UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Two component fluidization. LeClair, Brian Peter 1964

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
UBC_1964_A7 L4.pdf [ 6.73MB ]
Metadata
JSON: 1.0059168.json
JSON-LD: 1.0059168+ld.json
RDF/XML (Pretty): 1.0059168.xml
RDF/JSON: 1.0059168+rdf.json
Turtle: 1.0059168+rdf-turtle.txt
N-Triples: 1.0059168+rdf-ntriples.txt
Original Record: 1.0059168 +original-record.json
Full Text
1.0059168.txt
Citation
1.0059168.ris

Full Text

TWO COMPONENT FLUIDIZATION hy B r i a n P. Le C l a i r B . A . S c , U n i v e r s i t y o f B r i t i s h Columbia,  I962  A THESIS SUBMITTED I N PARTIAL TULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  i n t h e Department o f  CHEMICAL ENGINEERING  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e required standard  Members o f t h e Department o f Chemical E n g i n e e r i n g  THE UNIVERSITY OF BRITISH COLUMBIA J a n u a r y , 196k  the  In presenting  this thesis in partial fulfilment  of  r e q u i r e m e n t s f o r an  a d v a n c e d d e g r e e a t the U n i v e r s i t y  of  B r i t i s h Columbia, I agree that a v a i l a b l e f o r r e f e r e n c e and mission for extensive p u r p o s e s may his  be  L i b r a r y s h a l l make i t f r e e l y -  study.  I f u r t h e r agree that  copying of t h i s t h e s i s f o r  g r a n t e d by  representatives,,  the  the Head o f my  w i t h o u t my  written  Department  of  permission.  The U n i v e r s i t y o f B r i t i s h Columbia,. V a n c o u v e r 8, Canada. Date  scholarly  D e p a r t m e n t or  I t i s u n d e r s t o o d that, copying, or  c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain  (jOu.. /£>  j  /?*  s h a l l not  per-  be  by publi-  allowed  .>  v i i  Abstract  S t u d i e s were made o f t h e d i s t r i b u t i o n o f components, when two m a t e r i a l s are f l u i d i z e d i n a l i q u i d .  The h y p o t h e s i s  t e s t e d was t h a t t h e  d i s t r i b u t i o n o f m a t e r i a l i s a function o f the bulk density d i f f e r e n c e of •,the component beds.  The component bed h a v i n g t h e g r e a t e s t b u l k  w i l l occupy t h e bottom o f t h e t o t a l bed.  density  I t i s p o s s i b l e f o r the b u l k  d e n s i t y o f one m a t e r i a l t o be g r e a t e r t h a n t h e o t h e r a t low v e l o c i t i e s , and l e s s t h a n t h e o t h e r a t h i g h v e l o c i t i e s .  A t some i n t e r m e d i a t e  the b u l k d e n s i t y d i f f e r e n c e between t h e two beds must be zero.  condition  This  situation,  c a l l e d t h e i n v e r s i o n p o i n t , produces homogeneous m i x i n g o f t h e two components. Mixtures  o f two m a t e r i a l s f o r which an i n v e r s i o n was p r e d i c t e d by t h e  stated hypothesis  were t e s t e d .  I n the intermediate  and t u r b u l e n t  flow  r e g i o n s i n v e r s i o n s d i d n o t o c c u r because macroscopic m i x i n g d e s t r o y e d t h e bulk density gradients being established.  However, i n t h e l a m i n a r  flow  r e g i o n , where m i x i n g was n e g l i g i b l e , i n v e r s i o n s d i d occur. The  q u a l i t y o f t h e i n v e r s i o n was a f f e c t e d as f o l l o w s .  F o r a sharp  c l e a r i n v e r s i o n o f t h e two m a t e r i a l s a t t h e p r e d i c t e d v e l o c i t y , t h e d i a m e t e r r a t i o o f t h e two groups o f p a r t i c l e s must be much g r e a t e r than one and t h e d e n s i t y r a t i o ( c o r r e c t e d f o r buoyancy) o f t h e two groups o f p a r t i c l e s must be much l e s s than one.  A l s o o f importance i s t h e a b s o l u t e  density  (corrected  f o r buoyancy) o f t h e p a r t i c l e s . P a r t i c l e s i z e d i s t r i b u t i o n a l s o appeared t o s t r o n g l y a f f e c t t h e q u a l i t y o f the i n v e r s i o n .  These d i s t r i b u t i o n s s e t up b a l k d e n s i t y  w i t h i n t h e s i n g l e component beds.  T h i s appeared t o cause m i x i n g o f t h e  two components and i n some cases even f o r m a t i o n before  gradients  o f the two i n v e r t e d beds  t h e p r e d i c t e d i n v e r s i o n v e l o c i t y was reached.  viii  The p r e d i c t i o n o f t h e bed e x p a n s i o n o f m i x t u r e s was a l s o s t u d i e d . c o r r e l a t i o n was developed on t h e assumption m i x t u r e c o u l d be t r e a t e d s e p a r a t e l y .  A  t h a t each component o f t h e  The o v e r a l l e x p a n s i o n t h u s would be  the sum o f the e x p a n s i o n s o f t h e i n d i v i d u a l components.  There was v e r y  good agreement between v a l u e s p r e d i c t e d by t h i s method and e x p e r i m e n t a l data.  The method p r e d i c t e d e x p a n s i o n w e l l f o r a l l degrees o f m i x i n g o f  the two components, b u t d i d n o t p r e d i c t w e l l when one o f tiie components was near i t s minimum p o r o s i t y f o r f ' l u i d i z a t i o n . The e m p i r i c a l e q u a t i o n s o f R i c h a r d s o n and Z a k i (k) f o r s i n g l e l i q u i d f l u i d i z a t i o n e x p a n s i o n s were checked.  component  The v a l u e s o f t h e index  "n"  O b t a i n e d from e x p e r i m e n t a l d a t a agreed w i t h i n + 5$ o f those c a l c u l a t e d u s i n g the c o r r e l a t i o n s .  The e q u a t i o n developed by R i c h a r d s o n and Z a k i  f o r d e t e r m i n i n g the f r e e s e t t l i n g v e l o c i t y o f a s i n g l e p a r t i c l e  from  e x t r a p o l a t e d e x p a n s i o n d a t a gave r e s u l t s which were w i t h i n + 15$ o f those o b t a i n e d u s i n g t h e s t a n d a r d drag c o e f f i c i e n t - R e y n o l d s number p l o t f o r an isolated  sphere.  vi  Acknowledgement  I am i n d e b t e d t o Dr. Norman E p s t e i n , under whose g u i d a n c e t h i s s t u d y was made, f o r h i s encouragement and a s s i s t a n c e d u r i n g t h e course of t h i s p r o j e c t . The a s s i s t a n c e ^ o f Mr. R. Muelchen and t h e Workshop s t a f f i s a p p r e c i a t e d f o r t h e i r p r o f i c i e n c y a t b u i l d i n g t h e equipment t o t h e specifications  required.  I a l s o w i s h t o thank t h e N a t i o n a l R e s e a r c h C o u n c i l o f Canada f o r f i n a n c i a l a s s i s t a n e e r r e c e i v e d , and the Department o f C h e m i c a l E n g i n e e r i n g a t U.B.C. f o r a d d i t i o n a l s u p p o r t .  i  Table o f Contents  * Page vi  Acknowledgement Abstract  vii  "  Nomenclature  ix  Introduction  1  Theory  4  (A)  Free S e t t l i n g V e l o c i t y o f a P a r t i c l e  4  (B)  Bed E x p a n s i o n C o r r e l a t i o n s  6  (c)  F r i c t i o n a l P r e s s u r e Drop i n a F l u i d i z e d Bed . . . .  9  (D)  Stratification  10  (E)  Theoretical Derivation f o r Inversion  12  (F)  M i x e d Bed H e i g h t P r e d i c t i o n s  l6 19  Apparatus (A)  General  (B)  Test Section  19 23  . .  29  Experimental Procedures (A)  General Operating Procedure  29  (B)  Flow Meters  29  (C)  Measurement o f V i s c o s i t y and D e n s i t y o f T e s t F l u i d .  34  (D)  Measurement o f P a r t i c l e D e n s i t y  35  (E)  Sizing of Particles  35 37  Results (A)  (B)  Experiments w i t h a S i n g l e Species  37  1.  Bed E x p a n s i o n  37  2.  D i f f e r e n t i a l P r e s s u r e ' Measurements  '  46  E x p e r i m e n t s w i t h two S p e c i e s  50  1.  Inversion of Mixtures  50  2.  P r e d i c t i o n o f Bed E x p a n s i o n f o r M i x t u r e s  ...  75  ii Page Conclusions  83  Literature Cited  89  Appendix I -  Bearet',  s Plots f o r Prediction of Inversion?!  Porosities  1-1  .  Appendix II - Sample Calculations and Error Analysis Appendix I I I - Materials Used  . . . . .  2-1 3-1  Appendix IV - O r i g i n a l Data  4-1  Appendix V - Measurement of Longitudinal P a r t i c l e Concentration (Proposed Method)  5©!  iii  Tables Page 1.  O r i f i c e Meter S i z e s  21  2.  A c c u r a c y o f Flow Meter C o r r e l a t i o n s  31  3.  L e a s t Squares E q u a t i o n s f o r M e t e r s  31  k.  Summary o f F l u i d i z a t i o n R e s u l t s f o r P a r t i c l e s i n Water  5.  Summary o f F l u i d i z a t i o n R e s u l t s f o r P a r t i c l e s i n G l y c o l . . .  39  6.  Comparison o f R e s u l t s w i t h R i c h a r d s o n and Z a k i C o r r e l a t i o n s - Water  'kO  7.  Comparison o f R e s u l t s w i t h R i c h a r d s o n and Z a k i C o r r e l a t i o n s -  41  . .'  . . .  38  Glycol • 8.  I n v e r s i o n R e s u l t s f o r N i c k e l and B a l l o t i n i  5§  9/  I n v e r s i o n R e s u l t s f o r Alundum and B a l l o t i n i  "57  10.  I n v e r s i o n R e s u l t s f o r .Lead and S t e e l  62  11.  I n v e r s i o n R e s u l t s f o r N i c k e l - G l a s s and B a l l o t i n i  12.  Quality-of-Inversion Predictions  '  71  iv L i s t of  Illustrations  Figure  Page  1.  F r i c t i o n a l P r e s s u r e Drop A c r o s s a F l u i d i z e d Bed  11  2.  P r e d i c t i o n o f F l u i d i z e d Bed I n v e r s i o n  15  3-  Schematic Diagram o f Apparatus  20  4.  Schematic  25  5-  Diagram o f E n t r y S e c t i o n To and E x i t  6.  Diagram o f D i f f e r e n t i a l P r e s s u r e Measurement System . . . .  28  7.  Flow-Meter C a l i b r a t i o n Curves f o r Water . . . .  32  8.  Flow-Meter C a l i b r a t i o n Curves f o r P o l y e t h y l e n e G l y c o l  9>  P l o t o f Alundum and Cataphote Bed Expansion  43  10.  V i s u a l O b s e r v a t i o n s o f F l u i d i z a t i o n o f Spheres  1+5  11.  F r i c t i o n a l P r e s s u r e Drop P r o f i l e s i n a B a l l o t i n i Bed  .  Diagram o f a S e c t i o n a l View o f the Column . . . . S e c t i o n from Column  .  . . .  26  33  . . .  48  F l u i d i z e d by P o l y e t h y l e n e G l y c o l 12.  F r i c t i o n a l P r e s s u r e Drop P r o f i l e s i n an Alundum BedF l u i d i z e d by P o l y e t h y l e n e G l y c o l  1+9  13.  P l o t of N i c k e l and B a l l o t i n i Bed Expansions  14.  D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n N i c k e l - B a l l o t i n i Bed  15-  P l o t o f Bulk D e n s i t y D i f f e r e n c e and V e l o c i t y f o r  53 .  .  54  the  N i c k e l - B a l l o t i n i Bed  55  16.  Schematic  Diagram o f how I n v e r s i o n Proceeded  17.  P l o t o f Alundum and B a l l o t i n i Bed Expansions i n  56 58  Polyethylene Glycol 18.  D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n A l u n d u m - B a l l o t i n i Bed .  19.  P l o t o f Bulk D e n s i t y D i f f e r e n c e and V e l o c i t y f o r  .  59  the  A l u n d u m - B a l l o t i n i Bed  60  20.  Schematic  Diagram o f How I n v e r s i o n Proceeded  21.  P l o t o f Lead and S t e e l Bed Expansions  22.  D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n L e a d - S t e e l Bed  23.  P l o t o f Bulk D e n s i t y D i f f e r e n c e and V e l o c i t y f o r L e a d - S t e e l Bed  .  6l  .  63 64 the 65  Figure 24.  25.  26.  •  Page  P l o t o f N i c k e l - G l a s s and B a l l o t i n i Bed Expansions i n Polyethylene Glycol  67  P l o t o f Bulk D e n s i t y D i f f e r e n c e and V e l o c i t y f o r the N i c k e l - G l a s s - B a l l o t i n i Bed  68  E f f e c t o f P a r t i c l e S i z e D i s t r i b u t i o n on the P o i n t o f 7*  Inversion 27.  P l o t o f Alundum-Crystalon Run N o . l  77  28.  P l o t o f Alundum-Crystalon Run No.2  78  29.  P l o t o f Alundum and B a l l o t i n i Bed Expansions i n Water .  79  ;>30.  P l o t o f N i c k e l - G l a s s and B a l l o t i n i Bed Expansions i n '• •  80  and Alundum Bed Expansions . . . . . . .  81  Water 31.  Plot of Nickel  32.  P l o t o f N i c k e l - G l a s s and B a l l o t i n i Bed Expansions w i t h D i f f e r e n t Volumes o f Each Component  33.  P a r t i c l e Size  34.  Beare P l o t f o r the Stokes' Law Region  35.  Beare P l o t f o r the Newtons' Law Region  36.  P l o t o f P R a t i o P r o f i l e s a t V a r i o u s Average P o r o s i t i e s  Distribution  . . .•  82 871-3  . .  1-4 5-2  IX Nomenclature  a r e a o f column,  ft.  2  A  -  cross-sectional  b*  -  index i n Lewis and Bowenaan e q u a t i o n ,  C  -  m o d i f i e d o r i f i c e meter c o e f f i c i e n t ,  dimensionless.  -t^L  P i s i n centipoises  and.the  /  V  P,-P  -  ^  2  rest engineering u n i t s . LL  C"  , where LL  P  m o d i f i e d o r i f i c e meter c o e f f i c i e n t ,  -— - /  P  /  p  -  ,  P, " P  V  all  2  engineering units. D  -  column diameter,  ft.  d  -  average p a r t i c l e  diameter,  Fp.  -  gravitational  Fp  -  drag f o r c e ,  g  -  acceleration  -  Newton's law c o n v e r s i o n f a c t o r ,  k  -  variable constant,  k'  -  c o n s t a n t i n Lewis and Bowerman e q u a t i o n ,  g  c  force,  f t . , mm.  lb-force.  lb-force, of g r a v i t y ,  ft./sec  2  (ft.)  (lb.)/(lb-force)  (sec. ) 2  dimensionless. dimensionless.  l/m k"  -  constant c o n t a i n i n g l i q u i d p r o p e r t i e s  and k ,  ^  vm-l)/2  P dimensional. ; L  -  vertical  distance  ' i n a f l u i d i z e d bed,  ft.;  vertical  M  2-m  ' distance  between a base p o s i t i o n i n the bed and an e l e v a t e d p o s i t i o n , M  -  weight o f s o l i d p a r t i c l e s  i n a f l u i d i z e d bed,  in  -  state-of-flow-index,  n  -  R i c h a r d s o n and Z a k i i n d e x ,  p  -  f l u i d pressure,  lbs.  dimensionless. dimensionless.  lb-force/ft.  App. -  f r i c t i o n a l pressure  loss  P  -  P ratio,  Q  -  (Ap/L )/(Ap/L )^ A. , p i p theoretical v o l u m e t r i c flow r a t e , f t . ^ / s e e .  R  -  particle  Reynolds number,  i n a f l u i d i z e d bed,  ^^P  ,  lb-force/ft.  -> d i m e n s i o n l e s s .  dimensionless.  ,  2  ft.  r  -  p a r t i c l e dianeterrratio, d  t  -  time o f e f f l u x  V  -  velocity  -  free s e t t l i n g velocity  -  superficial liquid velocity  V  0  Vj  ,  /d^  (  f o r f l u i d i n v i s c o m e t e r tube,  of f l u i d ,  e x t r a p o l a t e d to  of  € = 1.0,  i n a f l u i d i z e d bed,  -  superficial liquid velocity,  V |jp  -  slip velocity  is  V  -  volume o f  Vf-  -  t o t a l volume o f  -  weight of  W  -  weight o f a s p e c i f i c  V  -  d e n s i t y c o r r e c t e d f o r buoyancy r a t i o ,  ft/sec.  ft./sec.  "between p a r t i c l e  a f l u i d i z e d bed  Zaki p l o t  ft./sec.  V  m  ft./sec  when R i c h a r d s o n and  velocity  W  of p a r t i c l e  a particle,  -  S  sec.  ft./sec.  Vp s  dimensionless.  and  fraction,  f l u i d i z e d bed,  fluid,  ft./sec.  ft.3- .  lbs.  s o l i d s m i x t u r e i n f l u i d i z e d bed, fraction  of  lbs.  s o l i d s , i n f l u i d i z e d bed,  py  (  s  )/(  —p  lbs.  p$2.~p)>  dimensionless. €  -  p o r o s i t y o f f l u i d i z e d bed,  € f  -  minimum p o r o s i t y f o r f l u i d i z a t i o n ,  €m  -  average p o r o s i t y o f m i x t u r e ,  m  fJt.,fJLf p.g p,Pl  viscosity  of f l u i d ,  v . . . . v i s c o s i t y of  dimensionless. dimensionless.  dimensionless.  l b . / ( f t . )(sec. ) .  i ' l u i d i z e d suspension, l b . / ( f t . ) ( s e c ) .  -  d e n s i t y of f l u i d  Pg  -  d e n s i t y o f f l u i d i z e d suspension, l b . / f t .  p^  -  bulk density of  p  -  d e n s i t y of  <j)  -  weight f r a c t i o n  *s  lb./ft.3 .  f l u i d i z e d bed,  solid particles,  .  lb./ft.^.  gm./cm.^ , l b s . / f t . 3  o f a s o l i d component o f  .  a mixture,  subscripts 1, i  2, A, B s p e c i f i c f l u i d i z e d beds o f p a r t i c l e s j 1 and 2 a l s o denote upstream, and downstream t a p s , r e s p e c t i v e l y , on flowmeters, - any i n d i v i d u a l f l u i d i z e d bed f r a c t i o n .  free s e t t l i n g  conditions.  f r i c t i o n a l ; a l s o denotes g r a v i t a t i o n a l u n i t s o f f o r c e t e s t s e c t i o n b a s e d on empty tube.  1.  INTRODUCTION  F l u i d i z a t i o n i s a p r o c e s s w i d e l y used i n i n d u s t r y , b u t t h e t h e o r y and t e c h n i q u e s f o r d e s i g n o f l i q u i d f l u i d i z a t i o n equipment and p r o c e s s e s a r e n o t f u l l y understood a t the present time. theoretical  Thus a sound program based on  development and e x p e r i m e n t a t i o n must be c a r r i e d out t o d e v e l o p  r e l i a b l e design c r i t e r i a . The p r e s e n t work was f o r m u l a t e d t o s t u d y l i q u i d f l u i d i z a t i o n o f two component m i x t u r e s o f s o l i d s , f o r example, a m i x t u r e o f l e a d and s t e e l f l u i d i z e d by water. The two m a t e r i a l s would have s p e c i f i e d d i a m e t e r and d e n s i t y r a t i o s such t h a t i n v e r s i o n o f t h e m a t e r i a l s w i l l o c c u r a t some o v e r a l l p o r o s i t y above t h e minimum f l u i d i z a t i o n p o r o s i t y . C o n s i d e r a f l u i d i z e d bed composed o f m a t e r i a l A and m a t e r i a l B such that  PsA *PsB  A  N  ^  C  'B  >  *  F o r  i n conjunction with s p e c i f i e d r a t i o s of  p a r t i c u l a r r a t i o s of  dr^/d^  PSA^PSB  , the- f l u i d i z e d bed w i l l  respond i n t h e f o l l o w i n g v/ay t o changes i n s u p e r f i c i a l l i q u i d v e l o c i t y . At low f l o w r a t e s ' the f l u i d i z e d bed w i l l be made up o f two l a y e r s ,  one  above t h e o t h e r , such t h a t a l l t h e heavy s m a l l p a r t i c l e s w i l l form a f l u i d i z e d assemblage a t t h e bottom o f t h e column q u i t e d i s t i n c t from t h e l i g h t l a r g e ones w h i c h have formed an assemblage above t h e s m a l l heavy particles.  S i m i l a r l y a t h i g h v e l o c i t i e s t h e f l u i d i z e d b e d w i l l a g a i n be  composed o f two d i s t i n c t s t r a t a , b u t now t h e l a r g e l i g h t p a r t i c l e s w i l l be a t the bottom and the heavy s m a l l p a r t i c l e s w i l l be a t t h e t o p o f t h e bed. At some i n t e r m e d i a t e v e l o c i t y between t h e two extremes i n v e r s i o n o c c u r s . Trie i n v e r s i o n mode has been d e f i n e d as t h e p o i n t o f changeover, o r the p o i n t o f homogeneous f l u i d i z a t i o n o f t h e two s p e c i e s o f p a r t i c l e s . I n v e r s i o n o f the s o r t d e s c r i b e d above can o c c u r because o f t h e n a t u r e of p a r t i c u l a t e  fluidization.  W i l h e l m and Kwauk ( l ) have d e s c r i b e d  p a r t i c u l a t e f l u i d i z a t i o n , u s u a l l y b u t not always synonymous w i t h  liquid  f l u i d i z a t i o n , a s " c h a r a c t e r i z e d by the s e p a r a t i o n o f i n d i v i d u a l p a r t i c l e s much i n the manner o f a gas.  A mean f r e e p a t h can be o b s e r v e d , and  the  l e n g t h o f the p a t h i s found t o i n c r e a s e w i t h v e l o c i t y . " Thus l i q u i d f l u i d i z a t i o n i s o b s e r v e d t o be an o r d e r e d e x p a n s i o n o f the p a r t i c l e s i n the bed, w i t h o u t r a p i d l a r g e s c a l e c i r c u l a t i o n and m i x i n g o f p a r t i c l e s . Because o f t h i s , the p o s i t i o n o f the p a r t i c l e s i n a f l u i d i z e d bed w i l l  be  governed almost e x c l u s i v e l y by drag and g r a v i t a t i o n a l f o r c e s , on w h i c h the i n v e r s i o n phenomenon i s based. Q u a l i t a t i v e o b s e r v a t i o n s o f i n v e r s i o n s have been d e s c r i b e d by e a r l i e r w o r k e r s , namely, Hancock ( 2 ) 1936  and J o t t r a n d ( 3 ) .  