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Axial dispersion of the continuous phase in liquid-liquid extraction spray columns and internal sampling… Lim, Choon Jim 1971

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AXIAL DISPERSION OF THE CONTINUOUS PHASE IK LIQUID-LIQUID EXTRACTION SPRAY COLUMNS AND INTERNAL SAMPLING TECHNIQUES by CHOON JIM LIM B. Sc., Nanyang U n i v e r s i t y , 1968 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1971 o In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced deg ree a t t he 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 a g r e e 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 s t u d y . I f u r t h e r a g r ee 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 by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r 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 not 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 . Depar tment o f CHEMICAL ENGINEERING The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date June 2, 1971 i ABSTRACT An i n t e r n a l sampler, a p l a s t i c cup probe, was constructed t o replace a funnel-probe f o r sampling the dispersed phase (methyl i s o b u t y l ketone) 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. The dispersed phase sample can be withdrawn from the column by the p l a s t i c cup probe without being contaminated with the continuous phase water. For runs i n which the mass t r a n s f e r i s from the continuous phase to the dispersed phase, the p l a s t i c cup probe r e s u l t s agree with those obtained by the funnel-probe. On the other hand, f o r runs i n which the d i r e c t i o n of mass t r a n s f e r i s reversed, the p l a s t i c cup probe tends t o give s l i g h t l y lower dispersed phase concentrations than does the funnel-probe at the same sampling e l e v a t i o n . I t i s b e l i e v e d that both methods of measuring concentrations are correct w i t h i n l e s s than 2$. The e f f e c t of mass t r a n s f e r on the a x i a l d i s p e r s i o n c o e f f i c i e n t o f the continuous phase i n a 1.5-in. I.D. l i q u i d - l i q u i d e x t r a c t i o n spray column was studied f o r various s u p e r f i c i a l v e l o c i t i e s of two phases, and f o r various p a r t i t i o n a b l e solute ( a c e t i c a cid) concentrations i n the continuous phase fed t o the column. Tracer s o l u t i o n (sodium ch l o r i d e solution) was i n j e c t e d s t e a d i l y i n t o the continuous phase i n the column. A x i a l con-centration p r o f i l e s of the t r a c e r were measured upstream, with respect t o the continuous phase, from the t r a c e r d i s t r i b u t o r . The steady state form of the d i s p e r s i o n equation was used to c a l c u l a t e the a x i a l d i s p e r s i o n c o e f f i c i e n t of the continuous phsse. The r e s u l t s obtained show that there i s no e f f e c t of mass t r a n s f e r on the a x i a l d i s p e r s i o n c o e f f i c i e n t w i t h i n the range of the i n v e s t i g a t i o n . Drop s i z e d i s t r i b u t i o n and holdup of the dispersed phase i n the column a l s o were measured. The drop s i z e d i s t r i b u t i o n always shows two peaks. It was found that there i s no e f f e c t of mass t r a n s f e r on both the drop s i z e d i s t r i b u t i o n and on the dispersed phase holdups w i t h i n the range of i n v e s t i g a t i o n . i i i TABLE OF CONTENTS Page I. INTRODUCTION - - - 1 A) PREVIOUS WORK - 1 a) Holdup and Drop Size D i s t r i b u t i o n of the Dispersed Phase 1 b) Int e r n a l Sampling Techniques and Concentration P r o f i l e s 3 c) A x i a l Dispersion 9 B) OBJECT OF THE RESEARCH - 12 I I . EXPERIMENTAL METHODS 15 A) APPARATUS AND FLOW SHEET - - 15 B) GENERAL OPERATING PROCEDURE FOR STARTING UP THE COLUMN - 32 C) ANALYTICAL TECHNIQUES --- 38 a) Methyl Isobutyl Ketone - A c e t i c A c i d - Water System 38 b) Methyl Isobutyl Ketone - Sodium Chloride -Water System kO c) Methyl Isobutyl Ketone - Sodium Chloride -A c e t i c A c i d - Water System k2 I I I , STUDY OF INTERNAL SAMPLING TECHNIQUES — U5 A) EXPERIMENTAL PROCEDURES - k6 a) Sampling Technique Studies with the Hook-Probe, the Funnel-Probe, the Hypodermic Needles, and the P l a s t i c Cup Probes k6 i v b) Sampling Rate Studies with the P l a s t i c Cup Probes, the Hook-Probe, and the Funnel-Probe 50 c) Concentration P r o f i l e s of the Dispersed Phsse across Column Cross Sections 52 B) RESULTS AND DISCUSSION - 5k e) Sampling Rate Studies with the Hook-Probe, the Funnel-Probe, and the P l a s t i c Cup Probes — 58 b) Concentration P r o f i l e s of the Dispersed Phase across Column Cross Sections 6*4 c) Sampling Technique Studies with the Hook-Probe, the Funnel-Probe, the Hypodermic Needles, and the P l a s t i c Cup Probes T l IV. EFFECT OF INTERPHASE MASS TRANSFER ON THE AXIAL DISPERSION COEFFICIENT OF THE CONTINUOUS PHASE Qk A) THEORY - 8U a) Steady State I n j e c t i o n of Tracer Method 87 b) From the Concentration P r o f i l e s of the P a r t i t i o n a b l e Solute i n both Phases 89 B) EXPERIMENTAL PROCEDURES — - 93 8 ) E q u i l i b r i u m D i s t r i b u t i o n of HAc between Water -Saturated MU3K and MIBK - Saturated W8ter f o r Various Concentrations of HAc and NaCl 95 b) E q u i l i b r i u m D i s t r i b u t i o n of NaCl between Water -Saturated MIBK and MIBK - Saturated Water f o r Various Concentrations of HAc 96 V c) E f f e c t of Interphase Mass Transfer on Axi8l Dispersion C o e f f i c i e n t of the Continuous Phase •• 96 C) RESULTS AND DISCUSSION 101 a) J u s t i f i c a t i o n of Use of the MIBK - NaCl -HAc - Water System 101 1) D i s t r i b u t i o n C o e f f i c i e n t s of NaCl between Water - Saturated MIBK and MIBK - Saturated Water f o r Various Concentrations of HAc 101 2) D i s t r i b u t i o n C o e f f i c i e n t s of HAc between Water - Saturated MIBK and MIBK - Saturated Water f o r Various Concentrations of HAc and NaCl 105 3) Drop Size D i s t r i b u t i o n s of the Dispersed Phase — 108 k) Holdups of the Dispersed Phase 116 b) A x i a l Dispersion C o e f f i c i e n t from Tracer Measurements 121 c) A x i a l Dispersion C o e f f i c i e n t s from the P a r t i t i o n a b l e Solute Concentration P r o f i l e s i n both Phases 138 V. CONCLUSIONS AND RECOMMENDATIONS - . 155 VI. NOMENCLATURE 158 V I I . LITERATURE CITED l62 V I I I . APPENDICES A) DATA OF PART I I I STUDY OF INTERNAL SAMPLING TECHNIQUES iGl DATA OF PART IV EFFECT OF INTERPHASE MASS TRANSFER ON THE AXIAL DISPERSION COEFFICIENT OF THE CONTINUOUS PHASE COMPUTER PROGRAM FOR CALCULATING THE AXIAL DISPERSION COEFFICIENT FROM TRACER MEASUREMENTS AND A TYPICAL COMPUTER OUTPUT SAMPLE HAND CALCULATION AND COMPUTER PROGRAM FOR CALCULATING THE AXIAL DISPERSION COEFFICIENT FROM PARTITIONABLE SOLUTE CONCENTRATION PROFILES IN THE CONTINUOUS PHASE AND IN THE DISPERSED PHASE v i i LIST OF FIGURES Page 1. Letan end Kehat's Temperature Probe 8 2 . Schematic Flow Diagram f o r Column IT 3. Column Arrangement f o r Sampling Technique Studies 21 k. Column Arrangement f o r A x i a l Dispersion C o e f f i c i e n t Studies (Piston-Type Sampler at the Middle of the Test Section) 22 5. Column Arrangement f o r A x i a l Dispersion C o e f f i c i e n t Studies (Piston-Type Sampler at the Top of the Test Section) 23 6 . Hypodermic Needle and P l a s t i c Cup Probe I n s t a l l e d f o r Sampling 28 7. Piston of the Piston-Type Sampler 30 8. Nozzle Tip Patterns 31 9. Perspex Box (Pi) f o r the Column Photographs 33 10. Sampling Po s i t i o n s across the Cross Section of the Column 52 11. E f f e c t of Sampling Rate on the Dispersed Phase Concentration f o r the P l a s t i c Cup Probes 60 12. E f f e c t of Sampling Rate on the Dispersed Phase Concentration f o r the P l a s t i c Cup Probes 6 l 13. E f f e c t of Sampling Rate on Concentration f o r the Funnel and f o r the Hook Probes 62 ik. E f f e c t of Sampling Rate on Concentration f o r the Funnel-Probe ' 63 v i i i 15. Dispersed Phase Concentrations across the Cross Section of the Column and along the Test Section 66 16. Dispersed Phase Concentrations across the Cross Section of the Column and along the Test Section 67 17. Sampling Technique Studies with the Plastic Cup Probes, the Hypodermic Needles, the Funnel-Probe, and the Hook-Probe ik 18. Sampling Technique Studies with the Plastic Cup Probes, the Hypodermic Needles, the Funnel-Probe, 8 n d the Hook-Probe 75 19. Sampling Technique Studies with the Plastic Cup Probes, the Hypodermic Needles, the Funnel-Probe, and the Hook-Probe 78 20. Schematic Representation of the Column and of the Control Zone for Solute Mass Balances 85 21. Schematic Representation of the Arrangement for Determinating the Magnification Factor 100 22. Equilibrium Distribution of NaCl between Water -Saturated MIBK and MIBK - Saturated Water with Approximately 0.1 N NaCl in the Water Phase 102 23. System Water - HAc - MIBK at 25 °C, Weight % 10k 2k. Equilibrium Distribution of HAc between Water - Saturated MIBK and MIBK - Saturated Water, T = 70 — 7 O . 5 °F 107 25. Drop Size Distributions 8nd Drop Volume Distributions, i 3 Run 36 (C c = 0.000 Lb-Mole/Ft.) 111 26. Drop Size Distributions and Drop Volume Distributions, i 3 Run 31 (C c = 0.028 Lb-Mole/Ft.) 112 ix 27. Drop Size Distributions and Drop Volume Distributions, i 3 Run 2k (C = 0.0k3 Lb-Mole/Ft.) 113 28. Drop Size Distributions and Drop Volume Distributions, i 3 Run 28 (C = 0.066 Lb-Mole/Ft.) — - Ilk c 29 Holdup of the Dispersed Phase for Runs with Lp = 3 2 36.5 Ft./Hr. Ft., (Arranged in Time Sequence) 118 30. Reduced Concentration Profiles of Sodium in the Continuous Phase, (c* = 0.000 Lb-Mole/Ft^) 126 31. A x i a l Dispersion C o e f f i c i e n t f o r Runs with = 3 2 36.5 Ft./Hr. Ft. - — 129 32. Reduced Concentration Profiles of Sodium in the Continuous Phase, (C 1 = 0.028 Lb-Mole/Ft?) 131 c 33. Reduced Concentration Profiles of Sodium in the Continuous Phase, (c' = 0.0i+3 Lb-Mole/Ft^) 132 3^. Reduced Concentration Profiles of Sodium in the i 3 Continuous Phase, (C p = 0.066 Lb-Mole/Ft.) 133 X LIST OF TABLES Page 1. Key to Figure 2 — - — 18 2. Key to Figures 3, and 5 2k 3. Heights and Diameters of Column Sections 25 k. Heights of Sampling Points f o r Figure 3 25 5. Heights of Sampling Points for Figure k 26 6. Heights of Sampling Points for Figure 5 26 7. Atomic Absorption Measurements f o r D i f f e r e n t Concentrations of Sodium Chloride and A c e t i c A c i d i n MIBK - Saturated D i s t i l l e d Water kk 8. Operating Conditions f o r Sampling Rate Studies with the P l a s t i c Cup Probes, the Hook-Probe, snd the Funnel-Probe 50 9. Operating Conditions f o r Studies of Concentration P r o f i l e s of the Dispersed Phase 8cross the Column Cross Sections 53 10. Dispersed Phase Concentrations scross the Cross Section of the Column 69 11. Results of Sampling Technique Studies: Dispersed Phase Concentrations Average Over the Test Section 76 12. Results of Sampling Technique Studies: Continuous Phase Concentrations Average over the Test Section 77 13. Drop Size D i s t r i b u t i o n s and Drop Volume D i s t r i b u t i o n s (For Runs with = 36.5 Ft?/Hr. F t ? , and L c = 36.5 Ft?/Hr. Ft?) - - 115 x i 1*4. Holdups of the Dispersed Phase in the Column 119 15. Results of Axial Dispersion Coefficient Studies by Tracer Measurements 125 16. Comparison of E's Obtained by Using the Holdups as Measured with the E's Obtained by Using the Holdup of 2.85$: The Average Holdup of Runs 3^ , 35, 36, and 37 (Runs with No HAc in Two Phases) Which Were Made 8fter the Polyethylene Lining of the Piston Holes Had Aged — 130 17 . Concentrations of Sodium i n the Dispersed Phase and i 3 the Continuous Phase (C c £ 0.066 Lb-Mole/Ft.) 136 18. Comparison of the E's Obtained by Curve F i t t i n g Measured Partitionable Solute Concentrations by means of the Dispersion Equation with the E's Obtained by Tracer Measurements, and Comparison of Measured Concentrations of the Continuous Phase with Those Obtained from the Fitted Dispersion Equation : lM 19. E by Curve F i t t i n g with the Dispersion Equation Using Measured C p's and Smoothed C 's (both with Different v C Values of j ) - - - 1*15 20. Average Capacity Coefficient for Each Section within the Test Section of the Column for a l l the Runs with Mass Transfer 1^ 7 21. E by the Second Method 150 22. E by the Third Method (with the Flux Calculated by Equation 3*0 - - 152 x i i 2 3 . Comparison of the E's Obtained by the Third Method When the E's Are Based on Various Equations f o r the Flux of P a r t i t i o n a b l e Solute down the Column • 153 A - l . Sampling Technique Studies; Over e l l Mass Transfer Data - - 168 A - 2 . E f f e c t of Sampling Rate on Dispersed Phase Concentration f o r the P l a s t i c Cup Probes, Run 8 169 A - 3 . E f f e c t of Sampling Rate on Dispersed Phase Concentration f o r the P l a s t i c Cup Probes, Run 30 170 A-k. E f f e c t of Sampling Rate on Dispersed Phase Concentration f o r the Funnel-Probe 172 A - 5 . E f f e c t of Sampling Rate on Continuous Phase Concentration f o r the Hook-Probe, Run 11 173 A - 6 . Concentrations of Dispersed Phase i n Cross Sections Perpendicular to the Column Axis as Determined by Sampling with the P l a s t i c Cup Probes 17** A - 7 . Continuous and Dispersed Phase Concentrations Given by the P l a s t i c Cup Probes, the Hypodermic Needles, the Funnel-Probe, and the Hook-Probe • — 175 B - l . D i s t r i b u t i o n s of NaCl between Water - Saturated MIBK and MIBK - Saturated Water for Various Concentrations of HAc, T = 70 °F - 179 B - 2. E q u i l i b r i u m D i s t r i b u t i o n of HAc between MIBK - Saturated Water and Water - Saturated MIBK, T.= 70 °F l 8 0 B - 3 a . E q u i l i b r i u m D i s t r i b u t i o n of HAc between MIBK - Saturated W8ter and Water - Saturated MIBK, T = 7 0 . 5 °F, NaCl i n the Water Phase = 0 . 0 1 N — — l 8 l x i i i B - 3 b . E q u i l i b r i u m D i s t r i b u t i o n of HAc between MIBK-Saturated Water and Water-Saturated MIBK, T = 7 0 . 5 °F, NaCl i n the Water Phase = 0 . 1 N - 182 B-U. T y p i c a l Drop Size D i s t r i b u t i o n and Drop Volume D i s t r i b u t i o n Results, Run 28 183 B - 5 . Drop Size D i s t r i b u t i o n s i n the 1 l / 2 - I n . I. D. Column l8k B - 6 . Drop Volume D i s t r i b u t i o n s i n the 1 1 / 2 -In. I. D. Column 185 B - 7 . HAc Concentration P r o f i l e s i n the Continuous Phase and i n the Dispersed Phase 186 C - l . T y p i c a l Computer Output f o r C a l c u l a t i n g E from Tracer Measurements, Run 28 192 x i v ACKNOWLEDGEMENTS The author wishes to express h i s thanks to the f a c u l t y and s t a f f of the Chemical Engineering Department, The U n i v e r s i t y of B r i t i s h Columbia. S p e c i a l thanks are extended to Dr. S. D. Cavers f o r h i s invaluable 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 throughout the course of t h i s work. The author i s indebted t o the Chemical Engineering Workshop personnel f o r t h e i r assistance i n assembling the experimental equipment. The production of a covering f o r piston was s o l e l y the work of Mr. R. Muelchen. F i n a n c i a l assistance was most g r a t e f u l l y received from the National Research Council of Canada and from The U n i v e r s i t y of B r i t i s h Columbia i n the form of U. B. C. Graduate Fellowship. 1 I . INTRODUCTION The present studies are a continuation of Henton's ( l ) work on a x i a l d i s p e r s i o n snd i n t e r n a l sampling techniques i n l i q u i d - l i q u i d e x t r a c t i o n spray columns. A x i a l d i s p e r s i o n (also c a l l e d backmixing and l o n g i t u d i a l d i s p e r s i o n ) may be thought of as M 8 case of non-ideal flow i n which a random movement of f l u i d i s superimposed on, and i s i n the d i r e c t i o n o f , the main flow" (2). The e f f e c t of a x i s l d i s p e r s i o n i n l i q u i d - l i q u i d extractors i s to lower the mean d r i v i n g p o t e n t i a l f or mass t r a n s f e r . A) PREVIOUS WORK The f i r s t systematic study of spray columns was done by E l g i n and Browning ( 3 ) } i n 1935. They found that the mass t r a n s f e r c o e f f i c i e n t s were a f f e c t e d by flow r a t e s , d i r e c t i o n of solute t r a n s f e r , and drop s i z e . Blending and E l g i n (k) noticed that the spray column should have a funnel-shaped entrance at the dispersed phase i n l e t t o prevent sny disturbance of the dispersed phase entering the column. Blanding and E l g i n (k) and others (5,6,7 ,8) studied the optimum design of nozzles f o r forming the drops. Their r e s u l t s i n d i c a t e d that reproducible phenomena were most r e a d i l y obtained with sharp-edged nozzles. An extensive c l a s s i f i c a t i o n and d i s c u s s i o n of e x t r a c t i o n equipment, i n c l u d i n g mention of spray columns, has been prepared by Morello and Poffenberger (9). a) Holdup and Drop Size D i s t r i b u t i o n of the Dispersed Phase Hayworth and Treybal (5) observed that a short j e t of dispersed phase extends beyond the nozzle, and that the drops form as the r e s u l t 2 of a "necking i n " at the top of the jet. Very small drops, 8S well as large drops, are formed at some veloc i t i e s . Each of jet length and drop size increases with increasing dispersed phase velocity. Each reaches a maximum value 8nd then decreases. The maximum drop size i s reached before the maximum jet length. After the maximum drop size h8S been reached, drop size becomes less uniform and eventually large irregularly shaped drops 8nd small spherically shaped drops are formed simultaneously. Johnson and Bliss (10), and others (1,11,12,13) observed that when extraction was from the continuous to the dispersed phase no coalescence was detectable, but, when extraction was from the dispersed to the continuous phase, considerable coalescence occurred. Drop size distribution was studied by several workers (l,5,10,ll*,15). Rocchini (12) used close-up photography and a narrow depth of focus. He corrected for the distortion due to the curved glass of the column wall. Henton ( l ) , and Letan and Kehat (15) minimized this distortion by enclosing the glass section in 8 square Perspex box f i l l e d with continuous phase. Henton (l) concluded that drop size distribution i s independent of the continuous and of the dispersed phase flowrates studied. Letan and Kehat (15) showed that this result i s valid only at low flowrates of both phases.. In particular they showed that, at high flowrates of the continuous phase, the drop size increases considerably as the continuous phase flowrate increases, 8nd that this increase in drop size appears f i r s t at the top of the column, and last at the bottom of the column. Holdups of the dispersed phase in spray columns were measured by earlier workers at only a single elevation in each column. It was found that the holdups of dispersed phase increase slightly with increasing continuous phase flowrate, and are nearly linearly dependent on the 3 dispersed phase flowrate. Letan and Kehat (15) r e c e n t l y measured l o c a l holdup as a function of flowrates and a x i a l p o s i t i o n i n a spray column. They found t h a t , for a given dispersed phase flowrate, holdup i s constant along the column for low continuous phsse flowrates. At higher con-tinuous phase flowrates holdups are lar g e r at the bottom of the column than at the top. However, i f the continuous phase flowrates are not too high, there i s s t i l l a region of constant holdup at the bottom of the column , with holdup decreasing above t h i s constant region. Further increasing the continuous phase flowrates causes the constant holdup region at the bottom of the column to disappear, and the d i f f e r e n c e between the holdup 8t the bottom of the column and that at the top becomes quite l a r g e . b) I n t e r n a l Sampling Techniques and Concentration P r o f i l e s Geankoplis and Hixson ( l 6 ) i n pioneering work i n 1950 obtained continuous phase concentration p r o f i l e s i n a spray column by withdrawing samples through a movable hook-shaped tube ins e r t e d from the top of the column. Sampling was c a r r i e d out at low enough rates t o avoid a f f e c t i n g the e x t r a c t i o n process, and to avoid entraining the dispersed phase. Geankoplis continued the work with, f o r example, Vogt (17) and Kreager ( l 8 ) . A sharp change or end e f f e c t was found i n the solute concentration at the continuous phase i n l e t t o the column, but not at the dispersed phase i n l e t . Newman (19) suggested that t h i s end e f f e c t at the continuous phase i n l e t was the r e s u l t of v e r t i c a l mixing of the continuous phase due to the movement of the drops. Newman showed that Geankoplis' r e s u l t s were intermediate between t r u l y countercurrent, unmixed flow of the continuous phase, and the condition which would be produced by-very e f f i c i e n t s t i r r i n g ; completely uniform concentration i n that phase. However, i t should be noted that Morello and Poffenberger (9) had pointed out e a r l i e r that there i s r e c i r c u l a t i o n i n the continuous phase of a spray column. The phenomenon of c i r c u l a t i o n was investigated f u r t h e r by Gier and Hougen (20) i n both spray and packed columns. They drew o f f continuous phase samples through hypodermic needles. A l s o , for the f i r s t time, samples of dispersed phase were obtained, by a set of funnel-shaped samplers f a c i n g downward so as to t r a p the r i s i n g drops. For both kinds of samplers access was through the column w a l l . The samples obtained by means of the funnel-shaped samplers contained both dispersed and con-tinuous phases. A n a l y s i s of solute i n each phase of a funnel-probe sample wss c a r r i e d out at some time a f t e r the sample had been taken. A material balance was used t o c a l c u l a t e the value of the solute concen-r t r e t i o n i n the dispersed phase as i t was at the time of sampling. They found that concentration p r o f i l e s f o r the continuous phsse were s i m i l a r to those measured by Geankoplis and co-workers ( l 6 , 1 7 , l 8 ) . Gier and Hougen (20) established that the continuous phase was s e r i o u l y back-mixed i n spray columns, but l e s s so i n packed towers. The r i s i n g drops were observed to ascend continuously, although e r r a t i c a l l y , and d i d not descend and mixed backward over t h e i r paths. This plug flow behaviour of the dispersed phase a l s o was observed by Cavers and Ewsnchyna ( 2 1 ) . Cavers and Ew8nchyna (21) combined the sampling methods of Gier and Hougen ( 2 0 ) , and Geankoplis and Hixson ( l 6 ) with c e r t a i n modifications. They made use of a hook-probe f o r continuous phase sampling, and a.funnel-probe f o r dispersed phase sampling. Both hook and funnel probes were 5 made of s t a i n l e s s s t e e l . The probes were lowered i n t o the column from the top. From the concentration p r o f i l e s , they explained that the causes of the end e f f e c t at the continuous phase i n l e t were, f i r s t the backmixing of the continuous phase, and second the mass t r a n s f e r between the continuous phase and the drops while these are ag i t a t e d at the column i n t e r f a c e p r i o r t o coalescence. To c a l c u l a t e the concentration of the dispersed phase i n the column from the a n a l y s i s of the sample obtained with the funnel-probe the following equation was used: CD - 4 -. r ( c c - cc > 1 D The use of t h i s equation implied two assumptions: ( i ) V c and V D are independent of the solute t r a n s f e r r e d between phases, and ( i i ) at the time of sampling the concentration CQ was i d e n t i c a l to the concentration of the continuous phase as sampled with the hook-probe. Later ( l , 2 2 ) , hypodermic needles as w e l l as hook-probes were used f o r sampling the continuous phase., Furthermore, i t was r e a l i z e d that the funnel-probe might sample p r e f e r e n t i a l l y the continuous phase from the wakes of the drops, but that the hook-probe and the hypodermic needle samplers might not do so. Hence, i t was bel i e v e d that the second assumption might be i n er r o r and therefore considerable work was done on sampling techniques. Hawrelak (22) designed and constructed a piston-type sampler, i n one attempt to j u s t i f y the use of equation 1. The piston-type sampler withdrew, almost instantaneously, a sample con s i s t i n g of the e n t i r e 6 contents of a small height of the operating column. Bergeron (23) con-tinued this work, determined the minimum purging time required to change the solution present in the sampling probes, and found that the rate of sampling by hook and by funnel probes had no effect on the concentration measured.. However, he ran the column so that the phases were near e q u i l i -brium at the elevation of sampling, and therefore no very firm conclusions could be drawn. Hention et a l . (1,2*0 me^ e extensive studies of sampling by means of hypodermic needles, hook-probe, funnel-probe, and piston-type samplers. Their work was done for two kinds of operation. In one, mass transfer of solute was going on from the continuous to the dispersed phase. In the other, no mass transfer took place, but a sodium chloride tracer, insoluble in the dispersed phase, was injected into the continuous phase, and the steady state concentration of the tracer was measured in that phase upstream from the point of injection. For use in connection with the piston sampler, Henton (l) derived Equation 2 (below) for calculating the average concentration of the descending continuous phase (without the inclusion of any contribution from a r i s i n g back-mixing stream of continuous phase). 2 Although not necessary to the derivation of equation 2, a l i k e l y hypothesis i s that backmixing of the continuous phase takes place by the mechanism of transport i n drop wakes. Henton et a l . (2k) showed t h a t , f o r the t r a c e r experiments, both the hook-probe and hypodermic needles give the correct volumetric average continuous phase concentration. It seemed l i k e l y , although not completely proved, that the same conclusion could be drawn for the mass tr a n s f e r experiment ( l ) . However, i n the msss t r a n s f e r work the hook-probe r e s u l t s always l a y above those from hypodermic needle samplers by about 1.5%' The hypodermic needle r e s u l t s agreed with the continuous phase concentration calulated by equation 2. For the dispersed phase concentration agreement was reasonably good between funnel-probe r e s u l t s , and piston-type sampler r e s u l t s , i f both were based on equation 1, with the continuous phase concentration obtained from hypodermic needle samples. However, hook-probe r e s u l t s were not. accurate enough for c a l c u l a t i n g dispersed phase concentrations from p i s t o n samples. In Henton's t h e s i s ( l ) the probably erroneous conclusion (2k) was drawn that the concentration i n the continuous phase of a spray column does not change markedly between the main body of the continuous phase and the drop wakes. Inte r n a l sampling techniques have been used a l s o f o r other types of l i q u i d e x traction columns; Mar snd Babb (25), and Schmel and Babb (26,27), sampled the continuous phase only, i n pulsed columns, i n much the ssme manner as d i d Gier and Hougen (20). Claybaugh (28) sampled both phases i n a pulsed column. The continuous phase was sampled by the u s u s l hypodermic needle, while the dispersed phsse was sampled by an inverted s t e e l funnel-probe attached to the bottom side of a p l a t e . Chiu (29) used a copper cup soldered to the end of a hypodermic needle as a sampler for Scheibel columns. Continuous phase 8 samples were obtained when the cup was placed concave upward, and dispersed phase when i t was placed concave downward. Smoot and Babb (30) a l s o used hypodermic needles to sample both phases i n a pulsed column. In order to p r e f e r e n t i a l l y remove dispersed phase, the needles used t o sample the dispersed phase had 8 f l a r e d polyethylene sleeve p o i n t i n g downward. However, removal of the dispersed phase uncontaminated with the continuous phase was not achieved. In studying spray column l i q u i d - l i q u i d heat exchangers, Letan and Kehat (31) made successful use of the property of p l s s t i c materials whereby they are p r e f e r e n t i a l l y wetted by organic l i q u i d s . They constructed a temperature probe (as i l l u s t r a t e d i n f i g u r e 1 below), f o r measuring the temperature of r i s i n g drops. FIGURE 1. LETAN AND KEHAT'S TEMPERATURE PROBE. A thermocouple was i n s e r t e d i n t o the side of a "bead made from a £ inch polyethlene sleeve from a compression f i t t i n g . The temperature pro-f i l e s of both phases were measured (32,33,3*0, and 8 hydrodynamic model was proposed f o r heat t r a n s f e r i n a spray column. The model emphasizes the importance of the r o l e played by the W8kes of drops i n the mechanism of he8t t r a n s f e r . Letan and Kehat (3*0 suggested that the same mechanism would apply to the mass t r a n s f e r esse. However, when Duncan (35) attempted t o apply the model t o c a l c u l a t e the concentration p r o f i l e s of the con-tinuous phase from the dispersed phase, he found that the agreement with the experimental r e s u l t s was poor. . Letan and Kehat (3l) suggested that s i m i l a r polyethylene bead could be used f o r withdrawing sample of pure dispersed phase from l i q u i d e x t r a c t i o n columns. c) A x i a l Dispersion The di s p e r s i o n model, the mixing c e l l model, 8nd the rsndom walk model have been found u s e f u l f o r d e s c r i b i n g a x i a l d i s p e r s i o n i n solvent e x t r a c t i o n columns. The d i s p e r s i o n model assumes that the various f a c t o r s causing a x i a l mixing can be described by a d i f f u s i o n a l type process superimposed on plug flow (36). The random walk model i s based on E i n s t e i n ' s (37) s t a t i s t i c a l treatment of motion of t r a c e r molecules t r a v e l l i n g through a column. The mixing c e l l model represents the extractor 8S a number of completely mixed c e l l s connected i n s e r i e s . For d e s c r i b i n g the operation of spray columns the d i s p e r s i o n model i s more appropriate than are the other two (38), and consequently most of the work i n spray columns i s based on the di s p e r s i o n model. The i d e a l i z e d d i s p e r s i o n model equations were developed, f o r example by Miyauchi and Vermeulen (39,*+0), and by Sl e i c h e r (kl) by extending Damkohler's (k2.) equation of c o n t i n u i t y f o r a sing l e phase continuous flow system t o the two-phase flow case. The equations f o r each phase were solved simultaneously. Numerical c a l u l a t i o n s were c a r r i e d out by computer. Danckwerts' boundary conditions (U 3,1*1*,1*5) were applied to y i e l d expressions f o r the continuous and f o r the dispersed phase solute concentrations as functions of distance along the axis . of the column. Rod 0*6,1+7) approximated the d i f f e r e n t i a l equations by f i n i t e d i f f e r e n c e equations and solved g r a p h i c a l l y on a d i s t r i b u t i o n diagram. In 1^-in. I.D. spray column operation drops are observed t o proceed upward without backmixing over t h e i r path. However, i n a 3 - i n . I.D. column some bsckmixing of drops i s observed ( l , l * 8 ) . Based on the l-g-in.-I.D. column behaviour, the customary assumption has been that 8 x i a l d i s p e r s i o n occurs only i n the continuous phase, and not i n the dispersed phase. In general the a x i a l d i s p e r s i o n c o e f f i c i e n t of the continuous phase has been determined by i n j e c t i n g i n t o the continuous phase a t r a c e r which i s not soluble i n the dispersed phase. Brutvan (k$) determined a x i a l d i s p e r s i o n c o e f f i c i e n t s , E, of the continuous phase i n a simulated spray column. Glass beads were the dispersed phase and were allowed t o f a l l through a r i s i n g water phase. His columns were 1, 1.5, and 2 - i n . I.D., 8nd the diameters of the glass beads 3, 5, and 6 mm. His continuous phase s u p e r f i c i a l o p 3 2 v e l o c i t i e s ranged from 1*40 f t f / n r . f t 1 to 780 f t . / h r . f t . , and dispersed 3 2 3 ? phase s u p e r f i c i a l v e l o c i t i e s from 10 f t . / h r . f t . to 100 f t . / h r . f t . The a x i a l d i s p e r s i o n c o e f f i c i e n t , E, was found to increase with i n c r e a s i n g dispersed phase flowrste, and decreasing continuous phase flowrate, decreasing dispersed phase p a r t i c l e s i z e , and incr e a s i n g column 11 diameter. Hazlebeck and Geankoplis (ll*) were the first to measure E's in a true spray column. Water was the continuous phase and methyl isobufyl ketone (MIBK) the dispersed phase. Their column was 1.1*1-in. I.D. 3 2 The continuous phase superficial velocity ranged from 10 ft./nr. f t . to 3 2 1*5 ft./hr. f t . , and the dispersed phase superficial velocity from l&.k ft./hr. f t . to 50 ft./hr. f t l Axial dispersion coefficients were found to be independent of dispersed phase flowrate, and to vary with the superficial velocity of the continuous phase (L c) in the following manner: E - 9.00 (Lc) In the work of Brutvan (1+9), and in that of Hazlebeck 8nd Geankoplis (ll*), axial dispersion coefficients were obtained by intro-ducing a step change in the concentration of tracer (potassium chloride) entering the column in the continuous phase. Measurements were made downstream (in the continuous phase) from where the tracer was introduced. The S8me solvent system used by Hazlebeck and Geankoplis (ll*) was used also in this laboratary by Henton and Cavers (1*8). However, sodium chloride sloution was used as a tracer by the latter, and axial dispersion coefficients E, were determined by them by means of the steady state application of the dispersion model. Their columns were 1.5, and 3-in. I.D. Five sets of nozzle tips were used, having respectively, average diameters of 0.126, 0.103, 0.086, and 0.053 inch (all in the 1.5-in. I.D. column) end 0.102 inch (in the 3-in. I.D. column). The superficial velocity of continuous phase ranged from 12 9.0 f t . / n r . f t . t o 1*8.1+ f t . / h r . f t . , end that of dispersed phase from 30.1+ to 127.7. Henton end Cavers' (1*8) r e s u l t s show that the a x i a l d i s p e r s i o n c o e f f i c i e n t i s unaffected by the continuous phase super-f i c i a l v e l o c i t y , but decreases with increased dispersed phase super-f i c i a l v e l o c i t y . It increases with column diameter, but i s unaffected by column length. I t increases with drop s i z e at constant dispersed phase s u p e r f i c i a l v e l o c i t y ; however, i t remains approximately constant with drop si z e when the number of drops per u n i t volume remains constant. Comparison of the experimental r e s u l t s from the various researches described above shows that disagreement e x i s t s between the r e s u l t s of the various workers, indeed, i n Brutvsn's (1+9) simulated spray column, the glass beads were r i g i d . Therefore, they d i d not become d i s t o r t e d i n shape and undulate as drops do i n passing through a second f l u i d . Hence, the data may not r e a l l y be representative of the data expected from a l i q u i d - l i q u i d spray column. Furthermore, both Brutvan (1+9), and H8zlebeck and Geankoplis (ll*) d i d not take i n t o account the problems associated with the production of a p e r f e c t step function f o r the t r a c e r . B) OBJECT OF THE RESEARCH When the d i s p e r s i o n model i s used to describe the behaviour of l i q u i d - l i q u i d e x t r a c t i o n spray columns, i t requires experimental values of the a x i a l d i s p e r s i o n c o e f f i c i e n t , E. So f a r , the values of E which can be found i n the l i t e r a t u r e are from t r a c e r experiments (either steady state or unsteady state i n j e c t i o n of t r a c e r ) with no mass t r a n s f e r between phases. It i s b e l i e v e d that ,the main mechanism of a x i a l d i s p e r s i o n of the /if continuous phase i s the transport of the continuous phase i n the wakes of the drops moving up the column (1,32,33,3^,^8). In the t r a c e r experiments since t r a c e r i s not soluble i n the dispersed phase, the only d i f f u s i o n of the t r a c e r i s between the wakes and the main bulk of the continuous phase. However, when p a r t i t i o n a b l e solute i s present t h i s i s not only t r a n s f e r r e d between the bulk of the continuous phase and the wakes, but a l s o between the wakes and the drops, and, at l e a s t to some extent, between the bulk of the continuous phase and the drops (33,3*0. The presence of t h i s p a r t i t i o n a b l e solute may a f f e c t the behaviour of the i n t e r f a c e between the phases, and may, as w e l l , a l t e r the wake forms behind the drops, because the t r a n s f e r of the p a r t i t i o n a b l e solute across the i n t e r f a c e may give r i s e t o l o c a l v a r i a t i o n of i n t e r f a c i a l tension and r e s u l t a n t extension or contraction of the i n t e r f a c e (50,51). This phenomenon i s known as Marangoni e f f e c t . It has been found by S t e r n l i n g and Scriven (50) that for some solvent systems, and depending on the solute d i f f u s i v i t y i n the two phases, the v i s c o s i t i e s of the f l u i d s , and the dependence of i n t e r f a c i a l tension on composition, the Marangoni e f f e c t w i l l create i n t e r f a c i a l turbulence or Marangoni i n s t a b i l i t y f o r solute t r a n s f e r i n one d i r e c t i o n across the i n t e r f a c e but not f o r the other d i r e c t i o n . The Marangoni e f f e c t may increase with i n c r e a s i n g solute concentration d i f f e r e n c e between the two phases, because more solute w i l l be t r a n s f e r r e d across the i n t e r f a c e . It would seem that t h i s e f f e c t might change the value of the a x i a l d i s p e r s i o n c o e f f i c i e n t obtained. Recently Henton ( l ) determined the a x i a l d i s p e r s i o n c o e f f i c i e n t of the continuous phase from the concentration p r o f i l e s of the solute i n both phases. The solute was t r a n s f e r r e d from the continuous phase to the dispersed phase. He assumed that there i s no a x i a l d i s p e r s i o n i n the dispersed phase, and found that the B x i a l d ispersion c o e f f i c i e n t , E, of the continuous phase obtained i n t h i s way was d i f f e r e n t from that obtained by the t r a c e r experiments under s i m i l a r operating conditions. A r i s i n g from t h i s r e s u l t , one of the purpose of the present research was to study the e f f e c t of interphase mass t r a n s f e r on the s x i a l d i s p e r s i o n c o e f f i c i e n t of the continuous phase. A second object was t o search for a new i n t e r n a l sampler t o with-draw the dispersed phase without i t s being contaminated with the con-tinuous phase, 8nd t o compare the concentration p r o f i l e of the dispersed phase obtained by t h i s kind of sampler with those given by the funnel-probe and the hypodermic needles with the assistance of equation 1. I I . EXPERIMENTAL METHODS A) APPARATUS AND FLOW SHEET The experiments were done i n a 1.5-in. I.D. spray column of E l g i n design. The o r i g i n a l apparatus was constructed mainly by Lepage (52), but i t h8s been modified by other workers (1,12,22,23,53,5*+). A schematic flow diagram of the apparatus i s shown i n f i g u r e 2. A key to t h i s f i g u r e i s presented i n table 1. Because of the solvent and corrosive properties of methyl i s o b u t y l ketone (MIBK), snd a c e t i c a c i d (HAc), the construction materials were r e s t r i c t e d to gLass, graphite, polyethylene, T e f l o n , chromium and s t a i n l e s s s t e e l . D e t a i l e d d e s c r i p t i o n of most of the apparatus has been presented elsewhere (1,12,22,23,52,53), and w i l l not be repeated here. Lep8ge (52), 8nd Choudbury (53) gave the d e t a i l e d drawing of the two-end sec t i o n s , M, and U, of the column. Choudbury (53) presented a l s o a d e t a i l e d d e s c r i p t i o n of the dispersed phase d i s t r i b u t i n g nozzle. Construction d e t a i l s of the s t a i n l e s s s t e e l storage tank are t o be found i n Bergeron's t h e s i s (23), and those of the constant head t8nks are i n Desn's t h e s i s (55). Henton ( l ) designed the t r a c e r d i s t r i b u t o r and gave the d e t a i l e d drawing. Flows i n the column were the continuous water phase flowing downwards, and the dispersed MIBK phase flowing upwards. Water and MIBK were stored i n the approximately 8 - f t . s t a i n l e s s s t e e l tanks, A and D, r e s p e c t i v e l y . The c e n t r i f u g a l feed pumps, P-^ , and P 2, supply water and MIBK t o the constant head tanks, E, and F, r e s p e c t i v e l y , which i n turn supply these phases to the rotameters feeding the column. Part of the water phase at the constant head tank overflows back to the tank A, while the d e s i r a b l e amount flows through the c o n t r o l l i n g valve, J , and rotameter, G, i n t o the E l g i n head, M, of the column. Water flows down through the column proper, R, and leaves the lower end of the column by passing through the automatic i n t e r f a c i a l l e v e l c o n t r o l l i n g valve, X, to the storage tank, B. MIBK i s pumped from the feed tsnk, D, t o the constant head tank, F. Part of i t returns to the storage tank, D, and the d e s i r a b l e amount flows through the c o n t r o l l i n g v s l v e , K, and rotameter, H, to the dispersed phase d i s t r i b u t i n g nozzle, S. MIBK i s dispersed i n t o drops. The drops r i s e counter-currently t o the descending water phsse and coalesce at the i n t e r f a c e , Q. A f t e r coalescence, the MIBK i n the E l g i n head overflows d i r e c t l y without c o n t r o l t o the storage tank, C. The i n t e r f a c i a l l e v e l , Q, between water and MIBK i n the E l g i n head, i s c o n t r o l l e d by c o n t r o l l i n g the amount of the water phase lea v i n g at the bottom of the column. An automatic c o n t r o l system with negative feed back was used. This system was designed and assembled by Nielsen (5*0, end modified by the author. The i n t e r f a c i a l l e v e l measuring device consists a 6-in. long k watt fluorescent l i g h t , l , a polyethylene f l o a t , n, and a model BIT i n d u s t r i a l selenium p h o t o c e l l , m. The c o n t r o l elements are 8 Honeywell E l e c t r o n i k 15 s t r i p chart pneumatic c o n t r o l l e r , o, and a diaphragm valve, X. The d e t a i l e d c o n t r o l apparatus assembly i s described i n Nielsen's t h e s i s (5*0. With t h i s set up, i t was po s s i b l e to c o n t r o l the i n t e r f a c i a l l e v e l very e a s i l y . In the a x i a l d i s p e r s i o n c o e f f i c i e n t study, sodium chloride d i s s o l v e d i n MIBK-saturated water was used as the t r a c e r s o l u t i o n . This s o l u t i o n flows from storage tank, Y, through needle valve, a, and rotameter, b, t o the t r a c e r d i s t r i b u t o r , c, and i n t o the column. FIGURE 2. SCHEMATIC FLOW DIAGRAM FOR COLUMN 18 TABLE 1. KEY TO FIGURE 2 A Continuous phase feed t8nk. B Continuous phase r e c e i v e r and storage tank. C Dispersed phase r e c e i v e r and storage tank. D Dispersed phase feed tank. E Continuous phase constant he8d tank. F Dispersed phase constant head tank. G Continuous phase feed rotameter. H Dispersed phase feed rotameter. I Continuous phase i n l e t ssmple va l v e . J Continuous phase flowrate c o n t r o l v a l v e . K Dispersed phase flowrste c o n t r o l V8lve. L Dispersed phsse i n l e t sample va l v e . M E l g i n head. N Continuous phase i n l e t p i p e s . 