i c u l a t e p h a s e ,, was d e te r m in e d by a tim e
o f c o n ta c t e x p e rim e n t,
A s m a l l a m o u n t,o f t r a c e r g a s , . h e l i u m , was a d d e d
t o t h e . f l u i d i z i n g a i r and. .th e u n i t . was r u n u n t i l . e q u i l i b r i u m was e s t a b ­
lis h e d .
The t r a c e r g a s was t h e n c u t . o f f a n d . i t s . c o n c e n t r a t i o n i n t h e
e x i t g a s w as .m o n ito re d ..
T he c r o s s .f l o w . p e t e i s r e l a t e d .to t h e ..s l o p e .of
t h e r e s i d e n c e t im e d i s t r i b u t i o n .
A lth o u g h May show ed r e s u l t s o f h i s t r a c e r s t u d i e s , .no e x p e r i m e n t a l
r e s u l t s w ere g i v e n f o r t h e s t u d y o f f i r s t o r d e r r e a c t i o n s y s te m i n a
f l u i d i z e d b e d , w h ic h h e a l s o c o n s i d e r e d .
The m odel .o f May was a p p l i e d t o g a s m ix in g e x p e r im e n ts by Van D eem ter
( 6 ) t o d e te r m i n e b o t h d e n s e p h a s e g a s v e r t i c a l d i f f u s i v i t y a n d t h e g a s
i n t e r c h a n g e b e tw e e n t h e two p h a s e s , w i t h o u t u s i n g t h e a s s u m p tio n o f . e q u a l
. d i f f u s i v i t y o f s o l i d s and d en se p h a s e g a s .
F o r th e c a s e .o f f i r s t o rd e r
i r r e v e r s i b l e c h e m ic a l r e a c t i o n , . h e c o n c lu d e d t h a t a x i a l d i f f u s i o n i s . i m ­
p o r ta n t .o n ly a t h ig h c o n v e rs io n s .
t h i s case.,, e i t h e r .
-No e x p e r i m e n t a l w ork was r e p o r t e d i n
-5 L a n n e au (7) u g e l a c a p a c i t a n c e p r o b e t o i n v e s t i g a t e t h e g a s f lo w i n
a f l u i d i z e d , b e d by m eans ,o f d e n s i t y m e a s u r e m e n ts .
From t h e r e s u l t s o f
h i s e x p e rim e n ts,,, c o n c lu s i o n s w e re draw n, a b o u t t h e d i s t r i b u t i o n , o f s o l i d s
b e tw e e n t h e b u b b le an d .e m u ls io n p h a s e s j .t h e g a s b a c k m ix in g ^ a n d ..t h e i n t e r
c h a n g e betw een, t h e two p h a s e s .
,B a se d -o n . t h i s ^ h e p o s t u l a t e d a two p h a s e
m o d el t o d e s c r i b e a f i r s t . o r d e r i r r e v e r s i b l e r e a c t i o n in . a f l u i d i z e d b e d .
■Lanneau. a l s o d e v e lo p e d c u rv e s .sh e w in g .th e; e f f e c t o f r e a c t i o n , r a t e a n d
i n t e r c h a n g e b e tw e e n t h e p h a s e s o n c o n v e r s io n ^ b u t no e x p e r i m e n t a l . r e s u l t s
.o f t h i s w e re g i v e n .
. O r d u t t . , . e t . a l . ( 8 ) s t u d i e d th e. d e c o m p o s itio n o f . o z o n e .over, i r o n
o x id e . c a t a l y s t i n a f l u i d i z e d b e d .
They a ssu m ed t h e b u b b le , p h a s e to
be. d i s c r e t e , a n d w e l l m ix e d a n d t o . c o n t a i n no s o l i d p a r t i c l e s . • The
e m u lsio n , p h a s e i s c o n s i d e r e d .u n d e r t h e c o n d i t i o n s ,of b o th p l u g flo w a n d
c o m p le te m ix in g ,
. The .i n t e r c h a n g e .o f ..r e a c ta n t s , b e tw e e n .the. .two p h a s e s
i s assum ed .to t a k e p l a c e by b u lk .flow. a n d . d i f f u s i o n .
c o n v e r s i o n s .r a n g e d fro m 10 $ t o 95 $ .
was t e m p e r a t u r e .
T h e ir e x p e rim e n ta l
. The .m ain v a r i a b l e i n t h i s s t u d y
F l o w . r a t e , b e d d iam e te r= , and, .th e am ount, o f . c a t a l y s t
w e re a l s o t a k e n a s .v a r i a b l e s
(p a ra m e te rs ).
■The c a l c u l a t e d . v a l u e s u s in g
b o th t h e m o d els show ed .r e a s o n a b l e a g re e m e n t, w i t h -the- e x p e r i m e n t a l r e s u l t s
■The e x p e r i m e n t a l v a lu e s t e n d e d t o l i e ..betw een t h o s e .o b t a i n e d fro m t h e
tw o m o d els..
. H e id e l.s , e t . ■. a j . ,
(9) s t u d i e d t h e i n f l u e n c e o f m ix in g a n d / o r
s e g r e g a t i o n p r o c e s s e s on c h e m i c a l . r e a c t i o n . e x i s t i n g , i n f l u i d i z e d b ed s
u s i n g h y d r o g e n a tio n , o f e t h y l e n e on c o p p e r c a t a l y s t .
d i f f e r e n t . m o d e l s t o a n a ly z e t h e i r r e s u l t s ,
They u s e d .t h r e e
-Two o f th em w e re t h e d i f f u s i o n
m o d el a n d t h e tw o - p h a s e m o d e l, w h ic h a r e s i m i l a r t o t h o s e . d e s c r i b e d
e a rlie r.
The t h i r d , .one was t h e .t w o z o n e m o d el b a s e d .o n t h e w ork o f
De M a r ia y e i . a l „ ,
(1 0 ).
De M a ria a n d c o -w o rk e r s f o u n d t h a t , i n f l u i d ­
i z e d b ed s * .t h e i n t e n s i t y o f m ix in g was d i f f e r e n t a t v a r i o u s r a d i a l p o s i ­
tio n s .
The c e n t r a l c o r e o f t h e f l u i d i z e d b e d was f o u n d t o b e m ix e d much
b e t t e r th a n th e r e g io n n e a r th e w a ll.
o f H e id e ls e t . . a l . «
B a se d on t h i s , t h e two z o n e m odel
d i v i d e d t h e f l u i d i z e d b e d .i n t o a w a l l z o n e a n d a
c e n t r a l z o n e ,..e a c h , c h a r a c t e r i z e d by a n a v e r a g e r e s i d e n c e tim e a n d a
m ix in g c o e f f i c i e n t o f i t s
own.
The p r o p o r t i o n b e tw e e n t h e w a l l .zone a n d
t h e c e n t r a l z o n e c a n be d e te r m in e d by t a k i n g t h e r a t i o o f t h e a r e a s u n d e r
t h e r e s i d e n c e t i m e . c u r v e s . f o r t h e two z o ii.e s.
The c o n v e r s i o n v a lu e s c a l ­
c u l a t e d u s i n g t h i s m o d el w e r e .f o u n d t o b e h i g h e r t h a n t h e o b s e r v e d r e s u l t s .
T h is m o d el was f o u n d t o be v a l i d o n ly f o r s h a llo w b e d s w h e re .th e a v e r a g e
r e s i d e n c e tim e s o f t h e two z o n e s show a p p r e c i a b l e d i f f e r e n c e .
When 4 l /
d
i s g r e a t e r t h a n 6 . 9 , t h e e f f e c t . o l r a d i a l . m i x i n g becom es g r e a t a n d t h e
.tw o zone, m odel w i l l b e t h e sam e a s a d i f f u s i o n m o d e l.
D a v id s o n a n d .H a r r is o n (11) d e s c r i b e d two m o d els f o r two p h a s e
. f l u i d i z a t i o n w h ic h a r e e s s e n t i a l l y t h e sam e a s t h a t u s e d by O r e u t t e t .
a l.
H e r e .,. a l s o Jjl t h e b u b b le s w e re a s su m e d t o b e o f s p h e r i c a l s h a p e .con­
t a i n i n g n o s o l i d p a r t i c l e s i n th e m .
The i n t e r c h a n g e o f r e a c t a n t s b e tw e e n
t h e two p h a s e s i s .c o n s i d e r e d .to t a k e p l a c e , b y b u lk f lo w a n d d i f f u s i o n .
The d i f f e r e n c e b e tw e e n t h e i r two m o d els i s t h a t , . , i n o n e . c a s e , t h e p a r t i f c -
-7 “
u l a t e p h a s e was t a k e n t o be p e r f e c t l y m ix e d , an d I n t h e o t h e r c a s e ,- p i s t o n
f l o w . i s a ssu m e d ,
Rowe (12) a l s o c o n s id e r e d t h e f l u i d i z e d b e d t o be com posed o f two
phases,
R o w e's m odel i s b a s e d on r e c e n t s t u d i e s done on th e n a t u r e o f
th e gas s o lid c o n ta c tin g in f l u i d i z e d b e d s .
T h is m odel c o n s i d e r e d th e
b u b b le s t o be s p h e r i c a l b u t h a v e an i n d e n t e d b a s e o f o n e - t h i r d t h e c o m p le te
s p h e r e v o lu m e, . T h is l o w e s t o n e ^ t h i r d . i s t h e wake o f p a r t i c l e s w h ich
t r a v e l s w ith th e b u b b le .
A l s o , . a .c lo u d o f g a s i s p r e s e n t a r o u n d .e a c h
b u b b le w h ich e x c h a n g e s t h e g a s w i t h th e b u b b le f r e e l y T h u s R o w e's
.m odel c o n s id e r e d t h e f l u i d i z e d b e d t o be com posed o f (a ) an. e m u ls io n
p h a s e , th ro u g h w h ic h g a s t r a v e l s a t a p p r o x im a te ly th e minimum f l u i d i z i n g
V e l o c i t y jl. an d (b) b u b b le s a l o n g , w i t h t h e i r wake a n d .th e . g a s c lo u d t r a v e l ­
l i n g th ro u g h , t h e f l u i d i z e d b e d a t t h e v e l o c i t y o f t h e b u b b l e s .
Mamuro a n d M uchi (13) p o s t u l a t e d , a p a r t i t i o n e d .m odel i n w h ic h th e
f l u i d i z e d b ed i s d i v i d e d i n t o a num ber o f c e l l s o f h e i g h t e q u a l t o t h e
d i a m e te r o f t h e g a s b u b b l e s „
E a c h c e l l i s -com posed o f two p h a s e s , t h e
b u b b le , p h a s e a n d t h e e m u ls io n p h a s e .
e m u ls io n p h a s e o f e a c h . c e l l an d i t s
a d ja c e n t.c e lls .
Gas b a c k m ix in g i s p r e s e n t i n t h e
e f f e c t s a r e . c a r r i e d o v e r o n ly t o t h e
The b u b b le p h a s e was assum ed t o c o n t a i n no s o l i d s a n d
g a s i s i n t e r c h a n g e d b e tw e en t h e two p h a s e s ,
The m o d els o f H a r r i s o n a n d D a v i d s o n , Rowe^ a n d . Mamuro a n d M uch! a r e ■
d e s c r i b e d i n d e t a i l i n th e l a t e r p a r t o f t h e t e x t .
T h e se f o u r m o d els w ere
u s e d t o a n a ly z e t h e e x p e r i m e n t a l d a t a o b t a i n e d i n t h i s i n v e s t i g a t i o n .
RESEARCH .OBJECTIVES
This- r e s e a r c h was c o n d u c te d t o im p ro v e th e u n d e r s t a n d i n g o f f i r s t
o r d e r , c h e m ic a l r e a c t i o n s t a k i n g ,p la c e , i n a f l u i d i z e d b e d .
V a rio u s
p h y s i c a l .m odels ,h a v e b e e n p o s t u l a t e d .by p r e v i o u s i n v e s t i g a t o r s , .many o f
them w ith o u t e x p e r i m e n t a l b a c k in g ,
, C o n v e rs io n s o f . r e a c t a n t s . c a l c u l a t e d
u s i n g t h e s e m odels, f o r t h e e x p e r i m e n t a l .c o n d it io n s w e re t o b e .com pared
v w ith t h e o b s e r v e d .v a lu e s t o d e te r m in e w h ic h of: t h e s e m o d els d e s c r i b e d
t h e a c t u a l b e h a v io r o f f l u i d i z e d bedsj,, and i f n e c e s s a r y ^ a .new .m odel -was
t o b e d e v e lo p e d .
A p s e u d o - f i r s t o r d e r i r r e v e r s i b l e g a s e o u s r e a c t i o n was t o be u,sed - f o r
t h i s . s t u d y w h e re t h e r e a c t i o n to o k p l a c e a t t h e s u r f a c e o f t h e c a t a l y s t .
, The system )
c h o s e n f o r . t h i s s t u d y was t h e r e a c t i o n o f c a rb o n m onoxide and
s te a m o v e r i r o n o x i d e . c a t a l y s t y i e l d i n g c a rb o n d i o x i d e and, h y d r o g e n .
. The
l i m i t i n g r e a c t a n t was c a rb o n m o n o x id e .
- The s p e c i f i c c o n c lu s i o n s t o be, draw n f r o m t h i s s t u d y were.:-.
A.
The e f f e c t . o f p a r t i c l e siz e ,* b e d h e ig h t,, a n d te m p e r a t u r e
on t h e c o n v e r s i o n i n a. f l u i d i z e d - b e d .
B.
,The. e f f e c t o f b a c k m ix irig i n th e. .e m u ls io n p h a s e on t h e c o n v e r s i o n .
C.
T h e .e x t e n t o f i n t e r a c t i o n b e tw e e n t h e e m u ls io n p h a s e a n d th e
b u b b le p h a s e .
i
COLOR
OC— froior a a
pec.
UEiGltT
' I
BIND AS LAID
REMOVE ADS
ERONT COVER IN
S-*:,
fy> SS
LAST NO. COMPL.
NARROW MARGIN
NO TPI PUBLISHED
BACK
DIVIDER
SPECIAL TRIM
LABELS
CALL NOS.
l in e s
iM M n k m n
CRITERION STYLE
f !
PROMT COVER LET.
BACK BONH E. F. C
GOLD
BLACK
X
!McCANDLESS, FRANK PHILIP
REMOVE COVERS
•THEORETICAL DISCUSSION
P r e s s u r e Drop i n F l u i d i z e d .Beds
Carman (14) d e r i v e d an e q u a t i o n f o r t h e p r e s s u r e d ro p i n a b e d o f
p a r t i c l e s c o m p a rin g i t t o flo w o f f l u i d i n p a r a l l e l c h a n n e ls u s i n g t h e
P o is e iu lle e q u a tio n .
At low R e y n o ld s n u m b e rs ^
A P
/xU
(I
-€)
(i)
L
F o r s p h e r e s , .Carman fo u n d t h i s a b o v e e q u a t i o n t o be
A P
' L
( Z )
I n t h e c a s e o f f l u i d i z e d b e d s a t i n c i p i e n t f l u i d i z a t i o n , ,t h e i n d i ­
v i d u a l p a r t i c l e s a r e l i f t e d . o u t o f c o n t a c t w i t h e a c h o t h e r an d t h e bed
ex p an d s.
A t . t h i s p o i n t , , t h e p r e s s u r e d ro p i s e q u i v a l e n t t o th e . buo y ed
w e ig h t o f t h e b e d an d t h e r e f o r e
-A j,
L
w h e re / ^ t a n d
s p e c tiv e ly .
= C/>s - / 9 ) g ( l ^ C
q)
a r e t h e d e n s i t i e s o f s o l i d an d f l u i d i z i n g .f l u i d ., , r e ^
. C om bining ,e q u a tio n s
Jo = 0 .0 0 1 1 4 g ,d
2
( 2 ) a n d ( 3 ) , w i t h £ 0 = O A rJS g i y e s
(3)
-1 0 Thus t h e m in im u m - f lu id iz in g v e l o c i t y , .U0 ^ c a n be c a l c u l a t e d know ing
th e p a r t i c l e , d ia m e te r , p a r t i c l e and f l u i d d e n s i t i e s , f l u i d v i s c o s i t y ,
a n d t h e v o id a g e a t i n c i p i e n t f l u i d i z a t i o n .
R e a c t i o n R a te C o n s ta n t
The r e a c t i o n r a t e c o n s t a n t i s
a f ix e d bed,
o b t a i n e d by o p e r a t i n g t h e r e a c t o r a s
- I f t h e . r e a c t i o n r a t e , ..r, i s e x p r e s s e d a s mpl.es o f g a s r e ­
a c t i n g p e r u n i t w e ig h t o f t h e . c a t a l y s t p e r u n i t .tim e ,
,F C
dy
•=.
- r dw
*
=
r
== .-k -C0 ( I - y)
(5)
-Q-O .--- ( 6 )
■d(w/F).
B ut
f o r a f i r s t o rd er r e a c tio n .
- .In ( l.- y )
=
(.7)
C om bining .e q u a tio n s
( 6 ) a n d (7) y i e l d s
k (w /F )
The s l o p e o f t h e l i n e o b t a i n e d by p l o t t i n g . - I n
(8)
(1 -y ) a g a i n s t
(w/F)
w i l l g iv e th e r e a c tio n r a t e c o n s ta n t, k .
F l u i d i z e d Bed R e a c t o r M odels
I.
■R o w e 's , MpI e l
(1,2) .
T h is m odel i s b a s e d .on r e c e n t s t u d i e s , done on
t h e n a t u r e .o f g a s - s o l i d c o n t a c t i n g .i n f l u i d i z e d b e d s .
In th e .e a r lie r
m o d e l s , t h e b u b b le s w e re t a k e n a s ,c o m p l e t e s p h e r e s w i t h no s o l i d s i n th em .
“1 1 —
X - r a y s t u d i e s o f b u b b le s r i s i n g in . f l u i d i z e d b e d s h a v e shown t h a t t h e y a r e
g e n e r a l l y s p h e r i c a l b u t h a v e a n i n d e n t e d b a s e o f o n e - t h i r d o f t h e c o m p le te
s p h e r e v o lu m e .
The lo w e s t o n e - t h i r d o f t h e s p h e r e t h a t e n c l o s e s t h e
b u b b le i s a wake o f p a r t i c l e s w h ic h t r a v e l s w i t h t h e b u b b l e .
T h is wake
c a r r i e s th e p a r t i c l e fro m th e b o tto m o f t h e b e d a n d d e p o s i t s i t a t t h e
to p .
I n a d d i t i o n t o t h e w ak e, s o l i d p a r t i c l e s f lo w i p s t r e a m l i n e s a ro u n d
t h e b u b b le w h ic h c a u s e s a s p o u t o f m a t e r i a l t o be draw n up b e h in d e a c h
b u b b le .
-The em pty b u b b le i s h i g h l y p e rm e a b le t o g p s w h ic h f lo w s i n t o i t s
b a se and o u t a t th e to p .
. S in c e t h e p a r t i c l e s
a r e f lo w in g downward r e l a t i v e
t o t h e b u b b l e , t h e s e p a r t i c l e s d ra g ,s o m e g a s w i t h th e m .
The c o m b in a tio n
o f t h e s e e f f e c t s i s a c lo u d o f g a s a ro u n d .e a c h b u b b le w h ic h i s i n c o n s t a n t
i n t e r a c t i o n w i t h t h e b u b b le J
D a v id s o n ( I g ) p r e d i c t e d 1 th e d i a m e t e r o f
t h i s s p h e r i c a l c lo u d o f g a s t o b e
dc
=
dB
(C f+ 2 / {CL- I ) I V i
(9)
w h e re cC i s t h e . r a t i o o f b u b b le t o i n t e r s t i t i a l g a s v e l o c i t y , U y C Z u n^ .
The g a s i n t h e e m u ls io n p h a s e m oves u pw ards a t t h e minimum f l u i d i z i n g
,v e lo c ity .
M aking a m a t e r i a l b a la n c e on a n i n f i n i t e s i m a l h e i g h t dH o f t h e
e m u ls io n p h a s e
FgO %
dy^
.=
k ( l - y 1 )P s % dH .
w h e re k i s e x p r e s s e d a s c u b ic f e e t p e r , p o u n d o f c a t a l y s t p e r S e c o n d ,
(10)
In te g ra tin g ,
In
( I ,-r. Yj.)
=
k H
(
12)
-k H
(13)
■5- -e
From, t h e b u b b le .cloud, .V olum ej ,we c a n .f in d .th e w e ig h t o f t h e l i m i t i n g
r e a c t a n t i n t h e c l o u d , W,qq, .
T h is g a s i s i n c o n t a c t w i t h t h e s o l i d s i n
t h e s h e l l b e tw e e n t h e c lo u d and t h e b u b b le s and w i t h t h e s o l i d s i n i t s
w ake,
The w e ig h t, o f s o l i d s i n c o n t a c t w i t h '.W;s,c i s g iv en - by
*s%
=
(14)
(Vc - 2 /3 ' W s
I n th e c a s e o f b u b b l e s , t h e tim e a v a i l a b l e f o r r e a c t i o n i s t h e
r e s i d e n c e tim e o f t h e b u b b le H /U g.
is
The o u t l e t c o m p o s itio n o f t h e b u b b le
g iv e n by
■■(k W6,c. Mco H)/WQg Ub
yc
=
(15)
I - e
The t o t a l c o n v e r s i o n i n s i d e t h e f l u i d i z e d b e d i s
y
w h e re
Ei
+ Ec y c.
a.nd Ec ar.e t h e f r a c t i o n s o f g a s p a s s i n g t h r o u g h .th e ..em ulsion,
p h a s e a n d .b u b b le cloud,,., r e s p e c t i v e l y ,
(1 6 )
•“1 3 “
•2.
M o d e ls . o f D a v id so n an d H a r r i s o n ( 1 1 ) .
T h ese two m o d els .assum e
t h a t t h e b u b b le s a r e o f u n ifo r m - s iz e th r o u g h o u t t h e b e d an d . t h a t th e
.c a ta ly tic , r e a c ti o n ta k e s p la c e e n t i r e l y i n th e p a r t i c u l a t e p h a s e .
. The
b u b b le s a r e . c o n s i d e r e d t o be. s p h e r i c a l , a n d g a s e x c h a n g e b e tw e e n th e
b u b b le s a n d t h e e m u ls io n p h a s e t a k e s p l a c e by b u lk f lo w a n d by d i f f u s i o n .
I t i s a l s o a ssu m e d . t h a t a l l th e . g a s i n e x c e s s .o f 'w hat i s r e q u i r e d .f o r
minimum f l u i d i z a t i o n p a s s e s t h r o u g h a s b u b b l e s .
•The d i f f e r e n c e b e tw e e n
t h e tyro, m odels, is . t h a t i n one c a s e , .th e p a r t i c u l a t e p h a s e is . t a k e n t o be.
p e r f e c t l y mixed,., a n d .in t h e o t h e r c a s e p i s t o n f lo w i s a ssu m e d .
s i m i l a r t o t h e s e w e re p r o p o s e d by S h e n an d J o h n s to n e
, M a th is an d W atson ( 3 ) , a n d - L e w i s .£ t , .q l .
(4 ).
M odels
( 2 ) * P a n s in g (16)>
The d i f f e r e n c e , b e tw e e n
t h e s e a n d t h o s e .p r o p o s e d - b y .o th e r s l i e s m a in ly i n t h e b u b b le, m e c h a n ic s .
S in c e .e a c h b u b b le i s a , d i s c r e t e e n t i t y > . i t i s n o t p o s s i b l e t o h a v e d i f r
■f u s i o n fro m -b u b b le , t o b u b b le .
a). , P e r f e c t M ix in g in . P a r t i c u l a t e P h a s e .
A m a te ria l
b a la n c e , o n a . s i n g l e - r i s i n g b u b b le g i v e s .
(q + k GS) (Cp
Cb )
=
Ua Y
cLC
w h e re q i s t h e v o l u m e tr i c f l o w . r a t e i n a n d o u t o f t h e b u b b l e ,
S i s ,t h e s u r f a c e a r e a , k Q i s th e , m ass, t r a n s f e r c o e f f i c i e n t
b e tw e e n t h e b u b b le a n d .th e . e m u ls io n , p h a s e w i t h a c o n c e n t r a t i o n
d riv in g f o r c e
( Cp ••• Cfc) .
I n t e g r a t i n g ,e q u a tio n (1%) u s i n g t h e b o u n d a ry c o n d i t i o n s ,.
• Cfa = C0 a t z = -0 y i e l d s
(17)
-1 4 -Qs/tlAV
(1 8 )
C b = Cp + (Co-Cp) e
Where Q, .= (q + k^S)
A - m a t e r i a l b a la n c e o n t h e t o t a l .e m u ls io n p h a s e g iv e s
NVU1 (C0 -
Cp ) ( I
e
-QH/TAV
A ) + U0 ( Cq - Cp ) = kWCp
(19)
The o v e r a l l c o n v e r s io n i n s i d e t h e bed may be o b t a i n e d by
m ix in g t h e s tr e a m s l e a v i n g t h e b u b b le p h a s e and- e m u ls io n p h a s e
a t t h e to p o f t h e b e d .
