UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Particle size segregation in particulately fluidised beds. Pruden, Barry Blythe 1964

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1964_A7 P78.pdf [ 11.52MB ]
Metadata
JSON: 831-1.0059109.json
JSON-LD: 831-1.0059109-ld.json
RDF/XML (Pretty): 831-1.0059109-rdf.xml
RDF/JSON: 831-1.0059109-rdf.json
Turtle: 831-1.0059109-turtle.txt
N-Triples: 831-1.0059109-rdf-ntriples.txt
Original Record: 831-1.0059109-source.json
Full Text
831-1.0059109-fulltext.txt
Citation
831-1.0059109.ris

Full Text

P A R T I C L E - 3 I Z E SEGREGATION  IX  PARTICULATELY  FLUIDISED BEDS by BARRY PRUDEN B.E.,  University  •  o f Saskatchewan,  1962  A THESIS SUBMITTED IiN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in  t h e Department of  CHEMICAL  We a c c e p t  this  the r e a u i r e d  Members  ENGINEERING  t h e s i s as conforming  to  standard  o f t h e ueparttnent  of  Chemical  Engineering THE UNIVERSITY OF BRITISH COLUMBIA January,  1964  In presenting the  requirements  British  Columbia,  available mission  for  for  for  I  agree  reference  extensive  representatives,,  cation  of  this  Department  in partial  that  the  copying of  I  this  the U n i v e r s i t y o f  for  i s understood  thesis  for,  that  of  per-  scholarly or by  c o p y i n g or  f i n a n c i a l g a i n s h a l l not  permission.  freely  f u r t h e r • agr.ee t h a t  by the Head o f my Department  The U n i v e r s i t y o f B r i t i s h C o l u m b i a , . V a n c o u v e r .8, C a n a d a . Date  at  f u l f i l m e n t of  L i b r a r y s h a l l , make i t  and s t u d y .  It  thesis  w i t h o u t my w r i t t e n  thesis  an advanced degree  purpo-ses may be g r a n t e d his  this  publi-  be a l l o w e d  ix  ABSTRACT  A paper by J o t t r a n d which d e a l s with p a r t i c l e segregation  i n l i q u i d - f l u i d i s e d beds i s examined  size  critically,  and an attempt has been made to extend and complement his t  work. I t i s assumed t h a t the d r i v i n g f o r c e f o r segregat i o n o f two groups of 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 bed  fluidised  i s the d i f f e r e n c e i n bulk d e n s i t y of the beds formed by  each group o f p a r t i c l e s s e p a r a t e l y when subjected, t o the same s u p e r f i c i a l v e l o c i t y o f the f l u i d . ing  equation  Accordingly  the f o l l o w -  f o r the bulk d e n s i t y d i f f e r e n c e between two  groups o f p a r t i c l e s with unequal diameters was d e r i v e d and studied  experimentally:  In the above equation, and  the s u b s c r i p t s L and S r e f e r t o l a r g e  s m a l l p a r t i c l e s r e s p e c t i v e l y , m i s the index o f f l u i d  regime (m = 1 i n Stokes r e g i o n , m = 2 i n Newton r e g i o n ) , and n i s the exponent i n a Richardson-Zaki  type expansion equa-  tion. I t was found that f o r equal d e n s i t y p a r t i c l e s the segregation hence €  L  tendency increased as the o v e r a l l p o r o s i t y , and  » was increased and as the diameter r a t i o  increased.  (r) was  The tendency e i t h e r to mix or t o segregate was  found  t o be v e r y s e n s i t i v e  t o changes i n y  e r e n c e between l a r g e p a r t i c l e s  and  fluid  divided  d e n s i t y d i f f e r e n c e between s m a l l p a r t i c l e s is was  the bulk d e n s i t y d i f f e r e n c e observed  segregated, ing  t h a t a bed w i t h one  i n the f a c t o r  difference, to  i t d i d not  segregate,  provided  v a l u e s o f m and fluid  I t was  segregation tendencies. bulk density difference i n s o f a r as m i x i n g  were k e p t  the Stokes  i t was  The  of a reduced  the l i m i t e d  an  particles  constant.  The  region to  as  the  the  changes i n  concluded  that  but  the  trends, that  the  predicted bulk density difference/  d e n s i t y was  by  of the  or. s e g r e g a t i o n a r e c o n c e r n e d ,  when t h e p a r t i c l e  suggested  relative  equation p r e d i c t e d the r i g h t  not u n i q u e l y c o r r e l a t e d w i t h the  applicability  occupy-  that, while  f o r the corresponding Finally  a b s o l u t e magnitude o f the was  found  It  completely  t o change s u f f i c i e n t l y ,  from  Newton r e g i o n , >to a c c o u n t  or  of p a r t i c l e s  i n c r e a s e the tendency  changed  as  i n c r e a s e d the b u l k d e n s i t y  L  r and y  the  fluid),  d e p e n d i n g on t h e  also  ( Pp ~P)  n were f o u n d  r e g i m e was  e i t h e r mixed  or the other s i z e  t h e u p p e r p o r t i o n o f t h e bed,  increase  and  by  i n t h e above e q u a t i o n .  c o u l d be  m a g n i t u d e s o f r and y.  (density d i f f -  data  varied  observed  phenomena,  at constant r  and  bulk density d i f f e r e n c e available.  y  .  was  viii  ACKNOWLEDGEMENTS  I w i s h t o a c k n o w l e d g e my a p p r e c i a t i o n t o D r . Norman Epstein f o r h i s advice The staff  and g u i d a n c e t h r o u g h o u t t h e p r o j e c t .  cooperation  o f Mr. R. M u e l c h e n  and t h e workshop  i n m o v i n g and r e b u i l d i n g t h e a p p a r a t u s i s a l s o  appre-  ciated. I w i s h t o thank t h e U n i v e r s i t y o f B r i t i s h for  financial  Graduate  assistance  Fellowship,  received  Columbia  i n t h e form o f t h e i r  and 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 f o r  t h e i r a d d i t i o n a l support. Barry  B. P r u d e n  ii  TABLE OP CONTENTS Page ACKNOWLEDGEMENTS  viii  ABSTRACT  ix  NOMENCLATURE INTRODUCTION  •x i . . . .  .  1.  P u r p o s e , Methods,  2.  L i t e r a t u r e Survey  Scope  1 .  DISCUSSION OF WORK BY JOTTRAND  •.  THEORY 1.  1  2 5'  '. . 12 Use o f E q u a t i o n s  APPARATUS  19 and 20  16  .  18  1.  General  .18  2.  The T e s t  3.  Temperature C o n t r o l  4.  C o n s t r u c t i o n and C a l i b r a t i o n  5.  Pumping Equipment  6.  Pressure  7.  Sampler  8.  Measurements  9.  Test  10.  Columns  18 .  Drop Equipment  24 o f Flow M e t e r s  . . . 24 26  . . . . . . . . . . . . .  26 .28  o f V i s c o s i t y and D e n s i t y  Liquids  Test Materials  EXPERIMENTAL  29 . . . . . . . . .  1.  Objectives  2.  General  Outline  28  32 34 34  of Experimental  Work  35  iii  Page 3.  Experimental  P r o c e d u r e s and P r o c e s s i n g o f D a t a . . 36  (a)  Velocity  (b)  P r e s s u r e D r o p Measurements  (c)  Sampling  (d)  Photography  RESULTS AND DISCUSSION  37  - P o r o s i t y Data  " . . 39 40 41  . . . . .  1.  Introduction . . ,  2.  D i v i n y l - Water Runs  3.  G l a s s Beads - P o l y e t h y l e n e G l y c o l Runs  41 .  41 48  (a)  2 and 3 mm.  G l a s s Beads, P l u i d i s e d  i n P.E.G.48  (b)  3 and 4 mm.  G l a s s Beads, P l u i d i s e d  i n P.E.G.55  (c)  4 and 5 mm.  G l a s s Beads, F l u i d i s e d  i n P.EiG.58  (d)  5 and 6 mm.  G l a s s Beads, F l u i d i s e d  i n P.E.G.61  (e)  2 mm.  A and 2 mm.  B G l a s s Beads, F l u i d i s e d 66  i n P.E.G 4.  Lead  5.  G l a s s Beads -- Water Runs  6.  39  . . .  S h o t - P o l y e t h y l e n e G l y c o l Run  .  69 73  (a)  3 and 4 mm.  G l a s s Beads,- F l u i d i s e d  i n Water 73  (b)  5 and 6 mm.  G l a s s Beads, F l u i d i s e d  i n Water 76  General  .83  .  CONCLUSIONS AND RECOMMENDATIONS  90  REFERENCES  94  APPENDIX I - O r i g i n a l D a t a APPENDIX I I - Sample C a l c u l a t i o n s and E r r o r s APPENDIX I I I - I n s t a b i l i t i e s  and End E f f e c t s  iv  LIST OF FIGURES Figure  *  Page  1.  Representation of Equation 8  2.  F l u i d i s a t i o n Apparatus  19  3.  Column Top S e c t i o n  20  4.  P r e s s u r e Drop Apparatus  21  5.  Sampler  27  6.  Expansion Curves f o r 24-28 and 28-32 Mesh D i v i n y l Fluidised  7.  7  i n Water . . . . .  43  Expansion Curves f o r 24-28 and 42-48 Mesh D i v i n y l Fluidised  i n Water  45  8.  R e s u l t s o f Sampling Runs  47  9.  Expansion Curves f o r 2 and 3 mm. G l a s s Beads F l u i d i s e d i n P.E.G.*  10.  49  Photographs o f 2, 3, and 4 mm. G l a s s Beads F l u i d i s e d i n P.E.G  11.  51  P r e s s u r e Drop Data - 2 mm. G l a s s Beads F l u i d i s e d i n P.E.G  12o  52  P r e s s u r e Drop Data - 3 mm. G l a s s Beads F l u i d i s e d IH P • b e G •  13.  t  • o « • 53  P r e s s u r e Drop Data - 2 and 3 mm. G l a s s Beads Fluidised  14.  o e e> • e • • o • o o o *> o e  i n P.E.G.  54  Expansion Curves f o r 3 and 4 mm. G l a s s Beads Fluidised  i n P.E.G.  56  V  Figure 15.  Page .Pressure Drop D a t a - 3 and 4 mm.-Glass Beads Fluidised  16.  57  P r e s s u r e Drop D a t a - 4 and 5 mm. Fluidised  "17.  i n P.E.G Glass  Beads  i n P.E.G  . . . 59  P h o t o g r a p h s o f 4 and 5 mm.  Beads F l u i d i s e d i n  P.E.G 18.  .60  E x p a n s i o n C u r v e s f o r 4 mm. Beads F l u i d i s e d  19.  21.  i n P.E.G.  Photographs  . . . • . . • • • . • . . . . 63 Beads  G l a s s Beads  Photographs  65 A. and 2 mm.  B. G l a s s  i n P.E.G. .  o f 2 mm.  .64  Fluidised  .'•  E x p a n s i o n C u r v e s f o r 2 mm.  Fluidised  Glass  .  o f 5 and 6 mm.  Beads F l u i d i s e d 23.  G l a s s Beads  i n P.E.G  i n P.E.G 22.  62  P r e s s u r e Drop D a t a - 5 and 6 mm. Fluidised  K. G l a s s .  i n P.E.G  E x p a n s i o n C u r v e s f o r 5 and 6 mm. Fluidised  20.  and 5 mm.  67  A. and 2 mm.  B. G l a s s  Beads  i n P.E.G  .68  24.  E x p a n s i o n C u r v e s f o r Lead Shot F l u i d i s e d  i n P.E.G.70  25.  P r e s s u r e Drop D a t a - Lead Shot F l u i d i s e d  i n P.E.G.71  26.  P h o t o g r a p h s o f Lead Shot F l u i d i s e d  27.  E x p a n s i o n C u r v e s f o r 3 and 4 mm. Fluidised  28.  i n Water  i n P.E.G.  Glass  . . . . .  P h o t o g r a p h s o f 3 and 4 mm.  G l a s s Beads  75 Fluidised 77  P r e s s u r e Drop D a t a - 3 and 4 mm. Fluidised  74  Beads  i n Water 29.  . .  i n Water  .  Glass  Beads 78  vi Figure 30.  Page E x p a n s i o n C u r v e s f o r 5 and 6 mm. Fluidised  . 31«  G l a s s Beads  i n Water  79  P h o t o g r a p h s o f 5 and 6 mm.  G l a s s Beads  Fluidised  i n Water 32.  P r e s s u r e Drop D a t a f o r 5 and 6 mm. Fluidised  33•  80 Glass  Beads  i n Water  . 82  E x p a n s i o n D a t a f o r 300 grams, and 600 grams o f 24-28 Mesh D i v i n y l  Fluidised  i n Water  •P.E.G, - p o l y e t h y l e n e g l y c o l - w a t e r  . . . . . III-5  solution.  vii  L I S T OF TABLES  Table  I. II. III. I?.  V. VI.  *  Page  I m p o r t a n t Flow M e t e r D i m e n s i o n s Calibration Properties  .24  of C a p i l l a r y Meter A  30  o f P a r t i c l e s and F l u i d s  42  C o m p a r i s o n o f . M e a s u r e d and C a l c u l a t e d  Bulk Density  Differences  84  Summary o f R e s u l t s  87  Comparison Diameters  o f Measured  and  Calculated  Particle 93  xi  NOMENCLATURE  A  = cross s e c t i o n a l  C  = coefficient  Cj) = drag C  0  area o f column, 20.262 s q . cm.  i n equation 13.  coefficient.  = orifice coefficient  d e f i n e d by equation 2 6 a .  CQ = o r i f i c e c o e f f i c i e n t d e f i n e d by.equation 26b. d  = particle  d-t = tube  diameter,  diameter.  D  = centre t o centre d i s t a n c e between p a r t i c l e s .  g  = gravitational  h  = height from which sample taken, measured from bottom o f bed, i n c h e s .  k  = constant when f l u i d  k»,  k", k  u , ,  acceleration,  32.2 f t . / s e c . ^ .  p r o p e r t i e s (/>>/•*•) a r e constant.  = constants.  K  = constant i n equations 7a and 7 b .  1  = d i s t a n c e over which p r e s s u r e  L  = bed h e i g h t , cm. u n l e s s otherwise s t a t e d .  m  = index of f l u i d regime i n equations 13-20 m = 1 i n Stokes region, m = 2 i n Newton r e g i o n .  n  = exponent i n R i c h a r d s o n - Z a k i equation, equation 2.  N  = t o t a l number of p a r t i c l e s .  AP = pressure drop = RA/0g_ gc p P q  drop i s measured, f t .  lb.force/ft.2  = pressure a t a g i v e n pressure tap, v  = volume occupied by p e l l e t s , f t . 3 = volumetric flowrate, f t V s e c .  lb.force-in/ft.3  xii . r  = diameter r a t i o =  di/dg  R  = f l o w m e t e r manometer r e a d i n g , f t .  R  m  = f l o w m e t e r manometer r e a d i n g ,  R  e  = particle  Re = free 0  R e y n o l d s number,  particle  inches.  dV/°  R e y n o l d s number,  R += R e y n o l d s number b a s e d  d\/ p Q  on t u b e d i a m e t e r  e  d V/> t  s  = exponent d e p e n d i n g number c u r v e .  S  = surface area of p a r t i c l e s , f t . ^  T  = t e m p e r a t u r e , °F u n l e s s  U  = local  V  = l i q u i d s u p e r f i c i a l v e l o c i t y b a s e d on empty t u b e i n fluidisation', ft./sec. p a r t i c l e v e l o c i t y w i t h r e s p e c t t o the l a b o r a t o r y i n sedimentation, f t . / s e c .  fluid  = intercept from p l o t V  velocity,  settling velocity,  v  = t o t a l volume o c c u p i e d by l i q u i d f l u i d i s e d bed.  V/  = weight  X  = exponent d e p e n d i n g on s l o p e o f R e y n o l d s number c u r v e .  y  = r a d i a l d i s t a n c e measured f r o m a x i s  Greek  Reynolds  ft./sec.  particle  of p a r t i c l e s ,  -  specified.  v e l o c i t y , value of V extrapolated of l o g V versus l o g € , f t . / s e c .  = terminal free  0  on s l o p e o f dra'g c o e f f i c i e n t  and  to € = 1  ft./sec.  particles  in a  grams. drag-coefficientof tube, f t .  Letters  € = p o r o s i t y = volume v o i d s / t o t a l = overall  porosity  i n mixed  volume  bed.  € = p o r o s i t y a s s o c i a t e d w i t h l a r g e p a r t i c l e s i n a mixed bed, o b t a i n e d f r o m e x p a n s i o n c u r v e o f l a r g e p a r t i c l e s a l o n e a t v e l o c i t y c o r r e s p o n d i n g t o mixed bed s u p e r f i c i a l velocity. L  xiii €  = p o r o s i t y a s s o c i a t e d w i t h s m a l l p a r t i c l e s i n a mixed bed, o b t a i n e d f r o m e x p a n s i o n c u r v e o f s m a l l p a r t i c l e s a l o n e a t v e l o c i t y c o r r e s p o n d i n g t o mixed bed superficial velocity. . •  s  PpCP  y  = density ratio  p  = fluid  density,  Ib./cu.ft.  p'  = fluid  density,  gm./cc.  p  = bulk d e n s i t y , o r weighted average d e n s i t y bed. I b . / c u . f t .  b  p  =  = particle  density,  Ib./cu.ft.  p' = p a r t i c l e <p -  density,  gm./cc.  P  bp = d e n s i t y  d i f f e r e n c e between manometer l i q u i d s ,  p. -  fluid  viscosity,  pl -  fluid  viscosity,  T  lb./ft.-sec. centipoise.  = average shear s t r e s s ,  lb./sq.ft.  p -p (B - r e d u c e d b u l k  density, =  Superscripts L  = large  mf = minimum S  =  small  w  = wall  in a  fluidisation  ^  s  fluidised  Ib./cu.ft.  INTRODUCTION  lo  P u r p o s e , Methods, Scope The  and  purpose of t h i s  experimental3_y  particle  size  the  of d i f f e r e n t  theoretically  v a r i a b l e s on fluidised  made w i t h r e s p e c t t o p a r t i c l e  in particulately  cussed.  effect  t o show  segregation i n particulately  C e r t a i n statements tion  s t u d y was  A simple  fluidised  formula  beds a r e  which a l l o w s  size  pointed  i s used  experimental  The tion,  experimental  methods u s e d  photography, p a r t i c l e  c u r v e s , and  static  transparent  column.  a. c o n c e n t r a t e d  pressure  sampling, profile  L i q u i d s used  aqueous s o l u t i o n  ( v i s c o s i t y = 120  centipoises).  this  formula  study.  include v i s u a l comparison of  observaexpansion  measurements i n a 2"  l a r g e p o r t i o n o f the (2 mm.  and  densities  D a t a were a l s o  obtained sizes  f o r runs  of d i v i n y l The  w i t h l e a d shot  was  study  r e g i o n , the  studied.  (2,5  and  2.0  mm,)  and  mm.)  screen  particles. was  restricted, to particulate  using spherical particles. Stokes  gm/cc).  - 6  work  done w i t h g l a s s beads o f v a r i o u s s i a e s gm/cc. t o 2.9  and  glycol  was  (2,2  ID,  i n t h e 3tudy were w a t e r  of polyethylene A  dis-  the r a t i o n a l a n a l y s i s  beds i s p r o p o s e d , and  t h e b a s i s f o r an  segrega-  out and  of segregation i n f l u i d i s e d as  beds.  Particle  size  s e g r e g a t i o n i n the  i n t e r m e d i a t e r e g i o n , and  Most d a t a  were o b t a i n e d  fluidisation  i n the  t h e Newton r e g i o n experimentally  2 more common i n t e r m e d i a t e r e g i o n .  2.  Literature The  Survey  first  report of s t r a t i f i c a t i o n i n l i q u i d f l u i d i s e d  beds was made by V e r s c h o o r  (4).  He worked w i t h sand  in  t h e r a n g e 100-120 mesh, and t h i s  to  lead  r a n g e seemed  sufficient  to segregation. Andrieu  ( 3 ) made a s y s t e m a t i c s t u d y  u s i n g 3 5 - 4 8 mesh s a n d . (a measure o f t h e w e i g h t  P r e s s u r e drop of particles  of segregation  i n t h e f l u i d i s e d bed supported  i n the i n t e r v a l  between two p r e s s u r e t a p s , c o r r e c t e d f o r b u o y a n t measured a t s e v e r a l i n t e r v a l s  t o the voidage  V o i d a g e was f o u n d  T h i s p r e s s u r e drop  failure  t o i n c r e a s e from  (1) p r e s e n t e d  This theory i s discussed i n d e t a i l and Z a k i  equal d e n s i t y p a r t i c l e s predicted basis  expansion  i n terms o f s e g r e g a t i o n .  (2)  i n concentrated i n the next  beds.  reported the f l u i d i s a t i o n of  w i t h two d i f f e r e n t  expansion  with experimental  f o r the  section,  diameters.  o f t h e mixed bed o f p a r t i c l e s  of the individual  correlation  was- r e -  t h e b o t t o m o f t h e bed t o  a theory t o account  of c l a s s i f i c a t i o n t o occur  Richardson  pressure  i n t h e bed by  t h e t o p , and t h i s was i n t e r p r e t e d Jottrand  f o r c e ) was  up h i s column u s i n g  taps at the various i n t e r v a l s . lated  particles  on t h e  c u r v e s , and o b t a i n e d  results.  a t h e o r y f o r p r e d i c t i n g bed e x p a n s i o n  They a l s o  They  good  proposed  which i s taken as t h e  3 basis  f o r the theory presented  L a p i d u s , and  Elgin  05)  in this  extended  thesis.  t h e work o f R i c h a r d s o n  Z a k i i n p r e d i c t i n g the b a t c h expansion sizes.  They n o t e d  diameter  ratios  r a t i o was  reduced.  systems,  appearance o f an particles  and  and  s y s t e m s and  the behavior of  agree  o f e q u a l d e n s i t y but d i f f e r e n t  with results  Kaye and of p a r t i c l e s explained theory.  Davies  their results R i c h a r d s o n and  R i c h a r d s o n and  Meikle of  Zaki  and  important free in  diameters.  They  Hindrance"  (18) a l s o s t u d i e d s e d i m e n t a t i o n  solids. McBride  (21),  give excellent  reviews  bibliographies  on p a r t i c u l a t e  fluidisa-  i n understanding  particularly  of s e t s  (5, 15)  particles.  Shannon  on  i n the f o l l o w i n g paragraph  the e f f e c t  beds.  are  of turbulence (high  number) on p a r t i c l e  fluidised  (19)  fluidisation.  mentioned  p a r t i c l e Reynolds  thesis  settling  ( 2 ) , D a l l a v a l l e and  aggregative  papers  Some  to t h i s  gives a cross-referenced bibliography of l i t e r a t u r e  The  dis-  sets of  i n terms o f a " M e c h a n i c a l  of equal d e n s i t y mono-sized  p a r t i c u l a t e and  between  runs.  (6) s t u d i e d h i n d e r e d  on f l u i d i s a t i o n  of the l i t e r a t u r e , tion  pertinent  o f e q u a l d e n s i t y but d i f f e r e n t  textbooks  the  liquid-  diameters.  obtained i n d i v i n y l  o f two-component m i x t u r e s  and  w i t h two  large  as  thus t o e x p l a i n the appearance or  o f t h e i r d a t a a r e complementary and and  interface with  t o draw an a n a l o g y  i n t e r f a c e when w o r k i n g  and  f o r mixed  i t s disappearance  They a t t e m p t e d  the behavior of t h e i r liquid  curves  t h e a p p e a r a n c e o f an  of p a r t i c l e s ,  Hoffman,  size  segregation  4 Jackson of  instabilities  disturbances the  upper  Cairns  at  of  diagrams, -  are  a  the  effect  They  is  also  to  They  was s t u d i e d  by  explain  at  high  velocity  fluidised  bed  described,.with  numbers voids.  to  velocity, to/IV,  Reynolds  fluidisa"swirling",  mixing (.Newton  properties region)  F u r u k a w a and  for a variable  analogous  small in  channeling,  the f r a c t i o n  is  from  disturbances  found, t h a t  Reynolds  presence  in particulate  spasmodic  proportional  turbulence  Mxing  encountered  Random p a r t i c l e  showed  large  bed.  an expression  (/i-V) w h i c h  b.id  of  of  to  in a particulately  high  the  b e d , w h i c h grow  who a t t e m p t e d  (7)  motion,  function  system. they  a deep  number.  bed a t  (11) d e r i v e d  fluidised  which  of  and. " b u b b l i n g " .  a strong  liquid  bod s u p p o r t  particles  percolation  mathematically  fluidised  phenomena  fluidised  Ohir.ae  an  of  Peclet  "rotation", in  the  and P r a u s n i t z  terms  tion  in a  portions  fluctuations in  predicted  (9)  in a  temperature  in a  the magnitude was d i s c u s s e d numbers.  of as  5-  5  DISCUSSION OF WORK BY JOTTRAND  T h i s work was prompted by s u g g e s t i o n s p a p e r hj duct  J o t t r a n d ( 1 ) . I t was o r i g i n a l l y  an e x p e r i m e n t a l  statements  study  made i n t h i s  t o prove  paper,  certain  as w e l l as statements  made i n  section Jottrand*s  Some r e m a r k s a r e made on a c r i t i c a l  between f l u i d i s a t i o n and h i n d e r e d The  (2) t y p e  this  difference  settling.  t h e o r y o f J o t t r a n d (1) i s based  on a  Richardson-  (volume  voids/total  equation  V=Vj€  (2) In  t o con-  (1) i s i n t r o d u c e d and d i s c u s s e d , and p e r t i n e n t g r a p h s  are presented.  Zaki  intended  or disprove  a d i s c u s s i o n b y E p s t e i n . , (30). I n t h i s theory  made i n a  equation,  n  € i s the void  fraction  v o l u m e ) , and n i s a n exponent which  i s constant  i n the Stokes  r e g i o n , and w h i c h depends on t h e f r e e - s e t t l i n g  Reynolds  number and t h e p a r t icle-to-*-tube d i a m e t e r  i n the i n t e r -  m e d i a t e and Newton r e g i o n s . that,  plot  of log V  versus  n and i n t e r c e p t v(  is  related  (v ) 0  and Z a k i  f o r a given set of uniformly sized  d e n s i t y which a r e s e t t l e d a  Richardson  ratio  .  line  with  fluid, slope  They f u r t h e r show t h a t t h e c o n s t a n t  to the free s e t t l i n g v e l o c i t y  logV  of constant  by a g i v e n  i s a straight  by t h e r e l a t i o n s h i p  (3)  particles  i n or fluidised  log€  ( 2 ) show  0  =  logV:+J  of a single  particle  where d i s t h e p a r t i c l e the  tube  d i a m e t e r , and  i n which the p a r t i c l e s  variable  V i s the f l u i d  (superficial velocity  d-fc i s t h e d i a m e t e r  are settled  velocity  based  with respect Jottrand  to the l a b o r a t o r y  makes t h e f o l l o w i n g  a)  Settling  b)  The  or f l u i d i s e d .  on the empty  v e l o c i t y ) i n f l u i d i s a t i o n , and  of  the  The  tube  particle  i n sedimentation.  assumptions:  or f l u i d i s a t i o n  occurs i n the  Stokes  region.  at  settling  grains are spheres, e q u a l l y  t h e nodes o f a r e g u l a r c)  increase  The  bed  spaced  array.  expansion i s accomplished  by a  i n t h e d i s t a n c e between t h e p a r t i c l e s ,  simultaneous  without  any  change i n o r i e n t a t i o n . d)  The  a negligible  fluid  p r o p e r t i e s a r e c o n s t a n t , and  p a r t i c l e - t o - t u b e diameter  e)  The  assumption  i s implied  d i f f e r e n c e between, c l a s s i f i c a t i o n a settling tion"  and  suspension.  t h a t t h e r e i s no bed  h i s p a p e r he u s e s  and  in  "fluidisa-  "sedimentation" interchangeably.  In single  ratio.  in a fluidised  Throughout  there i s  light  particle  o f t h e above assumptions, simplifies  (4)  to  18 p  kd  2  and (4a) (Any c o n s i s t e n t  V = Vj 0  set of u n i t s  c a n be  used).  