0 E l g i n head drain v a l v e . P^ C e n t r i f u g a l pump f o r continuous phase. Pg C e n t r i f u g a l pump f o r dispersed phase. PTS Piston-type sampler. Q Interfa ce. R Column proper. S Dispersed phase nozzle. T 1 » T 2 ' T 3 Thermometers. U Bottom c o n i c a l s e c t i o n . V Vent t o atmosphere. X Interface l e v e l c o n t r o l diaphram va l v e . 19 Y Tracer feed and storage tank. Continuous phase ou t l e t sample va l v e . 2>2 Dispersed phase o u t l e t sample val v e , a Tracer flowrate c o n t r o l valve, b Tracer feed rotameter, c Tracer d i s t r i b u t o r , d 22-gauge hypodermic needle samplers, e P l a s t i c cup probes, f Hook-probe. g Funnel-probe. h Funnel-probe c o n t r o l valve, i Hook-probe c o n t r o l v a l v e , j Funnel-probe rotameter. k Hook-probe rotameter. 1 Fluorescent l i g h t , m Photocell n Polyethylene f l o a t . o Pneumatic c o n t r o l l e r . Tubing. E l e c t r i c cable. 20 The arrangements and the v e r t i c a l dimensions of the columns f o r the experiments are shown i n f i g u r e s 3, ^, and 5. A key to these f i g u r e s i s presented i n table 2. The heights of the column sections were measured by Henton ( l ) and also by the author, and are shown i n table 3. The i n -side diameters (measured by Henton ( l ) ) a l s o are shown i n table 3- The heights of a l l the sampling points i n f i g u r e s 3, and 5 above the dispersed phase nozzle are given i n tables k, 5, and 6 r e s p e c t i v e l y . In a d d i t i o n , t a b l e s 5 and 6 include a l s o the height above the t r a c e r d i s t r i b u t o r and the reduced height f o r each sampling p o i n t . The reduced height i s defined as the distance below sampling point 10 divided by the distance between sampling points 1 and 10. The section of the column within which the samples were withdrawn was defined as the t e s t section of the column. For the column arrangement shown i n f i g u r e 3, the t e s t s ection (between sampling points 1 and 7) was 3.0*+ and f o r the column arrangements shown i n f i g u r e s k and 5, the t e s t sections (between sampling points 1 and 10) were both equal to U.53^7 f t . Four kinds of sampling probes were used i n the runs of the sampling technique study (except f o r run no. kj i n which the hook-probe was not used). These are (figure 2) the hook-probe, f , and hypodermic needles, d, for the continuous phase samples; and the funnel-probe, g, and p l a s t i c cup probes, e, f o r the dispersed (MIBK) phase samples. Detailed drawings of the hook and of the funnel probe are to be found i n Ewanchyna's t h e s i s (56). Both of them were made of s t a i n l e s s s t e e l , and are about 10 f t long. A water a s p i r a t o r was used to spply s l i g h t vacuum at the ends of the sampling l i n e s to suck samples out of the column. Because of a syphoning a c t i o n , once the sampling l i n e s have been f i l l e d with l i q u i d , no more suction i s necessary. Samples flow from the column F I G U R E 3. C O L U M N A R R A N G E M E N T F O R S A M P L I N G T E C H N I Q U E S T U D I E S . 22 FIGURE k. COLUMN ARRANGEMENT FOR AXIAL DISPERSION COEFFICIENT'STUDIES (PISTON-TYPE SAMPLER AT THE MIDDLE OF THE TEST SECTION) 23 FIGURE 5. COLUMN ARRANGEMENT FOR AXIAL DISPERSION COEFFICIENT STUDIES (PISTON-TYPE SAMPLER AT THE TOP OF THE TEST SECTION) 2k TABLE 2. KEY TO FIGURES 3, k and 5 M 6-in. long, 6-in. I.D, Pryex c o n i c a l pipe. N 10-in. long, l j j - i n . I.D. Pyrex c o n i c a l pipe with unflanged upper end. L 3 -ft. long, l§-in. I.D. Pyrex c o n i c a l pipe. R l / l 6-in. t h i c k , 1-^-in. I.D. polyethylene gasket through which sampling needles passed. S l / l 6-in. t h i c k , l | - i n . I.D./ Teflon gasket. Q l / 8 - i n . t h i c k , l | - i n . I.D. polyethylene gasket through which the t r a c e r d i s t r i b u t o r passed. P^ Perspex box f o r taking photograph of drops, see f i g u r e 9. P2 Perspex box f o r taking photograph of drops, see f i g u r e 6 of Kingsbury's t h e s i s (57). PTS Piston-type sampler. P Custon-made Pyrex c o n i c a l pipe, 3-in. to 1-g-in. reducer. B t o K Pyrex c o n i c a l pipe, see ta b l e 3. 1 t o 10 Sampling point numbers, see tables U, 5, snd 6. TABLE 3 . HEIGHTS AND DIAMETERS OF COLUMN SECTIONS LABEL (ON THE TOP FLANGE OF THE COLUMN SECTION) HEIGHT, INCHES INSIDE DIAMETER (FROM HENTON'S THESIS), INCHES B 6 . 0 3 5 1 . 5 0 0 C 6 . 0 1 * 9 1 . 5 0 8 D 5 . 9 7 9 1 . 5 0 1 * E 6 . 0 5 0 1 . 5 9 5 F 5 . 9 8 1 * 1 . 5 0 3 G 6 . 0 2 0 1 . 1 * 9 2 H 5 . 9 7 5 1 . 1 * 9 7 I 5 . 9 6 9 1 . 5 0 0 J 6 . 0 l * 8 1 . 5 0 0 K 1 2 . 0 7 1 PISTON SAMPLER 5 . 7 9 3 * Only the f i r s t three d i g i t s are considered s i g n i f i c a n t . * TABLE 1*. HEIGHTS OF SAMPLING POINTS FOR FIGURE 3 SAMPLING POINT NO. HEIGHT ABOVE THE NOZZLE TIPS., FT. INCHES 1 5 . 9 3 * * 7 1 . 2 1 2 5 . 1 + 2 6 6 5 . l l 3 ^ . 9 1 7 5 9 . 0 0 1* l * . l * 1 3 5 2 . 9 6 5 3 . 9 0 1 * 1 * 6 . 8 5 6 3 . 1 + 0 0 1 * 0 . 8 0 7 2 . 8 9 3 3 * + . 7 2 Only the f i r s t three d i g i t s are considered s i g n i f i c a n t . TABLE 5. HEIGHT OF SAMPLING POINTS FOR FIGURE 4 SAMPLING POINT NO. HEIGHT ABOVE THE NOZZLE TIPS, FT. HEIGHT ABOVE THE TRACER DISTRIBUTOR, FT. REDUCED HEIGHT, DIMENSIONLESS, ZR 1 1.898 0.512 1.0000 2 2.401 l.Ollt 0.8892 3 2.901+ 1.518 0.7782 1+ 3.411 2.021+ 0.6661+ 5 3.91*+ 2.528 0.5553 6 U .1+02 3.016 0.1+1+77 7 It .912 3.526 0.3355 8 • 5.415 1+.029 0.22UI+ 9 5.925 4.538 0.1121 10 6.1+33 5.01+6 0.0000 * Only the f i r s t three d i g i t s are considered s i g n i f i c a n t . * TABLE 6. HEIGHTS OF SAMPLING POINTS FOR FIGURE 5 SAMPLING HEIGHT ABOVE THE HEIGHT ABOVE THE REDUCED HEIGHT, POINT NOZZLE TIPS, TRACER DISTRIBUTOR, DIMENSIONLESS, NO. FT. FT. ZR 1 1.898 0.512 1.0000 2 2.1+01 1.011+ 0.8892 3 2.904 1.518 0.7782 1+ 3.1+11 2.024 0.6664 5 3.914 2.528 0.5553 6 1+.1+24 3.038 0.41+30 7 4.927 3.541 0.3320 8 5.437 4.051 O.2196 9 5.945 4.559 0.1076 10 6.433 5.01+7 0.0000 * Only the f i r s t three d i g i t s are considered s i g n i f i c a n t . through the needle valves, h, and i , and rotameters, j , and k, res-pectively. The funnel-probe withdrew both the continuous water phase and the dispersed MIBK phase. The hypodermic needles used are 22-gauge, and are 3 inches long. The bevel of the hypodermic needle i s facing in the upstream direction of the continuous phase while sampling, as shown in the l e f t hand side of the sketch in figure 6. The p l a s t i c cup probe consists of a hypodermic needle inserted into a -5-in. 0. D., and 0.2-in. high Teflon cup as shown in figure 6. Both the hypodermic needles used for sampling the continuous phase, and the plastic cup probes for sampling the dispersed phase were inserted through the polyethylene gaskets which were situated between successive sections of the Pyrex columns. The hook and the funnel probes were not used in studying the effect of mass transfer on the 8xial dispersion coefficient. However, a piston-type sampler was used to measure the holdup of the dispersed phase in the column. The piston block for the sampler was designed and constructed by Hawrelak, and the detailed drawing was presented in his thesis (22). Henton (l) used a polyethlene covered piston in the block. Because of the corrosive action of the f l u i d s , the cylinder had to be rechromed in the present work, and the piston had to be recontructed. The piston, including the holes through which the column operated, was covered with a layer of polyethylene as shown in figure 7. The same d i f f i c u l t y experienced eariler by Hawrelak (22) was encountered in the present work in contructing the piston; thus i t was d i f f i c u l t to make i t s l i p easily inside the cylinder, and, at the same time, insure no leakage. The rate of leakage of the piston-type sampler used was about one drop in four minutes. Samples from 1 " 1 " ^ Th ick , ! I.D. 2^"0.D. Polyethylene Gasket with Two 0.025" Dia. Holes for Needles Dispersed Phase 3 Long, 22 Gauge Hypodermic Needle 1" High, ^ I.D. 1"0. D. Telfon Cup FIGURE 6. HYPODERMIC NEEDLE AND PLASTIC CUP PROBE INSTALLED FOR SAMPLING ro Co the piston-type sampler were c o l l e c t e d i n the s p e c i a l l y made c o l l e c t i n g v e s s e l s which were c a l i b r a t e d and used by Henton ( l ) e a r l i e r . One set of dispersed phase d i s t r i b u t i n g nozzle t i p s was used throughout the experiments. The average i n s i d e diameter of these nozzle t i p s was measured by Henton ( l ) , and i s equal t o 0.103-in. The average v e l o c i t y of MIBK passing through these nozzle t i p s was 0.338 f t . / s e c . f o r the runs of the sampling technique study (except f o r run no. k"J i n which the v e l o c i t y was 0.358 f t . / s e c ) , and was 0.358 f t ./sec. f o r the runs of the a x i a l d i s p e r s i o n c o e f f i c i e n t study. In order t o maintain these v e l o c i t i e s f o r various MIBK s u p e r f i c i a l v e l o c i t i e s i n the column, some of the nozzle t i p s were blocked up by using Teflon caps. Figure 8 shows the t i p patterns used i n the experiments. Drop size d i s t r i b u t i o n s i n the column were measured i n the same way as by Henton ( l ) . A section of the column was photographed while i n operation, and the d i s t o r t i o n due t o the curved column glass was minimized by enclosing glass column sections i n square Perspex boxes f i l l e d with d i s t i l l e d water. Two of these boxes were used. One ( P l i n f i g u r e s k and 5) was b u i l t during Henton's work, and the other (P2 i n f i g u r e 5) during the present study. The former i s shown i n f i g u r e 9. (Figure V-9 i n Henton's t h e s i s shows the same box, but the dimensions are i n e r r o r ) . The l a t e r box (P2) was made s i m i l a r to the one of Henton and i s shown i n f i g u r e 6 of Kingsbury's t h e s i s (57). The sections of the column through which photographs were taken are shown i n f i g u r e s k and 5. The Exacta VX-IIa camera with a 1.6-in. extension r i n g and a Telemegor 5.5/250 photolens was used f o r the purpose. The camera aperature was set at f22 t o give a depth of focus greater than the i n s i d e diameter of the column. The arrangement 30 CLA1V3PING SLOT & SCREWS (NOT SHOWN ) KNURLED CYLINDER FOR TENSIONING SHEET g-IN. THICK POLYETHY-LENE COVER, RELIEVED APPROX. 0015 FIGURE 7. PISTON OF THE PISTON-TYPE SAMPLER 31 studies O Open © Blocked FIGURE 8. NOZZLE TIP PATTERNS was the same as that shown i n Henton's f i g u r e 19 ( l ) , except that the distance between the column center l i n e and the back of camera was 52 inches, instead of 69^/16 inches. The 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 m i l l i s e c o n d was used as the l i g h t source. B) GENERAL OPERATING PROCEDURE FOR STARTING UP THE COLUMN In a l l the experiments i n which mass t r a n s f e r took place solute was t r a n s f e r r e d from the continuous phase to the dispersed phase, except that f o r two runs (runs no. 5 and 7) the d i r e c t i o n of solute t r a n s f e r was reversed. Throughout the course of the experiments, demineralized water with r e s i s t i v i t y b e t t e r than 1 meghom cm. was used i n preparing the continuous phase. Technical grade MIBK supplied by Chemcell L t d . was used as the dispersed phase. Reagent grade g l a c i a l a c e t i c a c i d manu-factured by Nichols Chemical Corporation L t d . was the p a r t i t i o n 8 b l e s o l u t e . Sodium chloride supplied by F i s h e r S c i e n t i f i c Company was used as the t r a c e r . The demineralized water used was produced by passing c i t y water through a Barnstead Bantam BD-1 mixed bed demineralizer. MIBK and water are p a r t i a l l y m i s c i b l e , and t h i s mutual m i s c i b l i t y increases with i n c r e a s i n g a c e t i c a c i d concentration. In order to minimize the po s s i b l e e f f e c t s of t h i s on the experimental r e s u l t s obtained, each phase was saturated with the other phase before use. For runs i n which solute t r a n s f e r r e d from the continuous phase to the dispersed phase, the continuous phase feed s o l u t i o n was prepared by f i l l i n g the aqueous tank with demineralized water. Then the necessary A «-| 1/8"D.VENT^| I 11 DRILL AND TAP ^—V 8"N.P.T. V\ K V V \ \ \ \ - W l -TRANSLUSCENT 1/„"PERSPEX i —I '8 T T 732 tt J*fc= I* E / / / / / / -7 " 1 " 3 \ SECTION ON B-B mjco SECTION ON A-A MATERIAL: TRANSPARENT 3^" PERSPEX (UNLESS OTHERWISE SPECIFIED ) FIGURE 9. PERSPEX BOX (Pi) FOR THE COLUMN PHOTOGRAPHS amount of gl a c i a l acetic acid needed to produce a desirable acetic acid concentration was added, and also MIBK was added to produce a layer about an inch of MIBK at the top of the solution. The dispersed phase was the product of backwashing the MIBK from the previous run, and the solute concentration was very low. For runs in which solute transfer was reversed, the continuous phase was pure MIBK-saturated demineralized water. The dispersed phase was from the previous run and the amount of acetic acid needed to produce a desirable concentration was added. A layer of a few inches of water was maintained at the bottom of the MIBK feed tank following preparation of dispersed phase feed. To insure that the solutions were homogeneous and saturated with the other phase, the solutions in the tanks were stirred vigourously and, at the S8me time, pumped up to the constant head tanks and allowed to run back into the feed tanks. The homogenity was checked by periodically t i t r a t i n g the flows from the constant head tanks with standard sodium hydroxide solution. The column was started in the following way. F i r s t of a l l , the pumps (for the continuous phase and the dispersed phase), and the fluorescent light (which was attached to the Elgin head for the int e r f a c i a l level control) were switched on. The a i r supplied to the pneumatic controller was regulated to 20 psig., and the pneumatic valve controlling the continuous phase out of the column was closed by setting the controlled air pressure to zero psig. Secondly, a small amount of the dispersed phase was allowed to pass through the nozzle tips in order to vent away any air in the nozzle. Then the column was f i l l e d with continuous phase at the maximum possible rate. Finally, when the interface between water and MIBK reached the Elgin head, the continuous phase flowrate was slowed down to rotameter reading 35 10mm. (about 33 f t . / n r . f t . ) , and three minutes time was allowed f o r the i n t e r f a c e to reach the set point of the c o n t r o l l e r . Then the automatic c o n t r o l l e r was a c t i v a t e d by switching on the instrument power and the chart d r i v e . Slowing down the continuous phase flowrate was necessary, f o r , i f the l e v e l was allowed to approach the set point too r a p i d l y , the c o n t r o l system was unable to react q u i c k l y enough. Consequently, the c o n t r o l l e r was unable to b r i n g the l e v e l t o the set point before the f l o a t passed through the l i g h t path. Once the i n t e r f a c e had been s t a b l i z e d at the set p o i n t , the flowrates of the dispersed and the continuous phases were adjusted to the desi r e d flowrates slowly. For the a x i a l d i s p e r s i o n c o e f f i c i e n t study, the valve feeding the rotameter f o r the t r a c e r s o l u t i o n (sodium chloride s o l u t i o n ) was then opened slowly, t o allow the t r a c e r t o flow i n t o the column. This rotameter then was set at the d e s i r e d flowrate, u s u a l l y about 1$ of the continuous phase flowrate, but never more then 1.5$. In the sampling technique study, the continuous phase product out o f the column ran back i n t o the continuous phase storage tank, B, shown i n f i g u r e 2. At the end of an experiment the continuous phase product was pumped back t o the continuous phase feed tank, and the continuous phase product tank was f i l l e d with demineralized water. This was used to backwash the MIBK from the previous run i n the column, and t o prepare the MIBK f o r the next run. The continuous phase product from the backwashing operation was fed t o the continuous phase feed tank u n t i l the l i q u i d l e v e l i n that tank was about 6 inches from the top, and then the remainder was fed t o the d r a i n . The aqueous s o l u t i o n needed for the next run then was prepared as described p r e v i o u s l y . In the a x i a l d i s p e r s i o n c o e f f i c i e n t study, because the continuous phase 36 product was contaminated with tracer, this product could not be reused for the next run. The continuous phase product and the continuous phase backwashing product were fed to the drain together with large amounts of water. The time to obtain steady state operation after the column has been started was taken from Henton's (l) experimental results. For runs in which the superficial velocity of the continuous phase was equal to 3 2 18.2 f t . / h r . f t . , two hours were allowed for steady state to be reached, and for runs in which the superficial velocities of the continuous phase 3 2 were equal to 27.7 f t . / h r . f t . or were above this value (such as 3 2 3 2 36.5 f t . / h r . f t . and k&.k ft./hr. f t . ) one hour was allowed. After allowing the column to reach steady state, sampling through the probes was commenced (The details of the sampling procedures w i l l be described later in Part III and Part IV of this thesis). During the experiments, the rotameter readings of both phases and of the tracer (for the axial dispersion coefficient study only) were checked from time to time. If there W8S any deviation from the set point, the deviation was corrected immediately, and fifteen minutes time was allowed before the next sample was withdrawn. From time to time during the course of the steady state operation, samples of each of phases entering and leaving the column were taken in * order to check that conditions were not changing with time, and to provide for the making of materiel balances. For each run, the t o t a l rate of solute transfer across the interface in the column was calculated by the following equations. NW = LC (CC - C c ) 3a Results of analysis of these samples show that the times allowed for the column to reach steady state (measured for tracer runs without mass transfer) are sufficient also under the mass transfer conditions used in and NK " h K - CD> 3b Where was the t o t a l amount of solute out of the continuous phase i n passing through the column per unit time and per u n i t c r o s s - s e c t i o n a l area, and N was solute i n t o the dispersed phase. Both were expressed i n lb-mole per hour per square f o o t . Hawrelak (22) (in appendix II of h i s t h e s i s ) made a c a l c u l a t i o n of the volume change of both phases i n a s i n g l e - c o n t a c t - e x t r a c t i o n mixer. The two phases i n the mixer were assumed t o be i n e q u i l i b r i u m . He found that the change of volume of both phases was n e g l i g i b l e . Therefore, i n the c a l c u l a t i o n , f o r each run L„ and L were assumed constant throughout the column. C D In general, the values of N and were s l i g h t l y d i f f e r e n t from W K-each other. Hence the average value, N = (N + N.J/2, was used f o r K W c a l c u l a t i n g the percentage d e v i a t i o n . The percentage d e v i a t i o n was calculated f o r each run as a measure of the q u a l i t y of the experimental work. The equation used was as f o l l o w s . For the study of the a x i a l d i s p e r s i o n c o e f f i c i e n t , i n which t r a c e r s o l u t i o n was i n j e c t e d , the percentage d i f f e r e n c e between the t r a c e r i n j e c t e d i n t o the column, and that leaving the column with the continuous phase a l s o was calculated by the following equation. NTT - N, Percentage Deviation = X 100$ l+a N Tracer mass balance apparent l o s s = X 100% kb where Lq> i s the tracer feed s u p e r f i c i a l v e l o c i t y , i s the t r a c e r feed o concentration i n ppm., and Ctp i s the steady state t r a c e r concentration i n ppm. i n the continuous phase lea v i n g the column. Samples obtained with the funnel-probe consisted of MIBK and a small amount of water. Each sample was c o l l e c t e d i n a 50ml. measuring c y l i n d e r . A f t e r some time, the volume of MIBK, Vp , and the volume of water, V , were recorded. The phases were separated (by sucking out L the water phase with a p i p e t t e ) , and then were analyzed f o r solute a a concentrations. The r e s u l t s obtained were end C Q r e s p e c t i v e l y . The concentration of solute i n MIBK at the time of sampling, Cp , was ca l c u l a t e d by material balance of solute between the time o f sampling and the time of a n a l y s i s . Equation (repeated below f o r convenience) i s as f o l l o w s . a V C , °D = °D - " 7 " ( C C " C C ) 1 VD This equation involved the assumption t h a t there i s n e g l i g i b l e volume change of both phases when solute t r a n s f e r i s from the water phase t o the MIBK phase i n the sample. C^ f o r using equation 1 was the value obtained by analyzing sample obtained with the hypodermic needles. C) ANALYTICAL TECHNIQUES a) Methyl Isobutyl Ketone - A c e t i c A c i d - Water System D i r e c t t i t r a t i o n with carbon d i o x i d e - f r e e standard sodium hydroxide 39 solution with phenophthalein as the indicator was used to determine the amount of acetic acid in the water phase and in the MIBK phase. When ti t r a t i n g the MIBK phase 25 ml. SDAG - IK was added to render the MIBK, and the water phase added during t i t r a t i o n , miscible. Generally, 2 ml. of samples were tit r a t e d , hut, i f a smaller volume was removed from the column, or i f the concentration was very low or very high, other appropriate volumes were t i t r a t e d . The concentration of standard sodium hydroxide ranged "between 0.02 and 0.05 normal. A l l the samples were titrated to what appeared to be the same pinkish color which represents the end point. In t i t r a t i n g a blank solution of water phase, one drop of sodium hydroxide solution turned the color of the blank considerably darker than that reached at the end point of the samples. As a result, no blank correction was applied to the measured concentration of the water samples. A similar blank was prepared for the MIBK. It was found that three-or four drops of the sodium hydroxide solution were needed to change the color of the blank solution. Therefore, for each batch of the standard sodium hydroxide solution prepared the amount of the sodium hydroxide solution needed for the blank was determined, and this amount was subtracted from the volume of sodium hydroxide solution used to neutralize the acid in MIBK samples. In studying the possible error incurred in the t i t r a t i o n , ten samples were titrated of the same water phase, and ten samples of the same MIBK phase. The standard deviation of acid concentration measured i n the water phase W8S found to be 0.00003^ lb-mole/ft. and that of MIBK was found to be 0.0000H2 lb-mole/ft. # SDAG - lk is a mixture of 90$ V/V ethanol and 10 V/V methanol. ko b) Methyl Isobutyl Ketone - Sodium Chloride - Water System A Perkin-Elmer Model 303 atomic absorption spectrophotometer with sodium lamp no. 358-H, was used t o measure sodium concentration i n the samples. It has been found (58) that i f a solute i s d i s s o l v e d i n an organic solvent the absorption obtained w i l l be 2 t o 5 times greater than that obtained f o r an aqueous s o l u t i o n of a given element at a same concentration. As a r e s u l t , i n a l l the measurements, MIBK-saturated d i s t i l l e d water was used to prepare the standard sodium chloride s o l u t i o n f o r c a l i b r a t i n g the atomic absorption spectrophotometer f o r the aqueous phase. A l s o , i n d i l u t i n g samples f o r absorption a n a l y s i s MIBK-saturated d i s t i l l e d water was used. For the aqueous phase the c a l i b r a t i n g l i n e r e l a t i n g absorbances to concentration was found t o be s t r a i g h t . Absorbance i s defined as f o l l o w s . Absorbance = Log-^Q ( ) 1-Absorption The equation f o r t h i s l i n e was c a l c u l a t e d by the method of l e a s t squares. B r i t i s h Drug Houses supplied standard sodium chloride s o l u t i o n (N/lO) was used to prepare various concentrations of sodium c h l o r i d e needed to e s t a b l i s h the c a l i b r a t i n g l i n e . The use o f t h i s standard s o l u t i o n was checked by comparing the c a l i b r a t i n g l i n e produced by using i t with the c a l i b r a t i n g l i n e obtained by using the sodium standard (1000 ppm.) e s p e c i a l l y prepared and standardized by Harleco f o r use i n atomic absorption spectrophotometer techniques. I t was found that they both gave p r a c t i c a l l y the same c a l i b r a t i n g l i n e . Each sample whose concentration was higher than k ppm. was d i l u t e d with MIBK-saturated d i s t i l l e d water t o the c a l i b r a t i n g range. Samples of concentration l e s s than 0.05 ppm. were discarded on the grounds of u n r e l i a b i l i t y . There i s no standard sodium ch l o r i d e i n MIBK s o l u t i o n a v a i l a b l e ; t h e r e f o r e , a c a l i b r a t i o n curve f o r absorption of sodium i n the MIBK phase was determined i n the following way. Six mixtures, each of 8bout 20 ml. d i s t i l l e d water and 200 ml. t e c h n i c a l grade MIBK were prepared i n 250 ml. c o n i c a l f l a s k s . A s u i t a b l e amount of a c e t i c a c i d and sodium ch l o r i d e were added i n t o each f l a s k . The mixtures then were shaken vi g o r o u s l y and l e t stand f o r sev e r a l days. Then the absorption of sodium i n the MIBK phase f o r each o f the mixtures prepared was measured by means o f the Perkin-Elmer 303 atomic absorption spectrophotometer. Next 10 ml. of the MIBK phase from each of the c o n i c a l f l a s k s was pi p e t t e d i n t o a d i f f e r e n t 50 ml. beaker. A l l the beakers were put i n t o a fume hood and the MIBK was evaporated away by a i r currents at room temperature. A f t e r a l l the l i q u i d (MIBK plus d i s s o l v e d water) i n the beakers had been evaporated, 10 ml. of MIBK-saturated d i s t i l l e d water was added i n t o each beaker. The concentration of NaCl i n the r e s u l t i n g aqueous s o l u t i o n i n each beaker was measured f o r sodium by means of the Perkin-Elmer 303 atomic absorption spectrophotometer. Now, the NaCl concentration i n the MIBK phase was equal to the NaCl concentration i n the corresponding aqueous phase prepared as above(it was assumed that the volume of aqueous sodium ch l o r i d e s o l u t i o n was equal to the volume of MIBK-saturated water added. This c e r t a i n l y should be true at the very low sodium chloride concentration i n v o l v e d — u p to Itppra.). The NaCl concentration i n the aqueous phase could be cal c u l a t e d from the c a l i b r a t i o n curve f o r aqueous phase prepared f o r use with the Perkin-Elmer 303 atomic absorption spectrophotometer. Therefore, the NaCl concentrations i n the s i x mixtures prepared above were known. By com-b i n a t i o n with t h e i r corresponding absorptions measured i n water-saturated MIBK, the c a l i b r a t i o n curve f o r the absorption of sodium i n the MIBK phase could be obtained, c) Methyl Isobutyl Ketone - Sodium Chloride - A c e t i c A c i d - Water System S o l u b i l i t y of MIBK i n water increases with i n c r e a s i n g concentration of 8cetic a c i d i n the water phase. It was found th a t , because o f t h i s e f f e c t , the absorption increased s l i g h t l y with i n c r e a s i n g a c e t i c a c i d concentration i n the s o l u t i o n , f o r a given sodium chloride concentration i n the water phase. This increase i n the absorption was studied at various l e v e l s of sodium ch l o r i d e and a c e t i c a c i d concentrations (see t a b l e 7). The r e s u l t s are given i n t a b l e 7. The c o r r e c t i o n f a c t o r , reduced absorbance, of the sample saturated with MIBK at p a r t i c u l a r a c e t i c a c i d concentrations was defined as; the absorbance of that sample over the absorbance of sample saturated with MIBK, and having the same sodium chloride concentration but without a c e t i c a c i d . Reduced absorbance defined i n t h i s way f o r samples saturated with MIBK i s always equal to or greater than one. As ta b l e 7 shows, t h i s reduced absorbance depends on the concentration of the 8 c e t i c a c i d i n the sample, but shows l i t t l e or no dependence on the sodium chlo r i d e concentration. It was found that the r e s u l t s could be corr e l a t e d by the l e a s t squares method to give the following equation (for Reduced Absorbance ^ l ) Reduced Absorbance = 1.000 + 3.58 C c - 63.23 C c + 503.15 5 In a l l measurements of the sodium chloride concentration i n undiluted samples containing a c e t i c a c i d , the absorbance of sodium was divided by the corresponding reduced absorbance ca l c u l a t e d from the above equation. However, no correction was made i n the case of a sample which had been d i l u t e d , since the a d d i t i o n of MIBK-saturated d i s t i l l e d water would r e s u l t i n lowering of the a c e t i c a c i d concentrations t o a very low value, therefore the MIBK concentrations to a value approaching what i t would be without a c e t i c a c i d present. TABLE 7. ATOMIC ABSORPTION MEASUREMENTS FOR DIFFERENT CONCENTRATIONS OF SODIUM CHLORIDE AND ACETIC ACID IN MIBK-SATURATED DISTILLED WATER SOLUTION CONCENTRATION % ABSORPTION OF SAMPLES AVERAGE VALUES REDUCED GROUP NO. HAc, LB-MOLE/FT. NaCl, SAMPLE SAMPLE SAMPLE & N X IO 4 NO. 1 NO. 2 NO. 3 P ABSORBANCE ABSORBANCE X IO 3 ABSORPTION 1 a 0.00 0.2 18.0 17.8 17.8 17.8 0.0859 0.8601+ 2 b 0.00 0.2 20.5 20.5 20.5 20.5 O.O996 1.0000 3 b 12 .1+9 0.2 21.2 21.2 20.5 21.0 0.1021* 1.0281 1* b 31.h6 0.2 21.8 22.0 21.5 21.8 0.1068 1.0723 5 b 7*+.92 0.2 22.1* 22.8 22.8 22.7 0.1118 1.1225 6 a 0.00 0.1* 30.8 31.8 30.8 31.1 0.l6l8 0.8708 7 b 0.00 0.1* 35.1 35.3 35.0 35.1 O.I878 1.0000 8 b 12.1*9 0.1* 35.6 37.0 35.5 36.0 0.1938 1.0319 9 b 37.1*6 0.1* 37.7 37.0 1.k 37.1+ 0.2031* 1.0831 10 b 7* .92 0.1* 39.0 39.1 39.0 39.0 0.211+7 1.1+32 11 a 0.00 1.0 62.5 62.1 61.5 62.0 0.1*202 0.9292 12 b 0.00 1.0 61* .6 61* .9 61* .7 61* .7 0.1*522 1.0000 13 b 12 .1*9 1.0 66.3 66.1* 66.1* 66.1* 0.1*737 1.01+75 lU b 37. ke 1.0 67.5 67.3 67.lt 67.1* 0.1*868 1.0765 15 b Ik.92 1.0 69.O 68.9 68.7 68.9 0.5072 1.1216 16 a 0.00 2.0 82.0 8l.l* 81.5 81.6 0.7352 0.8955 17 b 0.00 2.0 85.O 81* .9 81* .9 81* .9 0.8210 1.0000 18 b 31M 2.0 86.9 86.8 86.8 86.8 0.8791* 1.0711 19 b Ik.92 2.0 88.1 87.8 88.3 88.1 0.92l*5 1.1261 20 a 0.00 0.3 25.2 25.2 O.1262 0.8632 21 b 0.00 0.3 28.6 28.6 0.11+62 1.0000 22 b 25.02 0.3 30.0 30.0 0.151*9 1.0595 23 b 50.52 0.3 30.5 30.5 0.1580 1.0807 4 b 65.23 0.3 31.5 31.5 O.1630 1.111*9 a : No MIBK present. b : Water phase i s saturated with MIBK. I I I . STUDY OF INTERNAL SAMPLING TECHNIQUES The f i r s t part of t h i s study was concerned with the construction of a sampling probe t o permit the withdrawal from the column of dispersed phase, uncontaminated with continuous phase. Such a probe was success-f u l l y constructed. It i s shown i n f i g u r e 6 and has been named the " P l a s t i c Cup Probe". It i s worth mentioning that Letan end Kehat (3l) i n s e r t e d a thermocouple i n t o the centre of a c y l i n d r i c a l polyethylene bead (r e f e r t o f i g u r e l ) t o measure the temperature of dispersed kerosene phase i n a spray column. They suggested that r e p l a c i n g the thermocouple by a hypodermic needle would permit the probe to be used to withdraw samples of dispersed organic phase. However, i t was found that such a probe, as suggested by them, d i d not permit sampling dispersed phase, uncontaminated with continuous phase. The second part of t h i s study consisted of comparing the con-centration p r o f i l e s of the dispersed phase i n the column obtained by means of the p l a s t i c cup probes with those given by the funnel-probe. ( I t w i l l be r e c a l l e d that when the l a t t e r probe i s used, equation 1 must be a p p l i e d , and continuous phase concentrations are needed; these were obtained by means of hypodermic needles.) In a d d i t i o n , i n order to gain more information concerning the samples taken by various kinds of sampling probes, the following experiments were done. Measurements were made of the e f f e c t of sampling rate on the concentrations of the samples obtained by the hook-probe, by the funnel-probe, and by the p l a s t i c cup probes. Furthermore, the concentrations of the dispersed phase were measured at various radius p o s i t i o n s i n the column, a l l at the same distance from the nozzle t i p s . A) EXPERIMENTAL PROCEDURES a) Sampling Technique Studies with the Hook Probe, the Funnel Probe, the Hypodermic Needles, and the P l a s t i c Cup Probes Several p r e l i m i n a r y experiments were done, i n order t o become acquainted with the technique of handling each kind of sampling probe. For the hook and the funnel probes, conservative values of the minimum purging times were found by Henton ( l ) . According t o him, the purging time of these two probes Is r e l a t e d to the sampling rate by the f o l l o w i n g equation. 