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Back-mixing in liquid-liquid extraction spray columns Henton, Jeffrey Ernest 1967

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The  U n i v e r s i t y o f B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of JEFFREY ERNEST HENTON  B.Sc,  U n i v e r s i t y o f Leeds, 1964  MONDAY, OCTOBER 2, 1967, AT 3:30 P.M. IN ROOM 207 CHEMICAL ENGINEERING BUILDING  COMMITTEE IN CHARGE Chairman: Dr. K.L. P i h d e r Dr. J.S.. F o r s y t h . Dr. R.M.R. B r a n i o n  B. N. Moyls Dr. N. E p s t e i n Dr. E . P e t e r s Dr. A. M i t c h e l l  E x t e r n a l Examiner: T. Vermeulen P r o f e s s o r , Department o f Chemical E n g i n e e r i n g U n i v e r s i t y of C a l i f o r n i a , B e r k e l e y , C a l i f o r n i a , U.S.A.  .Research S u p e r v i s o r :  S..D. Cavers  BACKMIXING IN LIQUID-LIQUID EXTRACTION SPRAY COLUMNS  ABSTRACT  Backmixing of the c o n t i n u o u s phase was in l i q u i d - l i q u i d for  spray columns of v a r i o u s  studied  geometries,  v a r i o u s f l o w r a t e s of the two phases, and f o r  v a r i o u s drop s i z e  distributions.  The d i s p e r s i o n or eddy d i f f u s i o n model was used to c h a r a c t e r i z e the a x i a l m i x i n g of the continuous phase, from a d i s t r i b u t o r  of sodium c h l o r i d e  ( s o l u b l e i n the continuous phase only)„ s t a t e form of the model was u t i l i z e d a x i a l eddy d i f f u s i v i t i e s  from these  The  steady  to c a l c u l a t e results.  The t r a c e r s t u d i e s showed t h a t the a x i a l diffusivity  tracer  eddy  i s independent of the continuous phase  f l o w r a t e and the column h e i g h t . A x i a l eddy d i f f u s i 2 2 v i t i e s between 7 - f t . / h r . and 3 1 - f t . / h r . were o b t a i n e d i n a 1 % - i n . I . D. column.  Low  d i s p e r s e d phase flow-  r a t e s and l a r g e drop s i z e s r e s u l t e d diffusivities. resulted between  eddy  I n c r e a s i n g the column diameter to 3 - i n .  i n s u p e r f i c i a l a x i a l eddy 6.3  i n high a x i a l  and 17.3 times  diffusivities  larger.  The hold-up of d i s p e r s e d phase was measured by means of a p i s t o n sampler.  The hold-up i n c r e a s e s  approximately l i n e a r l y with i n c r e a s i n g phase  dispersed  s u p e r f i c i a l v e l o c i t y and tends to be  higher  f o r i n c r e a s e d c o n t i n u o u s phase  velocities. increased  A smaller  slightly  superficial  drop s i z e r e s u l t e d i n an  hold-up.  Drop s i z e d i s t r i b u t i o n s were measured.. always  show two peaks, one at 0.02-in. diameter,  and the other value  They  at a much l a r g e r s i z e ,  the a c t u a l .  of which depends on the n o z z l e  t i p diameter  used to d i s p e r s e  the d r o p s .  The m i x i n g c e l l - p a c k e d bed analogy was p r e d i c t P e c l e t numbers i n a s p r a y column.  used to The ,  agreement between these and measured P e c l e t numbers i s good f o r drops of about 0.15-in.  equivalent  diameter but becomes p r o g r e s s i v e l y worse as the drop m s i z e i s reduced.  AWARDS 1964-1967  Commonwealth  Scholarship  1966-1967  F i n n i n g T r a c t o r Graduate  Scholarship  GRADUATE STUDIES  Field  of Study:  Related  Chemical  Engineering  Studies  Mass T r a n s f e r  S.D. Cavers  Statistics  D.A. Ratkowsky  Fluid  R„M„R. B r a n i o n  and P a r t i c l e Dynamics  Linear Algebra  Wm.R.  Simons  Other S t u d i e s Mass and Heat T r a n s f e r A n a l o g i e s Surface E f f e c t s Optimization Computer Programming  N. E p s t e i n J. Leja K..L. P i n d e r K. Teng  BACK-MIXING I N LIQUID-LIQUID EXTRACTION SPRAY COLUMNS by JEFFREY ERNEST HENTON B. S c . , U n i v e r s i t y o f Leeds,  196V  A THESIS SUBMITTED I N PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  i n t h e Department of CHEMICAL ENGINEERING  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e required standard  THE UNIVERSITY OF BRITISH COLUMBIA September, 1 9 6 7  In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements f o r a n advanced degree a t t h e 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 , I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study.  I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s  t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d b y t h e Head o f my Department o r b y h i s representatives„  I t i s understood that  copying  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n .  Department o f  C//<£TA7 / £ / 3 ^  £~/^<r / A/£~"<~~ f l / / ^ ^ ~  T h e " U n i v e r s i t y of " B r i t i s h Columbia V a n c o u v e r 8 Canada S  Date 2  (9scs&&u-  176  7  i  ABSTRACT  Backmixing spray  columns  phases,  dispersion  a x i a l mixing  were  measured  distributor only). axial  eddy  eddy  obtained large  o f sodium  column  sizes  between  hold-up  dispersed  phase  drop  increased size  phase  (soluble  flowrate  phase  to calculate  diffusivity  a n d t h e column  and 31-ft./hr. phase  were flowrates and  i n superficial axial  times  i s  height.  diffusivities.  Increasing eddy  larger.  w a s m e a s u r e d b y means  v e l o c i t y and tends  linearly  hold-up.  of a  with  A  piston  increasing  to be slightly  Superficial velocities.  i n an increased  from a  i n the continuous  t h e a x i a l eddy  resulted  phase  phase,  profiles  results.  a x i a l eddy  phase  to characterize  was u t i l i z e d  increases approximately  continuous  of the two  concentration  Low dispersed  a n d 17.3  Superficial  resulted  was u s e d  Axial  7-ft./hr.  i n high  of dispersed  The hold-up  that  D. c o l u m n .  6.3  liquid-liquid  flowrates  t o the continuous  tracer  between  t o 3-i&»  sampler.  for  showed  resulted  diameter  phase.  from these  diffusivities 1.  model  form o f t h e model  studies  i n  distributions.  respect  chloride  was studied  f o r various  diffusion  of the continuous  diffusivities  The  size  with  state  i n a 1^-in.  drop  drop  diffusivities  independent Axial  geometries,  o r eddy  upstream,  tracer  phase  o f the continuous  The steady  The  the  of various  andf o r various  The the  of the continuous  higher  smaller  ii  Drop s i z e d i s t r i b u t i o n s were measured.  They a l w a y s show two.peaks,  one a t 0 . 0 2 - i n . d i a m e t e r , and the o t h e r a t a much l a r g e r s i z e , t h e a c t u a l v a l u e o f w h i c h depends on t h e n o z z l e t i p d i a m e t e r used t o d i s p e r s e the drops.  •  The m i x i n g c e l l - p a c k e d bed a n a l o g y was used t o p r e d i c t P e c l e t  numbers i n a s p r a y column.  The agreement between t h e s e and measured  P e c l e t numbers i s good f o r drops o f about 0 . 1 5 - i n . e q u i v a l e n t b u t becomes p r o g r e s s i v e l y worse as t h e d r o p s i z e i s r e d u c e d .  diameter  iii  TABLE OF CONTENTS  INTRODUCTION  THEORY  -  P r e v i o u s work  !  -  M a t h e m a t i c a l models  -  O b j e c t o f t h i s work  -  A p p l i c a t i o n o f t h e d i s p e r s i o n model t o r u n s  j_o, ,  27  30  w i t h no mass t r a n s f e r -  A p p l i c a t i o n o f t h e d i s p e r s i o n model t o liquid-liquid extraction  APPARATUS.  32  ...  EXPERIMENTAL PROCEDURE  -  36  :  -  Column-operation  60  f  S a m p l i n g t e c h n i q u e s t u d i e s w i t h mass t r a n s f e r .  61  -  Search f o r a s u i t a b l e t r a c e r  -  Sampling t e c h n i q u e s t u d i e s w i t h no mass  67  transfer. -  A x i a l eddy d i f f u s i v i t y and d i s p e r s e d hold-up....  -  69 phase  t  C o n c e n t r a t i o n p r o f i l e s w i t h mass t r a n s f e r  70 84  RESULTS AND DISCUSSION -  Results o f sampling technique studies  86  Discussion o f sampling technique studies  cjx  iv  -  A x i a l eddy d i f f u s i v i t y , drop s i z e  distribution,  and d i s p e r s e d phase hold-up s t u d i e s i n t h e 10^  l-g--in. I . D. column -  A x i a l eddy d i f f u s i v i t y and drop  size  d i s t r i b u t i o n s t u d i e s i n t h e 3 - i n . I . D. 1J+3  column -  Visual  o b s e r v a t i o n s o f t h e m o t i o n o f t h e drops  -  C o n c e n t r a t i o n p r o f i l e s w i t h mass t r a n s f e r  15X 16U  CONCLUSIONS. NOMENCLATURE.  150  168  ,  ^3  LITERATURE CITED APPENDICES I II  DISPERSION MODEL THEORY.  ^  MIXING CELL - PACKED BED ANALOGY and SPRAY COLUMN ^9  PACKED BED ANALOGY III  ANALYSIS OF PISTON SAMPLE RESULTS TO PRODUCE THE AVERAGE CONTINUOUS PHASE CONCENTRATION, EXCLUDING THE CONTRIBUTION FROM WAKES, I N THE PISTON SAMPLE AT THE TIME OF SAMPLING..  IV V VI  ,  197  TABULATED RESULTS.  203  DETAILS OF THE APPARATUS  230  DIMENSIONS OF THE GLASS PORTIONS I N THE COLUMN TEST SECTIONS AND MEASUREMENT OF PURGE TIMES  256  V  LIST OF TABLES  1.  Key to Figure 9  .  38  2.  Key to Figure 21  3.  Sampling Studies with Hook and Bell-Probes and  ,  Piston.......... k.  Sampling Studies with Hook and Bell-Probes, Hypodermic Needles, and Piston  ^2  5.  Sampling Technique Studies with No Mass Transfer.....  94  6.  Time to Reach Steady State i n the l§--in. I. D. Column 135  under Conditions of no Mass Transfer 7. •  E f f e c t of Tracer Feed 'Rate on Reduced  Concentration  P r o f i l e s and A x i a l Eddy D i f f u s i v i t y i n the l i - i n . 136  I. D. Column 8.  Reproducibility of Results, f o r A x i a l Eddy D i f f u s i v i t y 137  i n the l | - i n . I, D. Column 9.  Cross-Sectional Homogeneity i n the 1-g-in. I. D. 139  Column 10.  E f f e c t of Sampling Rate on the Reduced  Concentration  P r o f i l e i n the 1^-in. I. D. Column 11.  2.I+0  E f f e c t of Order of Sampling on the Measured  Concen-  t r a t i o n P r o f i l e i n the l-g--in. I. D. Column 12.  E f f e c t of Column Height on the Measured  Concen-  t r a t i o n P r o f i l e and A x i a l Eddy D i f f u s i v i t y i n the 1^-in. I. D. Column...  l i + 2  vi  13.  Steady State Times for the 3-in. I. D. Column  1^7  Reproducibility of Results for the 3-in. I. D. Column... 15.  lk8  Cross-Sectional Homogeneity i n the 3-in. I . D. Column...........  16.  Comparison of Axial Eddy Diffusivity by Mass Transfer Studies and Tracer Studies  IV-1.  1^9  ,  156  ,  Data Sheet  20k  IV-2. Calculation of Quantities used for the Calculation of E.  207  ....  213  IV-3. Typical Computer Results IV-k. Axial Eddy Diffusivity Results for the 1^-in.  21^  I. D« Column.............. IV-5. Superficial Axial Eddy Diffusivity Results for the 3-in. I. D. Column....  ..  219  IV-6. Typical Drop Size Distribution Results  221  IV-7. Drop Size Distributions i n the l^--in. I. D. Column..  222  IV-8. Drop Size Distributions i n the 3-in. I. D. Column...  22^  IV-9. Concentration Studies with Mass Transfer i n the 1^-in. I. D. Column. IV-10.The Relation Between.E and &  225 226  IV-ll.Calculated Values of E for Various Values of K^a and J...  227  vii  I V - 1 2 . C a l c u l a t e d V a l u e s o f E f o r V a r i o u s Values o f m  I V - 1 3 . E q u i l i b r i u m Data f o r  Acetic Acid  228  Distributed  Between MIBK-Saturated Water and W a t e r - S a t u r a t e d MIBK a t 70°F.. VI-1.  Dimensions  o f t h e G l a s s P o r t i o n s i n t h e Column  Test Sections  1  229  256  viii  LIST OF FIGURES  1.  Schematic Diagram of a Spray Column.....  2  2.  Solute Concentration Profile in a Spray Column......  5  3.  Mass Balance Over a Section of a Spray Column  6  h.  Continuous Phase Recirculation  7  5.  Hook and Bell-Probes  12  6.  Concentration Profiles in a Spray Column  lh  7.  Concentration Profiles in a Spray Column  15  8.  Piston Sampler.  17  9.  Schematic Flow Diagram for the l§--in. I. D. Column..  37  10.  1^-in. I. D. Column  hi  11.  Short 1^-in.I. D. Column  12.  Long 1-g-in. I. D, Column..  13.  .1^-in. I. D- Column for Comparing Hook and B e l l -  , ,..  Probes and Piston Sampler Results lh.  43 44  ^  l|:-in. I. D. Column for Comparing Hypodermic Needle, Hook and Bell-Probes; and Piston Sampler Results....  15.  Nozzle Tip Patterns. J. D. = 0.126-in. ( l ^ - i n . I. D. Column)  16.  hQ  Nozzle Tip Patterns. I. D. = 0.103-in. (l-|-in. I. D, Column).  49  ix  17.  Nozzle T i p Patterns. I. D. = 0.086-in.  (l^-in. 50  I. D. Column) 18.  Nozzle Tip Patterns. I. D. = 0.053-in.  (l|-in.  I. D. Column) 19.  Photographic Conditions  20.  ,  I. D. Column..........  21.  Schematic Flow Diagram f o r the 3-in. I. D. Column  22.  Nozzle T i p Patterns. I . D. = 0,102-in. (3-in. I. D.  75  Optical D i s t o r t i o n Investigation, 3-in. I. D. Column  25.  ••  8l  •«•  Sampling Technique'Studies with Hook and Bell-Probes 90  and Piston... 26.  55  O p t i c a l D i s t o r t i o n Investigation, 1^-in. I. D. Column  2k.  cu  58  Column) 23.  53  Sampling Technique Studies with Hook and Bell-Probes, Hypodermic Needles and Piston  93  27.  Sampling Technique Studies with no Mass Transfer  95  28.  Reduced Concentration P r o f i l e s . . . . .  108  29.  A x i a l Eddy D i f f u s i v i t y i n the l | - i n . I. D.. Column  HO  30.  Comparison of A x i a l Eddy D i f f u s i v i t y as Determined i n t h i s Work with That of Other Workers.  30a.  112  Comparison of Dispersion Number i n This Work with That f o r Packed Beds  ;  113  X  31..  Predicted and Calculated Peclet Numbers,  32.  = 0.155-ln P Predicted and Calculated Peclet Numbers,  H5  d  = 0.135-ia  d  116  p 33•  Predicted and Calculated Peclet Numbers, d  34.  p  = 0.125-in  117  Predicted and Calculated Peclet Numbers, = 0.095-in  d  118  P 35-  Percentage Error in the Equivalent Diameter due to Optical Distortion in the 1 ^ - i n . I. D. Column  36.  121  Drop Size Distribution for Fun 5 0 , Average Nozzle Tip Diameter = Q . 1 0 3 - i n . . . .  37.  Photographs at Operating Conditions Corresponding to Runs Indicated.  38.  125  Magnification Factor =  3  ••••  Drop Size Distribution for Run 1 3 0 , Average Nozzle Tip Diameter = 0 . 1 2 6 - i n  39.  128  Distribution of Totai Percent of Volume of Drops for Run 5 0 , Average Nozzle Tip Diameter = 0 . 1 0 3 - i n . .  kO. kl.  3-27  Dispersed Phase Hold-up, d P Dispersed Phase Hold-up, d  129  = 0.155-in  130  = 0.135-in  131  = 0.125-in  132  = 0.095-in  133  P k2.  Dispersed Phase Hold-up, d  U3.  Dispersed Phase Hold-up, d  kk.  Superficial Axial Eddy Diffusivity in the 3 - i n . I . D.  p  Column 45.  lbk  Percentage Error in the Equivalent Diameter due to Optical Distortion in the 3 - i n . I. D. Column  1^6  xi  h6.  E q u i l i b r i u m Curve f o r A c e t i c A c i d  Distributed  Between MIBK- S a t u r a t e d Water and W a t e r - S a t u r a t e d MIBK a t 70°F  153 p  V7.  Minimizing  f o r Run J I  1+8.  The E f f e c t on E o f V a r y i n g t h e Methpd o f F l u x  158  ,  C a l c u l a t i o n and o f V a r y i n g K^a f o r Run J I  159  49.  The E f f e c t on E o f V a r i a t i o n s i n m f o r Run J I  160  50.  Measured and F i t t e d C o n c e n t r a t i o n P r o f i l e s f o r ,  ...  2.61  S o l u t e Mass B a l a n c e i n t h e Continuous Phase  ..  igfo.  RunJl.. 1-1.  I I I - l . Lower P o r t i o n o f a Spray Column  201  III-2.  The E f f e c t o f Time on a P i s t o n Sample  202  V-l.  P i s t o n Sample C o l l e c t i o n F l a s k f o r Large Hold-ups....  233  V-2.  Hypodermic Needle  234  V-3.  Sampling V a l v e f o r Hypodermic Needle  235  V-U.  T r a c e r I n j e c t i o n System...  236  V-5.  Tracer Distributor....  237  V-6.  0.126-in. I.D. N o z z l e T i p s , N o z z l e T i p Support  I n s t a l l e d f o r Sampling  P l a t e , and N o z z l e T i p Caps.......... V-7.  0 . 0 8 6 - i n . I.D. N o z z l e T i p s , N o z z l e T i p Support 239  P l a t e , and N o z z l e T i p P l u g s V-8.  .  0.053-in. I.D. N o z z l e T i p s , N o z z l e T i p Support P l a t e and N o z z l e T i p P l u g s . . . . ,  V'9«  238  Perspex Box f o r t h e 1^-in. I.D  r  2k0 Column Photographs...  2U1  xii  V-10.  L i g h t S h i e l d f o r t h e l§-in. I . D. Column Photographs.  242  V-ll.  Lower end o f t h e 3 - i n . I . D. Column  243  V-12.  S p e c i a l P y r e x Reducer f o r t h e 3 - i n . I . D. Column  244  V-13.  N o z z l e S h e l l f o r t h e 3 - i n . I . D. Column  24-5  V-l4.  N o z z l e T i p s , N o z z l e T i p Support P l a t e , and N o z z l e T i p P l u g s f o r t h e 3 - i n . I . D. Column  246  f o r t h e 3 - i n . I . D. Column N o z z l e . .  V-15-  Flow S t r a i g h t e n e r  V-l6.  N o z z l e S e c u r i n g P l a t e and R e t a i n i n g Nut f o r t h e 3 - i n . I . D. Column  ,  2  47  2U8  ,  V-17.  End P l a t e f o r t h e Bottom o f t h e 3 - i n . I . D. Column...  249  V-18.  E l g i n Head f o r t h e 3 - i n . I . D. Column  250  V-19.  Upper End P l a t e f o r t h e E l g i n Head o f t h e 3 - i n . I . D, Column  V-20.  •  251  ,.  Lower End P l a t e f o r t h e E l g i n Head o f t h e 3 - i n . 252  I . D. Column.. V-21.  Lower End P l a t e P a c k i n g f o r t h e E l g i n Head o f t h e 3 - i h . I . D. Column  253  V-22.  P e r s p e x Box f o r t h e 3 - i n . I . D. Column P h o t o g r a p h s . . .  254  V-23.  Flange f o r the Photographic Section of the 3 - i n . I . D. Column.  255  .'  "A  xiii  ACKNOWLEDGEMENTS The  a u t h o r would l i k e t o e x p r e s s h i s s i n c e r e g r a t i t u d e t o  Dr. S. D. Cavers f o r h i s a s s i s t a n c e , encouragement, and h e l p f u l c r i t i c i s m s o f f e r e d t h r o u g h o u t t h e course o f t h i s p r o j e c t . Thanks a r e extended t o a l l members o f the f a c u l t y and s t a f f o f the Department o f C h e m i c a l E n g i n e e r i n g , Columbia f o r t h e i r r e a d i n e s s  The U n i v e r s i t y o f B r i t i s h  and w i l l i n g n e s s i n d i s c u s s i n g b o t h  i c a l and p r a c t i c a l problems a s s o c i a t e d w i t h t h e work.  theoret-  Particular  a p p r e c i a t i o n i s o f f e r e d t o Dr. K. L. P l n d e r . f o r t h e l o a n o f a t e l e p h o t o l e n s and t o Mr. R. B r a n d t f o r making most o f t h e machined p a r t s e s s e n t i a l f o r t h i s study.. The  author i s indebted  t o Dr. Duncan o f the B r i t i s h Columbia  Research C o u n c i l f o r h i s suggesting  t h e use o f sodium c h l o r i d e a s a  t r a c e r and f o r p r o v i d i n g t h e u s e o f t h e a t o m i c a b s o r p t i o n  spectrophoto-  meter. F i n a n c i a l s u p p o r t was most g r a t e f u l l y r e c e i v e d i n t h e form o f s c h o l a r s h i p s from t h e Commonwealth S c h o l a r s h i p and F e l l o w s h i p  Committee  of t h e E x t e r n a l A i d O f f i c e , Ottawa, and, f r o m the F i n n i n g T r a c t o r Company, L t d . Funds f o r ' the equipment were p r o v i d e d b y t h e N a t i o n a l R e s e a r c h Council.  1  I INTRODUCTION  1.  PREVIOUS WORK  L i q u i d . - l i q u i d e x t r a c t i o n i s used w i d e l y f o r s e p a r a t i n g components which a r e more d i f f i c u l t o r expensive as d i s t i l l a t i o n ,  t o separate by o t h e r methods  e v a p o r a t i o n , or p r e c i p i t a t i o n .  u s u a l l y a r e p r e f e r r e d i f the two b o i l i n g p o i n t s , o r i f one  Extraction  components t o be  such  processes  s e p a r a t e d have  similar  o f the components i s heat' s e n s i t i v e or p r e s e n t  i n s m a l l amounts.  C o u n t e r c u r r e n t e x t r a c t i o n i n v e r t i c a l towers can be c a r r i e d  out  when the r a f f i n a t e and e x t r a c t phases d i f f e r a p p r e c i a b l y i n d e n s i t y . Although  s i e v e - p l a t e , bubble  found i n i n d u s t r i a l use  cap, and packed towers a r e more commonly  "...the spray tower i s the more a t t r a c t i v e f o r  e x p e r i m e n t a t i o n because of i t s i n h e r e n t s i m p l i c i t y , and a l s o because o f the g r e a t e r p o s s i b l e range of f l o w r a t e s o f the two  F i g u r e 1 shows d i a g r a m m a t i c a l l y how and removed from a spray tower.  (phases)..." ( l )  each phase i s i n t r o d u c e d i n t o  In the system- shown the l e s s dense  phase i s d i s p e r s e d through n o z z l e t i p s l o c a t e d a t the lower end o f the column. phase and  The d i s p e r s e d phase drops r i s e through  the d e s c e n d i n g  continuous  c o a l e s c e a t the i n t e r f a c e a t the upper end of the column.  Many workers have s t u d i e d spray column o p e r a t i o n . i n the main r e p r e s e n t s an a c c u m u l a t i o n  The  knowledge gained  of s m a l l c o n t r i b u t i o n s .  2  .DISPERSED PHASE OUTLET  CONTINOUS PHASE INLET  INTERFACE .  • • * •••*  *  •••  •  _  • . ••• •• • .«. ••••. •• -  •• • * •  •••••• . • •  .•  ••  ••  : . . . . ;.. .  •  DISPERSED PHASE NOZZLE TIPS CONTINUOUS ^ PHASE OUTLET  FIGURE 1.  DISPERSED PHASE INLET  SCHEMATIC DIAGRAM OF A SPRAY COLUMN  3  The d e s i g n s o f the c o n t i n u o u s  phase i n l e t and d i s p e r s e d phase o u t l e t  used I n the p r e s e n t s t u d y were f i r s t proposed by B l a n d i n g and E l g i n ( 2 ) . Optimum n o z z l e t i p d i a m e t e r s  and d i s p e r s e d phase f l o w r a t e s i n the n o z z l e  t i p s f o r r e p r o d u c i b l e , more o r l e s s u n i f o r m drop s i z e have been suggested by Johnson and B l i s s (3) and l a t e r b y o t h e r s  (U,5,6,7,8).  From about the e a r l y 1930's workers began t o perform  laboratory  s c a l e e x p e r i m e n t s i n a t t e m p t s t o d i s c o v e r s i m p l e laws o r t o f o r m u l a t e c o r r e l a t i o n s w h i c h a p p l i e d t o spray tower o p e r a t i o n  (2,3,9,10,11,12,13)•  T h e i r r e s u l t s i n d i c a t e t h a t the e x t e n t o f e x t r a c t i o n i s dependent upon t h e f l o w r a t e s o f the two phases, the d i r e c t i o n o f s o l u t e t r a n s f e r ( x . e . from d i s p e r s e d phase t o c o n t i n u o u s  phase o r v i c e v e r s a ) , which  phase' i s d i s p e r s e d , drop s i z e , column d i m e n s i o n s , 7  i n l e t solute concentrations.  and sometimes upon  A l l t h e s e workers a n a l y s e d o n l y the  column i n l e t and o u t l e t s o l u t e c o n c e n t r a t i o n s o f each phase. L i c h t and Conway  i n 1 9 5 0 p o i n t e d out t h a t the mass t r a n s f e r  p r o c e s s s h o u l d be c o n s i d e r e d a s t a k i n g p l a c e i n t h r e e s e p a r a t e s t a g e s i ) drop f o r m a t i o n , i i ) drop r i s e , and i i i ) drop c o a l e s c e n c e . and H i x s o n  ( l ) , a l s o i n 1950, r e v o l u t i o n i z e d t e c h n i q u e s  e x p e r i m e n t a t i o n b y t a k i n g samples o f the c o n t i n u o u s o p e r a t i n g column.  T h i s was a c c o m p l i s h e d  Geankoplis  i n spray column  phase from w i t h i n a n  b y l o w e r i n g a hook-shaped  sampling probe, (as shown i n the s k e t c h b e l o w ) i n t o the column and t h e n a p p l y i n g a s l i g h t vacuum t o the upper end o f the probe.  Continuous  phase/was drawn i n t o the probe w i t h o u t e n t r a i n i n g any d i s p e r s e d phase.  y  They o b s e r v e d t h a t t h e b a s i c f l o w p a t t e r n w i t h i n t h e column d i d n o t appear t o be a f f e c t e d b y t h e probe. Hawk (15) sampling  extended G e a n k o p l i s  I n 1951 G e a n k o p l i s , W e l l s and  and H i x s o n ' s work, a g a i n u s i n g an i n t e r n a l  p r o b e , t o measure t h e s o l u t e c o n c e n t r a t i o n p r o f i l e i n t h e  continuous  phase.  i n the continuous Geankoplis  A t y p i c a l experimental  solute concentration  profile  phase i s shown i n F i g u r e 2.  and co-workers n o t i c e d a sharp change, o r e n d - e f f e c t ,  i n s o l u t e concentration i n the continuous  phase a t t h e i n t e r f a c e .  They t h o u g h t " . . . t h a t t h e l o c a t i o n o f t h e end e f f e c t a t t h e c o n t i n u o u s phase i n l e t may be caused b y t h e i n h e r e n t t u r b u l e n c e e f f e c t o f c o a l e s c e n c e o f b u b b l e s a t t h e i n t e r f a c e . . . " (.15)-  They made an a l l o w a n c e  for this  end e f f e c t b y c a l c u l a t i n g a f i c t i t i o u s h e i g h t o f column i n w h i c h t h e r e w o u l d o c c u r t h e same amount o f mass t r a n s f e r a s appeared t o o c c u r a t c:  the i n t e r f a c e .  To c a l c u l a t e s o l u t e c o n c e n t r a t i o n s i n t h e d i s p e r s e d  phase a t v a r i o u s e l e v a t i o n s i n t h e column t h e use o f mass b a l a n c e s was attempted.  On t h e b a s i s t h a t t h e s u p e r f i c i a l f l o w r a t e s o f b o t h phases  5  LU I  to  2 <  O X  §  a  cc tn o z  is o  LU  hD _J O  co  DISTANCE  FROM THE COLUMN  TOP  INTERFACE  FIGURE 2-  OF  THE NOZZLE  TIPS  SOLUTE CONCENTRATION PROFILE I N A SPRAY COLUMN.  are not a f f e c t e d b y s o l u t e c o n c e n t r a t i o n  changes e x p e r i e n c e d i n t h e  column, a m a t e r i a l b a l a n c e on s o l u t e around t h e c o n t r o l zone shown i n Figure  3 r e s u l t e d i n the f o l l o w i n g equation. D  +  L  C°C ~ C C L  C  +  L  D D C  Thus C  D  =  0 I L j <C - ^ C  0  _L  \ +  C  D  1  6  .CONTROL ZONE  FIGURE 3 .  MASS BALANCE OVER A SECTION OF A SPRAY COLUMN.  A l t h o u g h some t u r b u l e n c e was observed i n t h e c o n t i n u o u s phase ( l ) -no a l l o w a n c e f o r i t s e f f e c t was i n c l u d e d i n t h e mass b a l a n c e . c o n t i n u e d h i s work i n v o l v i n g  Geankoplis  c o n t i n u o u s phase s a m p l i n g w i t h Kreager ( l 6 )  and l a t e r w i t h Vogt (17)> M o r e l l o and P o f f e n b e r g e r ( l 8 ) were t h e f i r s t t o suggest  positively  t h a t t h e c o n t i n u o u s phase d i d n o t move t h r o u g h t h e column i n e f f e c t i v e p l u g f l o w , b u t t h a t t h e r e was r e c i r c u l a t i o n w i t h i n t h a t phase.  They  s a i d t h a t t h e r e c i r c u l a t i o n , which was l a t e r t o be c a l l e d b a c k m i x i n g , may be caused by t h e r m a l c u r r e n t s , d e n s i t y d i f f e r e n c e s o r b y t h e f r i c t i o n o f t h e drops c a r r y i n g some o f t h e c o n t i n u o u s phase a l o n g w i t h them.  7  They p o r t r a y e d t h e i d e a d i a g r a m m a t i c a l l y a s shown i n F i g u r e k.  DISPERSED PHASE OUT  CONTINUOUS PHASE IN  CONTINUOUS DISPERSED PHASE IN  PHASE  FIGURE k.  OUT  CONTINUOUS PHASE RECIRCULATION.  I t can be seen t h a t t h e s i m p l e mass b a l a n c e  g i v e n i n E q u a t i o n 1 based  on p l u g f l o w o f b o t h phases i s n o t v a l i d . • '"  A l t h o u g h M o r e l l o and P o f f e n b e r g e r  backmixing,  ( l 8 ) gave a p h y s i c a l p i c t u r e o f  Newman ( 1 9 ) p o i n t e d o u t t h a t the" e n d - e f f e c t w h i c h had been  observed b y e a r l i e r w o r k e r s c o u l d be e x p l a i n e d i n terms o f b a c k m i x i n g of the continuous  phase.  A l s o he p r e s e n t e d  t h e f o l l o w i n g argument t o  show t h a t t h e s o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase a t some p o i n t i n t h e column cannot be c a l c u l a t e d b y a mass b a l a n c e o f t h e column.,. Newman a c c o u n t e d f o r b a c k m i x i n g of c o n t i n u o u s  over s h o r t s e c t i o n s  by considering a f l o w  phase c o u n t e r c u r r e n t t o t h e main f l o w o f c o n t i n u o u s  phase.  T h i s backniixing f l o w was e x a c t l y compensated "by an I n c r e a s e d  main  flow- o f continuous  phase.  f l o w o f continuous  phase was r a d i a l l y homogeneous a t a g i v e n column  elevation.  I t was assumed t h a t t h e r e s u l t i n g main  The p l u g f l o w model and Newman's b a c k m i x i n g model a r e  shown i n t h e f o l l o w i n g s k e t c h .  (b) BACKMIXING. MODEL  (a) PLUG FLOW MODEL  F o r p l u g f l o w o f b o t h phases, as shown i n ( a ) o f t h e above i  c^ i s g i v e n by E q u a t i o n 2.  sketch, '  c^ = L„ ( c - c°) + cj" D _C C C D  F o r /backmixing o f s o l u t e mass b a l a n c e  the continuous over t h e lower L c DD  i  phase, as shown i n (b) above, a s e c t i o n o f column y i e l d s  + ( L + L ) c = L c C B C DD  + L c ° + L c C C B B  Thus C  D  =  L  C  (c  C  " C C  }  +  4  +  .B L  (C  C  "  C  B  )  4 e q u a t i o n t o o b t a i n c^.  F o r t h e same r e a s o n c a p a c i t y c o e f f i c i e n t s and  H.T.U. v a l u e s f o r s h o r t s e c t i o n s o f column cannot be d e r i v e d from t h e knowledge o f t e r m i n a l c o n d i t i o n s and the s o l u t e c o n c e n t r a t i o n p r o f i l e i n the c o n t i n u o u s Campos (20)  phase. c a l c u l a t e d the h e i g h t o f tower i n which t h e r e would  o c c u r t h e same amount o f mass t r a n s f e r as appeared t o have produced e n d - e f f e c t a t t h e c o n t i n u o u s phase i n l e t o f t h e column. t h a t b a c k m i x i n g o f t h e c o n t i n u o u s phase may towers.  the  He n o t e d a l s o  cause e n d - e f f e c t s i n s p r a y  The e x i s t e n c e o f a b a c k m i x i n g stream i n t h e form o f wakes  t r a v e l l i n g w i t h t h e d i s p e r s e d phase drops has been p h o t o g r a p h i c a l l y (21,  22,  demonstrated  23,-24), and L i and Z i e g l e r (25)  say " I n  g e n e r a l t h e p r o c e s s o f b a c k m i x i n g i n s p r a y towers i s b e l i e v e d t o be I n i t i a t e d l a r g e l y i n t h e wakes o f d r o p l e t s " . have worked w i t h s p r a y column heat exchangers.  L e t a n and Kehat (26,  27)  They e x p l a i n c o n t i n u o u s  phase b a c k m i x i n g e f f e c t s by means o f a model i n which c o n t i n u o u s phase i s supposed  t o be c a r r i e d a l o n g i n t h e form o f wakes, w i t h t h e d i s p e r s e d  phase d r o p s .  G i e r and Hougen (28)  used hypodermic  s y r i n g e s t o draw o f f c o n t i n u o u s  phase samples and b e l l - s h a p e d probes t o c o l l e c t d i s p e r s e d phase  samples.  1 0  The accompanying sketch shows an example of each sort of probe used by them-  Probes of each sort were d i s t r i b u t e d along the length of the  column.  It  =3S  A b e l l - p r o b e sample contained both dispersed and continuous phases. The- sample was allowed to reach equilibrium*and then each phase was analysed f o r s o l u t e .  A simple mass balance on solute i n the b e l l -  probe, sample at the times of c o l l e c t i o n and a n a l y s i s r e s u l t s i n Equation 5V c + v " c = V c + Vc D D C C DD CC a  a  Therefore  In order to c a l c u l a t e c^ from Equation 6 an estimate of c^, at the ' e l e v a t i o n of the b e l l - p r o b e , was made from a p l o t of the concentration of solute i n the hypodermic syringe samples versus column height. i . e . no change i n concentration of^either-phase with time.  11  G i e r and Hougen c a l c u l a t e d v a l u e s o f H.T.U., based on c o n c e n t r a t i o n d i f f e r e n c e s i n t h e d i s p e r s e d phase, b y g r a p h i c a l i n t e g r a t i o n u s i n g t h e T h e i r F i g u r e 17 shows t h e s o l u t e  measured c o n c e n t r a t i o n p r o f i l e s .  - c o n c e n t r a t i o n i n t h e d i s p e r s e d phase as d e t e r m i n e d b y means o f • E q u a t i o n 6. f o r one o f t h e i r runs i n w h i c h s o l u t e was t r a n s f e r r e d f r o m the continuous  phase t o t h e d i s p e r s e d phase.  These  concentrations  a r e g r e a t e r t h a n those w h i c h c o u l d be o b t a i n e d f r o m c a l c u l a t i o n b y means o f E q u a t i o n 2 which i s based on p l u g " f l o w o f b o t h phases. r e s u l t i s i n agreement w i t h Newman's s u g g e s t i o n s  ( E q u a t i o n k).  This As a  r e s u l t the. H.T.U. v a l u e s c a l c u l a t e d b y g r a p h i c a l i n t e g r a t i o n were c o r r e s p o n d i n g l y lower t h a n those c a l c u l a t e d from t h e column t e r m i n a l c o n d i t i o n s assuming p l u g f l o w o f b o t h phases.  P a t t o n (29) t o o k samples  f r o m a n o p e r a t i n g spray column u s i n g t h e hypodermic n e e d l e and i n v e r t e d f u n n e l technique the continuous  o f G i e r and Hougen.  He f o u n d a c o n s i d e r a b l e drop i n  phase s o l u t e c o n c e n t r a t i o n a t t h e i n t e r f a c e w h i c h was  not matched b y a p r o p o r t i o n a l drop i n t h e s o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase.  He concluded  that the d i s c o n t i n u i t y i n the solute  c o n c e n t r a t i o n p r o f i l e i n the continuous to b u l k mixing o f the continuous  phase a t t h e i n t e r f a c e was due  phase i n t h e column.  A development• o f t h e s a m p l i n g  technique  of Geankoplis  and coworkers  ( l ) and o f G i e r and Hougen (28) was used b y Ewanchyna and Cavers (30, 3 l ) They made use o f a hook-shaped probe f o r c o n t i n u o u s  phase  and a b e l l - s h a p e d probe f o r d i s p e r s e d phase sampling.  sampling  The probes  were l o w e r e d i n t o t h e o p e r a t i n g column a t t h e ends o f s t a i n l e s s tubes as shown i n F i g u r e 5*  steel  Samples were drawn i n t o t h e probes and  12  FIGURE 5« HOOK AND BELL-PROBES  and a l o n g t h e sample lih.estoythe use o f a water a s p i r a t o r . a c i d was t r a n s f e r r e d between an aqueous continuous i s o b u t y l ketone (MIBK) d i s p e r s e d phase.  Acetic  phase and a methyl  The aqueous phase was  s a t u r a t e d w i t h MIBK and the MIBK phase s a t u r a t e d w i t h water.  The  "solute c o n c e n t r a t i o n p r o f i l e i n each phase was measured a t v a r i o u s combinations o f phase f l o w r a t e s .  P l o t s were made showing the dependenc  of c a p a c i t y c o e f f i c i e n t s on f l o w r a t e s and a l s o o f H.T.U. v a l u e s on flowrates.  The causes o f end e f f e c t s i n spray columns were e x p l a i n e d  c l e a r l y and v e r i f i e d  experimentally.  The measured c o n c e n t r a t i o n p r o f i l e s f o r a t y p i c a l r u n w i t h s o l u t e b e i n g t r a n s f e r r e d from t h e continuous  aqueous phase t o the-  d i s p e r s e d MIBK phase a r e shown i n F i g u r e 6.  The l i n e s FB and GE  are t h e measured c o n c e n t r a t i o n p r o f i l e s f o r t h e d i s p e r s e d phase andthe continuous  phase r e s p e c t i v e l y .  took p l a c e i n t h e d i s p e r s e d phase.  I t was assumed t h a t no backmixing T h i s assumption was based on the  v i s u a l o b s e r v a t i o n t h a t the drops appeared t o r i s e up t h e column without  c i r c u l a t i n g back on t h e i r paths (28, 30, 3 l ) -  assumed i n a d d i t i o n t h a t no b a c k m i x i n g takes phase then E q u a t i o n  I f i"t i s  p l a c e i n t h e continuous  2, which i s based on p l u g f l o w o f b o t h phases,  can be used t o c a l c u l a t e t h e l i n e GD.  When t h e drops o f d i s p e r s e d  phase a r r i v e a t t h e i n t e r f a c e they do not c o a l e s c e immediately b u t remain as p a r t o f a drop l a y e r t h e r e . takes  Undoubtedly mass t r a n s f e r  p l a c e i n t o these drops d u r i n g t h e i r s o j o u r n a t the i n t e r f a c e .  Ewanchyna  and Cavers a t t r i b u t e d t h e c o n c e n t r a t i o n jumps BA ( i n the  d i s p e r s e d phase) and CD t o t h i s i n t e r f a c e mass t r a n s f e r .  Ik  CONTINUOUS  Cr  5*PRASE u  z g  CONTINUOUS PHASE OUTLET  DISPERSED PHASE OUTLET  i—  < a:  o z o  INLET  DISPERSED P H A S E INLET"  o  INTERFACE  NOZZLE  UJ  h-  HEIGHT  -I  o  UP  COLUMN  CO  FIGURE 6.  CONCENTRATION PROFILES IN A SPRAY COLUMN.  They a t t r i b u t e d the change DE t o a x i a l m i x i n g o f the c o n t i n u o u s phase.  The l i n e GH i s the c o n c e n t r a t i o n  p r o f i l e which would be  expected f o r p e r f e c t m i x i n g o f t h a t phase under c o n d i t i o n s the  solute concentration  such t h a t  i n the aqueous stream l e a v i n g the column  was t h a t given by p o i n t G. phase s o l u t e c o n c e n t r a t i o n  I t can be seen t h a t the measured aqueous profile  (GE) l i e s between t h a t  f o r p e r f e c t m i x i n g (GH) and t h a t f o r t r u e c o u n t e r c u r r e n t  expected f l o w (GD).  E v i d e n t l y the continuous phase does undergo some a x i a l m i x i n g .  15  • Ewanchyna and Cavers (30,  31)  found t h a t the r e s u l t s o f r u n s  w i t h s o l u t e t r a n s f e r r e d from t h e d i s p e r s e d phase t o t h e phase s u p p o r t e d . t h e above i d e a s . -continuous (31,  32,  With solute t r a n s f e r r e d t o the  phase drops c o a l e s c e i m m e d i a t e l y  33,  3^)-  continuous  on r e a c h i n g t h e i n t e r f a c e  As a r e s u l t t h e r e was n e g l i g i b l e mass t r a n s f e r  a t t h e i n t e r f a c e and hence no jump i n the d i s p e r s e d phase c o n c e n t r a t i o n p r o f i l e there.  FIGURE 7.  The r e s u l t s o f a t y p i c a l r u n a r e shown i n F i g u r e 7-  CONCENTRATION PROFILES I N A SPRAY COLUMN.  16  The whole o f t h e s o l u t e c o n c e n t r a t i o n change (DE) i n t h e  continuous  phase a t t h e i n t e r f a c e was a t t r i b u t e d t o b a c k m i x i n g o f t h e  continuous  phase i n t h e column.  Choudhury (35)  c o n t i n u e d Ewanchyna's work.  backmixing of the continuous f o r (H.T.U.)  Qvera  u_  To a l l o w f o r  phase i n t h e d e r i v a t i o n o f an e x p r e s s i o n  v a l u e s , b a s e d on a l o g a r i t h m i c mean d i s p e r s e d  phase c o n c e n t r a t i o n d r i v i n g f o r c e , he i n t r o d u c e d a c o r r e c t i o n f a c t o r , F , as P r a t t (36)  had done f o r packed  towers.  The q u e s t i o n was r a i s e d as t o whether t h e s o l u t e c o n c e n t r a t i o n i n the continuous  phase e n t e r i n g t h e b e l l - p r o b e w i t h t h e d r o p s was  the same a s t h a t e n t e r i n g t h e hook-probe.  I t was thought t h a t t h e  b e l l - p r o b e might sample p r e f e r e n t i a l l y c o n t i n u o u s the immediate v i c i n i t y o f t h e d r o p s .  phase w h i c h was i n  J f t h i s continuous  phase were  not o f t h e same s o l u t e c o n c e n t r a t i o n as t h a t i n t h e main b u l k o f t h e continuous  phase t h e use i n E q u a t i o n 6 o f c^ f r o m a hook-probe sample  i n o r d e r t o c a l c u l a t e c^ i n a b e l l - p r o b e sample would be  (37)  invalid.  I n o r d e r t o t e s t t h e hook and b e l l s a m p l i n g  technique  designed  A sketch of t h i s  and c o n s t r u c t e d a p i s t o n sampler.  d e v i c e i s shown i n F i g u r e 8.  Hawrelak  By moving t h e p i s t o n from one s i d e o f  the p i s t o n b l o c k t o t h e o t h e r i t was p o s s i b l e t o remove a b u l k sample o f b o t h phases f r o m t h e column and a l l o w t h e column t o c o n t i n u e operating.  W i t h t h i s d e v i c e Hawrelak (37),  and l a t e r B e r g e r o n  (38);  17  BELL- PROBE-* COLJM N—  -HOOK-PROBE  A,  "ESS  PISTON BLOCK PISTON  FIGURE 8.  compared  PISTON'SAMPLER.  solute concentrations  i n t h e d i s p e r s e d phase c a l c u l a t e d  u s i n g t h e h e l l and . hook-probes w i t h those c a l c u l a t e d from r e s u l t s u s i n g t h e p i s t o n sampler and t h e hook-probe. assume t h a t t h e hook-probe  I t was n e c e s s a r y t o  sample was r e p r e s e n t a t i v e o f t h e c o n t i n u o u s  phase i n t h e column a t t h e sampling h e i g h t .  However, no d e f i n i t e  c o n c l u s i o n s were drawn, m a i n l y because t h e column was r u n under such c o n d i t i o n s t h a t t h e two phases were near e q u i l i b r i u m a t t h e sampling elevation.  Rocchini  ( 3 9 , ^ 0 ) s t u d i e d drop shape and measured drop s i z e  d i s t r i b u t i o n s i n a spray column by examining c l o s e - u p photographs taken o f an o p e r a t i n g  column.  18  Dispersed  phase hold-ups i n s p r a y towers have been c a l c u l a t e d  l a r g e l y from E q u a t i o n 7  (3)-  h = 100 u  However, Weaver, L a p i d u s and E l g i n (hi)  d e t e r m i n e d hold-ups by  I s o l a t i n g a s e c t i o n o f column between two q u i c k - a c t i n g b a l l  valves  arid m e a s u r i n g t h e volume o f each phase c o l l e c t e d .  (37)  Hawrelak  and B e r g e r o n (38) measured d i s p e r s e d phase h o l d - u p s , w i t h o u t d i s r u p t i n g t h e column o p e r a t i o n , w i t h t h e - a i d o f a. p i s t o n sampler described e a r l i e r .  I t has been found (3, 3 0 , ' 35 > 42) t h a t t h e  d i s p e r s e d phase hold-up  i n c r e a s e s .only s l i g h t l y w i t h i n c r e a s i n g  c o n t i n u o u s phase f l o w r a t e and i s n e a r l y l i n e a r l y dependent  on t h e  d i s p e r s e d phase f l o w r a t e . Hayworth and T r e y b a l (h)  and Johnson and B l i s s (3) have  o b s e r v e d t h a t t h e l e n g t h o f a j e t o f d i s p e r s e d phase l e a v i n g a n o z z l e t i p i n c r e a s e s t o a maximum and t h e n d e c r e a s e s a s t h e f l o w r a t e o f d i s p e r s e d phase i n c r e a s e s .  