two  Hancock ( 2 )  in  d i s c u s s e d and d e s c r i b e d i n v e r s i o n s o f the type d e s c r i b e d above.  The  o b s e r v a t i o n s made were: (1)  At s i m i l a r v e l o c i t i e s i n a column o f f l u i d i z e d mixed sands, the  "bulk d e n s i t y , yDg  , d e v e l o p e d by the bed  whereas w i t h a u n i f o r m (2)  I f one  i n c r e a s e s from the top downwards,  sand the b u l k d e n s i t y i s u n i f o r m down the  uniform  bed.  sand has a p a r t i c u l a r b u l k d e n s i t y a t a p a r t i c u l a r  l i q u i d v e l o c i t y , then i t i s p o s s i b l e f o r a n o t h e r u n i f o r m  sand o f a d i f f e r e n t  s o l i d d e n s i t y t o d e v e l o p the same b u l k d e n s i t y a t the s p e c i f i e d  liquid  v e l o c i t y i f the s i z e o f i t s p a r t i c l e s i s s u i t a b l y r e l a t e d t o the p a r t i c l e s i z e o f the former p a r t i c l e s . (3)  When two u n i f o r m sands d e v e l o p the same b u l k d e n s i t i e s a t a  p a r t i c u l a r l i q u i d v e l o c i t y , the t o t a l m i x t u r e behaves as one u n i f o r m J o t t r a n d (3)  bed.  has o b s e r v e d a s i m i l a r phenomenon b u t , as w i t h Hancock,  no q u a n t i t a t i v e measurements were r e c o r d e d .  I n J o t t r a n d ' s work a s p e c i a l  case i n v o l v i n g one component f l u i d i z e d and t h e o t h e r u n f l u i d i z e d i s reported.  The  c o n c l u s i o n drawn by J o t t r a n d was", however, e q u i v a l e n t t o  3- . t h a t drawn by Hancock, namely t h a t , t h e p r i m a r y f a c t o r g o v e r n i n g c l a s s i f i c a t i o n i n f l u i d i z e d beds i s t h e average bulk, d e n s i t y d e v e l o p e d by each o f t h e components o f t h e m i x t u r e f l u i d i z e d In order t o c o r r e l a t e data obtained  seperately.  on two component f l u i d i z a t i o n , t h e  l i t e r a t u r e was s e a r c h e d t o determine t h e b e s t method f o r measuring concentrations  a t v a r i o u s l o c a t i o n s i n t h e bed.  d a t a have been c o r r e l a t e d by bed e x p a n s i o n ( pressure  gradient  ( App/L v s  ;  V  s  Most l i q u i d  € vs. V  ) t h r o u g h t h e bed.  s  particle  fluidization  ) and d i f f e r e n t i a l A n a l y s i s showed t h a t  the b u l k d e n s i t y d i f f e r e n c e between two s e c t i o n s o f a bed was  e'quivalent  or at l e a s t p r o p o r t i o n a l to the d i f f e r e n c e i n d i f f e r e n t i a l f r i c t i o n a l pressure  g r a d i e n t between t h e s e c t i o n s .  f r i c t i o n a l pressure profiles  T h e r e f o r e measurements o f  l o s s p r o f i l e s c o u l d be used t o determine b u l k  and hence l o n g i t u d i n a l p a r t i c l e  density  d i s t r i b u t i o n s , i n a f l u i d i z e d bed.  k.  THEORY A.  Free S e t t l i n g V e l o c i t y  of a Particle  I f a p a r t i c l e i s f a l l i n g under t h e i n f l u e n c e o f g r a v i t y  in a fluid  medium, t h e p a r t i c l e w i l l a c c e l e r a t e t o a c o n s t a n t t e r m i n a l v e l o c i t y , V  Q  .  T i l l s v e l o c i t y i s dependent on t h e d i a m e t e r , shape and d e n s i t y o f t h e p a r t i c l e and t h e p r o p e r t i e s o f the- f l u i d through which i t i s f a l l i n g .  The  c o n s t a n t t e r m i n a l v e l o c i t y w i l l be a c h i e v e d when t h e b u o y a n c y - c o r r e c t e d gravitational accelerating upward d r a g f o r c e , F^.  f o r c e , F g , i s c o u n t e r b a l a n c e d by t h e r e s i s t i n g  F o r spheres,  6 F=  and  _l_C /> 7 T d V 8 2  0  2  2  D  On e q u a t i n g F g and F Q o f e q u a t i o n s 1 and 2, t h e drag c o e f f i c i e n t , C Q , i s t h e n g i v e n by  .  4dg (p -f) i 3V /> c  °D  =  3  s  2  0  The p a r t i c l e drag d a t a can be r e p r e s e n t e d i n terras o f a p l o t to the f r i c t i o n  factor  p r e s s u r e drop d a t a .  similar  - Reynolds number p l o t f o r p r e s e n t i n g p i p e l i n e  The drag c o e f f i c i e n t i s p l o t t e d a g a i n s t t h e Reynolds  number based on a c h a r a c t e r i s t i c p a r t i c l e dimension and on t h e r e l a t i v e v e l o c i t y between t h e p a r t i c l e and t h e f l u i d medium. Reynolds number c u r v e has been d i v i d e d  The d r a g c o e f f i c i e n t -  i n t o t h r e e r e g i o n s , t h e Stokes" Law  or l a m i n a r range, t h e i n t e r m e d i a t e r e g i o n , and t h e Newton o r t u r b u l e n t region.  I n each r e g i o n t h e curve has been approximated by a s t r a i g h t  For t h e i n d i v i d u a l ranges Crj iaay be approximated as f o l l o w s .  line.  Stokes*  Region  Re < 0-3 0  C V  D  0  = 24/Re  4  -  D  18/x  I n t e r m e d i a t e Region  0 3 < Re <  500  0  C = l8-6Re" ' 0  6  D  ,H4_ 0-714 0  u  0-428  Q  «\0-7l4  0 289  Newton Region  500 < Re < 500,000 0  C = 0-44  8  D  3g d(/3 -/3)l°c  •  5  s  9  :  G e n e r a l i z i n g , i t can be s t a t e d t h a t t h e drag f o r c e F Q i s g i v e n b y the f o l l o w i n g e q u a t i o n :  F  D  =kV  r n 0  d /i ' /o m  2  m  m H  io  At low v a l u e s o f Reynolds number, where f l u i d r e s i s t a n c e i s independent of d e n s i t y , m e q u a l s 1 . 0 , b u t t h i s i n d e x i n c r e a s e s t o 2 . 0 a t h i g h v a l u e s o f t h e Reynolds number, where f l u i d r e s i s t a n c e i s independent o f v i s c o s i t y . E q u a t i n g equations 1 and 1 0 , v/e o b t a i n a g e n e r a l i z e d e q u a t i o n f o r t h e f r e e settling or terminal velocity of f a l l of a p a r t i c l e :  6.  . /  k(/V/»  »  ,/m  £-1  <*  11  The c o n s t a n t , k, i n the e q u a t i o n v a r i e s from  1 ^-pin the Stokes' r e g i o n t o  i n . t h e Newton r e g i o n , f o r a s p h e r i c a l p a r t i c l e . B.  Bed E x p a n s i o n C o r r e l a t i o n s Numerous e q u a t i o n s have been developed f o r c o r r e l a t i n g b e d e x p a n s i o n  d a t a , b u t t h e r e does n o t seem t o be much agreement among workers a s t o which c o r r e l a t i o n i s b e s t .  A t t h e p r e s e n t t i m e , the most comprehensive  and e a s i e s t c o r r e l a t i o n s t o a p p l y a r e t h e s i m p l e power f u n c t i o n s r e l a t i n g p o r o s i t y and s u p e r f i c i a l l i q u i d v e l o c i t y .  Various studies reported i n  the l i t e r a t u r e on t h e v e l o c i t y - voidage r e l a t i o n s h i p i n m u l t i p a r t i c l e systems a r e a n a l y s e d i n the f o l l o w i n g  sections.  Happel (6) developed an e q u a t i o n f o r e x p a n s i o n r e l a t i o n s h i p s , b y u s i n g the N a v i e r - S t o k e s ' e q u a t i o n s w i t h o u t t h e i n e r t i a l terms t o d e s c r i b e the motion o f m u l t i p a r t i c l e systems.  The model o f a f l u i d i z e d o r  s e d i m e n t i n g b e d was t h a t o f a number o f c e l l s , each c o n s i s t i n g o f a s p h e r i c a l p a r t i c l e a t t h e c e n t e r e n c l o s e d b y a s p h e r i c a l envelope o f fluid.  The volume o f f l u i d w i t h i n t h e envelope was such t h a t t h e p o r o s i t y  o f a c e l l was e q u a l t o t h e o v e r a l l p o r o s i t y o f t h e bed, and the i t s e l f was assumed t o behave l i k e a f r e e s u r f a c e .  envelope  That i s , t o obey t h e  c o n d i t i o n o f zero shear s t r e s s a t t h e f l u i d - f l u i d boundary.  Disturbances  caused by p a r t i c l e s were c o n f i n e d t o t h e c e l l i n w h i c h t h e y were associated.  V  The r e l a t i o n s h i p developed on t h e s e p o s t u l a t e s i s g i v e n by  3 - 4-5(l-€)  ,/s  +4-5(l-€)  8/s  - 3(l-€)  2  7.  T h i s e q u a t i o n p r o v i d e s good agreement w i t h experiment  a t v e r y h i g h and  v e r y low voidage, and a t low Reynolds numbers, b u t i s poor o u t s i d e o f these regions. Hawksley (7) developed (l)  What i s important  an e q u a t i o n based  on t h e f o l l o w i n g p r o p o s a l s :  i s n o t the f l u i d d e n s i t y o r v i s c o s i t y b u t the  suspension d e n s i t y and v i s c o s i t y . V /€  f l u i d and p a r t i c l e s i s  s  .  (2) The r e l a t i v e v e l o c i t y between Thus the f l u i d i z e d b e d d e n s i t y and  v i s c o s i t y a r e g i v e n by the f o l l o w i n g e q u a t i o n s :  13  H-€ H-f *P £H(I-€)/(0-64+€)] =  e  S u b s t i t u t i o n o f equations 13 and 14 i n t o t h e Stokes' Law e q u a t i o n g i v e s  V  s  =  r  r  15  ~  —  18/xexp [ 4 l ( l - € ) / ( 0 - 6 4 + €)j  so t h a t  V  0  "  exp [41 ( l - € ) / ( 0 - 6 4 + € ) j  The agreement o f t h i s e q u a t i o n w i t h e x p e r i m e n t a l d a t a i s a g a i n good a t low Reynolds numbers b u t n o t a t h i g h Reynolds numbers. Richardson  and Z a k i ( 4 ) have developed  an e q u a t i o n based on the  dynamic e q u i l i b r i u m o f i n d i v i d u a l p a r t i c l e s as a f u n c t i o n o f the f l u i d i z e d bed and apparatus p r o p e r t i e s .  The e q u a t i o n i s based  a n a l y s i s development t o determine  on a - d i m e n s i o n a l  the v a r i a b l e s which a r e important and  how they are grouped, and a comprehensive group o f experiments t o determine  t h e powers on the v a r i o u s f u n c t i o n a l groups.  a n a l y s i s a n t i c i p a t e d the f o l l o w i n g groupings:  Dimensional  •8.  V  —  V  s  =  f  T  [<i^P  '  L  0  »  /J.  d —  D  1  t €  17  J  The e x p a n s i o n e q u a t i o n d e v e l o p e d was t h e f o l l o w i n g :  n  s  V  —  =  €  18  Vi where Vj i s t h e v e l o c i t y o b t a i n e d by e x t r a p o l a t i n g  the log-log p l o t of  s u p e r f i c i a l l i q u i d v e l o c i t y v e r s u s p o r o s i t y t o a p o r o s i t y o f one. The power  n  i s a f u n c t i o n o f b o t h t h e f l o w regime and t h e a p p a r a t u s :  n=4G5+  I95(d/D)  Re < 0-2 0  n= [ 4 4 5 + I8(d/D)] Re " ''  O2<Re < 2 0 0  0  0  0  n = 4-4 5 ReJ*  n =  19  20  200<Re < 500 0  2-39  Re. > 5 0 0  o  2  2  1  ?  --  c c  A l s o , i t has been shown b y R i c h a r d s o n and Zaki;- t h a t t h e f o l l o w i n g relationship holds:  »og V0 ' =  log Vj  +  d/D  23  The c o r r e l a t i o n s o f R i c h a r d s o n and Z a k i have been s u b j e c t e d t o rigorous  t e s t s b y comparing them w i t h e x t e n s i v e l i q u i d f l u i d i z a t i o n d a t a  from numerous l i t e r a t u r e s o u r c e s . a c c o r d i n g t o Leva ( 5 ) . predicting to  € = 1.0  E x c e l l e n t agreement has been o b t a i n e d ,  These c o r r e l a t i o n s a r e t h e most r e l i a b l e method o f  e x p a n s i o n o f l i q u i d f l u i d i z e d beds and a r e v a l i d v i r t u a l l y up .  9Lev/is and Bowerman (8) developed an e q u a t i o n o f t h e  •7  form  V (k'€ ')  =  2k  b  0  where k' and b' a r e s p e c i f i c c o n s t a n t s .  This equation i s intended to  t a k e i n t o account the e f f e c t s t h a t p a r t i c l e s may  e x e r t on each o t h e r .  As  t h e s e e f f e c t s s h o u l d decrease as i n t e r p a r t i c l e spaces i n c r e a s e , t h e o c c u r r e n c e o f bed voidage i n the r e l a t i o n s h i p shown above appears t o be reasonable. V  0  In t h e absence o f w a l l e f f e c t , when a c c o r d i n g t o e q u a t i o n 23  = Vj , e q u a t i o n 2k i s o b v i o u s l y e q u i v a l e n t t o e q u a t i o n 18 w i t h b'  to  n-1.  C  F r i c t i o n a l P r e s s u r e Drop i n a F l u i d i z e d  equal  Bed  The f r i c t i o n a l p r e s s u r e drop r e l a t i o n s h i p i n a f l u i d i z e d bed i s developed from the s u p p o s i t i o n t h a t t h e p a r t i c l e s i n a f l u i d i z e d bed e n t i r e l y supported by t h e f l u i d .  are  That i s , t h e w e i g h t g r a d i e n t o f the s o l i d  bed i s e q u a l t o t h e f r i c t i o n a l p r e s s u r e g r a d i e n t t h r o u g h the bed caused  by  mass f l o w :  Ap  -  Mg — A£ g s  or  [p -p)  25  %  c  Ape  g  L  g  c  These e q u a t i o n s were e x p e r i m e n t a l l y c o r r o b b r a t e d f o r numerous s o l i d s f l u i d i z e d i n l i q u i d s by W i l h e l m and Kwauk ( l ) . Most o f W i l h e l m Kwauk's d a t a agree w i t h t h e t h e o r e t i c a l e q u a t i o n w i t h i n 57°'  The  and results  o f R i c h a r d s o n and Z a k i (k) t e n d t o i n d i c a t e t h a t the above e q u a t i o n h o l d s f o r beds composed o f p a r t i c l e s w h i c h have a r e l a t i v e l y low d e n s i t y and i n which the p a r t i c l e t o column diameter r a t i o i s s m a l l .  10. F o r beds-composed o f l a r g e p a r t i c l e s o r v e r y heavy p a r t i c l e s , 26  c h a n n e l i n g , b r i d g i n g and o t h e r a g g r e g a t i v e e f f e c t s o c c u r and e q u a t i o n does not agree t o o w e l l w i t h experiment.  F i g u r e 1 shows a graph  relating  the f r i c t i o n a l p r e s s u r e drop a c r o s s a p a r t i c u l a t e l y f l u i d i z e d bed w i t h v e l o c i t y through t h e bed.  A l s o shown i s a diagram o f t h e p r e s s u r e drop  per u n i t l e n g t h through a f l u i d i z e d  D.  S t r a t i f i c a t i o n and  bed.  Classification  Ah i m p o r t a n t problem which had n o t been worked on e x t e n s i v e l y i n the p a s t i s s t r a t i f i c a t i o n and c l a s s i f i c a t i o n i n p a r t i c u l a t e l y f l u i d i z e d beds composed e i t h e r o f one m a t e r i a l o r o f a number o f m a t e r i a l s . Work i n the f i e l d o f s t r a t i f i c a t i o n by s i z e i s b e i n g c a r r i e d on a t t h e p r e s e n t time i n t h i s department and s h o u l d p r o v i d e some u s e f u l i n f o r m a t i o n . R i c h a r d s o n and Z'aki (k) showed t h a t i f a f l u i d i z e d bed i s composed o f p a r t i c l e s o f two d i s t i n c t s i z e ranges, t h e n the s m a l l p a r t i c l e s w i l l  form  a bed on top o f the bed o f l a r g e p a r t i c l e s , and t h e r e w i l l be a d i s t i n c t i n t e r f a c e between the two beds.  I n a f l u i d i z e d bed composed o f a  c o n t i n u o u s range o f p a r t i c l e s i z e s the s o l i d s w i l l t e n d t o arrange themselves of  the bed.  so t h a t t h e g r e a t e s t ' amount o f f i n e s w i l l be i n t h e upper p a r t Verschoor  (9)  observed t h a t s t r a t i f i c a t i o n of p a r t i c l e s w i l l •  o c c u r even f o r v e r y narrow s i z e ranges  (100  t o 120  mesh).  Andrieu  (lO)  s y s t e m a t i c a l l y s t u d i e d s t r a t i f i c a t i o n by s i z e i n w a t e r - f l u i d i z e d beds and found t h a t the p o r o s i t y o f t h e f l u i d i z e d bed i n c r e a s e d from the bottom t o the top o f the f l u i d i z e d bed, 'a c o n c l u s i o n w h i c h he deduced from observed decrease  the  i n the. p r e s s u r e g r a d i e n t and hence t h e apparent o r b u l k  d e n s i t y o f the f l u i d i z e d bed.  T h i s f i n d i n g i s c o n s i s t e n t w i t h Hancock's  f i r s t observation, previously discussed.  (2)  11  fixed b e d *  fluidized bed  -  log (Ap ) F  minimum velocity for fluidization (V ) mf  log ( V ) s  T y p i c a l F l u i d i z a t i o n curve r e l a t i n g f r i c t i o n a l p r e s s u r e l o s s a c r o s s f l u i d i z e d "bed t o s u p e r f i c i a l liquid velocity.  Figure l a .  tronsport fixed bed —  fluidized bed  log (Ap ) L F  * *mf =  log(V ) s  Figure l b .  T y p i c a l f l u i d i z a t i o n curve r e l a t i n g f r i c t i o n a l p r e s s u r e l o s s p e r u n i t h e i g h t a c r o s s a bed o f p a r t i c l e s to s u p e r f i c i a l l i q u i d velocity.  12.  E.  Theoretical Derivation f o r Inversion The  d r i v i n g force f o r segregation  o r s t r a t i f i c a t i o n o f two groups o f  p a r t i c l e s i n a p a r t i c u l a t e l y f l u i d i z e d bed' i s assumed t o be t h e d i f f e r e n c e i n b u l k d e n s i t y o f t h e beds formed by each group o f p a r t i c l e s when t h e y are i n d i v i d u a l l y s u b j e c t e d t o t h e g i v e n s u p e r f i c i a l l i q u i d v e l o c i t y .  The  b u l k d e n s i t y o f a f l u i d i z e d bed i s g i v e n by  PQ  The  = (i-«)/>s  €  +  27  P  d i f f e r e n c e i n b u l k d e n s i t y between two beds composed o f p a r t i c l e s  1  and 2 , r e s p e c t i v e l y , i s t h e r e f o r e 28  Many b e d e x p a n s i o n f u n c t i o n s e x i s t , b u t t h e s i m p l e s t e q u a t i o n which r e p r e s e n t s  e m p i r i c a l d a t a b e s t o v e r t h e whole range e n c o u n t e r e d i s  t h a t o f R i c h a r d s o n and Z a k i (k), w h i c h i s  29  o r from e q u a t i o n 2 3 , 30  The  and t h a t  f r e e s e t t l i n g v e l o c i t y i s given by equation  v  l/m  - k (/>,-/» M  0  d  11, which i s  (3-m)/m  Combining e q u a t i o n s 30 and 3 1 ,  = 10  -d/D  ,  II  *IP,-P)  l/m  d  (3-m)/m  n  13As p a r t i c l e s 1 and 2 a r e s u b j e c t e d t o t h e same s u p e r f i c i a l l i q u i d v e l o c i t y , i t follows that dj  J_  k'|lO {p -p)  3-m,  €,' = k'ilO  'd,  s}  dig  3-m  I  d  (Psz-P)  2 2  2  €  2 2  33  I f t h e assumption i s made t h a t b o t h groups o f p a r t i c l e s f l u i d i z e d w i t h i n the same f l o w r e g i m e , t h a t i s , i n a g i v e n r e g i o n o f Re  Q  r e g i o n o r t h e Newton r e g i o n ) , t h e n  and n^_ = n •  k^" = k " ,  = m  2  These c o n d i t i o n s c a n be a p p r o x i m a t e l y  2  ( e . g . t h e Stokes' 2  produced experimentally.  Also i f  i t can be assumed t h a t t h e p a r t i c l e s a r e s m a l l r e l a t i v e t o t h e column diameter, then 1 0 ^ 2 " ^ l V equation  D n  i s e q u a l t o 1.0 a p p r o x i m a t e l y .  Simplifying  33 a c c o r d i n g l y , /  «2 = |(/) €  where / =  (p -p)/{p sl  .  3*  U)  -p)  sZ  S u b s t i t u t i n g equation  J / m n , .l3-m)/mn  < I  r = d, / d  , and  2  > I  34 back i n t o 28.we have I  R  (3-rri)/mn  />B.-/>B2-(A|-/»[(I -  ^> - M ' - ^mn-l)/mn>]  Inspection o f equation  35 w i l l r e v e a l t h e f o l l o w i n g i n f o r m a t i o n :  (1)  3 5  suppose t h a t - _(3-m)/mn  i  ' y  *  e  ' '~ (  /-n-IVm.  >  3 6  The b u l k d e n s i t y o f bed 1 w i l l t h e n be l e s s t h a n t h e b u l k d e n s i t y o f b e d 2, and t h e l a t t e r w i l l occupy t h e bottom s e c t i o n o f t h e column w i t h b e d 1 above i t . 'This i s c l a s s i f i c a t i o n b y d e n s i t y . (2)  suppose t h a t (3-m)/mn  . 1-1  >  «I<I-  ^ ,  M  N  .  1  )  /  M  N  )  37  14. The h u l k d e n s i t y o f bed 2 w i l l be l e s s then the b u l k d e n s i t y o f bed 1,  and  thus bed 2 w i l l occupy the top o f the column w i t h bed 1 i n the bottom section. (3)  suppose t h a t  .  (3-m)/mn  ' - y  =  £  |  (  |  -  £».-•)/.»  1  3 8  The b u l k d e n s i t y o f bed 1 e q u a l s the b u l k d e n s i t y o f bed 2 and a c c o r d i n g t o Hancock ( 2 )  t h e r e s h o u l d be p e r f e c t m i x i n g o f the two s e t s o f p a r t i c l e s , ! ,  p r o d u c i n g one homogeneously f l u i d i z e d bed. p a r t i c u l a r value of  €|  I f t h i s c o n d i t i o n holds at a  , then f o r v a l u e s o f € |  l e s s then t h i s v a l u e ,  s i t u a t i o n 1 w i l l o c c u r and bed 2 w i l l be a t the bottom and bed 1 a t t h e .top.  