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Gas spouting of fine particles Chandnani, Pratap P. 1984

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GAS SPOUTING OF FINE PARTICLES  By PRATAP P. CHANDNANI B.Tech. I n d i a n I n s t i t u t e of Technology,  Bombay,  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Chemical  Engineering)  We accept t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d  July  1984  ® Pratap P. Chandnani,  1984  1982  In p r e s e n t i n g requirements  this thesis f o r an  of  British  it  freely available  agree that  in partial  advanced degree a t  Columbia, I agree that for reference  permission by  understood that for  h i s or  be  her  shall  be  DE-6  (3/81)  WQ.  s h a l l make  and  study.  I  I ,  If**  the  of  further this  Columbia  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  CKHl CArL  The U n i v e r s i t y o f B r i t i s h 1956 Main M a l l V a n c o u v e r , Canada V6T 1Y3 Date  Library  g r a n t e d by  permission.  Department o f  University  representatives.  not  the  the  copying or p u b l i c a t i o n  f i n a n c i a l gain  the  f o r extensive copying of  f o r s c h o l a r l y p u r p o s e s may department or  f u l f i l m e n t of  written  - ii ABSTRACT S p o u t i n g i s a w e l l e s t a b l i s h e d g a s - s o l i d s c o n t a c t i n g technique f o r coarse p a r t i c l e s ( d ^> 1 mm) which a r e not r e a d i l y p  fluidized.  S p o u t i n g of f i n e p a r t i c l e s (dp < 1 ram), however, i s a s p a r s e l y subject:  touched  the few r e p o r t s i n the l i t e r a t u r e a r e not i n complete harmony  w i t h each o t h e r , and they l e a d to a somewhat confused p i c t u r e about the s p o u t a b i l i t y of f i n e  particles.  E x p e r i m e n t s were conducted i n a 152-mm diameter t r a n s p a r e n t c o n i c a l - c y l i n d r i c a l h a l f - c o l u m n w i t h p a r t i c l e s r a n g i n g i n s i z e from 90 t o 1000  ym and i n d e n s i t y from 900 to 8900 kg/m . 3  The d i f f e r e n t f l o w  regimes which r e s u l t on v a r y i n g bed h e i g h t and gas v e l o c i t y f o r a g i v e n p a r t i c l e s p e c i e s were c a r e f u l l y observed, v i d e o - t a p e d and mapped.  The  c r i t e r i a of both G e l d a r t (1973) and M o l e r u s (1982) f o r s p o u t a b l e p a r t i c l e s ( c l a s s i f i e d as Group D by G e l d a r t ) were shown to be u n s a t i s factory.  F o l l o w i n g Ghosh (1965), however, i t was found t h a t f o r m a t i o n of  a s t a b l e spout was ensured o n l y i f a c r i t i c a l r a t i o (25.4 i n our e x p e r i m e n t s ) of i n l e t o r i f i c e s i z e to p a r t i c l e diameter was not exceeded. Measurements were a l s o made of bed p r e s s u r e d r o p s , s o l i d s c i r c u l a t i o n p a t t e r n s and r a t e s , dead zones, l o n g i t u d i n a l a n n u l a r gas v e l o c i t y p r o f i l e s , spout c o n t o u r s and f o u n t a i n h e i g h t s .  I t was found  t h a t the mechanism by which s p o u t i n g i s t e r m i n a t e d i n a c o a r s e p a r t i c l e bed, namely, f l u i d i z a t i o n of the a n n u l u s , c o u l d not account f o r i t s t e r m i n a t i o n i n the p r e s e n t beds.  The h y p o t h e s i s t h a t t e r m i n a t i o n was  caused i n s t e a d by c h o k i n g of the spout was r e i n f o r c e d by the f a c t the theory of c h o k i n g i n s t a n d p i p e s c o u l d be a p p l i e d p r e d i c t the end of s t a b l e s p o u t i n g .  that  to s a t i s f a c t o r i l y  - iii TABLE OF CONTENTS Page ABSTRACT  i i  LIST OF TABLES  vi  LIST OF FIGURES  v i i  ACKNOWLEDGMENTS  x i  CHAPTER 1 - INTRODUCTION  1  CHAPTER 2 - LITERATURE REVIEW  5  2.1  S p o u t a b i l i t y of F i n e P a r t i c l e s and the Conditions Affecting I t  5  2.1.1  E f f e c t of i n l e t s i z e  5  2.1.2  E f f e c t of p a r t i c l e s i z e and density  2.2  11  B a s i c S p o u t i n g Parameters  13  2.2.1  Minimum s p o u t i n g v e l o c i t y  13  2.2.2  Maximum s p o u t a b l e bed depth  14  2.2.3  Spout diameter  16  2.2.4  Fountain height  17  2.3  Regime Maps  17  2.4  L o n g i t u d i n a l Annulus F l u i d v e l o c i t y and O v e r a l l Bed P r e s s u r e Drop Annular P a r t i c l e V e l o c i t y P r o f i l e and S o l i d C i r c u l a t i o n Rate  19 23  I n d i r e c t Approaches R e l e v a n t to S p o u t i n g of F i n e P a r t i c l e s . . .  24  2.5 2.6  CHAPTER 3 - APPARATUS AND BED MATERIALS 3.1  C h o i c e and D e s c r i p t i o n Apparatus  27 of E x p e r i m e n t a l 27  - iv Page 3.2  Bed M a t e r i a l s  33  CHAPTER 4 - REGIME MAPS AND CRITERIA FOR FINE PARTICLE SPOUTING  41  4.1  E x p e r i m e n t a l Procedure  41  4.2  R e s u l t s and T h e i r A n a l y s i s  44  4.2.1  Influence  44  4.2.2 4.2.3  E f f e c t of p a r t i c l e s i z e E f f e c t of p a r t i c l e d e n s i t y  53 58  4.2.4  Minimum and maximum velocities  58  4.2.5  4.2.6  of i n l e t diameter  spouting  E f f e c t of bed h e i g h t , maximum s p o u t a b l e bed d e p t h , and s t a b l e j e t length  60  P r e d i c t i o n of regime transformation....  64  CHAPTER 5 - OVERALL BED PRESSURE DROP AND LONGITUDINAL FLUID VELOCITY IN THE ANNULUS  70  5.1  70  Measurement Technique 5.1.1  O v e r a l l bed p r e s s u r e  drop  5.1.2  Longitudinal f l u i d velocity i n the annulus  5.2  70  71  R e s u l t s and D i s c u s s i o n  72  5.2.1  O v e r a l l bed p r e s s u r e  drop  72  5.2.2  Annular l o n g i t u d i n a l gas velocity  79  - vPage CHAPTER 6 - ANNULAR PARTICLE VELOCITY AND CIRCULATION RATE  84  6.1  Measurement Technique  84  6.2  R e s u l t s and T h e i r I n t e r p r e t a t i o n  87  6.2.1  E f f e c t of bed d e p t h and U / U  90  6.2.2  E f f e c t of p a r t i c l e s i z e  92  6.2.3  E f f e c t of cone a n g l e  92  ms  CHAPTER 7 - SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT ...  95  7.1  Measurement Technique  95  7.2  R e s u l t s and D i s c u s s i o n  95  7.2.1  Spout shape and d i a m e t e r  95  7.2.2  Fountain height  98  CHAPTER 8 - CONCLUSIONS AND RECOMMENDATIONS  104  8.1  Conclusions  104  8.2  Recommendations F o r F u r t h e r Work  106  NOTATION  107  REFERENCES  110  APPENDICES A - Rotameter C a l i b r a t i o n Curves  113  B - S o l i d Free P r e s s u r e Drop Curves  117  C - S t a t i c P r e s s u r e Probe C a l i b r a t i o n I n a Loose Packed Bed  121  D - E x p e r i m e n t a l Data  123  D.l  P r e s s u r e drop v s . f l o w r a t e  126  D.2  A n n u l a r gas v e l o c i t y  135  D.3  Solid c i r c u l a t i o n rate  136  D.4  Spout diameter and r e g i o n of circulation  .• • • •  ^0  - viLIST OF TABLES Pages T a b l e 3.1  P r o p e r t i e s of bed m a t e r i a l s  36  T a b l e 3.2  P a r t i c l e size distributions  38  T a b l e 4.1  O p e r a t i n g c o n d i t i o n s i n t h i s work v s . those of H e s c h e l and K l o s e (1981)  42  E x p e r i m e n t a l v a l u e s of minimum s p o u t i n g v e l o c i t y v s . eq. (2.3)  61  E x p e r i m e n t a l v s . p r e d i c t e d maximum s p o u t a b l e bed depths  63  E x p e r i m e n t a l and p r e d i c t e d j e t p e n e t r a t i o n depths f o r H > ^ , Q = Q  65  P r e d i c t i o n of maximum s t a b l e s p o u t i n g v e l o c i t y (= U ) by c h o k i n g c r i t e r i o n v s . e x p e r i m e n t a l v a l u e [= U ( H ) ]  67  Maximum s p o u t a b l e bed d e p t h , e x p e r i m e n t a l v s . p r e d i c t i o n through the theory of choking  69  R a t i o AP /AP _ « Cn - e x p e r i m e n t a l and ,ms, raF theoretical  78  T a b l e 4.2 T a b l e 4.3 T a b l e 4.4  m F  T a b l e 4.5  c  g  T a b l e 4.6  T a b l e 5.1 T a b l e 7.1  u  L o n g i t u d i n a l l y averaged spout diameter (experimental vs. predicted)  101  - viiLIST OF FIGURES Page F i g u r e 1.1  Schematic diagram of a spouted bed  2  F i g u r e 2.1a  Regime map. Sand, dp = 0.42 -0.83 mm, D = 15.2 cm, d^^ = 1.25 cm (Mathur and G i s h l e r , 1955)  7  Regime map. Sand, d = 0.42 -0.83 mm, D = 15.2 cm, d = 1.58 cm (Mathur and G i s h l e r , 1955)  7  Phase diagram. Semicoke, dp = 1-5 mm, D = 23.5cm, d = 3.05 cm, (Mathur and G i s h l e r , 1955)  8  P r e s s u r e drop v s . v e l o c i t y d a t a of H e s c h e l and K l o s e ( 1 9 8 1 ) . PVC, d = 90 ym, = 1.27 g/cm , p = 0.565 g/cm , a i r a t 80% r e l a t i v e h u m i d i t y  9  c  F i g u r e 2.1b  p  c  j[  F i g u r e 2.2  c  ±  F i g u r e 2.3  3  P p  F i g u r e 2.4  3  b  T y p i c a l p r e s s u r e drop v s . v e l o c i t y c u r v e f o r a spouted bed of coarse p a r t i c l e s  10  G e l d a r t (1973) and Molerus (1982) c r i t e r i a on a l o g - l o g p l o t . P a r t i c l e s below t h e l i n e are termed 'non - s p o u t a b l e ' and above i t as ' spoutable' .  12  (AP / AP p) v s . (H/D ) f o r d i f f e r e n t v a l u e s o f 8 (Morgan and L i t t m a n , 1980)  22  D e t a i l s o f the two h a l f c y l i n d r i c a l columns  28  F i g u r e 3.2  Photograph of the o r i f i c e p l a t e s  29  F i g u r e 3.3  D i f f e r e n t i n l e t types ( w i t h o u t any c o n t r a c t i o n o f the i n l e t ) f o r column 2  30  F i g u r e 2.5  F i g u r e 2.6 F i g u r e 3.1  F i g u r e 3.4  m s  m  c  Schematic of the o v e r a l l  equipment  layout  32  F i g u r e 3.5  Photograph of the equipment  34  F i g u r e 3.6  Schematic diagram of the s t a t i c p r e s s u r e probe  35  - viii  Page  F i g u r e 4.1  F i g u r e 4.2a F i g u r e 4.2b  F i g u r e 4.3 F i g u r e 4.4a F i g u r e 4.4b F i g u r e 4.5 F i g u r e 4.6  F i g u r e 4.7  T y p i c a l pressure drop v s . f l o w r a t e c h a r a c t e r i s t i c s o b t a i n e d upon r e p e a t i n g c o n d i t i o n s of H e s c h e l and K l o s e (1981) C r i t i c a l i n l e t diameter range f o r spouting vs. p a r t i c l e diameter  the 45  steady 47  C r i t i c a l i n l e t diameter (mid - p o i n t s of the ranges shown i n f i g . .4.2a) v s . p a r t i c l e diameter  48  Regimes on s p o u t i n g p a r t i c l e s w i t h d < 350 um P Regime map. Sand, dp = 401 um, d^ = 4.5 mm  51  Regime map. d^ = 6 mm  51  Sand, dp = 401  50  Mm,  Photographs of the d i f f e r e n t regimes shown i n f i g . 4.4  52  T r a n s i t i o n betwen regimes a l o n g X X f i g . 4.4b w i t h i n c r e a s i n g f l o w  54  1  5  in  E f f e c t of i n l e t s i z e on v a r i o u s regimes. Sand, d„ = 516 pm (a) d = 6 mm (b) d = 12.7 mm (c) d = 19.05 mm (above the c r i t i c a l l i m i t f o r steady s p o u t i n g )  55 & 56  Regime map - e f f e c t of i n l e t diameter. G l a s s , dp = 710 ym (a) = 6.0 mm (b) d = 12.7 mm  57  G e l d a r t (1973) and M o l e r u s (1982) c r i t e r i a f o r s p o u t a b i l i t y on a l o g - l o g s c a l e  59  P r e s s u r e drop vs. f l o w r a t e c h a r a c t e r i s t i c s f o r d i f f e r e n t bed h e i g h t s . PVC, d = 186 um, d. = 4.5 mm  74  P r e s s u r e drop v s . f l o w r a t e f o r d i f f e r e n t bet h e i g h t s . Sand, d = 516 um, d. = 6 mm.  74  ±  ±  F i g u r e 4.8  ±  ±  F i g u r e 4.9 F i g u r e 5.1a  P  F i g u r e 5.1b  i  p  - ix -  Page F i g u r e 5.1c E f f e c t of p a r t i c l e s i z e on p r e s s u r e Sand, H= 41 cm, d^ = 6 mm F i g u r e 5.2a  F i g u r e 5.2b  F i g u r e 5.3  drop. 75  Stagnant zone and r e g i o n of c i r c u l a t i o n w i t h i n c r e a s i n g f l o w r a t e . PVC, dp = 186 ym, d^ = 4.5 mm, H = 19.5 cm, A i r a t 80% r e l a t i v e h u m i d i t y  76  Stagnant zone and r e g i o n of c i r c u l a t i o n w i t h i n c r e a s i n g dp. Sand, H = 41cm, d^ = 6 mm  77  L o n g i t u d i n a l annular gas v e l o c i t y - e x p t . v s . t h e o r . Sand, U/U s 1 • 18 , d. = 6 mm, d =516 ym l p L o n g i t u d i n a l annular gas v e l o c i t y d i s t r i b u t i o n . Sand, dp = 401 ym, d^ = 6mm, U/U = 1.18 ms E f e c t of p a r t i c l e s i z e , i n l e t diameter and bed h e i g h t on l o n g i t u d u a l a n n u l a r gas v e l o c i t y . Sand, U/U =1.18 ' ms Nodal p o i n t s f o r p a r t i c l e v e l o c i t y determination =  m  F i g u r e 5.4  me  F i g u r e 5.5  F i g u r e 6.1  F i g u r e 6.2 a & b  F i g u r e 6.3  F i g u r e 6.4  81  82 85  R a d i a l and a x i a l p a r t i c l e v e l o c i t y g r a d i e n t s i n the annulus. Sand, dp = 516 ym, H = 50 cm, d = 6 mm, U/U = 1.08  88 & 89  R a d i a l l y averaged a n n u l a r p a r t i c l e v e l o c i t y f o r d a t a i n f i g s . 6.2a and 6.2b  89  L  F i g u r e 6.2c  80  E f f e c t of bed h e i g h t and i n l e t f l u i d v e l o c i t y on s o l i d s f l o w r a t e i n the annulus. Sand, d]_ = 6 mm (a) dp = 401 ym (b) d = 516 ym P E f f e c t of p a r t i c l e s i z e on G . Sand, d i = 6 mm, (a) U / U = 1.08 (b) U/U = 1.18  91  a  ms  mg  F i g u r e 6.5  E f f e c t of cone angle on G . Sand, d = 516 ym, d._ = 6 mm, U / U = 1.08  93  a  mg  94  Page F i g u r e 7.1  D i f f e r e n t spout shapes  observed  96  F i g u r e 7.2  E f f e c t of bed h e i g h t on spout d i a m e t e r . Sand, d = 516 um, d. = 6 mm, U/U = 1.08 p ' i ms F i g u r e 7.3a E f f e c t of U/U on spout d i a m e t e r . Sand, d = 516 um, d^ = 6 mm  97  ras  p  F i g u r e 7.3b E f f e c t of U/U on spout d i a m e t e r . P o l y p r o p y l e n e , d = 299 um, d = 2.8 mm ~P  97  ms  99  ±  F i g u r e 7.4  V a r i a t i o n of spout diameter w i t h p a r t i c l e d = 6 mm, U/U = 1.08 ±  F i g u r e 7.5  F i g u r e 7.6 F i g u r e 7.7  size,  ms  E f f e c t of cone angle on spout shape. dp = 516 um, d-L = 6 mm, U/U = 1.08 ms E f f e c t of bed h e i g h t on H_ F E f f e c t of p a r t i c l e s i z e on  100  Sand, 100 102 102  - xi -  ACKNOWLEDGEMENTS  I g r e a t l y appreciate Dr.  N. E p s t e i n  Dr.  J.R.  the guidance and encouragement o f  a t every stage o f t h i s p r o j e c t .  Grace and Dr. C.J.  Lim  I am a l s o t h a n k f u l t o  f o r t h e i r v e r y h e l p f u l s u g g e s t i o n s an  discussions. A l l my f r i e n d s a l s o deserve s p e c i a l c r e d i t f o r making my s t a y here a p l e a s a n t  one.  Graduate f e l l o w s h i p from the U n i v e r s i t y of B r i t i s h Columbia f o the l a s t one year i s g r a t e f u l l y acknowledged.  - 1-  CHAPTER 1  INTRODUCTION  The s i g n i f i c a n c e of s o l i d - f l u i d c o n t a c t i n g d e v i c e s i n v o l v i n g t h e m o t i o n o f the f l u i d as w e l l as the s o l i d s has grown c o n s i d e r a b l y i n recent years.  F l u i d i z a t i o n i s the most w i d e l y a c c e p t e d t e c h n i q u e o f  t h i s type today.  In t h e f i f t i e s ,  the spouted bed t e c h n i q u e was  developed f o r p r o c e s s i n g c o a r s e p a r t i c l e s (dp _> 1 mm) f o r which gas f l u i d i z a t i o n becomes i n c r e a s i n g l y non-uniform as the p a r t i c l e s i z e i s i n c r e a s e d ( s l u g g i n g o r poor q u a l i t y a g g r e g a t i v e f l u i d i z a t i o n then o c c u r s - Mathur and E p s t e i n , 1974). A spouted bed i n v o l v e s a j e t of f l u i d i s s u i n g out of a c e n t r a l opening i n t o the bottom o f an i n i t i a l l y  f i x e d bed o f p a r t i c l e s .  As  shown i n F i g . 1.1, i f the i n j e c t i o n r a t e of the f l u i d i s h i g h enough, the  r e s u l t i n g c e n t r a l 'spout' causes a stream o f p a r t i c l e s t o r a p i d l y  r i s e above the bed i n t o a ' f o u n t a i n ' which showers  the p a r t i c l e s  back  onto the s u r r o u n d i n g 'annulus', where the p a r t i c l e s s l o w l y move downward and s l i g h t l y inward as a moving packed bed.  F l u i d from the spout  p r o g r e s s i v e l y l e a k s i n t o the a n n u l u s , w h i l e p a r t i c l e s from the annulus s h o r t - c i r c u i t back i n t o the spout.  The o v e r a l l system thereby becomes a  composite of a c e n t r a l l y l o c a t e d d i l u t e - p h a s e cocurrent-upward t r a n s p o r t r e g i o n surrounded by a dense-phase p e r c o l a t i o n o f the f l u i d .  moving packed bed w i t h c o u n t e r c u r r e n t  A more o r g a n i z e d motion of the s o l i d s than i n  a f l u i d i z e d bed i s thus e s t a b l i s h e d , w i t h e f f e c t i v e  fluid-solid  -  2 -  FOUNTAIN  BED  SURFACE  SPOUT ANNULUS SPOUT-ANNULUS INTERFACE  CONICAL  FLUID  F i g . 1.1.  S c h e m a t i c d i a g r a m of a s p o u t e d bed  INLET  BASE  - 3 -  c o n t a c t i n g and bed  include  rather  unique hydrodynamics.  the use  than the 100  i n a spouted bed um  range),  bed  r a r e l y exceeded 1 metre, a simple elaborate  less  of c o a r s e p a r t i c l e s ( e . g . i n the  mm  d i a m e t e r s which to date have o n l y o r i f i c e gas  gas d i s t r i b u t i o n g r i d , and  i s considerably  Other d i f f e r e n c e s from a f l u i d i z e d  i n l e t r a t h e r than an  a r e s u l t i n g bed  than that r e q u i r e d  pressure  drop which  to s u p p o r t the buoyed w e i g h t of  the s o l i d s as i n f l u i d i z a t i o n . Through the y e a r s , v a r i o u s m o d i f i c a t i o n s and spouted bed  concept have e v o l v e d .  r e c i r c u l a t i n g beds ( w i t h a d r a f t  analogs of  the  These i n c l u d e the s p o u t - f l u i d  bed,  t u b e ) , j e t ( s ) i n a f l u i d i z e d bed,  etc.  Some of these have been summarized by F i l l a e t a l ( 1 9 8 3 ) . A l t h o u g h the spouted bed  f o r coarse p a r t i c l e s ( d  been s t u d i e d q u i t e i n t e n s i v e l y , not much i n f o r m a t i o n of a spouted bed  for fine particles ( d  information available  p  < 1 mm).  on f i n e p a r t i c l e s p o u t i n g  The  p  >^ 1 mm)  e x i s t s on  has the  fragmentry  differs  considerably  from one worker to a n o t h e r , i s sometimes even c o n t r a d i c t o r y and g i v e any  d e f i n i t e conclusions.  The  p r e s e n t work i n v o l v e s a  study of the f i n e p a r t i c l e spouted The previous  present research  focuses p r i m a r i l y  particles.  The  on d e v e l o p i n g  fails  to  detailed  bed.  w o r k e r s , on i d e n t i f y i n g and  regimes i n v o l v e d and  use  on t e s t i n g  characterizing  the r e s u l t s  the v a r i o u s  flow  c r i t e r i a f o r * s t a b l e spouting  hydrodynamic s t u d i e s i n c l u d e :  of  of  fine  regime maps, p a r t i c l e  * ' S t a b l e s p o u t i n g ' i m p l i e s a s t e a d y spout w a l l , steady w i t h a w e l l d e f i n e d shape e t c . as shown i n f i g . 1.1.  