An improved model for describing mass-transfer in bubble columns and three-phase fluidized beds.

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University of Windsor University of Windsor

Scholarship at UWindsor

Electronic Theses and Dissertations Theses, Dissertations, and Major Papers 1-1-1986

An improved model for describing mass-transfer in bubble

columns and three-phase fluidized beds.

Abdulghanni H. Nhaesi

University of Windsor

Follow this and additional works at: https://scholar.uwindsor.ca/etd

Recommended Citation Recommended Citation

Nhaesi, Abdulghanni H., "An improved model for describing mass-transfer in bubble columns and three-phase fluidized beds." (1986). Electronic Theses and Dissertations. 6799.

https://scholar.uwindsor.ca/etd/6799

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AN IMPROVED MODEL FOR DESCRIBING MASS-TRANSFER IN BUBBLE COLUMNS AND THREE-PHASE FLUIDIZED BEDS

by

Abdulghannl H. Nhaesl

A Thesis submitted to the

Facul ty of Graduate Studies and Research through the Department of

Chemical Engineering i n Pa r t i a l F u l f i l l me nt o f the requirements f o r the Degree

of Master o f Applied Science at the Uni ver si t y of Windsor

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UMI Number: EC54788

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A bdulghannl H. N h a t t l A il R ig h ts R s s s rv s d 1 0 8 6

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ABSTRACT

Mass t r a n s f e r bet ween gas ( o x y g e n ) and l i q u i d ( w a t e r ) phases 1n t h r e e - p h a s e f l u l d l z e d beds and b u b b l e col umns has been s t u d i e d 1n t h i s I n v e s t i g a t i o n .

The m a t e r i a l s used 1n t h i s s t u d y c o n s i s t e d o f s p h e r i c a l g l a s s beads w i t h d i a m e t e r s o f 0 . 3 cm and 0 . 5 cm ( s o l i d p h a s e ) , o i l - f r e e compr essed a i r as t h e gas p h a s e , and t a p w a t e r as t h e l i q u i d p h a s e . The gas s u p e r f i c i a l v e l o c i t i e s

empl oyed wer e 8 , 26 and 43 cm/ s and t h o s e f o r t h e l i q u i d phase 5 , 7 . 5 and 12 c m/ s .

The c o l l e c t e d d a t a wer e used t o draw c o n c e n t r a t i o n p r o  f i l e s as w e l l as 1n t h e p r e p r a t l o n o f p e r t i n e n t c o n t o u r d i a  gr ams. The c o n t o u r d i a gr a ms o b t a i n e d 1n t h i s I n v e s t i g a t i o n c o n f i r m e d t h e e x i s t e n c e o f two c l e a r l y d i s t i n g u i s h a b l e mass t r a n s f e r zones 1n t h r e e - p h a s e f l u l d l z e d beds and b u b b l e c o l  umns . Pl ug f l o w c o n d i t i o n s p r e v a i l 1n t h e r e g i o n c l o s e t o t h e d i s t r i b u t o r , whi ch 1s t e r me d t h e g r i d zone and d i s p e r  s i o n c o n d i t i o n s p r e v a i l 1n t h e b u l k z o n e . T h i s was u t i l i z e d 1n t h e d e v e l o p me n t o f a m a t h e m a t i c a l model f o r d e s c r i b i n g mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds and b u b b l e c o l  umns .

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The v a l i d i t y o f t h e e x i s t i n g ma t h e ma t i c a l model s f o r d e  s c r i b i n g mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds and bubbl e col umns has been a n a l y z e d f rom an e x p e r i m e n t a l s t a n d  p o i n t and t h e e f f e c t s o f f l u i d s u p e r f i c i a l v e l o c i t i e s on t h e v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t s has been d i s c u s s e d .

The r e s u l t s o b t a i n e d 1n t h i s st udy c l e a r l y I n d i c a t e t h a t t h e pr oposed model conf or ms more c l o s e l y t o t h e e x p e r i m e n t a l d a t a t ha n any o f t h e e x i s t i n g mode l s .

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D ED IC A TIO N

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ACKNOWLEDGEMENTS

My s i n c e r e t ha nk s and g r a t i t u d e a r e due t o HI S ALMIGHTY, ALLAH, WHO h e l pe d and b l e s s e d me d u r i n g t h e c o u r s e o f my s t u d i e s 1n g e n e r a l .

I woul d l i k e t o e x p r e s s my a p p r e c i a t i o n and g r a t i t u d e t o P r o f e s s o r A b d u l - F a t t a h A s f o u r , my s u p e r v i s o r . Hi s I n v a l u a b l e a d v i c e and c o n s t r u c t i v e c r i t i c i s m have been t h e c o r n e r s t o n e f o r my wo r k . C e r t a i n l y t h i s work woul d n o t have been p o s s i  b l e w i t h o u t h i s g u i d a n c e and s u p e r v i s i o n .

D i s c u s s i o n s w i t h D r . Manuel A 1 v a r e z - C u e n c a d u r i n g t h e I n  v e s t i g a t i o n wer e most h e l p f u l and a r e d e e p l y a p p r e c i a t e d .

I am I n d e b t e d t o P r o f e s s o r Mor t on Ne r e n b e r g o f t h e U n i  v e r s i t y o f West er n O n t a r i o f o r t h e gener ous use o f t h e i r comput er f a c i l i t i e s and h i s h e l p w i t h t h e m a t h e m a t i c a l mod e l i n g .

F i n a n c i a l s u p p o r t f o r t h i s p r o j e c t , f rom t h e N a t u r a l S c i  ences and E n g i n e e r i n g Resear ch C o u n c i l o f Canada (NSERC) and I m p e r i a l 011 company, 1s d e e p l y a p p r e c i a t e d .

Much a p p r e c i a t i o n goes t o Mr . D i e t e r L l e b s c h and Mr . L o i s Beaudry o f t h e c e n t r a l r e s e a r c h shop, and Mr . George Ryan, t h e t e c h n i c i a n o f t h e Chemi cal E n g i n e e r i n g D e p a r t me n t f o r t h e i r e x c e l l e n t s e r v i c e .

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TABLE OF CONTENTS

A B S T R A C T ...111

DEDICATION ... v

ACKNOWLEDGEMENTS ... v1

TABLE OF CONTENTS... . v 111 LI ST OF T A B L E S ... x

LI ST OF F I G U R E S ... x11

LI ST OF A P P E N D I C E S ... xv

NOMENCLATURE ... xv1

C h a p t e r page I . INTRODUCTION ... 1

Gener al ... 1

O b j e c t i v e s ... 3

I I . LITERATURE SURVEY ... 5

The F l u l d l z e d S t a t e ... 5

Advant ages and d i s a d v a n t a g e s o f t h r e e -phase f l u l d l z e d b e d s ... 6

Bubbl e Columns ... 7

Advant ages and d i s a d v a n t a g e s o f bubbl e col umns ... 8

Mass T r a n s f e r 1n T h r e e - p h a s e F l u l d l z e d Beds . . 9

Model s For D e s c r i b i n g Mass T r a n s f e r 1n T h r e e - p h a s e F l u l d l z e d Beds ... 18

G e n e r a l ... 18

Revi ew o f e x i s t i n g model s ... 19

I I I . E X P E R I M E N T A L ...31

Gener al ...31

E x p e r i me n t a l S e t - u p ... 34

The t w o - d i m e n s i o n a l col umn ... 34

The s t r i p p i n g col umn ... 37

The a i r s a t u r a t o r ... 38

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E x p e r i me n t a l Pr o c e d u r e ... 41

The Gas and L i q u i d S u p e r f i c i a l V e l o c i t i e s . . . 42

The E x p e r i me n t a l D a t a ...42

C a l c u l a t i o n o f V o l u m e t r i c Mass T r a n s f e r And D i s p e r s i o n C o e f f i c i e n t s ... 38

The v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t e v a l u a t e d by t h e p l ug f l o w model . . . 43