S t o k e s law  for a  7  d, microns Figure 1 - Representation and  o f E q u a t i o n 8,  E q u a t i o n 7c,  Dotted  Lines  Solid  Lines  E q u a t i o n 2 c a n now V =  (5)  be r e w r i t t e n  kd € 2  I f D i s the d i s t a n c e t o t a l volume o c c u p i e d  as  n  between g r a i n c e n t r e s ,  by t h e bed, and  which the spheres a r e touching,  € f m  v i s the  i s the p o r o s i t y at  then  and (6b)  |-€ =  where N i s t h e t o t a l number o f p a r t i c l e s . assume  and  a regular  I f the p a r t i c l e s  array  (7a)  v  (7b)  v  mf  = KNDjrf = KNd = KND  3  3  f r o m e q u a t i o n s 6a and 6b,  i - . n ^  ( 7 c )  Substituting  e q u a t i o n 7c i n t o 5  V - kd»[l-Cl-c |J-^]  (8)  A p l o t o f e q u a t i o n 8, t a k i n g n = 4.65,  t,  m  i s given  i n Figure  1.  € f m  as 0.465, and  d and D a r e i n m i c r o n s ,  V/k  —2 i n microns and  .  Jottrand  b a s e s h i s argument  argument he a t t e m p t s  shows a s i m i l a r p l o t i n h i s p a p e r , on a d i s c u s s i o n ' o f  t o show t h a t  the p l o t .  i t i s possible  In t h i s  for a  small  particle  t o descend a t a f a s t e r  p a r t i c l e s under c e r t a i n This  conditions,  surrounded  reaction  further  by l a r g e r  superficial  p a r t i c l e s , without  The f l u i d i s a t i o n v e l o c i t y  velocity  required  particles  sizes  of different  idisation velocity  velocity  laboratory.  i n a tube.  i s t h e same f o r a l l p a r t i c l e s . of a s e t of p a r t i c l e s  size  deep t o b r i n g  i n a given f l u i d i s  i n the f l u i d  r e l a t i v e to the  about complete s e g r e g a t i o n o f each  not  t h e same f o r a l l p a r t i c l e s  and  this  faster  velocity based  and t h e l a r g e r  i s the v e l o c i t y  velocity  Iti s  i f t h e p a r t i c l e s a r e mixed,  particles  then a l l "see" the tend  i n a c c o r d a n c e w i t h e q u a t i o n 4.  on t h e f r e e  stitial  t o compression) zone.  i s t r u e because t h e p a r t i c l e s  rate  with respect to  i s i f t h e s e t t l i n g chamber were  i n t h e s e t t l i n g ( a s opposed  same p o r o s i t y ,  The  i s t h e same f o r two s e t s o f p a r t i c l e s i n  l i q u i d i s reached, that  sufficiently  set of  I f two s e t s o f  g i v e n t u b e o n l y when dynamic s t e a d y s t a t e  the  a  i s the l i q u i d  o c c u p y t h e same t u b e , t h e f l u -  o f the p a r t i c l e s This  considering  velocity i n -  to f l u i d i s e a given  porosity  settling velocity  small  The s i t u a t i o n i s  and i n t e r s t i t i a l  particles to a certain  a  of a single  b e c a u s e t h e a u t h o r mixes up f l u i d i s a t i o n  settling velocity,  discriminately .  large  i n a s e t t l i n g suspension.  o f the surrounding p a r t i c l e s .  confused  velocity,  the  than surrounding  i s done by c o n s i d e r i n g t h e r e a c t i o n  particle, the  rate  t o descend a t The  interstitial  o f t h e l i q u i d i n t h e f l u i d i s e d bed,  cross sectional i s equal to  area.  ^- ,  The a v e r a g e  inter-  The minima i n F i g u r e  1  10  a r e m i s l e a d i n g , and d i s t a n c e D-d, d i s t a n c e D, are plots  or void  a g a i n s t d.  o f e q u a t i o n 7c  correspond not  f r a c t i o n € , r a t h e r than  i s plotted  Jottrand  is  d i s a p p e a r as s o o n as e i t h e r  to the l i m i t i n g  lines  minimum p o i n t s o f t h e  values  The  of expansion  contradicted 25).  by  beyond  observed  used  23,  study.  fluidisation  r u n s w i t h l a r g e g l a s s beads  Jottrand  have an  that of the  observable upper  (2  mm)  and  not  r e g i o n was  size,  velocities.  diameter  ratio  o f j2-\  no  on  classification  the s i z e  that there i s at least  settling  divinyl also  difference  in  glycol,  experimental powders o f occurs is  a twofold difference  T h i s statement  limit,  maintained.  g r o u n d s , t h a t f o r h i g h c o n c e n t r a t i o n s o f two  unless  and  observed  polyethylene  a l s o makes t h e a s s e r t i o n ,  water f l u i d i s a t i o n  i s also  work w i t h w a t e r  c o n d i t i o n was  i n the Stokes  d e n s i t y but d i f f e r e n t  porosi-  data  I t i s p o s s i b l e t h a t he  t h e u n s t a b l e bed  where f l u i d i s a t i o n  with  c o n d i t i o n as d i s c u s s e d i n Appendix  T h i s unstable bed-did  however, and  a  His statement  with density approximating  t h e u n s t a b l e bed  with  a t much h i g h e r  31).  26,  other laminar l i q u i d  i n this  curves  which i t  homogeneous beds  Jottrand did h i s experimental  s m a l l spheres spheres  stable  have been o b s e r v e d  t i e s „(Figures 1 0 , 1 7 , 2 1 ,  8  p o r o s i t y a t which' t h e minima i n  i s 0,8746, and  p r e c i s e upper l i m i t s  great  i n Figure  p o s s i b l e t o have a s t a b l e homogeneous bed  Figure 1 occur  III.  ceritre-to-centre  for various € .  s t a t e s t h a t "The  p r e c i s e upper l i m i t . "  (2,  Dotted  clearance  equal  during  sufficiently i n free  i m p l i e s t h a t a minimum  i s r e q u i r e d f o r s t r a t i f i c a t i o n to  occur  11  d u r i n g dense pha3e Stokes r e g i o n p a r t i c u l a t e f l u i d i s a t i o n , and a minimum r a t i o o f 4 : 1 ulate f l u i d i s a t i o n .  i n dense phase Newton r e g i o n  partic-  The n e c e s s i t y o f such l a r g e r a t i o s i s  c o n t r a d i c t e d b o t h by p r e v i o u s Stokes and Newton r e g i o n fluidisation.data  (4, 6, 8) and by d a t a which we have  We have found t h a t s e g r e g a t i o n of - l i l  obtained.  can occur f o r d i a m e t e r r a t i o s  i n the Stokes r e g i o n , and f o r diameter r a t i o s o f - l-i'3  i n the Newton r e g i o n .  We have a l s o found t h a t s e g r e g a t i o n  s i z e o f equal d e n s i t y p a r t i c l e s - i n p a r t i c u l a t e l y beds can occur from the p o i n t a t which the l a r g e r  by  fluidised particles  a r e f l u i d i s e d up to and beyond the p o i n t a t which t h e s m a l l e r p a r t i c l e s are e l u t r i a t e d .  12  THEORY  T h i s theory i s based on the assumption that the 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 o f two groups of 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 s e d . bed i s the d i f f e r e n c e i n bulk d e n s i t y of the beds formed by each group o f p a r t i c l e s s e p a r a t e l y when subjected to the g i v e n s u p e r f i c i a l v e l o c i t y of the f l u i d . density p  The bulk  o f a mixture o f o a r t i e l e s of d e n s i t y p "  'b  r  p  and flxiid  of d e n s i t y p i s given by (9)  p  =  {\-€)p-p€  b  where €  p  i s the void f r a c t i o n .  The d i f f e r e n c e i n bulk d e n s i t y  between beds o f p a r t i c l e s L ('large) and S (small) i s t h e r e fore  (10a)  0-€ )£-^ -  p^-p^-  L  L  O - ^ k + ^ s  and (!-*)<£-/>>.-(i-^(£-p)  (10b)  Eliminating- Vj from equations  (11)  2 and 3 ,  V = V € /IO t n  d/d  0  In the Stokes r e g i o n o f f l u i d i s a t i o n , the v e l o c i t y r e q u i r e d to f l u i d i s e a s i n g l e p a r t i c l e  (17) i s g i v e n by  equation 4. In the Newton r e g i o n of f l u i d i s a t i o n , the v e l o c i t y r e q u i r e d to f l u i d i s e a s i n g l e p a r t i c l e  (17) i s given by  13 (12)  2  V  0  Equation  =  4(/Q-/0)gd 3  Yo44)p—  (consistent  12 and 4 c a n be r e p r e s e n t e d  units)  by a s i n g l e  formula  (13)  V  =  0  fm-n/a  ,.„  (consistent  where m = 1 i n t h e S t o k e s r e g i o n , The  coefficient  and  1.745  C has a v a l u e  of  and 2 i n t h e Newton  0.0556  i n the Stokes  i n t h e Newton r e g i o n , and i s i n g e n e r a l  o f t h e f r e e s e t t l i n g R e y n o l d s number. development, r a t i o s  of  o f C, assumed c o n s t a n t  V  over small  region. region  a function  However i n f u t u r e  a r e u s e d , and t h e r e f o r e  0  units)  ranges o f f r e e  the values  settling  R e y n o l d s number, c a n c e l o u t . The  fluid  p r o p e r t i e s are constant,  (14) V = C  (p -p)<p-  Substitution  o f 14 i n t o 11 y i e l d s  Q  p  and  1  5  )  v  therefore  { l b )  =  =  (,  d  f o r a binary  v  mVm  C'(/g-p)' ^d /  (  so t h a t  ml/m  €"  system,  ,o ' <  *  d /d  A s s u m i n g t h a t m^=mg=m, n^=ng=n, and C j=C g ( S e t s o f particles to  having  low d i a m e t e r r a t i o s ,  and d e n s i t y  1)  (17)  Let  [ff] , y ,  ^-pvip^pi  ratios  close  14 Then €  (13)  s  =  € L r  ^-rn)/rT y./mn (d -d .)/nd V  | 0  s  L  S u b s t i t u t i o n o f e q u a t i o n 18 i n t o  t  e q u a t i o n 10b y i e l d s  ^0^}}  W  (W)  E q u a t i o n 19 i s t h e e x p r e s s i o n f o r 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 two s e t s o f p a r t i c l e s , i n p a r t i c l e diameters  allowing f o r difference  and p a r t i c l e d e n s i t y , when s u b j e c t e d t o  t h e same f l u i d i s i n g v e l o c i t y .  Allowance  f o rwall effect i s  i n c l u d e d , as w e l l as allowance  f o r region of f l u i d i s a t i o n  ( S t o k e s , i n t e r m e d i a t e o r Newton r e g i o n s ) inasmuch a s m and n change f r o m  region to region.  For sets of p a r t i c l e s  o f e q u a l d e n s i t y , e q u a t i o n 19  reduces t o  p -p = (/>-/>)€  (20) The opposing  s t r a t i f i c a t i o n by s i z e ,  In fact,  as p a r t i c l e (9),  m ) / m n  |Cr 8' i i  d  ) / n d  t-I  then the s l i g h t e s t  however, f a c t o r s o p p o s i n g  circulation  support The  "  hand s i d e would s i g n i f y  as w e l l as entrance  particle  t B  )  above e q u a t i o n shows t h a t i f t h e r e were no f o r c e s  value of the right tion.  (r  such  positive  stratifica-  s t r a t i f i c a t i o n , such  (7) and h y d r o d y n a m i c i n s t a b i l i t i e s effect  due t o t h e n a t u r e o f t h e  (3*6), a r e I n h e r e n t  minimum d i f f e r e n c e  i n the operation.  i n bulk density necessary t o  promote m e a s u r a b l e s t r a t i f i c a t i o n b y s i z e u n d e r v a r i o u s circumstances  i s therefore siibject to experimental deter-  15 mination.  Nevertheless  one  can g e n e r a l i z e t o the  effect  that  t h e g r e a t e r t h e v a l u e o f t h e b u l k d e n s i t y d i f f e r e n c e as d i c t e d by  equation  s e g r e g a t i o n by sizing  20,  size.  the g r e a t e r the Equation  o c c u r s more r e a d i l y  20  and  creasing m  i s always g r e a t e r than  sponding  decrease  d i c t s that the €  and  hence The  tion, as  the v a l u e  i n n).  of m the  d /d  of  L  (the e f f e c t  effect  of the  In a d d i t i o n , equation  s  of i n corre-  20 a l s o p r e -  s e g r e g a t i o n t e n d e n c y i s enhanced by i n c r e a s i n g €  L  , t h a t i s , by  effect  expanding the  of t u r b u l e n c e  fluidised  i s i n c l u d e d i n the  bed.  calcula-  i n s o f a r as m i n c r e a s e s from 1 t o a l i m i t i n g v a l u e o f  t h e f l o w r e g i m e changes f r o m t h e S t o k e s  Newton r e g i o n , and 2.39.  towards  therefore predicts that  the h i g h e r the v a l u e  and (D-p),  the lower  tendency  pre-  The  n  region to  of turbulence  on a s i n g l e  s t r e a m l i n e f l o w around  particle  the  the  to  effect  (17) - f r o m t h e c a ^ e  p a r t i c l e where t h e r e i s no  l a y e r s e p a r a t i o n (m=l); t h r o u g h s e p a r a t i o n o c c u r s and  the  changes c o r r e s p o n d i n g l y f r o m 4.65  change i n m r e p r e s e n t s m a t h e m a t i c a l l y  the  2  of  boundary  i n t e r m e d i a t e r e g i o n where  a wake i s formed  (m v a r i e s f r o m 1 t o  2);  t o t h e Newton r e g i o n , c h a r a c t e r i s e d by  a boundary l a y e r  is  of the s e p a r a t i o n p o i n t ,  and  i n contact with the sphere which flows  There i s another important the  particles  f r e e l y a r o u n d t h e wake i n s e p a r a t i o n effect  when a bed  effect  i n front  is fluidised,  o f p a r t i c l e random v e l o c i t y .  motionless,  but  move up  (m=2).  o f t u r b u l e n c e , however, t h a t i s  of p a r t i c l e s  is fluidised,  which  and  When a bed  this  is  of  the  i n d i v i d u a l p a r t i c l e s are  not  and  down and  velocity  sideways w i t h a  16 w h i c h has been shown The  effect  (11) t o be d e p e n d e n t on t h e p r o d u c t f-LV.  of p a r t i c l e  random v e l o c i t y  i n opposing  t i o n has been shown t o be most i m p o r t a n t (11, 7 ) . ences  I t was  t h e r e f o r e t h a t much l a r g e r  i n t h e Newton r e g i o n t h a n  19 and 20 by m e a s u r i n g  measureable  i n the Stokes r e g i o n .  were o b t a i n e d f o r use i n e q u a t i o n s  the diameter  t a k i n g the a r i t h m e t i c average. was n e c e s s a r y , t h e e x p a n s i o n (From  the expansion  was value  found  and v„ was  for d .  Where r e l i a n c e  curve  calculated  The d i a m e t e r  p  o f 100 p a r t i c l e s and on s c r e e n  sizes  ( l o g V v s . l o g € ) was  used.  curve f o r the i n d i v i d u a l s e t o f p a r t i c l e s ,  from a s t a n d a r d textbook  e q u a t i o n 2, a s s u m i n g a  calculated  from  The v a l u e o f n was t a k e n a s  curve of the s m a l l e r  particles.  compute m f o r t h e m i x t u r e , w h i c h t u r n e d o u t t o be  to m f o r the l a r g e s t numbers  number  particles,  the f r e e s e t t l i n g  curve  line  fitted  t o the drag  identical  Reynolds  f o r t h e s m a l l and f o r t h e l a r g e p a r t i c l e s  a straight  the drag-  c u r v e f o r s p h e r e s , u s i n g methods  (21)).  the s l o p e of the expansion  from  was t h e n  c o e f f i c i e n t - R e y n o l d s number  and  differ-  Use o f E q u a t i o n s 19 and 20 P a r t i c l e diameters  To  i n t h e Newton r e g i o n  i n b u l k d e n s i t y would be needed t o promote  stratification  1.  expected  stratifica-  were  calculated  coefficient-Reynolds  (17, 21) o v e r t h e g i v e n r a n g e .  This line  e q u a t i o n o f t h e form  C = k'Re* D  Cn i s a s i m p l e power f u n c t i o n o f d and VQ,  and R e  0  is  had a n  17 d i r e c t l y p r o p o r t i o n a l to d V  and V , 0  =  0  k"d  y  could he obtained, and in c a l c u l a t e d y= ^  so that a r e l a t i o n s h i p  from  (See equation 14) , m =  For cases where R  <  e Q  0.2,  m = r.  Where RQ  Q  >  500 , m = 2 .  The advantage of formulae 19 and 20 i s that y and r have t o be c a l c u l a t e d only once, g i v i n g the f o l l o w i n g simple equation f o r the bulk d e n s i t y d i f f e r e n c e . p -p I  DL  = C + C„€,  'tis  Knowing that €  1  L  h a v i o r of the mixed bed, elutriation  2  L  x  (CT and Cp are c  v a r i e s from about 0.45  constants) to 1, the  be-  from i n c i p i e n t f l u i d i s a t i o n to  can be a n t i c i p a t e d .  From a study of the bulk  d e n s i t i e s n e c e s s a ^ f o r s e g r e g a t i o n i n the case of mixed beds which c o n t a i n only two p a r t i c l e o v e r l a p p i n g ranges  sizes  (or two d i f f e r e n t ,  non-  of s i z e s ) , data can be obtained that w i l l  f a c i l i t a t e b e t t e r understanding of the s e g r e g a t i o n phenomena in fluidised  beds.  18  APPARATUS  1.  General A schematic  F i g u r e 2.  Liquid  drawing  o f the apparatus  i s shown i n  was s t o r e d i n t h e r e s e r v o i r R and was pumped  t o t h e c o l u m n , t h r o u g h c e n t r i f u g a l pump P.. Pump h e a t was r e moved i n h e a t by b y p a s s i n g  e x c h a n g e r H, fluid  passing through  Pump o u t p u t  through  the heat  valve V  p r e s s u r e was c o n t r o l l e d  t o the r e s e r v o i r .  exchanger,  fluid  flowed  After  t h r o u g h one  o f t h e o r i f i c e m e t e r s B, C, o r D, o r t h r o u g h t h e c a p i l l a r y m e t e r A. long  Fluid  (13')  temperature  run of straight  before the l i q u i d  t o minimize  t o be a d m i t t e d ,  in  t h e column  2.  The T e s t  section  end e f f e c t s ,  to allow to'be  Columns a 2" I.L\.x44-'  perspex  ( F i g u r e 4 ) , and a 2" I.D.x5' g l a s s  The g l a s s column was used column was u s e d  d u r i n g sampling  f o r a l l o t h e r runs»  r u n s , and  F l a n g e s on  t h e e n t r y a n d t o p s e c t i o n s o f t h e column were d e s i g n e d t h e two columns were i n t e r c h a n g e a b l e . taped  inserted  (Figure3 ) .  column w i t h p r e s s u r e t a p s  the perspex  A  The t o p s e c t i o n o f  and t o a l l o w a s a m p l e r  Two columns were a v a i l a b l e ,  column.  t h e r m o m e t e r T.  pipe provided a calming  e n t e r e d t h e column.  t h e colvimn was d e s i g n e d particles  was r e a d from  t o t h e column f o r m e a s u r i n g  so t h a t  A m e t e r s t i c k was  bed h e i g h t s .  19  FLUIDISATION APPARATUS A,B,C,D- fluid meters E - t e s t section F - entry section G - exit section H - heat exchanger P - pump T - thermometer R • reservoir  •—i  H  Fi,?ure 2 - F l u i d i s a t i o n  Apparatus  20  00  2COLUMN T O P I - Sampler  2  SECTION  holder  2 - Adjustable guide for I CM  3 - Fluid outlet 4 - Fluid inlet - flange is bolted:to t e s t section  ©  Figure >  3 - Columri Top S e c t i o n  21  CO QL  LU  or  3  d  3  CO CO (J LU  V  •  0  U U U U U U L I U  UUUUUUUUULIIJ  IJTJTJ-1JTJ  C-txHc  c o or LU Q  CO 3  2  LU  cr  LU O Z  <  CL  LU CT LU r-  LU  O  <  C~C3  1  1-  3  Q II  LU CD  LL.  CO LU CL EC O  O 3  O  LU ICO LU  11 • i • i • (i • •11 > • 11 < f*< i' 11 •••  <  5 c o o O cr cr o o cr cr 1 c o< co i— z cr CL <  o o  o  Q_  .• )•<•• | ,ii, |iiiii|ii>iii||iii||iiiiii|t|iii|ii,ii|iiiii |t|t iii (•* • ' • |> • t  F i g u r e 4 - P r e s s u r e Drop A p p a r a t u s  1  22 The circulation observed.  column e n t r y s e c t i o n was d e s i g n e d effects, Initially  which tended  the s o l i d s  glass disc  packed  support consisted  supported  i n g s e c t i o n was f o u n d  o f a 3/16" t h i c k  i n a i " brass p l a t e . t o produce  they produced  t h e same e f f e c t .  large-scale  Circulation  b r a s s p l a t e was used  sintered glass disc.  Porous  and  were f o u n d  were t r i e d still  circulation, packings shot, but  effects instead  were  still  o f the  b r a s s p l a t e s w i t h l a r g e and s m a l l  i n combination with s e v e r a l types o f packing, t o be i n a d e q u a t e .  Several sizes  of screen  i n combination with the packings l i s t e d  the c i r c u l a t i o n  t h e s e t e s t s were t h a t circulation  sintered  Several other  o b v i o u s when a p o r o u s  p o r e s were u s e d  rings,  T h i s type of calm-  n i c k e l s h o t , and 1 / 8 " l e a d  such as  of a 9"  w i t h •$-" R a s c h i g  bumping, and a l a r g e p r e s s u r e d r o p . were t r i e d ,  t h e phenomena  the calming s e c t i o n consisted  l o n g , 2" I.D. b r a s s s e c t i o n , and  t o obscure  t o minimise  effect  persisted.  the c i r c u l a t i o n  o f p a r t i c l e s u p one s i d e  t h e o t h e r s i d e ) was c a u s e d  above, and  The c o n c l u s i o n s o f  effect  (large  scale  o f t h e column and down  by t h e p r e s e n c e  o f a n elbow a t t h e  t o p o f t h e column, and one a t 9 " below t h e s o l i d ' s s u p p o r t . new t o p s e c t i o n was d e s i g n e d  ( F i g u r e 4) s o t h a t  t h e elbow a t  t h e t o p o f t h e column was e l i m i n a t e d , and t h e a p p a r a t u s redesigned  was  s o t h a t a l o n g (13') e n t r y s e c t i o n c o u l d be u s e d .  •The e n t r y s e c t i o n was made v e r t i c a l , lined  A  up w i t h i t .  and t h e c o l u m n was  ( F l a n g e s were l i n e d  up and b o l t e d  then  down.  Any p r o t r u d i n g g a s k e t was removed, and h o l e s were d r i l l e d f o r  •jr" t a p e r e d  p i n s , which ensured  s e c t i o n were l i n e d c o l u m n was  lined  negligible,  up  up  like  one  i t was  t h a t t h e column and continuous  found  pipe).  When t h e  that c i r c u l a t i o n  u s i n g a 1 6 mesh s c r e e n a s  solids  entry  was  support,  and  no  packing. For 3/32"  particles  s m a l l e r - t h a n 1 6 mesh, a 2" l a y e r  l e a d p a r t i c l e s was  used, which acted l i k e  above the s c r e e n s u p p o r t . lead was  packed bed  support  was  a packed  bed  some c h a n n e l i n g when, t h e  u s e d , but  the c i r c u l a t i o n  effect  negligible. Conclusions  as  T h e r e was  of  on t h e s t u d y  follows, f o r minimizing a)  The  b)  the  effect  were  circulation.  column has  p r e c i s e l y with  of c i r c u l a t i o n  t o be v e r t i c a l ,  and  lined  up  entry section,  A l o n g e n t r y s e c t i o n has  t o be u s e d .  We  used, a  13' entry section, c) be  A l o n g e n t r y s e c t i o n , w i t h no  s u p e r i o r t o a packed s e c t i o n w i t h o u t  packing,  the l o n g  seemed  to  entry  section. d)  A screen support  P o r o u s d i s c s and and  promoted e)  top o f the  Elbows s h o u l d column, and  adequate.  l a r g e pressure drops a c r o s s  c h a n n e l i n g and  t o the s o l i d s f)  p l u g s had  f o r t h e p a r t i c l e s was  be  them,  circulation. eliminated i f possible at  elbows s h o u l d n o t  be  placed  the  too c l o s e  support.  An  (which w i l l not  a d d i t i o n a l a i d i s a bed be  fluidised  i n the  of l e a d  particles  range of v e l o c i t i e s  that  24 one  d e s i r e s ) p l a c e d above t h e s u p p o r t  3<>'  Temperature C o n t r o l The  tube, the  heat  type..  C a r e was  temperature constant,  temperature.  T h i s was  r a t e to the heat 4.  e x c h a n g e r w h i c h removes pump h e a t  countercurrent  fluid  screen.  very  Table  to  keep  c o o l i n g water temperature.  o f Flow Meters  T h e r e were f o u r f l o w m e t e r s a v a i l a b l e , wide r a n g e o f f l o w s .  seven-  c l o s e («3°F) t o room  c o n t r o l l i n g room  Calibration  a  i n a l l runs  done by a d j u s t i n g t h e  e x c h a n g e r , and  C o n s t r u c t i o n and  and  taken  was  to handle  Important dimensions are g i v e n  a  in  I. TABLE I  Run  Diam,  in,  0.25  in.  0.20  in,  0.50  in.  C  0.40  in.  1.00  in,  D  0.85  in,  2.00  in.  Meter  Orifice  A  0.25  B  (capillary)  A calming and  l e n g t h upstream of a t l e a s t  downstream a t l e a s t  m e t e r s B, calming  C,  and  Diam,  D.  10  pipe diameters,  M e t e r A,  l e n g t h s o f 100  and  downstream r e s p e c t i v e l y .  a capillary  was  pipe  diameters,  allowed  flowmeter,  50 p i p e d i a m e t e r s The  50  had  upstream  pressure drop a c r o s s  for  the  and orifice  25 p l a t e s and t h e c a p i l l a r y meter was measured  by means o f two  manometers, a 60" i n v e r t e d U-tube manometer, and a 30" m e r c u r y filled  U-tube Meriam  manometer.  were c o n n e c t e d t o a m a n i f o l d  The t a p l e a d s f r o m t h e meters  system, so t h a t t h e p r e s s u r e  d r o p a c r o s s a n y meter c o u l d be measured manometers.  on e i t h e r o f t h e two  V e n t s and m e r c u r y t r a p s were p r o v i d e d .  r a n g e o f p r e s s u r e d r o p s w h i c h c o u l d be measured was 50-1600 l b . f o r c e / f t ^ . calibrated  The  accurately  The f l o w meters were d e s i g n e d and  by J.W. S m i t h .  C a l i b r a t i o n curves  and c a l c u l a t i o n s  o f e r r o r i n measurement o f v e l o c i t y a r e g i v e n by Le C l a i r . (14) Calibration  equations  f o r m e t e r s A, B, and C a r e a s f o l l o w s .  C a p i l l a r y meter A (21)  V*  1-468 X l O "  6  RA/0//A  Meter B water Polyethylene  log (-p -) =H 0 6 4 log ( R e ) + I 3 9 9 io  (22)  G l y c o l l o g l ^ ) =-0-936 logLJRe)-1-174  (23)  2  t  i o  Meter C water Polyethylene  loqJ^J)  = -1-018 log (Re ) + 1-848 )()  t  G l y c o l log^^J) = - 0 - 9 5 2 log,J[Re )+ 0-557 (25) t  C The v a l u e s  c'  o f ( IT- )» 2  (  a  n  d  Re were c a l c u l a t e d f r o m  (26a) (26b)  . (24)  ( c;/Re ) t  (/i'/p)y/)/RAp  t  26 (27) R  =  Manometer r e a d i n g i n f t ,  Ap = d e n s i t y o f t e s t fluid  - d e n s i t y o f manometer'  lbm/ft.3  d-fc = d i a m e t e r 5,  fluid  of test  section  in ft.  