fountain  c i r c u l a t i o n r a t e i n the a n n u l u s , l o n g i t u d i n a l annular f l u i d  velocity  d i s t r i b u t i o n , f o u n t a i n shape and h e i g h t , spout shape and d i a m e t e r , and o v e r a l l pressure drop. Comparison o f the d a t a o b t a i n e d w i t h e x i s t i n g c o r r e l a t i o n s f o r c o a r s e p a r t i c l e s , and use of the i n f o r m a t i o n from o t h e r r e l a t e d areas to e x p l a i n some of the observed of  t h i s work.  phenomena, c o n s t i t u t e d secondary  objectives  - 5 -  CHAPTER 2  LITERATURE REVIEW  "Although s p o u t i n g  of coarse  particles  e s t a b l i s h e d phenomenon, s p o u t i n g touched s u b j e c t .  The few r e p o r t s  (dp 2. 1  ) ^  111111  s a  of f i n e p a r t i c l e s i s a v e r y t h a t do e x i s t on s p o u t i n g  p a r t i c l e s a r e n o t i n complete harmony w i t h each o t h e r . problem s t i l l  well sparsely of f i n e  The b a s i c  r e v o l v e s around whether f i n e p a r t i c l e s a r e s p o u t a b l e o r  n o t , and i f s o , under what c o n d i t i o n s , and how do the r e s u l t i n g d i f f e r from a r e g u l a r spouted bed of c o a r s e The  present  review  beds  particles.  examines the l i t e r a t u r e a v a i l a b l e  on s p o u t i n g  of f i n e p a r t i c l e s , b o t h through d i r e c t and i n d i r e c t s t u d i e s .  Some of  the b a s i c hydrodynamic f e a t u r e s of a spouted bed r e l e v a n t t o the p r e s e n t study are a l s o r e v i e w e d .  2.1  Spoutability of Fine P a r t i c l e s and the Conditions A f f e c t i n g I t  2.1.1  E f f e c t of i n l e t size U n t i l 1981 i t was g e n e r a l l y thought t h a t f i n e p a r t i c l e s  ( s i z e as  s m a l l as 80 t o 100 mesh) can be made to spout only i f the o r i f i c e was  less  than 30 times the p a r t i c l e d i a m e t e r (Ghosh, 1965).  size  The  r e s u l t i n g j e t becomes so s m a l l that i t e n t r a i n s very few p a r t i c l e s and so  the r e g i o n of s o l i d c i r c u l a t i o n i s l i m i t e d  the spout.  to a region very c l o s e to  Ghosh based h i s c r i t e r i o n on the data c o l l e c t e d  diameter s p l i t column w i t h 165 um g l a s s beads.  The r e s u l t s  i n a 15.2 cm of Rooney  - 6 -  and H a r r i s o n (1974) were found to obey Ghosh's c r i t e r i o n f o r a c r i t i c a l inlet  to p a r t i c l e s i z e r a t i o which must n o t be exceeded  a c h i e v e steady s p o u t i n g . beyond t h i s c r i t i c a l  i n order to  They r e p o r t t h a t i n c r e a s i n g the i n l e t diameter  s i z e gave r i s e  to b u b b l i n g or s l u g g i n g .  The regime  maps of Mathur and G i s h l e r (1955) f o r sand p a r t i c l e s of 420 t o 830 ym, d i s p l a y e d i n f i g s . 2.1a and 2.1b, f o l l o w Ghosh's c r i t e r i a .  F i g . 2.2  shows that a much l a r g e r r e g i o n of s t e a d y s p o u t i n g i s t y p i c a l of a coarse p a r t i c l e spouted bed. In  1981, however, two E a s t German s c i e n t i s t s , H e s c h e l and K l o s e ,  r e p o r t e d s p o u t i n g of PVC powder h a v i n g a mean d i a m e t e r of 90 ym i n a 30 cm diameter c y l i n d r i c a l column w i t h an i n l e t s i z e of 25.4 mm, i . e . d j / d p = 282, f a r above the d-j/dp = 30 suggested by the p r e v i o u s workers.  T h e i r r e s u l t s showing p r e s s u r e drop v s . f l o w r a t e were most  unusual i n that they e x i b i t e d  two peaks as shown i n f i g . 2.3.  This i s  q u i t e d i f f e r e n t from the c h a r a c t e r i s t i c s of a r e g u l a r c o a r s e p a r t i c l e spouted bed, shown i n f i g . 2.4 f o r comparison.  The f i r s t peak i n f i g .  2.3 corresponds to a gas j e t b r e a k i n g through the bed i n an unsteady manner, f o r m i n g a c r a t e r shaped area around i t .  The c i r c u l a t i o n of  s o l i d s was r e p o r t e d to be apparent o n l y near the j e t and the 'annulus' was a t r e s t .  The f o o t of the second peak i s a t t r i b u t e d  steady s p o u t i n g of the bed, a f t e r which constant with flow.  to the onset of  the p r e s s u r e drop  remains  I n a c o n v e n t i o n a l spouted bed, however, s t e a d y  s p o u t i n g s e t s i n when the p r e s s u r e f i r s t drops ( f o o t of the peak i n Fig.  2.4) and there i s no second peak.  -  1  175  7 -  i  i  0  O  \  SLUGGING  c  150  fv 125  "  BED  z to. UJ  o  ^  f  STATIC  /  J  / o /  \  / - /  BUBBLING  A / P ^ / / o/  100  / /  o  /  UJ CD  0-  1  0  / /  *- /  /J z k Q w A I UJ 1 I * /  75  / o/  PROGRESSIVELY 50  INCOHERENT  SPOUTING  •/ °/ ,  0.15  0.20  1  0.25  ,  0.30  SUPERFICIAL.  AIR  1 0.35  ,  0.45  0.40  VELOCITY,  m/stc  0/ l F i g u r e 2.1a. Regime map. Sand, (3^=0.42-0.83 irm, D =15.2 cm, c  d ^ l . 2 5 cm (Mathur a n d G i s h l e r ,  1955).  SLUGGING  BUSBLif-'G  02  0  SUPERFICIAL  J  0 •> AIP  VELOCITY.  05 m/ c se  F i g u r e 2.1b. Regime ITHD. Sand, d =0.42-0.83 mm, D =15.2 cm, ^ P d ^ l . 5 8 cm (Mathur and G i s h l e r , 1955). c  -  04  0.6  0.8  SUPERFICIAL  AIR  8 -  1.0  1.2  V E L O C I T Y , m/jec  F i g u r e 2.2. Phase d i a g r a m . Semicoke, d^=l-5 ram, d.=3.05 cm (Mathur and E p s t e i n , 1974).  -  0-0  1.8  0.9  2.7  9 -  3.6  4.5  5.4  6.3  SUPERFICIAL GAS VELOCITY, cm/s. F i g u r e 2.3. P r e s s u r e d r o p v s . v e l o c i t y d a t a o f H e s c h e l and K l o s e (1981) 3 3 PVC, d =0.09 mm, p^=1270 kg/m , p =565 kg/m . F l u i d used: p  A i r a t 80% r e l a t i v e h u m i d i t y .  b  - 10 -  SUPERFICIAL  VELOCITY  F i g u r e 2.4. T y p i c a l p r e s s u r e drop v s . v e l o c i t y c u r v e f o r a spouted bed o f c o a r s e p a r t i c l e s .  - 11 -  2.1.2  E f f e c t of p a r t i c l e size and density Another c l a s s i f i c a t i o n a t t e m p t i n g to d i s t i n g u i s h  between  s p o u t a b l e and non-spoutable p a r t i c l e s was d e r i v e d by G e l d a r t (1973) and m o d i f i e d by Molerus (1982).  G e l d a r t (1973) concluded t h a t p a r t i c l e s f o r  which:  (p  2 - p ) d^ > 10 6 g(ym) P f P —  (2.1)  (cm ) tend to form s t a b l e spouts and c l a s s i f i e d them as "Group D' p a r t i c l e s . Molerus (1982) c l a s s i f i e d s p o u t a b l e p a r t i c l e s (Group D) as those f o r which the dynamic p r e s s u r e e x e r t e d by the f l u i d exceeds a d i s t i n c t v a l u e depending on the p a r t i c l e s i z e and d e n s i t y d i f f e r e n c e between the p a r t i c l e and the f l u i d .  He proposed  the l i m i t i n g c o n d i t i o n f o r  s p o u t a b i l i t y as:  (2.2)  The c r i t e r i a of G e l d a r t (1973) and Molerus (1982) both become l i n e a r on a l o g - l o g p l o t ( F i g . 2.5) and p r e d i c t : 1.  That p a r t i c l e s f a l l i n g below the g i v e n l i n e i n F i g . 2.5 a r e non-spoutable and those f a l l i n g above the l i n e a r e s p o u t a b l e .  2.  That i n c r e a s i n g  the p a r t i c l e s i z e and d e n s i t y d i f f e r e n c e between the  p a r t i c l e and the f l u i d enhance t h e i r 3.  spoutability.  No e f f e c t of i n l e t diameter on s p o u t a b i l i t y .  -, 12 -  d  (mm) P F i g u r e 2.5. G e l d a r t (1973) and M o l e r u s (1982) c r i t e r i a on a l o g - l o g p l o t . P a r t i c l e s b e l o w t h e l i n e a r e termed a s 'non-spoutable' and above i t as  'spoutable'.  - 13 -  2.2 2.2.1  Basic Spouting Parameters Minimum spouting v e l o c i t y T h i s i s the minimum s u p e r f i c i a l v e l o c i t y r e q u i r e d to m a i n t a i n a  c e r t a i n bed i n a s t a b l e s p o u t i n g c o n d i t i o n . B i n F i g . 2.4, bed s t a r t s  I t i s r e p r e s e n t e d by p o i n t  i . e . the v e l o c i t y a t w h i c h the p r e s s u r e drop a c r o s s  to r i s e a g a i n upon d e c r e a s i n g the f l u i d  number of e q u a t i o n s are a v a i l a b l e minimum s p o u t i n g v e l o c i t y , U , m s  commonly used one i s s t i l l  Although  i n the l i t e r a t u r e f o r p r e d i c t i n g  a the  (Mathur and E p s t e i n , 1974), the most  the M a t h u r - G i s h l e r e m p i r i c a l e q u a t i o n (1955)  which i s based on d a t a from both gas and  r  flow*.  the  d -, r d -.1/3  r  2g(p  l i q u i d spouted  - p ) H-]  n  beds:  l / 2  Ghosh (1965) a l s o d e r i v e d an e q u a t i o n f o r the minimum s p o u t i n g v e l o c i t y , based on a momentum balance between the p a r t i c l e s and fluid  a t the f l u i d  inlet.  the  H i s e q u a t i o n , which i s q u i t e s i m i l a r i n form  to the M a t h u r - G i s h l e r e q u a t i o n , p r o v i d e s some t h e o r e t i c a l  basis for i t :  1/2 [2kn'-|l/2 P p l f•2g( P_ - p ) U ms = [l ^3 - Jr - ||-£ — f— _ J I LI f  D  I  L  Hi  (2.4)  p  * I n the case of very f i n e p a r t i c l e s (dp < 350 urn) steady s p o u t i n g i s observed a t a v e l o c i t y g r e a t e r than t h a t shown i n f i g . 2.4, The gas s i m p l y bubbles through between p o i n t s B and C (somewhat a r b i t a r i l y chosen here) and steady s p o u t i n g s e t s i n o n l y a t p o i n t C. G e l d a r t (1981) recommends C as the p o i n t f o r d e t e r m i n i n g U f o r these p a r t i c l e s , s i n c e p o i n t C i s f a i r l y r e p r o d u c i b l e i n a f u l l column a l s o . ras  - 14 -  A more r e c e n t c o r r e l a t i o n  for U  m s  comes from G r b a v c i c e t a l  (1976) based on t h e i r f l o w model:  U  / U _ - ka  f  mS  For  , *  ,  = [ l'-Cl  a  -H/y  3  ]  (2.5)  a m a j o r i t y of systems,  a  a  « 1 -- m!-=• I 2  •.  k =1  and  whence ^fL mF  2.2.2  = 1 -  1 - H/^)  3  ( 2  -  5 a )  Maximum spoutable bed depth The maximum s p o u t a b l e bed d e p t h , H , M  a t which a s t a b l e  spout can be m a i n t a i n e d .  i s the maximum bed h e i g h t Mathur and E p s t e i n  (1974)  have r e p o r t e d t h r e e d i f f e r e n t mechanisms f o r spout t e r m i n a t i o n when the bed h e i g h t exceeds % .  They a r e :  1.  F l u i d i z a t i o n of the a n n u l a r s o l i d s .  2.  Choking of the spout.  3.  Growth  of an i n s t a b i l i t y a t the s p o u t - a n n u l u s  interface.  - 15 -  The  f i r s t mechanism i s known to occur i n a r e g u l a r spouted bed of  c o a r s e p a r t i c l e s and in  the second mechanism has been r e p o r t e d to p r e v a i l  the case of f i n e p a r t i c l e s ( L i t t m a n e t a l , 1977). Various correlations for H  E p s t e i n (1974) and Kim (1982). than 1 mm,  HJ»J  M  have been l i s t e d by Mathur and  For p a r t i c l e s w i t h average d i a m e t e r l e s s  i n c r e a s e s w i t h i n c r e a s i n g p a r t i c l e s i z e , and  when p a r t i c l e s i z e exceeds about 1.2 mm. H  M  v s . dp c u r v e , somewhere near d  showing an i n c r e a s i n g trend of H s t u d y , where d One  p  <  M  A maximum thus o c c u r s i n a  = 1 mm.  p  with d  decreases  p  Only the c o r r e l a t i o n s a r e thus r e l e v a n t to t h i s  1mm.  of the c o r r e l a t i o n s developed by L i t t m a n e t a l ( 1 9 7 7 ) , by  s i m u l t a n e o u s s o l u t i o n of p r e s s u r e and v e l o c i t y d i s t r i b u t i o n i n the annulus of a spouted bed u s i n g c o n t i n u i t y and  the v e c t o r form of Ergun's  equation, i s :  M  (D  2 c  -0.384  s  2 D) s  (2.6)  0.34.5  Z  Another e x p r e s s i o n comes from Morgan and L i t t m a n ( 1 9 7 9 ) :  / D  c  = (0.218 + 0.005/A + 2.5 x 10  Ik  A >  )  *  0.014  (2.7a)  - 16 -  D = 175 (A - 0.01) - j - ; i  / D  (2.7b)  C  0.01 < A < 0.014  where A i s d e f i n e d by e q u a t i o n ( 2 . 1 4 ) . I t has been r e p o r t e d by G e l d a r t e t a l (1981) t h a t % column i s u s u a l l y about 15% l e s s than t h a t i n a f u l l due to g a s - w a l l and p a r t i c l e - w a l l  2.2.3  i n a half  column, p r o b a b l y  friction.  Spout diameter Spout d i a m e t e r s a r e u s u a l l y measured  column.  in a half-cylindrical  L i m and Mathur (1974) used X - r a y photography t o determine s p o u t  shape and s i z e i n a f u l l column and found t h a t the f l a t s u r f a c e i n a h a l f column had n e g l i g i b l e e f f e c t on the spout geometry. An e m p i r i c a l c o r r e l a t i o n f o r the l o n g i t u d i n a l l y averaged spout diameter a t the minimum s p o u t i n g c o n d i t i o n i s due t o McNab (1972):  1.48 G ms 0  ms  For  D°c 0.41  4 9  6 8  (2.9a)  a gas v e l o c i t y above minimum s p o u t i n g we have, a c c o r d i n g to McNab  (1972):  D  s  U J L ms J  ms  1/2 (2.9b)  - 17 -  2.2.4 Fountain height Grace and Mathur (1978) proposed an e x p r e s s i o n f o r e s t i m a t i n g f o u n t a i n h e i g h t , Hp, based on a momentum i n t e g r a l over the f o u n t a i n :  1.46  V 2g  (2.10)  ( P -P ) p  f  The f o u n t a i n shape has been r e p o r t e d t o be a p p r o x i m a t e l y p a r a b o l i c i n most c a s e s .  2.3 Regime Maps The f i r s t regime maps r e l e v a n t t o f i n e p a r t i c l e s p o u t i n g appeared i n the work, of Mathur and G i s h l e r (1955) and a r e shown i n f i g s . 2.1a and 2.1b.  More r e c e n t l y L i t t m a n and Morgan (1984) suggested a  c h a r a c t e r i z a t i o n of s p o u t i n g regimes by a parameter C , where: Q  C  1 [1 - e ( Z ' ) ] ms dZ' , / s  =  V  = Z/H  (2.11)  AP  ms + mF  AP  (2.12a) ( 1  " mF> e  ( p  p "  P  f ^  H  - 18 -  AP AP  ms  (2.12b)  mF  T h i s a n a l y s i s i s based on momentum e q u a t i o n s f o r gas and s o l i d s . equation  (2.11) i s s u b j e c t e d  e  s  (0)  ms  to the boundary  conditions:  and e ( 1 ) s  mF  =1  i t i s observed t h a t o n l y f o r v a l u e s of C does e ( Z ' ) decrease m o n o t o n i c a l l y g  monotonically  0  ms  (2.13)  between 0.215 and 0.785  ( e ( Z ) should T  g  decrease  to be c o n s i s t e n t w i t h the p h y s i c a l o b s e r v a t i o n s ,  p a r t i c l e s enter  When  the spout throughout the bed h e i g h t ) .  since  However f o r C  Q  > 0.785, e ( Z ' ) was found to s t a b i l i z e o n l y when e ( 0 ) < 1, w h i c h g  s  would r e q u i r e p a r t i c l e s  t o be p r e s e n t a t the spout i n l e t .  The l a t t e r  has been e x p e r i m e n t a l l y observed when 855 um g l a s s beads a r e spouted w i t h a i r ( L i t t m a n e t a l , 1977). p a r t i c l e s with water, C e  g  (0) < 1 (Kim, 1982).  0  A l s o , i n the case of s p o u t i n g of f i n e  has been found to average around 0.85 and Kim (1982) a l s o suggested  t h a t s p o u t i n g of  f i n e p a r t i c l e s w i t h water c o n s t i t u t e d a new s p o u t i n g regime because h i s experimental  d a t a on H , D M  g  and AP  rag  were n o t s a t i s f a c t o r i l y  p r e d i c t e d by the c o r r e l a t i o n s f o r c o a r s e p a r t i c l e s .  He a l s o found  that  w h i l e spout t e r m i n a t i o n i n the case of f i n e p a r t i c l e s p o u t i n g w i t h a i r occurred  due to c h o k i n g of the spout, the t e r m i n a t i o n mechanism i n the  case of a water spouted f i n e p a r t i c l e bed was a n n u l a r f l u i d i z a t i o n .  - 19 -  Annular  f l u i d i z a t i o n a l s o p r e v a i l s as the spout  a c o n v e n t i o n a l spouted  bed of coarse p a r t i c l e s .  t e r m i n a t i o n mechanism i n C  0  < 0.215 i s  i n t e r p r e t e d as the case where v e r y s h a l l o w beds a r e used and the spout i s simply a hole blowing  through w i t h v e r y few p a r t i c l e s e n t r a i n e d  inside i t . Morgan and L i t t m a n (1982) a l s o use a parameter A, r e p r e s e n t i n g the r a t i o of j e t i n e r t i a regimes.  to bed p r e s s u r e drop f o r c e s , t o c h a r a c t e r i z e  T h e i r d i m e n s i o n l e s s p l o t of mA v s . A f o r p r e d i c t i n g the  maximum s p o u t a b l e h e i g h t e x i b i t s a break i n the p l o t f o r a v a l u e of A around 0.02.  T h i s break i s a t t r i b u t e d  s p o u t i n g regime.  to the t r a n s i t i o n to a new  A i s d e f i n e d as:  U  A =  mf T P > g d. U  (2.14)  f  and  can be m o d i f i e d f o r n o n - s p h e r i c i t y .  2.4 Longitudinal Annulus Fluid V e l o c i t y and Overall Bed Pressure Drop The predicting  e q u a t i o n which has proven to be the most s u c c e s s f u l f o r the l o n g i t u d i n a l annular f l u i d  v e l o c i t y f o r coarse  particles  i s a c o n t r i b u t i o n of Mamuro and H a t t o r i (1968/1970) f o r a bed a t i t s maximum s p o u t a b l e  bed h e i g h t :  U  a  TZ mF  3 1  -  (  l  -  z / h  m >  (2.15)  - 20 -  Darcy's law was assumed to be v a l i d i n the annulus and l e d t o :  AP AP  ms  (P  p  - P ) (1 - e > f  =  g^  A  0.75  (2.16)  The boundary c o n d i t i o n s used were:  ( i ) Z = 0, U (ii) Z = H , M  = 0 U  a  = U  a  (H  M  ) = U, mF = (  _  P p  P f )  ( 1  _ ^  (2.17)  g  mF  I t was found e x p e r i m e n t a l l y t h a t U than U p m  a  ( H ) i s about 10 to 15% l e s s M  ( E p s t e i n et a l , 1978) and hence eq. (2.15) s h o u l d be m o d i f i e d  to: U 1 - (1 -Z/  )•  (2.18)  L e f r o y and Davidson (1969) f o r m u l a t e d the f o l l o w i n g e q u a t i o n f o r l o n g i t u d i n a l p r e s s u r e d i s t r i b u t i o n , based on t h e i r e m p i r i c a l  findings:  (2.19)  - 21 -  I t was shown by E p s t e i n e t a l (1978) t h a t a p p l y i n g the v e l o c i t y relationship:  " §  = K'U/  (2.20)  where n, the f l o w regime index t y p i c a l l y v a r i e s from 1 (Darcy's law) a t the  bottom of the annulus to as much as 2 ( i n v i s c i d f l o w ) a t Z = H^.  By combining eqns. (2.19) and (2.20) a t any Z and a t Z = H^,  U  a  U  a  (  I  Sinfnz  K  V  1  /  (2.21)  n  J  R e c e n t l y , Morgan and L i t t m a n (1980) d e r i v e d a g e n e r a l s p o u t - a n n u l a r i n t e r f a c i a l boundary c o n d i t i o n f o r the p r e s s u r e distribution  P  a  a t the spout w a l l :  (  Z  AP  For  )  -  P  a  (  H  .  )  ms Z =H  any f l u i d - p a r t i c l e  predicted AP /AP m s  m F  Z  f  H  L  ( A P  ms  7  (AP / m s  * V z AP  m F  )  - Z z  =  H  1 J  < ' > 2  22  system, i n a bed of h e i g h t H < H^, they a l s o  v s . H/D  c  through a parameter 9 ( f i g . 2.6)  where 8 was c o r r e l a t e d by:  d.  = 7.18 (A -  •—• ) + 1.07; A < 0.07  (2.23)  - 22 -  i  1  ~i  r  H/O  c  F i g u r e 2.6. P a t i o o f minimum s p o u t i n g p r e s s u r e d r o p t o minimum f l u i d i z a t i o n p r e s s u r e d r o p v s . r a t i o o f bed h e i g h t t o column d i a m e t e r f o r d i f f e r e n t v a l u e s o f 6 (Morgan and L i t t m a n , 1980).  - 23  and A i s g i v e n by eqn.  (2.14).  -  T h e i r f i n d i n g s f o r s e v e r a l v a l u e s of 9  showed t h a t eq. (2.21) s a t i s f i e d the q u a r t e r c o s i n e p r o f i l e of L e f r o y and Davidson (1969) v e r y c l o s e l y . condition  I t a l s o s a t i s f i e d the G r b a v c i c  (1976):  -dP  a  dZ  Z  = constant * f(H)  = constant cons t a n t  (2.24)  w h i c h s t a t e s t h a t the p r e s s u r e g r a d i e n t or the v e l o c i t y  (eqn. (2.20))  at  any bed l e v e l i s independent of the bed h e i g h t above i t , f o r any particular H <^ Hj^.  column, f l u i d and s o l i d s .  Eqn.  (2.21) and  Thus eqn.  (2.15) a p p l i e s f o r  the G r b a v c i c c o n d i t i o n were e a r l i e r shown to  be imcorapatible w i t h each other by E p s t e i n e t a l (1978).  2.5  Annular P a r t i c l e V e l o c i t y P r o f i l e and For p a r t i c l e s  particles  t h a t f a l l i n the r e g u l a r spouted  regime (dp >^ 1 mm),  measured by Lim ( 1 9 7 5 ) . decreased  Solid Circulation  r a d i a l and  He found  bed  axial velocity  t h a t the annulus  Rate  of c o a r s e  p r o f i l e s were  particle  velocity  from the spout w a l l to the column w a l l a t any bed l e v e l , i . e .  a r a d i a l gradient exists. p o s i t i o n decreased  The  particle velocity  from the bed s u r f a c e to the  j u n c t i o n , a f t e r which i t i n c r e a s e d a g a i n  a t any f i x e d  radial  conical-cylindrical  to the gas i n l e t .  The  overall  s o l i d c i r c u l a t i o n r a t e i n c r e a s e d from the bottom to the top, h a v i n g a c o n s t a n t r a t e of i n c r e a s e beyond the c o n e - c y l i n d r i c a l  junction.  - 24 -  No i n f o r m a t i o n , however, i s a v a i l a b l e on the a n n u l a r p a r t i c l e v e l o c i t y i n the case of f i n e r s o l i d s (dp < 1 mm).  2.6 Indirect Approaches Relevant to Spouting of Fine P a r t i c l e s The g r i d r e g i o n of a f l u i d i z e d bed i s b e l i e v e d resemblance  to have a c l o s e  to a spouted bed, s i n c e gas i s s u i n g above the o r i f i c e s i s i n  the form of s m a l l 'spouts' and the u n d e r - f l u i d i z e d p a r t i c l e s r e s t on the p i t c h areas between the s p o u t i n g o r i f i c e s . submerged 'spouts' i s f l u i d i z e d .  The bed above these  F a k h i m i e t a l (1983) used  l o o k i n g a t the g r i d r e g i o n t o determine  t h i s way of  the h e i g h t of the e n t r a n c e  effect:  F i l l a e t a l (1983) have r e c e n t l y compared f u l l y developed  spouts  and gas j e t s i s s u i n g i n t o a f l u i d i z e d bed. They c o n c l u d e , t h a t a l t h o u g h the a v a i l a b l e spout and j e t models a r e both based on gas and s o l i d s mass and momentum b a l a n c e s , they d i f f e r i n a u x i l i a r y e q u a t i o n s .  These  a u x i l i a r y e q u a t i o n s , which have been t e s t e d a g a i n s t e x p e r i m e n t a l d a t a , relate  to p r e s s u r e g r a d i e n t s , gas e n t r a i n m e n t / d i s e n t r a i n m e n t , s o l i d s  c o n c e n t r a t i o n and p a r t i c l e v e l o c i t y p r o f i l e s .  However, a correspondence  may be e s t a b l i s h e d between the maximum h e i g h t a t which a bubble forms from the t i p of a j e t and the maximum s p o u t a b l e bed d e p t h . S i t (1981) was y e t another i n v e s t i g a t o r who a p p l i e d spouted bed  - 25  theory  -  to study mass t r a n s f e r from the spout to the dense phase where a  stream of gas  e n t e r s a f l u i d i s e d bed  I n h i s case a s t a b l e spout was entrance,  through a c e n t r a l l y p l a c e d  observed only up  above w h i c h i t d i s c h a r g e d  nozzle.  to about 15 cm from  the  as b u b b l e s .  A number of c o r r e l a t i o n s e x i s t i n the l i t e r a t u r e f o r e s t i m a t i n g the j e t p e n e t r a t i o n d e p t h , and (1983) and  S i t (1981).  these have been reviewed by B l a k e e t a l  Most of these s t u d i e s , however, i n v o l v e a  j e t i s s u i n g i n t o a f l u i d i z e d bed,  and  gas  the e f f e c t of f l u i d i z a t i o n ( o r  a u x i l i a r y f l o w i n t o the annulus) on the j e t p e n e t r a t i o n depth ( o r l e n g t h of the submerged s t a b l e spout) i s q u i t e s i g n i f i c a n t . Basov e t a l (1969) had the p r e s e n t work.  no a u x i l i a r y f l o w and  d 0.007 + 0.566d  where, h = j e t p e n e t r a t i o n depth i n dp = p a r t i c l e s i z e i n  i s therefore relevant  to  Q P  0.35 or  (2.26)  cm.  um.  = o r i f i c e f l o w r a t e i n cm  Blake represent  c o r r e l a t i o n of  His c o r r e l a t i o n i s :  h =  Qor  The  et a l (1983) suggest t h a t the f o l l o w i n g c o r r e l a t i o n s  the upper and  the lower l i m i t s , r e s p e c t i v e l y , of j e t  penetration i n a f l u i d i z e d  bed:  (2.27a)  - 26 -  p  0.707  0.451  2  (2.27b)  i i - "-  2  where V = gas v e l o c i t y through the o r i f i c e .  A l l the a v a i l a b l e d a t a have  thus been shown to have d e v i a t i o n s up to ± 45%. H a t t o r i and Takeda (1978) used a s i d e o u t l e t spouted bed w i t h an i n n e r d r a f t tube f o r c o n t a c t i n g p a r t i c l e s as s m a l l as 270 um.  In t h i s  system the c i r c u l a t i o n of s o l i d s depends on the e n t r a i n m e n t of p a r t i c l e s a t the bottom of the d r a f t tube.  These i n v e s t i g a t o r s  f o r p r e d i c t i n g the gas c o n v e r s i o n i n such a system.  proposed a model The c o n v e r s i o n i n  the case o f non-porous c a t a l y s t p a r t i c l e s i n c r e a s e d w i t h d e c r e a s e i n p a r t i c l e s i z e due to the h i g h e r s u r f a c e - t o - v o l u m e r a t i o o f the s m a l l e r particles.  - 27 -  CHAPTER 3  APPARATUS AND BED MATERIALS  3.1 Choice and Description of Experimental Apparatus Two 15.2 cm d i a m e t e r h a l f columns, h a v i n g an i n c l u d e d cone a n g l e of 36.4 and 60 degrees r e s p e c t i v e l y , were used ( F i g .  3.1).  A half  column i s b e l i e v e d t o r e p r e s e n t the b e h a v i o u r i n a f u l l column q u i t e a d e q u a t e l y f o r many purposes and f o r a wide v a r i e t y of m a t e r i a l s spouted ( G e l d a r t e t a l , 1981).  The major advantage i n u s i n g a h a l f column i s  t h a t i t a l l o w s d i r e c t o b s e r v a t i o n of s p o u t shape and d i a m e t e r , and r a d i a l p a r t i c l e v e l o c i t y g r a d i e n t s , as w e l l as v i s u a l i z a t i o n of the f l o w regimes i n v o l v e d a l o n g w i t h t h e i r The  of  points.  two columns were made of p l e x i g l a s s , w i t h the f l a t  made of g l a s s . 9.0,  transition  Semicircular orifices  of d i a m e t e r s 2.8, 4.5, 6.0, 7.5,  12.7, 16.0, 19.05, 23.2 and 28 mm were u t i l i z e d .  these o r i f i c e s  o r i f i c e of t h i s  surface  The i n l e t of each  p r o t r u d e d 2 mm i n t o the bed as shown i n F i g . 3.2. An type g i v e s very good s t a b i l i t y  to the spout (Mathur and  E p s t e i n , 1974). For  the 36.4 degree cone angle column, s p e c i a l o r i f i c e  w i t h the o r i f i c e  plates,  tapered a t the same cone a n g l e , were f a b r i c a t e d .  The  use of such p l a t e s a t the bottom p r o v i d e d a smooth i n l e t c o n n e c t i o n t o the  half c i r c u l a r i n l e t  fluid  (Fig.  3.3).  tube, a v o i d i n g any c o n t r a c t i o n of the i n l e t  Three d i f f e r e n t i n l e t s i z e s of t h i s type of o r i f i c e  were used - 25.4 (when no o r i f i c e p l a t e was u s e d ) , 12.7 and 10.1 mm.  A  CONICAL SECTION AUXILIARY FLOW LINES  19.3 cm  RESSURE TAP HONEYCOMBED FLOW STRAIGHTENERS F i g u r e 3.1. D e t a i l s o f t h e two h a l f c y l i n d r i c a l columns.  - 29  -  F i g u r e 3.2. P h o t o g r a p h o f the o r i f i c e p l a t e . Tube a t t a c h m e n t i s f o r a l i g n m e n t purposes.  ALL  DIMENSIONS  IN MMS.  o  -HALF CIRCULAR TUBE  HALF CIRCULAR TUBE FULL CIRCULAR TUBE  -FULL CIRCULAR TUBE HONEY COMBED FLOW STRAIGHTNERS  Figure  3.3. D i f f e r e n t i n l e t t y p e s (without c o n t r a c t i o n o f t h e i n l e t f l u i d )  f o r column 2.  - 31  cone angle of 36.4  degrees and  -  such an i n l e t d e s i g n was  the same column geometry as used by H e s c h e l and K l o s e A v e r t i c a l p i p e of 3.18  cm I.D.  and  made to m a i n t a i n (1981).  l e n g t h 30 cm,  with  a p p r o p r i a t e grooves f o r h o l d i n g the o r i f i c e p l a t e (see F i g . 3.2) u n d e r l y i n g w i r e mesh (250 mesh f o r dp = 98 o t h e r p a r t i c l e s ) , was  and  an  um and 65 mesh f o r a l l  used to connect the incoming a i r l i n e to the base  of the column ( i t c o u l d be used f o r each of the two  columns).  'Honeycombed' f l o w s t r a i g h t e n e r s were f i x e d i n s i d e the p i p e . A pressure pipe.  The  tap was  pressure  l o c a t e d 5 cm below the bed  tap was  i n l e t i n the  inlet  connected through a T - j o i n t to two U -  tube manometers c o n t a i n i n g a l i q u i d of s p e c i f i c g r a v i t y 0.827 and mercury ( s p . g r . 13.6), r e s p e c t i v e l y . l i q u i d was  to a v o i d any s p i l l a g e of the  Whenever i t was  lighter  fitted  k e p t c l o s e d when the p r e s s u r e drop was  with  high, i n  liquid.  The 60 degree cone angle column was work.  manometer f o r the  used f o r low p r e s s u r e drop measurements and was  an i n l e t v a l v e which was order  The  used f o r most p a r t s of  not used, the cone angle i s s p e c i f i e d .  The  this 60  degree cone angle column had an a u x i l i a r y f l u i d i z i n g l i n e to the annulus and  c o u l d t h e r e f o r e be operated  fluidized  a l s o as e i t h e r a s p o u t - f l u i d or a  bed.  In order  to remove any  polymers, the incoming a i r was columns w i t h a c o m b i n a t i o n  s t a t i c c l i n g while using small s i z e d humidified.  of R a s c h i g  Two  10.16  cm  diameter  r i n g s and B e r l saddles as  m a t e r i a l s were used i n p a r a l l e l f o r t h i s purpose ( F i g . 3.4). mesh was  p l a c e d a t d i f f e r e n t l e v e l s i n between the packings  good d i s p e r s i o n of a i r bubbles i n water.  packing  Fine  wire  to o b t a i n a  Both the h u m i d i f i e r s  - 33 -  were c a p a b l e of c o n t a c t i n g a i r and water c o u n t e r c u r r e n t l y t o ensure h i g h h u m i d i t y w h i l e u s i n g polymers.  A d r y a i r stream was a l s o connected t o  the h u m i d i f i c a t i o n s e c t i o n o u t l e t to c o n t r o l the h u m i d i t y . measured u s i n g d r y - b u l b and wet-bulb  H u m i d i t y was  thermometers.  A i r f l o w r a t e s were measured by e i t h e r of the two r o t a m e t e r s , which were c a l i b r a t e d u s i n g a d r y gas meter*. used f o r s m a l l f l o w r a t e s o n l y . by a p r e s s u r e gauge.  The s m a l l e r r o t a m e t e r was  The upstream a i r p r e s s u r e was measured  F i g . 3.4 summarizes  the o v e r a l l equipment  layout  and F i g . 3.5 i s a p i c t u r e o f the same. Annulus gas v e l o c i t y p r o f i l e s were measured by u s i n g a s t a t i c p r e s s u r e probe, t h e same probe as used by L i m (1975) - F i g . 3.6.  Two  c o n c e n t r i c s t a i n l e s s s t e e l tubes of unequal l e n g t h s h a v i n g an O.D. o f 1.6 mm and 4.8 ram r e s p e c t i v e l y , c o n s t i t u t e d the main body of the p r o b e . The two ends were f i t t e d w i t h 22 gauge hypodermic n e e d l e s , bent a t r i g h t a n g l e s 1.2 cm from t h e i r t i p s , t h e v e r t i c a l s e p e r a t i o n between the t i p s b e i n g 2 cm.  S t a t i c p r e s s u r e drops were measured u s i n g a  raicroraanometer** gr.  h a v i n g a l e a s t count o f 0.00254 cm b u t y l a l c o h o l ( s p .  0.821).  3.2 Bed Materials A wide v a r i e t y of p a r t i c l e s r a n g i n g i n s i z e from 90 urn to 1000 um and i n s p e c i f i c g r a v i t y from 0.9 to 8.9 were employed.  *Model A.L425, made by Canadian Meter Co. L t d . **Model MM-3, made by Flow Corp., Cambridge,  Mass.  Table 3.1  F i g u r e 3.5. P h o t o g r a p h o f t h e equipment.  - 35 -  to  inclined  manometer  — probe holder  120 cm  flat surfacey of c o l u m n  4.8 m m  O.D.  2 cm  d i a g r a m not to s c a l e  -H  [ 4 — ^ ^ - 2 2 Gauge  1.2 cm  hypodermic  needle  F i g u r e 3.6. S c h e m a t i c d i a g r a m o f t h e s t a t i c p r e s s u r e p r o b e .  Table 3.1:  Material  P r o p e r t i e s of bed m a t e r i a l s  d (degrees)  (degrees)  mF (cm/s)  0.586  76.7  30.6  0.49  0.564  0.556  66.5  32.1  1.67'  0.900  0.518  0.425  61.3  29.3  4.25  196  2.660  1.467  0.449  66.0  33.2  4.55  S i l i c a Sand  280  2.665  1.557  0.416  61.4  32.8  9.29  S i l i c a Sand  401  2.657  1.552  0.408  58.8  32.2  16.70  S i l i c a Sand  516.4  2.648  1.533  0.427  57.5  34.8  22.38  2.661  1.557  0.415  66.3  36.9  56.19  U  P (pm)  (g/cm )  (g/cm )  PVC  98  1.270  0.526  PVC  185.6  1.270  Polypropylene  299.5  S i l i c a Sand  S i l i c a Sand  1000  d  3  Bronze  176.4  7.906  4.649  0.412  52.0  26.3  Copper  458.5  8.811  5.190  0.411  57.8  29.2  Nickel  238.3  8.906  5.255  0.410  52.7  28.1  Nickel  545  8.912  5.258  0.410  52.0  27.4  Nickel  635  8.900  5.245  0.411  52.0  26.6  Glass  710  4.506  2.665  0.408  47.4  24.1  Glass  845  2.417  1.423  0.409  50.6  25.0  46.61  - 37 -  summarizes the p h y s i c a l p r o p e r t i e s of the p a r t i c l e s used.  The d i a m e t e r  used here i s the mean-diameter o b t a i n e d a f t e r s i e v e a n a l y s i s as f o l l o w s :  (3.1)  where  i s the weight f r a c t i o n of p a r t i c l e s h a v i n g an a p e r t u r e mean  d i a m e t e r , p ^ * T a b l e 3.2 g i v e s the s i z e d i s t r i b u t i o n f o r PVC, a  p o l y p r o p y l e n e , b r o n z e , copper and t h e t h r e e s i l i c a g l a s s and n i c k e l p a r t i c l e s were f a i r l y in  sands used.  The  s p h e r i c a l i n shape, and u n i f o r m  size. The d e n s i t i e s of each of the p a r t i c l e s were determined by  measuring the volume o f l i q u i d d i s p l a c e d when a known w e i g h t of s o l i d s i s poured i n t o a graduated c y l i n d e r .  The d e n s i t i e s of PVC (***GEON 30  and GEON 212) and polypropylene// were s u p p l i e d by the m a n u f a c t u r e r s . The b u l k d e n s i t y measurements were c a r r i e d out i n accordance w i t h the  procedure o f Oman and Watson ( 1 9 4 4 ) .  A 500 c . c . g r a d u a t e d c y l i n d e r  was p a r t i a l l y f i l l e d w i t h a known weight of s o l i d s , c l o s e d a t i t s open end and i n v e r t e d , then r e t u r n e d back q u i c k l y t o i t s o r i g i n a l  position.  The t e s t was r e p e a t e d s e v e r a l times t o ensure good r e p r o d u c i b i l i t y .  ***Trade  name used by B.F. G o o d r i c h Co. L t d .  //Supplied by H e r c u l e s Canada L t d .  The  Table 3.2: P a r t i c l e s i z e (a)  PVC (GEON 212)  d  (um) P  180  150  0.027  0.066  215  165  1  (b) d  0.488  1  (c)  0.42  (um)  0.028  0.425  135  105  d  0.469  0.0352  P  0.019  31 0.016  = 185.6 um  0.0078  458  384 ..  301  255  188  0.01712  0.6733  0.0424  0.0701  195  165  128  i  x. l  (d)  0.043  d  P  = 299.5 um  Bronze (um)  252  d  = 176.4 um P  x. l  63  Polypropylene  d  p  75  i  x.  d  90  PVC (GEON 30) (um)  P  125  i  x.  P  distributions  0.182  0.330  0.477  0.012  d  P  = 98 um  T a b l e 3.2: (e)  S i l i c a Sand  d P  X  i  dim)  i  [f)  (pm) p  d  =196  215  165  135  105  0.501  0.468  0.020  0.011  640  548  458  386  323  0.105  0.171  0.306  0.186  0.128  655  548  458  386  220  0.281  0.403  0.205  0.054  0.058  P  pm  S i l i c a Sand  d  X  coat'd....  223  i  i  d  P  = 401 um  .105  S i l i c a Sand d p  x.  1  i  (um)  d  P  = 516.4  \im  - 40 -  weight  of the s o l i d s d i v i d e d  the above procedure, T h i s enabled voidage  ( t h e annulus  by the volume occupied  by the s o l i d s  after  gave the random l o o s e-packed b u l k d e n s i t y , the c a l c u l a t i o n of a spouted  of e^, the spouted  bed i s a loose-packed  bed  annulus  bed) as:  (3.4)  T e s t s f o r a n g l e of repose carried  and angle of i n t e r n a l f r i c t i o n were  out i n accordance w i t h the methods o u t l i n e d  by Zenz and Othmer  (1960).  F o r measuring the angle of i n t e r n a l f r i c t i o n ( a ) , a c y l i n d e r  I.D. 6.4  cm, h a v i n g a 1 cm h o l e a t the bottom and open a t the top, was  utilized. drain.  of  S o l i d s were poured to a h e i g h t of about 35 cm and a l l o w e d to  The h e i g h t of the bed a t which a d e p r e s s i o n f i r s t o c c u r r e d i n  the c e n t e r of the bed s u r f a c e was n o t e d , and the r a t i o of t h i s h e i g h t to the c y l i n d e r  I.D. recorded as the tangent  f r i c t i o n (a).  The angle of repose  of the angle of i n t e r n a l  ( $ ) was measured as the angle made by  the heap of the d r a i n e d s o l i d s w i t h the h o r i z o n t a l .  The t e s t s were done  s e v e r a l times to ensure r e p r o d u c i b l e r e s u l t s . The minimum f l u i d i z a t i o n v e l o c i t y , U ~p, was m  e x p e r i m e n t a l l y i n the h a l f column by a c t i v a t i n g  determined  the a u x i l i a r y f l o w l i n e s  and m a i n t a i n i n g bed h e i g h t s above 80 cm to ensure u n i f o r m d i s t r i b u t i o n of f l o w .  - 41 -  CHAPTER 4 REGIME MAPS AND CRITERIA FOR FINE PARTICLE SPOUTING  As d i s c u s s e d controversy  i n c h a p t e r s one and two, there e x i s t s s i g n i f i c a n t  regarding  the s p o u t a b i l i t y of f i n e p a r t i c l e s .  p a r t of t h i s work t h e r e f o r e i n v o l v e d previous  The f i r s t  t e s t i n g the g e n e r a l i z a t i o n s of the  workers (Mathur and G i s h l e r - 1 9 5 5 ;  Ghosh-1965; G e l d a r t - 1 9 7 3 ;  Rooney and H a r r i s o n - 1 9 7 4 ; H e s c h e l and K l o s e - 1 9 8 1 ; M o l e r u s - 1 9 8 2 ) . r e s u l t s were used t o o b t a i n regime maps l i k e 2.1a  The  the ones shown i n F i g s .  and. 2.1b, which summarize the d i f f e r e n t ' s t a t e s ' of a system under  various  operating  conditions.  The v a r i o u s  f l o w regimes a l o n g w i t h the  t r a n s i t i o n p o i n t s were c a r e f u l l y examined and v i d e o t a p e d , and the i n f l u e n c e of d i f f e r e n t parameters on these regimes s t u d i e d .  4.1  Experimental Procedure To  s t a r t w i t h , the work of H e s c h e l and K l o s e  (1981), which  e x h i b i t e d most unusual r e s u l t s , was r e p e a t e d i n a h a l f column of h a l f the s i z e used i n t h e i r work. were very c l o s e used to m a i n t a i n the i n l e t ) . and  to t h e i r s .  