The v o l u m e t r i c mass t r a n s f e r and a x i a l d i s p e r s i o n c o e f f i c i e n t s e v a l u a t e d by t h e a x i a l d i s p e r s i o n model . . ; . . 44

The v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t 1n t h e g r i d r e g i o n and t h e v o l u m e t r i c mass t r a n s f e r 1n bul k r e g i o n e v a l u a t e d by t h e t wo - z o n e m o d e l ... 44

The v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t I n t h e g r i d r e g i o n and t h e v o l u m e t r i c mass t r a n s f e r 1n bul k r e g i o n e v a l u a t e d by t h e proposed m o d e l ... 45

U n c e r t a i n t y A n a l y s i s ... 45

E f f e c t o f t he pr e s e nc e o f a bubbl e 1n t he mi x i n g c e l l ...46

U n c e r t a i n t y 1n t he c a l c u l a t i o n o f ( K^a) . . . 46

I V . RESULTS AND D I S C U S S I O N ...50

C o n c e n t r a t i o n P r o f i l e s ... 76

V a l i d i t y o f t h e Mass T r a n s f e r M o d e l s ...76

The pl ug f l o w m o d e l ...83

The a x i a l d i s p e r s i o n model ... 90

The t wo - z o n e model ...92

The proposed model ... 104

V a r i a t i o n o f t h e v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t s w i t h t h e d i a m e t e r o f t he s o l i d phase p a r t i c l e s ... 104

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L I S T OF TABLES

T a b l e D e s c r i p t i o n Page

4 . 1 The S e p a r a t i o n Boundar y P a r a m e t e r ... 59 4 . 2 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Two- Zone Model ( Dp* 0 . 0 c m ) ... . 63 4 . 3 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Pr oposed Model ( Dp* 0 . 0 c m ) ... 63 4 . 4 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Two- Zone Model (Dp * 0 . 3 c m ) ... 64 4 . 5 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Two- Zone Model ( Dp = 0 . 5 c m ) ... 64 4 . 6 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Pl ug Fl ow Model ( D^ = 0 * 0 c m ) ...80 4 . 7 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t he Pl ug Fl ow Model ( Dp* 0 . 3 c m ) ...80 4 . 8 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Pl ug Fl ow Model ( Dp= 0 . 5 c m ) ... 81 4 . 9 S t a n d a r d D e v i a t i o n o f t h e F i t f r om t h e

E x p e r i m e n t a l Da t a Usi ng t h e Pl ug Fl ow Mod e l . . . 81 4 . 1 0 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e A x i a l D i s p e r s i o n Model (Dp * 0 . 0 cm) . . . 85 4 . 1 1 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t he A x i a l D i s p e r s i o n Model ( Dp* 0 . 3 cm) . . . 85 4 . 1 2 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e A x i a l D i s p e r s i o n Model (Dp * 0 . 5 cm) . . . 85 4 . 1 3 A x i a l D i s p e r s i o n C o e f f i c i e n t s ( Dp * 0 . 0 cm) . . . 86 4 . 1 4 A x i a l D i s p e r s i o n C o e f f i c i e n t s ( Dp * 0 . 3 cm) . . . 87 4 . 1 5 A x i a l D i s p e r s i o n C o e f f i c i e n t s ( Dp* 0 . 5 cm) . . . 87 4 . 1 6 S t a n d a r d D e v i a t i o n o f t h e F i t f rom t h e

E x p e r i m e n t a l Dat a Usi ng t h e A x i a l D1spers1om

M o d e l ... 89 4 . 1 7 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t h e Pr oposed Model ( Dp* 0 . 3 c m ) ...100

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T a b l e D e s c r i p t i o n Page

4 . 1 8 V o l u m e t r i c Mass T r a n s f e r C o e f f i c i e n t s E v a l u a t e d

by t he Pr oposed Model ( Dp3 0 . 5 c m ) ... 100 4 . 1 9 A x i a l D i s p e r s i o n C o e f f i c i e n t s 1n t h e Bul k

Zone ( Dp = 0 . 0 c m ) ... 102 4 . 2 0 A x i a l D i s p e r s i o n C o e f f i c i e n t s 1.n t h e Bul k

Zone ( Dp3 0 . 3 c m ) ... 102 4 . 2 1 A x i a l D i s p e r s i o n C o e f f i c i e n t s 1n t he Bul k

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L I S T OF FIGURES

F i g u r e D e s c r i p t i o n Page

3 . 1 Schemat i c Di agr am o f t h e E x p e r i me n t a l

S e t - U p ... 33

3 . 2 Sampl i ng P o r t D i s t r i b u t i o n 1n t h e Column . . . . 35

3 . 3 P i c t o r i a l Vi ew o f T h r e e - P h a s e F l u l d l z e d B e d F a c 1 l i t y ... 36

3 . 4 P i c t o r i a l Vi ew o f Sampl i ng C e l l and Oxygen A n a l y z e r ... 39

4 . 1 C o n c e n t r a t i o n Cont our Di agr am ... 51

4 . 4 C o n c e n t r a t i o n Cont our Di agr am ... . . . . 55

4 . 5 V a r i a t i o n o f b w i t h t h e F l u i d V e l o c i t i e s . . . 56

4 . 6 V a r i a t i o n o f b w i t h t h e F l u i d V e l o c i t i e s . . . 57

4 . 7 V a r i a t i o n o f b w i t h t h e F l u i d V e l o c i t i e s . . . 58

4 . 1 0 Oxygen C o n c e n t r a t i o n s Measur ed a t Two P o s i t i o n s ... 65

4 . 1 1 Oxygen C o n c e n t r a t i o n s Measur ed a t Two P o s i t i o n s ... 66

4 . 1 2 C o n c e n t r a t i o n Cont our Di agr am ... 68

4 . 1 3 C o n c e n t r a t i o n Cont our Di agr am ... 69

4 . 1 4 Oxygen C o n c e n t r a t i o n Measured a t Two P o s i t i o n s ... 70

4 . 1 5 Oxygen C o n c e n t r a t i o n Measur ed a t Two P o s i t i o n s ... 71

4 . 1 6 V a r i a t i o n o f E x p e r i m e n t a l C o n c e n t r a t i o n s w i t h t he P a r t i c l e S i z e ... 73

4 . 1 7 V a r i a t i o n o f E x p e r i m e n t a l C o n c e n t r a t i o n s w i t h t h e P a r t i c l e S i z e ... 74

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F i g u r e D e s c r i p t i o n Page

4 . 1 8 E x p e r i m e n t a l and P r e d i c t e d Oxygen

C o n c e n t r a t i o n s ... 77 4 . 1 9 E x p e r i m e n t a l and P r e d i c t e d Oxygen

C o n c e n t r a t i o n s ... ... 94 4 . 2 3 E x p e r i m e n t a l and P r e d i c t e d Oxygen

C o n c e n t r a t i o n s ... 95 4 . 2 4 E x p e r i m e n t a l and P r e d i c t e d Oxygen

C o n c e n t r a t i o n s ... 97 4 . 2 6 V a r i a t i o n o f w i t h ... 98 4 . 2 7 V a r i a t i o n o f a E v a l u a t e d by t h e Pl ug

Fl ow Model w i t h t h e L i q u i d V e l o c i t y ... 106 4 . 2 8 V a r i a t i o n o f (K^a)pB w i t h t h e L i q u i d

B . l

S u p e r f a c l a l V e l o c i t y ,

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F1gur e D e s c r l p t 1 o n Page

B. 8 C o n c e n t r a t l o n Co nt o u r Di a gr am . . . . ... 163

B. 9 C o n c e n t r a t i o n C o n t o u r Di a gr am . . . . . . . 164

B. 1 0 C o n c e n t r a t i o n C o n t o u r Di agr am . . . . . . . 166

B . l l C o n c e n t r a t l o n C o n t o u r Di agr am . . . . . . . 166

B. 1 2 C o n c e n t r a t l o n Co nt o u r Di agr am . . . . . . . 167

B. 1 3 C o n c e n t r a t l o n C o nt o u r Di agr am . . . . ... 168

B. 14 C o n c e n t r a t l o n Co nt o u r Di a gr am . . . . ... 169

B. 15 C o n c e n t r a t l o n Co nt o u r Di a gr am . . . . . . . 170

B . 16 C o n c e n t r a t l o n Co nt o u r Di a gr am . . . . ... 171

B. 18 C o n c e n t r a t l o n Co nt o u r Di a gr am . . . . ... 173

B. 19 C o n c e n t r a t l o n Co nt o u r Di agr am . . . . ... 174

H. l R o t a me t e r Cal 1 b r a t l o n Cur ve ... ... 298

H. 2 R o t a me t e r Cal 1b r a t l o n Cur ve ... ... 299

H. 3 R o t a me t e r Cal 1b r a t l o n Cur ve ... ... 300

H . 4 R o t a me t e r Cal 1b r a t l o n Cur ve ... ... 301 H. 5 V e n t u r l m e t e r C a l i b r a t i o n Cur ve . . .