UCH -= (U - U0 )C m
+ U0 Cp
S u b s titu tin g e q u a tio n s
(20)
(18) and, (19) i n t o e q u a t i o n (20) a n d r e ­
arranging,, , t h e f r a c t i o n o f r e a c .t a n t w h ic h l e a v e s u n c o n v e r te d ,is
g i v e n by
C1 = J l
I - fi e - x + A
-
C°
1 -/9
k 'e : ^
(21)
.e"x + k '
w here
o
b)
P i s t o n glow I n t h e P a r t i c u l a t e P h a s e .
In th is case th e re is
,u n ifo rm c o n c e n t r a t i o n a c r o s s t h e h o r i z o n t a l p lq n e a n d no
i n th e v e r t i c a l d i r e c t i o n i s a ssu m e d .
c a b le i n t h i s c a s e , a ls o .
m ix in g
E q u a tio n (18) i s appli-?.
M aking a m a t e r i a l b a la n c e qn an i n ­
f i n i t e s i m a l h e i g h t dz .o f t h e b e d , . i t y i e l d s
-15'
U0 dcPr
+ ItW Cp
+ ( u - u0)
(
T
-
22)
,Uz
The d im e n s io n l e s s fo rm o f t h e a b o v e e q u a t i o n i s
(1 ^ /9 )
dS=
.dz
+
J L cI
d.z
+ k 'C p = 0
The c o r r e s p o n d in g fo rm o f e q u a t i o n
dC
-A.
dz
.( 2 3 )
(17) i s
+ JS (ch - Cn) = -O
H
n
E lim in a tin g C
P
( I - ./9 )H ^ CU
'
dz?
(24)
p
b e tw e e n e q u a t i o n s
a- (x
/v +
a. k H)
+
C4
dZ'
(23) a n d (24) y i e l d s
4. k l5L-,Ch = 0
(251
The s o l u t i o n o f t h i s l i n e a r s e c o n d o r d e r d i f f e r e n t i a l e q u a tio n .
i£. o f t h e fo rm
Ch , C 1BmI21
+ CsemmZ
(26)
w here m^ a n d m2 a r e t h e r o o t s o f t h e q u a d r a tic ., e q u a tio n , fro m
e q u a t i o n (2 5 ) s o t h a t
1 /2
-(x T k-1H) ± L (x + k ’H)
, 4 ( 1 - /9 )H k1x
(
2H (1 - / ? )
2? )
.CbJi 'is.: o b t a i n e d by a p p ly i n g , t h e b o u n d a ry c o n d i t i o n s t o e q u a t i o n
(26) a n d e v a l u a t i n g t h e . c o n s t a n t s .
..Cpll i s o b t a i n e d by s u b s t i t u t i n g
.-1 6 -.
C^h .i n t o e q u a t i o n
(24) a n d e v a l u a t i n g f o r 2 = H.
Ct a .and.-CpH i n t o e q u a ti o n
S u b s titu tio n of
( 2 0 ) y i e l d s t h e .f r a c t i o n , o f t h e r e a c t a n t
u n c o n v e r te d g i v e n by
C1 - S l
C0
.In1
I.
- m2
( I - m2Hg°
x U
) _
(I .
)
x IJ
(28)
The q u a n t i t y x may be c a l c u l a t e d u s i n g t h e e q u a t i o n d e r i v e d
by D avidson, a n d H a r r i s o n i f a v a lu e o f Dj3.,. th e. e q u iv a l e n t , b u b b le
d ia m e te r, i s a v a il a b l e .
6.34 H0 ,
^b(SD t ) 1 /2
w h ere Dq i s
1 /2
(Uo + 1,3 DG
g-
)
(29)
Dt 1/ 4
th e b in a ry d i f f u s i o n .c o e f f i c i e n t o f th e r e a c t a n t s .
V a lu e s .o fo r x. c a n a l s o b e . c a l c u l a t e d fro m e x p e r i m e n t a l r e s u l t s .
From e q u a t i o n ( 2 1 ) , a p l o t k l v e r s u s C 1 h a s a f i n i t e asym ptote..,
e"^" a t l a r g e v a lu e s o f k ' . . T hig m eans,, h o w e v e r f a s t t h e r e ­
a c ti o n ., a p o r t i o n o f t h e e n t e r i n g r e a c t a n t s ,m a n a g e s t o b y p a s s .t h e
b e d . . T h is p o r t i o n d e p e n d s o q h ly io n th e., f l u i d m e c h a n ic s o f t h e bed
a n d n o t on t h e n a t u r e o f r e a c t i o n .
T h is v a lu e o f x o b t a i n e d fro m
t h e p l o t i s m ore r e l i a b l e t h a n t h a t c a l c u l a t e d u s i n g . e q u a t i o n
s i n c e t h e t h e o r y l e a d i n g t o i t d o e s n o t h a v e much e x p e r i m e n t a l
b a c k in g .
( 2 9 )»
-1 7
3o
Mamuro an d M uchl (1 3 )»
They p o s t u l a t e d a p a r t i t i o n e d m odel i n
w h ic h t h e . f l u i d i z e d b e d i s d i v i d e d i n t o a num ber o f c e l l s o f h e i g h t e q u a l
t o t h e d i a m e te r o f t h e g a s b u b b l e s .
E a c h c e l l i s com posed o f two p h a s e s ,
t h e b u b b le p h a s e a n d t h e p a r t i c u l a t e p h a s e .
t a i n any p a r t i c l e s „
The b u b b le p h a s e d o e s n o t c o n ­
I n t h e p a r t i c u l a t e p h a s e ,, t h e g a s f lo w r a t e i s
t o t h e minimum . f l u i d i z i n g v e l o c i t y .
equal
Gas b a c k m ix ln g i s p r e s e n t i n t h e
e m u ls io n p h a s e o f e a c h c e l l a n d i t s e f f e c t s a r e c a r r i e d o v e r o n ly t o t h e
a d ja c e n t c e l l s .
ph ase.
F o r e a c h s t a g e , t h e c o n c e n t r a t i o n i s u n ifo r m i n e a c h
T h e re e x i s t s a g a s i n t e r c h a n g e b e tw e e n t h e tw o p h a s e s w h ic h i s
p r o p o r t io n a l to th e d i f f e r e n c e in c o n c e n tr a tio n and th e i n t e r f a c i a l
a r e a b e tw e e n th e . two p h a s e s .
M aking a , m a t e r i a l b a la n c e o n t h e e m u ls io n p h a s e o f t h e i ^ ^ b s ta g e y
f O1^1
Ce i= 1 ~ 'p Oic e i - (p M1 Ce1 - PM1 +1Ce 1+i )
+ k I s I 1JL ^ b 1 “ Ce1 )
~ .k / pS t1 “ £ JQe1
= 0
(30)
a n d f o r t h e b u b b le p h a s e
p b ll4=1 Cfr1^ 1 - Fjj 1 Cb1 ^ K1 B1 I 1(Cj)^ - Ce i )= .O
(3D
The b o u n d a ry c o n d i t i o n s a r e
(32)
and
•0
(33)
The h a c k m ix in g i s c o n s i d e r e d .a s a r i s i n g fro m e x c h a n g e o f p o s i t i o n
w h ic h o c c u rs ^ h e n t h e g a s b u b b l e s . r i s e a n d .th e p a r t i c l e s f a l l i n t o t h e
n e w ly v a c a t e d s p a c e .
.F o r t h e c a s e w h e re t h e r a t e o f f l o w . o f t h e b u b b le
p h a s e .is s m a l l .com pared t o t h e p a r t i c u l a t e phase,* t h e backm ix, .flo w o f
gas. i s g iv e n by
p M i+!
^ in f 5 H
( ^m f
F e i^
F o r th e . a l t e r n a t e c a s e w h e re t h e r a t e .o f flow , .i n t h e b u b b le p h a s e i s
l a r g e .com pared t o t h e e m u ls io n p h ase*
F
MU 1
=
( ^m f
ei
f Tc i ^
Fe i )
(35)
I f t h e g a s i n t e r c h a n g e r a t e . c o e f f i c i e n t * .Ki ., i s p r o p o r t i o n a l t o t h e
b a c k m ix in g i n t h e i
^fch.
'i; a n d ( i + l ) t h s t a g e s ., i t may be w r i t t e n i n t h e
fo rm
Ki
k ( F M i+i + F m1 )
(36)
w h e re k i s a c o n s t a n t .
C o n sid e fin .g , .th e t o t a l s u r f a c e a r e a o f .th e g a s b u b b le s * .. th e . -i n t e r f a c i a l
a r e a p e r u n i t v o l u m e Ui , o f t h e two p h a s e s i n t h e i ^ - 'i s t a g e y i e l d s
th e r e la tio n s h ip
at
= -£ £ u
(37)
C om paring ,e q u a ti o n (30) w i t h t h e b a s i c e q u a tio n , f o r th e . tw o -p h a s e
m o d el w i t h a x i a l . d i f f u s i o n * t h e g a s i n t e r c h a n g e . c o e f f i c i e n t s . o f t h e two
19m o d els a r e .fo u n d t o b e r e l a t e d by t h e f o l l o w i n g .e q u a ti o n
(38)
Ka -=S !'e y
A sSUjning c o n s t a n t b a e k m ix in g fro m s t a g e t o s t a g e ,
e M14.
1
=
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(39)
eM
T h e n e q u a t i o n ( 5 6 ) becom es
K1
C om bining e q u a ti o n s
.k /fe
(40)
2 k Kjyj
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(37) and (4-0),
.4 b . Ec v
(41)
12 £ F m
F
hv
may b e c a l c u l a t e d . u s i n g t h e e q u a t i o n o f D a v id so n a n d H a r r i s o n ,
"
kAB.
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g
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(42)
I + 0 ,7 1 1 (g d B ) i / ? f y ^ U^)
w h e re D ^ i s t h e b i n a r y d i f f u s i o n c o e f f i c i e n t f o r t h e two r e a c t a n t s a n d
d
'U
i s . t h e d i a m e te r o f t h e b u b b l e .
The e x p r e s s i o n k/^>
s h o u ld . y i e l d a , c o n s t a n t .v a l u e f o r d i f f e r e n t
b e d h e i g h t s k e e p in g th e , v e l o c i t y c o n s ta n t,
EXPERIMENTAL .CONSIDERATIONS
R e a c tio n .
The. r e a c t i o n , c h o s e n f o r. t h i s , s t u d y was w a t e r g a s. s h i f t r e a c t i o n , o v e r
i r o n o x id e, . c a t a l y s t
CO + Na O
..c a ta ly s t
------------ COa + Ha
The r e a c t i o n w as c o n d u c te d a t a te m p e r a t u r e r a n g e o f 4 1 0 °F t o 48o°F..
. The c o m p o s itio n o f c a rb o n m o n o x id e i n th e. i n l e t s tre a m -w a s . .k e p t s m a l l so
t h a t a . f i r s t o rd e r r e a c tio n is o b ta in e d .
The two i n l e t g as. s t r e a m com­
p o s i t i o n s w ere. 5fo a n d 10 $ ' c a rb o n , m o n o x id e, a n d t h e .r e m a in d e r , s te a m .
C a ta ly s t
T he c a t a l y s t , u s e d . w a s c h rp m ia -p ro m o fe d i r o n o x i d e c a t a l y s t m a n u fa c ­
t u r e d by t h e G i r d l e r .C a t a l y s t d e p a r tm e n t o f t h e C h e m e fro n C o r p o r a tio n ,.
. T h is . c a t a l y s t c o n s i s t s , ,o f .$,0$ F e a O.3 a n d 1 0 $ C rsO 3 a n d i s . c a l l e d t h e
-G -i; , c a t a l y s t .
The s i z e s o f c a t a l y s t u s e d I n t h i s s tu d y w a re .;0 . 1 6l .mm
d i a m e t e r a n d Q .lS l.m m d ia m e te r p a r t i c l e s „
The b u lk d e n s i t y was fo u n d t o
b.e 0J688 ' g m s /c c . and t h e p a r t i c l e d e n s i t y was fo u n d t o be 3 .4 6 gm s/.co.
. A p p a ra tu s
T he .flow, .d ia g r a m o f ,the e x p e r i m e n t a l -sy ste m I s shewn, i n F i g . , 2 .
C a rb o n m onoxide o f 99..,5$ p u r i t y was used, w i t h o u t f u r t h e r p u r i f i c a t i o n .
W a te r was., s to r e d , i n a n o v e rh e a d t a n k a n d was p r e s s u r i z e d by n i t r o g e n .
T he c a rb o n , m o n o x id e f l o w . r a t e was. m e a s u re d .by a r o t a m e t e r w h i l e .an
o r i f i c e , m e te r ,was us.ed, t,o m e a s u r e ,:t h e .w a te r f lo w r a t e ;
W a te r an d .c a rb o n
m o n o x id e were, m ix e d a n d w e re t h e n . in tro d u ced i n t o a p r e h e a t e r w h e re w a t e r
was c o n v e r t e d t o s te a m a n d t h e r e s u l t i n g g a s m ix tu r e was h e a t e d up to
t h e o p e r a t i n g te m p e r a t u r e b e f o r e e n t e r i n g th e c a t a l y s t b e d .
. The ro ta -*
m e t e r and o r i f i c e m e te r w ere a d j u s t e d t o g iv e, t h e r e q u i r e d i n l e t g a s
c o m p o s itio n ^ w h ic h was k e p t c o n s t a n t th r o u g h o u t a s e r i e s o f r u n s .
The
.e x p e rim e n ts f o r b o th f i x e d an d f l u i d i z e d b e d .w ere c a r r i e d o u t u s i n g .th e
sam e r e a c t o r b u t by c h a n g in g ,th e downward flo w .o f g a s t o upw ard f lo w .
The r e a c t i o n r a t e c o n s t a n t was o b t a i n e d by o p e r a t i n g t h e c a t a l y s t b ed as
a f ix e d .r e a c to r .
One s e t o f f i x e d b e d r u n s w a s ^m addofop e a c h s e r i e s o f
f l u i d i z e d bed r u n s .
The r e a c t o r was c o n s t r u c t e d fro m a .3 « f o o t l e n g t h o f 3 i p c h ' d i a m e te r
s c h e d u l e 40 s t e e l p i p e .
I t was f i t t e d w i t h a s t a i n l e s s s t e e l p o r o u s p l a t e
a t t h e b o tto m t o s u p p o r t t h e c a t a l y s t a n d t o 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 .
The r e a c t o r was h e a t e d e l e c t r i c a l l y by 2 2 -g a u g e N ic k e l-C h ro m iu m h e a t i n g
w i r e s wound a ro u n d th e r e a c t o r i n f o u r s e c t i o n s .
r e a c t o r was r e g u l a t e d by V a r ia c s e t t i n g s .
w e re i n s u l a t e d u s i n g i n s u l a t i n g , c e m e n t .
The t e m p e r a t u r e o f th e
The r e a c t o r , an d t h e p r e h e a t e r
The t e m p e r a t u r e m e a su re m e n ts o f
t h e c a t a l y s t b e d a n d th e i n l e t g a s s t r e a m w e re made w i t h i r o n - c o n s t a h t a n
th e r m o c o u p le s i n s e r t e d i n s i d e s m a l l s t e e l . t h e r m a l w e l l s .
Two t h e r m a l
w e l l s w ere p l a c e d 8 i n c h e s a p a r t a n d on o p p o s i t e s i d e s o f t h e b o tto m o f
th e r e a c to r .
E l u t r i a t e d . c a t a l y s t p a r t i c l e s w e re c o l l e c t e d a n d r e t u r n e d
by a .c y c lo n e s e p a r a t o r ab o v e t h e r e a c t o r , . w h i c h was a l s o i n s u l a t e d t o
p r e v e n t c o n d e n s a t io n o f t h e e x c e s s s te a m .
The e x i t g a s s t r e a m fro m th e
c y c lo n e was p a s s e d th r o u g h a c o n d e n s e r - w h e r e m o st o f t h e s te a m was c o n ­
d e n s e d o u t a n d t h e r e l a t i v e l y d ry g a s m ix t u r e l e a v i n g .w a s s a m p le d and
-2 2 a n a ly z e d .
Two p r e s s u r e t a p s w ere p l a c e d one I m m e d ia te ly a b o v e a n d th e
o t h e r below, t h e p o r o u s p l a t e d i s t r i b u t o r .
T h ese p r e s s u r e t a p s w e re u s e d
t o m ea su re t h e p r e s s u r e d ro p a c r o s s t h e b e d a n d t h e d i s t r i b u t o r .
Gas A n a ly s is
The s a m p le s o f t h e o u t l e t g a s w ere a n a ly z e d f o r c a rb o n m onoxide and
c a r b o n d i o x id e by g a s c h ro m a to g r a p h y , .u s in g an A e ro g ra p h - 200 c h ro m a to ­
g r a p h e q u ip p e d w i t h a .th e r m a l c o n d u c t i v i t y c e l l d e t e c t o r .
. The s e p a r a t i o n s
w e re made by an 1 8 - f o o t l o n g , . o n e - f o u r t h i n c h c o p p e r colum n p a c k e d w ith
s i l i c a g e l u s i n g h e liu m a s t h e . c a r r i e r g a s .
Oven t e m p e r a t u r e o f . 8 o°C
a n d a sa m p le s i z e .o f I m l..w e r e u s e d f o r t h e a n a l y s i s .
P r e l i m i n a r y E x p e rim e n ts
B e fo re e s t a b l i s h i n g a s t a n d a r d .e x p e r im e n ta l p r o c e d u r e , .p r e l i m i n a r y
e x p e r im e n ts on c a t a l y s t s t a b i l i t y
o u t.
an d f l u i d i z i n g p r o p e r t i e s w ere c a r r i e d
The c a t a l y s t p a r t i c l e s w e re f o u n d t o h a v e ro u g h e d g e s a n d t h e p r e s ­
s u r e d ro p a c r o s s t h e b ed was f o u n d .to v a r y d u r in g t h e f i r s t 7.2 h o u r s ;
th e n i t le v e le d o u t to a s te a d y v a lu e .
At. t h e o n s e t o f f l u i d i z a t i o n , t h e
p r e s s u r e d ro p a c r o s s t h e b e d was f o u n d t o d ro p a n d t h e n i n c r e a s e s lo w ly
w i t h i n c r e a s i n g f lo w r a t e o f g a s .
The c a t a l y s t a c t i v i t y was a l s o fo u n d t o d e c r e a s e d u r in g t h e f i r s t
th re e days.
A f te r t h a t , t h e . c a t a l y s t a c t i v i t y .r e m a i n e d .f a i r l y c o n s ta n t
f o r s e v e r a l h u n d r e d .h o u r s .
A f te r th e c a t a l y s t a c t i v i t y and th e p ressu re"
d ro p a c r o s s t h e b e d h a d a c h ie v e d s t e a d y v a l u e s , t h e b e d t e m p e r a t u r e was
d e te r m in e d .f o r t h e .d e s i r e d b e d .h e i g h t an d t h e r a n g e o f g a s f l o w . r a t e s ,
-2 3 The te m p e r a t u r e r a n g e u s e d was U lO 0F t o 4 8 0 °F a n d t h e b e d h e i g h t s u s e d
.w ere 1 2 " 1 0 " „ .a n d 8 " ,
Two d i f f e r e n t c a t a l y s t s i z e s w e re a l s o u s e d .
P ro c ed u re
The r e q u i r e d am ount o f c a t a l y s t was c h a r g e d i n t o t h e r e a c t o r and
t h e V a r la c s e t t i n g s w e re a d j u s t e d t o g iv e t h e d e s i r e d l i n e ' o u t te m p e ra -,
tu re ,
When t h e c a t a l y s t a c t i v i t y h a d become s t e a d y , . t h e r e a c t i o n m ix tu r e
was f e d i n t o t h e r e a c t o r a t t h e d e s i r e d r a t e .
B e f o re e a c h s e t o f r u n s ,
3-U hours were needed fo r the .reactor to a tt a in eq u ilib riu m c o n d itio n s .
. Gas sa m p le s were, t a k e n a t th e o u t l e t o f t h e r e a c t o r a t 1.5 m in u te i n t e r v a l s
a n d w ere i n t r o d u c e d i n t o t h e c h ro m a to g r a p h .
E a c h .ru n l a s t e d u n t i l two
c o n s e c u t i v e s a m p le s a n a ly z e d g a v e t h e same c o n v e r s i o n o f c a rb o n m o n o x id e .
I n o r d e r to .c o m p a r e t h e c o n v e r s i o n s a t th e s a m e . e x p e r i m e n t a l .c o n d i t i o n s
b e tw e e n t h e f i x e d b e d an d t h e , f l u i d i z e d b ed an d t o c a l c u l a t e t h e r e a c t i o n
v e l o c i t y c o n s t a n t t t h e u p - flo w o f t h e gas. s tr e a m was s w itc h e d t o dow nflow
f o r f i x e d .bed o p e r a t i o n s a t t h e e n d o f t h e s a m p lin g f o r f l u i d i z e d b e d r u n s .
The te m p e r a t u r e d i s t r i b u t i o n w i t h i n t h e b ed was o c c a s i o n a l l y c h e c k e d
by t a k i n g t e m p e r a t u r e r e a d i n g s fro m .th e two th e r m o c o u p le s i n s i d e t h e
bed.
The b ed t e m p e r a t u r e was a b l e t o b e m a i n ta i n e d w i t h i n ± 0 ,5 ° C o f t h e
d e s ir e d v a lu e .
The o p e r a t i n g p r e s s u r e o f t h e r e a c t o r was a tm o s p h e r ic
s i n c e t h e p r e s s u r e d ro p a c r o s s t h e c a t a l y s t b ed was fo u n d t o b e n e g l i g i b l e
a n d no p r e s s u r e d ro p c o r r e c t i o n s w e re m ade on t h e c a l c u l a t i o n s .
.The
c a t a l y s t c a r r y o v e r fro m t h e r e a c t o r was a l s o f o u n d t o be n e g l i g i b l e .
- 2 4 “;
A f l u i d i z e d b e d made o f 3- i n c h g l a s s tu b e was u s e d t o s tu d y t h e
v o id a g e a t minimum f l u i d i z a t i o n by o b s e r v i n g t h e ' e x p a n s io n o f t h e b ed
w i t h i n c r e a s i n g f lo w r a t e s .
The v o id a g e was c a l c u l a t e d fro m t h e w e ig h t
o f t h e c a t a l y s t b e d a n d . i t s b u lk - d e n s i t y when l o q s e l y p a c k e d .
R e p r o d u c i b i l i t y s t u d i e s w e re c o n d u c te d f o r b o th f i x e d and f l u i d i z e d
b e d r u n s i n o r d e r t o show t h a t no n o t i c e a b l e c h a n g e i n c a t a l y s t a c t i v i t y
to o k p l a c e d u r in g t h e .r u n s ..
. I n c a s e .o f any d i s c r e p a n c y , t h e w h o le g e t
o f f i x e d a n d f l u i d i z .e d b e d .r u n s w ere r e p e a t e d .
RESULTS AND DISCUSSIONS
R e a c ti o n R a te C o n s ta n t
The r e a c t i o n r a t e c o n s t a n t , k f o r e a c h o f t h e s e r i e s o f r u n s , was
c a l c u l a t e d u s i n g t h e m ethod d e s c r i b e d on p a g e 1 0 .
The r a t e c o n s t a n t was
o b t a i n e d by t a k i n g t h e s lo p e o f t h e s t r a i g h t l i n e r e s u l t i n g fro m p l o t t i n g
.- I n ( I - y) v ersu s
(W /P ).
R e g r e s s i o n a n a l y s i s was u s e d t o c a l c u l a t e
t h e s l o p e o f s u c h a s t r a i g h t l i n e w h ic h w i l l b e s t f i t ..the d a t a e n d p a s s
th r o u g h -the o r i g i n .
I f x ' s a n d .y 's . r e p r e s e n t t h e v a lu e s e f - I n
( I - - y)
a n d ( W / F ) . r e s p e c t i v e l y j . t h e s l o p e q f t h e l i n e . , i s . o b t a i n e d by t h e r e l a t i o n
b =
E .x y .
E x2
'
a n d .th e r e g r e s s i o n l i n e i s g i v e n by
y
=
bx
T h e .r e a c ti o n , v e l o c i t y . c o n s t a n t s o b t a i n e d u s i n g t h e a b o v e ,m e th o d .w ith ,
t h e d a t a .from t h e f i x e d b ed .ru n s a r e g i v e n i n T a b le I I I .
,A sam ple, p l o t
I s shown i n F i g u r e 3 .
S in c e e x p e r im e n ts w e r e .c o n d u c te d a t t h r e e d i f f e r e n t t e m p e r a t u r e s ,
t h e a c t i v a t i o n e n e rg y o f t h e r e a c t i o n was c a l c u l a t e d a s .s h o w n i n F i g u r e
4.
. F o r th e r e a c ti o n u sed i n
th is
i n v e s t i g a t i o n , , t h e a c t i v a t i o n e n e rg y
^
4
was fo u n d t o be 1 .6 x 10 c a l o r i e s .