The bed m a t e r i a l and the i n l e t f l u i d The tapered  o r i f i c e s shown i n F i g . 3.3 were  e x a c t l y the same i n l e t c o n d i t i o n s  Table 4.1 summarizes the o p e r a t i n g  i n t h a t of H e s c h e l and K l o s e  used  (no c o n t r a c t i o n a t  c o n d i t i o n s i n t h i s work  (1981).  Subsequent runs were a l s o made i n the 60 degree cone angle column w i t h i n l e t s i z e s from 2.8 to 28 mm and a wide v a i e t y of p a r t i c l e s ranging g/cm  3  i n s i z e from 170 um to 1000 um and i n d e n s i t y from 0.9 to 8.9  (Table 3 . 1 ) .  Table 4.1:  O p e r a t i n g c o n d i t i o n s i n t h i s work v s . those of Heschel and K l o s e (1981)  Heschel & K l o s e (1981) 1.  T h i s work  Column d i a . = 30 cm ( f u l l column)  1.  I n l e t diameter = 25.4 mm (no c o n t r a c t i o n of the f l u i d at the i n l e t ) 2.  S o l i d used:  PVC (d  = 90 urn) P  3.  Fluid:  A i r (R.H. = 80%)  4.  H = 40, 55 and 75 cm.  (Note:  Column d i a m e t e r = 15.2 cm ( h a l f column) I n l e t diameter = 25.4, 12.7 & 10.1 mm (no c o n t r a c t i o n o f the f l u i d a t the i n l e t )  2.  S o l i d used:  PVC (d = 98.8 P  3.  Fluid:  4.  H = 15 to 80 cm.  A i r (R.H. = 80%)  R.H. = R e l a t i v e h u m i d i t y )  um)  - 43 -  F o r o b t a i n i n g the regime maps ( e . g . F i g . 4.4),  s o l i d s were poured  i n t o the column, s t a r t i n g w i t h a low bed h e i g h t , and t h e i r l o o s e packed bed h e i g h t * measured.  The a i r f l o w r a t e was i n c r e a s e d g r a d u a l l y and the  t r a n s i t i o n p o i n t s ( t r a n s i t i o n between d i f f e r e n t regimes) n o t e d .  The  f l o w r a t e was then decreased to the minimum s p o u t i n g f l o w r a t e and then i n c r e a s e d a g a i n , the t r a n s i t i o n p o i n t s b e i n g noted once more. procedure was s u b s e q u e n t l y All  repeated  This  f o r l a r g e r bed h e i g h t s .  regime maps were c o n s t r u c t e d w h i l e d e c r e a s i n g  the f l o w , and  were then q u i t e r e p r o d u c i b l e when the f l o w was i n c r e a s e d once a g a i n . T h i s procedure was e s s e n t i a l i n order  to o b t a i n a l l the r e g i m e s , as  d u r i n g s t a r t - u p the bed o f t e n went s t r a i g h t from the f i x e d packed c o n d i t i o n to the b u b b l i n g regime ( t o p o i n t X i n F i g . 4.4a, f o r example, escaping  the steady  regimes). of U  m s  s p o u t i n g and the p r o g r e s s i v e l y i n c o h e r e n t  A l s o , t h i s procedure becomes c o n s i s t e n t w i t h the d e f i n i t i o n  based on d e c r e a s i n g The  spouting  f l o w (Chapter  2, Sec. 2.2.1).  regime t r a n s i t i o n s were marked by d i s t i n c t v i s u a l  o b s e r v a t i o n s , as d i s c u s s e d constructed  i n the next s e c t i o n .  for different i n l e t  The regime maps were  sizes.  Some p r e l i m i n a r y work was a l s o c a r r i e d  out i n a f u l l  column w i t h  a cone a n g l e  of 30° and diameter 15.2 cm to reproduce the q u a l i t a t i v e  observations  of H e s c h e l and K l o s e (1981).  employed f o r q u a l i t a t i v e l y c o n f i r m i n g and  The f u l l column was a l s o  the e x i s t e n c e of d i f f e r e n t  f o r c o l l e c t i n g data i n some l a t e r work.  *The l o o s e packed bed h e i g h t r e f e r s here to the bed h e i g h t o b t a i n e d by c o l l a p s e of the bed from the s p o u t i n g c o n d i t i o n .  regimes  - 44 -  The  e f f e c t of p a r t i c l e d e n s i t y and s i z e on s p o u t a b i l i t y  s t u d i e d f o r each of the s o l i d s l i s t e d i n Table 3.1. the i n l e t s i z e was  For e v e r y  few runs were a l s o repeated i n the f u l l  Results and  4.2.1  solid,  p r o g r e s s i v e l y i n c r e a s e d ( s e v e r a l bed h e i g h t s were  used f o r each i n l e t s i z e ) u n t i l no s t e a d y s p o u t i n g was  4.2  was  achievable.  column.  Their Analysis  Influence of i n l e t diameter The  o b s e r v a t i o n s i n the 36°  10.1  mm  h a l f - c o l u m n w i t h i n l e t s i z e s of  12.7  and  PVC,  were q u i t e d i f f e r e n t from those of H e s c h e l and K l o s e (1981).  mm  orifice.  was  o b t a i n e d w i t h the  K l o s e (1981) at the f o o t of t h e i r f i r s t peak ( F i g . 2.3).  drop f l u c t u a t e d .  The  rising  at the f o o t of  T h i s c o i n c i d e d w i t h the o b s e r v a t i o n s of H e s c h e l  i n c r e a s i n g the f l o w , bubbles  ym  The  The j e t broke through and d i s c h a r g e d as bubbles  up c e n t r a l l y , f o r m i n g a c r a t e r - s h a p e d area around i t , peak ( p o i n t A ) .  25.4,  and w i t h no f l u i d c o n t r a c t i o n at the i n l e t , u s i n g 98  p r e s s u r e drop v s . flow curve shown i n F i g u r e 4.1 12.7  A  the  and  Upon  grew i n number and s i z e and the  pressure  s o l i d s were c a r r i e d up i n the wake of the  bubbles  (which were m o s t l y at the c e n t e r of the column) and moved down i n the 'annulus' bed).  (which c o u l d be c a l l e d the 'emulsion  At the curved  phase' as i n a  fluidized  r e a r w a l l of the column, the s o l i d s appeared to be  moving downwards i n a p u l s a t i n g manner.  Further increase i n flow did  not cause any s i g n i f i c a n t r i s e i n p r e s s u r e drop, but s i m p l y l e d to s l u g g i n g , where the bubbles  became e q u a l to the diameter  of the column.  Thus the second peak r e p o r t e d by H e s c h e l and K l o s e (1981) d i d not appear  o •5?  0.0  0.2  0.4  0.6 Q  0.8  1.0  (std.l/s)  F i g u r e 4.1. T y p i c a l p r e s s u r e d r o p v s . f l o w r a t e c h a r a c t e r i s t i c s o b t a i n e d upon r e p e a t i n g t h e c o n d i t i o n s o f H e s c h e l and K l o s e (1981). PVC, d =0.098 mm, d.=12.7 mm, H=37. P F l u i d used: A i r a t 80% r e l a t i v e h u m i d i t y . 1  - 46 -  at a l l , and steady s p o u t i n g was never o b s e r v e d .  F u r t h e r i n c r e a s e of  f l o w l e d to pneumatic t r a n s p o r t o f the s o l i d s from the column.  The same  o b s e r v a t i o n s were a l s o made when the f u l l column was u t i l i z e d . Spouting was o n l y seen to occur when the i n l e t to l e s s than 25 times the p a r t i c l e d i a m e t e r . d i a m e t e r , b u b b l i n g or s l u g g i n g o c c u r r e d .  s i z e was reduced  Beyond t h i s l i m i t of i n l e t  The o c c u r r e n c e o f t h i s  c r i t i c a l v a l u e o f i n l e t diameter beyond which steady s p o u t i n g d i d not occur was confirmed f o r a wide v a r i e t y o f s o l i d s ( T a b l e 3.1) and the r e s u l t s a r e shown i n F i g . 4.2a.  The l i m i t i n g  i n l e t diameter f o r  s p o u t i n g i s shown as a range, s i n c e t h e o r i f i c e stepwise i n s i z e . highest i n l e t  The lower l i m i t o f each v e r t i c a l  line  r e p r e s e n t s the  s i z e employed at which s t e a d y s p o u t i n g was a c h i e v a b l e and  the upper l i m i t r e p r e s e n t s the lowest i n l e t spouting occurred. Fig.  s i z e s used i n c r e a s e d  s i z e used a t which no  The m i d - p o i n t o f each o f the i n l e t  s i z e ranges i n  4.2a was then taken as a r e p r e s e n t a t i v e v a l u e o f the c r i t i c a l  diameter  f o r steady s p o u t i n g .  inlet  These were p l o t t e d i n F i g . 4.2b and l i n e  CC^ o b t a i n e d by l i n e a r r e g r e s s i o n o f these p o i n t s ( a l m o s t no f o r c i n g through t h e o r i g i n was r e q u i r e d ) .  Hence f o r s t e a d y s p o u t i n g to o c c u r ,  d. < 25.4 d l p  (4.1)  L i n e s AA[ and BB^ were o b t a i n e d by l i n e a r r e g r e s s i o n o f the upper and  the lower l i m i t s , r e s p e c t i v e l y , i n F i g . 4.2a, w i t h o u t any f o r c i n g  through the o r i g i n .  These r e p r e s e n t t h e d e v i a t i o n s from Eq. (4.1) (AA^  -  47  ^£ (g/cm ) 0.90 3  Polypropylene V  1.27  PVC  O  S i l i c a sand  2.66  •  Glass  2.42  •  Glass  4.56  Bronze  7.90  X  Copper  8.80  A  Nickel  8.90  d F i g u r e 4.2a.  Critical inlet  (mm) P diameter range f o r steady s p o u t i n g  - 48 -  1  I I  l  1  1  1  1  1  1 C  SOLID  —  •  — — —  P  Polypropylene  p  3 (g/cm )  /  V PVC  li.27  y  O S i l i c a sand  2.66  /  •  Glass  4.56  %  Glass  2.42 7.90  X' Copper  8.80  A Nickel  8.90  _  Y  0.90  A Bronze  l  — —  y /  —  /  —  / A  /  #  OA/  BUBBLING  —  —  —  — STEADY SPOUTING A/OB  —  —  — —  0  —  •  c 1  1  0.2  1  1  0 .4  1  d  1  0.6 P  F i g u r e 4.2b. C r i t i c a l i n l e t d i a m e t e r Fig.4.2a)  1  1  0.8  1  1  1.0  (mm) ( m i d - p o i n t s o f t h e ranges shown i n  f o r steady spouting.  - 49  has a s l o p e of 28.2  and BB^  -  a s l o p e of 23.2).  The  r e s u l t s obtained i n  t h i s work support  the o b s e r v a t i o n s of Ghosh (1965) and  H a r r i s o n (1974).  The  i n l e t diameter 30  times  c r i t e r i o n of Ghosh, which p o s t u l a t e s a the p a r t i c l e d i a m e t e r , i s f a i r l y  upper l i m i t of d e v i a t i o n ( s l o p e of l i n e AAj = 28.2). t h i s work do not agree w i t h those of H e s c h e l p r o b a b l y mistook  of Rooney and  c l o s e to the  The r e s u l t s of  and K l o s e ( 1 9 8 1 ) ,  ym PVC,  sand showed three regimes:  300  ym p o l y p r o p y l e n e and 196  ym  silica  f i x e d bed, b u b b l i n g and steady s p o u t i n g upon  i n c r e a s i n g and d e c r e a s i n g the f l o w , p r o v i d e d Eq.  (4.1) was  i n c r e a s i n g the f l o w , the j e t f i r s t broke through as bubbles 2.4)  who  non-homogenous f l u i d i z a t i o n f o r s p o u t i n g .  S p o u t i n g of 186  Fig.  critical  obeyed.  Upon  (point B i n  and formed a steady spout when the f l o w r a t e was f u r t h e r  i n c r e a s e d ( p o i n t C i n F i g . 2.4). increased with i n c r e a s i n g flow.  The The  r e g i o n of s o l i d  circulation  c i r c u l a t i o n of s o l i d s was  very poor  and a v e r y l a r g e s t a g n a n t zone e x i s t e d a t a l l times ( F i g . 4.3b). The above 400  r e g i o n of s o l i d c i r c u l a t i o n was ym i n s i z e were u t i l i z e d .  h i g h e r bed depth  These p a r t i c l e s a l s o allowed a much  to be spouted w i t h a v e r y s m a l l or no s t a g n a n t  thus r e p r e s e n t i n g a more p r a c t i c a l system. the maximum i n l e t diameter maps s i m i l a r  to F i g . 4.4a  zone,  For such p a r t i c l e s , p r o v i d e d  f o r steady s p o u t i n g i s not exceeded, regime were o b t a i n e d .  p i c t o r i a l l y r e p r e s e n t e d i n F i g . 4.5. by the presence  much enhanced when p a r t i c l e s  of a steady  The  v a r i o u s regimes are  Steady s p o u t i n g i s c h a r a c t e r i z e d  f o u n t a i n , h a v i n g a d e f i n i t e shape  ( a p p r o x i m a t e l y p a r a b o l i c ) and a steady spout-annulus d i s t u r b a n c e s or waves ( F i g . 4.5a).  interface with  no  P r o g r e s s i v e l y incoherent spouting  I  8  (b)  (a) F i g u r e 4.3. Regimes w i t h s p o u t i n g p a r t i c l e s w i t h d^< and C i n F i g . 2 . 4 , show  0.35 ran. (a) B u b b l i n g  o c c u r s between p o i n t s B  (b) s t e a d y s p o u t i n g s e t s i n beyond p o i n t C (Fig.2.4) - t h e t r a c e r  the region o f c i r c u l a t i o n .  particles  (a)  (W  F i g u r e 4 5. P i c t u r e s o f d i f f e r e n t r e g i e s shown i n F i g . 4.4. incoherent spouting  (c) b u b b l i n g  (d)  ( C )  (a) s t e a d y s p o u t i n g  (d) s l u g g i n g . Sand, d =0.516 mn, p  (b) p r o g r e s s x v e l y  d.=6.0 nm.  -  (P.I.S.)  -  53  s e t s i n when the f o u n t a i n shape g e t s d i s t o r t e d and waves s t a r t  to appear along the spout-annulus  i n t e r f a c e near the bed s u r f a c e .  The  t r a n s i t i o n from P.I.S. to b u b b l i n g o c c u r s when the j e t s i n k s below the bed  s u r f a c e and d i s c h a r g e s as b u b b l e s .  T h i s t r a n s i t i o n can  be  v i s u a l i z e d as the a m p l i t u d e o f the waves ( o r d i s t u r b a n c e s ) i n P.I.S. becoming equal to the spout r a d i u s , l e a d i n g to a p i n c h p o i n t and the f o r m a t i o n of a bubble.  thereby  When the r i s i n g bubbles become e q u a l to the  s i z e of the column, as they approach the bed s u r f a c e , s l u g g i n g s e t s i n . An i n t e r e s t i n g phenomenon o c c u r s when the bed h e i g h t i s between B and C i n F i g . 4.4b.  For example, on i n c r e a s i n g the f l o w along the  X j X g , steady s p o u t i n g o c c u r s between X  2  and X . 3  Beyond X , 3  line  P.I.S. s e t s  i n and upon f u r t h e r i n c r e a s e of f l o w to Xu., steady s p o u t i n g once a g a i n occurs.  Spouting beyond X^,  however, l e a d s to a v e r y h i g h f o u n t a i n and  the bed s u r f a c e i s c o n i c a l as compared to i t s i n v e r t e d cone shape between X  2  behaviour  and X . 3  F i g . 4.6  further elucidates this point.  This  i s a l s o r e t r a c e a b l e upon d e c r e a s i n g the f l o w .  F i g u r e 4.7  demonstrates the e f f e c t of i n l e t s i z e on the d i f f e r e n t  regimes.  As the i n l e t s i z e i n c r e a s e s , the r e g i o n of s t e a d y  decreases  ( a l s o shown i n F i g s . 4.4  and 4.8)  and  spouting  upon exceeding  the  limit  i n Eq. ( 4 . 1 ) , i t v a n i s h e s a l t o g e t h e r .  4.2.2  Effect of p a r t i c l e The  F i g . 4.2.  size  e f f e c t of i n c r e a s i n g p a r t i c l e s i z e i s p a r t i a l l y r e f l e c t e d i n I n c r e a s i n g the p a r t i c l e s i z e a l l o w s a b i g g e r i n l e t s i z e to be  used f o r steady s p o u t i n g .  A l s o , use of b i g g e r p a r t i c l e s m a g n i f i e s  the  (a) F i g u r e 4.6.  (b)  T r a n s i t i o n between regimes a l o n g  (c) i n F i g . 4.4b  with increasing flow rate.  (a) s t e a d y s p o u t i n g (b) p r o g r e s s i v e l y i n c o h e r e n t s p o u t i n g (c) s t e a d y s p o u t i n g  - 56 -  - 58  -  r e g i o n of steady s p o u t i n g as d e p i c t e d by F i g s . 4.4b, p a r t i c l e s w i t h mean diameter  g r e a t e r than 1 mm,  4.7b  and 4.8b.  the r e g i o n of  s p o u t i n g i s much l a r g e r and P.I.S. i s almost n o n - e x i s t e n t . Fig.  4.2.3  For  steady  ( R e f e r to  2.2).  E f f e c t of p a r t i c l e density The  c r i t e r i a of s p o u t a b i l i t y g i v e n by G e l d a r t (1973) and  (1982) ( E q u a t i o n s 2.1  and 2.2  r e s p e c t i v e l y ) suggest  that  1  Molerus  non-spoutable'  p a r t i c l e s can become 'spoutable' i f t h e i r d e n s i t y i s i n c r e a s e d s u f f i c i e n t l y (Chapter 2, S e c t i o n 2.1.2).  For example i n F i g . 4.9  p a r t i c l e a t p o i n t K i s i n the n o n - s p o u t i n g  zone.  a  However, i f i t s  d e n s i t y i s r a i s e d , k e e p i n g i t s s i z e the same, i t can be made to spout ( p o i n t L i n F i g . 4.9). p a r t i c l e s ( s i z e 170  However, d a t a c o l l e c t e d over a wide v a r i e t y of  to 1000  um and d e n s i t y 0.9  to 8.9  n e g l i g i b l e e f f e c t of d e n s i t y on s p o u t a b i l i t y . i n f e r r e d from F i g . 4.2.  A l s o , i n F i g . 4.9,  full  4.2.4  (1982).  ) show  T h i s can e a s i l y  be  a number of s t a b l e s p o u t i n g  p o i n t s f a l l i n the s o - c a l l e d 'non-spoutable' and Molerus  g/cm  r e g i o n s of G e l d a r t (1973)  Some of these r e s u l t s were a l s o c o n f i r m e d  i n the  column.  Minimum and  maximum spouting v e l o c i t i e s  The minimum s p o u t i n g v e l o c i t y , U , m s  was  p r e d i c t e d by  the  M a t h u r - G i s h l e r e q u a t i o n , Eq. ( 2 . 3 ) , w i t h an average d e v i a t i o n of ± 10%. For p a r t i c l e s g r e a t e r than 400  um i n s i z e , U  m g  was  taken as  the  s u p e r f i c i a l i n l e t v e l o c i t y a t which the p r e s s u r e drop a c r o s s the bed  - 59 -  F i g u r e 4.9. G e l d a r t ' s on  (1973) and  Molerus'  (1982) c r i t e r i a f o r s p o u t a b i l i t y  a l o g - l o g s c a l e . Data p o i n t s shown r e p r e s e n t p a r t i c l e s f o r  s t e a d y s p o u t i n g was a c h i e v a b l e i n t h i s  work.  - 60  rose a g a i n upon d e c r e a s i n g the f l o w . in size, U  m s  was  -  For p a r t i c l e s s m a l l e r than 400  um  taken as the minimum v e l o c i t y a t which steady  s p o u t i n g o c c u r r e d (Chapter 2, S e c t i o n 2.2.1, p o i n t C i n F i g . 2.4). Table 4.2 than 400  summarizes the r e s u l t s .  um i n s i z e , when p o i n t B i n F i g . 2.4  between e x p e r i m e n t a l v a l u e s and 40%,  I t i s seen t h a t f o r p a r t i c l e s l e s s i s used, the d e v i a t i o n s  those p r e d i c t e d by Eq. (2.3) are  over  but when p o i n t C i s chosen ( s t e a d y s p o u t i n g occurs o n l y beyond C ) ,  the d e v i a t i o n s a r e much s m a l l e r . g r e a t e r than 400 (dp > 400  um),  The  prediction  of U  um by Eq. (2.3) are much improved.  as i s c o n v e n t i o n a l l y done, B was  r e p r e s e n t the e x p e r i m e n t a l v a l u e of  m s  for particles  For these p a r t i c l e s  the p o i n t chosen to  U . m s  As seen from the regime maps i n F i g s . 4.4,  4.7  and 4.8,  above a  c e r t a i n minimum bed h e i g h t there e x i s t s a maximum s p o u t i n g v e l o c i t y beyond which s t a b l e s p o u t i n g ceases  to o c c u r .  This'maximum s p o u t i n g  v e l o c i t y approaches the minimum s p o u t i n g v e l o c i t y , narrowing  the r e g i o n  of steady s p o u t i n g , as the i n l e t s i z e i s i n c r e a s e d to i t s c r i t i c a l ( F i g . 4.7,  f o r example).  value  The maximum s p o u t i n g v e l o c i t y i s a l s o an  i n d i c a t o r of regime t r a n s f o r m a t i o n and  can be p r e d i c t e d as d i s c u s s e d i n  S e c t i o n 4.2.6.  4.2.5  E f f e c t of bed  height, maximum spoutable bed  depth,  and  stable j e t length It i s interesting and 4.8  to note  t h a t the regime maps i n F i g . 4.4,  are q u i t e r e p r o d u c i b l e by k e e p i n g  c o n s t a n t v a l u e and changing  4.7  the flow r a t e s e t a t a  the bed h e i g h t .  In F i g . 