They n o t i c e d t h a t t h e s i z e o f t h e  drops formed a t t h e ends o f t h e j e t s o f d i s p e r s e d phase a l s o i n c r e a s e s t o a maximum w i t h i n c r e a s i n g d i s p e r s e d phase f l o w r a t e .  However, t h e  d i s p e r s e d phase f l o w r a t e a t w h i c h t h e maximum drop s i z e o c c u r s i s l o w e r t h a n t h a t a t which t h e maximum j e t l e n g t h o c c u r s .  The c l a i m  was made t h a t u n i f o r m l y s i z e d drops a r e produced a t d i s p e r s e d f l o w r a t e s l o w e r t h a n t h o s e which g i v e t h e maximum drop s i z e .  phase The  f o r m a t i o n o f many s m a l l drops a l o n g w i t h l a r g e r drops has been  19  observed under some o p e r a t i n g c o n d i t i o n s , (h, and E l g i n  k'S)'.  (hi) found no n o t i c e a b l e change i n drop  a l o n g the l e n g t h o f a spray column.  Weaver, L a p i d u s , size  distribution  G a r w i n a n d Smith (U3) r e p o r t  t h a t t h e d i s p e r s e d phase drop s i z e i s independent  o f t h e continuous  phase f l o w r a t e .  2..... MATHEMATICAL • MODELS  In to  order to describe f u l l y a turbulent f i e l d i t i s necessary  know t h e v e l o c i t y v e c t o r a t a l l p o i n t s . a n d a t a l l t i m e s .  such knowledge i s u n a v a i l a b l e . of  Therefore, a measurement o f some e f f e c t  t h e t u r b u l e n c e u s u a l l y i s made i n o r d e r t o c h a r a c t e r i z e the e x t e n t  Of t h e t u r b u l e n c e .  Even when the f l o w p a t t e r n s i n t h e t u r b u l e n t  f i e l d a r e o f a complicated, nature a simple mathematical adequately d e s c r i b e s the mixing t a k i n g place. of  However,  f l o w r e a c t o r s has been based  model o f t e n  I n the past the d e s i g n  l a r g e l y upon two i d e a l i z e d models:  p l u g f l o w , and c o m p l e t e l y mixed f l o w .  P l u g f l o w assumes a f l a t  v e l o c i t y p r o f i l e , whereas c o m p l e t e l y mixed f l o w assumes t h a t the fluid  i n t h e v e s s e l i s p e r f e c t l y mixed.  The t h r e e most p o p u l a r  models which l i e between t h e two extreme c a s e s a r e the d i s p e r s i o n , mixing c e l l , and random walk models.  F o r t h e case of f l u i d  through a l o n g column o r bed t h e mathematical t h r e e models a r e e s s e n t i a l l y the same (hk, are'fundamental  implications of a l l  4 5 , 46).  d i f f e r e n c e s between t h e premises  models a r e based.  flow  However, t h e r e  upon which t h e  B r i e f o u t l i n e s o f t h e s e models a r e p r e s e n t e d  below t o g e t h e r w i t h summaries.of some o f the more important  researches  2.0  which have u t i l i z e d m i x i n g of o n l y one  them, f o r i n t e r p r e t i n g ' e x p e r i m e n t a l d a t a . phase i s c o n s i d e r e d i n each  Axial  case.  DISPERSION MODEL  I t i s assumed t h a t a x i a l m i x i n g due law s i m i l a r t o F i c k ' s Law  to turbulence follows a  f o r molecular d i f f u s i o n .  On t h i s b a s i s  a mass b a l a n c e on s o l u t e i n the continuous phase over an i n c r e m e n t a l s e c t i o n o f column y i e l d s E q u a t i o n 8 f o r the case o f no mass t r a n s f e r to  o r from the continuous phase. Ee i c  c  - L  z^  c 0  ( A l s o see Appendix  c  c  =  e^c  1.)  c  2>t  oz  8 I t i s assumed t h a t r a d i a l homogeneity p r e v a i l s .  Wilson  s o l v e d an e q u a t i o n s i m i l a r t o E q u a t i o n 8 f o r m o l e c u l a r of  heat from a p o i n t source i n t o a f l o w i n g f l u i d .  In  1949  B e r n a r d and Wilhelm  eddy d i f f u s i v i t i e s  G i l l i l a n d and Mason (52)  to  to  (51)  i n packed  of used  columns.  a p p l i e d the model t o the  steady state, o p e r a t i o n o f a n . . , a l r - f l u i d i z e d bed.' i s independent  50)  solution  i n open d u c t s on the assumption  I s o t r o p i c homogeneous t u r b u l e n c e . a s i m i l a r method t o determine  diffusion  Wilson's  has been used t o g e t h e r w i t h e x p e r i m e n t a l d a t a (4'8, 49, c a l c u l a t e eddy d i f f u s i v i t i e s  (47)  A t steady s t a t e c^  o f t and E q u a t i o n 8 can be i n t e g r a t e d  (Appendix  l)  give Ee  dCp  = L^Cp - • J  dz  9  21  where t h e c o n s t a n t o f i n t e g r a t i o n , J , i s t h e net f l u x o f s o l u t e down t h e column.  I f t h e t e s t s e c t i o n i s , from the v i e w p o i n t o f  the c o n t i n u o u s phase, upstream f r o m t h e f e e d p o i n t o f t r a c e r ,  then  J = 0 and E q u a t i o n 9 y i e l d s E q u a t i o n 10 on  In  (c  c  )  integration.  _ L^f. " Ee  G i l l i l a n d and Mason (52,  53)  10  .  i n j e c t e d a t r a c e r gas a t a  constant  r a t e i n t o t h e bed and measured t r a c e r c o n c e n t r a t i o n s a t v a r i o u s p o i n t s i n the bed below t h e l e v e l o f t r a c e r i n j e c t i o n .  From the  s l o p e o f a p l o t o f I n ( c ^ ) v e r s u s z t h e y were a b l e t o c a l c u l a t e t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y ,  (eE).  The above method f o r  e s t i m a t i n g a x i a l eddy d i f f u s i v i t i e s cannot be u t i l i z e d f o r t h e cases o f s i n g l e phase o r c o - c u r r e n t f l o w s because t h e p r o c e s s  of  a x i a l m i x i n g would n o t , i n t h i s c a s e , c a r r y t h e t r a c e r upstream i n t h e c o n t i n u o u s phase w i t h r e s p e c t t o t h e t r a c e r i n j e c t i o n p o i n t . The model has been a p p l i e d s u b s e q u e n t l y s i e v e - p l a t e e x t r a c t i o n columns (5^, v e s s e l s (56),  t o t h e study o f p u l s e d  55),  gas-sparged  r o t a t i n g - d i s k c o n t a c t o r s (57,  f l u i d i z e d bed c a t a l y s t r e g e n e r a t o r s  Continuous  58);  a n  d  tubular commercial  (59)*  phase a x i a l eddy d i f f u s i v i t i e s  have been  determined  m o s t l y by c o n s i d e r i n g the e f f e c t downstream, w i t h r e s p e c t t o t h e c o n t i n u o u s phase, o f an u n s t e a d y s t a t e i n j e c t i o n o f t r a c e r .  Equation  8 has been s o l v e d f o r i n j e c t i o n o f t r a c e r a c c o r d i n g t o a D i r a c  22  D e l t a F u n c t i o n o r s i n g l e p u l s e , a s t e p f u n c t i o n , and a s i n u s o i d a l function.  These t h r e e d i f f e r e n t methods o f t r a c e r i n j e c t i o n a r e  d i s c u s s e d b r i e f l y below.  Dirac Delta Function  W i t h no a x i a l m i x i n g a transverse-homogeneous s i n g l e p u l s e o f t r a c e r i n j e c t e d i n t o a moving s t r e a m would appear downstream as a s i n g l e pulse a t a l l times.  W i t h some a x i a l m i x i n g ,  spreading  w i t h r e s p e c t t o d i s t a n c e w i t h i n t h e column o f t h e t r a c e r p u l s e results.  Panckwerts (60) and L e v e n s p i e l and S m i t h ( 6 l ) showed how  t o i n t e r p r e t t h e p l o t o f t r a c e r c o n c e n t r a t i o n v e r s u s t i m e f o r some p o i n t downstream from t h e p l a c e o f t r a c e r i n j e c t i o n .  Such a p l o t  i s c a l l e d a C-curve (60) and t h e second moment o r v a r i a n c e o f t h i s curve i s r e l a t e d t o t h e a x i a l eddy d i f f u s i v i t y .  A x i a l eddy d i f f u s -  i v i t i e s have been d e t e r m i n e d by t h e D i r a c D e l t a F u n c t i o n  method  f o r packed columns (62, 63, 64), p u l s e d s i e v e - p l a t e columns (54, 55/ 100), c o i l e d t u b e r e a c t o r s (66), and l i q u i d - f l u i d i z e d beds (67). Van d e r Laan (68) showed how t o d e t e r m i n e t h e a x i a l eddy d i f f u s i v i t y from t h e v a r i a n c e o f a C-curve f o r a f i n i t e l e n g t h o f v e s s e l b y u s i n g t h e a p p r o p r i a t e boundary c o n d i t i o n s (60, 69)-  A r i s (70)  p o i n t e d out t h a t i t i s I m p o s s i b l e t o i n j e c t a p e r f e c t p u l s e o f t r a c e r i n t o a column. necessary  A l s o he showed, however, t h a t i t i s n o t  f o r t h e t r a c e r i n j e c t i o n t o be i n t h e f o r m o f a p e r f e c t  p u l s e i f one t a k e s t h e d i f f e r e n c e o f t h e second moments o f t h e C-curves measured a t two d i f f e r e n t p o i n t s i n t h e column,  Aris'  1  t h e o r y was l a t e r c o r r e c t e d by B i s c h o f f ( 7 l ) L e v e n s p i e l (72,  73),  who, t o g e t h e r w i t h  presented the theory i n d e t a i l .  A x i a l eddy  d i f f u s i v i t i e s i n l i q u i d - l i q u i d s p r a y columns a t f l o o d i n g c o n d i t i o n s (74),  i n packed beds (75),  and i n o r i f i c e p l a t e g a s - l i q u i d r e a c t o r s  (76) have been d e t e r m i n e d by  taking  the d i f f e r e n c e of the variances  of C-curves.  Step F u n c t i o n A s t e p f u n c t i o n o f t r a c e r can be i n t r o d u c e d i n t o a column by suddenly s t o p p i n g o r s t a r t i n g t h e f l o w o f t r a c e r .  A p l o t o f down-  stream t r a c e r c o n c e n t r a t i o n v e r s u s t i m e i s c a l l e d an F-curve o r b r e a k t h r o u g h curve..  (60)  The g r a d i e n t o f t h e F-curve a t a p a r t i c u l a r  v a l u e on t h e t i m e a x i s i s r e l a t e d t o t h e a x i a l eddy d i f f u s i v i t y . G i l l i l a n d and Mason (53) i n 1952,  examined an F-curve f o r a f l u i d i z e d bed  b u t a t t h a t t i m e a t h e o r e t i c a l a n a l y s i s o f such a c u r v e  had n o t been d e v e l o p e d .  I n 1953  Danckwerts (60)  showed how t o  c a l c u l a t e t h e a x i a l eddy d i f f u s i v i t y f r o m an e x p e r i m e n t a l F - c u r v e . A x i a l eddy d i f f u s i v i t i e s have been d e t e r m i n e d from b r e a k t h r o u g h c u r v e s f o r packed beds ( 4 6 , 60,  77,  78,  79,  80, 8 l , 82),  columns ( 4 2 ) , and r o t a t i n g d i s k c o n t a c t o r s (83).  spray  B r u t v a n (84)  d e t e r m i n e d a x i a l eddy d i f f u s i v i t i e s from b r e a k t h r o u g h c u r v e s i n a s p r a y column where t h e " d i s p e r s e d phase was s o l i d s p h e r e s .  A  s t a t i s t i c a l a n a l y s i s o f e x p e r i m e n t a l b r e a k t h r o u g h c u r v e s has been d i s c u s s e d by K l i n k e n b e r g (85).  l e v e n s p i e l and B i s c h o f f  (73)  i n d i c a t e d how t o e l i m i n a t e t h e e f f e c t on t h e F-curve o f t h e p a r t i c u l a r method o f t r a c e r i n j e c t i o n used.  The procedure i n v o l v e d  t a k i n g measurements a t two e l e v a t i o n s i n a column.  M i l l e r and  2k  K i n g (86) examined the s l o p e s o f F - c u r v e s measured a t two  axial  d i s t a n c e s i n a packed bed t o c a l c u l a t e a x i a l eddy d i f f u s i v i t i e s . I t s h o u l d be n o t e d t h a t the F-curve i s the time i n t e g r a l o f the C-curve (79)-  T h i s f a c t has been demonstrated e x p e r i m e n t a l l y  (87).  Sinusoidal Function Under t h e i n f l u e n c e of a x i a l m i x i n g i n a column a s i n u s o i d a l f u n c t i o n o f t r a c e r c o n c e n t r a t i o n s u f f e r s b o t h a t t e n u a t i o n and lag.  phase  L e v e n s p i e l and B i s c h o f f (73) d e r i v e d e q u a t i o n s r e l a t i n g the  P e c l e t number t o the a t t e n u a t i o n and phase l a g o f a s i n u s o i d a l i n p u t of t r a c e r .  The  s i n u s o i d a l input or frequency  r e s p o n s e method  has been used t o d e t e r m i n e P e c l e t numbers f o r gas f l o w and f l o w t h r o u g h random and o r d e r e d packed beds (63, 88, 92, 93, 9k,  104).  Ebach and White (63)  showed how  liquid  89, 90,  to  91*  evaluate  r e s u l t s f o r p e r i o d i c t r a c e r i n p u t f u n c t i o n s w h i c h are n o t s i n u s o i d a l .  I n l i q u i d - l i q u i d e x t r a c t i o n columns two phase f l o w w i t h mass t r a n s f e r i s e n c o u n t e r e d .  The  countercurrent  performance o f such  columns has been p r e d i c t e d on the b a s i s o f E q u a t i o n 8 m o d i f i e d i n c l u d e a mass t r a n s f e r term (95>  96, 91,  to  98) as shown b e l o w  I-l T h e o r e t i c a l c o n c e n t r a t i o n p r o f i l e s i n e x t r a c t i o n columns have been c a l c u l a t e d f o r v a r i o u s o p e r a t i n g c o n d i t i o n s (99, 100,  101,  102,  103).  25  Theoretical concentration  p r o f i l e s . h a v e been compared w i t h  mental p r o f i l e s f o r various l i q u i d - l i q u i d e x t r a c t i o n Agreement was good f o r p u l s e d  experi-  devices.  columns (58, 102) and moderately-  good f o r some c o n d i t i o n s o f s p r a y column o p e r a t i o n gas a b s o r p t i o n - t o w e r o p e r a t i o n s  (103) and f o r  (105).  G o t t s c h l i c h (106) a p p l i e d E q u a t i o n 8 t o a packed column. I n d o i n g so he m o d i f i e d  the equation t o take i n t o account stagnant  l a y e r s o f f l u i d around t h e p a c k i n g e l e m e n t s .  He r e p o r t s t h a t t h e  m o d i f i c a t i o n improves t h e agreement o f e x p e r i m e n t a l r e s u l t s and t h e t h e o r e t i c a l model.  (107)  Van Deemter, Zuiderweg, and K l i n k e n b e r g  used t h e d i s p e r s i o n model t o c o r r e c t f o r n o n - i d e a l i t y i n chroma t o g r a p h y due .to a x i a l d i s p e r s i o n .  MIXING CELL MODEL Kramers and A l b e r d a (90) drew an a n a l o g y between s i n g l e phase f l o w i n a packed b e d and a s e r i e s o f p e r f e c t m i x i n g v e s s e l s . They assumed a l o n g b e d %nd r e s t r i c t e d t h e magnitude o f t h e p a r t i c l e P e c l e t number.  On t h e s e b a s e s t h e y showed t h a t t h e d i s p e r s i o n  model and m i x i n g c e l l model y i e l d t h e same f r e q u e n c y r e s p o n s e diagram f o r a s i n u s o i d a l l y v a r y i n g t r a c e r i n p u t . (kk, for  Other w o r k e r s  6h, 92, 108, 109) have f o l l o w e d Kramers and A l b e r d a ' s approach s i n g l e phase f l o w .  I t has been shown t h a t f o r t h e a n a l o g y t o  be v a l i d t h e P e c l e t number', Pe', must be g i v e n by E q u a t i o n  11,  Pe'- = 2 1  J  11  where )v i s t h e r a t i o o f t h e l e n g t h o f a m i x i n g c e l l , c L , t o t h e c h a r a c t e r i s t i c p a c k i n g d i m e n s i o n , d (See Appendix I I . ) P  In a  packed b e d t h e a x i a l d i s t a n c e between l a y e r s o f p a c k i n g i s t a k e n t o be e q u a l t o t h e h e i g h t o f a m i x i n g c e l l . A r i s and Amundson (108) and Jacques and Vermeulen ( 4 6 ) used t h e P o i s s o n p r o b a b i l i t y d i s t r i b u t i o n f u n c t i o n t o d e s c r i b e t h e r e s i d e n c e t i m e d i s t r i b u t i o n o f a t r a c e r m o l e c u l e on t h e b a s i s o f t h e m i x i n g c e l l model. E p s t e i n ( H O ) has developed  charts f o r a correction factor  which m o d i f i e s l o g mean d r i v i n g f o r c e s f o r s i n g l e phase f l o w i n packed beds.  The model i s based on t h e a n a l o g y between a f i x e d  bed o f p a r t i c l e s and a s e r i e s o f p e r f e c t m i x e r s . T h e o r e t i c a l arguments have been p r e s e n t e d r e l a t i n g t h e d i s p e r s i o n model t o a s e r i e s o f p e r f e c t m i x i n g c e l l s w i t h b a c k f l o w between m i x e r s (45, 100, 111, 112, 113).  L i and Z i e g l e r (25)  r e c e n t l y have p u b l i s h e d a r e v i e w o f t h e e x p e r i m e n t a l and t h e o r e t i c a l work done on t h e a p p l i c a t i o n o f t h e d i s p e r s i o n and t h e m i x i n g c e l l models t o spray and packed t o w e r s . RANDOM WALK MODEL The t h e o r y f o r t h e random w a l k model i s b a s e d on E i n s t e i n ' s s t a t i s t i c a l treatment  (115).  S m a l l p a c k e t s o f f l u i d a r e assumed  t o move i n an i n t e r m i t t e n t f a s h i o n , t h e m o t i o n b e i n g over a  d i s t a n c e , and l a s t i n g f o r a l e n g t h o f t i m e , b o t h o f w h i c h a r e t a k e n t o be p u r e l y random q u a n t i t i e s .  J a c q u e s and Vermeulen  (46)  show t h a t t h e random w a l k model, t h e m i x i n g c e l l model, and t h e d i s p e r s i o n model r e s u l t i n t h e same m a t h e m a t i c a l e q u a t i o n f o r r e s i d e n c e time d i s t r i b u t i o n s .  A x i a l eddy d i f f u s i v i t i e s f o r  packed beds have been d e t e r m i n e d u s i n g t h e random w a l k model and i n p u t o f t r a c e r a c c o r d i n g t o a s t e p f u n c t i o n (46,  116, 117).  OBJECT OF THIS RESEARCH In I963 G e r s t e r (127) summarized t h e work w h i c h had been done on t h e e f f e c t o f a x i a l m i x i n g upon t h e performance o f e x t r a c t i o n columns.  He s u g g e s t e d t h a t much f u r t h e r work i n t h e  f i e l d o f a x i a l eddy d i f f u s i o n was needed. P r e v i o u s work t o d e t e r m i n e a x i a l eddy d i f f u s i v i t i e s i n spray columns has been c a r r i e d out by H a z l e b e c k and G e a n k o p l i s (42) and  by B r u t v a n (84).  The f o r m e r i n v e s t i g a t i o n i n v o l v e d t h e use  of w a t e r as t h e aqueous phase and MIBK as t h e d i s p e r s e d phase i n a l - ^ - i n . I.D. column.  Only one s e t o f n o z z l e t i p s , w h i c h produced  drops o f about 0.135-in. d i a m e t e r , was used t h r o u g h o u t t h e work. The s t e p f u n c t i o n i n p u t a p p l i c a t i o n o f t h e d i s p e r s i o n model was used a s d e s c r i b e d e a r l i e r * to  "The a x i a l <eddy d i f f u s i v i t y was'found  2  2  i n c r e a s e l i n e a r l y between 1 2 - f t . / h r . and 22«ft./hr- f o r  c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t i e s between l O - f t . / h r . f t .  3 and  2  45-ft'./hr. f t . r e s p e c t i v e l y .  F o r a g i v e n c o n t i n u o u s phase  s u p e r f i c i a l v e l o c i t y t h e a x i a l eddy d i f f u s i v i t y was c o n s t a n t f o r d i s p e n s e d phase s u p e r f i c i a l v e l o c i t i e s between 1 8 . 4 - f t . / h r . f t and 5 0 - f t . / h r . f t . B r u t v a n performed e x p e r i m e n t s I n 1 - i n . , l§--in. and 2 - i n . I.D. columns w i t h w a t e r as t h e c o n t i n u o u s phase and g l a s s beads, o f d i a m e t e r s 3, 4, 5, and 6-mm. t h e d i s p e r s e d phase.  r e s p e c t i v e l y , as  He, a l s o , used t h e s t e p f u n c t i o n i n p u t  a p p l i c a t i o n o f t h e d i s p e r s i o n model.  V a r i o u s d i s p e r s e d phase o  p  o  p  s u p e r f i c i a l v e l o c i t i e s between l O - f t ' / h r . f t . and 1 0 0 - f t r / h r . f t . and c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t i e s between l 4 o - f t . / h r . f t o  .  and 7 8 0 - f t . / h r .  g  f t . were s t u d i e d .  He found t h a t t h e a x i a l eddy  d i f f u s i v i t y i n c r e a s e d w i t h i n c r e a s i n g column d i a m e t e r , i n c r e a s i n g d i s p e r s e d phase f l o w r a t e , d e c r e a s i n g c o n t i n u o u s phase f l o w r a t e and d e c r e a s i n g d i s p e r s e d phase p a r t i c l e s i z e .  Both the i n v e s t i -  g a t i o n s o f H a z l e b e c k and G e a n k o p l i s and o f B r u t v a n d i d n o t t a k e i n t o account t h e problems a s s o c i a t e d w i t h t h e p r o d u c t i o n o f a p e r f e c t s t e p f u n c t i o n as mentioned e a r l i e r .  No work has been  r e p o r t e d where a x i a l eddy d i f f u s i v i t i e s i n s p r a y columns were d e t e r m i n e d by means o f t h e s t e a d y s t a t e a p p l i c a t i o n o f t h e d i s p e r s i o n model. A c c o r d i n g l y , t h e o b j e c t o f t h e p r e s e n t work was t o measure a x i a l eddy d i f f u s i v i t i e s i n an o p e r a t i n g l i q u i d - l i q u i d s p r a y column.  The s t e a d y s t a t e form o f t h e d i s p e r s i o n model was used  i n t h e s e i n v e s t i g a t i o n s . S i n c e l i t t l e was known o f t h e e f f e c t o f v a r i o u s o p e r a t i n g parameters  on eddy d i f f u s i v i t y i t was  d e c i d e d t h a t t h e e f f e c t s o f f l o w r a t e s o f t h e two phases,  column  l e n g t h , and column d i a m e t e r on t h e a x i a l eddy d i f f u s i v i t y s h o u l d he i n v e s t i g a t e d ,  A minor o b j e c t i v e i n t h e form o f a p r e l i m i n a r y  study was t o f i n d s u i t a b l e methods: f o r s a m p l i n g t h e c o n t i n u o u s and d i s p e r s e d phases o f an o p e r a t i n g s p r a y column.  30  THEORY  APPLICATION OF THE DISPERSION MODEL TO. RUNS WITH NO MASS TRANSFER I n t h e p r e s e n t work t h e d i s p e r s i o n model d e s c r i b e d i n t h e I n t r o d u c t i o n was used.  The g e n e r a l a s s u m p t i o n s upon w h i c h t h i s  model i s b a s e d a r e l i s t e d below. 1.  B a c k m i x i n g o f t h e c o n t i n u o u s phase can.be r e p r e s e n t e d b y F i c k ' s Second Law o f D i f f u s i o n w i t h a c o n s t a n t a x i a l eddy d i f f u s i v i t y t h r o u g h o u t t h e column.  2.  The m o l e c u l a r d i f f u s i v i t y o f any s o l u t e c o n s i d e r e d i s n e g l i g i b l e compared t o t h e a x i a l eddy d i f f u s i v i t y .  3-  R a d i a l homogeneity p r e v a i l s ' a t c o n s t a n t a x i a l  4.  The v e l o c i t y p r o f i l e i n t h e c o n t i n u o u s phase i s f l a t .  5«  V o l u m e t r i c f l o w r a t e s a r e c o n s t a n t t h r o u g h o u t t h e column.  6.  A t e s t s e c t i o n o f column i s c o n s i d e r e d i n w h i c h no hydrodynamic  position.  p r o p e r t y i s a f f e c t e d by t h e column t e r m i n a l c o n d i t i o n s . 7.  There i s no b a c k m i x i n g o f t h e d i s p e r s e d phase.  D e t e r m i n a t i o n o f A x i a l Eddy D i f f u s i v i t i e s I n a d d i t i o n t o t h e above a s s u m p t i o n s t h e f o l l o w i n g a s s u m p t i o n s were made f o r d e t e r m i n i n g a x i a l eddy d i f f u s i v i t i e s . 1.  The a x i a l eddy d i f f u s i v i t y i n t h e c o n t i n u o u s phase i s n o t  31  a f f e c t e d by t h e c h e m i c a l n a t u r e o f the s o l u t e . 2.  The  s o l u t e d i s s o l v e s o n l y i n t h e c o n t i n u o u s phase,  The t h e o r y i s developed f o r a t e s t s e c t i o n o f column which l i e s , from t h e v i e w p o i n t o f the c o n t i n u o u s phase, upstream from the p o i n t of i n j e c t i o n of t r a c e r .  The downstream f l o w o f t r a c e r  due t o b u l k f l o w o f the c o n t i n u o u s phase i s equated  t o the b a c k f l o w  o f t r a c e r by a x i a l eddy d i f f u s i o n t o g i v e L  c  c  c  = Ee  dc  c  cTz-  12 E - i s t h e a x i a l eddy d i f f u s i v i t y and eddy d i f f u s i v i t y . a t steady s t a t e .  (Ee) i s the s u p e r f i c i a l a x i a l  O b v i o u s l y E q u a t i o n 12  r e s u l t s from E q u a t i o n 8  As mentioned e a r l i e r , a l s o , t h e s o l u t i o n o f  E q u a t i o n 12 i s L  (c )  z = In Ee  where c  CO  CO  i s the value of c  E q u a t i o n 13  C  a t z = 0.  t h a t a p l o t of In c  13 I t can be seen f r o m  v e r s u s z has a s l o p e o f L  0  C  Ee"  i f the model h o l d s good.  D e r i v a t i o n s o f E q u a t i o n s 12  and 13  are  g i v e n i n Appendix I .  P r e d i c t i o n of P e c l e t Number by the M i x i n g C e l l  Analogy  As mentioned i n t h e I n t r o d u c t i o n t h e a n a l o g y between s i n g l e  32  phase f l o w through a packed bed and through a s e r i e s o f p e r f e c t mixers r e s u l t s i n the f o l l o w i n g l i m i t a t i o n on the p a r t i c l e  Peclet  Number, Pe'. (See Appendix I I . ) Pe'- =  2  J  where  >=^ d  P  where d^_ i s the d i s t a n c e between l a y e r s o f p a c k i n g p i e c e s .  I t i s suggested t h a t the above analogy can be extended  to  spray column o p e r a t i o n by a l l o w i n g the c o - o r d i n a t e axes o f r e f e r e n c e t o move a t the same v e l o c i t y as the r i s i n g d i s p e r s e d phase d r o p s . As  shown i n Appendix I I ; on t h i s b a s i s a spray column tends,  mathematically  speaking, towards a packed bed.  I f the drops  assumed t o be a r r a n g e d i n some, simple l a t t i c e s t r u c t u r e , ~\ expressed p u r e l y i n terms o f h .  are can be  T h e r e f o r e the p r e d i c t e d drop  P e c l e t number i s a simple f u n c t i o n o f h o n l y .  Equations f o r  p r e d i c t i n g the drop P e c l e t number, Pe, from the hold-up, been d e r i v e d i n Appendix I I f o r s i x d i f f e r e n t l a t t i c e  h, have  arrangements  o f drops.  APPLICATION OF THE  DISPERSION MODEL TO LIQUID-LIQUID EXTRACTION  On the b a s i s o f the d i s p e r s i o n model the reduced c o n c e n t r a t i o n o f s o l u t e i n the continuous phase of a l i q u i d - l i q u i d column i s g i v e n by E q u a t i o n l h .  extraction  33  C  = Aexp j ^ Z ) + Bexp ( ^ Z )  c  - Q  14 where  15  \  = c<- M + p , 2  16  2oc= L H + I^aH Q  Ee  P  ,  L D  17 2  = ( L  D  mL-pEe  18 Q = Jm  .  CO  D  , C  y  19 and A.and B a r e c o n s t a n t s o f i n t e g r a t i o n . i n c l u s i v e c o r r e s p o n d t o E q u a t i o n s 1-13;  E q u a t i o n s ik t o 19  1-14, 1-15;  1-10,  1-11,  and I - l 6 i n A p p e n d i x I . I f the solute concentration p r o f i l e s are a v a i l a b l e f o r b o t h phases o f a l i q u i d - l i q u i d e x t r a c t i o n spray column t h e capacity  c o e f f i c i e n t , (Kj-,a), can be c a l c u l a t e d b y means o f  E q u a t i o n 20. V  =  h  f H  D C  D  *  / ( c " D) c  C  20  34  The i n t e g r a l i n E q u a t i o n 20 i s e v a l u a t e d l e n g t h o f t e s t s e c t i o n , H.  g r a p h i c a l l y over the  The v o l u m e t r i c  f r a c t i o n of continuous  phase, e, i n t h e column can be measured b y means o f a p i s t o n sampler (37)-  For steady-state  operation  t h e n e t f l u x , J , o f s o l u t e down  t h e column must be t h e same a t any e l e v a t i o n i n t h e column.  J can  be c a l c u l a t e d from a knowledge o f t h e s u p e r f i c i a l ^ v e l o c i t i e s of, b o t h phases and s o l u t e c o n c e n t r a t i o n s  i n t h e streams e n t e r i n g and l e a v i n g  the column b y means o f E q u a t i o n 21. J * \  [(L cJ c  - L ^ ) + (L c° - L c J ) ] c  D  ^  Boundary c o n d i t i o n s f o r E q u a t i o n Ik have been s u g g e s t e d by Danckwerts (60).  These c o u l d be used t o c a l c u l a t e t h e v a l u e s o f A  and B i n t h a t e q u a t i o n .  Then, i f an e s t i m a t e o f t h e a x i a l eddy  d i f f u s i v i t y , E, were a v a i l a b l e , t h e c o n c e n t r a t i o n  p r o f i l e of solute  i n t h e c o n t i n u o u s phase c o u l d . b e p r e d i c t e d b y means o f E q u a t i o n l 4 . However, t h e boundary c o n d i t i o n s r e l y on t h e - a s s u m p t i o n t h a t t h e d i s p e r s i o n model i s a p p l i c a b l e a t t h e ends o f t h e s p r a y column. Some doubt e x i s t s a s t o whether t h i s a s s u m p t i o n i s v a l i d because t h e hydrodynamic f l o w p a t t e r n s a r e much d i f f e r e n t i n t h e E l g i n head a t t h e upper end o f t h e column, and i n t h e c o n i c a l s e c t i o n a t t h e l o w e r end o f t h e column, t h a n i n t h e column p r o p e r .  A n o t h e r method f o r c a l c u l a t i n g v a l u e s o f A and B c o n s i s t s o f f i t t i n g E q u a t i o n lk t o a measured s o l u t e c o n c e n t r a t i o n the c o n t i n u o u s phase.  profile i n  I n c a r r y i n g o u t t h i s curve f i t t i n g , an e s t i m a t e  o f t h e a x i a l eddy d i f f u s i v i t y , E, i s o b t a i n e d .  Since Equations  35  15 t o 1 9 i n c l u s i v e i n v o l v e E, v a l u e s o f E can be chosen by t r i a l and e r r o r t o produce t h e b e s t f i t o f E q u a t i o n 14 t o t h e measured concentration p r o f i l e .  One method o f f i t t i n g E q u a t i o n 1 4 t o an e x p e r i m e n t a l p r o f i l e i s toy means o f t h e l e a s t squares t e c h n i q u e .  Estimates of the values  o f A and B a r e o b t a i n e d b y m i n i m i z i n g t h e sum o f t h e squares o f t h e d i f f e r e n c e s between measured c o n c e n t r a t i o n s and t h o s e g i v e n b y E q u a t i o n 14.  g i v e n by E q u a t i o n 22, must  That'is, the value o f  be a minimum.  ^  =  5[°C  " AQM\Z)  - Bexp(> Z) + Q ]  2  2  22 I f E q u a t i o n 22 i s d i f f e r e n t i a t e d p a r t i a l l y w i t h r e s p e c t t o A and t h i s ' r e s u l t equated t o z e r o , and t h e n a g a i n w i t h r e s p e c t t o B, and that- r e s u l t equated t o z e r o , two s i m u l t a n e o u s  e q u a t i o n s i n A and B,  E q u a t i o n s 23 and 2 4 , r e s u l t . .  A^expC^Z))  2  + B^exp^Z^xpOgZ)) ^ ( ( ^ e x p C X ^ ) ) + Q^expO^Z)  23 A^(exp(> Z)exp(^ Z)) + B^(exp(> Z)) 1  2  2  2  ^(C^expO^Z)) + Q ^ e x p ^ Z )  24 E q u a t i o n s 23 and 2 4 can toe s o l v e d f o r A and B.  T h i s process can  toe r e p e a t e d f o r v a r i o u s assumed v a l u e s o f t h e a x i a l eddy d i f f u s i v i t y , 2  E.  The v a l u e o f E w h i c h r e s u l t s i n t h e l o w e s t v a l u e o f A . i s one  e s t i m a t e o f t h e t r u e v a l u e o f E.  36  i APPARATUS  The o r i g i n a l a p p a r a t u s was d e s i g n e d and b u i l t by Le Page ( l l 8 ) . However, i t has been m o d i f i e d by o t h e r s (37, 38, 39) and by t h e author.  A schematic f l o w diagram  o f one arrangement o f t h e a p p a r a t u s  used i n t h e p r e s e n t work i s shown i n "Figure 9«  T h i s arrangement  was used f o r t r a c e r s t u d i e s w i t h no i n t e r p h a s e mass t r a n s f e r i n a l-§--in. I.D. column.  A key t o F i g u r e 9 i s p r e s e n t e d i n Table 1.  A l l c o n t r o l v a l v e s were s t a i n l e s s s t e e l needle v a l v e s w i t h Teflon packing.  The c e n t r i f u g a l pump, P  supplies the constant  head t a n k , E, w i t h d e - i o n i s e d water from t h e s t o r a g e tank,. A. Water f l o w s from t h e c o n s t a n t head t a n k , E, t h r o u g h t h e c o n t r o l v a l v e , J , and r o t a m e t e r , G, t o t h e E l g i n head, M, o f t h e column. Water flows, down, as t h e c o n t i n u o u s phase, t h r o u g h t h e column p r o p e r , R, l e a v i n g . a t t h e l o w e r end o f t h e column and p a s s i n g through t h e i n t e r f a c e c o n t r o l v a l v e , X, and r o t a m e t e r , Y, t o t h e r e c e i v i n g t a n k , B.  MIBK i s s u p p l i e d t o t h e c o n s t a n t head t a n k , F, b y t h e  c e n t r i f u g a l pump, P  from t h e s u p p l y t a n k , D.  From t h e c o n s t a n t  head t a n k , F, MIBK f l o w s t h r o u g h t h e c o n t r o l v a l v e , K, and r o t a m e t e r , H, t o t h e d i s p e r s e d phase n o z z l e , S, a t t h e l o w e r end o f t h e column. MIBK r i s e s , i n t h e form o f d r o p s , t h r o u g h t h e d e s c e n d i n g water i n the column and c o a l e s c e s a t t h e i n t e r f a c e , Q,  From t h e " E l g i n head  MIBK f l o w s d i r e c t l y t o t h e r e c e i v i n g t a n k , C.  I t i s possible to  TABLE 1  (Key t o F i g u r e  9)  Continuous phase f e e d t a n k . Continuous phase r e c e i v e r and storage Dispersed  phase r e c e i v e r and storage  Dispersed  phase f e e d tank.  Continuous phase c o n s t a n t Dispersed  phase c o n s t a n t  tank. tank.  head tank. head "tank.  Continuous phase f e e d r o t a m e t e r . Dispersed  phase f e e d r o t a m e t e r .  Continuous phase i n l e t  sample  valve.  Continuous phase f l o w r a t e c o n t r o l v a l v e . Dispersed  phase f l o w r a t e c o n t r o l v a l v e .  Dispersed  phase i n l e t  Elgin  sample  valve.  head.  Continuous phase i n l e t  pipes.  E l g i n head d r a i n v a l v e . C e n t r i f u g a l pump f o r c o n t i n u o u s phase. C e n t r i f u g a l pump f o r d i s p e r s e d phase. Piston-type  sampler.  Interface. Column p r o p e r . Dispersed  phase n o z z l e .  Thermometers  Bottom c o n i c a l  section.  Vent t o atmosphere. Interface  level control  valve.  Interface  level control  rotameter.  T r a c e r c o n s t a n t head t a n k . Tracer flowrate Tracer feed Tracer  control  valve.  rotameter.  distributor.  22-gauge hypodermic n e e d l e sampler  t a k e a b u l k sample from the column w i t h the p i s t o n sampler, d e t a i l s o f w h i c h a r e t o be f o u n d elsewhere (37/  38).  PTS,  A drawing of  t h e p i s t o n sample c o l l e c t i o n v e s s e l f o r d i s p e r s e d phase hold-ups g r e a t e r t h a n 12$  i s shown i n Appendix V.  The p i s t o n sample  c o l l e c t i o n v e s s e l f o r d i s p e r s e d phase hold-ups l e s s t h a n 12$ i s s i m i l a r and i s d e s c r i b e d elsewhere (37)-  B o t h o f t h e p i s t o n sample  c o l l e c t i o n f l a s k s were c a l i b r a t e d by w e i g h i n g them when t h e y c o n t a i n e d v a r i o u s amounts o f w a t e r .  Sodium c h l o r i d e d i s s o l v e d i n M I B K - s a t u r a t e d water was as t r a c e r .  used  A c o n c e n t r a t e d s o l u t i o n o f t h i s f l o w s from t h e c o n s t a n t  head t a n k , Z, t h r o u g h t h e c o n t r o l n e e d l e v a l v e , a, and r o t a m e t e r , b, t o t h e t r a c e r d i s t r i b u t o r , c, i n t h e column.  Time average p o i n t  samples were t a k e n from t h e column t h r o u g h 22-gauge, 3 ~ i n . l o n g hypodermic n e e d l e s , d.  The f l o w r a t e o f t h e s e samples  was  r e g u l a t e d by means o f s i m p l e s t a i n l e s s s t e e l - p o l y e t h y l e n e s t o p c o c k valves.  The hypodermic n e e d l e s were i n s e r t e d t h r o u g h p o l y e t h y l e n e  g a s k e t s w h i c h were between 6 - i n , s e c t i o n s o f t h e P y r e x g l a s s  column.  (See Appendix V f o r d e t a i l e d drawings o f t h e t r a c e r d i s t r i b u t o r and o f t h e sample v a l v e s . )  Samples c o n t a i n i n g t r a c e r were a n a l y s e d  f o r sodium w i t h a P e r k i n - Elmer 303 a t o m i c a b s o r p t i o n s p e c t r o phometer. The major p a r t o f t h e work was column o f l - | - i n . I.D.'  D e t a i l s o f t h e end s e c t i o n s o f t h i s column  a r e t o be f o u n d e l s e w h e r e ( l l 8 , a r e shown i n F i g u r e 10.  c a r r i e d out w i t h a P y r e x g l a s s  35).  Its vertical  The arrangements  dimensions  shown i n F i g u r e 11  and  12  hi  CM  INTERFACE 6"LONG, 6"I.P. P Y R E X  T—T  "DOUBLE T O U G H " PIPE  10" L O N G , L V ID. PYREX " D O U B L E TOUGH" P I P E WITH U N F L A N G E D U P P E R E N D  «  3' LONG, l>2" ID. PYREX "DOUBLE TOUGH" PIPE.  A  6" LONG, l ' / " I.D. PYREX 2  DOUBLE TOUGH PIPE (SEE T A B L E VI-I F O R M E A S U R E D DIMENSIONS)  B  V\s" THICK , l!£" I.D. POLYETHYLENE GASKET THROUGH WHICH SAMPLING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER) STYLE 1-2 (CORNING)  TEFLON GASKET  '/g THICK, life I.D. TEFLON GASKET THROUGH WHICH THE TRACER INJECTION NEEDLE PASSED I* LONGj'/fc" IO. PYREX "DOUBLE TOUGH" PIPE CUSTOM MADE PYREX "DOUBLE TOUGH" 3" TO I /a" REDUCER (30) 1  FIGURE 10.  l£-IN. I.D. COLUMT  were used together with that given i n Figure 10 f o r i n v e s t i g a t i n g the e f f e c t of column length on the a x i a l eddy d i f f u s i v i t y .  Details  of the column arragements used f o r the part of the work concerning sampling techniques are shown i n Figures 13 and 14. Two  sampling  techniques f o r measuring concentration p r o f i l e s were investigated. The f i r s t method was the use of the hook and bell-probes.mentioned earlier.  Both the hook-shaped probe and the bell-shaped probe  were made-from stainless s t e e l .  Details of these probes are to  be found elsewhere ( 3 0 , 118), and a diagram i s shown i n Figure 5« Samples were syphoned out of the column through these probes and through small needle valves and rotameters connected i n series with them.  The needle valves were used to control the flows, and  the rotameters to measure them. of a water aspirator.  The syphon was started by means  The second sampling method made use of  hypodermic needles as mentioned e a r l i e r .  The piston sampler,  mentioned i n the Introduction, was employed i n both sampling investigations. The drops were produced at a nozzle s i m i l a r i n design to that of Kreagerand Geankoplis ( l 6 ) .  With t h i s sort of nozzle  drops are formed at the ends of j e t s extending from short tubes p r e s s ^ f i t t e d into a plate forming the end of the spray nozzle. These tubes were chamfered to sharp edges at t h e i r delivery endsThe dispersed phase nozzle used with the l-|-in. I.D. column was designed by Choudhury, and a d e t a i l e d drawing i s to be found fn his  thesis (35)?  The nozzle t i p s and nozzle t i p support plate  are  described elsewhere (30, 35; 1 1 8 ) . The average inside diameter  of these nozzle t i p s was measured by the present author and was  ^3  INTERFACE 6" LONG, 6" I.D. PYREX "DOUBLE TOUGH" PIPE 10"LONG, l'/2" I.D. PYREX "DOUBLE TOUGH" PIPE WITH UNFLANGED UPPER END 6" LONG, I.D. PYREX "DOUBLE TOUGH" PIPE (SEE TABLE VI-I FOR MEASURED DIMENSIONS) •  M  N  /|€ THICK, |'/2 |.D. POLYETHYLENE GASKET THROUGH WHICH SAMPING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER)  l/g THICK, l ' / " |.D. TEFLON GASKET THROUGH WHICH THE TRACER INJECTION NEEDLE PASSED 2  CUSTOM MADE PYREX "DOUBLE TOUGH" 3" TO iVz" REDUCER (30) STYLE  FIGURE 11.  1-2 TEFLON GASKET (CORNING)  SHORT 1^-IN. I.D. COLUMN  kk  INTERFACE  •6" LONG, 6" I.D.  "DOUBLE TOUGH"  PYREX  PIPE  10" LONG, I'/g" I..0. PYREX "DOUBLE TOUGH" PIPE WITH UNFLANGED UPPER END 2' 6" LONG, 1/2 I.D. PYREX "DOUBLE TOUGH" PIPE  3' LONG, PIPE A  6"  I'/g" I.D. PYREX "DOUBLE TOUGH"  LONG,  ID.  V/2.  Vi$"  B  THICK,  I5^  THROUGH  PASSED  (EACH  S T Y L E  \/£  THICK,  WHICH  I'  6"  2  FIGURE 1 2 .  ID. T E F L O N  TRACER  l'/ " 2  MADE  GASKET  INJECTION  I.D. P Y R E X  "DOUBLE  LONG l | - I N . I.D. COLUMN  "DOUBLE  THROUGH  NEEDLE  IDOUBLE  REDUCER  IS  (CORNING)  GASKET  P Y R E X  P Y R E X  N E E D L E S  POSITION  NUMBER)  life"  I D .  SAMPLING  SAMPLING  B Y  TOUGH"  MEASURED  P O L Y E T H Y L E N E  WHICH  TEFLON  l'/2  LONG,  CUSTOM l'/ "  ..  "DOUBLE  FOR  1-2  T H E  LONG,  2'  I.D.  GASKET  INDICATED  PYREX  VI-1  PIPE (SEE TABLE DIMENSIONS)  PASSED  TOUGH"  TOUGH"  TOUGH"  PIPE  PIPE  3 "  TO  45  CM  ^  4=L rr  INTERFACE '6" LONG, 6" I.D. PYREX "DOUBLE TOUGH" PIPE 10" LONG, I.D. PYREX "DOUBLE TOUGH" WITH UNFLANGED UPPER END  3' LONG, l / ^ PIPE 1  I' 6"L0NG, IV PIPE  2  T LONG, l'/ " PIPE 2  I.D. PYREX "DOUBLE TOUGH*  I.D. PYREX "DOUBLE TOUGH"  I.D • PYREX "DOUBLE  CUSTOM MADE PYREX TO l!/ " REDUCER  TOUGH"  "DOUBLE TOUGH"  3"  2  D  FIGURE  /  13.  STYLE  1-2 TEFLON  GASKET (CORNING)  I.D. COLUMN FOR COMPARING HOOK AND BELL-PROBES AND PISTON SAMPLER RESULTS  If-IN.  INTERFACE 6" L O N G ,  6 " I.D. P Y R E X  10" L O N G , l ' / I.D. WITH U N F L A N G E D  PYREX UPPER  M  2  3' L O N G , l ' /  I' L O N G , l ' /  I.D. P Y R E X  2  2  I.D.  A  T L O N G , l'/ "  B  '/,  2  6  THICK,  THROUGH  STYLE  E  3" L O N G , SPACER  l> " 2  FIGURE Ik.  WHICH  l'/  I.D.  2  I.D. P Y R E X  "DOUBLE  GASKET PYREX  PYREX  PYREX  "DOUBLE  PASSED TOUGH"  (CORNING)  "DOUBLE  "DOUBLE  SPACER  GASKET  NEEDLES  I.D.  PIPE  TOUGH"  SAMPLING  TEFLON  PIPE  PIPE  TOUGH"  H  D  MADE  TOUGH"  2  K  CUSTOM  "DOUBLE  PIPE  TOUGH"  ||/ I.D. P O L Y E T H Y L E N E  2  LONG,  "DOUBLE END  "DOUBLE  PYREX  2'/ " L O N G , I /{ SPACER 1-2  TOUGH"  "DOUBLE  PYREX  C  I'  "DOUBLE  TOUGH"  TOUGH" TOUGH"  PIPE 3" T O  REDUCER  i f - I N . I*D. COLUMN FOR COMPARING HYPODERMIC NEEDLE, HOOK, AND BELL-PROBES, AND PISTON SAMPLER RESULTS  f o u n d t o be 0.103-in. (See Appendix V.)  T h i s n o z z l e and t h e s e  nozzle  t i p s were used f o r much o f the work d e s c r i b e d i n the p r e s e n t t h e s i s i n c l u d i n g a l l the work i n v o l v i n g mass t r a n s f e r between phases.  However,  the end p l a t e and n o z z l e t i p assembly wag. r e p l a c e d f o r c e r t a i n runs so. t h a t the e f f e c t o f d r o p s i z e on the a x i a l eddy" d i f f u s i v i t y , c o u l d be studied.  Thus s e t s o f n o z z l e t i p s o f average i n s i d e d i a m e t e r  0.126-in., 0.086-in., and 0-053-in-. r e s p e c t i v e l y were used i n a d d i t i o n t o those o f 0.103-in. a l r e a d y mentioned.  A dispersed  phase n o z z l e was  Pyrex glass  designed  f o r use i n a 3 - i n . I.D.  column used f o r p a r t o f the work and d e s c r i b e d l a t e r i n t h i s s e c t i o n o f the t h e s i s .  D e t a i l e d drawings o f the 0.126-in.,  0.086-in., and 0.053-in- I.D.  n o z z l e t i p s appear i n Appendix V.  