Pumping Equipment The  test  fluid  was d r i v e n b y a Paramount c l o s e - c o u p l e d  t y p e U-132 c e n t r i f u g i c a l pump, ' d r i v e n b y a 3-horsepower motor o p e r a t i n g a t 3450 R.P.M,  I n r u n s w i t h w a t e r , t h e pump  p r e s s u r e was a d j u s t e d t o 36 p . s . i . g . in  runs  was  f o r optimum r e s u l t s , and  w i t h p o l y e t h y l e n e g l y c o l , a pump o u t p u t  40 p . s i . i . g . was m a i n t a i n e d . lowered  pressure o f  ( I f t h e pump o u t p u t  below t h i s v a l u e , e x c e s s  output  pressure  foaming r e s u l t e d  from t h e  h i g h c i r c u l a t i o n o f P.E.G.) 6.  P r e s s u r e Drop Equipment P r e s s u r e d r o p measurements up t h e column were  formed by means o f t h e p r e s s u r e t a p s on t h e p e r s p e x shown i n F i g u r e 5, the manifolds, adjacent  taps  were c o n n e c t e d tetrachloride rubber  T h e s e t a p s were a l t e r n a t e l y  per-  column,  connected t o  s o t h a t t h e p r e s s u r e d r o p a c r o s s a n y two c o u l d be m e a s u r e d .  L e a d s from  the manifold  t o a d i f f e r e n t i a l manometer, i n w h i c h was u s e d .  Spring-loaded  tubing connecting the i n d i v i d u a l  served as v a l v e s f o r t h e i n d i v i d u a l  carbon  p i n c h clamps on t h e taps t o the manifolds  taps.  Particles  were  27  SAMPLER Figure 5 -  Sampler  28 prevented soldered  from e n t e r i n g the to short pieces  taps  inserted into holes  f l u s h with  the  i n s i d e of the  i n the  sample t u b e was  b r o n z e , and  a constant  v i s c o s i t y and  tube i s g i v e n  i n (31).  standard,  w i t h i n ±0.2$ i n the The  The  and  was  range  d e n s i t y of the  t u b e was  fluids.  The  a t 60°F. and  fluid The  efflux  was  in time  using  water as  true  the  measured  hydrometer  distilled  found t o g i v e t h e  was an  density  68°-80°F. p a r t i c l e s was  and  t h e n i t s w e i g h t when h a l f f u l l  The  b o t t l e was  then f i l l e d  viscosity  the  A  calibrated  c l e a n i n g and  d e n s i t y of the  c*.c. s p e c i f i c g r a v i t y b o t t l e .  to, remove any  c o n t r o l l e d to lo.l°F.  procedure f o r f i l l i n g ,  checked u s i n g a Westphal balance absolute  The  d e n s i t y were measured  0,2546t where t was  u s i n g a hydrometer s t a n d a r d i z e d  25  fluid  (R-933 S i z e 300)  g i v e n by  The  5.  Density  measurement o f h i g h v i s c o s i t y  seconds.  s a m p l e r i s shown' i n F i g u r e  temperature o i l bath,  c e n t i s t o k e s was in  up  components were c o p p e r .  Measurements o f V i s c o s i t y and  Oannon-Fenske v i s c o m e t e r for  lined  adjustable.  Kinematic in  c o l u n , and  copper  Sampler  sample volume was 8.  This  w h i c h were  column.  A schematic drawing of the The  small, screens  of copper t u b i n g .  t u b i n g was  7»  by  The  b o t t l e was  o r gas  weighed  o f p a r t i c l e s was  with d i s t i l l e d  d i s s o l v e d gas,  measured u s i n g  w a t e r , and  adhering  to the  a empty,  taken. boiled particles.  29 It  was  then c o o l e d , topped  measured from  temperature.  The  ments were t a k e n  9.  Appendix  Test  w i t h w a t e r , and  weighed a t  p a r t i c l e d e n s i t y was  t h e above measurements  t h e volume o f t h e s p e c i f i c  in  up  ( u s i n g an  experimental  gravity bottle).  value f o r  Three  f o r each s e t of p a r t i c l e s .  calculated  measure-  These are  given  1.  liquids Test  properties, stabilitj',  liquids  were c h o s e n on t h e b a s i s o f Newtonian  non-corrosiveness, low  toxicity,  transparency, hygroscopicity,  viscosity  L i q u i d s c h o s e n were w a t e r , and  index,  and  Canada.  Water p o s s e s s e s  p r o p e r t i e s and  low  Chemical  does n o t need t o be m e n t i o n e d  for solution  t o 70  c e n t i p o i s e s were i n v e s t i g a t e d  He  found  t h a t 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 up  The  Newtonian b e h a v i o r  of polyethylene g l y c o l  was  who. a l s o  concluded  compared  the s t r e s s - s t r a i n curves  "Viscometer)  by G a l l o w a y  (0 t o 1600  The  viscosities (33)-  to a  c e n t i p o i s e s showed N e w t o n i a n b e h a v i o r  t h e wide r a n g e o f r a t e s o f s h e a r encountered.  of  further.  up  o f 70  of  t h e r e q u i r e d p h y s i c a l and. c h e m i c a l  properties of polyethylene g l y c o l  viscosity  cost.  an aqueous s o l u t i o n  p o l y e t h y l e n e g l y c o l E-9000, s u p p l i e d by Dow  tions  then  a  over  sec"" ") t h a t 1  of "concentrated"  investigated  that these s o l u t i o n s  by S m i t h  were N e w t o n i a n .  (obtained with a  of the  same v i s c o s i t y .  He  did  solu(32), .He  Stormer  of 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 w i t h those  glycerol solutions  he  not,  of  30 u n f o r t u n a t e l y , present any data, o r s t a t e the range o f v i s c o s i ties  studied.  calibration  The f o l l o w i n g d a t a , T a b l e  o f t h e 0.25" I.D., 4'-7" l o n g c a p i l l a r y  When t h e d a t a were p l o t t e d straight  a s 8q/jfdt^ v e r s u s  l i n e was o b t a i n e d ,  • l i k e a Newtonian f l u i d  i s the Fanning  range,  i n the  meter.  APd-fc/4Iyx,  showing t h a t t h e l i q u i d  a  behaved  (34) over t h e range o f r a t e s o f shear  shown and a t t h e v i s c o s i t i e s (f  II,were t a k e n  noted*  Also the value  f r i c t i o n f a c t o r ) was c o n s t a n t  o f f.Re  over the  a l t h o u g h n o t e x a c t l y e q u a l t o 16 a s p r e d i c t e d by  laminar flow theory.  T h i s was p r o b a b l y due t o d i f f i c u l t y  i n measuring t h e diameter  exactly. TABLE I I  Calibration  qxl04  Re.  Ft?/sec.  Centistokes.  5.460 5.209 4.291 3.801 3.345 2,873 2.406 2.202 1.478 1.240 1.045 0.470  123.5 123.5 123.0 122.8 122.8 121.8 121.5 120.5 121.5 120.9 120.3 .119.8  *•  25.10 23.95 19.80 17.58 15.47 13.39 11.24 10.38 6,91 5.82 4.93 2.23  o f C a p i l l a r y Meter A  P.Re. mm  15.40 15.48 15.42 15.49 15.38 15.61 15.57 15.55 15.50 15.72 15.77 15.23  Rate o f Shear a t Wall . g £Pd /4L/i. AP Secr-L lbf./ft. c  f  6221 5619 4885 4347 3800 3320 2772 2534 1697 1443 1220  1509 1477 1183 1050 918.1 793.6 . 6.61.3 599.2 404.6 342.4 287.9 124.5  531  T h i s l i n e a l s o passed through t h e o r i g i n , the p o s s i b i l i t y o f p l a s t i c behavior.  2  thus  eliminating  31 The rates  h i g h e s t p r e s s u r e d r o p s , and t h u s t h e h i g h e s t  o f shear, a r e encountered  i n the test  s e c t i o n when  particles are fluidised  a t low p o r o s i t y .  is  on t h e p a r t i c l e s a s w e l l a s on t h e  a shear force a c t i n g  walls of the v e s s e l . t h e problem  This  problem  In t h i s  case t h e r e  was much more complex  o f f i n d i n g t h e r a t e o f s h e a r i n an empty  s e c t i o n , and. some g r o s s a s s u m p t i o n s  had t o be made.  than  test A force  b a l a n c e on a s e c t i o n o f column w i t h l e n g t h L y i e l d s TT * n .2 iLAPd?  (28) where and  T  Q V  = TovS  i s an average  fluid-solid  shear s t r e s s  8 i s t h e s u r f a c e a r e a o v e r which  Assuming t h a t  this stress  i n the s e c t i o n , is- distributed.  S i s the s u r f a c e a r e a o f the p a r t i c l e s  s u r f a c e a r e a o f t h e column i n t e r i o r s e c t i o n , S = [7Td  (29)  +  t  -gj'O-  plus the  then  €)][_  s i n c e t h e volume o f p a r t i c l e s i s  P - J-dfLO- «) v  and  t h e s u r f a c e t o volume r a t i o  f o rspherical particles i s  e q u a l t o 6/d , The /  average >  V50>  -r a v  shear s t r e s s  -  ~  A P  [4/d + f  i s , from 23 and 29,  6(l-€)/d]L  hence  ( ) 31  Jrfui , T^QC _ J w  H-  APQ tV t d  +  6(i-€y/d]L/i  32 The  highest  r a t e s of shear encountered i n the t e s t  s e c t i o n i n runs with polyethylene p a r t i c l e s a t low p o r o s i t y . fj.= 0.0941 lbm./ft.-sec,  g l y c o l were with l a r g e lead  For € = 0.45, d  = 0 . 0 9 7 " , and.  the r a t e of shear was c a l c u l a t e d t o  be 1644 sec"" ', u s i n g 1 and 31. 1  This  i s w i t h i n the range shown  i n t a b l e 2, and shows that i t i s h i g h l y probable t h a t the s o l u t i o n s of polyethylene liquid  g l y c o l behaved l i k e a Newtonian  i n a l l experiments. A quantity  o f sodium dichromate (225 gm.) and sodium  hydroxide (54 gm.) was added t o the 32 g a l l o n s of 40$ s o l u t i o n to i n h i b i t c o r r o s i o n .  V/ith the passage of time the s o l u t i o n  turned a dark orange-brown c o l o r , but t h i s d i d not prevent the observer from seeing  the phenomena occuring  i n the bed.  Some r u s t was observed, e s p e c i a l l y i n the mercury t r a p s , which were made of s t e e l pipe with c a s t i r o n plugs. pump i n t e r n a l s , 'copper p i p e s ,  The  rubber tubing and brass  fittings  d i d not appear to be c o r r o d i n g . Polyethylene and  slightly efflorescent.  costs 35 10.  g l y c o l i s i n f i n i t e l y s o l u b l e i n water, I t has a low ^ v o l a t i l i t y , and  0/lbo  Test  Materials  Test m a t e r i a l s particles.  used were l e a d , g l a s s , and d i v i n y l  The lead and g l a s s p a r t i c l e s were s p h e r i c a l , and  a v a i l a b l e i n a range o f s i z e s (0.5 mm. t o 6 mm.).  Divinyl  p a r t i c l e s were s p h e r i c a l , and a v a i l a b l e i n mesh s i z e s of -24 t o +48 ( T y l e r ) o  One hundred p a r t i c l e s from each s e t  33 (except  42-48 mesh) were measured, and t h e s e  are reported  i n A p p e n d i x 1«  measurements  When p o s s i b l e , 5 p a r t i c l e s  from  e a c h s e t were measured on 3 m u t u a l l y  p e r p e n d i c u l a r a x e s , and  these  i n t h e A p p e n d i x t o show  measurements a r e a l s o r e p o r t e d  the d e v i a t i o n ' o f the p a r t i c l e s particles and  (2 mm.  from ' s p h e r i c i t y .  g l a s s , and 24-28 mesh d i v i n y l ) a " l a r g e "  "small" diameter i s given  for 5 particles  When p o s s i b l e , p a r t i c l e s screens.  Particles  made out o f b r a s s size.  were s i z e d  were a l s o s i z e d  or a r b o r i t e with  A l l sets of p a r t i c l e s  divinyl  using  inside  c o l o r e d , when n e c e s s a r y , v a r i o u s mesh s i z e s in small  "home-made"  were p i c k e d  over  particles  using  p a r t i c l e s adhering  to the screens  attempt  overlap.  until  they  Results  t h e Ro-Tap s h a k e r ,  a r e shown  in  water w i t h  Particles  Particles  originally,  Any  i n an  were s c r e e n e d  several  few r e m a i n -  o f s c r e e n i n g by hand, and i n A p p e n d i x 1,  Divinyl  and c o u l d be " b l e a c h e d "  no r e s u l t a n t change i n d e n s i t y .  were  (The  overlap).  with  particles  by hand  the T y l e r s c r e e n s .  were d i s c a r d e d ,  (except  The  were s c r e e n e d  would p a s s t h r o u g h e a s i l y ,  i n g on t h e s c r e e n .  were c o l o r e d  and  u s i n g model a i r p l a n e d o p e .  of d i v i n y l  screens,  the correct  by hand  particles  Ro-Tap s h a k e r gave i n c o n s i s t e n t c u t s , w i t h  times,  u s i n g T y l e r mesh  or at the s u r f a c e .  (5-10 gm) b a t c h e s ,  to prevent  i n each s e t .  holes d r i l l e d  p a r t i c l e s ) t o remove odd shaped  with a i r bubbles  For small  by  with particles  boiling  EXPERIMENTAL  In lined,  this  and  the  presented,  section method  along  with  of  experimental  attaining  these  experimental  objectives  are  objectives  is  out-  procedures.  Objectives  1.  Experiments  predicts  the  right  particulately intended to  the  have  find  to an  the  were  trends  fluidised  find  the  interface  particle  up  to  insofar  beds  is  between  two  density  prove  as  that  density sets  of  difference  segregation.  the  particle  concerned.  minimum b u l k  minimum b u l k  measurable  set  The  formula  segregation  It  was  also  difference particles, that  in  in  order  and  to  accompanies  objectives  were  as  follows: To  1)  with, i n c r e a s i n g To  2) as  the  erence  diameter  (yO-yO) To  3) bulk are  density well  show  that  the  tendency  to  segregation  increases  the  tendency  to  segregation  increases  porosity. show  that  ratio is  is  increased,  and  as  the  density  diff-  increased.  show  that  difference  segregated.  equation in  the  20  binary  predicts system  the when  actual the  particles  3 5  4) particle  To d e m o n s t r a t e t h e e f f e c t  size 5)  segregation.  To f i n d  t h e minimum b u l k  o r d e r t o have an i n t e r f a c e 6)  To f i n d  on  t h e minimum b u l k d e n s i t y d i f f e r e n c e t h a t segregation.  To 3tud.y t h e e f f e c t  particle  size  segregation  of particle  was d i s c u s s e d  2.  O u t l i n e of Experimental  The screen  first  sizes  made t o show t h e e f f e c t particle  size  would be h i g h e r that  phenomenum  particles  can  exist  tions.  T h e s e r u n s were  and t h a t t h i s  evidence  concerning with  found  together  takes  place a t the given  the segregation  t h e sampler.  Since the  from a s m a l l s e c t i o n o f t h e bed,  diameter r a t i o  operating  which condi-  of the p a r t i c l e s  i s t h e r a t i o above w h i c h m e a s u r a b l e  particles  would  I t was a l s o hoped  i n t h e bed a t t h e g i v e n  Hence t h e h i g h e s t  on  gradient  removed a r e r e p r e s e n t a t i v e o f p a r t i c l e s  together  The  size,  p o r o s i t y beds.  c o u l d be o b t a i n e d  the  i n water.  various  I t was hoped t h a t s a m p l i n g  in particle  s a m p l e r removes p a r t i c l e s  beds.  Work  o f p o r o s i t y and d i a m e t e r r a t i o  i n higher  some i n d i r e c t  fluidised  r u n s were made w i t h  particles  segregation.  indicate a gradient  velocity  i n t h e s e c t i o n on T h e o r y .  experimental  of divinyl  random  i n particulately  This effect General  density difference i n  between two s e t s o f p a r t i c l e s .  accompanies measurable p a r t i c l e 7)  o f c h a n g i n g m and n on  segregation  conditions.  chosen f o r the run d e s c r i b e d  were -28 +32 T y l e r mesh d i v i n y l .  above  T h e s e were c h o s e n on t h e  36 basis  o f sampler  representative  tests,  b e i n g s m a l l enough t o f a c i l i t a t e  sampling,  but l a r g e  enough t o be  measured w i t h m i c r o m e t e r c a l i p e r s . sampling  were made w i t h c o m b i n a t i o n s  the e f f e c t  of diameter  ratio  Other  that  the formula p r e d i c t s  f o r segregated particles  on p a r t i c l e s i z e  interface,  segregation.  i n polyethylene glycol  t o show  the a c t u a l bulk d e n s i t y d i f f e r e n c e  Runs were t h e n made w i t h s e t s o f ratios  to find  b u l k d e n s i t y t h a t accompanies d i s a p p e a r a n c e and f i n a l l y  t i o n by s i z e .  {p^-p)  t o show  on r u n s w i t h 2 and  having s u c c e s s i v e l y lower diameter  t h e minimum  of  beds.  without  of screen sizes  E x p e r i m e n t a l d a t a were c o l l e c t e d 3 millimeter glass particles  runs  easily  effect  size  segrega  s h o t t o show t h e e f f e c  segregation.  o f m and n was s t u d i e d by c o m p a r i n g t h e  b e h a v i o r o f t h e s e t o f 3 mm. and  6 mm.  particles,  and  polyethylene g l y c o l .  objective 7,  of measurable  Runs were made w i t h l e a d  on p a r t i c l e  The  the disappearance  o f an  and 4 mm.,  and t h e s e t o f 5  mm.  when t h e s e were f l u i d i s e d . w i t h water'  and r e s u l t s  T h i s work a l s o has a b e a r i n g on are discussed with t h i s  objective i n  mind. 3»  Experimental In  this  Procedures  and P r o c e s s i n g o f D a t a  s u b - s e c t i o n the procedures  and  processing data are given.  and  p r o c e s s i n g expansion  f o r a l l runs  for collecting  The p r o c e d u r e  and p r e s s u r e d r o p  with various p a r t i c l e s  for collecting  d a t a i s t h e same  and f l u i d s .  The  sampling  37 procedure i s a l s o (a)  given,  V e l o c i t y - P o r o s i t y Data  These d a t a each c o m b i n a t i o n  were o b t a i n e d  of p a r t i c l e  f o r each p a r t i c l e  sizes  top  W i t h a l l manometer and  turned  on.  flow  was  turned  The  meter w i t h  s e l e c t e d by  fluidised  and  adjusted  became c o n s t a n t , test  liquid  valves  and  and  until  w i t h i n 3°F.  f l o w was  then  The  o f f , the  the  long  pump  then  zeroed  by  The  velocity  was  test  liquid  to the d e s i r e d particles  minimum f l u i d i s a t i o n ,  the  temperature,  fluid  The  was  velocity  of the  calculated  increased  readings  t e m p e r a t u r e , and  further increased  m e n t i o n e d above were t a k e n velocity  particles  was  21  to a given v i s c o s i t y  to 27).  until  o f bed  until  The  until  of  room taken.  the  the  readings  elutriation  Velocity  u s i n g the meter  v e l o c i t y was  no a i r  point  height,  i n s t e p s , and  approached.  The  the  The  lines.  manometer were  at each.step  f r o m t h e above r e a d i n g s ,  (Squations  liquid  then  manometer  manometer, o r c o n n e c t i n g  and  were  temperature  o f room t e m p e r a t u r e .  bleeding test  then  was  c o o l i n g w a t e r was  s e t t o z e r o , and  remained, i n t h e m a n i f o l d ,  and  e r r o r , and  the  column,  funnel with a  valves  height.  i n the  on t h e m e t e r s e l e c t e d were opened c a u t i o u s l y .  m e t e r was  tions  flow  put  range c o r r e s p o n d i n g  trial  to a reasonable  on,  was  s e c t i o n , by means o f a  stem.  and  used,  A weighed -amount o f p a r t i c l e s through the  size,  then  was correlacorrected  (0.000672 lb./ft.-sec. f o r w a t e r , 0.092  0.0941 lb./ft.-sec. f o r p o l y e t h y l e n e  glycol) using  the  38 standard drag c o e f f i c i e n t spheres  was  (17).  fitted  - R e y n o l d s number c u r v e f o r  (A s t r a i g h t  line  of the  t o the drag c o e f f i c i e n t  form  - R e y n o l d s number c u r v e Re  o v e r t h e range.'• o f . a c t u a l p a r t i c l e R e y n o l d s  numbers  encountered.  From t h i s  e q u a t i o n t h e r e l a t i o n s h i p between v e l o c i t y  viscosity  was  obtained i n the V  =  k>  reported  form  s  where k ' " i s a c o n s t a n t w h i c h d e n s i t y , and  depends on f l u i d  p a r t i c l e diameter.)  i n Appendix  II.  and  These  V e l o c i t y was  and  particle  correction lines then c o r r e c t e d  >  J  V(corrected) = V(measured) [ C o r r e c t i o n s were n o t made f o r v a r i a t i o n s  U (base)  fc  (measured  in liquid  using -|  )  are  s  J  density  w i t h t e m p e r a t u r e as t h e s e v a r i a t i o n s were s m a l l o v e r t h e temperature  ranges  encountered.  A p o r o s i t y c o r r e s p o n d i n g t o each v e l o c i t y lated  was  calcu-  using  (32)  € = I - w//j'L(20-273)  where 20.273 i a t h e c r o s s s e c t i o n a l a r e a o f t h e column,  and  W,  Results  and  L a r e i n gm.,  gm./cc, and  cm.  respectively.  were p l o t t e d  as l o g V v e r s u s l o g € ,  and  discussion.  Where n e c e s s a r y , l e a s t  squares l i n e s  culated .  are presented i n the were  cal-  •39 (b)  P r e s s u r e Drop Measurements  The  column shown i n F i g u r e 4 was u s e d .  menter was f i r s t the manifolds to  zeroed  and l i n e s .  by p u r g i n g and b l e e d i n g a i r o u t o f The bed h e i g h t was t h e n  tap c l o s e s t  2 and 5,  and so on up t h e column u n t i l t h e  t o t h e t o p o f t h e bed was r e a c h e d .  Then v a l v e s  were a d j u s t e d s o t h a t 2 and 4 were on o p p o s i n g  on t a p #2  m a n i f o l d s , and p r e s s u r e d r o p 2 and 6, 2 and 8 , a n d In to  adjusted  t h e d e s i r e d v a l u e , and p r e s s u r e d r o p was measured between  v a l v e s 2 and 3,  4,  The mano-  runs  was t h e n measured a c r o s s 2 and  so on up t h e column.  with polyethylene g l y c o l ,  the time r e q u i r e d  o b t a i n a n a c c u r a t e r e a d i n g was v e r y l o n g - 30 t o 45 m i n u t e s .  R e a d i n g s were t a k e n readings agreed.  every 5 minutes,  During  until  t h i s time, minute adjustments  made t o bed h e i g h t , and room t e m p e r a t u r e were  converted  from  and f l u i d  were  temperature  controlled. Readings i n centimeters  and  two c o n s e c u t i v e  to readings  o f carbon  o f pounds f o r c e - i n c h p e r c u b i c  data a r e r e p o r t e d as "pressure drop" t a p #2". (c) To  desired  versus  were  foot,  "distance  O r i g i n a l d a t a a r e g i v e n i n Appendix I . Sampling  o b t a i n a sample, t h e bed was a d j u s t e d  h e i g h t by a d j u s t i n g t h e f l u i d  s a m p l e r was l o w e r e d height.  tetrachloride  i n the test  velocity,  t othe and t h e  section to the pre-selected  The sample p o r t was opened by d e p r e s s i n g t h e s p r i n g  • (See F i g u r e 5 ) , and then c l o s e d ,  40  The sampler was removed, •  and the sample recovered i n a 50-ml. beaker.  A l l samples  were t a k e n a t the a x i s o f the tube, the sampler b e i n g a d j u s t e d t o an a x i a l p o s i t i o n beforehand. Beads i n the sample were measured u s i n g a S t a r r e t t micrometer c a l i p e r , and the a r i t h m e t i c average of 100 p a r t i c l e s i s r e p o r t e d i n F i g u r e 3. Samples were a l s o t a k e n a.t some o f f c e n t r e r a d i a l p o s i t i o n s , but l i t t l e r a d i a l v a r i a t i o n was found.  Several  samples were a l s o taken, a t one p o i n t t o check the r e p r o d u c i b i l i t y o f r e s u l t s , and the r e p r o d u c i b i l i t y was found t o be good (See Appendix I ) . (d)  Photography  P i c t u r e s were t a k e n by a p r o f e s s i o n a l photographer, who used a w h i t e background, and an e l e c t r o n i c f l a s h f o r illumination.  41  RESULTS AND  1.  DISCUSSION  Introduction In t h i s  section  the r e s u l t s  o b t a i n e d from  e a c h m i x t u r e o f p a r t i c l e s a r e d i s c u s s e d , and g r a p h s and  pictures are given.  pertinent  F i n a l l y a l l of the  a r e shown i n t a b u l a r f r o m , and d i s c u s s e d 7 experimental objectives  the  fluidising  results  with respect  to the  s e t out i n t h e p r e v i o u s s e c t i o n .  E x p e r i m e n t a l d a t a f r o m w h i c h a l l g r a p h s were p r e p a r e d are given  i n Appendix  I.  Properties  f l u i d s u s e d a r e summarized particle 2.  sizes are given  Divinyl  of a l l p a r t i c l e s  i n Table I I I .  i n Appendix  and  Measurements o f  I.  -'Water Runs  Plots  of v e l o c i t y - p o r o s i t y  f o r the separate screen s i z e s w e l l as f o r two  (expansion data) are given  (24-28,  28-32, and  42-48),  b i n a r y m i x t u r e s , i n F i g u r e s 6 and  7.  as  Calcu-  l a t e d v e l o c i t y - p o r o s i t y p l o t s a r e a l s o g i v e n i n each case f o r t h e m i x t u r e s ( e q u a l p o r t i o n s by w e i g h t These a r e based sized  bed.  m i x t u r e was  on t h e i n d i v i d u a l  For a given velocity, calculated  from  i n both  cases).  e x p a n s i o n o f e a c h monothe o v e r a l l  porosity  of the  42 TABLE I I I Particle  Particle and Fluid -  Avg, Diam, mm.  Glass 2 mm.A-1 2 mm.B-1 3 mm. -1 4 mm. -1 5 mm. -1 5 mm.K-1 6 mm. -1 3 mm. -3 4 mm. -3 5 mm, -3 6 mm. -3  1.86 2,04 2.77 3.95 4.88 4.86 5.78 2.77 3.95 4.88 5.78  Lead #9-2 #6-2  2.02 2.46  Divinyl 24-28-3 28-32-3 42-48-3  0.653 0.543 0.322  Fluid  and F l u i d  Properties  n '  gm./cc.  