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L I S T OF APPENDICES

Appendi x page

A. EXPERIMENTAL D A T A ... ...118

B. PROGRAM UC0N2 AND CONCENTRATION CONTOUR D I A G R A M S ...145

C. SUBROUTINE PFM AND Z X S S Q ... 175

D. SUBROUTINE ADM AND Z X S S Q ... 205

E. SUBROUTINE TZM AND Z X S S Q ... 235

F. SUBROUTINE PM AND Z X S S Q ... 265

G. THE UNCERTANITY A N A L Y S I S ... 295

E f f e c t o f The p r e s e n c e o f a b u b b l e 1n t h e m i x i n g c e l l ... 295

U n c e r t a i n t y 1n C a l c u l a t i o n o f ( K^a ) 296 H. INSTRUMENTAL CALIBRATION ... 297

R o t a me t e r C a l i b r a t i o n ... 297

V e n t u r l m e t e r C a l i b r a t i o n ... 297

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NOMENCLATURE LATIN ALPHABET

A c o n s t a n t 1n E q u a t i o n ( 2 . 1 4 )

a I n t e r f a c i a l a r e a p e r u n i t vol ume o f t h e r e a c t o r ADC a x i a l d i s p e r s i o n c o e f f i c i e n t

ADM a x i a l d i s p e r s i o n model

B c o n s t a n t 1n E q u a t i o n ( 2 . 1 5 ) b s e p a r a t i o n boundar y p a r a m e t e r

C d i s s o l v e d oxygen c o n c e n t r a t i o n 1n w a t e r Cb d i s s o l v e d oxygen c o n c e n t r a t i o n a t y * b

C1 d i s s o l v e d oxygen c o n c e n t r a t i o n 1n t h e g r i d zone C2 d i s s o l v e d oxygen c o n c e n t r a t i o n 1n t h e b u l k zone

★

C d i s s o l v e d oxygen e q u i l i b r i u m c o n c e n t r a t i o n c C - C*

s

a x i a l d i s p e r s i o n c o e f f i c i e n t

G c o n s t a n t 1n E q u a t i o n ( 2 . 2 4 ) I . D. I n s i d e d i a m e t e r

K-j » K2 c o n s t a n t s 1n E q u a t i o n ( 2 . 3 5 )

KJla v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t L col umn h e i g h t

M c o n s t a n t I n E q u a t i o n ( 2 . 2 8 ) n c o n s t a n t 1n E q u a t i o n ( 2 . 1 0 ) P c o n s t a n t 1n E q u a t i o n ( 2 . 1 1 ) PFM pl ug f l o w model

PM pr oposed model

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r b b u b b l e r a d i u s T-ZM t w o - z o n e model

V9 gas s u p e r f a c l a l v e l o c i t y l i q u i d s u p e r f a c l a l v e l o c i t y V minimum f l u 1 d 1 z a t 1 o n v e l o c i t y X _{h o r i z o n t a l c o o r d i n a t e s}

y v e r t i c a l c o o r d i n a t e s

SUPERSCRIPTS

+ I m m e d i a t e l y above t h e d i s t r i b u t o r I m m e d i a t e l y be l ow t h e d i s t r i b u t o r * a t e q u i l i b r i u m

SUBSCRIPTS

9 gas phase

I l i q u i d phase

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C h a p t e r I INTRODUCTION

1 . 1 Ge ne r a l

T h r e e - p h a s e f l u l d l z e d beds pr omot e I n t i m a t e c o n t a c t i n g bet ween a s o l i d , a l i q u i d and a ga s . Such beds have a v a  r i e t y o f p o t e n t i a l a p p l i c a t i o n s as c he mi c a l r e a c t o r s . P r e s  e n t I n d u s t r i a l a p p l i c a t i o n s I n c l u d e c a t a l y t i c h y d r o g e n a t i o n and d e s u l p h u r i z a t i o n o f p e t r o l e u m p r o d u c t s , p r o d u c t i o n o f ammonium b i s u l f i t e , and b i o c h e m i c a l p r o c e s s e s e s . P o t e n t i a l a p p l i c a t i o n s I n c l u d e heavy o i l u p g r a d i n g , coa l and r e s l d c o n v e r s I o n .

Mass t r a n s f e r I n t h r e e - p h a s e f l u l d l z a t i o n has r e c e n t l y become a s u b j e c t t h a t 1s r e c e i v i n g a l o t o f I n t e r e s t . Model s used t o d e s c r i b e mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds I n c l u d e , t h e p l ug f l o w mode l , t h e a x i a l d i s p e r s i o n model and t h e t w o - z o n e mo d e l . These model s y i e l d v a l u e s f o r t h e v o l u  m e t r i c mass t r a n s f e r c o e f f i c i e n t .

The a v a i l a b l e e x p e r i m e n t a l e v i d e n c e s ug g e s t s t h a t n e i t h e r t h e p l ug f l o w nor t h e a x i a l d i s p e r s i o n model w i t h c o n s t a n t c o e f f i c i e n t s s a t i s f a c t o r i l y d e s c r i b e t h e t r a n s p o r t p r o c e s s e s o c c u r l n g 1n t h r e e phase f l u l d l z e d beds .

A 1 v a r e z - C u e n c a ( 1 9 7 9 ) u t i l i z e d c o n c e n t r a t i o n c o n t o u r d i a  grams t o I n d i c a t e t h e p r e s e n c e o f two d i s t i n c t mass t r a n s f e r

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zones 1n t h r e e - p h a s e f l u l d l z e d beds and bubb l e col umns; v i z . , t h e f i r s t zone 1s 1n t h e v i c i n i t y t o t h e d i s t r i b u t o r and 1s t er med t h e " g r i d z o n e " . The second zone 1s away f rom t h e d i s t r i b u t o r and 1s known as t h e " b u l k z o n e " . The nar r ow t r a n s i t i o n a r e a bet ween t h e two zones 1s known as t h e " s e p a  r a t i o n bounda r y" and t h e d i s t a n c e bet ween t h e g r i d and t h e b u l k zone 1s known as t h e " s e p a r a t i o n boundar y p a r a m e t e r " . The e x i s t e n c e o f t h e s e two zones p r o b a b l y p r o v i d e s an e x p l a  n a t i o n f o r t h e f a i l u r e o f t h e p l u g f l o w model and a x i a l d i s  p e r s i o n model t o p r o p e r l y d e s c r i b e mass t r a n s f e r I n t h r e e -phase f l u l d l z e d beds and b u b b l e c ol umns.

On t h a t b a s i s A 1 v a r e z - C u e n c a ( 1 9 7 9 ) pr oposed a " t w o - z o n e " model whi ch r e s u l t s f rom I n t e r f a c i n g two p l u g f l o w model s a t t h e s e p a r a t i o n b o u n d a r y . The t w o - z o n e model p r o v i d e d a b e t  t e r d e s c r i p t i o n o f mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds as was p o i n t e d o u t 1n a s e r i e s o f p u b l i c a t i o n s by A l v a -r e z - C u e n c a and c owo -r k e -r s ( 1 9 8 0 , 1 9 8 1 and 1 9 8 4 ) .