4.7a,  f o r example,  Table 4.2:  Solid  PVC PVC PVC Polypropylene Polypropylene Polypropylene Sand Sand Sand Bronze Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Glass Glass Glass Glass Sand Sand  E x p e r i m e n t a l v a l u e s of minimum s p o u t i n g v e l o c i t y v s . E q u a t i o n 2.3  d  H  P (um)  i (mm)  (cm)  185.6 185.6 185.6 299.5 299.5 299.5 196 196 196 176.4 401 401 401 401 401 401 401 401 516.4 516.4 516.4 516.4 516.4 710 710 710 710 1000 1000  2.8 2.8 4.5 2.8 4.5 6.0 2.8 4.5 4.5 2.8 4.5 4.5 4.5 6.0 6.0 6.0 9.0 9.0 6.0 6.0 6.0 12.7 12.7 6.0 6.0 12.7 12.7 6.0 • 12.7  12.6 17.3 19.5 19.8 20.0 23.0 15.0 14.5 19.5 15.0 30.0 41.0 49.6 15.0 30.0 41.0 30.0 41.0 30.0 41.0 50.0 30.0 41.0 40.5 50.8 41.0 52.0 41.0 41.0  d  *Taken as p o i n t B i n F i g . 2.4. //Calculated as ^ d i e t e d - E x p t . Expt.  x  ^  U  ms* < Expt. 0.010 0.013 0.015 0.026 0.027 0.031 0.018 0.018 0.022 0.029  —  m / s )  U  ms Expt.  ( m / s )  0.013 0.021 0.025 0.027 0.028 0.033 0.022 0.024 0.029 0.035 0.093 0.118 0.125 0.0714 0.107 0.122 0.111 0.121 0.157 0.172 0.184 0.158 0.178 0.328 0.353 0.372 0.398 0.318 0.374  (m/s) ms Eq. (2.3) 0.015 0.018 0.022 0.028 0.030 0.037 0.025 0.028 0.033 0.041 0.095 0.108 0.119 0.072 0.102 0.119 0.117 0.136 0.133 0.158 0.173 0.164 0.196 0.281 0.313 0.361 0.407 0.298 0.382  % dev. //  +13 .96 -14 .29 -12 .00 +3 .70 +9 .24 +12 .12 + 13 .64 +16 .67 +13 .79 +17 .14 +2 .31 -8 .48 -4 .79 +0 .84 -4 .76 -2 .54 +5 .12 +12 .4 -15 .22 -7 .97 -6 .19 +3 .87 +10 .11 -14 .33 -11 .33 -2 .96 +2 .26 -6 .28 +2 .14  - 62  keeping  -  the f l o w r a t e f i x e d and i n c r e a s i n g  v e r t i c a l l i n e MQ  the bed h e i g h t a l o n g  e x h i b i t s p o i n t s N, 0 and P as the t r a n s i t i o n  the  points.  These p o i n t s are q u i t e c l o s e to the t r a n s i t i o n s o b t a i n e d by the e a r l i e r method. As d e s c r i b e d i n S e c t i o n 2.2.2, spout s p o u t a b l e bed h e i g h t , H , M  t e r m i n a t i o n a t the maximum  i n the case of f i n e p a r t i c l e s o c c u r s due  to  c h o k i n g of the spout. The d a t a f o r %  are shown i n t a b l e 4.3.  I t can be seen t h a t  the maximum s p o u t a b l e bed depth decreases w i t h i n c r e a s i n g i n l e t and d e c r e a s i n g p a r t i c l e s i z e . Rooney and H a r r i s o n (1974).  The  t r e n d i s the same as t h a t observed  The e q u a t i o n s reviewed  e q u a t i o n s o v e r p r e d i c t H^ by more than 100%  and hence cannot  These e q u a t i o n s ,  by  i n S e c t i o n 2.2.2  t e s t e d a g a i n s t e x p e r i m e n t a l d a t a and p r e s e n t e d i n Table 4.3.  recommended f o r f i n e p a r t i c l e s .  diameter  are  Both be  developed  s e m i - e m p i r i c a l l y based on coarse p a r t i c l e d a t a , do not r e p r e s e n t the f i n e p a r t i c l e b e h a v i o u r adequately.  Nor does the f o o t n o t e d e q u a t i o n .  A l t h o u g h G e l d a r t e t a l (1981) found  that H  M  i n a h a l f column i s  g e n e r a l l y about 10 to 15% lower than i n a f u l l column, t h i s still and  does not account  finding  f o r the h i g h d i s c r e p a n c y between the e x p e r i m e n t a l  the p r e d i c t e d r e s u l t s of the p r e s e n t  study.  However, when H^ i s c a l c u l a t e d by the new method d e s c r i b e d i n the next s e c t i o n ( T a b l e 4.6),  the d e v i a t i o n of the p r e d i c t e d v a l u e s  the e x p e r i m e n t a l ones i s l e s s than 30%,  from  which i s r e a s o n a b l e as d i s c u s s e d  later. In the b u b b l i n g regime, as shown i n F i g . 4.5,  a s t a b l e j e t of  Table 4.3:  Experimental  dp  Solid  v s . p r e d i c t e d maximum s p o u t a b l e  d. l (mm)  (ym)  H  M  (cm)  H  (Expt.)  bed  (cm)  M  (Eq.  2.6)  depths*  H  H  (cm)  M  (Eq.  (cm)  M  2.7)  PVC  186  2.8 4.5  28.3 26.4  + +  + +  + +  Polypropylene  299  2.8 4.5 6.0  26.2 22.0 20.5  + + +  + + +  + + +  S i l i c a sand  196  2.8 4.5  26.2 20.5  + +  + +  + +  S i l i c a Sand  401  4.5 6.0 7.5 9.0  49.6 46.8 45.6 43.6  128.9 121.2 116.4 101.1  @ @ @ @  77.4 63.9 55.1 48.8  S i l i c a Sand  516  6.0 7.5 9.0 12.7  58.5 55.4 52.5 48.5  108.1 103.6 91.4 80.6  @ @ @ @  95.5 82.3 72.8 57.9  Glass  710  6.0 7.5 9.0 12.7  55.5 55.0 52.1 50.8  85.9 81.2 76.1 72.4  198.5 158.5 132.1 93.6  196.5 169.3 150.0 119.2  +  cannot be determined f o r these, s i n c e H b a r e l y exceeds H changes s i g n i f i c a n t l y w i t h f l o w r a t e and along  and  c  the bed h e i g h t .  s i n c e the r e g i o n of  circulation  No r e p r e s e n t a t i v e v a l u e of D  c  can  thus be  used. @ A i s below the minimum value r e q u i r e d i n Eq. 2.7 * H  M  i s a l s o p r e d i c t e d by a new  // P r e d i c t e d by H  method i n the next s e c t i o n .  = 700(D /d )(D / d j c p c i 2  M  (A = 0.01).  2  /  3  [(1 + 35.9  x 10"  6  Ar)  1 / 2  - 1] /Ar, 2  see E p s t e i n and Grace  (1984).  - 64 -  l e n g t h h i s seen d i s c h a r g i n g as b u b b l e s .  The s t a b l e j e t l e n g t h  f l u c t u a t e s by about ± 3 era due to f o r m a t i o n  and d i s c h a r g e  of bubbles a t  its tip. I t i s f u r t h e r observed from F i g s . 4.4, 4.7 and 4.8 inlet fluid for  f l o w r a t e becomes equal  to the minimum f l u i d i z a t i o n  M  The s t a b l e j e t l e n g t h i s e x p e r i m e n t a l l y  independent of bed h e i g h t f o r H > H . M  m  flowrate  a deep enough bed (H _> H ) , a j e t d i s c h a r g i n g as bubbles i s  observed.  UF  t h a t as the  found to be  I n Eq. ( 2 . 2 5 ) , s u b s t i t u t i n g  f o r U thus g i v e s the s t a b l e j e t l e n g t h :  (4.2)  T a b l e 4.4  compares the e x p e r i m e n t a l  from Eqns. 4.2, 2.25 and 2.26. to the e x p e r i m e n t a l  4.2.6  data  I t i s observed t h a t Eq. (4.2) i s c l o s e r  than the other  two.  Prediction of Regime Transformation The phenomenon  formation  I n a standpipe  s l u g formation)  occurs  c r i t i c a l value, c a l l e d phenomeon decreasing  of t r a n s i t i o n from s t a b l e s p o u t i n g  to bubble  a t the spout top appears to be analagous to choking i n  standpipes. (or  r e s u l t s w i t h the p r e d i c t i o n s  where a f l u i d  i s carrying solids,  choking  as the gas v e l o c i t y i s reduced below a  the choking  v e l o c i t y (Leung, 1980).  The  e s s e n t i a l l y occurs due to i n c r e a s i n g s o l i d s c o n c e n t r a t i o n ( o r voidage) upon r e d u c i n g  the gas f l o w .  The  recommended  Table 4.4:  E x p e r i m e n t a l and p r e d i c t e d j e t p e n e t r a t i o n depths f o r • H  Solid  d  > V  *  =  d  i  1  h (cm)  h  (cm)  h  (cm)  L i m i t s of h (cm) (Eq. 2.27)  P ( um)  (mm)  S i l i c a Sand  516  6.0  35.2 ± 3  37.2  25.3  19.7 - 52.6  S i l i c a Sand  516  12.7  27.1 ± 3  30.9  25.3  7.7 - 20.5  Silica  Sand  401  6.0  24.0  ±3  29.8  22.9  15.8 - 42.2  S i l i c a Sand  401  9.0  21.6 ± 3  27.8  22.9  8.8 - 23.5  Glass  710  6.0  41.4  ±3  35.3  32.9  27.9 - 74.5  Glass  710  12.7  36.7 ± 3  32.3  32.7  Expt.  (Eq.  4.2)  (Eq.  2.26)  9.4  - 25.1  - 66 -  e q u a t i o n f o r p r e d i c t i n g the choking v e l o c i t y , U , i s : c  2gD(eT ' 4  i n which e , c  - l)/(U  7  - U )  c  T  2  = 0.074 p / 0  the voidage a t c h o k i n g , may  (4.3)  7 7  be p r e d i c t e d by the  s e m i - e m p i r i c a l e q u a t i o n of Smith (1978):  2 p  -9 ( 1  -  e  c  -  }  n  „ l  V^T  [ n £  f  c  9  U  T  2  iD  ]  ( 4  '  4 )  where UTJ i s the f r e e s e t t i n g v e l o c i t y of a s i n g l e p a r t i c l e , D i s the s t a n d p i p e diameter and n the R i c h a r d s o n - Z a k i i n d e x . These e q u a t i o n s w i t h D , s  the spout d i a m e t e r , r e p l a c i n g D, were  a p p l i e d to c a l c u l a t e U , which would then c o r r e s p o n d to U C  G  (=  v o l u m e t r i c f l o w r a t e through the s p o u t / s p o u t c r o s s - s e c t i o n a l area) a t the bed s u r f a c e a t the p o i n t of c h o k i n g ( t r a n s i t i o n from steady s p o u t i n g to b u b b l i n g ) .  F u r t h e r , by u s i n g the e x p e r i m e n t a l l y o b t a i n e d f l o w  d i s t r i b u t i o n between the spout and e x p e r i m e n t a l U (H) g  the annulus (Chapter 5 ) , the  a t c h o k i n g can be d e t e r m i n e d .  between the two v a l u e s are shown i n T a b l e 4.5. r e a s o n a b l y good, p a r t i c u l a r l y Eqn.  deviations  The p r e d i c t i o n i s  f o r h i g h e r bed d e p t h s , p r o b a b l y because  (4.4) i s based on data c o l l e c t e d  the v a l i d i t y of Eqn.  The  from a i r - s a n d systems.  (4.3) i s o f t e n q u e s t i o n e d (Leung, 1980)  d i a m e t e r s g r e a t e r than 50  to 100 mm,  i t was  Although f o r pipe  s u i t a b l e f o r t h i s work  Table  4.5:  P r e d i c t i o n of maximum s t a b l e s p o u t i n g v e l o c i t y (= U ) c r i t e r i o n v s . e x p e r i m e n t a l v a l u e [= U ( H ) ]  by c h o k i n g  c  S  H (cm)  Solid  d. l (mm)  U* (m/s) c (Theor.)  U (H) g  @  (m/s)  A  dev.  (Expt.)  Sand  (516  um)  50  6.0  6.16  6.71  -8.20  Sand  (516  Mm)  41  6.0  6.04  7.12  -15.17  Sand  (516  um)  30  6.0  5.98  7.59  -21.21  Sand  (516  ym)  41  12.7  6.02  5.58  +7.89  Sand  (401  ym)  41  6.0  5.24  5.87  -10.73  Sand  (401  um)  30  6.0  5.21  6.95  -25.03  G l a s s (710 um)  50  6.0  9.68  8.64  +12.03  G l a s s (710  41  6.0  9.61  11.44  -16.00  um)  @ C a l c u l a t e d as: [Q  c  " U (H) ( A a  c  -  A )]/A s  s  where the v a l u e s of U (H) used were determined a  * C a l c u l a t e d from eqns. (4.3) and ( 4 . 4 ) .  as shown i n Chapter  5.  - 68 -  where s p o u t - d i a m t e r , D , was a t most 30 mm. s  As the spout t e r m i n a t i o n o c c u r s due t o c h o k i n g of the spout a t maximum s p o u t a b l e bed depth ( H ^ ) , the v e l o c i t y a t the spout top can be equated  to U , i . e . : c  W  and knowing  U  c  ( 4  *  5 )  the f l o w d i s t r i b u t i o n i n the annulus (Chapter 5 ) , the t o t a l  i n l e t f l o w can be d e t e r m i n e d . the  =  T h i s f l o w , when equated  to A Q U ^ i n  M a t h u r - G i s h i e r e q u a t i o n , can be used to c a l c u l a t e Yty[.  shows t h a t t h i s method p r e d i c t s e x p e r i m e n t a l l y observed v a l u e s .  Table 4.6  w i t h i n about 30% of the However, s i n c e the p r e d i c t e d v a l u e i s  always g r e a t e r than the e x p e r i m e n t a l v a l u e i n the h a l f column, the d i f f e r e n c e can be accounted f o r i n p a r t by the o b s e r v a t i o n of G e l d a r t e t al  (1981)  column.  t h a t H^ i n a h a l f column i s about  15%  l e s s than i n a f u l l  The use f o r f i n e p a r t i c l e s of the M a t h u r - G i s h i e r e q u a t i o n ,  w h i c h i s an e m p i r i c a l c o r r e l a t i o n s f o r coarse p a r t i c l e s , may account f o r the  remaining 1 5 % d e v i a t i o n .  Table  4.6:  Maximum s p o u t a b l e bed depth ( H ^ ) , e x p e r i m e n t a l v s . p r e d i c t i o n  Solid  d  i  M (Expt.)  ( m m )  H  H  through  M * (Theor.)  % dev.*  S i l i c a Sand (401 um)  6.0  46.8  S i l i c a Sand (516 um)  12.7  48.5  62.6  + 29.1  S i l i c a Sand (516 um)  6.0  58.5  71.2  + 21.7  12.7  50.8  66.4  + 30.1  Glass (710 um)  * C a l c u l a t e d as Theor. - E x p t . Expt.  x  # C a l c u l a t e d by s u b s t i t u t i n g (U e q u a t i o n (Eq. 2 . 3 ) .  58.6  theory of c h o k i n g  •A  + U ( H ) • A )/A 0  M  for U  i n the M a t h u r - G i s h l e r  + 25.2  - 70 -  CHAPTER 5  OVERALL BED PRESSURE DROP AND LONGITUDINAL FLUID VELOCITY IN THE ANNULUS  5.1  Measurement Technique  5.1.1  Overall bed pressure drop The  o v e r a l l bed p r e s s u r e drop was measured by u s i n g e i t h e r o f the  two U-tube manometers connected  i n p a r a l l e l ( F i g . 3.4).  The manometers  c o n t a i n e d a l i q u i d of s p e c i f i c g r a v i t y 0.827 and mercury ( s p . g r . respectively. measuring  The manometer c o n t a i n i n g the l i g h t e r f l u i d was used f o r  lower p r e s s u r e drops and could be shut o f f by means of a v a l v e  ( F i g . 3.4) when the p r e s s u r e drop was beyond i t s range, i n which the Hg manometer was used. bed  13.6),  case  The p r e s s u r e tap was l o c a t e d 5 cm below the  inlet. As noted by Mathur and E p s t e i n (1974), the p r e s s u r e drop measured  by such a technique i n c l u d e s the p r e s s u r e drop both a c r o s s the o r i f i c e p l a t e and a c r o s s the bed.  F o r o b t a i n i n g the p r e s s u r e drop due t o the  bed a l o n e , the p r e s s u r e drop r e c o r d e d a t the same f l o w r a t e w i t h t h e column empty (no s o l i d s ) must be s u b t r a c t e d from  the measured v a l u e a t  the upstream p r e s s u r e tap l o c a t i o n as f o l l o w s :  AP = [ ( P  1/2 ) " (P - P )+ P ] E a tra a tm atm 2  2  2  - P a tm  (5.1)  - 71  -  where Pg i s the measured a b s o l u t e upstream the column, at  p r e s s u r e w i t h the bed i n  i s the measured a b s o l u t e upstream  the same f l o w r a t e and P t a  m  i-  empty column p r e s s u r e  atmospheric p r e s s u r e .  st n e  As  an  a p p r o x i m a t i o n , one can a l s o use:  AP - P  5.1.2  B  - P  (5.2)  E  Longitudinal f l u i d v e l o c i t y i n the annulus The a n n u l a r gas v e l o c i t y was determined by use of a s t a t i c  p r e s s u r e probe ( F i g . 3.6), which measured the v e r t i c a l s t a t i c p r e s s u r e g r a d i e n t a l o n g the a n n u l u s . spout and  The probe was  supported mid-way between the  the column w a l l s , w i t h the hypodermic  curved surface.  The probe was  needles f a c i n g the  capable of b e i n g lowered to any  l o n g i t u d i n a l p o s i t i o n i n the bed.  Measurements were taken a t 5  i n t e r v a l s , s t a r t i n g from 2 cm below the bed s u r f a c e .  cm  The p r e s s u r e  g r a d i e n t was measured by use of a micromanoraeter*. The above mentioned  technique i s based upon the assumption  the annulus i s a l o o s e l y packed  bed of s o l i d s .  A c a l i b r a t i o n of  p r e s s u r e drop v s . s u p e r f i c i a l f l u i d v e l o c i t y was l o o s e packed bed of the same m a t e r i a l . the maximum s p o u t a b l e bed depth ( H ) . M  was  that  t h e r e f o r e done i n a  The bed h e i g h t was w e l l above H a l f - c o l u m n no. 1 ( F i g . 3.1)  used, w i t h the a u x i l i a r y f l o w ( f l u i d i z a t i o n ) l i n e a c t i v e , so  the gas was  uniformly distributed.  Uniform f l u i d d i s t r i b u t i o n  *Model MM-3  made by Flow Corp., Cambridge, Mass.  that  was  - 72  f u r t h e r ensured by c h e c k i n g existed.  I t was  that no s i g n i f i c a n t r a d i a l  a l s o found that when the bed was  f l u i d i z a t i o n , f o r each of the s o l i d  ^measured " %  " ^  (  (where 0.02  -  m represents  gradients  c l o s e to minimum  materials  ( 1  " mF> £  ( 0  '  ^  0 2 )  (5  '> 3  the v e r t i c a l d i s t a n c e between hypodermic  n e e d l e s ) , which f u r t h e r confirmed  the r e l i a b i l i t y  of the  technique.  Appendix C summarizes the c a l i b r a t i o n f o r each of the bed  materials  investigated.  5.2  Results and  5.2.1  Discussion  Overall pressure drop For  similar  the case of s p o u t i n g 98 um PVC,  to those of H e s c h e l and K l o s e  maintaining  conditions  (1931) (Table 4.1),  pressure  v s . f l o w r a t e c u r v e s were s i m i l a r to t h a t shown i n F i g . 4.1. pressure  drop peaks as r e p o r t e d  were never o b t a i n e d  by H e s c h e l and K l o s e  even when 186  um PVC  and  the f u l l  The  (1981) ( F i g .  very drop two 2.3)  column were used.  The  peak shown i n F i g . 4.1  i s a t t r i b u t e d to the j e t b r e a k i n g  bed  i n the form of b u b b l e s , w i t h the manometer f l u c t u a t i n g about 1 to  1.5  cm of l i q u i d  of s p e c i f i c g r a v i t y 0.827.  The  through  the  f l u c t u a t i o n s became  g r e a t e r w i t h i n c r e a s i n g f l o w , which e v e n t u a l l y l e d to s l u g g i n g . P r e l i m i n a r y data c o l l e c t e d i n a f u l l column e x h i b i t e d the same t r e n d . Such a trend i s t y p i c a l of a f l u i d i z e d When the r a t i o of i n l e t  bed.  to p a r t i c l e diameter was  l e s s than  25.4  - 73 -  (Eq. 4 . 1 ) ,  steady s p o u t i n g was  a c h i e v e a b l e and  f l o w r a t e c h a r a c t e r i s t i c s shown i n F i g s . 5.1a  the p r e s s u r e drop v s .  and  5.1b  are t y p i c a l .  The  p r e s s u r e drop upon s p o u t i n g i n c r e a s e s s l i g h t l y w i t h i n c r e a s i n g f l o w , and more so w i t h f i n e r s o l i d s .  T h i s can be a t t r i b u t e d  to the i n c r e a s i n g  r e g i o n of c i r c u l a t i o n (more pronounced i n f i n e r s o l i d s — F i g s . 5.2a  and  b) w i t h i n c r e a s i n g f l o w . The 5.1a  p r e s s u r e drop i n c r e a s e s w i t h i n c r e a s i n g bed h e i g h t  and 5.1b)  and d e c r e a s i n g p a r t i c l e s i z e ( F i g . 5.1c).  zone d e c r e a s e s  (Figs.  The  w i t h i n c r e a s i n g s p o u t i n g v e l o c i t y ( F i g . 5.2a)  stagnant and  i n c r e a s i n g p a r t i c l e s i z e ( F i g . 5.2b), which i s a l s o r e f l e c t e d i n the p r e s s u r e drop curve f l a t t e n i n g out as i n F i g . 5.1c. The  measured A P / ^ p m s  m F  [minimum s p o u t i n g p r e s s u r e drop/minimum  f l u i d i z a t i o n p r e s s u r e d r o p , the denominator b e i n g g i v e n by (pp - pf) g ( l - e ^ )  H] , a l s o used as an a p p r o x i m a t i o n  regime c h a r a c t e r i z a t i o n parameter, C ,  by Morgan and L i t t m a n (1984)  0  (Eq. 2.12), i s t a b u l a t e d i n T a b l e 5.1.  The  A P / A P p a r e c a l c u l a t e d from F i g . 2.6 m s  of the  t h e o r e t i c a l v a l u e s of  f o r comparison,  m  seen t h a t agreement w i t h the e x p e r i m e n t a l data i s good.  and  i t is  I t i s also in  most cases seen t h a t the measured r a t i o A P / A P p i s u s u a l l y above ms  0.7  m  when the bed h e i g h t approaches the maximum s p o u t a b l e bed  depth.  T h i s i s not i n complete agreement w i t h the regime c h a r a c t e r i z a t i o n of Morgan and L i t t m a n (1984), who w i t h a gas, C  Q  s t a t e t h a t f o r s p o u t i n g of f i n e  i s above 0.785 (Chapter 2, S e c t i o n 2.3).  however, be noted  t h a t the v a l u e s of C  0  I t should,  obtained are a l l between  and 0.785, a c r i t e r i o n imposed f o r steady s p o u t i n g of c o a r s e (as opposed to f i n e ) by the above  particles  workers.  0.215  particles  - 74 i  2.0  4.0  r  6.0 Q  8.0  (std.l/s)  F i g u r e 5.1a. P r e s s u r e d r o p v s . f l o w r a t e f o r d i f f e r e n t bed h e i g h t s . PVC, d =0.186 mm, d.=4.5 mm. p l  ,H=50 cm H=4'l cm •H=30 cm  _L  0.0  1.0  . 2.0 Q (std.l/s)  F i g u r e 5.1b. P r e s s u r e d r o p  3.0  v s . f l o w r a t e f o r v a r i o u s bed h e i g h t s .  