S i m i l a r l y f o r values of  s i t u a t i o n 2 w i l l occur. by f i g u r e  €|  g r e a t e r than t h i s p a r t i c u l a r  €|  ,'  These s i t u a t i o n s are r e p r e s e n t e d d i a g r a m a t i e a l l y / c  2.  For s i t u a t i o n 3 f o o c c u r , the b u l k d e n s i t y d i f f e r e n c e must be 35,  t o z e r o , and t h e r e f o r e by e q u a t i o n  €,  =  1  -x  y l / m n (3-m)/mn r  The c o r r e s p o n d i n g v a l u e o f g i v e n by e q u a t i o n 3 4 ,  €  2  f°  equal  r  _  y  t h i s p a r t i c u l a r value of  39  is  o r by a p p l y i n g the c o n d i t i o n o f zero b u l k d e n s i t y  d i f f e r e n c e to equation 2 8 , which then s i m p l i f i e s to  S i n c e the v o i d f r a c t i o n i n a p a r t i c u l a t e l y f l u i d i z e d bed can v a r y o n l y from € f t o 1, a r e v e r s a l from s o r t i n g t o s i z i n g w i l l o c c u r i n such a m  15-  BED  I  EQUATIONS  BED  2  EQUATIONS  CASE  A  2  ~7[  CASE__3_ PERFECT MIXING  CASE  I  ~A  A  ' A  N  \  -A  \ \ \  •ftrft.  > 0  \  \  LOG(POROSITY) Figure 2.  P r e d i c t i o n o f F l u i d i z e d Bed I n v e r s i o n  16.  bed during i t s expansion only i f  €  where  €| and  respectively. region (m=l, of  r  and  mf  < €,  r  < €  and  2  y  are such that  < I  € a r e calculated from equations 39 and 3 * (or ko) 2  Beare ( l l ) has produced a p l o t f o r the laminar or Stokes  1  n=U.65) r e l a t i n g inversion conditions with p a r t i c u l a r values y  .  This' p l o t i s given i n Appendix I.  appears for the Newton region (m=2,  A s i m i l a r p l o t also  n=2«39) which can be compared to the  laminar p l o t .  F.  Mixed Bed Height Predictions Numerous workers have correlated l i q u i d f l u i d i z e d bed expansion  equations f o r uniform p a r t i c l e s , but very l i t t l e work has been done on c o r r e l a t i n g expansion data for f l u i d i z e d beds composed of mixed sizes or beds composed of more than one  s o l i d material.  Lewis and Bouerman (8)  studied f l u i d i z e d beds of non-uniform sized p a r t i c l e s and found that the performance of the system could be accurately predicted from equations f o r the constant  diameter spheres.  This can be done by using the equations to  calculate the performance f o r each narrow p a r t i c l e size f r a c t i o n , then summing the contributions f o r a l l f r a c t i o n s to give the o v e r a l l bed expansion.  I f a f l u i d i z e d bed i s composed, of a number of d i f f e r e n t  materials and i t can berassumed that the f l u i d i z e d bed i s separated  into  d i s t i n c t layers of d i f f e r e n t materials, then the contributions f o r each section can be s i m i l a r l y summed to give the o v e r a l l average porosity of the mixture as a function of v e l o c i t y . Suppose a f l u i d i z e d bed i s composed of W| density p^^  , vv  2  poiiinds of p a r t i c l e s of  pc^unds of p a r t i c l e s of density  p^  >  811(1  so on.  T&en  the volume of each section i n the f l u i d i z e d bed i s given by the following  equation,  i n w h i c h t h e s u b s c r i p t i r e f e r s t o any i n d i v i d u a l s e c t i o n i :  = T-L-  VI  '  The  x  i  €  I -  '  Psi  Ui  t o t a l volumes o f t h e b e d i s t h e sum o f t h e volume o f t h e d i f f e r e n t  Ejections.  *i  1  The  rsi  average p o r o s i t y o f t h e m i x t u r e i s t h e r a t i o o f volume o f l i q u i d i n  the b e d t o t h e t o t a l volume o f t h e f l u i d i z e d bed.  € = m  ' -  g  i  ^ Psi  Psi i  x  k 3  —  Ps y  _ i i _  _ <T  Psi  X  | !  —  ~ \ €  The  *L  x  L  .  X  _  Wj J  kk  .  Psi  above e q u a t i o n s h o u l d h o l d f o r a f l u i d i z e d b e d which i s s e p a r a t e d i n t o  l a y e r s , b u t n o t n e c e s s a r i l y when t h e m a t e r i a l s a r e mixed t o g e t h e r . here p o s t u l a t e d  t h a t e q u a t i o n (kk) a l s o a p p l i e s t o mixed beds.  It is  Thus t h e  average p o r o s i t y and t h e h e i g h t o f a f l u i d i z e d b e d o f mixed s p e c i e s c a n be p r e d i c t e d from a knowledge o f t h e p o r o s i t y - v e l o c i t y r e l a t i o n s h i p s o f t h e i n d i v i d u a l components. Hoffman, L a p i d u s and E l g i n (12) have s t u d i e d t h i s a s p e c t o f f l u i d i z a t i o n and have p r o p o s e d an e q u a t i o n f o r t h e o v e r a l l b e d e x p a n s i o n o f a b e d o f mixed s i z e s .  T h e i r work i s c o n c e r n e d w i t h p a r t i c l e s o f t h e  same m a t e r i a l b u t d i f f e r e n t s i z e s , d u r i n g t h e e x p a n s i o n o f w h i c h t h e p a r t i c l e s a r e c o m p l e t e l y s e g r e g a t e d by s i z e and do n o t mix. The e q u a t i o n t h e y propose i s e q u i v a l e n t t o  18.  45  where X: = W; / W,m •This e q u a t i o n  = weight f r a c t i o n of s i z e i i n the s o l i d  i s e q u i v a l e n t t o e q u a t i o n 43 o r 44 f o r c o n s t a n t  mixture.  density  s o l i d s , b u t E l g i n e t a l make t h e statement t h a t i t does n o t h o l d f o r f l u i d i z e d beds when t h e l a y e r s mix. The b a s i c assumption u n d e r l y i n g E l g i n ' s work i s t h a t a unique relationship particulate  e x i s t s between t h e s l i p v e l o c i t y and t h e h o l d up f o r any system.  The s l i p v e l o c i t y i s t h e r e l a t i v e v e l o c i t y between  the p a r t i c l e s and t h e f l u i d and i s g i v e n by  F o r a b a t c h - f l u i d i z e d bed, Vp  = 0  •  and t h e s l i p v e l o c i t y i s e q u i v a l e n t  t o t h e average i n t e r s t i t i a l v e l o c i t y i n t h e bed.  19-  APPARATUS  A.  General The equipment was designed so that a wide range of flows could be  pumped through the test section. displayed i n figure 3 loops.  A schematic diagram of the apparatus i s  The equipment i s an open system composed of two  The primary loop consists of the storage tank, pump and heat  exchanger which maintains the f l u i d at room temperature. c i r c u i t consists of the flow- and temperature-measuring  The secondary section and the  test column. (a)  Pump  The test f l u i d i s c i r c u l a t e d by a Paramount close-coupled type U 1 - 3 - 2 pump driven by a 3 h.p. motor operating at 3450 rpm. The pump was provided with a John Crane mechanical seal to prevent a i r being sucked into the pump.  The capacity of the pump i s 50 U.S. gallons per minute  against a t o t a l head of seventy feet of water and was supplied by Pumps and Power Limited, of Vancouver, B.C. (b)  Piping  The piping i s 2-inch I.D., type L, Noranada copper seamless pipe, and the f i t t i n g s used throughout were a l l copper or brass.  A l l shut-off  valves except the flow control valves are 2-inch brass gate valves.  The  two large control valves are globe valves and the small control valves are needle valves. (c)  Heat exchanger  The heat exchanger which removes heat generated by the pump i s a seven-tube b a f f l e d , counter-current type.  The cooling medium was on the  s h e l l side and the test f l u i d was i n the tubes.  In runs with low  v i s c o s i t y f l u i d s the temperature of the effluent l i q u i d was controlled by adjusting the cooling water throughput.  With high v i s c o s i t y f l u i d s ,  20.  A-test  section - 2 " l . D . X 5' long  B-calming  section - 152"  C - e x p a n s i o n exit D-equalizing E-  long  i i i i  section  entry  section  thermometer  F - capillary  flow  G G ,G -orifice | f  2  3  meter meters  B  HXH  1 k>4  heat  l  I  I  I  I i  • >  '[ exchanger  pump F i g u r e 3- Schematic Diagram o f A p p a r a t u s .  21.  where the c o n t r o l l i n g r e s i s t a n c e was  on the tube s i d e , the temperature  c o n t r o l l e d by a d j u s t i n g the flow through  the p r i m a r y  circuit.  was  Thermometer  E i n f i g u r e 3 - s used to measure the e f f l u x temperature t o the t e s t s e c t i o n , wa  (d)  Flow Meters  The  l i q u i d - m e t e r i n g s e c t i o n c o n s i s t s o f t h r e e sharp-edged o r i f i c e meter  runs and a c a p i l l a r y flow meter. 50 diameters  A c a l m i n g l e n g t h upstream o f at l e a s t  and downstream o f a t l e a s t 10 diameters  was  a l l o w e d on  meter runs, and a l l o r i f i c e meters were f i t t e d w i t h c o r n e r t a p s . c a p i l l a r y flow meter c o n s i s t s o f a 0 . 2 5 - i n c h  dianeter, stainless  orifice  The steel  tube 4 ' 7 "  l o n g w i t h a c a l m i n g l e n g t h upstream, and downstream o f 100  diameters  and  50 p i p e diameters  the flow meters was air-filled  respectively.  measured by means of one  pipe  The p r e s s u r e drop a c r o s s o f two manometers, a 6 0 - i n c h  i n v e r t e d U-tube manometer f o r r e l a t i v e l y  small pressure  drops,  and a 3 0 - i n c h m e r c u r y - f i l l e d U-tube Merian manometer f o r h i g h e r p r e s s u r e drops.  The  tap l e a d s from the meters are connected  so t h a t the p r e s s u r e drop a c r o s s any meter may manometers.  to a manifold  system,  be measured by one  or both  Vents were p r o v i d e d a t a l l h i g h p o i n t s . t o a l l o w complete  removal o f a i r from the l i n e s and mercury t r a p s were f i t t e d t o the mercury manometer.  P e r t i n e n t d e t a i l s as t o s i z e s o f o r i f i c e s are g i v e n i n t a b l e I.  Table  I  O r i f i c e Meter S i z e s Meter  Run  O r i f i c e Diameter inches  Run  Diameter inches  1  O.85  2.0  2  0.40  1.0  3  0.20  0.5  22. (e)  Test F l u i d s  The  test f l u i d  used f o r l a m i n a r  flow runs was  p o l y e t h y l e n e g l y c o l E-QOOO, s u p p l i e d by Dow Michigan. liquid. ments:  F o r the i n t e r m e d i a t e  an aqueous s o l u t i o n o f  Chemical Company, o f  r e g i o n runs, water was  used as the  test  These l i q u i d s were used because they meet the f o l l o w i n g r e q u i r e they are  ( l ) Newtonian, (2) n o n - c o r r o s i v e ,  to b a c t e r i a l a t t a c k , (1+)  possess  are ( 5 )  (6)  t r a n s p a r e n t , and  (3)  s t a b l e and  Viscosimeter  are not t o x i c .  (Ch.E.2002) c u r v e s f o r these  glycerol solutions.  resistant  h i g h v i s c o s i t y at h i g h g l y c o l c o n c e n t r a t i o n s , The Newtonian p r o p e r t i e s o f  the p o l y e t h y l e n e g l y c o l s o l u t i o n s were checked by comparing the  for  Midland,  s o l u t i o n s w i t h those  No non-Newtonian b e h a v i o u r  c o u l d be  Stormer obtained  detected  a f t e r the g l y c o l s o l u t i o n s were v i o l e n t l y s t i r r e d f o r a l o n g time. i n c r e a s e c o r r o s i o n r e s i s t a n c e , sodium dichromate and added.  These c h e m i c a l s  e f f e c t i v e l y stopped  To  sodium hydroxide  any c o r r o s i o n but caused  g l y c o l s o l u t i o n to t u r n a dark orange-brown c o l o r .  The  s o l u t i o n used  were the was  40yo by weight o f p o l y e t h y l e n e g l y c o l i n water, which had a v i s c o s i t y o f about 0 . 0 9 0  l b . / f t . s e c and a d e n s i t y o f 67.k  lb./ft.  3 a  t 70°F.  B.  Test  Section  The test section consisted of one of two t e s t columns, an ordinary 2-inch I.D. and 5-foot long i n d u s t r i a l Pyrex glass tube and a column constructed of perspex containing pressure taps at numerous positions up the column.  The perspex column was also 2-inch I.D. and  5 feet long.  A detailed schematic diagram of a pressure  i n figure k.  Each pressure tap was connected into one of two headers  i n such a way that f r i c t i o n a l pressure  tap appeared  drop measurements could be made  across alternate taps or from the bottom tap to any other tap. , The headers were connected to a 100-cm. long 8-mm. carbon tetrachloride.  glass U-tube containing  A diagram of the d i f f e r e n t i a l pressure measuring  system appears i n figure 6. The column attachment flanges were constructed  so that the column  could be aligned v e r t i c a l l y , and so that the calming section and column j o i n t could be properly aligned.  I t was found that the quality of  f l u i d i z a t i o n was affected markedly by these two factors.  Non-alignment  of column and calming section caused large eddies and channeling f l u i d i z e d bed.  i n the  Large scale c i r c u l a t i o n up one wall of the column and  down the other resulted from not having the column v e r t i c a l . The support f o r the f l u i d i z e d bed was a 16 mesh stainless s t e e l screen on top of which was a 2-inch deep f i x e d bed of lead spheres. The diameter of the spheres used i n a p a r t i c u l a r run was determined by the size and density of the material being f l u i d i z e d i n the .column during the run.  I f the lead spheres were too large, they caused channeling i n  the f l u i d i z e d bed and i f they were too small they f l u i d i z e d and disrupted the bed being studied.  The equalizing entry section consisted  of a 152-inch long section of straight copper pipe and a concentric  2k.  annulus d i s t r i b u t o r t o the s t r a i g h t p i p e . i s shown i n f i g u r e '5.  A diagram o f t h i s  distributor  The e x p a n s i o n e x i t s e c t i o n i s a s i m p l e o v e r f l o w •  from t h e 2 - i n c h diameter p i p e i n t o a l a r g e r chamber. s e c t i o n i s a l s o shown i n f i g u r e  5-  •  A diagram o f t h i s  25-  scale  F i g u r e k.  l"=  2"  Schematic Diagram of  a S e c t i o n a l V i e v o f the Column,  (glass backing flange omitted)  26.  F i g u r e 5-  Diagram o f E n t r y Section t o and E x i t S e c t i o n from Column.  27-  Key t o F i g u r e 4 1.  plastic  "0"-ring.  2.  p l u g w i t h l / l b " hole d r i l l e d through i t .  3-  150 T y l e r mesh s c r e e n c o v e r i n g p r e s s u r e t a p i n l e t .  4.  2 - i n c h I.D. e n t r y s e c t i o n t o column.  5-  3 / 8 " I m p e r i a l compression n u t .  6.  l / 4 " p i p e t o 3 / 8 " compression' I m p e r i a l c o n n e c t o r .  7-  2 - i n c h I.'.D. p^xspex column. . 1 1 .  8.  packed bed o f l e a d spheres.  9-  16 mesh s t a i n l e s s s t e e l support  10.  rubber  11.  b r a s s a d a p t e r f l a n g e f o r support  12.  brass flange.  13.  l / V ' i n c h I.D. copper t u b i n g .  lk.  rubber  screen.  gasket. screen.  gasket.  Key t o F i g u r e 5 1.. b r a s s c o n n e c t o r f l a n g e . 2.  2 - i n c h I.D. column e x t e n s i o n .  3.  2 - i n c h I.D. r e t u r n l i n e t o s t o r a g e  k.  4 - i n c h I.D. e x p a n s i o n  5>& 6 .  tank.  section.  alignment a p p a r a t u s f o r sampler used by  7-  2 - i n c h I.D. l i n e from f l u i d m e t e r i n g  8.  2 - i n c h I.D. c a l m i n g s e c t i o n below column.  9.  6 - i n c h I.D. e x p a n s i o n  section.  section.  B.Pruden ( 1 5 ) -  COLUMN AND PRESSURE TAPS MANOMETER  TAPS 4' APART  HEADERS  TAPS  2'  APART 3  TAPS r APART  spring pinch clamps F i g u r e 6.  Diagram o f D i f f e r e n t i a l P r e s s u r e Measurement System.  TJ  29-  EXPERIMENTAL PROCEDURES A.  Operating  Procedure  F o r each m i x t u r e o f s o l i d s t e s t e d t h e p r o c e d u r e was as f o l l o w s . Each component was r u n s e p a r a t e l y t o determine  t h e s i n g l e component  p r o p e r t i e s ; t h e n t h e two components were mixed t o g e t h e r and r u n t o determine how t h e m i x t u r e f l u i d i z e d .  D u r i n g each o f t h e t h r e e runs f o r each p a r t i c u l a r  m i x t u r e , e x p a n s i o n d a t a and f r i c t i o n a l p r e s s u r e l o s s d a t a were o b t a i n e d . V i s u a l o b s e r v a t i o n s o f t h e b e d were a l s o r e c o r d e d . 1.  Expansion  data.  At t h e v a r i o u s f l o w r a t e s a f t e r e q u i l i b r i u m was o b t a i n e d , t h e b e d h e i g h t , room t e m p e r a t u r e , recorded.  f l u i d temperature  and manometer r e a d i n g s were  When t h e t e s t f l u i d was p o l y e t h y l e n e g l y c o l t h e b e d took about  5 m i n u t e s t o come t o e q u i l i b r i u m a f t e r t h e f l o w r a t e was changed.  Water  f l u i d i z e d beds r e q u i r e d a much s h o r t e r time t o come t o e q u i l i b r i u m . 2.  F r i c t i o n a l p r e s s u r e drop d a t a .  At v a r i o u s l i q u i d f l o w r a t e s and b e d h e i g h t s , f r i c t i o n a l - p r e s s u r e drop p r o f i l e s were determined by measuring  the difference' i n pressure  between v a r i o u s p r e s s u r e t a p s and a base p r e s s u r e t a p . Manometers were b l e d b e f o r e any r e a d i n g s were t a k e n , t o ensure t h a t no a i r was i n t h e lines.  When t h e t e s t f l u i d was p o l y e t h y l e n e g l y c o l , t h e manometer took  about 15 m i n u t e s t o come t o e q u i l i b r i u m .  The sample c a l c u l a t i o n s p r e s e n t e d  i n Appendix I I f o r a p a r t i c u l a r m i x t u r e w i l l g i v e a good i n d i c a t i o n o f how d a t a were t a k e n and how t h e r e s u l t s were o b t a i n e d . B.  O r i f i c e Meter C a l i b r a t i o n s The method used f o r c a l i b r a t i o n o f t h e o r i f i c e s and t h e c a p i l l a r y  f l o w meter was a s f o l l o w s . temperature  A t steady s t a t e c o n d i t i o n s , when c o n s t a n t  and manometer r e a d i n g s p r e v a i l e d , t h e time t o c o l l e c t  fifty  30.  pounds o f f l u i d was  measured.  The  c a p i l l a r y f l o w meter was  only f o r high v i s c o s i t y polyethylene g l y c o l 1-inch  o r i f i c e meters were c a l i b r a t e d  solutions;  whereas the  against  Rej  section  and  ,  where  Re-j-is  C'  p,-p  2  L e a s t squares l i n e s o f the d a t a were c a l c u l a t e d . d e v i a t i o n s o f the d a t a from the l e a s t The c a l i b r a t i o n p l o t s  test  47.  P V  T  Maximum and mean  squares l i n e s are g i v e n i n T a b l e  appear i n F i g u r e s 7 and 8.  The  e q u a t i o n s f o r the o r i f i c e s meters are g i v e n i n T a b l e c a p i l l a r y f l o w meter was  calibrated  least 3-  i n the l a m i n a r flow  times the Reynolds number s h o u l d be a c o n s t a n t and e q u a l t o 1 6 .  actually  o f t h i s p r o d u c t as determined f r o m a l l c a l i b r a t i o n runs 15-395>  The main source o f the d i s c r e p a n c y can be  by r e f e r e n c e t o the e q u a t i o n f o r d e t e r m i n i n g the  f  E q u a t i o n 48  .Re  T  =  p. - p  —I—2  I±Q  P  r  L  7rD  range.  8L  g m  shows t h a t a s l i g h t e r r o r  diameter w i l l be g r e a t l y  1  C  factor The  was  understood  product;  I  4  2.  squares  A c c o r d i n g t o t h e o r y , f o r f l o w i n the l a m i n a r r e g i o n , the f r i c t i o n  average  solutions  C'/Rej  as  the f l u i d Reynolds i number i n the  fl  Re  ^-and  f o r both polyethylene g l y c o l  The d a t a f o r the o r i f i c e m e t e r s has been p l o t t e d  andWKater.  The  calibrated  J  U8  .  i n the measurement o f the c a p i l l a r y  m a g n i f i e d i n the  f-Re-f- product..  ,  The maximum and mean d e v i a t i o n s f o r the c a p i l l a r y f l o w meter are respectively  + 3 ' 5 $ and + 1.24$.  