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On t h e o t h e r hand, 1 t 1s s u p r l s l n g t o f i n d o u t t h a t A l -v r e z - C u e n c a ( 1 9 7 9 ) c o n t r a d i c t e d h i s d i s c o v e r y o f t h e p r e s  ence o f two d i s t i n c t mass t r a n s f e r zones 1n t h r e e - p h a s e f l u l d l z e d beds and bubb l e col umns by assumi ng p l u g f l o w c on d i t i o n s 1n bot h z o n e s , 1n t h e d e v e l o p me n t o f t h e t wo - z o n e model . C o n s e q u e n t l y , we q u e s t i o n t h e p h y s i c a l gr ounds on whi ch such a model has been bas e d.

A new model 1s r e p o r t e d 1n t h i s st udy f o r d e s c r i b i n g mass t r a n s f e r 1n t h r e e - p h a s e f l u 1 d 1 d 1 z e d beds and b u b b l e c ol umns . T h i s model has been d e v e l o p e d on p r o p e r p h y s i c a l gr ounds and as a r e s u l t 1 t conf or ms more c l o s e l y t o e x p e r i m e n t a l d a t a a t hi gh as w e l l as a t l ow s u p e r f i c i a l v e l o c i t i e s .

1 . 2 Obj e c t 1 v e s

The p r e s e n t s t u d y 1s c on c e r ne d w i t h mass t r a n s f e r bet ween gas ( o x y g e n ) and l i q u i d ( w a t e r ) phases 1n t h r e e - p h a s e f l u l d  l z e d be d s , where p u b l i s h e d d a t a a r e r e l a t i v e l y s c a r c e and most o f them a r e p e r f o r me d 1n smal l beds a t l ow l i q u i d and gas f l o w r a t e s . C o n s e q u e n t l y , such r e s u l t s have a l i m i t e d v a l u e as f a r as I n d u s t r y 1s c o n c e r n e d . The o b j e c t i v e s o f t h i s work I n c l u d e :

I ) c o n s t r u c t i o n o f a p l l o t - p l a n t s c a l e f l u 1 d 1 z a t 1 o n e x p e r i m e n t a l s e t - u p ,

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111) o b t a i n i n g more e x p e r i m e n t a l d a t a 1n t h e g r i d r e g i o n o f t h e f l u l d l z e d bed t han t hos e r e p o r t e d 1n t h e 1 1 t e r a t u r e ,

1 v ) d e v e l o p i n g a new ma t h e ma t i c a l model c a p a b l e o f de  s c r i b i n g mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d bed and bubbl e col umn,

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C h a p t e r I I LITERATURE SURVEY

2 . 1 The F I u 1 d l z e d S t a t e

When a s i n g l e f l u i d passes upward t hr ou g h a bed o f s o l i d p a r t i c l e s , s e v e r a l d i f f e r e n t f l o w r egi mes can be obs e r v e d as t h e v e l o c i t y 1s I n c r e a s e d . At l ow f l o w r a t e s , t h e f l u i d b a r e  l y t r i c k l e s t hr ough t h e t h e I n t e r s t i c e s bet ween s t a t i o n a r y p a r t i c l e s 1n t h e bed. I n t h i s case t h e dr ag on t h e s o l i d s 1n t he bed I n c r e a s e s w i t h v e l o c i t y ( f i x e d bed r e g i m e ) . T h i s d i s p l a y s I t s e l f as an I n c r e a s e 1n t h e p r e s s u r e drop acr os s t he bed. As t he v e l o c i t y 1s 1n c r e a s e d , t h e dr ag f o r c e s a l s o I n c r e a s e , u n t i l t h e drag e x a c t l y c o u n t e r b a l a n c e s t h e e f f e c  t i v e w e i g h t o f p a r t i c l e s . At t h i s s t a g e t h e bed expands so t h a t a l l t h e p a r t i c l e s a r e no l o n g e r t o u c h i n g and t h e bed 1s c o n s i d e r e d t o be f l u l d l z e d . The v e l o c i t y a t whi ch t h i s hap pens 1s known as t h e minimum f l u 1 d 1 z a t 1 o n v e l o c i t y (Vm^ ) . F u r t h e r I n c r e a s e 1n v e l o c i t y accompani ed by f u r t h e r I n c r e a s e

1n bed e x pa ns i on and t h e p r e s s u r e drop a c r o s s t h e e n t i r e bed r emai ns c o n s t a n t , beds o f s o l i d s may be f l u l d l z e d by e i t h e r a l i q u i d or gas, or bot h o f them ( t h r e e - p h a s e f l u l d l z e d b e d ) .

When t h e bed 1s f l u l d l z e d by a gas, d i s c r e t e bubbl es usu a l l y form 1n t he bed, whi ch 1s c h a r a c t e r l z e d by t h e f o r ma

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t 1on o f l a r g e b u b b l e s . The p a r t i c l e s a p p e a r t o a c t n o t as I n d i v i d u a l u n i t s , b u t as t o t a l u n i t s h a v i n g no v i s u a l f r e e p a t h . T h i s t y p e o f f l u 1 d 1 z a t 1 o n 1s known as " a g g r e g a t i v e f 1u 1 d 1 z a t l o n " . On t h e o t h e r hand when p a r t i c l e s a r e f l u l d  l z e d by a l i q u i d " p a r t i c u l a t e f 1u 1 d 1 z a t l o n " o c c u r s . The bed h e i g h t I n c r e a s e s s moot hl y w i t h v e l o c i t y b u t l a r g e - s c a l e bub b l i n g 1s n o t o b s e r v e d . Under t h e s e c o n d i t i o n s , t h e p a r t i c l e s a r e d i s c r e t e l y s e p e r a t e d f r om each o t h e r and e x h i b i t a mean f r e e p a t h whi ch a pp e a r s t o I n c r e a s e w i t h v e l o c i t y .

T h r e e - p h a s e f l u l d l z a t l o n d i s p l a y s c h a r a c t e r i s t i c s o f bot h l i q u i d and gas f 1u1d1 z a t l o n . The s o l i d expands u n i f o r m l y when t h e l i q u i d v e l o c i t y 1s above t h e minimum f l u 1 d 1 z 1 n g v a l u e s and t h e gas phase passes t h r o u g h t h e bed as d i s p e r s e d bubbl e f l o w . A t h i gh gas r a t e s , t h e t u r b u l e n c e 1s b r o u g h t by t h e gas w i t h i n t h e bed.

2 . 1 . 1 Adva nt a ges and d 1 s a d v a n t a g e s o f t h r e e - p h a s e f l u l d l z e d beds

F l u l d l z e d beds possess s e v e r a l a d v a n t a g e s o v e r o t h e r t y pe s o f m u l t i p h a s e r e a c t o r s , some o f t h e s e a d v a n t a g e s a r e l i s t e d be l ow:

I ) t h e e x c e l l e n t mi x i n g o f s o l i d s l e a d s t o e s s e n t i a l l y I s o t h e r m a l c o n d i t i o n s t r o u g h o u t t h e r e a c t o r . Mor e o v e r , t h e bed t e m p e r a t u r e 1s e a s i l y c o n t r o l l e d as a

r e s u l t o f t h e hi gh t he r ma l c a p a c i t y o f t h e l i q u i d , I I ) s o l i d s can be added or w i t h d r a w n c o n t i n u o u s l y f rom

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111) t h e r a t e o f h e a t t r a n s f e r bet ween t h e bed and t h e col umn w a l l 1s e x t r e m e l y h i g h .