Sand, d =0.516 mm, d.=6.0 mm. P • i  - 75 -  o oo  •d =0.401 mm P o  ID to  3 <3  O  <3"  O  d =1.0 P  CM  _L 3.0  J_  0.0  1.0  2.0 Q  F i g u r e 5.1c.  J  mm_  L  4.0  (std.l/s)  E f f e c t o f p a r t i c l e s i z e on p r e s s u r e drop. Sand, H=41  cm,  d^=6.0 mm.  S o l i d l i n e s represent  f l o w and dashed l i n e s r e p r e s e n t d e c r e a s i n g  increasing flow.  - 76  F l u i d u s e d : /Air a t 80%  -  r e l a t i v e humidity.  - 77 -  d  0.401  A  2  3  4 r  (nm)  5  6  7  (cm)  F i g u r e 5.2b. S t a g n a n t zone and r e g i o n o f c i r c u l a t i o n w i t h i n c r e a s i n g p a r t i c l e s i z e . Sand, d.j=6.0 mm,  H=41  cm.  T a b l e 5.1:  R a t i o AP / AP „ " C o - e x p e r i m e n t a l and t h e o r e t i c a l rns mF  A  Solid  i (mm) d  (Eq. 2.14) S i l i c a Sand 401 um S i l i c a Sand 401 um S i l i c a Sand 401 ym  3.79 x 1 0 3.79 x 1 0 " 3.79 x 1 0 ~  S i l i c a Sand 516 S i l i c a Sand 516 S i l i c a Sand 516 S i l i c a Sand 516 S i l i c a Sand 516 G l a s s 710 ym G l a s s 710 ym G l a s s 710 ym G l a s s 710 ym G l a s s 710 ym G l a s s 710 ym  6.4 x 1 0 " 6.4 x 1 0 6.4 x 1 0 ~ 3.02 x 1 0 ~ 3.02 x 1 0 " 0.021 0.021 0.021 0.01 0.01 0.01  - 3  Wm ym um um Mm  T denotes that H = H  3 3  3  - 3 3  M  3 3  H (cm)  6.0 6.0 6.0  30.0 41.0  6.0 6.0 6.0 12.7 12.7 6.0 6.0 6.0 12.7 12.7 12.7  41.0 50.0 58.5 41.0 55.5 30.0 41.0 55.5 30.0 41.0 50.8  46.8  L  T  T T  T T  AP /AP „ ms mF (Expt.)  AP  /AP „ ms mF (Theor.)  0.574 0.716 0.748  0.467 0.568 0.593  0.396 0.590 0.703 0.516 0.719 0.412 0.558 0.667 0.429 0.516 0.689  0.532 0.621 0.684 0.586 0.724 0.402 0.518 0.657 0.512 0.636 0.691  - 79 -  5.2.2  Annular longitudinal gas v e l o c i t y The f l u i d v e l o c i t y i n the annulus i n c r e a s e s a l o n g the bed h e i g h t  as observed i n F i g s . 5.3, 5.4 and 5.5.  No s i g n i f i c a n t r a d i a l g r a d i e n t s  of the f l u i d v e l o c i t y i n the annulus were observed i n the c y l i n d r i c a l p o r t i o n of the column.  T h i s i s c o n s i s t e n t w i t h the d a t a of S i t ( 1 9 8 1 ) ,  who used a s i m i l a r h a l f - c o l u m n .  H i s system was a submerged spout w i t h  the annulus a e r a t e d through a d i s t r i b u t o r p l a t e .  H i s data showed  that  r a d i a l g r a d i e n t s of a n n u l a r f l u i d v e l o c i t y e x i s t e d o n l y to about 5 cm from the d i s t r i b u t o r p l a t e , a f t e r which they were n e g l i g i b l e . The e f f e c t of bed h e i g h t was found to be n e g l i g i b l e ( F i g . 5.5). t h i s i s c o n s i s t e n t w i t h the c o n d i t i o n of G r b a v c v i c e t a l (1976):  U  * f(H)  a  (5.4)  Z = constant H^ = c o n s t a n t  i . e . the f l u i d v e l o c i t y i n the annulus a t any bed l e v e l i s independent of  the bed h e i g h t above i t f o r any p a r t i c u l a r bed. The e f f e c t of p a r t i c l e diameter and i n l e t s i z e on the a n n u l a r gas  v e l o c i t y i s shown i n F i g . 5.5.  The gas v e l o c i t y i n the annulus  i n c r e a s e s w i t h i n c r e a s e s i n b o t h p a r t i c l e d i a m e t e r and i n l e t d i a m e t e r . It i s interesting  to note that i n a l l the cases examined, the  a n n u l a r gas v e l o c i t y a t Z = % fluidization velocity. times U p m  i s w e l l below U p , m  the minimum  I t i s found that U (H{4) i s about 0.6 to 0.7 a  ( e . g . F i g u r e s 5.3 and 5.4). T h i s v a l u e of U ( H ) i s a  M  i  r  CN CM  _ _ -O u mF O CM  00  ft*,'  CO o  CN  00  10  20  _L 30 Z (cm)  40 '  50  60  F i g u r e 5.3. L o n g i t u d i n a l a n n u l a r gas v e l o c i t y - e x p e r i m e n t a l v s . t h e o r e t i c a l . Sand, d^=0.516 U/U /  mS  =1.18, d.=6.0 mm. L-D: L e f r o y - D a v i d s o n l  (1969), M-M: M a m u r o - H a t t o r i  mm,  (1968/1970).  -  81 -  F i g u r e 5.4. L o n g i t u d i n a l a n n u l a r g a s v e l o c i t y d i s t r i b u t i o n .  Sand,  d =0.40 mm, U / U ^ ^ l . 18, d^=6.0 nm. L-D: L e f r o y - D a v i d s o n (1969), M-H: Mamuro-Hattori  (1968/1970).  - 82 -  I _E 0.516 CN  10  \  l  —  6.0  41.0  A.  516  6.0  50.0  •  .516  12.7  50.0  •  -401  6.0  46.8  Q.401  6.0  35.0  r.401  9.0  43.6  CO  •  A  6 ft-  8 T  T  T  AO  f0  6  •  *n  t  • *3  J 0  10  20 Z  F i g u r e 5.5.  I 30  L 40  50  (cm)  E f f e c t o f p a r t i c l e d i a m e t e r , i n l e t s i z e and bed h e i g h t on l o n g i t u d i n a l a n n u l a r gas v e l o c i t y . Sand, U/U  =1.18.  - 82a -  s i g n i f i c a n t l y less bed  than the U (H{^) i n the case of a s t a n d a r d spouted a  of c o a r s e p a r t i c l e , where i t i s about 0.9  f u r t h e r s u p p o r t s the v i s u a l  to 1.0  times U p.  o b s e r v a t i o n of the spout  mechanism a t the maximum s p o u t a b l e bed depth, H^t e r m i a n t i o n mechanism i n the case of f i n e p a r t i c l e s  This  ra  termination  The  spout  occurs due  to  c h o k i n g of the spout, as compared to f l u i d i z a t i o n of the a n n u l a r i n a c o a r s e p a r t i c l e spouted bed.  solids  A l s o , i n a spouted bed of c o a r s e  particles:  * umF  U  where v"p(H ) i s the r a d i a l l y averaged p a r t i c l e v e l o c i t y M  a n n u l u s a t Z = H^.  The  (5.5)  i n the  term U* (H{4) i n E q u a t i o n (5.5) a  r e p r e s e n t s a s u p e r i m p o s i t i o n of the downward moving s o l i d motion on the gas movement i n the v e r t i c a l d i r e c t i o n . solids  I n the case of f i n e s o l i d s ,  the  i n the annulus move more s l o w l y as the p a r t i c l e s i z e i s reduced  ( C h a p t e r 6 ) , and so s u p e r i m p o s i n g the s o l i d m o t i o n on the gas s t i l l not a c c o u n t f o r the l a r g e d i f f e r e n c e between U (H{^) and U p. a  m  L e f r o y - D a v i d s o n (1969) e q u a t i o n , when used i n i t s o r i g i n a l  U  a  = U  mF  h i g h l y o v e r p r e d i c t s the v e l o c i t y  Sin (  2H, M  The form:  (5.6)  )  i n the annulus ( F i g s .  does  5.3  and 5 . 4 ) .  - 83 -  However, I n Eq. (5.6) when U p i s r e p l a c e d by U ( H ) , which i s ra  determined  a  M  e x p e r i m e n t a l l y , the p r e d i c t i o n i s v e r y good when compared  w i t h the e x p e r i m e n t a l d a t a .  The Mamuro-Hattori (1968/1970) e q u a t i o n ,  which has been q u i t e s u c c e s s f u l f o r coarse p a r t i c l e s , a l s o o v e r p r e d i c t s the gas v e l o c i t y i n the annulus U ]p. m  even when U ( H M ) i s s u b s t i t u t e d f o r 3  The e x p e r i m e n t a l p o i n t s and the p r e d i c t i o n s through v a r i o u s  e q u a t i o n s can be seen i n F i g s . 5.3 and 5.4 f o r the case of 401 and 516 um sand p a r t i c l e s .  The good f i t f o r the e x p e r i m e n t a l d a t a o b t a i n e d by  the m o d i f i e d L e f r o y - D a v i d s o n  e q u a t i o n should n o t be v e r y  surprising,  since t h i s equation, although e m p i r i c a l , f o l l o w s c l o s e l y  the r e s u l t s  o b t a i n e d by a s e m i - t h e o r e t i c a l a n a l y s i s of Morgan and L i t t m a n (1980) f o r a wide v a r i e t y of systems ( r e f e r t o S e c t i o n 2 . 4 ) . I t s h o u l d be noted  t h a t the f l o w regime i n d e x , n, i s s e t to u n i t y  (Darcy's law) i n u s i n g Eqn. (2.20) s i n c e the p a r t i c l e Reynolds number in  the annulus  i s w e l l below 10 f o r the case of f i n e  particles.  Measurements i n the c o n i c a l r e g i o n were n o t made due t o u n c e r t a i n t y of the gas f l o w p a t t e r n near  the i n l e t ( r e c i r c u l a t i o n ) and  of the voidage d i s t r i b u t i o n i n t h i s r e g i o n ( E l j a s ,  1975).  CHAPTER 6  ANNULAR PARTICLE VELOCITY AND CIRCULATION RATE  The  p a r t i c l e v e l o c i t y i n the annulus i n t h e r a d i a l and a x i a l  d i r e c t i o n s f o r coarse p a r t i c l e s has been measured by Lim (1975) u s i n g a h a l f column.  From these d a t a , he a l s o o b t a i n e d  the v o l u m e t r i c f l o w r a t e  of s o l i d s i n the annulus, w h i c h i s a measure o f s o l i d c i r c u l a t i o n r a t e . No i n f o r m a t i o n , however, e x i s t s on the s o l i d c i r c u l a t i o n r a t e f o r f i n e particle  6.1  spouting.  Measurement Technique The  p a r t i c l e v e l o c i t i e s were measured i n t h e l o n g i t u d i n a l as w e l l  as t h e r a d i a l d i r e c t i o n s a t t h e f l a t s u r f a c e o f the h a l f column.  The  f l a t s u r f a c e o f t h e column was d i v i d e d i n t o n o d a l p o i n t s along the r a d i a l and the a x i a l d i r e c t i o n s as shown i n f i g u r e 6.1.  At each a x i a l  p o s i t i o n ( a f i x e d Z) , the r a d i a l d i s t a n c e s o f n o d a l p o i n t s were 1.5, 3.0,  4.5 and 7.5 cm, r e s p e c t i v e l y , from t h e c e n t r e .  Measurements were  made w i t h the a i d o f c o l o r e d t r a c e r p a r t i c l e s (same as the bed m a t e r i a l but c o l o r e d by a water i n s o l u b l e d y e * ) .  At each node the t r a c e r  p a r t i c l e was v i s u a l l y f o l l o w e d and timed over a d i s t a n c e o f 2.4 cm, f o r example a l o n g X1X2 i n f i g u r e 6.1. a l s o served  as a nodal p o i n t .  of the curved  The spout-annulus  i n t e r f a c e ( r = r^)  Measurements were a l s o made a t the c e n t r e  s u r f a c e ( p o i n t C i n F i g u r e 6.1) f a r t h e s t away from t h e  *Waterproof Ink ( J i f f y Marker) by S h a c h i h a t a ,  Japan.  - 85 -  TOP VIEW  r (cm) v  r = 1 . 5 3,0  4.5  7.5 Z=50 cm  2.4 o n 45  SPOUT WALL  40 38 35  F i g u r e 6.1. N o d a l p o i n t s f o r particle velocity  30 27 25 22 (NOT TO SCALE)  20 18 15 11.7 7.9 4.1 0.0  d e t e r m i n a t i o n . S^S^ represent the i n t e r f a c e between t h e s t a g n a n t zone and t h e region o f s o l i d circulation.  j u n c t i o n of the f l a t f r o n t s u r f a c e and column.  the curved  P a r t i c l e v e l o c i t y at f i v e d i f f e r e n t r a d i a l ( r ^ . . . . ^ )  f o r each bed  l e v e l s was  A stagnant  thus  zone e x i s t e d  at the bottom i n most cases  the column w a l l i n F i g u r e 6.1. was  a l s o noted  positions  determined.  i n Chapter 5 ( a l s o r e f e r to F i g . 5.2).  6.1)  p o r t i o n of the  as d i s c u s s e d  T h i s zone i s bounded by S^S2  and  The r e g i o n of c i r c u l a t i o n (d/2 i n F i g .  along v a r i o u s bed  l e v e l s , Z.  The v o l u m e t r i c s o l i d s f l o w i n the annulus at any bed  , k+l G = G (Z) = / a a i r  level Z i s :  = d / 2  v ( r ) ( l - E . ) (2Ttr)dr p A  a  (6.1)  where v ( r ) r e p r e s e n t s the downward p a r t i c l e v e l o c i t y ( which p  varies  i n the r a d i a l d i r e c t i o n ) f o r any f i x e d bed  be f i t t e d r ^ , and r  l e v e l , Z.  as a s t r a i g h t l i n e between p o i n t s r^and r , r 2  4  and r s , r e s p e c t i v e l y , f o r any bed  l e v e l Z.  2  and  v (r) r3, r  - top v i e w ) .  3  and  T h i s w i l l lead  f o u r d i f f e r e n t r e g i o n s to be used f o r i n t e g r a t i o n i n e q u a t i o n (marked as 1, 2, 3, and 4 i n F i g . 6.1  can  p  For each of  (6.1) these  regions,  v (r) =  where c o n s t a n t s A^ and appropriately.  Equation  (6.1)  Ar t  +  B  (6.2)  i  can be e v a l u a t e d thus becomes:  f o r each r e g i o n  to  - 87 -  G  = 2u(l-e.) I J A . , i=l r  (A.r + B.)rdr l l  1  a  L  1  k  (6.2a)  ±  A.  . (6.2b)  1=1  where:  A. =  and  %  )  (6.3)  r.,, - r. l+l I  3. = v ( r . ) - A . r . p  f o r any f i x e d bed l e v e l ,  Z.  F o r bed l e v e l s where no s t a g n a n t zone e x i s t s , k=4 and r5  (d = D ) . c  =  F o r the bottom p o r t i o n , however, where a s t a g n a n t zone  does e x i s t , r^+i = d/2 (d < D ) , so that the c r o s s - s e c t i o n a l a r e a of c  the moving annulus i s a p p r o p r i a t e l y accounted T h i s method variation  f o r by e q u a t i o n ( 6 . 1 ) .  thus a c c o u n t s f o r the dead zone a t the bottom and the  of spout d i a m e t e r a l o n g the Z d i r e c t i o n  ( r j = D /2, g  a t any  Z).  6.2  Results and their Interpretation The p a r t i c l e v e l o c i t y i n the annulus i n c r e a s e s w i t h i n c r e a s i n g  bed l e v e l , Z, f o r the r e g i o n above the s t a g n a n t zone ( H * < Z < H); c  f o r Z < H ', c  however, the v e l o c i t y d e c r e a s e s w i t h i n c r e a s i n g Z f o r the  r e g i o n n e a r e r to the spout w a l l ( s e e F i g . 6.2). c o n t r a c t i n g c r o s s - s e c t i o n a l area f o r Z = H  c  T h i s happens due to  to Z = 0.  - 88 -  - 89 -  CO  en  o  (b) "3* O  O  O  J  O  ChO  I  !  L  0.4  0.6 0.8 Z'=Z/H F i g u r e 6.2b. V e r t i c a l p a r t i c l e v e l o c i t i e s i n t h e annulus. (same system a s a s i n F i g . 6 . 2 a ) . Arrows i n d i c a t e end o f s t a g n a n t zone.  -3* U3  O  1 |>  CN  0.0  0.2  0.4 0T6~ Z'=Z/H  F i g u r e 6.2c. R a d i a l l y  "078"  averaged annular p a r t i c l e v e l o c i t y f o r data  i n F i g s . 6 . 2 a and 6.2b. Arrows i n d i c a t e s t a g n a n t zone.  t h e end o f t h e  - 90 -  The r a d i a l l y averaged p a r t i c l e v e l o c i t y c a l c u l a t e d as:  (6.4)  (1 - eA )Aa  where G  a  as o b t a i n e d  by e q u a t i o n 6.2b i s used to generate F i g 6.2c.  These o b s e r v a t i o n s Lim  (1975) f o r coarse  a r e q u a l i t a t i v e l y c o n s i s t e n t w i t h the data of  particles.  The r a d i a l g r a d i e n t s of p a r t i c l e  v e l o c i t y i n the annulus a r e , however, much s t e e p e r f o r f i n e than those r e p o r t e d f o r c o a r s e  particles  p a r t i c l e s by L i m (1975).  I t was a l s o observed t h a t the p a r t i c l e v e l o c i t y a t the j u n c t i o n of the f l a t f r o n t w a l l and the curved v i e w ) was s i g n i f i c a n t l y lower  s u r f a c e ( p o i n t J i n F i g . 6-1 top  than the v e l o c i t y measured a t p o i n t C  ( F i g . 6.1-top v i e w ) , f a r away from the j u n c t i o n J ( e . g . J ' and C i n F i g . 6.2a).  T h i s shows t h a t there i s a r e t a r d i n g e f f e c t on the movement  of the p a r t i c l e s due to the merger of the two s u r f a c e s a t the j u n c t i o n J. The e f f e c t of v a r i o u s o p e r a t i n g parameters, which i n c l u d e bed h e i g h t , i n l e t a i r v e l o c i t y , p a r t i c l e s i z e and cone angle on the s o l i d c i r c u l a t i o n r a t e was a l s o i n v e s t i g a t e d .  6.2.1  Effect  of bed depth and U/U _ ms  The p a r t i c l e v e l o c i t y a t any p o i n t i n the annulus (and t h e r e f o r e the v o l u m e t r i c s o l i d s f l o w r a t e ) i n c r e a s e s w i t h i n c r e a s i n g bed depth ( F i g . 6.3).  The r e s u l t s of Lim (1975) w i t h coarse  p a r t i c l e s show t h a t  - 91 -  Z'=Z/H F i g u r e 6.3. E f f e c t o f H and U/U. on G . Sand, d.=6.0 mm. (a) d =0.40 mm, ms a i p (b) d =0.516 mm. Arrows i n d i c a t e end o f s t a g n a n t zone.  - 92 -  for H  < Z < H, where H  c  l i n e a r l y w i t h Z. F i g u r e 6.3, G  a  c  i s the h e i g h t of the cone, G  a  increases  For the case of f i n e p a r t i c l e s , however, as shown i n  v s . Z becomes a p p r o x i m a t e l y l i n e a r o n l y above the bed  l e v e l where the s t a g n a n t zone ceases the bottom of the bed corresponds  to e x i s t .  T h i s s t a g n a n t zone a t  to the n a t u r a l cone formed by the  r e g i o n of s o l i d c i r c u l a t i o n . The e f f e c t of U / U U/U  ms  ms  i s also reflected  f o r a g i v e n system i n c r e a s e s G  a  i n F i g . 6.3. I n c r e a s i n g  due to i n c r e a s i n g  entrainment  of p a r t i c l e s i n the spout.  6.2.2  E f f e c t of p a r t i c l e s i z e I n c r e a s i n g the p a r t i c l e s i z e f o r o t h e r w i s e i d e n t i c a l beds g i v e s  rise  to a h i g h e r p a r t i c l e v e l o c i t y a t any f i x e d p o i n t i n the bed.  r e s u l t s i n a h i g h e r s o l i d s f l o w r a t e as shown i n F i g u r e 6.4. F i g u r e 6.3, G  a  This  As i n  v s . Z/H above the s t a g n a n t zone i s a p p r o x i m a t e l y  linear.  6.2.3  E f f e c t of cone angle The e f f e c t of cone a n g l e i s shown i n F i g u r e 6.5.  i n c l u d e d cone angle from 60 degrees  to 36.4 degrees  a n n u l a r s o l i d s f l o w r a t e by about 35 t o 45 p e r c e n t .  Reducing the  i n c r e a s e s the I t was a l s o  observed  t h a t the s t a g n a n t zone i n the 60 degree cone a n g l e column- d i s a p p e a r e d when the 36.4 degree cone a n g l e column was used.  - 93 1 1 d (mm) p (g/cm )  _E  o -  VC  o  1  1  1  • 0.401  2.66  O 0.516  2.66  v 0.710  4.56  A  2-45./  0.845  1  1 A  A-"' ^  „  A- "  ' "  1  —A"  "  ^  V"  —  —  /  /  /  (a)  /  —  o -  CN  /  A  A / /  /,*  /  *•**  //  ja -  '  _ B  o 0 .0  i  0.2  d o  -  _ —-i—i  VD  car-—  /  p  (mm)  I 0.4  1  "  1  0.6  1  i 0  ,  8  i Z'=Z/H  p (g/cm ) p  ° 07401  2.66  O 0.516  2.66  in  o (b)  o  CN  0.0 Figure  Z'=Z/H 4. E f f e c t o f p a r t i c l e s i z e on G  d.=6.0 mm.  (a) U/U  =1.08,  (b) U/U =1.18. V e r t i c a l a r r o w/s s ii nnddiiccaat e e n d o f t h e s t a g n a n t niS  zone.  H=30 cm,  H=41 cm.  - 94 -  H (cm)  0.0  0.2  0.4 Z'=Z/H  0.6  0.8  F i g u r e 6.5. E f f e c t o f cone a n g l e on G^. Sand, d =0.516 inn, d_^=6.0 mm, U/U =1.08. V e r t i c a l arrows i n d i c a t e mS s t a g n a n t zone.  t h e end o f t h e  - 95 -  CHAPTER 7  SPOUT SHAPE, SPOUT DIAMETER AND FOUNTAIN HEIGHT  7.1  Measurement Technique The  spout diameter was measured along the bed l e v e l by t a k i n g  photographs  at the f l a t f r o n t s u r f a c e .  These p i c t u r e s were i n t h e form  of s l i d e s and were e n l a r g e d by p r o j e c t i n g on a s c r e e n . The m a g n i f i c a t i o n was r e c o r d e d and the t r u e spout d i a m e t e r thus d e t e r m i n e d . The  f o u n t a i n h e i g h t was d i r e c t l y measured as the d i s t a n c e from  the bed s u r f a c e t o the f o u n t a i n t o p .  7.2  Results and Discussion  7.2.1  Spout shape and diameter The spout d i s p l a y e d f o u r d i f f e r e n t shapes as shown i n F i g u r e  7.1.  The f i r s t  two types ( a and b) o c c u r r e d i n t h e 60 degree cone a n g l e  column, where t h e r e was a r a p i d e x p a n s i o n i n the cone r e g i o n and t h e l a s t two t y p e s ( c and d) were observed when the cone angle was 36.4 degrees.  The s l i g h t c o n t r a c t i o n o f the spout near the bed s u r f a c e as  shown i n F i g s . 7.1a and c appeared  i n most c a s e s .  