D u rin g t h e f l u i d i z e d b e d e x p e r im e n ts * t h e r e a c t o r was o p e r a te d , a t
f lo w r a t e s b elo w .t h e minimum f l u i d i z i n g v e l o c i t y a n d .th e c o n v e r s io n s
o b t a i n e d w ere a p p r o x im a te ly t h e same t h o s e i n t h e . f i x e d b e d r u n s f o r
-2 6 . t h e sam e flo w r a t e ^ a s shown I n t h e c a s e o f S e r i e s 9 -in T a b le V.
Row et S M odel
The t h e o r e t i c a l , . d i s c u s s i o n o f . t h i s m o d el i s g iv e n on p a g e 1 0 .
. B u b b le S iz e
F o r th e. c a l c u l a t i o n s f o r t h i s m o d e l t h e d i a m e te r o f t h e b u b b le was
assu m ed b a s e d on, t h e v a lu e s . r e p o r t e d I n t h e l i t e r a t u r e . - ( 8 , .1 5 ) «
U n til
r e c e n t l y , t h e b u b b le s w e re c o n s i d e r e d a s c o m p le te ly b jp h e r ic a l a n d . c o n ­
t a i n i n g no s o l i d s ,
.Many w r i t e r s th o u g h t o f b u b b le s a s t r a p p e d .p o c k e ts
o f gas r i s i n g th ro u g h th e f l u i d i z e d b e d .
R e c e n t s t u d i e s h a v e shown
t h a t -the g a s f lo w th r o u g h t h e b u b b le a n d t h e . r e s u l t a n t p a r t i c l e d r a g
g i v e s s t a b i l i t y t o t h e b u b b le w a l l s j u s t a s s u r f a c e t e n s i o n d o es
in th e case o f liq u id s
e s s e n t i a l l y e m p ty .
(1 8 ).
X - r a y s t u d i e s h a v e show n t h a t b u b b le s a r e
A g a s c lo u d was fo u n d .to be a ro u n d e a c h b u b b le w h ic h
e x c h a n g e s g a s w i t h t h e b u b b le s f r e e l y .
T h is c lo u d i s t h e r e s u l t o f g a s
f lo w in g up .th r o u g h t h e b u b b le a n d b e in g d ra g g e d down by t h e downward
.m o tio n .o f t h e p a r t i c l e s i n r e l a t i o n , t o .t h e b u b b l e .
.T he d i a m e te r o f t h e b u b b le i s
h e ig h t.
th e f u n c t i o n o f p a r t i c l e .s iz e and bed
O r c u tt (8 ) h a s e s t i m a t e d b u b b l e d i a m e t e r s f o r - f l u i d i s e d b e d s o f
v a r i o u s h e i g h t s . . The b u b b le d i a m e te r s u s e d h e r e a r e i n a g re e m e n t w i t h
O r c u t t 1S e s t i m a t e d , v a l u e s .
Rowe (12) h a s ,n o t e d t h a t t h e . c a l c u l a t i o n s made
u s i n g a , c e r t a i n v a lu e f o r t h e b u b b le d i a m e te r h a v e n e g l i g i b l e e r r o r j , p r o .v i d e d t h e b u b b le d i a m e te r i s n o t in . e r r o r by a f a c t o r o f f i v e o r s o .
t h e s i z e q f ,the. r e a c t o r u s e d ^ b u b b le d i a m e te r c a n n o t b e f i v e tim e s th e
W ith
-2 7 s iz e used.
B u b b le s i z e was o b s e r v e d i n a f l u i d i z e d b ed made o f a 5 - in c h
d i a m e te r g l a s s tu b e u s in g th e sam e p a r t i c l e s i z e an d b e d h e i g h t a s t h e
e x p e r i m e n t a l a p p a r a t u s an d i t was fo u n d t h a t th e b u b b le s i z e s w e re c l o s e
to th e s iz e u sed in th e c a lc u la t io n s .
The e f f e c t o f b u b b le s i z e on c o n ­
v e r s i o n was i n v e s t i g a t e d by c a l c u l a t i n g th e c o n v e r s io n s o f c a r b o n m onoxide
u s i n g v a r i o u s b u b b le s i z e s and v e r y l i t t l e
d i f f e r e n c e was n o t e d b e tw e e n
t h e c o n v e r s io n v a l u e s , . as shown i n T a b le IV .
C lo u d i D ia m e te r
The c lo u d d i a m e te r was c a l c u l a t e d h s i n g .e q u a ti o n (9) w h ic h was
p o s t u l a t e d by D a y id s o n ( 1 6 ) .
is
D a v id s o n 's t h e o r y assu m es t h a t t h e b u b b le
c i r c u l a r a n d t h a t t h e c lo u d w i l l a l s o be c i r c u l a r an d c o n c e n t r i c .
Rowe and P a t r i d g e
(19) fo u n d t h a t t h e b u b b le h a s a d e e p ly i n d e n t e d b a s e
w h ic h i s t h e wake o f p a r t i c l e s t r a v e l l i n g a lo n g w i t h i t . • The c lo u d was
a l s o i n d e n t e d fro m b elo w so t h a t i t d o e s .n o t e x te n d b e y o n d t h e lo w e r
m a r g in o f t h e b u b b le a n d i t i s s l i g h t l y d i s p l a c e d a h e a d o f t h e b u b b l e .
M u rray (20) h a s p u t f o r w a r d a s o p h i s t i c a t e d m a th e m a tic a l a n a l y s i s w h ic h
l e a d s t o t h e s h a p e a n d s i z e o f t h e c lo u d .
s im ila r a n a ly s is .
J a c k s o n (21) h a s a l s o made a
Rowe, e t . a l „ , (22) h a v e t a k e n p h o to g r a p h s o f b u b b le s
a n d t h e c lo u d s , a ro u n d them and h a v e fo u n d t h a t M u r r a y 's e q u a t i o n i s a
good f i t o v e r t h e u p p e r h a l f o f t h e c l o u d , w h ile D a v id s o n 's p r e d i c t i o n i s
to o l a r g e .
. B o th q u r v e s w e re f o u n d t o be s e r i o u s l y w rong o v e r t h e lo w e r
p a r t o f th e b u b b le .
I n t h i s i n v e s t i g a t i o n , D a v i d s o n i s .e q u a t i o n was u s e d
t o c a l c u l a t e t h e c lo u d d i a m e t e r , b u t c o n s i d e r i n g t h a t t h e wake o c c u p ie s
o n e - t h i r d t h e b u b b le vo lu m e.
/
- 28 Co n v e r s I o n
The o v e r a l l .c o n v e r s io n i n s i d e t h e f l u i d i z e d b ed was c a l c u l a t e d
u s i n g e q u a tio n s . ( 1 3 ) 1 5 , Jaiahdo(.16) „ ,E q u a tio n s
(13) and (15) g i v e t h e
■c o n v e r s io n s i n s i d e t h e e m u ls io n p h a s e a n d b u b b le p h a s e > r e s p e c t i v e l y , ,
.w h ere p lu g .flow was assum ed i n b o th c a s e s . . The r e s u l t s a r e t a b u l a t e d i n
T a b le V.
.S in c e t h e r e .is a . c e r t a i n am ount o f m ix in g t a k i n g , p l a c e i n t h e .em ul­
s i o n p h a s e d u e t o b u b b le s , - a n a l t e r n u t e . c a s e o f b a c k m ix in g was a l s o assum ed
i n t h e .em ulsion, p h a s e , . w h i l e c o n s i d e r i n g p l u g flo w i n t h e b u b b le p h a s e .
. T h e se r e s u l t s a re . a l s o t a b u l a t e d i n T a b le V.
. C o m p ariso n o f .t h e .c o n v e r s io n s c a l c u l a t e d u s i n g t h e two m o d els men­
t i o n e d ab o v e w i t h t h e o b s e r v e d v a lu e s a r e shown i n F i g u r e s 7 an d 8 .
.The
r e s u l t s shew t h a t t h e a s s u m p tio n o f p l u g f lo w i n t h e e m u ls io n p h a s e g av e
a much b e t t e r f i t t h a n b a c k m ix in g .
I n o t h e r w o r d s , t h e g a s flo w i n t h e
e m u ls io n p h a s e i s v e r y c l o s e t o p l u g ,flow .
F i g u r e 7 shows a .v e ry good
a g re e m e n t b e tw e e n the. c a l c u l a t e d a n d o b s e r v e d r e s u l t s f o r S e r i e s 10 and
F i g u r e 8 shows a good a g re e m e n t i n t h e c a s e .o f S e r i e s 6 ,.
A ll th e s e r i e s
o f r u n s e x c e p t S d r i e 1S .8 show s g o o d a g r e e m e n t.,. a s c a n be -s.een fro m T ab le. y„
S in c e t h e r e a r e s e v e r a l m eth o d s p o s t u l a t e d f o r c a l c u l a t i n g th e . c lo u d
s i z e ., a l l o f th em y i e l d i n g a d i f f e r e n t s i z e g a s c lo u d , t h e c lo u d s i z e was
k e p t a s . a n u n d e te r m in e d p a r a m e t e r i n t h e a b o y e m o d els an d .c a rb o n m onoxide
c o n v e r s i o n s w e re c a l c u l a t e d .
I n t h e s e c a l c u l a t i o n s t h e b u b b le s i z e s w e re
a ssu m e d a n d t h e r a t i o .o f d ia m e te r s .o f t h e .c lo p d a n d t h e b u b b l e , . dc/ d B ,
6.
“2 9 “
was t a k e n a s t h e u n d e te r m in e d p a r a m e t e r .
The v a lu e s o f t h i s p a r a m e t e r
u s e d ra n g e d f r o m .I . 001 t o 1 ,5 0 a t a n in c r e m e n t o f 0 .0 0 1 .
The maximum
v a lu e o f 1 .5 u s e d i s many tim e s a s l a r g e a s t h e l a r g e s t v a lu e o f c lo u d
s i z e .r e p o r te d i n th e l i t e r a t u r e f o r th e c o n d itio n s u sed i n t h i s
tig a tio n .
in v e s ­
The b e s t f i t was d e te r m in e d by t a k i n g t h e sum o f t h e s q u a r e s
o f th e d i f f e r e n c e b e tw e e n t h e c a l c u l a t e d an d .o b s e rv e d v a l u e s . o f c o n v e r s i o n
f o r each s e r ie s o f r u n s .
d i g i t a l c o m p u te r.
.The c a l c u l a t i o n s w ere p e r f o r m e d on a n IBM 1620
The F o r t r a n p ro g ra m s u s e d f o r t h e two c a s e s o f p l u g
f lo w an d b a c k m ix in g i n t h e e m u ls io n p h a s e a r e g iv e n i n T a b le s XIV and
XV.
The r e s u l t s a re - t a b u l a t e d i n T a b le s VI a n d V I I .
C o m p ariso n o f t h e b e s t f i t c o n v e r s i o n s c a l c u l a t e d u s i n g t h e two m o d els
m e n tio n e d ab o v e w i t h t h e o b s e r v e d v a lu e s a r e shown i n F i g u r e s 11 a n d 1 2 .
,T h e se f i g u r e s show t h a t th e a g re e m e n t i s onuch b e t t e r i n t h e p l u g flo w
c a s e th q n i n t h e c a s e o f .b ack m ix in g i n t h e e m u ls io n p h a s e .
, T h ese b e s t
f i t v a lu e s show some d e g r e e o f im p ro v em en t fro m t h e c a s e w h ere no u n ­
d e te r m in e d p a r a m e t e r s w ere used.? ,e v e n th o u g h t h i s im p ro v em en t was n o t
fo u n d t o be v e r y s i g n i f i c a n t . . S e r i e s 6 Shows good a g re e m e n t b e tw e e n t h e
c a l c u l a t e d an d o b s e r v e d r e s u l t s w h i l e S e r i e s 10 shows e v e n b e t t e r a g r e e ­
m e n t.
A l l t h e r e m a in in g s q r i e s o f r u n s e x c e p t S e r i e s .8 Show a g re e m e n t
w i t h t h e o b s e r v e d v a lu e s s i m i l a r t o t h a t o f S e r i e s 6 a n d 1 0 , w h ic h a r e
show n i n F i g u r e s 11 a n d 1 2 .
The. r a t i o s o f t h e d i a m e te r o f t h e c lo u d a n d t h e b u b b le a n d -the sums
o f th e s q u a re s o f th e d e v ia tio n f o r th e b e s t f i t d a ta f o r each s e r i e s o f
30r u n s a r e t a b u l a t e d I n T a b le s V I I I an d IX ,
I n t h e .c a s e w h ere p l u g flo w was
a ssu m e d I n t h e e m u ls io n p h a s e ^ t h e r e s u l t s show t h a t t h e c lo u d t o b u b b le
d i a m e te r r a t i o was t h e minimum f o r t h e b e s t f i t i n a l l t h e s e r i e s o f r u n s
e x c e p t i n S e r i e s rJ an d 8 , w h ere t h e maximum .v a lu e f o r t h e c lo u d t o b u b b le
d i a m e te r r a t i o u s e d y i e l d e d t h e b e s t f i t .
B u t, when b a c k m ix in g ,was assu m ed
i n t h e e m u ls io n p h a s e , b e s t f i t v a lu e s .w ere o b t a i n e d f o r t h e maximum .v a lu e
o f t h e . c lo u d t o b u b b le .d ia m e te r . r a t i o u s e d * . f o r a l l t h e s e r i e s o f r u n s .
A ssu m p tio n o f b a c k m ix in g y i e l d e d c o n v e r s i o n v a lu e s much lo w e r t h a n t h e
o b s e r v e d .o n e s .
S in c e o n ly a s m a ll am ount o f c a t a l y s t i s p r e s e n t i n t h e
c lo u d com pared t o t h e e m u ls io n p h a s e * a l o w ,c o n v e r s i o n i n t h e e m u ls io n
p h a s e w i l l lo w e r t h e o v e r a l l c o n v e r s i o n s u b s t a n t i a l l y .
T h a t i s why t h e
a s s u m p tio n o f b a c k m ix in g i n t h e e m u ls io n p h a s e y i e l d e d lo w e r c o n v e r s io n
v a lu e s a n d h e n c e a w o rs e f i t was o b t a i n e d t h a n i n t h e p l u g f lo w c a s e .
S i n c e p l u g flo w i s assum ed i n t h e b u b b le p h a s e f o r a l l .th e m o d e ls , a h i g h e r
c o n v e r s i o n may be o b t a i n e d i n t h i s p h a s e by a d d in g m ore s o l i d s
ph ase.
to t h is
.T h is c a n b e a c c o m p lis h e d by c o n s i d e r i n g a l a r g e r c l o u d , a n d h e n c e
t h e c lo u d t o b u b b le d i a m e te r r a t i o s w e re t h e maximum f o r t h e b e s t f i t
w hen b a c k m ix in g .was assu m ed i n t h e e m u ls io n p h a s e .
F o r t h e a s s u m p tio n o f p l u g f lo w in . t h e e m u ls io n phase,* th e c lo u d t o
b u b b le d ia m e te r r a t i o was f o u n d t o b e .th e maximum v a lu e , u s e d . f o r t h e b e s t
f i t f o r S e r i e s rJ a n d 8 * co m p ared t o t h e minimum c lo u d t o b u b b le d i a m e te r
r a t i o s i n th e. r e m a in in g ,s e r i e s o f r u n s .
The r e s u l t s show t h a t t h e e f f e c t
o f c lo u d s i z e on c o n v e r s i o n i s n o t to o g r e a t a s shown i n T a b le s VI and
V II.
T h e r e f o r e ^ Some o t h e r f a c t o r s s u c h a s i n a c c u r a c y i n t h e e x p e r i - 1-
-3 1 m e n ta l t e c h n i q u e ' may h a v e c a u s e d t h i s d i s c r e p a n c y .
I t h a s b e e n fo u n d e x p e r i m e n t a l l y t h a t t h e r e i s a c e r t a i n am ount o f
b a c k m ix in g i n t h e e m u ls io n p h a s e .- .S u t h e r l a n d (23) h a s shown t h a t t h e g a s
f lo w i n t h e f l u i d i z e d b e d w i t h o u t b u b b le s i s a lm o s t s t r e a m l i n e a n d a s t h e
g a s flo w r a t e i s
i n c r e a s e d , . b u b b l e s a r e fo rm e d a n d p a r t i c l e . m i x i n g i s
c a u s e d .b y t h e b u b b l e s .
S in c e b u b b le s a r e fo rm e d i n t h i s
in v e s tig a tio n
a l s o , .a s s u m p tio n o f p l u g flo w i n t h e e m u ls io n p h a s e d o e s n o t d e s c r i b e t h e
a c tu a l p ro c e s s .
. The p a r t i c l e m ix in g e x i s t i n g .in t h e f l u i d i z e d b e d may be
a c c o u n te d f o r by i n t r o d u c i n g a l o n g i t u d i n a l . d i f f u s i o n c o e f f i c i e n t f o r t h e
f lo w i n t h e e m u ls io n p h a s e a lo n g w ith , t h e a s s u m p tio n o f p l u g f lo w .
i n t h i s i n v e s t i g a t i o n ^ t h e d i f f u s i o n c o e f f i c i e n t a n d t h e c lo u d t o
b u b b le .d ia m e te r r a t i o w ere t a k e n a s u n d e te r m in e d p a r a m e t e r s s i n c e t h e
e q u ip m e n t u s e d did. n o t p e r m i t r e s i d e n c e tim e s t u d i e s .
C o n v e rs io n s w e re ■
, c a l c u l a t e d u s i n g t h i s m o d if ie d R ow e1s m odel w i t h p l u g f lo w i n t h e e m u ls io n
p h a s e a n d t h e tw o u n d e te r m in e d p a r a m e t e r s .
.The b e s t f i t . v a l u e s w ere
d e te r m i n e d by c a l c u l a t i n g t h e sum o f t h e s q u a r e s o f t h e d i f f e r e n c e b e tw e e n
t h e o b s e rv e d a n d t h e . c a l c u l a t e d . c o n v e r s i o n s f o r e a c h s e r i e s o f r u n s .
c a l c u l a t i o n s w e re done on a n IBM 1620. d i g i t a l c o m p u te r.
The
-The F o r t r a n
P ro g ra m u s e d i s g i v e n i n T a b le XYI,
. C o m p ariso n o f t h e b e s t f i t .v a lu e s o f . c o n v e r s i o n u s i n g m o d if ie d R o w e's
m o d el c o n t a i n i n g two u n d e te r m in e d p a r a m e t e r s w i t h t h e o b s e r v e d .v a lu e s
a r e shown i n F i g u r e s 15 a n d 1 6 .
F i g u r e 15 show s t h e f i t o f S e r i e s 1 0 .
H ere* v e r y g o o d a g re e m e n t i s s e e n b e tw e e n t h e o b s e r v e d a n d .the. c a l c u l a t e d
-3 2 .v a l u e s .
C om paring w i t h F i g u r e s 11 a n d 7 # . c o n v e r s i o n s - c a l c u l a t e d .u s in g
R o w e 's .m o d e l.c o n t a i n i n g two u n d e te r m in e d p a r a m e t e r s show some d e g r e e o f
im p ro v em en t i n t h e f i t w i t h t h e i n t r o d u c t i o n o f d i f f u s i o n c o e f f i c i e n t
a s a s e c o n d p a r a m e te r ^ bu t t h i s im p ro v e m e n t was fo u n d t o h e n o t verys ig n if ic a n t „
The s u m .o f th e . s q u a r e s o f e r r o r s an d t h e c lo u d t o b u b b le d i a m e te r
. r a t i o s f o r t h e b e s t . f i t d a t a a r e g iv e n , i n T a b le s V I I I an d I X , f o r e a c h I
o f th e . s e r i e s o f r u n s .
R e s u l t s show t h a t s m a l l e r sums o f t h e s q u a r e s
o f d e v i a t i o n b e tw e e n t h e o b s e rv e d a n d , c a l c u l a t e d r e s u l t s a r e o b t a i n e d
f o r S e r i e s 9* 1 0 , . an d 11 w i t h .th e i n t r o d u c t i o n o f t h e d i f f u s i o n c o ­
e f f i c i e n t a s a s e c o n d p a r a m e t e r i n t o t h e m o d e l.
In th e c a se o f S e rie s
6 , 7 * and .8 ^ b e s t f i t was o b t a i n e d f o r t h e .v a lu e o f z e r o f o r t h e d i f f u s i o n
c o e f f i c i e n t , a n d p l u g flo w i n t h e e m u ls io n p h a s e .
J u s t as in th e c a se of
one u n d e te r m in e d p a r a m e t e r m o d e l# .h e re a l s o t h e c lo u d t o b u b b le d i a m e te r
r a t i o was. fo u n d t o be t h e minimum v a lu e u s e d f o r t h e b e s t f i t i n a l l
.t h e s e r i e s , o r r u n s e x c e p t i n t h e c a s e o f S e r i e s 7 a n d . 8 ^ , w h e re t h e m a x i­
mum v a lu e u s e d . f o r t h e d i a m e te r r a t i o y i e l d e d t h e b e s t f i t .
,V ery low
v a lu e s f o r th e . d i f f u s i o n c o e f f i c i e n t w e re a l s o u s e d i n a l l t h e s e r i e s o f
ru n s f o r th e b e s t f i t e x c ep t in th e c a se o f S e rie s 11.
In S e rie s 1 1 ,
t h e p a r t i c l e s i z e u s e d was l a r g e r t h a n t h a t i n t h e o t h e r s e r i e s -of r u n s .
The b e d h e i g h t a l s o was l a r g e i n t h i s c a s e .
S in c e l a r g e r p a r t i c l e s r e ­
q u i r e a h i g h e r minimum f l u i d i z i n g v e l o c i t y , , a l a r g e r q u a n t i t y o f g a s i s
p a s s i n g th r o u g h t h e e m u ls io n p h a s e .
A ls o ,.th e s u p e r f ic i a l gas .v e lo c itie s
u s e d i n t h i s ,c a s e w e re h i g h e r , a n d a s a r e s u l t , . t h e b u b b le f r e q u e n c y was
-3 3 hIg h er0
S in c e m pre b u b b le s w e re f o rm e d , m ore m ix in g was t a k i n g p l a c e and
a h i g h e r v a lu e f o r t h e d i f f u s i o n c o e f f i c i e n t was n e e d e d t o a c c o u n t f o r
t h i s , m ix in g .
Thb r e s u l t s show t h a t S e r i e s No . ,8 show ed .maximum d i f f e r e n c e , b e tw e e n
t h e o b s e rv e d a n d t h e c a l c u l a t e d r e s u l t s u s in g a l l t h e m odels- c o n t a i n i n g
n o n e , . o n e , a n d two u n d e te r m in e d p a r a m e t e r s .
A l l t h e o t h e r s e r i e s show
v a r y i n g d e g r e e s o f d e v i a t i o n fro m v e r y s m a ll t o m o d e ra te ., .a s shown i n
T a b le V I I I .
I n t h e c a s e o f S e r i e s 8 ,> t h e f l u i d i z e d b e d was o p e r a t e d a t
a h ig h e r te m p e ra tu re th a n f o r th e o th e r s e r i e s o f r u n s .
In. a l l t h e o t h e r
s e r i e s o f .r u n s , . t h e f l u i d i z e d b e d was o p e r a t e d a t a .te m p e r a tu r e a t w h ic h
80 p e r c e n t t o 90. p e r c e n t c o n v e r s i o n o f .c a rb o n m onoxide was ,o b t a i n e d a t a
g a s f e e d r a t e o f j u s t ab o v e t h e m inim um f l u i d i z i n g v e l o c i t y .
In S e r ie s .8 ,
. t h e o p e r a t i n g te m p e r a tu r e , was i n c r e a s e d by 30 °B' k e e p in g a l l . t h e o t h e r
c o n d i t i o n s t h e sa m e .
.T h is i n c r e a s e i n te m p e r a t u r e s u b s e q u e n t ly i n c r e a s e d
t.he r a t e o f r e a c t i o n and a lm o s t c o m p le te .c o n v e rs io n was o b t a i n e d i n th e .
e m u ls io n , p h a s e .,
. S in c e t h e r e i s o n ly a s m a l l q u a n t i f y o f s o l i d s i n c o n t a c t
w i t h .th e g a s in . t h e b u b b le p h a s e > th e , i n c r e a s e i n r e a c t i o n r a t e , d i d .n o t
a p p re c ia b ly a f f e c t th e c o n v e rs io n in th e c lo u d .
. C om bining t h e two stre a m s.,,
th e . o v e r a l l c o n v e r s i o n s w ere, f o u n d t o be. s m a lle r , th a n , .th e o b s e r v e d v a l u e s ,
Some of. t h e l a c k o f a g re e m e n t b e tw e e n t h e c a l c u l a t e d and o b s e r v e d
c o n v e r s i o n s i n t h e c a s e o f S e r i e s ,8 a n d .o t h e r s may be e x p l a i n e d a s . f o l l o w s :
: I n t h e s e m o d els o f Eowe,. no c o n s i d e r a t i o n was g i v e n f o r t h e e x c h a n g e o f
g a s b e tw e e n t h e .c lo u d and th e .e m u ls io n p h a s e .
. From t r a c e r s t u d i e s i n
f l u i d i z e d .beds.,. Rowe. (22) fo u n d t h a t t h e r e , e x i s t s a phenom enon c a l l e d
-3 4 " c lo u d S h e d d in g ."