120 Purging time = 6 Sampling Rate (ml./min.) This equation was used throughout the present experiments, because i n t h i s work and i n that of Henton ( l ) , the same s t a i n l e s s s t e e l hook and funnel probe parts were used, and a l s o , i n both researches, each of the sampling l i n e s leading from the hook and the funnel probes t o the respective rotameters consisted of piece of 3 /32-in. I.D. Nylon tubing 27 f t . l ong. The t o t a l i n s i d e volume of each of the hook and the funnel probes ( i n c l u d i n g t h e i r respective sampling l i n e s ) was about 48 ml. Therefore, t h i s means that about 2.5 times the volume of the l i q u i d i n each probe and i t s sampling l i n e s was purged, before the sample was c o l l e c t e d . For the experiments i n t h i s subsection, the sampling rate used with the hook-probe W8S kept constant at 5.2 ml./min. For each run i n t h i s subsection the sampling rate with the funnel-probe was kept constant. (This sampling rate was based on the t o t a l volume of MIBK and water i n the sample.) However, the sampling rate was s l i g h t l y d i f f e r e n t from run t o run, ranging between 7 ml./min. and 11 ml./min., because i t was very d i f f i c u l t to regain the same rate from run t o run. As shown l a t t e r w i t h i n t h i s range there i s no a f f e c t o f sampling r a t e on the sample concentrations obtained. The rate of sample withdrawal by the hypodermic needles was approximately 1 ml./min., and the purging time used was 1§- rain. These sampling rates and t h i s purging time a l s o were used by Henton ( l ) . The volume of l i q u i d contained w i t h i n the hypodermic needle sampler, i n c l u d i n g the needle, the sampling l i n e , and the sampling valve (see f i g u r e 6), was 8bout 0.35 ml. This means t h 8 t , the volume purged before c o l l e c t i n g the sample, was about k times that the t o t a l volume of the hypodermic needle sampler i n c l u d i n g the parts l i s t e d above. The i n s i d e volume of each p l a s t i c cup probe, i n c l u d i n g the needle, the cup, the sampling l i n e , and the sampling valve was about 0.*t ml. As w i l l be discussed under the heading " Results and Discussion" the optimum sampling rate f o r the p l a s t i c cup probe was found t o be 1 ml./min. This sampling rate with the purging time o f 2 min. was used f o r the d i r e c t runs ( i n which solute was t r a n s f e r r e d from the continuous phase t o the dispersed phase). For the reverse runs ( i n which the solute was t r a n s f e r r e d from the dispersed phase to the continuous phase) the maximum p o s s i b l e sampling rate f o r the dispersed phase sample t o be withdrawn without continuous phase was about 0.3 ml./min. Therefore, f o r the reverse runs, sampling rate of approximately 0.3 ml./rain., and purging time of 6 min. were used. A l l of the experiments were done i n the column shown i n f i g u r e 3, except that run no. 47 was made i n the column shown i n f i g u r e 5. For a l l the runs, except f o r run no. 47, the dispersed phase s u p e r f i c i a l 3 2 v e l o c i t y was 69.0 f t . / h r . f t . For run no. 47, the s u p e r f i c i a l v e l o c i t y 3 2 of the dispersed phase was 73.0 f t . / h r . f t . In order to insure that the column was not operated with e q u i l i b r i u m concentrations of solute i n the two phases where samples were taken, high continuous phase flowrates were used. The s u p e r f i c i a l v e l o c i t y of the continuous phase 3 was maintained constant throughout each run and ranged from 44.7 f t . / h r . f t . t o 91.4 ft-?/hr. f t . In a l l the runs solute was t r a n s f e r r e d from the continuous phase t o the dispersed phase, except f o r runs 5 and 7. In these two the d i r e c t i o n of solute t r a n s f e r was reversed. When these experiments were made, the piston-type sampler was being r e b u i l t and, ther e f o r e , was not a v a i l a b l e . Hence, only the hypodermic needles, p l a s t i c cup probes, hook-probe and funnel-probe could be studied. (Although i n run no. 47 the piston-type sample was a v a i l a b l e , i t was used only f o r holdup measurement). Because of the long sampling and purging times required f o r the hook-probe and f o r the funnel-probe, only four samples were taken i n each run by each o f these sampling probes. Each sample of the four was taken at a d i f f e r e n t distance above the nozzle t i p s . The column was sta r t e d as described under the heading "General Operating Procedure f o r S t a r t i n g Up the Column". A f t e r the column reached steady s t a t e , samples were withdrawn, f i r s t by the hook-probe and by the funnel-probe, then by needles. Throughout the work, samples f o r a run were withdrawn, f i r s t at the lowest sampling p o i n t , then at the second lowest, and so on, the l a s t being taken at the highest sampling p o i n t . This order was used j u s t f o r the sake of e s t a b l i s h i n g a r o u t i n e , since i t has been found by Henton ( l ) that the order of sampling does not a f f e c t the concentration p r o f i l e s obtained f o r e i t h e r phase. In order to minimize the disturbance, when the hook-probe and funnel-probes were used a l l the hypodermic needles were withdrawn t o the column w a l l , and a l s o a l l the p l a s t i c cup probes were drawn as close as p o s s i b l e t o the column w a l l . When the hook-probe and the funnel-probe were r a i s e d from one sampling p o s i t i o n to another sampling p o s i t i o n , there was a l i t t l e disturbance of the i n t e r f a c i a l l e v e l of the phases i n the E l g i n head (indic a t e d by the movement of the instrument chart pen). Therefore, purging f o r the next set of samples was begun only a f t e r the l e v e l had s t a b i l i z e d again(about f i f t e e n minutes). A f t e r the l a s t samples were withdrawn by hook-probe and funnel-probe, these probes were r a i s e d above the i n t e r f a c e at the top of the column. Half an hour was allowed f o r the column to return to the steady state c o n d i t i o n before the lowest p l a s t i c cup probe was used to withdraw a dispersed phase sample. A sample was c o l l e c t e d by means of a p l a s t i c cup probe i n the following manner: A p l a s t i c cup probe sample was taken with the cup f a c i n g downward, and at the centre l i n e of the columnj one probe was used at a time, the other probes being drawn as close as p o s s i b l e to the column w a l l . It should be noted t h a t , during a l l t h i s sampling a l l the hypodermic needles s t i l l remained withdrawn t o the column w a l l . A f t e r the f i n a l p l a s t i c cup probe sample had been c o l l e c t e d , end the probe had been drawn close t o the column w a l l , again h a l f an hour was allowed to pass so ss t o insure that the column had returned t o the steady state condition before the f i r s t hypodermic needle continuous pha sample was taken. The hypodermic needle samples were c o l l e c t e d i n the same manner as that used i n c o l l e c t i n g the p l a s t i c cup probe samples. The needles not i n use again were kept withdrawn to the column w a l l . b) Sampling Rate Studies with the P l a s t i c Cup Probes, the Hook-Probe and the Funnel-Probe The experiments were done under the conditions shown In the fol l o w i n g t a b l e 8 TABLE 8. OPERATING CONDITIONS FOR SAMPLING RATE STUDIES WITH THE PLASTIC CUP PROBES, THE HOOK-PROBE AND THE FUNNEL-PROBE RUN NO. 3 2 FT./(HR. FT.) FT?/(HR. FT?) PROBES UNDER STUDY 8 59.98 68.97 hook-probe, funnel-probe 11 59.98 68.97 funnel-probe 12 kh.50 68.97 p l a s t i c cup probe 30 kQ.ko 36.50 p l a s t i c cup probe Runs no. 8, 11, 12, were done i n the column shown i n f i g u r e 3 > and run no. 30 was done i n the column shown i n f i g u r e 5. Throughout the experiments, care was taken to allow enough purging time before c o l l e c t i n g the samples. For hook-probe and funnel-probe approximately 120 ml. were purged before c o l l e c t i n g the samples, and f o r p l a s t i c cup probes approximately 2 ml. were purged. For hook-probe and funnel-probe, sampling rates were studied only at sampling p o s i t i o n 1. For the p l a s t i c cup probes, sampling rates were studied at sampling p o s i t i o n s 1, and 7 i n run no. 12; and at sampling p o s i t i o n s 1, 5, and 10, i n run no. 30. Hook-probe and funnel-probe were operated together as has been described i n to the preceding subsection on sampling technique studies (subsection a ) . For run no. 11, although no hook-probe samples were c o l l e c t e d , the hook-probe remained i n p o s i t i o n i n the column beside the funnel-probe. A f t e r the column reached steady s t B t e , samples were withdrawn at various rates by means o f the hook-probe and the funnel-probe. For each run, the purging times, the volumes of samples c o l l e c t e d , and the sampling times were recorded. A f t e r the l a s t set of samples had been taken, and the probes had been r a i s e d above the i n t e r f a c e at the top of the column, h a l f an hour was allowed to pass t o insure that the column was at the steady state c o n d i t i o n . Then, samples were withdrawn by p l a s t i c cup probe, and a l s o by hypodermic needle, at sampling point 1, at a rate of 1 ml./min. f o r each probe. For the p l a s t i c cup probe sampling rate study, the samples were c o l l e c t e d i n the same manner as has been described i n subsection 8 . At each sampling p o i n t , many samples were taken, one at a time, and a l l at d i f f e r e n t r a t e s . For each sample, the purging time, the volume of sample c o l l e c t e d , and the length of time over which t h i s volume was c o l l e c t e d were recorded. A f t e r a l l the p l a s t i c cup probe samples had been obtained hypodermic needle samples were taken, one at each sampling point at which the p l a s t i c cup probe sampling rate had been studied. The sampling rate of the hypodermic needles was 1 ml./min. c) Concentration P r o f i l e s of the Dispersed Phase across Column Cross Sections Concentration p r o f i l e s of the dispersed phase at esch o f two cross s e c t i o n s i n the column were measured by withdrawing samples by means of a p l a s t i c cup probe whose e l e v a t i o n above the nozzle t i p was kept constant, but which was placed at various d i s t a n c e s from the centre l i n e o f the column. The samples were withdrawn 8t each sampling p o s i t i o n s t u d i e d , from the l o c a t i o n s shown i n the f o l l o w i n g f i g u r e 10 (to s c a l e ) . FIGURE 10. SAMPLING POSITIONS ACROSS THE CROSS SECTION OF THE COLUMN The experiments were done i n the column shown i n the f i g u r e 5. Four runs were made. These covered the ranges of the dispersed phase and continuous phase s u p e r f i c i a l v e l o c i t i e s used i n the a x i a l d i s p e r s i o n c o e f f i c i e n t s t u dies. The conditions of the runs are shown i n the fol l o w i n g t a b l e 9. TABLE 9. OPERATING CONDITIONS FOR STUDY OF THE CONCENTRATION PROFILES OF THE DISPERSED PHASE ACROSS COLUMN CROSS SECTIONS RUN NO. FT?/(HR. FT?) 3 2 FT./(HR. FT.) 30 1+8.40 36.50 44 18.20 36.50 45 18.20 72.99 1+6 1+8.40 72.99 For each run, concentration p r o f i l e s f o r the dispersed phase were measured only at sampling p o s i t i o n s 1, and 8. Throughout these experiments of ( c ) , a sampling rate of 1 ml./min., and a purging time of 2 min. were used. A f t e r the column had reached steady s t a t e , dispersed phase samples were taken by means of a p l a s t i c cup probe at sampling p o s i t i o n 1, from the fol l o w i n g l o c a t i o n s shown i n f i g u r e 10: a, e, g, f , b, d, c, and h. (The sample from a was taken f i r s t , then the one from e, and so on down the l i s t ) . Then, samples were taken at sampling p o s i t i o n 8, i n a s i m i l a r manner. In run no. 30, no samples were taken at g, end d. Continuous phase samples were taken at the column centre l i n e i n esch run at sample points 1 and 8. In a d d i t i o n , f o r each run, the continuous phase and the dispersed phase were sampled at the column 5 4 centre l i n e et several other sampling points a l s o . In t h i s way a concentration p r o f i l e f o r each of the phases was obtained over the t e s t s e c t i o n . The dispersed phase samples from these other sampling points were obtained by means of p l a s t i c cup probes using the sampling rate and the purging time given immediately above. The continuous phase samples were withdrawn by the hypodermic needles at a sampling rate of 1 ml ./min. a f t e r a purging time of 1-| min. B) RESULTS AND DISCUSSION A probe was s u c c e s s f u l l y constructed to enable withdrawing from the 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 dispersed MIBK phase i n t e r n a l sample uncontaminated with the continuous water phase. As has been mentioned before, t h i s sampling probe (the p l a s t i c cup probe) was made by i n s e r t i n g a 3-in. long, 22-gauge hypodermic needle i n t o an inverted Teflon cup. By means of p l a s t i c cup probes, the concentration p r o f i l e of the dispersed phase i n the column can be measured e a s i l y . Time consumption i s l e s s than when the funnel probe i s used. However, i t was found that the surface of the Teflon cup at the end of the p l a s t i c cup probe apparently was attacked s l i g h t l y by the dispersed MIBK phase trapped i n the cup. As a r e s u l t , even though the 8ttack was very very slow, i t d i d change gradually the surface of the Te f l o n cup from hydrophobic to h y d r o p h i l i c . As a consequence of t h i s change, the maximum rate at which the dispersed phase could be withdrawn without being contaminated with the continuous phase was decreased slowly as the age of the p l a s t i c cup probe increased. The problem was overcome simply by r e p l a c i n g the Teflon cup a f t e r the probe had been used f o r a few months. Throughout the whole course of the experiments (including those of the a x i a l d i s p e r s i o n c o e f f i c i e n t study), three sets of p l a s t i c cup probes were used. I n i t i a l l y a few runs (runs no. 1, 2 and 3) were made i n order to become f a m i l i a r with the techniques of handling the various kinds of sampling probes. Table A - l i n appendix A l i s t s a l l the runs of the sampling technique studies. For each run, the amount of solute t r a n s f e r r e d out of (or i n t o ) the continuous phase, and i n t o (or out of) the dispersed phase were c a l c u l a t e d . The percentage d i f f e r e n c e between these two q u a n t i t i e s a l s o was c a l c u l a t e d . In a d d i t i o n , the amount of solute i n t o and out of the column due to the continuous phase and the dispersed phase flows, and the percentage d i f f e r e n c e between the solute i n and the solute out a l s o were c a l c u l a t e d . A l l these values are l i s t e d i n table A - l . Data f o r the d i s t r i b u t i o n of solute (HAc) between water-saturated MIBK, and MIBK-saturated water, 8t e q u i l i b r i u m , were taken from pre-vious work (Henton ( l ) , Ewanchyna (56), and Fleming and Johnson (59)), and a l s o from the present author's experimental measurements. The l i b r a r y computer program 'OLQF' (least squares f i t to polynomials i n one v a r i a b l e using orthogonal polynomials) was used to f i n d the best f i t t e d polynomial to a l l the e q u i l i b r i u m data . The r e s u l t i n g equation f o l l o w s : c j = o.oooii*oU + 2.(M86 C D - 5.838 7 Equation 7 was used to c a l c u l a t e the concentration of a con-tinuous phase (or of a dispersed phase) In eq u i l i b r i u m with a known dispersed phase (or continuous phase) concentration w i t h i n the column. It i s important f o r the column to be operated i n such a way that the phases within the column are f a r away from e q u i l i b r i u m , because, the fur t h e r the two phases i n contact are away from the e q u i l i b r i u m , the bette r the run C8n be used f o r the comparison of various sampling techniques. I f the phases are et or near e q u i l i b r i u m there w i l l tend t o be l i t t l e or no concentration gradient i n the continuous phase near the drops. Throughout the work, the percentage by which the continuous phase and the dispersed phase concentration i n the column were away from the respective e q u i l i b r i u m values, were calculated by the following equations. For the continuous phase concentration C - C % away from the eq u i l i b r i u m value = -5 £ X 100 8a For the dispersed phase concentration io away from the e q u i l i b r i u m value D D X 100 8b As a preparation f o r the di s c u s s i o n of the r e s u l t s of the» measurement of dispersed phase concentration p r o f i l e s across the cross section of the column, and t o make the accuracy of various sampling techniques more obvious, some important papers on the flow patterns r e s u l t i n g from the movement of drops or of spheres through f l u i d s w i l l now be reviewed b r i e f l y . Denbigh, Dombrowski, K i s i e l , and Place (6o), i n 19^2, photographed the wake downstream from a sphere i n a moving f l u i d . They showed that over a considerable f r a c t i o n of the wake close behind the sphere, the residence time was greater than i n the outer parts of the wakes. Hendrix, Shashikant, and Johnson (6l) measured the volumes of the o r i g i n a l material i n wake of s i n g l e organic drops t r a n s l a t e d when they r i s e through quiescent aqueous media, and found that the volumes t r a n s l a t e d were nearly independent of distance t r a v e l l e d f o r n o n - o s c i l l a t i n g drops, and decreased r a p i d l y with distance t r a v e l l e d f o r o s c i l l a t i n g drops. With reference to t h e i r f i g u r e k (volume t r a n s l a t e d i n drop wake as a f u n c t i o n of drop diameter) f o r the system: MIBK dispersed i n water, at the average drop diameter of 0.135-in. (as i n our spray column), the drops o s c i l l a t e d while r i s i n g through the continuous phase. This phenomenon also i s observed i n our column. Letan and Kehat (32, 33) i n studying spray column heat exchangers, showed that the main mechanism of bsck mixing i s transport i n drop wakes, and they suggested that at what they c a l l low dispersed phase holdup (up t o lh%), the volume of the wake i s equal to the volume of drop (36). According to t h e i r suggestion, then, the wakes of drops i n the pre-sent column, and those of the drops of Henton's ( l ) sampling technique study, can be considered as equal t o the volumes of the drops with which they are associated. Now, the r e s u l t s of both the sampling rate study, and the measurement of dispersed phase concentration p r o f i l e s across a c r o s s - s e c t i o n , are important considerations i n the work i n v o l v i n g various kinds of sampling probes. Therefore, the r e s u l t s of the sampling rate studies, and of the measurement of the dispersed phase concentration p r o f i l e s across column cross-sections w i l l be d i s -cussed before the r e s u l t s of the experiments i n which various sampling techniques are compared. 58 a) Sampling Rate Studies with the Hook-Probe, the Funnel-Probe, and the P l a s t i c Cup Probes The e f f e c t of varying the sampling rate on the concentrations o f the samples withdrawn by the p l a s t i c cup probes, by the hook and by the funnel probes, are summarized i n tables A-2, A-3, A-4, snd A-5 i n appendix A. These r e s u l t s are shown g r a p h i c a l l y i n f i g u r e s 11, 12, 13 and ik. The sampling rates used with the p l a s t i c cup probes ranged from 0.05 ml./min. up to 12 ml./min. A few of the samples were contaminated with small amount of the continuous phase. Since there was so l i t t l e continuous phase present i t wss impossible to correct the measured d i s -persed phase concentration f o r the presence of t h i s small amount of con-tinuous phase m a t e r i a l . Therefore, these samples were not used to study the e f f e c t of sampling rate on the concentration of the samplesj instead they were used to locate the maximum poss i b l e sampling rate at which the dispersed phase sample could be withdrawn uncontaminsted with the continuous phase. However, i n the case of those which contained measur-able amounts of the continuous phase, equation 1 was used t o ca l c u l a t e the dispersed phase concentrations at the time of sampling. In t h i s case, the continuous phase concentrations were provided by the hypodermic needle samples. It was found that the maximum sampling rate at which the dispersed phase sample could be withdrawn uncontaminated with the con-tinuous phase depended on the "age" of the p l a s t i c cup probe used but di d not depend on the height of the sampling point 8bove the nozzle t i p s . Figures 11, and 12, show that i f the sampling rates used with the p l a s t i c cup probes were lower th8n 0.8 ml./min., the concentrations of the dispersed phase samples increased with decreasing sampling rate. This result may indicate that there was solute transfer from the continuous phase to the dispersed phase trapped in the Teflon cup of the probe, before the dispersed phase could be withdrawn. On the other hand, the concentrations of the dispersed phase samples remain more or less constant, when the sampling rates used with the plastic cups are between0.8 ml./min., and the maximum rate of sampling for which the sample withdrawn is uncontaminated with the continuous phase. In other words, over this range the variation of the sampling r8te has no effect on the dispersed phase concentration measured. Furthermore, figures 11 and 12 also show that these concentrations of the dispersed phase are in most cases very close to the dispersed phase concentrations obtained from the plastic cup probe samples at high sampling rates (8t which the samples contained the measurable amounts of the continuous phase) with the assistance of equation 1, and the results of the hypodermic needle samples. From the above results, i t i s very obvious that the rate at which the samples are removed by the plastic cup probe i s very important, since; (i) i f the sample is withdrawn too slowly, MIBK drop "aging" w i l l occur, since a drop can be trapped by the cup and continue to receive solute from the continuous phase giving an incorrect solute concentration on t i t r a t i o n , ( i i ) i f the sample is withdrawn too fast, i t i s impossible to sample the dispersed MIBK phase alone uncontaminated with the continuous phase out of the column. Because of these facts, therefore, i t was desired to use a sampling rate of about 1 ml./min., throughout the experiments, since by using this sampling rate the above two problems could be avoided. 60 21 CO o X CO. u. m O m —i 6 z o o o < X 20 19 16 15 14 13 position 1 o a o 8 O Disp. phase £ j f 2 phases ir sample, cone. calc. by 1 0 0- 1-2 1-6 2-1 8 32 FIGURE 11. EFFECT OF SAMPLING RATE ON THE DISPERSED PHASE CONCENTRATION FOR THE PLASTIC CUP PROBES 6l CO o CO LL LU o CQ 3 0 2 9 ~ 2 8 O 8 2 0 O < 1 9 S a m p l i n g p o s i t i o n 1 0 S a m p l i n g p o s i t i o n 5 o R U N 3 0 O D» SP-3 3 [ 2 p h a s e s 1 o in s a i in s a m p l e , c o n e . c a l c . by e q . 1 0 0 - 4 0 8 SAIt 1-2 1-6 2 0 IL./A 2 * 4 6 * 6 FIGURE 12. EFFECT OF SAMPLING RATE ON THE DISPERSED PHASE CONCENTRATION FOR THE PLASTIC CUP PROBES co 30 o Z LL O 15 O z o o o < A o • 4 -RUN 11 A by hypo, needle O by hook probe CJ) Disp. phase cone, & eq.1 O by plastic cup probe by funnel probe, hypo, needle, 0 4 8 12 16 20 24 28 32 43 SAMPLING RATE ML./MIN. FIGURE 13. EFFECT OF SAMPLING RATE ON CONCENTRATION FOR THE FUNNEL AND FOR THE HOOK PROBES CA ro CO o X L L 19 18 17 ^ 16 O 15 o o o < • RUN 12 • by plastic cup probe Disp. phase cone, by funnel probe, hypo, needle & eq. 1 0 4 8 12 16 20 24 28 32 36 SAMPLING RATE ML./MIN. FIGURE lk. EFFECT OF SAMPLING RATE ON CONCENTRATION FOR THE FUNNEL PROBE ON (JO 6k The purpose of measuring the effect of sampling rate on the con-centrations of the continuous phase obtained was to provide reliable results of the sort Bergeron (23) had attempted to obtained, and at the same time, to ensure that the correct sampling rates were used in the axial dispersion studies. Figure 13 shows that the concentrations of the continuous phase withdrawn by the hook-probe are not affected by the rate of sampling over the range of sampling rates studied. The sampling rates used with the hook-probe in this study ranged from 2.2 ml./min. to 33.8 ml./min. In addition, figures 13 and ik show that the concentrations of the dispersed phase obtained by means of the funnel-probe are not affected by sampling rate between k.3 and 13 ml./min. The above results are consistent with the conclusions of Bergeron (23). If the sampling rates used with the funnel-probe were higher than 13 ml./min., the concentrations obtained for the dispersed phase de-crease s l i g h t l y with increasing rate of sampling. The dispersed phase concentration obtained by the funnel-probe at a sampling rate of 3^ ml./min. i s about 3fo lower than that obtained by the same probe at rates below 13 ml./min. b) Concentration Profiles of the Dispersed Phase across Column Cross Sections Concentrations of dispersed phase were measured at various locations across section each at a fixed distance from the nozzle t i p s . These samples were withdrawn by the pla s t i c cup probes at the positions shown in figure 10. The sampling rates used with the plastic cup probes were about 1 ml./min. and f o r each run, samples at the same el e v a t i o n above the nozzle t i p s were withdrawn at the same r a t e . Therefore, i f there was any e f f e c t of the sampling rate on the dispersed phase concentrations measured, the e f f e c t would be the same for a l l the samples at the same el e v a t i o n i n a given run. In a d d i t i o n , f or each run the concentration p r o f i l e of the dispersed phase was measured (with the p l a s t i c cup probes) along the center l i n e of the t e s t s e c t i o n of the column. A l s o , the concentrations of the con-tinuous phase were measured at the center l i n e of the column f o r the sampling p o s i t i o n s at which the c r o s s - s e c t i o n a l concentration p r o f i l e s of the dispersed phase were studied, and a l s o i n two of the runs, at sampling p o s i t i o n 5 (see t a b l e A-6). The r e s u l t s of a l l the runs are summarized i n t a b l e A-6 i n appendix A. Figures 15 8nd l6 show the r e s u l t s f o r two t y p i c a l runs g r a p h i c a l l y . With reference t o f i g u r e s 15 and l6, the c r o s s - s e c t i o n a l concentration p r o f i l e s of the dispersed phase were not f l a t , but instead were s l i g h t l y concave upward. However, they are p r a c t i c a l l y symmetrical about the column centre l i n e . These r e s u l t s were true generally over the ranges of t h i s part o f the..investigation. For each sampling e l e v a t i o n , the concentrations of the samples at the same distance away from the column centre l i n e were averaged. Three average concentrations were obtained: Ci» ^2> ^3' T h e s e a P P l y r e s p e c t i v e l y at the centre of the column, 13/32 inches and 5/8 inches away from the column centre l i n e . The percentage d i f f e r e n c e s between C2 and C^, 8nd between C3 and C i were c a l c u l a t e d . The concentration p r o f i l e s of the dispersed phase measured along the t e s t s e c t i o n were used to provide the gradient of a x i a l concentration at each sampling p o s i t i o n . For each run, and each 22 C O o X 20 c o _ . A 18 c o 16 o 14 o o < 12 T — r * i -O - Q - - 0 - - O POSITION 8 o o RUN 45 POSITION 1 - o O - Q - O °"-O" Points, a, e, g, f, in fig.10 "O Points, b, c, d, h, in fig.10 -ft-o o o 4-53 FT. o o o -0-75 -0-5 0 0 05 0-75 0 0 02 04 0-6 0-8 1 0 DIST. FROM COLUMN CENTRE, IN. REDUCED HT., Z R F I G U R E 15. D I S P E R S E D P H A S E C O N C E N T R A T I O N S A C R O S S T H E C R O S S S E C T I O N O F T H E C O L U M N A N D A L O N G T H E T E S T S E C T I O N ON % 1 6 X ^ 14 L L LU O 12 r 1 0 O O 8 O < IE .-o-O o -0-°" °o POSITION 8 RUN 46 o o o o POSITION 1 l _ - ° - o o ~ o O- Points, a, e, g, f, in fig. 10 ~ 0 Points, b, c, d,h, in fig. 10 « 4 5 3 FT. -0-75 -0-5 0 0 0-5 0-75 0 0 0-2 0-4 0-6 0-8 1 0 DIST. FROM COLUMN CENTRE, IN. REDUCED H T . , Z R FIGURE 16'. DISPERSED PHASE CONCENTRATIONS ACROSS THE CROSS SECTION OF THE COLUMN AND ALONG THE TEST SECTION ON 68 sampling e l e v a t i o n , the d i f f e r e n c e between C 2 and C^, and and were di v i d e d by t h e i r respective dispersed phase concentration g r a d i e n t s . The r e s u l t s obtained are the heights, , i n inches above the sampling e l e v a t i o n , at which the concentration of the dispersed phase at the column centre l i n e i s equal t o the dispersed phase concentration measured 8t 13/32 inches and 5/8 inches r e s p e c t i v e l y away from the column centre l i n e i n the r a d i a l d i r e c t i o n . The values of C^, C^, C^, the d i f f e r e n c e between and C-^  ( C 2 1 ) , and between and (C31), the percentage d i f f e r e n c e between C 2 and C-p and and C^, and a l s o the corresponding to C 2^ and are l i s t e d i n t a b l e 1 0 . The r e s u l t s show that f o r each run the percentage d i f f e r e n c e s between C 2 and are smaller than those between and The percentage d i f f e r e n c e between C 2 and C-^  i s about 1%, and that between C3 and about 3 $ . S i m i l a r l y , the Hp values corresponding to C 2 are smaller than corresponding t o C 3 . In a d d i t i o n to t h i s , except f o r run 3 0 , the value of Hp i s l a r g e r at sampling point 8 than i t i s at sampling point 1 . It should be noted that sampling point 8 i s higher above the nozzle t i p s than i s sampling point 1 . This means that the concentration d i f f e r e n c e across a cro s s - s e c t i o n increases with i n c r e a s i n g height above the nozzle t i p s . Results obtained above seem to bear no p a r t i c u l a r r e l a t i o n s h i p to the s u p e r f i c i a l v e l o c i t i e s of the phases, at l e a s t over the range of flowrates i n v e s t i g a t e d . The c r o s s - s e c t i o n a l concentration p r o f i l e s of the continuous phase were measured by Hawrelak ( 2 2 ) . He found them t o be e s s e n t i a l l y f l a t . In the present work, however, the c r o s s - s e c t i o n a l concentration p r o f i l e s of the dispersed phase were found to be s l i g h t l y concave upward. The upward concavity of the c r o s s - s e c t i o n a l concentration p r o f i l e s of TABLE 10. DISPERSED PHASE CONCENTRATIONS ACROSS THE CROSS SECTION OF THE COLUMN RUN NO. SUPERFICIAL a VELOCITY FT3/HR. FT? SAMPLING POSITION (SEE FIGURE 5) DISPERSED PHASE CONCENTRATION, LB-MOLE/FT3 X IO 3 = C21 V c i = C 31 % DIFFERENCE HEIGHT, H D, IN. AVER. OF * a, h AVER o OF * b,c,e,f AVER. OF * g, d Sli X 100 c l £32 x 100 C21 -r CONC. + GRADIENT C31 -f CONC. GRADIENT4 C 1 °2 C3 30 1+8.1+0 36.50 1 8 18.90 31.63 19.27 31.89 0.37 0.26 1.96 0.82 0.73 0.62 kk 18.20 72.99 1 8 1+.30 5.58 It.30 5.61* it.35 5.71 0.00 0.06 0.05 0.1k 0.00 1.20 1.09 ' 2.1+9 0.00 1.51 1.90 3.15 1+5 1+8.1+0 72.99 1 8 12.1+3 20.58 12.59 20.70 12.93 21.03 0.1k 0.12 0.50 0.1+5 1.15 0.58 1+.02 2.19 O.69 0.79 2.1+3 3.95 k6 18.20 36.50 1 8 8.26 lit .13 8.38 l i t . 35 8.60 14.65 0.12 0.22 0.31+ 0.52 1.+3 1.5l4 1+.12 3.68 0.91 1.25 2.62 • 2.97 a Upper value i s f o r the continuous phase ; lower value i s f o r the dispersed phase. + 3 Concentration gradient, (lb-mole/ft.)/ inch Sampling p o s i t i o n s r e f e r to fi g u r e 10. TO the dispersed phase most probably i s due to their being different re-sidence times of the drops at a given cross-section of the column. If the drops close to the column wall in average have longer residence times than those close to the column centre l i n e , then the concentration of the drops close to the wall w i l l be higher than that of those close to the column centre l i n e . Although there i s no clear evidence to support the above argument, the following experimental facts may serve as an indication that i t is correct. As the drops rise up the column, the drop velocities increase to the terminal velocities in a short distance of travel above the nozzle tips according to Letan and Kehat (32). Therefore, in the rest of the column a l l the drops are at their terminal ve l o c i t i e s . The terminal velocities of each r i s i n g drop depends on i t s equivalent diameter (62). Strom and Kintner (63) have studied the wall effect for the f a l l of single organic drops through an aqueous phase. They found that for a given equivalent diameter of the organic drop, the terminal velocity of the drop decreases with decreasing column diameter. The decrease in terminal velocity i s greater for larger drops. The same phenomena were found also in the rate of rise of single a i r bubbles in a quiescent l i q u i d by Seije and Kintner (6k). However, there i s no work, so far as can be found, comparing the wall effect on the terminal velocity of drops near the wall with that on the terminal velocity of drops close to the column centre l i n e . Nevertheless i t i s very l i k e l y that the work of Strom and Kintner (63), and that of S e i j i and Kintner (6k) may serve as indications that drops close to the wall w i l l be more or less affected by the presence of the wall, and, as a result, the terminal velocity of a drop is smaller when i t rises close to the column wall, than when i t rises close to the column centre l i n e . Consequently, at a given cross-section i n the column, drops close to the wall w i l l have experienced a longer average residence time than those close to the column centre l i n e . This d i f f e r e n c e w i l l increase with height above the nozzle t i p s , because the drops higher up the column w i l l have been exposed longer to the e f f e c t of the column w a l l . Therefore, the upward concavity of cross-s e c t i o n a l concentration p r o f i l e may be expected to increase with height up the column, at l e a s t f o r constant d r i v i n g force mass t r a n s f e r between the phases (68). The p o s s i b l e explanation of the f l a t c r o s s - s e c t i o n a l concentration p r o f i l e s of the continuous phase may derive from the f a c t that the dispersed phase holdups studied by Hawrelak (22), and a l s o i n the present work, are very low; t h e r e f o r e , the small upward concavity of the dispersed phase c r o s s - s e c t i o n a l concentration p r o f i l e s could, from material balance considerations, only cause a small downward concavity of the c r o s s - s e c t i o n a l concentration p r o f i l e s of the continuous phase. However, the l a t t e r concavity may have been more or l e s s removed f o r the following reason: It has been suggested by Letan and Kehat (22) that the v e l o c i t y p r o f i l e of the continuous phase i s f l a t t e n e d by i n c r e a s i n g the holdup of the dispersed phase i n ' the column. This means th8t the countercurrent flow of the dispersed phase against that of the continuous phase causes mixing within the cont inuou s pha s e. c) Sampling Technique Studies with the Hook-Probe, the Funnel-Probe, the Hypodermic Needles and the P l a s t i c Cup Probes Samples were withdrawn from the operating spray column by the p l a s t i c cup probes, by the hypodermic needles, by the hook-probe and by 72 the funnel-probe along the t e s t s ection of the column, at the sampling points shown i n f i g u r e 3., except i n the esse of run 47. The sampling points f o r run 47 are shown i n f i g u r e 5. Kuns i n which the d i r e c t i o n o f solute t r a n s f e r i s from the continuous phase to the dispersed phase, are c a l l e d the d i r e c t runs. Runs i n which the d i r e c t i o n of solute t r a n s f e r i s the reverse of that just described are c a l l e d reverse runs. Runs 5, and 7 are reverse runs; a l l the others sre d i r e c t . The r e s u l t s of a l l the runs are presented i n Table A-7 i n appendix A. For each run the average concentrations of the dispersed phase and of the continuous phase over the t e s t s e c t i o n of the column were ca l c u l a t e d from the r e s u l t s produced by each kind of sampling probe. The method o f averaging was t o use gr a p h i c a l i n t e g r a t i o n . Concentration p r o f i l e s were p l o t t e d over the t e s t s e c t i o n . The area under each curve was div i d e d by the length of the t e s t s e c t i o n . For s i m p l i c i t y , the f o l l o w i n g notation i s used. For the dispersed phase, C ^ p i s the average concentration over the t e s t s ection of the column given by the p l a s t i c cup probes, and C ^ ^ i s the average concentration given by the funnel-probe and the hypodermic needles with the assistance of the equation 1. C j, i s the average concentration of the dispersed phase i n the funnel-probe sample at the time of a n a l y s i s . For the continuous phase, C ^ Q J J i s the average concentration over the t e s t s e c t i o n of the column given by the hypodermic needles, and C i s the average con-ACH centration given by the hook-probe. The d i f f e r e n c e s between C ^ p and CADFN' 8 n < * between CACH a n c i CACN' 8 r w i c o r r e s P o n d i n S percentage d i f f e r e n c e s a l s o were c a l c u l a t e d f o r each run. In a d d i t i o n , the d e v i a t i o n of the ac t u a l average operating conditions, from average operating conditions i n which the phases wi t h i n the column t e s t section would be i n equ i l i b r i u m , was calculated by equations 8a and 8b f o r the continuous phase and the dispersed phase r e s p e c t i v e l y . Table 11 i s summary of these data f o r the dispersed phase, and Table 12 f o r the continuous phase. The r e s u l t s f o r t y p i c a l runs are shown g r a p h i c a l l y i n f i g u r e s 17, 18 and 19. It i s found t h a t , f o r each run, the dispersed phase concentration p r o f i l e obtained from the samples taken with the p l a s t i c cup probes i s s l i g h t l y d i f f e r e n t from that obtained from the funnel-probe samples with the assistance of the hypodermic needle data and equation 1. For the d i r e c t runs the dispersed phsse concentration p r o f i l e s obtained from the p l a s t i c cup probes are s l i g h t l y higher than are the respective dispersed phase concentration p r o f i l e s obtained by means of the funnel-probe and with the assistance of the hypodermic needle data 8nd equation 1 (See f i g u r e s 17 and i8 . ) On the other hand, f o r the reverse runs, i n order to sample out only dispersed phase,the sampling r a t e used with the p l a s t i c cup probes had to be r e s t r i c t e d to about 0.3 ml./min. At t h i s sampling r a t e , the dispersed phase concentration p r o f i l e s obtained are s l i g h t l y lower than those p l o t t e d from the funnel-probe r e s u l t s based on hypodermic needle samples and equation 1. (See f i g u r e 19.) For the d i r e c t runs, C values are about 0.6$ higher (except f o r run 6, where C i s 1.42$ h i g h e r . ) , then C values. For the ADP ' ADFN reverse runs C values are about 2$ lower than the values of ADP °ADFN. The s l i g h t l y lower C.