Amt. Used. gm.  2.907 2.907 2.896 2,803 2.525 2.221 2.457 2.896 2.803 2.525 2.457  200 200 200 300 300 300 220 ,1225 300 300 220  4.74 4.41 4.11 4.28 4.20 4.28 4.19 2.56 2.54 2.34 2.34  0.081 0.088 0.134 0.249 0.304 0.261 0.369 1.32 1.69 1.89 2.44  0.35 0.42 0.76 1.94 2.90 2.62 4.00 1112 2029 2805 4260  1.000 1.000 1.035 1.059 1.059 1.059 1.059 2.000 2.000 2.000 2.000  1000 1000  3.94 4.26  0.370 0.539  1.80 3.25  1.059 1.059  300 300 300  2.78 2.85 2.89  0.378 0.335 0.182  10.83 10.59 2.936 2.936 2.924  V  Re  0  0  m  f t ./sec'.  74,1 54.6 17.6  1.333 1.333 1.333  Properties 1. fl 2,  p.  3. / i - '  = 0.0920 l b . m a s s / f t  3ec .,  p' =  1.070 gm./cc.  = 0.0941 lb.mas s / f t . - s e c . , p' = 1.070 gm./cc-. = 1.00 c e n t i p o i s e ,  P' = 1.000 gm./cc.  43 —r~  P  DIVINYL-WATER ©  2 4 - 2 8  TYLER MESH _  ©  2 8 - 3 2  TYLER MESH  O MIXTURE-EXPERIMENI] -MIXTURE-PREDICTED (D24-28  MESH,-  UNSTABLE BED -1-4 -0-3  J  _ l  L  L06 Figure  -01  -0-2 l 0  €  6 - E x p a n s i o n C u r v e s f o r 24-28 a n d 28-32 Mesh Divinyl  P a r t i c l e s , Fluidised. with  Water  44 I t was v i s u a l l y green, while the  observed  (24-28 mesh p a r t i c l e s  28-32 and 42-48 mesh p a r t i c l e s  42-48 mesh p a r t i c l e s  particles  T h e r e was a d i s t i n c t ,  porosities, beds.  were w h i t e ) t h a t ,  formed a bed above t h e 24-28 mesh  a t a l l p o r o s i t i e s when t h e s e  together.  were c o l o r e d  two s e t s were  fluidised  horizontal interface at a l l  and t h e r e was no o b s e r v a b l e  i n t e r m i x i n g o f t h e two  When t h e 24-28 mesh and 28-32 mesh p a r t i c l e s  were  fluidised. together  i t was o b s e r v e d t h a t t h e 28-32 mesh  particles  t h e t o p p o r t i o n o f t h e bed a t a l l p o r o s i -  ties.  occupied  T h e r e was a f u z z y ,  of which decreased  with  wavy i n t e r f a c e , t h e r e l a t i v e  i n c r e a s i n g bed h e i g h t ,  some i n t e r m i x i n g o f t h e two b e d s . m i x i n g and t h e f u z z y sizes in  larger size, find  and t h e r e  I t was f e l t  was  that the i n t e r -  i n t e r f a c e were due i n p a r t t o o v e r l a p o f  i n the mixture.  each s e t ) .  height  (See A p p e n d i x  T h i s made i t n e c e s s a r y  I f o r size t o study  distributions particles  of a  where t h e s i z e d i s t r i b u t i o n s were s m a l l e r , t o  t h e minimum d i a m e t e r r a t i o ,  and hence t h e minimum  bulk  density difference f o r segregation. The particles  p o i n t s above t h e e x p a n s i o n curve  i n Figure  6 a r e f o r an' u n s t a b l e  e x i s t s a t ' p o r o s i t i e s above- 0.80,  f o r 24-28 mesh  bed c o n d i t i o n w h i c h  The bed c o u l d be expanded  t o p o r o s i t i e s above 0.80, b u t a s u d d e n d i s t u r b a n c e c a u s e t h e bed h e i g h t s w i r l i n g and v o r t e x  would  t o d r o p due t o t h e sudden a p p e a r a n c e o f formation.  This  swirling  could  o n l y be  e l i m i n a t e d by c o l l a p s i n g t h e bed and e x p a n d i n g i t s l o w l y again  from r e s t .  The p o i n t s a r e r e p r o d u c i b l e .  45  -0 4 h  -0-6  -0-8 >  o  o O  -l-Oh  -1-4  L0G € l0  F i g u r e 7 - Expansion Curves  f o r 24-28 and 42-48 Mesh  Fluidised  i n Water  Divinyl,  46 The particles  p o i n t s below t h e e x p a n s i o n  i n Figure 7 are calculated  of-bed v a l u e s t o o b t a i n the p o r o s i t y when i t was f l u i d i s e d ties  u s i n g i n t e r f a c e and t o p o f t h e 42-48 mesh bed  a b o v e t h e 24-28 mesh b e d .  The p o r o s i -  i n a l l c a s e s a r e h i g h e r , a t t h e same v e l o c i t i e s ,  the corresponding p o r o s i t i e s tion  for this  divinyl  i n the s i n g l e bed.  behavior i s offered  than  An e x p l a n a -  i n t h e next s u b - s e c t i o n .  A sampling  r u n was made w i t h 600 grams o f 28-32 mesh  i n water.  The r e s u l t s  the a r i t h m e t i c average is  c u r v e f o r 42-48 mesh  plotted  diameter  a g a i n s t reduced  as p a r a m e t e r ,  a r e shown i n F i g u r e 8.  (One p o i n t  o f 100 p a r t i c l e s  bed h e i g h t  Here  i n a sample  (h/L), with  porosity  i s missing f o r the curve a t p o r o s i t y  = 0.8, w h i c h i s h / L = 0, m e a n d i a m e t e r = 0.0238)  The c u r v e  shows t h a t  on t h e o v e r -  all  particle  porosity  s e g r e g a t i o n i s dependent  o f t h e b e d , and t h a t  density particles porosity  size  t h e tendency  f o r equal  t o s e g r e g a t e i s enhanced by i n c r e a s i n g t h e  of the p a r t i c u l a t e l y  a l s o taken a t p o r o s i t y =0.87.  fluidised At t h i s  bed.  Samples were  porosity,  t h e bed was i n t h e u n s t a b l e c o n d i t i o n mentioned and  i n Appendix I I I .  The samples show t h a t  however,  previously,  t h e r e i s more  m i x i n g , as e x p e c t e d , a t t h i s p o r o s i t y due t o t h e s w i r l i n g and  vortex formation i n the bed.  given normal  i n A p p e n d i x I.)  ( A l l sampling  results are  A l l samples show a n a p p r o x i m a t e l y  d i s t r i b u t i o n about  t h e mean, and a n e x a m i n a t i o n o f  the sampling r e s u l t s w i l l  show r o u g h l y what d i a m e t e r s o f  particles  t o be f o u n d  may be e x p e c t e d  mixed p a r t i c l e s  of this  type.  t o g e t h e r i n a bed o f  No c o n s i s t e n t  method o f  HEIGHT OF SAMPLE / Figure 8. Results of Sampling Run  TOTAL BED HEIGHT  48 treating  the sampling  diameter  ratio,  3.  d a t a c o u l d be  p o r o s i t y , and  found  relating  minimum  h/L.  G l a s s Beads - P o l y e t h y l e n e G l y c o l Runs (a)  2 and  3 mm.  G l a s s Beads F l u i d i s e d  i n Polyethylene  Glycol The and  expansion  curves  f o r a 50-50 m i x t u r e  i n F i g u r e 9.  The  o f 2 and  experimental  the p r e d i c t e d r e s u l t s , at high p o r o s i t i e s . low  effect,  entrance,  takes p l a c e .  effect  is difficult  minimised column.  not  T h i s may  except  be  to avoid i n any  of  the  e x p l a i n e d as f o l l o w s .  support  effect liquid  t h a t most  observed  i n a l l runs.)  to account  f o r , but  i t is certainly  when t h e r e a r e two  u p p e r bed  (See  due  f o r t h e bed  predicted, at high  t o the  entrance  fluidisation  f i g u r e 7,  i s more s e n s i t i v e t o  i s t h a t the curve  This  beds i n t h e  u n d e r g o e s smoother  cussion.)  changes, so the r e s u l t  effect  kept  the  ( T h i s was  higher p o r o s i t i e s .  r a p i d l y than  32,  i n a column t h e r e i s an  with resultant  curve  shown  favourably with  7,  apparent  I t i s a t t h e bed  would mean t h a t t h e t o p bed  approaches the  are  u s i n g equation  absence of the mixing  The  particles,  where t h e f l o w p a t t e r n o f t h e  i n t h e t o p bed The  r e s u l t s agree  w h i c h was  changes c o n s i d e r a b l y . mixing  3 mm.  particles  - F i g u r e s 6 and  When p a r t i c l e s a r e expanded to the  and  ( O v e r a l l p o r o s i t i e s were p u r p o s e l y  runs w i t h l a r g e r p a r t i c l e s . )  due  3 mm.  calculated  i n d i v i n y l - w a t e r runs  u n s t a b l e bed  f o r 2 mm.  and  dis-  velocity  f o r t h e mixed bed •  of smaller p a r t i c l e s porosities.  more  49  GLASS BEADS Re = 0-35-0-76 e  -10 O  2mm.  3  3 mm.  O MIXTURE - - PREDICTED  CURVE  FOR MIXTURE  -1-5  of  eg  O /  -2-0  /  /  /  Cf  / /  /  /  0  -2-5 /  -0-3  -0-2 LOG *  -01  | 0  F i g u r e 9 - E x p a n s i o n C u r v e s f o r 2 and Fluidised  i n Polyethylene  3 mm. Glycol  Glass  Beads,  50 A clear when t h e 2 and  i n t e r f a c e was 5 mm.  observed  at a l l p o r o s i t i e s  beads were f l u i d i s e d  together  (Figure  10). I n d i v i d u a l p r e s s u r e drop  curves  beads a r e shown i n F i g u r e s 11 and  12  i n both  cases,  however, t o be co-existing be  joined  t h e b e s t method o f p l o t t i n g ,  t o f i t two  which i s the  straight  interface,  which i s the average Pressure drop glass particles  and  and  t h e mixed bed,  was  i n slopes  of  3  mm.  Good agreement i s drops.  j o i n e d by d o t t e d  lines,  lines  follows.  the p o r o s i t i e s  found  The  From t h e  The indi-  o f t h e beds o f l a r g e to the v e l o c i t y  h e i g h t o f t h e bed  i n t e r f a c e above number 2 t a p was o f number 2 t a p f r o m  then  in  of  by u s i n g e q u a t i o n 32.  a s s u m i n g t h a t t h e i n t e r f a c e was  as  would be t o o c l o s e  and-would c a u s e c o n f u s i o n . )  which corresponded  then  o f 2 and  a c t u a l pressure  because these  l a t e d , knowing t h e h e i g h t and  intersection  f o r mixtures  were o b t a i n e d .  larger particles height of the  the  the d i f f e r e n c e  curves  curves,  small p a r t i c l e s ,  two  of  l i n e s were l o c a t e d as  v i d u a l expansion  since for  bulk density difference.  t o the t h e o r e t i c a l l i n e s , theoretical  found,  lines,  p o i n t s a r e not  i n succeeding graphs,  T h i s was  can  a r e g i v e n i n F i g u r e 13.  experimental  the  t h e p o i n t s on t h e g r a p h  shown between t h e t h e o r e t i c a l and (The  mm.  pressure  that p l o t t i n g  t o magnify e r r o r s .  sets of p a r t i c l e s  3  There- i s  experimental  c o n s i d e r i n g the f a c t  d a t a i n t h i s manner t e n d s  and  respectively.  good agreement between t h e o r e t i c a l and drop  f o r 2 mm.  The  calcu-  t h e bed  bottom,  l o c a t e d at the top of  the  F i g u r e lg - 2 mm.  ( w h i t e ) , g mrr. and 4 mm. t  g l a g a "Bead3 F l u i d i s e d Re  0  =0.35  (white)  i n P.3.G.  (2 mm. beads) and 1.94 (4 mm.  beads)  1.  L = 34.3 cm., € = 0.648, V = 0.0204 f t . / s e c .  2.  L = 73.3 cm., c = O.S35, V = 0.0426 f t . / s e c .  Particles  Pict. No.  'b "^  €  L  L  ( c a l c s  Lb./ft.3  2  and 3 mm, beads  1  0.649  11.2  2  and 3 mm,  beads  2  0.776  13.5  3 and 4 mm. beads  1  0.588  7.1  3 and 4 mm. beads * 2  0.695  9.5  -  )  52  0  1  2  3  4  5  6  7  8  9  10 II  12  HEIGHT ABOVE NO. 2 TAP - INCHES F i g u r e 11 - P r e s s u r e Drop C u r v e - 2 mm. Fluidised  i n Polyethylene  A G l a s s Beads, Glycol  0  I  2 3 4 5 6 7 8 9  10 II 12  HEIGHT ABOVE No.2 TAP-INCHES F i g u r e 12 - P r e s s u r e Drop Fluidised  C u r v e - } mm.  i n Polyethylene  Glass  Glycol  Beads,  54  HEIGHT ABOVE No.2 TAP (INCHES) I 2 3 4 5  5 10 15 20 HEIGHT ABOVE No.2 TAP (INCHES) F i g u r e 13  - Pressure  Fluidised  Drop D a t a - 2 and  i n Polyethylene  3 mm.  Glycol  Glass,  bed  of l a r g e p a r t i c l e s .  l i n e s were f o u n d drawn t h r o u g h upper l i n e  from  s l o p e s o f t h e two  e q u a t i o n 1.  The  was  drawn, w i t h t h e c o r r e c t  e q u a t i o n s 19 and  20 and  c a p t i o n s , F i g u r e s 10,  (b)  3 and  4 mm.  17,  4 mm.  21,  23,  The  value of  (200 gm.  f o r t h e 3 mm,  and  o f '3 nun..., 300  4 mm.  beads.  c u r v e s and  pictures  a r e shown i n F i g u r e s 15 and  The  10  porosity  be-  curves agree  drawn) but t h e agreement  = 6.810.  T h i s i s p r o b a b l y due  to^ t h e u p p e r one.  i n measured p r e s s u r e d r o p s  On  good  to errors i n predicting  i n the lower  curve  t h e .other hand,  a r e s m a l l e r , and  with  = 0.725  i s n o t as  i n t h e method o f  (see Appendix I I ) , e r r o r s  being propagated  of the  beads t h a n t h e r e i s between t h e 3 and  p o r o s i t y w h i c h become m a g n i f i e d pressure drop  at  respectively.  the experimental curves very c l o s e l y at p o r o s i t y  at  to  there i s a sharper i n t e r f a c e  p r e d i c t e d p r e s s u r e drop  (no d o t t e d l i n e was  of  curve of the s m a l l e s t p a r t i c l e s  Note t h a t i n t h e p i c t u r e  mm.  Again there i s a  the expansion  3 mm.  4  gm.  approach  tween t h e 2 and  picture  i n P.E.G.  f o r the e x p e r i m e n t a l p o i n t s f o r the mixture  expanded bed  L  31.  tendency  P r e s s u r e drop  € ,  i n bulk density  29, and  a r e shown i n F i g u r e 14.  high porosity.  the  intersecting  G l a s s Beads, F l u i d i s e d  f o r the mixture  beads),  slope,  then  h e n c e i s t h e v a l u e quoted, on  Graphs o f v e l o c i t y - p o r o s i t y b e a d s , and  was  s l o p e , and  the i n t e r f a c e p o s i t i o n .  as above, i s t h e v a l u e u s e d  theoretical  lower l i n e  the o r i g i n with the c o r r e c t  the lower l i n e . a t calculated  The  furthermore  errors each  56 1  r  T  r  -00GLASS BEADS , Re = 0-76 -2-7 —5 mm. ©4 mm. — 3 mm. 0  -0-5  —4 85 04 85 — 3 84 €3 8 4  mm. mm. mm. mm.  PREDICTED EXPERIMENT PREDICTED EXPERIMENT  -10  >o CD O  -1-5  -20  -0-2  J  L  -01  0  L0G € (0  Fiicrure 14  - E x p a n s i o n Curves Fluidised  f o r 5. 4,  i n Polyethylene  and  Glycol  5 mm.  Glass,  1  57  r  400  300  200  h  100  -  0  PREDICTED  ij O B S E R V E D INTERFACE LIMITS! 5  10  DISTANCE ABOVE No.2 T A P (inches) F i g u r e 15 - P r e s s u r e Drop D a t a - 3 and  4 mm.  Glass  Beads,  58 observed  point i s calculated  were f l u i d i s e d could it  i n polyethylene g l y c o l  he compared  was e x p e c t e d  with f l u i d i s a t i o n  that t h i s diameter  t h e minimum d i a m e t e r (c)  i n F i g u r e 17.  behavior  i n w a t e r where  r a t i o would he c l o s e t o t o o b t a i n an  G l a s s Beads P l u i d i s e d  and p r e s s u r e d r o p  of p a r t i c l e s  interface.  i n P.E.G.  plots are given f o r  fluidised  The e q u a t i o n f o r t h i s  Pictures  t o g e t h e r a r e shown  mixture,  as c a l c u l a t e d  e q u a t i o n 19, i s  p - p = 21 »7€ The  particles  beads i n F i g u r e s 14 and 16 r e s p e c t i v e l y .  o f t h e two s i z e s  from  These  so t h a t t h e i r  behavior  r a t i o necessary  4 and 5 mm.  Expansion 4 and 5 mm.  independently.  -17.  large negative q u a n t i t y i s present  because t h e 4  mm.  beads  ( d e n s i t y = 2.803 gm./cc.) a r e more dense t h a n t h e  5 mm.  beads  that  ( d e n s i t y = 2.525 g m . / c c . ) .  a t low p o r o s i t i e s  The e q u a t i o n  the smaller p a r t i c l e s  t h e bottom o f t h e b e d , t h a t t h e p a r t i c l e s o o r o s i t i e s around. 0.80  (where  p  - p  should  predicts occupy  s h o u l d mix a t  = 0 ) , and t h a t t h e  bt bs sma3.1er p a r t i c l e s bed  should  at high porosities.  does happen colored  (5 mm.  white).  there i s mixing, porosities porosity  occupy t h e upper p o r t i o n o f t h e F i g u r e 18 shows t h a t t h i s  beads a r e c o l o r l e s s ,  The p r e s s u r e d r o p  4 mm.  curves a l s o  i n fact  beads a r e show t h a t  o r a v e r y low b u l k d e n s i t y d i f f e r e n c e a t  0,629 and 0.791, and p a r t i a l  o f 0,886.  The e x p e r i m e n t a l  segregation at a  velocity-porosity  curve  0  4  8  10  12  DISTANCE A B O V E F i g u r e 16  16 No.2  - P r e s s u r e Drop D a t a - 4 and Fluidised  i n Polyethylene  20  24  T A P - INCHES 5 mm. Glycol  G l a s s Beads  F i g u r e 17 - 4 g£j 5 TO. G l a s s Beads F l u i d i s e d  i n P.E.G.  »  R  e  0  Picture L cm.  lie.  = 1.94 - 2.90  (4 ma. a r e white)  €  V ft./sec.  lb./ft.3  1  25.8  0.566  0.550  0.0199  -5.0  2  30.0  0.623  0.611  0.0313  -3.1  3  53.3  0.791  0.766  0.0832  -0.6  4  77.3  0.854  0.832  0.1150  +0.7  61 f o r the mixture curve  o f 4 and 5. mm. beads a g r e e s  p r e d i c t e d by e q u a t i o n 33.  with data obtained  c l o s e l y with the  The above i s i n agreement.  from o t h e r workers  (14, 35)..  Some 5 nun. beads o f a low d e n s i t y (5 mm. fluidised above.  s e p a r a t e l y , and w i t h t h e 4 mm,  The e x p a n s i o n  curves  K) were  beads mentioned  f o r t h e two s e t s o f beads  ( F i g u r e I S ) a r e n e a r l y c o i n c i d e n t , and p o r o s i t i e s a r e v e r y nearly equal at a l l v e l o c i t i e s . wholly at  t o d e n s i t y , a g a i n w i t h t h e h i g h e s t b u l k d e n s i t y bed  t h e bottom,  using  The s e p a r a t i o n i s t h u s due  The e q u a t i o n f o r t h e m i x t u r e ,  e q u a t i o n 19, was found  P-O 'bL  which p r e d i c t s particles  = 35.Oe,  'bs  L  t o be  - 36.6,  segregation at a l l porosities  occupying  calculated  with  the l a r g e r  t h e u p p e r p o r t i o n o f the'"bed, a s was  observed. (d)  5 and 6 mm. G l a s s Beads, F l u i d i s e d  Expansion  curves  f o r 5 mm.  fluidised  with p o l y e t h y l e n e g l y c o l  Predicted  and e x p e r i m e n t a l  sets of p a r t i c l e s  are also  i n P.E.G.  and 6 mm. g l a s s  a r e shown i n F i g u r e 19.  c\.irves f o r a m i x t u r e  o f t h e two  shown i n F i g u r e 19.  The p r e s s u r e  d r o p c u r v e s , F i g u r e 20, a r e c o n s i s t e n t w i t h v i s u a l tions,  illustrated  f o l l o w e d by p a r t i a l  particles  observa-  i n F i g u r e 21, o f m i x i n g a t low' p o r o s i t i e s s e g r e g a t i o n , and s e g r e g a t i o n w i t h an  interface at high p o r o s i t i e s .  The e q u a t i o n  f o r the mixture,  62 T  r  i  1  r  1  1  -i  r  1  -00 G L A S S BEADS  -0-5  Re = 0  1-9-2-6  ©Smm.K  p =2-25  gm./cc.  o4  p =2-80  gm./cc.  mm.  -o  -10 CD" O _J  o  -.1-5  OQ  .0'  o'  20  I  16  -  0  J  L  0  V  Expansion Curves  Beads,  L  -0-1  -0-2 L  Figure  I  - f o r 4 mm.  a n d 5 mm.  Fluidised i n Polyethylene  Glycol  K  Glass  -0-5  -10-  >  G L A S S B E A D S , Re = 2 - 9 - 4 - 0  o  0  o o  -1-5  -  J  -0-25  I  L  J_  L  ©  6  mm.  •  5 mm.  e  MIXTURE-EXPERIMENT  -  MIXTURE-PREDICTED _l  -0-2  -015 L0G  | 0  L  J  I  I  -01  €  Figure 19. Expansion Curves for 5 and 6mm. Glass Beads Fluidised in PE.G.  L  -005  DISTANCE FROM No.2 1 2 3  DISTANCE  A B O V E No.2  F i g u r e 20 - P r e s s u r e Drop D a t a - 5 and Fluidised  TAP-INCHES 4 5  i n Polyethylene  6  TAP-INCHES  6 mm. Glycol  Glass  Beads  Figure  21 - 5 mm.  and 6 mm.  Fluidised  R  =  e o  ~  (white) G l a s s  Beads,  i n P.E.G.  2.9  -  4.0  Picture  L  No.  cm.  1  30.9  0.668  0.656  0.0490  1.3  2  43.3  0.764  0.748  . 0.0932  2.7  ~  53.3  0.807  0.790  0.1084  3.1  4  73.3  0.860  0.838  0.1390  3.4  e  L  Ft./sec.  lb./ft.>  66 calculated  from p  This  -  equation  formula p  =  19»  is  9.2 €,  -  predicts mixing  d e n s i t y d i f f e r e n c e = 0 ) , and bed  a t a p o r o s i t y o f 0.456 from  the  observed  t h e minimum b u l k d e n s i t y d i f f e r e n c e  s e g r e g a t i o n w i t h an at  4.2  t h e end  of this  interface section,  can be  (bulk  behavior  of  f o r segregation,  inferred.  the  and  T h i s i s done  where d a t a from a l l r u n s  are  compared. (e)  2 mm,  A and  P. E«G o The  2 mm,  2 mm.  B G l a s s Beads, P l u i d i s e d  ,  particles  were s e p a r a t e d  w i t h p l a t e s i n which h o l e s o f a s p e c i f i c into 5 size particles,  ranges. and  no  The  sizes  was  two  particles, (B).  different  of average  characteristics in  the S t o k e s  value f o r n  diameters  found,  4  p  'tn.  -  p  'bs  =  chosen,  1.863  and  20,  4,4€. L  "density  gm./cc).  The  of equal d e n s i t y mm,  (A) and  u s i n g the  v a l u e o f n f o r t h e two  equation  drilled)  2.036  be  was  experimental sizes =  f o r t h e above m e n t i o n e d to  mm,  expansion  Assuming t h a t f l u i d i s a t i o n  r e g i o n (m = l' ) and  from  were  separately to obtain  the bulk d e n s i t y d i f f e r e n c e was  then  s i z e ranges  (Figure 22).  (average  size  ( d e n s i t y = 2.9  T h e s e were f l u i d i s e d  (by s c r e e n i n g  w i t h t h e l a r g e s t number o f  overlap,were  s e p a r a t e d " u s i n g Bromoform result  in  4.57), particles  67  GLASS BEADS-Re = 0 - 3 6 - 0 5 5 0  o 2 mm. A  Figure  22 - E x p a n s i o n C u r v e s f o r 2 min. A and Beads, F l u i d i s e d  in•Polyethylene  (Some p o i n t s a r e m i s s i n g  at l o g ^ Q g  2 mm,  Glycol -  0.325),  B  Glass  68  Figure  23-2  P.F.. A a n d 2 mr . B Fluidised  R  Picture  =  e o  T  5  0.35  -  "7"  no.  cit.  1  17.3  0.609  2  53.3  3  91.3  in  (white) Gla-^s  Beads'  P.E.G.  0.55  T  ~V  /g-^ fcolc.) s  ft./sec.  lb./ft.3  0.590  .0080  2.6  0.873  0.861  .0420  3.8  0.926  0.910  .0550  4.0  69 Thei-e i s no  constant  i n t h e above e q u a t i o n ,  bulk d e n s i t y equations, small  p a r t i c l e s are Expansion  and  of the  partial  curves  two  because the d e n s i t i e s  curves  f o r the  P i c t u r e s ( F i g u r e 23) sizes,  show t h a t t h e r e  (2) a t h i g h p o r o s i t y .  The the trend  due  bed,  expected  c a u s e an a p p a r e n t  and  where t h e  4.  Both s e t s of  particles  i n both  cases  from e x t r a p o l a t i o n . particles,  increase i n porosity.  the r e s u l t s  by s i z e  predict  o f the runs r a t i o as  with  low  in a particulately  as  2  mm.  1.09,  fluidised i n the  region.  Lead Shot - P o l y e t h y l e n e G l y c o l  fluidised  24 and  Richardson  f r e e p a r t i c l e R e y n o l d s numbers a r e  Expansion shot  the  expansion  b u l k d e n s i t y e q u a t i o n d o e s , however,  correctly,  are  of  t o s e g r e g a t i o n w i t h i n the s e t s o f  is stratification  Stokes  The  0.93» and  beads show t h a t , even f o r a d i a m e t e r there  25  particles,  curves  and  Run  p r e s s u r e drop curves  i n polyethylene g l y c o l are given  f o r lead  i n Figures  respectively.  The  calculated  bulk d e n s i t y formula  from e q u a t i o n p - p  and  a t low p o r o s i t y ,  i s d e v i a t i o n from the  the p o r o s i t y i s h i g h e r than  w h i c h would  are given  w h i c h show m i x i n g  show d e v i a t i o n a t a p o r o s i t y o f  T h i s c o u l d be  of the l a r g e  individual particles  segregation at high p o r o s i t y .  Zaki equation  i n previous  identical.  g i v e n i n F i g u r e 22. mixture  as  19,  = 67.1€  L  was  -  found  14.9,  to  be  f o r the l e a d  1  1  r  1  70  r  -i  -0-3 /  L E A D SHOT, Re = 1-8-3-3  /-I  0  3  /  2-46mm.  /  © 2 02mm.  -0-5  O MIXTURE - E X P E R I M E N T -  MIXTURE - PREDICTED  / / &  -0-7  >o  CD O  -0-9  - I I  -1-3  J  L  J  -0-2  -01 L O G  Figure  24 -  I _J  ,o  €  Expansion Curves  Fluidised  i n Polyethylene  f o r Lead Glycol  Shot.  L  0  5 DISTANCE  10 FROM  No.2  15 TAP  -INCHES  Figure 25. Pressure Drop data - Lead Shot Fluidised in P.E.G.  ^  72 w h i c h would over,  one  predict  segregation at a l l porosities.  might expect  an  interface  throughout,  t h e o r e t i c a l hulk d e n s i t y d i f f e r e n c e theoretical  w i t h an  o f 5 and  6 mm.  glass,  i n t e r f a c e at t h e o r e t i c a l  differences  o f u n d e r 2.3  encountered  (and  segregation  observed) bulk d e n s i t y and  i n the  fluidisation  o f 3 and  t i o n w i t h an  i n t e r f a c e at t h e o r e t i c a l bulk d e n s i t y d i f f e r e n c e s  o f u n d e r 4.8  pounds p e r c u b i c f o o t .  the p i c t u r e s  of lead  pictures  shot  o f t h e 5 and  indicates  same, w i t h m i x i n g segregation,  and  However, c o m p a r i s o n  porosities,  finally  s e g r e g a t i o n w i t h an  1.211  f o r the lead  lb./ft.5  particles).  at € = L  Figure  21,  the  partial  i n approximately  (1.184 f o r t h e  bulk density difference (38.8  the  interface  I I I ) and  5 and  of  and  f o l l o w e d by  They a r e f l u i d i s e d  comparable  F i g u r e 26,  glass f l u i d i s a t i o n ,  same R e y n o l d s number r e g i o n (see T a b l e r a t i o s are  segrega-  s y s t e m s behave a p p r o x i m a t e l y  a t low  high porosities.  where t h e r e was  fluidisation,  6 mm.  t h a t t h e two  glass,  the  i n the  where t h e r e was  pounds p e r c u b i c f o o t ,  4 mm.  s i n c e the  i s much g r e a t e r t h a n  bulk d e n s i t y d i f f e r e n c e s  fluidisation  More-  at the  diameter  6 mm.  glass,  The  much h i g h e r  theoretical  i n the case  of the l e a d  particles  0.8,  f o r the g l a s s p a r t i c l e s )  versus  i s due  3.2  l b . / f t . 