Gas i s s h e d .fro m t h e c lo u d i n d i s c r e t e am ounts i n t o
th e p a r t i c u l a te p h a se .
A ls o , t h e r e e x i s t s th e . e x c h a n g e o f g a s b e tw e e n
t h e two p h a s e s by m eans o f b u lk f lo w .
Row;e fo u n d t h a t t h e g a s e n t e r s t h e
b u b b le a t t h e b o tto m and l e a v e s a t t h e t o p .
T h is g a s l e a v i n g t h e to p is.
d r a g g e d down by t h e downward .m o tio n o f t h e p a r t i c l e s a n d r e - e n t e r s t h e
b o tto m o f t h e b u b b le a g a i n .
D u rin g t h i s p r o c e s s , some o f t h e g a s i s l o s t
t o t h e s u r r o u n d i n g ,e m u ls io n p h a s e .
D i f f u s i o n i s a n o t h e r m echanism by
w h ic h th e e x c h a n g e o f g a s ta k e s p l a c e b e tw e e n t h e two p h a s e s * s i n c e t h e r e
i s a c o n c e n t r a t i o n g r a d i e n t b e tw e e n t h e two p h a s e s .
As A lre a d y m e n tio n e d , some o f t h e l a c k o f a g re e m e n t b e tw e e n t h e c a l ­
c u l a t e d and o b s e r v e d v a lu e s c a n be a t t r i b u t e d t o t h e s o l i d s m ix in g c a u s e d
-by t h e m o tio n o f b u b b l e s „
T h is s o l i d s m ix in g c a n be a c c o u n te d f o r by
in tr o d u c in g a d if f u s io n c o e f f i c i e n t i n th e lo n g itu d in a l d i r e c t i o n .
In
t h i s i n v e s t i g a t i o n , an a v e r a g e v a lu e f o r t h e d i f f u s i o n c o e f f i c i e n t was
u s e d f o r a l l t h e d i f f e r e n t flo w r a t e s
in. one s e r i e s .
t h e d e g re e , o f m ix in g i s a f u n c t i o n o f flo w , r a t e .
As c a n be e x p e c t e d ,
At g a s f lo w ..r a te s v e ry
n e a r t o t h e minimum, f l u i d i z i n g v e l o c i t y , t h e g a s f lo w i n th e . .e m u ls io n
p h a s e i s v e r y n e a r l y p l u g f lo w .
A t h i g h e r g a s f lo w r a t e s , a h i g h e r v a lu e
f o r th e d i f f u s i o n c o e f f i c i e n t m u st be u s e d t o d e s c r i b e t h e h i g h e r d e g r e e s
o f s o l i d s m ix in g .
The r e s u l t s o f T a b le ! 'V a n d F i g u r e s 5 , 6 , I ,..9 , .1 0 , .1 1 ,
a n d 13 show t h a t c o n s i d e r i n g no d i f f u s i o n , b e t t e r a g re e m e n t was o b t a i n e d
a t low flo w r a t e s
t h a n a t h i g h f lo w r a t e s .
I n m o st o f t h e c a s e s , ,th e
p r e d i c t e d v a lu e s o f T co n y ersld m w e r e o h ig h e r th a n t h e o b s e r v e d v a lu e s a t
h i g h e r flo w r a t e s .
U s in g ,a p p r o p r i a t e v a lu e s f o r t h e d i f f u s i o n c o e f f i c i e n t
-3 5 '
f o r t h e s e h i g h e r .flo w r a t e s , t h e o v e r a l l f i t .c a n be im p r o v e d .f o r t h e s e
s e rie s of ru n s,
.The o b s e r v e d c o n v e r s io n v a lu e s w ere com pared w i t h th e . c o n v e r s io n s
c a l c u l a t e d c o n s i d e r i n g t h e w h o le r e a c t o r a s b ack m ix a n d p l u g f lo w and
t h e r e s u l t s a r e g iv e n i n T a b le V a n d F i g u r e s 5 a n d 6 .
The f i g u r e s show
t h a t t h e p r e d i c t e d v a lu e s a r e much l a r g e r t h a n t h e o b s e r v e d o n e s .
It
i s w rong t o . c o n s i d e r t h e w h o le r e a c t o r a s e i t h e r a p l u g f lo w on a b a c k m ix r e a c t o r s i n c e t h e b y p a s s due t o t h e b u b b le s w h ic h i s t h e t r u e
c h a r a c t e r i s t i c o f a f l u i d i z e d b ed i s n o t ta k e n in to c o n s id e r a tio n .
.EVen though, c o n v e r s i o n s c a l c u l a t e d a s su m in g th e. .whole r e a c t o r a s backm ix
show some, d e g r e e o f a g reem en t, w i t h th e . o b s e r v e d v a lu e s * i t s t i l l ,does
n o t d e s c r i b e t h e b e h a v io r o f f l u i d i z e d b e d s a t i s f a c t o r i l y .
-3 6 M qdels o f D a v id s o n a n d H a r r i s o n
The t h e o r y l e a d i n g t o t h e s e m o d els i s g i v e n on p a g e 1 3 .
C o n s id e r in g
p e r f e c t m ix in g i n th e . p a r t i c u l a t e phase,,, t h e o v e r a l l c o n v e r s i o n o f c a rb o n
m onoxide i n t h e ,f l u i d i z e d , b ed .,was c a l c u l a t e d . u s i n g e q u a t i o n (2 1 )..
The
num ber o f t r a n s f e r u n i t s , .x , ,u s e d i n t h e . c a l c u l a t i o n s was o b t a i n e d b y .
p l o t t i n g t h e f r a c t i o n o f r e a c t a n t s u n c o n v e r te d v e r s u s t h e d i m e n s io n l e s s
r e a c tio n v e lo c ity c o n s ta n t, k ‘ .
The num ber o f t r a n s f e r u n i t s was c a l r
. c u l a t e d fro m t h e a s y m p to te o f t h e r e s u l t i n g c u rv e a t l a r g e v a l u e s . o f t h e
v e lo c ity c o n s ta n t.
.The same v a lu e f o r t h e num ber o f t r a n s f e r u n i t s was
u s e d .f o r a l l th e ru n s in th e s e r i e s .
. The r e s u l t s a r e t a b u l a t e d i n
T a b le IV ,
. Now,',. c o n s i d e r i n g p l u g flo w in , t h e ,e m u ls io n p h a s e , th e . f r a c t i o n o f
c a rb o n , m onoxide u n c o n v e r te d i n t h e f l u i d i z e d b e d was c a l c u l a t e d u sin g e q u a ti o n s
(27) a n d ( 2 8 ) .
,The v a lu e o f t h e num ber o f t r a n s f e r u n i t s , ,x.,
. u s e d i n t h i s .mofLel was a l s o t h e same, a s t h a t u s e d ,- in th e , baCkmix c a s e
'f o r t h e Same s e r i e s . o f r u n s .
H e r e , a l s o , . t h e same v a lu e o f th e. num ber
o f t r a n s f e r ,u n i ts was .u se d f o r a l l .t h e .,runs I n one s e r i e s . . The r e s u l t s
a r e t a b u l a t e d i n T a b le V.
C arbqn m o n o x id e c o n v e r s i o n s c a l c u l a t e d u s i n g t h e two m o d els ,m e n tio n e d
above, w e r e co m p ared w i t h t h e o b s e r v e d v a l u e s a n d a r e shown i n F i g u r e s 9
a n d .1 0 ,
. I n m o st o f t h e s e r i e s o f r u n s o n ly f a i r a g re e m e n t b e tw e e n t h e
p r e d ic te d an d .o b s e rv e d v a lu e s o f .c o n v e rsio n ., was ,o b t a i n e d w h i l e i n some
•c a s e s - g o o d a g re e m e n t was show n, ,as i n t h e c a s e o f S e r i e s 10 shown i n
F ig u re 9 .
F i g u r e . 10 shows S e r i e s 6 i n t h e c a s e o f w h ic h o n ly f a i r a g r e e ­
-3 7 m ent was o b t a i n e d .
A ssu m p tio n ' o f U ackm ixing i n t h e e m u ls io n p h a s e was
f o u n d t o p r e d i c t -c o n v e rs io n s c l o s e r t o th e o b s e rv e d . v a l u e s .
In th e c a se
o f b o th o f t h e s e m o d e l s , .a g re e m e n t b e tw e e n th e o b s e r v e d and c a l c u l a t e d
c o n v e r s io n s was f o u n d t o be b e t t e r a t lo w e r flo w r a t e s t h a n a t h i g h e r
f lo w r a t e s .
. A p a rt fro m ,th e a s s u m p tiq n o f p l u g f lo w .and b a c k m ix in g i n t h e e m u l­
s i o n p h a s e , t h e v a l u e o f t h e number- o f t r a n s f e r u n i t s e s t i m a t e d a l s o
n e e d s ■e x p e r i m e n t a l v e r i f i c a t i o n .
I t r e p r e s e n t s t h e am ount o f r e a c t a n t
t r a n s f e r r e d b e tw e e n t h e two p h a s e s .
O t c u t t (8 ) f o u n d t h a t t h e v a lu e o f
t h e ..number o f t r a n s f e r u n i t s d i d n o t c h a n g e to o much w i t h flo w r a t e s and
t h a t an a v e r a g e v a lu e y i e l d e d s a t i s f a c t o r y r e s u l t s th r o u g h a w id e r a n g e
o f flo w r a t e s .
In th is
i n v e s t i g a t i o n a l s o , . one v a lu e f o r t h e num ber o f
t r a n s f e r u n i t s was u s e d f o r a l l t h e r u n s i n one s e r i e s .
S in c e t h e m e th o d .o f e s t i m a t i n g t h e num ber o f t r a n s f e r u n i t s s t i l l
n e e d s e x p e r i m e n t a l . v e r i f i c a t i o n . , , i t was .ta k e n a s an u n d e te r m in e d p a r a .m e t e r a n d .c o n v e r s io n s w ere c a l c u l a t e d .u s in g b o th t h e m o d e ls .
c u l a t i o n s w ere done u s in g an IBM 1,620 d i g i t a l c o m p u te r.
P ro g ram s u s e d a r e g i v e n i n T a b le s XVII. a n d X V I lI .
The c a l ­
The F o r t r a n
The b e s t f i t was
d e te r m in e d by c a l c u l a t i n g t h e sum o f t h e s q u a r e s o f t h e . d i f f e r e n c e b e ­
tw e e n t h e c a l c u l a t e d and .o b s e r v e d .c o n v e r s io n s . f o r e a c h s e r i e s o f .r u n s .
The b e s t f i t d a t a y i e l d e d th e minimum .v a lu e f o r t h e sum o f t h e s q u a r e s
of e rro rs.
. The r e s u l t s a r e show n i n T a b le s X an d XI?
-JS -O b se rv e d c o n v e r s i o n s w ere co m p ared w i t h t h e b e s t f i t v a lu e s o f t h e
c o n v e r s i o n c a l c u l a t e d u s in g t h e tw o m o d els w h ere p l u g f lo w .a n d b a c k m ix in g w e re .a s s u m e d i n t h e e m u ls io n p h a s e a n d u s i n g t h e ,num ber o f t r a n s ­
fe r u n its ,.x a s
u n d e te r m in e d p a r a m e t e r , a s shown i n F i g u r e s 13 and 1 4 .
. The f i g u r e s show t h a t i n th e . c a s e o f S e r i e s 1 0 , a v e ry good a g re e m e n t was
o b t a i n e d . f o r ' t h e c a s e . o f p l u g . f l o w i n . t h e e m u ls io n p h a s e w h ile f a i r a g r e e ­
m ent was o b t a i n e d . f o r t h e c a s e o f b a c k m ix in g ,
in th e c a se o f S e r ie s 8 ,
. b o t h t h e a s s u m p tio n o f p l u g f lo w a n d b a c k m ix in g r e s u l t e d i n f a i r a g r e e ­
m ent ,
i n d l l .th e s e r i e s o f r u n s , .t h e a g re e m e n t b e tw e e n t h e c a l c u l a t e d
.a n d o b s e r v e d .c o n v e r s io n s was f o u n d t o be b e t t e r u n d e r t h e a s s u m p tio n o f
p l u g f l o w . i n t h e e m u ls io n p h a s e t h a n b a c k m ix in g ,
-The v a lu e s o f t h e num ber
o f t r a n s f e r u n i t s f o r t h e b e s t f i t a r e g iv e n i n T a b le X I I I a n d t h e sums
o f s q u a r e s f o r th e ' b e s t f i t a r e g iv e n i n T a b le X I I ,
■The . r e s u l t s show
t h a t a ..s m a l le r num ber o f t r a n s f e r u n i t s w ere o b ta in e d - f o r t h e a s s u m p tio n
o f p l u g flo w t h a n b a c k m ix in g i n t h e .e m u l s i o n p h a s e ,
F o r t h e p l u g ,f l o w
c a s e , t h e num ber o f t r a n s f e r u n i t s r a n g e d fro m 0 . OQ.t o -Q, 59 > -w h ile i t
r a n g e d fro m Q.,JL5 t o I .Ip f o r t h e c a s e o f b a c k m ix in g ,
. These, v a lu e s - f o r
th e .n u m b e r o f t r a n s f e r u n i t s w e re f o u n d t o be s m a l l e r t h a n v a lu e s . e s t i ­
m a te d f o r th e . m odel, c a l c u l a t i o n s .w ith o u t, -SJfy ,u n d e te r m in e d p a r a m e t e r s .
When b a c k m ix in g was assu m ed in t h e e m u ls io n p h a s e A lo w e r c o n v e r s i o n s
w e re o b t a i n e d ,i n s i d e t h e .e m u ls io n p h a se , a n d t h e r e f o r e m ore g a s was n e e d e d
to- be .t r a n s f e r r e d b e tw e e n th e tw o p h a s e s t o i n c r e a s e t h e o v e r a l l c o n v e r ­
s io n .
. T h a t i s why th e. num ber o f t r a n s f e r u n i t s was fo u n d t o
be. h i g h e r i n
t h e c a s e . o f b a c k m ix in g i n t h e .e m u l s i o n p h a s e t h a n p l u g f l o w i n th e . same
phase„
S in c e t h e E e s n l t s i n d i c a t e t h a t th e. a s s u m p tio n o f p l u g flo w i n
t h e e m u ls io n p h as.e g i v e s a b e t t e r f i t th an , i n t h e c a s e o f b a c k m ix in g
a n d s i n c e a . c e r t a i n am ount o f p a r t i c l e m ix in g w a s . fo u n d t o e x i s t
i n t h e . f l u i d i z e d b e d , ..th is m ix in g c a n be a c c o u n te d f o r by i n t r o d u c i n g
a l o n g i t u d i n a l d i f f u s i o n c o e f f i c i e n t a lo n g w i t h t h e .a s s u m p t i o n o f p l u g
f lo w i n t h e e m u ls io n p h a s e .
T h is .h as b e e n c o n s i d e r e d an d t h e a p p r o p r i a t e
e q u a ti o n s w e re d e r i v e d by May ( 5 ) ,
.I n t h i s
i n v e s t i g a t i o n b o th t h e num­
b e r o f . t r a n s f e r u n i t s a n d ..the d i f f u s i o n , c o e f f i c i e n t w ere t a k e n a s un-.
d e te rm in e d , p a r a m e t e r s a n d c o n v e r s i o n s w e re c a l c u l a t e d f o r v a r i o u s v a lu e s
o f t h e two p a r a m e t e r s .
H ere,, a l s o , t h e sums o f t h e s q u a re s , o f e r r o r s
w e re c a l c u l a t e d t o d e te r m in e t h e b e s t. f i t .
The c a l c u l a t i o n s w e re .done
on a n IBM 1620. d i g i t a l c o m p u te r a n d t h e F o r t r a n P r o g ra m .u s e d i s g iv e n
i n T a b le XIX.
Sum o f t h e s q u a r e s o f t h e b e s t f i t v a lu e s o f .c o n v e r s io n
u s i n g n o n e ,.o n e y a n d tw o u n d e te r m in e d p a r a m e t e r s i n t h e m o d els o f
D a v id s on a n d .H a rriso n , w ere c o m p a red a n d t h e r e s u l t s a r e ,shown i n
T a b le X I I .
, The ..,values o f th e. num ber o f t r a n s f e r , u n i t s a n d t h e d i f -■
f u s io n c o e f f i c i e n t f o r th e b e s t f i t . v a l u e s
a lo n g w i t h t h e . v a l u e s o f
t h e num ber o f t r a n s f e r u n i t s f o r t h e c a s e o f n o n e , .o n e , ,a n d .two u n d e t e r ­
m in e d p a r a m e t e r s a r e g iv e n i n T a b le X I I l .
The r e s u l t s show t h a t i n S e r i e s 9 % ,1 0 ,.a n d 1 1 ,.,a b e t t e r f i t was
.o b t a i n e d .w ith t h e i n t r o d u c t i o n o f t h e d i f f u s i o n c o e f f i c i e n t a s a s e c o n d
u n d e te r m in e d p a r a m e t e r ,
,I n S e r i e s 6 , 7 , , a n d .8 , . a v a l u e . o f z e r o f o r th e
d i f f u s i o n c o e f f i c i e n t y ie ld e d , -th e b e s t f i t ,
E x cep t f o r th e c a se o f
S e r i e s 1 1 , ,th e im p ro v e m e n t i n t h e f i t w i t h t h e i n t r o d u c t i o n , o f a d i f f u s i o n
c o e f f i c i e n t a s a s e c o n d u n d e te r m in e d p a r a m e t e r was n o t v e r y s i g n i f i c a n t .
A c o m p a ris o n o f t h e b e s t f i t v a lu e s o f t h e m o d if ie d m o d els o f Rowe
a n d t h a t o f D a v id s o n a n d H a r r i s o n a s su m in g p l u g f lo w i n t h e e m u ls io n p h a s e
a n d c o n t a i n i n g tw o u n d e te r m in e d p a r a m e t e r s a r e show n i n R ig u r e s 15 a n d 1 6 .
T h e se f i g u r e s show t h a t b o th o f t h e two p a r a m e t e r m o d els y i e l d e q u a l l y
good f i t in th e c a s e o f S e r ie s 6 and 1 0 .
I n a l l t h e r e m a in in g s e r i e s of,
r u n s e x c e p t i n t h e . e a s e o f S e r i e s 8 ,. .v e ry g o o d f i t was ,o b t a i n e d u s i n g
t h e two p a r a m e t e r m o d e ls s i m i l a r ,
shown i n F i g u r e s 15 a n d 1 6 .
t o t h o s e o f S e r i e s 6 a n d 10 w h ic h a r e
J n t h e r a s e o f S e r i e s 8 , . o n ly a f a i r a g r e e ­
m ent was o b t a i n e d u s i n g ,th e two p a r a m e t e r m o d e ls .
I n t h e c a s e o f S e r i e s 8 , a .g o o d a g re e m e n t b e tw e e n t h e c a l c u l a t e d and
t h e o b s e r v e d r e s u l t s a r e s e n n a t low: f lo w r a t e s , , w h ile t h e a g re e m e n t was
f o u n d t o be. p o o r a t. h i g h flo w r a t e s .
f o u n d .to l i e
ab o v e t h e o b s e r v e d .o n e s .
A l l t h e c a l c u l a t e d v a lu e s w ere
,K eep in g t h e n u m b er o f t r a n s f e r u n i t s
a s a n u n d e te r m in e d p a r a m e t e r , t h e p r e d i c t e d c u rv e was lo w e r e d f o r t h e b e s t
f i t so t h a t h a l f o f t h e o b s e r v e d p o i n t s w ere h i g h e r a n d .th e r e s t lo w e r
th a n th e p r e d ic te d v a lu e s ,
W ith t h e i n t r o d u c t i o n o f d i f f u s i o n c o e f f i c i e n t
a s a s e c o n d u n d e te r m in e d p a r a m e t e r ,, n o s i g n i f i c a n t im p ro v em en t was o b ­
ta in e d f o r th is s e r ie s .
T h is may b e due t o t h e u s e o f a n a v e r a g e v a lu e
f o r t h e d i f f u s i o n c o e f f i c i e n t f o r a l l th e. d i f f e r e n t f l o w . r a t e s u s e d i n
S e rie s 8 .
U s in g v a r y i n g v a lu e s o f d i f f u s i o n c o e f f i c i e n t w i t h f l o w . r a t e s ,
t h e p r e d i c t i o n , c u r v e c a n be l i f t e d a t low f lo w r a t e s
f lo w r a t e s t o c o r r e s p o n d w i t h t h e o b s e r v e d . v a l u e s .
a n d lo w e r e d a t h i g h
-4 1 M odel
Mamuro
an d —
Much!
-----— (,o
j ^f. —;
— -— ^——
I------U sin g .e q u a ti o n ( 4 1 ) , th e v a lu e s o f k /^>
w e re c a l c u l a t e d f o r t h e
th r e e d i f f e r e n t l e d h e ig h ts u se d i n t h i s i n v e s t i g a t i o n .
te m p e r a tu r e ., an d p a r t i c l e s i z e w e re k e p t c o n s t a n t .
.The f lo w h a t e ,
The v a lu e s o f k / ft
were, f o u n d .to b e f a i r l y c o n s t a n t f o r a l l t h e t h r e e b e d h e i g h t s .
S in c e
t h e b u b b le d i a m e t e r i s a f u n c t i o n o f b e d h e i g h t , .t h r e e , d i f f e r e n t b u b b le
d i a m e te r s w ere u s e d f o r t h e t h r e e b e d h e i g h t s ,
e q u a tio n s
(42) a n d . ( 4 3 ) .
S in c e t h e .c o n d i t i o n s e x i s t i n g fh , t h i s i n v e s ­
t i g a t i o n C o rre s p o n d e d w i t h e q u a t i o n
was t a k e n a s Fm.
was c a l c u l a t e d . u s i n g
(35)
,minimum f l u i d i z i n g v e l o c i t y
The r e s u l t s a r e show n i n F ig u re . I rJ.
The r e s u l t s , show t h a t t h i s m o d el i s p a r t i c u l a r l y u s e f u l i n s c a l e - u p
.o f f lu i d iz e d bed r e a c t o r s .
,S in c e k / ^
i s , f a i r l y c o n s t a n t f o r w id e
r a n g e s o f b e d .h e i g h t s & b u b b le s i z e s i n r e a c t o r s o f d i f f e r e n t h e i g h t s
c a n b e c a l c u l a t e d u s i n g , e q u a t i o n ( 4 l ) ^ fro m w h ic h a l l o t h e r unknown
p a r a m e t e r s may b e c a l c u l a t e d a s d e s c r i b e d by D a y id s o n a n d H a r r i s o n
(1 1 ),
F f f e c t o f T e m p e ra tu re
I n t h i s , i n v e s t i g a t i o n ^ t h e f l u i d i z e d b e d was o p e r a t e d a t t h r e e
d i f f e r e n t te m p e ra tu re s ,
The t h r e e d i f f e r e n t t e m p e r a t u r e s u s e d w ere
4 l6 ° F ., ,4 5 0 0F., .a n d - 4 8 o ° F , ,c o r r e s p o n d in g t o S e r i e s 9,.. 7 , a n d 8 , , r e s p e c t i v e l y .
S in c e t h e r a t e o f r e a c t i o n i n c r e a s e s i n t e m p e r a t u r e , , t h e a c t i v a t i o n e n ­
e r g y o f t h e r e a c t i o n was c a l c u l a t e d f r o m th e . f i x e d b e d . r e s u l t s a n d i t
was fo u n d t o b e 1 , 6 x IO ^ c a l o r i e s .
In a l l th e th r e e s e r i e s o f r u n s ,,t h e
sam e p a r t i c l e s i z e a n d b e d h e i g h t w e re u s e d .
A c o m p a r is o n o f t h e o b ­
s e r v e d .c o n v e r s io n s a t t h e t h r e e te m p e r a t u r e s i s show n i n F i g u r e 1 8 .
/
-4 .2 F ig u r e 18 shows t h a t t h e l i n e s f i t t e d th r o u g h t h e t h h e e s e t s o f
p o i n t s o f o b s e r v e d .c o n v e r s io n s l i e p a r a l l e l t o e a c h o t h e r .
F o r t h e same
f e e d . r a t e , a p p r o x im a te ly t h e same, i n c r e a s e i n c o n v e r s i o n ^ras n o t e d f o r
t h e two in c r e m e n ts i n t e m p e r a t u r e .
Model c a l c u l a t i o n s show t h a t a n i n c r e a s e i n t h e q u a l i t y o f f i t was
o b t a i n e d w ith a d e c r e a s e i n t e m p e r a t u r e u s i n g a l l t h e m o d e ls .
The t h r e e
s e r i e s o f r u n s i n v o lv e d t h r e e r a n g e s o f f e e d r a t e s a s shown i n F i g u r e 1 8 .
F o r t h e ra n g e o f c o n v e r s io n s d e s i r e d > h i g h e r f e e d r a t e s w e re n e e d e d f o r
t h e h i g h e r t e m p e r a t u r e s w h i l e r e l a t i v e l y low flo w .r a t e s , w e re u s e d f o r t h e
lo w te m p e r a tu r e s e r i e s . .