^ values as compared with those of the ADFN C A T V p values f o r the d i r e c t runs may be due to the fo l l o w i n g reasons: 3 9 -co o LL O O o < 20 8 18 16 A 0 0 0 Q ° 9 Aq. phase cone, by hook probe ( j ) Aq. phase corse, by hypo, needle O Disp. phase cone, by plastic cup probe Q Dasp. phase cone, by funnel probe, hypo. needle, &eq.1 l I I i J  25 35 45 55 65 75 HT. ABOVE NOZZLE TIPS, FIGURE IT. SAMPLING TECHNIQUE STUDIES WITH THE PLASTIC CUP PROBES, THE HYPODERMIC NEEDLES, THE FUNNEL PROBE, AND THE HOOK PROBE 75 38 % 36 i)- 32 U J 03 ^8 O O 16 O O 14 < x 12 0 0 Q Q Q RUN 6 (I) Aq. phase cone. (P Aq. phase cone O Disp. phase cone, by plastic cup probe Q Dssp. phase cone, by funnel probe, needle & eq.1 25 35 45 55 65 75 FIGURE 18. SAMPLING TECHNIQUE STUDIES WITH THE PLASTIC CUP PROBES, THE HYPODERMIC NEEDLES, THE FUNNEL PROBE, AND THE HOOK PROBE T A B L E 11. R E S U L T S O 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 : D I S P E R S E D P H A S E C O N C E N T R A T I O N S A V E R A G E D O V E R T H E T E S T S E C T I O N . ( A L L C O N C E N T R A T I O N S I N L B - M O L E / F T 3 X I O 3 ) R U N N O . S U P E R F I C I A L V E L O C I T Y 8 F T 3 / H R . F T ? A V E R A G E C O N C E N T R A T I O N O V E R T E S T S E C T I O N O F T H E C O L U M N C - C A D P A D F N % D I F F E R E N C E , C A D P " C A D F N X 1 Q 0 ° A D F N C * A D % A W A Y F R O M E Q U I L I B R I U M . C * - c C A D C A D P X 1 0 0  C AS C A D P ° A D F N C A D F k 52.26 68.26 19.18 19.06 19.25 0.12 0.63 21.30 10.0 + 5 52.26 68.97 11.29 11.1*5 10.82 -0.16 -1.1*3 6.21 -81.8 6 H.50 68.97 lit .81 l*t .60 l*t .92 0.21 1.1*2 17.20 13.9 + 7 kk.50 68.97 15.22 15.56 lit .58 -0.3U -2.23 9.60 -58.5 9 91.35 68.97 18.39 18.29 l8.1t6 0.10 0.5** 19.19 1*.2 hi kQ.ko 72.99 16.12 16.02 16.39 0.10 0.62 18.50 12.9 C A D F : ^ u n n e ^ - Probe ( at time of a n a l y s i s ) . CADP : B y P l a s" f c i c C U P P robe. ^ADFN: B y funnel probe and hypodermic needle with the assistance of eq. 1. C* : Dispersed phase cone, i n equilibrium with hypodermic needle sample cone. AID Q Upper value i s f o r continuous phase; lower value i s for dispersed phase. + Reverse runs. TABLE 12. RESULTS OF SAMPLING TECHNIQUE STUDIES: CONTINUOUS PHASE CONCENTRATIONS AVERAGE OVER THE TEST SECTION. (ALL CONCENTRATIONS IN LB-MOLE/FT3 X IO 3) RUN NO. SUPERFICIAL VELOCITY 8 FT?/HR. FT? AVERAGE CONCENTRATION OVER TEST SECTION OF THE COLUMN CACN ' CACH % DIFFERENCE, CACH " CACN ^ 1 0 Q C ACN * CAC % AWAY FROM EQUILIBRIUM, C - C* -A 0! AC x 1 0 Q C* CAC C ACN C ACH 4 52.26 68.97 Ul.Ol 41.69 0.68 1.66 37.20 10.2 + 5 52 .26 68.97 13.62 13.02 -0.6o -4.41 22.45 -39.3 6 44.50 68.97 33.23 33.48 0.25 0.75 29.20 13-8 + 7 44.50 68.97 19.77 19.48 -0.39 -2.01 29.95 -34.0 9 91.35 68.97 37.08 37.18 0.11 0.30 35.70 3.9 CACN : ^ y h y P 0 ^ ™ 1 0 needle. CACH : B y n o o l c ~ P r o 1 : , e • * C ^ Q : Continuous phase cone, i n equilibrium with the p l a s t i c cup probe sample cone, a Upper value i s f o r continuous phase; lower value i s f o r dispersed phase. + Reverse runs. 78 2 6 CO o T -2 4 X CO. H 2 2 LL s 2 0 LU O 1 8 CQ 1 6 mJ a O 1 4 Z o o 1 2 o 1 0 < X 8 l I I •9--9-0 -9 - -— 0 -R U N 7 -O Aq. phase cone, by hook probe Aq. phase cone, by hypo, needle O Disp. phase cone, by plastic cup probe O Disp. phase cone, by funnel probe, hypo, needle & eq.1 i i i i i 25 35 45 55 65 75 FIGURE 19. SAMPLING TECHNIQUE STUDIES WITH THE PLASTIC CUP PROBES, THE HYPODERMIC NEEDLES, THE FUNNEL PROBE, AND THE HOOK PROBE In c a l c u l a t i n g the dispersed phase concentration from the funnel-probe equation 1 has been used: °D = °D ~ ( C C - cc ) 1 where C Q was given by the hypodermic needle samples. The volumetric r a t i o of the continuous phase, and the dispersed phase i n the funnel-probe samples at the sampling rate used i s about l / l 2 . I t i s very probable that t h i s small amount of the continuous phase comes from that p o r t i o n of the continuous phase close to the drops. For the d i r e c t runs, the main route of solute t r a n s f e r i s from the bulk continuous phase to the wakes of the drops, and from the wakes of the drops to the drops themselves (33). Of course, there i s 8lso some t r a n s f e r from the bulk of the continuous phase to the drops. The wakes are c a r r i e d up the column from the lower concentration region of the continuous phase by the drops. A l l the 8bove reasoning shows that the concentration of the por t i o n of the continuous phase which comes i n t o the funnel-probe together with the dispersed phase should have, at l e a s t s l i g h t l y lower concentration than the volumetric average concentration of the continuous phase at the point of i n t e r e s t , ( i t has been found by Henton, Hawrelak, Forsyth and Cavers (2*4) for t r a c e r runs with no mass t r a n s f e r that the 8ver8ge solute concentration i n the continuous phase over the p i s t o n height calculated by gr a p h i c a l i n t e g r a t i o n of hypodermic needle r e s u l t s was s l i g h t l y greater than the average solute concentration of the descending continuous phase i n the p i s t o n c a l c u l a t e d by 8n equation s i m i l a r to equation 2, but for the t r a c e r case. This r e s u l t was obtained because the continuous phase 80 concentration so ca l c u l a t e d from the p i s t o n sample excludes the p s r t of the continuous phase concentration contributed by the r i s i n g back flow stream (or wake of the dro p s ) ) . Therefore, i n mass t r a n s f e r runs the continuous phase concentration given by the hypodermic needle sample i s , at le a s t s l i g h t l y higher thsn that p o r t i o n of the continuous phase taken i n t o the funnel-probe sample at the time of sampling. From equation 1, i f a too high value of CQ i s used f o r c a l c u l a t i n g Cp, then the r e s u l t i n g Cp w i l l be too low. However, as has been mentioned above, the r a t i o of V c over V D i s about l / l 2 f o r a l l the funnel-probe samples taken; thus, when the hypodermic needle sample concentration i s used f o r C Q i n equation 1 i n c a l c u l a t i n g the Cj) from a funnel-probe sample, the r e s u l t i n g Cp would be only very s l i g h t l y lower than that obtained when the true C Q i s used f o r c a l c u l a t i o n . Now, the average concentrations of the dispersed phase given by the p l a s t i c cup probe samples are s l i g h t l y higher than those given by the funnel-probe samples with the assistance of the hypodermic needle samples and equation 1. Therefore, i t i s very reasonable t o conclude t h a t , f o r the d i r e c t runs, the p l a s t i c cup probes give r e l i a b l e con-centrations of the dispersed phase. For the reverse runs, the sampling rate used f o r the p l a s t i c cup probe i s about 0.3 ml./min. Figures 11 and 12 suggest that at t h i s sampling rate there i s solute t r a n s f e r between the continuous phase, and the dispersed phase trapped i n the cup of the p l a s t i c cup probe before the sample i s withdrawn from the probe through the hypodermic needle. Because of t h i s the concentrations of the dispersed phase given by the p l a s t i c cup probes f o r the reverse run would be lower than they should be, by a small percentage. Therefore, the dispersed phase concentrations given by the p l a s t i c cup probes f o r the reverse runs are not as r e l i a b l e as those f o r the d i r e c t runs. In the reverse runs the wake concentration would be higher than that of the bulk of the continuous phase. Result would be that the funnel-probe, hypodermic needle and equation 1 r e s u l t s would be too high. Therefore, the true r e s u l t f o r the dispersed phase i n f i g u r e 19 f o r example would seem to l i e somewhere between the two sets of points p l o t t e d f o r the dispersed phase. E v i d e n t l y e i t h e r method of sampling would seem to be quite adequate fo r reverse run s t u d i e s . The concentration p r o f i l e s of the continuous phase obtained by means of the hook-probe 8 r e s l i g h t l y d i f f e r e n t from those obtained by means of the hypodermic needles. For the d i r e c t runs, the concentration p r o f i l e s obtained by the hook-probe are higher than those obtained by the hypodermic needles. In f a c t , the values of C i n average are about 0.9$ higher than those of C._.T. This ACH r e s u l t i s i n agreement with that found by Henton ( l ) . For the reverse runs, the concentration p r o f i l e s obtained by the hook-probe are lower than those obtained by the hypodermic needles. The average values of C A C H a r e about 3.2$ lower than those of C A C N . This i s consistent with the r e s u l t s obtained f o r the d i r e c t runs, i f we consider that for the reverse runs, the r e s u l t s obtained should be reversed. The most l i k e l y reasons f o r the value of C A r l „ being higher ^ A L U than that of the C A„, T f o r each of the d i r e c t runs, and the value ACN ' of C being lower than that of C f o r each of the reverse runs ACH ACN may be as f o l l o w s . The f i r s t reason i s that the hook-probe may tend t o suck i n m a t e r i a l from an e l e v a t i o n higher up the column than the probe's a c t u a l p o s i t i o n . The concentration of the continuous phase increases with height above the nozzle t i p s f o r the d i r e c t runs, and decreases for the reverse runs. Due to the sucking i n of material from an e l e v a t i o n higher up the column, the hook-probe sample then should give a higher concentration f o r a d i r e c t run, and a lower one f o r a reverse run than the true concentration at the e l e v a t i o n of the probe. The second reason i s that the comparatively large s i z e of the hook-probe may d e f l e c t the drops i n such a way that the e x t r a c t i o n i s l e s s complete i n the neighourhood of the hook-probe i n l e t . Therefore, the continuous phase entering the hook-probe would have higher concentration than i t should f o r a d i r e c t run, and a lower concentration f o r a reverse run. With reference t o Table II of Henton, Hawrelak, Forsyth, and Cavers (2*0 , f o r t r a c e r experiments, the average t r a c e r concentrations over the p i s t o n sampler given by hypodermic needle samples, and those given by the hook-probe samples are i n agreement with each other. This shows that the f i r s t suggestion above, that the hook-probe tends to suck i n material from an e l e v a t i o n higher up the column than i t s a c t u a l p o s i t i o n , i s not t r u e . I f i t were t r u e , the average t r a c e r concentrations given by the hook-probe samples would be lower than those given by the hypodermic needle samples. (Tracer concentration i n the column decreases with i n c r e a s i n g height up the column i n the steady state t r a c e r studies r e f e r r e d t o above). Therefore, i t i s reasonable to conclude that the hook-probe gives higher continuous phase concentrations th8n those given by the hypodermic needle samples at the same sampling e l e v a t i o n f o r d i r e c t runs, and lower continuous phase concentrations than those given by the hypodermic 83 needle samples for reverse runs due to the second reason given above: that , because of the comparatively large s i z e of the hook-probe, the drops are d e f l e c t e d by i t i n such a way that e x t r a c t i o n i s l e s s complete i n the neighbourhood of the hook-probe i n l e t . 8l» IV. EFFECT OF INTERPHASE MASS TRANSFER ON THE AXIAL DISPERSION  COEFFICIENT OF THE CONTINUOUS PHASE A) THEORY The diffusion model i s used in the present study to describe the behaviour of the li q u i d - l i q u i d extraction spray column. The assumptions upon which this model is based are summarized below. 1. The operation i s at steady state. 2. Axial dispersion of the continuous phase can be represented by Fick's law of diffusion with the axial dispersion coefficient constant throughout the column. 3. Molecular diffusion and G. I. Taylor's (67) diffusion due to the continuous phase velocity pr o f i l e both are negligible as compared to axial dispersion of the continuous phase brought about by the r i s i n g drops. k. The superficial velocities of each phase, Ln, and L , are constant L D throughout the column. 5. Concentration gradients of each phase i n the r s d i a l direction are negligible. 6. There is no backmiximg of the dispersed phase. The derivation given in the following pages draws heavily upon Henton's work. Figure 20 shows schematically a case on which a solute i s being extracted from the continuous phase into the dispersed phase when the two flow countercurrently through the column. The flux of backmixing solute i s related to the concentration gradient by the 85 C C L D D Z POSITIVE z T dZ L c c c ~ J Z Z + dZ ZONE L c , " J Z+dZ C Q 4- dCQ i — ^  L D ' C D L D ' Cp+dCj C I D FIGURE 20. SCHEMATIC REPRESENTATION OF THE COLUMN AND OF THE CONTROL ZONE FOR SOLUTE MASS BALANCES following equation. d C c J = Ee z dZ The equation of conservation of s o l u t e , f o r a c o n t r o l zone of the continuous phase of dZ thickness, can be w r i t t e n as below f o r u n i t time: Accumulation of solute = (Net increases i n solute due t o the continuous phase flow) - (Net losses o f the solute due to the a x i a l d i spersion) - (Net losses of solute due to mass t r a n s f e r across the i n t e r f a c e ) 10 Because the column i s operated at steady s t a t e , the accumulation of solute i s equal to zero. The other three terms are given by the fol l o w i n g equations. Net losses of solute due to the a x i a l d i s p e r s i o n = - J„ - (- J ) Z Z + dZ d 2C_ = - EeS dZ 11a d z 2 Net losses of solute due to mass t r a n s f e r across the CL, in t e r f a c e = K Da ( — - C n ) SdZ l i b m u 87 Net increases in solute due to dC the continuous phase flow = - LpS dZ 11c ^ dZ The above equations 11a, l i b , and 11c are substituted into equation 10, and the resulting equation is rearranged into the following form: d 2C dC C dZd dZ m We can write a similar equation for the dispersed phase. However, because there i s no axial dispersion in the dispersed phase there i s no term corresponding to the f i r s t term of equation 12. The resulting equation i s as follows. dC C In the present work, the axial dispersion coefficient, E, of the continuous phase, was determined from equation 12 by the following methods. a) Steady State Injection of Tracer Method For the case in which solute i s dissolved only in the continuous phase, equation 12 can be simplified as below: d 2C dC Ee —f- - Ln — = 0 lk d Z 2 c d Z Equation lk r e s u l t s because the concentration of the dispersed phase, Cp, and 8lso K^a, are both zero. Equation lk can be integrated t o : dC Where - J i s the i n t e g r a t i o n constant. P h y s i c a l l y J i s equal t o the net f l u x of solute down the column. I f the t r a c e r s o l u t i o n i s introduced i n t o the column s t e a d i l y and i t s concentration p r o f i l e i n the continuous phase i s measured upstream from the point of i n j e c t i o n , i t s net f l u x down the column w i l l be zero. Let Z be the distance from the tr a c e r i n j e c t i o n p o i n t , measured p o s i t i v e l y upward i n f i g u r e 2 0 . Therefore, Z = H - Z, and dZ = -dZ. Then equation 15 becomes: dC L C = -Ee — £ 16 C C dZ A second i n t e g r a t i o n then i s c a r r i e d out, with the boundary condition C = C at Z = 0 . Equation IT r e s u l t s : I f the d i s p e r s i o n model i s a p p l i c a b l e , equation IT shows ths t a p l o t of ln(C /C ) versus Z w i l l give a s t r a i g h t l i n e with slope equal t o - L c/Ee, which permits the c a l c u l a t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t , E. b) From the Concentration P r o f i l e s of the P a r t i t i o n a b l e Solute i n Both Phases In the l i q u i d - l i q u i d e x t r a c t i o n spray column, i f the con-centration of each phase has been measured, the caps c i t y c o e f f i c i e n t K^a o f the column operation can be evaluated from equation 13. This equation 13 i s rearranged and then integrated as below: H . / ( £ £ - C D ) m where H i s the height of the section of the column i n which Krja Is t o be c a l c u l a t e d . Once K^a i s known equation 12 can be used t o determine the 8xial d i s p e r s i o n c o e f f i c i e n t of the continuous phase i n the column. In applying equation 12, and, indeed, equation 18 i t i s necessary t o have the concentration p r o f i l e of the continuous phase as w e l l as that of the dispersed phase. Three methods were used i n the present work t o c a l c u l a t e E from the p a r t i t i o n a b l e solute concentration p r o f i l e s i n both phases by equations 12, and 18. The f i r s t method assumes that the capacity c o e f f i c i e n t , K^a, and 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, are constant throughout the t e s t section of the column. In order to eliminate the disperse phase concentration, C^, i n equation 12, consider the net f l u x of solute down the column at e l e v a t i o n Z. The f o l l o w i n g equation gives t h i s net f l u x . (The equation should be in t e r p r e t e d with the help of f i g u r e 20.) J = L Q G Q - LQ C ° , d C c - L c c c - E e T T " h C D dZ 19 Let Z = Z R H , where Zp i s the reduced height (refer to t a b l e s 5 and 6) and H i s the height of the t e s t s ection of the column. Then equations 12 and 19 are combined t o eliminate Cp. The f o l l o w i n g equations are obtained. _ ^ _ 2 a — - 0 c c = y 20 where 2 Ee Lp ( L - mL ) K a H 2 P = _ 2 2 — 21b m JK an2 y = _J>— 2ic LpEe Equation 20 has been solved a n a l y t i c a l l y by Henton ( l ) f o r the case /3 £ 0, and ( a 2 + f3) * 0, t o give C c = AexpCX,^) + Bexp(\ 2Z R) - Q 22 A and B are i n t e g r a t i o n constants, and \ ( , \ 2 and Q are given by the following equations. \ 1 = a +y/ a 2 + p 23B X 2 = a - «Ja z + P 23b y Jm Q = - ~ = - 23c B (L - L m) ^ D C Equation 22 can be used t o estimate the a x i a l d i s p e r s i o n c o e f f i c i e n t , E, of the continuous phase, i f A and B are known. In t h i s work a l e a s t squares technique was used t o estimate A and B f o r a given value of E. The axi8l d i s p e r s i o n c o e f f i c i e n t , E, that gives the minimum value of the sum of the squares of the d i f f e r e n c e s between measured concentration p r o f i l e s of the continuous phase and those given by the equation 22 was considered to be the true E of the column. The d e t a i l e d d e s c r i p t i o n of the method can be found i n Henton's t h e s i s ( l ) , as w e l l as i n "RESULTS AND DISCUSSION" of t h i s s e c t i o n and a l s o i n appendix D. The second method of obtaining E from the concentration p r o f i l e s i s by d i r e c t a p p l i c a t i o n of equation 12 without s o l v i n g i t a n a l y t i c a l l y . The t e s t section of the column i s d i v i d e d i n t o several small sections. (The word subsection, which i s used l a t t e r , i s reserved f o r subdivisions of a s e c t i o n as defined here.) Each s e c t i o n used i n t h i s c a l c u l a t i o n included that region of the column from one sampling point t o the next one below: That i s s e c t i o n 1 included the region of the column between sampling points 10 and 9, and section 2 included the region of the column between sampling points 9 and 8, and so on. In a d d i t i o n i t was assumed that K^a, and m are constant f o r each s e c t i o n . Let Z = Z R H as before. Then equation 12 can be w r i t t e n f o r any s e c t i o n , i , as below. L dC C E± = 2k e d 2 C „ H dzg The value of (Kp.a)., ( — ) . , and ( ). can be c a l c u l a t e d T> 'i» MZfl'i' vdZ2 ' i from the concentration p r o f i l e s , and m i s taken t o be the average value of DI i n each s e c t i o n . (The methods of c a l c u l a t i n g Oty&)±, dC d 2 C c ( — - ) . , ( — , and m w i l l be described i n the following "RESULTS d Z R 1 dZg 1 AND DISCUSSION" and a l s o i n appendix D). In short, E ^ can be c a l c u l a t e d . The value of E f o r the continuous phase over the whole i t e s t s e c t i o n i s assumed equal to the a r i t h m e t i c average values of a l l the E 's. The t h i r d method of c a l c u l a t i n g E made use of equation 19, the m a t e r i a l balance of the f l u x down the column. The equation i s w r i t t e n f o r each sampling p o i n t , say j , and rearranged i n the f o l l o w i n g form ( l e t Z = Z H). R where J i s the solute f l u x down the column. For each sampling p o i n t , dC (-r-C-) . i s c a l c u l a t e d at that sampling p o i n t . (The method of c a l c u l a t i n g d Z R J dC ( ~ ) w i l l be described i n the f o l l o w i n g "RESULTS AND DISCUSSION" and dZ„ 1 R a l s o i n appendix D.) Then E_^  can be c a l c u l a t e d . Again i t i s assumed that the E f o r the whole t e s t section i s equal to the a r i t h m e t i c average value of the E 's obtained f o r each sampling point along the t e s t s e c t i o n as described above. B) EXPERIMENTAL PROCEDURES In t h i s laboratory Henton ( l ) has made an extensive study of the a x i a l d i s p e r s i o n c o e f f i c i e n t by the steady state i n j e c t i o n of t r a c e r . Therefore, with considerable background knowledge concerning t h i s method a v a i l a b l e , i t was desired to use the same method to approach the problem of studying the e f f e c t of mass t r a n s f e r on the a x i a l d i s p e r s i o n coefficient. Some of Henton's (l) experiments with the steady state injection of tracer were repeated. In addition other runs were made using similar operation conditions, except that solute of various concentrations was transferred from the continuous phase to the dispersed phase. At the same time the tracer solution was injected steadily. Hence, as described under the heading "THEORY", for runs with no mass transfer E can be calculated from the tracer concentration profile in the continuous phase, and for runs with mass transfer across the phases, E can be calculated, both from the tracer concentration p r o f i l e , and from the partitionable solute concentration profiles in both phases. Therefore, comparison can be made between the E by tracer from a no mass transfer run, with E by tracer from a similar run in which mass transfer i s taking place. Furthermore, the comparison also can be made between E from the partitionable solute concentration p r o f i l e s , with E by tracer in the same run. In this way the effect of mass transfer on E can be studied. The quaternary system MIBK-NaCl-HAc-water was used in this study. MIBK and water are the two immiscible solvents, NaCl i s the tracer, and HAc i s the partitionable solute. This quaternary system can be thought of the combination of two ternary systems: HAc as solute in MIBK-saturated water and water-saturated MIBK; and NaCl as tracer i n MIBK-saturated water and water-saturated MIBK. For the quaternary system to be useful, two important properties are required: f i r s t that the effect of NaCl on the distribution of HAc between the two phases, and second that the effect of HAc on the distribution of NaCl between the phases should be, at least, very small. These two effects were measured before the axial d i s p e r s i o n experiments were done. Other important measures of the behaviour of the system i n the column, such as holdup of the dispersed phase, and the drop siz e d i s t r i b u t i o n of the dispersed phase were measured i n conjunction with the a x i a l d i s p e r s i o n c o e f f i c i e n t s t u d i e s . a) E q u i l i b r i u m D i s t r i b u t i o n of HAc between Water-Saturated MIBK and MIBK-Saturated Water f o r Various Concentrations of HAc and NaCl The d i s t r i b u t i o n c o e f f i c i e n t f o r HAc i n the MIBK-NaCl-HAc-w8ter system was determined as a fun c t i o n of HAc concentration i n the aqueous phase up to 0.068 lb-mole/ft. This work was done f o r three sodium concentration l e v e l s i n the aqueous phase; for a zero concentration of NaCl i n the aqueous phase, and f o r concentrations of 0.01 and 0.1 normal i n that phase. The d i s t r i b u t i o n c o e f f i c i e n t s were determined i n the fol l o w i n g way: 1. Approximately one l i t e r of each of 0.1, and 0.01 normal NaCl stock s o l u t i o n s were prepared. 2. Approximately 20 ml. each of d i s t i l l e d water, or 0.01 normal NaCl s o l u t i o n , or 0.1 normal NaCl s o l u t i o n , and 20 ml. MIBK were pi p e t t e d i n t o a graduated c y l i n d e r . 3. The amount of HAc required to give the desired concentration was added. k. The mixture was allowed to come to equ i l i b r i u m by shaking o c c a s i o n a l l y over 2k hours, 8nd l e t stand f o r several days. 5. 2 ml. of each of the MIBK and the aqueous phase were pipet t e d i n t o 250 ml. c o n i c a l f l a s k s separately, and were t i t r a t e d for HAc concentration by means of the method described under the d i s p e r s i o n experiments were done. Other important measures of the behaviour of the system i n the column, such ss holdup of the dispersed phase, and the drop siz e d i s t r i b u t i o n of the dispersed phase were measured i n conjunction with the a x i a l d i s p e r s i o n c o e f f i c i e n t s t u d i e s . a) Equilibrium D i s t r i b u t i o n of HAc between Water-Saturated MIBK and MIBK-Saturated Water f o r Various Concentrations of HAc and NaCl The d i s t r i b u t i o n c o e f f i c i e n t f o r HAc i n the MIBK-NaCl-HAc-water system was determined as a function of HAc concentration i n the aqueous phase up to 0.068 lb-mole/ft. This work was done f o r three sodium concentration l e v e l s i n the aqueous phase. For a zero concentration of NaCl i n the aqueous phase, and f o r concentrations of 0.01 and 0.1 normal i n that phase. The d i s t r i b u t i o n c o e f f i c i e n t s were determined In the fol l o w i n g way: 1. Approximately one l i t e r of each of 0.1, and 0.01 normal NaCl stock solutions were prepared. 2. Approximately 20 ml. each of d i s t i l l e d water, or 0.01 normal NaCl s o l u t i o n , or 0.1 normal N8C1 s o l u t i o n , and 20 ml. MIBK were pipet t e d i n t o a graduated c y l i n d e r . 3. The amount of HAc required to give the desired concentration was added. k. The mixture was allowed to come to eq u i l i b r i u m by shaking o c c a s i o n a l l y over 2k hours, and l e t stand f o r several days. 5. 2 ml. of each of the MIBK and the aqueous phase were pipet t e d i n t o 250 ml. c o n i c a l f l a s k s separately, and were t i t r a t e d f o r HAc concentration by means of the method described under the heading "ANALYTICAL TECHNIQUE". b) E q u i l i b r i u m D i s t r i b u t i o n of NaCl between Water-Saturated MIBK and MIBK-Saturated Water f o r Various Concentrations of HAc The d i s t r i b u t i o n c o e f f i c i e n t s f o r NaCl i n the MIBK-NaCl-HAc-water system were determined as a f u n c t i o n of HAc concentration i n the aqueous phase. This concentration ranged from 0.0 to 0.068 lb-mole/ft? The solutions prepared i n (a) with NaCl concentration of approximately 0.1 normal i n the aqueous phase were used f o r the measurements. The concentrations of NaCl i n each phase of the mixtures were analyzed f o r sodium by means of a Perkin-Elmer 303 atomic absorption spectrophotometer as described under the heading "ANALYTICAL TECHNIQUES". c) E f f e c t of Interphase Mass Transfer on A x i a l Dispersion C o e f f i c i e n t of the Continuous Phase The experiments were done i n the columns shown i n f i g u r e s k 8 n d 5. The only d i f f e r e n c e between these two column arrangements was t h a t , f o r the one i n f i g u r e it, the piston-type sampler was s i t u a t e d between sampling points 5 and 6, whereas f o r that i n f i g u r e 5, i t was situated between sampling points 9 and 10. By these arrangements the dispersed phase holdup at two points along the t e s t section of the column could be measured. Runs 13 to 21 i n c l u s i v e , except f o r run 20, were performed i n the column as shown i n f i g u r e *t; the other runs were done i n the column as shown i n f i g u r e 5. I t has been shown i n part I I I "STUDY OF INTERNAL SAMPLING TECHNIQUES", that the p l a s t i c cup probes give r e l i a b l e concentration p r o f i l e s of the dispersed phase. Henton ( l ) has shown that hypodermic needles give correct continuous phase concentration p r o f i l e s . Because of these r e s u l t s , and a l s o because both p l a s t i c cup probes and hypodermic needles were l e s s time consuming to use than were hook and funnel probes, throughout these experiments, the p l a s t i c cup probes were used f o r measuring dispersed phase concentration p r o f i l e s , and hypodermic needles f o r continuous phase concentration p r o f i l e s . The sampling rate used f o r both kinds of samplers was 1 ml./min. The columns were operated i n the f o l l o w i n g manner: 1. The column was s t a r t e d up as described under the heading "GENERAL OPERATING PROCEDURE FOR STARTING UP THE COLUMN". 2. The t r a c e r s o l u t i o n (approximately 1 normal NaCl i n MIBK-saturated water) was fed i n t o the column through the t r a c e r d i s t r i b u t o r at approximately 1% of the volumetric flowrate of the continuous phase. 3. A f t e r the column reached steady s t a t e , f o r run 13 t o run 30 i n c l u s i v e , about ten photographs of the drops wi t h i n the column were taken between sampling points J and 8. For run 31 to run 38 i n c l u s i v e , i n order to check the v a r i a t i o n of drop s i z e d i s t r i b u t i o n s along the t e s t s e c t i o n of the column, besides the set of photographs as described above, another set of about ten photographs a l s o was taken between sampling points 3 end k. k. Then ten dispersed phase samples were withdrawn by the pla s t i c cup probes, 8nd also ten continuous phase samples were withdrawn by the hypodermic needles. The samples were withdrawn in the manner as described under the heading "STUDY OF INTERNAL SAMPLING TECHNIQUES". 5. Half hour was allowed after the last hypodermic needle sample was taken. Then three piston samples were taken by the piston-type sampler with an interval of ten minutes between successive samples.* The piston-samples, of course, each contained a continuous phase and a dispersed phase. For each sample the to t a l volume of the sample, and also the volume of the continuous phase and the volume of the dispersed phase were recorded. Samples of each of dispersed and continuous phases feeds and products were collected priodically during the experiments. The room temperature, and the temperature of continuous phase and dispersed phase out of the column were recorded. The concentration of NaCl in aqueous samples, and HAc concentrations i n a l l samples were determined by the methods as described under the heading "ANALYTICAL TECHNIQUES". For runs 3*f, 35, 36, and 37 each product leaving the column was collected over a suitable time interval and weighed. These data, when combined with information with respect to the density of each phase, provide another check on the volumetric flowrates. The density of each phase was measured by means of a Westphal Balance. For runs 3^, 35, 36, and 37 in which no HAc was present, the MIBK product was fed back into the MIBK supply tank, D, (see figure 2) The hole coming into alignment with the column axis contained with d i s t i l l e d water or exit continuous phase. 99 f o r r e c i r c u l a t i o n , and no p l a s t i c cup probe samples were taken. The photographic negatives were examined by the Recordak Model M. P. E. microfilm reader situated i n UBC main l i b r a r y M i c r o f i l m Section. For each set of photographs taken, the drop s i z e s of 500 drops were measured i n the following way: For each set of photographs taken ( i . e . one run), the photographic negatives were selected randomly f o r drop siz e measurements. Enough were so taken that the images of at l e a s t 500 drops were a v a i l a b l e . Then e l l the projected images of the drops within the c e n t r a l UGfo of the column image on each photographic negative selected were traced on graph paper. Their h o r i z o n t a l and v e r t i c a l dimensions were measured ( i n cm.). Where the negatives selected provided more than 500 drops, a l l the drops over part of the area of the f i n a l negative were ignored, whereas a l l the drops i n the remaining area of t h i s f i n a l negative were traced on graph paper and measured. This part of the a r e 8 of the f i n a l t r a c i n g was such that the drop siz e d i s t r i b u t i o n s reported are based on 500 drops. The dimensions of the drop images measured above were corrected fo r o p t i c a l magnification. The magnification f a c t o r was determined i n the f o l l o w i n g wsy: Three column sections(D i n f i g u r e U, and C and G i n f i g u r e 5) were used for photographing the drops. Therefore, the magnification f a c t o r was determined for each s e c t i o n . The space between the Perspex box 8 n d the column was f i l l e d with d i s t i l l e d water. The column se c t i o n was f i l l e d with MIBK-sturated demineralized water. Three c y l i n d r i c a l s t a i n l e s s s t e e l beads of diameter 0 . l 8 5-in. and height 0 . 25 -in. were suspended i n s i d e the column. (Each bead was supported by a glass rod passed through a c y l i n d r i c a l hole whose center l i n e coincided-with the axis of the b e 8 d . ) Figure 21 i s a schematic 100 RUBBER STOPPER SIMPLIFIED BY OMITTING THE PERSPEX BOX FIGURE 21. SCHEMATIC REPRESENTATION OF THE ARRANGEMENT FOR DETERMINATING THE MAGNIFICATION FACTOR representation of the arrangement. The ssme photographic conditions were used for the c a l i b r a t i o n photographs as f o r the photographs taken to determine drop siz e d i s t r i b u t i o n as described on page 29. The images of the beads were measured under the same conditions as described above for the measurement of the images of the drops. From the a c t u a l s i z e of the beads and the siz e of t h e i r respective images, the magnification f a c t o r s were c a l c u l a t e d . For column section D with Perspex box PI, the magnification f a c t o r was a l s o determined f o r the column section f i l l e d with MIBK-saturated demineralized water s o l u t i o n I N i n HAc, and l a t e r with MIBK-saturated demineralized water s o l u t i o n 1 N i n HAc and 0.01 N i n NaCl. It was found that the magnification f a c t o r s were the same as when the column was f i l l e d with MIBK-saturated demineralized water. Column sections C and D which were used with Perspex box PI produced a magnification f a c t o r of 50.6. Column section G, used with Perspex box P2 gave a f a c t o r of ^9.9. C) RESULTS AND DISCUSSION a) J u s t i f i c a t i o n of the Use of the MIBK- NaCl-HAc-Water System l ) D i s t r i b u t i o n C o e f f i c i e n t s of NaCl between Water-Saturated MIBK and MIBK-Saturated Water f o r Various Concentrations of HAc The r e s u l t s of the measurements sre shown i n table B-1 i n appendix B. Figure 22 i s a p l o t 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 s of NaCl between MIBK-saturated d i s t i l l e d water and water-saturated MIBK against the HAc concentrations i n the water phase. The d i s t r i b u t i o n Q 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 H A C C O N C , L B . M O L E / F T . 3 X 1 0 3 FIGURE 22. EQUILIBRIUM DISTRIBUTION OF NaCl BETWEEN WATER-SATURATED MIBK AND MIBK- o r o SATURATED WATER WITH APPROXIMATELY 0.1 N OF NaCl IN THE WATER PHASE c o e f f i c i e n t i s defined as the concentration of NaCl i n the water phase over that i n the MIBK phase. The r e s u l t s show that the d i s t r i b u t i o n c o e f f i c i e n t decreases with in c r e a s i n g HAc concentration In the water phase. When there i s no HAc i n the system 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 shout 1*4,000. The values 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 decrease to about 8,000 as the concentration i n the water phase increases to 0.068 lb-mole/ft. The reason may be the f o l l o w i n g . Consider f i g u r e 23, a phase diagram f o r the system water-HAc-MIBK at 25° C with the data having been taken from Sherwood, Evans and Longcor (65). As the concentration of HAc i n the MIBK phase increases the s o l u b i l i t y of water i n MIBK al s o increases. The increase of the wster concentration i n the MIBK phase means that the p o l a r i t y of MIBK s o l u t i o n i s increased t h e r e f o r e , i t i s reasonable that the amount of NaCl diso l v e d i n the MIBK phase increases with the incr e a s i n g HAc concentration. The present values 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 are l a r g e r than those found by Henton ( l ) . Henton's measured value i s about 7,000 f o r the d i s t r i b u t i o n c o e f f i c i e n t of NaCl between MIBK-saturated water and water-saturated MIBK without HAc present. The d i f f e r e n c e between the two sets of experimental r e s u l t s may be due to the d i f f e r e n t methods employed i n the measurements. Henton's Data Book U, page 12588 shows that Henton measured 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 n the following way: 15 ml. of k N sodium chloride s o l u t i o n was mixed with 90 ml. of MIBK. 80ml. of MIBK was separated from the water phase In a c y l i n d r i c a l separatory funnel a f t e r the mixture had reached e q u i l i b r i u m . The amount of NaCl i n that 80 ml. of MIBK was extracted by 20 ml. of MIBK-saturated d i s t i l l e d water. Then the aqueous extract was analyzed f o r sodium by the Perkin-Elmer 303 105 atomic absorption spectrophotometer ( c a l i b r a t e d with known concentrations of NaCl i n d i s t i l l e d water). The amount of N8C1 i n the 80 ml. of the MIBK phase was taken to be equal to the amount of NaCl i n the 20 ml. water e x t r a c t . Therefore, the concentration of NaCl i n MIBK i n contact with k N sodium chloride s o l u t i o n could be c a l c u l a t e d . Then the d i s t r i b u t i o n c o e f f i c i e n t was c a l c u l a t e d . Because of the great d i f f e r e n c e of NaCl concentration between the water and the MIBK phases, i f a small amount of the o r i g i n a l water s o l u t i o n was removed with the MIBK phase at the f i r s t separation step, a large e r r o r would r e s u l t i n the NaCl concentration measured In the MIBK. Such a small amount of contamination by the water phase might be due to small drops of water phase s t i c k i n g to the w a l l of the c y l i n d r i c a l separatory funnel and these coming out together with the MIBK phase during the f i r s t separation step. Although the d i s t r i b u t i o n c o e f f i c i e n t of NaCl between the two phases does decrease with i n c r e a s i n g HAc concentration i n both phases, wit h i n the range of HAc concentration studied, the values 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 s t i l l are very l a r g e . Therefore, i t i s safe to use NaCl as the t r a c e r f o r the experiments. 