3 at  €=  to the m u l t i p l i e r  (p  L  0.8 -p)  P L  in  e q u a t i o n 19.  A higher  ( p -p  ) t h e n , does n o t a p p e a r t o  P i n c r e a s e the tendency  to segregate,  a p p a r e n t l y not a f a c t o r tion.  Le C l a i r  particles  i n determining  (14) a l s o  together  (lead  so t h a t d e n s i t y l e v e l i s particle  size  finds that, i n f l u i d i s i n g s h o t and  steel balls),  segregadense  a large bulk  73 d e n s i t y d i f f e r e n c e accompanies t h e s e p a r a t i o n particles  i n t o d i s c r e t e beds.  smaller bulk  ( g l a s s b a l l o t i n i and alundum) i n t o  beds. It  with  He a l s o f i n d s t h a t a much  d e n s i t y d i f f e r e n c e accompanies t h e s e g r e g a t i o n  o f l e s s dense m a t e r i a l s discrete  of the  would seem, t h e n ,  particle  size  R  rather  =  that the quantity t o c o r r e l a t e  segregation ^  n o t be  (p—p)  ( T a b l e 4) t h i s  would  should  , but  **  P - P  Prom p r e v i o u s /3 = 0 . 1 1 3 €  f3  = 0.106€  formula  L  - 0.0251  Lead  L  - 0.0484  5 and 6 mm.  The new e q u a t i o n s  shot  observed  denominator  phenomena. —  p)  would be r e p l a c e d  that, all. other  segregation  Glass  behavior  better correlate p a r t i c l e s , the  (p-p).  by  equal,  the tendency t o  does n o t i n c r e a s e a s t h e d e n s i t y d i f f e r e n c e b e i s increased.  Beads - Water Runs  (a)  3 and 4 mm.  G l a s s Beads, F l u i d i s e d  C u r v e s o f e x p a n s i o n f o r 3 mm. are given  beads.  t o o b j e c t i v e number 2, i t c a n be  f a c t o r s being  tvreen s o l i d , and f l u i d 5.  r  For equidensity  Thus, vrith r e g a r d s said  glass  above p r e d i c t s i m i l a r  f o r b o t h s y s t e m s , w h i c h shows t h a t the5 the  give  i n Figure  27.  and A mm.  The c a l c u l a t e d and  i n Water glass  beads  experimental  ( y e l l o w ) and #9  F i g u r e 26 - #6  Fluidlaed  L  e  a  shot.  d  i n P.E.G.  Reo = 1« 00 - 3.25  Picture  L  ho.  crc.  1  24.3  0.642  2  28.3  3  P ~ D (CQlcJ  V  €  ft./sec.  bt 'bs , lb./ft.  0.628  0.0631  16.3  0.773  0.730  0.1220  '21.2  53.3  0.337  0.807  0.1840  25.1  4  71.1  0.878  0.844  0.2210  26.9  5  Bed a t r e s t  after falling  from L =  71.1  5  CU: .  T  1  1  1  1  1  / /  Figure  27 - E x p a n s i o n C u r v e s f o r 5 and 4'mm. Fluidised  i n Water  Glass  Beads,  76 expansion curves f o r the mixture are a l s o ( F i g u r e 28) and  visual  at a l l p o r o s i t i e s . i n d i c a t e d , by interface was  o b s e r v a t i o n s i n d i c a t e an  that  was  a circulation  Figure  28.  effects,  which  t o s e g r e g a t e , were n o t s u f f i c i e n t T h e r e were many i n t e r p a r t i c l e h e a r d , and  o f c o l o r i n g m a t t e r from  This  resulted  the  particles.  than expected  which  effect  the  The  5 and  from t h a t 6 mm.  porosities This  effect  could  bed.  could  i n the r a p i d  ( F i g u r e 28), which  a s t h e u n s t a b l e bed  lowering porosity (b)  curve i s such t h a t  in  tendency  removal  i t is interesting  f o r a given velocity.  the c i r c u l a t i o n  centi-  the  to desegregate  which  (over  is illustrated  tend to o f f s e t  and  fluctua-  5 t o 10  the d e v i a t i o n of the expansion curve f o r the  from the p r e d i c t e d  30.  velocity  collisions,  W i t h r e g a r d t o F i g u r e 27,  and  and  b e i n g thrown v i o l e n t l y  above t h e t o p o f t h e b e d . These  The  At h i g h p o r o s i t i e s  effect  meters  t h e same way  i s also  observed d i d not remain h o r i z o n t a l ,  tions with p a r t i c l e s  that  interface  presence of the i n t e r f a c e  c o n t i n u a l l y moving.  t h e r e was  a c t u a l l y be  Pictures  t h e p r e s s u r e d r o p c u r v e s , F i g u r e 29.  wavy and  0.89)  The  shown.  to' n o t e  mixture are  lower  be due  to  possibly acts i n  (Appendix  III) in  expected.  Glass'Beads,  Fluidised  e x p a n s i o n c u r v e s f o r t h e 5 mm.  and  i n Water 6 mm.  beads,  the expansion curve f o r the mixture are g i v e n i n F i g u r e These  particles  at a l l porosities,  tended  t o s e g r e g a t e , but not  as shown by t h e p i c t u r e s  completely,  i n F i g u r e 31»  I  Figure  2  eo  4  23 - 3 mm. and 4 mn. (brown) G l a s s Beads, Fluidised  R  3  i n Water  = 1110 - 2020  Picture No.  L cm.  1  19.6  0.538  2  31.5  3 4  €  € i  V  &r€» * tC0  ft./sec,  lb./ft.3  0.531  0.232  0.4  0.710  0.687  . 0.542  1.9  44.8  0.797  0.767  0.725  2.3  81.3  0.388  0.849  0.934  3.6  Ts  DISTANCE FROM No.2 TAP-INCHES I 2 3 4 5 6  0  4  8  12  16  20  24  DISTANCE FROM No.2 TAP-INCHES j  Figure  29 - P r e s s u r e Drop D a t a - 5 and 4 mm. Fluidised  i n Polyethylene  Glycol  Glass  Beads,  79  •5fe / /  -0-0  /  >-0-2  /  o  6  e> o  /  ^  GLASS-WATER  /  /  / /  © 5 mm.  /  / /  O 6 mm.  -0-4  © MIXTURE  -0-6  J  J  L  I  L  -02  -0 1 L0G € |Q  F i g u r e 50 - E x p a n s i o n  C u r v e s f o r 5 and 6 mm.  Fluidised  in. Water  Glass  Beads  30  P i Rrura 3- L  —  5  JB&*  and  6  Flu.id i s ed R  e o  BOB.  (brown) Glas  3  Beads,  i n P » J5 • \F •  = 2800 - 4260  ft./sec.  p - p (colcJ 'bL 'bs l b . / f t ,3  0.649  0.536  -0.4  0.805  0.794  0.861  0  75.8  0.861  0.847  1.000  0.5  123.3  0.914  0.898  1.150  0.7  Picture No.  L cm.  €  1  30.3  0.655  2  54.0  3 4  V  81/ The  pressure drop  experimental straight t i o n up was to  d a t a a r e g i v e n i n F i g u r e 32,  p o i n t s f o r each p o r o s i t y f a l l  line  indicating l i t t l e ,  the bed.  incomplete  Even a t p o r o s i t i e s  segregation.  i n polyethylene  The  R  (6 mm.)  e o  = 4.0  (6 mm.)  e o  €  g r e a t e r t h a n 0,92  there  were  as  calculated  from  p -p  = 9= 2 €  i s expected  = 0.45,  L  = 4260  p -p  = 5.8 €  and  bi (  - 4.2  L  bs  bs  p -p 'bi 'bs  - 4.2  L  = 0) i n t h e  i n the second  case at  o v e r 0,763 ( € t  = 0.751), c o r r e s p o n d i n g t o a b u l k d e n s i t y lb./ft,3  d i f f e r e n c e t h a t c o u l d be £  L  = 1) was  1,62  The  obtained  case  = 0.725.  L  observed  o f o v e r 2.8  i n the f i r s t  £  first  S e g r e g a t i o n was  difference  only at  maximum b u l k d e n s i t y  i n the second  l b . / f t . 3 w h i c h by  porosities  case  results  show t h a t s e g r e g a t i o n was  porosities  ( o v e r € = 0,92)  argument.  The  fluidised  values  giving  o f m and  incomplete  evidence  These v a l u e s were changed  when t h e same p a r t i c l e s  even a t  to the  were f l u i d i s e d  and  high  above were  4.28  t o ra = 2 and  i n water.  not  Experiment-  n when t h e p a r t i c l e s  i n p o l y e t h y l e n e g l y c o l were 1.059  respectively.  (at  comparison should  have been enough t o promote c o m p l e t e s e g r e g a t i o n . al  31  are  Mixing case at  bulk d e n s i t y v a r i a -  glycol.  bi  R  single  where t h e same p a r t i c l e s  bulk d e n s i t y equations,  e q u a t i o n 19  on a  the  Compare t h e p i c t u r e s i n F i g u r e  t h e p i c t u r e s i n F i g u r e 21,  fluidised  i f any,  and. a l l o f  n =  2.34  82 i  400  i  i  i  i  T  i  1  1  r  300  200  5 8 6 mm. G L A S S - H 0 2  100  0  j  0  2  J  i  4  6  8  L  ©  € = 0-857  -O-  € = 0-803  -O-  € = 0-660  -  PREDICTED  J  I  I  I  10 12 14 16 18 2 0 22 2 4  DISTANCE FROM No.2 T A P -INCHES F i g u r e 32 - P r e s s u r e Drop D a t a - 5 and 6 mm. G l a s s Particles  L  Fluidised  i n Water  m  Cairns and P r a u s n i t z (7) have shown that there should he a great d e a l o f mixing under the c o n d i t i o n s o f high f r e e p a r t i c l e Reynolds number which, p r e v a i l e d i n the water runs, and that mixing should be g r e a t e s t at p o r o s i t i e s of 0,7. This mixing, however seems to be accounted  f o r i n the present  theory by the values of m and n i n equations 19 and 20. That i s , the change i n the experimental "n", and the change in "m" as p r e d i c t e d from  the drag c o e f f i c i e n t - Reynolds  number curve, appear to be s u f f i c i e n t to allow f o r p a r t i c l e random v e l o c i t y without any f u r t h e r change i n the mathematical model. 6.  General The  c a l c u l a t e d and experimental v e l o c i t y - p o r o s i t y  curves agree q u i t e c l o s e l y .  T h i s i s i n accord with data  from other workers (2, 14, 35). At high p o r o s i t i e s the agreement i s not as good as a t low p o r o s i t i e s . interpreted  T h i s has been  (see previous s u b - s e c t i o n on "2 and 3 mm. g l a s s  beads f l u i d i s e d  i n P.E.G.", and Appendix I I I ) i n terms of a  mixing e f f e c t a s s o c i a t e d with, the change i n f l u i d  flow  pattern at the bed support. Table IV gives a comparison o f c a l c u l a t e d  (from  equation 19) and observed bulk d e n s i t y d i f f e r e n c e s , as w e l l as the o v e r a l l p o r o s i t y o f the bed (c) and the c a l c u l a t e d p o r o s i t y of the bed of l a r g e p a r t i c l e s mixture, hence  (V was known f o r the  € could be found from the graph L  i n d i v i d u a l component).  f o r the  The c a l c u l a t e d and observed  bulk  84  TABLE IV C o m p a r i s o n o f Measured and C a l c u l a t e d  Bulk  Density  Differences All  Fluid and Particles  bulk density  differences  i n l b . mass/ft.^  O v e r a l l From i n d i v i d u a l Bulk d e n s i t y difference-: For ose x p a n s i o n c u r v e s •••. C a l c u l a t e d Measured i t y * " "" " * "* *' ' (from €  €  L  €  s  -*  $  g^aph)  13.9 12.1 9.6  14.0 12.0 8.2  9.2 7.5  10.9 9.3  9.7 9.2  2.7 2.4 -2.8  1.3 -0.9 -4.1  2.0 0.0 0.0  3.8 3.0 1.9  2.3 1.3 0.0  1  2  2 mm. and 0.872 3 mm. g l a s s 0.766 i n P.E.G. 0.613  0.795 0.700 0.562  0.912 0.809 0.667  3 mm. and 0.810 4 mm. g l a s s 0.725 i n P.E.G.  0.764 0.689  0.857 0.772  0.886 4 mm. and 5 mm. g l a s s 0.791 i n . P.E.G. 0.629  0.861 0.767 0.611  0.906 0.827 0.648 -  5 mm. and 0.860 6 mm. g l a s s 0.807 i n P.E.G. 0.667  0.840 0.789 0.658  0.873 0.819 0.684  2.4 1.9 1.0  Lead s h o t i n P.E.G.  0.876 0.776 0.648  0.848 0.754 0.640  0.900 0.795 0.657  29.5 21.6 5.0  3 mm. and 0.898 4 mm. g l a s s 0.798 i n P.E.G. 0.723  0.357 0.775 0.698  0.927 0.832 0.752  7.6 5.4 4.7  4.0 3.0 2.1  1.5 4.5 5.0  5 mm. and 0.857 6 mm. g l a s s 0.803 i n P.E.G. 0.660  0.845 0.794 0.600  0.871 0.817 0.672  1.8 1.3 0.6  0.7 0.4 -0.4  0.0 0.0 0.0  13.4 12.4 11.7  1*  Calculated  using  - Bulk density  2//  Calculated  using  formulae obtained  42.0 35.5 27.9  difference =  28.2 14.2 0.0  ( l - €  L  ) x  f r o m e q u a t i o n 19.  85 d e n s i t y d i f f e r e n c e s agree well  segregated,  c l o s e l y when t h e p a r t i c l e s a r e  f o r example i n t h e c a s e where 2 and 3  beads were f l u i d i s e d  i n polyethylene g l y c o l .  The c a l c u l a t e d  bulk d e n s i t y d i f f e r e n c e s a r e g r e a t e r , as expected, there  i s observable mixing  beads f l u i d i s e d The difference  case  i n polyethylene  pressure drop was found  a.  as i n t h e case  High  mm.  when  o f t h e 5 and 6  mm.  glycol.  method o f d e t e r m i n i n g  bulk density  t o be o f d o u b t f u l u s e where:  p r e s s u r e drops  were measured, a s i n t h e  of the run with l e a d . b.  Bulk d e n s i t y d i f f e r e n c e s cases,  were s m a l l .  the predicted d i f f e r e n c e  T h i s was  because,  i n both  i n pressure  gradient  was o f t h e same o r d e r a s t h e a b s o l u t e e r r o r i n •4  measurement.  Visual  t o supplement  this  o b s e r v a t i o n s and p h o t o g r a p h s were  method, w h i c h was a d o p t e d  used  t o o b t a i n some  q u a n t i t a t i v e measurements o f s e g r e g a t i o n . V/ith r e g a r d . t o t h e 7 o b j e c t i v e s which were s e t o u t i n the previous 1. increased  section:  I t was found with  i n runs  shot  o f course,  at a l l p o r o s i t i e s , the  w i t h 2 mm.  A and B g l a s s beads  (Figure  w i t h 5 and 6 mrn. g l a s s beads' ( F i g u r e 2 1 ) , and  i n runs with lead obvious,  to segregate  i n c r e a s i n g p o r o s i t y i n the sampling run  ( F i g u r e 8 ) , i n runs 23),  t h a t the tendency  (Figure 26).  T h i s tendency  was n o t  i n c a s e s where t h e r e was an i n t e r f a c e except  t h a t i n 3ome c a s e s  i n t e r f a c e was more d e f i n e d a t h i g h e r  ( F i g u r e 10)  porosities.  86 2.  Comparison o f F i g u r e s  2 3 (r = 1.09) and .10  (r = 1.489 and 1.426) shows t h e i n c r e a s i n g t e n d e n c y t o segregation as the diameter r a t i o  i s increased.  F i g u r e 21 ( r = 1.184) and F i g u r e 10 ( r = From t h e r e s u l t s  This  Polyethylene 3. formula  i s discussed  fully  i t would  does n o t i n c r e a s e as  t h e d e n s i t y d i f f e r e n c e between p a r t i c l e s creased.  A l s o compare  1.489 and 1.426).  of the run with lead p a r t i c l e s  seem t h a t t h e t e n d e n c y t o s e g r e g a t e  \  and f l u i d  is in-  i n the s u b - s e c t i o n  "Lead-  Glycol." When t h e p a r t i c l e s a r e w e l l s e g r e g a t e d ,  obtained  from e q u a t i o n  19 ( s e e T a b l e  the  V) p r e d i c t s  q u i t e c l o s e l y t h e a c t u a l b u l k d e n s i t y d i f f e r e n c e , a s shown i n Table  V.  The. agreement between t h e p r e d i c t e d and  b u l k ' d e n s i t y d i f f e r e n c e s f o r t h e 2 and 3 mm. v e r y good, as i s t h e agreement  i n the case  observed  p a r t i c l e s is-  o f t h e 3 and 4  mm.  particles. 4.  The e f f e c t  o f c h a n g i n g m and n i s d i s c u s s e d i n  •j'  the  sub-section  The  value  "5 and 6 mm.  o f m was changed  Particles  Fluidised  f r o m 1.059 t o 2, and t h e v a l u e  o f n f r o m 4.28 t o 2.34, by c h a n g i n g t h e t e s t above s e t o f p a r t i c l e s .  The e f f e c t  the bulk d e n s i t y d r i v i n g  force equation  T a b l e V.  The e q u a t i o n  in•Water."  liquid  f o r the  o f c h a n g i n g m and n on  f o r 5 and 6 mm.  c a n be s e e n i n particles  was changed  from p  -p  ' B L  'bs  = 9.2€.L  - 4.2  (m = 1.059, n = 4.28)  = 5.8€  -4.2  (m = 2 , n =  to p-p b L  bs  L  2.34),  TABLE V Summary o f R e s u l t s  Mixture  ~  r  ' Glass 2 mm. A 2 mm. B  y 7  K  e  °  &~4>s L  (jgxlOO) 4.4 €  1.093  1.000  0.42  Ub/cu  -  ,t3  Remarks  mix a t low € , partial?, segregat i o n above € = 0.75  ; L  L  (3.9 € ) L  L  Glass 2 mm. A 3 mm.  1.489  18.1 €  Glass 3 mm. 4 mm.  1.426  Glass 4 mm. 5 mm.  1.235  Glass 4 mm. 5 mm. K.  1.229  Glass 5 mm. 6 mm.  1.184  0.995  - 0.6  L  0.76 (15.9€ -  0.5)  L  22.1€ 0.948  - 5.9  L  1.94 (19.9€ -  21.7€ . - 17.4 L  2.90  segregate with interface, a l l  5.5)  L  0.839  segregate with interface, a l l  f l i p o v e r with no interfaces  ( 2 2 . 9 € - 19.2) L  35.0€ 0.662  2.62  -36.6  segregate, .' 5 mm. K o c c u p y ( 4 8 . 2 € - 50.9) t o p p o r t i o n o f bed t  L  9.2€ 0.954  4.00  - 4.2  t  (10.6€ -  4.S)  L  mix a t low € • segregate i n t e r med. € ; i n t e r f a c e , € > 0.77 L  u  L  Lead #6 #9  1.211  0.976  67.1 €  - 14.9  L  3.25 (11.3€ -  2.5)  L  mix a t low € ; segregate i n t e r med. £ j i n t e r f a c e , c > 0.80 L  L  L  Glass 3 mm. 4 mm.  1.426  0.951  - 5.9  L  2029 (10.1€ -  5.1)  L  5.8€  Glass 5 mm. 6 mm.  1.184  Divinyl 24-28 28-32  1.20  24-28 42-48  11.4€  0.956  (6.4€  2.21  1.000 1.000  - 4.2  L  4260  75.2 75.2  t  - 4.6)  5.2 (4.3€  130 € (108.€  mixing with tendency t o segregate, a l l €  )  L  )  sharp all €  L  L t  L  fuzzy all €  € l L  segregate with interface, a l l € (some i n t e r mixing).  interface interface  L  88 showing 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 d r i v i n g decreased was  also  when 'the, p a r t i c l e s t r u e o f t h e 3 and  5.  The  were f l u i d i s e d  4 mm.  the bulk d e n s i t y equation individual  Ib./cu.ft.  f o r 5 and  P.E.G., and fluidised tion  expansion  about  35.5  i n P.E.G..  o f T a b l e V,  i n T a b l e V, curve)  6 mm.  interface  was  (see T a b l e  with  fluidised  f o r lead  show t h a t t h e r e i s n o t a u n i q u e f o r s e g r e g a t i o n w i t h an  unless the  fluid  2.8 in  examina-.  minimum interface  d e n s i t i e s are fixed  (see  item  above). 6.  The  minimum b u l k d e n s i t y d i f f e r e n c e  which  accompanies measurable s e g r e g a t i o n i s r e l a t i v e l y In  a d d i t i o n t o b e i n g d e p e n d e n t on t h e  it  depends a l s o  on t h e p a r t i c l e and  particle  fluid  v e r y s m a l l f o r low  density particles  density particles,  a l l other things being  7.  An  velocities  f o r the  t h e change o f m and 4 mm.  fluidised  n,  ratio, being  f o r high  equal. have t o  i n c r e a s e i n random  effect  a p p a r e n t l y accounted  t h e 5 and  6 mm.  be  particle  The  when c o m p a r i n g t h e b e h a v i o r  g l a s s b e a d s , and i n w a t e r and  size  larger  a t h i g h p a r t i c l e R e y n o l d s numbers.  random p a r t i c l e v e l o c i t y was  3 and  and  small.  densities,  e x t e n s i o n t o the t h e o r y d i d not  made i n o r d e r t o a c c o u n t  of  from  particles  T h e s e d a t a , t o g e t h e r w i t h an  p a r t i c l e and  from  obtained  L  bulk density d i f f e r e n c e  2  which  t o be a b o u t  glass particles  Ib./cu.ft.  €  This  V).  (calculated  found  was  with water.  minimum b u l k d e n s i t y d i f f e r e n c e  a c c o m p a n i e s s e g r e g a t i o n w i t h an  the  particles  force  of  for i n. the  g l a s s beads,  i n P.E.G. ( s e e s u b - s e c t i o n "5 and  6  mm.  8'9 g l a s s beads f l u i d i s e d  i n water").  In a l l cases, the c a l c u l a t i o n  o f 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 beds as 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 bed o f l a r g e r p a r t i c l e s , right  trends.  5 mm.  beads  was  The b u l k d e n s i t y e q u a t i o n f o r t h e 4 mm.  ( F i g u r e V) p r e d i c t s a f l i p o v e r  d e n s i t y a t low this  e  L  actually  t h e 2 mm.  observed.  A and 2 mm.  B  3 mm.  and 4 mm. fluidised 5 mm.  f o r t h e 2 mm.  beads, 5 mm.  and 6 mm.  i n polyethylene g l y c o l .  4 mm.  and  5 mm.  K beads o c c u p y i n g  €  L  ), and  The b u l k d e n s i t y e q u a t i o n f o r .  ( F i g u r e V) beads p r e d i c t s  as do t h e e q u a t i o n s  and  (negative bulk  » p o s i t i v e bulk d e n s i t y at high  tion,  shot  u s i n g e q u a t i o n 19, showed t h e  X beads p r e d i c t s  segrega-  A and 3 mm.  beads,  beads and t h e l e a d The e q u a t i o n f o r t h e  s e g r e g a t i o n , but w i t h t h e  t h e t o p o f t h e bed, a s was  observed.  However, t h e a b s o l u t e m a g n i t u d e o f t h e b u l k d e n s i t y d i f f e r e n c e does n o t u n i q u e l y c o r r e l a t e w i t h t h e o b s e r v e d mixing,  s e g r e g a t i o n , o r s e g r e g a t i o n w i t h an i n t e r f a c e ,  v a r y i n g the p a r t i c l e d e n s i t y . is  Table  the bulk d e n s i t y d i f f e r e n c e  by t h e d e n s i t y d i f f e r e n c e between  p a r t i c l e s and t h e t e s t V.  fluid.  when  A somewhat b e t t e r c o r r e l a t i o n  o b t a i n e d by u s i n g ft, w h i c h . i s  divided  phenomena o f  Values  of(3  the l a r g e r are also given i n  90  CONCLUSIONS AND RECOMMENDATIONS  Segregation  i s a c o n t i n u o u s phenomenum.  tendency t o s e g r e g a t i o n  increases  for different  diameter,  constant  particulately  fluidised  beds.  increases  as  increasing porosity  density particles i n  The t e n d e n c y t o s e g r e g a t e  as t h e d i a m e t e r r a t i o  The  with  of the p a r t i c l e s  tendency t o segregation  tion  High bulk  of high  fluid  density pa,rticles  (e.g.  i s important,  l e a d ) , and l o w b u l k o f 'low d e n s i t y  however, when p a r t i c l e s together.  4 and 5 mm.  glass  of a  i n polyethylene  (see R e s u l t s glycol),  and D i s c u s s i o n ,  o r have  f l u i d i s e d above o r below o r mixed w i t h  particles,  d e p e n d i n g on t h e r e l a t i v e  Mixing  i n turbulent  different  Under these c o n d i t i o n s i t  possible to obtain a "flipover"  particles  segrega-  The d e n s i t y d i f f e r e n c e between p a r t i c l e s and  density are f l u i d i s e d is  and f l u i d i s  d e n s i t y d i f f e r e n c e s accompany  d e n s i t y d i f f e r e n c e s accompany s e g r e g a t i o n particles.  i s increased.  does n o t seem t o i n c r e a s e  t h e d e n s i t y d i f f e r e n c e between p a r t i c l e  increased.  The  large  smaller  particle densities.  f l o w does n o t t e n d  to offset  segregation  more t h a n i s p r e d i c t e d by changes i n "m" and "n"  in  19.  equation  light  At l e a s t  of the experimental  stabilities particle  - particle  velocity  this  does n o t seem t o be s o i n  evidence.  circulation,  However, t h e i n bumping, and random  - b r i n g a b o u t a p h y s i c a l change i n t h e b e d ,  which a p p e a r s t o be more dynamic  i n turbulent  flow.  The  difference  a c c u r a t e l y by segregated,  i n hulk d e n s i t y i s predicted  e q u a t i o n 19 when t h e p a r t i c l e s a r e  and  when t h e e x p a n s i o n  particles  concerned  The  t r e n d i s p r e d i c t e d by  right  curves f o r the  the e q u a t i o n f o r bulk  of p o r o s i t y  f o r two  sets' of  i s , a high p o s i t i v e bulk d e n s i t y difference  predicts (wO)  individual  obey t h e R i c h a r d s o n - Z a k i e q u a t i o n ( 2 ) .  d e n s i t y as a f u n c t i o n that  completely  s e g r e g a t i o n w i t h an  bulk density difference  mixing at the s p e c i f i c  interface, predicts,  porosity.  and  particles, correctly  a very  low  f a i r l y accurately,  However, t h e r e i s no  c o r r e l a t i o n between t h e magnitude o f t h e b u l k d e n s i t y d i f f e r e n c e s and lieved  that  a  a l l of the observed  "reduced"  phenomena.  I t i s be-  b u l k d e n s i t y , ^ , s h o u l d be  used,  where  p = There are values of cases  over which mixing  0 t o 0.01), and  segregation occurs t i o n w i t h an  (/S=  0.01  "reduced"  A more t h o r o u g h bed, III.  over which  A more t h o r o u g h  (9) m a t h e m a t i c a l  , A l l of the runs spherical particles.  A  study  s t u d y c o u l d be made o f t h e  observed  treatment  segrega-  bulk density.  r e p o r t e d i n the d i s c u s s i o n o f r e s u l t s , Comparison o f t h i s  ina l l  partial  t o 0 . 0 4 ) , f o l l o w e d by  ()S>0.04).  interface  c o u l d be made o f t h i s  values of  i s observed  and  phenomenum and  of i n s t a b i l i t i e s  made i n t h i s  unstable  i n Appendix Jackson's  c o u l d be made.  s t u d y were done w i t h  s t u d y c o u l d be  conducted  under  similar  : c o n d i t i o n s - t o observe  t r u l y mono-sized p a r t i c l e s  t o study the behavior o f  (e.g. b a l l  b e a r i n g s ) , as i t i s .  c e r t a i n , t h a t b u l k d e n s i t y d i f f e r e n c e s and (3 v a l u e s f o r s e g r e g a t i o n would be l o w e r ( A l l runs  i f mono-sized p a r t i c l e s  w h i c h were s i z e d  closely  is  were study  within a  range). I t was assumed i n t h i s s t u d y t h a t - t h e  Zaki  necessary  t h a t were made i n c o n n e c t i o n w i t h t h i s  were made w i t h p a r t i c l e s given  92  the behavior of nonspherical p a r t i c l e s .  , I t would be o f i n t e r e s t  used.  \  (2) d e s c r i p t i o n o f t h e w a l l e f f e c t  reason t o b e l i e v e  particles'calculated (equation-3)» "Theory",  Richardson-.  i s correct.  