However, a somewhat  expanding spout shape near the bed s u r f a c e was observed f o r v e r y h i g h f l o w r a t e s and bed h e i g h t s below X 1 X 5 i n F i g . 4.4b ( a l s o r e f e r to F i g s . 4.6a  and c ) . The spout diameter i n c r e a s e d w i t h i n c r e a s i n g bed h e i g h t as shown  i n F i g u r e s 7.2 and 7.3a.  The spout diameter above the end of the  (a)  (b)  - (c) /  (c) a'=36.4* low f l o w r a t e ,  \l  (d)  0  F i g u r e 7.1. D i f f e r e n t s p o u t shapes o b s e r v e d , (a) a =60,  low f l o w r a t e ,  (d)a'=36.4, h i g h f l o w  ON  rate.  i  °  (b)a=60, high flow rate,  - 97 -  J 10  L  J 20  !_ 40  30 Z (cm)  F i g u r e 7.2. E f f e c t o f b e d h e i g h t o n s p o u t d i a m e t e r . Sand, d =0.516 mm, U / U ^ l . 0 8 , d.=6.0 mm.  P  o  i -»—  r  *  a  i  H (cm) • 30 50  A  "  -  U / U  mS  = 1  -  0 8  ^ = 1 . 1 8  J 10  L 20  J  1 30 Z (cm)  1  L 40  F i g u r e 7.3a. E f f e c t o f U / U ^ on s p o u t d i a m e t e r . Sand, d =0.516 mm, d.=6.0 rrm. i  ^  - 98 -  stagnant  zone was n e a r l y u n i f o r m f o r deep beds.  I n c r e a s i n g the i n l e t as i l l u s t r a t e d  by F i g u r e 7.3.  above the stagnant expansion  f l u i d v e l o c i t y i n c r e a s e d the spout F o r deep enough beds, the spout  f o l l o w e d E q u a t i o n (2.9b) v e r y  a f i x e d v a l u e o f U/U  Decreasing  diameter  zone was n e a r l y u n i f o r m ( F i g . 7.3a) and the spout  I n c r e a s i n g the p a r t i c l e diameter  The  diameter  ms  closely. i n c r e a s e d the spout diameter f o r  as shown i n F i g u r e 7.4.  e f f e c t o f cone angle on D  s  i s d i s p l a y e d by F i g u r e 7.5.  the cone angle a f f e c t s t h e spout s i z e and shape o n l y i n the  c o n i c a l r e g i o n * and has n e g l i g i b l e e f f e c t i n t h e remaining the b e d , where D  s  portion of  i s n e a r l y u n i f o r m along Z ( F i g . 7 . 5 ) .  McNab's c o r r e l a t i o n  ( E q . 2.9) u n d e p r e d i c t e d  the l o n g i t u d i n a l l y  averaged spout diameter by as much as 35% i n some c a s e s , as shown i n T a b l e 7.1.  7.2.2  Fountain height Fountain height increased with increase i n U/U  ms  as shown i n  F i g u r e s 7.6 and 7.7. T h i s o c c u r s because, f o r a g i v e n bed, the h i g h e r the i n l e t gas v e l o c i t y , the h i g h e r i s the p a r t i c l e v e l o c i t y i n the spout ( L i m , 1975), w h i c h i n t u r n l e a d s to a h i g h e r f o u n t a i n ( E q . 2.10). I n c r e a s i n g the bed h e i g h t lowers the f o u n t a i n h e i g h t ( F i g s . 7.6 and 7.7), w h i l e a p a r t i c l e s i z e i n c r e a s e l e a d s t o an i n c r e a s e i n f o u n t a i n h e i g h t as shown by t h e r e s u l t s i n F i g u r e 7.6. *The c o n i c a l r e g i o n i n the case o f the 60° cone angle extends t o the end o f the stagnant zone. When the cone angle i s 36.4°, no stagnant zone was o b s e r v e d .  - 99 -  -  100 -  F i g u r e 7.4. V a r i a t i o n o f spout diameter w i t h p a r t i c l e s i z e . d.=6.0 mm,  u/u^i'oe.  solid V ™ p _ 1  .401 .516 g l a s s .710 g l a s s .845  10  0 p  ( g / c m ]  2.66 O 2.66 u  4.56 • 2.45 A  30  20  Z (an) T  •3- •" 6 -8-8 ' - s f e  -0-D-0-  o o o  10  a  =60  a'=36.4°  -L 20  30 Z (cm)  40  50  F i g u r e 7.5. E f f e c t o f cone a n g l e on spout shape. Sand, d =0.516 mm, U/U =1.08, d.=6.0 mm. mS I  T a b l e 7.1:  Solid  PVC  L o n g i t u d i n a l l y averaged  d P ( ym) 186  d. l (mm)  spout diameter  H  (cm)  (experimental vs. predicted)  U  D  U  g  (mm)  (Expt.)  D  (mm s (Eq. 2."  ms  4.5  19.5  3.98  17.6  13.8  PVC  186  4.5  19.5  4.12  18.2  15.2  Sand  196  4.5  15.0  2.12  11.3  6.4  Sand  196  4.5  15.0  3.77  14.7  8.4  Polypropylene  299  2.8  19.8  1.03  11.8  7.9  Polypropylene  299  2.8  19.8  1.30  14.2  8.9  Propylene  299  2.8  19.8  2.42  16.1  12.0  Sand  401  4.5  30.0  1.08  13.6  11.1  Sand  401  4.5  30.0  1.18  14.6  11.8  Sand  401  4.5  41.0  1.18  15.3  11.5  Sand  401  6.0  30.0  1.08  13 .9  10.5  Sand  401  6.0  30.0  1.18  14.7  12.2  Sand  401  6.0  41.0  1.08  14 .9  10.5  Sand  401  6.0  41.0  1.18  15.5  12.2  Sand  401  9.0  41.0  1.08  15.1  10.9  Sand -  516  6.0  41.0  1.08  16.5  12.6  Sand  516  6.0  41.0  1.18  17.3  13.7  Sand  516  12.7  41.0  1.08  16.9  12.7  Glass  710  6.0  30.0  1.08  19.8  12.5  Glass  845  6.0  30.0  1.08  20.9  17.9  - 103 -  The f o u n t a i n shape was a p p r o x i m a t e l y p a r a b o l i c i n a l l c a s e s . , The f o u n t a i n shown i n F i g . A.6a does not extend over the e n t i r e c r o s s - s e c t i o n a l area of the column and i s t h e r e f o r e c a l l e d an 'underdeveloped'  fountain.  i n v e r t e d ( i . e . opposite increased  The bed s u r f a c e  i n t h i s case appears as an  the c o n i c a l base) cone.  As the f l o w r a t e i s  f u r t h e r ( w i t h H <_ X 1 X 5 as i n F i g . 4.4b),  the bed s u r f a c e  becomes c o n i c a l i n the same sense as the column base and the f o u n t a i n spreads over the e n t i r e a n n u l u s , as seen i n F i g u r e 4.6c. the f o u n t i a n i s termed where d  p  ' f u l l y developed.'  I n t h i s case  I n the case of p a r t i c l e s '  > 400 ym, e i t h e r of the f o u n t a i n types ( F i g . 4.6a or 4.6c)  may p r e v a i l , depending on the f l o w r a t e .  - 104 -  CHAPTER 8  CONCLUSIONS AND RECOMMENDATIONS  8.1  Conclusions 1.  provided  F i n e p a r t i c l e s ( d < 1ram)can be made t o spout p  t h a t the f l u i d  p a r t i c l e diameter.  i n l e t diameter  This supports  steadily  does n o t exceed 25 times the  the o b s e r v a t i o n s of Mathur and G i s h l e r  ( 1 9 5 5 ) , Ghosh (1965), Rooney and H a r r i s o n (1974) but does n o t agree w i t h the o b s e r v a t i o n s of H e s c h e l 2.  and K l o s e  (1981).  P a r t i c l e d e n s i t y has no s i g n i f i c a n t e f f e c t on s p o u t a b i l t y ,  thus c o n t r a d i c t i n g the c r i t e r i a of G e l d a r t (1973) and Molerus  (1982) f o r  spoutability. 3.  The v a r i o u s regimes observed  ym a r e spouted  when p a r t i c l e s w i t h d  ( p r o v i d e d d-^ _< 25.4 d ) are:  < 350  F i x e d bed, b u b b l i n g and  p  steady spouting.  p  When the p a r t i c l e s w i t h d ^> 400 ym a r e employed, p  the a s s o c i a t e d regimes a r e :  F i x e d bed, s t e a d y s p o u t i n g , p r o g r e s s i v e l y  i n c o h e r e n t s p o u t i n g , bubbing and s l u g g i n g .  The r e g i o n of steady  s p o u t i n g i n c r e a s e s w i t h i n c r e a s i n g p a r t i c l e s i z e and d e c r e a s i n g size.  The M a t h u r - G i s h l e r e q u a t i o n (Eq. 2.3) was found  reasonably w e l l . failed  inlet  to p r e d i c t U  m s  However, a l l the c o n v e n t i o n a l e q u a t i o n s f o r H^  t o r e p r e s e n t the e x p e r i m e n t a l v a l u e s a d e q u a t e l y .  I t was a l s o  e x p e r i m e n t a l l y found i n the b u b b l i n g regime t h a t the s t a b l e j e t l e n g t h was  independent of the bed h e i g h t f o r H >_ H . M  F a k h i m i e t a l (1983) was found well at U = U raF  The theory developed by  to p r e d i c t t h i s s t a b l e j e t l e n g t h q u i t e  - 105  4.  A change i n the spout  -  t e r m i n a t i o n mechanism i n the case  of  f i n e p a r t i c l e s p o u t i n g ( c h o k i n g v s . annular f l u i d i z a t i o n as i n c o a r s e p a r t i c l e s ) was  confirmed.  Furthermore,  s t a n d p i p e s was  s u c c e s s f u l l y a p p l i e d to p r e d i c t the regime t r a n s f o r m a t i o n  from steady s p o u t i n g w i t h i n ± 14%.  the theory of c h o k i n g i n  T h i s approach a l s o p r e d i c t e d  w i t h i n ± 30%, which i s f a r b e t t e r than the p r e d i c t i o n s of conventional 5.  The  ratio C  « AP /AP  Q  m s  m F  used as a regime  These workers s t a t e t h a t C  0  f o r the case of f i n e p a r t i c l e s p o u t i n g . e x p e r i m e n t a l v a l u e s of C 6.  the  equations.  c h a r a c t e r i z a t i o n f a c t o r by Morgan and L i t t m a n (1984) was most c a s e s .  by  The  below 0.7  in  s h o u l d be g r e a t e r than 0.785 However, the t h e o r e t i c a l  and  were i n good agreement.  Q  l o n g i t u d i n a l gas v e l o c i t y i n the annulus  r e p r e s e n t e d by the L e f r o y - D a v i d s o n e x p e r i m e n t a l v a l u e of U ( H ) was a  M  was  well  (1969) e q u a t i o n , p r o v i d e d  used i n s t e a d of U .  the  The  mF  M a m u r o - H a t t o r i (1968/1970) e q u a t i o n , which has been v e r y s u c c e s s f u l w i t h c o a r s e p a r t i c l e s (dp >^ 1mm), particles.  I t was  found  always o v e r p r e d i c t e d U ( Z ) a  t h a t U (H{4) « (0.66 a  p a r t i c l e s as opposed to U (H^) « (0.9 - 1.0) a  c o a r s e p a r t i c l e s , which f u r t h e r supports  to 0.7) U  m F  U  m F  for fine for fine  i n the case of  the p o s t u l a t e d change i n spout  t e r m i n a t i o n mechanism i n the case of f i n e p a r t i c l e s (where no  annular  f l u i d i z a t i o n , as f o r c o a r s e p a r t i c l e s , o c c u r s ) . 7.  The  r a d i a l g r a d i e n t s of p a r t i c l e v e l o c i t y were found  much s t e e p e r than f o r c o a r s e p a r t i c l e s .  The  to be  solid circulation rate  - 106 -  i n c r e a s e d w i t h i n c r e a s i n g p a r t i c l e s i z e , U/U , bed h e i g h t and ras  d e c r e a s i n g cone a n g l e . eliminated 8.  Decreasing  the s t a g n a n t zone near the i n l e t . The spout diameter  h e i g h t and p a r t i c l e s i z e .  i n c r e a s e d w i t h i n c r e a s i n g f l o w r a t e , bed  A l t e r i n g the cone angle a f f e c t e d the spout  shape o n l y i n the c o n i c a l r e g i o n . w i t h i n c r e a s i n g U/U s m  8.2  the cone angle from 60° to 36.4°  a n  The f o u n t a i n h e i g h t a l s o i n c r e a s e d  d p a r t i c l e s i z e and d e c r e a s i n g bed h e i g h t .  Recommendations f o r Further Work 1.  Q u a n t i t a t i v e d a t a on the v a r i o u s regime t r a n s f o r m a t i o n s i n an  e x a c t l y s i m i l a r f u l l y c y l i n d r i c a l column should be c o l l e c t e d f o r comparison. 2. occurrence  The theory of s t a b i l i t y may be a p p l i e d to study the of waves ( o r d i s t u r b a n c e s ) a t the s p o u t - w a l l as the bed goes  from the s t e a d i l y s p o u t i n g regime to p r o g r e s s i v e l y i n c o h e r e n t s p o u t i n g to  the f o r m a t i o n of a bubble a t the spout  be used to p r e d i c t regime t r a n s f o r m a t i o n .  top.  T h i s approach may a l s o  - 107 NOTATION Aa/ A a  d /d n  c  2  2  1  c  A  D e f i n e d by Eq. (2.14)  Ar  d  ( p P  p " f> P  P  f  g  /  y  2  ^a  Annulus c r o s s - s e c t i o n a l  area  A  c  Column c r o s s - s e c t i o n a l area  (m )  A  s  Spout c r o s s - s e c t i o n a l  (m )  area  (m ) 2  2  2  Co  D e f i n e d by eq. (2.11)  d  Diameter of s o l i d c i r c u l a t i o n r e g i o n  (cm)  di  Inlet  (mm)  d  P  d  Pi  diameter  Particle  diameter  ( ym)  A p e r t u r e mean d i a m e t e r  (ym)  D  Standpipe  (mm)  Dc  Column diameter  (cm)  Ds  Spout d i a m e t e r  (mm)  g  Acceleration  (m/s )  G  P u ms V o l u m e t r i c f l o w r a t e of s o l i d s  (g/cm s)  h  J e t p e n e t r a t i o n depth  (cm)  H  Loose-packed bed h e i g h t  (cm)  »c  H e i g h t of the cone  (cm)  H e i g h t of the s t a g n a n t zone  (cm)  ms  H  c  diameter  due to g r a v i t y  2  2  (cm /s) 3  H  F  Fountain height  (cm)  H  M  Maximum s p o u t a b l e bed depth  (cm)  k  Constant  - 108 K'  Constant  m  H d./D M 1 c  n  Flow regime i n d e x  P  Pressure  2  w  (kN/m ) 2  P (Z)  F l u i d p r e s s u r e a t spout-annulus  P  Atmospheric  a  a t m  P3  interface  pressure  A b s o l u t e p r e s s u r e measured upstream w i t h the s o l i d s  Pg  (kN/m ) 2  (kN/ra ) 2  (kN/m ) 2  A b s o l u t e p r e s s u r e measured upstream w i t h o u t the s o l i d s  (kN/m )  AP  P r e s s u r e drop a c c r o s s the bed  (kN/m )  A?nis  Minimum s p o u t i n g p r e s s u r e drop  (kN/m )  AP p  Minimum f l u i d i z a t i o n p r e s s u r e drop  (kN/m )  Q  I n l e t f l u i d flow rate  (std.l/s)  Inlet fluid  (std.l/s)  m  Q  mr  U U (Z) a  2  flow rate a t choking  Minimum f l u i d i z a t i o n f l o w r a t e  (std.l/s)  Superficial inlet fluid velocity  (cm/s)  S u p e r f i c a l annulus any bed l e v e l , Z  (cm/s)  fluid velocity at  U (H)  U  a  at Z = H  U (H )  U  a  at Z = H  U  c  S u p e r f i c i a l choking v e l o c i t y i n standpipe  (cm/s)  U p  S u p e r f i c i a l minimum f l u i d i z a t i o n v e l o c i t y  (cm/s)  U  S u p e r f i c i a l minimm s p o u t i n g v e l o c i t y  (cra/s)  U (0)  Fluid inlet velocity  (cm/s)  U (Z)  S u p e r f i c i a l f l u i d v e l o c i t y i n spout  (cm/s)  U (H)  U  (cm/s)  a  a  M  m  m s  s  S  S  s  at Z = H  (cm/s) M  (cm/s)  - 109 -  Ux V  P  V  P  Vgfl  Terminal v e l o c i t y  of a s i n g l e p a r t i c l e  Annular p a r t i c l e v e l o c i t y  (cm/s)  R a d i a l l y averaged a n n u l a r p a r t i c l e v e l o c i t y  (cm/s)  Particle velocity  (cm/s)  i n the spout a t Z = H  Weight f r a c t i o n of p a r t i c l e s a p e r t u r e mean d i a m e t e r of d P  Z p  (cm/s)  h a v i n g an i  V e r t i c a l d i s t a n c e from the f l u i d i n l e t  (cm/s)  Bulk, d e n s i t y  (g/cm )  Fluid density  (g/cm )  P a r t i c l e density  (g/cm )  b p f p P Annulus e  c  voidage  Voidage a t c h o k i n g Voidage a t minimum f l u i d i z a t i o n  e (Z')  Spout v o i d a g e a t Z' = Z/H  e (0) s  e a t Z' = 0 s  e (1) s  e a t Z' = 1 s  9  D e f i n e d by eq. (2.22)  a  Angle of i n t e r n a l  g  a  1  3  friction  (deg)  Cone i n c l u d e d a n g l e  (deg)  Angle of repose  (deg)  -  110 -  REFERENCES  1.  Basov, V.A., Markhevek, V . I . , M e l i k - Akhnazarov and Orochko, R . I . , " I n v e s t i g a t i o n of the S t r u c t u r e of A Non-Uniform F l u i d i z e d Bed", I n t . Chem. eng., 9_, 263 (1969).  2.  B l a k e , T.R., Wen, C.Y. and Ku, C.A., "The C o r r e l a t i o n of J e t P e n e t r a t i o n Measurements I n f l u i d i z e d Beds U s i n g Nondimensional hydrodynamic P a r a m e t e r s " , to be p u b l i s h e d i n AIChE Symp. s e r i e s (1984).  3.  Eastwood, J . , Matzen, E.J.P., Young, M.J. and E p s t e i n , N., "Random Loose P o r o s i t y of Packed Beds", B r i t . Chem. Eng., 14_, 1542(582), (1969).  4.  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F i l l a , M. , M a s s i m i l l a , L. and V a c c a r o , S., "Gas J e t s i n F l u i d i z e d Beds And Spouts: A Comparison of E x p e r i m e n t a l Behaviour and M o d e l s " , Can. J . Chem. Eng., j>l_, 370 ( 1 9 8 3 ) .  9.  G e l d a r t , D. , "Types of Gas F l u i d i z a t i o n " , Powder T e c h n o l . , (1973).  285  10.  G e l d a r t , D., Hemsworth, A., Sundavara, R. and W h i t i n g , K . J . , "A Comparison of S p o u t i n g and J e t t i n g i n Round And Half-Round F l u i d i z e d Beds", Can. J . Chem. Eng., 59_, 638 (1981).  11.  Ghosh, B., "A Study on the Spouted Bed, P a r t I - A T h e o r e c t i c a l A n a l y s i s " , I n d i a n Chem. Eng., _7 ( 1 ) , 16 (1965).  12.  G r a b a v c i c , Z.B., V u k o v i c , D.V., Z d a n s k i , F.K. and L i t m a n , H., " F l u i d Flow P a t t e r n , Mimimum Spouting V e l o c i t y and P r e s s u r e Drop i n Spouted Beds", Can. J . Chem. Eng., _54_, 33 (1976).  13.  G r a c e , J.R. and Mathur, K.B., "Height And S t r u c t u r e of the F o u n t a i n R e g i o n Above of the Spouted Beds", Can. J . Chem. Eng., 5_6_, 533 (1978).  -  I l l  -  14.  H a t t o r i , H. and Takeda, K., " S i d e - O u t l e t Spouted Bed With Inner D r a f t Tube F o r S m a l l - s i z e d S o l i d P a r t i c l e s " , J . Chem. Eng. J a p a n , J J _ ( 2 ) , 125 (1978).  15.  H e s c h e l W. and K l o s e , E., "The Flow Behaviour Of Very F i n e P a r t i c l e s I n The Spouted Bed", Chem. Techn., 33_, 122 ( 1 9 8 1 ) .  16.  Kim, S.J., Ph.d. T h e s i s , R e n s s e l a e r P o l y t e c h n i c I n s t i t u t e , N.Y. ( 1 9 8 2 ) .  17.  Leung, L.S., "The Ups And Downs of G a s - S o l i d s Flow: A Review", i n ' F l u i d i z a t i o n ' , Ed. by Grace, J.R. and Mastsen, J.M., Plenum P r e s s , N.Y., 25 (1980).  18.  L e f r o y , G.A. and D a v i d s o n , J.F., "The Mechanics T r a n s . I n s t n . Chem. E n g r s . , 47_, T120 ( 1 9 6 9 ) .  19.  Lira, C . J . , "Gas Residence time D i s t r i b u t i o n and R e l a t e d Flow P a t t e r n s i n Spouted Beds", Ph.D. T h e s i s , U n i v . B r i t i s h Columbia, Vancouver (1975).  20.  L i m , C . J . and Mathur, K.B., 'Residence Time d i s t r i b u t i o n Spouted Beds", Can. J . Chem. Eng., 52, 150 (1974).  21.  L i t t m a n , H., Morgan, M.H., I I I , V u k o v i c , D.V., Z d a n s k i , F.K. and G r b a v c i c , Z.B., "A Theory f o r P r e d i c t i n g The Maximum'Spoutable H e i g h t I n A Spouted Bed", Can. J . Chem. eng., _55_, 427 (1977).  22.  Mamuro, T. and H a t t o r i , H., "Flow P a t t e r n Of F l u i d I n spouted Beds", J . Chem. Eng. J a p . , j _ , 1 ( 1 9 6 8 ) / C o r r e c t i o n , J . Chem. Eng. J a p . , 3, 119 (1970).  23.  Mathur, K.B. and G i s h l e r , P.E., "A Technique F o r C o n t a c t i n g Gases W i t h S o l i d P a r t i c l e s " , AIChE J . , 1_, 157 ( 1 9 5 5 ) .  24.  Mathur, K.B. and E p s t e i n , N., 'Spouted (1974).  25.  McNab, G . S . , " P r e d i c t i o n of Spout Diameter', Tech., 17_, 532 ( 1 9 7 2 ) .  26.  M o l e r u s , 0., ' I n t e r p r e t a t i o n Of G e l d a r t ' s Type A, B, C and D Powders By T a k i n g I n t o Account I n t e r p a r t i c l e Cohesion F o r c e s " , Powder T e c h n o l . , 33_, 81 ( 1 9 8 2 ) .  27.  Morgan, M.H. I l l and L i t t m a n , H., "General R e l a t i o n s h i p s F o r The Minimum S p o u t i n g P r e s s u r e Drop R a t i o , A P / A P p , and The S p o u t - A n n u l a r I n t e r f a c i a l C o n d i t i o n I n A Spouted Bed", i n ' F l u i d i z a t i o n ' , Ed. by Grace, J.R. and Masten, J.M., Plenum P r e s s , N.Y., 287 (1980).  Of Spouted  Troy,  Beds,  of Gas i n  Beds', academic Prese N.Y.  ms  B r i t . Chem Eng. P r o c .  m  - 112 -  28.  Morgan, M.H. , I I I and L i t t m a n , H. , I & EC Fundamentals, _21_, 23 (1982).  29.  Morgan, M.H., I I I and L i t t m a n , H., "Spout Voidage D i s t r i b u t i o n , S t a b i l i t y and P a r t i c l e C i r c u l a t i o n Rates I n Spouted Bed Of Coarse P a r t i c l e s " , t o be p u b l i s h e d i n Chem. Eng. S c i .  30.  Rooney, N.M. and H a r r i s o n , D., "Spouted Beds Of F i n e P a r t i c l e s " , Powder T e c h n o l . , 9_, 227 ( 1 9 7 4 ) .  31.  