T he r e a r e , however , a number o f d l s a d v a n t g e s o f t h r e e -phase f l u l d l z a t l o n whi ch may make I t s use u n d e s i r a b l e . Those d i s a d v a n t a g e s can be summer l zed as f o l l o w s :

I ) n o n - u n i f o r m r e s i d e n c e t i me because o f t he. e x c e l 1 e n t mi x i n g o f s o l i d s . Ther e by a n o n - u n i f o r m s o l i d p r o d u c t 1s o b t a i n e d ,

I I ) b a c k ml x l n g o f r e a c t a n t s and p r o d u c t s w i l l a l s o o c  c ur w h i l e t h e y a r e absor bed on t h e movi ng c a t a l y s t . T h i s r e s u l t s I n , l o s s o f y i e l d and l o w e r i n g o f c on v e r s i o n ,

I I I ) t h r e e - p h a s e f l u l d l z e d beds a r e c h a r a c t e r i z e d by r e l a t i v e l y hi gh p r e s s u r e d r o p . T h i s may make t h e i r use u n e c o n o m i c a l ,

1v ) e r o s i o n o f t h e v e s s e l may oc c ur as a r e s u l t o f t h e s o l i d m o t i o n .

2 . 2 Bubbl e Columns

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At h i g h e r gas v e l o c i t i e s w i t h an I n c r e a s i n g number o f b u b b l e s , t h e f l o w becomes u n s t a b l e and c o a l e s c e n c e s e t s 1n l e a d i n g t o l a r g e r d i a m e t e r b u b b l e s . T h i s f l o w r e g i me ( wher e l a r g e b u bbl e s w i t h smal l bubbl e s a r e p r e s e n t ) I s c a l l e d h e t e r o g e n o u s r e g i m e .

2 . 2 . 1 Adv a nt a ge s and d 1 s a d v a n t a g e s o f b u bb l e col umns

The mai n a d v a n t a g e s o f t h e bubbl e col umn o v e r o t h e r t y p e s o f I 1 q u 1 d - g a s c o n t a c t o r a r e as f o l l o w s :

I ) t h e absence o f any movi ng p a r t s . Thus no s p e c i a l me c h a n i c a l s e a l s a r e r e q u i r e d when h i g h p r e s s u r e c o n d i t i o n s a r e use d,

I I ) good mass and h e a t t r a n s f e r c h a r a c t e r l s t 1 c s ,

I I I ) s i mp l e c o n s t r u c t i o n and minimum ma i n t e n a n c e a r e r e -q u 1 r e d ,

1v ) smal l f l o o r space r e q u i r e m e n t s .

Bubbl e col umns a l s o s u f f e r f rom s e v e r a l d i s a d v a n t a g e s . The f o l l o w i n g a r e some o f them:

I ) 1n bubb l e col umns w i t h h i gh l e n g t h t o d i a m e t e r r a  t i o , c o a l e s e c e n c e o f b u bb l e s w i l l o c c u r , and hence a d e c r e a s e o f t h e 1 n t e r f a c 1 a l a r e a a l o n g t h e h e i g h t o f t h e col umn,

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2 . 3 Mass T r a n s f e r 1n T h r e e - P h a s e F I u i d 1 z e d Beds

Resear ch work 1n t h r e e - p h a s e f 1u 1 d 1 z a t l o n , whi ch spans ov e r t h e l a s t two d e c a d e s , has been c o n c e r ne d w i t h h y d r o d y  nami cs and mass t r a n s f e r . A g r e a t deal o f t h e e f f o r t has been d e v o t e d t o t h e f i r s t t o p i c , howev e r , 1n t h e case o f mass t r a n s f e r , r e l a t i v e l y much l e s s work has been done. A1-v a r e z - C u e n c a ( 1 9 7 9 ) a t t r i b u t e d t h i s I m b a l a n c e t o t h e f a c t t h a t t h e s t udy o f hy dr ody na mi c s r e q u i r e s r e l a t i v e l y s i mp l e and smal l e q u i p m e n t , wher eas s t u d y i n g mass t r a n s f e r r e q u i r e s r e l a t i v e l y l a r g e and e l a b o r a t e e x p e r i m e n t a l s e t - u p s .

The a x i a l d i s p e r s i o n c o e f f i c i e n t s p e c i f i e s t h e m i x i n g 1n a r e a c t o r . For e x a mp l e , when t h e a x i a l d i s p e r s i o n c o e f f i  c i e n t , E , a pp r oa c he s a v e r y hi gh v a l u e , t h i s means t h a t t h e f l o w 1s p e r f e c t l y mi x e d . On t h e o t h e r hand when t h e a x i a l d i s p e r s i o n c o e f f i c i e n t , Ey, e q u a l s z e r o , I t means t h a t t h e r e 1s no mi x i n g 1n t h e d i r e c t i o n o f f l o w , and t h a t p l u g f l o w c o n d i t i o n s e x i s t .

I n t h e p h y s i c a l a b s o r p t i o n o f gases I n l i q u i d s , t h e v o l u  m e t r i c mass t r a n s f e r c o e f f i c i e n t can be r e p r e s e n t e d by t he f o l l o w i n g e q u a t i o n :

N = K^a( C* - C) ( 2. 1)

Whe r e ,

N = t h e r a t e o f a b s o r b t l o n o f t h e gas I n t h e f l u i d . C ■ t h e c o n c e n t r a t i o n o f d i s s o l v e d gas

1n t he b u l k o f t h e l i q u i d .

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10

= t h e mass t r a n s f e r c o e f f l c e n t .

a ■ t h e I n t e r f a c i a l a r e a bet ween t h e gas and l i q u i d p e r u n i t vol ume o f t h e r e a c t o r .

The v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t 1s t h e p a r a m e t e r used 1n mass t r a n s f e r p r o c e s s e s t o d e s c r i b e t h e d e g r e e o f p h y s i c a l a b s o r p t i o n o f a gas 1n a l i q u i d . Hence when ( K^a)

I n c r e a s e s t h e r e s i s t a n c e d e c r e a s e s .

A s ur v e y o f mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d bed 1s now 1n o r d e r .

The r a t e s o f I 1 q u 1 d - g a s mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds have been s t u d i e d by a number o f w o r k e r s . A 1 v a r e z - C u e n c a ( 1 9 7 9 ) c i t e d 1n h i s work t h a t Ma s s 1 m1 l l a e t

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11

O s t e r g a a r d and S u c h o z e r b r s k 1 ( 1 9 6 8 ) I n v e s t i g a t e d t h e r a t e o f t r a n s f e r o f oxygen f r om t h e gas phase t o t h e l i q u i d phase 1n beds o f p a r t i c l e s f l u l d l z e d by w a t e r and a m i x t u r e o f car bon d i o x i d e and n i t r o g e n . The s o l i d phase c o n s i s t e d o f 0 . 1 and 0 . 6 cm g l a s s b e a d s . E x p e r i me n t s wer e c a r r i e d o u t 1n a col umn t h a t measur ed 10 cm I . D and 29 cm h i g h . The maximum gas m i x t u r e s u p e r f i c i a l v e l o c i t y was 8 . 4 c m/ s . L i q u i d sam p l e s wer e t a k e n a t s i x p o i n t s 1n t h e col umn and a n a l y z e d v o -1u m e t e r l c a l l y w i t h ba r i um h y d r o x i d e . The p l u g f l o w model was empl oyed t o c a l c u l a t e v a l u e s o f t h e mass t r a n s f e r c o e f 

f i c i e n t ( K ^ a ) . The f o l l o w i n g o b s e r v a t i o n s wer e made by t h o s e a u t h o r s :

I ) t h e v a l u e s o f ( K^a ) I n c r e a s e d w i t h gas v e l o c i t y , b u t wer e r e a l t l v e l y I n d e p e n d e n t o f t h e l i q u i d v e  l o c i t y ,

I I ) beds o f 0 . 6 cm p a r t i c l e s wer e f e a t u r e d by hi gh r a t e o f mass t r a n s f e r , on t h e o t h e r hand beds o f 0 . 1 cm p a r t i c l e s wer e c h a r a c t e r l z e d by l ow r a t e s o f mass t r a n s f e r ,

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12

Ac c o r d i n g to O s t e r g a a r d and S u c h o z e r b r s k l ( 1 9 6 8 ) t he v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t I n c r e a s e d w i t h I n c r e a s  i ng t h e gas s u p e r f i c i a l v e l o c i t y (Vg ) . T h i s f a c t 1s g e n e r  a l l y a d m i t t e d , b u t no c o n s i s t e n c y e x i s t as f a r as t h e e f f e c t o f l i q u i d s u p e r f i c i a l v e l o c i t y (Vz ) 1s c o n c e r n e d . For I n  s t a n c e , A1 v a r e z - Cu e n c a and Ne r e n b e r g ( 1 9 8 1 ) r e p o r t e d t h a t ( K^a) a v e r a ge d o v e r t h e e n t i r e col umn I n c r e a s e s w i t h V^. I t 1s obvi ous t h a t t he f l o w r a t e r anges c ov e r e d 1n t h e f o r me r st udy wer e s m a l l . C o n s e q u e n t l y , t h e e f f e c t s o f j e t s c o u l d not be o b s e r v e d .