There  t h a t i t i s n o t , s i n c e a l l d i a m e t e r s ofwith the a i d o f the w a l l e f f e c t  equation  and u s i n g t h e method d e s c r i b e d I n t h e " s e c t i o n -  were l o w e r  a r i t h m e t i c average  t h a n t h e c o r r e s p o n d i n g measured  diameters  (Table. V I ) , w i t h t h e e x c e p t i o n  x  of  the screen s i z e s ,  (Because  which were h i g h e r i n two c a s e s .  of t h i s discrepancy the bulk d e n s i t y a n d  t i o n s were c a l c u l a t e d u s i n g t h e measured d i a m e t e r s the c a l c u l a t e d  diameters  important  important and  The w a l l e f f e c t  was  when c o n s i d e r i n g t h e s c r e e n sizes-, b u t i t was  wheri c o n s i d e r i n g t h e l a r g e r s i z e s  f o rthis  and n o t  f o r t h e s c r e e n . s i z e s as suggested  i n t h e p r e v i o u s , s e c t i o n - "Theory"-.) not  equa-  reason i t was.concluded  not d e s c r i b e , the w a l l e f f e c t  t h a t e q u a t i o n 3-does  correctly.  s t u d y c o u l d be made o f t h i s w a l l  of particles,  effect.  A more, t h o r o u g h . •  TABLE V I Comparison  o f Measured Particle  P a r t i c l e nominal size mm. 2 mm.  A  and C a l c u l a t e d  Diameters  Measured a r i t h m e t i c C a l c u l a t e d d i a m e t e r avg. diam. mm. mm. 1.863  1.83  3  mm.  2.774  2.45  4  mm.  3.950  3.69  5  mm.  4.878  4.62  4.856  4.82  5.776  5.44  5 mm. 6  K  mm.  24-28 T y l e r  mesh  0.653  0.646  28-32 T y l e r  mesh  0.543  0.595  42-48 T y l e r  mesh  0.322*  0.397  *  G e o m e t r i c mean o f s c r e e n  sizes.  94  REFERENCES  1.  J o t t r a n d , R., Chem. Eng. S c i . 3, 12 (1953).  2.  R i c h a r d s o n , J . F . and Vl.H. Z a k i , Trans. I n s t n . Chem. . Engrs., 1 2 , 35 (1954).  3.  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, France, (1956).  4.  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, 155 (1950).  5.  Leva, M., " F l u i d i s a t i o n " p. 92, KcGraw H i l l , New York, (1959). Kaye, B.H., and R. J-'avies, Symposium on t h e I n t e r a c t i o n between F l u i d s and P a r t i c l e s , T h i r d congress o f t h e European F e d e r a t i o n o f Chemical E n g i n e e r i n g , I n s t i t u t i o n o f Chemical E n g i n e e r s , London, A, A2 1'962.  6.  7.  C a i r n s , E . J . , and J.K. P r a u s n i t z , A.I.Ch.E. J o u r n a l , 6, 554 ( I 9 6 0 ) .  8.  C a i r n s , E . J . , and J.M. P r a u s n i t z , I n d . Eng. Chem., 51, 1441 (1959).  9.  J a c k s o n , R.A. Trans. I n s t , o f Chem..Engrs., 41, 13 (1963).  (London),  10.  S t e i n o u r , H., I n d . Eng. Chem., %6, 618 (1944).  11.  Furukawa, J . , and T.S. Ohmae, I n d . Eng. Chem., 50, 321 (1958).  12.  Leva, M., and W.W. Weintraub, Chem. Eng., 57 110, (1950).  13.  Happel, J . , and II. Brenner, A.I.Ch.E.J., 2* 506 (1957).  14.  Le C l a i r , B.P., K.A.Sc. T h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Vancouver, Canada, 1964. Zenz, F.A., and D.F. Othmer, " F l u i d i s a t i o n and F l u i d P a r t i c l e Systems", p. 311, I 9 6 0 .  15. 16. 17.  P r e s l e r , A.F., Ph.D. T h e s i 3 , Iowa S t a t e C o l l e g e , 1956.  McCabe, W.L., and J.C. Smith, " U n i t O p e r a t i o n s o f Chemical E n g i n e e r i n g " , p. 91, McGraw H i l l , New York, ,\,.,. 1956";  95 18.  R i c h a r d s o n , J . F . , and R.A. M e i k l e , T r a n s . I n s t . Chem. Eng. 22, 357 ( 1 9 6 1 ) .  19.  Shannon, P.T., Ph.D. t h e s i s , Chicago, 1 1 1 . , 1 9 5 9 .  20.  D a l l a v i l l e , J . P . , and Y.D. M c B r i d e , Oak R i d g e N a t . Lab., U.S.A.E.C. R e p o r t O.R.N.L.-2565, 1958.  21.  L a p p l e , C.E., F l u i d and P a r t i c l e M e c h a n i c s , p . 277, Edwards B r o t h e r s I n c . , Ann A r b o u r , M i c h i g a n , 1951.  22.  R i c h a r d s o n , J . F . , and Z a k i , W.N., 65 (1954).  23.  L e w i s , W.K., and E.W. Bowerman, Chem. E n g . P r o g . , 48, 603 ( 1 9 5 2 ) .  24.  Leivris, W.K., E.R. G i l l e l a n d , Chem., 4JL, 1104 ( 1 9 4 9 ) .  25.  Wilhelm, 201  111.  Inst,  Chem. E n g . S c i . , 3»  and W.C. B a u e r ,  I n d . Eng.  R.H., and Kwauk, M. Chem. E n g . P r o g . , 4 4 , (1948).  26.  H a n r a t t y a n d Bandukwala, A . I . C h . E . J . ,  27.  Loeffler, 310  o f Technology,  A . L . J r . , and B.F. R u t h ,  2,  293 ( 1 9 5 7 ) .  A.I.Ch.E.J.,  5,  (1959).  28.  H a s s e t t , N . J . , B r . Chem. Eng., 6, 777  29.  H a r r i s o n , D., e t a l . , T r a n s . I n s t . Chem. E n g . 29, 204 ( 1 9 6 1 ) . E p s t e i n , N., P r o c e e d i n g s o f t h e Symposium on t h e I n t e r a c t i o n between P a r t i c l e s and F l u i d s , p . 43-44, I n s t i t u t i o n o f C h e m i c a l E n g i n e e r s , London, 1962. A.S.T.K. manual D 4 4 5 - 5 3 T .  30. 1.  (1961).  32.  S m i t h , J.W., "Two Component F l u i d i s a t i o n " , a n u n p u b l i s h e d p r o g r e s s r e p o r t t o D r . N. E p s t e i n , U . B . C , 1962.  33*  G a l l o w a y , L.R., Ph.D. 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 C o l u m b i a , V a n c o u v e r , B.C., 1964.  34.  A l v e s , G.E., C o - A u t h o r i n L a p p l e , C E . e t a l . " F l u i d and P a r t i c l e M e c h a n i c s " , p . 130, Edwards B r o t h e r s I n c . , Ann A r b o u r , M i c h i g a n , 1951. ;  35.  Hoffman, R.F., L a p i d u s , L., and E l g i n , J o u r n a l , 6, 321 ( I 9 6 0 ) . "  J.C., A.I.Ch.E.  96 36.  A d l e r , I . L . , and J . H a p p e l , Chem. Eng. P r o g r e s s S y m p o s i u m . S e r i e s , 58, 98 ( 1 9 6 2 ) .  37.  P e r r y , J.H., " C h e m i c a l E n g i n e e r s Handbook". t h i r d - M c G r a w - H i l l , New Y o r k , 1950.  38.  B u t l e r , R., and K e r r , S . , "An I n t r o d u c t i o n t o N u m e r i c a l Methods", p . 8, S i r I s s a c P i t m a n and Sons L i m i t e d , London, 1961, '  39.  McCracken, D.D., "A G u i d e t o F o r t r a n Programming", W i l e y and Sons, I n c . , New Y o r k , 1962.  ,  edition,  i  John  APPENDIX I  Appendix I  -  1-1  O r i g i n a l Data TABLE OF CONTENTS Page  a)  1.-5  V e l o c i t y - P o r o s i t y Data 1/  24-28  mesh d i v i n y l i n water  2/  28-32  mesh d i v i n y l i n water  3/  42-48  mesh d i v i n y l  4/  Mixture,  24-28  and  5/  Mixture,  24-28  and  6/  3 mm. g l a s s beads i n water . . . . . . . . . . . 1 - 1 0  7/  4 mm. g l a s s beads i n water  1-11  8/  5 mm. g l a s s bead s i n water « . . . . . . « . . «  1—11  9/  6 mm. g l a s s beads i n water  1-12  1-6 j  i n water  I-7  . . . . „ . . . . .  1-8  28-32  mesh d i v i n y l i n water .  1-8  42-48  mesh d i v i n y l i n water .  1-9  10/  Mixture, 3 and 4 mm. g l a s s beads i n water  . . , 1-12  11/  Mixture, 5 and 6 mm. g l a s s beads i n water  . . . 1-13  12/  2 mm, A. g l a s s beads, i n P.E.G. . . . . . . . . '. 1 - 1 4  13/  2 mm. B. g l a s s beads i n P.E.G. . . . . . . . . . 1 - 1 5  14/  3  15/  4 mm. g l a s s beads i n P.E.G.  . . . . . . . . . . 1-16  16/  5 mm. g l a s s beads i n P.E.G.  . . . . . . . . . .  17/  6 mm', g l a s s beads i n P.E.G.  18/  5 mm.' K. g l a s s beads i n P.E.G, . . , . . . . . . 1 - 1 8  mm. g l a s s beads i n P.E.G.  1  .  .  .  .  .  .  .  .  .  .  1-15  1-16 •  . . . . . . . . , . 1-17  ; 1 9 / - : Mixture, 2 mm. A., and 3 mm. g l a s s beads i n * S O Cx  O  O  9 O  0  S  «  ©  O  •  V  9  O  «  •  O  •  O  6  O  Q  X""16  20/  Mixture, 3 and 4 mm. g l a s s beads i n P.E.G. . . . 1-19  21/  Mixture, 4 and 5 mm. g l a s s beads i n P.E.G,  22/  Mixture, 5 and 6 mm. g l a s s beads i n P.E.G. . . . 1 - 2 1  . , 1-20  1-2 23/  No. 6 l e a d  shot  i n P.E.G  .1-21  24/  No. 9 l e a d  shot  i n P.E.G  1-22  25/  M i x t u r e , No. 6 and No. 9 l e a d  * P.E.G. - P o l y e t h y l e n e G l y c o l - w a t e r b) '  c)  shot  i n P.E.G.  .1-22  solution.  P r e s s u r e Drop D a t a 1/  2 mm.  A. g l a s s beads i n P;E.G  .1-24  2/  3 mm.  A. g l a s s beads i n P.E.G  1-25  3/  2 and 3 mm.  g l a s s beads i n P.E.G  1-26 •  4/  3 and 4 mm.  g l a s s beads i n P.E.G  1-26  5/  4 and 5 mm.  g l a s s beads i n P.E.G  1-27  6/  5 and 6 mm. g l a s s beads i n P.E.G  7/  No. 6 and No. 9 l e a d  8/  3 and 4 mm.  g l a s s beads i n w a t e r  1-30  9/  5 and 6 mm.  g l a s s beads i n w a t e r  1-31  Particle  shot  .  i n P.E.G.  . . . . . .  1-28 1-29  S i z e Data  Item 1/  Key  2/  24-28 mesh s c r e e n s i z e  ( T a b l e 2)  3/  2 8 - 3 2 mesh s c r e e n s i z e  ( T a b l e 2)  4/  2 8 - 3 2 mesh s c r e e n s i z e  (Ro-Tap)(Table  5/  28-32 mesh - s a m p l i n g  6/  S a m p l i n g r u n , p o r o s i t y = 0.6 ( T a b l e 3)  . ll  1-33 . . . . . . .  1-34  , . 1-34 2 ) . . . . 1-34  r u n ( T a b l e 2)  1-34 . . . .  S a m p l i n g r u n , p o r o s i t y = 0.7 ( T a b l e 4  1-34 1-35  8/  S a m p l i n g r u n , p o r o s i t y = 0.8 ( T a b l e 5)  9/  S a m p l i n g r u n , p o r o s i t y = 0.87 ( T a b l e 6) . .  . . . .  1-35  .1^-36  1-3 Item  Page 2 mm.  A. g l a s s  ( T a b l e 7)  .1-36  11/ . 2 mm.  B. g l a s s  ( T a b l e 7)  1-36  12/  3 mm.  glass  ( T a b l e 7)  13/  4 mm.  glass  ( T a b l e 8)  14/  5 mm.  glass  ( T a b l e 8)  15/  5 mm.  K.  16/  6 mm.  glass  17/  No.  6 l e a d shot  ( T a b l e 9)  1-38  18/  No.  9 l e a d shot  ( T a b l e 9)  1-38  19/  2 mm.  10/  glass  1-36 . . . . . . . . . .  ... .  1-37  ( T a b l e 8)  (Table  1-37  9)  1-33  A. g l a s s , - d e v i a t i o n f r o m t r u e  sphere  ( T a b l e 10) 20/  3 mm.  1-39  g l a s s , - d e v i a t i o n from t r u e  sphere  ( T a b l e 11) 21/  4 mm.  22/  5 mm.  1-39  g l a s s , - d e v i a t i o n from  (Table  12)  true  sphere  '  g l a s s , - d e v i a t i o n from t r u e  1-49 sphere  ( T a b l e 13) 23/  6 mm.  1-40  g l a s s , - d e v i a t i o n from t r u e  sphere  ( T a b l e 14) 24/  No.  1-41  6 lead shot,  - d e v i a t i o n from t r u e  sphere  ( T a b l e 15) 25/  No.  d)  P a r t i c l e Density 1/  1-41  9 lead shot,  ( T a b l e 15)  1-37  . . . .  - d e v i a t i o n from t r u e  sphere .  1-41  Data  Divinyl particles  1-42  I  "4  Page  e).  2/  Glass p a r t i c l e s  1-42  3/  Lead  1-42  Liquid  \  particles  D e n s i t y and V i s c o s i t y  Data  1-43  1-5  a)  V e l o c i t y - P o r o s i t y Data  Notes: The f o l l o w i n g v e l o c i t i e s and p o r o s i t i e s were c a l c u l a t e d from the g i v e n data.  The " v e l o c i t i e s g i v e n were not corrected  f o r v i s c o s i t y change with temperature. The f o l l o w i n g symbols were used: A - meter A was used to measure flowrate B - meter B was used to measure flowrate C - meter G xvas used to measure flowrate D - meter D was used to measure flowrate The l e t t e r by i t s e l f  ( i e A,B,C, or D) a f t e r the r e a d i n g  denotes a r e a d i n g i n inches of mercury, with t e s t l i q u i d above the mercury.  A l e t t e r with an a s t e r i s k * denotes a reading i n  inches of t e s t l i q u i d ,  i n an i n v e r t e d a i r manometer.  Thus a  reading o f 20,27 B* would mean that meter B was used, and a r e a d i n g of 20.27 inches of t e s t l i q u i d  was obtained, u s i n g the  i n v e r t e d a i r manometer. The l e t t e r U a f t e r a bed height value denotes an uns t a b l e bed.  A bed-height value i n brackets denotes the height  of the i n t e r f a c e i n a mixed  bed.  1-6 TABLE 1 24-28 mesh d i v i n y l fluidised  (sample #2) i n water. 300 gm. d i v i n y l ,  above a bed o f 3/32" lead spheres, 3" high  " >  =  Data Bed Height, cm.  Fluid Temp'., OF  •8.40 8,80 9.40 9.80 11.04 12.2  Bed at r e s t 74.6 00.18 B 74.6 00,41 B 74.6 00.53 B 74.6 1,18 B 74.5 • 1.93 B 74.3 2.94 B 74.2 3.35 B 74.0 3.97 B 74.0 5,12 B 74.0 6,00 B 7,22 B 73.9 74.0 ' 8.92 B 74.0 10.39 B 74.0 11.80 B 74.0 11.78 B 74.0 . 13.91 B 74.0. 18.53 B 74.0 18.53 B 74 ,0 16.21 B 74.0 16.39 B 74.0 20.81 B 74.0 20.81 B 74.0 22.45 B 74.0 22.45 B  13.6  14 .0 14.9 16.3 17,3 18.8 20,8 23.3 25.0 25.0 28.1 37.4 32.0 U 32.4 29.6 U 42.5 36.0 U 47.5 39.2 U  Reading in.  Calculated Room Temp.,  Porosity  Velocity Ft./Sec.  0.400 28.1 0.427 28.1 0.464 28.1 0.485 27.3 0.543 0.587 27.3 0.630 27.1 • 0.640 27.1 27.0 0.662 27.0 0.691 27,0 0.708 0.732 26.9 0.758 26,9 26,9 0.784 0.793 26.9 0.798 26.9 26*99 0.821 26.9 0.865 0.8/2 26,9 26.9 0.844 0.830 26.9 0.881 26.9 0.860 . 26,9 26.9 0.894' 26.9 0.871  0.0295 0.0434 0.0511 0.0713 0.0898 0.1095 0.-1164 0.126 0.142 0.153 0.167 0.134 0.198 0.210 0,210  0,227  0.260 0,260 0.244 0,246 0,275 0,275 0.285 0.285  1-7  TABLE 2 28-32 mesh d i v i n y l  (sample #3) i n water. 300 gm.  divinyl,  f l u i d i s e d above a bed o f 3/32" lead spheres, 3" high  Data Bed.jht Height', cm.  Fluid Temo., OF."  •8.3 "9.4 10.4 12.3  70.5 70.5 71.8 71.3 71.8 71.3 71.9 71.9 71.9 72.0 72.0. 72.0 72.072.0  13.1  13.9 14.9 15.9 17.1 18.4 20.2  22.5  24.4 26.8  Reading, in. m  2.8 B*  6.0 B* 16.1 B* 23.2 B* 2.12 B 2,70 B 3.32 B 4.03 B 4.81 B 5.73 B 7.18 B 8.20 B 9.41 B  , Room Temp o , OC 18,3 18,3 18,3 18,3 18.3 18.3 18.3 18,7 18.7 18.7 18,8 13.8 13.8 18.8  Calculated  Porosity  Velocity, Ft./Sec.  .464  .  .515 .590 .615 .637 .662 .683 .705 .726 6750 .776 ,793 .812  .0325 .0455 . 0740 .0851 .0942 .1055 .1162 .1273 .1333 .1502 .1670 .1777 .1896  600 gm. 28-•32 mesh d i v i n y l 16.7 18.1  19.0  20.0  22.3 24.0  25.5 28.2  31.3  34.5 36.7 40.4  •71.9 71.9 71.9 71.9 71.9 71.9 71.9 71.9 71,9 72.0 72.0 72.0  _  22.1  B* 3.9 B* 5.5 B* 11.1 B* 16.0 B* 21.2 B* 30.2 B* 3.35 B 4.31 B 4,99 B 6.10 B  • 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0 19.0  .396 .443 .469 .496 .548 .580 .604 .642- " .678 .708 .725 .750  .0318 .0382 .0445 .0623 .0737 . 0342 .0994 .1167 .1314 .1407 .1547  1-8 TABLE 3  42-48 mesh d i v i n y l  i n water. 300 gm.  above a bed o f 3/32" l e a d  s p h e r e s , 3" h i g h  Data  Calculated  Bed Height, cm.  Fluid Temp., op  Reading  8.00 14.60 18.90 27.10 17.85 24 .90 30.40 32.60 44 .00 51.00 38.10 23.00 12.10  76.0 76.0 76.1 76.1 77.0 77.0 76.9 77.2 77.1 77.1 77.2 77.2 77.3  _  in.  0.70 1.42 2.61 1.32 2.43 3.20 3.46 4.70 5.03 4.45 2.12 0,86  divinyl^fluidised  B B B B B B B B B B B B  Room Temp. » OC  Porosity  23.6 23.6 23.6 23.6 23.7 23.7 23.7 23.8 23.8 23.8 23.9 24.0 24.0  0.370 0.654 0.733 0.814 0.719 0.797 0.834 0.845 0.886 0.901 0.868 0.781 0.568 .  Velocity Ft./Sec.  0.1034 0.0750 0.1000 0.1138 0.1180 0.1363 0.1407 0.1285 0.0937 0.0613  TABLE 4  24-28 mesh d i v i n y l  - as i n  1, 300 gm.  28^32 mesh d i v i n g:£ - a s i n  2, 300 gm.  Fluidised  above a bed o f 3/32"  lead  Data Bed 4 Heightf cm.  Fluid Temp., OF  16.8 19.3 21.1  70.6 70.6 70.6  Reading  spheres, l i "  high  Calculated  in.  Room Temp. » OC  0,35 B 0,35 B  23.8 23.8 23.8  Porosity  Velocity Ft./See.  0,400 0,477 . •0.522  0.0404 0.0541  1-9  TABLE A c o n t i n u e d  21o8  70.6 70.6  0,78  24.8  70.6 70.6  26.7  70.6  0.93 1.54 2.12  29.5  70.6 70.6 70.6  23.0 22,3  30.7 31.6  34.0  1.11  3.11 3.45 • 3.81  70.6 70.6 70.6 68.0  36.1  40.2 22.0 24.7 23.0  30.7 31.0  33.3. 35.5  4.02 5.26 6.56  68.2  0,79 1,58  68.4  2.50  68.4 68.4 63.4  3.33 3.40 4,17 4,86  68 „ 4  39.7  68.4 68,4  41.5 47.8 45.2 51.2  6,15 6,34 8,60  68.4 68.4  8.14 9.52  68.4  B B B B B B B B B B B B B B B B B B B B B B B  23.8 23.8 23.8 23.8 23.8 23.8 23.8 23.8 23.8  23.3 23.8 20.6 20.6 20.6 20.6 20.6 20.6 20.6 20.6 20.6 20.6  0.537 0.561  0.0589  0.547  0.0695 0.0640  0.593 0.635 0.653  0.0811 0.0942 0.1128'  0,671 0.681  0.1184 0.1241 0.1272  0.703 0.721  0.1444 0.1601  0.749 0.542 0.592 .  0.0594 0.0822  0.640  0.1096  0.671  0,1167 0.1178  0.674 0.607 0.716  0.1297 0.1393 0.1556  0.746  0.1636 0.1822  0.757  20.6  0.789 0.777  20.6  0.803  0.1775 0.1910  TABLE 5 • 24-28 :  42-48  mesh d i v i n y l as i n 1 , mesh d i v i n y l , as i n 1 ,  300  gm.  3 0 0 gm.  P l u i d i s e d above a bed o f 3 / 3 2 " l e a d s h o t , l - j - " h i g h  Data Bed Height, cm. (Interface)  Fluid Temp., op  18,3  75.2  Calculated  Reading in.  Room Temp., oc  Porosity  26,5  0.449  . 0.768  B*  (8.4) 20.3 (8.7)  (Porosity of 4 2 - 4 8 )  Velocity Ft./Sec.  0.01753  (0.491) 75.1  .  1.91  B*  26.5  0.503 (0.565)  0.02704  1-10 TABLE 5 c o n t i n u e d  26.5. (10.1) 33.0 (11.6) 38.8 (12.8) 44.8 (13.4) 71.7 (16.0) 59.2 (15.0) 35.5 (12.05)  74.9  9.50 B*  26.4  74.9 •  19.40 B*  26.3  74.7  2.21 B  26.3  74.2  2.58 B  26.3  74.0  4.90 B  26.3  74.0  4.11 B.  26.2  1.80 B  26.3  '74.0  0.619 (o.692) 0.694 (0.764) 0.740 (0.807) 0.775 (0.839) 0.860 (0.909) 0.830 (0.886) 0.716 (0.785)'  0.05761 0.08054 0.0957 0,1079 0.1392 0.1282 0.0870  TABLE 6 f;  3 mm. g l a s s beads  (sample #12)  i n water. 225 gm. b e a d s .  A v e r a g e d i a m e t e r = 2.896 mm. P a r t i c l e d e n s i t y = 2.896 gm./cc.  Data Bed Height, cm.  11.6 12.8 15.7 19.4 23.4 27.3 41.3 21.8 16.1 13.0 11.6 14.6  Calculated  Fluid Temp.,  Read i n g  Oj>  in.  70.0 69.8 69.8 69.6 • 69.6 70.1 70.1 69.8 69.8 69.8 69.8 69.8  2.95 3.72 5.37 7.21 9.15 10.96 15.92 - 8.38 5.55 3.72 2.87 4.64  Room Temp.,  Porosity  OF  C C C C c ; C C C C C C C v  72.4 72.4 72,4 72,4 .72.4 72.4 72.4 72.4 72.4 72.4 72,4 72.4  Velocity Ft./See,  .669 .700 .756 .802 .836 .860 .907 .824 .762 .705 .669 .737  0.423 0.475 0.569 0,658 0,739 0.808 QWO 0.708 0.578 0.475 0,419 0.530  1-11  TABLE 7 4 mm. g l a s s beads  1  (Sample #13) i n water o  9  Average diameter =: 3.95 mm. 300 gm. beads 0 P a r t i c l e d e n s i t y = 2.803 gm../cc.  Calculated  Data Bed Height, Cm.~ 9.7 11.3 12.9 14.7 17.3 20.0 23.5 26.131.3 38.9 43.3 33-5 21.9  Fluid Temp.  OF  Reading, in.  Room Temp.,  Porosity Velocity,  OF  •  _  _  69.0 69.0 69.0 69.0 68.9 68.8 69.1 69.1 69.1 69.1 69.1 69.1  1.59 2.53 53.46 5.22 6.85 8,81 10,47 12.77 16.00 18.98 14.02 7.09  Ft./Sec.  0 C C C C  c  C C C  0 C  c  72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.3 72.2 72.2 72.2 72.2  0.313 0.393 0.459 0.561 0.642 0.726 0.790 0.871 0.973 1.058 0.912 0.652  0.533 0.591 0,641 0.695 0.736 0.775 0.798 0.831 0.864 0.883 0.842 0.759  TABLE 8 5 mm. g l a s s beads  (sample #14) i n water.  Average diameter = 4,873 mm. 300 gm. beads. P a r t i c l e d e n s i t y = 2.525 gm./cc.  Calculated  Data Bed Height, Cm.  Fluid Temp., op  Read i n g ,  11.5  69.3 69.8 •' 69.8 '  18.93 B  12.0 12.6  in.  23.03 B 28.05 B  Room Temp,, op  Porosity  70.0 70,0 70,0  0.490  Velocity Ft./Sec.  0.511 0.535  0.264 0.289 0.317  1-12  14.0 15.9 17.8 20.5 25.2 26.0 32.3 43.3  69.8 69.5 69.3 69.5 '69.5 69.5 69.5 69.5  2.44 3.61 4.72 6.30 7.95 9.61 12.73 17.44  C C  70,0 70.1 70,1 •70.1 70,1 70,1 70,1 70.1  G  C C C C C  0.581 0.631 0,671 0,711 0,747 0.774 0,818 0.865  0.387 0.469 0.534 0.616 0.690 0.758 0,870 1.015  J  TABLE 9 6 mm.  g l a s s beads  (sample #15) i n w a t e r .  A v e r a g e d i a m e t e r = 5.776 mm. Particle density  220 gm.  = 2.457 gm./cc.  Data Bed Height, cm. 7.9 9.3 9.9 10.9 12.5 14 .6 15.8 16.8 • 20.6 22,2 25.4 . 28.8 14.0  Fluid Temp., °F  Calculated:  Read i n g , in.  Room Temp., op  Porosi ty  1.71 ::2".24 .3.20 4.61 6,51 7.72 8,69 11,88 12.83 15.40 17.85 6.02  C c  C C C C C  0  C C C C  70.1 70,1 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70,1 70.1  Velocity Ft./Sec.  ... 69.0 69.0 69.0 •69.2 69.2 69.2 69.2 69,2 . 69.2 69.2 69.2 69.2  beads.  •  0.44 0,525 0.554 0.595 0.647 0.697 0.720 0.737 0.786 0.801 0,826 0.847 0.684  _  0.3247 0.3707 0,4416 0,528 0.626 0.680 0.721 0.841 0.873 0.955 1.027 0.602  TABLE SO 225 gm,  3nim. g l a s s beads  300 gm. 4 mm.  glass  Fluidised  beads  (as i n 6 ) . (as i n 7 ) .  i n water  * 1-13  Data Bed Height, cm.  20.8 17.8 16.7 18.5 19.7 19.7 22.4 23.8 27.1 29.6 31.8 32.1  42.0  51.3 63.3 79.3 91.3  Fluid Temp., op  Calculated  Reading in.  27.54 B  69.0  69.0 69.0 69.0 69.0 69.1 69.3 69.5  14,62  11.42 17,82  B B B  22,56 B 1.35 C  70,0 70.0  69.5 69.0 69.0 68.8 68,4 68,5 68,5  2,15 C 2.64 C 3.77 C 4.41 C 5.13 C 6,80 C 7.96 C 10.26 C 13.12 C .16.18 C 18.30 C  Room Temp,, op  Porosity  69.2 69.2 69.2 69.2 69.2 69,2 69,4 69.4 69.4 69,4 69.4 69.3 69,1 69.1 69,1 69.1 69,0  0.563 0.489  0.315 0.234  0,508 0.538 0,538 0,594  0,286 0,289  Velocity Ft./Sec,  0.452  0,208  0,256 0.363  0.618 0.664  0.402  0,473  0.693  0.714  0,517 0,557  0.823  0.732  0.755 0.783  0.639 0.691  0.856  0,883  0.978  0.835  0,900  1.039  TABLE 11 beads, as i n 8 ,  220 gm, 6 mm,  glass  300 gm, 5 mm,  g l a s s b e a d s , as i n 9.  Fluidised  i n water  Data  Calculated  Bed Height, cm.  Fluid Temp.,  Reading  op  in.  Op  19.0 19.9 20.6 21.7 22.8 24.5  70.4  20.08 B  70.4 70.4 70.4 70.4 70.4 70,4 70.4 70.0 70.4 70.4 70.4 70.4  28.2  30.2 34.4 39.1 49.8 57.3 73.3  70.4  70.4 70.3 70.1  70.0  70.0 70.0 70.0 70.0 70.0 70.0  '70.0  23.86 B  28.12 2.05 2.67 3.98 4.82 6.18 7.95 11,55  B C C C C C C C 13.72 C 17.75 C  Room Temp.,  Porosity  Velocity Ft,/Sec,  0.484 0.501 0.527 0.549 0.581  0.636  0.660 0.701  0.737' 0.794 0.821 0.860  0.271  0,294 0,317 0.355 0,404 0.491  0,540 0,610 0.690  0,829 0.902 1.023  1-14 TABLE 12 2 mm.  A. g l a s s  beads,  fluidised  P.E.G. sample  2  P a r t i c l e a v e r a g e d i a m e t e r = 1.863 mm Particle density  i n P.E.G.  (sample 10)  = 2,90? gm./cc.  200 gm.  Data. Bed Height, cm.  7.0 8.5 10.8 12,1 12.7 11.4 13.2 15.4 16.3 16.9 19.3 23.7 27.2 46.0 60.0  Fluid Temp,, op 75.2 75.2 74.6 74.2 75.1 75.2 . 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 75.2 .  Read i n g in. 3.62 7.34 10.72 16.88 19.10 14.87 20.76 24.10 25.80 26.97 4.37 5,67 6.44 9,52 10,81 Repeat  5.87 6.32 7.40 8.30 9.82 11.40 12.80 14.20 16.70 17.20 22.70 33.00 47.0  73.2 73.2 73.2 73.2 73.2 73.2 73.2 73.2 73.2 73.8 73.6 73.8 73.8  Calculated  —  A A A A A A A A A A B* B* B* B* B*  Room Temp,, op  Porosity  74.8 74.8 74,8 74.8 75.2 74.0 74,4 74.4 74.4 74.4 73.8 73.8 73.8 73.8 73.8  0.5173 0.603 0.687 0.721 0.734 0.704 0.745 0.781 0.795' 0.800 0.825 0.857 0,876 0.925 0.944  Ft./Sec.  r u n , 194 gm. 2 mm. L i q u i d sample #5,  1.91 4.62 6.93 10.77 14.86 18.20 21.33 21.33 28.54 5.50 8.10 9.80  —  A A A A A A A A A B* B* B*  67.6 67.8 68,0 68.0 68,1 68.1 68,1 68.1 68,2 68.2 68,4 68.4  Velocity  0,00396 0.00803 0,0116 0,0181 0.0209 0,0163 0.0227 0,0264 0.0282 0,0295 0.0310 , 0,0366 0.0382 0,0465 0.0500  A,  0,439 0.479 0.550 0.603 0.665 0.711 0.743 0.768 0.768 0.809 0.855 0.900  0.930  _  0.00198 0.00478 0,00717 0.0115 0,0154 ' 0.0188 0.0221 0.0221 0.0296 0.0341 0.0419 0,0461  1-15 TABLE 13 2 mm. B. g l a s s "beads, f l u i d i s e d i n P.E.G. P«E.G. sample 2 P a r t i c l e average diameter = 2,036 mm,  (sample 11)  P a r t i c l e d e n s i t y = 2,903 gm./cc. 200 gm.  .Data Bed Height, cm. 6.2 7.3 7.9 8.8 9.7  11.2 12.2  Fluid Temo. OF  Reading  71.0 71.0 71.0 71.1 71.2 71.2 71.2 71.2 71.2 71,6 72.6 72.6  23.4 42.0 31.0  Porosity  in.  Room Temp., op  _  _  O.46  71.0 71.0 71,0 71.0 71.0 71.0 71.0 71.0 71.0 71.0' 71.0 71.0  0.531 0.572 0.616 0.652 0.698 0,723 • 0.743  0.01203  0.791 0,856  0,0279 0.0346  4 .79 6.56 9.36 11.85 16,03 19.28  71.2  13.1 14.8 16,2  Calculated  21,20  24.18 27.46 6.46  10.22 8,10  A A A A A A A A A B* B* B*  Velocity Ft./^ec.  0,772  0.930  0.891  0.00484 0.00663 O.OOQ48  0.01628 0.01953 0.02153 0.02A55 0.0481 0.0430  TABLE 14  3 mm. g l a s s beads, f l u i d i s e d i n P.E.G. P 0 E, G. sample 1 .Particle average diameter = 2.774 i n . (sample 12) P a r t i c l e d e n s i t y = 2,896 gm./cc. 200 gm.  Bed Height, cm.  Fluid Temp., °F  6.00 8,40  72.2  Data Reading in.  Room Temp., OF  13.37 A  69.0  Calculated Porosity Velocity Ft./oec. 0.437 0.595  0.0144  1-16  9.20 9.52 10.50 11.30 14.30 17.5 22.5 33.0  v  .  72.2 72,2 71.9 71.9 71.8 71.8 71.8 71.5  17.28 19.15 . 23.45 27.09 7.40 10.70 15.39 23.35  4 mm.  glas3  A A A A B* B* B* B*  69.1 69.1 69.5 69.5 69.8 69.8 70.4 70.4  Table  15  beads,  fluidised  P.E.G. sample Particle  0.630 0.643 , 0.676 0.699 0.762 0.806 .0.849 0.897  0.0180 0.0199 0.0243 0.0280 . 0,0407 0.0491 0,0601 0.0749  i n P.E.G.  3  a v e r a g e d i a m e t e r = 3.950 mm.  (Sample  13)  P a r t i c l e d e n s i t y = 2.803 gm./cc, 300  gm.  Data  Calculated  Bed Height, cm,  Fluid Temp., op  Reading  10.5 11.7 12,5 12.8 14 ,2 14.2 16,6 18,2 23.0 29,2 30.7 34,2 43^6 55.3  73.2 73.2 73.1 73.1 73.1 73.1 73,5 73.3 73.2 73.2 73.0 73.0 73.5 74.0  Q.06 14.32 19.00 20.83 27.31 3.70 7.25 9.81 19.07 32.81 35.33 40.98 56.52 70.18  in. A A A A A B* B* B* B* B* B* B* B* B*  Room Temp., °F 72,2 72,2 72,6 72.6 72,6 72.6 72,4 72.6 71.2 71.2 71.2 71.2 71.2 71,2  Porosity  Velocity Ft./Sec. .00962 .0152 .0202 00221 .0290 .0283 .0404 .0472 .0678 .0906 .0933 ,1022 .1214 .1367  .497 .549 .578 .588 .628 .628 .682 .710 .7.70 .819 .828 .846 .879 . .905  TABLE 16 5 mm.  g l a s s beads,  fluidised  P.E.G. sample  i n P.E.G.  3  P a r t i c l e a v e r a g e d i a m e t e r = 4.878 mm. Particle  (Sample  d e n s i t y = 2,525 gm./cc. 300  gm.  14)  1-17  Data Bed Height, cm.  