The average v e l o c i t y of MIBK I n the d i s p e r s e d phase d i s t r i b u t o r n o z z l e t i p s was m a i n t a i n e d  c o n s t a n t f o r each s e t o f n o z z l e t i p s  by b l o c k i n g o f f n o z z l e t i p s w i t h T e f l o n caps o r p l u g s as the MIBK f l o w r a t e was  r e d u c e d . P a t t e r n s of open n o z z l e t i p s used i n t h i s  work a r e shown i n F i g u r e s 15, l6,  17,  and 18, one f o r each s e t of  n o z z l e t i p s and f o r t h e v a r i o u s d i s p e r s e d phase f l o w r a t e s used.  Drop s f z e d i s t r i b u t i o n s i n the l§-iri. I.D. d e t e r m i n e d by p h o t o g r a p h i n g  column were  a 4 ^ i n . l e n g t h o f column s i t u a t e d  between 7 - i n . and 11-in..above t h e t o p of the p i s t o n sampler b l o c k . The. camera used was  an E x a c t a VX I I a) w i t h a 1.6-in. e x t e n s i o n  r i n g and a Telemegor 5-5/250 t e l e p h o t o l e n s . was  The.camera a p e r a t u r e  s e t a t f22 t o g i v e a d e p t h o f f o c u s g r e a t e r t h a n t h e i n s i d e  diameter  o f the column.  Adox KB-14  (20 ASA)  f i l m was  used-  OOPEN  FIGURE 15.  # BLOCKED  NOZZLE TIP PATTERNS. I.D. = 0.126-IN. ( l f - I N . I.D,. COLUMN)  k9  O FIGURE 16.  OPEN  # BLOCKED  NOZZLE TIP PATTERNS. I.D. - 0.103-IN. ( i f - I N . I.D. COLUMN) '  1  OOPEN  FIGURE 17.  •BLOCKED  NOZZLE TIP PATTERNS. I.D. = 0.086-IN. (l^-'IR. I.D. COLUMN)  •o • o• • '© o • • o © o ®'  oo••••*  o i i t o i o o o «• o • om « o« Qo «  4,-73-0  ©o ©o© • ® 'o o • • o • c  ®®oo«o©0O  r  o• • • o ®o o  © • O O O €) O «  L  • o•• o ••o oi » o « o o » o , • o«•oo• on ©e o L  o • O • • • Oj  o OPEN  FIGURE 18.  •  -91*  •BLOCKED  NOZZLE TIP PATTERNS. I.D. = 0.053-BT. ( l f - I N . I.D. COLUMN)  The s e c t i o n o f column photographed was surrounded by a p a r a l l e l s i d e d P e r s p e x box f i l l e d , " w i t h d i s t i l l e d  w a t e r t o reduce the  d i s t o r t i n g e f f e c t o f t h e round column.  Back l i g h t i n g was  effected  w i t h a B r a u n Hobby F 6 0 e l e c t r o n i c f l a s h u n i t w i t h a one m i l l i s e c o n d f l a s h duration.  The s e c t i o n o f column photographed was  shielded  from e x t r a n e o u s l i g h t w i t h a c a r d b o a r d box w h i c h a l s o s u p p o r t e d the  e l e c t r o n i c f l a s h head and a l i g h t - d i f f u s i n g s c r e e n o f e i g h t F i g u r e 19  s h e e t s o f t r a c i n g paper. of  f l a s h , column, and camera.  shows t h e r e l a t i v e  positions  D e t a i l e d drawings o f t h e P e r s p e x  box and t h e c a r d b o a r d s h i e l d a r e g i v e n i n Appendix V. A few e x p e r i m e n t a l r u n s were c a r r i e d out w i t h t h e 3 - i n . I.D. P y r e x g l a s s column shown i n F i g u r e 2 0 .  I n o r d e r t o produce and  m a i n t a i n h i g h c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t i e s t h r e e c o n t i n u o u s phase f e e d t a n k s , p r e s s u r i z e d t o about 15 n i t r o g e n , were used. F i g u r e 21.  A s c h e m a t i c f l o w diagram i s p r e s e n t e d i n  D e t a i l e d drawings o f t h e end s e c t i o n s and d i s p e r s e d  phase d i s t r i b u t o r n o z z l e a r e g i v e n i n Appendix V. the  p.s.i.g. with  F i g u r e 22 shows  p a t t e r n s o f open and c l o s e d n o z z l e t i p s used f o r v a r i o u s  d i s p e r s e d phase f l o w r a t e s .  Sodium c h l o r i d e t r a c e r was  injected  i n t o the column t h r o u g h t h e same t r a c e r d i s t r i b u t o r as used i n the  l - ^ - i n . I.D. column.  The t r a c e r d i s t r i b u t o r was l o c a t e d on  the  c e n t r e l i n e o f t h e column and t r a c e r f l o w e d i n t o i t t h r o u g h  a 3 - i n - l o n g , l8-gauge hypodermic n e e d l e w h i c h passed t h r o u g h a l / 8 - i n , t h i c k , 3 - i n . I.D., and 3 27/32-in. O.D. Samples were  Teflon gasket.  withdrawn as w i t h t h e l J r - i n . I.D. column e x c e p t t h a t  BACK OF CAMERA it  II  f]  FLASH UNIT  DIFFUSING SCREEN  COLUMN  PERSPEX BOX  LIGHT SHIELD  FIGURE 19. PHOTOGRAPHIC CONDITIONS  CAMERA  5^  INTERFACE 1—9"  LONG, 9" I.D.  Q.V. F. PIPE  10-3/4 LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE 6" LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE (SEE TABLE Vl-I FOR MEASURED DIMENSIONS) '/|6 THICK, 3" liD. POLYETHYLENE GASKET THROUGH WHICH SAMPLING NEEDLES PASSED (EACH SAMPLING POSITION IS INDICATED BY NUMBER) 6" LONG, 3" I.D. PYREX "DOUBLE TOUGH" PIPE WITH BOTH ENDS UNFLANGED (SEE TABLE VI-I FOR MEASURED DIMENSIONS)  l/ " THICK, 3" i.D. 8  POLYETHYLENE  GASKET  THROUGH WHICH THE TRACER NEEDLE PASSED  CUSTOM MADE PYREX "DOUBLE TOUGH" 6" TO 3" REDUCER  F I G U R E 20.  3 - I N . I . D . COLUMN  FIGURE 21.  SCHEMATIC PLOW DIAGRAM FOR THE 3-E*. I.D. COLUMN  TABLE 2 (Key t o F i g u r e 21)  .Continuous  phase f e e d t a n k s .  D i s p e r s e d phase f e e d and r e c e i v e r t a n k . Interface l e v e l c o n t r o l rotameters. Interface level control valves. Continuous  phase f e e d  D i s p e r s e d phase f e e d  rotameters. rotameters.  Continuous  phase i n l e t sample v a l v e .  Continuous  phase f l o w r a t e c o n t r o l v a l v e s . -  D i s p e r s e d phase f l o w r a t e c o n t r o l v a l v e s . E l g i n head. Continuous  phase i n l e t p i p e s .  Nitrogen cylinder. E l g i n head d r a i n v a l v e . C e n t r i f u g a l pump f o r c o n t i n u o u s phase f e e d . C e n t r i f u g a l pump f o r d i s p e r s e d phase f e e d . C e n t r i f u g a l pump f o r c o n t i n u o u s phase o u t l e t . P r e s sure gauge. Pressure r e l i e f valve. Interface. Column p r o p e r . D i s p e r s e d phase n o z z l e .  57  Thermometers  U V Z  -  Bottom c o n i c a l  section.  Vent, t o atmosphere. ' T r a c e r c o n s t a n t head tank.  a  Tracer flowrate control valve.  b  Tracer feed rotameter.  c  Tracer distributor..  d  22-gauge hypodermic needle  samplers.  58  the hypodermic needles, passed through l / l 6 ^ i n . thick, 3-in. and 3 2'7/32-in. O.D. column.  I.D.,  polyethylene gaskets to the centre l i n e of the  The eighth 6-rin. section of column above the tracer  d i s t r i b u t o r was  cut from a 1-ft. long piece of Pyrex glass pipe.  The piece selected was remote from the ends so that i t s bore reasonably uniform.  This section of column was  was  held i n place by  four aluminum" t i e rods, between two large diameter aluminum flanges shown i n Appendix V.  A f l a t - s i d e d Perspex box, also shown i n  Appendix V surrounded t h i s 6-in. long piece of column.  The space  between the glass and the Perspex was f i l l e d with d i s t i l l e d water. Photographs were taken of the column through the Perspex box the use of a cardboard  with  l i g h t - s h i e l d , a t r a c i n g paper d i f f u s i n g  screen and an e l e c t r o n i c f l a s h as with the l^-.in.. column. Photographic  conditions were the same as before except that  l i g h t i n g was by means of a Kakonet - II e l e c t r o n i c f l a s h unit with a f l a s h duration of 0.5-millisecond.  6o  EXPERIMENTAL PROCEDURE  1.  COLUMN OPERATION  C i t y water'was passed t h r o u g h a B a r n s t e a d Bantam BD-1 mixed bed d e m i n e r a l i z e r t o g i v e b e t t e r t h a n 1 megohm-cm. r e s i s t i v i t y water.  I n a l l experiments t h e c o n t i n u o u s phase was  d e m i n e r a l i z e d water and t h e d i s p e r s e d phase was t e c h n i c a l grade m e t h y l i s o b u t y l ketone (MIBK) s u p p l i e d b y C h e m c e l l L t d .  Each  phase was k e p t s a t u r a t e d w i t h t h e o t h e r by m a i n t a i n i n g a l a y e r o f one phase i n t h e f e e d t a n k o f t h e o t h e r .  The f l o w r a t e s o f b o t h  phases f e d t o t h e column were r e g u l a t e d w i t h s t a i n l e s s needle v a l v e s and metered w i t h r o t a m e t e r s .  steel  Four d i f f e r e n t drop  s i z e - d i s t r i b u t i o n s were produced i n t h e i f - i n . I.D. column b y means o f f o u r s e t s o f n o z z l e t i p s o f r e s p e c t i v e average d i a m e t e r s 0.126-in., 0.103-in., 0.086-in., and 0.053-in.  inside Only  one s e t o f n o z z l e t i p s o f average i n s i d e d i a m e t e r 0.102-in. was used w i t h t h e 3 - i n . I.D. column.  The d i s p e r s e d phase average  v e l o c i t y i n t h e d i s t r i b u t o r n o z z l e t i p s was h e l d a t 0 . 3 6 - f t . / s e c . , 0. ' 3 6 - f t . / s e c ,  0.38-ft./'sec., 0 . 6 8 - f t . / s e c . , and 0 - 3 7 - f t . / s e c . f o r  t h e - 0 . 1 2 6 - i n . , '0.103-in., 0.086-in., 0.053-in., 'and 0.102-in. 1. D. t i p s r e s p e c t i v e l y b y u t i l i z i n g o n l y a p o r t i o n o f t h e t o t a l n o z z l e t i p s a v a i l a b l e w i t h t h e h e l p o f T e f l o n caps o r p l u g s as d e s c r i b e d under t h e h e a d i n g A p p a r a t u s .  The h i g h e r n o z z l e t i p  61  v e l o c i t y o f 0.68-ft./sec.  i n t h e Q.053-in. I . D . t i p s was found t o  be n e c e s s a r y i n o r d e r t o produce drops o f a narrow range o f s i z e s . The i n t e r f a c e i n t h e E l g i n head was m a i n t a i n e d steady t o w i t h i n t l / l 6 - i n . b y c o n t r o l l i n g t h e f l o w o f c o n t i n u o u s phase • " • . ' • -J l e a v i n g t h e column by means o f a s t a i n l e s s s t e e l needle v a l v e . A rotameter, i n series w i t h t h i s v a l v e , i n d i c a t e d the flowrate. The d i s p e r s e d phase f l o w from t h e column head t o t h e r e c e i v i n g t a n k was u n r e s t r i c t e d . 2.  SAMPLING TECHNIQUE STUDIES WITH MASS TRANSFER  An attempt was made t o r e l a t e t h e samples t a k e n by t h e b e l l and hook-probes t o samples t a k e n by means o f t h e p i s t o n .  Early  i n the-work each o f t h e s a m p l i n g l i n e s l e a d i n g from t h e b e l l and hook-probes,  r e s p e c t i v e l y , used by e a r l i e r workers  (38) was  r e p l a c e d by 27-ft. o f s m a l l e r b o r e (3/32-in. I.D.) N y l o n t u b i n g . I t was found t h a t a c o n s e r v a t i v e e s t i m a t e o f t h e minimum purge time f o r each o f t h e s e new s a m p l i n g l i n e s was g i v e n by t h e f o l l o w i n g e q u a t i o n . (See Appendix V I )  120 Purge time, (min. ) = D  —  —  :  —-—•>—-,  / .  r  s a m p l i n g r a t e (ml./min,)  I n a l l Of t h e work i n v o l v i n g t h e hook o r b e l l - p r o b e d e s c r i b e d i n t h i s t h e s i s t h e s e probes were p o s i t i o n e d a s c l o s e l y as p o s s i b l e t o t h e c e n t r e l i n e o f t h e column.  The t i m e s f o r t h e column t o  r e a c h steady s t a t e o p e r a t i n g c o n d i t i o n s a t v a r i o u s f l o w r a t e s o f . each phase was t a k e n from t h e work o f B e r g e r o n  (38),  62  I n a l l e x p e r i m e n t s a c e t i c a c i d was t r a n s f e r r e d from t h e c o n t i n u o u s aqueous phase t o the d i s p e r s e d MIBK phase.  A t the  end o f an experiment t h e aqueous phase p r o d u c t was t r a n s f e r r e d t o the aqueous phase f e e d t a n k and the aqueous phase p r o d u c t t a n k was f i l l e d w i t h d e - i o n i s e d w a t e r .  T h i s water was used t o back-  wash MIBK f r o m t h e p r e v i o u s r u n i n t h e column i n o r d e r t o p r e p a r e a f e e d s t o c k o f MIBK low i n a c e t i c a c i d c o n c e n t r a t i o n f o r t h e next run.  " The aqueous phase backwashing  p r o d u c t was f e d t o t h e aqueous  phase f e e d t a n k u n t i l t h e l i q u i d l e v e l i n t h a t t a n k was  about  6 - i n . from t h e t o p and t h e n the remainder was f e d t o t h e d r a i n .  Reagent grade g l a c i a l a c e t i c a c i d , manufactured by N i c h o l s C h e m i c a l C o r p o r a t i o n L t d . , was used f o r p r e p a r i n g t h e aqueous a c e t i c a c i d s o l u t i o n used as c o n t i n u o u s phase' f e e d i n t h e f o l l o w i n g manner.  I f n e c e s s a r y t h e aqueous phase f e e d t a n k was  filled  t o w i t h i n about s i x i n c h e s from t h e t o p by a d d i n g d e - i o n i s e d water.  The contents, of t h i s t a n k were pumped up t o the aqueous  phase c o n s t a n t ' head t a n k and a l l o w e d t o r u n b a c k i n t o t h e f e e d t a n k u n t i l t h e s o l u t i o n was  homogeneous.  Homogeneity was  checked  by p e r i o d i c a l l y t i t r a t i n g t h e f l o w from the c o n s t a n t head t a n k w i t h c a r b o n a t e - f r e e s t a n d a r d sodium h y d r o x i d e s o l u t i o n .  (The  h y d r o x i d e s o l u t i o n was p r e p a r e d as recommended by S w i f t and' was  sodium (119)  s t a n d a r d i z e d by t i t r a t i n g a g a i n s t s t a n d a r d p o t a s s i u m  hydrogen p h t h a l a t e s o l u t i o n . )  From a knowledge o f t h e volume  of l i q u i d i n t h e aqueous phase f e e d t a n k and the c o n c e n t r a t i o n of a c e t i c a c i d . i n s o l u t i o n i n t h a t t a n k the amount of g l a c i a l  63  a c e t i c a c i d t o be added i n order t o produce a s u i t a b l e a c e t i c a c i d c o n c e n t r a t i o n , i n the aqueous phase f e e d was T h i s amount o f g l a c i a l a c e t i c a c i d was phase f e e d tank.  The  contents  calculated.  poured i n t o the aqueous  o f t h i s tank then were c i r c u l a t e d  t o g i v e a homogeneous s o l u t i o n as  before.  In t h i s study the s e t o f n o z z l e t i p s o f average i n s i d e diameter 0.103-in. was  used.  In most o f these experiments a l l o f  the d i s p e r s e d phase d i s t r i b u t o r n o z z l e t i p s were kept open. Therefore  a high ketone f l o w r a t e was  o b t a i n e d w i t h the use  average n o z z l e t i p v e l o c i t y of 0»36-ft./sec. f l o w r a t e was  of an  A high ketone  r e q u i r e d i n o r d e r t o produce a h i g h d i s p e r s e d phase 6 i n connection  hold-up so t h a t the a p p l i c a t i o n of E q u a t i o n  the p i s t o n sampler would r e s u l t i n a s m a l l e r r o r i n the ated value of c t h a t the column was  A high aqueous phase f l o w r a t e was  brium i n the v i c i n i t y of the p i s t o n sampler.  calcul-  used  o p e r a t i n g under c o n d i t i o n s f a r from  with  so  equili-  Under these  con-  d i t i o n s s o l u t e c o n c e n t r a t i o n g r a d i e n t s which are s u b s t a n t i a l l y d i f f e r e n t from zero i n b o t h phases over the p i s t o n h e i g h t are t o be e x p e c t e d .  Without t h i s c o n d i t i o n a comparison between the  v a r i o u s sampling t e c h n i q u e s  a)  would be  meaningless.  Sampling w i t h hook and b e l l - p r o b e s and  The b e l l and  apparatus was  piston  s e t up as shown i n F i g u r e 13•  Each of the  hook-probes were p o s i t i o n e d so t h a t t h e i r r e s p e c t i v e  e n t r a n c e s were  below the c e n t r e l i n e o f the p i s t o n .  d e s i r e d MIBK f l o w r a t e i n t o the empty column was  The  established,  and aqueous-feed phase wag pumped i n t o the column a t the maximum possible rate.  When the i n t e r f a c e reached the d e s i r e d  level  t h e f l o w r a t e o f the aqueous continuous phase was reduced to the o p e r a t i n g i v a l u e and the v a l v e c o n t r o l l i n g the aqueous phase f l o w r a t e from the f o o t o f the column was opened and a d j u s t e d t o m a i n t a i n the i n t e r f a c e l e v e l .  A f t e r a l l o w i n g the column t o r e a c h  steady s t a t e c o n d i t i o n s sampling through the probes was commenced. Samples were c o l l e c t e d i n 50^ml. graduated c y l i n d e r s which were c l o s e d w i t h ground-glass s t o p p e r s immediately a f t e r the samples were t a k e n .  Samples were c o l l e c t e d w i t h each probe a t the  l o c a t i o n mentioned above.  The probes then were moved 1 - i n . up  the column, and a second s e t o f samples was taken.  Sets o f  samples were c o l l e c t e d a t an a d d i t i o n a l f o u r 1 - i n . i n t e r v a l s up the column,  When the probe samples had been taken the probes  were r a i s e d above the i n t e r f a c e , and a p i s t o n sample was  collected  a f t e r a h a l f - h o u r i n t e r v a l ' i n the c a l i b r a t e d custom made  vessel  J  shown i n F i g u r e V - 1, Appendix V.  The volumes of each phase i n  samples taken w i t h the b e l l - p r o b e and w i t h the p i s t o n were recorded.  Sometime d u r i n g the course o f steady s t a t e  operation  column i n l e t and o u t l e t samples o f b o t h phases were taken.  A l l o f the samples c o n t a i n i n g two phases were shaken v i g o r o u s l y many times i n o r d e r t o b r i n g the two phases t o equilibrium.  The c o n c e n t r a t i o n o f a c e t i c a c i d i n each phase o f  65  each sample was determined hy t i t r a t i n g w i t h s t a n d a r d sodium h y d r o x i d e . s o l u t i o n u s i n g p h e n o l p h t h a l e i n as i n d i c a t o r .  When  t i t r a t i n g t h e MIBK phase SBAG-1K* was added t o r e n d e r t h e MIBK and  aqueous phases m i s c i b l e .  In a d d i t i o n t o t h e experiments d e s c r i b e d above an experiment was performed w i t h a m o d i f i c a t i o n o f t h e hook-probe as  shown i n the s k e t c h below.  b)  Sampling w i t h hook and b e l l - p r o b e s , hypodermic n e e d l e s , and 1  piston  •  |  Short Pyrex spacers were i n c l u d e d i n t h e column above and below t h e p i s t o n b l o c k as shown i n F i g u r e Ik.  *  Hypodermic n e e d l e s  SDAG-lK.is a m i x t u r e o f 9 0 $ v/v e t h a n o l and 1 0 $ v/v methanol.  66  were i n s e r t e d through polyethylene gaskets between the spacers i n a manner s i m i l a r to that shown i n Figure V - 2, Appendix V.  The  minimum purge time' f o r these needles was found to be l e s s than 4-5-sec. at a sampling rate of 3A-ml./min.  In a l l of the work  i n v o l v i n g hypodermic needles described i n t h i s t h e s i s a needle was purged f o r at l e a s t -l§--min. before t a k i n g a sample.  A  hypodermic needle sample was taken always w i t h the open end of the t  needle on the centre l i n e of the column unless otherwise i n d i c a t e d . The column was brought to steady state operating conditions and probe samples were taken as before.  Then the probes were r a i s e d  above the i n t e r f a c e and the column was allowed to a t t a i n steady state operating c o n d i t i o n s .  Samples were c o l l e c t e d by means of  the hypodermic needles i n the f o l l o w i n g manner.  Two needles,  separated by not l e s s than 10 inches, were used concurrently, the other needles being- withdrawn to the column w a l l so as not to protrude i n t o the column.  The valves at the end of each of the  two needles were opened so as to give sampling rates of about l-ml./mln.  The samples were c o l l e c t e d i n 10-ml. graduated c y l i n d e r s .  A f t e r the f i n a l hypodermic needle sample was c o l l e c t e d the column was allowed to reach steady state operating conditions and then a p i s t o n sample was taken.  The concentration of a c e t i c a c i d i n each  phase of each sample was determined by t i t r a t i n g w i t h sodium hydroxide s o l u t i o n as before.  \  3-  SEARCH FOR  SUITABLE TRACER  An i n v e s t i g a t i o n and p r e l i m i n a r y t e s t s were made t o f i n d a t r a c e r f o r use i n t h e d e t e r m i n a t i o n o f a x i a l eddy d i f f u s i v i t i e s w i t h no mass t r a n s f e r between the d i s p e r s e d and t h e c o n t i n u o u s phases.  The n e c e s s a r y t r a c e r p r o p e r t i e s a r e l i s t e d below:  a)  high s o l u b i l i t y  b)  insolubility  c)  c o n c e n t r a t i o n must be measurable a t low v a l u e s ,  d)  must not d i s t u r b the f l u i d f l o w p a t t e r n s when i n j e c t e d i n t o  i n w a t e r - s a t u r a t e d MIBK,  an o p e r a t i n g e)  i n MIBK - s a t u r a t e d w a t e r ,  column,  must not adsorb a t MIBK - water i n t e r f a c e o r a t any  solid-  l i q u i d i n t e r f a c e i n t h e column, f)  must n o t r e a c t c h e m i c a l l y w i t h w a t e r , MIBK, o r any  solid  s u r f a c e i n t h e column, and g)  t h e m o l e c u l a r d i f f u s i v i t y i n MIBK -> s a t u r a t e d w a t e r must be n e g l i g i b l e compared w i t h t h e a x i a l eddy d i f f u s i v i t y . The t r a c e r s c o n s i d e r e d , the method o f q u a n t i t a t i v e  a n a l y s i s f o r t h e i r c o n c e n t r a t i o n , and t h e i r s h o r t c o m i n g s , i f any, a r e l i s t e d below. a)  Ferric nitrate.  A n a l y s i s f o r t h i s compound would be by the  t h i o c y a n a t e method making use o f c o l o r i m e t r y .  Ferric  n i t r a t e hydrolyses i n MIBK-saturated water, f e r r i c hydroxide precipitating. b)  Hydrochloric acid.  . A n a l y s i s would be by t i t r a t i o n ,  Very  low c o n c e n t r a t i o n s a r e n o t e a s i l y measurable. c)  P o t a s s i u m c h l o r i d e . A n a l y s i s would be c a r r i e d out by means  of c a n d u c t i m e t r y .  Very low c o n c e n t r a t i o n s a r e n o t e a s i l y  measurable. d)  Water s o l u b l e dyes.  S o l u t i o n s o f these compounds would be  analysed c q l o r i m e t r i c a l l y .  Even c o m p l e t e l y i o n i s e d dyes,  such as c r y s t a l v i o l e t , d i s s o l v e i n w a t e r - s a t u r a t e d MIBK. e)  Cupric sulphate.  A n a l y s i s would be by t h e d i t h i z o n e method  making use o f c o l o r i m e t r y . f)  Sodium c h l o r i d e .  Dithizone i s quite unstable.  A n a l y s i s would be f o r sodium b y means o f  atomic a b s o r p t i o n spectrophotometry.  The m o l e c u l a r  d i f f u s i v i t y o f sodium c h l o r i d e i n water i s 0.00005-ft./hr. a t 65°F f o r c o n c e n t r a t i o n s between  0 and 1-molar (128).  No d a t a i s a v a i l a b l e f o r t h i s d i f f u s i v i t y i n MIBK-saturated water, b u t i t i s e x p e c t e d t h a t the v a l u e would be c l o s e l y s i m i l a r t o t h a t f o r . p u r e water and t h i s v a l u e has been used. A x i a l eddy d i f f u s i v i t i e s i n t h i s work were found t o be  2 always g r e a t e r than 7 - f t . / h r .  Thus t h e c o n d i t i o n t h a t the  m o l e c u l a r d i f f u s i v i t y i s n e g l i g i b l e compared w i t h the a x i a l e d d y . d i f f u s i v i t y i s met. A s o l u t i o n o f sodium c h l o r i d e i n MIBK - s a t u r a t e d water was found t o be a s u i t a b l e t r a c e r .  The d i s t r i b u t i o n  coefficient*  f o r sodium c h l o r i d e between MIBK - s a t u r a t e d water and water s a t u r a t e d MIBK was found t o be 7060.  * The d i s t r i b u t i o n c o e f f i c i e n t i s d e f i n e d here as t h e concen- t r a t i o n o f sodium c h j o r i d e i n t h e aqueous l a y e r d i v i d e d by the c o n c e n t r a t i o n o f t h a t compound i n t h e ketone l a y e r where c o n c e n t r a t i o n s a r e e x p r e s s e d i n t h e u n i t s o f weight p e r u n i t volume o f s o l u t i o n .  4.  SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER The  a p p a r a t u s was s e t up a s shown i n F i g u r e s  with the f o l l o w i n g modifications.  The t h i r d  9 and 14  polyethylene  g a s k e t below t h e p i s t o n was exchanged w i t h t h e T e f l o n f u r t h e r down t h e column.  gasket  The hypodermic n e e d l e s u p p o r t i n g t h e  t r a c e r . d i s t r i b u t o r remained i n t h i s T e f l o n gasket so t h a t  there  were o n l y two hypodermic needle s a m p l i n g p o s i t i o n s between t h e t r a c e r d i s t r i b u t o r and t h e p i s t o n .  The MIBK l e a v i n g t h e E l g i n  head passed d i r e c t l y t o t h e MIBK f e e d t a n k . MIBK f e e d s t o c k s were f r e e o f " a c e t i c a c i d .  The aqueous and The f l o w s o f MIBK  and aqueous phases were s t a r t e d and t h e i n t e r f a c e l e v e l was e s t a b l i s h e d as d e s c r i b e d under t h e h e a d i n g 1: The operating  i n the present section of the t h e s i s  Column O p e r a t i o n .  e x p e r i m e n t s were performed under t h e f o l l o w i n g conditions  Continuous, phase superficial velocity, ft?/hr. f t ?  36.5 36.5 27.7  D i s p e r s e d phase superficial velocity, .  '-  ft?/hr. f t  2  128 30.4 128  A one m o l a r sodium c h l o r i d e t r a c e r f e e d s o l u t i o n was p r e p a r e d by d i s s o l v i n g a weighed amount o f sodium c h l o r i d e i n MIBK saturated  w a t e r (H9)-  T h i s s o l u t i o n was s t a r t e d i n t o t h e  column as soon as t h e i n t e r f a c e , l e v e l had been e s t a b l i s h e d i n the E l g i n head.  The column was r u n f o r one hour t o a l l o w  steady s t a t e c o n d i t i o n s  t o be a t t a i n e d .  study of steady s t a t e times a r e discussed  (Experiments f o r t h e later.)  F i v e hook-  probe samples  were taken from e q u a l l y spaced p o s i t i o n s  the h e i g h t o f the p i s t o n b l o c k . was .5-ml./min.• Four hypodermic  throughout  The hook-probe sampling r a t e needle samples were taken,  one through each o f the gaskets immediately above and below the p i s t o n b l o c k , and one through each o f those a p p r o x i m a t e l y s i x i n c h e s above and below the p i s t o n b l o c k . sample was  taken.  F i n a l l y a piston  H a l f hour time i n t e r v a l s were a l l o w e d between  t a k i n g each probe sample, between t a k i n g the l a s t probe and the f i r s t  hypodermic  l a s t hypodermic  needle sample,  and between t a k i n g the  needle sample and the p i s t o n sample.  aqueous phase o f each sample was Of a P e r k i n - E l m e r 303  sample  The  a n a l y s e d f o r sodium by means  atomic a b s o r p t i o n spectrophotometer.  5.  AXIAL EDDY DIFFUSIVITY AND  DISPERSED PHASE HOLD-UP  a)  S t u d i e s i n the l f - I n . . I.D.  column.  I n i t i a l l y a few experiments were performed i n o r d e r t o see whether or not the d i s p e r s i o n model would d e s c r i b e the e x p e r i m e n t a l d a t a a d e q u a t e l y and, t h e r e f o r e , whether o r not a x i a l eddy d i f f u s i v i t i e s c o u l d be determined from t h i s model. These experiments were c a r r i e d out i n a manner i d e n t i c a l t o t h a t f o r the main b u l k o f experiments which i s d e s c r i b e d below. I t was  found t h a t a p l o t o f the l o g a r i t h m of t h e c o n c e n t r a t i o n  of t r a c e r v e r s u s h e i g h t up the column was the d i s p e r s i o n model was  linear;  accordingly  adopted.  In a d d i t i o n , b e f o r e the main b u l k o f e x p e r i m e n t a l d a t a was  c o l l e c t e d some experiments were c a r r i e d out t o j u s t i f y  some o f the e x p e r i m e n t a l t e c h n i q u e s used.  S i n c e these e x p e r i -  ments u s u a l l y were c a r r i e d out i n c o n j u n c t i o n w i t h a x i a l eddy, d i f f u s i v i t y determinations  t h e i r d e s c r i p t i o n w i l l be g i v e n  f o l l o w i n g t h a t o f t h e main experiments.  The apparatus used f o r  the s u b s i d i a r y experiments d e s c r i b e d under i i ) t o v i i i ) i n c l u s i v e below was i d e n t i c a l t o t h a t used f o r t h e main e x p e r i ments.  i)  A x i a l eddy d i f f u s i v i t y  The  determinations.  column was s e t up as shown i n F i g u r e s 9 and 10 except  t h a t t h e MIBK l i n e from t h e E l g i n head l e d d i r e c t l y t o t h e MIBK f e e d tank so t h a t MIBK r e c y c l e d through t h e apparatus. As r e q u i r e d , some n o z z l e t i p s o f t h e d i s p e r s e d phase d i s t r i b u t o r were b l o c k e d  o f f w i t h T e f l o n caps o r p l u g s a c c o r d i n g t o  the. p a t t e r n s shown i n F i g u r e s 15 t o 18  t o ensure t h e d e s i r e d  average v e l o c i t y o f d i s p e r s e d phase i n t h e n o z z l e t i p s .  The  f l o w o f MIBK i n t o t h e column was s t a r t e d , and t h e r e a f t e r maintained  a t the d e s i r e d r a t e .  Water was pumped i n t o the  column a t the maximum p o s s i b l e r a t e u n t i l the i n t e r f a c e i n the E l g i n head reached a predetermined l e v e l .  The f l o w r a t e o f  water was then reduced t o t h e e x p e r i m e n t a l  value and water  was a l l o w e d  t o leave, the column a t such a r a t e so as t o m a i n t a i n  the d e s i r e d constant  interface level.  The t r a c e r ( l - m o l a r  sodium c h l o r i d e s o l u t i o n i n MIBK - s a t u r a t e d water) was f e d t o the column a t a p p r o x i m a t e l y aqueous phase.  1$ o f the v o l u m e t r i c f l o w r a t e o f the  A f t e r a l l o w i n g t h e column t o r e a c h  steady  state  o p e r a t i n g c o n d i t i o n s t e n aqueous phase samples were taken by means o f the hypodermic n e e d l e s ,  one a t a time.  The f i r s t  sample was taken with, the lowest needle in the column, the second sample from the next needle up the column, and so on.  The samples  were withdrawn from the centre of the column and at a rate less than 1-5$ of the volumetric flowrate of aqueous phase though the column.  The description of experiments performed to investigate  radial concentration gradients and also the effect of sampling rate upon the column operation are discussed later.  When a  hypodermic needle was not "being used i t was withdrawn to the column wall.. The flowrate of each phase from the column was determined by weighing a sample collected over a suitable time interval.  The average of the temperatures of the fluids i n the  upper and lower sections of the Elgin head, of the f l u i d at the lower end of the column, and of the ketone phase entering the column was recorded. Finally three piston samples were taken at intervals of ten minutes and the volumes of the two phases in each sample recorded. The tracer concentration i n each of the ten hypodermic needle samples and in the aqueous phase leaving the column were measured by means of spectrophotometer.  an atomic absorption,  (Analysis was for sodium.) The calibration  line for the atomic absorption spectrophotometer always was found to be a straight line.  The equation for this line was cal-  culated by the method of least squares.  Samples whose concen-  trations were less than 0.05-microgm. sodium/ml. were discarded on the grounds of unreliability.  The probable error in the  concentration of a sample determined by this method was less than 2 $ .  E x p e r i m e n t s were performed a t a l l p o s s i b l e c o m b i n a t i o n s o f the  following operating conditions.  c o n t i n u o u s phase superficial velocity, ft?/hr. f t  d i s p e r s e d phase superficial velocity, ft?/hr. f t  2  9-0 18.2 27.7 36.5 kQ.k For  2  nozzle t i p average i n s i d e diameter, i n .  36.5 54.7 -73-0 91.2 110 128 .  '  0.053 0.086 0.103 0.126  each s e t o f n o z z l e t i p s about 10 photographs o f t h e  drops w i t h i n the column were t a k e n as d e s c r i b e d e a r l i e r the  under  h e a d i n g A p p a r a t u s a t t h e o p e r a t i n g c o n d i t i o n s shown i n each  l i n e shown i n the f o l l o w i n g t a b l e . c o n t i n u o u s phase superficial velocity, ft?/hr. f t  d i s p e r s e d phase superficial velocity, ft?/hr. f t  2  9.0 27.7  2  36.5 36.5 36.5 54.7 91-2  kQ.k  27.7 27.7  Some, b u t not a l l , o f t h e photographs were t a k e n d u r i n g runs f o r d e t e r m i n i n g a x i a l eddy d i f f u s i v i t i e s .  However, t h o s e  not t a k e n d u r i n g r u n s were t a k e n under column o p e r a t i n g conditions  i d e n t i c a l t o those which a p p l i e d d u r i n g runs.  p h o t o g r a p h i c n e g a t i v e s were examined by means o f a model M.P.E. m i c r o f i l m r e a d e r .  The  Recordak  The drop s i z e d i s t r i b u t i o n s  were  d e t e r m i n e d by measuring t h e v e r t i c a l and h o r i z o n t a l d i m e n s i o n s of t h e p r o j e c t e d images o f the' d r o p s .  W i t h the p h o t o g r a p h i c  Ik  c o n d i t i o n s d e s c r i b e d e a r l i e r the depth o f f o c u s i n c l u d e d the whole o f the column c r o s s - s e c t i o n .  Only the drops l y i n g  within  the c e n t r a l U6$> o f the column image, as p r o j e c t e d on the s c r e e n , ware examined, because as determined by experiments  described  below, the drops f a l l i n g w i t h i n t h e s e l i m i t s were not optically.  F i v e hundred drops were measured f o r each s e t o f  column o p e r a t i n g c o n d i t i o n s g i v e n i n the l a s t  ii)  distorted  table.  O p t i c a l d i s t o r t i o n of drops.  As mentioned  e a r l i e r o p t i c a l d i s t o r t i o n was  reduced con-  s i d e r a b l y by s u r r o u n d i n g the round g l a s s column w i t h a f l a t - s i d e d Perspex box. The  D e t a i l s o f the box a r e p r e s e n t e d i n Appendix  space between the box and the column was  water.  The  V.  f i l l e d with d i s t i l l e d  same p h o t o g r a p h i c c o n d i t i o n s were used f o r the  c a l i b r a t i o n photographs as f o r the photographs  taken t o determine  drop s i z e d i s t r i b u t i o n s as d e s c r i b e d under the heading A p p a r a t u s . The same 6 - i n . l o n g s e c t i o n o f column was  used f o r the  calib-  r a t i o n s as was  used f o r the a c t u a l drop s i z e  distribution  measurements.  The Perspex box was n o t s h i e l d e d from extraneous  l i g h t as i n t h e drop s i z e d i s t r i b u t i o n s t u d i e s s i n c e the photographs were taken i n a darkroom.  Photographs were t a k e n o f a  5 / 3 2 - i n . diameter b a l l b e a r i n g s i l v e r s o l d e r e d t o a s t e e l wire.  The b a l l ! was  stainless  photographed a t p o s i t i o n s shown i n  F i g u r e 2 3 f o r each o f the h o r i z o n t a l p l a n e s l o c a t e d -§-in. above and ^ - - i n . below the c e n t r e o f the P e r s p e x b o x .  Two  sets  7 5  FIGURE 23.  OPTICAL DISTORTION INVESTIGATION, lf-IN. I.D. COLUMN  o f photographs were taken, and  one w i t h MIBK - s a t u r a t e d water,  one w i t h a s o l u t i o n o f sodium c h l o r i d e i n MIBK - s a t u r a t e d  water i n t h e column.  F o r t h i s second s o l u t i o n t h e c o n c e n t r a t i o n  o f sodium was lOO-microgm./ml.  iii)  E f f e c t of t r a c e r feed rate The  f e e d r a t e o f t r a c e r s o l u t i o n i n t o t h e column  "be low enough so as n o t t o d i s t u r b t h e f l u i d f l o w w i t h i n t h e column.  should  patterns  The e f f e c t o f t r a c e r f e e d r a t e was s t u d i e d  u s i n g t h e s u p e r f i c i a l v e l o c i t i e s o f t h e two phases, and o f t h e t r a c e r f e e d s o l u t i o n s u p p l i e d t o t h e column, g i v e n i n each l i n e o f the f o l l o w i n g t a b l e .  Only t h e n o z z l e t i p s o f  in.  study.  I . D. were used f o r t h i s  Continuous phase, ft?/hr. f t ? ;  Dispersed .  ft?/hr. f t ?  27-7 . 27-7 '• 27.7 18.2 • . •• . 18.2 18.2 iv)  Steady-state  The  phase,  ••' 30.4 30.4 - 30.4  73 73 '. . 73  0.103-  Tracer solution, ft?/hr. f t ?  0.16 0.31 0.62 0.10 0.20  ., :  0.40  time.  experimental  conditions f o r sections i v ) to v i i i )  i n c l u s i v e a r e shown i n each l i n e o f t h e f o l l o w i n g t a b l e  Continuous phase superficial velocity, ft?/hr.f t  D i s p e r s e d phase superficial velocity, ft?/hr.f t  2  2  128 30.4 30.4  9 9 27-7  The time taken f o r t h e column t o r e a c h steady s t a t e  operating  c o n d i t i o n s was e s t i m a t e d by t a k i n g samples by means o f t h e first,  f o u r t h , seventh, and t e n t h hypodermic n e e d l e s above the  t r a c e r d i s t r i b u t o r , and a l s o by c o l l e c t i n g aqueous phase l e a v i n g the column.  One o f each o f these samples was taken between  3-min. and 21-min. a f t e r s t a r t - u p and then a t i n t e r v a l s between 5  v)  _ m  i  n >  and 30-min. u n t i l 2-hr. a f t e r  varying  start-up.  Reproducibility of r e s u l t s .  S e v e r a l o f the experiments f o r d e t e r m i n i n g a x i a l eddy d i f f u s i v i t y and hold-up were r e p e a t e d under i d e n t i c a l  operating  c o n d i t i o n s i n o r d e r t o t e s t 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 .  vi)  C r o s s - s e c t i o n a l homogeneity.  In a d d i t i o n t o t h e sample taken from t h e c e n t r e o f t h e column by means o f t h e hypodermic needle immediately above the t r a c e r d i s t r i b u t o r f o u r samples were taken a t t h e same e l e v a t i o n but a t p o s i t i o n s on a 1 - i n . c i r c l e c o n c e n t r i c w i t h t h e column. T h i s experiment was c a r r i e d out f o r each o f the runs l i s t e d i n s e c t i o n i v ) above.  78  v i i ) . E f f e c t o f sampling  Samples.of  rate.  the continuous phase were taken a t 0.25-ml./min.,  0.'75-ml./min.•, and 1.5-ml./min. f o r the continuous phase s u p e r f i c i a l v e l o c i t y o f 9 - f t . / h r . f t . and a t 0.5-ml./min.,  l.O-ml./min., and  2.O-ml./min.' f o r the continuous phase s u p e r f i c i a l v e l o c i t y o f O  p  27-7-ft./hr. f t f  •  '  Only the f i r s t  f o u r sampling p o s i t i o n s above the  t r a c e r d i s t r i b u t o r were s t u d i e d . viii)  E f f e c t o f o r d e r o f sampling.  •'„ ' . Samples were taken c o n s e c u t i v e l y from the lowest p o s i t i o n up t o the h i g h e s t one.  sampling  A second s e t of samples was  taken w i t h t h i s sampling o r d e r r e v e r s e d .  Both sampling o r d e r s  were used i n each o f the experiments d e s c r i b e d i n the t a b l e given i n s e c t i o n i v ) .  ix)  E f f e c t o f column l e n g t h . .  In a d d i t i o n t o - t h e s t a n d a r d experiments performed  with  the column o f h e i g h t 1 0 - f t . 3 l / 8 - i n . , as shown i n F i g u r e 10, a s i n g l e experiment was performed one o f h e i g h t 6 - f t . ' 3 f - i n . ,  i n each o f two o t h e r columns,  andthe  other of height l 6 - f t .  Uf-in. as shown i n F i g u r e s 11 and 12 r e s p e c t i v e l y .  Each o f t h e s e  l a s t two experiments was c a r r i e d out w i t h a continuous phase s u p e r f i c i a l v e l o c i t y o f \ l 8 , 2 - f t i / h r . f t . , and a d i s p e r s e d phase o  2  s u p e r f i c i a l v e l o c i t y o f 5^-7-ft./hr.: f t .  The average  I.D. o f the  n o z z l e t i p s i n b o t h experiments was  b)  S t u d i e s i n the 3 - i n . I.D.  0.103-in.  column.  A l t h o u g h the g r e a t b u l k o f the work d e s c r i b e d i n t h i s t h e s i s was  c a r r i e d out i n a l ^ - i n .  I.D.  column, some t r a c e r  experiments were c a r r i e d out i n a 3 - i n . I.D.  column.  This  column i s shown i n F i g u r e 20 and a f l o w s h e e t i s g i v e n i n F i g u r e 21. in  In o r d e r t o produce a continuous phase  superficial  the column g r e a t e r t h a n l O O - f t . / h r . f t . i t was  velocity  necessary to  p r e s s u r i z e the aqueous phase f e e d tanks t o 15 p . s . i . g . w i t h nitrogen.. I.D. was  Only one s e t o f n o z z l e t i p s o f 0.102-in. average used.  I t was  not p o s s i b l e t o measure the d i s p e r s e d  phase hold-up because a p i s t o n sampler f o r t h i s column was a v a i l a b l e . As w i t h the l-jjf-in. I.D.  not  column, experiments were  c a r r i e d out i n c o n j u n c t i o n w i t h the a x i a l eddy d i f f u s i v i t y experiments t o j u s t i f y some o f t h e e x p e r i m e n t a l t e c h n i q u e s used for  the 3 - i n . I.D.  column.  The experiments w i t h t h i s column are  d e s c r i b e d below.  i)  O p t i c a l d i s t o r t i o n of drops.  The p h o t o g r a p h i c t e s t s e c t i o n was I.D.  a 6-In. l o n g , 3 - i n .  l e n g t h o f Pyrex Double Tough g l a s s p i p e which was  a 1 - f t . l o n g f l a n g e d s e c t i o n as d e s c r i b e d e a r l i e r .  c u t from  T h i s pipe  was  surrounded by a f l a t - s i d e d Perspex box and the space between  the  p i p e and the box was  f i l l e d w i t h d i s t i l l e d water.  The  p h o t o g r a p h i c c o n d i t i o n s were s i m i l a r t o t h o s e used f o r t h e l - | - i n . I.D. column*  A Kakonet - I I e l e c t r o n i c f l a s h u n i t was used f o r  l i g h t i n g purposes. b a l l bearing.  Photographs were t a k e n o f a 5/32-in. d i a m e t e r  The b a l l was photographed a t p o s i t i o n s shown i n  F i g u r e 2k f o r each o f t h e h o r i z o n t a l p l a n e s l o c a t e d 1-^-in. above and 1-^-in. below t h e c e n t r e  o f t h e P e r s p e x box.  Two  s e t s o f photographs, were t a k e n , one w i t h MIBK - s a t u r a t e d w a t e r , and one w i t h a s o l u t i o n o f sodium c h l o r i d e i n MIBK s a t u r a t e d water i n the column. c o n c e n t r a t i o n o f sodium was ii)  F o r t h i s second s o l u t i o n the  100-microgin./ml.  