S in c e h i g h e r f e e d . r a t e s c a u s e .m o re .s o l i d s m ix in g ,
t h e e f f e c t o f t h e l o n g i t u d i n a l d i f f u s i o n c o e f f i c i e n t i s m ore i m p o r ta n t
f o r th e h ig h e r te m p e ra tu re s e r i e s .
An a v e r a g e d i f f u s i o n c o e f f i c i e n t f o r
t h e w h o le s e r i e s .o f r u n s o n ly lo w e r s t h e w h o le c o n v e r s i o n c u r v e ,
A b e tte r
f i t may be o b t a i n e d .f o r S e r i e s 8 , by u s i n g a . v a r i a b l e d i f f u s i o n c o e f f i c i e n t .
I n t h e c a s e o f S e r i e s g , . r e l a t i v e l y lo w f lo w r a t e s w e re u s e d a n d h e n c e a
b e t t e r f i t was o b t a i n e d u s in g a l l t h e m o d e l s .
An i n t e r m e d i a t e . f i t was
o b t a i n e d f o r S e r i e s Y , . a s c a n be s e e n fro m T a b le s V I I I a n d Z I I .
T a b le s
IX a n d X I I I show t h a t t h e num ber o f t r a n s f e r u n i t s f o r t h e b e s t f i t was
h i g h e r f o r h ig h e r ' t e m p e r a t u r e s u s i n g one. u n d e te r m in e d p a r a m e t e r w h i l e no
d e f i n i t e t r e n d was s e e n u s in g t h e t w o - p a r a m e te r m o d e l.
The v a lu e s o f
d i f f u s i o n c o e f f i c i e n t s a n d .c lo u d S i s e a l s o d i d n o t show a n y d e f i n i t e
tre n d .
-4 3 E f f e c t o f B ed .E e l g h t
T h re e d i f f e r e n t b e d h e i g h t s w e re a l s o u s e d i n t h i s i n v e s t i g a t i o n .
The l e n g t h t o d i a m e te r r a t i o s u s e d w e re 4 . 0 0 , 3 .3 3 , a n d 2 . 6 7 , c o r r e s ­
p o n d in g t o S e r i e s 6 , .7 , and 1 0 , r e s p e c t i v e l y .
I n a l l t h r e e . c a s e s , .th e
p a r t i c l e s i z e a n d t e m p e r a t u r e w ere k e p t t h e sam e.
c o n v e r s i o n s i s shown i n F ig u r e 1 9 .
A c o m p a ris o n o f t h e
S in c e t h e r a t e o f r e a c t i o n i s d e p e n d e n t
on t h e am ount o f c a t a l y s t p r e s e n t,,, a n i n c r e a s e i n c o n v e r s i o n was o b t a i n e d
w i t h a n i n c r e a s e i n b e d h e i g h t f o r t h e same g a s f e e d r a t e .
H e r e , a ls o ,-
t h e r a n g e o f g a s flo w r a t e s u s e d was w i d e r f o r t h e h i g h e r b e d h e i g h t s .
M odel c a l c u l a t i o n s show t h a t a g o o d f i t was o b t a i n e d f o r S e r i e s 6
(L/D = 4 . 0 ) w h ile a b e t t e r f i t was .o b t a i n e d f o r S e r i e s 7 (L/D = 3 .3 3 )
a n d a n e v e n b e t t e r f i t was o b t a i n e d f o r S e r i e s 10 (L/D = 2 . 6 7 ) f o r a l l
t h e m odel c a l c u l a t i o n s .
T h is c a n be s e e n fro m T a b le s V I I I a n d X I I .
. The r e s u l t s show t h a t t h e num ber o f t r a n s f e r u n i t s c a l c u l a t e d u s i n g
t h e m eth o d o f .Q r c u tt (8) shows a n i n c r e a s e w i t h t h e b e d h e i g h t w h i l e no
d e f i n i t e t r e n d was n o t i c e d i n t h e .c a s e o f b e s t f i t v a l u e s .
The v a lu e s
f o r t h e d i f f u s i o n c o e f f i c i e n t a l s o show ed .no d e f i n i t e t r e n d w i t h t h e
bed h e ig h ts .
E f f e c t o f P a r t i c l e S jz e
The f l u i d i z e d b e d w as o p e r a t e d u s i n g two d i f f e r e n t s i z e s o f c a t a l y s t
p a r t i c l e > a ls o .
The a v e r a g e s i z e , o f t h e c a t a l y s t p a r t i c l e s w e re Q . l 6l mm
a n d .0 .1 8 1 mm, c o r r e s p o n d in g t o S e r i e s 6 a n d 1 1 , r e s p e c t i v e l y .
tw o s e r i e s o f r u n s A .th e same b e d h e i g h t (L/D = 4 . 0 )
F or th e s e
an d te m p e r a t u r e
-44-'
( 4 5 0 °F) w ere u s e d .
The minimum, f l u i d i z i n g v e l o c i t y i s a f u n c t i o n o f
p a r t i c l e s i z e a n d t h e q u a n t i t i e s o f g a s f lo w in g th r o u g h t h e e m u ls io n
p h a se .-.o f t h e two s e r i e s w ere .fo u n d t o b e YQO c c /m in a n d 1950 c c /m in u s i n g
t h e s m a ll a n d t h e l a r g e s i z e p a r t i c l e s , , . r e s p e c t i v e l y .
.A c o m p a ris o n o f
t h e o b s e r v e d .c a r b o n m onoxide .c o n v e r s io n s f o r t h e two s e t s o f p a r t i c l e s i s
show n i n F ig u r e 2 0 .
Mod.e'1 c a l c u l a t i o n s .show t h a t a b e t t e r f i t was o b t a i n e d f o r t h e c a s e
o f s m a l l e r p a r t i c l e s t h a n t h e o t h e r * a s shown ,in T a b le s V I I I a n d X I I .
. The g a s flow, , r a t e s u s e d i n S e r i e s 11. .w ere v e r y much h i g h e r t h a n t h o s e
in S e rie s 6 .
As a , r e s u l t , a h i g h e r d e g r e e o f p a r t i c l e m ix in g was
p r e s e n t in S e rie s 1 1 .
T a b le s IX a n d X I t I show a l a r g e v a lu e f o r t h e
d i f f u s i o n c o e f f i c i e n t was u s e d f o r t h e b e s t f i t i n t h e c a s e o f S e r i e s
I l j 1 w h ile , a minimum v a lu e was u s e d .in S e r i e s 6 . . The v a lu e s o f c lo u d t o
b u b b le d ia m e te r r a t i o a n d t h e .num ber o f t r a n s . f e r u n i t s u s e d f o r t h e
b e s t f i t c a l c u l a t i o n s .were f o u n d t o be t h e same i n b o th . S e r ie s . 6 a n d 1 1 .
CONCLUSIONS
The p r im a r y o b je c t o f t h i s r e s e a r c h was t o g a i n b e t t e r u n d e r ­
s ta n d in g o f f i r s t o rd e r r e a c tio n s ta k in g p la c e in a f lu id iz e d bed .c a ta ly t i c
re a c to r.
S e v e r a l p h y s i c a l .m odels a r e a v a i l a b l e i n t h e
l i t e r a t u r e , .many
o f them w ith l i t t l e
o r no e x p e r i m e n t a l v e r i f i c a t i o n , c o n v e r s io n s c a l c u l a t e d
u s i n g .th e s e .m odels
w e re t o be .co m p ared w i t h t h e o b s e r v e d v a l u e s t o d e t e r ­
m in e how. w e l l t h e y d e s c r i b e t h e b e h a v io r o f f l u i d i z e d b e d s .
S in c e t h e
r e l a t i o n s h i p s u s e d t o c a l c u l a t e Some o f t h e c r i t i c a l p a r a m e t e r s i n t h e s e
m o d e ls s t i l l ..need e x p e r i m e n t a l b a c k i n g , t h e s e p a r a m e t e r s w e re k e p t a s
u n d e te r m in e d i n t h e s e m o d els a n d b e s t f i t v a lu e s o f c o n v e r s i o n w e re
c a lc u la te d .
. C om paring t h e e x p e r i m e n t a l a n d c a l c u l a t e d r e s u l t s ,■ i t was f o u n d t h a t
c o n v e r s i o n s C a l c u l a t e d u s i n g t h e u n m o d if ie d m o d e l.o f Rowe show ed . b e t t e r
a g re e m e n t w i t h t h e o b s e rv e d r e s u l t s t h a n t h o s e c a l c u l a t e d . u s i n g t h e
m o d els, .of D a v id s o n a n d H a r r i s o n .
, B a c k m ix in g .was a l s o assum ed i n t h e '
e m u ls io n p h a s e f o r R ow ejs m odel c a l c u l a t i o n s , a n d t h e f i t was fo u n d t o
be w o rse t h a n t h e p l u g f l o w . c a s e .
R o w e 's m odel was f u r t h e r m o d if ie d by
c o n s i d e r i n g t h e c lo u d s i z e a s a n u n d e te r m in e d p a r a m e t e r a n d t h e b e s t f i t
c o n v e r s i o n s w e re c a l c u l a t e d , f o r b o t h p l u g f lo w a n d b a c k m ix in g , i n th e
e m u ls io n p h a s e .
No a p p r e c i a b l e im p ro v e m e n t i n f i t was o b t a i n e d fro m th e
c a s e w here n o u n d e te r m in e d p a r a m e t e r s w e re u s e d .
The m odels o f D a v id s o n a n d H a r r i s o n W ere a l s o m o d if ie d by c o n s i d e r i n g
t h e num ber o f t r a n s f e r u n i t s a s a n u n d e te r m in e d p a r a m e t e r .
The r e s u l t s
-4 6 show t h a t a s s u m p tio n s o f p l u g f lo w i n t h e e m u ls io n p h a s e s t i l l y i e l d e d
b e t t e r a g re e m e n t w i t h t h e o b s e r v e d . r e s u l t s .
S i g n i f i c a n t im p ro v e m e n t i n
f i t was a l s o o b t a i n e d by c o n s i d e r i n g t h e num ber o f t r a n s f e r u n i t s a s an
u n d e te r m in e d p a r a m e t e r .
B u b b le s p l a y a v e ry im p o r ta n t p a r t i n t h e m ix in g t a k i n g p l a c e i n
th e f lu id iz e d b ed .
B u b b le s a r e r e s p o n s i b l e f o r p a r t i c l e m ovem ent due
t o t h e wake t h a t i s p r e s e n t b e h in d .-each b u b b l e .
I t i s w rong t o assum e
p l u g flo w .o r b a c k m ix in g o f g a s I n t h e e m u ls io n p h a s e ,ev en th o u g h t h e
a c t u a l c o n d i t i o n e x i s t i n g i s C l o s e r t o p l u g . f l o w , . The m ix in g t h a t i s
p r e s e n t i n t h e e m u ls io n p h a s e may b e a c c o u n te d . f o r by i n t r o d u c i n g a
lo n g itu d in a l d iffu s io n c o e ff ic ie n t in th a t p h ase.
The l o n g i t u d i n a l d i f f u s i o n c o e f f i c i e n t was i n t r o d u c e d a s a s e c o n d
u n d e te r m in e d p a r a m e t e r i n t o t h e m o d e l o f Rowe a n d t h a t o f D a v id s o n a n d
H a r r i s o n a s su m in g p l u g flo w i n t h e e m u ls io n p h a s e o f b o th t h e m o d e ls .
S l i g h t im p ro v em en t i n t h e f i t was n o t ic e d , f o r m o st o f t h e s e r i e s o f
ru n s.
.C om paring t h e two tw o - p a r a m e te r models,-, no s i g n i f i c a n t d i f f e r e n c e
i n f i t was s e e n b e tw e e n th em .
Gas i s t r a n s f e r r e d b e tw e e n t h e e m u ls io n p h a s e a n d t h e b u b b le p h a s e
by m eans o f b u lk f lo w an d d i f f u s i o n .
T h is q u a n t i t y was e x p r e s s e d i n t h e
m o d els o f D a v id s o n a n d H a r r i s o n a s t h e n u m b er o f t r a n s f e r u n i t s an d was
f o u n d t o be im p o r ta n t f o r t h e p r e d i c t i o n o f t h e b e h a v io r o f f l u i d i z e d b e d s .
The num ber o f t r a n s f e r u n i t s f o r t h e b e s t f i t r e s u l t s Vwas fo u n d t o be
. d i f f e r e n t , fro m t h e ,c a l c u l a t e d ..values, d u e t o I n a c c u r a c i e s I n t h e i r m eth o d
o f e s tim a tio n .
I n R o n e i $ m o d e l, t h e ex ch an g e, o f g a s b e tw e e n th e . tw o p h a s e s was n o t
t a k e n .in to c o n s i d e r a t i o n .
c a n t and i s
At lo w f lo w r a t e s , t h i s e x c h a n g e i s n o t. s i g n i f i ­
c o m p e n s a te d f o r by t h e e f f e c t o f t h e b u b b le c l o u d .
At h i g h
f lo w r a t e s ,..t h e g a s in te r c h a n g e , s h o u ld be i n c l u d e d i n Row e1s m odel f o r
b e tt e r p re d ic tio n .
The. d e g re e , .of s o l i d s m ix in g i s a . f u n c t i o n o f flo w r a t e S in c e .more
a n d m ore b u b b le s a r e fo rm e d w i t h i n c r e a s e i n g a s flo w r a t e .
A d iffe re n t
v a l u e f o r t h e . d i f f u s i o n c o e f f i c i e n t m u s t b e u s e d f o r b a c h f lo w r a t e t o
d e s c r i b e t h e b e h a v io r o f t h e f l u i d i z e d bed w e l l .
. R or t h e r a n g e o f flo w
. r a t e s .u s e d i n t h i s i n v e s t i g a t i o n . , . .l o n g i t u d i n a l d i f f u s i o n was. n o t a b i g
,f a c to r.
F or. a s i m p l i f i e d m odel w i t h no undeterm ined p a r a m e t e r s , . R o w e 's
m o d el .was f o u n d t o d e s c r i b e th e b e h a v io r , o f .the. f l u i d i z e d b b d r a t h e r
w e l l a n d was ,found, t o b e much b e t t e r th a n . th e . m odels, o f D a v id s o n a n d
H a r r i s o n f o r th e . c o n d i t i o n s u s e d in. t h i s , i n v e s t i g a t i o n .
SUGGESTIONS FOR FUTURE ,WORK
T h e re a r e s e v e r a l p o s s i b l e a r e a s f o r , e x t e n s i o n o f t h e p r e s e n t w o rk .
The. f i r s t a r e a I n v o lv e s o p e r a t i n g t h e , f l u i d i z e d b e d a t h i g h e r g a s v e l o c i ­
tie s .
I n t h is ; i n v e s t i g a t i o n t h e .maximum f lo w , r a t e u s e d w as..4 .5 tim e s
t h e minimum f l u i d i z i n g V e l o c i t y .
i1
I n o r d e r t o o p e r a t e - a t .h ig h e r g a s flow ; .
r a t e s > h i g h e r b e d h e ig h ts , a r e n e e d e d .
. One, o f t h e d i f f i c u l t i e s enr-
.c o u n te r e d in . h i g h f lo w r a t e s i s . t h e . , . c a t a l y s t c a r r y o v e r w hich, may be
c o r r e c t e d by a c o n s t a n t c a t a ly s t f e e d i n t o t h e r e a c t o r .
t
V ,
I
„
'
'
'
•
•
M
•
'
A n o th e r p o s s i b i l i t y i s ,to d o t r a c e r s t u d i e s i n th e , p r e s e n t f l u i d i z e d
b e d t o f in d , a c t u a l . d i f f u s i o n c o e f f i c i e n t s f o r t h e s y s te m .
.T h is i s
e s p e c i a l l y n e e d e d f o r f l u i d i z e d ,beds o p e r a t e d a t l a r g e , f e e d . r a t e s ,
A t h i r d a r e a i n v o lv e s t h e s c d l e - u p o f r e a c t o r s .
So f a r , s c a l e - u p
h a s b e e n f o u n d t o be t h e h a r d e s t p ro b lem , f a c i n g t h e d e s ig n o f f l u i d i z e d
|
bed r e a c to r s .
The same r e a c t i o n s y s te m a s t h a t u s e d i n t h i s , ih v .e s t i - .
I
g a tio n may be used in la r g er f lu id iz e d beds to ob tain th e ,c o r r e la tio n s
I
n ecessa ry fo r s c a le -u p .
A n o th e r a r e a . I i e s i n d e v e l o p i n g . p h y s i c a l . . m o d e l s . f o r , f i r s t o r d e r
r e v e r s i b l e r e a c t i o n s o r s e c o n d o rd er r e a c t i o n s . . T h is w i l l c e r t a i n l y be
m ore d i f f i c u l t t h a n f o r t h e f i r s t o r d e r , r e a c t i o n s .
■
i;
.T here, a r e s o m e .f ix e d
b e d d a t a . a v a i l a b l e .f o r t h i s ty p e o f r e a c t i o n s y s te m i n t h e l i t e r a t u r e . .
The same system s may b e ,u s e d i n t h e f l u i d i z e d b e d s t o d e v e lo p
a p p r o p r i a t e p h y s i c a l m o d e ls .
.
49
-
■APPENDICES
NOMENCLATURE
=
C ro ss s e c t i o n a l a r e a o f t h e r e a c t o r , , f t 2
=
I n t e r f a c i a l a r e a o f p h a s e s p e r u n it volume, o f b e d , . f t 2/ f t 3
=
C o n c e n t r a ti o n o f CO i n th e . .f e e d , lb - m o le s / f t 3
=■ C o n c e n t r a ti o n o f CO I n t h e b u b b le ^ i b - m o l e s / f t 3
=
C o n c e n t r a ti o n o f CO i n . t h e e m u ls io n p h a s e , . I b - m o l e s / f t 3
“
Ce
=
C o n c e n t r a ti o n o f CO i n t h e s t r e a m l e a v i n g t h e bed,-. I b - m o l e s / f t 3
=
D ia m e te r o f t h e p a r t i c l e s , , f t
=
D ia m e fe r o f t h e b u b b l e , ,,ft.
=
D ia m e te r o f t h e b u b b le, c l o u d , ,.f t
— Gas p h a s e d i f f u s i o n c p e f f .i c l e n f > . f .t 2/ s e c
.=
F r a c t i o n , o f g a s i n t h e e m u ls io n p h a s e
=
F r a c t i o n o f g a s i n t h e b u b b le p h ase.
= Feed r a t e , f t 3/se,c
=
Flow r a t e i n th e , b u b b le, p h a s e p e r u n i t c r o s s - s e c t i o n a l a r e a ,
ft/s e c
=
F lo p , r a t e i n .th e e m u ls io n p h a s e p e r u n i t , c r o p s - s e c t I o n a l a r e a ,
f t/s e .c
=
B a c k m ix in g f lo w r a t e p e r u n it - c r o s s - s e c t i o n a l , a r e a , f t / s e c
=
Gas i n t e r c h a n g e r a t e c o e f f i c i e n t p e r u n i t b e d volum e
I f t 3/ ( S e p ) ( f t 3 )
.=
A c c e l e r a t i o n due t o g r a v i t y , ,.f t/ s e .c 2
-=
H eight, .o f t h e c a t a l y s t , b e d , . f t
=
Bed h e i g h t a t i n c i p i e n t f l u i d i z a t i o n , f t
=
R e a c tio n , r a t e c o n s t a n t , . I b v m o l e s / ( l b - c a t ) ( s e c )
51k'
D im e n s io n le s s r e a c t i o n v e l o c i t y c o n s ta n t ,k w / 'U A
k
Mass t r a n s f e r c o e f f i c i e n t b e tw e e n b u b b le and, e m u ls io n p h a s e s ,
S
. £ t 2/ s e c —£ t 2
K
Gas i n t e r c h a n g e r a t e c o e f f i c i e n t p e r u n i t ' v o lu m e , ..f t 3/ s e c - f t 2
L
F lu id ig e d bed h e ig h t ,..f t
I
H eight, o f a c e l l , f t
M
M o le c u la r w t , l b s
R o o ts o f th e q u a d r a t i c e q u a t i o n
Kil j In2
=
H
■=! Humber o f b u b b le s p e r u n f t -volume
A b s o lu te ; p r e s s u r e , atm
P
q.
.= V o lu m e tr ic f l o w , r a t e i n a n d .o u t o f b u b b l e , , f t 3/ s e e
Q
=. (q..+ k g S )j, f t 3/ s e c
r
=i R e a c t i o n r a t e , . l b - m o l e s / ( l b - c a t ) ( s e c )
f
.=
T e m p e ra tu re o f th e b e d , , °F
t
T im e ,s e c
u.
S u p e r fic ia l v e lo c ity of g a s ,,f t / s e c
Uo
= Minimum f l u i d i z i n g . v e l o c i t y , . f t / s e c
uA
i= A b s o lu te , r i s i n g v e l o c i t y o f b u b b l e , . f e e t / s e c
V
=
W
= W e ig h t o f t h e C a t a l y s t , . l b s
WSC
=
W eight, o f g a s i n t h e b u b b le , c l o u d , l b s
=
W e ig h t o f s o l i d s i n t h e b u b b le c l o u d , , l b s
QH./U^V
.X
y
Volume o f a b u b b l e , . . f t 3
=
=
num ber o f t r a n s f e r u n its
F r a c t i o n o f CO r e a c t e d
52 T'
V e r ti c a l c o o rd in a te
R a t io o f b a b b le t o i n t e r s t i t i a l g a s v e l o c i t y ,, .UB.C/U0
I - H0/II
Mean y o id a g e f r a c t i o n o f t h e . c a t a l y s t b e d
I n c l i n a t i o n o f passage,*, d e g re e s .
V is c o s ity o f th e f l u i d
•Bulk D e n s i ty o f t h e , c a t a l y s t
.F o m f a c t o r o f g a s b u b b le s
SAMPLE CALCULATIONS
M odel C a l c u l a t i o n s :
I n t h e s e c t i o n o f t h e o r e t i c a l d i s c u s s i o n ,, a num ber o f e q u a ti o n s w ere
p r e s e n t e d w h ic h p e r m i t t e d th e c a l c u l a t i o n o f t h e c o n v e r s i o n o f c a r b o n mon­
o x id e f o r t h e v a r i o u s m odels c o n s i d e r e d i n t h i s i n v e s t i g a t i o n .
Sam ple C a l c u l a t i o n s a r e p r e s e n t e d f o r r u n n o . I o f t h e S e r i e s 7T e m p e r a t u r e ,. p a r t i c l e s i z e , an d b e d h e i g h t w e re k e p t t h e sam e f o r a l l t h e
ru n s in th e s e r i e s .
ROWE1S MODEL
A.
.P lu g Flow i n b o th E m u ls io n a n d B u b b le P h a s e :
V e l o c i t y o f t h e b u b b l e , ,Ub -
0 .78 (g r B) 1//2
g .= 3,2 .2 f t p e r r ,s q u a r e :;s e e
r B ,= 0 .0 1170 f t
Ug = O.905 f t p e r s e c
<* -
dB €
A n f
= O.776
Ufflf = 0 . 008 l f t p e r s e c
=as.7
D ia m e te r o f t h e c l o u d , dg = dB
( o C + 2 ) / ( c C - I ) j 1 /3
= .0 .0 8 4 4 f t
W eight o f s o l i d s i n t h e c l o u d , Ws c = (Vc - . 0 . 6 6 7 Vb-)/^
Vc = 0 . 000318,2 c u b ic f t
Vb = 0 .0 0 0 3 0 3 c u b ic f t
■== 4 5 .0 l b p e r c u b ic f t
Ws c = 0 .0 5 2 3 l b s
-5 4 W eig h t o f g a s i n t h e p lo u d , Wqq =
0 . 67VB +
£ (Ve - -0,67 Vb )
:= 0 .0 4 2 2 l b p e r c u b ic f t
1 GO
9 .5 x IO "^ gms
F re q u e n c y o f B u b b le s , f B ,= Q, Bc/V e
Q .= Q,0 00494 c u b ic f t p e r s e c
0.166
-C
Vc = 0 . 0005.182
fg & 0.55
C o n v e r s io n i n t h e E m u ls io n P h a se
^i
..:k
I - EXP
k O0 (W - f B Ws c. /) / B
E 1 .]
= 0 .0005555 c u b ic f t p e r l b o f c a t a l y s t p e r s e c
C0 = 0 ,.0001515 l b m o le s o f c a rb o n m onoxide p e r sec.