Fluid Temp., op  11.2 12.5 13.4 14.0 14.5 15.4 16.9 16.9 18.9 22,8 26.9 33.7 42.6 52.5 24.3  74.3 74.3 74.1 73.9 73.7 73.7 73.8' 73.8 73.9 74.0 74.0 74.0 74.4 74.4 74.4  Calculated  Read i n g  Room 'emp., OF  Porosity  —  0.477 0.531 0.563 0.581 0.596 0.619 0.619 0.653 0.690 0.743 0.782 0.826 0.862 0.888 0.759  Velocity  x  in.  -  • 75.31 19.92 24 .03 27.74  4.24  7.61 7.61 12.20 21.70 32.94 4.41 5.76 7.11 26,13  A A A A B* B* B* B* B* B* B B B B*  72,8 72,8 72,7 72,7 72,7 72.6 72.6 72.6 73.0 73.0 73.0 73.4 73.6 73.6  •H./^ec. _  0.0160 0.0208 0.0250 0.0289 0.0305 0.0305 0.0415 0.0514 0.0724 . 0.0917 0.1112  0.1321  ' 0.1477 ' 0.0800  TABLE 17 6  mm. g l a s s b e a d s ,  fluidised in  P.E.G.  P.E.G. sample # 4 Particle  a v e r a g e d i a m e t e r = 5.776 mm.  Particle  d e n s i t y = 2,457 gm./cc 220  gm.  Data Bed Height, cm.  Fluid Temp., op  8.6 8.8 9.5 10.4 11,6 13.1 15.8 18.6 21.7  -72.4 72,4 72.4 72.4 72.6 73.0 73.2 73.3  Calculated  Reading  Porosity.  in|  Room Temp., °F  —  —  0,496 0.498 0.535 0.575 0.619 0.663 0,720 0.763 0,797  15.65 20.04 27.33 9.70 11.75 23,17 35.36 52,40  A A A B* B* B* B* B*  69,9 69.9 69,9 69.9 69.9 69.9 69,9 69.9  Velocity Ft./3ec. —  0,0162 0,0703 0.0283 . 0,0472 0.0524 0.0743 • 0.0938" 0.116  1-18 TABLE 17 continued  25.1 26.5 28.4 38.3  68.04 B* 6.43 B 7,02 B 10.01 B  73.4 73.4 73.4 73.4  69.9 69.9 69.9 69.9  0.824 0.833 0.845 0.885  0.133 0.140 0.149 0.178  TABLE 18 5  mm. K. (Kimble ) g l a s s i n P. E. G. p  Par t i d e  P  ft  sample 4  average diameter = 4.856 :mm.  (sample 16)  P a r t i c l e d e n s i t y = 2 .218 gm./cc. 300 gm.  Data Bed Height, cm. 12.0  13.0  13.8 14.7 15.3 16.6 17.5 22.5 25.6 39.4 49.1  Fluid Temp.,  OF  20,5 70.5 ' 70.5 70.5 70.5 70.5 70.5 70.5 70.5 70.5 70.5  Calculated  Read i n g , in.  8.39 11.37 14.38 16.97 22.29 27.37 9.59 13.12 33.31 43.02  A A A A A A B* B* B* B*  Room Temp., op  Porosity  67.2 67.2 67.2 67.2 67.2 67.2 67.2 67.2 67.2 67.2 67.2  0.444 0.487 0.516 0.546 0.564 0.598 0.619 0.7034 0.739 0.831 0.864  Velocity Ft./Sec.  0.00854 0.0116 0,0146 0.0173 0.0227 0.0279 0.0473 0.0567 0.0918 0.105  TABLE 19 2 mm, A g l a s s beads 200 gm. as i n 12 3ynm, g l a s s beads 200 gm, as i n 14 Fluidised  i n P.E.G. (sample #1)  Data  Calculated  Bed Height,  Fluid Temp.,  Reading  Room Temp.,  cm.  OF "  in.  OF  Porosity  Velocity Ft./Sec.  .1-19 TABLE 19 c o n t i n u e d  12.0 (6.0) 16.7 (6.7) 17.3 (7.2) 19.5 (7.6) 23.0 (9.4) 26.6 (10.7) 29.3 (11.5) 51.0 (14.3) 39.7 (12.6) 29.3 (11.5) 62.8 (15.5) 90 (17.5)  0.435 71.4  8.61 A  69.5  0.594  0.00883  71.4  10.20 A  69.7  0.608  0.01046  71.3  14.12 A /" 69.8  0.652  0.0145  71.2  19.71 A  69.8  0.705  0.0201  71.6  23.90 A  69.9  0.745  0.0246  71.5  26.98 A  70.0  0.769  0.0277 0.0415  71.2  7.65 B*-  70.0  0.867  71.1  5.91 B*  69.6  0.829  3.65 B*  70.0  0,769  0.0279  71.0  0.0361 *  71.1  9.00 B*  68.8  0.892  0.0454  71.0  11.21 B*  68.2  0.925  0.0485  TABLE 20 3 mm.  glass  beads 200 gm, a s i n 14  4 mm.  glass  beads 200 gm. a s i n 15  F l u i d i s e d i n P.E.G., sample 3  Calculated  Data Bed Height, cm.  Fluid Temp. op  Reading  19.7 21.8 23.1 23.5 24 .8 26,5 30.2 39.3  73.6 •73.4 73.4 73.2 73-1 73.1 73.1 73.2  13.78 19.18 22.95 23.99 27.33 4.65 7.22 13.75  in. A A A A A B* B* B*  Room Temp.,, op  Porosity Velocity (Overall) Ft./Sec.  71.2 71.2 71.2 71.2 71.2 71.2 71.2 71.2  0.559 .602 .624 .631 .650 .672 .713 .779  .0148 .0205 .0245 .0255 .0290 ,0320 .0405 .0567  '  TABLE 20 c o n t i n u e d  32,3 47.3 67.3.  '  73.8 74.0 74.0  9.25 B* 19.08 B* 28.46 B*  71.2 71.2 71.2  '.731 .816 .871  .0461 .0669 .0839  TABLE 21 4 mm.  glass  beads 300 gm. a s i n 15  5 mm.  glass  beads 300 gm. a s i n 16  Fluidised  i n P.E.G. sample 3  Calculated  Data Bed Height, cm. 21.3 22.3 24.2 26.1 28.6 29.8 34.5 39.6 46.8 61.5 68.3 89.3 97.3  ,  Reading  Fluid Temp.. op  in.  Op  A A A A A B* B* B* B* B* B* 58.90 B* 63.92 B*  67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6 67.6  8.17 10.55 14.99 20.13 26.93 4.64 8.68 13.91 22.11 37.35 43.84  71.5 . 71.5 71.5 71.5 71.5 71.5 71.5 71.5 71.4 71.4 71.4 71.4 71.4  Room Temp. ,  Overall Porosity  Velocity Ft./Sec.  0.477 0.501 0.540 0.573 0.611 0.626 0.677 0.719 0.7620.819 0.837 0.875 0.886  0.00842 0.0109 0.0154 0.0207 0,0277 0.0319 0.0445 0.0573 0.0724 0.0965 0.105 0.123 0.128  TABLE 22 5 mm.  glass  beads 300 gm, a s i n 16  6 mm.  glass  beads, 220 gm. a s i n 17  Fluidised  i n P.E.G. sample  Calculated  Data  Bed  Fluid  Reading  Height, cm.  Temp., op  in.  #4  Room Temp.,  OF  Overall Porosity  Velocity Ft./Sec.  1-21  TABLE 22 continued  19.8 20.6 21.4 22.3 23.4 24.4 26.6 30.4 35.1 43.3 40.5 53.3 66.3 96.3  74.0 74.1 74.1 74.1 74.2 74.1 74.0 74 .-2 74.0 74.0 74.2 74.3 74.3 74.2  11.56 13.69 16.80 19.81 23.49 27.36 6,43 11.24 19.95 33.37 28.36 49.77 65.88 97,43  A A A A A A B* B* B* B* B* B*. B* B*  69.4 69.4 69.4 69.4 69,4 69.4 69.4 70.2 70.2 70.2 70.2 70.2 70.2 70.2  .481 .501 .520 .539 .561 .579 .614 .662 .707 0.763 0.746 0.807 0.845 0,893  .0123  .0146 .0180 ,0212 .0252 .0292 .0383 .0507 .0676 .0891 J -.0811 .1097 .1273 .1567  TABLE 2 3 #6 lead shot f l u i d i s e d i n P.E.G. P.E.G. sample #6 P a r t i c l e average diameter = 2.46 mm,  (sample 17)  P a r t i c l e d e n s i t y = 10.592 gm./cc. 1000 gm.  Calculated  Data Bed Height cm. 8.35 12,3 13.3 15.7 17.2 19.2 21.7 24.3 28.7 33.3 39.3 46.8 35.3 13.7  r  Fluid Temp,, op  73.0 73.0 73.0 73.0 73.1 73.0 73.2 73.0 73.0 73.0 73.0 73.0 73.0  • Reading in.  1.46 2.00 4.09 5.46 7.45 9.85 12.43 16.17 20.02 24.06 27.92 21.85 3.07  B B B B B B B B B B B B B  Room Temp., op  69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 68.8 68.8 68.8 68.8  Porosity  Velocity Ft,/Sec.  .478 .646 .673 .723 .747 ,773 .800 .821 .848 .869 .889 .907 .877 .683  .0632 .0668 . 1101 .1283 .1516 .1754 .199 .229 .256 .283 .305, ,262 .0947  1-22  TABLE 24 #9 l e a d shot f l u i d i s e d i n P.E.G. P.E.G. sample #7 P a r t i c l e average d i a m e t e r = 2.02 mm. (sample 18) P a r t i c l e density  = 10.817 gm./cc. 900 gm.  Data obtained from B..P. Le C l a i r (14)  Bed Height, cm.  Fluid Temp., op  7.0 8.5 9.7 10.9 12.3 19.3 16,3 18,5 20.4 24,2 27.1 31.1 35.3  mm  73.9 73.8 73.9 74.0 74.0 74.0 73.9 73.9 74.0 74.0 74.1 '74.0  Data Reading, in.  Room Temp., op  _  _  5.7 B* 9.5 B* 15.0 B* 1 , 9 0 B* 3.10 B 4.50 B 6.15 B 7.45 B 9.95 B 11.70 B. 13.60 B 15.55 B  73.4 73.4 73.4 73.4 73.4 73.4 73.4 73.4 73.4 73.4 73.6. 73.6  Calculated Porosity Velocity Ft./Sec. 0.441 0.540 0.597 0.691 0.682 0.727 0.760 0.789 0.809 0.839 0.856' 0.875 0.890  0.0343  0.0449  0.0566 0.0734 0.0950 0.1173 0.1381 0.1476 0.1772 0.192 0.210 0.236  TABLE 25 #6 and #9 l e a d s h o t , f l u i d i s e d i n P.E.G. P.E.G. sample #8 1000 gm. o f each s i z e , (samples 17 and 18)  Bed Height, cm.  Fluid Temp., op  16.1 17.7 18.3  _  75.0 75.0  Data Reading in.  Room Temo., Op  _  16.91 A  22.22 A  71.4 71.4  Calculated Overall Velocity Porosity Ft./Sec. 0.460 0,509 .525  0.0172 0.0226  1-23 TABLE 25 c o n t i n u e d  19.0 24.0 25.5 30.5 33.7 39.0 44.9 48.5 55.7 61.8 66.4 73.9 77.5 56.1 •'• 44.1 '"•  75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75.0 75-0 75.0 75.0 75.0 75.0 75.0  28.38 1.16 1.53 3.20 4.47 6.52 9.92 10.29 12.61 13.98 15.70 17.44 13.40 12.85 8.56  A B B B B B B B B B B B B B B  71.4 71.4 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8 70.8  "  .542 .542 .659 0.715 0.742 0.777 0.806 0.821 0.844 0.858 0.869 0.882 0,888 0.845 0.803  0.0289 0.0601 0.0641 0.0941 0.114 0,138 0.163 0,176 0.195 0.207 0.220 0.232 0.2Y7 0.197 0.159  1-24 b)  P r e s s u r e Drop D a t a  Particle  sample w e i g h t s  samples a r e t h e same as Tap .to  sizes,  and  liquid  i n the corresponding  run  i n 1.  numbers a r e g i v e n .  and  The  t h e number o f i n c h e s t h e p r e s s u r e  datum.  Thus i f t a p numbers 2-7  pressure drop  i s between t a p s  apart.  In a l l r u n s  mixture  o f 2 and  bed  support.  2 and  3 mm.  except  3 mm.  t a p number tap  2 and  t a p #2  5  c h l o r i d e , with test  Readings are  i s 8.8  liquid  i n cm.  inches  3 mm.,  and  cm.  T h i s d i s t a n c e i s g i v e n i n the case particles.  given  corresponding  7, w h i c h a r e  r u n s w i t h 2 mm.,  particles,  corresponds  i s above a  are g i v e n , the  .  the  from  o f 2,  Of C a r b o n  3,  the and  tetra-  above.  TABLE 1 2 mm.  A g l a s f j beads i n P o l y t h y l e n e G l y c o l No.  2 t a p = 1.5  cm.  from  bottom o f  Tap No.  3.4 8.4 8.4 11.4 11.4 11.4 11.4 17.0 17.0 17.0 17.0 26.0 26.0  2-3  Reading cm.  2-4 2-5  2-3 2-4 2-6 5-6  2-3 2-5 3-4 2-7 2-3  2-3  1  3.65 6.31 10.60 2.77 5.62  10,32  2.60 1.90 5.42 1.S0 8.44 1.48 1.48  bed  Calculated  Data Bed Height, cm.  (P.E.G.)  Room Temp.,  Porosity  OF  69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 67.8 67.8  Pressure Drop Lb -in/ft.' f  0.593 0.598 0,598 0.704 0.704 0.704 0.704 0.801 0.801 0,801 0,801 0,870 0.870  47,42 88; 48 137.71 35.99 73.02 134.08 33.78 24.68 70.42 24 .68 109.65 19.27 19.27  1-25 TABLE 1 c o n t i n u e d  26.0 26.0 26,0 26.0 26.0 26.0.  2-5 2-7 2-9 2-11 10-11 : 5-6  67.8 67.8 67.3 67.8 67.8 67.3  3.75 6,13 8.24 10.42 1.00 1,12  „  0,870 0.870 0.870 0.370 0,370 0,870  48.84 .79.83 107.31 135.70 13.02 14.58  TABLE 2 3 iran, g l a s s beads i n P. E.G. #2 t a p = 1.7 cm . from b o t t o m o f bed  Data Bed Height cm.  Tap No.  7.7 7.7 10.3 10.3 10.3 10.3 14.7 14.7 14.7 14.7 19.4 19.4 19.4 19.4 19.4  2-3 3-4 ' 2-3 2-5 4-5 4T5 2-3 4-5 2-5 2-7 2-3 2-5 2-7 2-7 2-9  f  Reading cm. 3.9 3.7 3.0 8.51 3.00 3.00 2.07 2.09 6,20 10,35 1,79 5.01 8.13 8.13 11.39  Calculated Room Temp., op 72.2 72.0 71.8 70.9 71.3 ' 71.6 71.9 72.4 72,6 72.8 73.2 72.5 72.5 72.5  Porosity  Pressure Drop Lbf-in/ft3  0.558 0,558 0.670 0,670 0.670 0,670 0.769 0,769 0.769 0,769 0.825 0,325 0.825 0.825 0,825  50.36 47.99 33.72 110.22 33.79 38.77 26.73 - 26.99 80.04 ' 133.53 23.08 64.54 104.92 104.92 146.99  #2 t a p = 0 icm. f r o m bed b o t t o m 30.6 30.6 30.6 30.6 30.6 30.6 30,6  2-3 3-4 3-6 3-8 3-10 3-12 11-12  1.95 1.17 3.32 5.40 7.39 9.24 1.11  70.4 70.4 70.4 70.4 70.4 70.4 70.4  0.889 0.889 0.389 0.889 0.839 0.389 0,389  •  Reject 15.16 43.03 69.99 95.78 119.76 14.38  1-26 TABLE 3 2 and 3 mm. .jj-2 t a p = 1.7  g l a s s beads i n P.E.G. cm. f r o m b o t t o m o f bed  Data, Bed Height, •cm.  Tap So.  17.5 •17.5':  2-3 2-5 2-7 3-8 3-6 3-4 2-3 2-5 2-7  17.5 17.5 17.5  17.5 29.0 29.0 29.0  29.0 29.0 29.0  29.0 29.0 29.0  .  ,  Reading  Porosity  cm.  Room Temp., op  Pressure Droo Lbflin/ft3  3.74 10.97  72,2 72,2  0.613  48.28 141.62 220.62 210.55  17.09 16.31  72.2 72.2 72.2  3.42 2.80 8,18  72.2  10.48  2-9  2-11 3-4  3-6 3-10 3-12  Calculated  0.613 0.613 0.613 0.613  70,0  12,56 15.79  2,35 . 8.01 14,73 18,16  44.15  36.33  0.776  70.0  0.776 0.776  70.2 70.2 70.2 70.2 71.6 71.6  0.776  70,0  19.07  135.29  0.613  106,14 162,96 •204.77  0,776 0.776 0.776 0.776 0.776  247,31 30,48  103,38  190,21 234,51  #2 t a p = 1,1 cm. from b o t t o m o f bed 53.1 53.1 53.1 53.1 53,1 53.1 53.1 53.1 53.1 53.1  2-3 2-5 2-7 2-9  2.07  2-11  6,16 10.20 12,85 14.59  2-18  17.31 20.77  2-14  2-22 20-22 8»11  0.872 0.872 0.872 0.872 0,872 9.872 0.872 0.872 0.872 0,872  70.7  70.5 70.6 70.6 72.2 72.2 72.2 70.4 70.4 70.6  23.36 1.34 2,89  26.30 79.81  132,12  166.44 138.35  223,46  '263.13 302.76 17.37  *  37.43  TABLE 4  3 and 4 mm,  Calculated  Data  >  Bed Height cm.  g l a s s beads i n P.3.G.  Tap Ko.  Read i n g cm.  Room Temp., op  Porosity •  Pressure Drop, Lbf-in/ft'  1-27  TABLE 4 c o n t i n u e d  31.5 31.5 31.5 31.5 31.5 31.5 31.5 31.5 31.5 45.8 45.8 45.8 45.8 45.8 45.8 45.8 45.8 45.8 67.3 67.3  2-6 2-8 2-10 2-4 2-3 2-5 2-7 , 2-Q 2-11 2-14 2-.11 2-9 2-7 2-5 2-3 2-6 2-8 2-10 7-8 11-12  10.16 14.39 18,38 5.39 2.51 7.65 12,33 16.41 20,52 20,40 16.24 13.53 10.39 6.37 2.19 8.08 11.89 14.68 1.62 0.90  71.8 71.8 71.8 71.8 71.8 71.8 71,8 71.8. 71,8 71.8 71,8 . 71,8 71.8 71,8 71,8 71,8 71,8 71.8 71.8 71.8  0.725 0.725 0.725 0.725 0,725 0.725 0.725 0.725 0.725 0.810 0.810 0.810 0,810 0.810 0.810 0.810 0.810 0.810 0.871 0.871  -  131.28 185.93 236.49 69.64 32.43 98.84 159.32 212.03 265.14 263.59 209.34 174.82 134.25 82.31 28.30 104.40 153.63 189.68 20,93 11.63  TABLE 5 4 and 5 mm.  g;lass  heads i n P,E,G,  Data Bed Height, cm.  Tap No.  Reading  30.0 30.0 30.0 30.0 30.0 5^.3 53-3 53.3 53.3 53.3 53.3 53.3 77.3 77.3 77.3 77.3  2-3 2-4 2-6 2-8 2-10 2-3 2-5 2-7 2-9 2^11 2-14 2-18 2-26 2-22 2-18 2-14  2.80 6.06 11.85 17.67 23.25 1.69 4.71 8.18 11.78 15.20 20.25 27.34 30.30 25.74 20.76 15.41  cm.  Calculated Room Temp.,  Porosity  Pressure j^rop, lbf-in/ft3  72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72.2 72,2  0,629 0.629 0.629 0.629 0.629 0.791 0.791 • 0.791 0.791 0.791 0.791 0.791 0.856 0.856 0.856 0.856  36,15 78.23 152.97 228.10 300.13 21.82 60.30 105.60 152.07 196,22 261.41 352,93 391.14 332,28 267.99 193.93  Oj?  1-28 TABLE 5 c o n t i n u e d  53.3 53.3 53.3 53.3 53.3 97.8 97.8 97.8 97.8 97.8 97,8 97.8  2-11 2-9 2-7 2-5 2-3 2-5 2,-9 2^14 :i2^18 2-22 T2-26 2-32  72.2 72,2 72.2 72,2 72.2 68.2 68.2 68.2 68.2 68,2 68,2 68.2  11,94 9.50 7.08 4.51 2.10 3.52 7,93 13.07 17,65 21.62 25,40 30.89  0,856 0,856 0.856 0.356 0,856 0.386 0.886 0.836 0.886 0.886 0.886 0.386  154.13 122.64 , 91.40 58.22 27.11 45.61 102.75 169.35 228.69 280.13 329.10 400.24  TABLE 6 5 and 6 mm.  g l a s s beads i n P. E. 3 ,  Data Bed Height, cm.  Tap No,  30.9 30.9 30.9 30.9 30,9 30.9 30.9 44.8 44.3 44.3 44.8 44.8 44.8 53.3 53.3 53.3 53.3 53.3 53.3 53.3 53 = 3 53.3  2-3 2-5 2-7 2-Q 2-8 2-6 2-4 2-3 2-5 2-7" 2-9 2-11 2-14 2-3 2-5 2-7 2-9 2-11 2-18 2-4 2-6 2-8  Reading cir,. ' 2.37 6.99 11.61 16.28 13.90  9.47  4.68 1.74 5.17 ' 8.49  11,94  15.26 19.92 1.70 4,72 7,77 10.45 13.41 22,92 3.22 6.25 9,11  Calculated Room Temp.,  Porosity  70.2 70.2 70.2 70.3 70.2 70.2 70,2 70.0 70,0 70.1" 70.1 70.0 70.0 69.9 69.9 69.9 69.9 69.9 69.9 69.9 69,9 69.9  0.667 0.667 0.667 0.667 0,667 0,667 0,667 0.771 0,771 0.771 0.771 0,771 0,771 0.807 0.807 0,807 0.807 0,807 0.807 0.807 0.807 0.807'  OF  Pressure Drop, Lbf-in/ft? 30.74 .". 90,66 150.58 211.15 180.28 122.83 60,70 22.58 67,09 110.17 154.93 1S88QQ11 258.48 22.07 61.27 100.85 135.64 174,06 297.50 41.80 81.13 118,25  1-29 TABLE 6 c o n t i n u e d  53.3 53.3 73.3 73.3  73.3  73.3 73.3  73.3  73.3 73.3 73.3  2-10 2-14 2-26 2-14 2-22 2-18 2-11 2-9  2-7  2-5 2-3  •  11.81 17.39 27.14 14.38 22.70 18.62 11.18 8.91 6.48 4.00 1.56  69.9 69.9 70.1 70.1 70.1 70.1 70.1 70.1 70.1 70,1 70.1  0.807 0.807 0.860 0.860 0.860 0.860 0.860 0.860 0.860 0.860 0.860  153.29 225.71 352.06 186.54 294.46 241.54 145.02 115.58 84 .06 51.89 20.24  TABLE 7 #6 and #9 l e a d s h o t i n P.E.G.  Data Bed Height, cm. 24.7 24.7 , 24.7 24.7 24.7 24.7 38.8 v 38.8 • 38.8 38.8 38.8 38.8 38.8 38.8 38.8 38.8 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3  Tap No.  Reading cm.  2-3 4-5 6-7 2-4 5-6 7-8 2-4 2-6 2-8 2-10 2-12 10-11 6-7 4-5 2-3 8-9 24-26 2-3 2-5 2-7 6-11 6-9 6-7 10-11 10-14  16.64 16.64 16.35 33.32 17.22 16.82 22.25 45.70 66.82 87.88 109.06 10.19 10.32 11.13 11,12 10.22 9.48 7.86 23.23 37.82 35.13 21.66 7.38 6.59 23.80  Calculated Room Temp.,  Porosity  70.0 70.0 70.0 70.0 70.0 70.0 70.8 70.8 20.8 70.8 69.7 69.7 69.7 69.7 69.7 69.7 68.8 70.2 70.2 70.2 70.2 70,2 70.4 70.4 68.8  0,648 0.648 0,648 0.648' 0.648 0.648 0.776 0.776 0.776 0.776 0.776 0.776 0.776 0.776 0.776 0.776 0.876 0.876 0,876 0.876 0,876 0.876 0,876 . 0.876 0.876  OF  Pressure Drop, Lbf-in/ft3 214.49 214.49 210.75 429.49 221,97 216,81 286,36 588,16 859.97 1131. o:1405.8 131.35 133.02 143.46 143.34 131.74 122.39 101.31 299.43 487.50 452.83 279.11 95*13 84.95 307.26  1^30 Table 7 continued  70.3 70.3 70.3 70.3 70.3  10-18 16-18 16-22 16-26 16-18  46.11 11.55  70.4 70.4 70.4 70.4 70.4  32.72 56.25  11.52  0.876 0.876 0.876 . 0.876 0.876  595.28  149.11  422.42  726.19  148.72  TABLE 8 3 and 4 mm.  glass  leads i n  water  Data Bed Height, cm. 32.9 32.9 32.9  32.9  32.9 32.9 32.9 32.9 32.9 32.9 45.1 45.1 45.1 45.1 45.1 45.1 45.1 45.1 45.1 45.1 45.1 45.1 89.9 89.9 89.9 89.9 89.9 89.9 89.9  Tap No.  2-3 2-5 2-7 2-9 2-11 2-10 \ 2-8 • 2-6 2-4 2-3 2-4 2-6 2-8 2-10 2-12 2-16 2-14 2-11 2-9 2-7 2-5 2-3 2-3 2-5 2-7 2-9 2-11 2-14 2-18  Reading cm.  2.23  6.90 11.44 15.59 19.41 17.64 13.63 9.36 4.70 2.25 3.51 7.15 10.52 13.66 16.33 22.39 19.57 15.16 11.95 8.77 5.29 1.72 0.90 2.71 4.64 6.52 8.28 10.87 14.30  Calculated Room Temp.. op 68.8 68.8 68.9 69.0 68.9 68.9 68.9 . 68.9 68.9 68.9 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0  Porosity  0.723 0.723 0.723 0.723 0.723 . 0.723 0.723 0.723 0.723 0.723 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.798 0.898 0.898 0.898 0.898 0.898 0.898 0.898  Pressure Drop Lbf-in/ft3  32.71 101.22 - 167.82 222.71 284.74 258.78 199.95 137.31 68.95 33.01 . 5.1.49 . 104.89 154.32 200.39 239.56 328.46 287.09 222.40 175.31 128.66 77.60 25.23 , 13.20 39.76 . 68.07 95.65 121.47 159.46 209.78  1-31 TABLE 8 c o n t i n u e d  89.9 89.9 89.9 89.9 89.9 89,9 89.9 89.9 89.9 89.9 89.9 89.9  2-22 2-26 2-32 2-28 2-24 2-20 2-16 2-12 2-10 2-8 2-6 •2-4  69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0 69.0  17.67 20.81 25.08 22.44 19.49 16,25 12,75 9,22 7.60 5,60 3.80 1,90  0.898 0.898 0.898 0.898 0.898 0,898 0.898 0.898 0.898' 0.398 0.898 0.898  259.22 305,28 365.80 329.19 285.92 238,39 187,04 135,26 111.49 82.15 55.75 27.87  TABLE 9 5 and 6 mm,  g l a s s; beads i n  water  Calculated  Data Bed Height, cm.  Tap No.  30.9 30.9 30.9 30.9 30.9 30.9 30.9 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 53.5 55.3 58.5 73.3  2-8 2-6 2-4 2-3 2-5 2-7 2-9 2-4 2-6 2-8 2-10 2-12 2-16 2-18 2-14 2-11 2-9 2-7 2-5 2-3 2-14 2-14 2-3  Porosity  cm.  Room Temp., Op  Pressure Droo Lbf-in/ft^  12.72 8.48 4.18 ,2.00 6,29 10.40 14,81 2.41 4.89 7.42 9,98 12.30 17,32 20.29 15.17 11.34 8.83 6.20 3.89 1.25 14 .90 14.20 0.86  70.3 70.3 70.3 70,3 70.3 70,3 70,3 70,3 70,3 70,3 70,3 70,3 70,3 70.3 70,3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3  0.6598 0.6598 0.6598 0.6598 0.6598 0.6598 0.6598 0.803 0.803 0.803 0.803 0.803 0.803 0,803 0.803 0.803 0.803 0.803 0.803 0.803 0.810 0.820 0.857  186.60 124.40 61.32 29.34 92.27 152.57 217.26 35.35 71.74 108.35 146.41 180,44 254.23 297,65 222.54 166,36 129.54 90.95 57.07 18.34 218.58 208.31 12.61  Reading  1-32 TABLE 9 c o n t i n u e d  73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3 73.3  2-5 2-7 2-9 2-11 2^14 2-18 2-22 2-26 2-24 2-22-16 2-12 2-10 2-8 2-6 2-4  2.97 4.65 6.40 8.25 11.11 14.75 18.29 22.00 20.08 16.55 13.18 9.19 7.44 5.48 3.70 1.87  70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3 70.3  0.857 0.857 0.857 0.857 0.857 0.857 0,857 0.857 0.357 0.357 0.857 0.857 0.357 0.857 0.857 0.357  40.92 68.22 93.89 121,03 162.98 216,38 268,31 322,74 294,57 242.79 193.35 134.32 109,15 30,39 54.28 * 21  Ay  c)  P a r t i c l e Size  Data'  Samples o f 100 were t a k e n f r o m p a r t i c l e s used. and  each n o m i n a l  They were measured w i t h m i c r o m e t e r  t h e ^measurements a r e r e p o r t e d i n t h i s s e c t i o n .  ments a r e a l s o  g i v e n t o show t h e d e v i a t i o n  size of calipers, Measure-  of the p a r t i c l e s  from t r u e s p h e r e s .  1/  Key TABLE  1  Key  Size  range  l e s s than 0.0190 0.0200 0.0210 — 0.0220 — 0.0230 — 0.0240 — 0.0250 — 0.0260 — 0.0270 — 0.0280 — 0.0290 — 0.0300  0.0189 i n . 0.0199 0.0209 0^.0219 0.0229 0.0239 0.0249 0.0259 0.0269 0.0279 0.0289 0.0299 0.0309  -  — '  -  label a b c d e f g h i j k 1 m  2/  24-28 T y l e r  screen size  d i v i n y l , hand  screened.  3/  28-32 T y l e r  s c r e e n s i z e d i v i n y l , hand  screened.  4/ . 2 8 - 3 2 T y l e r Ro-Tap s h a k e r . 5/  Not u s e d  28-32 T y l e r  24-28 mesh d i v i n y l .  screen s i z e d i v i n y l , screened  i n the  i n runs. screen size  T h i s was used  d i v i n y l , mixed w i t h some i n the sampling  runs.  1-34 .  TABLE 2  D a t a f o r i t e m s 2, 3, 4 and 5 e x p l a i n e d above  Size  range  Percent  2 a b c d e f  0 0 0 0 0 5  S  h i j k 1 Average Diameter  oarticles 3  i n s i z e range  0 l 38 36 34 24 1 0 0 0 0 0  23  30 27 15 0 0 ( i n . ) 0.0257  A  5  0 1 16  0  29  32 19 3 0 0 0 0 "  0  0.0221  0.0214  6/  S a m p l i n g r u n , p o r o s i t y = 0.6.  7A  °ampling r u n ,  :  4 20 • 25 22 12 6  6  2 2 1 0 0.0222  p o r o s i t y = 0.7.  TABLE 3 D a t a f o r i t e m 6 above  h/L Size  : 1.0 range  . a  b c d e f g h i j k Average (in.)  2  Q 42-/ 29 . 11 4 0 1 0 1 0 0.0210  Percent 0.68  3 13 36 29 17 2 0 0 0 0 0 0.0209  of  particles 0.32  1 6 19 26 26 12 4 3 2 1 0 0.0220  i n s i z e range 0.20 0.40  0 6 10 21 30 16 7 3 2 4 1 0.0226  1 8 35 30 15 9 ' 1 0 0 1 0 0.02108  1-35 .TABLE 4 D a t a f o r i t e m 7 above  h/L Size  1.0  Percent 0.72  7 21 51 17 3 0 0 0 0 1 0.02035  1 14 36 30 15 4 0 0 0 0 0.02097  of p a r t i c l e s 0.48  i n s i z e range 0 0.24  range a b c d e f 6 h i 3  Average (in.)  0 4 15 35 21 16 7 1 1 0 0.02202  1 4 16 30 33 12 3 1 0 0 0.02185  8/  Sampling r u n , p o r o s i t y  = 0.8.  9/  Sampling run, p o r o s i t y  = 0.87.  1 3 14  4 2 28 5 1 5 0 1 0.02191  TABLE 5 D a t a f o r i t e m 8 above  h/L Size  1.0  Percent of p a r t i c l e s 0.50 0.74  range  a b c d e f g h i j k Average (in.)  3 60 23 10 1 3 0 0 0 0 0 0.0199  4 11 35 34 16 0 0 0 0 0 0 0.0208  2 8 ' 31 37 13 6 2 0 0 0 0 0.0213  i n s i z e range 0.10  0.20  0 4 21 28 32 10 5 0 0 0 0 0.0218  0  0 0 6 0 19 5 8 25. 28 19 30 15 2 14 2 9 2 11 0 2 0 2 0.0220 0.02382  1-36 TABLE 6 D a t a f o r i t e m 9 above  h/L Size  = 1.0 range a b c d e f  £  h i j Average (in.)  1 24 51 18 6 0 0 0 0 0 0.02043  10/  Percent 0.75  of o a r t i c l e s i n s i z e 6.75 0.25  range 0  0 q 38 34 18 1 0 0 0 0 0.02103  2 11 33 32 • 17 5 0 0 0 1 0.02112  2 mm.  A Glass.  Average  d i a m e t e r = 1.834  2 mm.  B glass.  Average  d i a m e t e r = 2.036.,  3 mm.  glass.  1 8 18 21 32 13 4 3 0 0 0.02182  0 0 10 24 29 14 610 6 6 0.02282  mm.,  0.0722 i n . 11/ 0.08015 i n . 12/  Average  d i a m e t e r = 2.774  mm.,  0.1092 i n . - TABLE 7 D a t a f o r i t e m s 10, 11, and 12 above  range, Thousandths o f an i n c h  Size  Percent 10  69.0 70.0 71.0 •72.0 73.0 74.0 75.0 :  -  69.9 79.9 71.9 72.9 73.9 74.9 75.9  6 9 8 12  23  17 16  •  of p a r t i c l e s i n s i z e range 11  -  12  —  —  —  —  —  --  --  1-37  TABLE 7 c o n t i n u e d  76.0 - 76.9 77.0 - 77.9 78.0 - 78.9 79.0 - 79.9 80.0 - 80.9 81.0 - 81.9 82.0 - 82.9 83.0 - 83.9 84.0 - 84.9 L e s s - t h a n 100.0 100.0 - 101.9 • 102.0 - 103.9 104.0 - 105.9 106.0 107.9 108.0 - 109.9 110.0 - 111.9 112.0 - 113.9 114.0 - 115.9 116.0 - 117.9 118.0 . 119.9 13/  2 7 11 16 19 20 21  7 2 — — — — —  — —  _ — — —  3  — —  1  —  —  —  —  • —  _  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  —  — —  1 2 4 7 9 24 27 12 5 6  3  4 mm.  glass  beads.  A v e r a g e d i a m e t e r = 3.950  mm.,  5 mm.  glass  beads.  A v e r a g e d i a m e t e r =; 4.878  mm.,  5 mm.  K. g l a s s  0.1555 i n . 14/ 0.1920 i n . 15/ 4.856 mm.,  beads.  Average d i a m e t e r =  0.1911 i n . TABLE 8 D a t a f o r i t e m s 13, 14 and 15 above  S i z e range, Thousandths of an i n c h 145.0 147.5 150.0 152.5 155.0 157.5  -  147.4 149.9 152.4 154.9 157.4 159.9  Percent 13 2 5 17 20 29  12  of p a r t i c l e s i n size 14  range 15  1-38 TABLE 8 c o n t i n u e d '  160.0 162.5 165.0  — —  -  177.5 180.0 182.5 185.0 187.5 190.0 192.5 195.0 197.5 200.0  —  —  —  179.9 182.4 184.9 187.4 • 189.9 192.4 194.9 197.4 199.9 224.4  16/  3 2 3 8 17 18 18 12 14 5  — — —  —  — —  -  6 rmii. g l a s s  beads.  -  —  —  —  -  _  6 5 4  162.4 164.9 167.4  mm  2 8 13 16 18 16 14 11 2  A v e r a g e d i a m e t e r = 5.776  mm.,  0.2274 i n . 17/  #6  lead  s h o t , a v e r a g e d i a m e t e r = 2.46  mm.,  #9  lead  s h o t , a v e r a g e d i a m e t e r = 2.02  mm.,  0.09685 i n . 