I t 1s o f I n t e r e s t t o n o t e t h a t t h e o c c u r r e n c e o f maximum v a l u e s o f ( a ) whi ch wer e obs e r v e d by O s t e r g a a r d and Su c h o z e r b r s k l ( 1 9 6 8 ) a t y * 50 cm has been c o n f i r m e d by A l v a -r e z - Cu e nc a and Ne -r e nbe -r g ( 1 9 8 1 ) f o r beds o f g l a s s bead p a r  t i c l e s me as ur i ng 0 . 3 cm and 0 . 5 cm d i a m e t e r s .

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13

I ) t he d e c r e a s e o f h y d r o s t a t i c p r e s s u r e w i t h I n c r e a s  ing d i s t a n c e from t h e d i s t r i b u t o r w i l l cause an I n  c r e a s e 1n gas vol ume. T h i s may w e l l a f f e c t t he a b  s o r p t i o n c o e f f i c i e n t , b ut t h e I n f l u e n c e may p r o b a b l y be d i s r e g a r d e d 1n t h e p r e s e n t c a s e , where t he maximum change 1n t h e s t a t i c p r e s s u r e 1s o f t he o r d e r o f 20%,

I I ) t he a b s o r p t i o n o f oxygen causes t h e gas mass f l o w r a t e t o dec r e a s e w i t h I n c r e a s i n g d i s t a n c e . A l s o , t h i s e f f e c t may p r o b a b l y be d i s r e g a r d e d 1n t he s e s yst ems, where t h e maximum r e d u c t i o n 1s o f t h e o r  der o f 5%,

I I I ) a x i a l m i x i n g 1n t he gas phase may be n e g l e c t e d 1n t he s e e x p e r i m e n t s s i n c e t h e gas phase c o n s i s t s o f pure oxygen,

1v ) a x i a l m i x i n g 1n t he l i q u i d phase may I n f l u e n c e t he a b s o r p t i o n c o e f f i c i e n t s .

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( K . a ) 1s a p p r o x i m a t e l y p r o p t l o n a l t o V „ . On t he o t h e r hand

* g

( K^a) was found t o d e c r e a s e w i t h I n c r e a s i n g w h i c h , o b v i  o u s l y , c o n t r a d i c t s t h e f i n d i n g s o f O s t e r g a a r d and Fosbol

( 1 9 7 2 ) .

Dhanuka and St epanek ( 1 9 8 0 ) s t u d i e d g a s - l 1 q u 1 d mass t r a n s f e r 1n a t h r e e - p h a s e f l u l d l z e d beds. The v a l u e s o f ( K^a) were c a l c u l a t e d from t h e e x p e r i m e n t a l d a t a by means o f t h e p l u g f l o w model . They c l a i m e d t h a t t h e v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t I n c r e a s e s w i t h I n c r e a s i n g t h e gas s u p e r f i c i a l v e l o c i t y b u t 1s I n d e p e n d e n t o f t h e l i q u i d s u p e r f i  c i a l v e l o c i t y ( v ^ i * The v a l u e s o f ( K^a) o b t a i n e d 1n t h e i r study a gr e e d w i t h i n ± 30% w i t h t ho s e r e p o r t e d by O s t e r g a a r d and Coworker ( 1 9 7 2 ) and Lee and W o r t h i n g t o n ( 1 9 7 4 ) .

V a i l e t al . ( 196 8) p r e s e n t e d d a t a on l o n g t u d l n a l m i x i n g o f t h e gas and l i q u i d phases 1n a t h r e e phase syst em. T h e i r equi pment c o n t a i n e d a r e a c t o r whi ch measured 1 4 . 6 cm I . D and 150 cm h i g h . The I n v e s t i g a t i o n s were conduct ed w i t h two d i s t r i b u t o r g r i d s . A i r was used as t h e gaseous p h a s e , t a p w a t e r as t h e l i q u i d phas e, and t h e s o l i d phase was spheres o f s l u r r y . Gas v e l o c i t y , Yg , ranged from 1 . 5 t o 9 . 9 c m/ s . Two l i q u i d v e l o c i t i e s were empl oyed; v i z . , 1 . 7 and 3 . 0 7 c m/ s , r e s p e c t i v e l y . The e x p e r i m e n t a l d a t a were p r oce sse d u s  ing t h e a x i a l d i s p e r s i o n mo d el . Ya1l e t a l . ( 1 9 6 8 ) r e p o r t e d t h a t E I n c r e a s e d w i t h V b u t d e c r e a s e d w i t h V , .

y g *•

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15

was employed t o st udy t h e s e e f f e c t s . The r e s u l t s o f t h e study o f M l c h e l s e n and O s t e r g a a r d ( 1 9 7 0 ) can be summarized as f o l l o w s :

I ) beds o f 0 . 6 cm p a r t i c l e s were c h a r a c t e r i z e d by a v e r y low de g r e e o f m i x i n g 1n t h e l i q u i d phase. The I n t e n s i t y o f m i x i n g 1s I n d e p e n d e n t o f t he gas f l o w r a t e and I n c r e a s e d s l i g h t l y w i t h I n c r e a s i n g l i q u i d v e l o c 1 t y ,

I I ) beds o f 0 . 1 cm p a r t i c l e s a r e c h a r a c t e r i z e d by a hi gh de g r e e o f m i x i n g . The I n t e n s i t y o f m i x i n g I n  c r e a s e d w i t h d e c r e a s i n g l i q u i d f l o w r a t e and I n  c r e a s i n g gas f l o w r a t e . I t was n o t i c e d t h a t a v a r i  a t i o n 1n d i s p e r s i o n o c c u r r e d w i t h changes 1n V& and

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Cherry e t a l . ( 1 9 7 8 ) I n v e s t i g a t e d t he par amet er s I n f l u  encing d i s p e r s i o n 1n a t h r e e - p h a s e f l u l d l z e d beds. The ob j e c t i v e s o f t h e i r study were to de t e r mi n e t he e f f e c t o f l i q  ui d v e l o c i t y , gas v e l o c i t y and p a r t i c l e s i z e on t he mass t r a n s f e r c h a r a c t e r i s t i c s o f t h r e e - p h a s e f l u l d l z e d beds. The e xper i ment s were c a r r i e d o ut 1n 15 cm 1 . 0 (6 i n ) and 7 . 5 cm

(3 i n ) I . D columns, using gl a ss beads o f d i f f e r e n t d i a me t e r s ( 0 . 3 , 0 . 4 6 and 0 . 6 cm) as t he s o l i d phase. The l i q u i d v e l o c  i t i e s (aqueous g l y c e r o l ) ranged from 5 to 12 cm/ s, and the gas v e l o c i t i e s ranged from 4 to 16 cm/ s. They concluded t h a t the v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t , ( K ^ a ) , i n c r e a s e d w i t h I n c r e a s i n g t he gas v e l o c i t y and p a r t i c l e d i a m e t e r . F u r  t her mor e, they c l a i med t h a t t h e r e 1s no c o n s i s t e n t r e l a t i o n  ship between l i q u i d v e l o c i t y and ( K ^ a ) . They al so r e p o r t e d t h a t t he a x i a l d i s p e r s i o n c o e f f i c i e n t s , E , 1n t he 15 cm I . D column were h i g h e r than t hose 1n the 7 . 5 cm I . D . They j u s t i  f i e d t h a t by I n d i c a t i n g t h a t t he s o l i d motion and backml xl ng are more p e r m i t t e d I n t he l a r g e column.