2) D i s t r i b u t i o n C o e f f i c i e n t s of HAc between MIBK-Saturated Water and W8ter-Saturated MIBK f o r Various Concentrations of HAc and NaCl Three sets of measurements were made f o r the eq u i l i b r i u m d i s t r i b u t i o n of HAc between MIBK-saturated water and water-saturated MIBK. There was no NaCl present i n the f i r s t s e t . For the second and t h i r d sets the concentrations of NaCl i n the water phase were approximately 0.01 N and 0.1 N r e s p e c t i v e l y . The r e s u l t s are summarized i n tables B-2 and B-3 i n appendix B, and are a l s o shown g r a p h i c a l l y i n f i g u r e 2k. A second order polynomial was used t o f i t the e q u i l i b r i u m data of the f i r s t s e t . The r e s u l t i n g equation i s given below. * 2 C c a 0.0002836 + 2.01751 C p - 6.11123 CJJ 26 Equation 26 was used t o c a l c u l a t e d the HAc concentrations i n the water phase from each of measured dispersed phase concentrations fo r each set of e q u i l i b r i u m data. Then the d i f f e r e n c e between the measured and the calculated HAc concentration i n the water phase was ca l c u l a t e d f o r each i n d i v i d u a l experiment. It was found t h a t , f o r the f i r s t set of data with no NaCl present, the standard d e v i a t i o n i s O.357 X 10 J lb-mole/ft., f o r the second set with 0.01 N sodium chloride i n the water phase, the standard d e v i a t i o n i s 0.622 X 10 o lb-mole/ft., and f o r the t h i r d set with 0.1 N NaCl i n the water phase, -3 3 the standard d e v i a t i o n i s 1.2kk X 10 l b - m o l e / f t . These f i g u r e s show that the standard d e v i a t i o n i s increased with i n c r e a s i n g NaCl concentration i n the water phase. This r e s u l t means that the e q u i l i b r i u m data deviate more from equation 26, with i n c r e a s i n g NaCl concentration i n the water phase. Figure 2k shows that the e f f e c t of NaCl on the HAc d i s t r i b u t i o n between water and MIBK i s t o favor d i s t r i b u t i o n i n t o the MIBK phase. This e f f e c t i s increased with i n c r e a s i n g NaCl concentration i n the water phase. The reason may be t h a t , with more NaCl present, more 107 0 10 20 30 40 HAC CONC. IN MIBK PHASE, C D , LB. MOLE/FT. 3X10 3 FIGURE 2k. EQUILIBRIUM DISTRIBUTION OF HAc BETWEEN WATER-SATURATED MIBK AND MIBK-SATURATED WATER, T = 70 — 70.5 °F NaCl d i s s o l v e s i n the MIBK phase, which then becomes more p o l a r . Therefore, i t would be expected that more HAc would d i s s o l v e In the MIBK phase. However, the e f f e c t of NaCl on the d i s t r i b u t i o n of HAc between the water and MIBK phases i s very small f o r the second set of ex-periments with NaCl 0.01 N i n the water phase. For a l l the a x i a l d i s p e r s i o n runs made with NaCl as t r a c e r , the concentration of NaCl with i n the t e s t section of the column was w e l l below 0.01 N. Therefore, i t was safe t o assume that the e f f e c t of NaCl on the HAc d i s t r i b u t i o n i s n e g l i g i b l e within the range of the a x i a l d i s p e r s i o n experiments. 3) Drop Size D i s t r i b u t i o n s of the Dispersed Phase It has been found by Henton ( l ) that there i s no v e r t i c a l o p t i c a l d i s t o r t i o n of the drops due to the column w a l l i n the photographs taken by the present method. He al s o found that h o r i z o n t a l o p t i c a l d i s t o r t i o n i s independent o f the height of the drops i n the photographic t e s t section of the column, but that the h o r i z o n t a l d i s t o r t i o n i s greater f o r the drops close t o the sides of the photographs than f o r those near the c e n t r a l p o r t i o n of the photographs. He showed that , w i t h i n the k6% c e n t r a l p o r t i o n of the column as i t appears i n the photographs, the h o r i z o n t a l d i s t o r t i o n i s smaller than ± 1%. For each run, i n which the drop s i z e d i s t r i b u t i o n was determined, the h o r i z o n t a l and v e r t i c a l dimensions of the images of 500 drops located w i t h i n t h i s k6% c e n t r a l p o r t i o n were measured. As 109 suggested by Henton ( l ) the h o r i z o n t a l and v e r t i c a l dimensions of the images of the drops were corrected only f o r o p t i c a l magnification and not f o r o p t i c a l d i s t o r t i o n . The drops were assumed t o be oblate spheriods. The f o l l o w i n g equation was used to ca l c u l a t e d the equivalent diameter, d , of the drops, s 3 2 d s = h d p d 27 Where h^ = the v e r t i c a l dimension of the drop image corrected f o r o p t i c a l magnification. p, = the h o r i z o n t a l dimension of the drop image corrected a f o r o p t i c a l magnification. The equivalent drop diameters, d , f a l l between 0.00 and 0.25 i n . The computer program w r i t t e n by Henton ( l ) was used to do the f o l l o w i n g c a l c u l a t i o n s . The program d i v i d e d the range of the drop diameters i n t o increments of 0.01 i n . The percentage of the t o t a l number of drops, and the percentage of t o t a l volume contributed by the drops i n each 0 . 01 -in. s i z e range were ca l c u l a t e d f o r t o t a l of 100, 200, 300, 1+00, and 500 drops. Drop s i z e d i s t r i b u t i o n s were measured at an average distance of 5.l6 f t . above the nozzle t i p s between sampling points 7 and 8 f o r 10 runs. In order to check f o r v a r i a t i o n of drop siz e d i s t r i b u t i o n s along the t e s t section of the column another 500 drops were measured f o r each of runs 31 and 36 by means of photographs taken between sampling points 3 and 1+. These drop s i z e d i s t r i b u t i o n s apply at an average distance of 3.l6 f t . above the nozzle t i p s . The computer output of run 28 i s given i n ta b l e B-1+ i n appendix B. The r e s u l t s of a l l the measurements 8nd 110 c a l c u l a t i o n s are summarized i n tables B-5 end B-6 i n appendix B. The r e s u l t s of four t y p i c a l runs (runs 36, 31, 24, and 28) are given i n t a b l e 13, and shown g r a p h i c a l l y i n f i g u r e s 25, 26, 27, and 28. (These runs and the corresponding f i g u r e s have been arranged i n order of i n c r e a s i n g HAc concentrations i n the continuous phase fed to the column). Each of these runs had the same continuous phase and dispersed phase s u p e r f i c i a l v e l o c i t i e s , but d i f f e r e n t HAc concentrations i n the continuous phase fed to the column. For each run, there are two peaks i n the equivalent diameter on the drop size d i s t r i b u t i o n p l o t . The f i r s t peak i s between 0.01 and 0.05 i n . , and the second peak (except f o r runs 20, 23, end 29) i s between 0.13 and O.lk i n . Tn runs 20 and 23, the second peak i s between 0.12 and 0.13 i n . , and i n run 29 between O.lk and 0.15 i n . Because the volume contributed by the small drops i s n e g l i g i b l e , i n the p l o t s of percentage of t o t a l drop volume against the equivalent drop diameter, there i s only one peak. This corresponds to the peak of the large drops i n the drop si z e d i s t r i b u t i o n p l o t s . The above r e s u l t s are consistent with those o f Henton ( l ) and Rochini (12). For runs 36, 31, 2k, and 28 (see t a b l e 13 and a l s o f i g u r e s 25, 26, 27, and 28), the d i s t r i b u t i o n s o f drop s i z e are p r a c t i c a l l y the same, except the equivalent diameters of drops corresponding t o the peaks f o r the smaller drops are not a l l the same. This i s because f o r the runs with no HAc i n the continuous phase, the con-tinuous phase i n the column i s very c l e a r . However, the continuous phase becomes misty when there i s HAc present i n the continuous phase, and t h i s solute i s being extracted out of the continuous phase. The misting of the continuous phase i s due to separation from the continuous I l l 30 CL g LU Q O Z LL < O g O LU o o H < 10 LL LU o _ o * ~ L U LU O 40 3 Z Q < . GC O y 30 CL co ° x GC r\ 5 ^ - I U J o " H CO i. °-O cc 20 10 RUN 36 0 4 8 12 16 20 X10 2 24 FIGURE 25. DROP S I Z E DISTRIBUTIONS AND DROP VOLUME DISTRIBUTIONS, RUN 36 . ( C Q = 0.000 LB-MOLE/FT 3) 112 C/) CL Q & LL <f o g O LU Z N LL LU o _ c/) X o < o * ~ U J UJ (3 3 Z Q < . cr - J O *4 a. 'co O T -a LU H Z o -I— c/> L L o O g 31 0 4 8 12 16 20 24 EQUIV. DROP DIA., d s , IN.X102 FIGURE 26. DROP SIZE DISTRIBUTIONS AND DROP VOLUME DISTRIBUTIONS, RUN 31 (cj = 0.028 LB-MOLE/FT?) o O H* o UJ s o r3 3^ 3 ro -3 CO H N M O H CO a G 3^ r H . s .00 CO 3 o < o i r j o M CO a •-3 r H CO ro -c-%0F TOTAL DROP VOL. DUE TO DROPS IN EACH SIZE RANGE -»> ro w ^ o o o o m 0 „ < • o 39 0 0 • CJ) 2 S O O ro ro % OF TOTAL NO. OF DROPS IN EACH SIZE RANGE ro co ^ > o o o o z ro T T r o II o o ON. ON I s o M I w ro CD w CO M o h-i co M b2 *J O •9 as . uo co 9 o M CO H •s •-3 M O a CO 5d ro CP %0F TOTAL DROP VOL. DUE TO % OF TOTAL NO. OF DROPS DROPS IN EACH SIZE RANGE IN EACH SIZE RANGE o o o o o O o m A N cz — a 00 o a a > • ro a & z 0) X ro o o ro ro ro o CA) o o 1 1 ] 30 ro oo TABLE 13. DROP SIZE DISTRIBUTIONS AND DROP VOLUME DISTRIBUTIONS (FOR RUNS WITH Lp = 36.5 FT?/HR. FT?, and L c = 36.5 FT?/HR. FT?) % OF DROPS IN GIVEN SIZE RANGE FOR A TOTAL $ OF TOTAL DROP VOLUME CONTRIBUTED BY DROPS IN RANGE OF 500 DROPS. GIVEN SIZE RANGE FOR A TOTAL OF 500 DROPS. OF d s , 24 28a 3 1 a 36a 31b 36b 24a 28a 3l a 368 31b 36b 0.00 - 0.01 0.0 0.0 0.0 0.2 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.01 - 0.02 0.4 1.2 12.4 18.8 11.8 16.8 0.0 0.0 0.1 0.1 0.1 0.1 0.02 - 0.03 12.0 9.0 19.4 25.8 26.2 22.4 0.2 0.1 0.3 0.4 0.4 0.2 0.03 - o.o4 20.0 10.8 16.8 11.0 15.6 10.0 0.7 0.3 0.7 0.5 0.6 0.3 0.04 - 0.05 5.8 7.8 4.0 4.8 7.0 3.8 0.4 0.5 0.4 0.5 0.6 0.2 0.05 - 0.06 4.2 4.4 3.2 2.2 2.6 1.0 0.5 0.5 0.5 o.4 0.5 0.1 0.06 - 0.07 2.4 5.8 1.2 2.2 2.0 0.6 0.5 1.2 0.3 0.7 0.5 0.1 0.07 - 0.08 2.8 2'.4 2.6 0.2 0.6 1.4 1.0 0.8 1.2 0.1 0.3 0.4 0.08 - 0.09 2.4 3.8 1.6 1.2 0.4 0.4 1.2 1.8 1.0 0.8 0.2 0.2 0.09 - 0.10 1.6 2.2 3.0 1.0 1.4 1.4 1.1 1.4 2.6 1.0 1.3 0.8 0.10 - 0.11 3.0 1.8 3.0 0.6 1.8 1.0 2.7 1.6 3.8 0.8 2.2 0.9 0.11 - 0.12 5.4 6.8 5.0 4.4 2.6 1.6 6.3 7.8 8.0 7.9 4.1 1.8 0.12 - 0.13 11.4 15.8 9.0 9.6 7.6 6.6 17.9 23.3 19.0 21.4 15.9 9.7 0.13 - 0.14 15.4 16.0 10.2 11.0 9.6 14.2 30.2 29.4 25.0 30.3 24.6 25.4 0.l4 - 0.15 8.0 7.6 5.0 3.6 4.8 10.0 18.8 17.1 15.2 12.1 15.0 21.8 0.15 - 0.16 2.4 3.2 1.2 0.6 3.2 3.8 6.9 8.8 4.5 2.6 12.0 10.2 0.16 - 0.17 0.8 0.8 0.8 0.6 0.6 1.6 2.8 2.6 3.6 2.9 2.7 5.3 0.17 - 0.18 0.4 0.4 0.4 0.4 0.4 1.0 1.6 1.6 2.2 2.6 2.2 4.0 0.18 - 0.19 0.4 0.0 0.0 0.8 0.8 0.6 2.0 0.0 0.0 5.7 5.1 2.8 0.19 - 0.20 0.2 0.2 0.6 0.6 0.0 0.0 1.1 1.1 4.7 5.1 0.0 0.0 0.20 - 0.21 0.0 0.0 0.0 0.4 0.2 0.4 0.0 0.0 0.0 4.0 1.9 2.7 0.21 - 0.22 0.2 0.0 0.4 0.0 0.2 0.4 1.5 0.0 4.3 0.0 2.2 3.0 0.22 - 0.23 0.0 0.0 0.2 0.0 0.4 0.4 0.0 0.0 2.4 0.0 4.6 3.2 0.23 - 0.24 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.24 - 0.25 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 2.9 0.0 Drop d i s t r i b u t i o n s were measured at an average of 5.l6 f t . above the dispersed phase nozzle t i p s between sampling points 7 and 8. Drop d i s t r i b u t i o n s were measured at an average of 3.l6 f t . above the dispersed phase nozzle t i p s between sampling points 3 and 4. phase of extremely small MIBK d r o p l e t s , because s o l u b i l i t y of MIBK i n the continuous phase decreases with decreasing HAc concentration i n the continuous phase (refer to f i g u r e 23). The misting becomes more serious with i n c r e a s i n g HAc concentration i n the continuous phase. Because of t h i s misting, the small drops of the dispersed phase taken i n the photographs were not clear enough t o permit accurate s i z e measurements. The same phenomenon has been observed by Rocchini (12). However, we sre i n t e r e s t e d r e a l l y only i n the s i z e d i s t r i b u t i o n of the large drops; t h e r e f o r e , the conclusion can be drawn that the presence of HAc, and of NaCl t r a c e r , w i t h i n the concentration range of the present experiments, do not a f f e c t the drop siz e d i s t r i b u t i o n s of the dispersed phase of i n t e r e s t i n t h i s work; those of the larger s i z e drops. F i n a l l y , r e f e r to ta b l e 13 (for runs 31 and 36). E v i d e n t l y the drop s i z e d i s t r i b u t i o n s measured between sampling points 3 and k a l s o have two peaks on the drop siz e d i s t r i b u t i o n p l o t . The equivalent diameters of drops corresponding to these peaks 8re the same as those measured between sampling points 7 and 8, for the corresponding runs (nos. 31 and 36). k) Holdups of the Dispersed Phase Holdups of the dispersed phase were measured f o r a l l the runs i n which measurements were made of a x i a l d i s p e r s i o n c o e f f i c i e n t s . The r e s u l t s are summarized i n table ik. A l l the holdups measured by Henton ( l ) under s i m i l a r operating conditions a l s o are shown i n tab l e lk f o r comparison purposes. It was found that the r e s u l t obtained when a holdup i s measured depends s l i g h t l y on the "sge" of the p i s t o n -type sampler used. In the present instance t h i s observation was made for the runs at the dispersed phase s u p e r f i c i a l v e l o c i t y , L , of 3 2 ^ 36.5 f t . / h r . f t . Figure 29 i s a p l o t of holdup against run number (arranged i n time sequence) f o r these runs. Figure 29 shows t h s t holdup of the dispersed phase was almost constant f o r the f i r s t 12 runs. It then decreased and f i n a l l y become constant again at a s l i g h t l y lower value. This lower holdup i s consistent with that measured by •3 Henton ( l ) under s i m i l a r operating c o n d i t i o n s . For Lp of 72.99 ft./ 2 h r . f t . , the holdups of the dispersed phase measured i n the present work are consistent with those measured by Henton ( l ) f o r s i m i l a r runs. As has been mentioned i n part I I I under the heading "RESULTS AND DISCUSSION" the Teflon p l a s t i c cup probe works w e l l i n sampling the dispersed phase because i t s surface i s wetted by that phase. However, the p l a s t i c surface of t h i s probe changes gradually from hodrophobic t o h y d r o p h i l i c . The p l a s t i c cup probes as they "aged" began t o c o l l e c t water phase along with the dispersed phase i n the sample. The p i s t o n used f o r the holdup measurement i n a l l the present experiments had a polyethylene l i n i n g i n the holes through which the column operated. I n i t i a l l y , the dispersed phase probably wetted the i n s i d e of the hole of the polyethylene p i s t o n , as time passed the polyethylene quite l i k e l y became more h y d r o p h i l i c and the wetting decreased, and, f o r l a t e r runs, i t was wetted by the dispersed phase no more than was the metal p i s t o n of Henton ( l ) . Hence, lower holdups were obtained f o r the l a s t 6 runs of f i g u r e 29. This may be the explanation , then, of the high holdups obtained 5 J I I I I I i i I I i i i i i i i i i i < 1 — X W a QXft LU 2 Lc» FT.3/HR.FT.2 ~~ • LL O 1 6 182 9 27-7 - J o 3 6 - 5 _ o I I I I I I i i 48-4 I I I I I I I I I I I I 17 18 19 21 20 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 RUN NO., ARRANGED IN TIME SEQUENCE FIGURE 29. HOLDUPS OF THE DISPERSED PHASE FOR RUNS WITH L^ = 36.5 FT?/HR„ FT? (ARRANGED IN TIME SEQUENCE). TABLE l 4 . HOLDUPS OF THE DISPERSED PHASE IN THE COLUMN RUN NO. (COLUMN NO. IMMEDIATELY BELOW CORRESPONDS TO COLUMN NO. UNDER HEADING 'HOLDUPS') SUPERFICIAL VELOCITY, FT?/HR. FT? HOLDUPS OF DISP 0 PHASE, % AT VARIOUS CONC. OF HAc IN THE CONT. PHASE FED TO THE COLUMN8 1 2 3 k 5 6* LC L D 1 0.000 2 0.028 3 0.028 4 • 0.042 5 0.066 6* 0.000 34 20 21 25 29 6k 18.20 36.50 2.84b ' 3.19b 3.22° 3.28b 2.90b 2.8d 35 32 17 22 26 63 27.70 36.50 2.8ob 2.78b 3.25c 3.17b 3.l6b 2.8d 36 31 18 24 28 62 36.50 36.50 2.86b 2.99* 3.31° 3.19* 3.17b 2.8d 37 33 19 23 27 30 66 48.40 36.50 2.92b 2.73b 3.18C 3.21b 3.21b 3.06b 2.9d 15 57 18.20 72.99 7.38° 6.7d Ik 38 56 27.70 72.99 6.4ic 7.35b 6.8d -13 136 36.50 72.99 7.23c 7.3d 16 137 48.40 72.99 c 7.52 7.4d The upper number immediately below t h i s heading i n the table corresponds to the column number under heading 'RUN NO.'; the lower number i s the concentration of HAc i n the continuous phase fed t o the column, lb-mole/ft3 Piston sampler at the top of the t e s t section (axis of the p i s t o n sampler 6.18 f t . above nozzle t i p s ) . P i s t o n sampler at the centre of the t e s t section (axis of the p i s t o n sampler 4.l6 f t . above nozzle t i p s ) . P iston sampler at the centre of the t e s t section (axis of the p i s t o n sampler 4.15 f t . above nozzle t i p s ) . A l l runs i n t h i s column were made by Henton ( l ) . 120 for the f i r s t 12 runs shown in figure 29. The volume of a piston-sample i s 117 ml. The average holdup of the dispersed phase for the f i r s t 12 runs with of 36.5 f t ? / 2 hr. f t . i s 3.21$. This i s equivalent to 3.76 ml. of the dispersed phase. For the last 6 runs with of 36.5 ft./hr. f t . the average holdup was 2.82$. This i s equivalent to '3.3 ml. of dispersed phase. The above numerical values show that the volume of the dispersed phase wetting the polyethylene wall of piston hole i s very small (i.e. about 3 2 0.k6 ml.). For the runs at a L equal to 72.99 f t . / h r . f t . the volume of the dispersed phase in the piston sample i s about 8.5 ml. A l l the runs with equal to 72.99 ft./hr. f t . were m8de before those of o o equal to 36.5 ft./hr. f t . , except for run 38 which was made after those of Lp equal to 36.5- Therefore, except for run 38, each of the runs with LQ of 72.99 would be expected to produce a piston sample containing an extra 0.U6 ml. of dispersed phase as a result of using 8 polyethylene instead of a metal wall in the holes d r i l l e d through the piston block. However, an increase of 0.U6 ml. in the volume of the dispersed phase in the piston sample would be much less significant for the higher holdups of the runs 8t equal to 72.99 ft?/hr. ft2. In spite of the above d i f f i c u l t i e s with the piston, the dispersed phase holdups measured as shown in figure 29, s t i l l provide the following valuable information. F i r s t , they show th8t, within the range of the dispersed phase superficial velocity studies, there i s no obvious effect of the continuous phase superficial velocity on the dispersed phase holdup in the column. This i s consistent with the results obtained by Henton ( l ) . Second, they show that the dispersed phase holdup in the column i s not affected by the HAc concentration i n the continuous phase fed i n t o the column. T h i r d , the holdups for the f i r s t 12 runs In f i g u r e 29 are almost the same. Now, f o r runs 17, 18, 19 and 21 the holdups of dispersed phase were measured between sampling points 5 end 6, ( i . e . at k.16 f t . above the nozzle t i p s ) , and f o r the other runs (runs 20, 22, 23, 2k, 25, 26, 27, and 28) were measured between sampling points 9 and 10 ( i . e . 6.18 f t . above nozzle t i p s ) . Therefore, the r e s u l t s of these runs i n d i c a t e that there i s no v a r i a t i o n of holdup of dispersed phase between the two heights given above at the average holdup o f 3.21$ (which appli e s f o r the above 12 r u n s ) . The agreement between the holdups of these runs i s consistent with Letan and Kehat (32) r e s u l t t h a t , f o r a given low dispersed phase s u p e r f i c i a l v e l o c i t y , holdup of the dispersed phase i s constant along the column at the 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 s u p e r f i c i a l v e l o c i t i e s of the continuous phase used i n the present work were considered by them t o be the low s u p e r f i c i a l v e l o c i t i e s . b) A x i a l Dispersion C o e f f i c i e n t from Tracer Measurements The r e s u l t s of part (a) above show that i t i s safe to use the system MIBK-NaCl-HAc-Water to study the e f f e c t of mass t r a n s f e r on the a x i a l d i s p e r s i o n c o e f f i c i e n t . Four preliminary runs (runs 13, lk, 15, and 16) were made to t e s t the a p p l i c a b i l i t y of the system used and the s u i t a b i l i t y of the experimental method. The dispersed phase used was l e f t over from the i n t e r n a l sampling technique study. It therefore contained HAc. It i s very d i f f i c u l t to extract a l l the HAc from the dispersed phases. Therefore, no experiment was made i n t h i s preliminary stage with no HAc t r a n s f e r between the phases, and s u f f i c i e n t HAc con-centration was provided i n the continuous phase i n each of these four runs t o insure that mass t r a n s f e r was from the continuous phase to the dispersed phase. In runs 13 and l4 low l e v e l of HAc con-centration was required i n the continuous phase feed: about 4.3 X 10 lb-mole/ft? In runs 15 8nd 16 t h i s concentration was about 30 X 10~3 3 3 l b - m o l e / f t . The dispersed phase s u p e r f i c i a l v e l o c i t y was 72.99 f t . / h r 2 f t . , and the continuous phase s u p e r f i c i a l v e l o c i t i e s ranged from 18.2 f t ? / n r . f t ? t o 48.8 f t ? / h r . f t ? For each run, the logarithm of the reduced sodium (or sodium c h l o r i d e ) concentration W8S p l o t t e d against the height above the t r a c e r d i s t r i b u t o r . The r e s u l t s were summarized i n ta b l e 15 (below). A s t r a i g h t l i n e was obtained f o r each run i n the p l o t . The a x i a l d i s p e r s i o n c o e f f i c i e n t s estimated are approximately the same f o r a l l the runs, and a l s o are very close to that of run 38 (made under s i m i l a r operating conditions but with no mass t r a n s f e r ) and a l s o t o those obtained by Henton(l), a l s o under s i m i l a r operating conditions but with no mass t r a n s f e r . It W8S found by Henton ( l ) t h 8 t , i n the main, the a x i a l d i s p e r s i o n c o e f f i c i e n t decreases as the dispersed phase s u p e r f i c i a l v e l o c i t y i n c r e a s e s . Consistent with t h i s r e s u l t i s the f a c t that i n the experiments the concentration of sodium tends to be r e l a t i v e l y high throughout t e s t section at low s u p e r f i c i a l v e l o c i t i e s of the dispersed phase. As a r e s u l t , the concentrations of sodium remain at measurable values at a r e l a t i v e l y large number of sampling p o i n t s . For t h i s reason, the dispersed phase s u p e r f i c i a l v e l o c i t y was reduced 3 2 t o 36.5 f t . / h r . f t . f o r the bulk of the experiments. These 123 experiments were made at a l l the pos s i b l e combinations of the following conditions. DISPERSED PHASE SUPER-FICIAL VELOCITY, CONTINUOUS PHASE SUPER-FICIAL VELOCITY, HAc CONC, IN CONT. PHASE FED TO THE COLUMN, 1^, FT?/HR. FT? L . FT?/HR. FT? C' ' cj, LB-MOLE/FT? X I O 3 36.5 18.2 0 27.7 28 36.5 h3 k8.k 66 In a d d i t i o n to the above, run 38 was made. In run 38, L^ was equal to 27.2 f t 3 / h r . f t ? and Lp was equal to 72.99 f t ? / h r . f t ? and there was no mass t r a n s f e r between the phases. For a l l the runs, HAc concentration i n the dispersed phase fed to the column, C*, was made as low as i p o s s i b l e . The values of C^ are l i s t e d i n ta b l e 15. A l l the c a l c u l a t i o n s were performed with the IBM 360/67 e l e c t r o n i c computer. A computer program (given i n appendix C) was wr i t t e n to ca l c u l a t e the fo l l o w i n g q u a n t i t i e s : t r a c e r mass balance, reduced concentration of sodium, a x i a l d i s p e r s i o n c o e f f i c i e n t , and Peclet number. In analyzing f o r sodium the measured absorption was corrected f o r the presence of HAc and extra MIBK i n the water phase due t o the presence of HAc, by d i v i d i n g by the reduced absorption given by equation 5. The Peclet number, Pe, was defined as L„ P e » (J5 + f L ) (% ve l - e ' VE ' * when appropriate; see p. ks 28 Henton ( l ) a l s o used t h i s d e f i n i t i o n . In equation 28, d^ i s the equivalent drop diameter corresponding to the second peak i n the drop s i z e d i s t r i b u t i o n p l o t , e.g. 0.135-in. i n run 2k. The reduced concentration of sodium was ca l c u l a t e d by the following equation. A c t u a l concentration X 1000 Reduced concentration = 29 Concentration i n the continuous phase le a v i n g the column The a c t u a l concentration o f the sodium i n each continuous phase sample i s equal to the concentration of sodium i n the sample minus the concentration of sodium i n the continuous phase fed to the column. This sodium came from the HAc and demineralized water used to prepare the continuous phase. For a l l the experiments made, the sodium concentration i n the continuous phase fed t o the column was l e s s than 0.2 ppm. By means of the reduced concentration given by equation 29, the sodium concentration p r o f i l e s f o r various column operating conditions could be compared. The d e t a i l e d steps of the c a l c u l a t i o n of the d i s p e r s i o n c o e f f i c i e n t , E, were the same as that described by Henton ( l ) , except that Henton d i d not correct f o r the sodium i n the continuous phase fed to the column. Henton d i d not make t h i s c o r r e c t i o n because there was no HAc i n h i s continuous phase, and he used MIBK-saturated demineralized water to prepare the sodium chloride s o l u t i o n s f o r c a l i b r a t i n g the atomic absorption spectrophotometer. The computer output f o r run 28 i s given i n appendix C. The r e s u l t s of a l l the runs are summarized i n table 15. In table 15, the r e s u l t s of Henton's ( l ) experiments under s i m i l a r operating conditions are al s o presented f o r purposes of comparison. The Peclet numbers f o r the present work can be compared with TAPUT 15. RESULTS 07 AXIAL DISPERSION COtTrtCmfT STUDIES Bt TOACEF MEASUREMENTS AVERAGE IMS IDF DIAMETER OF NOZZLE TIPS • 0.10V tN. AVERAGE VELOCITY Of DISPERSED PHASE IN N0Z7.IX TIPS - O. t f F T . / S F C . CCLUMN DIAKTTTF - 1 , * j - T N . CCIUMN HEIGH? (N077.LE TIPS TO INTERFACE) - 1 0 - F T . <* W - H * . (SEE FIGURES *• AND 5 ) . HEIGHT OV THE COLUMN TEST SECTION • UpT. 6 ?/*> -IN. (SEl FIGURES *• AND 5). L C - CONTINUOUS PHASE SUPERFICIAL VELOCITY. F T ? ' H R , FT? LJJ * DISPERSED PHASF SUPERFICIAL VELOCITY, FT?, HI*, FT? Ly • TRACER FEEn SUPERFICIAL VELOCITY. FT^/KP . FT? • Wf CONCENTRATION IN THE CONTINUOUS PHASE FED TO THE COLUMN, LB-MOLE/FT? X 10? r£ - HAC roNcrrrfATioN IN W E nispEssro PKACE FED TO '•HE COLUMN, I B - M O U / F T ? X J O : E - AXIAL DISPERSION CCiPFFICIFNT WITH 9*>i CONFIDENCE LIMITS. F T ? / H R . PP - 9i:KtiV CT SAfPlf CONCENTRATION? USVS F f * KITIMATION OF AXTAL DISPEP.SION COEFTtCrEN?. HOLDUP - VOLUMETRIC yThCtlTTAZZ OP l ISmtSED PHASE IN COLUMN. PE - PECLET NUXrES PASED CN A^. CALCULATED PY F C . ? f l . <Jp - THE EfiUn.rVAlENT DLAKETE-« OF DTSPFRSFJD PHASE CORRESPONDING TO THE SECOND PEA It 171 7HT DROP S17X PrSTRTRUTION PLOT, INCH. rSROP • TRACER FAUNCE APPAPFNT LOSS. CALCULATED BY EO. l«b. AVER. TEMP. - THF AVERAGE OF ROOM TEMPERATURE (SAME AS THE CONTINUOUS PHASE AND DISPERSED PHASE FEED TEMPTRATUHE), DISPERSED PHASE PRODUCT TEMPERATURE AND CONTINUOUS PttfSK PRODUCT TEMPERATURE, ° F . h 4 c REDUCES SODIUM COHCrMTOATrOKS *T 5AKPLIK0 P0IHT8 PP HOIDUP rt C1R0B, NO. 1 TEW. 1 2 3 4 5 6 7 8 9 10 °r 13' 16.50 72.99 0.368 4.34 0.87 0.97 i 1.70 138.05 15.24 2.01 0.36 0.00 0 . 0 0 . 0.00 0.00 0.00 O.OO 4 7.23 1.13 0.79 64 .'4* 27.70 72.99 0.260 4.35 0.B7 9.1.0 1 0.86 293.79 55.1 ' 14 .07 2.83 0.47 0.00 0.00 0.00 0.00 0.00 5 6.41 1.4o 3.89 64 15* 16.20 72.99 0.235 31.26 1.68 11.1.9 2 0.71 418.1k 159.42 65.81 30.75 11.07 4.26 2.17 1.29 0.34 0.13 9 7.38 0.99 -O.67 64 16 18.10 72.99 0.5BA 28.73 2.55 12.71. t 4.31 134.59 13.74 1.23 0.30 0.07 0.06 0.00 0.00 0.02 0.04 4 7.52 0.90 3.03 60 38 27.70 7? .99 0.2S5 O.OC 0.00 12.25 * 0.59 291.67 78.01 20.82 6.09 ?.05 0.59 0.20 0.06 0.01 0.02 7 7.35 0.94 O.38 60 * 18.20 36.50 0.206 0.00 0.00 20.65 1 0.93 627.55 356.78 245.19 152.06 102.26 66.94 34.56 23.99 17.36 9.23 10 2.64 0.71 0.41 68 20 18.20 36.50 o.?ch 2B.79 1.21. 27.13 I 1.10 772.9*' 476.91 334.28 254.70 186.64 116.14 85.19 59.76 44.46 31.61 10 3-19 0.1.8 0.125 -2.10 70 25 18.20 36.50 0.208 1.2.62 6.25 27.67 1 1.1.6 813.38 546.72 350.31 234 . 46 194.32 142.78 95.74 64.42 46.72 35.29 10 3.26 0.46 0.135 -0.11 68 29 19.20 56.50 0.208 66.12 1. .27 25.18 i 1.1.3 666.55 406.63 260.09 186.70 133.19 108.23 66.24 46.45 28.8? 19.94 10 2.90 0.57 0.145 -3.75 £8 35 27.70 36.50 0.265 0.00 0.00 21.57 1 0.93 501.37 252.06 125.38 65.45 37.25 17.05 9.54 • 3.86 2.02 1.49 10 2.60 0.69 0.37 68 32 27.70 36.50 0.285 28.20 l.il ia .55 i 0.1.5 4TS.31 191.27 92.25 39.81 17.90 9.29 3.54 1.96 0.91 o.3e 10 2.78 0.81 1.42 64 22 27.70 36.50 0.285 1.3.66 !• .95 21 .00 1 1.12 540.57 240.13 122.75 57.04 31.51 14.25 7.15 4.69 2.54 1.36 10 3.17 0.01 0.135 1.46 66 26 27.70 36.50 0.285 66.36 2.59 25.60 t 2.1.0 616.09 284 .68 218.01 117.97 82.08 47.78 23.49 16.27 5.35 3-. 34 10 3.16 0.52 0.135 -i.es 68 36 36.50 36.50 0.368 O.OO 0.00 21.99 t 1.10 418.08 219.75 85.02 37.41 13.71 5.01 2.4 3 0.96 0.56 o.ofi 9 2.86 0.67 0.135 0.81 71 31 36.50 36.50 0.363 28.19 4.43 23.1.7 1 2.61 391.74 130.52 52.01 23.66 6.90 3.00 1.19 0.82 0.52 0.31 10 2.99 C.60 0.135 2.73 56 24 36.50 36.50 0.36S 1.2.93 6.28 21".37 t 2.16 526.02 228.03 86.67 32.35 20.74 8.03 2.65 1.31 0.96 0.58 10 3-19 0.55 0.135 0.61 66 28 36.50 36.50 O.368 66.1.8 I. .26 21.99 ± 1.95 300.27 114.11 35.58 15.99 8.24 4.70 1.49 0.53 0.17 0.00 a 3.17 0.61 0.135 -2.26 68 37 48.40 36.50 0.721 0.00 0.00 21.33 I 1.21 297.87 115.14 33.74 7.95 3.00 1.03 0.25 0.05 0.04 0.02 ' 7 2.93 0.6B 0.85 67 33 48.40 36.50 0.721 28.01 2.79 21.0". 2 1.60 225.65 57.53 15.03 4.61 1.31 0.61 0.15 O.05 0.05 0.00 7 2.93 0.74 1.41 70 23 1.6.1.0 36.50 0.721 "3.77 5.11 26.k6 1 5.31. 259.87 44.67 10.38 3.77 2.13 1.11 0.64 0.16 0.12 0.01 8 3-21 0.51 0.125 -* .33 6S 27 48. 40 36.50 0.721 65.76 2.1.3 27.1.3 2 1* .98 215.29 60.67 11.69 3.33 1.79 0.76 0.34 0.19 0.14 0.11 9 3.21 0 .«9 0.135 0.15 64 30 18.1.0 36.50 0.721 69.19 4.05 27. Oil 1 4.85 438.80 142.67 35.69 10.62 3.37 1.17 0.88 0.4] 0.32 0.12 9 3.06 0.52 1.61 60 64* 18.20 36.50 0.200 0.00 0.00 2li.27 t 0.87 574.64 421.40 273.44 1B3.72 122.93 Bo.36 53.39 36.77 28.33 18.32 10 2.8 0.61 - 5 . 5 ! 73 63* 27.70 36.50 0.310 0.00 0.00 22.69 t 0.65 468.70 298.94 154.47 79.92 39.52 20.37 12.03 6.25 3.52 1.65 10 2.8 0.65 1.01 73 62* 36.50 36.50 0.350 0.00 0.00 26.19 t 0.62 466.73 218.69 93.48 55.69 23.24 11.61 5.91 2.83 1.38 0.69 10 2.6 0.57 0.94 12 66* i.e.to 36.50 0.68C 0.00 0.00 27.31 * 1.18 252.25 125.44 37.92 19.so 7.38 2.51 1.28 0.42 0.15 0.04 8 2.9 0.54 1.28 72 P r e l l a l r a r y r u i n . Henton'a ( l ) «xp.*rl>ae.ital reiul*-« H 126 0 1 2 3 4 5 HT. ABOVE TRACER DISTRIBUTOR, FT. FIGURE 30. REDUCED CONCENTRATION PROFILES OF SODIUM IN THE CONTINUOUS PHASE; c* = 0.000 LB-MOLE/FT. those of Henton and Cavers (^7) by using t h e i r f i g u r e 8 . This f i g u r e i s a p l o t of the d i s p e r s i o n number ( r e c i p r o c a l of the Peclet number) against Reynolds number f o r t h e i r 1.5 i n . column work. Dispe r s i o n numbers ca l c u l a t e d f o r the present runs f a l l on the same area of the graph as do the d i s p e r s i o n numbers of Henton and Cavers ( ^ 7 ) . Figure 30 shows the reduced concentration of sodium p l o t t e d on a l ogarithmic scale against distance above the t r a c e r d i s t r i b u t o r on an a rithmetic scale f o r the runs with no HAc t r a n s f e r between the 3 2 phases. The dispersed phase s u p e r f i c i a l v e l o c i t y was 3 6 . 5 f t . / h r . f t . , 8nd the continuous phase s u p e r f i c i a l v e l o c i t i e s ranged from l 8 . 2 to 3 2 k&.k f t . / h r . f t . The l i n e s on the f i g u r e are the best f i t t e d s t r a i g h t l i n e s obtained by the l e a s t squares method. A l l the reduced con-centration p r o f i l e s i n the semi-logarithmic graph appear t o be s t r a i g h t l i n e s . With reference t o t a b l e 1 5 , the d u p l i c a t i o n of the r e s u l t s as between Henton ( l ) and the present worker i s not too good. The values of the a x i a l d i s p e r s i o n c o e f f i c i e n t c a l c u l a t e d i n the present work are s l i g h t l y lower than those obtained by Henton ( l ) . However, f o r some runs, the 95$ confidence i n t e r v a l f o r the a x i a l d i s p e r s i o n c o e f f i c i e n t estimated from the present r e s u l t s overlaps i n part with the corresponding i n t e r v a l f o r E obtained from the duplicate experiment of Henton ( l ) . In a d d i t i o n , the v a r i a t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t f o r the present four runs with no mass t r a n s f e r i s smaller than i n Henton's case. (The a x i a l d i s p e r s i o n c o e f f i c i e n t s would be expected to be equal because the dispersed phase s u p e r f i c i a l v e l o c i t y was kept the same i n each run, and Henton(l) found the a x i a l d i s p e r s i o n c o e f f i c i e n t to be independent of the continuous phase s u p e r f i c i a l v e l o c i t y over the range of h i s i n v e s t i g a t i o n . ) Figure 31 i s a p l o t o f a x i a l d i s p e r s i o n c o e f f i c i e n t versus the s u p e r f i c i a l v e l o c i t y of the continuous phase, Lc, with HAc concentration i n the continuous phase fed to the column as parameter. It confirms that the a x i a l d i s p e r s i o n c o e f f i c i e n t s do not depend upon the continuous phase s u p e r f i c i a l v e l o c i t y at l e a s t over the range studied, and i t shows a l s o that there i s l i t t l e or no e f f e c t of HAc concentration i n the continuous phase fed t o the column on the a x i a l d i s p e r s i o n c o e f f i c i e n t s . Table 16 provides 8 comparison o f E obtained by using the holdup measured with those obtained by using a holdup of 2.85$. These l a s t E's are i n e f f e c t calculated from holdups corrected f o r the extra dispersed phase wetting the imaged polyethylene w a l l of the p i s t o n sampler. Table l6 shows that the use of measured holdups produces only a small error i n E. Except i n t a b l e l6 the E's reported i n t h i s t h e s i s are uncorrected with respect t o any extra holdup due to unaged polyethylene w e l l , and have been cal c u l a t e d on the holdups a c t u a l l y measured i n the experiments. The reduced concentration p r o f i l e s of sodium f o r the runs with mass t r a n s f e r are shown i n f i g u r e s 32, 33, and 3*+. These are again semi-logarithmic p l o t s of the reduced concentrations of sodium against distance from the t r a c e r d i s t r i b u t o r . The concentration of HAc i n the continuous phase fed t o the column W8s approximately, 0.028, 0.0^3, 0.066 l b - m o l e / f t . i n f i g u r e s 32, 33, and 3k r e s p e c t i v e l y . The l i n e s on f i g u r e s 32, 33, and 3k again are the best f i t t e d s t r a i g h t l i n e s obtained by the l e a s t squares method. These f i g u r e s show t h a t , f o r each run the values 129 3 0 2 8 2 6 cc 2 4 2 2 LL ~ 2 0 LU 18 16 12 I I I I " "8-Xf / — — - © — O "8 u 0- ~ — o -— — LD= 3 . 6 - 5 0 F T . 3 / ( H R .FT.2) _ C Q , LB . M O L E/FT. 3 O 0-000 o 0-028 - o 0-043 0-066 o I 0-000 I (HENTON'S W I ORK) I 10 5 0 3 0 FIGURE 31. AXIAL DISPERSION COEFFICIENT FOR RUNS WITH Lj, = 36.5 FT?/HR. FT? 16. COMPARISON OF E'S OBTAINED BY USING THE HOLDUPS AS MEASURED WITH THE E'S OBTAINED BY USING THE HOLDUP OF 2.85$ : THE AVERAGE HOLDUP OF RUNS 34, 35, 36, AND 37 (RUNS WITH NO HAc IN TWO PHASES) WHICH WERE MADE AFTER THE POLYETHYLENE LINING OF THE PISTON HOLES HAD AGED MEASURED HOLDUP 2 . E, FT./HR. 2. E, FT./HR. OF THE DISPERSED RUN PHASE, % USING MEASURED USING HOLDUP NO. HOLDUP. OF 2.85$ 20 3.19 27.13 27.04 22 3.17 21.90 21.83 23 3.21 26.46 26.36 24 3.19 24.37 24.28 25 3.28 27.67 27.55 26 3.16 25.60 25.52 27 3.21 27.43 27.33 28 3.17 21.99 21.92 29 2.90 25.18 25.17 30 3.06 27.04 26.98 31 2.99 23.47 23.43 32 2.78 18.55 18.57 33 2.73 21.04 21.07 3k 2.84 20.65 20.65 35 2.80 21.57 21.59 36 2.86 21.99 21.99 37 2.93 21.33 21.33 131 0 1 2 3 4 5 HT. ABOVE TRACER DISTRIBUTOR, FT. FIGURE 32. REDUCED CONCENTRATION PROFILES OF SODIUM IN THE CONTINUOUS PHASE; C c = 0.028 LB-MOLE/FT3. 132 0 1 2 3 4 5 HT. ABOVE TRACER DISTRIBUTOR, FT. FIGURE 33. REDUCED CONCENTRATION PROFILES OF SODIUM IN THE CONTINUOUS PHASE; Cr. = 0.0*4 3 LB-MOLE/FT3 133 1 0 0 0 0 1 2 3 4 5 HT. ABOVE TRACER DISTRIBUTOR, FT. FIGURE 3k . REDUCED CONCENTRATION PROFILES OF SODIUM IN THE CONTINUOUS PHASE; cj = 0.066 LB-MOLE/FT? of the reduced sodium concentration tend to deviate more from the best f i t t e d s t r a i g h t l i n e than do those shown i n figu r e 30 f o r the runs with no mass t r a n s f e r . The deviations become very pronounced f o r the mass t r a n s f e r runs with high continuous phase s u p e r f i c i a l v e l o c i t i e s , f o r example, f o r runs with L c = kQ.k f t ? / h r . ft2. In a d d i t i o n , the deviations increase with the concentration of HAc i n the continuous phase fed t o the column. These deviations may be due t o the reasons which w i l l be given i n the following two paragraphs. In s e v e r a l runs the absorptions due to sodium were measured i n the dispersed phase withdrawn by the p l a s t i c cup probes. Because of the d i f f i c u l t y involved i n c a l i b r a t i n g the absorbance curve i n the MIBK phase, and because at that time the author d i d not r e a l i z e the po s s i b l e importance of a small amount of sodium i n the MIBK phase, no c a l i b r a t i o n curve f o r sodium absorption i n MIBK was m8de simultaneously. The c a l i b r a t i o n curve ( r e l a t i n g sodium absorbance and the corresponding sodium concentration i n the MIBK phase), prepared during the measuring 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 s of sodium between MIBK and water, was used here to c a l c u l a t e the approximate sodium concentrations i n MIBK f o r those runs. (As a j u s t i f i c a t i o n , i t was found that the c a l i b r a t i o n curves r e l a t i n g sodium absorbance and the corresponding concentration i n the water phase were not much d i f f e r e n t from run t o r u n ) . Table IT below gives the concentration p r o f i l e s of sodium i n the MIBK phase f o r runs with the HAc concentration i n the continuous phase fed to the column equal 0.066 lb-mole/ft. In a d d i t i o n , i n t a b l e l T the con-centrations of sodium i n the wster phase are given f o r each sampling point as w e l l as the e q u i l i b r i u m concentrations of sodium i n the 135 MIBK phase corresponding to those in the water phase. The equilibrium concentrations of sodium in the MIBK phase were calculated by dividing the concentration of sodium in the continuous phase by the corresponding distribution coefficient from figure 22. Table IT shows that the sodium concentrations actually measured in MIBK phase from the plastic cup probe samples are much higher than are the corresponding equilibrium concentrations. This abnormal phonomenon i s most probably due to the following. The concentration of sodium in the continuous phase near the tracer distributor in contact with the dispersed phase i s very high as compared with the sodium concentration in the MIBK phase. The sol u b i l i t y curve of the system MIBK-HAc-Water (figure 23) shows that the solu b i l i t y of water in the MIBK phase increases with increasing HAc concentration. In the column, the HAc concentration in both phases increased with height above the tracer distributor. That i s , HAc was transferred from the continuous phase to the ris i n g dispersed phase, and, as a result, water also. It i s very reasonable that, when water and HAc were transferred into the dispersed phase, some sodium was carried over into the dispersed phase together with them particularly near the tracer distributor. Of course, i f time was allowed, the excess sodium would transfer back to the continuous phase u n t i l the equilibrium value was obtained. This reasoning i s supported by the results from the plastic cup probe samples which contained both phases (see table IT): the sodium concentration in the dispersed phase was very low, and could not even detected by the atomic absorption spectrophotometer. If, as has been mentioned, the excess sodium in the MIBK phase would eventually diffuse back into the continuous phase to reach TABLE IT. CONCENTRATIONS OF SODIUM IN THE DISPERSED PHASE AND THE CONTINUOUS PHASE (C = 0.066 LB-MOLE/FT.) RUN NO. SUPERFICIAL VELOCITY , 3 2 FT./HR. FT. CONCENTRATIONS OF SODIUM IN PPM. AT SAMPLING POINT 1 2 3 4 5 6 T 8 9 10 29 18.20 36.50 a 191.2 b 0.015 c O.OIO 116.2 O.098 0.006 T4.2 0.049 0.004 53.1 O.060 0.003 3T.8 ' 0.022 0.002 30.T 0.008 0.002 18.T 0.054 0.001 13.1 O.o4o 0.001 8.1 0.023 0.001 5.6 0.031 0.000 26 2T.T0 36.50 a 156.4 b 0.060 c 0.009 T2.03 0.040 0.005 54.96 0.022 0.004 29.6T 0.046 0.002 20.59 0.015 0.002 11.96 0.084 0.001 5.86 0.008 0.001 4.04 0.110 0.000 1.45 * 0.000 0.000 0.91 0.024 0.000 28 36.50 36.50 a T2.8 b 0.109 c 0.006 2T.6 0.068 0.002 8.55 0.136 0.001 3.83 0.115 0.000 2.16 0.053 0.000 1.24 0.012 0.000 0.39 0.281 0.000 o.i4 0.10T 0.000 o.o4 0.026 0.000 "0.00 0.000 2T 48.40 36.50 a T6.0T b 0.019 c 0.005 21.36 0.002 4.09 0.132 0.001 1.30 0.639 0.000 O.69 0.250 0.000 0.29 0.044 0.000 0.13 0.025 0.000 O.OT 0.026 0.000 0.05 # 0.000 0.000 0.04 0.015 0.000 + Upper value i s f o r the continuous phase; lower value i s f o r the dispersed phase, a This row i s f o r sodium concentrations i n the continuous phase, b This row i s f o r sodium concentrations i n the dispersed phase. c This row i s f o r sodium concentrations i n the dispersed phsse i n e q u i l i b r i u m with that i n the cont. phase (ca l c u l a t e d from fig u r e 22). Two phases i n the sample. 