Steady-state time.  The e x p e r i m e n t a l c o n d i t i o n s f o r s e c t i o n s i i ) and i i i ) a r e g i v e n i n each l i n e o f the f o l l o w i n g t a b l e . Column  I.D. = 3 - i n .  .Average n o z z l e t i p I.D. = 0.102-in. Continuous phase superficial velocity, ft?/hr... f t ?  . ••  D i s p e r s e d phase superficial velocity, ft^/hr. ft? ,  18.2 .100 •  36.5  18.2  109 ,  36.5  Samples were taken..by means, o f the f i r s t , f o u r t h , s e v e n t h , and t e n t h hypodermic n e e d l e s above t h e t r a c e r d i s t r i b u t o r , and a l s o by c o l l e c t i n g aqueous phase l e a v i n g the column.  One o f each o f  81  CAMERA  FIGURE 2k.  OPTICAL DISTORTION INVESTIGATION, 3-IN. I.D. COLUMN  82  these samples was taken between 2-min. and 10-rmin. after startup and. then. at intervals varying between 5-min- and 30-min. until 1^-hr.  iii)  after start-up.  Reproducibility  of results.  Several of the experiments for. determining axial eddy diffusi v i t y were repeated under identical operating conditions in order to test the reproducibility of results. .  iv)  Cross-sectional homogeneity. In addition to the samples taken from the centre of the  column by means of the f i r s t and f i f t h hypodermic needles above the tracer distributor samples were taken, from; positions; 'shown in the following sketch at each of the two above mentioned sampling elevations.  These sets of samples were collected for each of  the column operating conditions shown in the following  . Continuous, phase superficial'velocity, .  ft-Vhr. f t 18.2 100 18.2 100 18.2 100  2  table.  Dispersed "phase superficial velocity, ft?/hr. f t •  36.5 36.5 73 73 109 109  2  83  v)  A x i a l eddy d i f f u s i v i t y d e t e r m i n a t i o n s .  The experiments performed t o determine a x i a l eddy d i f f u s i v i t i e s were c a r r i e d out i n a manner s i m i l a r t o t h a t f o r the l f i n . I.D. column. . The e x p e r i m e n t a l c o n d i t i o n s a r e g i v e n i n Table IV-5, Appendix  IV.  A sampling r a t e o f 3-nil./min. was  used i n a l l experiments i n the 3 - i n * I«D. column.  Photographs were taken o f the f l u i d s w i t h i n the c a l i b r a t e d g l a s s s e c t i o n d e s c r i b e d e a r l i e r which was i n s t a l l e d as the e i g h t h 6 - i n . s e c t i o n above t h e t r a c e r d i s t r i b u t o r .  This  section  of column' was surrounded by a f l a t - s i d e d Perspex box as shown i n Appendix V.  The p h o t o g r a p h i c c o n d i t i o n s were s i m i l a r t o  those used f o r t h e i f - i n .  I.D. column.  A Kakonet  f l a s h u n i t was used f o r l i g h t i n g purposes.  - II electronic  The column o p e r a t i n g  c o n d i t i o n s f o r which photographs were t a k e n a r e shown i n each l i n e o f the f o l l o w i n g t a b l e . D i s p e r s e d phase superficial velocity,  Continuous phase superficial velocity, ft?/hr. f t  TtJ/hr. f t  2  . 18.2 36.5 75 • 220  6.  2  36.5 36.5 36.5 36.5  CONCENTRATION PROFILES WITH MASS TRANSFER  The l f - i n . and 10.  I.D. column was  s e t up as shown i n F i g u r e s 9  The t r a c e r d i s t r i b u t o r , and t h e T e f l o n gasket t h r o u g h  which the t r a c e r s u p p l y hypodermic  needle passed, were r e p l a c e d  by a s t a n d a r d l / l 6 - i n . t h i c k T e f l o n g a s k e t .  Acetic acid  was  t r a n s f e r r e d from the c o n t i n u o u s phase t o the d i s p e r s e d phase. The c o n c e n t r a t i o n p r o f i l e i n each phase was measured.by means o f the b e l l - p r o b e and hypodermic  n e e d l e s as d e s c r i b e d below.  , The column was brought t o t h e o p e r a t i n g c o n d i t i o n as d e s c r i b e d under s e c t i o n 2 o f E x p e r i m e n t a l P r o c e d u r e .  The  times  a t w h i c h steady s t a t e c o n d i t i o n s were a t t a i n e d were determined by t a k i n g samples by means o f t h e l o w e s t and the h i g h e s t hypodermic n e e d l e s and o f t h e aqueous phase l e a v i n g t h e column a t various times a f t e r s t a r t - u p .  A l l hypodermic  needle samples  i n t h i s p a r t o f the work were t a k e n a t S/^-ml./min.  During  a c t u a l runs samples were t a k e n w i t h the b e l l - p r o b e a t the l e v e l s  of the f i r s t ,  third, f i f t h ,  seventh, n i n t h , and t e n t h hypo-  dermic needles up t h e column,  A b e l l - p r o b e sampling r a t e o f  5.2-ml./min. was used f o r i each sample taken.  Samples were not  taken by means o f t h e b e l l - p r o b e a t a l l l e v e l s o f the n e e d l e s because  o f the l e n g t h y procedure o f sampling w i t h t h e b e l l -  probe.  The b e l l - p r o b e was r a i s e d above the i n t e r f a c e and a f t e r  a h a l f - h o u r i n t e r v a l aqueous phase samples were taken w i t h the hypodermic  needles c o n s e c u t i v e l y s t a r t i n g w i t h the lowest one.  Samples o f the i n l e t and o u t l e t streams o f the column were taken a t t h e b e g i n n i n g o f s t e a d y - s t a t e o p e r a t i o n , a f t e r the b e l l probe samples had been taken, and a f t e r t h e hypodermic samples had been t a k e n .  needle  F i n a l l y a p i s t o n sample was taken i n  o r d e r t o measure t h e d i s p e r s e d phase hold-up.  Each b e l l - p r o b e  sample was shaken, v i g o r o u s l y many times t o b r i n g t h e two phases to e q u i l i b r i u m .  Each phase o f each sample was a n a l y s e d f o r  a c e t i c a c i d by t i t r a t i n g w i t h s t a n d a r d sodium hydroxide as d e s c r i b e d e a r l i e r .  solution  The column O p e r a t i n g c o n d i t i o n s s t u d i e d  a r e g i v e n i n each l i n e o f t h e f o l l o w i n g  table.  Run  D i s p e r s e d phase • • superficial velocity,  Continuous phase superficial velocity, ,  Jl  J2 J3 jk  J5  •  ft^/hr. f t ?  36.5 ' • 18.2 : 36.5 ;  k&.k kQ.k  '  ft^/hr. f t ?  5^-7 . 5U.7 91.2 91.2 128  RESULTS AND  An i n i t i a l I n v e s t i g a t i o n was  DISCUSSION  undertaken to assess  methods o f removing samples o f e i t h e r phase f r o m the spray column.  various  operating  P r e v i o u s measurements o f c o n c e n t r a t i o n p r o f i l e s  w i t h i n a l i q u i d - l i q u i d e x t r a c t i o n spray column a t The U n i v e r s i t y o f B r i t i s h Columbia, i n v o l v e d the t a k i n g o f samples by means the hook, and the b e l l - p r o b e s mentioned e a r l i e r (35, 37,  38,  of 39).  As d i s c u s s e d under the h e a d i n g I n t r o d u c t i o n some doubt e x i s t e d as t o whether the s o l u t e c o n c e n t r a t i o n i n the Continuous phase e n t e r i n g the hook-probe:was the same as t h a t i n the  continuous  phase e n t e r i n g , the b e l l - p r o b e a l o n g w i t h the d r o p s .  Accordingly  v a r i o u s methods o f s a m p l i n g  o f the phases were i n v e s t i g a t e d i n  t h i s work.  A d i s c u s s i o n of the: r e s u l t s i s presented  -  o f t h e ,. s a m p l i n g  technique  as a whole a f t e r a l l o f these r e s u l t s a r e  studies  given.  T h i s procedure' has been adopted i n o r d e r t h a t comparisons  and  c o n t r a s t s between the r e s u l t s of v a r i o u s i n v e s t i g a t i o n s can  be  seen more e a s i l y .  1 . . RESULTS OF SAMPLING TECHNIQUE STUDIES  a) Sampling w i t h hook and b e l l - p r o b e s and p i s t o n w i t h mass t r a n s f e r between the phases. Samples were taken from the o p e r a t i n g spray column w i t h the hook and t h e b e l l - p r o b e s a t v a r i o u s l o c a t i o n s shown f o r a  t y p i c a l r u n i n the a b s c i s s a o f F i g u r e 2 5 p i s t o n sample a l s o was taken.  In each such r u n a  The c o n c e n t r a t i o n o f a c e t i c a c i d  i n the ketone phase o f a b e l l - p r o b e sample was c a l c u l a t e d by means.of e q u a t i o n  6 as d e s c r i b e d  earlier.  V a C  D  =  C  D  +  ,  C  FT  ( C  / a C " C C  \ }  6 The  v a l u e o f c^ was taken t o be t h e c o n c e n t r a t i o n o f a c e t i c  a c i d i n the hook-probe sample taken from t h e same sampling e l e v a t i o n as t h e b e l l - p r o b e sample.  An average c o n c e n t r a t i o n i n  each phase over the p i s t o n h e i g h t was determined from t h e r e s u l t s o b t a i n e d w i t h each probe by g r a p h i c a l i n t e g r a t i o n o f the r e s p e c t i v e c o n c e n t r a t i o n p r o f i l e s o f the. s o r t shown i n Figure 2 5 '  The average c o n c e n t r a t i o n o f a c e t i c a c i d i n t h e  ketone phase o f the p i s t o n sample was c a l c u l a t e d b y means o f Equation  6 where c^ was taken t o be t h e average c o n c e n t r a t i o n  i n t h e aqueous phase over t h e p i s t o n h e i g h t c a l c u l a t e d from the hook-probe sample r e s u l t s I t i s assumed t h a t b a c k m i x i n g o f t h e continuous be r e p r e s e n t e d  by "packets"  d i s p e r s e d phase drops.  o f continuous  Presumably these  m a i n l y t h e wakes o f r i s i n g drops*.  phase r i s i n g w i t h t h e "packets"  are, i n fact,  On t h i s b a s i s i t i s shown i n  Appendix I I I t h a t f o r a p i s t o n sample t h e average of a c e t i c . a c i d i n t h e continuous  phase can  concentration  phase, e x c l u d i n g t h a t i n  * Note t h a t the d e r i v a t i o n o f E q u a t i o n I I I - 8 i n Appendix I I I i s g e n e r a l i n t h a t wakes are. not mentioned. In t h e model used t h e r e c^ i s t h e average c o n c e n t r a t i o n o f s o l u t e i n t h e d e s c e n d i n g continuous.phase a t the e l e v a t i o n under c o n s i d e r a t i o n .  such wakes, i s g i v e n by E q u a t i o n  c  III-8.  C  III-8 The average c o n c e n t r a t i o n o f a c e t i c . a c i d i n the d i s p e r s e d phase o f each p i s t o n sample was by means o f E q u a t i o n 6.  c a l c u l a t e d a second time  However, i n s t e a d o f ' u s i n g c  hook-pro^e sample r e s u l t s as mentioned above, c from E q u a t i o n - . 1 1 1 - 8 . a p p l i e d t o the p i s t o n  p  from the  was determined  sample.  The r e s u l t s o f sampling the phases, i n the o p e r a t i n g  spray  column w i t h the hook and the b e l l - p r o b e s and t h e p i s t o n f o r each o f s e v e r a l runs a r e g i v e n i n Table 3 -  The r e s u l t s o f a  t y p i c a l e x p e r i m e n t a l r u n a r e shown g r a p h i c a l l y i n Figure. 2 5 »  b ) Sampling w i t h hook a n d ' b e l l - p r o b e s , hypodermic n e e d l e s , and p i s t o n w i t h mass t r a n s f e r between the phases. F u r t h e r runs were made i n which samples were t a k e n as j u s t d e s c r i b e d under a') b u t i n which c o n t i n u o u s •. phase  samples  a l s o were withdrawn by means o f hypodermic n e e d l e s i n o r d e r t o p r o v i d e an independent check on the hook-probe results.  sample  I n a d d i t i o n t o the average c o n c e n t r a t i o n s o v e r the  p i s t o n h e i g h t c a l c u l a t e d as d e s c r i b e d under a) a l l  calculations  I n v o l v i n g the hook-probe were r e p e a t e d f o r the hypodermic needle  results.  TABLE 3.  a  92.5 90.4 93-7 12^.  4  69.O  5 . b  7k:  7 C  9  d  k  87.5 11^. 87.5 11^. 87.5 113.  6  8  BELL PROBES AND  PISTON  C o n c e n t r a t i o n o f a c e t i c a c i d a t the time o f sampling, .'. . •_ . :• . l b . - m o l e s / f t ? - x "1(P" -• • • AverAverage age i n over Average Q S u p e r f i c i a l B e l l and hook probes a t p o s i t i o n piston piston in flowrates by hook h e i g h t p i s t o n by and ft3/hr.ft?by hook E q u a t i o n s 1 2 p i s t o n " and b e l l I I I - 8 and 6 3 " 4 5 * 6 7  Run  2  SAMPLING STUDIES WITH HOOK AND  ' -  87.5 3r  i;L  46.8 48.0 18.6 19.I 55-1 54.6 21.6 " 2^.5 - 60.7 25.8 ^3-9 45.2 18.2 18.7 3k.Q 39-6  48.8 49.4 50.0 20.4 ,21.3 22.3 57-3 58.0 58.6 2^.4 23.9 24.0 62.3 63.7 64.5 25.5 26.8 2 7 . 1 45.9 46.3 46.5 19.5  10.7  ik.6 40.1  15.1 40.2  40.7 ki.3 1 5 . 6 16.1 42.2 4 l . 7  33-0 35.5 35-0 13.2 .13.2 14.1  35.7 36.2 13.8 14.4  Ik.6  40.5  IQ.4  50.7 21.9 59-6 24.2 65.1 28.5 47.2 20.1 41.7 16.6  50.7 22.4 60.1 25.0 65.6 27.5 46.8 PQ-7  42.3 T5.9  49.4 20.9 58.0 : 10.6 i 63.2 13.8 , 46.1/ 16.0 40.8  49.4 21.1 58.0  49.5 21.6 55.8  2^.8  63.2 26.6 46.1  P1.6  .  62.3 23.^ 45.5 1Q.0  40.8  39-5  15.5  .15.5  43.2  41.7  .41.7  40.4  36.7 36.9 .14.6 14.6.  35.6 12.7  35-6 14.0  35.3 14.2  Hookprobe sampling rate, , ml./min.  Bellprobe sampling rate, ml./min.  8.6  20  •8.6  20  8.6  17  4  17  5  20  5  -  5  17  F o r each r u n the upper number i n each column r e f e r s t o the c o n t i n u o u s phase, the lower number t o the d i s p e r s e d phase. Each r u n was c a r r i e d out a t room temperature. The hook-probe was 0.9 i n c h e s above the sampling-.position i n d i c a t e d . The v a l u e s shown f o r the r e s p e c t i v e c o n c e n t r a t i o n s of a c e t i c a c i d i n the hook probe samples have been t a k e n from a p l o t o f the measured c o n c e n t r a t i o n s v e r s u s d i s t a n c e up the column. 'The b e l l -probe was above the i n t e r f a c e throughout the r u n . ^The hook-probe was m o d i f i e d as shown i n the sketch on page The p o s i t i o n s a t which samples were taken are i n d i c a t e d by. number i n the a b s c i s s a o f F i g u r e 25-  90  005  •  XT  CONTINUOUS PHASE  u.  z>  <-> 0 0 4 — CO UJ  i  GO*  a  o < o  002 DISPERSED PHASE  o < o z  o  &  . RUN  6  or j—  001 - O  BY  HOOK-PROBE  o  Q  BY  BELL-PROBE,HOOK-PROBE 8  o  a  AQUEOUS PHASE OF PISTON  O  KETONE PHASE OF PISTON  A  KETONE PHASE OF RSTON SAMPLE  z.  z o  000  EQN. 6  SAMPLE  SAMPLE  Ill- 8 BY EQNS. III-3 a 6 BY HOOK  a PISTON  4  PISTON SAMPLER  BY EQN.  '—  4  2 FIGURE 2 5 .  3  SAMPLING  4  5  POSITION, SCALE  6  SAMPLING TECHNIQUE STUDIES WITH HOOK AND BELL-PROBES AND PISTON  Table h shows the r e s u l t s o f sampling w i t h the hypodermic n e e d l e s , and f u r t h e r r e s u l t s o b t a i n e d w i t h . t h e probes and the p i s t o n .  The  bell-  r e s u l t s of a t y p i c a l experimental  a r e shown - g r a p h i c a l l y i n F i g u r e  c) Sampling  hook and the  run  26.  w i t h hook-probes, hypodermic n e e d l e s ; and  piston  w i t h no mass t r a n s f e r , between the phases.  F o r each r u n a s t r a i g h t . l i n e was  f i t t e d by the method o f  l e a s t squares t o a p l o t o f the n a t u r a l l o g a r i t h m o f the s o l u t e • c o n c e n t r a t i o n versus h e i g h t up the column f o r the hook-probe r e s u l t s and the hypodermic needle, r e s u l t s r e s p e c t i v e l y . e q u a t i o n f o r t h i s s t r a i g h t l i n e was  transformed  The  i n t o the  e q u a t i o n f o r the c o n c e n t r a t i o n - v e r s u s h e i g h t up the column. I n t e g r a t i o n of the t r a n s f o r m e d . e q u a t i o n c o n c e n t r a t i o n - o v e r the p i s t o n h e i g h t . of s o l u t e i n the continuous determined  produced  an  The average  average concentration  phase of a p i s t o n sample  d i r e c t l y by a n a l y s i s f o r s o l u t e .  was  This concentration  i n c l u d e d t h e . c o n t r i b u t i o n of. the wakes.  The  r e s u l t s o f sampling  technique  s t u d i e s under c o n d i t i o n s  o f no mass t r a n s f e r a r e p r e s e n t e d i n T a b l e 5« a t y p i c a l run a r e shown g r a p h i c a l l y i n F i g u r e  2.  The r e s u l t s o f 27•  DISCUSSION OF SAMPLING TECHNIQUE STUDIES In o r d e r t o understand' f u l l y what m a t e r i a l e n t e r s a  sampling d e v i c e i t would be n e c e s s a r y t o know e x a c t l y the c o n c e n t r a t i o n of s o l u t e a t every p o i n t i n the column and  TABL13 k. SAMPLING STUDIES WITH HOOK AND BELL-PROBES. HYPODERMIC NEEDLES. AND PISTON HookBellC o n c e n t r a t i o n o f a c e t i c a c i d a t the time o f sampling, l b . -moles/ft ?xio' Superficial probe prooe. sampling sampling B e l l and hook probes a t p o s i t i o n Run flowrate, „ ft./hr.ft. mS.^Ain. H G D 1 7 5 -  13  a  ., 15 16  28.9 29.6 9.87 10.6 26.8 27.3 9.83 10.2, 27.3 28.1? 9.6 1 0 . ?  87.5 11387.5 . 113. 87.5 11^.  -3. 29.9 10.9 28.2 10.5 29-7 10.9  b b  30.9 11-3 28.9 io.a 29.% 10.8  31.8 11.9 29.2 11.2  b  32.h  12.U  31.0 11.8  C o n c e n t r a t i o n o f a c e t i c a c i d a t t h e time o f sampling, l b . - m o l e s / f t . average over piston height by means o f hook and bellprobes  Run  13  15 16  hypodermic  needle a t p o s i t i o n  B  D  E  G  H  26.5  27.6 27-3  28 .h- .28.8 30.9  31.8  31.8  32.3  33-3  25-3  26.O 26.3  26.3  27.0 28.9  29.U  29.J+  29.9  30.7  25-3  26.3 27.O  27-3  27.0 29-9  30.4  30.4  3l>h  32.3  =  30.5 • 11.0 '• 28. k 10.7 29.1 11.7  hypod-ermic needles and b e l l probe  29.9 11.0 28.0 10.7 28.9 11.7  3  5  17  5  17  5  17  x 10  average i n p i s t o n b y means o f hypod-ermic needles and piston  29-9 11.3 28.0 lo.k  28.9 11.1  hookprobe and piston  30.5 8.3 28. k 8.3 29.1 10.0  equations  III-8  and 6  30.1 10.5 27.9 10.3' 28.9 10.3  ^ F o r each r u n t h e upper number i n each column r e f e r s t o the c o n t i n u o u s phase, t h e lower number t o t h e ^ d i s p e r s e d phase. Each r u n was c a r r i e d out a t room temperature. c  Samples were taken 5/8-in. above the p o s i t i o n i n d i c a t e d . * The p o s i t i o n s a t which samples were taken a r e i n d i c a t e d by number o r l e t t e r i n t h e a b s c i s s a o f F i g u r e 26. .  93  CONTINUOUS PHASE  DISPERSED PHASE  0009  O007 -  RUN 13  - O A  9  •  o  A  FIGURE 26.  BY HOOK-PROBE BY HYPODERMIC NEEDLES BY BELL-PROBE, HOOK-PROBE, 8  EQN. 6  AQUEOUS PHASE OF PISTON SAMPLE BY EQN. 111-8 KETONE PHASE OF PISTON SAMPLE BY NEEDLES a KETONE PHASE OF PISTON SAMPLE BY EQNSjIP^a 6 KETONE PHASE OF PISTON SAMPLE BY HOOK 8 PISTON L PISTON _ J ~" B C D E •SAMPLER'^ F G H j 1 2 3 4 5 6 7 SAMPLING POSITION, S C A L E : K - H l " SAMPLING TECHNIQUE STUDIES WITH HOOK AND BELL-PROBES, HYPODERMIC NEEDLES AND PISTON  TABLE 5.  SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER Sodium c o n c e n t r a t i o n s ,  Hook-probe samples  Hypodermic needle samples Run  L  C>  '  ft?/hr.  ft. /hr. 3  Height above p i s t o n centre, i n .  0  ft?  ft?  -8.96 -2.90  2.9  8.96  Average over piston  microgm./ml.  -2.88 - l A 4  0.0  2.88 0.22  O.67'  0.65  Ik  1-7  3.62  3-6  73  0.24  0.68  O.63  7^  1.7  3,9  3.8  73  39,8 3^.2  46,3  46,1  72  128.  12.6  2.0  0.25  0.035  6.7k i . 7 1  O.98  0.60 0.39  44  36.5  73-  35-2  8.0  1-5  0-33  3.6  7-0  k.7  3-5  44a  36.5  128  15.8  1.6  0.21 0.03  O.63  I.67  1.03  0.67 O.36  44b  27-T  128.  47.0  6.6  1.6  0.31  3.72  7 A  5.3  3-6  69  36.5  61.3  3^.9  19.8  60.2  54.6  46.0  46.8  Temp.  1.44  36.5  110.  Piston sample  age over piston  ^3  30.4  Avert-  Height above p i s t o n centre, i n .  2.6  2.8  °F  VO  50  o o tr ¥l0f-  O 0  00  o  Q:  fee h-  2 UJ  z  o o  RUN 4 4  I tr o •  HOOK-PROBE HYPODERMIC NEEDL  0-5  •i-J  L__J_  -8  *  -6  I  - 4 - 2  »;  L—i__J  0  •  »  6  8  HEIGHT ABOVE PISTON CENTRE, IN. FIGURE 27.  SAMPLING TECHNIQUE STUDIES WITH NO MASS TRANSFER I.  from which, p o i n t every volume element o f the sample o r i g i n a t e d . A l t h o u g h i t t u r n s out t h a t some c o n c l u s i o n s can be drawn f o r the case of no mass t r a n s f e r between the phases,  sufficient  knowledge i s not a v a i l a b l e t o do so f o r the case of mass transfer.  F o r t u n a t e l y the b u l k o f the work d e s c r i b e d i n t h i s  t h e s i s d e a l s w i t h the case where c o n c l u s i o n s  can be  drawn:  measurement of a x i a l e d d y . d i f f u s i v i t i e s where no mass t r a n s f e r between the phases occured. sampling techniques  The  comparative s i m p l i c i t y o f  the  i n the absence of mass t r a n s f e r suggests  t h a t the r e s u l t s of these  s t u d i e s be d i s c u s s e d  first.  Under c o n d i t i o n s of no mass t r a n s f e r the measured c o n c e n t r a t i o n of s o l u t e i n the continuous  phase of a p i s t o n  sample i s the average c o n c e n t r a t i o n i n t h a t phase over p i s t o n h e i g h t a t the time of sampling. account r a d i a l and the a p p r o p r i a t e and  T h i s average takes  a x i a l v a r i a t i o n s i n c o n c e n t r a t i o n , and  into includes  c o n t r i b u t i o n s from the d e s c e n d i n g continuous  from the r i s i n g aqueous phase i n the wakes.  from Table  the  I t can be  phase  seen  5 t h a t the average s o l u t e c o n c e n t r a t i o n i n a p i s t o n  sample i s found t o be,  t o a l l i n t e n t s and purposes, the same as  the average s o l u t e c o n c e n t r a t i o n over the p i s t o n h e i g h t c a l c u l a t e d from the hook-probe or the hypodermic needle r e s u l t s . e i t h e r the hook-probe or the hypodermic needles  Therefore  can be used t o  g i v e the average c o n c e n t r a t i o n of s o l u t e i n the continuous of a spray  phase  column under c o n d i t i o n s a p p l i c a b l e when t r a c e r s t u d i e s  are b e i n g c a r r i e d  out.  97  A l t h o u g h , as mentioned under t h e heading Theory, the d i s p e r s i o n model e n v i s a g e s no r a d i a l c o n c e n t r a t i o n d i f f e r e n c e s i n the continuous phase, presumably such do occur i n o p e r a t i n g columns, f o r example i n the wakes o f r i s i n g d r o p s .  However, i f the d i s p e r s i o n model i s  t o be a p p l i e d some average c o n c e n t r a t i o n must be used, and t h a t o b t a i n e d from a p i s t o n sample (and a l s o , as shown i n T a b l e 5, hy means o f the hook-probe or the hypodermic n e e d l e s ) would seem t o be a reasonable choice.  Due t o the many p r a c t i c a l problems which would  be encountered i n i n c o r p o r a t i n g s e v e r a l p i s t o n samplers a l o n g the l e n g t h of the column and of the l e n g t h y purge time needed i n t a k i n g hook-probe samples hypodermic n e e d l e s have been used f o r t a k i n g samples i n the work i n v o l v i n g t r a c e r s t u d i e s o f a x i a l eddy diffusivity.  With t h i s r a t i o n a l e f o r the use o f the hypodermic n e e d l e s e s t a b l i s h e d , i t i s i n t e r e s t i n g t o s p e c u l a t e on t h e mechanism l y i n g b e h i n d the agreement noted i n T a b l e 5 between hypodermic n e e d l e s , and hook-probe r e s u l t s under c o n d i t i o n s o f no mass transfer.  Among the t e n a b l e p o s t u l a t e s a r e the two  alternatives  t h a t e i t h e r the hook-probe and the hypodermic n e e d l e s b o t h sample the d e s c e n d i n g continuous phase and the r i s i n g wakes r e p r e s e n t a t i v e l y , or the c o n t r i b u t i o n o f the wakes t o the average s o l u t e c o n c e n t r a t i o n i n a p i s t o n sample i s n e g l i g i b l e . former e x p l a n a t i o n perhaps i s p o s s i b l e .  The  However, i t seems  u n l i k e l y t h a t i t i s t r u e because the p h y s i c a l n a t u r e s o f the hook-probe and o f the hypodermic needles a r e d i f f e r e n t  enough  t h a t these sampling d e v i c e s would be expected t o withdraw  continuous phase i n d i f f e r e n t p r o p o r t i o n s from the wakes and from the descending aqueous phase.  The second a l t e r n a t i v e ,  then,  seems more l i k e l y t o be v a l i d than does the f i r s t and i f t h i s i s accepted two p o s s i b i l i t i e s a r i s e .  E i t h e r the volume o f the  wakes i s s m a l l r e l a t i v e t o the t o t a l volume o f the continuous phase, o r the c o n c e n t r a t i o n o f s o l u t e i n the b u l k o f the continuous phase i s almost the same as t h a t i n the wakes. and Kehat  Letan  ( l 2 l ) suggest t h a t the wakes have almost the. same  volume as the drops f o r heat t r a n s f e r s t u d i e s i n a spray column. The p r e s e n t s t u d i e s o f sampling t e c h n i q u e s f o r c o n d i t i o n s o f no mass t r a n s f e r i n c l u d e c o n d i t i o n s o f d i s p e r s e d phase as h i g h as 16$.  hold-up  T h e r e f o r e , a c c e p t i n g the views o f L e t a n and  Kehat, i n t r a c e r s t u d i e s i t would appear l i k e l y t h a t the s o l u t e c o n c e n t r a t i o n i n the wakes i s almost the same as i n the b u l k o f the continuous  For  phase.  continuous phase s u p e r f i c i a l v e l o c i t i e s g r e a t e r than  about 3 6 - f t ? / h r . f t ? the r a t e o f decrease o f t r a c e r c o n c e n t r a t i o n w i t h h e i g h t up the column i s so g r e a t t h a t the t r a c e r c o n c e n t r a t i o n is.measurable o n l y i n the samples taken a t the first  two o r t h r e e sampling p o i n t s above the t r a c e r  distributor.  Because o f t h i s l i m i t a t i o n the work o f sampling under c o n d i t i o n s o f no mass t r a n s f e r was r e s t r i c t e d t o low continuous phase s u p e r f i c i a l v e l o c i t i e s .  (The work i n c l u d e s b o t h h i g h  and low d i s p e r s e d phase s u p e r f i c i a l  velocities.)  When the s t u d i e s of sampling t e c h n i q u e s f o r runs i n which mass t r a n s f e r took p l a c e between the two phases a r e c o n s i d e r e d , it  i s found t h a t d e f i n i t e c o n c l u s i o n s can not be drawn as t o  the exact s i g n i f i c a n c e o f the r e s u l t s o b t a i n e d . are  However, t h e r e  i n d i c a t i o n s t h a t the hypodermic n e e d l e s withdraw continuous  phase which i s r e p r e s e n t a t i v e of the descending phase a t the sampling e l e v a t i o n .  A comparison between the hook-probe and  the hypodermic needle r e s u l t s can be made w i t h the h e l p o f F i g u r e 26.  From t h i s f i g u r e i t can be seen t h a t the s o l u t e  c o n c e n t r a t i o n p r o f i l e i n the continuous phase o b t a i n e d by means of  the hypodermic needles l i e s below t h a t o b t a i n e d w i t h the  hook-probe.  The average  s o l u t e c o n c e n t r a t i o n i n the  phase over the p i s t o n h e i g h t c a l c u l a t e d by g r a p h i c a l of  continuous integration  the hypodermic needle r e s u l t s l i e s v e r y c l o s e t o the  average  s o l u t e c o n c e n t r a t i o n o f the descending continuous phase ( i . e . wakes excluded), i n the p i s t o n sample c a l c u l a t e d by means o f Equation III-8.  T h i s agreement of t h e r e s u l t s o f the hypodermic  n e e d l e s w i t h those c a l c u l a t e d by means o f E q u a t i o n I I I - 8  shows  t h a t , i f the model o f Appendix I I I i s c o r r e c t , e i t h e r the hypodermic needle samples c o n t a i n no continuous phase o r i g i n a t i n g In  the wakes, or continuous phase from t h i s source i n hypodermic  needle samples does not c o n t r i b u t e v e r y much t o the measured hypodermic needle sample c o n c e n t r a t i o n s .  Again t h i s small  c o n t r i b u t i o n c o u l d be the r e s u l t of the wakes b e i n g o f s i m i l a r s o l u t e c o n c e n t r a t i o n t o t h a t o f the b u l k o f the continuous phase, or the r e s u l t of the i n c l u s i o n o f o n l y a s m a l l r e l a t i v e volume of wake f l u i d  i n the hypodermic needle  100  samples.  The f i r s t  o f these l a s t two a l t e r n a t i v e s seem much l e s s  p l a u s i b l e than i t d i d f o r sampling i n t r a c e r s t u d i e s .  In the  mass t r a n s f e r case, f o r t r a n s f e r out o f the continuous phase, the wake c o n c e n t r a t i o n would be low f o r two r e a s o n s : backmixing of  d i l u t e m a t e r i a l from t h e lower end o f t h e column, and t r a n s f e r  out o f t h e wake i n t o t h e d i s p e r s e d phase.  Only t h e f i r s t o f  these two f a c t o r s o p e r a t e s i n t h e case o f t h e t r a c e r  studies.  U n f o r t u n a t e l y f u r t h e r i n f o r m a t i o n i s needed t o draw more d e f i n i t e c o n c l u s i o n s f o r the runs w i t h mass t r a n s f e r .  As t h e r e  was no evidence which i n d i c a t e d t h a t t h e n e e d l e s gave  erroneous  r e s u l t s t h e i r use as sampling d e v i c e s was adopted i n t h e f i v e mass t r a n s f e r runs performed diffusivity.  i n o r d e r t o i n v e s t i g a t e a x i a l eddy  However, t h i s procedure perhaps was no worse i n  i t s e f f e c t than was the assumption  ( r e q u i r e d f o r the d i s p e r s i o n  model) o f constant r a d i a l c o n c e n t r a t i o n i n t h e continuous phase at  a p a r t i c u l a r a x i a l p o s i t i o n which would not, o f course, have  been completely  The  valid.  s o l u t e c o n c e n t r a t i o n p r o f i l e i n the d i s p e r s e d phase i s  s u b s t a n t i a l l y the same whether i t i s c a l c u l a t e d from hook-probe and b e l l - p r o b e r e s u l t s by means o f E q u a t i o n 6 o r from hypodermic n e e d l e s and b e l l - p r o b e r e s u l t s by means o f t h e same e q u a t i o n . (See T a b l e 5-) c  p  The reasons f o r t h i s f a c t a r e t h a t the v a l u e s o f  from hypodermic needle r e s u l t s and from hook-probe r e s u l t s  d i f f e r b y r o u g h l y two p e r c e n t o n l y , and —  f o r a bell-probe  D sample i s o f t h e o r d e r o f l / 7 o n l y .  With t h i s r a t i o o f V  to V  a two  percent  change i n c  has  o n l y a n e g l i g i b l e e f f e c t on  v a l u e of C p c a l c u l a t e d by means of E q u a t i o n conclusions regarding c from the b e l l - p r o b e and with  p  Therefore  no  can be drawn from the f a c t t h a t c the hypodermic needle r e s u l t s agrees  C p o b t a i n e d from the b e l l - p r o b e and  However, due  6.  the  the hook-probe r e s u l t s .  t o the c a l c u l a t e d value o f c^ f o r a b e l l - p r o b e •  sample b e i n g i n s e n s i t i v e t o s m a l l e r r o r s i n  i t would be  expected t h a t t h i s value of c^ i s the t r u e s o l u t e  concentration  i n the d i s p e r s e d phase e n t e r i n g the b e l l - p r o b e i f i t can assumed t h a t the c  be  used does i n v o l v e o n l y a s m a l l e r r o r .  Now,  as Table k shows, the average s o l u t e c o n c e n t r a t i o n i n the d i s p e r s e d phase of a p i s t o n sample c a l c u l a t e d from hypodermic needle and p i s t o n r e s u l t s agrees w i t h the average s o l u t e c o n c e n t r a t i o n i n the d i s p e r s e d phase over the p i s t o n h e i g h t c a l c u l a t e d from hypodermic needle and b e l l - p r o b e V  A l s o , the average v a l u e :  5, and  results.  C  of —  D  f o r a p i s t o n sample i s about  t h e r e f o r e the v a l u e o f c^ o b t a i n e d from E q u a t i o n  6  a p p l i e d t o a p i s t o n sample i s much more s e n s i t i v e t o the of c^ used i n E q u a t i o n  6 than i t i s f o r a b e l l - p r o b e  Hence the agreement of the v a l u e s the c o r r e c t n e s s of the v a l u e of c  of course,  sample.  of c^ as noted above i m p l i e s p  used i n the p i s t o n  the c o n c e n t r a t i o n g i v e n by the hypodermic n e e d l e s . relies,  value  case:  A l l this  on the assumption t h a t o n l y s m a l l e r r o r s  a p p l y t o the c o n c e n t r a t i o n s  g i v e n by the hypodermic  needles.  Thus one might complain t h a t the argument g i v e n here i n v o l v e s an assumption of what i s b e i n g proved..  However, a l t h o u g h  this  102  complaint i s j u s t i f i e d t o a degree,  i t s h o u l d be r e a l i z e d t h a t i n  p r e s e n t i n g the argument the very d i f f e r e n t — ^ -  r a t i o i n the p i s t o n  D sample from t h a t i n t h e b e l l - p r o b e sample strenghtens t h e case f o r the c o r r e c t n e s s o f the hypodermic needle samples.  I f these a r e  c o r r e c t , o r even r e a s o n a b l y so, then t h e v a l u e o f the d i s p e r s e d phase c o n c e n t r a t i o n from the b e l l - p r o b e r e s u l t s a l s o i s c o r r e c t . One f u r t h e r comparison  should be made.  Table k shows t h a t  C p o b t a i n e d from t h e p i s t o n r e s u l t s i n c o n j u n c t i o n w i t h the hookprobe r e s u l t s i s lower than t h a t o b t a i n e d from t h e p i s t o n and hypodermic needle r e s u l t s o r the p i s t o n r e s u l t s and E q u a t i o n I I I - 8 . T a b l e 3 shows s i m i l a r low v a l u e s o f c ^ when t h e hook-probe a n a l y s e s a r e used i n s t e a d o f continuous phase c o n c e n t r a t i o n s from Equation I I I - 8 i n t h e c a l c u l a t i o n o f c ^ f o r t h e p i s t o n .  These  l a s t o b s e r v a t i o n s , o f course, a r e c o n s i s t e n t w i t h t h e f a c t mentioned e a r l i e r , t h a t t h e value o f c^, o b t a i n e d from E q u a t i o n agrees w i t h the hypodermic needle  III-8  results.  Now, a low value o f c ^ i s o b t a i n e d from a p i s t o n sample i f a high value o f c^ i s used i n E q u a t i o n 6.  R e c a l l i n g t h a t c^, from  E q u a t i o n I I I - 8 assumes t h e i n c l u s i o n o f no wakes, and t h a t i f wakes were i n c l u d e d , the v a l u e o f c^ would be reduced, and, t h e r e f o r e t h e v a l u e o f c ^ c a l c u l a t e d from p i s t o n r e s u l t s  raised,  we can see t h a t i f i t were p o s t u l a t e d t h a t t h e hook-probe sample i n c l u d e d an a p p r e c i a b l e and e f f e c t i v e c o n t r i b u t i o n from t h e wakes, the value o f c ^ c a l c u l a t e d from p i s t o n and hook-probe r e s u l t s would be i n c r e a s e d i n comparison  t o the v a l u e o f c  103  c a l c u l a t e d from needle and b e l l , and  p i s t o n , a l l o f which a r e i n r e a s o n a b l e  from hook-probe and  C p r e s u l t s from hook and  hook-probe c o n c e n t r a t i o n s from drop wakes. not low.  and E q u a t i o n .111-8  agreement.  However, c^  p i s t o n r e s u l t s a r e lower than the v a l u e s o f  o b t a i n e d by the o t h e r methods. low  hook and b e l l ,  Hence i t seems i m p o s s i b l e  p i s t o n measurements a r e due  that to  the  the  r e f l e c t i n g appreciable contributions  In o t h e r words c^ f o r the hook-probe i s h i g h , k c^ from the p i s t o n sample based  Furthermore i n Run  hook-probe a n a l y s e s  i s lower, indeed,  on  than the d i s p e r s e d phase  c o n c e n t r a t i o n a t the d i s p e r s e d phase i n l e t  nozzle.  l e n d s s t r o n g support  This to  result,  o f course,  i s i m p o s s i b l e , and  hypothesis  t h a t c^ from the hook-probe r e s u l t s g e n e r a l l y i s  too  c^  the  high.  It  seems advantageous.to compare hook-probe r e s u l t s  with  r e f e r e n c e t o the d i s p e r s e d phase c o n c e n t r a t i o n s , as has been done above, i n s t e a d of comparing d i r e c t l y the hook-probe and needle r e s u l t s .  There are two  reasons f o r t h i s approach.  the d i f f e r e n c e o b t a i n e d between the v a l u e s  the i m p o s s i b l e  hypodermic n e e d l e s  r e s u l t o f c^ b e i n g  First,  of c^ i s n u m e r i c a l l y  much l a r g e r than i s t h e d i f f e r e n c e between the v a l u e s the hook-probe and. the  hypodermic  o f c^ from  respectively,  Second,  c a l c u l a t e d as even lower than  t h a t i n the d i s p e r s e d phase e n t e r i n g the column i s missed when the d i r e c t comparison i s made between c^ from the and  c^ from the hypodermic  The  p o s t u l a t e c o u l d be  hook-probe  needles.  put forward  t h a t the  hook-probe  10k  tends t o suck i n m a t e r i a l from some e l e v a t i o n h i g h e r up t h e column than i t s a c t u a l p o s i t i o n .  However, when an attempt was  made t o l e s s e n such an e f f e c t h y . d i r e c t i n g t h e end o f the hook h o r i z o n t a l l y , as shown i n t h e s k e t c h on page,65, no change i n the r e s u l t s were o b t a i n e d .  Perhaps the c o m p a r a t i v e l y l a r g e  J  s i z e o f the hook-probe d i s t u r b s t h e f l o w p a t t e r n s i n t h e column t o produce h i g h continuous phase c o n c e n t r a t i o n s a t i t s inlet.  F o r example, i f t h e hook-probe d e f l e c t s drops i n such  a way t h a t e x t r a c t i o n i s l e s s complete i n t h e neighbourhood o f the hook-probe i n l e t , then h i g h c o n t i n u o u s phase c o n c e n t r a t i o n s would be measured by t h i s probe.  From p l o t s such as t h a t shown i n F i g u r e 26,  and assuming t h a t  the hypodermic needle samples a r e r e p r e s e n t a t i v e o f t h e continuous phase, i n the column a t the sampling h e i g h t , i t can be seen t h a t the continuous phase e n t e r i n g t h e hook-probe appears t o be r e p r e s e n t a t i v e o f t h a t phase i n the column a p p r o x i m a t e l y 1 - i n . above the probe e n t r a n c e .  As a r e s u l t t h e continuous phase  c o n c e n t r a t i o n p r o f i l e s g i v e n by Ewanchyna (30, somewhat i n e r r o r .  31) appear t o be  However, t h i s e r r o r i s o n l y s l i g h t and h i s  c o n c l u s i o n s mentioned under t h e heading I n t r o d u c t i o n r e g a r d i n g the end e f f e c t a t t h e continuous phase i n l e t o f the column a r e still  3.  substantially  valid.  AXIAL EDDY DIFFUSIVITY, DEOP SIZE DISTRIBUTION, AND  DISPERSED  PHASE HOLD-UP STUDIES IN THE l f - I N . I.D. COLUMN The a x i a l eddy d i f f u s i v i t y , E, c h a r a c t e r i z e s the e x t e n t t o which s o l u t e i s backmixed up the column, presumably t h r o u g h the  agency  o f wakes r i s i n g b e h i n d d i s p e r s e d phase d r o p s .  In t h i s  work v a l u e s o f E have been determined by means o f t r a c e r w i t h no mass t r a n s f e r between the phases.  studies  I f mass t r a n s f e r were  p r e s e n t some degree o f t u r b u l e n c e a t the s u r f a c e s o f the drops would be expected due t o i n t e r f a c i a l phenomena such as the Marangoni  effect.  However, the e f f e c t o f t h i s  interfacial  t u r b u l e n c e on the s i z e o f the wakes and on the manner i n which s o l u t e i s t r a n s f e r r e d out o f and i n t o the. wakes would be: . expected t o be n e g l i g i b l e compared w i t h the e f f e c t o f the o s c i l l a t i n g motion o f the d r o p s .  Consequently the v a l u e s o f  E determined by t r a c e r s t u d i e s would be expected ( s u b j e c t t o the l i m i t a t i o n s d i s c u s s e d on page 154.  ) t o be a p p l i c a b l e f o r  the case o f mass, t r a n s f e r .  A d i s c u s s i o n o f the r e s u l t s o f the main b u l k o f experiments precedes t h a t o f the p r e l i m i n a r y experiments performed i n o r d e r t o t e s t the a p p l i c a b i l i t y of. the d i s p e r s i o n model and the  suit-  a b i l i t y o f the e x p e r i m e n t a l method.  a)  A x i a l eddy d i f f u s i v i t y , drop' s i z e d i s t r i b u t i o n , and  hold-up  studies. i)  D e t e r m i n a t i o n o f a x i a l eddy d i f f u s i v i t i e s and P e c l e t numbers.  The c a l c u l a t i o n s t o be d e s c r i b e d here were performed on an IBM 7040 e l e c t r o n i c computer.  A d a t a s h e e t , a hand c a l c u l a t i o n ,  and a computer output f o r a t y p i c a l run a r e g i v e n i n Appendix  These  c a l c u l a t i o n s produced the f o l l o w i n g  IV.  quantities:  s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s , a x i a l eddy d i f f u s i v i t i e s ,  P e c l e t numbers, reduced c o n c e n t r a t i o n s , and mass b a l a n c e s . n a t u r a l logarithms p l o t t e d versus best  of the concentrations  h e i g h t down the column.  The  o f the samples were The e q u a t i o n  f o r the  s t r a i g h t l i n e through these p o i n t s was c a l c u l a t e d by the  method o f l e a s t squares.  The v a l i d i t y o f t h i s method f o r  c a l c u l a t i n g the s t r a i g h t l i n e i n v o l v e d the u s u a l assumptions concerning  the n o r m a l i t y o f t h e d i s t r i b u t i o n o f t h e n a t u r a l  l o g a r i t h m o f the c o n c e n t r a t i o n of the continuous  (125).  The s u p e r f i c i a l  phase was d i v i d e d by the a b s o l u t e  velocity  magnitude  of the s l o p e o f t h i s l i n e t o g i v e the s u p e r f i c i a l a x i a l eddy diffusivity,  ( E e ) . (See -Equation-13•)  The a x i a l eddy d i f f u s -  i v i t y , E, w a s . c a l c u l a t e d , by d i v i d i n g t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y by the v o l u m e t r i c i n the column.  f r a c t i o n , e, o f continuous  phase  The P e c l e t - number, Pe, was c a l c u l a t e d by means  of the f o l l o w i n g e q u a t i o n .  . 11-18 The i n t e r p r e t a t i o n t o be p l a c e d on the drop diameter, d^, i s d i s c u s s e d below..  