The mass t r a n s f e r o f oxygen between a i r and dexogenated w a t e r 1n t h r e e - p h a s e f l u l d l z e d beds c o n t a i n i n g ( 0 . 1 , 0 . 3 and 0 . 5 cm g l a ss beads) was s t u d i e d by A l v a r e z - C u e n c a ( 1 9 7 9 ) . Ex per i ments were performed 1n a t wo - d i me n si o na l p l e x i g l a s s column which had 51 sampling taps from which l i q u i d samples could be wi t hdrawn and a n a l y z e d . The column measured 250 cm

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17

ranged from 4 to 28 c m/ s . The l i q u i d v e l o c i t i e s ranged b e  tween t h e a p p r o p r i a t e minimum f l u 1 d 1 z 1 n g v e l o c i t y and t h e upper l i m i t ( 10 c m/ s ) p e r m i t t e d by t h e e x p e r i m e n t a l s e t - u p .

The c o n c e n t r a t i o n p r o f i l e s a t low gas r a t e s ( 4 cm/ s) were g e n e r a l l y S - s h a p e d . The oxygen c o n c e n t r a t i o n r emai ned p r a c  t i c a l l y c o n s t a n t w i t h i n t h e g r i d r e g i o n . F u r t h e r m o r e t he c o n c e n t r a t i o n I n c r e a s e d 1n t h e b u l k r e g i o n o f t h r e e - p h a s e Tl u1d1zed bed. T h e r e f o r e t h e s t e e p r i s e 1n c o n c e n t r a t i o n took p l a c e 1n t h e s o l i d - f r e e zone above t h e bed. At hi gh r a t e s (28 c m / s ) , t h e c o n c e n t r a t i o n I n c r e a s e d r a p i d l y w i t h h e i g h t , so t h a t t he S- shaped c ur ve s became l e s s pr onouc ed.

A l v a r e z - C u e n c a e t a l . ( 1 9 7 9 , 1 9 7 9 a ) a n a l y z e d , from an e x  p e r i m e n t a l p o i n t v i e w , t he v a l i d i t y and l i m i t a t i o n s o f t he t h r e e - f l o w model s, l . e , t he p l u g f l o w model , a x i a l d i s p e r  sion model and t h e t w o - z o n e model which was proposed by A l -v a r e z - Cu e n c a ( 1 9 7 9 ) . A c c o r d i n g to t h e i r a n a l y s i s t he f o l l o w 

ing c o n c l u s i o n s were r e p o r t e d :

I ) a t low gas s u p e r f i c i a l v e l o c i t y ( Vg a 4 c m/ s ) t h e c o n c e n t r a t i o n p r o f i l e s 1n beds o f 0 . 1 cm p a r t i c l e s i z e were f a i r l y r e p r e s e n t e d by t he p l u g f l o w and t h e a x i a l d i s p e r s i o n mode l s ,

I I ) a t hi gh gas and l i q u i d s u p e r f i c i a l v e l o c i t i e s n e i  t h e r t h e pl ug f l o w model nor t h e a x i a l d i s p e r s i o n model s a t i s f a c t o r i l y d e s c r i b e d t h e c o n c e n t r a t i o n

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111) t h e t w o - z o n e model p r e s e n t e d a s i g n i f i c a n t I m p r o v e  ment 1n c ompar i son w i t h t h e a x i a l d i s p e r s i o n model and t h e p l u g f l o w mo d e l . However, 1 t was n o t s uc  c e s s f u l 1n p r e d i c t i n g t h e S- s h a p e d c o n c e n t r a t i o n p r o f i l e s o b s e r v e d a t low gas and l i q u i d s u p e r f i c i a l v e l o c 1 t i e s .

A l v a r e z - C u e n c a e t al . ( 1 9 8 4 ) c on c l u d e d t h a t ( K^ a ) I n  c r e a s e d l i n e a r l y w i t h t h e gas v e l o c i t y r e g a r d l e s s o f t h e model use d. They a l s o r e p o r t e d t h a t t h e v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t d e t e r m i n e d by means o f t h e t w o - z o n e model I n c r e a s e d w i t h I n c r e a s i n g t h e l i q u i d s u p e r f i c i a l v e  l o c i t y . F u r t h e r m o r e , A l v a r e z - C u e n c a and N e r e n b e r g ( 1 9 8 1 ) s t a t e d t h a t ( K^a ) c a l c u l a t e d from t h e p l u g f l o w model I n  c r e a s e d w i t h I n c r e a s i n g t h e l i q u i d s u p e r f i c i a l v e l o c i t y .

2 . 4 Models f o r D e s c r i b i n g Mass T r a n s f e r I n T h r e e - P h a s e FLUTUIZFP~BKDS' --- ---2 . 4 . 1 Ge ne r a l

A m a t h e m a t i c a l m o d e l , I s an e x p r e s s i o n c a p a b l e o f symbol  i z i n g a r e a l p r o c e s s . I n t h e d e v e l o p m e n t o f any m a t h e m a t i c a l model one has t o b e a r 1n mind t h a t good m a t h e m a t i c a l models

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I n t he l i g h t o f t h e p r e s e n t l i t e r a t u r e s e a r c h , 1 t has been n o t i c e d t h a t even when s i m i l a r e x p e r i m e n t a l and t h e o r l -cal c o n d i t i o n s e x i s t e d , d i f f e r e n t r e s u l t s were o b t a i n e d . T hi s c o n t r o v e r s y m i g h t be a t t r i b u t e d t o absence o f a d e q u a t e m a t h e m a t i c a l model s .

The s i m p l e s t r e a c t o r model 1s t h e p l u g f l o w model ( PFM) . No r e a l r e a c t o r can be d e s c r i b e d by such a m o d e l , however , some r e a c t o r s c l o s e l y approach t he I d e a l b e h a v i o r d e s c r i b e d by t he pl ug f l o w model . I n s e v e r a l o t h e r cases t h e a x i a l d i s p e r s i o n model has been w i d e l y u t i l i z e d t o d e s c r i b e mass t r a n s f e r 1n t h r e e - p h a s e f l u l d l z e d beds.

The t wo - z o n e model has been d e v e l o pe d by A l v a r e z - C u e n c a ( 1 9 7 9 ) and was shown to g i v e b e t t e r f i t f o r t h e e x p e r i m e n t a l data t han t h e pl ug f l o w model and t h e a x i a l d i s p e r s i o n model e s p e c i a l l y a t v e r y l a r g e gas and l i q u i d s u p e r f i c i a l v e l o c i  t i e s .

2 . 4 . 2 Rev1ew o f e x 1 s t 1 n g models 1) The p l u g f 1ow model ( PFM)

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a) n o n- u n 1 f o r m v e l o c i t y p r o f i l e ,

b) v e l o c i t y f l u c t u a t i o n due t o m o l e c u l a r o r t u r b u  l e n t d i f f u s i o n ,

c) s h o r t c i r c u i t i n g , by p a ss i n g and c h a n n e l i n g o f f l u i d .