The c a l i b r a t i o n e q u a t i o n developed  meter by w e i g h t i n g the 8 0 d a t a p o i n t s e q u a l l y i s  V  c  = I-468 XlO"  6  P t  P g  49.  f o r the  Table 2 A c c u r a c y o f Flow Meter C o r r e l a t i o n s meter 111  mean d e v i a t i o n  maximum d e v i a t i o n  glycol  + 2-3$  + ivf,  1", g l y c o l  + 2-9$  +  9%  water  + 2.0$  +  9$  1", w a t e r  + 2-9$  -  2  >  lit 2  >  13$  Table 3 L e a s t Squares E q u a t i o n s f o r M e t e r s Polyethylene g l y c o l solution -!-" meter 1" meter Water  ' log-5*- = -O.93631og(  Re ) T  = -0.95231og( Re T  log  Re  )  -1.174 -0-5574  T  c" meter 1" meter  l o g p"gy= -1.064iog( Ref)i+jl.399 =-1.0l8 log(Re-r) + 1-848  l o g £L  Re  1 T  32.  10°  2  3  4  5  6  7  8  TEST  9  IO  1  SECTION  F i g u r e 7«  2  3  4  RE  Flow-Meter C a l i b r a t i o n Curve f o r Water.  5  6  7  8  9  |Q  2  2  i  r  I  I  1—i—I—i—i—i—i—r—  I  V ORIFICE  I  ORIFICE  o  POLYETHYLENE  GLYCOL  i I i I—I—I I I 5  6  7  8 9  |0  i 3  I 2  TEST Figure 8.  i  I  i L  3  SECTION  4  J  l_L  5  6  7  8 9  |0  RE  Flow-Meter C a l i b r a t i o n Curves, i'or P o l y e t h y l e n e  Glycol.  4  3h.  C.  Measurement o f V i s c o s i t y and D e n s i t y o f T e s t L i q u i d . The k i n e m a t i c v i s c o s i t y and f l u i d d e n s i t y o f t h e t e s t l i q u i d were  measured i n a c o n s t a n t t e m p e r a t u r e o i l b a t h w i t h a p r e c i s i o n t e m p e r a t u r e c o n t r o l l e r c a p a b l e o f c o n t r o l l i n g w i t h i n + 0.1°F.  scientific Samples  o f t h e t e s t l i q u i d were t a k e n a t t h e end o f each r u n , and d u r i n g t h e r u n f o r some o f t h e l o n g e r r u n s .  D u p l i c a t e measurements a t t h r e e t e m p e r a t u r e s ,  70, 75 and 80°F., were made o f t h e samples.  These t e m p e r a t u r e s were chosen  because t h e y b r a c k e t e d t h e t e m p e r a t u r e o f t h e f l u i d i n t h e t e s t column f o r almost a l l t h e r u n s . I The d e n s i t y o f t h e f l u i d s was measured u s i n g t h e d e p a r t m e n t a l s e t o f s t a n d a r d hydrometers  (Ch.E 1566).  These hydrometers a r e s t a n d a r d i z e d a t  60°F., whereas t h e p r e s e n t e x p e r i m e n t s were c o n d u c t e d i n ' t h e range o f 6o-80°F.  The p o s s i b l e e r r o r due t o t h e t e m p e r a t u r e e f f e c t was c h e c k e d  using  a W e s t p h a l b a l a n c e and- d i s t i l l e d w a t e r was employed as an a b s o l u t e s t a n d a r d . The hydrometers used were found t o g i v e t h e t r u e d e n s i t y w i t h i n + 0.2$. A Cannon-Fenske v i s c o s i m e t e r (R933> S i z e 300) tube was e s p e c i a l l y c a l i b r a t e d f o r measurement o f t h e h i g h v i s c o s i t y p o l y e t h y l e n e g l y c o l  solutions.  The tube was c a l i b r a t e d b y comparing t h e d i s c h a r g e t i m e f o r a tube (C-8) p r e v i o u s l y c a l i b r a t e d by De V e r t e u l l (13) w i t h t h e t i m e t a k e n i n t h e t e s t viscosimeter.  A p r e c i s i o n o f + 0.1$ was o b t a i n e d .  The p r o c e d u r e used f o r  f i l l i n g , c l e a n i n g and measuring t i m e s o f e f f l u x from tubes i s g i v e n i n t h e ASTM manual, DU1+5-53T (lU).  F o r t h i s t u b e , R933, w i t h i n t h e  recommended range o f k i n e m a t i c v i s c o s i t i e s (50-200 c e n t i s t o k e s ) , .the v i s c o s i t y i n c e n t i s t o k e s i s g i v e n by  u = 0-2546 t where t = e f f l u x t i m e i n seconds.  50 The c o r r e c t i o n f o r k i n e t i c energy i s  35-  n e g l i g i b l e p r o v i d e d the e f f l u x time i s g r e a t e r than 200  seconds, and  n e g l e c t e d i n t h i s case as the e f f l u x times were o f the o r d e r o f 400  D.  seconds.  Measurement o f P a r t i c l e D e n s i t y . P a r t i c l e d e n s i t y was measured u s i n g a number o f 25-ml.  bottles. the  was  Two  gravity  random samples were taken from the b u l k o f the m a t e r i a l and  p a r t i c l e d e n s i t y was measured by the f o l l o w i n g method.  were o b t a i n e d by f i r s t filling  specific  Measurements  w e i g h i n g the s p e c i f i c g r a v i t y b o t t l e empty, next  i t t w o - t h i r d s f u l l o f p a r t i c l e s and weighing, then f i l l i n g i t  c o m p l e t e l y and w e i g h i n g and f i n a l l y removing the p a r t i c l e s and w e i g h i n g the bottle f u l l  o f water.  From t h e s e weighings and the temperature i n the  laboratory,- the volume and the weight o f p a r t i c l e s c o u l d be determined,  and  thus the d e n s i t y o f the p a r t i c l e s .  E.  S i z i n g of P a r t i c l e s . Two methods were used t o measure the average diameter o f the p a r t i c l e s .  For  s p h e r i c a l p a r t i c l e s g r e a t e r than 2 mm.,  the m i c r o m e t i c method was. used.  A f t e r s c r e e n i n g the p a r t i c l e s through a s e r i e s o f s i e v e s developed by B. Pruden  ( 1 5 ) , a random sample o f 100 beads were measured u s i n g a  micrometer. measurements. the  The diameter u s e d f o r the beads was F o r beads o f 2 mm.  100  o r g r e a t e r the maximum d e v i a t i o n o f  measured d i a m e t e r s from the average was For  the average o f  about + 5-0$>.  s m a l l e r beads and p a r t i c l e s , the a r i t h m a t i c average o f two  a d j a c e n t s c r e e n s i z e s was  used.  The p r o c e d u r e was  as f o l l o w s .  About  500  grams o f p a r t i c l e s were s c r e e n e d between a d j a c e n t T y l e r s i e v e s o f the 4 t h r o o t s e r i e s i n a Ro-tap machine f o r 10-minute i n t e r v a l s . s c r e e n i n g , p a r t i c l e s which remained between the two  A f t e r the  first  s p e c i f i e d s i e v e s were  36. c o l l e c t e d and s c r e e n e d a g a i n .  The second, t h i r d and f o u r t h s c r e e n i n g s  c a r r i e d o u t on such p a r t i c l e s o n l y .  were  Each s c r e e n i n g was about 10 minutes  l o n g , a f t e r w h i c h t h e s i e v e s were r e g u l a r l y c l e a n e d .  I t was f o u n d t h a t  by about t h e f o u r t h s c r e e n i n g a n e g l i g i b l e amount o f m a t e r i a l was p a s s i n g through the smaller sieve.  37EXPERIMENTAL RESULTS A. Experiments 1.  Bed E x p a n s i o n  w i t h a S i n g l e Species  Measurements  To be a b l e t o p r e d i c t i n v e r s i o n and b e d expansions  of mixtures o f  two o r more s p e c i e s o f p a r t i c l e s u s i n g s i n g l e component e q u a t i o n s and d a t a , numerous runs were made w i t h s i n g l e component f l u i d i z e d beds. experiment of l o g V 21,  s  F o r each  on f l u i d i z a t i o n o f a p a r t i c u l a r s p e c i e s , c u r v e s were p l o t t e d against l o g €  .  T y p i c a l c u r v e s a r e shown i n f i g u r e s 13,  17,  27, 2 8 , 3 0 , and t h e s l o p e s and i n t e r c e p t s o b t a i n e d a r e g i v e n i n t a b l e s  k and 5-  The d a t a were c o r r e l a t e d i n t h i s form because o f i t s s i m p l i c i t y  and because R i c h a r d s o n and Z a k i (h) have shown t h a t i t works q u i t e w e l l o v e r t h e complete range o f f l u i d i z a t i o n . The r e s u l t s o b t a i n e d f o r t h e s l o p e s have been compared w i t h v a l u e s p r e d i c t e d by using the e m p i r i c a l equations t a b l e s 6 and J.  o f R i c h a r d s o n and Z a k i i n  The agreement i s good i n almost e v e r y  case.  T a b l e s 6 and 7 a l s o compare f r e e s e t t l i n g v e l o c i t y , V f r o m t h e e x p e r i m e n t a l i n t e r c e p t s and e q u a t i o n 2 3 , w i t h N^j  0  , as computed as c a l c u l a t e d  f r o m t h e s t a n d a r d d r a g c o e f f i c i e n t - R e y n o l d s number c o r r e l a t i o n s f o r f r e e s e t t l i n g o f spheres.  D i s c r e p a n c i e s between t h e r e s p e c t i v e v a l u e s , w h i c h  range as h i g h as 30$ b u t average l e s s than IU70, c o u l d be due t o t h e n o n - s p h e r i c i t y and n o n - u n i f o r m i t y o f t h e p a r t i c l e s . T r i a l r u n s were made w i t h a m i x t u r e o f alundum and g l a s s m i c r o - b e a d ( c a t a p h o t e ) p a r t i c l e s t o determine another  t h e e f f e c t on a f l u i d i z e d b e d o f h a v i n g  f l u i d i z e d b e d above o r below t h e p a r t i c u l a r b e d b e i n g s t u d i e d .  When t h e f l u i d i z e d m i c r o - b e a d b e d was above t h e alundum b e d t h e e x p a n s i o n c u r v e f o r t h e alundum d e v i a t e d s l i g h t l y from t h e c u r v e o b t a i n e d when t h e r e was n o t  b e d above.  As c a n be seen i n f i g u r e 9 , t h e alundum b e d i s  Table 4 Summary o f F l u i d i z a t i o n R e s u l t s f o r P a r t i c l e s i n Water  Wo.  Parti cles d>-mm.  rs  Re > cm.  J  0  Material  >  f t / sec  log(Vj )  n  Figure  1  1.08  2.91  Ballotini  198  0.590  -0.250  2.56  0.021  29  2  O.767  3-95  Alundum  129  0.543  '-0.280  2.87  0.015  • .27  3  0.645  3-95  Alundum  97.8 O.516  -0.310  2-95  0.013  28  4  0.912  3-95  Alundum  171  0.606  -0.235  2.76  0.018  31  5  I.83  2.92  Ballotini  511  0-904  -0.080  2.31  O.O36  29  6  1.08  3.17  Crystalon  195  0.582  -0.256  2-77  0,021  27  7  0.542  4.50  NickelGlass  89-3 0.532 '  -O.285  3-02  0.011  30  Table 5  Summary o f F l u i d i z a t i o n R e s u l t s f o r P a r t i c l e s i n P o l y e t h y l e n e  No.  Part i c l e s d,mm  ^  s  cm  3  Material  Re  log(Vj )  0  Glycol  Figure  a•  ft/sec.  8  0.456  8.90  Nickel  O.025  0.0236'  -1.635  4-75  0.009  13  9  0.645  3-95  Alundum  0.031 '  0.0205  -1.700  5.36  0.013  17  10  2.28  2.73  Ballotini  O.507  0.0959  -I.O63  4.59  0.045  13  11  1.08  2.91  Ballotini  0.077  O.O3O9  -1.530  ' 5.13  0.021  17  12  3-15  7.83  Steel  5.97  O.77O  -O.185  4.13  0.062  21  13  2.05  Lead  2.04  0.404  -0.433  4.19  0.040  21  14  0.  NickelGlass  0.0168  O.OI63•  -1.800  4.84  0.011  24  542  11-33 4.50  40.  Table 6  Comparison o f R e s u l t s w i t h R i c h a r d s o n - Z a k i and F r e e S e t t l i n g C o r r e l a t i o n s . Water  Re  No.-  0  v  Experiment 1  198.0  2  129-1  3  97-8  Correlation  '  .  o ft/sec. Expt. Correl'n  n Expt.  Correl'n  210.0  0.590  0.626  2.56  2-53  144  0.543  0.606  2.87  2.83  102  0.516  0.538  2-95  2-97  4  171  198  0.606  0.701  2.76  2.80  5  511  537  0.904  0.951  2.31  2.38  6  195  218  O.582  0.651  2.77  2.72  7  89-3  82  0.532  0.487 •  3-02  2.98  •  41.  Table 7  Comparison o f R e s u l t s w i t h R i c h a r d s o n - Z a k i and Free S e t t l i n g C o r r e l a t i o n s . Polyethylene Glycol. V  ReNo.  Experiment C o r r e l a t i o n  n  ft/sec.  Experiment C o r r e l a t i o n  Experiment C o r r e l a t i o n  8  0.025  0.022  0.0236  0.0207  4.75  4.83  9. ' .  0.031  0.023  0.0205  0.0153  5.36  4.90  10  0.507  0-575  O.0959  O.IO87  4.59  5.20  11  0.077  0.068  0.0309  0.0274  5.13  5.07  12  5-97  4.90  O.77O  0.633  4.13  4.72  13  2.04  2-39  0.404  0.474  4.19  4.74  14  0.0168  O.OI36  O.O163  0.0132  4.84  4.86  42.  compressed s l i g h t l y by the presence o f the micro-beads ( c a t a p h o t e ) , b u t t h i s e f f e c t d i s a p p e a r s as t h e bed i s expanded. was  Because the d e v i a t i o n  v e r y s m a l l i t i s assumed t h a t h a v i n g one f l u i d i z e d bed on t o p o f  a n o t h e r doesn't  i n f l u e n c e the f l u i d i z a t i o n o f the l o w e r bed.  The  e x p a n s i o n c u r v e f o r the c a t a p h o t e bed was not i n f l u e n c e d a t a l l by t h e alundum bed f l u i d i z e d below i t .  having  Thus s i n g l e component d a t a can be  used t o determine o v e r a l l bed e x p a n s i o n s f o r m i x t u r e s , p r o v i d e d t h e beds do n o t mix.  R e s u l t s p e r t a i n i n g t o e x p a n s i o n c u r v e s f o r two components  which do mix a t c e r t a i n p o r o s i t i e s w i l l be g i v e n i n a l a t e r  section.  The e x p a n s i o n s o f s e v e r a l o f t h e w a t e r f l u i d i z e d beds d i s p l a y i n t e r e s t i n g behaviour. of  an  The e x p a n s i o n c u r v e i s composed o f two s e c t i o n s  d i f f e r e n t ' s l o p e s , and the e x p a n s i o n seems t o p r o c e e d d i f f e r e n t l y i n  t h e two r e g i o n s , as seen i n f i g u r e s 27,  28 and 30-  The bed expands a t  a g r e a t e r r a t e w i t h r e s p e c t t o v e l o c i t y above p o r o s i t i e s o f about t h a n i t does a t p o r o s i t i e s below 5 5 $ ' t h e d/D  T h i s b e h a v i o u r seems t o depend on  r a t i o , the v e l o c i t y of the f l u i d ,  The phenomenum was  55$  and the p o r o s i t y o f t h e bed.  n o t o b s e r v e d when p a r t i c l e s were f l u i d i z e d i n  p o l y e t h y l e n e g l y c o l s o l u t i o n s o r when v e r y l a r g e p a r t i c l e s were f l u i d i z e d i n water.  Diagrams b a s e d on v i s u a l o b s e r v a t i o n s o f how beds appeared t o  f l u i d i z e and the p a r t i c l e f l o w p a t t e r n s a r e g i v e n i n f i g u r e 1 0 .  At  p o r o s i t i e s o f about 55$ b u b b l i n g and v o i d wave f o r m a t i o n s b e g i n t o appear i n the f l u i d i z e d bed. undoubtedly  The v o i d waves grow as the bed expands.  a cause f o r t h e change i n s l o p e o f the e x p a n s i o n  These are  curve.  O b s e r v a t i o n s s i m i l a r t o the above were a l s o n o t e d by C a i r n s and P r a u s n i t z (l6)  i n t h e i r study of macroscopic C a i r n s and P r a u s n i t z ( 1 7 )  mixing i n f l u i d i z a t i o n .  a l s o measured the l i n e v e l o c i t y p r o f i l e s i n  water f l u i d i z e d beds i n a 2 - i n c h column u s i n g a t r a c e r t e c h n i q u e . f o u n d t h a t the v e l o c i t y p r o f i l e s b e g i n t o change t h e i r shape from  They a  43-  -0-5  e 0  -0-6  € 0  ALUNDUM (cataphote) CATAPHOTE (alundum) ALUNDUM CATAPHOTE MIXTURE  -0-8  -0-9 Ui  o  -0-3 F i g u r e 9-  -0-25 -0-2 -015 LOG(POROSITY)  -01  P l o t o f Alundum and Cataphote Bed E x p a n s i o n j and w i t h Cataphote above Alundum.  Individually  r a d i a l l y f l a t p r o f i l e and develop humps a t 3 "to 3 ' 5 p a r t i c l e f r o m t h e w a l l , a t p o r o s i t i e s o f about 55$-  diameters  The h e i g h t o f t h e humps  r e l a t i v e t o t h e average v e l o c i t y depends on t h e p a r t i c l e d e n s i t y . There appears t o be a l i m i t t o w h i c h a f l u i d i z e d bed c a n be' expanded b e f o r e i t becomes h y d r o d y n a m i c a l l y u n s t a b l e .  On e x p a n s i o n o f  a b e d s l o w l y from a f i x e d to..a .dense and then a more d i l u t e f l u i d i z e d b e d , the b e d expanded u n i f o r m l y u n t i l a p o r o s i t y o f 8 5 $ .  The b e d was s t a b l e ,  and d i s t u r b a n c e s w h i c h moved t h r o u g h i t a f f e c t e d t h e q u a l i t y o f f l u i d i z a t i o n b u t d i d not-cause  any s u s t a i n e d o s c i l l a t i o n s .  I f a b e d was  expanded above 8 5 $ p o r o s i t y , any d i s t u r b a n c e b e g i n n i n g i n t h e b e d became a m p l i f i e d as i t moved through t h e b e d and s e t up c o n t i n u o u s v o i d waves and o s c i l l a t i o n s , w h i c h remained u n t i l t h e p o r o s i t y o f t h e b e d was decreased.  A f t e r decreasing the p o r o s i t y , the o s c i l l a t i o n s slowly  d i s a p p e a r e d and t h e b e d r e t u r n e d t o a homogeneous f l u i d i z e d  state.  A c c o r d i n g t o J a c k s o n ( l 8 ) , f l u i d i z e d beds w i l l remain s t a b l e and w i l l not be a f f e c t e d - b y d i s c o n t i n u i t i e s u n l e s s t h e bed i s expanded above a certain limit.  D i s t u r b a n c e s i n a f l u i d i z e d b e d grow as t h e y move up  t h r o u g h t h e bed, b u t i f a b e d i s . n o t deep enough, t h e d i s t u r b a n c e w i l l have moved o u t o f t h e b e d b e f o r e i t has become l a r g e enough t o d i s r u p t it.  S l i s and W i l l e m s e  have developed  ( 1 9 ) have a l s o o b s e r v e d t h e s e d i s t u r b a n c e s and  a t h e o r y t o account f o r t h e i r v e l o c i t y o f p r o p a g a t i o n .  The f l u i d i z a t i o n o f p a r t i c l e s i n t h e p o l y e t h y l e n e g l y c o l s o l u t i o n s was much more u n i f o r m i n appearance t h a n w i t h w a t e r .  I t was n o t u n t i l  t h e b e d wascexpanded t o about 7 5 $ p o r o s i t y t h a t n o t a b l e c i r c u l a t i o n . o f the p a r t i c l e s occurred.  There was some tendency f o r p a r t i c l e movement  down t h e w a l l s o f t h e tube and up t h e c e n t r e , b u t i t was n o t v e r y pronounced.  The p a r t i c l e s , however, - were c o n t i n u a l l y coming t o g e t h e r  11 • # » • f  • •«•  »•»•  € = 0-85  i  €=0-70 ballotini  € = 0-55 spheres  in  € = 0-43  water  '»«»»>...  t  € = 0-85  € = 0-65 nickel  F i g u r e 10.  € = 0-50 spheres  in  € = 0-45  water  V i s u a l O b s e r v a t i o n o f F l u i d i z a t i o n o f Spheres.  i n s m a l l groups, t h e n f a l l i n g through t h e "bed as a group, d i s p e r s i n g , and r i s i n g again.  T h i s e f f e c t was p a r t i c u l a r l y n o t i c e a b l e w i t h n i c k e l spheres  where 5 o r 6 p a r t i c l e s w o u l d f a l l as a v e r t i c a l c h a i n . such as t h e l e a d and s t e e l b a l l s , t h e r e i s e v i d e n c e  For large p a r t i c l e  o f mass movement o f  groups o f p a r t i c l e s , b u t i n these runs t h e p a r t i c l e Reynolds/ was g r e a t e r than 2 . 0 .  number  P a r t i c l e f l o w c o n s i s t e d o f a "random eddying  motion  and t h e r e were f a i r l y l a r g e v a r i a t i o n s i n t h e l o c a l s o l i d s c o n c e n t r a t i o n s t h r o u g h o u t t h e bed.  However, d i s t u r b a n c e s s i m i l a r t o those o b s e r v e d i n  deep, w a t e r - f l u i d i z e d beds were n o t p r e s e n t i n beds f l u i d i z e d b y t h e polyethylene' g l y c o l s o l u t i o n s .  Such beds c o u l d be expanded o u t t h e t o p  o f t h e column w i t h o u t l a r g e s c a l e v o i d s f o r m i n g a.s they d i d i n w a t e r f l u i d i z e d beds.  Beds f l u i d i z e d i n p o l y e t h y l e n e g l y c o l s e g r e g a t e d by  s i z e t o a much g r e a t e r e x t e n t t h a n t h e y d i d i n w a t e r , and a t h i g h p o r o s i t i e s s e v e r a l beds d i s p e r s e d t o t h e p o i n t t h a t no i n t e r f a c e between bed and f l u i d c o u l d be  2.  observed.  D i f f e r e n t i a l P r e s s u r e Measurements. D i f f e r e n t i a l p r e s s u r e measurements were made on beds f l u i d i z e d w i t h  polyethylene g l y c o l solution. results.  F i g u r e s 1 1 and 12 a r e examples o f these  The r e s u l t s o b t a i n e d a r e w i t h i n 5$ o f t h e t h e o r e t i c a l v a l u e s f o r  a l l p o r o s i t i e s below 8 5 $ .  