In o r d e r t h a t c o n c e n t r a t i o n p r o f i l e s c o u l d be  compared f o r v a r i o u s column o p e r a t i n g c o n d i t i o n s the reduced c o n c e n t r a t i o n a t each sampling p o i n t was c a l c u l a t e d by means of the f o l l o w i n g e x p r e s s i o n .  reduced c o n c e n t r a t i o n =  a c t u a l c o n c e n t r a t i o n x 1000 c o n c e n t r a t i o n i n the aqueous phase l e a v i n g the column  Mass b a l a n c e s were c a l c u l a t e d f o r t h e aqueous phase, t h e ketone phase, and the t r a c e r , r e s p e c t i v e l y , over the column. of reduced c o n c e n t r a t i o n p r o f i l e s f o r one s u p e r f i c i a l  A set velocity  of ketone phase and v a r i o u s s u p e r f i c i a l v e l o c i t i e s o f aqueous phase i s shown i n F i g u r e 28.  The l i n e a r i t y o f each p l o t i n  F i g u r e 28 i n d i c a t e s t h a t E q u a t i o n 13,  and hence t h e d i s p e r s i o n  model concept, describe, the backmixing o f the continuous  phase.  The reduced c o n c e n t r a t i o n p r o f i l e , the d i s p e r s e d phase hold-up, the a x i a l eddy d i f f u s i v i t y , t h e P e c l e t number and t h e mass b a l a n c e r e s u l t s f o r each r u n a r e g i v e n i n T a b l e IV-k,  Appendix IV..'  As t h i s t a b l e shows a t t h e l e v e l o f a c c u r a c y p o s s i b l e i n the p r e s e n t experiments, t h e r e was no dependence o f a x i a l eddy d i f f u s i v i t y on t h e c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t y , L^-. „•• Continuous phase has been found (21,  22,  23)  i n the wakes o f r i s i n g d i s p e r s e d phase d r o p s .  t o move up the column' The v e l o c i t y o f  the drops i s n e g l i g i b l y a f f e c t e d by a s m a l l change i n the low v a l u e s of L>£ used i n the t r a c e r s t u d i e s . C o r r e s p o n d i n g l y t h e f l o w r a t e o f continuous phase up t h e column i n t h e wakes o f drops i s s u b s t a n t i a l l y u n a f f e c t e d by such a change i n the s u p e r f i c i a l v e l o c i t y o f the c o n t i n u o u s phase.  I f the a x i a l mixing of the  continuous phase i s caused by t h e drops and t h e a s s o c i a t e d - wakes it  i s not s u r p r i s i n g t h a t t h e a x i a l eddy d i f f u s i y i t y i s  independent o f used i n t h i s work.  f o r t h e narrow range o f low v a l u e s of. L Q  108  FIGURE 2 8 .  REDUCED CONCENTRATION PROFILES  109  F i g u r e 29 shows t h e dependence o f a x i a l eddy d i f f u s i v i t y on the d i s p e r s e d phase f l o w r a t e f o r one continuous and v a r i o u s drop s i z e s . approximately decreased  constant  The a x i a l eddy d i f f u s i v i t y remained as t h e d i s p e r s e d phase f l o w r a t e was  from high v a l u e s b u t a t low d i s p e r s e d phase f l o w r a t e s  the a x i a l eddy d i f f u s i v i t y i n c r e a s e d r a p i d l y . less  phase f l o w r a t e  pronounced a t s m a l l drop s i z e s .  This effect i s  The e f f e c t  of increasing  t h e drop s i z e f o r a g i v e n d i s p e r s e d phase s u p e r f i c i a l  velocity  was t o i n c r e a s e t h e a x i a l eddy d i f f u s i v i t y . At f i r s t  i t was expected t h a t an i n c r e a s e i n t h e number o f  drops o f a g i v e n s i z e p e r u n i t a larger  volume o f continuous  volume o f column would r e s u l t i n phase b e i n g c a r r i e d  up t h e column  i n t h e i r wakes and hence an i n c r e a s e i n t h e a x i a l eddy d i f f u s i v i t y , E . However, as mentioned above,, t h e o p p o s i t e e f f e c t low  i s observed a t  s u p e r f i c i a l v e l o c i t i e s , L^, o f d i s p e r s e d phase.  The  reason  f o r t h e d e c r e a s e i n E w i t h an i n c r e a s e i n t h e number o f drops c o u l d be due t o t h e i n c r e a s e i n i n t e r f e r e n c e o f t h e wakes o f drops by n e i g h b o u r i n g  drops.  T h i s i n t e r f e r e n c e would t e n d t o  d e t a c h t h e wakes from t h e drops, r e s u l t i n g Apparently  a t low v a l u e s  of  i n a lower v a l u e o f E.  the d e c r e a s e i n E due t o . i n t e r f e r e n c e  o f wakes predominates over t h e i n c r e a s e i n E due t o t h e l a r g e r number o f d r o p s . counterbalance An  A t high values o f  each  the two.effects  on E  other.  i n c r e a s e i n t h e drop s i z e , d^, f o r a g i v e n value o f  would be e x p e c t e d t o r e s u l t  i n an i n c r e a s e i n E due t o an  i n c r e a s e i n t h e s i z e o f each wake and a l s o due t o l e s s i n t e r f e r e n c e o f wakes by n e i g h b o u r i n g  drops.  However, t h e  v a l u e o f E would be expected t o decrease due t o a s m a l l e r  110  FIGURE 29. AXIAL EDDY DIFFUSIVITY' IN THE if-IN. I.D. COLUMN  number o f drops and hence fewer wakes.. A p p a r e n t l y the e f f e c t s r e s u l t i n g i n ah i n c r e a s e i n E when d^ i s i n c r e a s e d over!, those, which.would  predominate  t e n d - t o decrease E.  F i g u r e 30 shows the a x i a l eddy d i f f u s i v i t y , E, p l o t t e d a g a i n s t the s u p e r f i c i a l v e l o c i t y  o f continuous phase, L^, f o r  four, d i f f e r e n t v a l u e s - o f , t h e . • ' s u p e r f i c i a l ' . v e l o c i t y  of dispersed  -  phase, Lp.  The drop s i z e , d^, was  E i s independent o f  0.135-in.  As mentioned  earlier  and decreases w i t h an increase i n L^.  Also  shown i n Figure. 30 a r e the r e s u l t s o f Hazelbeck and G e a n k o p l i s  (42).  They used a l.kl-in.  I.D.  column, a drop s i z e , d , o f  0.134-in. and water and MIBK as the c o n t i n u o u s and d i s p e r s e d phases: r e s p e c t i v e l y . ' They used an aqueous s o l u t i o n o f potassium c h l o r i d e as t r a c e r and the s t e p f u n c t i o n method. dependence o f E °h.  f o r v a l u e s of  They found no  between l8.U-ft./h r . f t .  and; ^ 9 . 5 - f t . / h r . f t . , b u t found t h a t E i n c r e a s e d l i n e a r l y w i t h L . c  As d i s c u s s e d on page 107 o f t h i s t h e s i s i t . would expected t h a t E s h o u l d be n e a r l y independent o f  be f o r the  narrow  range o f low v a l u e s o f I _ used f o r . the experiments d e s c r i b e d i n t h i s t h e s i s and- a l s o those d e s c r i b e d by Hazelbeck.and G e a n k o p l i s . The f a c t t h a t . t h e s e workers w i t h i n i n c r e a s e i n -L^ ^may  (42), found a marked i n c r e a s e i n E have, been due t o problems  associated  w i t h t r a n s i e n t response t e c h n i q u e s d i s c u s s e d under the heading Introduction. Ee F i g u r e 30a i s a p l o t o f the d i s p e r s i o n number, -y— , a g a i n s t d . P the Reynolds number, . . .This f i g u r e shows a summary, p r e p a r e d  112  T H I S WORK"  —  —  -  C O L U M N I D . ' 1-5-IN. dp a 0 1 3 5 - IN. L , C U . F T . / ( H R . SQ.FT.) D  O Q  H A Z L E B E C K  ond  GEANK0PLIS(4gl  COLUMN ID.« I-4I-IN. d « 0-134-IN. p  L^«l8-4 to 49-5,  30-4  CU.FT.AHR.  SQ.FT.)  36 5 54-7 7 3  30  _  o  »-'20  6  co UJ  10  0J[MilllliiliiiiiiMj||lil|iii||||||MuL  0  10  20  30  40  f  50  CU.FTV(Hft. SQ.FT.)  FIGURE 3 0 . COMPARISON OF AXIAL EDDY DIFFUSIVITY AS DETERMINED IN THIS WORK WITH THAT OF OTHER WORKERS  20  0-1  0-5  10  5  10  50  REYNOLDS NUMBER =  FIGURE 30a.  d p  100 U  500  1000 2000  g  COMPARISON OF DISPERSION NUMBER AS DETERMINED I N THIS WORK WITH THAT FOR PACKED BEDS :  by L e v e n s p i e l and B i s c h o f f (73),  of the data i n the l i t e r a t u r e f o r  gas and l i q u i d f l o w t h r o u g h packed beds.  A l s o p l o t t e d are the  r e s u l t s f o r l i q u i d - l i q u i d s p r a y tower o p e r a t i o n d e t e r m i n e d i n t h i s work.' I t can be seen f r o m F i g u r e 30a t h a t t h e r e s u l t s for  s p r a y tower o p e r a t i o n more o r l e s s c o i n c i d e w i t h t h o s e f o r  l i q u i d f l o w t h r o u g h packed beds, f o r t h e l i m i t e d range o f R e y n o l d s number i n v e s t i g a t e d .  T h i s agreement s u p p o r t s t h e  correctness of the r e s u l t s of a x i a l e d d y . d i f f u s i v i t y i n a spray column p r e s e n t e d i n t h i s t h e s i s . . • . I n a d d i t i o n , i t l e n d s s u p p o r t t o t h e a p p l i c a t i o n o f t h e m i x i n g c e l l -.packed bed a n a l o g y t o s p r a y column o p e r a t i o n d e s c r i b e d below.  P l o t s o f drop P e c l e t numbers.versus d i s p e r s e d phase hold-up for  t h e f o u r d i f f e r e n t drop s i z e d i s t r i b u t i o n s s t u d i e d a r e  p r e s e n t e d i n F i g u r e s 31,  32,  33,  and 3^ r e s p e c t i v e l y .  Peclet  numbers, p r e d i c t e d on t h e b a s i s o f t h e m i x i n g c e l l - packed bed. a n a l o g y (kk, 6k, 90, 92,- 108,  109)  were c a l c u l a t e d f o r  s i x l a t t i c e arrangements o f d r o p s as shown i n Appendix I I . A l l o f t h e p r e d i c t e d P e c l e t numbers l i e i n the range between t h o s e f o r t h e l a t t i c e arrangements o f o r t h o r h o m b i c - 2 and rhombohedral - 1 r e s p e c t i v e l y .  The v a l u e s o f t h e P e c l e t  numbers f o r t h e s e two cases' a r e p l o t t e d i n each o f F i g u r e s 31,  32:,  33,  and 3^ i n o r d e r t h a t a comparison between t h e  c a l c u l a t e d and t h e p r e d i c t e d P e c l e t numbers can be made. The agreement between t h e e x p e r i m e n t a l Pe and. t h e p r e d i c t e d Pe i s v e r y good f o r l a r g e drops and becomes p r o g r e s s i v e l y worse  115  116  117 A  12  /  A  • AO 0 9 -  0-6  EXPERIMENTAL o  CL  03  I  I  L  L  90  A  18 2  •  27-7  O  36 5 48-4  THEORETICAL ORTHORHOMBSC-2 LATTICE r l LATTICE! I  1  L _ J  I  10  FIGURE 33.  1  CU.FT./(HR. SQ.FT)  V  00  C  PREDICTED AND CALCULATED PECLET NUMBERS, d 1?  l - i  I  15  = 0.125-IN.  0 o  o  Oy  o  V  EXPERIMENTAL  O A  c  CU.FT./IHR. SQ.F: 90 18 2 27-7  O  36-5  V  48-4  THEORETICAL ORTHORHOMBIC-2 LATTICE RHOMBOHEDRAL-I 01 0  LATTICE  10 h ,  15  %  FIGURE 34. PREDICTED AND CALCULATED PECLET NUMBERS, d = 0.095-IN. J?  119  as t h e drop s i z e i s reduced. g i v e n i n t h e t a b l e below. 31,  32,  A summary o f t h e comparison i s  However, o n l y by l o o k i n g a t F i g u r e s  3 3 / a n d 3^- can t h e t r e n d o f t h e e x p e r i m e n t a l p o i n t s away  from t h e p r e d i c t e d v a l u e s be seen c l e a r l y . d  P  , in.  .0.155  Percentage number o f e x p e r i m e n t a l p o i n t s i n t h e p r e d i c t e d Pe range  ^7  Percentage number o f e x p e r i m e n t a l p o i n t s w i t h i n 10$> o f t h e p r e d i c t e d Pe range  87  L a r g e s t percentage d i f f e r e n c e between t h e e x p e r i m e n t a l Pe and the n e a r e s t s i d e o f t h e p r e d i c t e d Pe range c a l c u l a t e d a l o n g a l i n e of constant h  0.125  0.135  63  0.095  53  17  70  ^3 !  . 20  28  The d r o p s , o f course,, do. n o t l i e i n an o r d e r e d  . 30  ^5  lattice  arrangement b u t a r e p o s i t i o n e d i n a random fashion r e l a t i v e t o one another a t a n y . i n s t a n t i n t i m e . i n d i c a t e t h a t t h e assumption.of  However, t h e above r e s u l t s  a. s i m p l e ; l a t t i c e , arrangement o f  drops i s o f s o m e . l i m i t e d use i n a p p l y i n g t h e m i x i n g c e l l packed bed analogy i n o r d e r t o make a f i r s t e s t i m a t e o f t h e P e c l e t number.  The m i x i n g c e l l - packed analogy p r e d i c t s a decrease w i t h a decrease i n d  P  a t c o n s t a n t h and i t p r e d i c t s a decrease  In E w i t h an i n c r e a s e i n h a t c o n s t a n t d^.  The e x p e r i m e n t a l  r e s u l t s shown i n F i g u r e 29 b e a r out t h e s e p r e d i c t i o n s qualitatively.  in E  120  ii)  C a l i b r a t i o n f o r o p t i c a l d i s t o r t i o n and drop s i z e measurements. F i g u r e 23 p r e s e n t e d e a r l i e r shows t h e p o s i t i o n s o f t h e  5/32-In. b a l l b e a r i n g . p l a c e d i n the column when the o p t i c a l d i s t o r t i o n was b e i n g measured. the  The camera, o f c o u r s e , viewed  column i n e l e v a t i o n from t h e f r o n t .  W i t h t h e camera l e n s  used t h e d e p t h o f f o c u s was such t h a t a l l t h e . d r o p s i n t h e column were i n . f o c u s . c a s e s , and.changed  D i s t o r t i o n s were s m a l l i n a l m o s t a l l  o n l y s l i g h t l y i n most cases when t h e b a l l  .moved f r o m one p o s i t i o n t o a n o t h e r .  was  Hence i t seemed r e a s o n a b l e  t o d i v i d e t h e c r o s s - s e c t i o n o f the column i n t o r e g i o n s i n each of w h i c h t h e o p t i c a l d i s t o r t i o n ' w a s t a k e n to.be c o n s t a n t . b o u n d a r i e s between r e g i o n s are. shown, i n F i g u r e 35'  The  These bound-  a r i e s w e r e - p l a c e d - e q u i d i s t a n t , from a d j a c e n t p o s i t i o n s o c c u p i e d by t h e b a l l d u r i n g t h e t a k i n g o f t h e photographs f o r c a l i b r a t i o n for optical distortion.  The o p t i c a l d i s t o r t i o n o f t h e b a l l  was  found t o be independent o f t h e h e i g h t o f t h e b a l l i n t h e photog r a p h i c t e s t s e c t i o n o f t h e column and a l s o independent o f t h e c o n c e n t r a t i o n o f t r a c e r i n t h e column.  By c o n s i d e r i n g o n l y t h e  drops w h i c h were l o c a t e d i n t h e c e n t r a l p o r t i o n s o f t h e photographs i t was p o s s i b l e t o a v o i d making d i s t o r t i o n c o r r e c t i o n s , s i n c e t h e c o r r e c t i o n s a p p l i c a b l e t o such drops were o n l y - 1$>. A c c o r d i n g l y o n l y drops i n t h e r e g i o n shown as "drop s i z e measurement f i e l d " i n F i g u r e 35 were measured f o r c a l c u l a t i n g drop s i z e distributions.  The p a r t o f t h e column.shown i n F i g u r e 35 w h i c h was used f o r drop s i z e measurements c o n t a i n e d t h e whole o f t h e c e n t r a l  121-  IDROP SIZEl MEASUREMENT FIELD  CAMERA  FIGURE 35.  PERCENTAGE ERROR IN THE EQUIVALENT DIAMETER DUE TO OPTICAL DISTORTION I N THE l | - I N . I.D. COLUMN  122  p o r t i o n , b u t n o t a l l o f t h e p e r i p h e r a l a r e a o f the column section.  cross-  As a r e s u l t a d i s p r o p o r t i o n a t e number o f drops a p p e a r i n g  i n t h e c e n t r a l p o r t i o n o f t h e column c r o s s - s e c t i o n , as opposed t o t h o s e near t h e column w a l l , were c o n s i d e r e d f o r drop s i z e d i s t r i b u t i o n measurements.  I f t h e r e were any w a l l e f f e c t on .  drop s i z e d i s t r i b u t i o n s i t was not t a k e n i n t o a c c o u n t . With.no l i q u i d i n t h e p h o t o g r a p h i c t e s t s e c t i o n o f t h e column, t h e b a l l was p o s i t i o n e d a t t h e c e n t r e of. t h i s t e s t The g l a s s column and-Perspex box were removed-without  section.  disturbing  the b a l l .  A photograph o f t h e b a l l i n a i r t h e n was t a k e n i n t h e  u s u a l way.  The d i a m e t e r o f t h e p r o j e c t e d image o f t h e b a l l i n  t h i s photograph was measured.  :  The enlargement f a c t o r f o r c a l -  c u l a t i n g t h e ;,apparertt .dimensions, o f t h e b a l l d u r i n g c a l i b r a t i o n s t u d i e s and o f drops d u r i n g drop s i z e - d i s t r i b u t i o n measurements was determined, by d i v i d i n g the;measured.diameter o f t h e p r o j e c t e d image o f t h e b a l l photographed i n a i r by t h e a c t u a l diameter of the b a l l .  The v e r t i c a l and h o r i z o n t a l d i m e n s i o n s o f t h e images o f 500 drops were measured f o r each r u n i n w h i c h drop s i z e t i o n s were d e t e r m i n e d . spheroid.-  distribu-  Each d r o p was assumed t o be an o b l a t e  T h i s a s s u m p t i o n has bgen f o u n d t o be r e a s o n a b l y good  f o r drops i s s u i n g f r o m t h e 0 . 1 0 3 - i n . I.D. n o z z l e t i p s ( 3 9 ) * The measured drop d i m e n s i o n s were c o r r e c t e d f o r o p t i c a l m a g n i f i c a t i o n , b u t no c o r r e c t i o n for- o p t i c a l d i s t o r t i o n was a p p l i e d . e q u i v a l e n t drop d i a m e t e r , d , was c a l c u l a t e d f o r each d r o p by  The  means of t h e f o l l o w i n g e q u a t i o n  h^ = t h e v e r t i c a l d i m e n s i o n o f the drop image, and -p^,. = ' t h e h o r i z o n t a l d i m e n s i o n o f t h e drop image. Out o f 13,000 drops measured  o n l y one d r o p was f o u n d t o have an  e q u i v a l e n t drop d i a m e t e r o f g r e a t e r than 0 . 2 5 - i n . not  T h i s drop was  c o n s i d e r e d t o be t y p i c a l and was not c o n s i d e r e d i n drop  s i z e d i s t r i b u t i o n ...calculations,.:. from O.OO-in. t o 0 . 2 5 - i n . was d i v i d e d up i n t o  The range o f d  i n c r e m e n t s of 0 . 0 1 - i n .  An IBM - "(OkO e l e c t r o n i c computer  was  used t o c a l c u l a t e ' t h e p e r c e n t a g e of t h e t o t a l number o f d r o p s , and t h e percentage o f t o t a l drop,volume increments.  found i n each o f t h e s e  T h e s e . c a l c u l a t i o n s were performed f o r the f i r s t  100 drops measured, t h e f i r s t 200 drops measured, t h e f i r s t 300,  t h e f i r s t kOO,  of d a t a .  and the f i r s t 500 drops measured  i n each s e t  I t was found t h a t the c a l c u l a t e d drop s i z e d i s t r i b u t i o n s  f o r . 4 0 0 and 500 drops r e s p e c t i v e l y were a l m o s t t h e same f o r each of t h e s e t s of d a t a .  E v i d e n t l y a.sample  s i z e o f 500 drops i s  s u f f i c i e n t l y l a r g e t o be r e p r e s e n t a t i v e o f the whole p o p u l a t i o n of drops i n the column.  A c c o r d i n g l y a l l subsequent d i s c u s s i o n  i n v o l v i n g drop s i z e i s based on a t o t a l o f 500 drops f o r each set  of d a t a .  A t y p i c a l s e t o f r e s u l t s ' f o r t h e drop s i z e d i s t r i b -  124  ution calculations  i s g i v e n i n T a b l e I V - 6 and p l o t t e d  i n Figure  A summary o f a l l o f t h e r e s u l t s i s p r e s e n t e d i n T a b l e I V - 7 -  36.  In  each case t h e r e was a peak between 0 . 0 1 - i n . and 0 . 0 3 - i n . i n t h e e q u i v a l e n t d i a m e t e r on t h e drop s i z e d i s t r i b u t i o n p l o t s . . addition  In  a second peak appeared a t a h i g h e r drop d i a m e t e r .  The  mean of the two l i m i t s o f t h e e q u i v a l e n t drop d i a m e t e r r a n g e , of w i d t h 0 . 0 1 - i n . , i n w h i c h t h e second peak o.ccured was t a k e n t o be t h e d r o p d i a m e t e r , d^, used i n t h e P e c l e t number c a l c u l ations.  F o r example, from F i g u r e 36 t h e drop d i a m e t e r o f 0.135-  i n . was used t o c a l c u l a t e  Pe f o r Run 50.  c l o s e - u p photographs o f a l f - i n .  R o c c h i n i (39)  I.D. s p r a y column u s i n g t h e  0.103-in. I.D. n o z z l e t i p s and w i t h t h e t r a n s f e r from t h e c o n t i n u o u s phase t o t h e d i s p e r s e d phase. conditions resulted drops were examined.  took  of a c e t i c  acid  His photographic  i n a very short depth of focus i n which R o c c h i n i d i d not use any means f o r r e d u c i n g  o p t i c a l d i s t o r t i o n b u t he c o r r e c t e d t h e drop s i z e measurements f o r o p t i c a l d i s t o r t i o n by means o f a c a l i b r a t i o n g r a p h . drop s i z e d i s t r i b u t i o n s w h i c h he p r e s e n t s (39) exactly  The  have peaks a t  t h e same e q u i v a l e n t - d r o p d i a m e t e r as shown i n F i g u r e  36.  I n t h e p r e s e n t work t h e second peak, was v e r y h i g h and narrow f o r drops produced f r o m t h e 0.053-in-. I.D. n o z z l e t i p s and v e r y low and b r o a d f o r t h e 0.126-in. I.D. t i p s .  Obviously the pro-  d u c t i o n o f i r r e g u l a r l y s i z e d drops a t t h e n o z z l e t i p s would r e s u l t i n a b r o a d peak.  However, i t i s f e l t t h a t the main r e a s o n  f o r t h e change i n t h e shape o f t h e peaks i s t h e i n v a l i d i t y o f t h e a s s u m p t i o n t h a t t h e l a r g e r drops a r e o f o b l a t e s p h e r o i d shape.  20  EQUIVALENT FIGURE 36.  DROP  DIAMETER, IM.  DROP SIZE DISTRIBUTION FOR RUN 50, AVERAGE NOZZLE T I P DIAMETER = 0.103-IN.  126  T y p i c a l photographs of drop's produced i n the. l f - i n . I.D.  column by  the f o u r d i f f e r e n t s i z e s o f n o z z l e t i p s a r e shown i n F i g u r e  37-  From photographs .such as t h e s e i t can be seen t h a t l a r g e r drops a r e more i r r e g u l a r i n shape t h a n s m a l l e r d r o p s .  T y p i c a l drop  s i z e d i s t r i b u t i o n h i s t o g r a m s f o r the 0.103-in. I.D. 0,126-in. ;T.D.- n o z z l e t i p s are p r e s e n t e d  and  the  i n F i g u r e s 36 and  38  respectively.  F o r each o f the t h r e e s m a l l e s t n o z z l e t i p d i a m e t e r s .the second peak i n t h e drop s i z e d i s t r i b u t i o n p l o t was by r u n c o n d i t i o n s .  I n the case pf t h e . n o z z l e t i p s o f average  0.126-in. the. l o c a t i o n of the- peak was r u n c o n d i t i o n s . . . The drop d i a m e t e r , was  not i n f l u e n c e d  t a k e n as 0.155-in.  influenced s l i g h t l y  dp, f o r t h e s e n o z z l e  I.D.,  by  tips  Garwin and Smith (43) r e p o r t t h a t t h e  drop s i z e . i s i n d e p e n d e n t - o f t h e c o n t i n u o u s  phase f l o w r a t e .  T h i s c o n c l u s i o n i s c o n s i s t e n t w i t h t h e above o b s e r v a t i o n s . F i g u r e 39 i s a t y p i c a l example o f p l o t s made t o show t h e o f t o t a l drop volume v e r s u s e q u i v a l e n t drop d i a m e t e r .  percent  There  was  no n o t i c e a b l e peak f o r the v e r y s m a l l d r o p s - i n t h i s s o r t o f p l o t s i n c e the c o n t r i b u t i o n o f t h e s e t o t h e t o t a l volume  was  negligible. i i i ) Hold-up s t u d i e s . P l o t s a r e g i v e n i n F i g u r e s 40, 4 l , 42, and 43 f o r the d i s p e r s e d phase hold-up•(measured by means of t h e p i s t o n ) t h e d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y f o r each o f t h e nozzle t i p sizes studied.  •  '  Weaver, L a p i d u s , and E l g i n  .  .  '  '  '  /  •  •  versus four  (41)  •  127  AVERAGE NOZZLE TIP DIA. = 0.053-IN. (RUN 148)  AVERAGE NOZZLE TIP DIA. = 0.103-IN. (RUN 65)  FIGURE 37.  AVERAGE NOZZLE TIP DIA. = 0.086-IN.  (RUN  96)  AVERAGE NOZZLE TIP DIA. = 0.126-IN. (RUN 126)  PHOTOGRAPHS OF DROPS AT OPERATING CONDITIONS CORRESPONDING TO RUNS INDICATED. MAGNIFICATION FACTOR = 3.  000  005 EQUIVALENT FIGURE 38.  010 DROP DIAMETER, IN.  015  020  DROP SIZE DISTRIBUTION FOR RUN 130, AVERAGE NOZZLE T I P DIAMETER = 0.126-IN.  0-25  005  EQUIVALENT FIGURE 3 9 .  0 85  010 DROP  DIAMETER,  0*5  DISTRIBUTION OF TOTAL PERCENT OF VOLUME OF DROPS FOR RUN 5 0 , AVERAGE NOZZLE T I P DIAMETER = 0 . 1 0 3 - I N .  FIGURE kO.  DISPERSED PHASE HOLD-UP, d  = 0.155-IEF.  131  FIGURE bl. .DISPERSED PHASE HOLD-UP, d- =  0.135-Iffi  132  FIGURE 42. DISPERSED PHASE HOLD-UP, d  = 0.125-IN.  133  o/  FIGURE 43.  DISPERSED PHASE HOLD-UP, d  = 0.095-IN.  extended the t h e o r y r e l a t i n g s l i p v e l o c i t y and hold-up i n f l u i d i z e d beds t o s p r a y column o p e r a t i o n .  They show t h a t t h e s l i p  i s e x p e c t e d t o decrease w i t h i n c r e a s i n g hold-up.  velocity  As a r e s u l t a  p l o t o f hold-up v e r s u s d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y , i s e x p e c t e d t o be c u r v e d , concave upwards.  L^,  F i g u r e s 40, 41, 42,  and 43 b e a r out t h i s p r e d i c t i o n f o r v a l u e s of  l e s s than  6 0 - f t ? / h r . f t ? However, no e x p l a n a t i o n , c o u l d be f o u n d f o r t h e l i n e a r i t y of t h e hold-up c u r v e s f o r v a l u e s o f 6 0 - f t . / h r . f t . . The v e l o c i t y ,  greater than  u, o f r i s e o f t h e d i s p e r s e d phase  drops;was o f the o r d e r o f l O O O - f t . / h r . and e x p e r i m e n t s were c a r r i e d o u t . f o r c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t i e s , L , between 9 - f t ? / h r . f t ? and 4 8 . 4 - f t ? / h r . f t ?  Increasing L  w i t h i n t h i s narrow range would be e x p e c t e d t o r e s u l t i n o n l y a s m a l l decrease i n u and t h e r e f o r e o n l y a s l i g h t i n c r e a s e i n the  hold-up.  A l t h o u g h F i g u r e s 40, 4l,. 42, and 43 show no  r e g u l a r dependence o f t h e hold-up on L  there i s a s l i g h t  tendency f o r t h e hold-up t o be somewhat h i g h e r a t h i g h e r c o n t i n u o u s phase f l o w r a t e s .  F o r a g i v e n d i s p e r s e d phase  f l o w r a t e d e c r e a s i n g the drop s i z e s h o u l d r e s u l t i n an i n c r e a s e d hold-up s i n c e u s u a l l y s m a l l e r drops have a s m a l l e r terminal velocity.  However, no e f f e c t o f t h i s s o r t was  noticed  i n g o i n g from a drop d i a m e t e r , d^, o f 0.155-in. t o one of 0.135-in. as can be seen by comparing F i g u r e s 40 and 4 l .  The  r e a s o n f o r t h i s might be t h a t drops o f about 0.155-in. e q u i v a l e n t d i a m e t e r a r e so l a r g e t h a t t h e y a r e much d i s t o r t e d from t h e o b l a t e s p h e r o i d shape.  The d i s t o r t i o n u s u a l l y r e s u l t s i n  a large frontal area of each drop ( l l 4 ) which in turn increases the drag and lowers the terminal velocity.  Comparison of  Figures 4 l , h2, and 43, however, shows an increase in the holdup as the drop size is decreased. b)  Results of the preliminary experiments. The sampling positions 1 to 10 inclusive mentioned below  are shown in the abscissa of Figure 28. i)  Time to reach steady-state. . The solute concentrations in samples taken by means of the  first,.fourth, seventh, and tenth hypodermic needles, shown in Figure 9, above the tracer distributor, and in the aqueous phase leaving the column were, plotted versus time after start-up. Table 6 shows the time to reach steady-state at the last sampling position to do so.  TABLE 6.  TIME TO REACH STEADY-STATE IN THE if-IN. I.D. COLUMN UNDER CONDITIONS OF NO MASS TRANSFER.  Run  32  33  3^  L , ft?/hr. ft?  9-0.  9-0  27-7  30.4  30.4  c  L , ft?/hr. ft? D  128  time to reach steadyestate, min. 100 Temperature, °F  71  115 68  ^5 69  Table 6 shows that the time to reach steady state varies l i t t l e when L i s varied over a wide range. Hence the effect of 1^. on  136  t h e time t o r e a c h steady s t a t e was n o t t a k e n i n t o a c c o u n t .  Table  6 a l s o shows t h a t t h e time t o r e a c h steady s t a t e d e c r e a s e s C o n s i d e r a t i o n o f T a b l e 6 suggested  r a p i d l y w i t h an i n c r e a s e i n L^. t h a t 1-hr.  would be. a c o n s e r v a t i v e e s t i m a t e o f t h e t i m e r e q u i r e d was g r e a t e r .than 3 0 - f t . / h r . f t .  t o r e a c h steady, s t a t e when  and t h a t 2-hr. would be a c o n s e r v a t i v e e s t i m a t e o f t h i s time f o r values of L  c  o 2 *3 2 between 9 - f t . / h r . f t . and 30-f.t./hr. f t . These  steady s t a t e t i m e s f o r v a r i o u s v a l u e s o f  were adopted f o r a l l  the . s t u d i e s i n v o l v i n g t r a c e r i n t h e l f - i n .  column.  ii)  E f f e c t . o f t r a c e r feed r a t e . T a b l e :7 shows t h e r e s u l t s o f t e s t s performed t o i n v e s t i g a t e  any e f f e c t s o f t r a c e r f e e d r a t e on t h e r e d u c e d c o n c e n t r a t i o n p r o f i l e s o r on t h e a x i a l eddy d i f f u s i v i t y TABLE 7,  EFFECT OF TRACER FEED RATE ON REDUCED CONCENTRATION . PROFILES AND AXIAL' EDDY DIFFUSIVITY I N THE i f - I N . I.D. COLUMN.  Run ¥ ft?/ hr.  ¥ ft?/ 'nr.  f t ? ,. f t ?  35 27-7 4o . 27.7 36 27.7. 67 57 68 The  values.  30.4 30.4 30.4  ft?/ hr.. . ft?, ,  0.16 0.31 •0.62  E. •  Reduced c o n c e n t r a t i o n a t sampling p o s i t i o n s  1  .2  .3 -.  4•  5  98' 599 411 271 l62 557 380 246 152 9^ 621 389 251 160 104  18.2 73 ' 0.10 350 157 18.2 73: 0.20 '^33 166 18.2- '73 ' . 0.40 307 142  50 76 48  6  7  67 42 60 40 66 42  ft?/ hr. 8~-  32 27 29  9 19 18 20  • 8 2.8 1-3 11 2.1 0.85 35 0.35 .5 18 8 3.3 1.4 0.51 0.20  24  reduced c o n c e n t r a t i o n a t a g i v e n s a m p l i n g  point varies  c o n s i d e r a b l y f o r v a r i o u s t r a c e r f e e d r a t e s i n many c a s e s .  Temp. °F  10. 12 32.5 11 32.6 12 32.8  69 70 71  - 10.3 72 - 11.0 74 - 10.7 73 •  137  However, the resulting overall concentration profile and axial eddy diffusivity are not affected appreciably by tracer-feed rate.  It i s concluded that the effect of tracer feed rate on  the value of the axial eddy diffusivity i s negligible for tracer fLowrates of less than 2$ of the continuous phase superficial velocity.  ....>•  i i i ) Reproducibility of results. Three runs were duplicated to provide a check on reproducib i l i t y of results.  The reduced concentration profiles and the  calculated values:of.the axial eddy diffusivity for these experiments are given in Table 8. TABLE 8.  REPRODUCIBILITY OF RESULTS FOR AXIAL EDDY DIFFUSIVITY IN THE 1-|-IN. I.D. COLUMN. ' • . .  Run ft?/ ft?/ hr. hr. ft? 32 47 33 42 3^ 40  ft? V .1  2  3'  4  5  6  7  8  9 155 79 48 28 14 157 .86, 46 28 14 7-8 566 487 391 330 297 259 571 492 397 252 288 250 30.4 523 408 257 166 93 58 38 28 30.4 . 557 380 246 152 9k 60 40 27  9,0. 128 575 256 9.0 128., 529 308. 9,0 30.4 755 644 9.0 30.4 : 75^ 668 27-7 27-7  Temp.  Reduced concentration at samplingr position 9  hr.  °F  10  3.8 2.0 5-3 2.9  8.6 8.9  223 179 29.3 221 179 28.7 19 12 33-0 18 11 32.6  71 71 68 73 69 70  The reproducibility of the calculated value of the axial eddy diffusivity i s good although point reduced concentrations are not exactly the same in duplicate runs. iv)  Cross-sectional homogeneity. The dispersion model requires that .at any elevation i n the  column the concentrations of solute in the continuous phase be  uniform. not  A c c o r d i n g l y i t was n e c e s s a r y t o check on whether o r  c r o s s - s e c t i o n a l homogeneity e x i s t e d .  Samples were withdrawn  a t t h e l e v e l o f t h e f i r s t hypodermic n e e d l e above t h e t r a c e r d i s t r i b u t o r ( F i g u r e 9) f o r each o f t h e t h r e e r u n s l i s t e d i n T a b l e 9«  T h i s l o c a t i o n was chosen because o f a l l t h e s a m p l i n g  • l o c a t i o n s i t would be t h e one most l i k e l y t o e x h i b i t nonu n i f o r m i t y o f .solute c o n c e n t r a t i o n . run  Samples were t a k e n i n each  a t t h e p o s i t i o n s shown i n t h e s k e t c h below:  The c o r r e s p o n d i n g r e d u c e d c o n c e n t r a t i o n s appear i n T a b l e 9. A l s o shown i s t h e r e d u c e d c o n c e n t r a t i o n a t p o s i t i o n 1 f o r a sample t a k e n i n each r u n about kO m i n u t e s b e f o r e t h e f i v e  samples  mentioned above. / A l t h o u g h t h e c o n c e n t r a t i o n of s o l u t e i s n o t e x a c t l y u n i f o r m over t h e c r o s s - s e c t i o n o f t h e column, t h e v a r i a t i o n i s n o t l a r g e compared w i t h t h e v a r i a t i o n o f c o n c e n t r a t i o n w i t h t i m e a t t h e c e n t r e of t h e c r o s s - s e c t i o n . . P o s i t i o n 1 was the  first  s a m p l i n g p o s i t i o n above t h e t r a c e r d i s t r i b u t o r .  The  s m a l l v a r i a t i o n i n c o n c e n t r a t i o n over t h e c r o s s - s e c t i o n a t t h i s  139  TABLE 9. Run  32 33 34  CROSS-SECTIONAL HOMOGENEITY IN THE l f - I N . I.D.. COLUMN remp.  Reduced c o n c e n t r a t i o n a t sampling p o s i t i o n . .  C> ft?/ hr.ft.  ft?/ hr.ft..  9-0 9-0 27.7  127-7 . 578 575 30.4 754 723, •30. V. •: 532-. 525  L  a  1,  2  la  lb  l  '  568 • 7^5 526 .  ic  Id  577 751 537  573 755 519  sample taken earlier  575 755 523  F  71 68 69  sampling e l e v a t i o n i n d i c a t e s that t r a c e r l e a v i n g the d i s t r i b u t o r spreads over t h e c r o s s - s e c t i o n i n a s m a l l i n c r e m e n t a l column height.  (37) s t u d i e d a l f - i n .  Hawrelak  I.D. s p r a y column w i t h  t h e t r a n s f e r o f . a c e t i c a c i d from t h e continuous, phase t o t h e d i s p e r s e d phase.  He t o o k samples f r o m v a r i o u s p o s i t i o n s a t a  g i v e n c r o s s - s e c t i o n by means o f hypodermic,needles  and. found no  r a d i a l concentration gradients.  v)  Sampling r a t e . T a b l e 10 shows t h e reduced c o n c e n t r a t i o n s o f s o l u t e i n .samples  t a k e n from t h e f i r s t f o u r s a m p l i n g p o s i t i o n s above t h e t r a c e r distributor  a t various sampling r a t e s .  for superficial  3  velocities  Sampling r a t e s o f l.O-ml./min.  of, c o n t i n u o u s phase g r e a t e r t h a n  2  27.7 f t . / n r . f t . and o f 0.75 ml./min. f o r s u p e r f i c i a l  velocities  o f c o n t i n u o u s phase, between . 9 . . O - f t . / h r . f t . and 2 7 . 7 - f t . / h r . f t . appear t o be s m a l l enough so a s n o t t o d i s t u r b t h e o p e r a t i o n o f t h e column.  A c c o r d i n g l y t h e s e s a m p l i n g r a t e s were used f o r a l l  TABLE 10. EFFECT OF :SAMPLING BATE ON THE REDUCED CONCENTRATION PROFILE I N THE l | - I N . I.D. COLUMN Run  L  '•  ft?/ hr.ft. p  D ft?/ hr.ft.  Temp.  Reduced c o n c e n t r a t i o n a t s a m p l i n g p o s i t i o n  L  Sampling r a t e = 1.0 ml./min.  Sampling r a t e = 0.5 ml./min.  °F  . Sampling'rate = 2.0 ml./min.  Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Position tion tion tion tion tion tion tion tion tion tion tion  3^  Run  27-7  L  30.4  1  2  3  4  1  2  3  4  1  2  3  4  523  388  255  158  523  4o8  257  166  522  387  25^  155  Temp.  Reduced c o n c e n t r a t i o n a t sampling p o s i t i o n  C  Sampling r a t e = 1.5 ml./min.  Sampling r a t e = 0-75 ml;/min.  Sampling r a t e . h r . f t . h r . f t . - . .= 0.25 ml./min.  69  °F  Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Posi- Position tion tion tion tion tion tion tion tion tion tion tion  33 32  9-0 9.0  30.4 128  1  2  3  4  1  2  3  4  1  2  3  749 575  642 257  566 155  485 . 80  755 575  644  566 155  487 79  751 573  644  568 155  256  255  4 .  488, 79  68 71  o f t h e t r a c e r s t u d i e s i n t h e T g - i n . I.D. column.  vi)  Order o f s a m p l i n g . The. u s u a l o r d e r o f s a m p l i n g was t o t a k e a sample by means  o f t h e f i r s t hypodermic needle above t h e t r a c e r d i s t r i b u t o r , t h e n by means o f t h e n e x t h i g h e r n e e d l e , and so on. (See F i g u r e s 9 and 10 f o r s a m p l i n g p o s i t i o n s . ) F o r t h r e e r u n s samples were t a k e n i n t h e r e v e r s e o r d e r , t h a t i s s t a r t i n g w i t h t h e h i g h e s t hypodermic n e e d l e .  As w e l l i n t h e s e same r u n s samples  were t a k e n i n t h e u s u a l o r d e r .  The r e s u l t s a r e g i v e n i n T a b l e 1 1 .  I t i s e v i d e n t from T a b l e 11 t h a t t h e o r d e r i n w h i c h samples a r e t a k e n does n o t a f f e c t t h e measured c o n c e n t r a t i o n p r o f i l e .  vii)  E f f e c t o f column h e i g h t . F o r one s e t o f column o p e r a t i n g c o n d i t i o n s t h r e e e x p e r i m e n t s  were performed w i t h t h r e e d i f f e r e n t l e n g t h s o f column.  (See  F i g u r e s 10, 1 1 , and 1 2 . ) T a b l e 12 shows t h e r e d u c e d c o n c e n t r a t i o n p r o f i l e o f s o l u t e i n t h e t e s t s e c t i o n and t h e c a l c u l a t e d v a l u e o f the a x i a l eddy d i f f u s i v i t y f o r each r u n . The  l e n g t h o f t h e column appears t o have no s i g n i f i c a n t  e f f e c t upon t h e a x i a l eddy d i f f u s i v i t y .  TABLE 11. Run  L  C  '  EFFECT OF THE ORDER OF SAMPLING ON THE MEASURED CONCENTRATION PROFILE I N THE 1^-IN. I.D. COLUMN Order  o f sampling  Reduced c o n c e n t r a t i o n a t s a m p l i n g p o s i t i o n  hr.ft.  D ft?/ hr.ft.  33  9-0  30.4 •  u s u a l ( l t o 10) r e v e r s e (10 t o l )  32  9-0  128  u s u a l ( l t o 10) 57H.-. 256 155. r e v e r s e (10 t o l ) 572 253. 155  3^  27-7  30.4  u s u a l ( l t o 10) 523 r e v e r s e (10 t o l ) 526  ft3/  L  1  2  755 7^7  644  642  4o8 374  3  4  566 564  487 485 79 79 166 153 '  257 254  5  6  391 389 •48 48  330 327 28 28  93 97  .58 61  7  8  9  297 297  259 258  223 215  14. 9.0 14 8.9 28 38 40 27  Temp.  10  179 178  3-0 ' 2.0 3-8 2.0 19 . 12 18 11  °F  68 71 " 69  TABLE 12..EFFECT OF COLUMN HEIGHT ON THE MEASURED CONCENTRATION PROFILE AND AXIAL EDDY DIFFUSIVITY IN. THE T|-IN. I.D. COLUMN Run  174 51 175  Column l e n g t h (nozzle t i p s t o interface) 6-ft.' 3 l / 8 - i n . 10-ft. 3?-in. 16-ft. 4|-in.  Reduced concerL t r a t i o n a t s a m p l i n g p o s i t i o n s  L ft?/ h'tt.ft.  ft?/  18.2 18.2 18.2  54.7 54.7 54.7  hr.ftf  1 426 561 562  2 ' 286 298 299  3 136 138 146  5  6  7  8  81-. 39 83 37 73 45  20 18 23  9.9 11 9-9  5-7 5.8 5.2  4.  9 ' 3-0 2.7 2.7  E  10  ft?/hr.  1.4 T-5 1-5  14.9 14.5 • 14.5. .  Temp. °F  68 71 68  .  143  4.  AXIAL EDDY DIFFUSIVITY AND DROP SIZE DISTRIBUTION STUDIES IN THE 3-IN. I.D. COLUMN. The r e s u l t s  o f t h e p r e l i m i n a r y experiments c o n c e r n i n g steady-  s t a t e time, r e p r o d u c i b i l i t y  of results,  and c r o s s - s e c t i o n a l v h o m o -  g e n e i t y a r e d i s c u s s e d a f t e r those o f t h e main e x p e r i m e n t s .  a)  Main Experiments. • • . The v a l u e o f - t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , Ee, f o r  each run.- was  c a l c u l a t e d in- a manner s i m i l a r  t o that  already  d e s c r i b e d f o r t h e 1-|—in. I.D... column. . A summary o f t h e r e s u l t s • f o r t h e 3 - i n . I.D. column i s g i v e n i n T a b l e IV-5.  F i g u r e 44  shows t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y p l o t t e d a g a i n s t d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y . figure  The curve shown i n t h i s  was drawn t h r o u g h t h e p o i n t s by eye.. As w i t h t h e l f - i n .  I.D. column, t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y d e c r e a s e s w i t h i n c r e a s i n g d i s p e r s e d phase f l o w r a t e .  However, t h e r e appears  t o be some tendency, f o r h i g h e r s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y v a l u e s ' f o r the. 3-in.'I..D. column t o be a s s o c i a t e d w i t h superficial velocities  o f t h e . c o n t i n u o u s phase.  s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y r e s u l t s  higher  Comparison o f t h e  f o r t h e 3 ~ i n . I.D.  column w i t h those f o r t h e i f - I n . I.D. column shows t h a t a t a drop s i z e , d^> o f 0.135-in. and f o r a g i v e n s u p e r f i c i a l  velocity  of each phase t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y i n t h e 3 - i n . I.D. column was between 6.3 and 17•3 times t h a t i n t h e l f - i n . I.D. column.  I t was e v i d e n t t h a t t h e c o n t i n u o u s phase underwent  c h a n n e l l i n g . (See later.)  T h i s f a c t , no doubt, r e s u l t e d i n an  i n c r e a s e i n a x i a l m i x i n g o f t h e continuous phase I n t h e 3 i n . I.D. -  FldURE kk.  SUPERFICIAL AXIAL EDDY DIFFUSIVITY I N THE 3-IN. I.D. COLUMN  145  G i e r and Hougen ( 2 8 ) s a y t h a t t h e "...  column.  bulk mixing  effect  would be e x p e c t e d t o be most s e r i o u s i n spray columns o f h i g h diameter t o height r a t i o . "  However, the r e s u l t s o f the e x p e r i m e n t s  d e s c r i b e d i n t h i s t h e s i s show t h a t t h e d i a m e t e r , o f t h e column i s i m p o r t a n t m i x i n g o f the c o n t i n u o u s  b u t not t h e  i n a s s e s s i n g t h e e x t e n t o f the  height,  axial  phase. A c t u a l eddy d i f f u s i v i t i e s were not  c a l c u l a t e d f r o m the s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s because t h e d i s p e r s e d phase hold-up, h, was column.. Previous, workers (3, .6,  30,  h o l d - u p / h, by means o f - E q u a t i o n  7•  . 100 h _ . • u  not measured i n t h e 3 i u . 31,  ^3)  have e s t i m a t e d  the  h  7  However, i n t h e . p r e s e n t work i t was  not p o s s i b l e t o measure t h e  v e l o c i t y o f r i s e o f t h e d i s p e r s e d phase drops w i t h any due  I.D.  _  accuracy  t o t h e s w i r l i n g m o t i o n o f t h e drops ( d e s c r i b e d l a t e r ) .  As  a r e s u l t E q u a t i o n 7 c o u l d not be u s e d t o e s t i m a t e the h o l d - u p , h.  The to  p e r c e n t a g e e r r o r i n t h e e q u i v a l e n t d i a m e t e r o f drops  o p t i c a l ^ d i s t o r t i o n was  used f o r the , l f - i n . independent of  I.D.  due  d e t e r m i n e d i n a manner s i m i l a r t o t h a t column.  The  optical distortion  was  t h e v e r t i c a l p o s i t i o n o f t h e b a l l and o f t h e  c o n c e n t r a t i o n o f t r a c e r i n . t h e column.  