137 the equilibrium value, then i t may be expected that at least part of the sodium carried into the dispersed phase by HAc and water in the' lower sections of the column w i l l transfer back to the continuous phase in the upper sections of the column while the drops are r i s i n g . Because of t h i s , there are two opposite directions of transfer of sodium in the column; one i s from the continuous phase into the drops, and the other i s from the drops back into the continuous phase. Hence, whether, the sodium concentration in the continuous phase at any elevation in the column is higher or lower than the value purely due to the axial dispersion of the continuous phase depends upon which direction of transfer of sodium is the more important. For lower continuous phase superficial velocities, the concentrations of sodium in the continuous phase are high and, also, do not decrease very rapidly with height above the tracer distributor. (See figures 30, 32, 33, end 3^.) Therefore, the small amount of excess sodium transferred into or back from the dispersed phase does not contribute an observable effect on the semi-logarithmic plots of sodium concentration in the continuous phase. On the other hand, for high superficial velocities of the continuous phase, the sodium concentrations in the continuous phase decrease very rapidly with height above the tracer distributor. For example, at the continuous phsse superficial velocity of kQ.h f t . / h r . f t . usually only the f i r s t seven or eight sampling points are available for sodium concentration measurements, because the sodium concentrations in the samples withdrawn above these sampling points usually are too low to be analyzed accurately by the atomic absorption spectrophotometer. Therefore, when the sodium picked up by the dispersed phsse near the tracer distributor i s in pert t r a n s f e r r e d back i n t o the continuous phase et the higher end of the t e s t s e c t i o n , a s i g n i f i c a n t e f f e c t on the sodium concentration i n the continuous phase i s produced ther e . This explanation would be consistent with the concave upward nature of the curve at LQ = k&.k f t 3 / h r . ft2, i n f i g u r e 3k. A somewhat s i m i l a r , although l e s s d e f i n i t e concavity, e x i s t s i n f i g u r e 33 at same value of LQ. c) A x i a l Dispersion C o e f f i c i e n t s from the P a r t i t i o n a b l e Solute Concentration P r o f i l e s i n Both Phases The HAc concentration p r o f i l e s i n both phases were measured f o r the runs i n which HAc t r a n s f e r took place from the continuous phase t o the dispersed phase. As has been mentioned under the heading "THEORY", these concentration p r o f i l e s provide another way o f estimating the a x i a l d i s p e r s i o n c o e f f i c i e n t , E, f o r the operation taking place i n the column. For a l l the runs of t h i s part of the experimental work the HAc concentration p r o f i l e s measured i n both phases are l i s t e d i n table B-7 of appendix B. Three methods were used as described under "THEORY" f o r estimating E from the HAc concentration p r o f i l e s . A l l the c a l c u l a t i o n s were performed with the IBiM 360/67 e l e c t r o n i c computer. Because Henton ( l ) had made f i v e runs ( J l , J 2 , J 3 , 34, and J5) with HAc t r a n s f e r from the continuous phase t o the dispersed phase, and because he used only the f i r s t method given, h i s runs were included i n the present work and E's were ca l c u l a t e d from them by the second and t h i r d methods mentioned above. The computer program and a d e t a i l e d d e s c r i p t i o n of the steps are presented i n appendix D. F i r s t of a l l the UBC "OLQF" l i b r a r y subroutine was used t o f i n d the best f i t t e d polynomial f o r the concentration p r o f i l e of each phase. Next 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, of HAc between the MIBK 8nd the water phases f o r the present experiments was c a l c u l a t e d from the f o l l o w i n g equation which r e l a t e s e q u i l i b r i u m concentrations of HAc i n the two phases: 2 c = 0.0002836 + 2.01T51C- - 6.11123CL 26 0 D jj Here i s the HAc concentration i n the continuous phase i n e q u i l i b r i u m with 0^, the HAc concentration i n the dispersed phase. This i s the equation that best f i t t e d the e q u i l i b r i u m data measured by the author. (Refer to t a b l e B-2 In appendix B.) For Henton's f i v e runs, m, was c a l c u l a t e d from the f o l l o w i n g e q u i l i b r i u m equation. C = 0.000012408 + 2.07898C - 6.41063C 2 30 v» U JJ This i s the best f i t t e d equation obtained by the present author from Henton's measured e q u i l i b r i u m data. These two e q u i l i b r i u m equations are not much d i f f e r e n t , except that equation 30 gives s l i g h t l y higher m's at high HAc concentrations i n the continuous phase. In c a l c u l a t i n g the values of K^a end m, the t e s t s e c t i o n of the column was d i v i d e d i n t o nine s e c t i o n s . Each section included that region of the column from one sampling point t o the next one below; that i s s e c t i o n 1 included the region of the column between sampling points 10 and 9, and section 2 included the region of the * at zero concentration of HAc i n the water phase. column between sampling points 9 and 8, and so on. The number of t r a n s f e r u n i t s , NTU, f o r any s e c t i o n , i , was calculated by the f o l l o w i n g equation. 31 The t r a p e z o i d a l method of i n t e g r a t i o n was used. The i n t e g r a t i o n was repeated several times. In each i n t e g r a t i o n the s e c t i o n was f u r t h e r divided i n t o smaller and smaller subsections, u n t i l the d i f f e r e n c e between two consecutive NTU^'s obtained was smaller than 0 . 0 0 1 . In c a l c u l a t i n g each value of NTU i, the values of m at the bottom end top of each subsection had t o be obtained. (Each value of m corresponded to a value of Cg, i . e . t o a value et the bottom or top of the subsection. The vslue of C c was substituted i n the appropriate equation (26 or 30) to give Cp. The corresponding m then was obtained by d i v i d i n g Cg by Cp.) The values of m (corres-ponding to the l a s t NTU^ of the s e r i e s o f i n t e g r a t i o n s described above) were recorded and used f o r c a l c u l a t i n g m^  of the p a r t i c u l a r s e c t i o n under study: mi of the section being taken as the a r i t h m e t i c average of the m's at the boundaries of a l l the subsections wi t h i n the s e c t i o n . The capacity c o e f f i c i e n t , Kjja, of the section was calculated from NTUi by t n e following expression. L_ X NTU, Height of the s e c t i o n 32 Ikl The f i r s t method of estimating E for the column operation was similar to that used by Henton. Both K a, and m were assumed to be D constant throughout the test section of the column. In this calculation m of the test section was taken to be the arithmetic average of the m^ 's of the a l l nine sections within the test section, K^a was calculated by the following equation. h x Ji ( N T O i ) K B = — 33 D Height of the test section The net flux, J, down the column was calculated by the following equation, J - 5 [<Ve " YD> + <V$ " YD>] * This equation 3^  gives the value of flux down the column calculated as an average of the values measured at the top of the column 8nd at the bottom of the column. For each run, the value of E was assumed equal to 1 for the f i r s t t r i a l . Equation 22 (below) was f i t t e d to the measured concentration prof i l e of the continuous phase, and A and B were then estimated by means of the least square technique as described by Henton (l) and also in appendix D. C C = Aexp(\ 1Z R) + B e x p C X g ^ ) - Q 22 2 In this procedure the value of A , the sum of the squares of the differences between respective measured C 's and C Q ' S calculated from equation 22 with E taken as equal to 1, was calculated. Thus, 2 10 2 A = 2 Z (C c - AexpCX^) - BexpCXgZ^) + Q) 35 The curve f i t t i n g was repeated with the value of E increased by one for each successive t r i a l , u n t i l E was equal to 60. The value p of E corresponding to the minimum value of A was taken as the estimated E of the test section for the run under study. Table 18 gives, for each run, the value of E estimated, the measured continuous phase concentration p r o f i l e , and the continuous phase concentration profi l e calculated by equation 22, the E estimated being u l t i l i z e d . In addition, table 18 gives for each run the continuous phase concentration profiles calculated again by equation 22 but now making use of the E obtained from the tracer study. Because of measuring errors in the experiments, the flux down the column measured at the top of the column was not exactly the same as that measured at the bottom of the column. Therefore, the process of calculation was repeated, based on the use of flux, J, measured at the top of the column and given by the following equation 36. J = (L C 1 - L C°) 36 C C D D Again the calculation was repeated. This time the flux, J, used was that measured at the bottom of the column and given by equation 37. J = ( L C ° - L C C I D ' 37 Now, i f the HAc concentration in the continuous phase i s calculated at each sampling point by the polynomial which best f i t t e d the measured value of C , the result i s slig h t l y different from the value c measured at the same sampling point. In order to know whether such small differences would affect the value of E estimated, the whole of the above calculations were repeated once again. This time i n 2 calculating the value of A by equation 35 the values of C^ used were those calculated by the polynomial which best f i t t e d the measured continuous phase concentration p r o f i l e s . In other words, instead of using the directly measured C values, smoothed values C were used. The various values of E which resulted from using C c measured, and C smoothed, and the different fluxes (equation 3k, c 3 6 , and 3 7 ) , are l i s t e d i n table 1 9 . In addition, i n table 19 the values of flux calculated by equationS34, 3 6 , and 37 are l i s t e d also for a l l the runs. With reference to table 1 8 , the values of E obtained by the present method are often quite different from those obtained by the tracer technique; also, the values of E are not constant for the runs with the same dispersed phase superficial velocity. The fluxes J, down the column, calculated for a run from equations 36 and 37 are s l i g h t l y different. Also, they are each a few percent away from the average value of the flux calculated by equation 3^ (except in the case of run J 5 where the situation i s very much worse). However, as table 18 shows, the values of E estimated by using these different values of J can be greatly different from one another. This TABLE 18. COMPARISON 0? THE E ' S OPTAIKTD BY CURVE FITTIBC THE MEASURED PAHTrTIONABLE SOUJfE CONCFJtTiATIONS BT MEANS Of THE DISPERSION EQUATION "FIRST METHOD" WITH E ' S OBTAINED BY TRACER MEASUREMENTS, AND COMPARISON 0? MEASUHED CONCENTRATIONS 07 THE CONTINUOUS PHASE WITH THOSE OBTAINED FROM THE FITTED DISPERSION EQUATION RUN K O . S U P E R F I C I A L V E L O C I T Y . • 3/ 2 4. L B - M O L E / F T ? x io 3 FOR T E S T S E C T ! on E , BY TRACER S T U D Y , E , BT T H I S METHOD, C C OBTADIED BY MEASUREMENT AND BY L E A S T SQUARES F I T TO T H E D I S P E R S I O N E Q U A T I O N , • . L B - M O L E / F T ? X 10? A T SAMPLIXO P O I N T S STANDARD ERROR BETWEEN CALCULATED AND MEASURED CONCENTRATIONS X I O 3 F T ? / H R . r r? / K R . 1 2 3 1 5 6 7 8 9 10 16 18.10 72.09 28.73 1.9835 12.71 13 15.911 15.901 15.901 17.030 17.097 17.097 18.087 18.121 18.121 19.113 19.085 19.085 20.010 19.981 19.981 21.020 20.795 20.795 21.5I0 21.593 21.593 22.230 22.332 22.332 22.935 23.03I 23.031 23.718 23.691 23.691 0.0^ 2 0.032 20 18.20 16.50 28 .T9 1.9958 27.13 51 11.281 11.292 11.550 15.331 15.291 15.139 16.136 16.121 15.795 16.759 16.612 16.I91 17.166 17.189 17.202 18.166 18.098 17.931 18.586 18.672 18.658 19.3T0 19.236 19.397 19.818 19.787 20.137 20.231 20.311 20.818 0.021 0.106 2? 27 .TO 36.50 13.66 1.9335 21.90 10 25.891 25.900 26.131 27.822 27.817 27.535 29.503 29.399 28.961 30.725 30.717 30.319 31.723 31.867 31.653 31.788 32.917 32.888 31.077 33.870 31.027 31.805 31.767 35.102 35.616 35.601 36.099 36.263 36.359 36.993 0.036 0.132 23 ua .io 36.50 13.T7 1.9018 26.16 23 35.007 31.9T1 31.968 36.722 36.838 36.826 37.967 37.973 37.980 38.750 38.819 38.832 39.513 39.505 39.516 10.152 I0.093 I0.098 10.721 10.592 10.592 11.063 11.030 11.021 I1 . I19 I1 .I07 11.397 11.722 11.722 11.709 0.023 0.023 2b 36.50 36.50 12.93 1.91S1 21.37 60 30.190 30.172 30.636 32.283 32.399 32.121 33.951 33.853 33.186 35.030 35.006 31.718 36.038 35.918 35.811 36.767 36.7ja 36.791 37.173 37.153 37.657 38.056 38.077 38.133 38.561 38.63I 39.119 39.009 39.118 39.706 0.025 0.131 25 18.20 36.50 12.62 1.9651 27.67 12 19.101 19.308 19.600 20.611 20.688 20.512 21.690 21.875 21.511 22.957 22.955 22.5T2 23.910 23.961 23.653 25.18B 21.937 21.761 25.950 25.880 25.868 26.768 26.821 26.991 27.779 27.751 28.121 28.518 28.617 29.213 O . O l l 0.116 26 2T.T0 36.50 66.36 1.8952 25.60 23 30.075 30.022 29.905 33.168 33.328 33.167 36.329 36.253 36.111 38.919 38.933 39.087 11.331 11.385 11.171 13.639 13.682 13.690 15.900 15.791 15.721 17.868 17.775 17.639 19.668 I9.617 19.120 51.130 51.265 51.017 0.031 0.061 2T 18.1.0 36.50 65.78 1.8331 27.13 21 19.803 19.763 . I9.738 52.536 52.681 52.730 51.887 5 L 8 9 0 51.936 56.799 56.671 56.695 58.160 58.121 58.122 59.329 59.339 59.316 60.3I2 60.336 60.298 61.253 61.173 61.125 61.8I9 61.867 61.81I 62.310 62.123 62.367 0.027 0.031 28 36.50 36.50 66.19 1.8187 21.99 21 15.013 11.950 11.981 17.583 17.757 17.705 50.095 50.076 50.016 52.033 52.090 52.050 53.898 53.853 53.839 55.511 55.135 55.117 57.111 56.830 56.863 58.113 58.089 58.1I0 59.112 59.211 59.276 59.900 60.176 60.251 0.051 0.057 29 18.20 36.50 66.12 1.9327 25.18 33 23.351 23.511 23.850 25.818 25.637 25.391 27.772 27.622 27.161 29.578 29.516 29.078 31.399 31.117 31.051 33.250 33.291 33.090 31.921 35.135 35.131 36.833 37.001 37.223 38.992 38.867 39.323 I 0 . 7 5 ! 10.666 11.351 0.019 0.153 30 18.10 36.50 69.19 1.825I 27.01 31 50.292 50.3I0 50.3T8 51.102 53.928 53.831 56.265 56.520 56.116 58.971 58.551 58.I92 60.015 60.189 60.186 61.339 61.561 61.61) 61.663 62.696 62.787 63.512 63.661 63.781 61.590 61.177 61.616 65.310 6J.139 65.287 0.073 0.081 31 36.50 36.50 28.19 1.9612 23.17 13 21.812 21.816 21.791 22.611 22.136 22.551 22.959 23.135 23.232 23.758 23.796 23.816 21.382 21.387 21.391 21.881 21.921 21.890 25.117 25.390 25.331 25.836 25.813 25.730 26.06J 26.188 26.068 26.717 26.509 26.396 o.olo 0.051 32 27.70 •>6.50 28.20 1.9750 18.55 27 18.658 18.659 18.7I8 19-518 19.511 19.361 20.327 20.330 20.155 21.105 21.105 20.981 21.822 21.827 21.772 22.529 22.508 22.521 23.123 23.137 23.215 23.676 23.729 23.863 21.103 2I.280 21.161 21.700 21.771 21.992 0.017 0.051 33 18.1.0 36.50 28.01 1.9596 21.01 7 23.153 23.151 23.113 23.913 21.013 21.095 21.687 21.602 21.655 25.055 25.113 25.131 25.511 25.550 25.515 25.911 25.928 25.903 26.319 26.219 26.210 26.5II 26.528 26-W9 26.830 26.766 26.719 26.932 26.963 26.901 0.018 0.028 J l + 36.50 5^.70 81.37 1.9208 11.9" 18 30.660 P . 2 8 1 30-121 31.300 35.950 35.613 10.370 10.027 39.697 13.T0O 13.512 13.320 17.710 16.778 16.689 19.170 19.ST2 I9.TC6 53.720 52.160 52.607 55.210 55.096 55.313 57.210 57.558 57.890 58.820 59.850 60.256 0.276 0.301 J ? 4 18.20 51.70 83.32 2.0270 11.5" 11 9.010 8.981 10.523 10.050 10.258 6.839 11.810 11.793 7.398 13.960 13.517 9.121 15.300 15.115 12.129 17.000 17.385 15.171 19.130 19.565 18.727 22.310 21.931 22.789 21.250 21.171 27.366 ST-3fg 27.188 32.505 0.088 1.131 J3' 36.50 91.20 80.75 2.0068 11.1** 3 s . 15.180 15.535 15.777 16.690 16.581 13.878 18.270 18.053 15.550 19.T3C 19.736 17.726 21.130 21.561 20.139 23.070 23.111 22.659 25.500 25.500 25.175 27.590 27.712 28.570 30.110 30.061 31.930 32.510 32.517 35.568 0.066 0.061 Jl* I18.I0 91.20 80.13 l ."603 11.1** 10 25.250 25.292 25.197 27.710 27.635 23.118 30.350 30.163 26.696 32.780 32.729 30.525 35.120 35.301 31.332 37.510 37.759 37.935 10.060 10.263 11.588 I2 . I90 12.T69 15.223 15.250 15.215 18.796 18.020 17.686 52.298 0.066 l.ool J5* 18.10 127.00 82.90 2.0167 9.3" 60 11.630 15.190 16.390 17.360 18.850 20.2)0 21.730 23.13C 25.100 27.590 Upper value Is f o r continuous phase; lower v a l u e l a f o r d i s p e r s e d p h a s e . Upper v a l u e * ere c o n c e n t r a t i o n s -Measured; middle v a l u e s a r e c o n c e n t r a t i o n s c a l c u l a t e d frost l e a s t squares f i t u s i n g E o b t a i n e d by t h i s oratbod; lower values are c o n c e n t r a t i o n s c a l c u l a t e d f r o n least squares f i t u s i n g E from t r a c e r measurements. Henton ( l ) o b t a i n e d t h * p r e l l a i n a r y d a t a f o r the J r u n s . These d a t a have been t r e a t e d by the methods o f the present study t o p r o v i d e the sjuabers a b o v e . These v a l u e s are taken f r o n the run wi th s i m i l a r o p e r a t i n g c o n d i t i o n s , but no BBSS t r a n s f e r between the p h a s e s . TABLE 19. E BY CURVE FITTING DISPERSION EQUATION USING MEASURED CC'S AND SMOOTHED CC«S (BOTH WITH DIFFERENT VALUES OF J) RUN NO. E BY TRACER STUDY, FT./HR. J , FLUX DOWN THE COLUMN CALCULATED BY EQUATIONS LISTED, _ LB-MOLE/HR. F T / E BY CURVE FITTING THE DISPERSION EQUATION, FT?/HR. A OF EQUATION 35 CALCULATED BY MEANS OF THE MEASURED VALUES OF CC, USING DIFFERENT J'S A OF EQUATION 35 CALCULATED BY MEANS OF THE SMOOTHED VALUES OF CC, USING DIFFERENT J'S J l EQ. 34 J2 EQ. 36 J3 EQ. 37 J l J2 J3 J l J 2 J3 16 12.7-+ 0.38947 0.41320 0.36573 13.0 35.0 7.0 13.0 35.0 7.0 20 27.13 0.08507 0.08625 0.08390 51.0 52.0 50.0 51.0 52.0 50.0 22 21.90 0.43643 0.44554 0.42732 40.0 47.0 33.0 4o.o 47.0 33.0 23 26.46 1.28211 1.30579 1.25842 23.0 60.0 60.0 29.0 60.O 60.O k 24.37 0.77809 0.79128 0.76489 60.0 60.0 49.0 60.0 60.0 49.0 25 27.67 0.12147 0.12522 0.11771 42.0 44.0 39.0 42.0 44.0 40.0 26 25.60 0.62752 0.64474 O.61029 23.0 28.0 18.0 23.0 28.0 18.0 27 27.43 1.85966 1.89428 1.82504 24 .0 56.0 7.0 24.0 57.0 .7.0 28 21.99 1.14995 1.15756 1,14234 24.0 29.0 20.0 24.0 28.0 19.O 29 25.18 0.22110 0.22322 O.21899 33.0 34.0 33.0 33.0 34.0 33.0 30 27.04 1.95734 1.97560 1.93907 34.0 49.0 19.0 34.0 49.0 19.0 31 23.47 0.52310 O.52870 0.51768 13.0 19.0 5.0 12.0 20.0 5.0 32 18.55 0.29274 0.29640 O.28907 27.0 31.0 24.0 27.0 31.0 24.0 33 21.04 0.83959 0.84570 0.83348 7.0 20.0 7.0 7.0 22.0 7-0 J I 14.9 0.74122 0.77872 0.70372 18.0 28.0 9.0 19.0 28.0 9.0 J2 14.5 0.11895 0.13853 0.09937 41.0 45.0 37.0 4l.o 45.0 36.0 J3 11.1 0.09404 0.09920 0.08888 32.0 33.0 30.0 32.0 33.0 30.0 J4 11.1 O.47670 O.52662 0.42694 40.0 51.0 29.0 40.0 51.0 29.0 J5 9.25 I.15668 2.24261 O.05875 60.0 60.0 60.0 60.0 60.0 60.0 result Indicates the important effect of J on the E estimated by the present method. On the other hand, table 19 shows that for each run the value of E estimated i s almost the same, whether i t is based on the raw measured values of C^ ,, or on the smoothed values from the best f i t t e d polynomial of the measured continuous phase concentrations. Henton (l) also noted the sensitivity of the value of E estimated to the value of J. He also noted the sensitivity of E to small variations in K^a and m. From the equilibrium equations 26 and 30, i t is evident that m does decrease slightly with increasing HAc concentration in the phases. Hence m changes 8long the test section. Table 20, shows that K^a is not constant 8long the test section either. For most of the runs (except run J2, jk and J5) K^a decreases with increasing height above the dispersed phase nozzle t i p s . In runs J2, Jk, and J5, K^a increases with height above the dispersed phase nozzle t i p s . Because small variations in both K^8, and m have a very great effect on the E estimated ( l ) , and also because there is no theoretical background to support the use of an arithmetic average m for the test section (as has been used here), i t may be that the use of constant average values of these quantities along the test section of the column is not very suitable. Consequently, the results for E may be error. In spite of the differences between the E's estimated by the present method and the corresponding values of E obtained by means of the tracer method, table 18 shows that the values of C^ calculated by this method are in very good agreement with the corresponding measured values of C . In addition, table l 8 shows that for each TABLE 20, AVERAGE CAPACITY COEFFICIENT FOR EACH SECTION WITHIN THE TEST SECTION OF THE COLUMN FOR ALL THE RUNS WITH MASS TRANSFER RUN K Da, OF AVERAGE CAPACITY COEFF., KpS (1/HR.), OVER THE SECTIONS LYING BETWEEN THE SAMPLING NO. THE TEST POINTS LISTED IMMEDIATELY BELOW SECTION, 1/HR. 1,2 2,3 5,6 6,7 7,8 8,9 9,10 16 1+2.952 57.288 52.994 48.346 44.868 42.921 41.812 39.973 34.794 23.849 20 19.939 28.305 22.018 19.067 18.049 18.104 . 18.584 18.962 -18.771 17.585 22 22 001 30.033 26.156 23.214 21.161 19.902 19.287 19.140 19.324 19.815 23 18.921 24.401 23.847 .57  23.169 22.104 10.831 16.064 1 100 5.842 24 22.180 26.050 24.132 22.655 21.528 20.723 20.276 20.308 21.068 22.959 5 20.899 26.013 23.988 22.385 .113 20.108 19.325 18.735 18.319 18.073 26 23.927 38.847 3 .355 28.454 25.211 23.434 22.175 20.078 15.587 7.833 27 26.580 29.514 28.916 28.181 27.239 26.087 24.873 23.968 24.071 26.420 28 21.830 5 469 5.2 4 24.720 3.957 22.896 1.510 19.768 17.632 15.134 29 19.0^ 3 30.163 24.698 21,275 19.102 17.633 16 .474 5.342 14.055 12.560 30 25.919 35.362 30.381 25.712 22.315 20.7 9 21.072 23.042 26.048 28.805 31 18.858 21.613 21.421 0.795 19.796 18.590 17.427 16.594 16.383 17.095 2 22.142 4.5 5 24.428 24.151 23.661 22.933 21.95  20.725 19.237 .557 33 18.472 19.405 19.922 20.287 0.408 20.168 19 M3 18.008 5.764 12.685 J l 43.824 5 . 49 58.057 54.495 49.127 42.978 37.104 32.429 30.038 31.131 J2 50.380 48.567 47.387 46.914 47.401 48.711 50.590 52.763 54.791 56.126 J3 76.762 74.853 79.997 82.903 83.478 81.998 78.925 74.675 69.755 64.598 Jk 96.350 84.472 84.620 84.673 85.722 88.590 93.931 102.396 114.067 128.010 J5 139.016 100.829 117.620 132.282 143.766 151.231 154.673 154.425 150.991 145.194 148 run (except run J 2 , J 3 , j U , and J 5 ) the values of C c calculated by equation 22 with E determined by the tracer study also are quite close to the measured values of C . C The second method of estimating" E from the HAc concentration profiles was introduced because i t was hoped that i t would provide a way of avoiding the errors caused in E by measuring J, and also by the variations of Yi^a and m along the test section of the column. In calculating the E by this method equation 2k (below) was used. L dC. E = 2k 2 d % e ( - A . H 2 < 1 The test section of the column was divided into nine sections as used in calculating (K a) , and ra , where i i s any section. It W8S assumed D i i that the values of both (K a) , and m in each section were constant. D 1 i (K^a)^ and m# for each section were calculated as described near the begining of the present subsection of thesis snd in appendix D. d C d2C, (- — ) 9 and ( ) t were obtained by differentiating the best f i t t e d d Z R d ^ i ,_2 i polynomial representing the HAc concentration profile of the continuous d C_ d 2C c phase. A l l of (C /m - C ) , (—-) and ( ) were evaluated at C D i d Z p i d z 2 i the mid point of each section. and in (Cc/m - Cp)^ were evaluated by means of the best f i t t e d polynomials respresenting the concentration p r o f i l e s i n respective phases. The ra used was the m^  mention above. dC d 2 c c Once the values of (K_a) , (C_/m - C n ) . , ( ) and ( — — ) had been C u 1 dZp i d z 2 i obtained, the value of E^ f o r the section was cal c u l a t e d by equation 2k. For each run, the arithmetic average of E^ , f o r a l l the sections was taken as the E f o r the t e s t s e c t i o n . For a l l the runs, the values of E f o r the column ( i . e . f o r the t e s t s e c t i o n ) , and f o r each section w i t h i n the t e s t s e c t i o n of the column are l i s t e d i n ta b l e 21. The sample hand c a l c u l a t i o n of E by t h i s second method i s given i n appendix D. Unfortunately, t a b l e 21 shows the values of E obtained are d i f f e r e n t from those of the t r a c e r r e s u l t s ; i n f a c t f o r some runs, the E's of some of the sections within the t e s t s e c t i o n have a negative v a l u e j when the averaging i s done some of the E's f o r the t e s t s e c t i o n i t s e l f are negative as a r e s u l t . In short, the agreement between the E's estimated by t h i s second method Over the t e s t s e c t i o n of the column show even worse agreement with the E's of the t r a c e r study than do those given by the f i r s t method. D i f f i c u l t y a r i s e s from the f o l l o w i n g , ( i ) Small deviations of K^a and m s t i l l have a very great e f f e c t on the E estimated; ( i i ) Although t h i s method has removed the p o s s i b l e er r o r due t o measuring of J , and avoided the assumption that K^a and m are constant 2 2 throughout the t e s t s e c t i o n , another f a c t o r (d CQ/dZ^J^ has been ? 2 introduced. (d^C^/dZp^ appears i n the denominator of the equation 2 2 2k. Within the range of and L c studied the values of (d C c / d Z R ) i TABLE 21. E BY THE SECOND METHOD SUPERFICIAL i CC> E, E, AVERAGE E OVER THE SECTIONS OF THE COLUMN BETWEEN THE SAMPLING RUN VELOCITY p NO. 3 2 BY BY THIS POINTS LISTED IMMEDIATELY BELOW, FT./HR. FT./HR. FT. LB-MOLE TRACER + METHOD 2 FT^ STUDY, 6,7 8,9 2 , FT 0/HR . 1,2 2,3 ,^5 5,6 7,8 9,10 X 10J FT./HR. 16 48.4 72.9 28.73 12.74 6.84 75.23 26.25 32.9k 21.51 9.33 -1.89 O.92 -48.10 -54.66 20 18.2 36.5 28.79 27.13 -15.48 5.74 5.17 4.50 2.37 -57.08 -63.99 -16.43 -10.55 -9.07 22 27.7 36.5 43.37 21.90 18.61 3.60 2.59 4.18 14.38 52.60 68.74 25.08 3.38 -7.10 23 k8.k 36.5 43.77 26.46 30.64 30.42 22.23 15.53 13.11 21.92 47.96 61.71 43.22 19.62 24 36.5 36.5 42.93 24.37 11.49 27.35 22.38 17.80 13.80 10.61 8.42 6.78 3.14 -6.91 25 18.2 36.5 42.62 27.67 1.42 24.47 18.75 12.99 7.24 1.44 -4.34 -10.13 -15.96 -21.65 26 27.7 36.5 66.36 25.60 36.24 -4.02 16.52 36.19 51.10 55.67 49.40 4o.94 38.24 42.13 27 48.4 36.5 65.78 27.43 21.03 30.70 26.99 24.79 24.43 25.72 26.93 23.84 12.23 -6.39 28 36.5 36.5 66.49 21.99 29.96 53.71 47.80 41.86 35.92 29.97 24.01 18.06 12.08 6.22 29 18.2 36.5 66.42 25.18 -20.27 2.20 1.57 3.17 46.66 -27.43 -27.16 -42.06 -191.39 52.02 30 4 . k 36.5 69.19 27.04 37.25 20.33 21.70 24.75 30.99 43.56 65.89 76.61 40.32 11.11 31 36.5 36.5 28.19 23.47 37.68 -40.85 -3.38 26.55 48.76 63.32 70.15 69.27 60.64 44.65 32 27.7 36.5 28.20 18.55 39.96 4l.9l 41.43 40.94 0.4 39.96 39.47 38.98 38.49 37.98 33 48.4 36.5 28.01 21.04 48.51 72.78 66.74 60.68 54.61 48.53 42.46 36.37 30.24 24.21 J l 36.5 54.7 81.37 14.9 6.46 2.82 7.15 11.62 15.16 16.68 15.24 9.64 -1.34 -18.86 J2 18.2 54.7 83.32 14.5 39.41 34.16 26.09 24.00 26.61 32.52 40.43 49.27 57.60 63.97 J3 36.5 91.2 80.75 11.1 .18.70 42.45 36.47 30.49 24.52 18.68 12.86 6.92 0.95 -5.02 k 48.4 91.2 80.43 11.1 65.61 705.59 •222.74 -101.05 -109.06 •265.OI 387.02 107.05 56.61 32.67 J5 48.4 127.0 82.93 9.25 59.95 62.91 62.12 61.33 60.56 59.88 59.18 58.50 57.87 57.23 + Arithmetic average of nine sectional E's listed beside. 151 were very smell negative or positive values. Because of this fact, E calculated by this second method appears to be very sensitive to 2 2 l i t t l e changes in (d C^/dZ^)^. It i s worth mentioning that this same method of estimating E has been used before by Thomas and Chui (66). They estimated values of E for sn osc i l l a t i n g baffle contactor by this approach, 8nd claimed that the results obtained were close to those determined from tracer measurements. However, they performed a l l the calculations by hand, and apparently these included considerable personal adjustment in determining (dC c/dZ R) i and (d Cc/d7^)±. Furthermore, in Table 1 of the paper (66), they even ignored a negative sign of E estimated. Finally E's for the present work were estimated by the third method under the heading "THEORY". For this method the smoothed values of CQ and were used. These values were calculated by the polynomials which best f i t t e d the corresponding concentration p r o f i l e s . The value of E was calculated at each sampling point. Therefore, there were ten values of E for each run. The E over the test section of the column was taken to be the arithmetic average of these ten E's. Again the process of calculation was repeated by using different fluxes calculated from equations 3^, 36, and 37. Table 22 shows values of E based on the average flux of partitionable solute (HAc) down the column as given by equation 3^ . Included in this table are the values of E at each sampling point and the average value obtained as described above. Table 23 compares the average value of E over the test section for each run for each of the three ways of calculating the flux as mentioned above. By this method of calculating E, the effects of K^a and m on TABLE 22. E BY THE THIRD METHOD (WITH THE FLUX CALCULATED BY EQUATION 34) RUN E, E, E, 2 . AT THE SAMPLING POINTS LISTED IMMEDIATELY BELOW, FT./HR. # BY BY THIS NO. TRACER STUDY, METHOD/ 2 2 1 2 3 4 5 6 7 8 9 10 FT./HR. FT./HR. 16 22.7k 16.12 14.33 18.74 18.72 17.52 16.96 18.10 20.78 21.55 14.85 -o.4o 20 27.13 37.90 20.49 24.88 29.22 32.34 33.71 34.13 35.03 38.4o 48.44 82.35 22 21.90 30.91 16.22 20.32 24.94 28.54 29.81 29.00 27.67 28.03 34.64 69.95 23 26.46 27.63 26.22 24.51 25.22 28.18 31.75 33.46 31.76 27.19 22.11 25.96 4 24.37 38.15 26.52 26.25 27.24 29.62 33.30 37.93 42.79 4 .4  52.21 58.16 25 27.67 35.18 29.63 29.84 30.35 31.18 32.39 34.05 36.20 38.99 42.50 46.70 26 25.60 25.67 25.23 29.09 30.48 30.00 28.46 26.61 24.96 23.47 21.46 16.98 27 27.43 27.38 26.48 25.37 24.94 24.95 25.07 24.93 54 24.74 28.39 44.36 28 21.99 31.47 33.39 31.49 29.81 28.41 . 27.44 27.06 27.61 29.72 34.67 45.14 29 25.18 .84 25.38 30.62 35.15 37.65 37.57 35.52 32.62 29.73 27.53 26.60 30 27.04 27.30 .8  27.93 30.15 1 86 32.04 30.08 26.62 23.11 21.37 23.94 31 23.47 19.50 21.25 24.77 26.48 26.51 25.03 22.24 18.50 14.14 9.78 6.31 32 18.55 30.65 33.23 32.76 32.26 31.73 31.17 30.55 29.89 29.15 28.32 27.4  3 21.04 31.87 42.99 40.20 7.45 4. 5 32.16 29.68 7.43 25.51 24.23 24.29 J l 14.9 18.52 13.64 14.66 15.46 15.93 16.05 15.98 16.11 17.47 22.47 37.45 J2 14.5 43.01 48.28 46.62 44 3 42.45 4l.o4 40.36 40.36 41.00 42.10 43.46 J3 l l . l 35.67 39.82 40.19 39.79 38.87 37.56 36.02 34.23 32.23 30.10 27.86 it l l . l 2 86 20.06 23.98 26.85 29.44 32.21 35.12 38.13 40.57 4l.6o 4o.6 l J5 9.25 598.6 1030.0 848.4 724.1 633.5 564  511.6 467.7 431.1 400.5 374.5 Run conditions: LQ, Lp, and C C see page 150 table 21. + Arithmetic average of the ten E»s a t t h e sampling points l i s t e d beside. TABLE 23. COMPARISON OF THE E'S OBTAINED BY THE THIRD METHOD WHEN THE E'S ARE BASED ON VARIOUS EQUATIONS FOR THE FLUX OF PARTITIONABLE SOLUTE DOWN THE COLUMN RUN NO. E, FROM TRACER STUDY, 2. FT./HR. AVERAGE E FOR THE TEST SECTION, BASED ON DIFFERENT J'S J l > CALCULATED BY EQ. 34 * J2 CALCULATED BY EQ. 36 * J3 CALCULATED BY EQ. 37 16 12.74 16.12 31.48 0.75 20 27.13 37.90 38.93 36.87 22 21.90 30.91 35.91 25.91 23 26.46 27.63 54.40 0.86 24 24.37 38.15 47.16 29.14 25 27.67 35.18 37.15' 33.22 26 25.60 25.67 29.77 21.57 27 27.43 27.38 45.95 8.80 28 21.99 31.^7 3^.45 28.50 29 25.18 31.84 32.40 31.27 30 27.04 27.30 34.48 20.12 31 23.47 19.50 25.10 13.90 32 18.55 30.65 33.57 27.73 33 21.04 31.87 41.83 21.90 J l 14.9 18.52 26.18 10.86 J2 14.5 43.01 48.44 37.58 J3 l l . l 35.67 37.28 34.06 Jl* l l . l 32.86 43.77 21.95 J5 9.25 598.6 1097.8 87.30 FOR VALUES OF J SEE TABLE 19 the values of E estimated are to t a l l y eliminated, but that of the flux, J, s t i l l remains. Table 23 shows that there i s a large effect of small variations of J on the value of E calculated for a given run. However, table 22 (which gives values of E calculated by using the average flux from equation 3*0 suggests the following: The runs 3 2 i n table 22 for equal 36.5 f t . / h r . f t . were made at various continuous phases superficial v e l o c i t i e s . When a comparison:is made of the E's obtained from these runs by the third method a reason-able conclusion seems to be that the superficial velocity of the continuous phase does not affect E. In addition, these runs were made at various HAc concentrations i n the continuous phase fed to the column. From table 22 i t seems l i k e l y that this factor also does not affect E. A l l these findings are consistent with the conclusions drawn from the tracer results. F i n a l l y , again with reference to table 22, the values of E calculated at individual sampling points do not change much from point to point for a given run, except at a few sampling points where the values of E are very large or very small. These last values may be due to experimental error. If we exclude them, the difference between the average value of E and the corresponding E from the tracer results i s not great for most of the runs. However, for each of runs J2, J3, Jk, and J5 a very large difference exists between the average E and the E from the tracer work. 155 V. CONCLUSIONS AND RECOMMENDATIONS A better understanding of sampling techniques u s e f u 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 spray columns has r e s u l t e d from the present work. A new i n t e r n a l sampler, a p l a s t i c cup probe, was s u c c e s s f u l l y constructed to enable withdrawing from the spray column a dispersed phase i n t e r n a l sample uncontaminated with the continuous phase. This p l a s t i c cup probe provides an independent check of the dispersed phase concentration as obtained by the funnel probe (with the assistance of equation 1 8nd hypodermic needle data of continuous phase concentrations). It has been proved that both the p l a s t i c cup probe and the funnel probe give r e a l i a b l e dispersed phase concentrations i n the column. The advantages of the p l a s t i c cup probe over the funnel probe are as f o l l o w s , ( i ) Use of the p l a s t i c cup probe i s l e s s time consuming, ( i i ) Use of the p l a s t i c cup probe r e s u l t s i n the withdraw of a smaller volume of purge l i q u i d and smaller volume of sample, ( i i i ) The dimensions of the p l a s t i c cup probe are smaller; therefore p o s s i b l e e f f e c t s on the flow pattern i n the column are l e s s ; ( i v ) With the p l a s t i c cup probe only dispersed phase i s withdrawn; t h e r e f o r e , the a n a l y s i s of the sample i s e a s i e r , and any uncertainty about the correct continuous phase concentration to use i n equation 1 no longer enters i n t o the s i t u a t i o n . For the above reason, the p l a s t i c cup probe should be used i n place o f the funnel probe f o r furth e r work i n v o l v i n g the measuring of concentration p r o f i l e s of the dispersed phase. A pos s i b l e improvement can be made i n the p l a s t i c cup probe; that i s a conduc t i v i t y c e l l perhaps could be b u i l t i n s i d e the cup of the probe. Then the dispersed 156 phase concentrations could be measured continuously. The hook probe gives continuous phase concentrations sl i g h t l y higher for the direct runs, and lower for the reverse runs, than those obtained by means of a hypodermic needle at the same sampling elevation. This phenomenon i s believed to be due to the comparatively large size of the hook probe which results in the drop being deflected in such a way th8t extraction i s less complete i n the neighbourhood of the hook probe i n l e t . With the assistance of the plastic cup probe, the dispersed phase concentrations were carefully studied by withdrawing samples from various locations within cross section at constant height above the nozzle t i p s . The cross-sectional concentration profiles of the dispersed phase, for direct runs were found to be slightly concave upward. The axial dispersion coefficients measured by means of tracer are found to be not affected by mass transfer from the continuous phase to the dispersed phase within the ranges of the variables investigated in the present work. As auxilliary studies, drop size distributions and holdups of the dispersed phase were measured both for the runs with mass transfer and for those without mass transfer. The results showed that there i s no effect of mass transfer on the drop size distributions and the dispersed phase holdups. Three methods were used to estimate,with the assistance of the dispersion equation, the axial dispersion coefficient from the partitionable solute concentration profiles in the two phases. • In the f i r s t method used the values of s x i a l dispersion coefficient obtained were very s e n s i t i v e to small changes i n the f l u x , J , of solute down the column, the value of the capacity c o e f f i c i e n t , K^a, and 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. In the second method used the E's obtained were s e n s i t i v e t o small changes of 2 2 (d Cg/dZp), and i n the t h i r d method t o small changes of J . Among the three methods mentioned above, the r e s u l t s given by the t h i r d method, with J c a l c u l a t e d by equation 3*4 (the average value of J's measured at the top and the bottom of the column) are clo s e s t t o those of the corresponding runs given by the t r a c e r s t u d i e s . It has been observed ( l ) that there i s a x i a l d i s p e r s i o n of the dispersed phase i n a 3-in. I. D. column. Therefore, f o r f u r t h e r work, i t i s recommended that both the a x i a l d i s p e r s i o n of the continuous phase and the a x i a l d i s p e r s i o n of the dispersed phase be studied i n the large column. Then attempts can be made to c o r r e l a t e a l l the data a v a i l a b l e f or a x i a l d i s p e r s i o n c o e f f i c i e n t s i n spray columns. Such a c o r r e l a t i o n would a s s i s t p r e d i c t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t s f o r columns of intermediate s i z e between 1.5-in. and 3-in. I . D. when operated w i t h i n the range of s u p e r f i c i a l v e l o c i t y studied i n the present work. It might a l s o a s s i s t i n the p r e d i c t i o n of a x i a l d i s p e r s i o n c o e f f i c i e n t s f o r columns of s i z e somewhat outside the range mention and f o r s u p e r f i c i a l v e l o c i t i e s somewhat la r g e r or smaller than those studied here. 158 V I . NOMENCLATURE A Constant of In t e g r a t i o n . a I n t e r f a c i a l area per u n i t volume of column, f t 2 / f t ? B Constant of i n t e g r a t i o n . C Average solute concentration i n the continuous phase D •3 backmixing stream, lb-mole/ft? CQ Solute concentration i n the continuous phase, lb-mole/ft? or microgm./ml. CQ Solute concentration i n the continuous phase of a funnel-probe sample at the time of a n a l y s i s , lb-mole/ft? CQQ Value of C c when Z = 0, mlcrogm./ml CQ Solute concentration i n the continuous phase i n l e t stream, lb-mole/ft? CQ Solute concentration i n the continuous phase o u t l e t stream, lb-mole/ft? Cjj Solute concentration i n the dispersed phase, lb-mole/ft? C® Solute concentration i n the dispersed phase of a funnel-'s probe sample at the time of a n a l y s i s , lb-mole/ft. C^ Solute concentration i n the dispersed phase i n l e t stream, lb-mole/ft? ,o Cp Solute concentration i n the dispersed phase o u t l e t stream, lb-mole/ft? * Solute concentration i n a continuous phase i n 3 e q u i l i b r i u m with dispersed phase of concentration Cp, lb-mole/ft. Cp Solute concentration In a dispersed phase i n e q u i l i b r i u m with continuous phase of concentration C^, lb-mole/ft? dp Value of d s at the second peak of 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 . 