A t p o r o s i t i e s g r e a t e r than 8 5 $ t h e p a r t i c l e s  were s u f f i c i e n t l y s e g r e g a t e d b y s i z e t h a t t h e p o r o s i t y c a l c u l a t e d from bed h e i g h t was n o t r e p r e s e n t a t i v e o f t h e b u l k o f t h e b e d , and t h u s e x p e r i m e n t a l r e s u l t s were s i g n i f i c a n t l y g r e a t e r t h a n t h e t h e o r e t i c a l predicted values. F u r t h e r a n a l y s i s o f t h e r e s u l t s shows t h a t f o r low p o r o s i t i e s the e x p e r i m e n t a l v a l u e s o f p o r o s i t y a r e somewhat l e s s than t h e t h e o r e t i c a l v a l u e s , w h i l e a t h i g h p o r o s i t i e s the experimental r e s u l t s are l a r g e r than  47-  t h e t h e o r e t i c a l ones.  T h i s c o n d i t i o n h a s been e x p l a i n e d by A d l e r and  Happel (20) as b e i n g caused b y t h e n a t u r e o f t h e e n t r a n c e s e c t i o n .  They  have s t u d i e d t h e e f f e c t o f c a l m i n g • s e c t i o n p a c k i n g and l o o s e - p a c k e d b e d h e i g h t t o d i a m e t e r r a t i o on d i f f e r e n t i a l p r e s s u r e drop a c r o s s a f l u i d i z e d bed.  The r e s u l t s o b t a i n e d i n d i c a t e t h r e e t r e n d s .  ( l ) With no p a c k i n g  i n the calming section, the r a t i o of experimental d i f f e r e n t i a l pressure g r a d i e n t t o t h e o r e t i c a l p r e s s u r e g r a d i e n t c a l c u l a t e d from e q u a t i o n 26, known as t h e P r a t i o , i s a f u n c t i o n o f t h e l o o s e r - p a c k e d b e d h e i g h t t o d i a m e t e r r a t i o and t h e p o r o s i t y o f t h e f l u i d i z e d bed.  (2)  F o r packed  c a l m i n g s e c t i o n s , where t h e p a c k i n g i s above t h e support as i n o u r c a s e , t h e P r a t i o i s o n l y a f u n c t i o n o f t h e p o r o s i t y o f t h e f l u i d i z e d bed. A l s o o f importance  i s t h e f a c t t h a t t h e P r a t i o v a r i e s from about O.9O a t  p o r o s i t i e s o f 60$ t o about 1.10  a t p o r o s i t i e s o f 90$>.  (3)  When t h e  p a c k i n g was below t h e support s c r e e n t h e P r a t i o s were always l e s s t h a n 1.0.  T h i s c a n be r e a d i l y c o n f i r m e d by o b s e r v i n g W i l h e l m and Kwauks'  results  (l).  When measuring  the f r i c t i o n a l pressure l o s s through the f l u i d i z e d bed  by t h e method used i n t h i s work, t h e p r e s s u r e l o s s due t o w a l l f r i c t i o n i s a l s o measured.  The r e s u l t o b t a i n e d c a n be t r e a t e d as t h e sum o f t h e  p r e s s u r e l o s s due t o t h e f l u i d i z e d b e d plu..- t h e p r e s s u r e l o s s due t o t h e wall.  C a l c u l a t i o n s were made t o determine  p r e s s u r e l o s s c o u l d cause.  t h e maximum e r r o r t h a t t h e w a l l  The h i g h e s t f r e e s e t t l i n g p a r t i c l e  velocities  i n w a t e r and i n p o l y e t h y l e n e g l y c o l were used i n t h e c a l c u l a t i o n .  The  maximum p r e s s u r e l o s s p e r f o o t o f column i n t h e p o l y e t h y l e n e g l y c o l f l u i d i z e d b e d was computed t o be 0.039 l b - f o r c e /. f t ? — f t , and i n t h e w a t e r f l u i d i z e d b e d 0.002 l b . f o r c e /. f t ? _ f t .  The measured f r i c t i o n a l  p r e s s u r e l o s s e s i n t h e f l u i d i z e d b e d were never l e s s t h a n 5 l b - f o r c e / f t ? — f t , and t h u s t h e e r r o r due t o w a l l f r i c t i o n was n e v e r g r e a t e r t h a n I70.  48.  SYMBOL  POROSITY  588 695 758 811 868 926  O €  e  ©  THEORETICAL CURVE -\ BASED ON ( p - p ) = L( p - p){\-€)q/qc 0  F  s  I  0  2 F i g u r e 11.  4  6  8 10 12 14 16 18 20 2 2 L, INCHES  F r i c t i o n a l P r e s s u r e Drop P r o f i l e s i n a B a l l o t i n i Bed F l u i d i z e d by P o l y e t h y l e n e G l y c o l .  1.9.  BED 12.  HEIGHT,  INCHES  F r i c t i o n a l P r e s s u r e Drop P r o f i l e s i n an Alundum Bed F l u i d i z e d by P o l y e t h y l e n e G l y c o l .  50.  B. 1.  Experiments  w i t h two s p e c i e s .  Inversion of Mixtures. M i x t u r e s o f two groups o f p a r t i c l e s , f o r w h i c h s i n g l e component d a t a  had a l r e a d y been measured, were f l u i d i z e d • u s i n g p o l y e t h y l e n e g l y c o l s o l u t i o n s and water. Many d i f f e r e n t m i x t u r e s were t e s t e d when the f l u i d i z i n g medium was w a t e r , b u t no v i s i b l e i n v e r s i o n s were o b t a i n e d . i n t h e f o l l o w i n g manner.  Most m i x t u r e s expanded  A t low v e l o c i t i e s t h e bed was s e p a r a t e d i n t o two  d i s t i n c t s e c t i o n s and as t h e f l u i d v e l o c i t y was i n c r e a s e d t h e two components mixed t o g e t h e r .  The m i x i n g i n c r e a s e d as t h e f l u i d  i n c r e a s e d u n t i l a homogeneous mixed b e d was o b t a i n e d .  velocity  On f u r t h e r i n c r e a s e  i n f l u i d v e l o c i t y no s e p a r a t i o n o f t h e bed i n t o two s e c t i o n s was  observed.  T h i s was n o t unexpected as most p r a c t i c a l i n v e r s i o n s a r e p r e d i c t e d t o o c c u r a t a p o r o s i t y o f about 85$, and i n w a t e r f l u i d i z a t i o n t h e f l u i d i z e d bed i s v e r y u n s t a b l e a t t h e s e p o r o s i t i e s .  I t appears t h a t  macroscopic  m i x i n g i n t h e w a t e r - f l u i d i z e d beds masked t h e i n v e r s i o n s , and t h a t t h e d r i v i n g f o r c e f o r s e g r e g a t i o n due t o b u l k d e n s i t y d i f f e r e n c e was n o t g r e a t enough t o overcome the f o r c e s p r o d u c i n g m i x i n g a f f e c t s and i n s t a b i l i t i e s i n t h e f l u i d i z e d bed. B i n a r y m i x t u r e s o f p a r t i c l e s were a l s o f l u i d i z e d i n p o l y e t h y l e n e g l y c o l s o l u t i o n s , and v e r y d e t a i l e d r e s u l t s were o b t a i n e d f o r f o u r m i x t u r e s . The r e s u l t s o b t a i n e d appear i n T a b l e s 8 - 11, and a r e f o l l o w e d by a g e n e r a l a n a l y s i s o f two component f l u i d i z a t i o n . The i n t e r p r e t a t i o n o f d a t a was as f o l l o w s .  Expansion  as l o g a r i t h m (mean p o r o s i t y ) a g a i n s t l o g a r i t h m ( s u p e r f i c i a l velocity).  d a t a were p l o t t e d liquid  The e x p e r i m e n t a l p o i n t s o b t a i n e d a r e g i v e n and t h e e x p a n s i o n  c u r v e p r e d i c t e d by e q u a t i o n (kk), u s i n g s i n g l e component d a t a , i s drawn as a bold line.  The agreement between e x p e r i m e n t a l and p r e d i c t e d  expansions  i s v e r y good, as c a n be seen i n F i g u r e s 1 3 , 1 7 , '21 and 2k.  The  f r i c t i o n a l p r e s s u r e drop d a t a were p l o t t e d a s d i f f e r e n c e i n p r e s s u r e from a base p o s i t i o n t o a h i g h e r p l a n e v e r s u s h e i g h t L, w h i c h i s t h e d i s t a n c e between t h e base p o s i t i o n and t h e h i g h e r p l a n e . superficial liquid velocity. and 2 2 .  The parameter i s  These d a t a a r e d i s p l a y e d i n F i g u r e s lk,  18  The d i f f e r e n t i a l p r e s s u r e g r a d i e n t s f o r t h e i n d i v i d u a l components  were o b t a i n e d b y measuring t h e s l o p e s o f t h e s t r a i g h t l i n e s i n t h e l a t t e r plots.  The d i f f e r e n c e i n b u l k d e n s i t y o f t h e two beds i s n u m e r i c a l l y  e q u a l t o t h e d i f f e r e n c e i n d i f f e r e n t i a l .-pressure g r a d i e n t f o r t h e beds. Development i s g i v e n below.  (AP  F  /L),  (A^/L), - ( A | > / L )  2  =  (!-€,)(/>„-/»g/g  26  c  = (I-«,)(/>„ -/>)0/g -(l-^)(/te-/>>Q/Qc c  51  The b u l k d e n s i t y d i f f e r e n c e has a l r e a d y been shown t o be g i v e n b y  PB|-/°B2=^ - |HPsl -P) ~ |  €  <l- )(Ps2 ~P) €  2 8  2  Thus  PB\ ~PB2 = [(Ap /L)|- ( A p / L ) ] g / g F  F  2  52  c  The measured d i f f e r e n t i a l p r e s s u r e d i f f e r e n c e s , w h i c h a r e t h u s e q u i v a l e n t to the bulk density d i f f e r e n c e s , are p l o t t e d against the s u p e r f i c i a l l i q u i d v e l o c i t i e s i n F i g u r e s 1 5 , 1 9 , 2 3 and 2 5 -  The b o l d l i n e i s t h e  curve o b t a i n e d b y u s i n g s i n g l e component e x p a n s i o n d a t a and t h e o r e t i c a l d i f f e r e n t i a l p r e s s u r e s t o determine  the i n v e r s i o n p o i n t , as f o l l o w s .  a particular superficial liquid velocity  €^ and ^ £  w  e  r  e  At  r e a d from t h e  s i n g l e component e x p a n s i o n c u r v e s , and t h e s e v a l u e s were u s e d i n e q u a t i o n 51  t o calculate the difference i n d i f f e r e n t i a l f r i c t i o n a l pressure  g r a d i e n t between t h e two components.  Table 8 Inversion Results f o r Nickel and B a l l o t i n i M i x t u r e Properties of Mixture Components  d,mm.  O.I+56  2.28  Ps  8.9O  2-73  Material  Nickel  Ballotini  Wt. o f Sample  I+59.O gm.  r  Buoyancy ratio  0.212  Size ratio  .5.01  Predicted inversion p o r o s i t y ( € ) by equation ( 3 9 ) m  Predicted inversion porosity (€ ) u s i n g s i n g l e component data. Experimental inversion porosity m  Flow regime  400.0 gm.  0.817  0.842  O.783 Stoke s  53-  -0-8 -1-0 -1-2 -  €> - NICKEL (d=0-456mm.) ©-BALLOTINI (d=2-28mm.) 0 - M I X T U R E : 459gm. NICKEL AND 4 0 0 g m . BALLOTINI - - P R E D I C T E D CURVE FOR MIXTURE  -0-3 F i g u r e 13.  -0-2 -0-1 LOG(POROSITY)  P l o t o f N i c k e l and B a l l o t i n i Bed E x p a n s i o n s .  0  BED  HEIGHT,  INCHES  F i g u r e l U . D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n . N i c k e l - B a l l o t i n i Bed.  55-  50  1  r  1  1  1  1  40 30 20 10 0 -10 ro H  -20  LL  ^  -30  _i  -40  C/) GO  CJ-50  CQ  I  -60  —  m  o.  -70 -80  /  PREDICTED CURVE" BASED ON SINGLE _ COMPONENT DATA 0 EXPERIMENTAL "  /  -90  / /  -100 -110 -120  ©2  1  0 '  0  1  0 004  1  0 008  V 15.  s  ,  1  1  1 ,-  0 012  0 016  0 020  FT./SEC.  P l o t o f B u l k D e n s i t y D i f f e r e n c e and V e l o c i t y f o r t h e N i c k e l - B a l l o t i n i Bed.  0  • o«o  #  • «~ o o o 'o  0 OS #  • ••  (2)  •o •  #  »o o o. o  •o* o • o  (3)  (4)  0  ••••v.* •vvv  •oo o .o» •o*°  0  °-!  o o o • o • oo o o o oo o°ot o o o • o o o o (5)  NICKEL OO  o  BALLOTINI  INVERSION OF AND BALLOTINI  NICKEL MIXTURE CA  Figure l 6 .  Schematic Diagram o f how I n v e r s i o n Proceeded.  Table 9 Inversion Results f o r Alundum and B a l l o t i n i M i x t u r e ,  Properties of  d,mm  Ps  Mixture • Components  0.645  1.08  3-95  2.91  Material  Alundum  Wt. o f sample  4 4 7 0 gm. 3 2 0 0 gm.  Buoyancy ratio  r  0.640  size ratio  r  1.67  predicted, inversion p o r o s i t y ( € ) by equation ( 3 9 )  Ballotini  0.80 5 •  m  •predicted inversion porosity using single component d a t a . experimental i n v e r s i o n • porosity ( € )  O.806  O.763  m  f l o w regime  Intermediate  58.  € ALUNDUM (d=0-645 mm.) © BALLOTINI (d=l079mm.) 9 MIXTURE: 447gm.ALUNDUM  -0-2 F i g u r e 17.  -0-1 LOG(POROSITY)  P l o t o f Alundum and B a l l o t i n i Bed E x p a n s i o n s i n Polyethylene Glycol.  /  0  50 45 40 35 30 oo  m -  25  SYMBOL  VELOCITY FLUID -  20  I 2 3 4  15  OF  FT./SEC.  •00096 •00316 •00589 •0119  € 3  10  0  0  8  10  Figure 18.  12  14  16 BED  18 2 0 HEIGHT  22  2 4 26 INCHES  D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n A l u n d u m - B a l l o t i n i Bed.  28  30  32  34  36  38  40  42  60.  0  0004  0 0 0 8 0012 0016 V , FT./SEC.  0020  s  F i g u r e . 19-  P l o t o f B u l k D e n s i t y D i f f e r e n c e and V e l o c i t y A l u n d o m - B a l l o t i n i Bed.  for  OOCiSC  • •• • • (i)  ••  (2) ALUNDUM INVERSION  o  AND BALLOTINI  OF  BALLOTINI  ALUNDUM MIXTURE  Table 10 I n v e r s i o n R e s u l t s f o r Lead and S t e e l M i x t u r e d,mm  Properties of  Ps  3-15  2.05  7.83  11-33  Lead  Mixture  Material  Steel  Components  Wt. o f sample  800.0  gm.  buoyancy ratio  O.659  size ratio  1.536  predicted porosity  inversion by equation  900.0  gm.  0.803  (39)  predicted inversion porosity using single component d a t a  0.688  experimental i n v e r s i o n p o r o s i t y (€„}  0.721  f l o w rdgime  Intermediate  0  -0-2  T  © © ®  LEAD STEEL MIXTURE  0-4 •  S  /  0-6  •0-8  -10  -1-2  -1-4  -1-6  0-25  -0-2 -015 -01 LOG(POROSITY)  F i g u r e 21.  -005  P l o t o f Lead and S t e e l Bed Expansions.  0  SYMBOL I  2 3 4  6 22.  € Q  ©  8 10 BED HEIGHT,  VELOCITY OF FLUID - FT./SEC. •054 •097 • 182 •237  12 14 INCHES  16  D i f f e r e n t i a l P r e s s u r e P r o f i l e s i n L e a d - S t e e l Bed.  18  1  20  65-  45  i  i  i  I  I  40 35  •  —  30 25 20 15 CO OQ -J  —  10 5  :  3®  —  CM  m I  -  CD  0 -5  / ® 2 ~® I  -10 -15  —  —  /  PREDICTED B A S E D ON  •20 -25  —  -30  —  -35  —  /  e  -40 004  i 008  COMPONENT DATA EXPERIMENTAL  1  1  012  016  V F i g u r e 23-  CURVE SINGLE  s  1  0-20  1  024  , FT./SEC.  P l o t o f B u l k D e n s i t y D i f f e r e n c e and V e l o c i t y f o r t h e L e a d - S t e e l Bed.  Table  11  Inversion Results f o r Nickel-Glass and B a l l o t i n i M i x t u r e . Properties of  d,mm  0.542  1.08  4 . 50  2.91  Material  NickelGlass  Ballotini  Wt. o f sample  296.O gin.  290.0  Ps  Mixture Components  buoyancy ratio  X  0-537  size ratio  r  1.99  predicted porosity  inversion by e q u a t i o n ( 3 9 )  0.804  predicted inversion . porosity using single component d a t a  0.841  experimental inversion porosity  O.8O7  f l o w regime  Stokes  gm.  67-  LOG(POROSITY) Figure 2U-  Plot of Nidkel'-Glass and Bal|otini- Bed-'-Expansio'ris iii Polyethylene-"-Gl-ycoi.- c  68.  -50  1  1  0  0004  1  1  •  I  0 0 0 8 0012 0016 V , FT./SEC. s  Figure 25-  P l o t of Bulk Density Difference N i c k e l - G l a s s - B a l l o t i n i Bed.  and V e l o c i t y f o r  1  0020  69The  s u p e r f i c i a l l i q u i d v e l o c i t y at w h i c h homogeneous f l u i d i z a t i o n  o c c u r r e d f o r the f o u r m i x t u r e s was  (39)  c l o s e t o t h a t p r e d i c t e d by e q u a t i o n  .and t h a t p r e d i c t e d from s i n g l e component d a t a .  V i s u a l observations  showed  a g r a d u a l t r a n s i t i o n from heavy component p r e d o m i n a n t l y a t t h e bottom t o the heavy component p r e d o m i n a n t l y a t t h e top o f t h e bed, o f the f l u i d was  increased.  An i n s t a n t a n e o u s  beds as d e s c r i b e d i n the t h e o r y d i d not o c c u r . i n v e r s i o n s proceeded i s ' i n t e r e s t i n g . was  as the  velocity  f l i p - o v e r o f the component The way  i n w h i c h the  As the s u p e r f i c i a l l i q u i d  velocity  i n c r e a s e d , m i x i n g o f the two components began a t the i n t e r f a c e between  the two beds, p r o d u c i n g  a r e g i o n o f mixed bed.  Further increase i n v e l o c i t y  caused the mixed bed r e g i o n t o expand b o t h upwards and downwards, u n t i l i t e n g u l f e d t h e whole f l u i d i z e d bed.  F i n a l l y , as the v e l o c i t y  was  i n c r e a s e d f u r t h e r , the heavy s m a l l p a r t i c l e s began t o move out o f mixed bed  and form a bed above the mixed bed.  The mixed bed was  d e p l e t e d o f heavy s m a l l p a r t i c l e s as the v e l o c i t y was number o f s m a l l p a r t i c l e s l e f t i n the mixed bed was  slowly  increased u n t i l  very small.  g i v e a shcematic r e p r e s e n t a t i o n o f the i n v e r s i o n o f two The  the  the  Figures  mixtures.  v e l o c i t y i n t e r v a l o v e r w h i c h the i n t e r f a c e between beds  was  i n d i s t i n g u i s h a b l e o c c u r r e d between b u l k d e n s i t y d i f f e r e n c e s o f a p p r o x i m a t e l y • -15  and +k l b s m / f t . 3  In t h i s region of small bulk d e n s i t y d i f f e r e n c e s  between the two components, the f a c t o r s c a u s i n g m i x i n g ,  such as v e l o c i t y  d i s t r i b u t i o n and p a r t i c l e s i z e d i s t r i b u t i o n , have- a g r e a t e r e f f e c t t h a n the s m a l l b u l k d e n s i t y g r a d i e n t s , and the beds remain mixed and do segregate.  not  *  I n o r d e r t o have an almost i n s t a n t a n e o u s  inversion, the'region  of  s m a l l b u l k d e n s i t y d i f f e r e n c e must c o r r e s p o n d t o a s m a l l change i n superficial liquid velocity.  F o r a sharp c l e a r i n v e r s i o n the r a t e o f  change o f b u l k d e n s i t y w i t h r e s p e c t t o v e l o c i t y must be l a r g e .  Considering  70.  equation  2 8 , t h e p o r o s i t y i s t h e o n l y v a r i a b l e on t h e r i g h t hand s i d e  which i s a f u n c t i o n of v e l o c i t y .  Therefore the gradient o f bulk  density  d i f f e r e n c e w i t h r e s p e c t t o p o r o s i t y must be d i r e c t l y r e l a t e d t o t h e gradient o f bulk density difference with respect to v e l o c i t y .  Thus  ,(3-m)/mn  PB\  -PBZ-  IP:'•I  -P)  [ < l - yI * ~  D i f f e r e n t i a t i n g with respect to  r  =  (  To have an i n v e r s i o n w i t h r  € | , we have  ^  s l  y  ~^'[y(mn-l)/mn-  s  | < r  and t h u s  (3-m)/mn >  '  53; f t i s apparent t h e r e f o r e t h a t f o r a l a r g e  of bulk density d i f f e r e n c e with respect to p o r o s i t y , r p j —p)  53  ' ]  < | , i t i s necessary that  ^(mn-|)/mn  (  28  l^' ~ ^(mn-ll/mn *  (3-m)/mn  dlPm -Psi  R e f e r r i n g to equation  €  must be l a r g e and y  must be s m a l l .  must be l a r g e ,  A n a l y s i s of the data  shows t h a t t h e s e f a c t o r s do i n d e e d have t h e p r e d i c t e d e f f e c t on t h e quality of inversion.  gradient  A c o m p a r i s o n o f m i x t u r e s appears i n t a b l e 1 2 .  71-  T a b l e 12 Quality-of-Inversion Mixture  NickelBallotini  Predictions  Nickel-Glass Ballotini  Alundum Ballotini  1.84 gm/cc  1.84 gm/cc  1.84 gm/cc  r  5.01  1.99  1.67  r  0.212  O.537  0.640  10.6 gm/cc  2.21  P%\ - P  ^PB\~PB^^ \ €  Comments:  . v e r y good • clear-cut inversion  gm/cc  f a i r inversion  1.44 gm/cc mixed b e d over most of f l u i d i z a t i o n region - poor inversion.  72.  P a r t i c l e size distributions  a f f e c t e d the p r e c i s e n e s s  and caused them t o o c c u r o v e r a range o f v e l o c i t i e s .  o f the  inversions  If a fluidized  bed  i s composed o f m a t e r i a l o f a range o f s i z e s , t h e r e w i l l be a p o r o s i t y g r a d i e n t t h r o u g h 'the f l u i d i z e d bed w h i c h w i l l gause a b u l k gradient.  T h i s has been shown t o be  w o r k e r s (h,  8,  9)-  so by A n d r i e u ( 1 0 )  density  and numerous o t h e r  A n d r i e u has a l s o shown t h a t the p o r o s i t y g r a d a t i o n  t h u s the b u l k d e n s i t y g r a d a t i o n  i n c r e a s e as the o v e r a l l average p o r o s i t y  i s increased.  Both components i n the m i x t u r e have p a r t i c l e  distributions  and t h u s b o t h have b u l k d e n s i t y d i s t r i b u t i o n s .  arise,  (l)  The b u l k d e n s i t y d i s t r i b u t i o n s  size Three c a s e s  o f b o t h beds i s e q u a l . . ( 2 )  b u l k d e n s i t y d i s t r i b u t i o n o f the s m a l l heavy p a r t i c l e s ' i s g r e a t e r t h a t o f the l a r g e l i g h t p a r t i c l e s .  (3.)  Case ( 2 )  The b u l k d e n s i t y d i s t r i b u t i o n  s m a l l p a r t i c l e s cannot be  i s t h e most l i k e l y f o r two  d e n s i t y d i s t r i b u t i o n w i l l be g r e a t e r f o r the s m a l l p a r t i c l e bed.  of  of  reasons.  s i z e d as w e l l as l a r g e p a r t i c l e s , the  The  than  the heavy s m a l l p a r t i c l e s i s l e s s t h a n the b u l k d e n s i t y d i s t r i b u t i o n the l a r g e p a r t i c l e s .  