S i t , Song - P., " G r i d Region And C o a l e s c e n c e Zone Gas Exchange I n F l u i d i z e d Beds", Ph.D. T h e s i s , M c G i l l U n i v e r s i t y (1981).  32.  Smith, T.N., " L i m i t i n g Volume F r a c t i o n s i n V e r t i c a l Penumatic T r a n s p o r t ' , Chem. Eng. S c i . , 33_, 745 ( 1 9 7 8 ) .  33.  Zenz, F.A. and Othmer, D.F. , " F l u i d i z a t i o n and F l u i d - P a r t i c l e Systems", R e i n h o l d P u b l i s h i n g Corp., N.Y. ( 1 9 6 0 ) .  - 113 -  APPENDIX A ROTAMETER CALIBRATION CURVES  - 115 -  - 116 -  Air  f l o w r a t e c o n v e r t e d to standard  upstream p r e s s u r e ) from a c t u a l o p e r a t i n g  c o n d i t i o n s (20°C and 1 atm conditions:  Q (20°C, 1 atm) = Q* (1.7)  where  Q  ?  * +°  = a i r f l o w r a t e a t 20°C and 1 atm  Q* = a i r f l o w r a t e under o p e r a t i n g  T and P  T  = i n l e t upstream temperature (°C)  P  = i n l e t upstream guage pressure  (kPa).  - 117 -  APPENDIX B  SOLIDS FREE PRESSURE DROP CURVES  - 121 -  APPENDIX C  STATIC PRESSURE PROBE CALIBRATION IN A LOOSE PACKED BED  Table C . l :  Pressure drop-velocity  A  Material  r e l a t i o n s h i p s f o r l o o s e l y packed bed  A  2  3  Ai+  A  5  Variance  S i l i c a Sand (dp = 401 um)  -0.002213  0.429850  -0.000968  0.000000  0.000000  0.028674  S i l i c a Sand (dp = 516 um)  10.609846  -1.269200  +0.118332  -0.003496  0.000038  0.015006  Glass (dp = 710 ym)  0.071533  1.611811  -0.018936  0.000228  -0.000001  0.000267  U = Ai + A where U and  2  (Ah) + A  ( Ah) + A 2  3  = f l u i d v e l o c i t y i n cms/s  Ah = d i s p l a c e m e n t of the microraanometeric f l u i d i n mms.  ( Ah) + A ( A h ) 3  4  5  5  - 123 -  APPENDIX D  EXPERIMENTAL DATA  Table D . l :  No. 1 2 3 4 5 5a 6 7 7a 8 9 10 11 12 13 14 15 16 17 18 18a 19 20  Particle sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand glass glass glass PVC  Run Nos. used f o r subsequent d a t a  d  p  (um) 401 401 401 401 401 401 401 401 401 401 401 516 516 516 516 516 516 516 516 710 710 845 185.6  H  (cm) 30.0 30.0 41.0 30.0 30.0 35.0 41.0 41.0 46.8 30.0 43.6 30.0 30.0 41.0 41.0 50.0 48.5 41.0 50.0 30.0 55.5 30.0 15.0  presentation  d. l  (mm)  4.5 4.5 4.5 6.0 6.0 6.0 6.0 6.0 6.0 9.0 9.0 6.0 6.0 6.0 6.0 6.0 12.7 6.0 6.0 6.0 6.0 6.0 2.8  U/U  a  1  (deg.  ms 1.08 1.18 1.18 1.08 1.18 1. 18 1.08 1.18 1.18 1.08 1.08 1.08 1.18 1.08 1.18 1.08 1.08 1.08 1.18 1.08 1.08 1.08 1.95  60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 36.4 36.4 60 60 60 60  Table D.1:  Continued...  jn No.  Particle  d  p  (um)  H (cm)  d^  (mm)  a* (de^  U/U ms  21 22 23 24 24a 24b 24c 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40  PVC PVC PVC PVC PVC PVC PVC Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Polypropylene Sand Sand Sand Sand Sand Sand Bronze Bronze  185.6 185.6 185.6 185.6 185.6 185.6 185.6 299 299 299 299 299 299 299 299 196 196 196 196 196 196 176.4 176.4  15.0 15.0 14.5 14.5 19.8 19.8 19.8 19.8 19.8 19.8 20.0 20.0 20.0 23.0 23.0 15.0 15.0 15.0 15.0 19.5 19.5 15.0 15.0  2.8 2.8 4.5 4.5 4.5 4.5 4.5 2.8 2.8 2.8 4.5 4.5 4.5 6.0 6.0 2.8 2.8 4.5 4.5 4.5 4.5 2.8 2.8  2.48 3.69 3.70 5.50 2.00 3.00 3.59 1.03 1.30 2.42 3.63 5.00 6.37 3.42 5.01 1.68 3.18 2.12 3.77 1.61 3.66 1.24 2.03  60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60  - 126 -  D.1 S i l i c a sand:  Pressure  drop v s . f l o w r a t e  dp = 401 urn, d-£ = 6 mm, H = 30 cm  • Q  Note:  AP( t )  AP( +)  0.107  1.14  0.86  0.156  1.63  0.98  0.214  2.25  1.09  0.292  2.64  1.26  0.381  2.81  1.31  0.467  3.01  1.52  0.553  3.46  1.94  0.740  3.96  2.23  0.860  4.11  2.49  0.955  4.61  2.90  0.971  5.26  2.60  1.198  5.60  3.61  1.327  3.70  3.70  1.457  4.67  4.54  1.627  5.70  5.70  AP(+) - P r e s s u r e drop w i t h i n c r e a s i n g f l o w AP(+) - P r e s s u r e drop w i t h d e c r e a s i n g f l o w  - 127 -  S i l i c a sand:  d  p  = 401 ym, d^ = 6 mm, H = 41 cm  •  Q  AP( +)  AP( +)  0.083  1.35  -  0.136  1.75  -  0.215  2.42  0.89  0.295  3.13  1.11  0.386  3.75  1.92  0.564  4.96  2.49  0.663  5.51  3.22  0.881  7.09  3.88  1.110  7.86  5.51  1.128  8.60  4.48  1.257  9.07  4.94  1.405  8.95  5.31  1.544  5.90  5.90  1.734  6.22  6.22  1.820  6.84  6.84  1.951  6.96  6.95  2.144  6.98  6.98  - 128 -  S i l i c a sand: •  Q  d  p  = 516 um, d^ = 6 mm, H =• 30 cm  AP(+)  AP( +)  0.083  0.67  0.46  0.136  1.28  0.68  0.215  1.63  0.82  0.385  2.00  0.98  0.561  2.31  1.04  0.757  2.78  1.13  1.000  3.60  1.18  1.242  4.01  1.26  1.384  4.22  1.45  1.430  4.29  2.61  1.442  3.67  2.22  1.529  3.61  2.84  1.550  3.02  3.00  1.729  3.11  3.10  1.915  3.18  3.18  2.248  3.20  3.20  2.464  3.32  3.32  2.750  3.41  3.41  - 129 -  S i l i c a sand: •  Q  d  D  = 516 ym, d^ = 6 mm, H = 41 cm  AP(+)  AP( 4-)  0.083  0.67  -  0.135  1.24  -  0.214  1.45  -  0.382  2.01  1.42  0.559  2.40  1.61  0.757  3.01  2.15  0.998  3.65  2.58  1.238  4.55  2.89  1.486  4.88  3.98  1.553  -  3.17  1.724  5.36  3.22  1.965  4.67  2.046  3.76  3.74  2.500  3.88  3.85  3.010  4.06  4.06  3.388  4.09  4.09  -  - 130 -  S i l i c a sand: • Q  d = p  516 ym, d^ = 6 mm, H = 5 0 cm  AP(t)  AP(+)  0.093  0.68  0.136  1.15  0.89  0.215  1.65  1.28  0.385  2.31  1.71  0.561  3.02  2.20  0.760  4.12  2.98  1.000  5.63  3.39  1.242  6.48  4.08  1.539  8.08  4.31  1.647  8.36  4.52  1.683  8.41  3.71  1.760  -  3.74  1.873  -  1.927  8.96  4.39  2.061  4.42  4.40  2.125  4.48  4.45  2.286  4.58  4.55  2.400  4.60  4.60  2.561  4.62  4.62  2.980  4.65  4.65  •  -  4.08  - 131 -  S i l i c a sand: •  Q  d  p  = 1000 ym, d^ = 6 mm, H = 41 cm  AP( +)  AP( +)  -  1.57  1.16  1.75  1.35  1.29  1.88  1.68  1.71  2.15  1.82 '  1.81  2.36  2.16  2.16  2.55  2.62  2.48  2.86  2.88  1.51  3.05  3.15  1.51  3.31  3.58  1.51  3.52  4.00  1.51  3.72  4.67  1.52  4.00  1.52  1.52  4.25  1.54  1.54  4.50  1.59  1.59  - 132 -  Glass:  d  p  = 710 ym, dji = 6 mm, H = 41 cm  Q  AP(t)  AP(+)  -  1.62  2.95  1.85  3.86  3.76  2.12  4.42  4.25  2.40  5.28  4.80  2.87  6.62  5.72  3.08  7.50  6.39  3.31  8.36  4.92  3.52  8.45  4.98  3.78  5.05  5.01  4.00  5.11  5.10  4.26  5.15  5.15  4.96  5.36  5.36  5.66  5.37  5.37  - 133 -  PVC:  d  = 196 um,  p  d  ±  = 6 mm AP  Q  H = 14.5 cms  0.025  0.35  0.042  0.61  0.072  _  H = 19.5 cms  H = 26.0 cms  0.80  1.05  1.15  1.51  0.091  0.94  0.110  0.50  1.32  1.88  0.126  0.51  0.72  1.01  0.161  0.52 0.82  1.28  0.200  -  0.225  0.55  0.300  0.64  1.00  1.73  0.408  0.71  1.31  2.25  0.495  0.78  1.71  2.76  0.568  0.88 1.95  3.03  2.22  3.36  0.600  -  0.625  1.00  0.680  1.16  0.700  -  - 134 -  S i l i c a Sand: •  Q  d  p  = 196 ym, d^ = 4.5 ram, H = 19.5 cm  AP(+)  AP( +)  0.097  2.55  1.56  0.132  3.62  1.83  0.158  3.87  2.18  0.215  -  2.18  0.230  3.85  1.50  0.295  1.53  1.52  0.383  1.61  1.60  0.472  1.69  1.67  0.658  2.05  2.05  0.895  2.83  2.83  1.000  3.30  3.30  - 135 D.2:  Z  U  17.5 21.5 26.5 31.0 33.5  a  4.85 5.90 6.81 7.61 7.96  Run No. 12 Z  6.85 8.14 9.21 10.14 11.62 12.12  Run No. 18a  16.5 21.0 26.5 31.0 36.0 41.0 46.0 55.0  Z  U  17.5 21.5 26.5 31.0 33.5 36.0 41.0 46.3  a  5.04 6.02 6.85 7.48 8.00 8.32 8.98 9.20  Run No. 14 U a  16.5 21.0 26.5 31.0 36.0 41.0  Annulus Gas V e l o c i t y  11.45 15.60 19.12 21.47 23.86 25.12 26.88 28.21  Z 15.5 21.0 26.5 31.0 36.0 41.0 46.0 49.0  Z 17.5 21.5 26.5 31.0 33.5 36.0 41.0 43.0  U  a  5.42 6.48 7.33 8.16 8.56 8.79 9.18 9.19  Run No. 15 IT a  6.42 7.78 9.27 10.09 11.63 12.17 13.10 13.93  Z 15.7 21.0 26.5 31.0 36.0 41.0 46.0 48.0  LI a 7.56 8.83 9.71 10.64 11.84 12.93 13.41 13.56  - 136 -  D.3:  Solids Circulation  Rate  Run No. 4 Z/H  Run No. 5 G  ZH  G  a 0.986 0.900 0.833 0.733 0.600 0.500 0.390 0.263 0.137  21.2 20.1 18.2 14.6 10.8 6.7 5.8 5.2 2.2  a 0.986 0.900 0.833 0.733 0.600 0.500 0.390 0.263 0.137  Run No. 6 Z/H 0.976 0.854 0.732 0.659 0.610 0.537 0.439 0.366 0.285 0.193 0.100  24.4 21.9 20.2 15.5 13.0 7.5 7.2 5.6 2.7  Run No. 7 G a  ZH  27.4 22.6 21.5 20.5 19.9 17.9 9.2 6.3 5.6 5.5 3.6  0.976 0.854 0.732 0.659 0.610 0.537 0.439 0.366 0.285 0.193 0.100  o  G a 34.2 28.7 25.8 25.2 24.0 21.2 10.1 7.6 6.5 6.4 4.2  - 137 -  Run No. 10 Z/H  Run No. 11 a  ZH  28.3 27.8 25.2 21.5 18.0 13.8 11.2 7.6 5.9 4.0  0.976 0.900 0.833 0.733 0.667 0.600 0.500 0.390 0.263 0.137  G  0.976 0.900 0.833 0.733 0.667 0.600 0.500 0.390 0.263 0.137  G  a  34.8 32.6 28.5 25.7 21.6 16.7 13.1 8.1 6.7 4.2  •  Run No. 12 Z/H  Run No. 13 G a  0.976 0.927 0.854 0.732 0.659 0.610 0.537 0.488 0.439 0.366 0.285 0.192 0.100  36.4 32.9 31.1 28.8 28.2 27.4 25.9 20.9 15.8 11.3 8.1 7.0 3.6  ZH 0.976 0.927 0.854 0.732 0.659' 0.610 0.537 0.488 0.439 0.366 0.285 0.192 0.100  G  a  41.7 39.0 35.2 34.3 32.5 31.7 30.1 22.2 17.4 11.8 8.9 7.4 5.3  - 138 -  Run No. 14 Z/H  Run No. 16 G  ZH  G  a 0.980 0.900 0.800 0.760 0.700 0.600 0.540 0.500 0.440 0.400 0.360 0.300 0.234 0.158 0.082  51.3 42.6 41.3 39.8 36.3 35.3 34.2 32.4 31.1 24.3 16.8 12.2 9.0 7.3 4.8  a 0.976 0.854 0.732 0.610 0.546 0.442 0.378 0.249 0.115  Run No. 17  44.5 41.2 39.5 37.0 35.6 32.7 30.0 16.0 9.7  Run No. 18  Z/H  G  ZH  G a  0.986 0.900 0.800 0.700 0.600 0.500 0.448 0.362 0.310 0.204 0.094  64.0 59.9 52.6 46.8 43.3 39.9 40.2 38.2 32.4 21.8 10.4  0.986 0.900 0.833 0.733 0.667 0.600 0.500 0.370 0.243 0.191 0.098  64.4 63.1 61.4 58.4 57.5 53.9 50.9 46.8 33.5 24.8 14.1  - 139 -  Run No. 19 Z/H  G a  0.980 0.880 0.813 0.713 0.647 0.580 0.480 0.390 0.263 0.191 0.098  66.6 66.0 62.7 61.0 60.1 56.4 60.4 47.5 42.4 31.4 18.6  - 140 -  D.4:  Spout Diameter and Region of C i r c u l a t i o n  Run No. 1 z  D  30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  13.0 13.0 13.0 13.0 13.0 13.5 13.5 14.0 15.1 17.1 9.4  s  Run No. 2 d 15.2 15.2 15.2 15.2 15.2 13.3 10.2 7.6 6.1 4.0 2.9  Z 30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  Run No. 3 Z  D  d  14.6 14.8 14.8 15.1 15.1 15.1 15.1 15.1 15.1 16.9 18.5 9.1  s  13.5 13.5 13.5 13.5 14.1 14.1 14.5 15.6 17.0 17.0 9.5  d 15.2 15.2 15.2 15.2 15.2 13.3 10.3 7.8 6.3 4.1 3.0  Run No. 4 Z  s 40.0 37.0 35.0 30.0 25.0 22.0 20.0 15.0 11.7 7.9 4.1 1.6  D  D  d s  15.2 15.2 15.2 15.2 15.2 15.2 14.8 9.1 7.3 5.8 4.1 3.0  30.0 27.0 25.0 22.0 18.0 15.0 11.7 7.9 4.1 1.6  "12.5 12.5 13.0 13.0 14.0 14.0 14.5 16.1 14.5 10.5  15.2 15.2 15.2 15.2 13.3 10.4 7.8 6.3 4.1 3.0  -  141 -  Run No. 5 z  30.0 27.0 25.0 22.0 18.0 15.0 11.7 7.9 4.1 1.6  Run No. 6  D  d  14.0 14.0 14.0 14.0 14.5 14.5 16.1 16.5 14.5 10.6  15.2 15.2 15.2 15.2 13.3 10.5 8.1 6.3 4.3 3.0  s  Z  40.0 35.0 30.0 27.0 25.0 22.0 18.0 15.0 11.7 7.9 4.1 1.6  Run No. 7  Z  D s  40.0 35.0 30.0 27.0 25.0 22.0 18.0 15.0 11.7 7.9 4.1 1.6  15.0 15.0 15.0 15.0 15.0 15.5 15.5 15.5 16.5 17.5 14.0 10.6  D  s  13.0 13.5 14.1 14.1 14.1 14.1 14.1 14.5 14.5 14.5 13.1 10.1  d  15.2 15.2 15.2 15.2 15.2 15.2 13.3 9.2 7.4 5.8 4.1 3.0  Run No. 8  d 15.2 15.2 15.2 15.2 15.2 15.2 13.3 9.4 7.5 6.4 4.6 3.0  Z 30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  D  s  13.0 13.0 13.0 13.0 13.0 13.5 14.5 15.5 16.5 19.5 11.0  d 15.2 15.2 15.2 15.2 15.2 13.3 10.5 7.9 6.6 4.2 3.0  - 142 -  Run No. 9 z  40.0 35.0 30.0 25.0 20.0 15.0 11.7 7.9 4.1 1.6  Run No. 10  D s  d  14.5 14.5 14.5 14.5 15.0 15.6 17.0 18.1 18.1 11.5  15.2 15.2 15.2 15.2 14.6 9.3 7.5 5.8 4.1 3.1  Z  30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  Run No. 11  D s  d  14.0 14.5 15.0 15.0 15.5 15.5 16.0 17.5 19.0 17.1 11.0  15.2 15.2 15.2 15.2 15.2 15.2 13.2 9.6 7.3 4.4 3.1  Run No. 12  Z  D s  d  Z  30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  15.0 15.0 15.5 15.5 16.0 16.5 17.1 18.1 19.5 17.2 11.1  15.2 15.2 15.2 15.2 15.2 15.2 13.4 9.6 7.5 4.9 3.2  40.0 38.0 35.0 30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  d  D  15.0 15.0 15.0 15.0 15.0 15.5 15.5 16.1 16.2 17.1 19.2 20.4 17.5 13.1  15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 13.3 9.7 7.4 4.4 3.1  - 143 -  Run No. 13 z  40.0 38.0 35.0 30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  D  s  15.5 15.5 15.5 15.5 15.5 15.5 16.0 16.0 16.5 17.1 19.3 20.6 17.5 13.5  Run No. 14  d 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 13.5 9.9 7.7 4.9 3.3  Z 49.0 45.0 40.0 38.0 35.0 30.0 27.0 25.0 22.0 20.0 18.0 15.0 11.7 7.9 4.1 1.6  Run No. 15  Z 40.0 35.0 30.0 25.0 20.0 15.0 11.7 7.9 4.1 1.6  d  16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 16.5 17.1 17.5 18.5 20.0 17.5 12.1  15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 15.2 13.3 9.7 7.6 4.8 3.1  Run No. 16  s  d  16.5 16.5 16.0 15.8 16.8 18.0 19.1 20.4 20.4 9.5  15.2 15.2 15.2 15.2 15.2 13.3 9.8 7.6 4.5 3.2  D  D s  Z 40.0 35.0 30.0 25.0 22.4 18.1 15.5 10.2 4.7 2.4 1.2  D  d*  s  15.1 15.1 15.1 15.1 15.1 15.1 15.0 15.0 13.5 9.5 6.0  -  -—  -  144  -  Run No. 17 z 50.0 45.0 40.0 35.0 30.0 25.0 22.4 18.1 15.5 10.2 4.7 2.4 1.2  D  Run No. d*  s  16.1 16.5 16.5 16.5 16.5 16.5 16.2 16.0 15.8 15.2 14.0 8.9 6.0  Z  -  29.4 26.4 24.4 21.4 19.4 17.7 14.4 11.1 7.3 3.5  D  29.4 26.4 24.4 21.4 19.4 17.4 14.4 11.7 7.9 4.1  19.0 19.0 19.0 19.0 19.5 19.5 22.0 25.2 24.5 23.5  *No stagnant  18.1 18.5 19.1 19.1 19.5 20.0 20.4 23.3 25.5 16.0  —  , -  -  Run No. 20 d*  s  zone e x i s t e d  d s  —  Run No. 19 Z  D  18  Z  -  15.0 13.1 11.7 7.9 7.0 4.2 2.9 1.6  —  and d = D . c  D  s  8.1 10.2 11.5 12.0 10.0 8.5 7.1  d 8.1 5.9 4.5 3.7 3.3 2.5 2.0 1.35  - 145 -  Run No. 21  z 15.0 13.1 11.7 7.9 7.0 4.2 2.9 1.6  D s  8.1 10.1 13.2 12.5 10.5 9.6 7.0  Run No. 22 d 6.8 5.2 4.8 4.2 3.7 3.1 2.6 1.8  Z 15.0 13.1 11.7 7.9 7.0 4.2 2.9 1.6  Run No. 23  D s  d  —  8.0 5.8 4.4 3.6 3.2 2.5 2.0 1.3  10.0 12.6 14.3 14.4 11.6 10.0 8.0  Run No. 24  Z  D s  d  13.1 11.7 9.6 7.9 5.6 4.1 3.1 1.6  14.5 17.2 18.4 17.9 15.8 13.7 12.0 10.1  6.8 5.2 4.8 4.2 3.7 3.1 2.6 1.8  *No s t a g n a n t zone e x i s t e d and d = D„.  Z 13.3 11.7 9.6 7.9 5.6 4.1 3.1 1.6  D s  d  19.9 20.8 21.8 19.8 17.2 14.5 11.8 10.2  7.9 6.4 5.8 5.4 4.5 3.8 3.3 2.2  - 146 -  Run No. 24a z  19.8 17.0 15.011.7 9.6 7.9 5.6 4.1 3.1 1.6  D  s  16.7 18.8 20.5 20.8 18.8 16.2 13.7 12.9 9.6  Run No. 24b d  15.2 11.3 9.3 6.6 5.2 3.9 2.9 2.3 1.9 1.5  Run No. 24c Z  19.0 17.0 15.0 11.7 9.6 7.9 5.6 4.1 3.1 1.6  d  -  15.2 13.0 11.2 8.2 6.9 5.9 4.8 4.3 3.7 2.9  Z  19.4 17.0 15.0 11.7 9.6 7.9 5.6 4.1 3.1 1.6  D  s  —  d  15.2 12.5 10.7 6.9 8.2 5.7 4.8 4.0 3.1 2.4  - 147 -  Run No. 25  z 19.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.1 1.6  D s  11.4 11.5 10.6 11.9 12.8 13.7 13.7 11.9 9.3  Run No. 26  d 10.2 8.8 8.0 6.7 5.9 5.1 4.4 3.7 3.0 2.4  Z 19.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.1 1.6  Run No. 27  Z 19.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.1 1.6  D s  13.0 14.0 14.5 18.2 19.8 18.2 13.5 10.9 7.3  D s  d  -  15.0 10.2 9.2 8.0 7.3 6.6 5.4 4.4 3.8 3.0  11.6 11.6 12.1 13.7 14.7 14.7 12.6 10.0 6.9  Run No. 28  d 15.2 11.3 10.4 8.9 8.1 7.2 5.9 5.0 4.2 3.3  Z 20.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  D s  d  25.3 26.4 23.9 20.7 20.7 20.0 17.1 14.3 12.5 9.3  15.2 11.3 10.2 8.6 7.9 7.0 5.6 4.9 4.3 3.2  - 148 -  Run No. 29 z  20.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  Run No. 30  D s  d  20.9 23.8 24.5 25.1 22.5 20.9 17.7 14.5 11.6 9.0  15.2 11.4 10.4 8.8 8.0 7.2 5.8 5.4 4.4 3.3  Z 20.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  Run No. 31 Z  22.0 20.0 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  22.2 25.5 28.4 26.8 23.9 21.4 17.7 15.2 12.8 9.9  . d •  15.2 11.9 10.8 9.2 8.3 7.4 5.9 5.6 4.6 3.3  Run No. 32  s  d  26.5 28.8 28.8 26.8 25.9 22.9 20.9 17.4 14.8 13.4 9.9  15.2 12.7 11.6 10.5 9.0 8.0 7.3 6.1 5.3 4.5 3.5  D  D s  Z 22.0 20.0 18.0 15.0 11.7 9.6 8.5 5.6 5.6 3.4 1.6  D s  d  26.7 29.0 30.5 30.5 28.0 25.0 23.0 19.0 19.0 13.5 10.0  15.2 13.3 12.2 11.5 10.6 9.3 8.6 7.4 5.7 4.7 3.5  - 149 -  Run  z  Run  d  Z  -  -  9.5 10.3 10.8 14.0 13.0 10.6 6.1  6.2 5.8 5.1 4.2 3.8 3.2 2.6  15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  s  Run  15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  33  D  15.0 11.7 9.6 8.5 5.6 4.1 . 3.4 1.6  Z  No.  No.  —  11.4 11.4 12.3 12.7 11.8 10.9 3.2  10.6 6.2 4.9 4.3 3.6 3.1 2.7 2.3  15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  d  s  -  10.8 7.7 6.7 6.0 4.9 4.7 3.8 2.8  6.7 13.3 15.8 18.4 14.8 13.3 6.7  Run Z  34  D  35  d  D  No.  D  No.  s —  15.0 15.0 15.9 14.6 13.7 10.9 8.2  36  d 12.3 7.7 6.7 6.2 5.0 4.1 3.5 2.8  - 150 -  Run No. 37 z  19.5 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  D s  -  11.4 11.4 12.5 12.5 13.6 13.6 11.9 9.8 8.7  Run No. 38  d 13.8 • 8.5 5.8 4.6 4.2 3.8 3.2 2.8 2.3 2.2  Z  19.5 18.0 15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  Run No. 39 Z  15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  D s  d  15.3 15.3 17.4 19.6 20.7 20.2 17.4 14.7 11.4 9.3  15.2 11.8 9.7 8.6 7.7 7.1 5.5 4.7 3.7 3.4  Run No. 40  D s  d  6.7 6.9 6.9 6.9 7.4 6.7 6.2 4.2  8.4 6.6 5.7 5.1 4.8 4.2 3.2 3.0  Z  15.0 11.7 9.6 8.5 5.6 4.1 3.4 1.6  D s  d  4.9 6.0 7.4 8.1 7.7 7.4 6.0 4.9  11.8 8.6 7.2 6.4 5.6 4.8 4.1 3.5  - 151 -  D.5:  Solid  d  p  Fountain Height  d.  U/U  ms  H  H  p  Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand  196 196 196 196 196 196 196 196 196 196 196 196  2.8 2.8 2.8 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5  1.14 1.43 1.86 1.84 2.41 3.00 3.56 4.13. 4.81 5.66 1.58 1.88  15.0 15.0 15.0 14.5 14.5 14.5 14.5 14.5 14.5 14.5 19.5 19.5  36.5 45.5 58.5 41.0 54.5 69.0 75.5 77.5 79.5 84.5 74.5 90.5  Bronze Bronze Bronze Bronze  176.4 176.4 176.4 176.4  2.8 2.8 2.8 2.8  1.24 1.53 1.76 2.03  15.0 15.0 15.0 15.0  24.2 38.0 42.1 52.0  Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand  401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401 401  4.5 4.5 4.5 4.5 4.5 4.5 4.5 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 9.0 9.0  1.08 1.18 1.08 1.18 1.08 1.18 1.20 1.08 1.18 1.32 1.50 1.67 1.87 1.01 1.08 1.11 1.18 1.01 1.08 1.13 1.23 1.27 1.02 1.09  30.0 30.0 41.0 41.0 49.6 49.6 49.6 15.0 15.0 15.0 15.0 15.0 15.0 30.0 30.0 30.0 30.0 41.0 41.0 41.0 41.0 41.0 30.0 30.0  10.7 18.0 9.0 17.2 8.8 14.2 16.6 10.0 19.0 26.0 32.1 42.2 46.0 9.4 12.8 15.1 19.5 7.1 10.8 14.2 19.5 21.0 10.4 12.5  \  - 152 -  Solid  d  p  d, i  Sand Sand Sand  401 401 401  9.0 9.0 9.0  Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand Sand  516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516 516  6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 6.0 12.7 12.7 12.7  Glass Glass Glass  710 710 710  Glass Glass Glass Glass Glass Glass  845 845 845 845 845 845  U/U  ms  H  H„ F  1.02 1.07 1.10  41.0 41.0 41.0  10.1 13.0 15.8  1.01 1.02 1.06 1.11 1.14 1.16 1.015 1.05 1.06 1.11 1.16 1.21 1.24 1.015 1.05 1.10 1.12 1.14 1.16 1.19 1.01 1.04 1.08  30.0 30.0 30.0 30.0 30.0 30.0 41.0 41.0 41.0 41.0 41.0 41.0 41.0 50.0 50.0 50.0 50.0 50.0 50.0 50.0 41.0 41.0 41.0  10.2 11.2 14.1 16.2 18.2 20.7 8.2 9.5 10.9 13.0 15.8 18.5 20.0 5.8 8.5 10.8 13.2 14.5 16.5 18.5 9.5 13.5 18.2  6.0 6.0 6.0  1.01 1.05 1.24  30.0 30.0 30.0  14.0 20.0 29.5  6.0 6.0 6.0 6.0 6.0 6.0  1.02 1.05 1.07 1.11 1.17 1.23  30.0 30.0 30.0 30.0 30.0 30.0  11.8 14.3 15.4 19.0 22.3 26.8  

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