W = 2 . 5 0 lb s
F
= 7 ,5 0 x IO "^ l b m o le s o f . c a r b o n m onoxide p e r s e c
E 1 = 0 .8 5 4
Y1 = 0 , 9 7 0 5
C o n v e r s io n i n t h e B u b b le Phase.
y c = I - EXP ( k C0 M Ws c H/WGc Ub ]
M = 2 8 l b s p e r pound,.m ol,e
H. = 1 .0 f t
y c = 0 .0 1 6
O v e r a ll C o n v e r s io n I n s i d e t h e F l u i d i z e d Bed
y
.= E1 y i + E0 y 0
= 0 , 8.167
jPg
-55Bo
B a c k m ix in g i n t h e E m u ls io n P h a s e an d P lu g Plow i n t h e B u b b le P h a se
Y jA
k
-
Y i = k(W - -fg Wg e ) /P
',O rO O 5355
c u b ic P t p e r l b o f c a t a l y s t p e r s e e
W = 2 . 5 0 lb s
fg ^ P.35
Wgg = Po05,23 l b s
F
= Q .0 0 0 4 l2 .c u b ic f t p e r s e c
Y i / ( ,I •“ Yj[) = 3,.22
C o n v e rs io n i n t h e E m u ls io n P h a se
Y1 = 3.22/3.22 + I
=T O„767
C o n v e rs io n i n t h e B u b b le P h a s e
J c = ■O.OI6
O v e r a l l C o n v e r s io n i n t h e F l u i d i z e d .Bed
Y = E i YjL + Ec Yc
- 0.6394
Co
M o d ifie d -Rowe's Model, w i t h P lu g Flow an d L o n g i t u d i n a l
D iffu s io n C o e f f ic ie n t:
The m eth o d o f . c a l c u l a t i o n i s shown i n T a b le XV w h ere t h e
F o r t r a n P ro g ra m u s e d f o r t h e c a l c u l a t i o n s i s g i v e n .
-56MODELS OF DAVIDSON AND HARRISON
A.
B ackm ixj,ng i n th e E m u ls io n P h a s e :
/S = (U - -U0 )/U
U •= .0 .0 0 9 6 3 f t p e r s e c
U0 = O.OOSlO f t p e r s e c
P
- O .I 66
Q o n y e rsio n . I n s i d e t h e F l u i d i z e d Bed
y
= 1 - .
-
I
I
+ /^ k t e
- /.e ^
+k'
0 ,1 6 6
.k ' = 2 ,7 0
B,
x
= 1 .9 3 5
y
- 0.7 1 6 8
P lu g Flow i n t h e E m u ls io n P h a s e
,1 /2
M =
- ( x + k fH) ± [ (x + k 'H ) 2 - 4 ( 1 - p
).H kA xl
2H (1 - / 3 )
H
= ,1 .0 f t
m. . = —4 .0 4
m2 = - I ..578
C o n v e rs io n I n s i d e th e. F l u i d i z e d Bed
y
= .1
V m 1 m2
Ui1 ( I - m2 H U0/ x U)
■- m2 ( I —JH1H U0 )
x U
j
J
-
-,57?
U = 0.00.963 f t per sec
U -= 0,00810 -ft p er sec
y
C.
= 0 .9 5 2 5
M o d ifie d M odel o f D a v id s o n arid .H a r ris o n a s su m in g P lu g Plow i n t h e
E m ulsion. P h a s e C o n ta in in g a L o n g i t u d i n a l D i f f u s i o n C o e f f i c i e n t :■
The e q u a t i o n s u s e d . f o r th e s e , c a l c u l a t i o n s a r e g i v e n by May (5)
a n d a r e g i v e n i n t h e fo rm o f a F o r t r a n P ro g ra m in. T ab le. X V J II.
. The, Whole. R e a c t o r a s P lu g plow
- I n . ( I - y) = k Cao (W/P)
k
•= 0 .0005335 c u b ic f t p e r l b o f c a t a l y s t p e r 1 s e c
c Ao = 0 .0 0 0 1 5 1 5 l b m o le s p e r c u b ic f t
¥
= 2 .5 l b s
F
=; 7 .4 2 0 -x 1 0.-G l b m o le s p e r s e c
- I n (I
y) = 2 .7 .2
C o n v e rs io n I n s i d e t h e F l u i d i s e d .Bed R e a c to r
y
= Q.9339
The W hole R e a c to r a s B ackm ix
y / ( I - -y) ■=- k ¥ /P
k. = .0.0005335 cubfc f t p er lb. of c a t a ly s t per see
¥ .= -2 .5 lb s
F .= -0.000494 c u b ic f t p e r sec.
y / (1..- y) .= .2 ,7 1
C o n v e r s io n I n s f d e th e . F l u i d i z e d Bed R e a c t o r
y = .0 .7 3 0
'
-58model
OF MAMDRO M D MDCHI
icAB 'I.
6. C0J o ,? 7 5 . DS1 / 2 . :gV 4 / aB + 3 / 1*. Ho,
1 /2
r
aB
i .+ 0 .7 1 1 (g dB)
/(u
- u0)
C0 = -.0001515 l.U m o le s p e r c u b ic f t
Dq = O.OOO747 s q u a r e . f t p e r s e c
dp = 0 .0 8 5 3 f t
g
,= 3 2 .2 f t p e r s e c 2
U
= .O.QO963 ft per sec
U0 = O.OO752 f t pier s e c
KAB = ^
c u b ic f t p e r h r p e r s q u a r e f t
F=, = Kffi
R T/P
R'
= 0 .7 3 0 2
T
= 910°R
P
= 1 atm
F e v - 2650 .c u b ic f t p e r h r p e r s q u a r e f t
V f
= dp f c /
12 9%
= 0.78
F m = 0 .0 0 8 1 0 f t p e r s e c
k /p >
= 0 .0 0 1 9 2
'
table
SERIES
6 '
I:
-5 9 -
EXPERIMENTAL CONDITIONS
TEMP
( 0F)
■ CATALYST
WT ( lb )
'
HEIGHT OF
■BED ( f t )
PARTICLE
SIZE
450
5 .0 0
1 .0 0 0
A
7
. 450
2 .5 0
0 .8 3 3
A •
8
48 O
.9
416
IQ
450
' 11.
■ 450
2 .5 0 ,
.
.
Omf
(c c /m ln )
.
675
.
690
710
. 0 .8 3 3
0 .8 3 ^ .
A
675
2 .0 0
• ■ ■ 0 .6 6 7
A
; ■ 700
3 ,0 0
1 .0 0 0
B
1950
2 .5 0
.
-6o~
TABLE J I ;
TYLER. MESH
SIZE
CATALYST SIZE DISTRIBUTION
. BATCH A ,
W e ig h t (.gms)
• % Wt .
BATCH B
W e ig h t (gms)
fo Wt
6 0 -6 5
3 9 8 .6
4 2 .0 0
5 2 5 .6 '
5 7 .6 2
65-80
1 7 6 .1
1 8 .5 0
262.I
2 8 ,7 6
8 0-100
2 1 .8
2 .2 9
■ 1 5 .8
1 .7 4
1 0 0 -1 4 0
1 3 .6
1 .4 3
1 7 ,2
1 .8 8
1 4 0 -1 7 0
' 4 1 .7
4.3,6
1 1 ,8
1 ,2 9
I 7 O - 2 OO
200 +
2 5 .8
2 .7 0 '
5 .3
0 ,5 9
2 7 4 .2
2 8 .8 0 .
7 4 .0
8 .1 1
-6.1-
TABLE III: FIXED BED DATA
SERIES
' NO.
6
7
8
GAS FLON
Rate (cc/rnln)
I
2195
0.908
1,965
.0 .6 4 5 '
2
2620
0.84.5
1 .4 9 0
,6 .5 4 0
. 3
2&55
Q..8l8
.1,335
o ,4 9 6
4
3% .
(U745
1 .1 1 0
0.44,2
5
3822
.0.710
0.937
0 .3 7 1
I
1023
0 ,8 4 2
1 . 8,35
1 .1 5 5
2
1480
1 .4 9 0
■0.795
-3
18-55
0 .6 8 0
1 .1 4 6
0.63.6
4
2195
0.655
1 . 06.3
0 .5 3 7
5.
2625 ‘
0 ,6 3 0
0 .9 9 2
0 .4 5 1
■6
2860
0 .6 1 0 .
0 ,9 4 0
I
.33.10
0,935
2.73
3920.
0.815
1 .6 8 7
0 . 30 I 5
4490
0,773
1 ,4 8 2
0 .2 6 2 5
5050 ■
0 .7 2 0
1 ,2 7 3
0.2340
,.'5*3
O.737
1.335.
^ ,1 1 7
# 5
Q ,6o4
Q<927
I . .2,4 6
3
11.72
O . 36 Q
0 .4 4 7
.1,007
4
^368.
0 .3 1 0
- 6 .3 7 1
.Q&863.
2
.
3
,4.
1
?
-In (I -r. y)
RUN
. NO.
2
.
.
CONVERSION
■
0.775
.
'
v
(W/P)
.0 .4 1 4
.0.3565
v 62 x
. ( c o n tin u e d )
TABLE I I I :
RUN.
NO.
GAS FLOW
R ate, (c c /m ln )
CONVERSION
- I n ( I - y)
(W/F)
.1
.840.
0 .8 4 0 ’
1 . 8.3.
1 .1 2 2
2
126$
0.680 '
1 .1 4
O.744
3 '
1680
O .545
0,878
0,561,
^060
,0.44.5
P,52.0.
0.459
I
2488,
0 .8 8 8
2,19
.O . 57 I
■ 2
.2771
■0 .8 4 2
1 ,8 4 7
0.5.13
3
3370
. 0,774
1.4856 "
0.431
4
3875
-0 .6 7 3
1 .1 1 6
0.366
. 5
4380 .
0 .6 0 5
0.929
0 ,3 2 4
SERIES
NO.
.10
4.
11
S e rie s #6
k = 7 .7 .1 x IO"4
%
t'
= 5 .3 3 5 x I O ^
1
#7
.
- 1 .5 5 0 x IO " 3
#9
= 1 ,6 6 8
x l.O"4
#10 -
= 4 .3 5 7 x IO "4
#11 ^
= .9 ,7 6
x IO "4
lb -s e c
TABLE IV :
EFFECT OF. BUBBLE SIZE .ON CONVERSION USING ROWE'S MODEL
Flow. R a te
(F.t'3/ s e c )
O„0416
0.000'1-92
B u b b le D ia m e te r ( f t )
'
0.1041
0.1667
0.8039
'0.8031
0,8027
-O„00074.5
0 .5 ) 6 9
0,5)45
0,5 ))7
,0.000990
0 .4 0 9 7 •
.0.4060
0.4048
0 „001290
0.3163
0.3127
0.3113
TABLE .V:
WU-o
OBSERVED AND CALCULATED. CARBON MONOXIDE .CONVERSIONS
O b serv ed
- R ow els
Babkm ix in i
E m u lsio n
P h a se
M odels
D a v id s o n 's M odels
P lu g Flow i n B ackm ix I r L P lu g .Flow 'In The E n t i r e . The E n t i r e
' R e a c to r as R e a c t o r a s
E m u lsio n
E m u lsio n
E m u ls io n
B ackm ix
P lu g Flow
P h a se
P h a se
P h ase.
.
.S E R I E S
N O .,
6, ‘
1 .2 0
, 0,8 5 0
0.7110
0.8559
0 .8 0 8 4
6.9525
0,828
- 0.991
1 .4 6 2
0.750
0.5864
0.6880
0.7659
0.9058
0,796
0.979
.2 .1 1 5
0.555
0.4105
0 .4 8 1 4
0.6869
0 .8 1 5 4
0.733
0.939
2 .6 5 0
0.420
0.5510
0 .5 8 7 4
0.6585
0.7 5 7 8
0 .6 8 0
.0 ,8 8 1
5 .1 4 0
0*250
0,2820
0.5296
0.6018
0 .7 1 5 6
0 .6 4 2
0.852
5.740
0.205
0.2584
0*2787
0.5625
0.6702
0 ,6 0 0
0.771
SER
IE S
N O ,,
7 .
1 .2 0 0 •
, 0.8 0 0
0.6594
0,8052
0 .7 1 6 8
0,-8806
0.730
0.934
1.462
-O.. 710
. 0.5 2 6 5
0 ,6 6 1 5
. 0 .6 6 7 5
0 ,8 0 1 0
0.690
6.892
1 .8 1 0
0.6 2 7
0.4262
0,5350
0.6145 '
0 .7 2 0 4
0.642
0,855
2 .1 1 5
0.530
0.5670
0,4.607
0.5763
.0 .6 6 5 6
0 .6 1 2
0.787
2 .4 0 0 .
0.455
0,5241
0.4065
0.5455
0,6222
0 :5 7 7
0 .7 4 4
2 .6 5 0
0.547
0.2950
0.5694
0.5 2 1 2
O.5896
0 .5 5 1
OVflO
■5.140
0 .5 0 0
0.2504
0.5132
.0 .4 8 1 4
0 ,5 5 7 0
0.499
0.648
TABLE V:
n/Uo
(continued.)
O b serv ed
Rowe1s
Backm ix I n
E m u lsio n
P h a se
M odels
P lu g Flow, i n
E m u lsio n
P h a se
D a v id s o n 's M o d e ls .
B ack m ix "i n P lu g F lo w i n
E m u lsio n
E m u lsio n
P h a se
P hase.
.8 E R I . E 3
The E n t i r e
R e a c to r as
Backm ix
The E n t i r e
R e a c to r a s
P lu g Flow
N 0. 8
2 .1 8 5
0,800
0 .4 2 9 7
0.4737
0.7376
0.8062
0.812
0.986
2 .4 5 0
0 .6 6 4
0.3860
0 .4 2 5 2
0.7162
O.78II
0.793
0.978
2.730
0.604
0.3492
0 .3 8 4 4
0.6952
.0.7568
0 .7 7 4
0.967
3.000
0,535
0.3189
0.3533
0.6750
0.7302
0 .7 5 7
0.955
3.230
0.497
0,3019
0.3296
0 .6 6 6 8
0.7269
0 .7 4 3
0 .9 4 4
3.785
0.450
0.2605
0,2859
0.6338
0.6855
O . 7 I .2
0.915
4 .2 5 0
0 .4 0 0
0.2350
0.2578
0,5986
0 .6 4 7 1 "
.0.689
0.889
. S E R I
ES
N 0;
-9
. . .
0.875
0.721
1.095
0.555
0.4596
0.6068
0.4678
0,5846
0 .4 8 1
0.602
1.350
0.450
0.3731
0.4917
0.3986
0 ,4 8 4 1
0 .4 2 8
0.528
1,675
0 .3 4 7
0 .3 0 1 1
0.3965
0.3385
0.3991
0.377
. 0.4 5 6
1 .9 5 0
0,280
0 .2 5 8 7
0.3409
0.3015
0,3483
0 .3 4 1
0.408
0 .7 2 7
■TABLE V-:
n/Ho
(con tin u ed )
O b serv ed
Rowe1s . M odels,
Ba'ckmix I n P lu g Flow i n
E m u lsio n
E m u lsio n
P h a se .
P h a se
D a v id s o n 's M odels
B ackm ix I n P lu g Flow i n
E m u isio n
E m u lsio n
P h a se
P h a se
' . . SERI ES
NO.
The E n t i r e
R e a c to r as
Backm ix
The E n t i r e
R e a c to r as
P lu g Flow
10
1,200
O . 72 O
0,5681
0.7352
0 ,6 1 2 4
0.7071
0.638
0.830
1 .4 6 2
0.574
0.4690
0,69$Q
0 .5 4 8 6
0,6068
0.592
.0.766
1 .8 1 0
0 .4 9 0
0.3780
0.4888
0.4863
0,5158
0.539
0 .6 7 7
2 .1 1 5
0*415
0.3250
0 .4 2 0 6
0 .4 4 5 4
0.4590
0 .4 9 9
-0 .6 3 1
.2 ,4 0 0
0,365
0.2869
0.3709
0 .4 1 4 0
0 .4 1 7 1
' 0*468
O.582
2*650
0 ,3 2 4
0*2607
0.3368
0.39P9
0.3875
0.443
0 .5 4 8
.S E R I E S N
...
.Q.
.11
1 .0 6 6
O.88O
0.6734
0.8639
0.6972
0 .9 2 4 0
0.699
0,905
1 .2 7 5
0.7 4 5
0.5672
0.7268
0.6510
,0 ,8 448
0 .6 6 0
0.860
1.4.20
■0.631
0^5123
0,6565
0 .6158
0,7943
0 ,6 3 6
0.8 2 9
1 ,5 7 2
0.5 1 0
.0 ,4 6 4 7
0;5943
O.5885
4.7^26
0 .6 1 2
-0,793 .
1 .8 4 5
0.373
.0.3988
0;5095
0.5473
0*6918
0.572
0*742
2 ,1 1 5
0.300
0^3513
0 ,4 4 8 2
0.5122
0.6426
0 ,5 4 0
0.694
2 .3 7 0
0.270
0 .3 1 5 1
0.4013
0 .4 8 3 4
0.6 0 3 0
0 .5 1 1
0.659
TABLE .VI ;
S e rie s
No.
EPEECT OP CLOUD SIZE ON -CONVERSION USING- ROWE ’ S" MODEL "WITH
PLUG PLOW IN .THE EMULSION PHASE
# 0
D ia m e te r ■o f 'C lo u d /p la m e te f r o f B u b b le ( d c/
1 .0 0 1
'
'
■ IV l " ‘
1 ,2
'
' 1 .3
1 .4 '
)
1 .5
i.200
0,8335
0,834$
0.8360
0,8368
9.8374
0.8378
1.462
. 0 , 6874 :
0.6$00
0.6$20
0.6535
0,6$46
0.6555
2.115
,0 ,4 8 0 4 '
.0.4848.
0.4881
■ ..0 .4 9 0 6
0.4925
0.4939
.2,650
O.3862
0,3$15 .
0\3$53
0,3583
O.40O5
0 .4022
3 .1 4 0
0,3283
0.3341
0.3383 .
0.3415
0,3435
0,3458
J.TitO
0 ,2 7 7 4
0.28-35 :
0.2881
0.02536
0.2915
0,02605
0.2941
0.02663
0.2962
0.8046
O.8051
0.8055
. 0.8057
6
-.9.0236$.
1 .2 0 0
.0.8031
. 0 ,0 2455
i 1
> T' 'L'
.0 ,8 0 4 0
1,462
0.6613
0.662$
0.6641
0,6651
.0.6657
0.6662
1 ,8 1 0 ■
0.5347
0.5370
Q .!# 6 7
0 ,5 4 0 1
0,-5409
0.5417
2 .1 1 5
0.4604
0.4631
.0.4,652
.0,4-668
0.4678
0.4687
2,4.00
0 .40,02
.0.4092 .
0 .4 1 1 4
■0.4132
.0 ,4 1 4 4
0.4153
2,65.0
O.369.O
0.3722
0,3746
0.3765
0.3778
0.3788
3.140
0.3.12$
0.0187 '
P-.3164- . .
0.3150
. -»*-• • ■
0,3211.
• 0 .3 2 2 4
0.3236
0 ,1 7 1 5
0.01668
8 ,8 . '
0 .0 2 7 1 1
7
s.s
0.1780
... . .
0.01635
-0.01611
TABLE .VI:
S e rie s
No.
(continued)
VDo
1 .5
0.4730
0.4809
0.4869
.0 .4 914
0.4948
0 ,4 9 7 4
2 .4 5 0
0.4243
,0.4331
0.4396
0 ,4 4 4 5
0.4482
0.4511
2.730
0.3834
0,3929
0,3999
0 .4 0 5 1
0.4091
0 .4 1 2 1
5.000
0,3523
0.3622
0.3696
0,3751
0.3793
0.3825
3.230
0.3285
0.3388
0 .3 4 6 4
0,3521
0.3564
0.3598
3.7Q5
0 ,2 8 4 8
0.2957
0.3039
0.3099
0.3145
0.3180
4 .2 5 0
0.2566
O.268O'.
0,2764
0 .2 8 2 7
0.2875
0.2912
0.3227
0.29577
0.2766
0.2628
0.2527
0 .2 4 5 1
1,095
.0.606P
0.60(69
0,6070
0.6070
0.6071
0.6071
1,350
0,4917
0.4920
0 .4 9 2 2
.0 ,4 9 2 4
, 0 .4 9 2 5
0 ,4 9 2 7
1 .6 7 5
0 .3 9 6 4
0.3969
0.3973
.0.3975
0.3978
0.3979
1,950
0.3408
0 .3 4 1 4
0 .3 4 1 9
0 .4 3 2 2
0.3425
0.3427
0.01084
0.01093
0.01101
0.01107
S 9S 0
s .s .
1.001
2 ;1 8 5
8
9
D ia m e te r o f C lo u d /D ian re t.e r o f B u b b le ( d c /d ^ )
1 .4
' 1 .1
1,2
1 .3
O.OIO 56
■ W f — i p . — . . . . . . . . . . . . . . . . . . . ..
.
0.01072
............
.
r .
-I r
r , > , - . r T M-
(con tin u ed )
S e rie s
No.
n/n<)
1.001
0.7351
0.7357
0.7361
0.7365
0.7367
0.7369
1 .4 6 2
0.60 4 9
0.6060
0,6068
O.6O74
0.6079
0,6083
1 ,8 1 0
0.4887
0.4902
0 .4 9 1 4
.0.4923
0.4929
0 .4 9 3 4
2 .1 1 5
0 .4 2 0 5
0.4223
0.4237
0.4247
0.4255
0.4261
2 .4 0 0
0,3707
0,3727
0 .3 7 4 2
0,3754
0.3762
0.3769
2,650
0.3366
0.3387
0 .3 4 0 4
0 .3 4 1 6
0 .3 4 2 5
0.3432
0 .0 0 1 4
0.001603
O.OOI77
0.001908
0.002021
.0.002112
1 ,0 6 6
0,8638
0 .8 6 4 4
0.8649
0.8653
0.8655
O.8658
1 .2 7 5
0.7263
Q.7285
0.7302
0 .7 3 1 4
0.7323
O.733I
1 .4 2 0
0.6558
0.6588
0 .6 6 1 0
0.6627
0.6640
0 .6650
1 .5 7 2
0.5935
0,5971
0.5998
0 .6 0 1 9
0 .6 0 3 5
0 .6 0 4 7
.
1 ,8 4 5
0.5085
0 .5 1 3 1
0 .5 1 6 5
0.5191
0 .5211
0.5226
■
2 .1 1 5
0 .4 4 7 0
.0 ,4 5 2 3
Q.4563
0.4592
0 .4 6 1 5
0.4632
2 .3 7 0
0 .4 0 0 0
0.4058
0 .4 1 0 2
0 .4 1 3 4
0 ,4 1 5 9
0 ,4 1 7 8
0.06507
0.07165
0 .0 7 4 1 2
O.07717
0.07953.
0.08138
S.S.
11
S .S .
1 .5
1 ,2 0 0
10
'
D ia m e te r o f C lp u d /D ia m e te r o f B u b b le (d ^ /d ^ )
1 .4
1 . 1'
1 .3
1.2
- 6 9 ’“
TABLE .VI:
TABLE V I I :
S e rie s
No.
6
EFFECT OF CLOUD SIZE .ON CONVERSION USING ROWE'S MODEL
WITH BACKMIZING IN .THE EMULSION PHASE
1 .0 1
1 .1
1 .2
' 1 .3
1 .4
<<Vdt,L
1 .5
0.7 1 1 0
0 .7 1 2 2
0.7133
0 .7 1 4 0
.0 .7 1 4 6
O.7151
1 .4 6 2
.0 ,5 8 6 4
O.5887
0,5907
0 .5 9 2 2
0.5932
0 .5 9 4 1
2 .1 1 5
0 .4 1 0 6
0 .4 1 4 5
0.4 1 7 7
0 .4 2 0 4
0 .4 2 2 0
0 .4 2 3 5
2.650
0.3307
0.3354
0 .3 3 9 2
0 .3 4 2 3
0 .3 4 4 3
0.3460
5 .140
0.2817
0.2868
0.2910
•0.2944
0.2966
0.2983
3.740
0.2385
0 .2 4 3 9
0 .2 4 8 5
0 .2 5 2 1
.0 .2 5 4 4
0 ,2 5 6 4
0 .0 7 2 5 5
0.07058
0.06907
0.06796
0.06731
0.06677
1 .2 0 0
0.6394
0 .6 4 0 1
.0 .6 4 0 8
0,-6412
0.6416
0 .6 4 1 9
1 ,4 6 2
0.5263
0 .5 2 7 7
0,5289
0.5298
0.5305
0 .5 3 1 0
1.810
0.4262
0.4284
0 .4 2 9 9
•0.4312
0 .4 3 2 2
0.4329
2 .1 1 5
0.3669
0.3695
0.3713
0.3728
0.3739
0 .3 7 4 8
2 .4 0 0
0 .3 2 4 1
0.3269
0.3289
0.3306
0 .3 3 1 8
0.332B
2.650
0 .2 9 4 7
0 .2 9 7 7
0.2998
0.3016 '
0 .3 0 2 9
0 ,3 0 4 0
3 .1 4 0
0 ,2 5 0 4
0.2537
0.2 5 6 0
0 .2 5 7 9
0 .2 5 9 4
0 .2605
0 .1 4 8 8
0 .1 4 5 2
0 .1 4 2 2
0 .1 4 0 0
0 .1 3 8 4 '
0.1371
-7 0 -
S .S .
'
1 .2 0 0
S .S .
7I
D ia m e te r o f t h e C lo u d /D ia m e te r o f t h e B u b b le
u /u 0
TABLE V I I :
S e rie s
No.
8
( c o n tin u e d )
S .S .