and  As  bulk Also,  the s m a l l heavy p a r t i c l e s w i l l be a t a h i g h e r p o r o s i t y at i n v e r s i o n t h a n the l a r g e l i g h t p a r t i c l e s , so t h a t the b u l k d e n s i t y d i s t r i b u t i o n  will  a g a i n be g r e a t e r f o r the s m a l l heavy p a r t i c l e s t h a n f o r the l a r g e p a r t i c l e s . . Case ( 3 )  i s very u n l i k e l y .  As the d e n s i t y r a t i o and  p a r t i c l e s approach u n i t y , t h e p r o b a b i l i t y As case ( 2 )  i n the s m a l l p a r t i c l e bed  See  i n w h i c h i t a f f e c t s the  The beds w i l l b e g i n t o mix when the  b u l k d e n s i t y a t the bottom o f the top bed the top o f the bottom bed.  f i g u r e 26a.  i s e q u a l t o the b u l k d e n s i t y As the b u l k d e n s i t y  at  variation  i s g r e a t e r t h a n i n the l a r g e p a r t i c l e bed,  s m a l l p a r t i c l e s w i l l b e g i n t o form a s i n g l e component bed bed b e f o r e  the  o f case ( l ) i n c r e a s e s .  i s the m o s t . l i k e l y , the way  f l u i d i z e d m i x t u r e w i l l be d i s c u s s e d .  size r a t i o of  the  above the mixed  the average b u l k d e n s i t y d i f f e r e n c e s between the beds i s z e r o .  73-  T h i s i s i l l u s t r a t e d i n f i g u r e 2 6 b , and a c c o u n t s f o r t h e f a c t t h a t t h e observed i n v e r s i o n  p o i n t always f e l l t o t h e l e f t o f t h e t h e o r e t i c a l  cross-over point i n Figures 15,  1 9 , 23 and 25•  The components w i l l  f i n a l l y s e p a r a t e c o m p l e t e l y i n t o two beds when we have t h a t which i s shown i n f i g u r e 2 6 c  situation  T h i s was r e a d i l y n o t i c e a b l e w i t h t h e  n i c k e l - b a l l o t i n i m i x t u r e , where t h e p a r t i c l e s i z e d i s t r i b u t i o n o f t h e n i c k e l p a r t i c l e s was much l a r g e r t h a n t h a t o f t h e b a l l o t i n i p a r t i c l e s . A f t e r t h e i n v e r s i o n p o i n t was reached and an apparent homogeneous f l u i d i z e d bed  appeared, as t h e s u p e r f i c i a l l i q u i d v e l o c i t y was i n c r e a s e d a n i c k e l  bed  began t o f o r m on t o p o f t h e mixed bed.  but  a mixed b e d r e g i o n remained u n t i l a much g r e a t e r v e l o c i t y than t h e  inversion  The n i c k e l b e d became  larger  v e l o c i t y was reached.  The case ( l ) s i t u a t i o n w o u l d be s i m i l a r t o t h a t o f t h e alondumb a l l o t i n i mixture.  Here, a f t e r t h e i n v e r s i o n p o i n t was r e a c h e d , a  b a l l o t i n i b e d began t o f o r m a t t h e bottom o f t h e mixed b e d and an alundum bed  a t t h e t o p . As t h e s u p e r f i c i a l l i q u i d v e l o c i t y was i n c r e a s e d , t h e  r e g i o n o f mixed bed d e c r e a s e d u n t i l i t d i s a p p e a r e d a t t h e c e n t r e o f t h e bed.  T h i s i s shown i n f i g u r e 2 6 d .  74.  shaded  M- measured average bulk density difference  mixed  section — bed  region  .bottom TOM  BED  bottom BOTTOM  BED  bottom TOP  26 a.  26c.  "beds b e g i n n i n g t o mix.  26b.  i n i t i a l bottom b e d nov on t o p complete s e g r e g a t i o n .  Figure.26.  BED  i n i t i a l bottom bed beginning t o form b e d a t t o p o f mixed bed.  26d.  alundum-ballotini mixture s i t u a t i o n 1.  E f f e c t o f P a r t i c l e Si'£e D i s t r i b u t i o n s on t h e P o i n t o f Inversion.  75-  22  P r e d i c t i o n , o f Bed Expansion E q u a t i o n kk;  expansions  developed  f o r Mixtures.  i n an e a r l i e r s e c t i o n t o p r e d i c t bed  f o r m i x t u r e s o f d i f f e r e n t m a t e r i a l s , was  t e s t e d f o r numerous  m i x t u r e s i n f l u i d i z i n g media o f w a t e r and p o l y e t h y l e n e g l y c o l The  solutions.  e q u a t i o n p r e d i c t s the e x p a n s i o n o f the mixed beds v e r y w e l l .  In  the i n v e r s i o n . r u n s made w i t h p o l y e t h y l e n e g l y c o l s o l u t i o n s , the e x p e r i m e n t a l d a t a c o v e r the complete range o f m i x i n g o f t h e two components, and e q u a t i o n kk s t i l l p r e d i c t s the e x p a n s i o n t o a h i g h degree o f Comparisons o f e x p e r i m e n t a l and p r e d i c t e d expansions g l y c o l s o l u t i o n s are given i n f i g u r e s 13; the p r e d i c t e d e x p a n s i o n  17;  accuracy.  i n polyethylene  21 and 2k.  I n each c a s e ,  i s r e p r e s e n t e d by the dark b o l d l i n e and  the  e x p e r i m e n t a l d a t a by the c i r c u l a r p o i n t s . Many runs o f d i f i ' e r e n t m a t e r i a l s were made i n w a t e r - f l u i d i z e d beds M i x t u r e s f o r which the . X r a t i o was  t o t e s t e q u a t i o n kk t h o r o u g h l y . and the r  r a t i o s m a l l , r e p r e s e n t e d by f i g u r e s 2 7 ;  s i m i l a r l y mixtures w i t h small by f i g u r e s 30 and 3 1 ; on how  y r a t i o s and l a r g e r  were t e s t e d t o determine  28 and 2 9 ; ratios,  and represented  the e f f e c t o f these f a c t o r s  w e l l the e q u a t i o n p r e d i c t e d the a c t u a l e x p a n s i o n .  I t was  found  t h a t f o r l a r g e r r a t i o s , the e q u a t i o n d i d not p r e d i c t the e x p a n s i o n a t low p o r o s i t i e s .  large  well  I n the r e g i o n where one o f the components i s n e a r the  minimum p o r o s i t y o f f l u i d i z a t i o n , the p r e d i c t e d curve d e v i a t e d from t h e experimental data.  The l a t t e r f e l l much c l o s e r t o the e x p a n s i o n  line  f o r t h a t component w h i c h i s n e a r the minimum f l u i d i z a t i o n v e l o c i t y d i d the p r e d i c t e d r e s u l t s .  T h i s can be seen i n F i g u r e  31  A s e r i e s o f runs was made w i t h v a r i o u s r a t i o s o f n i c k e l - g l a s s b a l l o t i n i t o t e s t e q u a t i o n kk when t h e r e was volume o f each component p r e s e n t . fairly well for a l l ratios.  than  and  l a r g e d i f f e r e n c e s i n the  The e q u a t i o n p r e d i c t e d the  R e s u l t s are g i v e n i n f i g u r e  32.  results  76.  I t i s i n t e r e s t i n g t h a t an e q u a t i o n w h i c h i s based on the assumption t h a t t h e two m a t e r i a l s are c o m p l e t e l y s e g r e g a t e d i n t o two beds p r e d i c t s the expansion mixed.  even when t h e two components are p a r t i a l l y o r c o m p l e t e l y  T h i s seems t o i n d i c a t e t h a t the b u i l d i n g b l o c k t h e o r y o f Happel (6),  t h a t a f l u i d i z e d bed i s made up o f c e l l s , each o f w h i c h i s a s s o c i a t e d w i t h a p a r t i c l e , and t h a t t h e s i z e o f the c e l l s i s dependent o n l y on the p a r t i c l e and t h e s l i p v e l o c i t y o f the f l u i d , i s sound. - Thus t h e c e l l s w i l l be the same s i z e whether t h e y are i n the m i x t u r e o r i n a c o m p l e t e l y segregated  bed.  77-  -0-35 F i g u r e 27-  -0-3 -0-25 -0-2 LOG(POROSITY)  -015  P l o t o f A l u n d u m - C r y s t a l o n Run N o . l .  -01  78.  LOG(POROSITY) F i g u r e 28.  P l o t o f A l u n d u m - C r y s t a l o n Run No.2.  Figure 29-  P l o t o f Alundum and B a l l o t i n i Bed E x p a n s i o n s i n Water.  80.  -0-35  -0-3  Figure 30.  -0-25 -0-2 -015 LOG(POROSITY)  P l o t o f N i c k e l - G l a s s and B a l l o t i n i Bed E x p a n s i o n s i n Water.  -01  81.  LOG (POROSITY) F i g u r e 31.  P l o t o f N i c k e l and Alundum Bed Exp  i  i  MIXTURE:  i  r~  BALLOTINI (B)  -1-3 1 — 1 1 1 I I I I I -0-46 -0-42 -0-38 -0-34 -0-3 -0-26 -0-22 -018 LOG( POROSITY) F i g u r e 32.  I I  -014  -01  P l o t o f N i c k e l - G l a s s and B a l l o t i n i Bed E x p a n s i o n s w i t h D i f f e r e n t Volumes o f Each Component.  I I  - 0 06 00 r°  83CONCLUSIONS 1.  The s u p e r f i c i a l l i q u i d v e l o c i t y w h i c h produces homogeneous  fluidization  o f two s p e c i e s does so a t a mean p o r o s i t y f o r t h e f l u i d i z e d m i x t u r e i s very close t o that p r e d i c t e d by equation component d a t a . n  l ~ 2> l n  m  =  m  Equation  39 and t h a t p r e d i c t e d by s i n g l e  39 i s b a s e d on t h e f o l l o w i n g f o u r a s s u m p t i o n s :  2> ^12= ^2> and (^1 " c^X^n  are s a t i s f i e d approximately; equation  which  i s small.  These c o n d i t i o n s  each i s i n e r r o r b y a s m a l l amount.  Thus  39 can be e x p e c t e d t o g i v e o n l y an approximate v a l u e f o r t h e  i n v e r s i o n p o r o s i t y , and c o r r e s p o n d i n g  velocity.  The s i n g l e component d a t a  a l s o cannot p r e d i c t i n v e r s i o n v e l o c i t i e s p r e c i s e l y , because t h e p o r o s i t y v e l o c i t y r e l a t i o n s h i p s o b t a i n e d f o r t h e s i n g l e component beds a r e average v a l u e s o v e r t h e whole bed.  P o i n t c o n d i t i o n s i n the f l u i d i z e d bed describe  the s i t u a t i o n b e t t e r t h a n average v a l u e s , e s p e c i a l l y when t h e p a r t i c l e s are n o t p e r f e c t l y u n i f o r m mixture  i n size.  Homogeneous m i x i n g i n t h e f l u i d i z e d  i s a f u n c t i o n o f the r e l a t i v e bulk density d i s t r i b u t i o n i n the  s i n g l e component beds. 2.  The e x p e r i m e n t a l  m i x t u r e p o r o s i t y a t homogeneous f l u i d i z a t i o n i s l e s s  t h a n t h a t p r e d i c t e d b y s i n g l e component d a t a .  T h i s was a n a l y z e d  and i t  was f o u n d t h a t t h e o n l y cause c o u l d be p a r t i c l e s i z e d i s t r i b u t i o n i n t h e two s i n g l e component beds.  Also, the bulk density gradation i n the small  p a r t i c l e b e d must be g r e a t e r t h a n t h a t i n t h e l a r g e p a r t i c l e bed.  This  would cause t h e p o i n t o f homogeneous f l u i d i z a t i o n t o be r e a c h e d b e f o r e t h a t p r e d i c t e d from s i n g l e component d a t a .  The two c o n d i t i o n s which. Cause  t h e b u l k d e n s i t y g r a d a t i o n t o be g r e a t e r i n t h e s m a l l p a r t i c l e b e d a r e : (1)  t h e l a r g e p a r t i c l e s can be s i z e d b e t t e r t h a n t h e s m a l l p a r t i c l e s ;  (2)  t h e s m a l l p a r t i c l e s a r e a t a h i g h e r average p o r o s i t y , t h u s t h e e f f e c t  o f p a r t i c l e s i z e d i s t r i b u t i o n on t h e b u l k d e h s i t y w i l l be much g r e a t e r  8k. •than f o r t h e l a r g e p a r t i c l e s , which are a t a much l o w e r p o r o s i t y . 3.  F o r a c l e a r - c u t i n v e r s i o n i n the f l u i d i z e d bed t h e r e g i o n o f low  b u l k d e n s i t y d i f f e r e n c e s , where m i x i n g f o r c e s are predominant, must be t r a v e r s e d by a s m a l l change i n v e l o c i t y . a large value of k.  T h i s i s a c c o m p l i s h e d by  r and a c o r r e s p o n d i n g l y s m a l l v a l u e o f  I n c o n t r a s t t o beds f l u i d i z e d by p o l y e t h y l e n e g l y c o l  y  having  .  solutions,  i n v e r s i o n s i n w a t e r - f l u i d i z e d beds were n o t o b t a i n e d because t h e extreme t u r b u l e n c e , p a r t i c l e c i r c u l a t i o n , and p o r o s i t y d i s t r i b u t i o n s d i s r u p t e d the bed t o o much.  B u l k d e n s i t y g r a d i e n t s d i d not get a chance t o d e v e l o p ,  as m i x i n g f o r c e s were,.;much more predominant.  The p o r o s i t y o f the s m a l l  p a r t i c l e beds r e q u i r e d t o produce homogeneous f l u i d i z a t i o n was greater than 85$.  usually  At p o r o s i t i e s i n t h i s range, w a t e r - f l u i d i z e d beds are  hydrodynamically unstable. 5.  The p r e d i c t i o n o f mixed bed e x p a n s i o n b a s e d on s i n g l e component d a t a  u s i n g e q u a t i o n kk i s v e r y good.  The e q u a t i o n p r e d i c t s the e x p a n s i o n 6'ver  the .measured r a n g e ofrflMdization: .forhmixt\ar«'s^^  •ratios-" •  ;  as g r e a t as 10:1. range o f y  and  I t a l s o p r e d i c t s the e x p a n s i o n v e r y w e l l f o r a wide r ratios.  <  The p r e d i c t e d v a l u e s b e g i n t o d e v i a t e from the  e x p e r i m e n t a l v a l u e s when one o f the two components o f the m i x t u r e i s c l o s e t o i t s minimum p o r o s i t y f o r f l u i d i z a t i o n . b a s e d on the assumption  Even though the e q u a t i o n i s  o f no m i x i n g o f the component beds, i t p r e d i c t s  the e x p a n s i o n o f the f o u r m i x t u r e s w h i c h p a s s e d t h r o u g h a l l s t a g e s o f m i x i n g as t h e y were f l u i d i z e d .  T h i s seems t o i n d i c a t e t h a t the  holdup  i n a f l u i d i z e d bed i s o n l y a f u n c t i o n o f t h e i n d i v i d u a l p a r t i c l e s t h e s u p e r f i c i a l l i q u i d v e l o c i t y , and u n a f f e c t e d by p a r t i c l e 6.  and  interactions.  The R i c h a r d s o n and Z a k i method o f p l o t t i n g d a t a f o r s i n g l e components  appears t o be e x c e l l e n t , as most d a t a f e l l on a s t r a i g h t l i n e h a v i n g a ' s l o p e v e r y n e a r l y e q u a l t o t h a t p r e d i c t e d by the R i c h a r d s o n and Z a k i e q u a t i o n s .  85The d a t a began t o t a i l o f f a t v e r y h i g h p o r o s i t i e s , b u t t h i s i s p r o b a b l y caused by s i z e s t r a t i f i c a t i o n i n t h e f l u i d i z e d 7»  Equation 23,  bed.  d e v e l o p e d by R i c h a r d s o n and Z a k i f o r c a l c u l a t i n g t h e f r e e  s e t t l i n g v e l o c i t y o f the p a r t i c l e s from t h e e x p a n s i o n l i n e s v e l o c i t y i n t e r c e p t at a p o r o s i t y of 100$,  g i v e s answers which a r e o f t e n 1 0 - 2 0 $  d i f f e r e n t from t h o s e c a l c u l a t e d u s i n g the d r a g c o e f f i c i e n t - R e y n o l d s ' number p l o t f o r spheres.  T h i s c o u l d be caused by a number o f f a c t o r s , two  of  w h i c h may be t h e n o n - s p h e r i c i t y and n o n - u n i f o r m i t y o f the p a r t i c l e s .  On  t h e o t h e r hand, t h e r e i s a l s o t h e p o s s i b i l i t y t h a t e q u a t i o n 23 does not adequately c o r r e c t f o r the w a l l e f f e c t .  R i c h a r d s o n and Z a k i have assumed  t h a t t h e w a l l e f f e c t i s o n l y a f u n c t i o n o f t h e p a r t i c l e t o column d i a m e t e r r a t i o ; and have i g n o r e d o t h e r p o s s i b l e v a r i a b l e s such as f l u i d 8.  regime.  The f r i c t i o n a l p r e s s u r e drop e q u a t i o n b a s e d on a s i m p l e f o r c e b a l a n c e ,  p o p u l a r i z e d by W i l h e l m and Kwauk, p r e d i c t s t h e e x p e r i m e n t a l r e s u l t s w e l l , e x c e p t a t v e r y h i g h p o r o s i t i e s where t h e r e i s a l a r g e amount o f s e g r e g a t i o n by s i z e o f the p a r t i c l e s .  The average e r r o r i s a p p r o x i m a t e l y 5$-  e r r o r due t o assuming the w a l l p r e s s u r e l o s s was n e g l i g i b l e found t o be l e s s t h a n 1 $ .  The  was  A l s o i t 1-has been shown t h a t measurement o f  p r e s s u r e l o s s p r o f i l e s i s an e x c e l l e n t method f o r d e t e r m i n i n g l o n g i t u d i n a l b u l k d e n s i t y and p o r o s i t y d i s t r i b u t i o n s i n f l u i d i z e d beds.  86. Recommendations f o r F u r t h e r Work 1.  Determination  o f the e f f e c t  i n v e r s i o n p o i n t i s important.  o f p a r t i c l e s i z e d i s t r i b u t i o n on T h i s may  the  be a c c o m p l i s h e d by the f o l l o w i n g  procedure: (a)  F l u i d ! z e ammixture o f two m a t e r i a l s o f known p r o p e r t i e s  o b t a i n e x p a n s i o n and d i f f e r e n t i a l p r e s s u r e (b)  d a t a f o r the  mixture.  A t a v e l o c i t y j u s t l e s s t h a n the i n v e r s i o n v e l o c i t y ,  s e p a r a t e l y t h e upper and l o w e r p o r t i o n s o f t h e bed.  and  remove  Measure the average  p a r t i c l e d i a m e t e r o f the s m a l l heavy p a r t i c l e s w h i c h w e r e ' i n the top  bed.  Dp the same f o r the l a r g e p a r t i c l e s w h i c h were i n the s m a l l p a r t i c l e  bed.  (c)  W i t h t h e s m a l l p a r t i c l e s w h i c h were i n the l a r g e p a r t i c l e  and the l a r g e p a r t i c l e s w h i c h were i n the s m a l l p a r t i c l e bed f l u i d i z e the r e m a i n i n g d a t a s h o u l d be (d)  m i x t u r e . . E x p a n s i o n and d i f f e r e n t i a l  bed  removed,. pressure  obtained.  At a v e l o c i t y  j u s t g r e a t e r t h a n the i n v e r s i o n v e l o c i t y ,  s e p a r a t e l y the upper and l o w e r beds o f the m i x t u r e .  remove  Measure the average  p a r t i c l e d i a m e t e r o f the l a r g e p a r t i c l e s w h i c h remained i n the top  bed  and o f the s m a l l p a r t i c l e s w h i c h remained i n the bottom bed. I f the p a r t i c l e s i z e , d i s t r i b u t i o n was  approximately  G a u s s i a n and i f  p a r t i c l e s i z e d i s t r i b u t i o n i s i m p o r t a n t ) the f o l l o w i n g r e s u l t s obtained.  should  be  F i g u r e 33 i s a diagram o f t h e p a r t i c l e s i z e d i s t r i b u t i o n i n  the s m a l l heavy p a r t i c l e bed and t h e l a r g e - l i g h t p a r t i c l e bed.  The  average  d i a m e t e r o f the s m a l l p a r t i c l e s measured i n ' p a r t (b) s h o u l d be i n the shaded r e g i o n A.  The  average d i a m e t e r o f the s m a l l particles measured i n  p a r t (d) s h o u l d be i n the shaded r e g i o n B. p a r t i c l e bed,  S i m i l a r l y f o r the l a r g e  t h e average d i a m e t e r o f the p a r t i c l e s removed i n pafct  s h o u l d be i n the shaded r e g i o n D, and the average d i a m e t e r o f the  (b)  particles  87-  d  d small heavy p a r t i c l e size distribution. Figure 33'  -  large l i g h t p a r t i c l e size distribution.  P a r t i c l e Size Distributions  removed i n part (d) should be i n the shaded region C.  I f the above  conditions are consistent with the experimental r e s u l t s f o r average p a r t i c l e diameters,, then p a r t i c l e size d i s t r i b u t i o n i s a very important f a c t o r a f f e c t i n g inversions.  The above procedure may be c a r r i e d out a  number of times u n t i l the' inversion occurs over a very narrow v e l o c i t y range. 2.  Most mixtures subjected to inversion runs i n the present research  were approximately  '}0~50 mixtures by volume. Numerous experiments  should be run where the i n i t i a l amount of each component added i s d i f f e r e n t from 50$ by volume.  If the r e s u l t s are similar to those  obtained i n the present report, i t can be concluded that the r e l a t i v e proportions of each material has noteffect on the mixing and segregation i n the f l u i d i z e d mixture.  I f the inversions obtained are clear-cut,  then runs made with very small amounts of one material added to another  88.  can be used to measure rates of mixing.  The time f o r the small amount  of material to mix homogeneously i n the component of large volume could be measured.  