159 d s Equivalent drop diameter = the diameter of a sphere whose volume i s the same as that of the drop, f t . E Continuous phase a x i a l d i s p e r s i o n c o e f f i c i e n t , f t . / h r . e = 1 - h/100; Volumetric f r a c t i o n of continuous phase i n the column. H Test s e c t i o n length between sampling points 1 and 10. (see f i g u r e s k and 5); f t . H Distance between sampling point 10 and t r a c e r i n j e c t i o n point; (see f i g u r e s k and 5.); f t . h Volume percentage of dispersed phase i n the column, %. h j V e r t i c a l dimension of a drop image corrected f o r magnification, f t . J Net f l u x of solute down the column, lb-moles/(hr. f t . ) = - Ee(dC c/dZ); Flux of solute due to a x i a l d i s p e r s i o n . Kp Mass t r a n s f e r c o e f f i c i e n t based on (Cc/m - C^) d r i v i n g lb-moles f o r c e , (hr.) (ft2.) (lb-moles/ft?) 3 2 L c S u p e r f i c i a l v e l o c i t y of the continuous phase, f t . / ( h r . f t . ) 3 2 lip S u p e r f i c i a l v e l o c i t y of the dispersed phase, f t . / ( h r . f t . ) Lvp 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 feed, f t ? / ( h r . ft2.) m =(cc/cD) e q u i l . D i s t r i b u t i o n c o e f f i c i e n t f o r the solute between the continuous phase and the dispersed phase, dimensionless. ^ T o t a l amount of solute t r a n s f e r e d out of the continuous 2 phase i n passing through the column, b a s i s of 1 f t . of 2 c r o s s - s e c t i o n a l area, lb-moles/(hr. f t . ) . N^ T o t a l amount of solute t r a n s f e r e d i n t o the dispersed phase 2 i n passing through the column, b a s i s of 1 f t . of cross-2 s e c t i o n a l area, l b - m o l e s / ( f t . hr.) 160 N = (Ny + N K)/2; Average value of N w and N„ , lb-moles/(hr. f t . ) C d C D NTU _ / — ^ Number of t r a n s f e r u n i t s , dimensionless. m D P e = (Lg/e - L p / ( l - e) ) dp/E, Peclet number f o r two phase flow. H o r i z o n t a l dimension of a drop image corrected f o r magnification, f t . p S Cro s s - s e c t i o n a l area of the column, f t . t time, h r . T Temperature °F or °C V-g Volume of the continuous phase backmixing stream i n a 3 p i s t o n sample, f t . V Volume of the continuous phase i n a funnel-probe sample 3 or a p i s t o n sample, f t . Vp Volume of the dispersed phase i n a funnel-probe sample or a p i s t o n sample, f t ? v Average volume of a continuous phase backmixing "packet" B associated with each dispersed phase drop, f t . 3 Vp Average volume of 8 dispersed phase drop, f t . Z Distance along the column, i n the d i r e c t i o n of the con-tinuous phase flow, r e l a t i v e to co-ordinate axes st a t i o n a r y with respect to the laboratory, f t . Z = 0, 8t sampling point 10. (see f i g u r e s k and 5.) Z = H -Z Distance along the column, i n the d i r e c t i o n of the dispersed phase flow, r e l a t i v e to co- ordinate axes sta t i o n a r y with respect t o the laboratory, f t . 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A., Chem. Eng. Sci., 10, 28l (1959) 46 Rod, V., B r i t . Chem. Eng. 9, 301 (196*0 1+7 Rod, V., B r i t . Chem. Eng. 11, I+83 (1966) 165 48 Henton, J. E. and Cavers, S. D., Ind. Eng. Chem. Fundamentals 9, 384 (1970) 49 Brutvan, D.R., Ph. D. thesis, Rensselaer Polytechnic Institute, Troy, New York, 1958 50 Sternling, C. V. and Scriven, L. E., A. I. Ch. E. J. 5, 514, (1959) 51 Sternling, C. V. and Scriven, L. E., Nature 187, No. 4733, 186 (i960) 52 Le P8ge , N. A. W., B. A. Sc. thesis, The University of Br i t i s h Columbia, 1956 53 Choudhury, P. R., M. A. Sc. thesis, The University of B r i t i s h Columbia, 1959 54 Nielsen, D. E., B. A. Sc. thesis, The University of Br i t i s h Columbia, 1969 55 Dean, R. R., B. E. thesis, University of Saskatchewan, 1954 56 Ewanchyna, J. E., M. A. Sc. thesis, University of Saskatchewan, 1955 57 Kingsbury, E. R., B. A. Sc. thesis, The University of Br i t i s h Columbia, 1970 58 Instructions for model 303 Atomic Absorption Spectrophotometer, Perkin-Elmer Corporation, 2-l6 (1968) 59 Fleming, J. F. and Johnson, H. F., Chem. Eng. Progr. 4j), 497 (1953) 60 Denbigh, K. G., Dombrowski, N., K i s i e l , A. J. and Place, E. R., Chem. Eng. Sci. 17, 573 (1962) 61 Hendrix, C D . , Shashikant, B. D and Johnson, H. F., A. I. Ch. E. J. 13, 1072 (1967) 166 62 Treybal, R. E., Liquid Extraction, P. l82, 2nd Ed., M cGraw-Hill Book Co., Inc., New York, 1963 63 Strom, J . R. and Kintner, R. C , A. I. Ch. E. J. 4, 153 (1958) 64 S e i j i , U., and Kintner, R. C., A. I. Ch. E. J . 2, 420 (1956) 65 Sherwood, T. K., Evans, J. E. and Longcor, J. V., Ind. Eng. Chem. 31, 1144 (1939) 66 Thomas, W. J . and Chui, Y. T., Trans. Am. Inst. Chem. Engrs. 4j, 315 (1969) 67 Taylor, G. I., Proc. Roy. Soc. 223A, 446 (1954) 68 Kintner, R.C., "Advances in Chemical Engineering" Vol. 4, P. 85 (1963) VIII. APPENDICES A) DATA OF PART III STUDY OF INTERNAL SAMPLING TECHNIQUES TABLE A - l . SAMPLING TECHNIQUE STUDIES, OVER-ALL TRANSFER DATA RUN NO. SUPERFICIAL VELOCITY, FT?/HR. FT? INLET AND OUTLET CONCENTRATIONS, 3 3 LB-MOLE/FT. X 10 OVER-ALL HAC TRANSFER INTO OR OUT OF A PHASE. OVER-ALL HAC BALANCE INTO AND OUT OF THE COLUMN. WATER PHASE MIBK PHASE WATER PHASE, V MIBK PHASE, N 8 INTO THE COLUMN, a V OUT OF THE COLUMN, NOUT N - N IN 0U1 % X 100 NIN X 100 LC CCIN C COUT CDIN C DOUT 52.26 68.97 53.73 24.13 6.17 27.11 1.546 1.444 6.83 3.233 3.131 3.23 5 52.26 68.97 0.31 26.55 24.22 3.60 1.371 1.422 -3.64 1.687 I.636 3.06 6 44 50 68.97 49.86 19.13 5.59 24.65 1.368 1.314 3.97 2.6o4 2.551 2.05 7 44.50 68.97 0.28 35.53 29.24 5.5  1.569 1.634 -4.08 2.029 1.964 3.28 8 59.98 68.97 46.13 22.56 4.25 23.9^  1.4l4 1.358 4.03 3.060 3.004 1.84 9 91.35 68.97 38.87 28.14 6.19 20.14 0.980 0.962 1.84 3.478 3.960 0.46 11 59.98 68.97 31.93 20.07 6.39 16.14 0.712 0.673 5.66 2.356 2.317 1.67 12 44.56 68.97 49.91 19.78 5.60 24.80 1.341 1.324 1.24 2.607 2.591 0.64 30 48.40 36.50 69.19 43.11 4.S5 37.63 1.262 1.226 2.94 3.497 3.460 1.06 44 18.20 72.99 62.32 8.96 3.37 16.42 0.971 0.953 1.89 1.380 1.362 1.31 45 48.40 72.99 63.03 22.64 5.57 31.70 1.955 1.907 2.48 3.457 3 4lO 1.37 6 18.20 36.50 0.14 17.76 4.20 25.05 0.771 O.761 1.36 1.248 1.238 0.80 47 48.40 72.99 50.12 19.93 5.10 24.57 1.461 1.421 2.78 2.798 2.758 1.44 3 The units of N , N N , and N are LB-MOLE/HR. FT2, 00 169 TABLE A-2. EFFECT OF SAMPLING RATE ON DISPERSED PHASE CON-CENTRATION FOR THE PLASTIC CUP PROBE, RUN 8 SAMPLING PURGING SAMPLING SAMPLING VOLUME OF SAMPLE, CONC. OF SAMPLE, POSITION TIME, TIME, RATE, ML. (SEE MIN. MIN. ML./MIN. LB-MOLE/FT. X 10 FIG. 3) MIBK WATER MIBK WATER PHASE PHASE PHASE PHASE 1 15.0 20.0 0.09 1.70 0.00 20.07 1 15.0 25.5 0.l4 3.50 0.00 20.01 1 5.0 l4.0 0.31 4.40 0.00 19.78 1 5.0 10.5 0.36 3.80 0.00 19.70 1 3.0 8.0 O.69 5.50 0.00 19.58 1 2.0 7.5 0.80 6.00 0.00 19.70 X * 1.5 4.0 1.56 6.25 0.00 19.56 1 1.0 7.0 2.93 19.00 1.50 19.79 37.99 7 15.0 20.0 0.05 2.03 0.00 15.23 7 10.0 20.0 0.15 3.00 0.00 15.20 7 10.0 17.0 0.23 3.95 0.00 15.04 7 5.0 10.0 0.54 5.35 0.00 15.04 7 3.0 7.0 0.76 5.35 0.00 14.95 7 2.0 6.0 1.01 6.15 0.00 14.77 7 1.5 3.0 1.78 5.35 0.00 14.77 1.0 7.0 3.04 20.00 1.30 15.12 29.17 7 1.0 1.5 12.00 9.30 8.80 16.77 32.38 Note. Hypodermic needle samples at the sampling rate of 1 ml./min. and purging time of !§• min. also were taken at the above sampling positions, sampling position 1: cont. phase cone. = 46.67 lb-mole/cu. f t . X 10^  sampling position 7: cont. phase cone. = 3*+ .^8 lb-mole/cu. f t . X 10^  Dispersed phase concentration 8t the time of sampling calculated from the plastic cup probe sample with the assistance of the hypodermic needle sample and equation 1 = 0.01958 lb-mole/cu. f t . Dispersed phase concentration at the time of sampling calculated as in foot note* = 0.01477 lb-mole/ cu. f t . *** Dispersed phase concentration at the time of sampling calculated as in foot note* = 0.01477 lb-mole/cu. f t . Percentage away from equilibrium calculated by eq. 8b sampling position 1 = 18.8$ sampling position 7 = 15.7$ 170 TABLE A-3. EFFECT OF SAMPLING RATE ON DISPERSED PHASE CON-CENTRATION FOR THE PLASTIC CUP PROBES, RUN 30 SAMPLING PURGING SAMPLING SAMPLING VOLUME OF SAMPLE, CONC. OF SAMPLE POSITION TIME, TIME, RATE, ML. (SEE MIN. MIN. ML ./MIN. LB-MOLE/FT. X K T FIG. 5) MIBK WATER MIBK WATER PHASE PHASE PHASE PHASE 1 10.0 15.0 0.27 4.05 0.00 19.20 1 5.0 15.0 0.33 5.00 0.00 19.12 1 5.0 8.0 0.57 4.55 0.00 19.33 1 4.0 10.0 0.6i 6.10 0.00 18.96 1 4.0 8.5 O.83 7.05 0.00 19.12 1 4.0 5.0 1.00 5.00 0.00 19.05 1 4.0 5.0 1.20 6.00 0.00 19.20 1 3.0 k.o 1.55 6.20 0.00 19.12 1 3.0 3.0 2.k0 7.20 0.00 19.17 1 2.0 2.5 4.86 11.10 1.05 20.61 5 10.0 20.0 0.12 2.40 0.00 28.98 5 8.0 11.5 0.28 3.20 0.00 29.20 5 8.0 12.0 0.4o 4.75 0.00 28.80 5 5.0 9.0 0.43 3.85 0.00 29.05 5 k.o 11.0 0.64 7.00 0.00 28.61 5 k.o 8.5 0.77 6.55 0.00 28.55 5 3.0 5.5 i.ko 7.00 0.00 28.52 5 3.0 6.0 1.55 9.20 TRACE 28.83 5 2.0 3.5 1.75 6.12 TRACE 28.91 10 15.0 23.0 0.13 3.00 0.00 35.04 10 10.0 15.0 0.29 4.4o 0.00 34.86 10 10.0 10.0 0.44 4.4o 0.00 34.20 10 5.0 12.0 0.51 6.10 0.00 34.35 10 k.o 9.5 0.82 7.75 0.00 34.32 10 - k.o 6.0 1.23 7.4o 0.00 34.08 10 3.0 6.0 2.13 12.80 0.00 34.11 1 0 * 2.0 k.o I.89 7.55 TRACE 34.36 10* 1.0 2.5 6.60 8.50 8.00 35.57 63.85 TABLE A-3. (CONTINUED) 171 Note. Hypodermic needle samples at the sampling rate of 1 ml./min. and purging time of 1-| rain, also were taken at the 8 b o v e sampling positions. sampling position 1: cont. phase cone. = 50.29 lb-mole/ft? X 10^  3 3 sampling position 5: cont. phase cone. = 60.02 lb-mole/ft. X 10 3 sampling position 10: cont. phase cone. = 65.34 lb-mole/ft. X 10 * Dispersed phsse concentration at the time of sampling calculated from plastic cup probe sample with the assistance of hypodermic needle sample and eq. 1 = 34.17 lb-mole/ft? X 10^  Percentage away from the equilibrium calculated by equation 8b sampling position 1 = 26.2$ sampling position 5 = 10.4$ sampling position 10 = 3.5$ TABLE A-4. EFFECT OF SAMPLING RATE ON DISPERSED PHASE CONCENTRATION FOR THE FUNNEL PROBE RUN SAMPLING PURGING SAMPLING SAMPLING VOLUME OF SAMPLE, CONC. OF SAMPLES AT DISP. PHASE CONC. NO. POSITION TIME, TIME, RATE, N IL. TIME OF ANALYSIS, AT TIME OF SAMPLING (SEE MIN. MIN. ML./MIN. , 3 3 FIG. 3) WATER MIBK LB-MOLE/FT". X 10 LB-MOLE/FT. X 10 PHASE PHASE WATER PHASE MIBK PHASE BY FUNNEL AND HYPO. SAMPLES AND EQ. 1 11 1 25.0 10.0 4.38 2.9 40.9 23.65 12.05 14.59 1 '26.0 9.3 5.T9 3.9 50.1 23.62 12.03 14.56 1 20.0 T.O 6.43 4.0 41.0 23.65 12.14 14.67 1 12.0 5.0 9.60 4.9 43.1 23.40 12.09 14.56 1 10.0 4.0 11.70 5.5 41.3 23.25 12.20 14.64 1 5.0 2.0 17.50 5.6 29.4 23.29 12.05 14.39 1 5.0 1.0 29.00 9.0 20.0 23.33 12.14 14.14 1 5.0 1.0 43.00 20.5 22.5 23.62 12.35 14.08 12 1 20.0 8.0 6.19 4.0 45.5 27.60 13.98 16.60 1 15.0 6.0 8.17 4.5 44.5 27.10 13.83 16.40 1 10.0 k o 11.00 5.0 39.0 26.96 14.02 16.49 1 5.0 2.0 22.10 9.9 34.3 27.55 14.25 16.27 1 5.0 1.0 32.60 11.9 20.9 28.15 14.53 15.97 Hypodermic needle samples end p l a s t i c cup probe samples also were taken at the above sampling p o s i t i o n f o r each run (both with sampling rate of 1 ml./min. and purging time of 1^ and 2 min. r e s p e c t i v e l y . ) run no. sampling p o s i t i o n hypodermic needle sample cone. p l a s t i c cup probe sample cone. 11 1 0.02978 lb-mole/cu. f t . 0.01462 lb-mole/cu. f t . 12 1 0.03710 lb-mole/cu. f t . O.OI663 lb-mole/cu. f t . Percentage away from equilibrium calculated by equation 8b run 11 = 3.4$ run 12 = 13.0$ 173 TABLE A-5. EFFECT OF SAMPLING RATE ON CONTINUOUS PHASE CONCENTRATION FOR THE HOOK PROBE, RUN 11 SAMPLING POSITION (REFER TO FIG. 3) PURGING TIME, MIN. SAMPLING TIME, MIN. SAMPLING RATE, ML ./MIN. VOLUME OF SAMPLE, ML. CONC. OF SAMPLE, 3 LB-MOLE/FT. 3 X 10 1 50.0 5.3 2.22 12.20 29-97 1 35.0 k.O 3.43 13.70 29.81 1 23.3 2.3 5.28 13.20 29.93 1 18.0 2.0 6.80 13.60 29.81 1 9.3 1.0 12.90 12.90 29.87 1 5.0 1.0 25.20 25.20 29.87 1 5.0 1.0 33.80 33.80 29.81 Concentration of hypodermic needle sample at sampling p o s i t i o n 1 f o r t h i s run i s equal t o 29.78 lb-mole/ft? X I O 3 Percentage away from e q u i l i b r i u m c a l c u l a t e d by equation 8a = 3.8$ 174 TABLE A-6. CONCENTRATIONS OF DISPERSED PHASE IN CROSS SECTIONS PERPENDICULAR TO THE COLUMN AXIS AS DETERMINED BY SAMPLING WITH THE PLASTIC CUP PROBES RUN NO. SAMPLING POSITION (SEE FIG. 5) CONC. OF DISP. PHASE ACROSS CROSS SECTION OF THE COLUMN 3 3 AT POSITIONS GIVEN BELOW (SEE FIG. 10),LB-MOLE/FT. X 10 8 b c e f g a h 30 1 8 18.90 31.63 19.49 32.21 19.10 31.73 19.23 31.77 19.27 31.85 44 1 8 lt.287 5.570 4.277 5.681 4.287 5.579 4.352 5.663 4.296 5.644 4.352 5.719 4.342 5.709 4.314 5.579 45 1 8 12.1*5 20.60 12.60 20.71 12.49 20.62 12.54 20.78 12.64 20.67 12.86 21.03 12.99 21.02 12.40 20.55 46 1 8 8.2l* ll*.13 8.42 14.18 8.28 14.51 8.36 14.33 8.45 14.37 8.57 14.79 8.63 14.51 8.28 14.13 RUN SUPERFICIAL CONC. ALONG THE COLUMN CENTRE AT SAMPLING POSITIONS NO. VELOCITY8, ^ 2 GIVEN BELOW6(SEE FIG. 5), LB-MOLE/FT3, X IO 3 FT./HR. FT. 1 2 3 5 7 8 9 30 1*8.1*0 36.50 18.90 25.01 28.46 31.63 34.13 1*1* 18.20 72.99 9.661 4.287 4.398 4.584 4.956 5.375 13.57 5.570 5.905 1*5 1*8.1*0 72.99 31.89 12.45 13.76 14.92 39.52 17.39 19.71 44.96 20.60 21.54 1*6 18.20 36.50 21.22 8.24 9.09 9.80 28.53 11.50 13.06 33.21 14.13 15.16 8 Upper value i s for the continuous phase ; lower value i s for the dispersed phase. Upper value i s for the continuous phase ; lower value i s for the dispersed phase. L c • «s • CCN* C C H : "DFN* * C v c : VD : TABLE A-7. CONTINUOUS AND DISPERSED PBASES CONCENTRATIONS GIVEN BY PLASTIC CUP PROBES, THE HYPODERMIC NEEDLES, THE FUNNEL PROBE AND THE HOOK PROBE (ALL CONCENTRATION IN / 3 3x LB-MOLE/FT. X 10 ) Dispersed phase concentration by p l a s t i c cup probes. Continuous phase concentration by fu n n e l probe a t time o f a n a l y s i s . Dispersed phase concentration by fu n n e l probe at time o f a n a l y s i s . Continuous phase concentration by hypodermic needles. Continuous phase concentration by hook probe. Dispersed phase concentration from f u n n e l probe sample wi t h a s s i s t a n c e o f hypodermic needle sample and equation 1. Continuous phase concentration i n e q u i l i b r i u m with at the same sampling p o s i t i o n . Dispersed phase concentration i n e q u i l i b r i u m w i t h C ^ at the same sampling p o s i t i o n . Volume o f water phase i n funnel probe sample, ml. Volume o f MIBK phase i n fu n n e l probe sample, ml. RUN NO. SAMPLING POSITION (SEE FIG. 3) FUNNEL PROBE SAMPLE CCN CCH °D7 C DFN C* D * CCN " C C * °D " °DP S P ' CDFN WATER PHASE MIBK PHASE X 100$ * X 100$ °DP X 100$ a C C v c <« VD ** 1 42.23 2.9 21.86 49.8 45.15 45.16 21.80 21.69 23.5 7.8 7.2 0.05 3 40.75 3.4 20.28 45.5 42.35 42.85 20.08 20.16 39.1 22.1 8.3 9.1 -0.40 5 37.35 3.1 18.38 46.1 39.52 0^.75 18.36 18.23 35.4 20.7 11.6 11.3 0.71 • 7 2.50 2.9 16.03 47.1 36.72 37.66 15.86 15.77 30.8 18.6 19.2 14.7 0.56 + Run 4 i s a d i r e c t run . T A B L E A-7. (CONTINUED) RUN SAMPLING FUNNEL PROBE SAMPLE * C - C * C - C c - c NO. POSITION CN C D DP DP DFN (SEE * * C* p c _ n FIG. 3) WATER PHASE MIBK PHASE CCN CCH CDP CDFN C C CD DP a X 100$ X 100$ X 100$ c 8 V C a V C c D D + 5 1 16.56 3.2 8.13 53.3 9.45 9.03 8.53 8.55 4.5 -45.7 -89.6 -0.23 3 19.70 3.0 9.86 4o.O 12.11 11.95 10.27 10.43 20.9 5.8 -42.1 -77.1 -1.56 5 23.28 3.4 11.64 i l l .2 14.93 14.22 12.19 12.33 24.4 7.0 -38.8 -74.1 -1.15 7 27.35 4.1 13.83 44.7 18.13 17.35 14.53 14.68 29.0 8.7 -37.5 -67.0 -1.03 + 6 1 35.17 3.3 17.47 46.2 37.67 37.90 17.40 17.29 33.6 19.5 12.1 12.1 0.63 3 31.13 4.6 15.84 43.9 34.62 34.48 15.69 15.44 29.8 17.8 16.2 13.4 1.59 5 29.13 3.8 13.98 43.8 31.92 32.08 13.98 13.74 27.2 16.4 17.4 17.3 1.72 7 24.57 3.0 12.19 45.8 28.88 29.05 12.12 11.91 23.6 15.2 22.4 25.4 1.73 7+ 1 23.19 4.7 10.95 43.5 14.51 14.04 11.63 11.89 23.6 6.9 -38.5 -40.7 -2.24 3 27.00 4.5 13.42 42.0 17 082 17.56 14.04 14.40 28.5 8.7 -37.5 -38.0 -2.56 5 30.59 4.5 15.68 4o.9 21.58 21.11 16.35 16.67 32.6 10.6 -33.8 -35.2 -1.96 7 34.80 4.0 18.38 4i.o 25.45 25.12 18.98 19.29 37.5 12.7 -32.1 -33.1 -1.63 + 9 1 36.65 3.5 19.55 44.0 38.12 38.18 19.47 19.43 37.7 19.6 1.10 0.7 0.21 3 36.19 3.1 19.96 45.3 37.57 37.66 18.86 18.77 36.4 19.4 3.2 2.8 0.48 5 34.06 3.0 18.17 55.0 36.67 36.84 18.10 18.03 35.1 18.9 4.5 4.2 0.39 7 31.72 3.1 16.95 45.9 35.69 35.77 16.80 16.68 32.6 18.4 9.5 8.7 O.71 + Runs 6 and 9 are d i r e c t runs, and runs 5 and 7 Bre reverse runs. TABLE A-7. (CONTINUED) RUN NO. SAMPLING POSITION (SEE FIG. 5) FUNNEL PROBE SAMPLE CCN CCH CDP ^FN * CC * CD # CCN " CC * CC X 100$ # c - c D DP <* X 100$ c - c DP DFN X 100$ WATER PHASE MIBK PHASE c a c V C C 8 D V D hi 10 36.25 h.o 18.46 47.5 39.24 18.18 18.21 20.30 10.4 -0.17 8 33.68 3.9 17.17 45.1 37.29 16.88 16.75 19.22 12.2 0.77 6 30.70 3.9 15.68 45.6 35.29 15.38 15.32 18.13 15.2 0.39 4 27.60 3.4 14.12 46.1 32.50 13.86 13.76 16.61 16.6 0.72 + Run 47 i s a direct run. 178 B) DATA OF PART IV EFFECT OF INTERPHASE MASS TRANSFER ON THE AXIAL DISPERSION COEFFICIENT OF THE CONTINUOUS PHASE TABLE B - l . DISTRIBUTIONS OF NaCl BETWEEN WATER-SATURATED MIBK AND MIBK-SATURATED WATER FOR VARIOUS CONCENTRATIONS OF HAc, T = TO °F TEST NO. cc> 3 LB-MOLE/FT. X I O 3 NaCl IN WATER PHASE LB-MOLE/FT. 3 X 10 NaCl IN MIBK PHASE DISTRIBUTION COEF.8, -4 X 10 DILUTION FACTOR i ABSORP-TION ABSORBANCE MEASURED CONC., ppm. ACTUAL CONC., ppm. % ABSORP-TION ABSORBANCE CONC., ppm. 1 3.487 1,000 53.9 0.3363 2.105 2,105 1.912 6.3 0.0283 0.064T 3.254 3 8.942 1,000 52.1 0.319T 2.002 2,002 4.386 T.l 0.0315 0.0T03 2.849 5 15.015 1,000 54.5 0.3420 2.141 2,l4l T.536 8.4 0.0381 0.0819 2.615 T 20.639 1,000 49.2 0.2941 1.843 1,843 10.5T2 11.8 0.0545 0.1106 1.66T 9 25.475 1,000 54.0 0.33T2 2.111 2,111 13.306 12.8 0.0595 0.1194 1.T68 11 30.593 1,000 53.9 O.3362 2.105 2,105 16.2T5 12.8 0.0595 0.1194 1.T63 13 32.954 1,000 55.2 0.348T 2.182 2,182 1T.55T 13. TO o o64o 0.12T3 1.T14 15 "42.121 1,000 54.9 0.3458 2.164 2,164 23.102 IT.20 0.0682 0.1588 1.363 IT 46.350 1,000 56.3 0.3595 2.250 2,250 25.644 18 .TO 0.0899 0.1T2T 1.303 19 51.119 1,000 56.6 O.3625 2.268 2,268 28.456 20. TO 0.1013 0.1926 1.178 21 54.T18 1,000 55.8 0.3546 2.219 2,219 30.368 22.90 0.1104 0.2121 1.046 23 63.648 1,000 55.1 0.34T8 2.ITT 2,ITT 36.441 26.90 0.1355 0.2526 0.858 25 68.158 1,000 55.2 0.348T 2.182 2,182 38.9T2 28.30 0.1445 0.2684 O.813 2T 0 1,000 56.0 0.3565 2.231 2,231 0 4.95 0.0200 0.0502 4.448 C : Concentration of HAc in the water phase. C C^: Concentration of HAc in the MIBK phase. Distribution Coefficient = concentration of NsCl in water phase, concentration of NaCl in MIBK phase. TABLE B-2. EQUILIBRIUM DISTRIBUTION OF HAc BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK,T = TO °F (ALL CONCENTRATION IN LB-MOLE/FT. X 10 ) TEST NO. HAc CONC. IN MIBK PHASE, Cp. HAc CONC. IN WATER PHASE, C c HAc CONC. IN WATER PHASE BY EQ. 26, CCFT CC " CCFT 1 2.119 4.417 4.496 -0.079 2 3.139 5.874 6.529 -0.656 3 4.697 9.663 9.610 0.053 4 6.188 12.7T9 12.529 0.250 5 8.015 16.254 16.068 0.186 6 9.528 18.9T8 18.967 0.011 7 11.153 22.2T3 22.049 0.225 8 12.891 25.5T6 25.307 0.250 9 lit .292 2T.643 27.906 -0.263 10 15.63T 30.512 30.378 0.134 11 IT.139 33.326 33.112 0.214 12 18.it 51 35.489 35.476 0.013 13 18.608 35.904 35.757 0.147 14 21.690 41.195 41.220 -0.025 15 24.437 45.993 46.027 0.603 16 25.558 4T.88T 47.906 -0.019 IT 27.340 50.723 50.923 -0.200 18 28.640 53.189 53.098 0.091 19 30.210 54.926 55.697 -0.771 20 32.T20 58.927 59.788 -0.861 21 33.292 60.600 60.709 -0.109 22 3T.664 67.917 67.612 0.305 23 38.449 68.888 68.826 0.062 24 38.561 68.826 68.998 -0.173 25 41.083 73.455 72.843 0.612 l 8 l TABLE B - 3 a . EQUILIBRIUM DISTRIBUTION OF HAc BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK, T = 7 0 . 5 °F, NaCl IN WATER PHASE i 0 . 0 1 N 3 3 (ALL CONCENTRATION IN LB-MOLE/FT. X 10 ) TEST HAc CONC. HAc CONC. HAc CONC. NO. IN MIBK IN WATER IN WATER c - c C CFT PHASE, PHASE, PHASE BY EQ. 26 °D cc c CFT 2 2.924 5 . 9 6 0 6 . 1 0 2 -O.I38 4 5 . 7 4 7 11.911 1 1 . 6 6 9 0.242 6 8.649 17.^33 17.286 0 . 1 4 7 8 1 2 . 0 4 6 2 3 . 5 0 7 2 3 . 7 2 8 - 0 . 2 2 1 10 14.486 2 8 . 1 6 3 2 8 . 2 6 4 - 0 . 1 0 1 12 17.118 3 2 . 5 0 5 33.074 - 0 . 5 6 9 lk 2 0 . 2 6 8 38.151 38.715 - 0 . 5 6 4 16 2 3 . 8 6 7 4 4 . 6 8 5 4 5 . 0 0 6 - 0 . 3 2 1 18 2 6 . 9 1 5 49.488 5 0 . 2 0 7 - 0 . 7 1 9 20 2 9 . 9 5 4 5 6 . 0 4 0 5 4 . 5 9 7 1 .443 22 35.204 6 3 . 2 3 2 6 3 . 7 5 7 - 0 . 5 2 5 2k 3 5 . 0 8 0 6 2 . 8 7 2 6 3 . 5 6 1 - 0 . 6 8 9 182 TABLE B-3b. EQUILIBRIUM DISTRIBUTION OF HAc BETWEEN MIBK-SATURATED WATER AND WATER-SATURATED MIBK, T = 70.5 °F, NaCl IN WATER PHASE * 0.1 N (ALL CONC. IN LB-MOLE/FT? X IO 3) TEST NO. HAc CONC. IN MIBK PHASE, °D HAc CONC. IN WATER PHASE, cc HAc CONC. IN WATER PHASE BY EQ. 26 C CFT °C " CCFT 1 1.912 3.»+87 1+.082 -0.591+ 3 U.386 8.9*42 8.997 -0.550 5 7.536 15.015 15.1+1+ -0.129 7 10.572 20.639 20.951 -0.312 9 13.306 25.1+75 26 .080 -0.605 11 16.275 30.593 • 31.51+3 -0.950 13 17.557 32.95*+ 33.867 -0.913 15 23.102 1+2.121 1+3.683 -1.562 17 25.61+1+ 1+6.350 1+8.053 -1.703 19 28.1+56 51.119 52.279 -l.l60 21 30.368 51+.718 55.957 -1.239 23 36 M l 63.61+8 65.705 -2.057 25 38.972 68.158 69.963 -1.805 T A B L E B-1*. T Y P I C A L D R O P S I Z E D I S T R I B U T I O N A N D D R O P V O L U M E D I S T R I B U T I O N R E S U L T S , R U N 28 183 WATER SUPERFICIAL VELOCITY = 36.50 CU.FT./1HR. SQ.FT.) KETONE SUPERFICIAL VELOCITY = 36.50 CU.FT./IHR. SO.FT.) NUZZLE TIP AVERAGE DIAMETER = 0.103 IN.  COLUMN DIAMETER = 1.5 IN. CONDITIONS CORRESPON TO RUN 28 RANGE OF EQUIVALENT DROP DIA. IN INCHES PERCENTAGE OF DROPS IN GIVEN SIZE RANGE FOR TOTAL NUMBER UF DROPS SHOWN AT HEAD OF LIST PERCENTAGE OF TOTAL DROP VOLUME CONTRIBUTED BY DROPS IN GIVEN SIZE RANGE FOR TOTAL NUMBER OF DROPS SHOWN A T HEAD OF I. IS T 100 0.0 2.0 9.0 10.0 5.0 0. 0 • 0.01' 0.02-0.03 1 0. 04-O.Ub 1 0. 06-0.07' 0. 08-0.09' 0. 10' 0.11' 0. 12-0.13' 0. 14-0.15' 0. 16-•0.01 •0.0 2 •0.03 •0.04 '0.05 200 0.0 1.5 9.5 11.0 6.5 300 0.0 1.7 10.7 10.7 7.0 400 0. 0 1 . 5 9.5 9.5 7.5 •0.U6 •0.07 •0.08 •0.09 •0. 10 0.11 3.0 6.0 2.0 3.0 4.0 I .0 8.0 18.0 13.0 9.0 6.0 1.0 3. / 6.3 1.3 4.3 3.0 1.7 ~T7CT 15.7 15.3 7.3 3.0 0.7 6.0 1.5 3.7 2.7 1.5 500 0.0 1.2 9.0 10.8 7.8 4.4 5.8 2.4 3.8 2.2 1.8 6.8 15.8 16.0 7.6 3.2 0.8 100 0.0 0.0 0. 1 0.2 0. 3 0.3 1.2 0.6 1.4 2.4 0.8 8.5 24.0 22.6 18.8 15.6 3. 1 200 0.0 0.0 0.1 0.3 0.4 0.5 1.2 0.5 1.9 2 .3 1.3 7.4 23.0 26.5 19.8 11.1 1.6 300 0.0 0 .0 0. 1 0.3 0.5 0.5 1.3 0 .4 2.1 2 .0 1.6 8.2 23.6 29.0 16.8 8.6 2.2 400 0 .0 0.0 0.1 0.3 0.5 ~UT5~ 1 .2 0.5 1 .7 1.7 1 .3 500 0.0 0 .0 0.1 0 .3 0.5 0.5 1.2 0.8 1.8 L .4 1.6 / .8 23.3 29.4 17.1 i .8 2.6 4.0 6.0 1.5 4.0 3.5 1.5 •0. 12" •0.13 •0.14 •0.15 •0. 16 •0.17 6.5 16.0 14.5 9.0 4.0 0.5 1.5 1 5.0 16 .7 8.2 3.2 0.5 8.5 21 .5 30.3 18.1 8.8 1 .6 0.17' 0. 18« 0.19' 0. 20« 0.2 1' 0. 22-•0.18 '0.19 •0.20 •0.21 •0.22 •0.23 0.0 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.0 0.0 0.0 0.0 0.7 0.0 0.0 0.0 0.0 0.0 0.5 0.0 0.3 0.0 0.0 0. 0 0.4 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.1 0.0 0 .0 0.0 0.0 0.0 2 .8 0.0 0 .0 0.0 0 .0 0.0 2.0 0.0 1.4 .0 .0 0.0 0.0 L .6 0.0 L . I 0.0 0 .0 0.0 0.23' 0. 24-•0.24 •0.25 ~OTD~ 0.0 1)70 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 B-5. DROP SIZE DISTRIBUTIONS IN THE 1^ -TJJ. I . D. COLUMN PERCENTAGE OF DROPS IN GIVEN SIZE RANGE FOR A TOTAL OF 500 DROPS RINGE ^0 OF d s , I N / \ a a a a a a a a 8 a b a b 20 22 23 24 25 26 27 28 29 31 31 36 36 0.00 0.01 . 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.2 0.01 - 0.02 2.0 3.0 1.0 0.4 0.0 0.0 0.6 1.2 0.8 12.4 11.8 18.8 16.8 0.02 - 0.03 5.2 13.6 10.0 12.0 3.0 9.2 23.8 9.0 10.0 19.4 26.2 25.8 22.4 0.03 - o.o4 7.2 12.2 14.2 20.0 7.8 13.8 13.0 10.8 15.2 16.8 15.6 11.0 10.0 0.04 - 0.05 k k 8.0 4.0 5.8 4.8 6.6 5.8 7.8 6.8 4.0 7.0 4.8 3.8 0.05 - 0.06 k.2 2.6 5.2 4.2 3.0 2.8 2.2 4.4 5.0 3.2 2.6 2.2 1.0 0.06 - 0.07 5.6 3.6 3.0 2.4 1.8 2.8 2.4 5.8 4.2 1.2 2.0 2.2 0.6 0.07 - 0.08 2.8 2.4 3.2 2.8 2.4 3.2 2.2 2.4 3.4 2.6 0.6 0.2 1.4 0.08 - 0.09 5.6 2.6 2.8 2.4 3.0 2.4 2.6 3.8 4.0 1.6 0.4 1.2 0.4 0.09 - 0.10 6.8 3.2 6.2 1.6 3.0 3.6 3.8 2.2 2.0 3.0 1.4 1.0 1.4 -0.10 - 0.11 Q k 4.8 4.0 3.0 5.0 4.2 4.8 1.8 3.6 3.0 1.8 0.6 1.0 0.11 0.12 10.4 7.6 9.6 5.4 6.6 9.0 6.8 6.8 4.0 5.0 2.6 4.4 1.6 0.12 - 0.13 14.8 9.6 15.2 11.4 20.4 14.0 10.2 15.8 9.8 9.0 7.6 9.6 6.6 0.13 - 1k 11.8 11.6 11.8 15.4 26.2 14.4 14.2 16.0 8.8 10.2 9.6 11.0 14.2 1k - 0.15 7.6 8.2 5.6 8.0 7.0 9.3 4.8 7.6 12.8 5.0 4.8 3.6 10.0 0.15 - 0.16 2.2 4.0 2.8 2.4 2.6 3.0 2.2 3.2 5.0 1.2 3.2 0.6 3.8 0.16 - 0.17 0.4 1.0 0.6 0.8 1.6 0.8 0.8 0.8 2.0 0.8 0.6 0.6 1.6 0.17 - 0.18 0.4 0.6 0.2 0.4 0.8 0.2 0.0 0.4 1.4 0.4 0.4 0.4 1.0 0.18 - 0.19 0.2 0.4 0.4 0.4 0.6 0.6 0.0 0.0 0.4 0.0 0.8 0.0 0.6 0.19 - 0.20 0.0 0.4 0.0 0.2 0.2 0.0 0.0 0.2 0.6 0.6 0.0 0.6 0.0 0.20 - 0.21 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.4 0.4 0.21 - 0.22 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.4 0.2 0.0 0.4 0.22 - 0.23 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 0.2 0.4 0.0 0.4 0.23 - 0.24 0.0 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 0.0 0.0 2k — 0.25 0.0 0.2 0.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.2 0.0 0.0 Drop d i s t r i b u t i o n s were measured at an average of 5.l6 f t . above the dispersed phase nozzle t i p s between sampling points 7 and 8. Drop d i s t r i b u t i o n s were measured at an average of 3.l6 f t . above the dispersed phase nozzle t i p s between sampling points 3 and 4. TABLE B-6. DROP VOLUME DISTRIBUTIONS IN THE l | - I N . I . D. COLUMN PERCENTAGE OF TOTAL DROP VOLUME CONTRIBUTED BY DROPS IN GIVEN SIZE RANGE FOR A RANGE T0TA1 j OF 500 DROPS OF d s , INTv. a a a a a 8 a 8 8 a b a b 20 22 23 24 25 26 27 28 29 31 31 36 36 0.00 - 0.01 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 0.01 - 0.02 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.1 0.1 0.1 0.1 0.02 - 0.03 0.1 0.2 0.1 0.2 0.0 0.1 0.3 0.1 0.1 0.3 0.4 0.4 0.2 3 o ok 0.2 0.4 0.5 0.7 0.2 0.4 0.5 0.3 0.5 0.7 0.6 0.5 0.3 O.Qk - 0.05 0.3 0.6 0.3 0.4 0.2 0.4 0.5 0.5 0.4 0.4 0.6 0.5 0.2 0.05 - 0.06 0.5 0.3 0.7 0.5 0.3 0.3 0.3 0.5 0.6 0.5 0.5 0.4 0.1 0.06 - 0.07 1.1 0.7 0.6 0.5 0.3 0.5 0.7 1.2 0.8 0.3 0.5 0.7 0.1 0.07 - 0.08 0.9 0.8 1.0 1.0 0.6 1.0 0.9 0.8 1.0 1.2 0.3 0.1 0.4 0.08 - 0.09 2.6 1.2 1.4 1.2 1.0 1.1 1.5 1.8 1.7 1.0 0.2 0.8 0.2 0.09 - 0.10 4.5 2.1 4.2 1.1 1.5 2.2 3.1 1.4 1.2 2.6 1.3 1.0 0.8 0.10 - 0.11 7.2 4.3 3.7 2.7 3.3 3.6 5.4 1.6 3.0 3.8 2.2 0.8 0.9 0.11 - 0.12 12.1 8.6 11.9 6.3 5.7 10.2 10.0 7.8 4.4 8.0 4.1 7.9 1.8 0.12 - 0.13 21.9 14.3 23.6 17.9 23.0 20.0 18.7 23.3 13.3 19.0 15.9 21.4 9.7 3 O lk 21.5 21.5 22.9 30.2 36.0 25.4 33.2 29.4 15.3 25.0 24.6 30.0 25.4 O.lk - 0.15 17.2 18.5 13.5 18.8 11.9 20.7 14.2 17.1 27.0 15.2 15.0 12.2 21.8 0.15 - 0.16 6.0 11.4 8.3 6.9 5.2 8.0 7.4 8.8 12.6 4.5 12.0 2.6 10.2 0.l6 - 0.17 1.4 3.3 2.1 2.8 4.1 2.5 3.3 2.6 6.3 3.6 2.7 2.9 5.3 0.17 - 0.18 1.5 2.3 0.8 1.6 2.4 0.8 0.0 1.6 5.2 2.2 2.2 2.6 4.0 0.18 - 0.19 1.0 1.9 2.0 2.0 2.0 2.8 0.0 0.0 1.8 0.0 5.1 5.7 2.8 0.19 - 0.20 0.0 2.2 0.0 1.1 0.8 0.0 0.0 1.1 3.1 4.7 0.0 5.1 0.0 0.20 - 0.21 0.0 1.2 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.9 4.0 2.7 0.21 - 0.22 0.0 0.0 0.0 1.5 0.0 0.0 0.0 0.0 0.0 4.3 2.2 0.0 3.0 0.22 - 0.23 0.0 0.0 0.0 0.0 1.3 0.0 0.0 0.0 0.0 2.4 4.6 0.0 3.2 0.23 - 0.24 0.0 2.0 0.0 0.0 0.0 0.0 0.0 0.0 1.9 0.0 0.0 0.0 0.0 0.24 - 0.25 0.0 2.2 2.3 0.0 0.0 0.0 0.0 0.0 0.0 0.0 2.9 0.0 0.0 Drop distributions were measured at an average of 5.16 f t . above the dispersed phase nozzle tips between sampling points 7 and 8. Drop distributions were measured at an average of 3.16 f t . above the dispersed phase nozzle tips between sampling points 3 and 4. 186 TABLE B-T. ACETIC ACID CONCENTRATION PROFILES IN BOTH PHASES RUN NO. SUPERFICIAL VELOCITY,' FT?/HR. FT? AC2TIC ACID CONCENTRATIONS IN THE CONTINUOUS PHASE AND THE DISPERSED PHASE," LB-MOLE/FT3. X IO3 i ERROR BY EQ. "(8 CIN c l C2 C 3 C5 c6 C7 C8 C 9 c i o C OUT 13 36.50 72.99 I-.336 0.870 2.609 1.218 2.671 1.218 2.795 1.255 2.857 1.329 2.91.1. 1 .".91 3.0UI. 1.516 3.168 1.553 3.292 1.590 3.379 1.615 3.1.78 1.61.0 2.187 1.872 6.99 lU 27.70 72.99 0.870 2.199 0.932 2.211 0.99"* 2.799 0.99". 2.373 1.031 2.510 1.106 2.572 1.11.3 2.61.6 1.155 2.696 1.193 2.808 1.21.2 2.907 1.317 1.967 1.7lli 6.78 15 18.20 72.99 31.261 1.678 3.891 1.865 1<.065 1.927 I..351 2.050 >> .72". 2.076 5.159 2.113 5.283 2.138 5.59"i 2.1.86 5.81.0 2.5">S 6.588 2.710 7.210 2.9"i6 3.605 8.U10 2.17 16 1J6.1»0 72.99 28.T?7 2.5W 15.911 5.590 17.030 6.1.76 lR.087 7.123 19.11.3 7.819 20.010 8.1.00 21.020 8.826 21.5"<0 9.31.8 22.230 9.708 22.935 10.181 23.718 10.367 11.1.99 13.388 5.83 20 18.20 36.50 28.791 "..235 l*.28l 6.062 15.331 6.1.75 16.136 6.860 16.759 7.175 17."i66 7.1.1.1 18.166 7.805 18.586 8.155 19.370 8.1.1.9 19.818 8.771 20.231 9.066 13.103 11.992 0.839 22 27.70 36.50 It 3.661 ". .9I49 25.89'' 9.660 27.822 11.068 29.503 12.17". 30.725 13.056 31.723 13.966 32.788 l"i .519 3"..OT7 15.191 3". .805 15.856 35.61.6 36.263 16.976 21.9"<8 20.928 3.07 23 U8.I4O 36.50 "•3.773 5.106 35.007 1*.012 36.722 15.357 37.967 16.62". 38.750 17.". 31 39.513 18.1.28 "10.152 19.011 1*0.721. 19.617 1.1.083 19.953 1.1.1.19 20.2".!. It 1.722 20.31.5 29.851 22.291 7.28 Sk 36.50 36.50 ".2.932 6.277 30.U90 12.162 32.283 13.283 33.95". l"i .539 35.030 15.357 36.038 16.251. 36.767 16.837 37.1.73 17.599 38.056 18.070 38.561 18.530 39.009 19.079 27.233 21.253 I..71 25 18.20 36.50 li 2.62I| 6.21.9 19.".0l< 8.306 20.61". 8.777 21.690 9.1.30 22.957 9.909 23.910 10.380 25.188 10.873 25.950 11.1.00 26.768 11.972 27.800 12.31.2 28.5""8 12.812 19.000 17.823 1.76 26 27.70 36.50 66.359 2.587 30.075 10.179 33.168 12.912 36.329 l"i.8oi 38.9"<9 16.HO I1I.33U 17.987 "•3.639 18.907 1.5.900 20.526 1.7.868 21. It 82 1.9.668 51.130 22.888 25."'>'1 32.696 3.09 27 1.8 .".0 36.50 65.779 2.U-U 1.9.803 19.570 52.536 22.033 51. .887 2". .1.18 56.799 26.656 58.160 27.927 59.329 29.052 60.31.2 30.188 61.253 31.369 61.8I.9 62.310 32.617 39.5">3 35.328 5.62 28 36.50 36.50 66.1485 "..259 "15.013 1B.35B ".7.583 20.120 50.095 21.750 52.033 23.351 53.898 25.33^ 55.51"' 26.509 57.1""". 27.228 58.11.3 28.227 59.112 29.01.9 29.931 35.556 3"i.771 1.36 29 18.20 36.50 66.1.19 I..270 23.351 9.25? 25.8^8 10.207 27.772 n .382 29.578 12.322 31.399 12.968 33.250 31..92'' 1'. .".95 36.8 3 3 15.567 38.992 16.155 1.0.75"" 16.933 20.60". 27.003 0.50 30 I48.U0 36.50 69.19". h .Oli5 50.292 18.902 5*..102 22.1.32 56.265 25.006 58.971 27.139 60.015 28.1.63 61.339 29.".61. 62 .663 31.111 63.512 31.626 61. .590 33.170 65.3".0 U3.11IJ 37.627 2.9"i 31 36.50 36.50 28.187 1. .Itjfi 21.81? 8.295 22.611 22.959 9.61.6 23.758 10.353 ?i. ..38? 2". .881. 11.111 ?5.1.1.7 11.531 25.536 11.71.6 26.062 12.186 26.717 12.391 18.617 13.701 3.20 32 27.70 36.50 28.200 It .kill 18.658 7.639 19.518 8.3I.6 20.327 8.69". 21.105 9.2".7 21.822 22.529 10.158 23.123 10.51.8 23.676 10.752 2l).l(03 11.162 21. .700 11.500 16.252 13.282 33 1.8.1.0 36.50 28.013 2.785 23."<53 9."<T7 23.9^3 10.212 2". .687 10.589 25.055 25.51.". 11.681 25.911 11.987 26.319 12.21.2 26.51.1' 12.558 26.830 12.925 26.932 19.321 13.976 2.9'' Upper numbers are for the continuous phase; lower numbers are for the dispersed phase. C^: HAc concentration in the phase fed to the column. ^OUT: ^ c c o n c e n t r B t l ° n * n l ^ phase leaving the column. Cj C : HAc concentrations at the sampling points I , 2, 3 ( , and 10 respectively. 187 APPENDIX C. a) Notation AA(I) A HI, AH2, AH3 B(I) BM, BC BML1, BML2 C(I) CA(I) CB(I) CBB(l) CE(l) CW(l) COMPUTER PROGRAM FOR CALCULATING AXIAL DISPERSION COEFFICIENTS FROM TRACER MEASUREMENTS An array containing the concentrations of the calibration solutions for atomic absorption spectrophotometer. Holdups of the dispersed phase. An array containing absorbances of the samples. Slope and constant term of the following equation ln (concentration of tracer) = (BM) (height above tracer distributor) + BC Upper and lower bounds of the 95$ confidence limits of BM above. An array containing absorptions of the samples. An array containing concentrations of the samples after d i l u t i o n . An array containing concentrations of the samples after correction for blank (sodium concentration in the continuous phase fed to the column). An array containing concentrations of the samples before correction for blank. An array containing the values of ln (CB(l)). An array containing the concentrations of HAc in the continuous phase samples. 188 CZ(l) An array containing the reduced concentrations of the samples. D(l) An array containing the dilution factors. ED Axial dispersion coefficient. EDL1, EDL2 Upper and lower bounds of the 95% confidence limits of ED above. ERR Tracer mass transfer balance apparent loss, % } calculated by equation kb. FT Tracer superficial velocity, FT./HR. FT. FK Dispersed phase superficial velocity, FT^/HR. FT? 3 2 FW Continuous phase superficial velocity, FT./HR. FT. TRUN Run no. NB Number of sampling points at which the concentration was available for estimation of axial dispersion coefficient. PE Peclet number. SM, SC Slope and constant term of the calibration equation: Concentration (ppm.) = (SM) (absorbance) + SC T(l) An array containing the values of the T- distribution for (NB-2) degree of freedom and 95% confidence l i m i t s . TP Temperature, °F TTNA Absorbance of tracer solution injected into the column after diluted 10,000 times. WINN Absorbance of continuous phase fed to the column. ZZ(l) An array containing sampling position, f t . above the tracer distributor. 189 b) Computer Program c CALCULATION OF E FROM TRACER RESULTS DIMENSION C ( 1 6 ) , D ( 1 1 ),CC( 16 ),B{16),CA{ 11 ) ,CB( 11 ) t C E ( 11) ,CZ( 11 ) ,V( 1 16 ) ,T(8 >, ZZ(10),CW( 10),WC( 1 0 ) , A A ( 5 ) , C B B ( 11) READ(5,1) ( Z Z ( I ),! = !,10) READ(5,2) ( T U ) , I = 1,8) R t A 0 < 5 , 2 ) (AA( I ) ,1 = 1,5) 100 READ(5,3) I RUN,FK , FW,FT,AH 1,AH2,AH3,TP,WINN,TTNA,DP READ(5,4) ( C ( I ) , I=1, 16) READI5.5) ( 0 ( 1 1 , 1 = 1 , 1 1 ) R E A 0 ( 5 , 6 ) ( C W ( I ) , 1 = 1,10)  READ(5,7) I J K . I F I G AHH1=1.0 - AH1/100.0 AHH2=1.0 - AH2/100.0 AHH3=1.0 - AH3/100.0 AH=(AH1+AH2+AH3)/3.0 AHH=( AHH1+AHH2+AHH3 ) /3.0  DO 200 1=1,16 V ( I ) = C ( I ) * 1 0 0 . 0 C C ( I ) = 1 . 0 / ( 1 . 0 - C ( I ) ) 200 B ( I ) = A L 0 G 1 0 ( C C ( I ) ) DU 3 0 0 J = 1 , 1 1 I = 11 - J I F ( D ( I ) .GT.2.0) GO TO 400 WC(I)=1.00013+3.58156*CW(I)-62.22 5*CW(I) **2+503.146*CW(11**3 300 B ( I ) = B ( I ) / W C ( I ) 4 0 0 AAA=AA(1)+AA(2)+AA(3)+AA(4)+AA{5) AAN=6.0 IF ( AA( 5 ) .EQ.O. 00) AAN = 5.0  SUMX = B( 1 2 ) + B ( 13)+B(14)+B( 1 5 ) + B ( 1 6 ) SUMXY = B( 12)*AA( 1) +6( 1 3 ) * A A ( 2 ) + » ( 1 4 ) * A A ( 3 ) + S ( 15 ) *AA( 4) +B( 16 )*<U (•> ) S U M X 2 = B ( 1 2 ) * * 2 + B ( 1 3 ) * * 2 + B ( 1 4 ) * * 2 + B ( 1 5 ) * * 2 + B ( 1 6 ) * * 2 SM = (SUMX*AAA-SUMXY*AAN)/(SUMX**2-SUMX2*AAN) SC = (SUMX2*AAA-SUMXY*SUMX)/(SUMX2*AAN-SUMX**2) TTNA=( SM*TTNA+SC )» 10000. WNA= SM*WINN+SC IF(WINN.EQ. 0.000) WNA=0.0000 DU 500 1=1,11 C A ( I ) = S M * B ( I ) + S C C B B ( I ) = C A ( I ) * D ( I ) 5 0 0 C B ( I ) = C B B ( I ) - W N A  WRITE(6,8) IRUN,FW,FK,FT,TP WRITE(6,9) NNNN=AAN+10 DO 6 0 0 1=12,NNNN J = I - 1 1 600 WKITE(6,10) A A ( J ) , V ( I ) , B ( I )  I F ( S C . L E . 0 . 0 0 0 0 ) WRITE(6,11) SM,SC I F ( S C . G E . 0 . 0 0 0 0 ) WRITE(6,12) SM,SC WRITE(6,13) I F I G DO 7 00 1=1,11 1D = D(1 ) I F ( C B ( I ).LT.O.OOOl) C B ( I ) = 0.0001  C Z ( I ) = C B ( I ) / C B ( 1 1 ) * 1 0 0 0 . C f c ( I ) = A L O G ( C B ( I ) ) 700 WRITE(6,14) I , I D , V ( I ) , R ( I ) , C A ( I ) , C B B ( I ) , C B ( I ) , C E ( I ) •CZ( I ) 190 E R R = ( F T * T T N A - C B ( 1 1 ) * F W ) * 1 0 0 . 0 / ( T T N A * F T ) W R I T E ( 6 , 1 5 > WN A , E R-t » AH S 1 = 0 . 0 S 2 = 0 . 0 , S 3 = 0 . 0 S 4 = 0 . 0 S 5 = 0 . 0 L =1 8 0 0 I F I C B ( L ) . L T . 0 . 