1 .1
1 . 0 1 ''
1 .2
1 .3
1 .4
' 1 .5
2 .1 8 5
0.4297
0.4368
0 ,4 4 2 8
0,4472
0.4506
0.4532
2 .4 5 0
0.3860
0.3938
0 .4 0 0 3
0 .4 0 5 2
0.4089
0 .4 1 1 8
2.730
0.3492
0,3576
0.3646
0.3698
0.3737
0.3767
3.000
0.3212
0.3300
0.3373
' 0 ,'3428
.0.3469
0.3501
.3.230
0,2998
0.3089 .
0,5165
0 .3 2 2 2
0.3264
0.3297
3,785
0 ,2 6 0 4
0.2 7 0 1
0.2 7 8 2
0 .2 8 4 2
0.2888
0.2923
4 .2 5 0
0.235P
0 ,2 4 5 1
0.2535
.0.2598
0 .2 6 4 5
0.2682
. 0,427.12
0,3993
0 .3 7 7 0
0:3609
0:3490
0 .'3400
1,095
0.4596
0.4597
■0.4598
p;4599
0.4599
0.4599
1 . 3.50
0 .3 7 3 1
0,3737
0:3739
0 .3 7 4 1
0 .3 7 4 2
1 ,6 7 5
0.3011
0.5016
0,3020
0.3023
.0.3026
0.3027
1.950
.0.2587
0.2594 -
0.2598
0 .2 6 0 2
0.2605
0.2607
0.01742
0.01731
.0.01723
0.01716
0.01711
S .S .
yQ
D ia m e te r o f t h e C lo u d /D ia m e te r o f t h e B u b b le (d c / d b )
n/n<)
0 .0 1 7 5 7
•
0 .3 7 3 4
;■
■TABLE .V II:
Series
No,
(continued)
Diameter of the Cloud/Diameter of Bubble (dcdb)
U/Uo
1 .4
1 .0 1
1 .1
1 .2 0 0
0,5681
0 ,5 6 8 6
0,-5691
0,5694
0.5697
0.5699
1 .4 6 2
0 ,4 6 7 1
0,4681
0.4689
0.4695
0 .4 7 0 0
0.4705
1,8 1 0
0.5780
0.5794
0/5806
0.5815
0.5822
0.5827
2 .1 1 5
0,5250
0,5267
0.5281
0.3291
0.5299
0.5505
2 .4 0 0
0.2869
0.2 8 8 7
0.2902
0 ,2 9 1 4
0.2925
0.2930
2,650
0,2607
0.2626
0.2645
0,2655
0.2665
0,2672
.0.06525
0.06574
'0'.'06249
0.06157
0.06086
0,0605
1.066
0 .6 7 5 4
0.6759
0 .6 7 4 4
0.6748
0.6751
0.6753
1 .2 7 5
0,5670
0,5690
" 0.5706-
0.5719
0 .5728
0.5735
1 ,4 2 0
0 .5 1 2 1
0.5 1 4 7
"0.5169
0.5186
0.5199
0.5209
1 .5 7 2
0,4645
0.4676
0 .4 7 0 4
0 .4 7 2 4
0.4740
0.4752
1 .8 4 5
0.5985
0 .4 0 2 4
0.4059
0 .4 0 8 4
■0.4104
■0.4119
2 .1 1 5
0.5507
0 .5 5 5 4
'0,5594
0,5624
0.5647
0 .3 6 6 4
2 .5 7 0
0,5144
0.5197
0.09515
0.5240
0 .3 2 7 2
0.5298
0.3317
0.09476
0 .0 9 4 5 5
0 .0 9 4 4 4
0.09438
1 .2
'
1 .5
10
SeSe
11
S.S.
0.09578
'
1 .5
■TABLE .V III:,
S e rie s
No,
SUM .OF THE SQUARES OF ERRORS FOR THE BEST F IT DATA USING'THE .MODELS OF ROWE
HAVING NONE, ONE AND TWO UNDETERMINED -PARAMETERS
Best' F i t Data .Using
as V a ria b le
P lu g Flow i n
t h e E m u lsio n
P h ase ■
B ackm ixi n g ­
i n t h e Em ul­
s i o n P h a se
6
0 .Q23770
0.07255
0.023690
0.072550
0.02369
7
0.018659
0 .1 4 8 7 7
0 .0 1 6 1 1 4
0.013710
0 .01611
8
0 .3 2 1 6 4 0
0.42862
0.245070
0.340000
0.24507
9
0,015810
0.01755
O.OIO 56 O ■
O .O I 7570
0 .0 0 3 4 2
.. 10
0 .0 0 1 4 2 8
0.06525
0 .0 0 1 4 0 9
0.065250
0 ,0 0 0 7 4
^
11
0,065590
0.09578
0 .0 6 5 0 7 0
0.095780
0.04673
'
P lu g Flow i n
E m u lsio n P h a se
B ack m ix in g
i n E m u lsio n
P h a se
B e s t F i t D a ta U s in g G0Zd l3
and D i f f u s i o n C o e f f i c i e n t
a s V a r ia b l e
TABLE IX-:
S e rie s
Io „
CLOUD TO BUBBLE DIAMETER RATIO AND DIFFUSION COEFFICIENT -VALUES FOR
THE BEST FIT DATA USING THE .MODELS OF ROWE
No U n d e te rm in a te P a r a m e te r s
P lu g Flow
B ackm ixlng
i n E- p h a s e
i n E- p h a s e
dc/ d and D a s U n d e te r ­
m in a te P a r a m e te r s
P lu g Flow I n E- p h a s e
D
dc/db
dc/ d ’ a s ' U n d e te rm in a te
P a r a m e te r s
P lu g Flow
B ack m ix in g
I n E- p h a s e
i n E- p h a s e
^oAb
Vdb
4c/db
6
1.010
1.010
1.001
I ".500
1.001
0 .0 0 0 0
7
1 .0 1 2
1 .0 1 2
1.500
1 .500
1.500
0 .0 0 0 0
8
1 .0 1 2
1.012
1 .5 0 0
1 . 5GQ
1 .5 0 0
0.0000
9
1 .0 1 2
1 .0 1 2
1 .0 0 1
1 .5 0 0
1 .0 0 1
0.0,001
10
1 .0 1 5
1 .0 1 5
1 .0 0 1
1 .5 0 0
1.001
O.OO'Ol
. 11
1 .0 1 0
1 ,0 1 0
1 .0 0 1
1.500
1 .0 0 1
.0.0050
■
—C
-F
I
TABLE Xi
EFFECT OF NUMBER OF TRANSFER .UNITS ON CONVERSION USING THE .MODEL .OF
DAVIDSON AND HARRISON WITH BACEMIX IN THE EMULSION PHASE
Number .o f T r a n s f e r U n i t s , X
S e rie s
No,
5
B est F it x
x ■= 0 .1 5
0 ,1
1 ,2 0 0
0 ,7 2 4 4
0.7 1 9 2
0.7469
0 .7 6 7 1
O . 782 O
0.7929
1 .4 6 2
0.6 1 2 6
0.6027
0 .6 5 4 4
0.6916
0.7186
0.7385
2 „115
0 ,4 5 3 4
0.4 3 7 4
0 .5 2 0 1
0,5775
0 . 6l 80
0 .6 4 7 1
2,650
0.3809
0.3623
O.4571 ,
.0.5209
0.5651
0.5963
3 ,1 4 0
0.3361
0.3160
0,4169
0.4832
0.5283
0.5597
3 .7 4 0
0.2962
0.2750
0.3798
0,44.66
0.4912
0 .5 2 1 8
0.06097
0.06276
0 .0 8 4 4 4
0 .1 4 1 5
0.2006
0.2520
0.6848
0.6464
0.6686
0 ,6 8 4 8
0.6967
0.7053
1 .4 6 2
0.6113
0 .5 4 0 8
0,5820
0 .6 1 1 3
0.6323
.0 .6 4 7 5
1 .8 1 0
0 ,5 4 2 2
0.4465
0,5032
,0 .5 4 2 2
0,5697
0^5892
2 .1 1 5
0.4984
0.3905
0 .4 5 5 1
0 .4 9 8 4
0.5283
0 .5 4 9 4
2 .4 0 0
0 .4 6 5 2
0 .3 4 9 8
0.4196
0.4652
0.4963
0 .5 1 7 9
2,650
0 .4 4 1 2
0 .3 2 1 8
0,3945
0 .4 4 1 2
0.4725
0 .4 9 4 1
3 .1 4 0
0 ,4 0 3 4
0 .2 7 9 8
0.3 5 6 1
0 ,4 0 3 4
0.4543
0 .4 5 5 4
0.0508
0 .1 1 6 4
0.0612
0.0508
O.O 5551
0 .0 6 4 4 2
u /o 0
S »S 6
0 ,4
0.7
1.0
1 .3
x .= 0 .7
1 .2 0 0
7
SeSe
.
TABIiE X:
(contInued)
Number o f T ran sfer U n it s y.x
Series
-No..
8
n/Uo
Best Fit x
x.
-0 .7 4 _
0 .1 .
.0 .4
0 ,7
1 .0
1 .3
-
2 .1 8 5
0 .6 3 2 2
0 .4 5 5 5
0 .5 5 4 5
0 .6 2 4 5
0 .6 7 4 8
0.7112
2 .4 5 0
0 .6 0 4 6
0 .4 1 4 2
. Q ,5213
0 ,5 9 6 4
0 .6 4 9 8
0 .6 8 8 3
2 ,7 3 0
0 .5 7 9 6
0 .3 7 9 2
0 ,4 9 2 4
0 .5 7 1 1
0 .6 2 6 7
0 .6 6 6 4
3 ,0 0 0
0 .5 6 0 1
0 .3 4 9 5
0 .4 6 5 0
0.5518
0 .6 0 8 3
0 .6 4 4 6
3 ,2 3 0
0 .5 4 4 8
0 .3 3 5 0
0 ,4 5 8 4
0 .5 3 5 9
0 .5 9 3 5
0 .6 3 8 5
3 .7 8 5
0 .5 1 4 4
0 .2 9 4 7
0 ,4209
0.5Q 54
0 .5 6 3 6
0 .6 0 4 6
4 ,2 5 0
0 ,4 8 5 0
0 .2 6 7 9
0 .3 9 3 8
0 .4 7 6 2
0 .5 5 2 2
0 .5 7 1 1
0 .0 4 6 5 5
0 .3 3 2 1
0 ,0 9 9 6 7
0 .0 6 1 4 6
0 ,0 9 7 6 3
.
B
s .s .
' b .0 4 7 0 9
On
I
x = .1 ,1 5
.q
y
s.s.
1 .0 9 5
0 .4 7 3 1
0 .4 6 0 8
0 .4 6 5 8
0 ,4 6 9 4
0 .4 7 2 0
0 .4 7 4 0
1 .3 5 0
0 .4 1 2 7
0 .3 7 8 6
0 .3 9 3 0
0 .4 0 3 0
0 .4 1 0 0
0 .4 1 5 0
1 .6 7 5
0 .3 5 7 2
0 .3 0 9 7
0 .3 3 0 6
0 .3 4 4 4
0 .3 5 3 7
0 ,3 6 0 1
1 .9 5 0
0 ,3 2 1 4
0 .2 6 8 8
0 .2 9 2 8
0 .3 0 7 8
0 .3 1 7 7
0 .3 2 4 5
O.OO9918
0 .0 1 5 4 8
0 .0 1 2 0
0 ,0 1032
0 .0 0 9 9 5
0 .0 0 9 9 3 8
-TABLE X:
(continued)
Number o f T ra n sfer U n its i x
S e rie s
Wo, ■
n/Uo
B est F i t x
.*.= -0.75..
. 0.1
0 .4
0.7
1 .0
1 .3
1 .2 0 0
0,6 0 5 4
0.5736
0 ,5 9 1 1
.0 .6 0 3 7
0.6129
0.6196
1 ,4 6 2
0.5359
0 .4 7 8 5
0 .5 1 0 5
0.5329
0.5488
-4.5602
1 .8 1 0
0 .4 7 1 0
0.3942
0 .4 3 7 8
0 .4 6 7 1
0.4873
0,5016
2 .1 1 5
0 ,4 2 9 1
. 0.3458
0 .3 9 3 0
0.4249
0 .4 4 6 4
2 .4 0 0
0.3974
0.3074
073600.
0.3931
.0 .4 1 5 0
0.4300
2,650
O.3744
0.2823
0,3367
0 ,3 7 0 1
.0.3919
0.4067
. 0 ,0 1872
.0.04982
0 ,0 2 4 0 4
’ 0 ,0 1 8 7 5
0 .0 2 0 2 2
0 .0 2 4 2 4
10
4
s.s.
'
0 .4 6 1 4
.:x = 0 ,1 5
11
s.s. ’
1 .0 6 6
0,6759
0.6 7 4 4
0.6 8 2 2
0.6879
0.6922
0.6953
1 .2 7 5
0.5822
0.5733
0 .6 0 3 1
0 .6 2 1 6
0,6351
0.6449
1 .4 2 0
.0.5270
0 .5 2 0 5
0 ,5 5 4 4
0 ,5 7 8 4
0.5956
0.6081
1 .5 7 2
0 .4 8 2 7
0.4747
0:5159
0.5446
0.5649
0.5795
1 .8 4 5
0 ,4 2 1 9
0 .4 1 2 0
.0.4624
D.4966
0,5203
0,5370
2 .1 1 5
0,3768
0.3657
0 ,4 2 1 7
0 ,4 5 8 7
0 .4 8 3 9
0 ,5 0 1 5
2.370
0.3426
0.3306
0,3905
0.4289
0,4548
0.4-727
0.09269
0.09285
O .I O I 51
0.12052
0.13984
0.15651
TABLE X I j
EFFECT OF EUHBER .OF TRANSFER .UNITS ON CONVERSION USING THE MODEL OF
DAVIDSON AND HARRISON WITH'PLUG FLOW IN THE EMULSION PHASE '
______ , .
Series
No.,
_______ Number o f T r a n s f e r U n i t s , x
Best F it x
- x = 0.0 .. ';. o . i
Vu-O
■■■??"■■■ ■■: '
- 0;3. .I-.
-0,5
. 0 , 7.
■ 0 .9 .
-
i
I ..200
0.,83Q
0 ,8 4 4 2
.0.8649
0.8821
0.8968
!.,462
.0.681
O.7054
0,7439
0,7759
0,8030
0,8260
0.472
.O.5O85
0 „ 570.8
,0.6215
-0 ,6 6 3 4
0 .69.84
0.376
0.4.189
0 . 490.9
■ 0 .5 4 8 4
0.5953
0.6539
0.5 1 8
0,3637
o ,4 4 il
-0,50.18
0 .5 5 0 6
0,5903
.0.266
0,3149
0.3962
0.4586
0.02306
0,03275
0.086&2
•- - -
0 .1 6 2 2 "
2 .1 1 5
6
2,650
3.740
. •- - -•- - •;
S.S .
S.S.
o;5o80
'
-" 0.2446
-
0 . 54-77 ■
0.3263
x .= Of 164
-
7
•
0,9094
■
I.200
0.8127
0,8 0 8 3
0.8212
0.8324
0 .8 4 2 1
.0.8506
1.462
.0.6798
0.6 7 1 7
0.6957
0.7162
0.7338
'0 .7 4 8 9
1 ,8 1 0
,0,5610
,0,5496
0,5830
0,6109
0,6345
-0.6544
2.115
0 .4 9 0 6
0.4775
0.5158
0,5473
■0,5734
0,5952
2 .4 0 0
0,43-94
0,4251
0 . 4-667
0,5004
0.5279
Oi55Q7
2,650
0.4041
0,3890
0 .4 3 2 7
0.4676
0#4957
Q.5187
3,140
,0.3510
0.01310
0.3348
0.3813
0 ,4 1 7 4
0,4459,
0,4688
0. OlUIT
0 .0 1 6 8 9
0 .0 3 2 0 4
0.05301
---
-
. 0 .07621 '
TABLE XI; : (con tin u ed )
Number o f , T ran sfer U n it s , ,x
S e rie s
NO' :
n/Uo
8
...
•B e s t P i t x
. x .= O . 59 O
0 .1
0 .3
0 .5
.
0 .7
.
0 .9
2 .1 8 5
0 .6 4 7 8
0 .4 9 8 5
0 .5 6 8 2
0 .6 2 5 4
Q.6727
0 .7120
2 .4 5 0
0 .6 1 5 2
0 .4 5 2 2
0 ,5 2 7 7
0 ,5 8 9 3
0 .6 3 9 8
0 „ 6816
2 .7 )0
0 ,5 8 2 9
0 .4 1 3 1
0 .4 9 3 2
0 ,5 5 7 9
0.6107
0.6540
3.000
0 .5 5 4 2
0 .3 8 2 3
0 .4 6 3 8
0 ,5 2 9 1
0 .5 8 1 9
0.6252
3 .2 5 0
.0 .5 4 6 3
0 .3 6 1 7
0 .4 4 9 4
0 .5 1 9 4
0 .5 7 5 9
0 .6221
).7 8 5
0 ,5 0 5 7
0 .3 1 8 7
0 .4 0 8 5
0 ,4 7 8 9
0 .5 3 5 1
0 .5 8 0 5
4 .2 5 0
0 .4 7 5 3
0 .2 9 0 4
0 .3 8 0 0
0 ,4 4 9 2
0 .5 0 3 7
0 .5 4 7 3
0 .0 3 7 5 0
0 .2 4 1 9 6
0 .0 9 3 4 5
0 .0 4 1 6 6
0 .0 4 3 0 6
0 .0 7 3 3 2
0 ,5 8 4 2
0 .5 8 5 5
0 ,5 8 6 6
S ,S .
x . = 0 .0
1 .0 9 5
O .58I
0.5812
0 .5 8 2 8
.
1 .3 5 0
0 .4 7 0
0 .4 7 4 1
. 0 .4 7 8 9
0 i.4830
0 .4 8 6 7
0 .4 8 9 9
1 ,6 7 5
-0 .3 7 9
0 .3 8 4 1
0 .3 9 1 4
0 .3 9 7 5
0.4028
0 .4 0 7 3
1 .9 5 0
0 .3 2 5
0 .3 3 0 9
0 .3 3 9 5
0 .3 4 6 5
0 .3 5 2 5
0 .3 5 7 5 .
0 .0 0 4 1 7
0 .0 0 5 2 4
0 .0 0 7 1 1
0 .0 0 8 9 3
0 .0 1 6 5
0 .0 1 2 2 4
Q
s . s .
•TABLE X I:
( c bnt lim ed )
Number.of T ran sfer U n it s , x
S e rie s
No,
%/0o
B est F i t x
x .= 0 .277
1 .2 0 0
O.6898
0 .6 8 4 1
0 .6 9 0 5
6961
1 .4 6 2
0 .5 7 5 8
0 .5 6 5 2
0 .5 7 7 1
.O..5874
1 .8 1 0
0 .4 7 4 9
0 .4 6 0 1
0 .4 7 6 6
2 .1 1 5
0 .4 1 4 1
0 .3 9 7 3
2 .4 0 0
0 .3 7 0 2
2 .6 5 0
0 .3 3 9 9
0 .1
0 .3
01,7
•0.5
.
0 .9
0 ,7011
0 .7 0 5 5
0.5,962
0 .6 0 3 9
0 .4 9 0 5
0.5022
0.5122
■0.41.61
0 .4 3 1 6
0*4444
0.35<20
0 .3 5 2 0
.0 ,3 7 2 3
0 ;3 8 8 8
0 .4 0 2 1
0 .3 2 0 8
0 ,3 4 2 1
0 .3 5 9 0
0 .3 7 2 5
0 .3 8 3 6
0 .0 0 2 7 4 8
0 ,0 0 1 4 4 2
0,002817
0.005607
0 .0 0 9 0 7 8
.
10
S .S .
,0 .0 0 1 4 2 4
.
x ■= 0 .0
11
SeSe
•
0 .4 5 5 0
oo
0
1
-
1 .0 6 6
. 0 .8 9 1
O.8989
0 .9 0 3 9
0 ,9 0 8 3
0 .9 1 2 1
.0 .9 1 5 5
1 .2 7 5
0 ,7 4 7
O.7627
0 .7 7 9 6
0 .7 9 4 1
0 .8 0 6 8
O.8178
1 .4 2 0
0 .6 7 2
0 .6 8 8 2
0 .7 1 0 4
0 .7 2 9 4
O.7457
,0 .7 5 9 9
1 .5 7 2
0 .6 0 5
0 .6 2 5 3
0 ,6 5 2 4
0 ,6 7 5 5
0 .6 9 5 2
0 .7121
1 .8 4 5
•0 ,5 1 6
0 .5 3 9 3
0 ,5 7 3 0
0 .6 0 1 1
0 .6 2 4 8
0 .6 4 4 8
2 .1 1 5
0 ,4 5 2
0 .4 7 6 5
0,5.143
0 .5 4 5 4
0 .5 7 1 3
0 .5 9 2 9
2 .2 7 0
0 .4 0 2
0.42&7
0 .4 6 9 5
0 .5 0 2 7
0 .5 2 9 8
0 .5 5 2 2
0 .0 7 1 9 5
0 .0 9 9 9 9
0 .1 5 2 5
0 .2 0 4 9
0 .2 5 4 7
0 .3 0 1 0 6
-
-TABLE XU-:
S e rie s
No.
SUM OF THE SQUARES OF ERRORS FOR THE BEST F IT DATA USING THE-MODELS
OF DAEIDSON AND HARRISON WITH NONE, ONE, AND TWO UNDETERMINED PARAMETERS
P lu g Flow i n
t h e E m u lsio n
P h a se
B ack m ixing i n
th e E m u lsio n
P hase
B e s t F i t D a ta U s in g
x a s V a r ia b l e ,
P lu g Flow- i n
B a c k m ix in g i n
t h e E m u lsio n
t h e E m u lsio n
-P h a s e .
P h a se
B e s t F i t D a ta f o r U s in g
x and D i f f u s i o n C o e ffie c ie n ts as V a ria b le s
6
0 .6 7 3 9 9
0 .3 3 4 1 9
0 .0 2 2 5 4 0
0 .0 6 0 9 7 0
0 .0 2 2 5 4 0
7
0.18502
0 .0 8 2 4 7
0.0131Q 0
0 . 050850 '
0 .0 1 3 1 0 0
8
■0..,24471
0 .1 3 6 6 8
0 ,0 3 7 5 1 0
0 .0 4 6 5 5 0
0 .0 3 7 5 1 0
9
0.00943
0.Q1077
0 „004.170 ■
0 .0 0 9 9 1 8
O.OOO785
10
0 ,0 2 0 6 2
.0 .0 2 0 0 6
0 .0 0 2 4 2 5
0,018720
0 ,0 0 1 3 4 1
11
0 .4 2 4 8
0 .1 6 7 9 5
0.071950
0 .0 9 2 6 9 0
0 ,0 4 6 3 4 0
H
I
'T able
CO
% .
No
x iii;
. number of tra n sfer u n it s and d i f f u s i o n - c o e f f i c i e n t s ■values
DATA USING THE MODELS OF DAVIDSON AND HARRISON
Np U n d e te rm in a te .
P a ra m e te rs
P lu g Flow
B a ck m ix irig .
i n E -p h a s e
iri E -p h a s e
•X
X
x a s U n d e te rm in a te
P a r a m e te r
B ack m ix in g
P lu g Flow
i n E -p h a s e
i n E -p h a s e
X
X
for the b e s t f i t
x arid D a s . U ndetersm in a te P a r a m e te r s
P lu g Flow i n E -P h a s e
X
D
6
1(988
1.9 8 8
0 .0 0 0
0 .1 5 0
0 .0 0 0
0 .0 0 0 0
7
1 .9 ) 5
1 .9 ) 5
■0.164
0 .7 0 0
0 ,1 9 0
0 .0 0 0 0
8
i.6 o o
1 .6 0 0
0 .5 9 0
0 .7 5 0
0 .5 7 0
0 .0 0 0 0
9
Q .557
0 .5 5 7
0 .0 0 0
1 .2 5 0
0 .0 0 2
. 0 ,0 0 1 5
10
0 .9 8 )
0 .9 8 3
0 .2 7 7
0 .7 5 0
0 .0 0 2
0 .0 0 1 5
Ii
1 .5 5 0
1 .5 5 0
0 .0 0 0
0 .1 5 0
0 .0 0 1
0 .0 0 2 5
.CO
PO
-.83-
TABLE XIV:
FORTRAN PROGRAM FOR ROWE'S MODEL CALCULATION WITH PLUG FLOW
IN THE EMULSION PHASE
DIMENSION B(7) ,QQ(T)-.YYA(T)
3 RE AD SljiXMA X,XM INiDX
31 FORMAT(SFlOoO)
; X= XM IN
READ32,H,RHQG,GAO,B ILLSN,VELK,FE,W,DB
32 FORMAT(SFlOoO)
;
RE AD 3-3 s N
33 FORMAT(12)
REAb 3A, (B(K) ,QQ(K) »YYA(|<) ,K = I s N)
6T3 SUM=OoO
' 004831=1,N
" BETA=B(I)
Q=QQ( I I
YAGT = YYAf I )
34 FORMAT(3F10o0 )
DC=X-K-DB
'
Up = O oT8 -KSQRT F ( 16ol*DB) '
VB-3ol415926*DB**3/6o0
Ve=3ol415926*DC**3/6d0
WSC^AS o0* (VC- (2 ok-VB/3 o ) )
W G C = ((2o*VB/3,1+o776*(VC-(2.*VB/3.