I n t h e d ev e l opme nt o f t h e p l u g f l o w model , I t 1s assumed t h a t t h e r e 1s no a x i a l m i x i n g 1n e i  t h e r f l u i d phase. Under s t e a d y s t a t e c o n d i t i o n s , t h e d i f f e r e n t i a l e q u a t i o n and t h e boundary c on d i t i o n s d e s c r i b i n g mass t r a n s f e r a r e as f o l l o w s :

The c o n c e n t r a t i o n o f t he d i f f u s i n g s p e c i e s I s

c e n t r a t l o n and y 1s t h e d i s t a n c e above t h e g r i d . E q u a t i o n ( 2 . 2 ) can be I n t e g r a t e d by s e p a r t l n g t he v a r i a b l e s , t hen u si ng t h e boundary c o n d i  t i o n s g i v e n by e q u a t i o n ( 2 . 3 ) as f o l l o w s :

■ KAa <C* ' C>

(

2

.

2

)

y = 0 C = C,₀ ( 2. 3)

*

denot ed by C. C r e p r e s e n t s t h e e q u i l i b r i u m c

on-/

C dC Kja U . 4 )

C

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21

The e x p e r i m e n t a l d a t a were f i t t e d t o E q u a t i o n ( 2 . 5 ) 1n o r d e r t o c a l c u l a t e ( K ^ a ) as d e s c r i b e d 1n C h a p t e r 3 . The comput er program used I s g i v e n 1n Appe ndi x C.

11) The a x i a l d 1 s p e r s l o n m o d e l ( ADM)

The a x i a l d i s p e r s i o n model 1s a two p a r a m e t e r model whi ch t a k e s I n t o a c c o u n t some d e g r e e o f b a c k -m i x i n g 1n t h e d i r e c t i o n o f f l o w . The a x i a l d i s p e r  s i o n c o e f f i c i e n t c h a r a c t e r i z e s t h e d e g r e e o f b a c k -m i x i n g d u r i n g f l o w and a c c o u n t s f o r m i x i n g b o t h by m o l e c u l a r d i f f u s i o n and by t u r b u l e n t e d d i e s . The a x i a l d i s p e r s i o n model 1s based on t h e f o l l o w i n g a s s u m p t l o n s :

a) t h e c o n c e n t r a t i o n and t h e f l u i d v e l o c i t y a c r o s s t he v e s s e l d i a m e t e r a r e c o n s t a n t ,

b) t h e m a g n i t u d e o f d i s p e r s i o n ( a x i a l d i s p e r s i o n c o e f f i c i e n t ) 1s I n d e p e n d e n t o f p o s t i o n w i t h i n

t he v e s s e l .

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22

d2C „ dC *

Ev H “ Vjl — + K£a <C -C) = 0 <2 *6 >

y dy * dy *

The L a n g m u l r ' s Boundary c o n d l t 1 o n s ( L a n g m u l r , 1 912) a r e g i v e n by:

y - L § - 0 ( 2. 7 )

VjCtO) - V4C(0) - Ey ( 2. 8 )

wh e r e , ' + ' I n d i c a t e s t h a t t h e f l o w 1s above t h e r e f e r e n c e l e v e l ( g r i d l e v e l 1n our c a s e ) , and

I n d i c a t e s t h a t t h e f l o w 1s bel ow t h e r e f e r e n c e l e v e l ( g r i d l e v e l 1n our c a s e ) .

E q u a t i o n ( 2 . 6 ) 1s a d i f f e r e n t i a l e q u a t i o n whi ch has t h e f o l l o w i n g s o l u t i o n :

C - Aepy + B eny ( 2. 9)

where

n = (2.1 0)

p = v „ i 2. i i )

£ 2E.

i

eE.

p - (1 + 4 P ^ ) 1 / 2 ( 2 . 1 2 )

£

e « - 4 - (2.13)

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23

**-nV)l(C*-Co>eln' P)L**

A p[Eyn( 1 - e ln' p, L) - V ^ l - £ e tn‘ p, L) ] v . ( c * - c n)

8 ’ Eyn( 1 - e (n- p)L) - Vt ( l - £ e ln- p,L)

E x p e r i m e n t a l d a t a a r e f i t t e d t o E q u a t i o n ( 2 . 9 ) to p r o v i d e v al ue s f o r t h e c o n s t a n t s A, B, p and n. These c o n s t a n t s ar e then used i n E q u a t i o n s ( 2 . 1 0 ) t o ( 2 . 1 5 ) to d e t e r m i n e t he v a l u e s o f t h e v o l u m e t r i c mass t r a n s f e r and t h e a x i a l d i s p e r 

sion c o e f f i c i e n t s .

111) The t w o - z o n e model ( T - Z M )

The work o f A l v a r e z - C u e n c a ( 1 9 7 9 ) r e v e a l e d t h e pr ese nce o f two d i s t i n g u i s h a b l e mass t r a n s f e r zones i n t h r e e - p h a s e beds and bubb l e col umns, 1 . e , t h e g r i d zone and t h e b u l k zone. The e x i s t e n c e o f such two d i s t i n g u i s h a b l e mass t r a n s f e r zones l e d A l v a -r e z - C u e n c a ( 1 9 7 9 ) and A l v a -r e z - C u e n c a e t a l . ( 1 9 7 9 a and 1980) to t he I d e a o f I n t e r f a c i n g two p l u g f l o w models a t t he boundary o f s e p e r a t l o n between t he g r i d and b u l k z o n e s . The d eve l opment o f t h e model 1s as f o l l o w s :

a) G r i d zone

E q u a t i o n ( 2 . 1 6 ) r e p r e s n t s t h e pl ug f l o w model used 1n t h e g r i d r e g i o n :

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24

where 1s t h e v o l u m e t r i c mass t r a n s f e r c o e f f i c i e n t 1n t he g r i d zone.

The boundary c o n d i t i o n a r e :

y = 0 C = Cq (.2.17)

The s o l u t i o n o f E q u a t i o n ( 2 . 1 6 ) 1s g i v e n by

C* - C = (C* - CQ)e“0y (.2.18) where

(K.a)Tr

9 -

h

TG (2-19)

I

b) Buik zone

E q u a t i o n ( 2 . 2 0 ) r e p r e s e n t s t h e pl ug f l o w mod el used 1n t he b u l k zone :

dC (K0a ) TR *

3y - y TB (c - C) y i b (2.20)

where (K a) 1s t h e v o l u m e t r i c mass t r a n s f e r

& TB

c o e f f i c i e n t 1n t he bul k zone. The boundary con d i t i o n a r e :

y - b C - Cb (2.21)

The s o l u t i o n t o E q u a t i o n ( 2 . 2 0 ) I s g i v e n by:

C* - C - G e~ay (2.22)

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G = (C* - C0)e^a"9,b

25

(2.24)

A l v a r e z - C u e n c a ( 1979) and A l v a r e z - C u e n c a and N e r e n b e r g ( 1 9 8 1 ) c l a i m e d t h a t t h e t wo - z o n e model r e p r e s e n t e d a s i g n i f i c a n t Improvement o v e r t h e a x i a l d i s p e r s i o n model o r pl ug f l o w model . Ac c o r d i n g t o A l v a r e z - C u e n c a ( 1 9 7 9 ) , t h e b e t t e r p e r  f ormance o f t h e t wo - z o n e model can be a t t r i b u t e d t o t a k i n g I n t o a c c o u n t t h e t h e e x i s t e n c e o f two zones 1n which t he mass t r a n s f e r r a t e s a r e d i f 

f e r e n t .

However, as I n d i c a t e d e a r l i e r one can que s  t i o n t h e p h y s i c a l grounds on which t he t wo - z o n e model was d e v e l o p e d , s i n c e 1 t was t a c i t l y a s 

sumed 1n t h e dev el opment o f t h a t model t h a t pl ug f l o w c o n d i t i o n s p r e v a i l 1n t h e e x i s t i n g two mass t r a n s f e r z o n e s . T h i s assumpti on c o n t r a d i c t s t he f a c t t h a t two d i s t i n c t zones e x i s t , 1n which d i f f e r e n t mass t r a n s f e r c h a r a c t e r l s t 1 c s a r e p r e s e n t .