F i g u r e 45 shows t h i s .  p e r c e n t a g e e r r o r a t v a r i o u s p o s i t i o n s i n the c r o s s - s e c t i o n o f the column.  A l s o s h o w n i n F i g u r e 45 i s the p o r t i o n o f t h e c r o s s -  s e c t i o n i n w h i c h drop s i z e measurements were made. the l f - i n .  I.D.  J u s t as f o r  column r e s t r i c t i n g the d r o p s i z e measurements t o .  the f i e l d shown i n . t h i s f i g u r e made i t u n n e c e s s a r y t o a p p l y any  correction for"optical distortion.  A summary o f t h e drop  I D R O P SIZE] MEASUREMENT FIELD  CAMERA  FIGUEE if-5.  PERCENTAGE ERROR I N THE EQUIVALENT DIAMETER DUE TO OPTICAL DISTORTION I N THE 3-IN. I.D. COLUMN  Ikl  s i z e d i s t r i b u t i o n s measured appears i n T a b l e I V - 8 .  The second  peak i n each drop s i z e d i s t r i b u t i o n p l o t appeared between 0 . 1 3 - i n . and 0 . I k - i n . . e q u i v a l e n t drop d i a m e t e r . b)  P r e l i m i n a r y Experiments.  i)  Steady-state time.  _  The c o n c e n t r a t i o n o f . t r a c e r i n samples t a k e n by means o f the. f i r s t , . t h i r d , s e v e n t h , and t e n t h hypodermic  n e e d l e s above t h e  t r a c e r d i s t r i b u t o r ( F i g u r e s 20 and 2 l ) and i n t h e aqueous phase l e a v i n g t h e column were p l o t t e d v e r s u s time a f t e r s t a r t - u p .  Table  shows t h e t i m e t o r e a c h s t e a d y - s t a t e a t t h e l a s t s a m p l i n g p o s i t i o n t o do. s o . TABLE' 13.  STEADY-STATE TIMES FOR THE 3-IN. I.D. 'COLUMN.  177  Run • • •.'  ISO  203  L , ft?/hr. f t ?  18.2  Lp, f t ? / h r . f t ? ,  36.5  36.5  t i m e t o r e a c h , steady-state?, min..  55  25  57  Temperature,  70  70  69  c  °F  100  18.2 109  A l t h o u g h t h e time t o reach, s t e a d y - s t a t e v a r i e d l i t t l e f o r a wide range o f d i s p e r s e d phase s u p e r f i c i a l v e l o c i t i e s i t d e c r e a s e d markedly f o r . an i n c r e a s e i n t h e s u p e r f i c i a l v e l o c i t y o f cont i n u o u s phase.  The time f o r the.column  s t a t e c o n d i t i o n was.taken  t o reach a steady-  t o be 1-hr. f o r c o n t i n u o u s phase  s u p e r f i c i a l v e l o c i t i e s o f l e s s t h a n l O O - f t . / h r . f t . and 30-min. o 2 f o r c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t i e s o f I G O - f t . / h r . f t .  13  148  and  ii)  greater.  R e p r o d u c i b i l i t y of results. The r e d u c e d c o n c e n t r a t i o n p r o f i l e s and t h e s u p e r f i c i a l  a x i a l eddy d i f f u s i v i t i e s f o r d u p l i c a t e r u n s a r e p r e s e n t e d i n " T a b l e 14.  TABLE 14. REPRODUCIBILITY OF RESULTS FOR THE 3-IN. I.D.. COLUMN . Reduced c o n c e n t r a t i o n a t s a m p l i n g p o i n t s  Run  ft ./  Temp.  2  ft?/ ft?/ h r  2  ft.  ftT  hr. .1  177 18.2 36.5 933 186 18.. 2 36.5 921 191 48.4 54.7 1080 207 48.4 54.7 1077 201 100 109 1118 208 100 109 ' 1131  .2  3  4  5  6 •  863 844 8 l l 777 707 888 819 785 761 731 933 780 701 .546 457 892 731 608 532 444 613 167 101 40 18.8 565 193 109 37 13-7  T a b l e l 4 shows t h a t , a l t h o u g h  °F  7  8  9  680 689  656 656  636 620  593 188 595 190  395 367  317 310  273 249  257 •145 70 218 138' 69  6.03 1.09 5.17 2.13 1.14  10  -  70 70  53-6 67 56.5 68  point concentrations are not  e x a c t l y r e p r o d u c i b l e , t h e r e d u c e d c o n c e n t r a t i o n p r o f i l e s and s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s f o r d u p l i c a t e r u n s a r e q u i t e similar.  iii)  C r o s s - s e c t i o n a l homogeneity. The r e d u c e d c o n c e n t r a t i o n s  o f s o l u t e a t t h e p o s i t i o n s shown  i n t h e f o l l o w i n g s k e t c h a r e g i v e n i n T a b l e 15 f o r t h e l e v e l s o f  149  the f i r s t and f i f t h hypodermic n e e d l e s above t h e t r a c e r  distri-  (See F i g u r e s 20 and 21.)  butor.  TABLE 15.- CROSS-SECTIONAL HOMOGENEITY I N THE 3-IN. I.D. COLUMN Run l  177 180 197 195 203 201 Run  L  c  D ft?/  Reduced c o n c e n t r a t i o n a t s a m p l i n g p o i n t s Temp..  L  ft?/ hr.ftf hKftr 2  l8.2 100 18.-2 100 18.2 100 '  36.5 36.5 73 73 . 109 109  c  V  L  2  la.  18.2 100. 18.2 100  36.5 36.5 73 73 18.2~- 109 100 109  . 1.  °F lc  lh .  Id l e . I f  937 •933 937 917 901 838 833 816 784 737 980 988 960 972 968 1290 1263 1097 947 889 916 911 909 897 893 1277 1198 1120 990 895  939 936 933 919 791 811 847 855 958 958 966 968 913 1019 1021 1034 903 903 907 907 893 920 1008 1034  70 70 67 • 68 69 67  Reduced c o n c e n t r a t i o n a t s a m p l i n g p o i n t s Temp..  f t.?/ ft?/ hr.ft. h r . f t . 5a  177 180 197 :i95 .203 201  lb  807 230 664 194 611 41  5b  5  798 225 682 184 599 4o  733 218 69k  169 603 4o  5c  5d  5e  5f  5g  5h  773 206 672 151 576 39  762 196 724 144 553 38  776 223 696' 161 591 41  760 225 684 163 601 41  751 220 698 170 609 40  742 208 708 176 611 39  • ' 1  °F  70 70 67 68 69 67  150  Table 15 shows that the assumption of radial homogeneity i s less valid for the  I.D. column than for the 1-jjr-in. I.D. column.  Visual observations of the very small dispersed phase drops during experimental runs showed that large scale axial swirling motions occurred in the continuous phase of the 3-in. I.D. column as mentioned later. . However, the plot of the natural logarithm of the tracer concentration versus column height i s straight for the runs in the 3-in. I.D. column as required by the dispersion model equation (Equation 13). Therefore a lack of cross-sectional homogeneity in the 3-in. I . D . column seems not to be too serious as far as the determination of superficial axial eddy diffusivities is concerned.  5.  VISUAL OBSERVATIONS OF THE MOTION OF THE DROPS The motion of the drops in the Tg-in. I.D. column was very  erratic but always.in an upwardly direction. of drops ever taking a downward course.  There was no evidence  The very small drops of  about 0".02-in. diameter moved up the column very slowly.  Due to  the small size of these drops their motion would have reflected any.large scale turbulence or channelling in the main bulk of the continuous phase.  However no such effects were observed.  These  general flow characteristics were the same for the various' flowt  rates of the"two phases and for the four different 'drop size distributions studied i n the T§-in. I.D. column. Evidently the drops moved up the column in effective plug flow.  Thus the  151  assumption o f no a x i a l eddy d i f f u s i o n i n t h e d i s p e r s e d (28,  31,  phase  35) i s v a l i d .  In c o n t r a s t t o t h e o b s e r v a t i o n s o f the drop motion i n t h e T§-in. I.D. column the drop b e h a v i o u r i n the 3 - i n . I.DI column was q u i t e d i f f e r e n t .  Not o n l y d i d t h e v e r y s m a l l drops  exhibit  an a x i a l s w i r l i n g motion b u t l a r g e r drops o f t e n took a downward course f o r a s h o r t d i s t a n c e a l o n g t h e column. continuous phase underwent c h a n n e l l i n g .  Obviously the  As d i s c u s s e d e a r l i e r  this  phenomenon r e s u l t e d i n r a d i a l inhomogeneity o f t h e c o n t i n u o u s phase Due t o t h e s w i r l i n g motion o f t h e drops t h e assumption o f no b a c k m i x i n g of" the d i s p e r s e d phase i s i n v a l i d .  6.'  CONCENTRATION PROFILES WITH MASS TRANSFER  F i v e runs were performed w i t h t h e t r a n s f e r o f a c e t i c  acid  from the c o n t i n u o u s aqueous phase t o t h e d i s p e r s e d ketone phase i n the T§-in. I.D. column as d e s c r i b e d u n d e r ' E x p e r i m e n t a l P r o c e d u r e . Samples' were taken from w i t h i n t h e o p e r a t i n g column by means o f the hypodermic probe.  needle samplers and a l s o by means o f t h e b e l l -  The c o n c e n t r a t i o n , c^, o f a c e t i c a c i d i n t h e 'ketone  phase  o f each b e l l - p r o b e sample a t t h e time o f sampling was c a l c u l a t e d by means o f E q u a t i o n 6 and t h e c o n c e n t r a t i o n , c^, o f a c e t i c i n t h e hypodermic  needle sample a t t h e sampling elevation-. C  D = D C  +  "^C V  ( c  D  C  " C C  }  .  acid  For each run the concentration p r o f i l e s of solute i n both phases over the t e s t s e c t i o n were p l o t t e d .  Smoothed values of the con-  centrations of solute i n each phase at the sampling p o s i t i o n s were read from these p l o t s .  The value of the d i s t r i b u t i o n c o e f f i c i e n t ,  m, at each of the ten. hypodermic needle sampling p o s i t i o n s was c a l c u l a t e d from the e q u i l i b r i u m curve f o r a c e t i c a c i d d i s t r i b uted between MIBK - saturated water and water - saturated MIBK at 70°F.  The a r i t h m e t i c average of these ten values of m was  c a l c u l a t e d and used i n subsequent c a l c u l a t i o n s .  The e q u i l i b r i u m  curve i s shown i n Figure k6 and the e q u i l i b r i u m data used t o prepare t h i s p l o t appear i n Table IV-13, Appendix IV. coefficient,  The capacity  K^a, was c a l c u l a t e d by means of the smoothed concen-  t r a t i o n s and Equation 20.  I n t e g r a t i o n was c a r r i e d out over the  t e s t s e c t i o n only.  20 The experimental r e s u l t s are presented i n Table IV-9, Appendix IV. The d i s p e r s i o n model characterizes the extent of backmixing of the continuous phase.  I t i s l i k e l y that the continuous phase which  i s backmixe'd enters the wakes of drops and i s transported some distance up the column as wake m a t e r i a l before passing back i n t o the main bulk of the continuous phase.  In the t r a c e r  experiments  described e a r l i e r t h i s backmixing was studied by measuring the extent to which a solute t r a c e r , soluble only i n the continuous phase, was c a r r i e d up the column.  153  000  FIGURE k6.  000 0 02 0 04 A C E T I C ACID C O N C . IN MIBK LB.-MOLES/CU.FT.  006 PHASE,  EQUILIBRIUM CURVE FOR ACETIC ACID DISTRIBUTED BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK AT 70°F  154  When mass t r a n s f e r can t a k e p l a c e t h e s i m p l e c o n d i t i o n s of the t r a c e r work no l o n g e r o b t a i n and c a u t i o n must be e x e r c i s e d i n u s i n g t h e t r a c e r r e s u l t s and t h e d i s p e r s i o n model.  The  d i f f e r e n c e s which  can a r i s e a r e t h a t the wakes a r e no l o n g e r t y p i c a l o f t h e l o c a t i o n f r o m w h i c h t h e y were drawn,.and mass t r a n s f e r can s t i l l o c c u r f r o m a wake w h i l e i t i s t r a v e l l i n g w i t h t h e d r o p . : I n the case o f mass t r a n s f e r f r o m the c o n t i n u o u s  t o the  dispersed  phase, s o l u t e , i n t h i s case s o l u b l e i n b o t h p h a s e s , i s t r a n s p o r t e d with.continuous as was  phase up the column i n t h e wakes o f t h e r i s i n g drops  t h e case i n t h e t r a c e r s t u d i e s .  t h a t the c o n t i n u o u s  phase, i m m e d i a t e l y  However, i t i s p r o b a b l e p r i o r t o e n t e r i n g a wake,  had been i n t h e n e a r v i c i n i t y o f t h e a s s o c i a t e d d r o p . t h i s continuous  along  Consequently  phase would be l o w e r i n s o l u t e c o n c e n t r a t i o n t h a n  t h e b u l k o f t h a t phase a t , t h e same e l e v a t i o n .  Therefore  the amount  o f s o l u t e c a r r i e d up the .'column . i n the r i s i n g . w a k e s would be l e s s t h a n t h a t p r e d i c t e d from t h e t r a c e r s t u d i e s w h e r e i n no d e p l e t i o n o f t r a c e r c o u l d have t a k e n  such  place.  • I n a d d i t i o n t o t h e above e f f e c t t h e r e i s the d i s s i m i l a r i t y o f t h e d i f f u s i o n p a t t e r n o f s o l u t e between the wake and t h e ( •continuous  phase.  surrounding  I n t h e case o f t h e n o n - p a r t i t i o n e d t r a c e r  d i f f u s i o n must i n e v i t a b l y be f r o m the wake t o the c o n t i n u o u s i n which the c o n c e n t r a t i o n of t r a c e r i s l e s s .  phase  However, i n the case  o f mass t r a n s f e r , as d e s c r i b e d i n t h e p r e s e n t work, t h e wakes a r e moving towards a r e g i o n o f h i g h e r c o n c e n t r a t i o n o f s o l u t e and f o r e m o l e c u l a r . d i f f u s i o n o f s o l u t e i s f r o m the c o n t i n u o u s towards t h e wake.  there-  phase  As- has been d i s c u s s e d e l s e w h e r e i n t h i s t h e s i s  155  molecular  d i f f u s i o n can be n e g l e c t e d w i t h r e s p e c t t o eddy d i f f u s i o n ,  and hence i t i s f e l t t h a t t h i s p a r t i c u l a r d i s t o r t i o n o f t h e wake composition  can be n e g l e c t e d .  There i s y e t , however, one more f a c t o r t o be c o n s i d e r e d .  Mass  t r a n s f e r i n e v i t a b l y w i l l occur between t h e wake and t h e drop i t s e l f by t h e t r a n s f e r o f t h e p a r t i t i o n a b l e s o l u t e from t h e wake t o t h e drop.  F o r t h e moment bur c o n c e r n i s w i t h t h e wake i t s e l f and such  mass t r a n s f e r .would s t i l l f u r t h e r . d e p l e t e t h e s o l u t e i n t h e wake and  so when p a r t s o f t h i s wake a r e c a s t o f f a t h i g h e r l e v e l s t h e  amount,of s o l u t e t r a n s f e r r e d b y t h e b a c k m i x i n g method w i l l be l o w e r t h a n t h a t had mass t r a n s f e r n o t t a k e n p l a c e .  I n p a s s i n g one might  mention t h a t because p a r t o f t h e drop i s exposed t o t h e wake r a t h e r t h a n t o the. s u r r o u n d i n g  continuous  phase mass t r a n s f e r t o t h e drop  w i l l b e : l o w e r t h a n would.have been t r u e i f ' t h e wake had n o t e x i s t e d . E v i d e n t l y t h e d i s p e r s i o n m o d e l . s h o u l d be used w i t h c a u t i o n f o r the case o f mass t r a n s f e r between t h e phases.  I n s p i t e of the  above mentioned d e f i c i e n c e s o f t h e d i s p e r s i o n model i t was used i n t h i s work t o a n a l y s e t h e r e s u l t s o f f i v e r u n s i n v o l v i n g mass t r a n s f e r . F o r each r u n E q u a t i o n iki • C  = Aexp. ( A Z ) + Bexp ( A ) Z  c  X  2  ~ Q  was f i t t e d t o t h e measured c o n c e n t r a t i o n p r o f i l e o f a c e t i c a c i d i n the continuous  phase o v e r t h e t e s t s e c t i o n f o r a v a l u e o f  2 6 0 - f t . / h r . f o r ' t h e a x i a l eddy d i f f u s i v i t y , E.  Values of A  and B were e s t i m a t e d b y means, o f t h e l e a s t squares t e c h n i q u e as  iU  l$6  d e s c r i b e d under Theory.  These c a l c u l a t i o n s were performed  IBM-7040 e l e c t r o n i c computer.  on an  The f l u x of s o l u t e , J , down the  column was c a l c u l a t e d by means o f E q u a t i o n  21: L  D  C  21 The curve f i t t i n g was r e p e a t e d f o r v a l u e s o f E decreased by one f o r each s u c c e s s i v e t r i a l )il  0  r  X2  r e a c l i e  ^  a  v  a  l  u  e  ( i . e . 59, 58, 57, e t c . ) u n t i l . e i t h e r  °f 10^-  Numbers g r e a t e r than  10^  c o u l d not be handled by the IBM-7040 e l e c t r o n i c computer. lower l i m i t o f E was between 5 and 9i n the s m a l l e s t sum o f squares, A  The  The v a l u e of E which r e s u l t e d  , o f the d e v i a t i o n s between  the c a l c u l a t e d and measured v a l u e s o f c^, was taken t o be the e s t i m a t e o f E.  The v a l u e s o f E c a l c u l a t e d by t h i s method and  the v a l u e s o f E c a l c u l a t e d by means o f t r a c e r s t u d i e s f o r s i m i l a r column o p e r a t i n g c o n d i t i o n s a r e g i v e n i n t a b l e l 6 .  TABLE 16. COMPARISON OF AXIAL EDDY DIFFUSIVITY BY MASS TRANSFER AND TRACER STUDIES.  Tracer studies  Mass t r a n s f e r s t u d i e s E,  Run ftV/hr..ftT Jl  J2 J3 J4 J5.  36.5 18.2 36.5  48 A 48.4  ft?/hr.ft?  54.T 5U.7 91.2 91.2 127  T a b l e IV-10 shows the p o i n t v a l u e s o f  Run ft?/hr.  ft?/hr.  16, 42  31 39 53  k9  51 138 139  lk3  15 15 ll ll  9  and E f o r the e s t i m a t i o n  1-57  o f E i n each o f the f i v e r u n s .  I n each r u n the v a l u e o f t h e  a x i a l eddy d i f f u s i v i t y , E, determined  from c o n c e n t r a t i o n p r o f i l e s  w i t h mass t r a n s f e r was l e s s than E c a l c u l a t e d from t r a c e r s t u d i e s f o r t h e same column o p e r a t i n g c o n d i t i o n s .  The e s t i m a t i o n o f E f o r each r u n was r e p e a t e d s e v e r a l t i m e s . ' The f i r s t r e p e t i t i o n i n v o l v e d the replacement  i n the c a l c u l a t i o n s  o f J as g i v e n by E q u a t i o n 21 by J as g i v e n by E q u a t i o n J = (L  c  c'J - L  25:  c°)  D  . 2 5 The  second r e p e t i t i o n c o n s i s t e d o f r e p l a c i n g t h e v a l u e o f J  used by t h a t g i v e n by E q u a t i o n .  J  26:  = ( C C " D L  C  L  C  C  }  F u r t h e r r e p e t i t i o n s i n v o l v e d the use o f v a r i o u s a r b i t r a r i l y chosen v a l u e s o f m and K^a.  T a b l e s IV-11 and IV-12, Appendix I V  show t h e values' o f E c a l c u l a t e d f o r each o f t h e t h r e e v a l u e s o f J used and a l s o f o r t h e v a r i o u s v a l u e s o f m and K^a used f o r each run.  T y p i c a l s e t s o f r e s u l t s a r e shown g r a p h i c a l l y i n F i g u r e s  47, 48, 49, and 50 Figure'47  shows how  E i s varied a r b i t r a r i l y .  passes through a minimum v a l u e as However, t h e minimum v a l u e o f £ i s not  pronounced enough t o enable E t o be e s t i m a t e d w i t h any g r e a t accuracy.  I n a d d i t i o n , the t r u e v a l u e o f E i n any case may  not correspond e x a c t l y w i t h t h e minimum v a l u e o f & because o f  159  FIGURE 1+8.  THE EFFECT ON E OF VARYING THE METHOD OF-FLUX CALCULATION AND OF VARYING K^a FOR RUN J I  i6o '  I 84  188  1-92  m FIGURE 4 9 .  THE EFFECT ON E OF VARIATIONS IN m FOR RUN J l  196  l6l  O  MEASURED  CONCENTRATION  E Q U A T I O N 14 F I T T E D T O T H E EXPERIMENTAL POINTS  '  i  1 2  I  |  i  3  4  5  i ;  l  6  7  j  ;—i  __L_  9  10  8  SAMPLING POSITION, S C A L E : K6 -H U  FIGURE 5 0 ,  MEASURED AND FITTED CONCENTRATION PROFILES FOR RUN J l  162-  the f a c t t h a t the u n d e r l y i n g assumptions on w h i c h the l e a s t squares f i t t i n g t e c h n i q u e i s b a s e d have no sound b a s i s as i n t h i s case.  applied  These assumptions are t h a t the c o n c e n t r a t i o n  of  s o l u t e i n t h e c o n t i n u o u s phase a t each s a m p l i n g p o i n t comes from a n o r m a l d i s t r i b u t i o n and  t h a t each such d i s t r i b u t i o n has  the  same v a r i a n c e a t a l l s a m p l i n g p o i n t s (125)«  F i g u r e 48  shows the e f f e c t on E o f c a l c u l a t i n g J by  v a r i o u s methods.  the  T h i s f i g u r e a l s o shows the e f f e c t o f a r b i t r a r y  changes i n the v a l u e o f K^a-used i n the c a l c u l a t i o n . The  d i f f e r e n c e s i n the v a l u e s of J used a r i s e because the  f l u x of s o l u t e down the column as c a l c u l a t e d a t the upper a t the l o w e r ends of the column a r e not e q u a l . a r e due  s o l e l y to experimental  between the v a l u e s J.  The  20 may  error.  and  These d i f f e r e n c e s  Large d i f f e r e n c e s r e s u l t  o f E c a l c u l a t e d from the v a r i o u s v a l u e s  e r r o r i n t h e v a l u e of K^a be 'quite l a r g e due  of  c a l c u l a t e d by means of E q u a t i o n  t o the d i f f e r e n c e ( Q c  C D  )  being  m s m a l l compared w i t h ^ c ^ o r  c^.  v a l u e of E i s ' h i g h l y d e p e n d e n t m  Hence s m a l l e r r o r s i n c^, m, " The  F i g u r e 48  shows t h a t the c a l c u l a t e d  upon t h e v a l u e of K^a  used.  o r c^ r e s u l t i n a l a r g e e r r o r i n E.  e f f e c t on the c a l c u l a t e d v a l u e of E of the v a l u e o f m  used i s shown- i n F i g u r e 49• substantial. (Table IV-9)  Evidently t h i s e f f e c t i s quite  As mentioned e a r l i e r the v a l u e of m used was  initially  the a r i t h m e t i c average of m a t the t e n hypodermic  163  needle sampling p o s i t i o n s .  The v a l u e s o f m a t t h e h i g h e s t and  l o w e s t hypodermic n e e d l e s f o r Run J I were 1.86 and 1.99 r e s p e c t ively.  The assumption  obviously i s not v a l i d .  o f constancy o f m over t h e t e s t Furthermore  section  t h e r e a r e no t h e o r e t i c a l  grounds f o r t a k i n g t h e a r i t h m e t i c average o f m a s t h a t v a l u e o f m which s h o u l d be used.  I n t h e l i g h t o f F i g u r e 4-9 and t h e s e  f a c t s t h e c a l c u l a t e d v a l u e o f E can be c o n s i d e r a b l y i n e r r o r . F i g u r e 5 0 shows t h e measured c o n c e n t r a t i o n s f o r Run J I . Superimposed'is  t h e curve c a l c u l a t e d from E q u a t i o n Ik  using.the  v a l u e o f K^a c a l c u l a t e d b y means o f E q u a t i o n 20, t h e v a l u e o f J c a l c u l a t e d f r o m E q u a t i o n 21, and t h e v a l u e o f m - c a l c u l a t e d as t h e a r i t h m e t i c mean o f m a t t h e t e n hypodermic n e e d l e p o s i t i o n s A l t h o u g h the value o f E corresponding t o t h i s  sampling curve  may be i n e r r o r , t h e agreement between t h e - c u r v e and t h e e x p e r i m e n t a l p o i n t s i s good.  164  CONCLUSIONS A b e t t e r understanding  o f s a m p l i n g methods has r e s u l t e d  from t h e work d e s c r i b e d i n t h i s t h e s i s .  A t low continuous  phase f l o w r a t e s a hook-probe sample i s r e p r e s e n t a t i v e o f t h e c o n t i n u o u s . p h a s e i n t h e column a t t h e s a m p l i n g e l e v a t i o n . However, a t h i g h f l o w r a t e s o f t h e phases such a sample appears t o be r e p r e s e n t a t i v e o f c o n t i n u o u s  phase i n t h e column a t some  h e i g h t above t h e s a m p l i n g e l e v a t i o n . . Hypodermic n e e d l e s (22-gauge) do, however, w i t h d r a w c o n t i n u o u s  phase w h i c h i s  r e p r e s e n t a t i v e o f that, i n the. column a t t h e s a m p l i n g h e i g h t . The d i s p e r s e d phase s o l u t e c o n c e n t r a t i o n o b t a i n e d from t h e b e l l - p r o b e sample i s r e p r e s e n t a t i v e o f t h e d i s p e r s e d phase i n the '• column a t t h e s a m p l i n g e l e v a t i o n .  Equation  III-8 i n  c o n j u n c t i o n with' t h e r e s u l t s o f a p i s t o n sample and t h e t e r m i n a l c o n d i t i o n s o f t h e column g i v e s t h e average s o l u t e c o n c e n t r a t i o n i n t h e continuous  phase, e x c l u d i n g t h e c o n t r i b u t i o n from t h e  wakes, o f t h e p i s t o n sample a t t h e time o f sampling.  This  c a l c u l a t e d value o f t h e s o l u t e c o n c e n t r a t i o n i n the continuous phase t o g e t h e r w i t h Equation,-6 r e s u l t s i n t h e average s o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase o f t h e p i s t o n sample a t the t i m e o f s a m p l i n g . T h i s work has t e s t e d the' d i s p e r s i o n model as a means o f d e s c r i b i n g a x i a l mixing o f the continuous The  phase o f a s p r a y column.  p r e d i c t i o n b y t h i s model o f an e x p o n e n t i a l decay o f s o l u t e  c o n c e n t r a t i o n upstream, w i t h r e s p e c t t o c o n t i n u o u s  phase f l o w ,  165  f r o m t h e i n j e c t i o n p o i n t o f a t r a c e r s o l u b l e o n l y i n t h e continuous phase, i s i n agreement w i t h e x p e r i m e n t a l  results.  The a x i a l eddy  d i f f u s i v i t y , which c h a r a c t e r i z e s the a x i a l mixing of the c o n t i n uous phase, was c a l c u l a t e d f r o m such r e s u l t s . effects  o f column d i a m e t e r ,  In addition the  column h e i g h t , drop s i z e , and f l o w -  r a t e s o f t h e two. phases have been measured e x p e r i m e n t a l l y . a x i a l eddy d i f f u s i v i t y o f t h e c o n t i n u o u s of the s u p e r f i c i a l v e l o c i t y  phase s u p e r f i c i a l v e l o c i t y  phase i s independent  o f t h e continuous  column h e i g h t and remains a p p r o x i m a t e l y  phase and o f t h e  c o n s t a n t as t h e d i s p e r s e d  i s d e c r e a s e d from h i g h  values.  However, t h e a x i a l eddy d i f f u s i v i t y i n c r e a s e s r a p i d l y d i s p e r s e d phase s u p e r f i c i a l v e l o c i t y This effect  i s less.pronounced  The  as t h e  i s decreased t o low values.  a t s m a l l drop s i z e s .  The e f f e c t  o f i n c r e a s i n g t h e d r o p s i z e f o r a g i v e n d i s p e r s e d phase superf i c i a l velocity effect  i s t o i n c r e a s e t h e a x i a l eddy d i f f u s i v i t y .  The  o f i n c r e a s i n g t h e column d i a m e t e r i s t o i n c r e a s e t h e  a x i a l eddy d i f f u s i v i t y .  F o r t h e same f l o w r a t e s o f r e s p e c t i v e  phases i n each o f t h e two columns t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y f o r the continuous  phase i s between 6.3 and  17-3  t i m e s g r e a t e r i n t h e 3 ~ i n . I.D. column t h a n i n t h e l § r - i n . I.D. column f o r t h e s i n g l e v a l u e o f d  (0.135-in.) i n v e s t i g a t e d .  The m i x i n g c e l l - p a c k e d bed a n a l o g y , when a p p l i e d t o a spray column, p r e d i c t s t h e P e c l e t number a d e q u a t e l y phase drops o f about 0.155-in. d^.  f o r dispersed  F o r drops o f s m a l l e r  e q u i v a l e n t d i a m e t e r t h e agreement between t h e p r e d i c t e d P e c l e t  166  number and t h e measured P e c l e t number becomes worse. I n t h e p r e s e n t work drop s i z e d i s t r i b u t i o n s were measured i n o r d e r t o d e f i n e t h e p h y s i c a l systems e x i s t i n g i n t h e v a r i o u s backmixing studies.  T h i s was an a u x i l l i a r y s t u d y and n o t a complete  i n v e s t i g a t i o n o f drop s i z e d i s t r i b u t i o n s f o r v a r i o u s n o z z l e t i p s i z e s , n o z z l e t i p v e l o c i t i e s , and t h e l i k e . . F o r t h e r e s t r i c t e d c o n d i t i o n s i n v e s t i g a t e d drop s i z e d i s t r i b u t i o n p l o t s show two peaks.  F o r a l l t h e drop f o r m a t i o n c o n d i t i o n s i n v e s t i g a t e d i n t h i s  work t h e f i r s t peak o c c u r s a t an e q u i v a l e n t drop d i a m e t e r o f about 0 . 0 2 - i n . and i n d i c a t e s a l a r g e number o f d r o p s o f t h i s size.  The second peak i s h i g h and narrow f o r drops o f about  0.095-in. e q u i v a l e n t d i a m e t e r (formed at. 0.053~in. I.D. n o z z l e t i p s ) and becomes p r o g r e s s i v e l y f l a t t e r and b r o a d e r as t h e e q u i v a l e n t d i a m e t e r i s i n c r e a s e d t o about 0.155'-in. (formed a t 0.126-in. I.D. n o z z l e t i p s ) .  The p i s t o n sampler proved t o be an e x c e l l e n t d e v i c e f o r use i n measuring t h e d i s p e r s e d phase h o l d - u p .  T h i s hold-up was  f o u n d t o be a l m o s t independent o f t h e c o n t i n u o u s phase s u p e r f i c i a l v e l o c i t y a s , i n d e e d , would be e x p e c t e d . The hold-up i n c r e a s e s a p p r o x i m a t e l y l i n e a r l y w i t h d i s p e r s e d phase f l o w r a t e s above 6 0 - f t . / h r . f t . F o r a g i v e n d i s p e r s e d phase f l o w r a t e t h e • hold-up i n c r e a s e s w i t h d e c r e a s i n g drop s i z e e x c e p t when d^ i s g r e a t e r t h a n about O . l U - i n .  167  A x i a l eddy d i f f u s i v i t i e s can be c a l c u l a t e d f r o m r u n s i n v o l v i n g mass t r a n s f e r by f i t t i n g t h e d i s p e r s i o n model e q u a t i o n t o e x p e r i mental concentration values obtained  profiles.  However, t h e eddy d i f f u s i v i t y  were v e r y s e n s i t i v e t o s m a l l changes i n t h e f l u x  o f s o l u t e down t h e column, t h e v a l u e o f t h e mass t r a n s f e r c o e f f i c i e n t , and t h e v a l u e o f t h e d i s t r i b u t i o n The  capacity  coefficient.  e f f e c t o f s m a l l . c h a n g e s i n o t h e r parameters such as s u p e r f i c i a l  v e l o c i t i e s and d i s p e r s e d  phase hold-up on t h e c a l c u l a t e d v a l u e s o f  the a x i a l eddy d i f f u s i v i t y were n o t i n v e s t i g a t e d .  Investigations  i n t o t h e v a l i d i t y o f t h e boundary c o n d i t i o n s proposed b y Danckwerts (60)  as a p p l i e d t o an e x p e r i m e n t a l column might l e a d t o t h e a c c u r a t e  p r e d i c t i o n of solute concentration  p r o f i l e s by means o f t h e  d i s p e r s i o n model e q u a t i o n and. a x i a l eddy d i f f u s i v i t y v a l u e s measured i n t h i s work by t r a c e r e x p e r i m e n t s w i t h no mass t r a n s f e r .  NOMENCLATURE  Constant o f i n t e g r a t i o n . i I n t e r f a c i a l a r e a p e r u n i t volume o f column, ft?/ft? Constant o f i n t e g r a t i o n . Average s o l u t e c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase b a c k m i x i n g stream, l b . - m o l e s / f t . Reduced c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase. S o l u t e c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase, l b . - m o l e s / f t . o r microgm./ml. S o l u t e c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase o f a b e l l - p r o b e sample o r a p i s t o n sample a t t h e t i m e o f analysis, lb.-moles/ft. Value o f  when z = 0, microgm./ml.  S o l u t e c o n c e n t r a t i o n .in t h e c o n t i n u o u s phase i n t h e j'k* c e l l o f a s e r i e s o f p e r f e c t m i x e r s , l b . - m o l e s / 1  "Tt? o r microgm./ml. S o l u t e c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase i n l e t , lb.-moles/ft? S o l u t e c o n c e n t r a t i o n i n t h e c o n t i n u o u s phase o u t l e t , Tb.-moles/ft? S o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase, lb.-moles/ft?  169  S o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase i n t h e c e l l o f a .series o f p e r f e c t m i x e r s , l b . - m o l e s / f t ? or microgm./ml. S o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase o f a b e l l - p r o b e sample o r a p i s t o n sample a t t h e t i m e o f • analysis, lb.-moles/ft. S o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase i n l e t , lb.-moles/ft. S o l u t e c o n c e n t r a t i o n i n t h e d i s p e r s e d phase o u t l e t , lb.-moles/ft? Constant of i n t e g r a t i o n . Height of a mixing c e l l , f t . Value o f d  g  a t t h e second peak o f a drop s i z e ,  d i s t r i b u t i o n p l o t , i n . or f t . ' E q u i v a l e n t drop d i a m e t e r = t h e d i a m e t e r o f a sphere whose volume i s t h e same as t h a t o f t h e d r o p , f t . C o n t i n u o u s phase a x i a l eddy d i f f u s i v i t y f o r t h e case o f t h e d i s p e r s e d phase moving r e l a t i v e t o t h e co-ordinate axes, f t . / h r . C o n t i n u o u s phase a x i a l eddy d i f f u s i v i t y f o r t h e case o f t h e d i s p e r s e d phase s t a t i o n a r y r e l a t i v e t o t h e  2 co-ordinate axes, f t . / h r . V o l u m e t r i c f r a c t i o n o f c o n t i n u o u s phase i n t h e column. Test s e c t i o n height, " f t . Volume p e r c e n t a g e o f d i s p e r s e d phase i n t h e column, °jo.  170  V e r t i c a l d i m e n s i o n o f a d r o p image c o r r e c t e d f o r magnification,f t . J  Wet f l u x o f s o l u t e down t h e column, Mass t r a n s f e r force,  c o e f f i c i e n t based on  2  lb.-moles/(hr.ft.). m " °D  driving  lb.-moles (.hr.)( ?)(lb.-moles/ft^) f t  S u p e r f i c i a l v e l o c i t y of t h e c o n t i n u o u s phase b a c k 2  's  m i x i n g stream r e l a t i v e t o t h e l a b o r a t o r y , f t . / ( h r . f t . ) . Superficial velocity.of  t h e c o n t i n u o u s phase f o r t h e  case o f . t h e d i s p e r s e d phase moving r e l a t i v e t o c o - o r d i n a t e axes f i x e d w i t h r e s p e c t t o t h e l a b o r a tory, ,ft?/( h r . f t ? ) . S u p e r f i c i a l v e l o c i t y o f t h e c o n t i n u o u s phase f o r the  case o f t h e d i s p e r s e d phase s t a t i o n a r y  to co-ordinate axes.  relative  These may be e i t h e r f i x e d o r o  2  moving r e l a t i v e t o t h e l a b o r a t o r y , f t . / ( h r . f t . ) . S u p e r f i c i a l v e l o c i t y of t h e d i s p e r s e d phase r e l a t i v e o 2 to the l a b o r a t o r y , f t . / ( h r . f t . ) .  Lp  L„p  S u p e r f i c i a l v e l o c i t y of the t r a c e r to the l a b o r a t o r y ,  (  Cp\  —  C  Distribution  feed r e l a t i v e  o 2 ft./(hr.ft.).  c o e f f i c i e n t f o r t h e s o l u t e between t h e  / GQ  D' * c o n t i nuous phase and t h e d i s p e r s e d phase, (lb.-mole s / f t ?)/(lb.-mole s / f t ? ) .  (  Ud \  (  L^d \  p^  P e c l e t number f o r two phase, f l o w  P e c l e t number f o r s i n g l e phase f l o w .  H o r i z o n t a l d i m e n s i o n o f a d r o p image c o r r e c t e d f o r magnification, f t .  2 S t  C r o s s - s e c t i o n a l a r e a o f t h e column, f t . .  Time, h r . L^+L \ 'Continuous phase i n t e r s t i t i a l v e l o c i t y r e l a t i v e t o e 1—e/ / ' the r i s i n g drops, f t . / h r .  (  \ '• U  -I  phase  n  11-e, AL,  Average l i n e a r v e l o c i t y o f t h e d i s p e r s e d drops r e l a t i v e t o t h e l a b o r a t o r y , f t . / h r .  Volume o f t h e c o n t i n u o u s phase b a c k m i x i n g stream  3 i n a p i s t o n sample, f t . V  Volume o f t h e c o n t i n u o u s phase i n a b e l l - p r o b e  •  3  sample or. a p i s t o n sample, f t . V^  Volume o f .the.dispersed  phase i n a b e l l - p r o b e  sample'  3 or a p i s t o n sample-, f t . VT-,  Average volume o f a c o n t i n u o u s phase b a c k m i x i n g " p a c k e t " a s s o c i a t e d w i t h each d i s p e r s e d  phase  3 drop, f t . Vp-  .  3 Average volume o f a d i s p e r s e d phase d r o p , f t .  172  y=z + u t  D i s t a n c e a l o n g t h e column, i n t h e d i r e c t i o n o f t h e c o n t i n u o u s phase f l o w , r e l a t i v e t o c o - o r d i n a t e axes s t a t i o n a r y w i t h r e s p e c t t o t h e d i s p e r s e d phase drops, f t .  Z = z/H  Dimensionless  d i s t a n c e a l o n g t h e column i n t h e  d i r e c t i o n o f t h e c o n t i n u o u s phase f l o w , z  D i s t a n c e a l o n g t h e column, i n t h e d i r e c t i o n o f t h e ' c o n t i n u o u s phase f l o w , r e l a t i v e t o c o - o r d i n a t e axes stationary with respect t o the laboratory, f t . ft:  H  o<=  2  P=  -  Ee  L  DJ  L  D  E e C  ^ 2[ =  ftT1  aH  ( D mL^Ee  L  CO  Cc  3N2 '  A  e  x  p  (  \  Z  X= °< v / ^ P  >  X=p<-ySf  ,  +  £>  1  )  -  B  e  x  P(^  Z 2  )  +  Q  ]  ' (lb.-moles/ft?)  f t T l  f t :  1  D e n s i t y o f t h e c o n t i n u o u s phase, l b . / f t . V i s c o s i t y o f t h e c o n t i n u o u s phase, l b . / h r . f t .  173,  LITERATURE CITED  1.  G e a n k o p l i s , C. J . and H i x s o n , A. N., I n d . Eng. Chem.  42, 1141 (1950) 2.  B l a n d i n g , F. H. and E l g i n , J.C., T r a n s . Am. I n s t . Chem. E n g r s . 3§_, 305 (1942)  3.  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J o s t , W., D i f f u s i o n , p. 477, Academic P r e s s I n c . , New Y o r k , i960  183  APPENDIX I  DISPERSION MODEL THEORY The assumptions upon w h i c h the m a t h e m a t i c a l model i s based a r e g i v e n under the h e a d i n g o f Theory. C o n s i d e r t h e c o n t r o l zone i n t h e C-phase, shown i n F i g u r e I - l , d u r i n g t h e i n c r e m e n t a l time d t .  The case c o n s i d e r e d i s one  i n which mass t r a n s f e r i s t a k i n g p l a c e between t h e phase and t h e d i s p e r s e d phase.  continuous  A s o l u t e mass b a l a n c e  over t h e  c o n t r o l zone g i v e s t h e f o l l o w i n g terms. i)  S o l u t e o u t due t o mass t r a n s f e r . Kp/c^  - c \Sa(dz)(dt) D  \ m ii)  I  S o l u t e o u t due t o C-phase f l o w . L S^c c  iii)  c  + | b c y d z ) j (dt) c  S o l u t e i n due t o C-phase f l o w . L Sc (dt) c  iv)  c  S o l u t e i n due t o eddy d i f f u s i o n . , E  (^-.( C ^ cj C  +  c  d  Z  ^  S  e  (  d  t  )  =  E  e  S  ( ) ( d z  d t  H E e S p f c ^ (dz) ( d t )  C - P H A S E , D-PHASl  CONTROL ZONE  FIGURE I - T .  SOLUTE MASS BALANCE I N THE CONTINUOUS PHASE  185  v)  S o l u t e out due t o eddy d i f f u s i o n . E/))c \(dz')eS(dt) c  Terms i ) t o v) i n c l u s i v e have "been shown on F i g u r e I - l as arrows w i t h the c o r r e s p o n d i n g numbers as g i v e n here i n d i c a t e d b e s i d e them.  vi)  Accumulation  of solute.  /V \Se(dz)(dt) c  These terms'combine i n t o the f o l l o w i n g mass b a l a n c e .  KJJ // cc -- c c D \j Sa Sa (dz) (dz) ((ddt t))++LL SScc (dt (dt)+L ) + L c sp S A cc^A (dz) (dz) ( d )t+)E+^ E AC c J A Se (dz) ( d t ) (dt c c  D  c  c  c  c  C  c  (  +Ac \Se(dz)(dt)=L Sc (dt)+E/^c \Se(dz)(dt)+E/^c \(dz)Se(dt) c  c  c  c  c  fey The above e q u a t i o n can be r e a r r a n g e d t o g i v e  I-l At- steady s t a t e E q u a t i o n I - l reduces  to  2 \ Ee/d  c \  - L p / d c ^ - K^a/Cp - c ^ = 0 dz / > Vm / dz ; p  2  v  1-2 E q u a t i o n 1-2  can be r e a r r a n g e d t o g i v e  186--  Ml?/ v U / ~ z  1-3  The n e t f l u x , J , o f s o l u t e down t h e column a t t h e e l e v a t i o n z i s g i v e n b y E q u a t i o n I-k. J = L c c  - E/dc \e - L c  c  c  D  D  I-k 1-3  The s u b s t i t u t i o n o f c ^ f r o m ' E q u a t i o n J = L c c  ,2  G  - Ee/dc^-f L E e ^ d c \ V  d  V  1  z  dz  2  /dc \  -  Q  D  i n t o Equation. --I-k y i e l d s c  D  dz y  a  /  -/L c N \m  c  /  1-5 E q u a t i o n 1-5  can be r e a r r a n g e d t o g i v e  -/vW  cl -/M/ cY , 2 / ' I L_. A d z / \Ee/\dz / ,dz / \D/ / •» i \ I , 2 c  dc  V  +  /  V  c  V  ^  V L^Ee / \ D '  -f^v N  \ mEe , . _ . ' \l DD / L  lV E e  1-6 C o n c e n t r a t i o n s and d i s t a n c e s c a n be p u t on a d i m e n s i o n l e s s b a s i s by means o f E q u a t i o n s 1-7 °C  =  c  and 1-8.  co c c  1-7 z  = ZH  ..  1-8 These two e q u a t i o n s now can be used t o t r a n s f o r m E q u a t i o n i n t o Equation  1-6  1-9.  d Z  2 I  \dZ  1-9  187  where o i , p and. Y a r e g i v e n by E q u a t i o n 1-10, 1-11, and 1-12. ;  1-10 (Lp - m L ^ K p a H P  2  ml^Ee 1-11 L Eec D  If  p ^ 0  and  (c*  2  L  °  1-12 I-12a)  + p) > 0  I-12b)  t h e s o l u t i o n o f E q u a t i o n 1-9 i s g i v e n b y E q u a t i o n C  = Aexp Q Z ) + Bexp  c  X  fo Z) 2  1-13.  - Q  1-13 A and B a r e c o n s t a n t s o f i n t e g r a t i o n and  and Q a r e  g i v e n b y E q u a t i o n s 1-14, 1-15, and I - l 6 r e s p e c t i v e l y .  1-14 ^  2  =  cc-JJ7$  1-15  P ." C O D " C  ( L  m L  C  1-16  )  Other s o l u t i o n s o f E q u a t i o n 1-9. a r e a p p r o p r i a t e when t h e c o n d i t i o n s g i v e n b y E q u a t i o n I-12a) and I-12b) a r e n o t met.  However, t h e  a p p l i c a b i l i t y o f t h e s e o t h e r s o l u t i o n s i s more l i m i t e d t h a n t h a t o f E q u a t i o n 1-13  and no e x t r a i n f o r m a t i o n can be o b t a i n e d b y t h e i r u s e .  When t h e c o n d i t i o n g i v e n b y E q u a t i o n I-12b) i s n o t s a t i s f i e d problems i n v o l v i n g i n s t a b i l i t y may a r i s e . F o r a s o l u t e w h i c h d i s s o l v e s o n l y in- t h e c o n t i n u o u s phase C  D  =  °>  '  . '  188  and E q u a t i o n I-k  reduces J = L c G  c  to - Ee  1-17 If,  i n addition,  continuous phase samples a r e withdrawn from  the p o r t i o n o f the column which, f o r the c o n t i n u o u s phase, i s upstream from t h e f e e d p o i n t o f t r a c e r J = Then E q u a t i o n 1-17  then  0. becomes  1-18 The  s o l u t i o n of Equation I - l 8 i s  1-19 where D i s a c o n s t a n t o f i n t e g r a t i o n . c  C  = c  CO  But when  z = 0.  Therefore,  1-20 E q u a t i o n 1-20  can be r e a r r a n g e d . t o g i v e  1-21  189  APPENDIX I I  A.  MIXING CELL - PACKED BED ANALOGYj(kk, 6k,  90, 92,  10Q, 1 0 9 )  C o n s i d e r a s e r i e s o f p e r f e c t m i x e r s as shown i n t h e s k e t c h below.  Suppose t h a t a s o l u t e i s e x t r a c t e d from a moving  c o n t i n u o u s phase b y a s t a t i o n a r y d i s p e r s e d phase.  }  f  j-  2  • 11  j )  J-H \  j+  V  2  L e t the i n t e r -  190  stage s u p e r f i c i a l v e l o c i t y o f t h e c o n t i n u o u s  phase be L ,  s o l u t e c o n c e n t r a t i o n f o r the continuous phase i n the be  c  the  p  mixer  ., and t h e s o l u t e c o n c e n t r a t i o n f o r the d i s p e r s e d phase i n o,j th  the j  mixer be  c^ y  L e t the mass t r a n s f e r c o e f f i c i e n t ,  the i n t e r f a c i a l a r e a per unit, volume o f mixer,  K^;  a; and the h e i g h t  o f a m i x i n g c e l l , . d ^ , , be the same f o r each mixer.  