18/ 0.07953 i n . TABLE 9 D a t a f o r i t e m s 16, 17, and  Size  range, Thousandths o f an i n c h  75.0 76.0 77.0 78.0 79.0 80.0 31.0 82.0 83.0 84.0 90.0 92.0 94.0  _  —  — — —  —  —  -  —  75.9 76.9 77.9 78.9 79.9 80.9 81.9 82.9 83.9 34.9 91.9 93.9 95.9  Percent 16  -  of  18  above  ^articles in size 17  -  —  —  —  —  —  — —  —  4 13 28  range 18 3 2 7 11 14 19 20 21 3 1  -  1-39 TABLE 9 c o n t i n u e d  _  96.0 - 97.9 98.0 - 99.9 100.0-101.9 102.0-103.9 104.0-105.9 215.0-217.4 217.5-219.9 220.0-222.4 222.5-224.9 225.0-227.4 227.5-229.9 230.0-232.4 232.5-234.9 235.0-237.4 237.5-239.9 240.0-242.4 242.5-244.9  15 22 9 4 5  — — — —  1 3 7 14 27 12 13 13 4 1 1 1  _  _  —  —  —  _  —  —  —  —  —  _ —  —  —  — —  —  —  -  —  -  —  19/  2 mm.  A glass, deviation  20/  3 mm.  glass,  deviation  from t r u e  sphere.  21/  4 mm.  glass,  deviation  from t r u e  sphere.  fromltrue  sphere.  TABLE 10 D a t a f o r i t e m 19 a b o v e  Particle No. 1 2 3 4 5  Largest diameter in.  Smallest diameter in.  .0745 .0751 .0751 .0755 .0761  .0731 .0748 .0732 .0743 .0742  TABLE 11 D a t a f o r i t e m 20 above  Particle No. 2  D i a m e t e r measurements on 3 axe's, i n c h e s 1 2 0.1165 0.1102  0.1035 0.1081  3 0.1152 0.1121  1-40 TABLE 11 c o n t i n u e d  0.1082 0.1107 0.1151  3 4 5  0.1096 0.1101 Q.1150  0.1065 0.1112 0.1202 •  TABLE 12 D a t a f o r i t e m 21 above  D i a m e t e r measurements on 3 axes, inches 1 2  Particle Mo. 1 2 3 4 5  0.1482 0.1617 0.1567 0.1535 0.1486  3 0.1518 0.1545 0.1642 0.1483 0.1545  0.1515 0.1596 0.1563 0.1502 0.1476  22/  5 mm.  g l a s s beads, d e v i a t i o n  from t r u e  23/  6 mm.  g l a s s beads,  from t r u e s p h e r e .  24/  Wo.  25/  No. 9 l e a d  6 lead  deviation  sphere.  s h o t , d e v i a t i o n f r o m t r u e -sphere. s h o t , d e v i a t i o n from t r u e  sphere.  TABLE 13 D a t a f o r i t e m 22 a b o v e  Particle No. 1 2 3 4 5  D i a m e t e r measurements on " 3~axes, i n c h e s 1 2 0.1946 0.1823 0.1852 0.1972 0.1965  0.1870 0.1931 0.1881 0.1943 0.1918  3 0.1825 0.1860 0.1922 . 0.1972 0.2008  1-41 TABLE 14 D a t a f o r i t e m 23 above  D i a m e t e r measurements on 3 axes, inches 1 2  Particle Ko. 1 2 3 4  0.2194 0.2270 0.2333 0.2211 0.2313  5  0.2231 0.2392 0.2156 0.2270 0.2262  •*>  0.2300  0.2272 0.2328 • 0.2348 0.2322  TABLE 15 D a t a f o r i t e m s 24 and 25 above  Particle No.  Largest diameter in.  Smallest diameter in.  Largest diameter in.  24 1 2 3 4 5  0.1011 0.0895 0.0970 0.0951 0.0972  Smallest diameter in 25  0.0991 0.0856 0.0956 0.0920 0.0968  0.0825 0.0815 0.0800 0.0812 0.0793  0.0820 0.0810 0.0792 0.0749 0.0793  1.-42 d)  Particles  2 2 3 4 5 5 6  Particle  Readings 1  mm. A g l a s s 2.906 mm. B g l a s s 2.913 glass mm. 2.873 mm. glass 2.790 glass mm. 2.528 mm. K g l a s s 2.218 mm. glass 2.465 lead 10.590 #6 lead #9 10.817 24-28 d i v i n y l 2.9369 28-38 d i v i n y l 2.924 42-48 d i v i n y l 2.924  Density ^ata.  Densities  2  3  2.911 2.901 2.896 2.813 2.525  2.904 2.904 2.919 2.800 2.523  —  —  2.450 10.594 10.845 2.9360 2.945 2.920  •  — —  2.9358  -  —  i n gm./cc.  Average i 2.907. 2.906 2.896 2.803 2.525 2.218 2.457 10.592 10.831 2.936 2.936 2.922  1-43 eO>  Liquid  D e n s i t y and V i s c o s i t y  Sample  Temperature  Density gm/cc.  1 1 1 1 1 2 2 2 2 2 3 3 3 3 4  65.0 70.0 74.0 75.0 76.0 69.3 72.7 73.1 75.1 78,7 72.20 73.20 74.00 75.60 70.00 72.18 74.00 75.60 • 66.60 69.00 74.00 72,20 74.02 76.62 71.00 72.20 73.40 74.00 75.61 70 75 80 73.8 68,6 69.4 72.10 74.05 74.20 76.6  1.0684 1.0668 1.0667  4 4 5 5 5 5 5 5 6 6 6 6 6 7 7 7 . 7 8 8 8 8 8 8  Op  Data  Viscosity lbm./ft.-sec.  .09540 .08835 .08669 ..08500 0.09778  —  1.0660 1,0768 1.0758 —  1.0750 —  1.0672 1.0672 1.0669 —  1.0687 —  1.0702 1.0691 1.0713 1.0705 1.0682 — — —  1.0700 —  1.0692 1.0690  — — —  1.0667 1,0709 — — —  1,0700 1.0692  •  —  O.O0035  0.08725 0.08118 0.0.914 —  0.08813 0.08511 0.09562 0.09137 0.08818 0.08510 — — —  0.09229 0.08880 0.08436 —  0.09557 mm  0.09211 0,08884 0,09617 0,08610 0,07932 0,0889 —  0,101660 0,09630 0,09268 — —  APPENDIX  Sample C a l c u l a t i o n s  II  and  Errors  II-2  TABLE OP  CONTENTS  1.  Porosity  calculations  2.  Porosity  -  3.  Velocity  calculations  4.  Velocity -  5.  Flowmeter c a l i b r a t i o n e r r o r s  6.  Velocity corrections  7.  Pressure drop i. ii.  errors  errors  Predicted  Pressure drop  9.  Calculation Errors  calculations  Experimental  8.  10.  for viscosity variation  -  errors  of bulk d e n s i t y  i n the bulk d e n s i t y  difference difference  formulae formulae  II-3  In t h i s s e c t i o n , maximum p e r c e n t  1.  Porosity  errors  sample  c a l c u l a t i o n s are given,  i n t h e computed v a l u e s a r e c a l c u l a t e d  calculations  P o r o s i t i e s were c a l c u l a t e d €  =  and  1-  from  *_  W = w e i g h t o f p a r t i c l e s i n gm. = particle density L = bed h e i g h t A = cross (a)  i n gm./cc,  i n cm.  s e c t i o n a l a r e a o f column,  F o r r u n #6, h = 8.4  W = 300  1  0.5  20.262 sq.cm.  cm.  gm,  f)'= 2.896 1 0.005 gm./cc. L = 8.4 t 0.1  cm.  t u b e d i a m e t e r = 2 i 0.01 €=  (b)  inches.  1 - 3 0 0 / ( 2 . 9 8 6 ) ( 8 . 4 ) ( 2 0 . 2 6 2 ) = 0.595  F o r r u n #6, L = 33.0 t 0.4  cm.  € = 1 - 3 0 0 / ( 2 . 9 8 6 ) ( 8 . 4 ) ( 2 0 . 2 6 2 ) = 0.897  2.  Porosity  (a)  -  errors  F o r c a l c u l a t i o n 1-a ( s e e r e f e r e n c e methods).  38 f o r  11-4 Relative  Kelative  error  in  -  i n {!-€)  error  0.005. 0 . 1 ,  +  TMb*  - _  874*  0.01,  0.01  ~2~~  = i 0.0253 Maximum a b s o l u t e  i n ( l - € ) .= t ( 0 . 0 2 5 3 ) ( 0 . 4 0 5 ) = 1 0.0102  error  = maximum Maximum p e r c e n t (b)  error i n € = t Q ' ^ ?  2  absolute  X 100 = 1  i n (1-,) . i ( f ^ = 1  Maximum a b s o l u t e  1.7%  g ^ f r  ^  Maximum p e r c e n t The  error  ( 0 . 0 2 5 5 ) ( 0 . 1 0 3 ) = ± 0.00263  i n€ = ± j?'^; ? 6  e x p e c t e d maximum p e r c e n t  less at high porosity,  although  error i n porosity i s  A study  calculations  ( n o t e t h e e f f e c t o f changes  and e ) , w i l l  show why t h i s i s t r u e . ,  •3.  calculations  (a)  error i n €  x 100 = ± 0.3%  the r e l a t i v e error  t h e same i n b o t h c a s e s .  Velocity  S^,  (0.0255)  i n (1-e) = 1  error  %  = maximum a b s o l u t e  roughly  i n€  S i m i l a r l y , f o r c a l c u l a t i o n 1-b  H . l a t i v . error  is  error  i n(l-€)  o f t h e above  i n magnitude  of 1 - €  M e t e r A, r u n #6 —6  V = 1.468 x 1 0 " Where  AP//X  English  units)  A P = RA/p-^  From A p p e n d i x I , R Using  ( c a l i b r a t i o n equation,  m  = 13.87 i n . ( r u n #6)  t h e v a l u e g i v e n by P e r r y  69.OOF,  (37) f o r d e n s i t y  o f mercury a t  II-5 Ap  = 778.95  V = 1.468 x I O "  (b)  bed h e i g h t  6  lbm./ft.3  x 15.87 x 778.95 = 0.0144 12 0.0915  Meter B - r e a d i n g  = 22.5 cm.,  fluid  room temp. = 70.4 ± 0.1 OF,  i n inches  p  I  °F  r e a d i n g = 15.59 i n .  R  -=rr% = — Rbp R  P.E.G., r u n #6,  temp.. = 71.8 ± 0.1  J~ -\A/°/ A  =  ft./sec.  p)  (English  units)  i f density of a i r neglected. .  1 = 12 , ./L R 15.39  =  0.8830  R  f t )  0.001583  2  sec.  (sample  #1)  r  ^> =  (0.001383)(0.3830)  Re.= 7.24  (equation  V = Re.x-^-x ~ = 0.0601  (c)  = 7.24 x 0.001385 x 6  ft./sec.  test  Run 2 5 , Bed h e i g h t fluid  23)  Meter B - r e a d i n g a3  = 0.001221  i n inches  fluid.  = 53.3  cm.  R = 20.02/12  fJL = 0.0941 l b . / f t . - s e c .  (sample  #6)  p  (sample  #6)  p  =66.76 l b . / c u . f t . =  P.E.G.  temp. = 73.0 ± 0.1 °F, room temp. = 69.0 ± 0.1 °F  Rm = 20.02,  ^-  o f mercury,  0.001410  II-6 d e n s i t y o f m e r c u r y a t 69.0 OF - 845.56 I b . / c u . f t .  (reference  Ap = (845.56 - 66.76) = 778.80 I b . / c u . f t . Wx* R Z 5  = 12x66.76 = 0.05138 20.02x778.80  r  j£sp-  0 , 2 2 6 7  -£SL Re  - (0.001410) (0.2267) = 0.0005195  t  Re  t  V  = 30.50  ( e q u a t i o n 23)  = Re.x-x-t  ^  P  d  = 30.30 x 0.001410 x 6 = 0.2562  (d) M e t e r B - r e a d i n g test  o f mercury, water as  program was used t o c a l c u l a t e t h e r e s u l t s  when u s i n g w a t e r a s t e s t  fitted  i n inches  fluid.  A computer  obtained  ft./sec.  t  from P e r r y  fluid.  P r o p e r t i e s o f w a t e r were  (37) and g r a p h e d .  Straight lines  were  t o the curves o f viscosity-temperature,  p.' = 1.454 - 0.0225T  ( c e n t i p o i s e ) T i n ° C . and d e n s i t y -  temperature, = 1.00637 - 0.000120T efficients properties.  (gm./cc.) T i n ° F . and t h e c o -  f r o m t h e s e l i n e s were u s e d i n e v a l u a t i n g The program,  i n Fortran  by t h e f o l l o w i n g : 9 10  READ 10, PW, PD, MAN, N FORMAT  (2F9.0, 214)  PRINT 25, PW, PD 25  FORMAT  (2F8.2)  water  (39) l a n g u a g e , i s g i v e n  II-7 • 11  PVOL = PW/PD  22  READ 12, FTEMP, BEDH, RDG,  12  FORMAT  RTEMP  (4F9.0)  FDENS = 1.00637 - FTEMP * 0.00012 POR = 1.0 - PVOL/(BEDH * 20.262) TC = (FTEMP - 32.0) *  (5.0/9.0)  FVI3C = 1.454 - TC * 0.0225 DELR = 12.59168 - RTEMP * 0.00219 DELP = RDG * DELR * 5.203 CRE = FVI3C/3QRT IF 14  (FDENS * 62.438 * DELP).  (MAN-3) 14, 15, 14  REL = (1.399341 - 0.43429 * LOG ( C R E ) ) / l . 0 6 4 2 3 9 RE = 10.0 * * REL GO TO 17  15  REL = (0.43429 * LOG(CRE) - 1 . 8 4 8 7 3 5 ) / ( - l . 0 1 8 7 2 3 ) RE:=.T10.0 ** REL  17  VEL = (RE * FVISC/FDENS * 0,.004032)/62.438 PRINT 30, VEL, POR,  30  FORMAT  BEDH, RE  (2E20.8, F8.3, F10.2)  N = a - 1 IF  (N)  9, 9, 22  END Variables are: PW = w i g h t o f p e l l e t s , MAN  gm.  PD = d e n s i t y  o f p e l l e t s , " gm./cc.  = manometer number, A = 1, B = 2, e t c .  N = number o f t i m e s bed h e i g h t  i s changed.  II-8 PVOL = t o t a l volume o f p e l l e t s , c c , FTEMP = f l u i d  temperature,  °F.  RTEMP = room temp., <>C. TC = f l u i d  temperature,  °C.  FVISC = f l u i d  viscosity, centipoise  FDENS = f l u i d  d e n s i t y , gm./cc.  ORE a> d i m e n s i o n a l  orifice  coefficient  RE = R e y n o l d s number VEL  = velocity,  4.  Velocity - errors (a)  ft./sec.  F o r c a l c u l a t i o n 3a, f l u i d  p. = 0.0915 ± 0.0002, p  = 66.61 ± 0.05  &p= 778.95 - 0.1 (mercury Rm=  temp. = 7 2 . 2 °F  d e n s i t y from  Perry (37))  13.87 1 0.04 i n c h e s  E r r o r i n constant Relative  error  in calibration  i n V = 0.017 + 0.04 + 0.0002 + 0.1 13.87. 0.0915 778.95 =  Maximum p e r c e n t (b)  e q u a t i o n = ± 1.7% ( r e f e r e n c e 14)  0.0221  e r r o r i n V = 2.21%  F o r c a l c u l a t i o n 3b,  E r r o r due t o n e g l e c t i n g a i r d e n s i t y : Air  p r e s s u r e = 50 p . s . i . a . ,  Using  temperature  = 70.4 °F  t h e I d e a l Gas Law. p. *  r  = 50 x 144 x 29 = 0.25 l b m . / c u . f t . 1,545 x 530.4  II-9 Relative This and  0.255 e r r o r i n A/0 = 66.59 x 100 = +0.58%  error  i s halved  i n c a l c u l a t i o n o f the s q u a r e r o o t  term,  when c a r r i e d t h r o u g h t h e c a l c u l a t i o n i t r e p r e s e n t s a  +0.2% e r r o r i n v e l o c i t y . (c)  i n calculation 3b.  Error  Relative  error  in~  = ± J^J^  Relative  error  i n / ^ = ± 0.0013 = r e l a t i v e  Relative  error  in  = ± 0.00261  !t /£'fmS^ d  ™  ±  =  R  1  Re  in-v/^  (0.0013 + 0.0002 +  *J  ToW = 1  From t a b l e  error  0.02)  bT39  (0.0050)  below, e r r o r i n c a l c u l a t i o n o f R -^ e  from  i s ± 2.3% f  ± ( 0 . 0 2 3 + 0.005) = ± 0.028  Relative  error  i n Re =  Relative  error  i n V = i (0.028 +  t  + §7§§ff  + % ^ )  = ± 0.0357 Maximum  percent  (d) Relative  e r r o r i n V = ± 3.6%  Error  error  i n c a l c u l a t i o n . 3c,  in .  0.002 = ± (0.0941  , +  0.02 6T776"  +  . 1 0.02, 0,';0.041 , 0.1 2 66.76 2 0 . 0 2 " 778.8 +  +  = ± 0.00893 Maximum  = t (0.89 + 2 . 3 ) = ± 3.19% ( T a b l e  percent  error  in R  percent  error  i n V = ± ( 3 . 1 9 + 0 . 5 1 + 0 . 5 ) = * 4.2%  e t  below) Maximum  11-10 (e)  Errors  i n calculations using  w a t e r as t e s t  fluid  i  are  i n t h e same o r d e r o f m a g n i t u d e a s t h e e r r o r s  P.E.G., a s e r r o r s  using  i n manometer r e a d i n g s and c a l i b r a t i o n  c o n s t a n t s a r e r o u g h l y t h e same. 5.  Flowmeter c a l i b r a t i o n  '  Meter  errors  Mean deviation  Maximum deviation*  B. (P.E.G.) + 2.3% C. (P.E.G.) + 2.9%  9%  B. (wat e r )  + 2.0%  9%  C. ( w a t e r )  2.9%  * This -the  6.  10%  least  squares  following  f o rviscosity  runs  (II-l)  C  CCR  (II-2)  V (corrected)  D  - ' 0  e o  variations  f o r P.E.G. - g l a s s  f o r P.E.G. - l e a d  f o r a l l water  P.E.G. l e a d  from  e q u a t i o n s were used t o c o r r e c t  0.0941 l b . / f t . - s e c .  ft' = 1 c e n t i p o i s e  deviation  line.  t o p, = 0.0920 l b . / f t . - s e c .  velocities r u n s , JJ. -  13%  i s t h e maximum s i n g l e p o i n t  Velocity corrections  The  .  runs.  8 8 1 5  = V  U. 0.7881 (calc.)(~^j)  r u n s , and  11-11 P.E.G. - g l a s s r u n s  (3 and 4 mm.,  5 mm. (H-3)  C  «  (11-4)  V (corrected) - V  D  R  K, 6 mm.,  5 and 6  -°-M07  e  P.E.G. - g l a s s r u n s OC R  4 and 5 mm.,  (3 mm.,  2 and 3  mm.)  (II-5)  C  (II-6)  V (corrected) = V (calc.)/ H?' *0.0920'  D  e  -°'  0.888 (calc.)#_J£_J \0920'  o  P.E.G. - g l a s s r u n s CC R  6  6  4  (2 mm.  A, 2 mm.  (II-7)  C  (II-8)  V '(corrected) - V ( c a l c ) ,  B  e o  "  9  1 , 0  1  Water - d i v i n y l (II-9) (11-10)  C  p \ 0.0920'  runs  -.667  D  OC R " eo  V (corrected) = V (calc.)  ( v  'Water - g l a s s  Cn OC R e " *  (11-12)  V (corrected) = V ( c a l c ) ,  0  2 7 0 2  .  v  Pressure i.  0.5 M- \ 1.0'  runs  (11-11)  7.  B.)  drop  calculations  Experimental  { 1.0  ;  1 5 6 3  955  4 mm., mm.)  5  mm.,  11-12 (a)  3 mm.  g l a s s beads i n P.E.G., a t p o r o s i t y = 0.670  room temp. = 71.8 ± 0 . 1  op  t a p s 2-3, r e a d i n g = 3.00  £ 0.02  P  (P.E.G.) = 66.61 + 0.02  P  ( C C I ) = 99.41 1 0.03  (b)  3 mm.  /> =  ( l i q . sample  e-3)  ( P e r r y (37) ) lb.-in./ft.3  g l a s s beads a t p o r o s i t y - 0.670 op.  t a p s 2-5, r e a d i n g = 8.51 drop =  lb./ft.3  CCI^  (3.00) (99.41-66.61) = 38.72 2.54  room temp. = 71.8 ± 0.1  Pressure  cm.  lb./ft.3  4  Pressure drop =  ( A p p e n d i x I , a-2)  ( A p p e n d i x I , a-2)  t 0.02  cm.  CCI4  (8.51) (99.41-66.61) = 110.22 2.54  ii.  Predicted  (c)  As  lb.in./ft.3  (a) a b o v e , p o r o s i t y = 0.670  (2.896)(62.43) l b . / f t . 3  Pressure gradient =  p  =  (1.067)(62.43) l b . / f t . 3  (l-€)(p-p) = (0.33) (1.829) (62.43) 'p  Pressure drop = for  (32.72) l b . / f t . 3  1 i n c h = 32.72  lb.-in.ft.3  taps 1 i n c h apart. (d)  3 mm.  Press gradient =  g l a s s beads a t p o r o s i t y = 0.889  (0.111)(2.896-1.067) 62.43 ( f r o m e q u a t i o n  = 12.85 Pressure'drop 8.  x  (a)  lb./ft.3  between t a p s 1 i n c h a p a r t = 12.85  Pressure drop -  1)  errors  Error i n calculation  73  lb.-in./ft.3  11-13 Relative  maximum e r r o r  i n pressure drop  = 0.02+ 0.05 = 0.0082 3.00 32.80 = +• 0.8%  (b) Relative  Error  *  i n c a l c u l a t i o n 7b  maximum e r r o r  i n pressure drop  = 0.02+ 0.05 •= 0.0048 8.51 32.80 = t 0.5%  .... ( c ) - E r r o r , i n c a l c u l a t i o n 7c Relative  maximum e r r o r  i n 1 - € = 2.13% ( c a l c u l a t e d  as i n  Relative  maximum e r r o r  i n pressure drop  .05 114.25  = .0213 +  = ± 0.0217 = ± 2.2% . • (d)  Error  i n c a l c u l a t i o n 7d  Relative  maximum e r r o r  i n 1- € = 0.01Q8 ( c a l c u l a t e d as i n 1-a)  Relative  maximum e r r o r  i n pressure drop  9.  Calculation  (a)  = 0.0198 +  of bulk density d i f f e r e n c e  Example - 3 and 4 mm.  0.05 114.25  =12,  formulae  beads, f l u i d i s e d  i n P.E.G.  D e n s i t y o f - P . E . G . = 1.070 gm./cc. 7=  2.305 - 1.070 = 0.9471 2.396 - 1.070  r = 5.950 = 1.426 2.774  (dimensionless)  m = 1.0593, u s i n g e q u a t i o n and  Cp. ( r e f e r e n c e 21)  n = 4.11 f o r 3 mm.  (dimensionless)  beads.  II-3t  and t h e d e f i n i t i o n  of Re  0  11-14 £=•"  0.4461,  ^rp*  = 0.005632  P - P f  =  ^ = 0 - 7 7 0 1  |  ( d 0  ^  ) / n d  t  = 0-9862  = 108.3 I b . / c u . f t .  0.9471  =  1  ,  0  5  4  9  (Table I I I )  Hence, from e q u a t i o n 19  0.9471 = 22.1 € - 6.0 L  10.  E r r o r s i n the bulk d e n s i t y d i f f e r e n c e formulae The  l a r g e s t e r r o r i n the c a l c u l a t i o n occurs  evaluation of r .  i n the  P a r t i c l e a v e r a g e d i a m e t e r s h a v e , s a y , an  e r r o r associated with  them o f ± 5%.  Then t h e r e l a t i v e , e r r o r  i n r i s ± 10%. From e q u a t i o n  19, and u s i n g v a l u e s  calculation, the  relative  A  error i n  1  0  from t h e previous  A  " .[J^ = ?  m n  n  (0.446) (10)  = ± 4.46%  ( r e f e r e n c e 3 8 ) , s i n c e t h e exponent on r i s 0.446. relative rexaxive  er-or i n 1 er or i nl ;  i d |mn-U/mn ^ V ^ ™-  +  -  (1.2040? (0.0446) (100) i _ 1.2040  = + 26.6% The  possible error.is  computed q u a n t i t y subtracted absolute  i n c r e a s e d as the value  i s decreased, because t h i s q u a n t i t y i s  f r o m 1, g i v i n g a s m a l l number w i t h  e r r o r a s t h e computed  larger relative  of the  error.  t h e same  quantity, but with  a much  APPENDIX  Instabilities  and  III  End  Effects  III-2  The U n s t a b l e Bed  An  u n s t a b l e bed phenomenon was e n c o u n t e r e d  fluidising divinyl  when  (24-28 T y l e r mesh, and 28-32 T y l e r mesh,  d e n s i t y = 2.936 gm./cc.) i n w a t e r a t room t e m p e r a t u r e . low p o r o s i t y t h e bed expanded s m o o t h l y  At  l i k e an a c c o r d i o n ,  i n a manner s i m i l a r t o t h e " p e r c o l a t i n g " bed d e s c r i b e d by C a i r n s and P r a u s n i t z ( 7 ) . A f t e r a p o r o s i t y o f a b o u t >was r e a c h e d ,  t h e bed c o u l d be expanded f u r t h e r ,  l y gradual increases disturb  0.76  with  extreme-  i n v e l o c i t y and c a r e n o t t o shake o r  the apparatus.  However, a s l i g h t  shaking or too  sudden a n i n c r e a s e i n v e l o c i t y would c a u s e s w i r l i n g and mixing c u r r e n t s throughout  t h e bed, t h e r e s u l t  o f which  was  t o l o w e r t h e bed h e i g h t f o r t h e same v e l o c i t y as b e f o r e t h e s w i r l i n g and m i x i n g v/as s t a r t e d . remained  stabilised  and  f o r the given  bed d i d n o t s t a b i l i z e w i t h t i m e , and c o u l d  again,  t h e bed  hydrodynamically u n s t a b l e , but maintained a f i x e d  bed h e i g h t , w h i c h was r e p r o d u c i b l e The  Once s t a r t e d ,  o n l y be  e i t h e r by c o l l a p s i n g and t h e n e x p a n d i n g  o r by e x p a n d i n g  then c o l l a p s i n g  been c o l l e c t e d phenomenum.  velocity.  i t slowly  t h e bed t o a much h i g h e r p o r o s i t y  i t to the d e s i r e d  on a bed o f p a r t i c l e s  height. which  Data  have  exhibits  this  300 grams o f 24-28 mesh d i v i n y l  were f l u i d i s e d ,  and v e l o c i t y - p o r o s i t y d a t a were t a k e n b o t h when t h e bed was expanded n o r m a l l y and when i t was i n t h e u n s t a b l e c o n d i t i o n . Below a bed h e i g h t o f 21 cm.  ( p o r o s i t y = 0,76) t h e - b e d  was  111-3 s t a b l e , and, c o u l d n o t be made u n s t a b l e by s h a k i n g t h e apparatus  o r imposing  s t e p changes i n v e l o c i t y .  h e i g h t s o f 21 cm. t o a b o u t 47.5 cm. t h e bed c o u l d e i t h e r be expanded it  c o u l d be r e n d e r e d  v e l o c i t y - by q u i c k l y metering  ( p o r o s i t y = 0.76 t o 0.89)  i n the normal f a s h i o n , o r  u n s t a b l e by i m p o s i n g opening  valve) s l i g h t l y  From bed  a valve  a s t e p change i n  ( o t h e r than- t h e  and t h e n s h u t t i n g i t ,  Over the  range o f bed h e i g h t s  (and p o r o s i t i e s ) above, i t became i n -  creasingly d i f f i c u l t  t o expand t h e bed s o t h a t i t r e m a i n e d  stable. it  Beyond a bed h e i g h t o f 47.5 cm.  became a l m o s t  graph  ( p o r o s i t y = 0.89)  i m p o s s i b l e t o expand t h e bed n o r m a l l y .  i n F i g u r e 6 shows t h e above r e s u l t s .  v e l o c i t i e s and p o r o s i t i e s  The  Bed h e i g h t s ,  corresponding to this  graph a r e  g i v e n i n Appendix I . Sampling  d a t a were t a k e n  on a n u n s t a b l e bed o f  2 8 - 3 2 mesh d i v i n y l a t a p o r o s i t y o f 0.87 d e n s i t y = 2.936 g m . / c c , temperature).  fluidised  (600 gm.  divinyl,  i n water a t room  The d a t a a r e r e p r e s e n t e d  i n the f o l l o w i n g  t a b l e , and show, t h a t t h e r e i s more m i x i n g when t h e bed i s i n the u n s t a b l e s t a t e than  i n the corresponding  stable  state.  h/L  A v e r a g e d i a m e t e r i n sample, i n c h e s , € = 0.8 € = 0.7 € = 0.87 unstable stablestable  1.0 0.74-0.75 0.48-0.50 0.20-0.25 0  0.02035 0.02097 0.02185 0.02202 0.02191  0.0199 0.0208 0.02130 0.02180 0.02382  0.02043 0.02107 0.02182 0.02282  '  111-4  The  o r i g i n a l data f o r t h i s  The  average  diameters  t a b l e are g i v e n i n Appendix  i n t h e samples a t p o r o s i t y =  a c t u a l l y show a s m a l l e r v a r i a t i o n i n g ones a t p o r o s i t y = 0.8.  End  due  t o Bed  It  was  found,  were f l u i d i s e d  was  of lead is  when f l u i d i s i n g  42-48 mesh and  a l o n e a t t h e same w a t e r v e l o c i t i e s was  in a l l fluidisation p a r t i c l e s was  due  used  runs,  t o the e f f e c t  except  as a p a r t i c l e  i n the p r e c e d i n g t a b l e ,  curves  f o r 600  of  the  This  support.  at e  -  bed  The  0.7,  by  effect the  with  h/L  Figure  grams 24-28 mesh d i v i n y l ,  grams o f i d e n t i c a l m a t e r i a l .  600  gram s e t o f p a r t i c l e s  For a given velocity,  shows a h i g h e r p o r o s i t y .  c o n s i s t e n t \-i\t-h t h e t h e o r y above t h a t t h e r e i s a  the entrance.  mixing  when a f i x e d  p a r t i c l e diameter  300  which'causes a decrease  at a l l  (Figure 7).  the bottom h a l f o f t h e 28-32 mesh d i v i n y l b e d .  shows e x p a n s i o n  (which  t h a n when t h e y  where t h e r e i s c o n s i d e r a b l e m i x i n g .  illustrated  effect  24-28  a b o v e t h e 24-28 mesh p a r t i c l e s  n e g l i g i b l e v a r i a t i o n of average in  by  Support  believed that t h i s  seen  normal  increase in s t r a t i f i c a t i o n  p o r o s i t i e s ) were expanded t o h i g h e r p o r o s i t i e s  entrance,  correspond-  t o g e t h e r , t h a t t h e 42-48 mesh p a r t i c l e s  formed a d i s c r e t e bed  I t was  the  increase i n porosity.  Effect  mesh d i v i n y l  than  0.87  T h i s i s o p p o s i t e to the  ( s t a b l e ) b e h a v i o r , w h i c h i s an s i z e w i t h an  w i t h h/L  I.  33 and  the  This i s  mixing  i n p o r o s i t y associated with  (In the p r e v i o u s s e c t i o n of t h i s  appendix i t  III-5  r  1  i  -0-8  8  -10  o  / 1  ,6  6'  > o  "T  *  /  9  /  / /  DIVINYL- WATER © 24-28*  300 gm.  © 24-28*  600 gm.  /  o  "TYLER MESH  H-4  -0-3 L0G  l0  0-2 €  -01  F i g u r e 55 - E x p a n s i o n D a t a f o r 500 gm. and 600 gm, of  24-23 T y l e r  Mesh D i v i n y l  i n Water  III-6 was shown t h a t t h e r e was a m i x i n g p o r o s i t y f o r an u n s t a b l e bed.  effect  That  p o r o s i t y a g a i n accompanied a m i x i n g bed  o f 42-48 mesh p a r t i c l e s ,  bed  of particles,  i s , a decrease i n effect.):  when f l u i d i s e d  with the l a r g e r g l a s s  References  S i m i l a r l y the  above t h e o t h e r  was n o t s u b j e c t t o t h i s m i x i n g  t h e r e f o r e expanded t o a h i g h e r p o r o s i t y . was n o t n o t e d  and a d e c r e a s e i n  e f f e c t and  The same  effect  particles.  ( 7 ) , ( 9 ) , and (11) may be c o n s u l t e d f o r  d a t a and d i s c u s s i o n on m i x i n g and i n s t a b i l i t i e s  i n fluidised  beds. Both of the e f f e c t s not  large effects,  the d i v i n y l in  water.  mentioned  i n this  a p p e n d i x were  and were o n l y n o t i c e a b l e when f l u i d i s i n g  particles  (24-28, 28-32, and 42-48 T y l e r  mesh)  

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

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.831.1-0059109/manifest

Comment

Related Items