This would be a measure of the random mixing of p a r t i c l e s ,  because the d r i v i n g force due to bulk density difference would then be negligible. 3-  Experiments may  be made to determine the experimental l i m i t s of  density and size difference which can be tolerated i n seeking an inversion. h.  Motion pictures of. inversions may  how  an inversion takes place.  also be taken.to record v i s u a l l y  8 . 9  Literature Cited  1.  W i l h e l m , R.H.,  2.  Hancock, R.T., The M i n i n g Magazine,  3.  J o t t r a n d , R . J . , Chem.Eng. S c i . , 3 , 12  4.  R i c h a r d s o n , J . F . , and Z a k i , W.N., 31,  35  and Kwauk, M., Chem.Eng.Progr., 4 4 , 2 0 1 (1948). 55_, 9 0 ( 1 9 3 6 ) . (1954).  Trans.Inst.Chem.Engrs.  (London),  (1954).  5.  Leva, M., F l u i d i z a t i o n , M c G r a w - H i l l Book Co. I n c . , New Y o r k , 1959-  6.  H a p p e l , J . , A.I.Ch.E. J o u r n a l , 4 , 1 9 7  7.  Hawksley, P.G.W., Paper No.7 i n "Some A s p e c t s o f F l u i d Flow", London, Edward A r n o l d and Co.,  (1958).  1951.  8.  L e w i s , E.W.,  9.  V e r s c h o o r , H., A p p l . S c i . R e s e a r c h , A2,  and Bowerman, E.W.,  Chem.Eng.Progr., 48, 6 0 3 ( 1 9 5 2 ) . 155(1950).  10-.  A n d r i e u , R., Ph.D. t h e s i s , U n i v e r s i t y o f Nancy, F r a n c e , 1 9 5 6 .  11.  B e a r e , J.W.,  12.  Hoffman, R.F., L a p i d u s , L., and E l g i n , J.C., A.I.Ch.E. J o u r n a l , 6 ,  13.  De V e r t e u i l , G.F., B.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h  321  B.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia,  (i960).-  1958.  14.  I958.  Columbia,  A.S.T.M. S t a n d a r d s on P e t r o l e u m P r o d u c t s and L u b r i c a n t s , Baltimore,  1 9 5 8 , page 2 0 1 .  15.  Pruden, B.B., M.A.Sc. t h e s i s , U n i v e r s i t y o f B r i t i s h Columbia, 1 9 6 4 .  16.  C a i r n s , E . J . , and P r a u s n i t z , J.M., A.I.Ch.E. J o u r n a l , 6 , 554  17.  C a i r n s , E . J . , and P r a u s n i t z , J.M., Ind. Eng. Chem., 5 1 ,  18.  J a c k s o n , R.A., T r a n s . I n s t n . o f Chem.Engrs. (London), 4 l ,  19.  S l i s , P.L., W i l l e m s e , T.W.,  20.  A d l e r , I . L . , and H a p p e l , J . , Chem.Eng.Symposium  8, 58,  209  (i960),  l44l,.(l959). 13(1963).  Kramers, H., A p p l . S c i . R e s . S e c . A,  (1959)-  98 (1962).  •  S e r i e s , No.38,  APPENDIX I - BEARE'S PLOTS FOR PREDICTION OF INVERSION POROSITIES.  1-2  Belov/ i s p r e s e n t e d region. G  .  Beare. s p l o t f o r t h e l a m i n a r o r S t o k e s ' f l o w 1  I t r e l a t e s i n v e r s i o n c o n d i t i o n s w i t h p a r t i c u l a r v a l u e s o f f and 02 =ri|= 4 . 6 5  The p l o t i s b a s e d on t h e s i m p l i f y i n g a s s u m p t i o n s t h a t  i n t h e Richardson-Zaki equations, and t h a t t h e Stokes' law equation f o r f r e e s e t t l i n g holds. Thus  V  s  =  V € ' = n  V  0|  € 2 n  o 2  and  d f ^ S l - /  0  ^  ii7^  4  ..68  ^2-^9,  ieTi  1  €  4-66  (  2  <> A  The b u l k d e n s i t y d i f f e r e n c e a t i n v e r s i o n e q u a l s z e r o . Therefore PB\  ~PBZ  =  Psi('- i) €  +  P\ €  -  Psz^~ z) €  -  Pz €  =  0  or  (I- €,)(Al - P ) = (l-*2>(A>s2-/» whence _  l" 2 €  PsZ  " ^31  ~P ~P  Define 1  Then  /  /°$2 ~P Ps\  ~P  d  d  l  2  A  )  and from equation A above,  i  •  4-65  ••ft]  r.2 * 2  a  -2  (c)  Manipulating equations B and C,  a €  l  ~  a  —  I  3-65/4-63 2/4-68 _. r  |  and  c  =  2  €,/a +  (a-i)/a  Using the two equations given above, a chart was developed by Beare to give the p o r o s i t i e s of the two beds at inversion f o r any p a r t i c u l a r r  combination of  and Cl .  The chart,appears i n figure 33-  A s i m i l a r chart was also developed by the present author f o r the Newton region.  The assumptions used are:  (2) Newton's law f o r free s e t t l i n g holds.  ( l ) 01  = rig = 2-39  and  The inversion p o r o s i t i e s are  then €  5LzJ  =  gS-78/4-78  1  1/4-78 _  j  and  €  2  =  €,/a +  (a-i)/a  These equations were used to develop the chart, which works on the same p r i n c i p l e as Beare's chart and appears i n figure 34.  1-3  POROSITY F i g u r e ^k.  BED  Beare P l o t f o r Stokes' Lav/ Region.  I  APPENDIX I I SAMPLE CALCULATION AND ERROR ANALYSIS  2-2  Reference L i t e r a t u r e Data:  D e n s i t y o f Mercury. P e r r y , J.H., e d i t o r , Chemical Engineers.' Handbook, T h i r d McGraw-Hill Book Co.Inc., New York, 1 9 5 0 , p . 1 7 6 .  Edition,  D e n s i t y o f Carbon T e t r a c h l o r i d e . R i d d i c k , J.A. and Toops, J r . , E.E., Organic S o l v e n t s , Volume 7 , Second E d i t i o n , I n t e r s c i e n c e P u b l i s h e r s , I n c . , New York, 1 9 5 5 , P-194.  Drag C o e f f i c i e n t - Reynolds' number d a t a . Zenz, A.F., 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 R e i n h o l d P u b l i s h i n g C o r p o r a t i o n , New York, i 9 6 0 , p . 2 0 3 -  D e n s i t y o f Water. .Chemical E n g i n e e r s ' Handbook, p . 1 7 5 ,  complete r e f e r e n c e  above.  V i s c o s i t y o f Water. C h e m i c a l E n g i n e e r s ' Handbook, p - 3 7 4 ,  complete r e f e r e n c e  above.  Systems,  A.  Porosity  o f Bed.  H = 2 0 . 0 + 0.5 cm.  ;  W = 400.0 + 1 . 0 gm.  ;  p '  = 4 . 0 0 + 0.05 gm./cc. 2 A = 2 0 . 2 6 + 0 . 1 8 cm .  €= 1 - 400.0/(20.0 x 20.26 x 4 . 0 0 ) =  0.724  - €  1  W//o H A  =  s  1 400  0.05 4~00  0.5 20.0  0.18 20.26  maximum e r r o r i n ( l - € ) = ( 0 . 0 4 8 7 ) ( 0 . 2 7 6 ) = maximum e r r o r i n € maximum p e r c e n t e r r o r i n  (0-0487)(0.276) x 100$ 0.724  €=  =  B.  C a l c u l a t i o n o f P r e s s u r e Loss i n a F l u i d i z e d Bed. ^£-  F  =  X = p  =  0.394 - j * - ( p  M  - p  1 0 . 0 + 0 . 2 cm.  )g/g  F  P  ;  67.O + 0 . 6 l b s . / f t . ( p  M  -p  )  f  =  = 1  » 10.0  +  33.0  c  . lbforce/ft.  M  = 100.0+ 0.3 lbs./ft.  ;  L = 3 - 0 + 0 . 3 1 inches.  ( 1 0 0 . 0 - 67.O) + 0 . 9 l b s . / f t .  maximum p e r c e n t e r r o r i n A p p / L  C.  + 1.86$  =  + °-°  3 1 3  3.0  ) 100$ = 5.77 $ '  Velocity of Fluid. V  = f(Re)  D = 2 . 0 + 0 . 3 1 inches  p  = 66.6 + 0.6 lbs./ft.'  3  3  3  2-4  fj.=  0 . 0 9 0 + 0 . 0 0 2 l b s . / f t . sec.  Re - t a k e n from c o r r e l a t i o n c h a r t , f o r w h i c h t h e mean e r r o r i s + 2 . 8 $ maximum e r r o r ' i n V  =  2.8$ + ( °-°3i3 •  =  7.48$  2.0  +  *  0 ^ OTQTCF  *  0,002 0.090  )  1 0 0  #  ^  .  3-1  APPENDIX I I I - MATERIALS USED  Material  Alundum  Particle Shape  Density gm./cc.  Average Diameter mm.  3-95  0.645 0.645  §ranular, jagged  Ballotini  Cataphote  glass spheres  Nickel  glass micro-beads granular. shot, spherical spherical  NickelGlass Steel  n i c k e l coated g l a s s spheres b a l l bearings  Crystalon Lead  2.91-  2.73 2.47  Appendix IV Run No.  3  2*.  0.767 0.912 1-52 1.08 1.08 I.83 2.28  2 4 11 1 2*  0.767  9  5 1*  C 3-50  II.30  1.08 2.05  4.50  0.456 0.384 0.542  7.80 •  3-15  8.91  * p o l y e t h y l e n e g l y c o l s o l u t i o n r u n numbers  6 3* 1* 10  3*  APPENDIX IV - ORIGINAL DATA  APPENDIX IV - INDEX  Run No.  Description  Page  Polyethylene-glycol 1  B a l l o t i n i - N i c k e l Mixture  4-4  2  Ballotini-Alundum Mixture  4-9  3  Lead-Steel Mixture  4-13  4  B a l l o t i n i - N i c k e l - G l a s s Mixture  4-l6  1  B a l l o t i n i ( l . 0 8 mm.)  4-17  2  Alundum (O.767 mm.)  4-l8  3  Alundum (0.645 mm.)  4-19  4  Alundum ( 0 . 9 1 2 mm.)  4-19  5  Ballotini (1.83mm.)  4-l8  6  C r y s t a l o n ( l . 0 8 mm.)  7  B a l l o t i n i - N i c k e l - G l a s s Mixture ( l )  4-21  8  B a l l o t i n i - N i c k e l - G l a s s Mixture (2)  4-25  9  Alundum-Cataphote M i x t u r e  4-26  10  Alundum-Nickel  4-28  11  Alundum-Crystalon  Water  12  '  13  Mixture Mixture ( l )  Ballotini-Alundum Mixture Alundum-Crystalon  Mixture ( 2 )  ,  4-20  4-29. 4-30 4-20  A l l o r i g i n a l d a t a f o r t h e e x p a n s i o n runs and t h e f r i c t i o n a l p f e s runs a r e i n c l u d e d i n t h i s s e c t i o n . as  follows:  E x p l a n a t i o n s o f t a b l e headings a r e  4-3. Ave. Diameter  -  t h e average d i a m e t e r o f the p a r t i c l e s b a s e d on t h e a r i t h m e t i c average o f t h e s c r e e n s i z e s .  From Run  -  r e f e r s t o the p a r t i c u l a r run i n which the s i n g l e component d a t a f o r t h e m a t e r i a l appears.  A c r o s s Taps  -  t h e f r i c t i o n a j . p r e s s u r e g r a d i e n t r e a d i n g was measured a c r o s s the f o l l o w i n g two p r e s s u r e t a p s .  Run 1 ( P o l y e t h y l e n e G l y c o l ) - a r u n i n w h i c h the f l u i d i z i n g medium i s the polyethylene g l y c o l s o l u t i o n ; s i m i l a r l y f o r w a t e r runs ( w a t e r ) .  Meter ( M e r c u r y ) , e t c . - r e f e r s t o the p a r t i c u l a r f l o w meter and manometer f l u i d used t o make t h a t p a r t i c u l a r r e a d i n g .  4-4. Run 1 (Polyethylene Glycol) M a t e r i a l : Glass B a l l o t i n i Wt. of Sample: 1+00 gms. Manometer Reading . arm 1 i n . inarm 2 9-15  14.00 0.60 3-90  5.5O 4-55 2.20 6.60 15.10 4.15 6.10  * *  *  * * *  -  in.  Temperature column °F 70.8 71.0  6.95 10-75 4.60 4 • 30  72.5  71.0 71.0  7.00 3.15 1.00 4.80 11.65 2.25 4.00  69.5 70.2  70.4 70.6  70.7 71.0  Manometer Reading arm 1 i n . arm 2  3-40 3-75  4.40 4.85 5.65 6.15 6.50 7.25  Temperature Bed Of Room •height 70.1  23.6  71-0 73-4 71.6 71.4 69.6  29.8 38.3 54.6 96.6  70.8  14.1  in.  Temperature column °F  0.25 0.35 0.70 1.10 1.60 2.30 2.60 3.10 3.50 4.10 4.50 4.85 5.45  Meter (Mercury)  74.0 73-9 74.0 74.0 74.0 73-9 73-9 73-873-8 73.8 73-8 73.8 73.8  cm.  17.5  70.9 71.0 71.0  20.2 31.8 45.3  70.9  71.8  Meter (Mercury)  Run 1 (Polyethylene Glycol) M a t e r i a l : Nickel Wt. of Sample: 447 gms.  0.90 1.10 1.60 2.05 2.60  Ave. Diameter: 2.28mm. Density: 2*73 gm./cm3.  - |" Meter ( A i r )  Ave. Diameter: Density:  Temperature Room °F 73-2 73-4 73.8 73-6 73-9 73-6 73-7 73.8 73-7 73-8 73-4 73.4 73-6  O.456 mm.  8.92 gm./cm^. Bed height 5.4 5-7 6-7 7-4 8.5 10.1 11.0 12.3 13.7 16.0 17.8  19.5 23.0  4-5 Run 1 (Polyethylene' Glycol) M a t e r i a l : Glass B a l l o t i n i Wt. of Sample: 400.0 gm. From Run Manometer Reading arm  1  59-0 56.8 54.3 52.0 59-2 57.3 55.5 53-7 51.9 52.6 53-6  cm  arm  2  cm  61.4 63.7 66.2 68.6 61.2'  63.O . 65.O  66.9 68.8 68.5 • • 67.1 55.O . 65.6 56.4 64.2 •• 50.7 55-6 52.3 53-9 52.6 53-7 51.7 54.5 • 50.5 55-7 47.4 57.8 47.3 59-0 45.4 61.0 43.5 63.O 42.3  44.1 46.5  49.8 51.4 48.5 48.5 51.5  64.3  62.4 59-9 56.4 54.6 57.5 57-5 54.7  Temp Column °F  70.8 70.8 71.0 71.0 71.0 71.0 72.0 72.0 72.0 72-5  73.O  72.4 . 72.4 71.2 71.0 71.0 71.0 71.0 71.0 71.0 71.2 71.0 71.0 71.0 71-5 71.2 69-5 69-6 70.0 70.O  Ave. Diameter: 2.28 mm. Density: 2.73 gm./cc. Temp Room  Op  70.1 71. i 71.0 71.0 71.0 71.0 72.5 72.5 73-2 73.4 73.8 73-3 73-3 71.2 71.5 71.6 71.8 71.6 71-4 71.5 71.5 71.4 . 71.4 71-1 71-2 71.4 69-6 69.8 70.4 70.7  Bed Height cm  Across Taps .  23.5  1-2 1-4 1-6 1-8 1-2 1-4 1-6 1-8 1-10 1-12 1-10 1-8 1-6 1-4 1-2 1-2 1-4 1-6 1-10 . 1-12 1-16 1-20 1-36 1-28 1-20 1-10 1-21-4 2-5 4-5  29.8  • 38.3  5426'  96.6  17-5  Run 1 ( P o l y e t h y l e n e , G l y c o l ) -Materials: Glass B a l l o t i n i ';''Wt J* o f 'Samples ' 1+00. O^gmV' From Run. 1 '  Nickel  ' 1+59-0 gm.  ;  1  . Manometer R e a d i n g Temperature . arm 1 i n . arm 2 i n . column °F  0.1+0  •1-55  1.80 2.65 3-35 1+.50 5.60 6.30 6.70 7.30 1+.50  3.10 1+.10  1.10  2-35  ' 4.95  6.35 7.1+5 8.55 • 9.05 9.90 6.50 5.85  8.20  Temperature Room °F  71.8 71.7 71.6 71.8 71.5 71.6 70.5 70..3 71.8 72.5  72.0  72.6 72.6 72.8 72.8 • 72.9 70.6  '71.6  73.5 71+.0 73-1  71.0 71.0  •5-" M e t e r ( M e r c u r y )  73-2  Bed . H e i g h t s cm. Ni glass  8.1+ *  12.2  25.O 28.0  1I+.5  31-5  16.0 - : - '  39-6 37-5  70.0 75-0 80.0  Viscosity 16/ft.sec. O.O96  0.087 O.O79  34.1 37-2  1+0.2  t+8.0  36.0  59-0 70.0  39-6  36.3 1+0.5  -  * - S u b t r a c t 2.80 from a l l v a l v e s i n column.  Run 1 V i s c o s i t y and- D e n s i t y Temperature  21-5  10.6 .  Temperature Op  75-0 78.1+ 63.8  Density gm./cc.  66.55 66.52 66.73  4-7 Run 1 (Polyethylene Glycol) Materials: Glass B a l l o t i n i Wt. of sample: 400.0 gm. From Run 1 Bed Height cm.  Manometer Reading arm 1 arm 2 cm. cm.  18.7 25-2  60.0 • 66.6  31-8  74.3  35-0 •39.1 48.3 49.9 42.9 37-3 34.3  31.3  31.3  37-4  27.8 32.8 36.6 41.0 45.7 5O.9  30.4  56.2  ,  33.5  46.1 39^7 34.2 28.1  26.5 24.6 35.7 39-1 42.8 47.0  51.1  26.7  31.4  34.8  38.8  44.3  50.2  72.0  77.8 -  71.1  67.2 58.3 56.6  63.4 69.0  71.8 74.8 77-6  72.9 69-3 65.I  60.6  56.6 75-7 79-6  81.5 70.8 67.4  63.7 59-5  55-6 79-2 74.6  71.3 • 67.5 62.1 56.4  Nickel 459-0 gm. 1  Temp. Column op  Temp. Room op  Across Taps  71.8  72.0 72.4 72.5 72.6 72 .4 72.5 72.5 72.6 72.8 72.8 72.9  2-3 2-5 2-7 2-11 2-9 2-7 2-5 2-3 2-3 2-5 2-7 2-9 2-11 2-14 2-11 2-9  • 71-9  71.6 71.6 . 71-5 71.6 71.6  71.6 71-5 71.7 71.7 71.8 71.8  70.5 70.6 • 70.3  . 70.4 70.2 70.5  71.8  72.0  72.0 72.0 72.0 71-9 72.0 72.0 71.0  71.0  71.0 71.0 71.0 71-0 "  v  '  73-0 73-0  70.6  • 71-1 71.4 71.6  71.4 71-5  73.5 73-4 73-4 73.4 73-5 73-3 73-8 73-9 73-1 73-0 73-0 73-1  72.8  73-2  2-7  2-5 2-3 2-14  2-18  2-22 2-11 2-9 2-7 2-5 2-3 2-14  2-11  2-9 2-7 2-5 . 2-3  4-8  Run 1 (Polyethylene Glycol) Materials: Glass B a l l o t i n i Wt. of Sample: 400.0 gm. From Run 1 Bed Height cm. . 37-7  Manometer Reading arm 1 arm 1 cm. cm. .50.8  45.9  67.2  37-1 51.4 47.5 43.9  40.6 37-4 32.8 30.1 27.9 26.2 25.1  Temp. Column  79-7 80.8  Temp. Room  Acros; Taps  71-0 • 71-0 71.0 71.0  73,2 73-4 73-4 73-4  72-5 72.0 71.8  74.O  2-3 2-5 2-7 2-9 2-3 2-5 2-7 2-9 2-11  Ojp  55.8 60.6 65.0 69.1 ' 55-2 59-0 62.5 65.7 68.8 73-2 75-9 78.1  Nickel 4 5 9 . 0 gm. 1  ,  71-5 71-5 71.4 71.4 71.3 •71.3 71.3  Op  73-6 73.6 73-4 73-3 73-2 73.3 73-4 73-4 73-2  2-14 2-18 2-22 2-26 2-32  Run 2 ( P o l y e t h y l e n e G l y c o l ) Material: Glass B a l l o t i n i Wt. o f Sample 320 gm. Manometer R e a d i n g arm 1 i n . arm 2  2.60  7-00 5.80 4.65  9-15 10.25 11.05 9-65 7.40  • Temperature Column °F  2-75  *  1.60 0.80 13.50 6.40  7.30 7.90 6.80 5.00 4.10  6-35 5.20  3.15  * i it " Meter ( A i r ) Run 2 ( P o l y e t h y l e n e G l y c o l ) Material: Alundum Wt. o f Sample: 440 gm. Manometer Reading arm 1 i n .  4.40  4.75 5-10  5.5O  . 6.05 6.5O  3.85 3-25 2.60 1-95 1-35  Arm 2 i n . 2-75 3-00 3-20 3.60 4.10 4.45 2.25 I.70 1.10 0.50 0.00-  Meter ( M e r c u r y )  Temperature Room °C  1.08 ram. 2.91 gm./cm^. Bed H e i g h t era.  24.0. 75-6 24.0 76.0 24.0 74.5. 24.2 74.7 24.3 74.7 24.3 75-0 24.5 75-0 75-2 24.6 75.6 . 24.6 24-7 74.9 24.9 74.8 74.8 24.8 74.6 24.6 75.O 24.6 75.0 25.0 75-3 25.O.. in Meter ( M e r c u r y )  2.25 5.30 5.50 4.65 3-70  5.5O 8.O5  3-35 2.47 12.40  in.  Ave. Diameter Density  Ave. Diameter: Density:  . Temperature Column °F  71-3 71.1 71.3 71-3 71.3 • 71.4 71.3 71.3 71-3 71.3 71.3  9.6 10.8 40.6 32.8 26.7  22.4 18.1 15.1 13-3 49.4 66.5  82.8 58.6 35-8 29.4 24.1  0.645 mm. 3.95 gm./crn^. Temperature Room °F  71.2 71.0 71.4 <I 70.9 71.2 71.5 71.2 71.0 71.2 71-3 71.4  Bed H e i g h t cm.  31.1 33-5 36.6 40.6 47.0 53.5 28.5 24.4 20.6 17-1 13.8  4-10 Run 2 (Polyethylene Glycol) Material: Alundum Wt. of Sample: 440.gm.  Ave. Diameter Density  Manometer Reading Temp. Column arm 1 arm 2 o in. in. . F  52.3 49.7 47.4 45.1 42.8 39-3 40.9 -44.5 48.1  51-7 52.5 50.5  48.6 46.7  44.8  42.0  38.8  55-2 . 57-7 59-9 62.2 6&.5 67.9 66.3 62.9 59-4 55-6 54.9 56.9 58.8 60.6 62.4 65.2 68.2  71.1 71.0 71.0 71.0 ' 71.2 71-3 71.4 71-5 71-5 71.2 71-5 71.7 . 71.6 71.6 71.6 71.7 71-7  Temp. Room °F  71.1 70.9 71.0 71.2 71.2 71.4 70.9 71.2 71.2 70.2 70.6 70.8 . 71.0 71.1 70.9 71.2 71-5  0.645 mm-  3.95 gm./cc.  Bed Height cm.  32.6  21.1  42.0  Across Taps  1-2 1-4 1-6 1-8 1-10 1-13 1-8 1-6 1-4 1-2 1-2 1-4 1-6 1-8 1-10 1-13 1-17  4-11 Run 2 (Polyethylene Glycol) Materials: Glass B a l l o t i n i Wt. of Sample: \ 320.0 gm. From Run 2  Alundum  v  Manometer arm 1  7-20 7.00 6.5O  8.30 9.9O 11.70 13-45 2.20 2.50 3.05 3-35 3.85 4.30 4.95 5.50 6.10 6.70 7-25 7-75 *  * * *  * * * *  Reading arm 2 7-40  2.40  2.90 3-40  '  Run 2 V i s c o s i t y and Density  70.0 75-0 80.0  Temperature Room °C  22.0 22.2 22.0 22.4 22.6 22 ..3 22.3 - 22-3 22.4 22.4 22.5 . 22.6 22.4 22.4 22.2 22.1 22.6 22.5 22-7  73-5 74.0 73-1 73-5 73-7 73-8 73-8 73-7 73-7 73-5 73-6 73-9 73-4 73-4 73-2 73-0 73-1 73-0 73-1  in Meter (Mercury)  Meter ( A i r )  Temperature op  2  ' Temperature Column °F  6.90 7.50 9-30 IO.85 12.70 14.50 0.50 0.80 1.25 . 1-55 2.00  3.90 4-35 4.80 5-25  447-0 gm.  •  Viscosity lb./ft.sec.  Temperature °F  Density gm./cc.  O.O79  70.0 75-0 80.0  66.67 66.61 66.55  O.O87 O.096  Bed •Height cm.  25-5 24.8 25.4 . 27.4 28.9 30.5 31-9 33-6 36.4 40.7 44.1 48.2 53-4 61.1 69.7 80.7 92.8 108.6 125.4  4-12 Run 2 (Polyethylene Glycol) Materials: Wt. of Samples From Run Manometer Reading arm 1 arm 2 cm. cm.  31.6 27-9 24.4  21.1 16.0 16.1 21.4 25.5 28.3 30.9 33-6 36.5 35-1 29.4 24.2  19.8 15.4 32.6 27.1 22.5 13.4  37.1 35.7 '34.2 32.9 31.6 29.8 27.1 24.6  22.1 18.8 14.9  13-1  43.9 47.6 51.1 54.4 59.4 59.2 54.1 50.1 47.4 44.8 42.1.  39-5  40.6 46.1  51.3 55-6 59.9 43.7 49.5 54.2 53.3  38.6 40.1 41.5 42.6  43.9 45.8 48.4  50.7 53-2 56.6 60.3 62.1  Alundum  Glass B a l l o t i n i 315-0 gm.  Temp. Column • °F  72.3 71-9 71.7 71.7 71-7 71-2 71.2 71.2 71.5 71.5 ' 7L5 71-5 73-8 73-8 73.9 73-9 73-9 74.3 74.9 74.8 74.8 73-5 73-5 • 73-2 73.0 . 73-2 73-3 73-273-2 73-2 73-0 73-2 73-1  440.0 gm.  ' 2  Temp • Room o F  72.5 72.2 72.4 72.0 72.0 71.8 71-8 71.2 . 72.2 71.3 71.1 71.6 72.8 72.9 73.9 74.0 74.2 74.3 74.9 75.0 . 74.8 72.8 73.2 72.9 72.8 73.2 . 73.6 73.0 72.5. 72.6 72.5 72.9 73-0  2  Bed Height cm.  34.0  1-4 1-6 1-8 1-10 1-13  45-9  .1.17  •  24.5  100.0  Across Taps  1^13 1-10 1-8 1-6 1-4 1-2 1^2 1-4 1-6 1-8 1-10 1-3 1-5 1-7 1-9 1-2 1-4 1-6 1-8 . 1-10 1-13 1-17 1-21 1-25 1-31 1-39 1-43  4-13  Run 3 ( P o l y e t h y l e n e G l y c o l ) Material: Lead Wt. o f Sample: 900.0 gm. Manometer arm 1 i n .  2.20 4.30 7.20 0.40  Reading arm 2 i n .  * * *  1.00 1.70 2.45 3.05 4.15 4.95 5.80 6.70  3.50 . 5-20 7.80 1.50 2.10 2.80 3.70 4.40  5-80 6.75 7-8ai ' 9.85  "  Temperature Column °F  73-4 73-4 73-4 73-6 73.4 73-4 73.4 73.4 73-4 73-4 73-6 73-6  Ave. Diameter Density  Manometer Temperature Redding a r m t j l ^ l i n T r j . e arm'.. 21. i n . Column °F  8.15  9-95 11.10  2.80 5.80  O.55 1.40  2.20 2.85 3-80 4.90 6.10 7.60 8.60  In Meter ( A i r )  Bed H e i g h t cm.  8.5 9-7 10.9 12.3 14.3  16.3 18.5 20.4 24.2  27.1 31.1 35-3  Meter (Mercury)  Run 3 ( P o l y e t h y l e n e G l y c o l ) Material: Steel Wt. o f Sample: 800 gm.  * *  Temperature Room °F  73-9 73.8 73-9 74.0 74.0 74.0 73-9 73-9 74.0 74.0 74.1 74.0  Meter ( A i r )  1.30 4.90 1-55 2.50 3-35 4.15 5.30 .6.60  2.05 mm. 11.33gm./cc,  Ave. Diameter Density  74.0 73-9 73-9 73-9 73-9 73-9 • 73-9 74.1 74.2 74.2 74.1  3.15mm. 7.83gm./cc.  Temperature Room °F  -  Bed Height  10.1  73-2 73-2 73-2 73-2 73-4  11.6 ' 13-0  73-5  16.9  73.5 73.4 . 73.3 73-3 73-4  Meter (Mercury)  14.7 15.8 I8.3  20.0 22.1 24.6  26.1  cm.  4-14 Run 3 ( P o l y e t h y l e n e G l y c o l ) Material: Lead Wt. o f Sample: QOO.O gm. From Run 3 Manometer arm  1  Reading  in.  14.30 **  2.45  *  9.70 13.50 2.05 2.50 3-00 3.50 4.30  * * .  5.6O  *  .5-55  6.45 6.95 7-85 '8.65 9.15 9.80 10.30 10.70 11.20 * **  Steel  800.0 3  Temperature  arm 2 . i n .  Column  11.10 3-70 6.30 9.90 13-20 1.00 1.40  11.80 2.25 2.95 4.00 4.70 55U5 5.90 6.50 6.90 7.40 7.80 8.15 3.55  I " Meter ( A i r ) t " Meter (Mercury)  °F  72.6 73-7 74.0 74.3 74.3 73-8 73-6 73.5 73-6 74.0 74.0  gm.  