I)))*RHOG*BILLSN
FB=Q-KBETAZVC - "
Y Ii I'dO-^EXPF (-VELKXCAO-K- (W-FB-K-WSC )/ FE )
Y€=l*-EXPF(-28b*VELK*CA0*WSC#H/(WGC*UB))
• Y = (Io-BETA)*YI+BETA^YC"
DIF=Y-YACT ■' 1
SUM= SUM+DI F-K-^-2 483 PR INT 3 82'» Y »YACTi5BET A,Q, Dl F
382 FORMAT!5H Y-= ,E 14.T »8H 'YACT = »E14oT, •
18H: BETA '
-= ' iF10o6 »5H Q = »E14oT»TH DIF=»E14oT)
PR INT43'» X ,SUM
’
X=XfDX
IF (X-XMAX)673,673,313
43 FORNiATt 5H X = ,Fi0o6,7 H S S = ,E14.7,//)
313 PR LNT74»H»RHOG»CAO,BILLSN»VELK»FE,WtDB
G O 'TO 3 '
74 FORMAT(16H .PARAMETERS ARE ,8(2 X »E14o7) )
END
-,8 4 )
FORTRAN PROGRAM FOR ROWE1S MODEL CALCULATIONS WITH BACKMIXlNG
IN THE EMULSION PHASE
.
rPflBJlFi XV:
DIMENSION BI 7) ?QQ(7) SYYA(7)
3 READ31»XMAX»XMIN»DX
31 FORMAT(3Fl0o0) •
32
33
673
'
34
X=XMIN ■
RE AD32 >H , RHOG»CAO? B I L L SN ^ VELK» F E »W» DB
FORMAT(SFlOoO)
REAi)33*N
FORMAT(12) .
READ 3 4 » (B(K),QQ(K)»YYA(K)>K=1»N)
SUM=O0O
D0483 1= 1'»N '
BETA=B(I) '
Q=PQ ( I.)
YACT=YYA(I)
FORMAT ( 3 F 1 0 . 0 )
DC=X*DB•
UB=0*78*SQRTF(16,1*DB)
VBe3kl415926*DB**3/6.Q
VC=3.1415926*DC**3/6oQ
WSC=45.0&(VC-(2.*VB/3.))
WGC= ((2o*VB/3.)+.776*(VC-(2.*VB/3.
11))*RH0G*BILLSN
Fb =Q^betazvc
YX= V E L K * ( W - F B * W S C ) / ( Q * ( 1 , 0 - B E T A ) )
YI= YX/( YX+loO)
YG= 1 . - EXRF ( - 2 8 . * VELK* CA0 * WS C* H/ ( WGC* UB) )
Y=(lo-BETA)*Yi+BETA*YC
D I F = Y - Y A C T ‘
1 !
SUM=SU m ^DIF**Z .
483 PRINT382,Y,YACT,BETA,Q,DIF
382 FORMAT (‘5 H Y' =" ,E 14 »7,8H:':YACT = »E14o7»
IBM BETA = '»FlOo 6 »5H Q'= ,E14.7,7M DlF=,E14»7)
" PR INT43 »X »SUM
XrXH-DXi ■
IFfX4xNAX)673,673»313
43 FORMAT!5H X = , F I O . 6 , 7 H S S = , E 1 4 . 7 , / / )
313 PRINT74 ,H »R'HOG,CAO ,BI LLSN »VELK ,FE ,W5DB
GO TO 3
74 FORMAT Il6H PARAMETERS ARE »8(2X ,E14.7) )
• end'
-8 5 -
TABLE %VI:
FORTRAN PROGRAM FOR ROWE-1S MODEL CALCULATIONS WITH PLUG FLOW
AND LONGITUDINAL DIFFUSION IN THE EMULSION PHASE ''
** WM aT oALUMKAL
CH o E 0 RESEARCH
*LI5T PRINTER"'
■
'"
- ' r: ’ • pIMENS IQN B ( 7) vQQ f 7) * YYA ( 7 )
M=I ' • • " / 7
.
1 I= I
•
READ 2 V X sXMINsXMAX?D E L X :
READ' 2 ?XD ?XDMAX 9 DELXD
R E A D .6 ?H vRHOG 9C A d ,B I LLSN?V E L R ,W?DB
RE&p W
^
REAp 4?TB(K) ,QQ{K) 9 YYA(K) 9 K.-I9 N) ;
2 Ep#AT.(7Pl0.'6)':
> - '
3 FQRNiAT s' 12 ) ' /
4 FORMAT.(BFlQoO)" '
6 FQRMAT(7F1O*0)
5
- ' F'
DdTI = IVN '
" BETA=B(T) '
Q^ Q Q (I)'
YACT=YYA!I) ■
GC=X*DB "
WB = Q . 7 8 * 5 QR T F ( 1 6 . 1 * D B )
VB5;S V'141 592 6*DE**3 / 6:0 O
V,6 i-3 i 14 l $ 9 & 6 f D C * * 3 / 6 . 0
.W-SC'iAS'oOf IVC^r
,(:2o*VB/3o ) )
^GC=('{ Z i * V 6 / 3
+
( VC*- ( 2 . * V B / 3 . )
1 TV x r h o g k-b iLLSN
"v '? '
■
:■
' FB=Q*BETA/VC
- ' '
W i : . 0 .. ' I"
.
'^B=QfHX ( I sO-BETA ) / ( . Q3 9 8 1 * X D )
C=VELKXHX{W-FBK-WSC) / ( . 0 3 9 8 1 * X D )
Xp=(XixSQRTFT:XBKK'2 + 4oKA*C) )/(2t*A)
-86-
TABLE XVI:
( c o n tin u e d )
Y I = I . 0 - ( ({XMI-XM2 )*EXRF(XMl +XM2) )/ '
■ i rxMl *EXPF(XMi)-XM' 2#EXPF»XM2) )")
Y C= I . 0 - ( EXPF( ( - 28. *VELK*CA0*W$C*H) / ( . WGC*UB) ) )
Y= I I o - B E T A Y I + BETA*YC
■
DIF=Y-YACT
.........
SUM=SUM+D IF*#2 •'
7 PRINT 8,Y,YA€T,BETA,Q*DIF
8 FORMAT! BHOY= ,ElAaTsSH YACT= ,E14<,7,8H
!BETA= Y FIO . 6 ■,§H Q= ','ElAaTWH DIF= ,E1A.7)
PRINT 9,X,SUM,XD
......
9 FORMAT(SHOX= ,F10.6,18H SUM QF SQUARES
I= 1:'-sElAoT,SH- XD= • ,F10o6,/lH0) '
" '
X=X+DELX
10
'
11
12
'
IF(X-XMAX)5,5,10
X=XMIN
XD = XD+DELXD
IF (XD-^DMAX)5,5,11
M=M+I '
■\
'
IF(M-S)1,1,12
CALL EXIT
END'
s
.
.
\*
■
''
'
"8 7 -
FORTRAN PROGRAM FOR THE CALCULATIONS OF THE MODEL OF DAVIDSON
AND HARRISON WITH PLUG FLOW IN THE EMULSION PHASE
TABLE XVII:
11
49
50
■
51
48
DIMENSION XKT(V),BETAT(V),CQNV(V)
FORMAT(12,AplOeO) /
':
READ 11,' NN»'H»XMAX»XMIN sDELX
FORMAT (3FIO eO)
READ 50,(XKT(J),BETAT(J),CONV(J)»J=1,NN)
X=XMIN
SUM=O,O
• '
Pb-18 I=I,NN
• 1
XK=XKT (Ij
Bf
ETA=BETATI II
XMI- ’((X+XK*H )+ ((X+XK*H) **2-4 =-$<-(le-BETA)
i*Ni4XK*X)**0.5)/(2,*H*(l.-@ETA)j ■
■.
■ XM2=' ((X+XK#M)-SQRTF((X+XK*H)**2-4.*(1.lBETA)*H*XK*Xb)/(2i*H*(i.-BETA) '
(IH= '(I./(XM1--XM2 ))f TXM 1*(1.-(XM2*H*
■ l(:l-,-BETA)/"X))*EXPF(:-XM2*H')rXM2* ' '
l(lc-(XMi*H*( 1 6 - B E T A ) Z X )),TEXRF(-XMT-^H)5
Y=Ie-CH
: i '- '
DIF=CONV (I)-Y ■ V' -■
''
1
SUM=SUM+DIF**2
IV Fp-MAtV 5H-Y ■= ,FlO 0 6 ,8 H CONV =? »F10«,6»YH DIF
I="-9 EIJ6 V',6 H' K =- ,F10.5,8H BETA= ',FlO«,6 ,V )
18 PRINT IV,Y-,CONV (I),DIF,XKT( I),BETAT(I)
'
- PRINT 19,XiSUM
'"
'
I' FORMAT {4H X= -,F10<,5,18VH S S = ,214.Ti/)
. X=X+DEIiXi
v, •
IF(X-XMAX)51,51,52
52 pBiWtiab'HiNN, ' ' : . -
-
FORMAT (5H H = ,F1Q.5,13H NBR OF PT = ,E14.V,/)
- GO "Tb''49 : ''
end : • '
20
-
88-
TABLE X V III-.' .EGRTRAN PROGRAM FOR.THE CALCULATIONS OF THE. MODEL OF DAVIDSON
AND HARRISON WITH THE BACKMIXING IN THE EMULSION PHASE
DIMENSION XKT(V),BETAT(V),CONV(V)
FORMAT( 12,4FIO oO )
READ 11,' NN:,H,XMAX,XMIN ,DELX
FORMAT (3F:
lti0d)
6'
READ 50,(XKT(J),BETAT(J ),CONV(J) , J = I ,NN) '
X=XMIN
'
51 SUM=OoO
DO :I 8 I= I,NN
. XK=XKT(I)
BETA=BETAT(I)
48 C H = ’
(1.0-BETA*EXPF(-X)+BETA*XK*
• IEXPF (-1X ) )/(1.0-BETA*EXPF(-X)+XK)
11
49
50
'
■Y=I o-Chi
" '
-
DlF=CQNV(I)-Y
SWM=SUM+DIF**2
IV FORMAT (.5H:Y = ,FlOo 6,8H CONV= ,FlO e 6 , VH DIF
l= :>:,EiJoV:,.6H: K. =' ^Fio. 5,.BH BETA= ,FlQeS,/)
11
P RI NT' IV' i Y: , CONV( I ) , D I F , XKT ('% ! , B E T A T ( I )
' '
'k PRINT 19 ^X,SUM: . " " V
': ' " ' ' '
I FORMAT (4H X= -,F10.5,18 H S S. =,E14oY,0o
X=X+DELX
' IF(X-XMAX)51,51,52
52 PRINT 2 0 ,H,NN
20 FORMAT ( 5 H H = ,F10o5,13H 'NB R OF PT = ,E14.V,/)
; GO.iT O 49
:
' :
: '
'
• END
■
.8 9
TABLE XIX:
FORTRAN PROGRAM FOR CALCULATIONS OF THE MODEL OF DAVIDSON AND
HARRISON WITH PLUG FLOW,. LONGITUDINAL D IF F . .IN EMULSION PHASE
DIMENSION U (7),0(7)
DIMENSION Y A C K 7)
COMMON Al' ,A2,A3 ,A4,R1,R2,R3
M=I/ '
1
I= I
READ
RE-iD
REAb
READ
READ
2 ,-X-*XMINsXMAXs DELX
2 X D ,XDMAXYDELXD
2,X|(.,UQ,'XL,G,AR,E
3,%!
'
H K U ( J K J = I 9N)
READ 2 »(YACK J ) »J = 1»N)
2 FPRM1AT (7F1Q66)
" ''
3 FORMAT!12)
4 F O R M A T ( 4 H R 1 = 9E16«892 % 93HR2=,ElSeS9 ■
-12XY3MR3=: ?E IS o8)1 ' r
';
' :v
5
8 = f UQ * XL ) 7 ( X D* E )
■■ D = K Ut I)4 UO)* X L )/( XD*E) ,
• ■
GS= ( XK*G) / I A R ^ ( U ( I ) - U O ) )
P R I N T •20,X9XD9A 9B 9D 9GS
20 FORM-ATOM 'X^VElS'* 8'»2 X'» 3HXD = 9ElSe
• I8»2XO H A - 9E16.8,2X,2HD=9E16.8,2X,2
2HD=YElSo:8 92-X:93HGS=9El<6e8)
A l = I >0- \ ''
'A Z fA z-B ' :
, ;•
-
A3=-(A*B+A*D+GS*D)
A4f - =A*D*GS.
CALL C U B R T ......
PRINT 4,R19R2,R3
XMi=(R2-B)*R3*EXRF(R3)-(R3-B)*R2*
1EXPF(R2)^(A*B*R34EXPF(R3))/(A+R2
2)'- (A*E3*R2*EXPF(R2) )/(A+R3 5
' .'
XM 2 = (R 3 B ')* R I* E X P F (RI )- 1R I- 8 )* R 3«"
IEXPF(R 3 )+ (A*B*R1*EXPF(R1))/!A+R3
2)T(A*B*R3#EXPF(R3))/(A+R1)
-v:
-9 0 -
TABLE XIX:
( c o n tin u e d )
XM3=(Rl-g)*R2*EXPF(R2)-(R2-B)*Rl*
1EXPF(R1)+(A*B*R2?EXPF(R2))/(A+R2
2 ) “ ( A*B*Rl*E'x'PF'( R'i ) )■/( A+R2 )
;i
P=RI*EXPF( Rl)*( A*( R3--B) / (A+R2 )-A*
1 (R'2TBd /1 A+ R3 ):)+ R2-x-EkPF (R2)*(A*(R1
2-B )V {A+R3)- A * ( R 3 - B ) / ( A+RX) )+R3*EXPF(R 3 ) *
3(A*(R2-B)/(A+Rl)-A*(Rl-B)/(AtR2i)
' •
'Y=1.6^CX#l*E*RFi Rl)* ((A+D)'/ CA+RI')+B) +
lXM2*EXRF'(R2')i:((A*P)/'(A+R2)+B)'\' v
2 + XM3*EXPF(R3)*I IA*D?)'/(AiRB)+ B )) /!P*(B+D) )
Q( I ) = (Y^YACTTi))**2'
:• V
' ' '•
'
‘ '
P Rr N T _ ' 2 1 , y , Y A C T ( I ) ' , Q ( I ) , U ( I )
21 FORMAT (3H''Y=,'E16?8,2X,5HYACT=,E16«8,2X:
• I ,2HQ=»E16e8,2X,2HU=,E16o8)
1 = 1+1
IF' (I-N)5,5,6
6 SUM=Q.Q ■ '
DO 7J = l ,fs!
SUM=SUMfQ(J)
7 CONTINUE
■
PRINT 31 ,SUM,XoXD
31 FORMAT (6H SUM= ,E14e 8/4H X=,E'14.8»
' 14 H■"XD ■= ’ E14 ®8 , / / )
I = I
8
'
9
10
'
.
X=XfDELX
IF (X-XMAX)5,5,8
■
X=XMIN
:
•
XD=XDfDELXD
:
IF (XD--XDMAX) 5,5 ,9
M=Mfl
IF (KI-6) 1 , 1 , 1 0
CALL EXIT .
END
Log
-9 1 -
Log
P ig . I
(U)
P r e s s u r e D rop I n F l u i d i z e d B ed.
V ent
W ater
W a te r
To F ix e d
RV
RM
CM
H
R
TC
CN
CY
TC_ TC
V ent
To F l u i d i z e d Bed
W a te r
F ig u re 2 .
D iag ram o f A p p a ra tu s
R e g u l a ti n g V a lv e
R o ta m e te r
O r i f i c e M e te r
H e a te r
R e a c to r
T h erm o co u p le
C ondenser
C y c lo n e
i
VD
no
i
-9 3 -
S e r i e s No. 10
S lo p e
CA o(W/P)
F igu re 3.
( lb - h r/f t3)
F it t e d Line f o r R ea ctio n V e lo c it y C o n stan t.
-In
-9 4 -
i
F igu re 4 .
/
t °k x
io
3
A c tiv a tio n Energy
C o n v e rs io n
-9 5 -
----- = P lu g Flow
— = B ackm ix
A - O b s e rv e d
U/Uo
F ig u re 5 .
E n tir e R ea cto r as Plug Flow and Backmix
C o n v e rs io n
-9 6 -
P lu g Plow
B ackm ix
O b se rv e d
u /u 0
F ig u re 6
W hole R e a c to r a s B ackm ix an d P lu g Flow
C o n v e rs io n
-9 7 -
P lu g Plow
Backm lx
O b se rv e d
0 .0
1 .0
2 .0
3 .0
4 .0
O/Uo
F ig u r e 7 -
R o w e's M odel C a l c u l a t i o n C o n s id e r in g t h e E m u ls io n
P h a se a s P lu g Flow a n d B ack m ix .
5 .0
C o n v e rs io n
98 -
P lu g Plow
Backmix
O b se rv e d
UA0
F ig u r e 8 .
R o w e's Model w i t h P lu g Plow and B a c k m ix in g i n th e
E m u lsio n P h a s e .
CONVERSION
-9 9 -
S e rie s
P lu g Plow
B ackm ix
O b se rv e d
n /U o
F ig u r e 9 .
C a l c u l a t i o n s u s i n g M odel o f D a v id s o n an d H a r r i s o n
C o n s id e r in g P lu g Plow a n d B a c k m ix in g i n t h e Em ul­
s io n p h a se.
C o n v e rs io n
-IO O -
S e rle s
P lu g Flow
Backm lx
O b se rv e d
%/Uo
F ig u re 1 0 .
M odel o f D a v id s o n a n d H a r r i s o n w i t h P lu g Flow an d
B a c k m ix in g I n t h e E m u ls io n P h a s e .
C o n v e rs io n
—101.—
P lu g Plow
Backmljc
O b se rv e d
U/Uo
F ig u re 1 1 .
B e s t P i t D a ta fro m R ow e's M odel C a l c u l a t i o n u s i n g
d c/ d ^ a s U n d e te rm in e d P a r a m e te r .
C o n v e rs io n
-1 0 2 -
P lu g Flow
B ackm ix
O b se rv e d
U/Uo
F ig u re 1 2 .
R o w e's M odels w i t h One U n d e te rm in e d P a r a m e te r
C onversion
-1 0 3 -
S e r i e s No. 10
------- = Plug Plow
------ = B ackm ix A = O b se rv ed
0 .2 7 7
" /U 0
F ig u re 1 3 .
B e s t P i t D a ta fro m D a v id s o n an d H a r r i s o n 's M odel
C a l c u l a t i o n s U s in g x a s an U n d e te rm in e d P a r a m e te r .
C o n v e rs io n
-1 0 4 -
S e r i e s No. 6
-------- = P lu g Plow - x = 0
------- = B a c k m ix in g - x = 0 .1 5
A = O b se rv e d
U/Uo
F ig u re 1 4 .
M odels o f D a v id s o n an d H a r r i s o n W ith One U n d e te r ­
m ined P a r a m e te r .
C o n v e rs io n
-1 0 5 -
S e r i e s No. 10
--------= D a v id s o n , x = 0 .2 0
0 .0 0 0 0 1
%/Uo
F igu re 15.
B e s t F i t D a ta fro m R o w e's M odel and D a v id s o n and
H a r r i s o n 's M odel C a l c u l a t i o n s U s in g Two U n d e te r ­
m in ed P a r a m e t e r s .
C o n v e rs io n
- 106-
Rowe
(Ic Zdtl = 1 .0 0 1 , D = 1
D a v id so n & H a r r i s o n
x — 0 ,0 « D = 0 .0
F ig u re 1 6 .
Two P a r a m e te r M odels o f Rowe an d D a v id s o n and
H a rris o n .
-1 0 7 -
2 .5
2. 0
A
A
A
1 .5
1.0
0 .5
0.0
1.0
0 .5
1 .5
Bed H e ig h t ( f t )
F igu re 1 7 .
Model o f Mamuro and Muchl.
- 108-
-
C o n v e rs io n
0.8
0 .0
1 .0
2 .0
3 .0
4 .0
u /u 0
F igu re 1 8 .
E f f e c t o f Temperature on C onversion .
5 .0
C onversion
- 109-
□ - L/D = 4 . 0 - S e r ie s No. 6
A - L/D = 5 .5 3 - S e r ie s No. 7
0 - L/D = 2 .6 7 - S e r ie s No. 10
U/Uo
F ig u re 1 9 .
E f f e c t o f Bed H eight on C onversion .
-1 1 0 -
C o n v e rs io n
0 . l 6 l ram
U/Uo
F igu re 2 0 .
E f f e c t o f P a r t ic le S iz e on C on version .
-IllLITERATURE ■CITED
1.
L e.va,. M. > " F l u i d i z a t i o n ^ " p „ 5» M cG fraw -R lll,. .New Y ork ( i 960 ) .
2.
S h e n i,. C, Y. a n d H. F . .J o h n s to n e ii. A .Io C h .E . . J . I ,
3.
M a t h i s J „ ,F. a n d C .-C . W a tso n i ,. A -Ii=Ch-E.
4.
349 (1955) •
> 2-, .518 (19 5 6 )..
L ew is# W. K., s, E . . R . , G i l l i l a n d * a n d W. G l a s s , .A .I .C h .E . . J . ,
419 (1959) .
'
'
5*
'
5.
May,- W. G
6.
Van D e e m te ri ,J . .J ,# . Chem. Ehg.. S o l . j 1,3> 143 (1961) .
7.
L a n n e a u >. K. P . , . T r a n s .. I n s t . .Che,m„ E n g r s .., -38,# 125 (I9 6 0 ) .,
8.
O r c u t t i J . . C. J . F . .D a v id s o n , a n d R . L . P l g f o r d 3, Chem.. E h g .
P y o g r . Sym posium S e r .,, 5 8 , .1 ( 1 9 6 2 ) .
9.
. Chem.. E n g . P r o g r ..* 55# .49 ( 1 9 5 9 ) .
H e if le lii K .> K. S c h a g e r l i ,F. .P e t t i n g # a n d G. S c h e lm a n h i
- Chem. E n g . .S e l. , 20# 557 ( I 9 6 5 )..
10.
De M a ria * F . * L . E . ,L o n g f i e l d * a n d -G, B u t l e r 3 , Chem. E n g . P r o g r .
Symposium. ,S en. ,. 5 8 , .16 (.1.9 6 2 ) .
— — r-
11.
D a v id s o n # ,J . F . an d .D. H a r r is o n # " F l u i d i z e d P a r t i c l e s , "
C hap. 6* C am bridge H n iv . P r e s s # E n g la n d ( I 9 6 3 ) .
12.
.Rowe, P . N-., .Chem. E h g . P y o g r . , ,6 0 *. 75 ( 1 9 6 4 ) .
13.
Mamuro# T . a n d I l M uch!, I n t e r n e t . Chem. E n g . # .5# 732 (19 6 5 )..
14.
.Carman# P . C. # . T r a n s . . I n s t . Chem. E h g r s . , 3 4 , . 7 9
15.
Y a s u ii,- G«. a n d L . .N. . J o h a n s on# -A .I, .C h , E . y . , .4 , ,445 ( 1 9 5 8 ).
16.
D av id so n # J . F . , -R. C. P a u l * .M, J . S . S m ith 3 an d H. > . D u x b u ry ,
T r a n s . I n s t . , Chem. . E n g r s . , . 3 7 , 323 ( 1 9 5 9 ).
17.
P ansing#, .w. . E . A . I . Ch . E.
18.
Rowe# .p . No i - Ghem. E n g . P r o g r . Sym posium S e y . ,
19.
Rowe3 P . N. a n d B. A. P a r t r i d g e # Chem. E n g . S c i . , ,1 8 # .51.1 ( 1 9 6 3 ) .
i 2> J l
(1 9 3 7 )»
( 1 9 5 6 ).
5 8 # .42 ( 1 9 6 2 ) .
-11220.
M u r r a y J . D .,. Chem. .Eng. P rogr. Symposium S e r . , 6 2 , 71 (1966) „
21.
Jackson, R .,,. T rans, I n s t .. Chem, E n g r s ., .4 1 , 1 3 ( 1 9 6 3 ).
22.
Rowe,, P, .W., j B. A. P a rtr id g e > an d E,. •L y a ll, .Chem. Eng. S c i . , .1 9 ,
973 ( 1 9 6 4 ) .
'
23.
S u th erla n d , ,K . S . * T rans. .,,Inst . Chem,. E n grs. , . 3 9 , ,188 ( 1 9 6 1 ) .
MONTANA STATF i
.
utuccttv __
_
_
_
_
_
_
_
3 1762 10005130
D378
A lS c
op. 2
Alumkal, W. T.
The w ater gas s h i f t r e a c tio n
in a f lu id i z e d bed c a t a ly t i c ..
NAME AND A O O r tt e e
OCi
C5
V3
Ce
7
S