At  steady th  s t a t e a solute, mass b a l a n c e f o r the  continuous  phase o f the j  mixer r e s u l t s I n the f o l l o w i n g e q u a t i o n .  n-1 E q u a t i o n I I - l can be r e a r r a n g e d t o g i v e  'C,j-1 "  " C j '  ...  C I f E i s r e p l a c e d by E  m  V. and L  / n  i s r e p l a c e d by L  u 1-2  11-2  Equation  o  becomes E q u a t i o n I I - 3 which i s a p p l i c a b l e t o the  continuous  phase o f a packed bed w i t h s o l u t e t r a n s f e r r e d from the phase t o t h e  fluid  packing.  •••(SK®-v I t i s assumed t h a t the s o l u t e c o n c e n t r a t i o n i n each p i e c e i s u n i f o r m throughout  the p i e c e a t the v a l u e c^. Sub-  s t i t u t i o n pf the c e n t r a l d i f f e r e n c e e q u i v a l e n t s o f as g i v e n i n E q u a t i o n s t o E q u a t i o n II-6  (8).  packing  differentials,  I I - U and T l - 5 , i n t o E q u a t i o n I I - 3 l e a d s  191  ( c  C,j+i " 2d. 1  c  c j-i  )  >  Il-k  ' c\  ( C„H1 - C„j  dC  C  2 c  +  C  C„j-l)  ,dz II-5  ( C c  ^- " 1  C c  ^M^"  i +  -)  +  • c,j i - c,j ( c  1  +  c  c„  m  )  V  J), j  i C  II-6 B y • c o n s i d e r i n g t h e i n t e r s t i c e s between t h e p a c k i n g o f a packed b e d a s p e r f e c t m i x i n g c e l l s ' an a n a l o g y  can be drawn  between a s e r i e s o f p e r f e c t , m i x e r s and a packed bed. II-2  pieces  F o r Equations  and I I - 6 t o b e : c o n s i s t e n t t h e f o l l o w i n g e q u a l i t y must be  satisfied.  2  41,  II-7  E  where  II-8  P  The r i g h t hand s i d e o f E q u a t i o n I I - 7 d e f i n e s t h e P e c l e t number Pe  »4  i/ iE  II-9  .1=0  192  The m i x i n g c e l l l e n g t h , cL, i s supposed ( 1 1 2 ) t o be t h e v e r t i c a l c e n t r e - t o - c e n t r e d i s t a n c e between t h e l a y e r s o f p a c k i n g p i e c e s i n an o r d e r e d p a c k i n g system.  A l t h o u g h e x a c t v a l u e s f o r d^ can  be c a l c u l a t e d f o r o r d e r e d p a c k i n g s , i t would be e x p e c t e d t h a t o n l y an average v a l u e f o r d^ c o u l d be c a l c u l a t e d f o r random packings.  .For a packed b e d t h e v a l u e o f X ' i s a p p r o x i m a t e l y one.  Thus f o r t h i s case E q u a t i o n s I I - 7 and I I - 9 y i e l d t h e f o l l o w i n g w e l l known" r e l a t i o n s h i p (kk, 6k,  9 2 , 108, 109, 122, 1 2 3 ) .  Pe'' = 2  B.  SPRAY COLUMN - PACKED BED ANALOGY. F o r a spray column o p e r a t i n g a t steady s t a t e and w i t h a .  s o l u t e w h i c h d i s s o l v e s o n l y i n t h e c o n t i n u o u s phase  Equation.1-2  reduces t o Ee//d c j = L / d c | 2  c  c  c  11-10 C o n s i d e r a spray column o p e r a t i n g a t s t e a d y s t a t e w i t h axes o f r e f e r e n c e moving a t t h e same v e l o c i t y , u, as t h e r i s i n g d i s p e r s e d phase d r o p s .  The drops appear s t a t i o n a r y , on a  b a s i s , r e l a t i v e t o t h e c o - o r d i n a t e system..  time-average  That i s , t h e system  appears as a packed b e d w i t h t h e p a c k i n g p i e c e s n o t touching" each o t h e r .  L e t y be t h e a x i a l p o s i t i o n r e l a t i v e t o t h e moving  c o - o r d i n a t e axes.  Thus,  y = z + ut 11-11  193  L e t t h e a x i a l m i x i n g o f t h e c o n t i n u o u s phase be c h a r a c t e r i z e d by an a x i a l eddy d i f f u s i v i t y , E , r e l a t i v e t o t h e moving -co-ordinate axes.  C o n s i d e r t h e c o n t r o l zone i n t h e c o n t i n u o u s phase a s shown  i n the f o l l o w i n g sketch.  L e t t h e c o n t r o l zone be f i x e d  relative  t o t h e moving c o - o r d i n a t e system and b e o f i n c r e m e n t a l h e i g h t ( d y ) ,  CONTINUOUS PHASE  DISPERSED PHASE  CONTROL. ZONE  y + dy  A s o l u t e mass b a l a n c e o v e r t h e c o n t r o l zone f o r u n i t a r e a o f column and f o r a n i n c r e m e n t a l time i n t e r v a l ( d t ) g i v e s j^(L +ue)c + c  e  E ' ^ C  P \^( d y ) ) C  c  ( d t ) = (Lp+ue)  ( c |Vcy y) c  +  d  + E e  ^ j (dt) !  + 'uec -ue / c + / ^ \ ( d y ) ( d t ) c  c  c  11-12 The l e f t - h a n d s i d e o f E q u a t i o n 11-12 r e p r e s e n t s t h e amount o f s o l u t e e n t e r i n g ' t h e c o n t r o l zone.  The terms i n t h e f i r s t s e t o f  square b r a c k e t s on t h e r i g h t - h a n d s i d e o f E q u a t i o n 11-12 r e p r e s e n t t h e amount o f s o l u t e l e a v i n g t h e c o n t r o l zone.  The terms' i n t h e  second s e t o f square b r a c k e t s on t h e r i g h t - h a n d s i d e o f E q u a t i o n 11-12 r e p r e s e n t t h e a c c u m u l a t i o n o f s o l u t e i n t h e c o n t r o l zone.  19k-  E q u a t i o n 11-12  simplifies to E e  H-13  But c  cY  /  =  c: dz  (12^)  /*%  (12M  d c  and C\  =  dz T h e r e f o r e E q u a t i o n 11-13  becomes  , 2  E e/d c C\  C  dc^ dz  ,dz  11-14-  A comparison o f E q u a t i o n s 11-10 E'  and I I - l h  shows t h a t  = E  11-15  The i d e n t i t i e s g i v e n i n E q u a t i o n s II-15 above, and i n I I - 1 6 , and 11-17  below:  1-e  L  c  = L  c  II-16 + ue  11-17 can be used w i t h t h e f o l l o w i n g d e f i n i t i o n o f Pe : Pe = / L„  n-18  195  and w i t h E q u a t i o n I I - 7 t o produce E q u a t i o n  H-19.  Pe - 2  11-19 F o r s i m p l e o r d e r e d l a t t i c e " arragements  of uniform s p h e r i c a l  drops t h e v e r t i c a l d i s t a n c e "between l a y e r s o f d r o p s , d^, i s a f u n c t i o n o f t h e hold-up, h, and t h e drop d i a m e t e r , d^.  The  P e c l e t number, Pe, c a l c u l a t e d from E q u a t i o n 11-19, i s a f u n c t i o n of h o n l y ,  The f u n c t i o n g i v i n g d^ and Pe a r e p r e s e n t e d i n t h e  f o l l o w i n g t a b l e f o r s i x s i m p l e l a t t i c e arrangements o f d r o p s . Each drop i s supposed t o be c o n c e n t r i c w i t h an i m a g i n a r y l a r g e r sphere whose d i a m e t e r i s - e q u a l t o t h e c e n t r e - t o - c e n t r e . d i s t a n c e between n e i g h b o u r i n g , d r o p s .  I n t h e s i x l a t t i c e arrangements  c o n s i d e r e d each i m a g i n a r y sphere touches each o f i t s n e a r e s t neighbours.  These l a t t i c e arrangements r e p r e s e n t t h e s t a b l e  systems f o r beds o f packed spheres and i t i s suggested b y t h e a u t h o r o f . t h i s t h e s i s t h a t t h e y a r e t h e ones most, l i k e l y t o be a p p l i c a b l e .for use i n a p p l y i n g t h e m i x i n g c e l l - packed b e d a n a l o g y t o a s p r a y column.  I t can be seen from t h e f o l l o w i n g t a b l e t h a t f o r a g i v e n v a l u e o f h a l l o f t h e p r e d i c t e d Pe v a l u e s l i e i n t h e range between t h e Pe v a l u e s f o r the. l a t t i c e arrangements o f o r t h o r h o m b i c and rhombohedral - 1.  - 2  196  LATTICE  Pe  DIAGRAM LAYERS 1,3,5  NUMBER OF NEAREST NEIGHBOURS  O LAYERS 2,4,6 (ONLY 2 LAYERS SHOWN)  CUBIC  u J6 h  ORTHORHOMBIC- 1  w  O O O  3  48 h  6  7T  \  PLAN  O O O O  O  O  o  o  o—1  64 h  8  7T  J8 h  1  V1EW  3  O  V  o -  '  VIEW  1  PLAN  r  V  O  O  —~rA  O* O  —  24/3 h  3  O  O  O - — - X J  J 9^3 h  36/3"  7T  h  N  T  ,  E  W  o  o  o — J  FRONT 1  «000»-0  V  ,  E  W  PLAN VIEW  O-  rX  O  O  FRONT  o  o O — * '  O'PfO RHOMBOHEDRAL-2  0  10  12 h  3  R  VIEW  V  O O O O O  32/3" h \  W  8  7T  TETRAGONAL  E  PLAN  O O O  C  3  ,  F  '  1  O O O  J 3fT h  W  12 O  ORTHORHOMBIC-2  E  FRONT  o°o"'o  7T  3  ,  O I  96 h  \  PLAN  o o o c o  r  J 12 h  FRONT  d  OOOOO  3  o o OPP  RHOMBOHEDRAL-I  F  V I E W  PLAN  12 W"n n±3d. c  O  < J y—*  i  FRONT VIEW  APPENDIX I I I  ANALYSIS OF PISTON SAMPLE RESULTS TO PRODUCE THE AVERAGE CONTINUOUS PHASE CONCENTRATION, EXCLUDING THE CONTRIBUTION FROM THE WAKES, I N THE PISTON SAMPLE.AT THE TIME OF SAMPLING The a n a l y s i s o f p i s t o n sample . r e s u l t s t o produce t h e average c o n t i n u o u s phase c o n c e n t r a t i o n , e x c l u d i n g t h e c o n t r i b u t i o n from t h e .wakes, i n t h e p i s t o n a t t h e t i m e o f s a m p l i n g i s based on a model i n w h i c h i t i s p i c t u r e d t h a t each drop c a r r i e s some c o n t i n u o u s phase w i t h i t , f o r example i n i t s wake (21, 2k, 26, 1 2 l ) .  22,  23,  I t i s assumed t h a t on t h e average a volume v^ o f  c o n t i n u o u s phase o f average s o l u t e c o n c e n t r a t i o n c^ i s - c a r r i e d up t h e column p a s t a g i v e n e l e v a t i o n by each r i s i n g d i s p e r s e d  . .  .  h  phase drop.  Thus t h e f r e q u e n c y , — , o f drops p a s s i n g t h r o u g h D Lg u n i t area a t a given e l e v a t i o n i s equal t o the frequency, — , B V  V  o f passage o f volumes, v^, o f c o n t i n u o u s phase i n t h e f o r m o f a backmixing  stream. i.e. V.  D  V-B  Thus  III-l  198*  The number o f d i s p e r s e d phase drops i n a p i s t o n sample i s  V  D  •  and t h e number o f p a c k e t s o f backmixed c o n t i n u o u s phase i n a p i s t o n sample i s  Therefore,  IP_  =  IB  or v = V _p_ JD v V B  B  III-2 From E q u a t i o n s I I I - l and I I I - 2 ,  V  B  h  or B L  D III-3  C o n s i d e r t h e l o w e r p o r t i o n o f a s p r a y column as shown i n Figure I I I - l .  I t i s assumed.that t h e d e s c e n d i n g c o n t i n u o u s  phase i s f u l l y mixed a t any g i v e n e l e v a t i o n .  A mass b a l a n c e on  s o l u t e o v e r t h e s e c t i o n o f column shown i n F i g u r e I I I - l y i e l d s  199  V B  V D  +  +  C C  L  C  =  L  C C C  Vc  +  +  L  D D C  The above e q u a t i o n can be r e a r r a n g e d t o g i v e Os  -  =  c)  C  L  C D V  (  C  C  "  C  C  .  }  „  /  i  V D  +  "  C  B  D> III-l*  Now c o n s i d e r a p i s t o n sample.  F i g u r e III-2a r e p r e s e n t s  t h i s sample a t t h e i n s t a n t o f sampling. the same sample b u t l a t e r i n t i m e :  F i g u r e III-2b. r e p r e s e n t s  when t h e sample i s a n a l y s e d .  A mass b a l a n c e on s o l u t e i n t h e p i s t o n sample over t h e time between sampling and a n a l y s i s y i e l d s V  D D C  V B  V  <c  +  -  v  V c  = VS  c  Vc  +  "  S u b s t i t u t i n g . " f o r Vg from E q u a t i o n H I - 3  III-5  i n E q u a t i o n I I I - 5 and  then r e a r r a n g i n g g i v e s  '  VD.( B C  V .V S C  g  -  -  C  +  D>  V c - c> c  c  III-6 Equating¥ D L  D  (  C  E  -  c  c  )  ,  as g i v e n by each o f E q u a t i o n s III-l*-  Vc( C C  C C  )  +  V D " D> C  C  =  a  n  d III-6 r e s u l t s i n :  V D " D') C  C  +  \(  C &  C~ ) C  C  III-T  200  Equation  I I I - 7 can be r e a r r a n g e d  to give  D L  C  V  +  C  V D III-8  The  c o n c e n t r a t i o n , c^, g i v e n By E q u a t i o n  I I I - 8 i s the average  s o l u t e c o n c e n t r a t i o n : i n a p i s t o n sample, e x c l u d i n g c o n t r i b u t i o n from the wakes, a t the time of  the  sampling.  BOTTOM OF COLUMN  I L  t  C C C  FIGURE I I I - l .  L  D  C  D  LOWER PORTION OF A SPRAY COLUMN  202  V  V  D  C  D  B  PISTON S A M P L E AT THE TIME OF S A M P L I N G (a)  PISTON S A M P L E A T T H E TIME OF ANALYSIS (b)  )  FIGURE I I I - 2 .  THE EFFECT OF TIME ON A PISTON SAMPLE  203  APPENDIX I V  CALCULATIONS AND TABULATED RESULTS FOR AXIAL EDDY DIFFUSIVITY DETERMINATIONS AND DROP SIZE DISTRIBUTIONS  a)  CALCULATIONS.  •  A specimen hand c a l c u l a t i o n i s p r e s e n t e d s t a r t i n g from a d a t a sheet shown i n T a b l e I V - 1 . ( A c t u a l d a t a s h e e t s were more . abbreviated  t h a n t h e one shown . i n T a b l e IV-1.)  RUN 50 Water f l o w r a t e = 27.7 f t ? / h r . . f t ? Ketone f l o w r a t e = 5U.7 f t . / h r . f t . 2 T r a c e r f l o w r a t e = 0.310 f t r / h r . f t . 3 /  2 Column I.D. = 1.5  i n . C r o s s - s e c t i o n a l a r e a o f column = 0.01227 f t .  Sampling r a t e = 1 ml./min. = 0.002119 f t ? / h r . = 0.1727 f t ? / h r . f t ? Ketone hold-up = U.7# .•  .204 DATA SHEET.  TABLE IV-1. RUN NO. 50  DATE: 25 AUG.  1966  Column' I.D. = 1.5-in. T r a c e r f e e d cone.=23,OOO-microgm./ml. N o z z l e t i p average I.D.=0.103-in. 9 open n o z z l e t i p s Water r o t a m e t e r r e a d i n g = 86-mm. L =27-7-ft? A i r . f t ? *Ketone r o t a m e t e r reading=108-mm. Lr=5k.7^-ft|/hr.ft| Tracer rotameter reading=7«5- « I^=0.310-ftv/hr.ft. Average temperature o f t h e f l u i d s i n the column = 72°F Steady s t a t e time=l-hr. Sampling r a t e = 1-ml./min. mm  ANALYSIS.OF SAMPLES (See f i g u r e 10 f o r sampling p o s i t i o n s )  / /  -  ' -  1 2  GI G2  3  03 ' G4 G5 •  k  5 6 •7  •  8  9 10 aqueous phase l e a v i n g column CALIBRATION OF ATOMIC ABSORPTION SPECTROPHOTOMETER ' Sample Absorption, cone., microgr. 1o " /ml. 0 1  3 5 7 9  0.0  I8.7 46.7 64.3 76.2 84.3  Absorption r e a d i n g on spectrophometer,  Dilution factor  Sample collection tube  Sampling position  25 10  54.7 58.0  5 5  48.3 31.8 4o.6  1 •1 1 • 1 1 1 100  G6 07 G8 G9 ' G10 Gil  • >  20.6 . 8.1  "3A 1.6 0.9  .  41.7  PISTON SAMPLE Trial  1 2 . 3  B  A  0.9.5 0.95 1.0  6.45 6.85 6.60  C  0.95 0.95 1.0  D  6.25 6.65 6.40  E  116.4 116.4 116.4  F  G  5-3 4.55 5-7 4.90 5-4 4.64  A=reading o f k e t o n e / a i r i n t e r f a c e l e v e l , ' m l . B=reading o f water/ketone i n t e r f a c e l e v e l , m l . C=corrected A from c a l i b r a t i o n curve, m l . D=corrected B from c a l i b r a t i o n curve, m l . E = t o t a l volume in' sample, m l . F=volume o f ketone i n sample, m l . G=hold-up o f d i s p e r s e d phase, #  AQUEOUS PHASE OUTLET SAMPLE  KETONE PHASE OUTLET SAMPLE  C o l l e c t i o n tfme=40-min. Weight o f c o l l e c t i o n f l a s k = 1-lb. 15-oz. Weight o f f l a s k + sample= 16-lb.' 2-oz. Weight o f sample=l4-lb.3-oz.  Collection Weight o f Weight o f Weight o f  time=10-min-i • " c o l l . flask=l-lb.5-oz. f l a s k + sample=6-lb.l4-oz. sample=5-lb.'9-oz.'.  205  C a l i b r a t i o n o f atomic a b s o r p t i o n spectrophotometer  Sodium cone.  Absorption  Absorbance  (Absorbance)'  (Cone.) (Absorbance)  0  0.0  0.0000  0.0000  .0.0000  0.0899  0.0081  0.0899  0.2733  0.074-7  0.8199  5  1&..7 46.7 64.3  0.4473  0.2001  2.2365  7  76.2  0.6234  0.3886  4.3638  9  84.3  0.804-1  0.6466  .7.2369  2.2380  1.3181  14.7470  .  1 3  Total  25  L e t t h e : c a l i b r a t i o n l i n e be - -cone. = (m^)(absorbance) + By l e a s t squares f i t  (2.,2380)(25) - (6)(l4.7^70) m  and k±  l  =  (2.2380)  2  =  - (6)(l.3l80)  ( 2 5 ) ( l . 3 l 8 l ) - (2.238o)(l4.7470) 6 1 < 3 1 ei) . (2.2380)  =-( )(  2  11.22  = -0.018  Therefore, cone. = (11.22)(absorbance) T a b l e IV-2  0.018  shows the c a l c u l a t i o n o f the s o l u t e c o n c e n t r a t i o n a t  the sampling p o s i t i o n s i n the column.  A l s o shown i n T a b l e IV-2  are q u a n t i t i e s r e q u i r e d ' f o r f u r t h e r computations.  The dimensions  o f each p i e c e o f Pyrex p i p e i n the t e s t s e c t i o n of the column are given i n Table V I - 1 ,  Appendix V I .  Water b a l a n c e  D e n s i t y o f M I B K - s a t u r a t e d w a t e r = 0.996 gm./ml. (Measured b y means of s p e c i f i c g r a v i t y b o t t l e ) Aqueous phase l e a v i n g t h e l o w e r end o f t h e column = 14 l b . 3 o z . i n 1*0 min. = 27.897  ft?/hr.ft n  2  p  Sampling r a t e = 1 ml./min. = 0.1727 f t r / h r . f t . O  T r a c e r f e e d r a t e = 0.310  p  ft./hr.ft.'  Aqueous phase f e d t o t h e column =27-7 Apparent l o s s =  ft./hr.ft.  27.7 + 0.310 - 0.1727 - 27.897 27.7  (100)$ = -0.22$  Ketone b a l a n c e D e n s i t y o f w a t e r - s a t u r a t e d MIBK = O.806 gm./ml. (Measured b y means of s p e c i f i c g r a v i t y b o t t l e ) Ketone phase l e a v i n g t h e E l g i n head o f t h e column = 5 l b . 9 o z . i n 10 min. = 54.07  ft./hr.ft.  Ketone phase f e d t o t h e column = 54.74 Apparent l o s s =  54.74 - 54.07 54.74  ft./hr.ft.  (100) $ = 1.22$  Tracer balance The amount o f t r a c e r l e a v i n g t h e column due t o s a m p l i n g i s neglected.  TABLE IV-2. CALCULATION OF QUANTITIES USED FOR THE CALCULATION OF E. sampling position (Figs. 9 and 10)  Height above tracer distributor =w,ft,  Dilution factor  Absorption  Absorbance  *  Measured cone., microgm. per m l .  Sample cone.  c>  =c  Log (C .) e  c  = q  2  2  w  q  microgm. per m l .  1  0.5115  25  54.7  0.3439  3.8406  96.015  4.564  0.2616  2.3345  20.8301  2  1.014  10  58.0  0.3768  4.2097  42.097  3-740  1.0282  3.7924  13^9876  3  1.517  5  48.3  0.2865  3.1965  15.9825  2.771  2.3013  4.2036  7.6784  4  2.020  "5  31.8  0.1662  1.8468  9.2340  2.223  4.0804  4.4905  4.9417  5  2.527  1  40.6  0.2262  2.5200  2.2500  0.9423  6.3857  2.3812  0.8543  6  3-015  1  20.6  0.1002  1.1062  I..IO62  0.1008  9.0902  0.3039  0.0102  7  3.518  1  8.1  0.0367  0.3938  0.3938  -0.9319  12.3763  -3.2784  0.8684  •8  4.028  l-  3.4  0.0150  O.1503  0.1503  -1.895  16.2248  -7.633I  3.5910  9  4-537  1  1.6  0.0070  O.0605  0.0605  -2.805  20.5844 -12.7263  7.8680  10  5.045  1  0.9  0.0039  0.0258  0.0258  100  41.7  0.2343  2.6108  -6.1317  60.6297  il*» . Total*  22.6875  261.08 167.559  8.709  72.3329  1 *  F o r p o s i t i o n s 1 t o 9 ( i n c l . ) o n l y . (Sample cone, a t p o s i t i o n 10 i s l e s s t h a n 0.05 microgm./ml.)  * * P o s i t i o n 11 r e f e r s t o t h e aqueous phase l e a v i n g t h e column.  208  T r a c e r l e a v i n g t h e lower end o f t h e column = (27'.897)(26l.08)=7,283 (microgm./ml. ) ( f t ? ) / ( h r . ) ( f t ? o f column) T r a c e r f e d t o t h e column = (0.310)(23,000).= 7,130 (microgm./ml.) • . ( ' f t ? ) / ( h r . ) ( f t ? o f column) Apparent l o s s =[7,130 - 7,283"] (100) $ = -2.15$ L TA30 J A x i a l eddy d i f f u s i v i t y The f o l l o w i n g s t a t i s t i c a l computations a r e b a s e d on t h e methods (125).  d e s c r i b e d b y B e n n e t t and F r a n k l i n  n = t h e number o f sample c o n c e n t r a t i o n s l e s s t h a n  0.05-microgm./  ml.. = 9 S(q,w)= g ( q ) ( v ) - S ( q ) 5 ( w ) n S(q ) 2  = -6.1317-(22.6875)(8.709) 9  =^( 1 ) " H a l . ' = 60.6297 - 8.709 • ' ' . 9 (  2  2  n  S(w ) = ^ ( w ) - ( $ w ) • n 2  2  2  2  =  -28.0856  = 52.2023 .  = 72.3329 - 22.6875 . 9  2  = 15.1415  v/s(.w ) = 3.8912 2  S  S  2  *'  =(S(q ))(S(w )-(S(q,w)) 2  [ r  2  'U^(sU))  w  q,w = ° ' ^  2  = (52.2023) (15. lkX5) - ( -28.0856 ) =0.01529 (7)(l5.lfl5) 2  :  6  A l e a s t squares f i t (125) o f the d a t a t o t h e e q u a t i o n q = (M)(w) + K yields.  .  •  K=(5q)(5w )2  S((g)(w))£w =  (n)(^(w )) - (^w) 2  2  (8.709)(72.3329)-(-6.1317)(22.6875) (9)(72.3329) - (22.6S75)  = 5.640  2  209  and M = S(q,w) = -1.8549 = -I.8549 15.1415  S"(w ) 2  i c o n f i d e n c e l i m i t s on M a r e (125) M + ( t o . ) (S ) - n-2,g<. q,v v  / S T Y  where t  0  , , = t h e v a l u e o f t h e t - d i s t r i b u t i o n f o r ( n - 2 ) degrees o f freedom and (l00)(l-©<) $ c o n f i d e n c e  Yo.05  =  2  '  3  6  k  6  (  1  2  5  limits.  )  95$ c o n f i d e n c e l i m i t s on M a r e -I.8549 t- (2.3646)(0.1236) = -I.8549 t 0.07511 3-8912 = -1.9300 t o -1.7798 ( I t s h o u l d be noted t h a t f o r runs where n = 2 no s t a t i s t i c a l t e s t r e g a r d i n g t h e c o n f i d e n c e o f r e s u l t s c a n be performed.  F o r runs  where n = 3 t h e 95$ c o n f i d e n c e l i m i t s on M a r e l i k e l y t o be wide since ^,0.05  =  1  2  '  7  1  -  '  I n f a c t t h e 95$ c o n f i d e n c e l i m i t s c a l c u l a t e d f o r runs where n = 3 a r e n o t l i k e l y t o r e p r e s e n t t h e t r u e s i t u a t i o n because i t i s not p o s s i b l e t o i n c l u d e n o n - s t a t i s t i c a l r e a s o n i n g i n t h e s t a t i s t i c a l analysis.  F o r example, t h e r e i s no r e a s o n t o doubt t h e  l i n e a r i t y o f t h e r e l a t i o n s h i p between  and UJ f o r runs where n i s  g r e a t e r t h a n 3•) The s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , ( E e ) , i s g i v e n b y the f o l l o w i n g e q u a t i o n .  210  (Ee) = - L  c  ~M~ (Ee) = -27.7 -1.8549  = 14.93 f t ? / h r .  The f l o w r a t e , L^, o f aqueous phase f e d t o the column can be measured and kept c o n s t a n t t o w i t h i n a p p r o x i m a t e l y 1$ o f L^. On the assumption: t h a t t h e r e c o r d e d v a l u e o f  comes from a  n o r m a l d i s t r i b u t i o n an e s t i m a t e o f t h e s t a n d a r d d e v i a t i o n , cT~ , r  of L  c  i s g i v e n b y (125) CT^  = (L /100) .  C  c  Therefore (J-  = 27.7 = 0.09233 300  L C  An e s t i m a t e o f t h e v a r i a n c e , C J ^ , o f M i s g i v e n b y cr  M  =  = 0.01529 = 0.001010 15.1415  s  S(w ) 2  The v a r i a n c e , C 7 , E e  m  o f (Ee) i s g i v e n b y t h e f o l l o w i n g e q u a t i o n  ''Ee  (Be)  £  = (14.93T  t  (125)  M J  o. 09233 \ 27.7 J  + /.o. 00101 13.4407  0.06791  Therefore 0~ = 0.2606 Ee In c a l c u l a t i n g remembered  95$ c o n f i d e n c e l i m i t s f o r (Ee) i t must b e  t h a t M was d e t e r m i n e d from n d a t a p o i n t s .  A reasonable  a p p r o x i m a t i o n i s t o assume t h a t (Ee) comes from a t - d i s t r i b u t i o n  211  Therefore the 95$ confidence limits  with (n-2) degrees of freedom. on (Ee) are " ^n-2,  ( ) Ee  O ^ ^  =-14.93 - (2.3646)(o.26o6) = 14.93 t 0.62 = 14.31  to  15.55  Now l~hold-up 100 • The three values of e calculated from hold-up measurements are e = 1 - 4.55 100  = 0.9545  e = 1  = O.95IO  - 4.90  100  e = 1 - 4.64 100  = 0.9536  The arithmetic average of e = 0.9545 + O.9510 + O.9536 = O.953O 3 The best estimate, O" , of the variance of e i s given by  gf  =  (n)(Se ) - (ge) 2  2  =  (n)(n-l)  (3)(2.72482421) - (2.8591) (3,(2)  = 0.000003303 The axial eddy diffusivity, E, i s given by '  E = (Ee) = 14.93 = 15.67 e 0.9530  2 The variance, o~n,, 'E of E i s given by  'Sit  +  Ee/  = (15.67 ) 2  K Ie/  70.2606^  r  U^.93  7  2  + 0. 000003303 (0.9530)  2  = 0.0748  2  212'  Therefore . <T = K  0.2735  On t h e assumption t h a t E comes from a t - d i s t r i b u t i o n w i t h degrees o f freedom t h e 95$ c o n f i d e n c e  (n-2)  l i m i t s f o r E are taken  t o be E t (t _2,0.05 n  ) (  =  1  5  '  6  t  +  = 15.67  - (2.3646)(0.2735)  t  0.65 = 15.02 t o 16.32  The P e c l e t number, P e , i s c a l c u l a t e d from t h e f o l l o w i n g equation. (d ) r Pe =  \ 1 - e  e/ 11-18  where d^ i s t h e d i s p e r s e d phase drop 54.74 + + 27.7 27.7 ^ Pe = /0.135) /Q.I35^ / /54.74 V [ 12 J [ 0T0W 0.953/  diameter.  = O.857  15-67 . T a b l e I V - 3 shows t h e r e s u l t s o f t h e above c a l c u l a t i o n s a s c a r r i e d o u t on 'an IBM-7040 e l e c t r o n i c computer.  b)  TABULATED RESULTS T a b l e I V - 4 "gives t h e reduced c o n c e n t r a t i o n p r o f i l e s , t h e  d i s p e r s e d phase h o l d - u p , t h e number o f e x p e r i m e n t a l  p o i n t s used  f o r t h e e s t i m a t i o n o f t h e a x i a l eddy d i f f u s i v i t y , t h e a x i a l eddy d i f f u s i v i t y , and t h e P e c l e t number f o r each r u n c a r r i e d o u t w i t h t h e 1-^-in. I.D. column. number o f e x p e r i m e n t a l  The reduced c o n c e n t r a t i o n p r o f i l e , t h e p o i n t s used f o r t h e e s t i m a t i o n o f t h e  TABLE IV-3. RUN  TYPICAL COMPUTER RESULTS  50  HATER FLOWRATE • 27.70 CU.FT./IHR. SO.FT.) KETONE FLOWRATE • 54.74 CU.FT./INR. SO.FT.I TRACER FLOWRATE - 0.510 CU.FT./IHR. SQ.FT.> _ _ NOZZLE TIP AVERAGE DIA. • 0.10) IN. EQUIVALENT. DROP OIA. « 0.135 IN. AVERAGE VELOCITY OF OISPERSEO PHASE IN NOZZLE TIPS • 0.56 FT./SEC. COLUMN HEIGHT INOZZLE TIPS TO INTERFACE 1 • lO^FT. 3 1/0-IN. COLUNN I.D. • 1.5 IN. TEMPERATURE » 72 »F 1  CALIBRATION OF ATOMIC ABSORPTION SPECTROPHOTOMETER ABSDRBANCE CONCENTRATIONS PER CENT SOO.CONC. ABSORPTION MICROGN./NL. 0.000 0 0.0 18.7 0.090 t 3 46.7 0.273 64.1 0.447 5• 7 76.2 0.623 0.804 9 84.3 CONCENTRATION POSITION ISEE F I G . 101 1 2  •  *  •  HATER KETONE TRACER KETONE  M  U.219*ABSORBANCE-0.018  OILUTION FACTOR  PER CENT ABSORPTION  25 10 5 4 5 1 » 1 1 1 1 9 1 10 1 100 11 •POSITION 11 REFERS TO  i  ARE  ABSORBANCE  54.7 58.0 48.3 31.8 40.6 20.6 B.l 3.4 1.6 0.9 41.7 THE AQUEOUS  MEASURED CONC.  SAMPLE CONC.  LOG.E CONC.  REOUCEO CONC.  96.004 0. 344 3.840 0.377 4.209 42.087 0.287 3.196 15.981 1.847 0. 166 9.233 0.226 2.520 2.320 0.100 1.106 1.106 0.393 0.037 0.393 0.015 0.150 0.150 0.007 0.061 0.061 0.004 0.026 0.026 0.234 261.089 2.611 PHASE LEAVING THE COLUMN)  4.564 3.740 2.771 2.223 ' 0.924 0.101 -0.933 -1.894 -2.805 -3.650 5.565  367.705 161.197 61.210 35.365 9.651 4.236 1.507 0.576 0.232 0.100 1000.000  MASS BALANCE APPARENT LOSS • -0.201 PER CENT MASS BALANCE APPARENT LOSS » 1.257 PER CENT MASS 8ALANCE APPARENT LOSS • -2.139 PER CENT HOLD-UP - 4.70 PER CENT  tOO.EICONC)" -1.8549«IHE1GHT ABOVE TRACER INJECTION)**.6414 95 PC CONFIDENCE LIMITS ON SLOPE ARE LOG.IOICQNC). -4.2718*IHEIGHT ABOVE TRACER INJECTI0NI.LOG.101281.86)  -1.9404 TO :  -1.7693 " :  NUMBER OF POINTS FOR ESTIMATION OF EOOY DIFFUSIVITY » 9 SUPERFICIAL AXIAL EOOY DIFFUSIVITY '14.93 SO.FT./HR.  95 PC CONFIDENCE LIMITS ARE 14.23 SO.FT./HR. TO 13.63 SQ.FT./HR.  AXIAL EOOY OIFFUSIVITY -15.67 SQ.FT./HR.  95 PC CONFIDENCE LIMITS ARE 14.93 SQ.FT./HR. TO 16.41 SQ.FT./HR.  PECLET NUMBER • 0.858  TABLE IV-k.  AXIAL EDDY DIFFUSIVITY RESULTS FOR THE l | - I N . I.D. COLUMN  AVERAGE INSIDE DIAMETER Of HOI til TIPS - 0.126 IN. C1SPERSED PHASE EOUIVALENT OA CP DIAMETER - 0. IS* I N . AVERAGE VELOCITY OF 0I3PERSE0 PHASE IN TIPS • 0.36 PT./SEC. COLUMN INSIDE DIAMETER • 1.5 IN. COLUMN HEIGHT IN022LE TIPS TO INTERFACE I • 10-FT. 1 l / > - I N . I5EE F I G . 10 FOR OIAC. OP IX • CONTINUOUS PHASE SUPERFICIAL VSLOCir/, CU.FT./IHR. SO.FI.I : LK . OISPERSED PHASE SUPERFICIAL VeioclTY, CU.FT./IHR. SU.FT.I IT • TRACER FEEO SUPERFICIAL V£LOCI*Yi CU.FT./IHR. SO.FT.I HnlD-UP • VOLUMETRIC PERCENTAGE OF OISPFRSED PHASE IN COLUMN PP • NUMBER OF SAMPLE C01CENTRATIONS USED FOR ESTIMATION OF AXIAL EOOV O I F F U M V I I T f » AKIAL EODT OIFFUSIYITT MlTH 93 PER CENT CONFIOENCF LIMITS. SO.FT./HR. PE • PECLET NUMBER BASED ON OISPERSED PHASE DROP OIAMETER tm • WATER BALANCE APPARENT LOSS. PER CENT ER? • KETONE BALANCE APPARENT LOSS. PER CENT ER) • TRACER BALANCE APPARENT LOSS. PER CENT  101lit  IM 126 9.0 12T 18.2 12a 27. T i ? ) 36. 3 48.4  no  >6.3 36.5 36.3 36.3 36.5  0.112 0.200 0.310 0.350 0.680  TEMP *F 71 71 70 72 72  837.33 760.53 694.03 612.47 520.28  LK  LT  «  r  720.74 576.77 532.74 357.07 206.90  ' 3 631.46 417.22 328.25 200.93 93.9)  *  wENTRAT IflN AT SA MPLING P OINTS IS FE F I G . 101 & 4 5 7 ll y 405.09 530.62 359.35 318.5? 282.61 254.1)7 198.41 304.01 147.83 105.04 76.49 6 c 75 184.81 89.88 34.84 56.47 1 9 . 74 ?6.22 108.89 47.00 24.43 14.15 7.92 5.2f 32.37 12.59 5.74 i.ll 1.37 0.62  E  Pt  10 10 10 10 10  30.4912.66 2'(.6111.73 3C.26t2.71 30.46*1.46 3 0 . 0 4 H . 34  0.5s 0.64 0.62 0.62 0.56  1.08 -l.o: 2. 35 2.65 0.14 - 1 . 35 1.23 -1.05 6. 11 1.45 3. 02 0. l< -1.45 1. 33 - 0 . 45  73.79 8.23 0.45 0.08 0.03  4.7 4.7 4.7 4.6 4.8  10 10 10 8 6  18.77*0.76 19.8510.86 19.4710.69 20.2710.96 19.7410.57  0.82 0. 77 0.79 0.78 0.78  -1.77 -0.9« - 5 . 91 1.37 1.26 - 3 . 62 -1.21 1.2« 36 1. 25 1.29 1.2C 0.54 44 0. I.2C  16  ERI  ER2  ER)  93.92 14.38 U.92  61.69 ?.86 0.16 0.02 0.02  49.10 1.23 0.04 0.00 0.01  28.76 0.61 0.00 0.00  6.8 6.7 6.7 7.0 7.2  10 10 7 6 5  13.4410.73 13.4810.29 13.8810.51 13.0011.10 13.7)14.03  1.05 1.06 1.04 1.07 1.00  2.28 1.71 9. 13 1.37 0.15 4. 04 1.13 -0.37 3. 4 ) 0.67 - 3 . 64 -1.41 1.94 1.19 9t 96  52.92 1.31 0.06 0.04 0.00  33.13 0.45 0.02 0.00 0.00  20.43 0.09 0.00 0.00 0.01  11.54 0.00 0.01 0.00 0.00  9.) 9.2 9.4 9.6 9.8  10 8 5 4 3  11.3910.46 10.8010.42 10.87ll.2) 11.1512.18 11.5516.27  1.13 1.21 1.19 1.14 1.10  -0.56 1.37 -1.04 1.17 0.48  0.36 0. 29 0.98 - 1 . 99 0.14 -11. 01 1.39 I . 40 1.39 Of 34 1. 71 1.00 1. 46 1.00 1.43 0. 20 0.57 - 1 . 05 l.OC - 3 . 24  9.0 18.2 27.7 36.5 48.4  34.7 54.7 54.7 54.7 54.7  0.112 0.200 0.310 0.350 0.682  72 T2 70 71 71  707.79 624.01 407.72 335.61 312.21  549.90 413.69 188.50 168.54 85.19  4)9.74 742.01 102.32 47.38 25.34  342.22 169.91 40.93 22.79 7.08  238.2? 87.33 16.77 9.55 1.73  201.20 52.99 10.24 3.18 0.49  146.76 31.38 4.91 1.36 0.14  82 01 80 1)1 132  9.0 18.2 27.7 36.3 48.4  73.0 73.0 73.0 73.0 73.0  0.112 0.200 0.310 0.350 0.680  71 70 70 71 70  742.70 469.37 247.88 400.42 235.96  584.97 200.41 18.00 123.95 98.01  386.07 102.20 26.40 27.75 7.16  280.12 48.95 11.08 4.28 0.64  163.41 22.06 3.51 0.94 0.20  133.78 11.41 1.10 0.27 0.03  83.59 6.13 0.41 0.11 0.01  9.0 18.2 86 27.7 85 36.5 133 48.4  91.2 91.2 91.2 91.2 91.2  0.112 0.200 0.310 0.350 0.680  71 70 72 72 70  643.46 322.17 169.13 111.50 101.15  442.38 127.69 49.23 18.66 11.64  263.43 53.90 8.32 2.28 0.93  190.87 16.60 2.39 0.S2 0.09  108.02 7.49 0.64 0.16 0.02  77157 3.24 0.16 0.13 0.01  a*  HOLO -UP 2.7 2.5 7.6 2.6 2.9  PP  215.17 46.51 11.59 2.46 0.27  124.30 ??.71 ?.47 0.46 9.05  TT 76 75 T9 TS  83  APPARATUS)  -  a.in 0.03  o.oi  ).  88 87 90 89 134  9.0 18.2 27.7 36.5 48.4  109.5 109.3 109.5 109.5 109.3  0.112 0.200 0.310 0.330 0.610  71 T3 74 73 TO  477.46 293.73 153.20 101.39 86.18  321.83 123.06 38.37 13.85 7.53  182. » 36.80 6.12 1.69 0.27  116.59 12.68 2.92 0.43 0.02  64.74 3.74 0.82 0.14 0.01  51.7) 2.13 0.24 0.07 0.00  26.18 0.46 0.10 0.05 0.00  18.38 0.14 0.03 0.03 0.01  10.31 0.00  6.24 0.00 0.03 0.05 0.02  12.0 12.1 11.8 12.1 12.1  10 10.7110.44 7 9.7510.82 6 12.3411.74 4 11.2712.98 9.63110.7 3  l.ll 1.23 1.00 1.09 1.29  0.91 -0.74 -1.53 -0.06 -0.48  9* 93 92 91 133  9.0 18.2 27.7 36.3 48.4  127.7 127.7 127.7 127.7 127.7  0.112 0.200 0.310 0.350 0.680  73. 75 73 75 71  393.54 304.16 136.22 80.62 73.37  354.25 145.78 31.81 8.82 6.30  189.80 29.3) 4.30 0.94 0.16  121.78 9.84 1.10 0.10 0.04  60.06 3.26 0.31 0.06 0.01  45.56 1.28 0.15 0.06 0.02  23.91 0.37 0.11 0.04 0.00  13.67 0.13 0.09 0.04 0.01  10.33 0.11 0.11 0.08 0.00  5.57 0.11 0.09 0.04 0.00  13.7 13.6 13.7 13.8 14.8  10 10.2510.46 7 9.3110.71 5 10.4311.61 3 9.5610.62 3 10. 7 4 1 6 . 0 4  1.19 1.3) 1.19 1.31 1.10  1.96 0.13 -3. 9 ) -0.88 -1.17 1. 6 ) -1.98 -0.31 - 0 . 39 1.01 0.99 3. 67 1.04 -111' - 1 . 69  o.ov 0.03 o.oo  1  215  ii  52222  2 Jo'-oS  0--0-  -iii  .T--?«- 777?"  ... a  ooooo  333s  sssss  Oil tM N C M IHi <NJ  liili l-Stif I I I M fx IMft  is*;;  SSSSg j~ooo  SCSSg  •*~o'o'o'  pi!  2S3SS SSSE2  Is--  mi  sssgs  S23SS  "ESSSS  •^o'ooo  sggss  SSoSS 0 00 c  5SISS  KS5SS  je'doo Voooo  53133 3S2SS  idddD  2SSSS  ;dodc  S5SS5 f~  |33S!  OO O O  22222  22222 15533 S52SS J--000 rg 51533 13333 j;ddo 22222  $« IJS25  SUSS 8  iiiii  usees  ^000  I1S55 IPs  SSJ25-;  SSSSJ SS2S5  77?7°  <; 0 ^ -  -SS3S  SS2«  o o  t  *•  IS22  •3S2--  pin  3SC55  ;22^ •»>  S3""  ---00  i i :  - - 0 0 0 ooooo  |SS = ~  ?5222 ?3222  22222 22222 22222  00^00 ^0000  oooc«  It!..-  32225 *TTT- •?•?•?•?•  35253  m  S2SS-  3315?  SSS22  552§S  im  HE!*  22CEs -4-  t t>  M  ?!!H IB!! !!!!!  o^oo^l oooo'c 2  i i i i l 2 2 J 2 <j|  Villinm  «n  «c* v* m «n  sssss Mil  ma || 5?SSS| SS33SJ SKS5?|  3SS27  TABLE IV-4.  CONTINUED (2)  AVERAGE INSIOE DIAMETER OF NO H i t TIPS • 0.066 IN. DISPERSED PHASE EQUIVALENT DROP DIAMETER • 0.US IH. AVERAGE VELOCITY OF DISPERSED PHASE IN NOZILE TIPS • 0.38 FT./SEC. COLUMN INSIOE OIAMETER • U S IN. COLUMN HEIGHT INOHLE TIPS TO INTERFACE) • 10-FT. 1 1/8-IN. ISCE FIG. ID FOR 01AG. OF APPARATUS) LM • CONTINUOUS PHASE SUPERFICIAL VELOCOy, CU.PT./IHA. SO.FT.) LK • DISPERSEO PHASE SUPERFICIAL VfLOCITY, CU.FT./IHA. SO.FT.I IT • TRACER FEED SUPERFICIAL VftOCiry, CU.FT./IHR. SO.FT.) HOLD-UP • VOLUMETRIC PERCENTAGE OF OISPERSEO PHASE IN COLUMN PP • NUMBER OF SAMPLE CONCENTRATIONS USED FOR ESTIMATION OF AXIAL EOUY DIFFUSIVITY t - AXIAL EOOY 0IFFUS1YITY WITH 9* PER CENT CONFIDENCE LIMITS. SO.FT./HR. PE • PECLET NUMBER BASED ON DISPERSED PHASE DROP DIAMETER EKI • WATER BALANCE APPARENT LOSS. PER CENT EA2 • KETONE BALANCE APPARENT LOSS. PER CENT ER1 • TRACER BALANCE APPARENT LOSS. PER CENT HOLD -UP  PP  2.9 2.8 2.9 2.9  1.0  E  PE  36.* 0.3*0 36. 5 0.6S0  70 TO A9  314.14 23*.63 97.90  REDUCED CONCENTRAT1 ON AT SAMPLING POINTS ISFE 6 4 9 3 49i.4» 433.99 17.67 98.41 49.02 30.50 147.93 3.4* 2.00 80.0* 31.96 10.11 149.29 0.44 2.09 1.38 74.26 20.27 10.93 0.29 0.07 0.0* 42.26 7.46 2.11  9.0 18.2 27.7 36.5 48.4  S4.7 *4.7 94.7 54.7 *4.7  0.112 0.200 0.310 0.3*0 0.680  72 73 73 73 73  961.61 389.16 146.91 93.48 34.4*  4*3.17 177.99 67.11 23.61 6.92  260.53 58.66 12.29 4.12 0.72  181.61 34.56 5.92 1.51 0.15  120.17 8.83 2.80 0.39 0.00  81.66 ».19 0.47 0.04 0.00  46.47 1.95 0.00 0.00 0.00  36.83 0.67 0.00 0.00 0.00  23.38 0.21 0.00 0.00 0.00  13.69 0.00 0.00 0.00 0.00  4.9 4.8 4.8 4.8 9.0  10 9 6 5 4  11.4710.56 10.1710.63 13.1112.61 14.1112.06 13.7713.03  1.03 1.16 0.93 0.87 0.87  -0.80 1.59 0^79 0.19 0.84  9.0 18.2 27.7 109 36.5 48.4  73.0 73.0 73.0 73.0 73.0  0.112 0.200 0.310 0.3*0 0.480  73 73 74 74 74  410.67 303.97 136.8* 80.32 22.19  28S.08 129.34 3*.29 13.16 2.29  161.50 36.06 6.1* 0.94 0.00  107.92 16.99 1.67 0.00 0.00  57.S2 4.5) 0.3* 0.00 0.00  42.32 1.6* 0.11 0.00 0.00  24.20 0.4* 0.07 0.00 0.01  16.80 0.20 0.07 0.00 0.00  10.63 0.00 0.09 0.00 0.00  9.81 0.00 0.1* 0.00  0.00  7.7 7.0 7.2 7.9 7.3  10 10.3910.39 7 9.0610.60 5 10.0210.74 3 8.92112.2 2 11.56  1.03 1.23 1.08 1.19 0.95  -0.8S 0.67 0.92 1.19 -0.64 -0.89 -0.51 1.19 2.48 0.67  111 112 11) 114 11*  9.0 18.2 27.7 16.* 48.4  91.2 91.2 91.2 91.2 91.2  0.112 0.200 0.310 0.350 0.680  72 72 71 71 70  422.19 22*.76 128.84 *9.68 36.61  2*6.99 78.04 28.08 8.57 2.42  12*. 99 21.44 9.16 0.70 0.21  74.49 7.87 0.90 0.1) 0.04  36.49 2.30 0.22 0.08 -0.02  24.99 0.66 0.00 0.06 0.02  14.94 0.20 0.00 0.03 0.04  7.89 0.03 0.00 0.01 0.06  4.29 0.00  9.6 9.6 10.1 9.8 10.5  10 7  8.8210.30 8.6110.29  3 9.1518.49 3 10.5114.03  1.13 1.18 1.01  0.04  ?.*7 0.00 0.00 0.06 0.02  0.92  l.ll  0.41 -0.71 -0.64 0.96 -0.02  0.96 I'll 0.S6 -2.49 0.98 2.80 0.14 -0.11 0.56 4.14  116 LIT 118 119 120  9.0 18.2 21.7 36. » 48.4  109. 5 0.112 109.* 0.200 109.5 0.310 109.* 0.3*0 109.* 0.680  69 70 70 70 70  S74.78 287.24 117.37 69.88 27.62  343.98 97.2* 24.99 6.72 1.75  168.56 2».5l 2.56 0.48 0.00  96.93 9.15 0.40 0.00 0.00  46.44 2.29 0.00 U.OD 0.00  31.44 0.76 0.00 0.00 0.00  17.23 0.22 0.00 0.00 0.00  10.07 0.00 0.00 0.00 0.00  5.64 0.00 0.00 0.00 0.00  2.89 0.00 0.00 0.00 0.00  12.6 12.3 12.2 12.7 12.9  10 8.9010.31 7 3.6610.32 4 8.2211.74 3 8.9114.42 2 10.08  1.03 1.09 1.18 1.1* 0.96  0.22 .1.12 -0.79 0.16 1.0*  1.43 -1.16 1.00 6.34 1.00 2.81 1.4) 3.42 1 .4) 1.89  121 122 123 124 12*  9.0 18.2 27.7 36. S 48.4  127.7 127.7 127.7 127.7 127.7  70 70 69  463.18 243.02 107.13 41.99 22.83  246.69 74.94 18.12 4.13 1.16  128.48 17.54 1.98 0.17 0.00  73.25 6.79 0.28 0.00 0.00  37.99 1.93 0.00 0.00 0.00  21.43 0.70 0.00 0.00 0.00  10.57 0.12 0.00 0.00 0.00  6.*0 0.00 3.00 0.00 0.00  3.57 0.00 0.00 0.00  2.07 0.00 0.00 0.00 0.00  19.4 14.9 19.0 15.6 iv.n  10 6 4 2 2  8.8*10.24 9.1210.6a 8.1811.0b 9.40 9.71  0.'<9 1.00 1.1) 0.96 0.93  RUN 96  n  LM  LK  IT  1 2 'fJ96.J9" srm "To 0.200 69 961.82 271.11  34.* 9.6" SSTV 36.* 0.310  18.2 98 2T.T 99 36.* 100 48.4 101 102 103 10* 10* 106  ior 108  no  TEMP  0.112 0.200 0.310 0.3*0 0.680  -  ri 71  1 282.IS 254.6} 184.  FIG. 10) •* 8 94.43 5.19 7.9* 1.20 0.66 0.18 0.10 0.00 0.03  KKV:J*  o .oo 0.~06  o.oo  lo  77.43 2.75 0.31 0.07 0.00  10 10 7 5  15  17.3511.16 16.2310.66 18.17*1.17 1B.1U2.14 17.1413.91  * 9.9910.61  ERI  ER2  ERS  0.83 0.76 0.7* 0.80  -1.62 -0.88 0.62 1.45 -0.97  1.25 -0.71 0.14 -1.82 1.25 2.8* 0.14 4.9* 1.25 -0.97 1.26 1.71 1.26 0.77 1.26 0.0* 2.37 1.25 2.37 -4. 54  V4  1.67 2.69 1.44 3.57 2.78  2.57 -0.31 -1.36 1.76 0.1) 3.06 0.2* -1.17 4.04 1.17 -0.31 3.98 0.53 1-42 4.26  ro V-  1  ON  TABLE I V - U .  CONTINUED ( 3 )  AVERAGE INSIDE DIAMETER OF N O / H E TIPS • 0.0*1 IN. DISPERSED PHASE EOUIVALENT ORUP DIAMETER • 0.04* I N . AVERAGE- VELOCITY OF OISPERSED PHASE IN N022LE TIPS • 0.68 F T . / S E C . COLUMN INSIDE DIAMETER • I . * IN. LULUMN HEIGHT I H O m t TIPS TO INTERFACE! « 10-FT. 1 1/8-IN. ISEE F I G . 10 FOR DIAG. OF LU •CONTINUOUS PHASE SUPERFICIAL VELOCITY, CU.FI./IHR.' SO.FT.I IK • DISPERSED PttASE SUPERFICIAL Ml LOC IT Y, CU.FT./IHR. SQ.FT. I LT • TRACER FEED SUPERFICIAL </««.o«IT7*, CU.FT./IHR. SO.FT.I HOLD-UP • VOLUMETRIC PERCENTAGE OF DISPERSED PHASE IN COLUMN PP • NUMBER OF SAMPLE CONCENT'AT IONS USED FOR ESTIMATION OF AXIAL EDDY DIFFUSIVITY E_« AXIAL EDDY DIFFUSIVITY WITH 9* PER CENT CONFIOENCE L I M I T S . SC.FT./HR. PE • PECLET' N i m E R ~BASE0 ON DISPERSEO PHASE DROP DIAMETER CHI • MATFR BALANCE APPARENT LOSS, PER CENT ER2 - KFTONE BALANCE APPARENT LOSS. PER CENT t R ) • TRACER BALANCE APPARENT LOSS. PER CENT RUN  LU  L«  IAS 147 1*6 1*5 l*»  9.0 18.2 27.7 36.* 48.4  16.* 16.* 36.* 36.* 36.*  9.0 1*2 18.2 1 * 1 27.7 1*0 16.* 1*9 48.4 1*1  9.0  1*8 1*7 1 0 . 2 1*6 27.7 1** 16.* 1*4 48.4  TEMP 1 ^F 498.46 68 68 28*. 99 0.200 68 161.17 9.110 68 89.06 0.1*0 D.680 68 21.28 IT  0.112  RED JCEO CON CENTRA!IC N A l SAMPLING POINTS ISEE F I G . 10) * * 6 7 8 9 2 1 li.*7 146.04 59.88 34.14 400.76 211.71 71.48 22.98 2.27 0.90 0.1* 107.67 12.7* 0.41 48.81 5.25 0.09 6.57 1.82 0.62 0.25 0.05 0.05 48.48 0.11 0.06 0.06 0.08 1.67 0.08 16.72 0.11 0.05 0.07 0.05 1.94 0.08 0.07 0.0* 0.20  0.04 0.00 0.04 0.00  o.oi  0.02 0.04  If.16 0.01 0.02 0.0* 0.0*  6.71 0.01 0.02 0.02 0.06  68 68 68 68 68  *60.75 287.1* 118.93 70.68 26.6*  192.12 122.05 25.34 5.54 1.30  213.61 24.81 3.44 0.41 0.01  12*.96 7.81 0.23 0.04 0.01  54.10 1.84 0.03 0.04 0.00  31.41 0.48 0.01 0.02 u.00  17.16 0.13 0.01 0.02 0.01  73.0 0.112 13.4 D.200 73.0 0.110 73.0 0.1*0 0.680  66 76*.71 67 127.39 67 104.00 72.49 68 28.74 68 _  465.25 113.56 26.37 *.S0 0.97  245.89 21.42  61.10 1.22 0.0* 0.04 0.0*  41.98 0.24 0.03 0.02 0.04  19.29 0.0*  0.18 0.06  161.00 5.11 0.44 0.04 0.0*  2.1*  1.57  4.17 0.02 fi.Ot! 0.02 O.00  **.7 8.112 3*.7 **.7 0.310 0.200 *A.T 0 . 1 * 0 SA.7  0.6AO  APPARATUS!  10 6.0) 0.09 0.07 0.06 O.OI 1.97 0.01 0.C1 0.02 0.01  i./r  J.ul 0.01 0.02 0.0*  9.0 91.2 0.112 69 161 162 18.2 91.2 O.200 68 91.2 68 161 2 7 . 1 160 16.* 91.2 0.110 68 1*9 .**•*. 91.2 0.1*0 _69  474.10 329.94 127.40 81.24 18.66  297.44 109.41 25.41 8.5* 0.11  171.87 28.** 2.10 0.5* 0.02  97.69 8.8* 0.42 0.03 0.00  44.40 1.84 0.06 0.00 0.01  21.90 0.47 0.02 0.00 0.01  15.58 0.1* 0.04 0.00 0.01  6.11 0.07 ".02 0.00 0.00  3.52 U.U3 0.02  o.oi 0.02  0.01  o.oo  9.0 109.* 168 167 IB.2 109.* 166 77.7 109.* 16* 16.* 109.* 164 46.4 109.*  68 68 68 69 67  451.70 244.*9 119.48 **.97 . 12.70  129.11 77.40 20.52 6.71 0.69  171.77 19.36 0.*7 0.07  104.22 4.87 0.12 0.11 0.07  51.12 1.13 0.11 0.09 0.0*  11.65 0.17 0.09 0.09 0.05  19.00 0.16 0.09 0.11 0.0*  10.7* 0.09 0.09 0.11 0.07  68 69 69 69 68  482.44 1*2.27 97.27 41.41 18.71  141.44 94.91 16.67 2.79 .0.65  118.97 17.96 1.19 0.2* 0.0*  76.14 4.83 0.18 0.07 0.01  29.4) 1.2* 0.115 0.07 0.01  20.21 0.28 0.03 0.07 0.03  9.51 0.12 0.01 0.04 0.0*  5.48 0.0* 0.05 0.0* 0.0*  171 172 III 170 16 1  9.0 18.2 27.7 16.* Aft.A  127.7 127.7 127.7 127.7 127.7  0.690 0.112 0.200 0.310 0.1*0 0.680 0.112  0.200 0.110 0.1*0 0.680  1.88  1.91  HCILO -UP 2.7 2.11  2.9 3.U  1.0 4.8  PP  ER) 4. 14 1.42 2.01 2.7) 1.68  7.4*t0.18 7.3710.66 7.0712.71 7.5910.32 8.69  1.21 1.17 1.11 1.15 1.07  -1.62 2.17 -0.27 2.17 1.13 -0.96 -0.06 1.26 1.04 1.26  0.51 1.24 2.89  S.1110.34 6.8210.51 8.0412.41 7.5812.15 7.84  0.6-1  0.9*  -0.80 2.6* 0.12 -1.41 0.03  8.0610.18 7.7*10.57 H.0111.86 8.1715.80 8.18  0.S7 0.89 O.i* 0.85 0.82  -1.45 -1.14 -0.74 0.51 -1.53 0.53 0.61 1.78 0.48 1.16  1.62 0.66 0.48 1.57 0.07  >.3910.17 7.9U0.38 t l . 0011.5.* 9.2915.0* 9.7*  0.70 0.85 0.81 0. 71 0.6"  0.91 -0.88 -1.09 0.65 1.04  3.75 1.66 1.29 1.08 1.26  7.9810.41 7.6610.34 7.56111.0 P.5411.49 n. 75  0.79  -1.62  1  10  8.2 n.i 8.0  10  8.3  EK2  1.96 -0.97 0.92 1.25 0.62 1.25 1.12 2.16 1.04 1.25  6'  7.9  6««  Pt 1.10 1.05 0.95 1.02 0.92  5.1 5.3 5.2 4.9  E  9.6610.71 8 9.89l0.*l> 6 10.70tl.79 4 9.82*1.97 10.78A2.3*  10  4 3 2  6  4 3 2 10  0.00 O.Uti  10.* 10.7 11.2 10.9 11.2  6.tiO 0.09 0.11 0.09 0.0*  l.rtl 0.07 0.11 0. 1 1 0.07  13.1 13.2 13.9 13.8 l*.l  10  2.57 0.0* 0.05 0.04 0.01  I.II 0.0* J.Oft 0.07 0.01  16.2 U.* 16.4 16.6 17.2  10  6  *  1  2  6  *  1  2  6  1 1  ?  l.o;  0.41 1.01  1.16  0.69 ).*5 5.19 1.21 6.16 1.21 4.26 1.21 0.69 -0.51  0.59 1.4* 1.02 1.02 1.4*  -0.74 l.H 1.42 1.11 -1.09 0.11 -1.7* 1.01 -1.17 1.14 0.51 - 2 . 0 * 0.41  1 -1.11  0.65 0.0 0. 75 0. 72  0.11  218  s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y , and t h e s u p e r f i c i a l a x i a l eddy d i f f u s i v i t y f o r each run- w i t h t h e 3 - i n - I.D. column a r e D i s p e r s e d phase hold-ups i n t h e 3 i n . I.D.  given i n Table IV-5.  _  column were n o t measured.  C o n s e q u e n t l y i t was n o t p o s s i b l e t o  reduce s u p e r f i c i a l a x i a l eddy d i f f u s i v i t i e s t o t r u e a x i a l eddy d i f f u s i v i t i e s o r t o c a l c u l a t e P e c l e t numbers. Measurements o f t h e d i s p e r s e d phase drop s i z e s were a n a l y s e d on an IBM-7040 e l e c t r o n i c computer.  No hand c a l c u l a t i o n s a r e  p r e s e n t e d due t o t h e i r voluminous n a t u r e .  