Temperature Room °F  Bed Height  74.4 72.6 72.8 73-0 73.0 72.8 73.0 72.8 '73-0 73-0 73.2 73-4 71.2 71.0 71.2 70.8 70.8 71.0 71.0 71.0  74.O  74.0 74.0 73.8 73-5 73-2 73-3 73-3 73-3  18.6 20.2 2211  24.4 ,  26.4 28.1 30.1 32.1 34.1 37-4  42.1  45.6 47-3 51.6 56.1 59-6 63.8 67.4 . 71-6 75-1  ^" Meter (Mercury)  Run 3 V i s c o s i t y and D e n s i t y Temperature F  70.0 75-0 80.0  Viscosity lb./ft.sec.  Temperature °F  0.081 0.088  70.0 75.0 80.0  O.O99  Density lb./ft.  66.64 66.60  66.49  cm.  i  '  4-15 Run 3 ( P o l y e t h y l e n e G l y c o l ) Material: Lead Wt. o f Sample: 9 0 0 . 0 gm. From Run 3 Manometer arm 1 cm. 42.5 48.9 48.7 48.5 48.5 48.8 48.6 48.8 48.8 50.4 50.4 50.3 50.4 50.5 50.4 50.5 50.5 50.4 50.4 46.6 46.7 49.O 49.2 48.7 48.8 48.4 45.O 44.8 44.6 51.1 46.9 47.I 46.8 46.9 47.2 49.2  Reading arm 2 cm. 66.8 60.7 61.0 60.8 61.O 60.4 60.8 60.2 60.6 . 58.6 58.8 58.7 58.7 58.4 58.7 58.4 53.6 58.4 58.7 62.4 62.4 59-3 60.0' 60.3 60.5 60.5 64.5 64.4 64.8 57-9 61.3 62.2 62.1 62.5 61.8 60.1  Steel 8 0 0 . 0 gm. 3  .  Temperature Temperature Column . Room °F °F 73-0 73-0 73-0 73-0 73-0 73-0 73-0 73-3 73-3 75.0 74.7 75-0 73-9 73.8 74.0 74.1 73-9 74.0 74.0 74.3 74.3 73-3 73-5 73.6 73-5 73-8 73-8 73.8 73-5 73-5 73-5 73.7 73.8 74.0 74.0 74.1  •'  71.2 71.4 71.4 71.4 70.9 71 .'0 71.2 71.0 71.2 73-7 73-5 74.3 72.9 72.5 73-2 73-4 72.3 72.8 73-0 72.7 72.6 71.4 71.6 71.8 72.0 72.0 72.2 72.3 72.0 71.9 71.7 71.7 71.8 71.8 72.0 72.1  •  Bed Height cm. 28.8  44.6  60.1  22-7  Across Taps 2-4 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 2-3 3-4 4-5 5-6 6-7 7-8 8-9 .9-10 10-11 11-12 12-14 14-16 22-20 20-l'8 18-16 16-14 14-12 12-9 9-6 6-3 3-2 2-3 3-4 4-5 5-6 6-7 7-8  4-i6  Run 4 ( P o l y e t h y l e n e Material: W.t..^ o f aSample:  Glycol) Nickel Glass 296.0 gm.  Manometer Reading arm 1 i n . arm 2 i n . 0.30 0.60 1.00 1-35 1.95 2.35 2-95 3-40 3.80 4. 30-  Temperature Column °F  0.50 0.80  75-0 75-0 75-1 74.9 74.8  1.15 1.45 1-95 2-35 2.85 3-20 3.50 • 4.00  74.9. 74.8 74.9 74.9 74.9  Ave.Diameter Density Temperature Room °F  0.542 mm. 4 . 50 gm/cc. Bed' Height cm. 7.2 8.4  73-4 73-6 74.0 73-6 73-6 73.8 73.6 73-6 73-8 73-6  0.8 10.8 12.7 14.6 17-3 20.1 23.3 28.3  Meter (Mercury)  Run 4 ( P o l y e t h y l e n e Material: Wt. o f Sample: From Run  Glycol) Glass B a l l o t i n i 2 9 0 . 0 gm. 1  Manometer Reading arm 1 i n . arm 2 i n . 0.35 0.70 1.20 1.65 2.10 2.60 3-15 3-65 4.20 4.65  0.50 O.85 1.30 1.70 2.10 2-55 3-00 3-40 3.85 4.20  Meter (Mercury) * Homogeneous M i x i n g P o i n t  Temperature Column °F 76.7 76.8 76.4 75-8 75-6 75-3 75-4 75-4 75-5 75-6  N i c k e l Glass 2 9 6 . 0 gm. 4 Temperature Room °F 74.8 74.8 74.4 74.1 74.3 74.2 74.4 74.2 74.3 74.4  Bed H e i g h t cm. 16.8 19-9 22.9 25-7 28.5 32.0 36.3 41.5 48.3 56.3  4-17  Run 1 (Water) Material: Wt. o f Sample:  Glass B a l l o t i n i 400.0 gm.  Manometer R e a d i n g arm 1 ' i n . arm 2 i n . 3.40 2.65 2.05 1.45 4.15 4.80 5-35 5.90. 6.50 7.10 7.85  8.5O 9.O5 10.15  11.40 12.65 13.85 15.10  c  :  I.30 O.65 0.05 0.45 2.00 2.60 3.05 3-45 4.00 4.50 5-10 5-65 6.10 7.00 8.00 9.00 9-95 10.95  •g-" Meter ( M e r c u r y )  Temperature Column OF 78.9 78.8 78.8 78.7 73.7 . 78.7 78.7 78.7 78.7 78.7 78.7 78.7  78.7 78.7 78.7 78.7 78.7  78.7  1.08 mm. Ave.Diameter Density 2 - 9 1 gm./cc.  Temperature Room• oc 24.3 24.3 24.3 24.3 24.3 24.2 24.2 24.2 24.2 24.2 24.2 24.0 24.0 24.0 24.0 24.0 24.0 24.0  Bed H e i g h t cm. 15.80  14.60 13-40 11.90 17-00 17.00  I8.7 19.4 20.3 21.0 22.1 22.9 23.6 25.2 26.8 28.6  30.3 32.1  4-18  Run 2 (Water) Material: Wt. o f Sample:  Alundum 500.0  Manometer Reading arm 1 i n . arm 2 i n 0.25 0.55 0.95 1-35 1.90  0.55  2-35 2.95 3.45 4.05  2.40  4.60  4.30 4.80 5.40  Temperature Column °F 69.5 69-5 69.5 69-5 69.5 ' 69.5 • 69.2 . 69.2 69-1  O.85  1.20  1-55 2.05 2.95 3-35 3-35  5.20 5-95 6.70 7-20  Temperature Room ' °C 22.5 22..5 22-5 22. 5 22.5 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 • 22.6 22.6  '  69.I ' 69.O 69.O 69.O 69.O  6.00 6.45 7.00  7-95  Ave. Diameter O.767 mm. Density: 3 . 9 5 gm/cc  gm.  69-0  Bed H e i g h t cm. 12.0 13-0 14.0  14.3 15-9 16.7 17-8 18.6 19-5 20.5  21.4 22.6 23.8 24.7 25.9  Meter (Mercury)  Run 5 (Water) Material:' Wt. o f Sample:  400.0  Manometer Reading arm 1 i n . arm2. i n O.85 1.95 3.40  4.60 5.9O 6.9O 8.10 9.45 10.60 11.80 13-10  Ave. D i a m e t e r Density  Glass B a l l o t i n i  1.05 2.00 3-30  4.25 5.30 6.10 7.00 8.00 9.05 10.00 11.00  •|" Meter ( M e r c u r y )  gm.  I . 8 3 mm. 2 . 9 1 gm/cc.  Temperature Column °F  Temperature Room oc  Bed H e i g h t cm.  70.2 70.2 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70.1  23.0 23-0 23-0 23.0 23-0 23.0 23-0 23.0 23.0 23.0 23-0  11.0 12.0  •  •  13-3  14.1 15.0 15.6 lb-. 2 lb. 9 17-6 18.2 18.7  •  4-19 Run 3 (Water) Material: Wt. o f Sample:  Alundum 5 0 0 . 0 gm. .  Manometer Reading arm 1 i n . arm 2 i n . 0.25 O.65 1.10 1.50 1-95 2.35 2.80 3.45 '4.10 4.80 5.50 6.15 6 . 50 7.45 8.10  0.50 0.95 1.30 1.70 2.05 2.40 2.80 3-35 3.90 4.45 5.05 5-55 6.00 6.60 7.10  Ave. Diameter . Density  Temperature Column °F 70.0 ' 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 • 70.0 71-1 71.1 71.1  Temperature Room .°C 23.2 - 23-2 23.2 23-'2 23.2 23.0 73-0 23.0 23.0 23.0 23.0 23.0 23.0 23.0 23.0  1 0 . 6 4 5 mm. 3 . 9 5 gm/cc. •Bed Height 12.6 14.0 15-3 16.2 17-3 18.1 19.0 20.3 21-5 22.7 24.3 25.6 26.3 28.4 29.6  •§" Meter (Mercury)  Run 4 (Wa t e r ) Material: Wt. o f "Sample:  Alundum 5 0 0 . 0 gm.  Manometer Reading arm 1 i n . arm 2 i n 0.30 0.80 1.20 1-95 2.55 3.20 3-80 4.45 5.15 5.80 6.70 7-70  0.50 1.00 1-35 2.00 2 . 50 3.10 3.60 4.10 4.70 5-20 5-95 6-75  Meter (Mercury)  Temperature Column °F 74.2 74.2 74.2 74.2 74.3 74.2 74.2 74.2 74.3 74.3 74.3 74.3  Ave. Diameter Density  0 . 9 1 2 mm. 3 . 9 5 gm/cc.  Temperature Room °C  Bed H e i g h t cm.  22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6 22.6  11.4 12.8 13.7 14.9 15.8 16.7 17-5 18.3 19.2 20.0 21.1 22.4  4-20  Run 6 (Water) Crystalon Material: 3 5 0 . 0 gm. Wt. o f Sample: Manometer R e a d i n g arm 1 i n . ant1 2 i n . 10.80 3-10 0.20  * *  0-75 1-55 2.50 3.35 4.30 5.50 7.20 8.80 10.30 11.70  *  Run 13 Materialr Wt. o f Sample: From  4-75 5.45 6.20 7.20 3.60 9.80 11.00 12.15  0.05  0.40 1.00  1.30 2.80 3-80 5-45 7.20 9-.40 10.60 11-95 13.60  13-60 2.70 3-00  3-55 4.20 5.00 5.80 7-10 8.50 10.25 11.25 12.30 13-75  * \" M e t e r ( A i r )  Temperature Room °C  70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.0 70.1 70.1 70.1 70.2  19.6 19.6 19-7 19-7 19.7 19.4 19.6  19.7 19.8  70.3  19.9  19-9 19.8 19.6  B£d H e i g h t cm. 11-3 9-8 12. 5 13.3 14.4 15.5 16.5 17.6 19.2 21.2 23.2 25.2 27.1  3" Meter ( M e r c u r y )  Crystalon  Alundum 3 5 0 . 0 gm. Run 3  Manometer R e a d i n g ana 1 i n . arm 2 i n . 14.00 *  Temperature Column °F  10.60 3-20 2.85 3-30 4.00  Meter ( A i r )  1 . 0 8 mm.  Ave. D i amete r • Density  350.0  gm.  Run 6  Temperature Column °F  Temperature Room °C  70.4 70.5 70.6 70.7 70.6  19-8 20.0 20.0 20.0 20.0  70-7 70.7 70.8 70.3 71.4 70.9 71.0 70.8  1  19-9 20.0 20.0 20.0 20.0 20.0 19.9 20.0  Meter ( M e r c u r y )  Bed H e i g h t cm. 21.7 22.9 23-7 25.6 27.7 30.1 32.6 36.7  . 41.3 47.3 51.7 56.0  63.O  4-21 Run 7 (Water) Material: Wt. o f Sample:  Glass B a l l o t i n i 320.  S gin.  Manometer R e a d i n g Temperature arm 1 i n . arm 2 i n . Column °F 4.60  *  3-20 6.60 11.50 ' 2.80  0.70 *  14.S0 * 0.15 0.90 1,80 2.60 3.50  3-40  '  8.40  * I " Meter ( A i r )  Run 7 (Water) Material: Wt. o f Sample:  7-30 12.80 2.85 3.45 4.35 5-25 '  72.3 72.3 72.4 • 72.5 72.5  22.9 23.0 23-0 23.0 23.0  Nickel-Glass 3 3 4 . 0 gm.  3.40  * * *  72.3 72.3 72.4  6.40  6.5O  8,00  2.10 0.50 0.10  4.5O 3-10 2.55  * ^" Meter ( A i r )  1.08 2.91  mm.  Bed H e i g h t cm. 9-1 9.9 10.6 11.4 12.3 13-4  14.2 15-2 16.0 17.1 18.1 19.2 20.1  Meter ( M e r c u r y )  Manometer R e a d i n g arm 1 i n . arm 2 i n . 3.10 7-10 12.70 0.20 0.90 2.00 3-10 4.50  Temperature Room °C 22.9 22.9 23-0 22-9 22.8 22.9 22.9 22.9  71-9 71.9 72.1  4.20 4.85 5-55 6.30 7.20 7.90 8.80 9.50  4.40 5.45 6.45 7.50  71.8 71.8  Ave. Diameter ' Density  .  Temperature Column °F  Ave. Diameter Density Temperature Room °C  67.2  19.6  67.7 67-3 67.4 67.6 67.8 68.1 68.3 68.3 68.4 68.5 68.6  19.5 19.5 19.6 19.6 19.8 20.0 20.0 19.7 19.6 19.6 19-5  \" Meter ( M e r c u r y )  0 . 5 4 2 mm. 4 - 5 0 gm/cc. Bed Height 7.0 7-6 8.4 9-1 10.0  11-3  12.3 13.8 15.0 11.4 9.6 ' 8.7.  4-22  Run 7 (Water) Mixture Wt. o f Sampler From Run  Glass B a l l o t i n i 3 2 0 . 0 gm. 7  Manometer R e a d i n g m l i n . arm 2 i n . 3-10  *  4.30  *  8.80 0.05  *  4-95 5.90  8.40  10.05 10.80 12.80  5.50 6.80 7.90 9.45 11.20  Glass  23-5 24.7 27.5  Nickel-Glass 99.O gm.  gm.  7  7  Temperature Room °C  Temperature Column °F 70.4  10.40  70.3 • 70.3  * \" Meter ( A i r )  15.0 16.1 17.4 19.2 21.1  Ballotini  320.0  4.90 13.00 2.80 3-50 4.45 5.3O 6.25 7.20 8.20 9-10 11.30  14.1  |" Meter ( M e r c u r y )  Manometer R e a d i n g arm 1. i n . arm 2 i n .  4.40  13.1  70.3 "70.2 70.2 70.2 70.2 70.2  7-15  '  10.1 10.5 11.3 12.2  22.0  7O.3  3-6o 4.20  * *  Bed H e i g h t cm.  70.2 70.2 •70.2 70.2  * •5" Meter ( A i r )  2.70 11.20 0.20 1.00 2.15 3.20  Temperature Room °C  70.5 70.3  3-Q5  Run 7 (Water ) Mixture Wt. o f Sample: From Run  gm. 7  70.6  2.50  0.S0  49-5  Temperature Column °F  4.90 6.30 10.30  1.15 1.90 2.70 3-90 5.45 7.00 9.20 10.10 12.50  N i c k e l Glass  7O.5 70.5 70.3  7O.3 7O.3 70.3 70.3 70.3  7O.3  . •  22.0 22.0 22.0 22.0 22.0 22.0 22.1 22.2 22.2 22.1 22.2 22.2  •g-" Meter ( M e r c u r y )  Bed H e i g h t cm. 11.1 13-0 14.1  15.4 17.0 18.4 20.0 . 21-4 23.2 24.6  26.7 29-3  4-23  Run 7 (Water) Material: Wt. o f Sample: From Run  Glas s B a l l o t i n i 3 2 0 . 0 gm.  ;  *  6.3O  70.8 70.9 70.8  .  2.75 3.50 4.30 5.30  70.7 70.7 70.6 70.6  6.40  3-10  *  0.00 O.65 1.30 2.10 3-10 4.30' 5.00 5.85 7.10  •  70.7 • 70.7 • 70-7 70.6 70.6  7.70  • 8.5O 9.70 11.00  Glass B a l l o t i n i 3 2 0 . 0 gm. 7 Temperature Column °F  6.00 11.50 2.60 3-20  71.0 71.0 71.0 71.0  3-75 4.45 5.20 6.20  70.9 70.9 71.0 71.0 71.0 71.0 71.0  6-75  7.40 8.5O  Meter ( A i r )  Temperature Room °C  Bed Height cm.  22.4 22.3 22.3  12.6 13-6  22.3 22.3 22.4 22.3 22.3 22.3 22.4 22.5 22.5  15.5 17-0 18.6 20.4 22.4  14.3  24-7 26.3 28.5 31-0  •5-" Meter (Mercury)  Manometer Reading arm 1 i n . arm 2 i n .  *  Temperature Column °F  10.10 13.60  Run 7 (Wate r ) Material: Wt. o f Sample From Run  •  7  Meter ( A i r )  8.40 *  I65.O gm.  7  Manometer Reading arm 1 i n . arm 2 ' i n . 3.7O * 7.60 * 11.30 * 0.15 1.00 2.00 3-20 4.60 6.15 7.15 8.80 10.30  N i c k e l Glass  Ndckel G l a s s 2 4 7 - 5 gm. 7 Temperature Room °F 22.6 22.7 22.6 22.5 22.5 22.6 22.7 22.7 22.8 22.8 22.9  •5-" Meter (Mercury)  Bed H e i g h t cm. 14.3 15.9 17^4 18.8 20.2 21.6 23-3 25.3 26.5 2£.l 30.3  4-24 Run 7 (Water) Material: Wt. o f Sample: From Ron Manometer arm 1  in.  Reading arm 2  2.80 * 6.70 * 13-30 *  Temperature in.  3-60 . 7-30 13.50 3-00 3-75  o.4o  *  Glass B a l l o t i n i 194.0 gm. 7  1.25 2.05 3-05 4.20 5.05 6.20 7.75  4.40  5.20 6.15 6.80 7-70 8.90  £ " Meter ( A i r )  Run 7 (Water) Material: Wt. o f Sample: From Run Manometer arm  1  in.  6.40 * 8.70 * 14.20 *  0.45  1.30 2.50 3-90 4.90 5.60  *  Column' • ° F  Nickel  300.0 7  Temperature Room  . 69.7  •jj-" Meter  Glass B a l l o t i n i 38.8 gm.  Nickel  2 in. 6.70 8.. 90 14.20 3.00 3-70  arm  4-75 5.80 6.65 7.20  Meter ( A i r )  Bed Height cm.  11.6 12.7  14.2  15-6 17-1  18.4  20.0 21.8 23.1  24.9  27-3  (Mercury)  -Glass  300.0 gm. 7  7  Reading  °C  23.0 23-0 23.0 23.0 23.0 23-0 23.1 23-0 23.0 23.0 23.0  70.O  69.8' 69-7 69-7 69.5 69.6 69.6 69-5 69.6 69.5  Glass gm. .  Temperature Column ° F  Temperature Room °C  70.0 70.0 69-8 6§. 69-7 69.6 69.5 69.4 69.4  22.9 23..0 23.0 23.0 23.0 23.0 23.0  10.0 11.0 12.4 13-8  23.0  15577  7  23.O  Meter  (Mercury)  Bed Height  8.0 8.4  •9-1  14.9  4-25 Run 7 (Water) Material: Wt. o f Sample: From Run  Glas s B a l l o t i n i 300.0 gm. 7  Manometer Reading arm 1 i n . arm 2 i n . 4.70 * ' 8.00 * 11.90 * 0.05 0.55 1-45 2-35 3-50 4.50 5.35 *  68.9 68.8 68.8 68.7 68.7 68.6 68.6 68.768.7  Meter ( A i r )  3.20 7.9O 12.20 0.0 0.50 1-25 . 2.20 3.20 4.40 5.40 6-35 7.45 8.80 9.9O 1  it  * * *  Temperature Room °C 22.2 22.2 22.2 22.3 22.2 22.2 22.3 22.3 22.4 22.4  68.7  Bed H e i g h t cm. 7.1 7-6 8.1» 8.7 • 9-4 10.4 11.4 12.5  13-614.3  •q:" Meter (Mercury)  Glass B a l l o t i n i 3 2 0 . 8 gm. 7  Manometer Reading arm 1 i n . arm 2 i n .  t  Temperature Column °F  4.70 7.80 11.60 .2.65 3-10 . 3-90 4.60 5-55 6.35 7-00  Run 8 (Water) Material: Wt. o f Sample: From Run  N i c k e l Glass 19.4 gm. 7  3-40 7.80 12.20 2.70 3-10 3-75 4.55 5.3O 6.3O 7.10 7.85 8-75 9.80 10.70  Meter (Water )  Temperature Column ° F 69.8 69.O 6Q.2 69.4 69.5 69.5 69.6 69.5 69-7 69.9 70.0 69.8  N i c k e l Glass 33^.0 gm. 7 Temperature Room °C 20.0  Bed Height 15.9 17.6 I8.9 20.1 21-3 23.1 25.1 27-0 29.5 31-4 33-3 35-7 38.3 41.3  69.9 70.0 Meter (Mercury)  4-26 Run 9 (Water) Material: Wt. o f Sample: ' Manometer arm 1  Reading  i n . arm 2  -0.15 -0.70 -0.45 0 0.35 1.25 1.90 2.95 3-80 4.70 0.65 6.70 . 7.80 8.90  Alundum 4 0 0 . 0 gm.  Temperature in.  O.55  2.05 2-35 2.80 3-05 3-80 4.40 5.20 5.90 6.70 7.40  8.20 9.O5  10.05  Column  Temperature  °F  Room  73-0 73-0 72.7 72.6 72.5 72.5 72.5 72.7 72.7 72.7 72.6 72.6 72.7 72.6  -0.50 -0.15 0.25 0.75 1.25 2.05 2.85 3-6o U.25 5.15 5-95 6.70 7-30 7.80  23.O 23.O 23.O  23-0 23.0 23.O  - 300.0 gm. o f c a t a p h o t e on t o p 2.25 67.6 2-55 67.6 2.95 67.8 3-40 • 67.9 3-85 68.0 4.45 68.1 5-15 68.8 5.70 68.9 6.25 69.0 6.90 69.I 7.60 69.2 8.20 69.2 8.70 69.8 9.10 69.9  5-" Meter ( M e r c u r y )  °C  23.O  * Above r u n w i t h o u t c a t a p h o t e b e d on t o p Below  0 . 9 1 2 mm. 3 - 9 5 gm/cc.  , Ave. Diameter Density  23.0 23-0 23.0 22.6 23.0 23.0 22.9  Bed H e i g h t cm.  8.5 9-9 10.4 11.1 11.5 12.6 13.5 14.4  15^3 16.2 17.1 18.1 19.2 20.5  -  20.0 20.0 20.2 20.2 20.2 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3  10.2 10.7 H-3  12.0 12.6 13.4  14.2  15.0 15.6 16.5 17.4 18.2 18.8 19-4  4-27 Run 9 (Water) Material: Wt. o f Sample: Manometer  1 in. -0.50 -0.15 0.25 0.75 11.25 2.05 2.85 3-6o 4.25 5-15 5-95 6.70 7-30 7.80  arm  Cataphote 300.0 gm.  Reading arm  2 in. 2.25 2-55 2.95  .3-40  3.85 4.45 5-15 5.70 6.25 6.90 7.60 8.20 8.70 • 9.10  Meter (Mercury)  Ave. Diameter Density  Temperature Column °F  67.6 67.6 67.8 67-9 68.0 68.1 63.8 68.9  69.O  69-1 69-2 69-2 .." '69.8 69.9  O.767 mm. 2.47 gm/cc.  Temperature Room C  Bed Height  20.2 20.2' 20.2 20.3 20.3 20.3 20.3 20.3 20.3 20.3 20.3 , 20.3 20.3 20.3  15.0  0  16.3 17.8 19.4 21.1 23.7 26.3 28.9 31.5 35-2 39.1 43-3 46.7 49.9  4-28  Run 1 0 (Water) Material: Wt. o f Sample:  Nickel 8 0 0 . 0 gm.  Manometer Reading arm 1 i n . arm 2 i n . 6.,60  *  10.60 14.60 0.0 0.40 1.90 4.10 2.40  * *  3-10 ' 6.90 10.60 2.60 3.00 4.20 0.70 1.00  * *  .' Ave. Diameter 0-384 Density 8 . 9 2 gm/cc.  Temperature Column ° F  '  72.2 . 72.3 72.4 72.5 72.4 72.7 72.6 72.5  * ^ " Meter ( A i r )  Run 1 0 (Water) Material: Wt. o f Sample: From Run  * . * * *  Alundum 400.0 gm. 10  3- 30 6.10 8.50 12.50 2.6 2.90 3-10 3.40  0.95 1.45 2.00 2 . 50 3-30 4.30 5.40 6.35 7.25 8.20 9.00  3.9O  4-35 4.70 5.40 6.20 7.00 '  .7.35 8.55 9.35 10.00  * -g-" Meter ( A i r )  Temperature Room °C .  22.5 22.5 22.5 22.6 22.7 22.7 22.8 22.6  Bed H e i g h t cm. '8.0 8.6 9.1 9.5 , 10.0 11.2 7.6 7.1  Meter (Mercury)  Manometer Reading arm 1 i n . arm 2 i n . 1.50 4.50 7.00 11.00 0.05 0.30 0.50  mm.  Nickel 8 0 0 . 0 gm. 10  Temperature Column °F 71.2 71.6 71-7 71.7 71-7 72.0 72.1  Temperature Room °C  Bed Height  22.8 23.0 23.0 23.0  15.5 15-9 16.2 17.0  23.3 23.4 23.4 23.2 23.3 23-3 22.8 23.0  17-7 I8.5 19-0  72.3 72.3 72.3 72.3 72.5 72.6 72.772.7 72.6 72.8 72.7 -2" Meter (Mercury)  23.3 23.2 23.1 23.0 23.0 23-0  19-7 20. 5 21.4 22.0 23.0 • 24.1 25.2 26.3 27.2 28.3 29.2  4-29 R ' 10 (Water) Material: Wt. o f Sample:  Alundum 500 gm.  Manometer Reading arm 1 i n . arm 2 i n .  -0.30 0.15 O.85 1-35 3-20 4.95 7-30 9.00 10.80 8.10 5-30 4.10 2.8S  1.10 6.50 5"  2.30 2-75 3.40  3.35 5-20  .  6.75 8.60 10.00 11.40  9.20 7.00 6.00 5.05 4.05 8.00  Meter (Mercury)  Ave. Diameter Density  Temperature Column °F  23.4 23.4 23.7 23.5 23.4 23.5 23-5 23.5 23-5 23.6 23.6 23.6 23.4 23.4 . 23-3  1-52 3.95  Temperature Room °C  65.O 6S.2  65.5 65.7 65.7 65.8 66.0 66.3 66.5 66.5 66.5 66.5 66.6 67.0 67.2  mm. gm/cc. Bed Height  10.9 11-3 12.0 12.4 13-5 14.4 15-7  I6.5  17.3 15.8 14.4  . 13-7 13.O 12-3 15.1'  4-30  Run 11 (Water) Material: Wt. oi' Sample: From Manometer arm 1  0.35  -0.10 0.30 1.10  2.00 3-00 3.90 5; 10 6.60  7.40 8.35 10.20  11.30 • 1"  Run 2  Temperature in.  8.80 11-30 2.30 2.60 2.90 3-60 4-35  5-15 5.90 6.90 8.00 8.80 9.90  11.00  11.80  Meter ( A i r )  Crystalon 350.0 gm. Run 6  350.0 gm.  Reading  i n . arm 2  1.30 * 4.00 *  Alundum  Column  71.6 71-6 71-5 71-7 71.8 72.3 72.5 .72.5 72.6 72.6 72.7 71-9 71-9 71-9 72.0  , °F  Temperature Column  22.0 22.0 22.0 22.0 22.0 22.1 22.1 22.2 22.0 22.0  23-7 23.7 23-5 23.4 23.1  •§•" Meter ( M e r c u r y )  °C  Bed H e i g h t cm.  18.6 • 19-5 21.0 21.9  23-0 25.I 27-1 29-5  31-5  34.2 37-3  39-8 43.O  46.7 49.3  4-31 Run 12 (Water) Material: ; Wt. o f Sample: From Manometer arm 1  -0.90 -0.55 -0.25 0.20 0-55 1.00 1.60 2.15 2.80 3-60 4.70 5.60 6.40  7.20 7.80 8.90 9.65 10.30 11.40  10.80 10.30 9.00 7-75 6-35 5.20 4.00 2.70 1.50 0.25 -o.?o  Glass B a l l o t i n i  Reading  i n . arm 2  in.  1.80 2.15 2.45' 2.90 3-20 3.60 4.05 4.5O  5.05 5-75 6.60 7.30 8.00 8.55 9.10 10.00 10.50 11.00 12.00 11.40 11.00 10.00 9.00 7.95 6.95 6.00 5.00 4.00 2.95 2.00  |" Meter ( M e r c u r y )  Alundum  Run 1  320.8 gm.  i+50.0 gm. Run 3  'Temperature Column °F  Temperature Room °C  67-8 68.2 68.3 68.3 68.6 68.9 69-0 69.2 69.5 69.8 70.0 70.0 70.0 70.0 70.2 70.2 70.3 72.0 72.3  20.3 20.5 20.2 20.2 20.2 20.2 20.2 20.2 20.2 20.3  71-9  71-9 71.9 72.2 72.0 71.9 71-9 71-9 72.1 72.0 72.O  20.3  20.3 20.3 20.4 20.5 20.5 20.6 20.8 21.0 21.0 21.0 21.0 20.7 21.0 21.0  21.0 21.0 21.0 21.0 21.0  Bed H e i g h t cm.  20.5 22.4 23-7 25-3 26.4 27-9 29-4 30.9 32.7 34.8 37-5 39-8 42.0 43-9  45-9 48.7 51.0 48.0 49-5 49.O 47.O  47-7 45.0 41.2  38.2 35-0 31-8 28.7 28.7 21.3  APPENDIX V - MEASUREMENT OF LONGITUDINAL PARTICLE CONCENTRATION (PROPOSED METHOD)  An i n f o r m a t i v e method o f measuring l o n g i t u d i n a l p a r t i c l e gradients,  and hence  segregation  by s i z e ,  i s a p l o t of P r a t i o  concentration vs.  vertical  p o s i t i o n i n the column, u s i n g average p o r o s i t y o f the bed as a parameter. Such a p l o t  i s s'hovn i n F i g u r e 36 f o r the f l u i d i z a t i o n o f 2 . 2 8 mm.  b a l l o t i n i by the p o l y e t h y l e n e g l y c o l s o l u t i o n . a measure  o f the  average f r a c t i o n  fraction  s o l i d s at  glass  The c u r v e s o b t a i n e d g i v e  a 'particular position relative  to  the  s o l i d s i n the b e d , as can be seen by a n a l y z i n g the f o l l o w i n g  equations  -p-  'W-'.  (Ap/L),  h t o r y  (A)  (l-«) (/>s-/» m  or  (|-€),  = (l-€) -P m  (B)  5-2  0-95h-  0-90  Figure 36.  P l o t o f P. R a t i o P r o f i l e s at V a r i o u s Average Porosities.  

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
China 16 0
United States 12 0
Japan 5 0
France 3 0
Russia 2 0
Finland 1 0
City Views Downloads
Shenzhen 12 0
Unknown 11 2
Tokyo 5 0
Beijing 4 0
Ashburn 4 0
Mountain View 2 0
Helsinki 1 0

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0059168/manifest

Comment

Related Items