However, t h e a l g e b r a i c  e q u a t i o n used, t o p r o c e s s t h e d a t a i s g i v e n below. Let  r = t h e v e r t i c a l • d i m e n s i o n o f t h e drop image as measured by means o f t h e m i c r o f i l m r e a d e r , mm., x =. the. h o r i z o n t a l d i m e n s i o n o f t h e drop image as measured, b y means o f t h e m i c r o f i l m r e a d e r , mm. f^= t h e c o n v e r s i o n f a c t o r f o r mm. t o i n . = 0,.03937> f = t h e enlargement f a c t o r = a . l i n e a r d i m e n s i o n o f t h e o b s e r v e d image d i v i d e d b y t h e same l i n e a r d i m e n s i o n of t h e a c t u a l o b j e c t - 4-309,  and  d = t h e e q u i v a l e n t d i a m e t e r o f t h e drop = t h e d i a m e t e r g  of a sphere h a v i n g t h e same volume as t h e d r o p . Then.,  -  d = (fjX^r/Xx^)) g  . The range o f d  f  2  between 0.00 and 0 . 2 5 - i n . was d i v i d e d up i n t o  TABLE IV-5.  SUPERFICIAL AXIAL EDDY DIFFUSIVITY RESULTS FOR THE 3-IN. I.D. COLUMN  AVERAGE INSIOE OIAMETER OF NOZZLE TIPS • 0.102 IN. OISPERSEO PHASE EQUIVALENT DROP DIAMETER • 0.135 IN. AVERAGE VELOCITY OF OISPERSEO PHASE IN NOZZLE TIPS • 0.37 FT./SEC. COLUMN INSIDE DIAMETER • 1.0 IN. COLUMN HEIGHT [NOZZLE TIPS TO INTERFACE) • 10-FT. 9 T/B-IN. (SEE F I G . 20 FOR D U G . OF APPARATUS! LU • CONTINUOUS PHASE SUPERFICIAL MBLOCITY, CU.FT./IHR. SQ.FT.) LK • DISPERSED PHASE SUPERFICIAL V C L O C I T ^ CU.FT./IHR. SO.FT.) LT - TRACER FEED SUPERFICIAL V£i.OeiTjf, CU.FT./(HR._ SQ.FT.I _ PP • NUMBER OF SAMPLE CONCENTRATIONS USED FOR ESTIMATION OF SUPERFICIAL AXIAL EDDY DIFFUSIVITY SE > SUPERFICIAL AXIAL EDDY DIFFUSIVITY MITH 99 PER CENT CONFIDENCE L I M I T S . SO.FT./HR. ER1 . MtTFR BALANCE APPARENT LOSS. PER CENT • : ER2 - TRACER BALANCE APPARENT LOSS. PER CENT  RUN  LM  LK  LT  TEMP *F  1  2  REDUCED CON CENTRATI ON AT SA MPLING P DINTS IS EE F I G . 201 9 6 7 -8 . 3 3  *  PP  SE  ER1  ER2  10  177 18.2 181 27.7 182 36.9 181 *8.4 ISA 79.0 180 100.0 179 220.0 185 285.0  36.9 36.9 36.9 36.5 36.3 36.3 36.5 36.5  0.090 0.100 0.150 0.190 0.200 0.290 0.410 0.410  70 69 68 66 69 70 67 70  933.27 939.04 972.18 923.97 938.87 816.43 991.99 487.7*  863.08 877.36 949.34 799.06 717.49 644.68 282.48 274.18  843.83 842.38 846.63 718.67 606.97 440.33 142.48 109.02  810.9* 759.66 7*1.07 602.38 451.6* 337.34 49.30 93.78  776.76 693.78 623.71 316.67 330.10 218.3* 33.00 28.72  707.25 676.66 998.60 490.81 283.24 171.58 21.28 16.72  680.2) 604.4* 383.77 *33.57 236.79 133.89 11.30 9.16  655.87 568.8* 525.69 327.9* 192.38 97.49 6.10 *. 1*  6)3.98 471.59 435.07 312.99 150.23 75.67 3.75 1.88  593.46 470.11 389.08 273.32 123.07 53. 16 2.19 0.87  10 10 10 10 10 10 10 8  187.9116.* 17*.7120.1 181.3121.8 179.811*.6 1 6 9 . 0 1 9.5 168.OllO.3 181.4114.5 21*.0113.6  -1.28 -1.83 0.75 1.40 -0.03 -0.94 -0.78 0.76  -0.29 -0.48 2.06 0.19 -3.00 -1.09 3.51 -1.26  19* 193 I ? 191 178 190 189 188 187  18.2 27.7 36.9 48.* 75.0 100.0 190.0 220.0 262.0  94.7 54.7 94.7 94.7 94.7 94.7 54.7 54.7 94.7  0.090 0.100 0.190 0.150 0.200 0.290 0.410 0.410 0.410  6B 69 71 70 71 71 70 70 70  1028.76 1022.09 1011.09 1079.77 999.69 1123.63 1163.87 1081.40 1199.62  974.63 973.11 938.87 933.1* 756.42 7*8.37 731.16 623.83 540.40  936.07 909.10 782.22 780.03 993.69 949.14 491.99 320.26 166.24  864.67 853.8B 724.39 700.88 428.97 366.41 299. 36 149.96 46.87  816.98 78*.30 639.31 5*5.95 319.98 23*.51 143.42 72.90 12.97  767.73 735.85 574.92 456.55 273.73 179.48 76.33 32.54 3.4*  711.99 662.86 499.13 39*.37 210.35 149.88 *7.72 11.63 2.31  672.35 620.22 *22.79 317.39 170.16 80.05 27.65 9.67 1.12  634.91 577.73 368.37 272.97 134.21 54.91 17.87 2.76 0.17  583.14 502.74 334.76 257.38 96.94 40.04 9.48 1.32 0.00  10 10 10 10 10 10 10 9 7  1 4 6 . 1 1 6.5 181.211*.5 1 4 6 . 7 1 8.0 144.91 9.5 1 5 2 . 0 1 6.9 1 3 7 . 2 1 8.1 140.91 4.1 1 * 4 . 8 1 8.2 121.6110.7  -1.70 -1.2* 1.59 -0.72 -0.25 -1.75 -0.16 0.0* -0.**  1.52 -6.18 1.68 -0.63 -4.12 -2.62 -4.76 1.9* -0.91  197 18.2 48.4 196 195 100.0  73.0 73.0 73.6  0.090 0.190 0.290  67 70 68  996.99 882.90 1089.17 896.39 1286.97 I0T1.40  783.93 700.69 634.73  730.68 914.79 400.63  692.97 400.69 166.89  623.84 396.02 122.51  608.65 287.76 61.29  5*1.26 211.93 37.89  486.45 161.29 23.20  495.21 132.63 12.09  10 10 10  113.71 104.21 94.01  7.7 5.4 6.4  *.71 -0.58 0.61 -2.20 -1.05 0.19  200 18.2 48.4 199 198 100.0  91.2 91.2 91.2  0.050 0.190 0.290  70 67 69  894.06 1036.04 1195.97  768.91 7*8.89 683.49  692.29 606.34 276.73  610.94 412.92 160.0*  537.10 288.99 89.92  486.32 220.71 38.56  *32.12 181.26 19.68  383.60 114.90 10.34  360.91 •87.42 5.35  323.60 74.25 3.5*  10 10 10  82.81 4.5 81.21 * . * 76.21 3.2  1.00 2.78 -1.51 -1.99 -1.46 1.01  203 18.2 202 48.4 201 100.0  109.0 109.0 109.0  0.090 0.190 0.290  69 68 67  903.74 1064.79 1117.61  822.91 851.97. 613.37  798.86 630.43 167.42  718.11 459.27 100.89  603.11 272.23 40.26  328.61 202.34 18.79  491.67 1)8.32 6.03  428.69 94.93 1.09  387.63 65.80 0.18  336.02 52.66 0.00  10 10 8  81.91 6.8 69.51 3.* 53.71 7.*  1.6* 1.00 0.4) *.98 -0.91 -0.90  206 18.2 205 48.4 20* 100.0  128.0 128.0 128.0  0.040 0.190 0.290  69 69 70  996.89 934.09 980.29  879.33 700.19 291.22  744.99 471.77 83.91  392.89 289.27 31.47  471.32 157.78 17.03  408.91 115.89 4.63  323.8* 6*. 79 2.06  279.32 38.37 0./2  23*.*B 2 * . 82 0.57  190.85 18.17 0.28  10 10 7  49.01 2.0 52.91 2.6 52.91 * . *  7.27 0.12 1 .46 -0.33 -0.64 -1 .*6  9  220  0.01-in. increments.  The number,of d r o p s , and t h e t o t a l drop .  volume a s s o c i a t e d w i t h t h e d r o p s , a p p e a r i n g i n each o f t h e s e i n c r e m e n t s were c a l c u l a t e d .  F o r each i n c r e m e n t t h e number o f  drops was c o n v e r t e d i n t o t h e percentage o f t h e t o t a l number of drops measured.  S i m i l a r l y t h e sum o f t h e volumes o f t h e drops  i n each i n c r e m e n t was c o n v e r t e d i n t o a percentage o f t h e t o t a l drop volume a s s o c i a t e d w i t h a l l o f t h e d r o p s . were performed f o r t h e f i r s t 100 t o t h e f i r s t 200,  300,  These  calculations  drops examined and were extended  400, and 500 drops examined.  s e t o f r e s u l t s appears i n T a b l e I V - 6 .  A typical  The r e s u l t s f o r t h e  500  drops examined f o r each.run . i n w h i c h drop s i z e s were measured appear i n T a b l e IV-7 for  f o r t h e l§--in. I.D. column and i n T a b l e  t h e 3 - i n . I.D. column.  IV-8  Due t o t h e o v e r l a p p i n g o f t h e drops i n  the photographs i t was n o t p o s s i b l e t o measure t h e drop s i z e s f o r runs when  was l a r g e .  T h e r e f o r e i t was assumed t h a t t h e drop s i z e  d i s t r i b u t i o n s were t h e same a t h i g h and low v a l u e s of L^. T a b l e I V - 9 shows t h e s u p e r f i c i a l - f l o w r a t e s , t h e measured c o n c e n t r a t i o n s , the c a l c u l a t e d  c a p a c i t y c o e f f i c i e n t , the hold-up,  and t h e e r r o r i n t h e mass b a l a n c e f o r each r u n i n v o l v i n g mass transfer.  T a b l e IV-10  e s t i m a t i o n o f E.  shows, t h e r e l a t i o n between £ & n c l E f o r t h e  The v a l u e s o f K^a and m were t a k e n from T a b l e  and t h e v a l u e s o f J were c a l c u l a t e d by means o f E q u a t i o n 21. IV-11  and IV-12  IV-9  Tables  show t h e e f f e c t on E o f v a r y i n g K^a, m, and t h e  method o f c a l c u l a t i o n o f J .  T a b l e IV-13  g i v e s the  equilibrium  c o n c e n t r a t i o n o f a c e t i c a c i d i n MIBK - s a t u r a t e d water and water s a t u r a t e d MIBK a t 70°F as d e t e r m i n e d i n t h i s work.  221  TABLE IV-6.  TYPICAL DROP SIZE DISTRIBUTION RESULTS  WATER  SUPERFICIAL  VELOCITY  =  KETONE NOZZLE  SUPERFICIAL TIP AVERAGE  VELOCITY DIAMETER  = =  CONDITIONS  COLUMN D I A M E T E R = CORRESPOND TO RUN  27*70 54.74 0.103 1.5 50  CU.FI./(HR.  SQ.FT.)  CU.FT./MHR. IN.  SQ.FT.)  IN.  RANGE OF EQUIVALENT DROP DIA.  P E R C E N T A G E OF DROPS IN G I V E N S I Z E RANGE FOR T O T A L NUMBER OF D R O P S  VOLUME C O N T R I B U T E D BY DROPS IN G I V E N S I Z E RANGE  IN  SHOWN  FOR  INCHES  AT  HEAD  OF  LIST  PERCENTAGE  OF  T O T A L NUMBER AT HEAD OF  SHOWN  100 0.00-0.01 0.01-0.02 0.02-0.03 0.03-0.04 0.04-0.05 0.05-0.06 0.06-0.07 0.07-0.08 0.08-0.09 0.09-0.10 0.10-0.11 0. 11-0.12 0.12-0.13 0. 13-0.14 0.14-0.15 0.15-0.16 0.16-0.17 0.17-0.18 0.18-0.19 0.19-0.20 0.20-0.21 0.21-0.22 0.22-0.23 0.23-0.24 0.24-0.25  200  300  0.0 0.0 15.0 15.5 25.0 24.5 6.0 7.0 5.0 4.0 3.0 3.0 0.0 0.5 1.0 2.0 0.0 2.0 2.0 2.0 3.0 3.5 4.0 2.5 3.0 5.0 16.0 13.5 9.0 9.5 6.0 4*0 2.0 1.5 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 o.o| b.o  0.0 15.7 25.0 5.3 3.3 2.7 0.7 1.7 2.3 2.3 4.3 3.0 6.3 12.3 10.0 3.7 1.0 0.0 0.0 0.0 0.3 0.0 0.0 0.0 0.0  400  500  0. 0 0.0 16.0 16.6 24.2 23.0 6.3 7.4 3.5 3.0 2.2 1.8 0.5 0.4 1.2 1.6 2. 2 2.2 2.0 2.0 3.7 3.0 3.0 3*6 7.0 7.2 13. 2 13.8 10. 0 9.2 3.5 3.6 0. 7 0.6 0.2 0.6 0.6 6.0 0.0 0.0 0.2 0.4 0.0 0.0 0.0 0.0 0.0 0.0 o. 6 6.6  100  200  300  6.6  DROP  OF DROPS LIST  400  500  0.0 0.1 0.4 0.2 0.3 0.3 0.1 0.5 1.2 1.6 4.0 4.2 12.7 29.5 27.3 11*3 3. i 1.3 0.0 0.0 2.0 0.0 0.0 0.0 6.6 0.0  0.0 0.1 0.3 0.3 0.3 0.3 0.1 0.6  0.0 0.0 0.0 0. 1 0.1 0. 1 0.4 0.4 0.4 0.2 0.3 0.2 0.4 0.4 0.3 0.5 0.5 0.4 0.1 0.2 6.0 0.4 0.8 0.7 0.0 1.1 1.2 1.6 1.7 1.9 3.1 3.9 4.6 5.4 3.6 4.3 5.0 9.4 11.6 33.7 31.0 27.8 23.2 26.9 27.7 18.3 13.3 11.8 7.7 6.4 4.1 0.0 0.0 0.0 0.0 6.6 0.0 0.0 0.0 0.0 0.0 0.0 2.7 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0.6  TOTAL  l . l  t.6  3.1 5.0 12.8 30.0 24.5 11*6 2.4 2.8 0.0 0.0 3.0 0.0 0.0 0.0 0.0  TABLE I V - 7 .  RANGE OF EOUIVALENT DROP DIA. IN INCHES  0.00-0.01 0.01-0.02 0.02-0.03 0.03-0.0* 0.04-0.0$ 0.05-0.06 0.06-0.07 0.07-0.08 0.08-0.09 0.09-0.10 0.10-0.11 0.11-0.12 0.12-0.13 0.13-0.14 0.14-0.15 0.15-0.16 0.16-0.17 0.17-0.18 0.18-0.19 0.19-0.20 0.20-0.21 0.21-0.22 0.22-0.23 0.23-0.24 0.24-0.25  DROP SIZE DISTRIBUTIONS I N THE l | - I N . . I.D. COLUMN  PERCENTAGE OF DROPS IN GIVEN SIZE RANGE FOR A TOTAL OF 500 OROPS. CONDITIONS CORRESPOND T3 RUN AT HEAD OF LIST AVERAGE NOZZLE TIP I.D. •» 0.103- IN.  AVERAGE NOZZLE TIP 1.0. » 0.126-1N. 126  128  130  75  86  92  0.2 22.4 16.6 6.0 1.6 0.6 2.0 1.6 2.8 3.2 3.6 3.4 6.0 5.2 6.4 8.2 5.6 2.4 0.6 1.2 0.4 0.0 0.0 0.0 0.0  0.0 29.4 17.4 5.4 2.0 3.2 2.4 2.2 2.2 2.2 3.0 2.6 3.4 3.4 6.2 5.2 2.6 4.2 0.8 1.0 0.8 0.2 0.0 0.2 0.0  0.0 28.2 16.2 4.8 3.0 2.4 1.2 3.0 3.0 2.0 2.8 3.0 2.4 4.6 6.2 6.6 5.4 2.8 1.2 0.8 0.2 0.2 0.0 0.0 0.0  0.4 21.6 16.0 8.2 5.0 1.8 1.6 2.4 2.4 2.2 3.0 2.0 2.6 4.2 5.8 8.6 5.8 2.8 1.2 0.6 1.2 0.2 0.2 0.2 0.0  0.2 21.6 17.8 5.6 3.0 3.2 2.8 1.8 2.0 2.4 2.4 3.4 3.2 3.4 6.0 5.6 6.4  0.0 19.0 19.4 8.2 2.0 2.2 2.2 1.0 1.6 2.0 3.0 3.4 4.0 4.0 7.0 5.6 7.6 2.8 3.2 0.4 0.4 0.6 0.2 0.0 0.2  4.6  1.8 1.8 0.4 0.4 0.0 0.2 0.0  66  50  1.0 0.0 0.0 9.6 18.6 22.0 16.0 20.0 23.4 10.3 6.6 6.2 4.6 4.0 3.-4 2.2 2.2 0.6 1.0 1.6 0.8 1.4 2.2 1.0 3.2 1.8 1.2 3.2 1.8 2.4 4.0 2.4 2.4 5.4 5.2 3.6 8.2 10.0 6.0 15.0 11.8 14.0 10. 9 7.8 8.4 2.2 3.6 4.2 1.4 0.2 0.2 0.2 0.2 0.2 0.2 0.0 0.0 0.2 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 ' 0.0 0.0 0.0 0.0 0.0 0.0 0.0" 0.0  0.0 16.6 23.0 7.4 3.0 1.8 0.4 1.6 2.2 2.0 3.0 3.6 7.2 13.8 9.2 3.6 0.6 0.6 0.0 0.0 0.4 0.0 0.3 0.0 0.0  65  63  55  AVERAGE NOZZLE TIP I .0. * 0.086-1N. 45  0.0 0.0 9.0 6.4 16.8 12.2 11.4 7.8 4.0 4.4 1.8 3.0 1.6 0.8 1.4 1.4 1.0 1.4 2.2 2.4 2.4 3.8 4.6 5.6 6.4 11.2 16.4 15.2 12.0 13.8 5.8 6.0 1.8 3.0 0.2 0.6 0.6 0.8 0.4 0.2 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 Q.O  96  99  0.0 0.0 19.8 20.3 22.0 23.^ 6.8 8.2 1.8 2.6 0.8 1.2  1.8 1.0  0.6 1.8 0.8 0.4 2.8 2.2 3.0 3.0 8.4 8.2 21.4 13.8 8.2 11.0 1.6 2.2 " 0.2 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  100  103  113  0.2 a.2  0.0 10.8 20.0 8.2 2.4 2.2 0.6 1.0 1.8 4.0 4.8 15.0 16.6 H.6 2.2 1.4 0.2 3.2  25.4 18.4 19.6 20.2 5.4 8.8 3.0 2.4 1.4 0.0 1 .2 0.8 1.2 0.8 1.6 2.2 1.4 2.0 4.6 3.8 9.6 11.4 14.8 17.8 9.0 7.4 1.2 3.6 0.4 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0  AVERAGE NOZZLE TIP 1.0. » 0.053-14. 148  146  144  151  144  0.0 0.8 0.2 0.2 0.2 11.4 10.4 13.2 13.2 7.0 9.6 10.0 8.6 10.2 13.0 1.2. 2.4 1.6 1.2 3.6 0.4 0.6 0.4 0.0 0.2 0.2 0.4 0.4 0.2 0.2 1.0 0.4 0.8 0.0 0.0 1.2 2.0 1.2 1.0 3.8 18.4' 17.8 14.0 18.0 16.4 44.2 42.8 43.4 45.0 47.4 9.4 7.6 11.4 7.4 8.6 2.4 4.4 3.2 2.6 4.4 0. 6 0.4 1.2 0.8 1.0 0.0 0.0 0.4 0.2 0.0 0.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 O.O 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  TABLE IV-7..  RANGE OF EQUIVALENT DROP OIA. IN INCHES  PERCENTAGE OF TOTAL OROP VOLUME CONTRIBUTED BY OROPS IN GIVEN SIZE RANGE F0« A TOTAL OF 500 OROPS. CONDITIONS CORRFSPOND TO RUM AT HEAO OF LIST AVERAGE NOZZLE TIP I.D. »0.126-1N. 126  O.OO-O.Ol 0.01-0.02 0.02-0.03 0.03-0.04 Oo04-0.05 0.05-0.06 0.06-0.07 0.07-0.08 0.08-0.09 0.09-0.10 0.10-0.11 0.11-0.12 0.12-0.13 0.13-0.14 0.14-0.15 0.15-0.16 0.16-0.17 0.17-0.18 0.18-0.19 0.19-0.20 0.20-0.21 0.21-0.22 0.22-0.23 0.23-0.24 0.24-0.25  CONTINUED  128  65  63  66  50  55  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 O.I 0.1 0.0 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.1 0.1 0.2 0.3 0.2 0.1 0.3 0.1 0.4 0.3 0.2 0.3 0.2 0.3 0.4 0.6 0.3 0.3 0.5 0.4 0.2 0.4 0.7 1.0 0.7 0.5 0.3 0.5 1.2 1.1 1.5 1.0 0.8 0.6 1.6 1.9 1.6 1.2 1.3 1.3 1.1 2.2 2.8 2.9 2.5 2.4 1.8 2.1 3.6 3.6 3.2 3.6 2.1 3.4 3.3 6.6 8.2 5.3 3.5 3.5 4.2 4.9 12.9 8.9 6.6 8.6 7.0 5.5 6.2 29.5 13.6 15.3 14.6 12.0 11.8 13.3 25.8 21.2 15.7 18.9 21.5 13.3 12.9 6.4 17.2 9.2 18.6 17.4 18.4 21.3 5.1 8.9 17.9 11.3 10.2 15.4 9.2 0.3 2.7 4.0 5.9 5.2 7.3 12.5 1.0 6.0 6.0 4. 7 3.0 8.S 1.9 l . l 2.2 5.5 1.3 6.8 2.2 . 2.2 1.4 0.0 1.5 1.6 1.4 2.4 3.8 0.0 0.0 0.0 0.0 1.5 0.0 1.4 0.0 0.0 2.0 0.0 1.7 1.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.9 0.3  0.0 0.1 0.3 0.3 0.4 0.3 0.4 0.9 1.1 1.5 2.8  0.0 0.1 0.4 0.3 0.3 0.1 0.2 0.4 0.7 2.1 2.7 5.4 11.5 34.0 24.8 15.1 0.8 1.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0.0 0.1 0.3 0.3 0.3 O.J 0.1  0.0 0.0 0.2 0.4 0.3 0.2 0.3 0.4 0.4 1.3 1.9 4.9 8.8 28.3 25.2 14.8 5.8 0.7 2.6 2.1 0.3 1.3 0.0 0.0 3.3  130  75  86  92  7.8  19.0 27.6 22.6 13.0 0.8 1.1 0.0 0.0 0.0 0.0 0.0 0.0 0.0  0.6 1.1  1.6 3.1 5.0 12.') 30.0 24.5  11.6 2.4 2.8 0.0 0.0 3.3  0.3 0.0 0.0 0.3  AVERAGE NOZZLE TIP 1.0. = 0.053-IN.  AVERAGE NOZZLE TIP I.D. = C.086-IN.  AVERAGE NOZZLE TIP I.D. « 0.103- IN. 45  96  98  100  103  0.0 C O 0.0 0.0 0.0 0.0 0. 1 0.1 0.2 0. 1 0. 1 0.4 0.4 0.4 0.4 0.2 0.4 0.4 0.3 0.4 0.3 0.2 0.3 0.4 0.3 0.3 0.1 0.2 0.3 0.0 0.1 0.6 O.J 0.3 0.2 0.4 0.3 1.0 0.6 0.4 0.5 0.6 0.3 1.2 1.6 1.2 2.7 2.3 1.5 2.0 2.7 4.1 4.2 6.B 5.0 5.2 14.8 15.1 IB.9 10.3 13.2 47.2 31.* 35.9 3d.4 23.0 22. 1 31.3 26.* IV. 4 25.2 5.5 7.9 4.5 11.7 13.5 0.8 4.2 1.7 T.8 a.2 0.0 0.0 0.0 0.0 1.9 0.0 0.3 0.0 0.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 3.9 0.0 0.0 3.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0 .0 0.0 0.0 0.0 0.0 0.0 o-.:) 0.0 0.0 0.0 0.0 0.3 0.0 o.o  113  148  146  144  151  149  0.0 0.0 " T o " 6.0 3.1 0.1 0. 1 0.1 0.1 0. 1 0.3 0.2 0.2 0.2 0.2 3.4 C.4 C. 1 0.2 C. 1 0.1 0.0 0.2 o.o 0. 1 0.1 0.0 0.0 3.4 0.1 0.1 0.1 0.1 O.U 3.2 0.4. 0.2 0.4 u.o 0.0 0.4 C.d I .5 0.7 0.7 0.5 l . l 1 b.8-18.3 13.8 lfl.5 15.7 3.4 56.2 54.9 54.8 58. 3 56.3 5.5 16. 313.3 18.3 12.7 13.5 22.9 5.3 10.3 6.9 6.3 9.1 31.7 1 . &1.2 3.4 2.3 2.7 23.2 0.0 0.0 1.3 0.7 0.0 6.5 0.0 0.0 0.0 0.0 3.0 0.0 0.0 0.0 4.9 CO 0.0 3.8 0.0 0.0 0.0 0.0 1.3 l.C 0.0 0.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 O.U 0.0 3.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 o.o 0.0 0.3 0.0 0.0 . 3.0 o.o 0.0 0.0 0.0 0.3 3.0 0.0  22k  TABLE I V - 8 .  DROP SIZE DISTRIBUTIONS I N THE 3 - I N . I.D. COLUMN  AVERAGE CONDITIONS RANGE  IN  TIP  OF  EQUIVALENT  DROP  NOZZLE  CORRESPOND  PERCENTAGE  01A .  IN  GIVEN  OF  THE  SIZE  DROPS  RANGE  INCHES  I.D. TO  =  RUN  0 . 1 0 2 -• I N . AT  8.4  0 . 0 0 - 0 . 0 1  182  184  OF  LIST  PERCENTAGE  OF  TOTAL  VOLUME  DROP  CONTRIBUTED IN  177  HEAD  GIVEN  BY  SIZE  THE  DROPS RANGE  179  177  182  184  179  2.4  1.0  0.6  0.0  0.0  0.0  0.0  29.8  32.8  32.2  13.0  0.1  0 . 1  0. 1  0.0  0 . 0 2 - 0 . 0 3  5.6  12.4  10.8  13.6  0.1  0.2  0.2  0.2  0 . 0 3 - 0 . O A  3.6  2.2  2.8  4.8  0.2  0.1  0.1  0.2  0 . 0 4 - 0 . 0 5  1.8  1.0  1.6  4.0  0.2  0.1  0.1  0.3  0 . 0 5 - 0 . 0 6  1.2  1.4  1.8  1.0  0.2  0.2  0.3  0.1  0 . 0 6 - 0 . 0 7  1.4  2.4  0.8  2.6  0.4  0.7  0.2  0.4  0 . 0 7 - 0 . 0 8  1.6  0.8  0.8  2.4  0.6  0.3  0.4  0.9  0 . 0 8 - 0 . 0 9  3.2  2.8  1.4  2.6  2.1  1.7  0.8  1.3  0 . 0 9 - 0 . 1 0  2.8  2.6  1.8  3.8  2.6  2.3  1.5  2.7  0 . 0 1 - 0 . 0 2  1  0 . 1 0 - 0 . 1 1  2.8  1.4  4 . 0  4.2  3.2  1.7  4.4  4.1  0 . 1 1 - 0 . 1 2  5.4  4.0  5.8  8.6  8.5  6.2  8.5  10.8  0 . 1 2 - 0 . 1 3  11.2  10.0  10.2  12.4  22.4  19.4  19.2  19.4  0 . 1 3 - 0 . 1 4  12.2  13.2  16.6  16.4  30.5  32.5  38*4  32.1  0 . 1 4 - 0 . 1 5  7.4  7.8  6.6  7.0  22.3  23.3  19.0  16.7  0 . 1 5 - 0 . 1 6  0.8  2.0  0.8  3.2  2.9  7.2  2.8  9.3  0 . 1 6 - 0 . 1 7  0.6  0.6  1.0  0.4  2.7  2.6  4.1  1.4  0 . 1 7 - 0 . 1 8  0.2  0.0  0.0  0.0  1.0  0.0  0.0  0.0  0 . 1 8 - 0 . 1 9  0.0  0.2  0.0  0.0  0.0  1.3  0.0  0.0  0 . 1 9 - 0 . 2 0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0 . 2 0 - 0 . 2 1  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0 . 2 1 - 0 . 2 2  0.0  0.0  0.0  0 . 0  0.0  0.0  0.0  0.0  0 . 2 2 - 0 . 2 3  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0 . 2 3 - 0 . 2 4  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0 . 2 4 - 0 . 2 5  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  TABLE I V - 9 . .  tvm h  CONCENTRATION STUDIES WITH MASS TRANSFER I N THE l | - I N . I.D. COLUMN  Concentration at stapling points* (See Figure 10), ld'x lb.-seles/ft?  h '  n  36.5  1  18.2  54.7  9.04 2.91  n  36.5  91.2  48.4  91.2  5  6  48.4 127.7  15.2  19.88  7  8  9  53.72 55.24 5 7 . a 23.3  10 58.82  25.95 27.2  10.05 11.84 13.96 15.33 17.00 19.43 22.31 24.25 27.32 4.21  7.4  5.72  7.50  9.82  21.43 23.07 25.50 27.59 30.41 8.76  10.81  12.2  15.0  17.9  11.1  32.54  12.40 13.55  25.25 27.71 30.35 32.7* 35.42 37.51 40.06 42.49 45.25 9.16  n  4  15.49 16.69 18.27 19.73 6.1  Jk  3  54.7 30.66 34.30 ,40.37 43.70 47.71 '49.47 9.11  J2  2  20.9  48.02 22.7  14.63 15.48 16.39 17.36 18.85 20.21 21.73 23.43 25.40 27.59 6.1  7.04  8.1  9.70  11.1  12.2  and  and  81.37 19.28 0.00  40.06  83.32  54.63  0.00  25-19  80.75 11.53 3.64  Average  h  •  %  42.54  1.92  4.6  3.3  56.24  2.04  4.5  2.75  122  71  79.03  2.02  9.3  0.39  90  *».  94.63  1.96  9.8  3.22  101  72  2.04 14.8  -3.42  85  70  V  K.B?  Tlaw to Tea* reach °r steady etate adn. 65 71  31.23  80.43 16.39 4.02  37.03  82.93  13.72  141.1  4.74 31.87  the upper matter refer* to the continuous phase, the lover matter to the dispersed phase. K.B. i s the error l a the aass balance. This ease balance traa calculated according to the following equation.  ro  TABLE I V - 1 0 . THE RELATION BETWEEN E AND A .  (The v a l u e s o f K^a, and m were t a k e n from T a b l e I V - 9 .  The v a l u e s o f J were c a l c u l a t e d from. E q u a t i o n 21.) The numbers l i s t e d under t h e v a r i o u s v a l u e s o f E t e s t e d = 10 Run  J  JI  0.743 0.119  J2  J3 J4 J5 Run JI  J2  J3 J4 J5 Run JI  J2  J3' J4 J5 Run  56.24 0.09k':79.03 0.477 94.63 0.0017 L41.1  J 42.54 56.24 0.09k: 79.03 O.U77 94.63 0.0017 L 4 I . I J  J3 Jk  J5  V 42.54  0.743 0.119 56.24 O.09J+: 79.03 0.477 94.63 0.0017 L4I.I J  0.119 0.094; 0.477 0.0017  m  E  1.92 2.0k  2.02 I.96 2.04 m  0.743 0.119  • J I 0.7^3  J2  V •42.54  E  1.92  2.04  2.02 I.96 2.04 m  E  1.92 2.04 2.02 I.96 2.04  m V 42.54 1-92  56.24 2.04 79.03 2.02 94.63 I.96 L4I.I 2.04  E  60  59  2800 820 1300 920 58  2800 760 1200 860 47  46  45  2100 110 510 180 83  2100  32  31  1300 770 42 260  840  1300 960 39 330 94o  18  17  670 8500 1000 3200 3600  660 9800 1300 3600  89 46o i4o 100  4000  58  57  56  ' 55  ^  •  54  53  52  2400 2400 2300  51  50  49  48  47  2300 210 660 300 38  2200 170 610 260 50  2200  34 i4oo 490 65 150 650  33 i4oo 620 51 200 74o  20  2700 2700 2600 690 . 630 570 1200 1100 1000 800 74o 680 38 31 25 42 44 4  2600 510 990 620 20  2500 930 560 ' 18  2500 4oo 880 500 18  4i  4o  39  3b  37  36  1900 63 320 6a 190  1800 71 280  1700 120 200  1700 160 170 45 370  1600 220  1600 290 110 78 500  35 1500 380 85 110 570  27  23  22  21  3  2000 73  410 110 130  2000  64  370 88 160  46o  1800 89 240 .44 53 230 • 270  350 820' 450 19 1  41  320  300 770 4oo 23  i4o 57  430  26.  25  24  55 530 1200  1100 1000 1700 2000 110 76 650 790 1300, 1500  970 2400 150 950 1600  920 2900 200 1100 1800  870 840 3400 4000 270 350 1300 1600 2000. 2200  15  14  12  11  10  30  29  28  1200 1200 43 420 1100  1100  16  i4oo  13  84o 720 660 660 • 680 770 11000 13000 15000 17000 20000 23000 1500 1800 2100 2500 2900 3300 4ioo 4700 5200 5900 66OQ 74oo. 4300 4800 5200 5700 6200; 68oo' 1  1  9  250 720 350 29  140  560 210 .65  1800 2500  2100 2700  2400 3000  19 690 7300 850 2800 3300  8  7  6  5  790  750  720  46oo 54oo 6300 560 700 44o  920 1000 1200 1300 1500 27000 31000 36000 42000 49000 57000 3800 44oo 5100 5800 6600 8200 9100 10000 7400 8000  TABLE I V - 1 1 . CALCULATED VALUES OF E FOR VARIOUS VALUES OF K^a AND J . (The v a l u e s o f m were 1  t a k e n from T a b l e I V - 9 ) Run  JI  m  J  J2  J3 Run  J4  40  5  12  5  5 12  22  45  50  55 ~  60  65  16  20  25  29  35  26  29  34  38  33 4l  6  10  16  21  24  27  0.782  1.92  E  60  I.92  E  . 60  60  5  '35  4o  45  50  55  56.24  60  65  70  75  b  m  J  6-  .43 . .80  o.ll9  a  2.04  E  30.  34  37.  4o  42  .42  44  . ^5  47  48  49 •  0.138  b  2.04  •E  34  38  4l  44  46  47  48  50  51  53  54  26  30  33  35  38  38  39  42  44  45  80  : 85  90  95  100  105  2.04  E .  •4l  0.0943  a  2.02  VE  0.0992  b  2.02  E  23  27  30  32  33  35  38  0.0893°  2.02  E  21  24  28  30  .30  .3.3  35  m  70  75  80  85  90  21  26  30  36  39  39  42  48  50  50.  28  m  J  65  70  75. 79-03  22  26  29  31  32  34  37  39  41  42  40  '42  44  S7  39  4l  100  105  110  0.477^  I.96  VE  0.527  1.96  E  32  37  4l  • 33 44  I.96  E  10  14  19  22  25  m  120  125  130  135  140  2.04  VE  '44  47  49  51  53  53  55  b  2.04  E  26  28  30  32  34  34  0.0594°  2.04  E  60  60  60  60  60  60  J  b  J  -0.056o  a  The f l u x o f s o l u t e down t h e column, J = \  b  The f l u x o f s o l u t e down t h e column,  °  42.54  .60  0.0017" J5  35  E  0.427° Run  30  1.92  0.0994° Run  25  " '  0.743^ 0.704° Run  .  J  =  94.63  (LQ Q  - kj) j)) c  The f l u x o f s o l u t e down t h e column, J = ( L ^ c ^ - L _ n ) c  115  44  46  48  53  • 55  57  59  28  31  33  35  37  14.1.1' 145  150  155  160  165  56  . 58  60  60  35  37  38  40  4l  60  60  60  60  60  ^c°C " ^D°D^ C  .95  -  +  ^ C ° C " ^D°D^  TABLE I V - 1 2 . CALCULATED VALUES OF E FOR VARIOUS VALUES OF m. (The v a l u e s o f J a n d K^a were t a k e n from Table I V - 9 ' ) Run Jl Run J2  Run J3 Run  Jk Run J5  J 0,7^3  k2.$k  J 0.119  56.2h  J 0.09L3  79.03  J 0.^77 J 0.0017 l L l . l  m  1.82  E  36  m  I.9U  E  kQ  m  1.92  E  kk  m  l.6k  1.66  1.88  1.90  1.92  1.94  32  28  2k  20  16  12  1.96  1.98  2.00  2.02  2.0^  2.06  2.08  k6  k5  kk  k  k2  Ll  2.00  2.02  3^  1.9k 1.96 I . 9 8  :  3  1.96 9  I.98 6  2.00  6  2.02  6  2.10  2.12  ^0  ko  39  2.0L  2.06  2.08  2.10  2.12  31  29  26  2k  22  19  ki  39  36  •1.86  1.88  I.90  1.92  I.9L  I.96  I.98  2.00  2.02  2.04  2.06  E  59 '  ' 55  51  L  ^3  39  .35  32  28  2L  21  m  I.9L  I.96  1.98  2.00  2.02  2.0*f  2.06  2.08  2.10  2.12  2.1U  E  60 -  60  60  60  53  k  37  3^  T  58  9  h5 : L l  229  "TABLE I V - 1 3 . EQUILIBRIUM DATA FOR ACETIC ACID DISTRIBUTED BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK AT 70°F.  (MEASURED IN THIS WORK.)  .Concentration of a c e t i c  acid,  coefficient,  lb.-moles/ft? Water phase' 0.001010  0.002218 O.OOM-089  .  . . o.006307 O.OO6743 . O.OII27 ' O.OI385 O.OI763 0.02564  0.02109 . 0.02802 0.03728 0.04663 .... 0.05794 0.06683 O.06802 0,07376 . O.07891 0.08381 0.08807 O.09625 0.1008 0.1051 0.1104 0.1150  MIBK phase' •  Distribution  0.0005545  0.001099 •0.001990  0.003079 0.003287 0.005485 0.006772 0.008619 0.01262  0.01040. 0.01412 O.OI9OI 0.02446 0.03111 0.03614 0.03738 . 0.04059 0.04368 0.04733 O.05050 • 0.05564 O.05881 0.0.6188 O.06569 ' O.06901  m 1.8214  2.0180 2.0547 2.0482  2.0512 2.0542 2.0453 2.0460 2.0314  2.0286• 1.9846 . 1.9609 1.9069 1.8622 1.8493 . I.8199 I.8171 1.8064 . 1.7709 1.7441 1.7297 1.7146 1.6978 1.6812 I.6671  230  APPENDIX V DETAILS OF THE APPARATUS F i g u r e s V - l t o V-23  i n c l u s i v e show the d e t a i l s of v a r i o u s  p o r t i o n s o f the l g r - i n . I.D." and 3 - i n . I.D. their accessories.  AH  s p r a y columns and  s t a i n l e s s s t e e l p a r t s were made from  Type.304 s t a i n l e s s s t e e l .  .  The p i s t o n sample c o l l e c t i o n f l a s k shown I n F i g u r e V - l was  used f o r d i s p e r s e d phase hold-ups g r e a t e r t h a n 12$.  c o l l e c t i o n f l a s k f o r hold-ups l e s s t h a n 12$ where (37)'  F i g u r e V-2  i s described else-  i s a diagram of t h e hypodermic  sampling system and F i g u r e V-3  The  needle  g i v e s , d e t a i l s of the s a m p l i n g  The t r a c e r i n j e c t i o n arrangement i s g i v e n i n F i g u r e V-4 d e t a i l s o f t h e t r a c e r d i s t r i b u t o r a r e shown i n F i g u r e F i g u r e s V-6, i n . I.D.,  V-7,  and V-8  show the 0.126-in. I.D.,  and t h e 0.053-i « I.D. n  valve.  and V-§. 0.086-  nozzle t i p s together w i t h the  r e s p e c t i v e n o z z l e t i p support p l a t e s and n o z z l e t i p caps o r p l u g s f o r use i n t h e 1 ^ - i n . I.D.  spray, column.  The n o z z l e t i p  support p l a t e s were p r e s s f i t t e d i n t o t h e n o z z l e d e s i g n e d Choudhury (35)* Choudhury was  by  The f l o w s t r a i g h t e n e r i n the n o z z l e d e s i g n e d not used i n t h e p r e s e n t work.  The  0.103-in.  n o z z l e t i p s , t h e c o r r e s p o n d i n g n o z z l e t i p support p l a t e and t i p caps a r e d e s c r i b e d elsewhere (30,  35)-  The  by  I.D. nozzle  i n s i d e diameter  of  each n o z z l e t i p i n each s e t o f n o z z l e s was a t r a v e l l i n g microscope.  Two  measured by means o f  such d i a m e t e r s  at r i g h t angles  to  each o t h e r were measured f o r each n o z z l e t i p . The a r i t h m e t i c average o f the n o z z l e t i p i n s i d e d i a m e t e r was  calculated for  each s e t o f t i p s . The P e r s p e x box used t o reduce o p t i c a l d i s t o r t i o n i n the 1-g-in, I.D.  An 0 - r i n g was  column i s shown i n F i g u r e V-9-  press  f i t t e d i n each o f the t o p and bottom o f the box t o p r e v e n t the l o s s o f w a t e r from between the. box. and the column.  The  l i g h t s h i e l d / which f i t t e d over the P e r s p e x box, F i g u r e V-10.  cardboard  i s shown i n  . The i n s i d e s u r f a c e s o f the l i g h t s h i e l d were p a i n t e d  w i t h b l a c k . i n k t o reduce, unwanted l i g h t r e f l e c t i o n s .  The  eight  s h e e t s o f t r a c i n g paper i n . t h e l i g h t s h i e l d s e r v e d as a d i f f u s i n g s c r e e n f o r the  light.  F i g u r e V - l l shows the n o z z l e and n o z z l e t i p s assembled i n the lower p o r t i o n . o f the 3 - i n . I.D.  column.  D e t a i l s of t h e  v a r i o u s p a r t s o f the.assembly a r e g i v e n i n F i g u r e s V-12 inclusive. V-17  The  B was  f o r a thermometer w e l l .  C was  f o r a drain valve.  and F i g u r e s V-19, parts.  V-17  d i a m e t r i c a l l y opposite holes l a b e l l e d B i n Figure  were o u t l e t s f o r the aqueous phase.  Figure V-l8  to  The t h i r d h o l e l a b e l l e d  The n o z z l e support f i t t e d i n t o E.  shows the E l g i n head f o r t h e 3 - i n - I'D. V-20,  and V-21  column  g i v e d e t a i l s of v a r i o u s component  The aqueous phase i n l e t p i p e s , shown as A i n F i g u r e  V-l8,  •were screwed i n t o the' h o l e s marked C i n F i g u r e V-19h o l e s l a b e l l e d B i n F i g u r e V-19  The  two  were t h e d i s p e r s e d phase e x i t s  and E i n the same F i g u r e accommodated a thermometer w e l l .  F  i n F i g u r e V-20  six  accommodated a n o t h e r thermometer w e l l .  h o l e s , C, i n F i g u r e V-20 flange.  were f o r b o l t s which h e l d a  The  standard  T h i s f l a n g e compressed t h e p o l y e t h y l e n e p a c k i n g shown  i n F i g u r e V-21.  F i g u r e V-22  E i n F i g u r e V-20  was  for a drain valve.  shows t h e P e r s p e x box used t o reduce o p t i c a l  d i s t o r t i o n i n t h e 3 ~ i n . I.D.  column.  O - r i n g s were p r e s s  fitted  i n t o the te>p and t h e bottom of t h e box. t o p r e v e n t t h e escape o f w a t e r f r o m between the .box and the- column.  Drop photographs were  t a k e n t h r o u g h a • 6-in... l o n g . s e c t i o n o f 3 - i n . I.D. from a l o n g e r p i e c e .  glass pipe  cut  T h i s 6 - i n . p i e c e used f o r photography  t h e r e f o r e had u n f l a n g e d ends. . I t was  held i n place, concentric  w i t h the r e s t o f t h e column, by means o f two f l a n g e s , one which i s shown i n F i g u r e V-23«  of  F o u r 9 ~ i ' l o n g aluminum t i e n  r o d s h e l d t h e f l a n g e s i n p o s i t i o n . . Each end o f t h e s e was and c a r r i e d a nut f o r - t i g h t e n i n g ' p u r p o s e s .  threaded  233 §14-35  FULL  LENGTH  PYREX  GROUND  GLASS  JOINT  ,0'Z m l . D I V I S I O N S (APPROX.  2ml8./cm.)  2 5 mm. DIA.  0 - 2 ml. D I V I S I O N S (APPROX.  2 mls./cm.)  O  HOOKS  FOR  SPRINGS  E O c\l O  4 0 mm. DIA.  TEFLON  STOPCOCK  (WITH  LARGE  HOLE  FOR  DIA. PAST  DELIVERY)  FIGURE V - l . PISTON SAMPLE COLLECTION FLASK FOR LARGE HOLD-UPS  3  LONG  22  HYPODERMIC  NEEDLE  !{g T H I C K , ijfg SAMPLING  2 ^  VALVE  II 3  2  HOLE  WITH  FOR  WALL FIGURE V-2.  HYPODERMIC NEEDLE INSTALLED FOR  I.D.',  OD. POLYETHYLENE  GASKET COLUMN  GAUGE  SAMPLING  0 0 2 5 " DIA.  NEEDLE  1  0-7 * 0-5" •0-25j—j L  II  • _ :  0125" i  r  Q  lO CD  SECTION BODY  MATERIAL:  ON  POLYETHYLENE  0 0 6 2 5 " R.  o LO  0 0 8 9 " D.  STEM  MATERIAL: STAINLESS  v FIGURE  V-3-  SAMPLING V A L V E F O RHYPODERMIC  STEEL NEEDLE  A-A  D  "A" N Y L O N  C O M P R E S S I O N NUT  2  LONG  18 G A U G E  HYPODERMIC •A" N Y L O N  VTZZZA  UNION  NEEDLE TRACER DISTRIBUTOR  zzzzzzzi W w w  LONG.VQD! 0 0 5 7 " ID.  V T H I C K , Ifc" i . D ; , 2 W O . D . T E F L O N GASKET WITH 0 0 5 7 " DIA. HOLE FOR NEEDLE  POLYETHYLENE COLUMN  iV'O.D., Ve" L D .  WALL  POLYETHYLENE TUBE FIGURE V-4.  TRACER INJECTION SYSTEM  ro  u>  237  \  in 6  • \  \  i  GLASS—*  \  \  s  o o  \ \ \  POLYETHYLENE  6  2^ ^ O 7  cO ro 6 6  M>25'tH SECTION  ON  •—A  A-A  I HOLE  0 043" D  4 HOLES 0157" SECTION  0063"D.  D  ON B - B  FIGURE V - 5 .  TRACER DISTRIBUTOR  238  10 HOLES / j " D ON RC.D. 3  »V  6  4 HOLES /, D. ON / " RC.D. 3  6  3  8  STAINLESS STEEL NOZZLE TIP SUPPORT  Vs  D.  h / l 6 D. 3  to\45° t  CHAMFER  SECTION  t  i  f  -1  \ \  '/ " D. 4  N  \ s  II  ON A-A  STAINLESS STEEL NOZZLE TIP FIGURE V-6.  \  TEFLON NOZZLE CAP  0.126-IN. I.D. NOZZLE TIPS, NOZZLE TIP SUPPORT PLATE AND NOZZLE TIP CAPS '  239  9 HOLE'S '/e" 0. ON V P.C.D.  3 HOLES  V  '/a" D. ON PC.D.  16 HOLES •/s" D. ON I" RC.I5  STAINLESS  STEEL  NOZZLE  TIP  SUPPORT  fK45° r  CHAMFER  N  0 0 8 6 "D. M/e" D. 0 0 8 6 " D. SECTION  ON  A-A  TEFLON NOZZLE TIP P L U G  STAINLESS STEEL NOZZLE TIP  FIGURE V-7.  0.086-IN. I.D. NOZZLE TIPS, NOZZLE T I P SUPPORT PLATE, AND NOZZLE T I P PLUGS  73 HOLES / " D. ON V TRIANGULAR PITCH STEEL NOZZLE TIP SUPPORT 3  32  STAINLESS  *  45°y  \ \  K0052  vCHAMFER  v  D.  -a,|  J3. II  / " D. ^-0052 D. 3  32  n  SECTION  ON  A-A  STAINLESS STEEL NOZZLE TIP  FIGURE V-8.  TEFLON NOZZLE TIP PLUG  0.053-IN. I.D. NOZZLE TIPS, NOZZLE T I P SUPPORT PLATE, AND NOZZLE T I P PLUGS  2hi  „ *1 ^'/<" '/„ D. V E N T  DRILL  A  T  AND  TAP  !  CM CM  •  A ill  TRANSLUSCENT '/8" P E R S P E X  — — r  f  SECTION  ON  A-A  /  ftp  / /  / * / / h-7/ '32  SECTION  ON  B-B  MATERIAL - TRANSPARENT V PERSPEX UNLESS OTHERWISE SPECIFIED  FIGURE V-9.  PERSPEX BOX FOR THE 1^-IN. I.D. COLUMN PHOTOGRAPHS  „ MATERIAL 'IGUBE V-10.  1  '/  3 2  PULPBOARD  PHOTOGRAPHIC S E C T I O N OF COLUMN F I T S H E R E  LIGHT SHIELD FOR THE 1±-IN? I.D. COLUMN PHOTOGRAPHS  243  SPECIAL PYREX REDUCER  NOZZLE  TIPS  NOZZLE TIP SUPPORT  NOZZLE PLUGS  TIP  NOZZLE  FLOW STRAIGHTENER TEFLON ^GASKET  777771 END  POLYETHYLENE  PLATE  NOZZLE NOZZLE FIGURE V - l l .  RETAINING  SECURING  GASKET  NUT  PLATE  LOWER END OF THE 3-IN. I.D. COLUMN  3 " DIA.*  FIGURE V-12.  SPECIAL PYREX REDUCER FOR THE 3-IN. I.D. COLUMN  24-5  2-875 2-719" 2-657" 2-469" n  D; D: D. D  / / / /  io ro ro  /  /  /  /  /  /  / / /  (  o  1  o  IO OJ  6  JL  T  2jfe" I.D/I6T.RI  MATERIAL: STAINLESS FIGURE V - 1 3 .  STEEL  NOZZLE SHELL FOR THE 3 - I N . I.D. COLUMN  85 H O L E S Vs D. ON TRIANGULAR PITCH STAINLESS  STEEL  NOZZLE  45° f CHAMFER  1 I  M/  II H  8  D.  l-O-IOfD.  SECTION  ON  A-A  SUPPORT  1  1 i  TIP  V  KMOf'D.  TEFLON NOZZLE TIP P L U G  STAINLESS STEEL NOZZLE TIP FIGURE V-lk.  NOZZLE TIPS, NOZZLE T I P SUPPORT PLATE, AND NOZZLE T I P PLUGS FOR THE 3-IN. I.D. COLUMN  MATERIAL: STAINLESS  STEEL  FIGURE V-15. FLOW STRAIGHTENER FOR THE 3-IN. I.D. COLUMN NOZZLE  2k8  .2 /i6 0.D./l6 T.PI. 9  M  -or  IKWWN JL _  .9  I " I 'I 'I  "  /  4  •'  •  B  •/a" N.P.T. 3 - '•  •  I  II I II I II I  0.D./I6T.PI  S E C T I O N ON  B-B  S E C T I O N ON A-A STAINLESS  STEEL  NOZZLE  SECURING  PLATE  II  %  0.D./I6 T.P.I SECTION ON C-C  STAINLESS FIGURE V-16.  STEEL  RETAINING  NUT  NOZZLE SECURING PLATE AND RETAINING NUT FOR THE 3-IN COLUMN  I D  2k9  8 HOLES  WITH  CLEARANCE BOLTS  FOR ON  %" 9 V 2 RC.D.  4'/ " R C D  TAP-V*" N.P.T.  B, B,B, 3 H O L E S D R I L L AND C, 1 H O L E D R I L L A N D T A P E,l HOLE V D.  1 "  IO'/  2  «  MACHINE MATERIAL:  FIGURE V - l ? .  ,  N.P.T.  D.  1 \ A ^ \ V l k V VM kA VV] I\  r  !V'  \\S  N  FLAT SECTION ON STAINLESS STEEL  A- A  END PLATE FOR THE BOTTOM OF THE 3 - I N . I.D. COLUMN  250  A  W  B C  UPPER END P L A T E OF ELGIN TEFLON COVERED GASKETS.  D E F G  9 " L O N G , 9 " I.D. Q.V.F. G L A S S SECTION. LOWER E N D P L A T E O F E L G I N HEAD. L O W E R E N D P L A T E PACKING. 10 LONG, 3" I.D. P Y R E X " D O U B L E TOUGH" PIPE WITH F L A T UNFLARED UPPER END.  STAINLESS  STEEL  PIPES  (AQUEOUS INLET).  FIGURE V-18. ELGIN HEAD FOR THE 3-IN. I.D. COLUMN  PHASE  HEAD.  B,B, 2 HOLES DRILL AND TAP 'A" N.P.T. b,C, 2 HOLES DRILL AND TAP %" N.P.T. ! FROM BOTH SIDES £, I HOLE DRILL AND TAP '/ " N.P.T. 2  MACHINE FLAT SECTION ON A-A MATERIAL-STAINLESS STEEL FIGURE V-19..' UPPER END PLATE FOR THE ELGIN HEAD OF THE 3-IN. I.D. COLUMN  . ...... . 2 5 2  B C  E F  8  H O L E S / . 6 D. ON 12VRC.D. 6 H O L E S D R I L L . AND T A P '/a" DEEP FOR Vie" B O L T S ON 5%" P.CD. I H O L E D R I L L A N D T A P VA" N.P.T. ON 7Vz" P.C.D. I H O L E DRILL A N D T A P '/a" N.P.T. ON 7 ' / " P.C.D. 7  U  2  T A P E AND F T H I S SIDE  MACHINE  FLAT  h — —  13 /  SECTION  ON  3  4  D.—  / - ^  *  A-A  MATERIAL^ STAINLESS  FIGURE V - 2 0 .  FROM  STEEL  LOWER END PLATE FOR THE ELGIN HEAD OF THE 3 - I N . I.D. COLUMN  253  4 V D ; SECTION  ON  A-A  MATERIAL^ P O L Y E T H Y L E N E FIGURE V-21.  LOWER END PLATE PACKING FOR THE ELGIN HEAD OF THE 3-IN. I.D. COLUMN'  25k  u  DRILL  '/ " D.  DRILL  2  A N D T A P % N.PT.  \ \ \ \ foo  in  2 r  A-  1  SECTION  r-3 /i6 D p-3'/2 P."  ON A - A  l 3  / /  / / in  \ '  =12 W  —5'/a" SECTION  — ON B - B  MATERIAL: T R A N S P A R E N T FIGURE V-22.  Vii' PERSPEX  PERSPEX BOX FOR THE 3-IN. I.D. COLUMN PHOTOGRAPHS  255  4  ^  H O L E S  —  ?/32  H  O N  9"  P C D .  -9VD. S E C T I O N  M A T E R I A L FIGURE V - 2 3 .  Q.  :  O N  A - A  A L U M I N U M  FLANGE FOR THE PHOTOGRAPHIC SECTION OF THE 3 - I N . I.D. COLUMN  •  ••  256  APPENDIX V I DIMENSIONS OF THE GLASS PORTIONS I N THE COLUMN TEST SECTIONS AND MEASUREMENT OF PURGE TIMES. a)  Dimensions o f t h e g l a s s p o r t i o n s i n t h e column t e s t  sections.  .The. l e n g t h and i n s i d e d i a m e t e r o f each p i e c e o f P y r e x "Double Tough" g l a s s p i p e i n t h e t e s t s e c t i o n s o f t h e 1-g-in. I.D. and 3 In.. •I.D. columns, were measured b y means o f v e r n i e r -  calipers.  The,I.D. was t a k e n t o be t h e average o f s i x r e a d i n g s  e q u a l l y spaced a l o n g t h e l e n g t h o f t h e g l a s s p i e c e .  These  measurements" a r e g i v e n i n T a b l e V I - 1 . TABLE V I - 1 .  DIMENSIONS' OF THE GLASS PORTIONS I N THE COLUMN TEST SECTIONS.:  Section of . column between : positions (See d i a g s . . 10 and 20)  Length I.D. (l§--in. (1^-ln. I.D. c o l I.D.column) umn) in..  in.  Length I.D.(3-in. (3-in.I.D. I.D. column ) column) in.  in.  Tracer d i s t r r i b u t o r and I  6.044  • 1.500  5.983  2.992  1 and 2  5.967  .1.500  6.022  3.026  2 and 3  5.969.  1.497 .  6.020  2.985 '  3 and 4  5.978  1.503  5.975  2.989  4 and 5  . 6.024  I.492  6.020  3.008  6.014  3*009 2.992  ' .  5 and 6  5.793*  1.497  6 and 7  5.975.  1.504  6.008  7 and 8  6.050  1.595  6.044  8 and 9  6.0^9  I.508  6.018  2.998  9 and 10  6.032  1.500  5.996  2.995  a  •  b  3.020  b  9  The p i s t o n sampler b l o c k r e p l a c e d a g l a s s s e c t i o n . T h i s p i e c e o f g l a s s was used as t h e p h o t o g r a p h i c t e s t I t was c u t from a l o n g e r p i e c e o f P y r e x "Double Tough"  section. pipe.  The t h i c k n e s s o f each p o l y e t h y l e n e g a s k e t was measured and . was f o u n d t o be l / l 6 - i n .  T h i s measurement d i d n o t change when  t h e g a s k e t was compressed between two p i e c e s o f g l a s s . b ) Measurement  o f purge t i m e s .  i ) Hook and b e l l - p r o b e s s a m p l i n g l i n e s . The column was b r o u g h t t o s t e a d y s t a t e o p e r a t i n g c o n d i t i o n s w i t h t h e t r a n s f e r o £ a c e t i c a c i d f r o m t h e c o n t i n u o u s phase t o t h e d i s p e r s e d phase as d e s c r i b e d under E x p e r i m e n t a l P r o c e d u r e . W i t h t h e probes a few i n c h e s b e l o w t h e i n t e r f a c e t h e f l o w o f samples i n t o t h e probes and a l o n g t h e s a m p l i n g l i n e s was and m a i n t a i n e d f o r about 2 - h r .  started  Without a l t e r i n g the sampling  r a t e s t h e probes were l o w e r e d t o about 1 - f t . above t h e n o z z l e tips.  Samples from each probe were c o l l e c t e d a t t i m e i n t e r v a l s  o f about 1-min. u n t i l 30-min. a f t e r moving t h e p r o b e s .  The  b e l l - p r o b e samples were.shaken v i g o r o u s l y many t i m e s t o b r i n g t h e two phases t o e q u i l i b r i u m . .  The hook-probe samples and t h e  ketone phase o f t h e b e l l - p r o b e samples were a n a l y s e d f o r a c e t i c a c i d as d e s c r i b e d e a r l i e r .  F o r each probe a p l o t was made o f  t h e c o n c e n t r a t i o n o f a c e t i c a c i d i n each sample v e r s u s t h e t i m e a f t e r moving t h e p r o b e s . •The purge t i m e was t a k e n t o be t h a t t i m e when t h e r e was' no change i n c o n c e n t r a t i o n w i t h i n c r e a s i n g t i m e . . Purge t i m e s were d e t e r m i n e d f o r v a r i o u s s a m p l i n g r a t e s  258  between 4-ml./min. and 20/-ml./min.  I t was found t h a t a c o n s e r v -  a t i v e e s t i m a t e o f t h e minimum purge t i m e f o r each o f t h e s a m p l i n g l i n e s was g i v e n by t h e f o l l o w i n g e q u a t i o n .  Purge time (min.) = ii)  —  120  >—r—7—  R  :  ,sampling r a t e (ml./mm.J  •  Hypodermic n e e d l e s . The i n s i d e d i a m e t e r o f a 22-gauge hypodermic n e e d l e i s so  s m a l l t h a t t h e purge t i m e f o r such a s a m p l i n g d e v i c e i s v e r y small.  A " c o n s e r v a t i v e : e s t i m a t e o f t h e minimum purge t i m e  estimated- i n t h e f o l l o w i n g manner.  was  A hypodermic n e e d l e sampler  was i n s e r t e d t h r o u g h one. o f t h e l§-in. I.D. p o l y e t h y l e n e g a s k e t s described e a r l i e r . of  T h i s g a s k e t was sandwiched between one  end  a 3 - f t . l e n g t h of l§-in. I.D. P y r e x p i p e and a l§-in. d i a .  d i s k of l / l 6 - i n . t h i c k polyethylene.  The gasket and d i s k were  clamped t o t h e end o f t h e p i p e by means o f an aluminum end p l a t e and f l a n g e . of  The p i p e was f i l l e d w i t h water and a s a m p l i n g r a t e  3/4-ml./min. t h r o u g h t h e n e e d l e was e s t a b l i s h e d .  The  water  was poured out o f t h e p i p e and t h e n t h e p i p e was f i l l e d w i t h an aqueous s o l u t i o n o f p o t a s s i u m permanganate. t h r o u g h t h e hypodermic  The f l o w o f l i q u i d  n e e d l e recommenced a t 3A-ml./min.  The  c o l o u r o f t h e p o t a s s i u m permanganate showed up i n t h e sample i s s u i n g from t h e n e e d l e i n l e s s t h a n 45-sec.  The change i n c o l o u r  was so r a p i d t h a t t h e t i m e between t h a t when t h e c o l o u r  first  appeared and t h a t when i t r e a c h e d f u l l s t r e n g t h was c o n s i d e r e d t o be n e g l i g i b l e .  A purge t i m e o f l-g-min. was c o n s i d e r e d t o be  c o n s e r v a t i v e f o r s a m p l i n g r a t e s o f a t l e a s t 3A-ml./min.  

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