0 5 0 0 ) GO TO 9 0 0 Z = Z Z ( L ) S 1 = S 1 + C E ( L ) S 2 = S 2 + Z S 3 = S 3 + Z * * 2 S 4 = S 4 + Z * C E ( L ) S 5 = S 5 + C E ( L ) * * 2 L = L+1  I F ( L . L T . l l ) GO TO 8 0 0 9 0 0 N b = L - l BN = NB NB = BN S S 1 = S 4 - S 1 * S 2 / B N S S 2 = S 5 - S 1 * * 2 / B N  S S 3 = S 3 - S 2 * * 2 / B N S S 4 = S Q R T ( S S 3 ) S S 5 = ( S S 2 * S S 3 - S S 1 * * 2 ) / ( ( B N - 2 . ) * S S 3 ) S S 6 = S Q R T ( S S 5 ) B M = S S 1 / S S 3 BC=( S 1 * S 3 - S 2 * S 4 ) / ( B N * S 3 - S 2 * * 2 )  S E D = - F W / B M E O = S E D / A H H Ptf = ( F K / ( l . - A H H ) + F W / A H H ) * D P / ( E D * 1 2 . ) N N = N B - 2 B M L = T ( N N ) * S S 6 / S S 4 B M L 1 = B M - B M L ' B M L 2 = B M + B M L S I G 1 2 = F W / 3 0 0 . S I G 2 2 = S E 0 * * 2 * ( 1 . / 9 0 0 0 0 . + S S 5 / M S S 3 * B M * * 2 ) ) S I G 2 = S Q R T ( S I G 2 2 ) S E D L = T ( N N ) * S I G 2 S E D L 1 = S E D - S E 0 L S E D L 2 = S E D + S E D L S I G 3 2 = ( 3 . * ( A H H l * * 2 +AHH 2 * * 2 +AHH 3 * * 2 ) - ( A H H 1 + AHH2 + A H H 3 ) * * 2 ) / 6 . 0 S 1 G 4 2 = E 0 * * 2 * ( S I G 2 2 / S E D * * 2 + S I G 3 2 / A H H * * 2 ) S I G 4 = S Q R T ( S I G 4 2 ) E D L = T ( N N ) * S I G 4 E 0 L 1 = E P - E D L  E 0 L 2 = E 0 + E D L I F ( N B . E Q . 2 ) W R I T E ( 6 , 1 6 ) 3 M , B C , NB , E D , P<E I F ( N B . N E . 2 ) W R I T E ( 6 , 1 7 ) B M , B C , B M L 1 , B M L 2 , N B , E D , E D L 1 , E D L 2 , P E I F ( I J K . E O . O ) S T O P GO TO 100 1 F O R M A T ( 1 0 F 8 . 5 )  "2 F O R M A T ( 8 F 8 . 4 ) 3 F O R M A T ( I 3 , 2 F 6 . 2 , F 6 . 3 , 3 F 6 . 2 , I 3 , 2 F 7 . 4 , F 5 . 3 ) 4 F O R M A T ( 1 6 F 5 . 3 ) 191 5 FURMAT(11F5.1 ) 6 FURMAT(10F8.6) 7 FURMAT(213) 8 FURMAT(1H1,30X,'RUN ' , I 3/3 1 X , 1 / 1 2 X , ' WATE t FLOWRATE =',F7.2 1, ' CU.FT./(HR. SO.FT.)'/12X » 'MIBK FLOWRATE = • ,F6.2,' CU.FT./(HR. 2 SO.FT.)'/12X,'TRACER-FLOWRATE =«,F6.3,' CU.FT./(HR. SQ.-T. ) '/12X , 3'NOZZLE TIP AVERAGE DI A. = 0.103 IN.•»5X,'EQUIVALENT DROP DIA. = 0 4.135 IN.'/12X t'AVERAGE VELOCITY OF DISPERSED PHASE IN NOZZLE TIPS 5 = 0.36 FT./SEC.'/12X,'COLUMN I.D.= 1.5 IN.',10X,'TEMPERATURE = ',13 6,/12X,'COLUMN HEIGHT (NOZZLE TIPS TO . INTERFACE) = 4.535 FT.')  9 FURMAT(/ 12X t 'CALIBRATION UF ATOMIC ABSORPTION SPECTROPHOTOMETER '/ 112X »'SOD.CONC. P E R C E N T ABSORBANCE•/12X,'PPM.',8X,•ABSORPT I 20N' /12X,36( ' * ' ) / 1 3 X , • O.OOU' , 9X , ' 0 . 0 ••, 9X , '0.000' ) 10 FURMAT(13X,F6.4,8X,F4.1,9X,-5.3) 11 FORMAT(/12X,•CONCENTRAT ION(PPM.) =•,F7.3,'*ABSORBANCE•,F6.3) 12 FURMAT( /12X, 'CONCENTRATION!P 3M.) =',F7.3, '»ABSORBANCE+ ' ,F5.3> 13 FURMATI/12X,'POSITION DILUTION PER CENT ABSORBANCE MEASURED S 1 AMPLE ACTUAL LOG.E REOUCED'/12X,'SEE F I G . FACTOR AiSOR^T 2IUN CONC. CONC. CONC. ' CONC. CONC.'/12X , 12 3, /12X,86<'-')) 14 FORMAT(I16,I12-,F10.1,F12.3,F11.3,F10.3,F8.3,F9.3,F11.3) 15 FURMAT(14X,'(POSITION 11 REFERS TO THE AQUEOUS PHASE LEAVING THi C 10LUMN '/14X,'ACTUAL CONC. = SAMPLE CONC.-(CONC. OF BLAN<=INLET CON 2T. PHASE ANALYSIS) )• //12X, • INLET CONT. PHASE ANALYSIS = ' t •=• 6 . 3 , ' PP 3M.•/12X,'TRACER MASS BALANCE APPARENT LOSS =',F7.3,' PER CENT'/12X 4, 'MIBK HOLDUP =',F5.2,' PER CENT') 16 F U R M A K / 1 2 X , ' LOG . E ( CONC ) = ' ,F8.4, '*(HEIGHT ABOVE TRACER INJECTION) + 1 ',F6.4/12X, 'NUMBER OF POINTS FOR ESTIMATION Or A < I A L DISPERSION CO 2EFFICIENT = »,I 2/12X,'AX IAL DISPERSION COEFFICIENT =',F6.2,' SQ.FT. 3/HR.•/12X,'PECLET NUMBER =',F6.3) 17 FURMAT(/12X,•LOG.E(CONC)=',F8.4,'^(HEIGHT ABOVE TRACER IMJECTION)+ 1•,r6.4/12X,'95 PER CENT CON-IDENCE LIMITS ON SLOPE ARE',F9.4,' TO' 2, F 9 . 4 / 1 2 X , 'NUMBER OF POINTS FOR ESTIMATION OF AXIAL DISPERSION COE 3 F F I C I E N T = ' , I 3 / 1 2 X , ' A X I A L DISPERSION COEFFICIENT =',F5.2,' SQ.FT./H 4R.'/12X,'95 PER CENT CONFIDENCE L I M I T S ARE',F6.2,' SO. FT./HR. TO'. 5 F 6 . 2 , ' SQ.FT./HR.'/12X,'PECLEI NUMBER =',F6.3/) END c) Typical Computer Output for Calculating E from Tracer Measurements, Run 28 TABLE C-l. TYPICAL COMPUTER OUTPUT FOR CALCULATING E FROM TRACER MEASUREMENTS, RUN 28 WATER FLUWRATE = 36.50 CU- .FT. / tHR. S O . F T . ) MlBK FLUWKATfc = 36 .50 CU.FI " . / (HR. SU. FT. ) TRACER FLUWKATfc = 0.368 C U . F T . / I H R . SO .FT . ) NUZZLE TIP AVtRAGt' OIA. = 0.103 IN. EQUIVALENT DROP 0 1 4 . = 0 .135 H . AVfcRAGb VELOC ITY OF""0TSPERS FD"PHAS E TM" "NOZZTT: TTP"S" = 0736' F T . / S F C . CULUMN I.U.= 1.6 IN.' TEMPERA T URE = 68 CULUMN HEIGHT INUZZLE TIPS TU INTERFACE) = 10.3? F T . CALlBRATIUN UF AfUMIC ABSURPTION SPECTROPHOTOMETER SUU.CUNC. C t N T _ _ A ^ n KB_ANCE PPM. "AUSURPTIUN" 0 .000 0.0 0.000 1.1498 36 .0 0.194 2.2997 58.7 0 .384 3.4495 71.4 0.544 4 .5 994" 81.1 0 .724 C U N C E N T R A T I U N ( P P M . ) = 6 .391*ABSnRBANCE-0.059 P U S I r I U N 0 1 L U T I U N P E R C E N T A B S U R B A N C E M E A S U R E D S A M P L E A C T U A L L O G . E R E D U C E D StE F I G . F A C T U K A B S U R P T I O N C O N C . C O N C . C O N C . ; U M ; . C O N O . 5 1 2 5 . U 6 8 . 6 0 . 5 0 3 3 . 1 5 7 7 8 . 9 1 3 7 8 . 8 6 7 4 . 3 6 8 3 0 U . 2 7 3 2 1 0 . 0 6 6 . 8 0 . 4 7 9 3 . 0 0 2 3 0 . o n 2 9 . 9 7 2 3 . 4 0 0 1 1 4 . U 3 3 1 0 . 0 3 0 . 2 0 . 1 5 6 0 . 9 3 9 9 . 3 9 2 9 . 3 4 6 2 . 2 3 5 3 5 . 5 « 2 4 5 . 0 2 7 . 9 0 . 1 4 2 0 . 8 4 9 4 . 2 4 5 4 . 2 0 0 1 . 4 3 5 1 5 . 9 9 0 •3 1 . U 5 9 . 0 0 . 3 5 5 2 . 2 0 9 2 . 2 0 Q 2 . 1 6 3 0 . 7 7 2 8 . 2 3 6 6 1 . 0 4 1 . 0 0 . 2 1 0 1 . 2 8 1 1 . 2 8 1 1 . 2 3 5 0 . 2 1 1 4 . 7 0 1 7 1 . 0 L 7 . 8 0 . 0 7 8 0 . 4 3 8 ( ) . 4 3 « 0 . 3 9 2 - 0 . 9 3 7 I . 4 9 ? 8 1 . 0 9 . 2 0 . 0 3 4 0 . 1 8 5 0 . 1 8 5 0 . L 3 9 - 1 . 9 7 0 0 . 5 3 1 9 1 . 0 5 . 7 0 . 0 2 3 0 . 0 9 0 0 . 0 9 0 0 . 0 4 4 - 3 . 1 3 5 0 . 1 6 6 1 0 1 . 0 3 . 7 0 . 0 1 5 0 . 0 3 6 0 . 0 3 5 0 . 0 0 0 - 9 . 2 1 0 0 . 0 0 0 11 1 0 0 . 0 6 2 . 0 0 . 4 2 0 2 . 6 2 7 2 6 2 . 6 9 7 2 6 2 . 6 5 1 5 . 5 7 1 1 0 0 0 . 0 0 0 (PUSITIUN 11 REFERS TU TH<= AOUEUUS PHASE LEAVING THE COLUMN ACTUAL CUNC. = SAMPLE CUNC. -( COAIC . UF 8 LA NK= I NL ET CONT . PHASE ANALYS IS ) ) INLET CUNT. PHASE ANALYSIS = 0.046 PPM. TRACER MASS BALANCE APPARENT LOSS = - 2 . 2 5 6 PER CENT  MIBK HOLOUP = 3.17 PER CENT ~ LUG.E ICUiMC) = - 1 .7138* (HE IGHT ABOVE TRACER I NJECT I ON)+5.0936 95 PER CENT CONFIDENCE LIMITS UN SLOPE A<E - 1 . 8 6 5 7 TO - 1 . 5 6 1 9 NUMBER Ur PUINTS FUR ESTIMATION OF AXIAL DISPERSION COEFF IC IENT= ft AXIAL DISPERSION COEFFICIENT =21.99 S U . F T . / H R . 95 PER CENT CUNF 1UENLE L1MTTS ARE 207TX4 SU. h I . /HRT " HI 2 3 . 9 5~ ~. F T . /HR ." Pt C LET NUMBER = 0.609 APPENDIX D. SAMPLE HAND CALCULATION AND COMPUTER PROGRAM FOR CALCULATING THE AXIAL DISPERSION COEFFICIENT FROM PARTITIONABLE SOLUTE CONCENTRATION PROFILES IN THE CONTINUOUS PHASE AND IN THE DISPERSED PHASE a) SAMPLE CALCULATION A specimen hand calculation i s presented starting from the data obtained from the experiment. The calculation closely follows the computer program as shown in (c) of this part. However, the calculation as presented i s not absolutely complete, because certain of the steps of calculation, such as curve f i t t i n g and integration of the concentration p r o f i l e s , were very tedious to present in this way. The aim of this hand calculation was two fold; to check the computer results, and to serve as an i l l u s t r a t i o n of the computer program. Run 28 was chosen for the hand calculation: Run 28 MIBK phase superficial velocity, Lp = 36.5 ft?/hr. ft2. Water phase superficial velocity, L c = 36.5 f t l / h r . ft2 Holdup of MIBK phase, h, = 3.17$ Height of the column test section = 4.53^7 f t . Height of the column = 10.3k f t . Column inside diameter = 1.5 i n . Number of nozzle tips used = 12 Average inside diameter of nozzle tips = 0.103 i n . Average velocity of MIBK phase in nozzle tips = O.36 ft./sec. Equivalent drop diameter (corresponding to the second peak of a drop size distribution plot) = 0.135 i n . i 3 Inlet water phase HAc concentration, C c = 0.066485 lbmole/ft. Outlet water phase HAc concentration, c£ = 0.035556 lbmole/ft? Inlet MIBK phase HAc concentration, C* = 0.004259 lbmole/ft 3. Outlet MIBK phase HAc concentration, c£ = 0.034771 lbmole/ft 3 NOTATION AND DATA NAME (IN PROGRAM) DESCRIPTION VALUE IRUN FK FW OLDUP WINT WOUT DINT DOUT Z(D Z(2) 2(3) Z(4) Z(5) Z(6) Z(7) Z(8) z(9) Z(10) CMW(I' CMW(2] CMW(3) CMW(4; CMW(5] CMW(6; CMW(7) CMW(8) CMW(9] CMW(lO) RUN NO. MIBK phsse superficial velocity Water phase superficial velocity MIBK phase holdup, % Inlet water phase HAc concentration Outlet water phase HAc concentration Inlet MIBK phase HAc concentration Outlet MIBK phase HAc concentration Reduced height, Zp, at sampling pt. 10 Reduced height, ZR, at sampling pt. 9 Reduced height, ZR, at sampling pt. 8 Reduced height, ZR, at sampling pt. 7 Reduced height, ZR, at sampling pt. 6 Reduced height, ZR, at sampling pt. 5 Reduced height, ZR, at sampling pt. 4 Reduced height, ZR, at sampling pt. 3 Reduced height, ZR, at sampling pt. 2 Reduced height, ZR, at sampling pt. 1 HAc cone, in cont. phase, at Z(l] HAc cone, in cont, HAc cone, in cont, HAc cone, in cont, HAc cone, in cont, HAc cone, in cont, HAc cone, in cont, HAc cone, in cont. phase, at Z(8) HAc cone, in cont. phase, at Z(9) HAC cone, in cont. phase, at z(lO) phase, at Z(2 phase, at z(3 phase, at Z(4 phase, at z(5 phase, at Z(6 phase, at Z(7 28 36.5 36.5 3.17 0.066485 0.035556 0.004259 0.034771 0.000 O.IO761 0.21966 0.33197 0.44299 0.55532 0.66642 0.77821 O.88916 1.0000 0.059900 0.059112 0.058143 0.057144 0.055514 0.053898 0.052033 0.050095 0.047583 0.045013 195 CMD(l) HAc cone. in MIBK phase at z ( D 0.029931 CMD (2) HAc cone. in MIBK phase at Z(2) 0.029049 CMD(3) HAc cone. in MIBK phase at Z(3) 0.028227 CMD (4) HAc cone. in MIBK phase at Z(4) 0.027228 CMD(5) HAc cone. in MIBK phase at z(5) 0.026509 CMD(6) HAc cone. in MIBK phase at (6) 0.025334 CMD(T) HAc cone. in MIBK phase at z(7) 0.023351 CMD(8) HAc cone. in MIBK phase at z(8) 0.021750 CMD(9) HAc cone. in MIBK phase at Z(9) 0.020120 CMD(10) HAc cone. in MIBK phase at Z(10) 0.018358 Equation 26 (below) i s used to calculate the relationship between HAc concentrations i n the two phases at equilibrium. cc = 0.0002836 + 2.01751 Cp - 6.11123 26 i i ) CALCULATIONS l ) F i t t i n g the Concentration Profiles for each Phase UBC "OLQF" library subroutine subprogram was used to f i t the HAc concentration profile for each phase. For the continuous phase the best f i t t e d equation i s as follows: C c = 0.0598552 - 0.00547154 ZR - 0.0093335 Zp D-l And for the dispersed phase: C D = 0.02979^7 - 0.0051125 2^  - 0.0064221 z\ D-2 196 The computer outputs corresponding to each of equation D-l and D-2 are shown in table D-l and table D-2 respectively. TABLE D-l C O N T I N U O U S P H A S E C U N C F N T R A T T O N P R O F I L E . * ********** *** * ** * ** * * * ** **** **** ** ** * D E G R E E GF P O L Y N C M I A L = 2 SUM UF S Q U A R E S = 0 . 6 0 3 2 9 7 E - 0 7 PARAKE T E N S 0 . 5 9 8 5 5 2 E - 0 1 - 0 . 5 4 7 1 5 4 E - 02 - 0 . 9 3 3 3 5 0 E - 0 2 V A L U E S OF Z R VALUF.S OF cr. F [ T T E D V A L U E S OF CC P E S [ D U A L S * * * * * **********:> [: ** * * * * * * * * . -p v ** * * * * * * * * * * * * ** * * * * * * * * * * * * * * * * * * 0 . 0 0 . 5 9 9 0 0 0 E - 01 0 . 5 9 8 5 5 2 E - 0 1 0 . 4 4 7 5 9 4 F . - 0 4 0 . 1 C 7 6 1 C . 0 . 5 9 L 1 2 0 E - 01 0 . 5 9 1 5 8 4 E - 0 1 - 0 . 4 6 3 6 5 O F - 0 4 0 . 2 1 9 6 6 0 0 . 5 8 1 4 3 0 L - O i 0 . 5 8 2 0 3 0 E - 0 1 - 0 . 6 0 0 14 4 E - 0 4 0 . 3 3 1 0 7 0 0 . 5 7 1 4 4 0 0 01 0 . 5 7 0 1 0 3 E - 0 1 0 . 1 3 3 7 3 8 F - 0 3 0 . 4 4 2 9 9 0 0 . 5 5 5 1 4 0 E - 01 0 . 5 5 5 9 9 8 E - 0 1 - 0 . 8 5 7 9 7 2 F - 0 4 0 . 5 5 5 3 2 0 0 . 5 3 8 9 8 0 E - 01 0 . 5 3 9 3 8 5 E - 0 1 - 0 . 4 0 5 1 6 3 E - 0 4 0 . 6 6 6 4 2 0 0 . 52 0 3 3 0 E - 01 0 .5 2 0 6 3 7 E - 0 i - 0 . 3 0 7 41 1 E - 0 4 0 . 7 7 8 2 1 0 0 . 5 0 0 9 5 0 E - 01 0 . 4 9 9 4 4 8 E - 0 1 0 . 1 5 0 2 3 4 E - 0 3 0 . 8 8 9 1 6 0 0 . 4 7 5 8 3 0 E - 01 0 . 4 7 6 1 1 L E - 0 1 - 0 . 2 8 0 5 5 2 F - 0 4 1 . 0 0 0 0 G 0 . 4 5 0 1 3 O E - 01 0 . 4 50 50 2 E - 0 1 - 0 . 3 7 2 0 4 5 E - 0 4 The standard error of these f i t t e d values i s 0.8684 X 10 3 lb-mole/ft. for the continuous phase concentration prof i l e and i s -L 3 2 . 0 6 7 X 10 lb-mole/ft. for the dispersed phase concentration p r o f i l e . 197 TABLE D-2 0 I S P E R S 1-0 P H A S F C O N C E N T R A T I O N P R O F I L E * $ £ * * * * * '4; * * * * * * ;;t * * * * * * * * * * * * * 3',: * /,: * * * D E G R E E O F P O L Y N O M I A L ^ 2 S U M or _ S J J U A J ? rs o . 341 fi30E-06 P A R A M E T E R S 0 . 2 9 7 9 4 7 E - 0 1 - 0 . 5 1 1 2 5 8 F - C 2 - 0 . 6 4 2 2 1 O E - 0 2 VALUES O F /R V A L U E S O F C U F I T T E D V A L U E S ' O F C D R F SID UA L S ****** * * * ^  0 . 0 0 . 107610 0 . 2 1 9 6 6 0 0 .331970 0 . 4 4 2 99G " '^ V ^ ' ^  *I: ^  ^  v v V - i * -0 . 2 9 9 3 1 0 E -0 . 2 9 0 4 9 0 E -0 . 2 8 2 2 7 0 E -0 . 2 7 2 2 6 0 F -0 . 2 6 5 0 9 0 E -* * * • ********* * * * * * * * * * * * * * * * * * 0 . 5 5 5 32C 0.656420 0.77021C 0.0 09 160 1.00000 01 •01 •01 01 •01 0. 2 53 34 0b-0 . 2 3 3 5 ICE-0.217500E 0. 20 12 O O F -0. 18 3 500 E-0 . 2 9 7 9 4 7 E - 0 1 0 . 2 9 1 7 0 2 E - 0 1 0 . 2 8 3 6 1 8 E - 0 1 0 . 2 7 3 8 9 7 F - C 1 0 . 2 6 2 6 9 6 E - 0 1 • 0 1 0 . 2 4 9 7 5 1 E - 0 1 0 1 0 . 2 3 5 3 5 4 E - 0 1 - 0 1 0 . 2 1 9 2 6 8 F - 0 1 • 0 1 0 . 2 0 1 7 1 5 E - 0 1 • 0 1 0 . 1 8 2 6 0 0 E - 0 1 0.136290F-0 3 •0.121L76b-03 -0 . 13401 1E-0 3 -0. 163 749E-03 0.2 39383E-03 0 . 3 5 8 8 5 0 E - 0 3 • 0 . 1 8 4 4 3 5 E - 0 3 - 0 . 1 7 * 7 6 1 F - 0 3 - 0 . 5 14 7 2 3 E - 0 4 0 . 9 7 9 5 6 5 F - 0 4 2) Calculating the Capacity Coefficients, K^a, and Distribution Coefficients, m. The test section of the column was divided into nine sections. Each section included that region of the column from one sampling point to the next one below; that is section 1 included the region of the column between sampling points 10 and 9, and section 2 included the region of the column between sampling points 9 and 8, and so on. The values of number of transfer unit (NTU), K^B, and m were calculated for each section. NTU of any section, i , i s given by the following equation. 31 The NTU is based on the dispersed phase concentration on the assumption that the dispersed phase does not backmix , 8nd that therefore the change in concentration of this phase represents mass transfer across the interface. In both the hand calculation and the computer program, the trapezoidal method of integration was used. The integration of above equation 31 for NTU\ was repeated several times. In each integration the section concerned was divided into smaller and smaller subsections, u n t i l the difference of two consecutive (NTUi)'s obtained was smaller than 0.001„ Then the last value of NTl^ was taken as the value of NTU^ for the section. In the f i r s t integraion above the section was divided into subsections based on a AZp interval of 0.01 (dimensionless). In the second integration the section was divided into subsections based on a AZ^ interval of 0.005, and so on. As an i l l u s t r a t i o n , for the case where Zp = 0.005, subsection 1 of a section was given by A Z R 1 = \l ~ 0^ -Subsection 2 was given by A Z R 2 = " ^ 1 = °-°° 5 and so on. Here, as i in AZp^ increases one i s moving downward in the column. The last subsection of the section wss given by A Z R n " ^ n " V n - l ) = °-°° 5 where Z ^ Q represents the begining point of the section concerned, and Zp n the ending point. If AZp n calculated as Zp n - Z R ^ - J J turns out to be less than 0.005, AZp n never the less i s taken as being equal t o ^ n " V n - l ) -For the hand calculation, section 1 i s taken as an example and the interval of a subsection within a section was taken to be 0.005, except for the last subsection where AZ^ = 0.00261. A l l the values calculated are l i s t e d in table D-3. The NTUj of the section is given by the equation D-3 22 NTU = i=l L * C D ( -YYD. YYD i - l D-3 = 0.20233 and m^  for the section i s given by equation D-4 23 «! - i g l (mt) - 1.82714 D-4 The Kp8 of the section i s calculated from equation 32 T A B L E D-3 S U B S E C T I O N ° D m Y D D = - - CJ J m u *<T> Y D D I - Y D D I _ 1 1 2 3 4 5 6 T 8 9 10 11 12 13 lk I T 18 19 20 21 22 0.00000 o .00500 0.01000 0.01500 0.02000 0.02500 0.03000 0.03500 0 .04000 0.04500 o.0500 0.05500 o.06000 0.06500 0.07000 0.07500 0.08000 0.08500 0.09000 0.09500 0.10000 0.10500 0.10761 0.059855 0.059828 0.059800 0.059771 0.059742 0.059713 0.059683 0.059652 0.059621 0.059590 0.059558 0.059526 0.059493 0.059460 0.059426 0.059392 0.059358 0.059323 0.059287 0.059251 0.059215 0.059178 0.059158 0.029795 0.029769 0.029743 0.029717 0.029690 0.029663 0.029636 0.029608 0.029580 0.029552 0.029523 0.029494 0.029465 0.029435 0.029405 0.029375 0.029345 0.029314 0.029283 0.029251 0.029219 0.029187 0.029170 1.8258 1.8259 1.8260 1.8261 1.8263 1.8264 1.8265 1.8266 1.8267 1.8269 1.8270 1.8271 1.8272 1.8274 1.8275 1.8276 1.8278 1.8279 1.8281 1.8282 1.8283 1.8285 1.8286 334.663 333.699 332.730 331.767 330.807 329.843 328.886 327.930 326.972 326.020 325.072 324.119 323.170 322.228 321.282 320.340 319.403 318.463 317.526 316.587 315.659 314.722 314.238 0.000026 0.008597 0.000026 0.008678 0.000026 0.008759 0.000027 0.008841 0.000027 0.008922 0.000027 0.009001 0.000028 0.009080 0.000028 0.009160 0.000028 0.009237 0.000029 0.009315 0.000029 0.009392 0.000029 0.009469 0.000030 0.009544 0.000030 0.009620 0.000030 0.009694 0.000031 0.009769 0.000031 0.009844 0.000031 0.009915 0.000032 0.009989 0.000032 0.010061 0.000032 0.010132 0.000017 0.005316 O O 0.20233 X 36.50 r= • • - '• • — (0.10761 - 0.00000) x 4.5347 = 15.1339^  l/hr. The same procedure was used f o r the other s e c t i o n s . The values of NTU , ra, and K^a of each section are l i s t e d i n ta b l e D-4 below. TABLE D-4 V m, NTU SECTION NO. MID-POINT AVERAGE VALUES 1/HR. OF THE SECTION 1 0.05380 1.82714 0.20233 15.134 2 O.I6363 1.83040 0.24545 17.632 3 0.27581 1.83462 0.27583 19.768 4 0.38748 1.83975 0.29668 21.510 5 0.49915 1.84571 0.31953 22.896 6 0.61087 1.85262 0.33068 23.957 7 0.72231 1.86033 0.34332 24.720 8 0.83368 1.86894 0.34756 25.214 9 0.94458 1.87835 0.35073 25.469 The values of NTU f o r the t e s t section i s equal t o the sum of a l l the i n d i v i d u a l NTU^ of the sections w i t h i n the t e s t section as given by equation D-5 below. 9 NTU • (NTU) D-5 1=1 1 = 2.71211 The value of K a f o r the t e s t s ection can be cal c u l a t e d by D equation 33 9 i = l K a = 33 D Height of the t e s t s e c t i o n 36.5 X 2.71211 4.53^7 = 21.82989 1/m» The value of ra f o r the t e s t s e c t i o n i s t a k e n a s an a r i t h m e t i c average of m^  f o r the nine sections w i t h i n the t e s t s e c t i o n 9 m(of the t e s t section) = — ^ - j m.^  = 1,84865 3) Evaluation of E f o r the Test Section Using the F i r s t Method Mentioned i n the Body of the Thesis Let be the experimentally measured value of the continuous phase concentration, and be the continuous phase concentration c a l c u l a t e d by equation 22 (below). C w = A e x p O v . ^ ) + BexpO^Zjj) - Q 22 The l e a s t squares technique was used i n t h i s method. Let 203 10 A2=r ( c c - c / io i=l (C c - A e x p Q ^ ) - BexpO^Z^) + Q) 35 Differentiate equation 35 with respect to A and B separately; then 2 2 equate the resulting equations to zero (That i s and are set dA oB equal to zero.) For simplicity, from now on£means The following equations result: AZ(exp(X1ZR)) + BZ(exp(XiZR)exp(X2ZR)) = ^l(Ccexp(\\)) + QHexp(X1ZR) D-6 2 AZ(exp(X iZ R)exp(\ 2Z R)) + B H (expO^ )) =5I(Ccexp(X2ZR)) + QZexpO^ ) D-7 Equations D-6 and D-7 are solved simultaneously for A snd B: A » }Z(Ccexp(K1ZR)). + QZ(exp(X1ZR)) X^expO^Zp)) + QZCexpO,^ )) Z(exp(X1ZR)exp(X2ZR)) X(exp(X1ZR)) Z(exp(X1ZR)exp(X2ZR)) (^exp(X1ZR)exp(X2ZR)) 2 XCexpO^ Zp)) D-8 20k B = XCexpCX^ ))' ZCCcexpCX^ )) +QZexp(\iZR) 2I(exp(X1ZR)exp(X2ZR)) Z_ (CQexp(\-L^)) + QKexpQ )^) 5I(exp(X Z ) ) 1 R (exp(XLZR)exp(X2ZR)) 2 ; (exp (XXZR)exp (X2Zr ) ) IT (exp (X^ ) ) D-9 The method of calculation i s by assuming a value of E. Once we have E, the values of 0t,y6> Y, 0,, X]_, andXg, can be calculated from equations 21-a, 21-b, 21-c, 23-c, 23-a, and 23-b. Knowing the values of Q, X]_, and Xg> A a n d B can be calculated from equations D-8 and 2 D-9. Finally A i s calculated by equation 35. The same process of calculation i s repeated several times with different values of E. The 2 value of E which gives the lowest A i s said to be the best, and this value i s taken as the estimated value of E for the test section of the column. In the computer program the values of E ranged from 1 to 60 increasing by 1 for each calculation. Therefore the whole calculation i s carried out 60 times. Because repeating step after step of the calculation by hand would be very tedious, in this specimen calculation only one value of E i s used to serve as an example. E equal to 24.0 i s used in the calculation below. This value corresponds to the 2 minimum A from the computer output for this run. The average value of the flux measured at the top 8nd at the bottom of the column i s used for the present hand calculation. This average flux i s calculated by equation 34 205 J - i ((LCCJ- l^ cg) + (LCC° - I^Gi)) = £ (36.5 X 0.066485 - 36.5 X 0.034771) + (36.5 X 0.035556 - 36.5 X 0.004259) = 1.149949 lb-moles/(hr.ft 2.) The other quantities needed for calculating A and B are calculated as below: a = £ (h + V ) 2 Ee L D *= 4.5347 ( 36.5 21.82989) 2 24.0 X 0.9683 36.5 = 4.917205 mLpEe = (36.5 - 1.84865 X 36.5) X 21.82989 X 4.534T2 1.84865 X 36.5 X 24.o"x 0.9583 = - 8.86750 JK aH 2 7 = _ £ LDEe = 1.149949 X 21.82989 X 4.5347g 36.50 x 24.0 x 0.9683 = 0.608574 « -0.0686297 ! » 4.917205 + 4.9172052+ (-8.86750) = 4.917205 + 3.912979 = 8.830184 \ 2 « a - J a 2 + /3 = 1.004226 ^(expO^Zp)) = exp(8.830184 X 0.00000) + exp(8.830184 X O.IO761) + exp(8.830184 X 0.21966) + exp(8.830184 X 0.33197) + exp(8.830184 X 0.44299) + exp(8.830184 X 0.55532) + exp(8.830184 X 0.66642) + exp(8.830184 X 0.77821) + exp(8.830l84 X O.88916) + exp(8.830l84 X 1.00000) = 1 + 2.586268 + 6.956234 + 18.753046 + 49.983013 + 134.771099 + 359.462989 + 964.623135 + 2,569.448095 + 6,837.544808 = 10,945.12868 207 5I(C c exp( X ^ ) ) = 0.059900 X exp(8.830184 X 0.00000) + 0.059112 exp(8.830184 X O.IO761) + 0.058142 exp(8.830184 X O.21966) + 0.057144 exp(8.830184 X 0.33197) + 0.055514 exp(8.830184 X 0.44299) + 0.053898 exp(8.830184 X 0.55532) + 0.052033 exp(8.530184 X 0.66642) + 0.050095 exp(8.830184 X 0.77821) + 0.047583 exp(8.830184 X O.88916) + 0.045013 exp(8.830184 X 1.00000) • 0.059900 + 0.059112 x 2.586268 + 0.058143 X 6.956234 + 0.057144 X 18.753046 + 0.055514 x 49.083013 + 0.053898 x 134.771099 + 0.52033 x 359.462989 + 0.050095 x 964.623135 + 0.047583 X 2569.448095 + 0.045013 X 6837-544808 = 0.059900 + 0.152879 + 0.404456 + 1.071624 + 2.774757 + 7.263893 + 18.703938 + 48.322796 + 122.262049 +307.778404 = 508.7947 QXTexp(XiZR) = -O.0686297 X 10,945.12868 = -751.16090 H C e x p t X ^ ) ) = exp(l.004226 X 0.00000) + exp(1.004226 X 0.10761) + + exp(1.004226 X 0.33197) + + exp(l.004226 X 0.55532) + exp(1.004226 X 0.21966) exp(1.004226 X 0.44299) exp(l.004226 X.0.66642) + exp(l.004226 X O.7782I) + exp(l.004226 X O.88916) + exp(l.004226 X 1.00000) = 1 + 1.114120 + 1.246801 + 1.395668 + 1.560275 + 1.746593 + 1.952745 + 2.184744 + 2.442245 + 2.729794 » 17.372985 Q5I ( e x p ( X 2 Z R ) ) » -0.0686297 X 17.372985 = -I.I92303 X X C c e x p C X g Z R ) ) = 0.05990 X 1 + 0.059H2 X 1.114120 + 0.058l43 X 1.246801 + 0.057144 X 1.395668 + 0.055514 x 1.560275 + 0.053898 x 1.7^6593 + 0.052033 x 1.952745 + 0.050095 x 2.184744 + 0.047583 X 2.442245 + 0.045013 X 2.729794 = 0.059900 + 0.0658579 + 0.0724928 + 0.0797541 + 0.0866171 + 0.0941379 + 0.1016072 + 0.1094448 + O.II62093 + O.1228762 = O.908807 2Kexp(X 1ZR)exp(X 2 ZR)) = 1 X 1 + 2.586268 X 1.114120 + 6.956234 X 1.246801 + 18.753046 X 1.395668 + 49.983013 x 1.560275 + 13^.771099 X 1.746593 + 359.462989 X 1.952745 + 964.623135 X 2.184744 + 2569.448095 X 2.442245 + 6837.544808 X 2.729791* = 1 + 2.881413 + 8.673040 + 26.173026 + 77.987246 + 235.390248 + 701.939554 + 2107.454606 209 + 6275.221763 + 18665.08879 = 28101.81114 YLiexpiXfo))2 » 1 + 2.5862682 + 6.95623^  + 18.7530462 + 49.9830132 + 134.7710992 + 359.4629892 + 964.6231352 + 2569.M80952 + 6837.5448082 = 54,434,863.25 ^(exptXgZg))2 = l 2 + 1.1141202 + 1.2468012 + 1.3956682 + 1.5602752 + 1.7465932 + 1.9527452 + 2.1847442 + 2.4422452 + 2.729791*2 = 33.232266 Therefore: A « 508.79^7 - 751.1609 0.908897 - 1.192303 54,434,863.25 28,101.81114 28,101.81114 33.232266 28101.81114 33.232266 -242.3662 x 33.232266 + 0.283406 X 28101.81114 54,434,863.25 X 33.232266 - 28101.811142 -8,054.37803 + 7964.22189 (18.089939 - 7.897118) X 10' 8 9Q.l56l4 10.192821 X 10 -8 = -8.845063 x 10' ,-8 54,434,863.25 508.79k7 - 751.16090 B = 28101.81114 O.908897 - 1.192303 10.192821 x 10° -54,434,863.25 X 0.283406 + 242.3662 X 28101.81114 = ~" 10.192821 X 10b O.08616238 " 10.192821 = - 0.00845324 S u b s t i t u t i o n of the values ofXi,X2> A, B and Q i n t o equation 22 produces the f o l l o w i n g equation. Cy « -8.845063 X 10~ exp(8.830184; Z R ) - 0.00845324 exp(l.004226 Z R ) + 0.0686297 Therefore, C t r at each sampling point can be c a l c u l a t e d . The w values of at each sampling point calculated by equation D-10 are l i s t e d i n the f o l l o w i n g t a b l e . 211 TABLE D-5 SAMPLING z . MEASURED CALCULATED BY POINT, p. CC' EQ. D-10, C , W ( c c - c^) LB-MOLE/FT^  LB-MOLE/FT3. 3 X 10 1 1.0000 0.045013 0.044950 0.063 2 0.88916 0.047583 0.047757 -0.174 3 0.77821 0.050095 0.050076 0.019 4 0.66642 0.052033 0.052090 -0.057 5 0.55532 0.053898 0.053853 0.045 6 0.44299 0.055514 0.055435 0.079 T 0.33197 0.057144 0.056830 0.314 8 0.21966 0.058143 0.058089 0.054 9 0.10761 0.059112 0.059211 -0.099 10 0.00000 0.059900 0.060176 -0.276 Hence, by equation 35 2 10 A = 5 Z ( c c - C ) i=l u w = 0.2340 X 10 In the computer calculation, the whole process of evaluating E was repeated with different J's (calculated by equation 34, 36 and 37) and also with smoothed values of the measured continuous phase concentrations obtained by means of equation D-l. 4) Evaluation of E for Each Section within the Test Section and of E for the Test Section by the Second Method Mentioned in the Body of the Thesis From equation 24 (below), once we have the values of K^a and ra for each section within the test section, we can calculate E, 2 2 provided that we know dC^/dZ^ end d CC/&Z^. L dC c E i = : 2k e d 2C c Equation D-l is differentiated with respect to Z r , to give dC (below): 1ZR dC —- » -0.00547154 - 0.018667 Z_ D - l l dZ R R Equation D - l l i s differentiated with respect to Z^ to give d 2C c (below): d 2C = -0.018667 D-12 d ZR dC 2 The values of C , C , £ and d C c used to calculate E from ° D d ZR dZ^ equation 24 for each section are evaluated at the mid-point of each section. For section 1, which included the region of the column between sampling points 10 and 9, we have 36.5 , „ , , ,0.059534N (-0.006475) + 15.134(- ) - 0.02950) E l = 4.5347 1.82708 (-0.018667) 4.5347s 2 = 6.2 FT./HR. Values of E for the other sections were obtained similarly, and a l l the values of E ere l i s t e d in table D-6. 5) Evaluation of E at Each Sampling Point within the Test Section and of E for the Test Section by the Third Method Mentioned in the Body of the Thesis The value of E at each sampling point can be calculated from equation 25, E i = 25 a fi. We need to know C c, C^, and (dC^/dZ^Jj at each sampling point and the flux, J, down the column. Here j i s any sampling point. In the calculations C^, and (^O^/dZ^Jj at each sampling point ere calculated by equations D-l, D-2 and D - l l respectively. There are three ways of calculating J which have been used in the present study that i s by using equations 3*+, 36 and 37. Therefore, for each sampling point there are three values of E. As an example, J calculated by equation 34 i s used for the hand calculation below TABLE D-6. E BY THE SECOND METHOD SECTION MID-POINT OF THE SECTION m, (SEE TABLE D-4) Cp > L 3 LB-MOLE/FT. (BY EQ. D-l) C D > 3 LB-MOLE/FT. (BY EQ. D-2) dC c  D Z E (BY EQ. D - l l ) d 2 c c (BY EQ. D-12) K a D (SEE TABLE D-4) E, 2 . FT./HR. (BY EQ. 24) 1 0.05380 1.82708 0.05953 0.02950 -0.00648 -O.OI867 15.13b 6.22 2 0.16363 1.83032 0.05871 0.02879 -0.00853 -O.OI867 17.632 12.08 3 0.27581 - 1.83454 0.05764 0.02790 -0.01062 -O.O.867 19.768 18.06 4 0.38748 1.83963 0.05633 0.02685 -0.01270 -O.OI867 21.510 24.01 5 0.49915 1.84561 0.05480 0.02564 -0.01479 . I  22.896 29.97 6 O.6IO87 1.85247 0.05308 0.02428 -0.01687 -O.OI867 23.957 35.92 7 0.72231 1.86018 0.05103 0.02275 -O.01895 -O.OI867 24.720 41.86 8 0.83368 1.86875 0.04881 0.02107 -0.02103 -O.OI867 25.214 47.80 9 0.94458 1.87814 0.04636 0.01924 -0.02310 -O.OI867 25.469 53.71 215 (J = 1.149949). At sampling point 10. (36.5 x 0.059855 - 36.5 X 0.029795) - 1.149949 E10= O.9683 .^5347 x (-0.005472) = 45.15 f t . / h r . The values of C C , C^, (dC^dT^)^, and E at each sampling point for run 28 are l i s t e d in table D-7 TABLE D-7 SAMPLING POINT C C LB-MOLE/FT? (BY EQ. D-l) CD LB-MOLE/FT3. (BY EQ. D-2) dcc dZR (BY EQ. D - l l ) E FT^/HR. BY EQ. 25 1 0.045050 0.018260 -0.024139 33.39 2 0.047611 0.020171 -0.022069 31.49 3 0.049945 0.021927 -0.019998 29.80 4 0.052064 0.023535 -0.017855 28.41 5 0.053939 0.024975 -0.015838 27.44 6 0.055600 0.026270 -0.013741 27.06 7 0.057010 0.027390 -0.011668 27.61 8 0.058203 0.028362 -0.009572 29.72 9 0.059153 0.029170 -0.007480 34.67 10 0.059855 0.029795 -0.005472 45.15 The average value of E over the test section of the column i s given by following equation. 10 1 0 j=l j = 31.^7 216 b) Notation for Computer Program AE(I,J) AEM AED(l) AEEEM(l) AKDA(I) AVERZ(l) C(I), CC(I), YCMW(l) CD(I), D(I), YCMD(l) CM) ( I ) CMW(l) DCCPl(l) Values of axial dispersion coefficient at each sampling point. Average distribution coefficient of the test section. An array containing values of axial dispersion coefficient of esch section within the test section calculated by the second method. An array containing average distribution coefficient of each section within the test section. An array containing average values of K^a for each section within the test section. An array containing the average reduced heights of the sections for the second method. Arrays containing the continuous phase concentrations calculated from the corresponding best f i t t e d polynomial. Arrays containing the dispersed phase concentrations calculated from the corresponding best f i t t e d polynomial. An array containing measured values of the dispersed phase concentrations, lb-mole/ft. An array containing measured values of the continuous phase concentrations, lb-mole/ft? An array containing the values of the f i r s t derivative of the best f i t t e d polynomial. 217 DCCP2(l) DELS DIMIN DINT DOUT EDDIF FAKDA FED FK FW FLUX(II) IRUN LK MMM M N OLDUP P(I) An array containing the values of the second derivative of.the best f i t t e d polynomial for the continuous phase concentration p r o f i l e . 2 10 2 = A = ]>Z (CMW(I) - C(l)) 1=1 Minimum values of DEL2. HAc concentration in the dispersed phase fed to the 3 column, lb-mole/ft. HAc concentration in the dispersed phase leaving the 3 column, lb-mole/ft. Axial dispersion coefficient. Capacity coefficient, K^a, of the test section. Average axial dispersion coefficient of the test section. 3 2 Dispersed phase superficial velocity, ft./hr. f t . 3 2 Continuous phase superficial velocity, f t . / h r . f t . An array containing flux down the column calculated by equations 3^ , 36, and 37 mentioned in the body of the thesis. Run no. Logical variable in 'OLQF1 library subroutine subprogram. Section no. The maximum degree of polynomial which best f i t t e d the concentration p r o f i l e s . Number of data points. Dispersed phase holdup. An array containing Kj + -^  coefficients of the polynomial which best f i t t e d the concentration p r o f i l e . 218 ENTUD(J) SS SUB IN TE(l) WINT WOUT X(I), Z(I) YF(l) An array containing NTU of the sections within the test section. Sum of squares; for continuous phase 10 ^ (CMW(l) - YF(l)) ; for dispersed phase 10 ? = X I (cm(I) - YF(l)) . 1=1 = AZ , width of the subsection used in integration. R Average value of axial dispersion coefficient of the test section. HAc concentration In the continuous phase fed to the column, lb-mole/ft? HAc concentration in the continuous phase leaving the column, lb-mole/ft? Arrays containing reduced height. For continuous phase i s an array containing concentrations calculated from the corresponding best f i t t e d polynomial. For dispersed phase i s an array containing concentrations calculated from the corresponding best f i t t e d polynomial. c ) COMPUTER PROGRAM C T H I S P R O G R A M IS U S E O TO C A L C U L A T E D A X I A L D I S P E R S I O N C O E F F I C I E N T S C OF THE T E S T S E C T I O N OF THE C O L U M N FROM P A R T I T I O N A B L E S O L U T E C O N C . C P R O F I L E S IN THE D I S P E R S E D P H A S E AND THE C O N T I N U O U S P H A S E D I M E N S I ON C M w ( l O ) , C M D ( 1 0 ) , Z ! 1 0 ) , R N T U P ( 2 0 > , A N T U D ( 2 0 ) , A K D A ( 2 0 ) , E M ! 2 0 1 0 ) , A E E E M ( 2 0 ) , A £ E D ! 2 0 ) » A E D ( 2 0 ) , C C ( 2 0 ) , C D ( 2 0 ) , A V E R Z 1 2 0 ) , D C C P 1 1 2 0 ) , D C 2 C P 2 ( 2 0 ) , Y C E ( 2 0 ) , X ( 5 0 ) , Y ( 5 0 ) , Y F ! 5 0 ) t WT( 50 ) , YDI 5 0 ) , SI 1 1 ) , S IGMA I 1 0 ) , A 3 « 1 0 ) , B ( 1 0 ) , P ( 3 0 ) , Y C M W ( 2 0 0 ) , Y C M D ( 2 0 0 ) , Y C M W E I 2 0 0 ) , C C E ( 2 0 ) , C D E ( 2 0 ) , Y D AD( 2 0 0 ) , D D I 1 0 ) , W W ( 1 0 ) , Z Z ( 1 0 ) , R E E M ( 2 0 0 ) , C ( 1 0 ) , 0 ( 1 0 ) , F L U X ( 3 > COMMON I B L O G I C A L L K  R E A D ( 5 , I ) { Z ( I ) , 1 = 1 , 1 0 ) R E A D ( 5 , 2 ) N , M , L K 11 =N I I I = M 9 9 R E A D ( 5 , 3 ) I R U N , F K , F W , O L D U P , W I N T , W O U T , D I N T , D O U T R E A D ( 5 , 1 ) ( C M O ( I ) ,1=1 , 1 0 )  R E A D ! 5 , 1) (CMW( I ) , 1 = 1 , 1 0 ) R E A D ( 5 , 2 ) J J J C L I N E A R F I T OF C O N T I N U O U S P H A S E C O N C E N T R A T I O N P R O F I L E C O D ( I ) = C O E F F I C I E N T S OF THE P O L Y N O M I A L WHICH B E S T F I T T E D THE O I S P . C P H A S E C O N C . P R O F I L E C WW! I ) = C O E F F I C I E N T S OF THE P O L Y N O M I A L WHICH B E S T F I T T E D THE C O N T . X P H A S E C O N C . P R O F I L E . DO 1 0 1 = 1 , 5 0 D ! I ) = 0 . 0 W W ! I ) = 0 . 0 1 0 P ( I ) = 0 . 0 W R I T E ! 6 , 4 )  N= I I M = I I I NWT=0 C A L L O L Q F ( M , N , Z , C M W , Y F , Y D , W T , N W T , S , S I G M A , A , B , S S . L K . P ) JJ=M+1 W R I T E ( 6 , 5 1 ) M , S S , ( P ! J ) , J = l , J J )  W R I T E ( 6 , 5 ) W R I T E I 6 . 6 ) ( Z ( I ) , C M W ! I ) , Y F ! I ) , Y D ! I ) , I = 1 , N ) DO 2 0 1 = 1 ,JJ W W | I ) = P I I ) 2 0 P ( I ) = 0 . 0 C L I N E A R F I T OF Q l S P E R S F O P H A S E C O N C E N T R A T I O N P R O F I L E  W R I T E ( 6 , 7 ) N = I I M=III NWT=0 C A L L O L O F ( M , N , Z , C M D , Y F , Y D , W T , N W T , S , S I G M A , A , B , S S , L K , P ) JJ=M+1  W R I T E ! 6 , 5 l ) H , S S , ( P ( J ) , J = l , J J ) WR I T E ( 6 , 8 ) W R I T E ( 6 , 6 > ( Z ! ! ) , C M D ( I ) , Y F I 1 ) , Y D ! I ) , 1 = 1 , N) DO 3 0 I =1 ,JJ D D ! I ) = P ( I ) 3 0 P ! I ) = 0 . 0  ~C TNTUO = NUMBER OF THE T R A N S F E R U N I T OF T H E T E S T S E C T I O N . C TKDA = C A P A C I T Y C O E F F I C I E N T OF THE T E S T S E C T I O N . C T E E D = S U P E R F I C I A L A X I A L D I S P . C O E F F I C I E N T OF THE T E S T S E C T I O N 220 C TED = A X I A L D I S P E R S I O N C O E F F . OF THE T E S T S E C T I O N . T N T U C = C 0 T E E D = C . C T E O = C . C • AEM=C .O C D I V I D E THE COLUMN INTO N INE S E C T I C N T H E N E V A L U A T E NTU OF E A C H S E C T C ION W P I T E ( 6 , 1 7 ) DO 40 M M 2 . 1 0 yMH = M H - l T F R V A l = 1 0 0 . 0 C SUB IN = THE S T E P S I Z E OF I N T E G R A T I O N SUP IN=C .01 NN = 0 W i R I T E(t , 9 ) fMM R N T U C ( 1 ) = 0 . 0  DO 50 J = 2 , 1 0 C X ( I ) = REDUCEO H E I G H T X ( 1 ) = Z ( M M - 1 ) NN=NN+I K = C E M ( M M M ) = 0 . 0  100 K = K+1 I F ( X ( K ) . G T . Z ( M M ) ) X ( K ) = Z ( M M ) C B E S T F I T T E O PCL YNGMI AL FOR T H E C O N C . P R O F I L E OF T H E C O N T . P H A S E 200 Y C M M K ) = W W ( 1 ) + W W < 2 ) * X ( K ) + V«V»<3)*X ( K ) * * 2+WW ( 4 )* X ( K J * * 3+WW ( 5 ) * X< K ) * * 4 C B E S T F I T T E D POL YNCM IA L FOR T H E C O N C . P R O F I L E OF T H E D I S P . P H A S E Y C M C ( K ) = 0 0 ( 1 ) + D C ( 2 ) * X ( K ) + D 0 ( 3 ) * X ( K ) » * 2 + 0 0 ( 4 ) » X ( K ) * » 3 » 0 0 ( 5 ) * X ( K ) * * 4 C E Q U I L I B R I U M E Q U A T I O N CKU=2 , 0 l 7 5 1 * * 2 - 4 . * 6 . I U 2 3 * ( YCMW (K ) - C . 0 0 0 2 8 3 5 6 ) YCMWEIK ) = ( 2 . 0 1 7 5 1 - S C R T ( C K W ) ) / ( 2 . 0 * 6 . 1 1 1 2 3 ) R E E M ( K ) = Y C M W ( K ) / Y C M W E ( K I I F ( X ( K ) . G T . Z ( M M J ) GC TO 3 0 0 Y Y C = Y C M W ( K ) / R E E M K ) —Y C M O I K )  I F ( Y Y C . G T . O . O O O O l ) GO T O 4 0 0 X ( K ) = X ( K J + S U B I N GO TO 2CO 4 0 0 Y C C ( K ) = 1 . 0 / Y Y 0 EM IMMM)=EM(MMM)+REEM IK ) I F ( X ( K ) . C - E . Z ( M M ) > GC TO 3 3 0  X I K + l ) = X ( K ) + S U 8 I N GO TC 1 0 0 3 0 0 K = K - 1 3 3 0 CK=K E M I f M M ) = E M ( M M M ) / C K C S T A R T T H E I N T E G R A T I O N T R A P E O I D A L METHOD  K K = K - l R N T U D ( J ) = C . C CO 6 0 1=1,KK 6 0 R N T U D ( J ) = ( Y C M C ( I ) - Y C M C ( I + 1 ) ) * ( Y C D ( I ) * Y D D ( I + 1 ) ) « 0 . 5 + R N T U D I J ) W R I T E R , 1 1 ) K N , S U B I N , R N T U O ( J ) I F ( A I 3 S ( F N T U C ( J ) - R N T U C ( J - 1 ) ) . L T . 0 . 0 0 1 ) GO TO 5 0 0  T E R V A L = T E R V A L * 1 0 0 . 0 5C S U B I N = 1 . C / T E R V A L 5 0 0 C C N T I N U E 221 ANTUC (MMM)=PNTUC (NN+1 ) A V E R Z ( M M M ) = ( Z ( M M - 1 ) * Z ( M M ) J / 2 . 0 AKCA ( M M M ) = F K * A N T U D ( f M M ) / ( 4 . 5 3 4 7 * ( Z ( M M ) - Z < MM-1) ) ) TNTUO=TNTUD+ANTUC(MMM )  AEM=AEM+EM(MMM) " C S T A R T T O C A L C U L A T E E ' S BY THE SECOND METHOD C C ( M M M ) = K W ( 1 ) * W W ( 2 ) * A V E R Z ( M M M ) + W W < 3 ) * A V E R Z ( M M M ) * * 2 + W W ( 4 ) * A V E R Z (MMM 1 ) * * 3 * W W ( 5 ) * A V E R Z ( M M M ) * * 4 C D ( M M M ) = C C ( 1 ) * D D ( 2 ) * A V E R Z ( M M M ) + D C ( 3 ) * A V E R Z ( M M M ) * * 2 + D D ( 4 ) * A V E R Z ( M M M 1 ) * * 3 + 0 D ( 5 ) * A V E R Z ( M M M ) » * 4  C W K = 2 . 0 17 5 1 * * 2 - 4 . * 6 . 1 1 1 2 3 * ( C C ( M M M ) - C . 0 0 0 2 8 3 5 6 ) C C E ( M M M ) = ( 2 . 0 17 5 1 - S Q R T ( C W K ) )/( 2 . 0 * 6 . 1 1 1 2 3 ) AEEEM(MMM ) = CC(MMM) / C C E ( M M M ) C C C P H M M M > = WW( 2 ) + 2 . C*WW(,3)*A VERZ (MMM)* 3 . 00*WW( 4 ) * A V E R Z ( "MM) * * 2 + 4 . 0 1 * W W ( 5 ) * A V E R Z ( M M M ) * * 3 D C C P 2 ( M M M ) = 2 . 0 * W W ( 3 ) * 6 . C * W W ( 4 ) * A V E R Z ( M M M ) + 1 2 . 0 * W W < 5 ) * A V E R Z ( M M K ) * * 2 CDE(MMM)=CC(MMM )/A£EEM(MMM) HH=CCCP1 ( MMM M F W / 4 . 5 3 4 7 HHH=CCCP 2 ( M M M I / 4 . 5 3 4 7 * * 2 A f E C ( M M M ) = ( A K C A ( M M M ) * ( C D E ( M M M ) - C D ( M M M ) )• HH)/HHH A E D ( M M M ) = A E E C ( M M M ) / ( l . C - C L O L P / 1 0 0 . 0 ) T r E O = T E E D + A E E D ( M M M )  T E C = T E C + A E C ( M M M ) 4 0 C C N T I N U E C FMMM= NUMBER CF S E C T I O N IN THE T E S T S E C T I O N FMMM=MMM F A K D A = T N T U 0 * F K / 4 . 5 3 4 7 F t E Q = T E E D / F M M M  F E C=T EC/FMMM AEM= AEM/FMMM W R I T E ( 6 , 1 4 ) I R U N , F W , F K , W I N T , W O U T , 0 I N T , C O U T , O L D U P , AEM , T N T U D , F A K D A , 1 F E D 0 0 70 1=1,MMM 7 0 W R I T E ( 6 , 1 5 ) I , A V E R Z ( I ) , A E E E M ( I ) , C C ( I ) , C D ( I ) , D C C P 1 ( I ) , C C C P 2 ( I)  1 , A N T U C ( I ) , A K C A ( I ) , A E D ( I ) W R I T E ( 6 , 1 6 ) C S T A R T TO C A L C U L A T E D E » S BY T H E F I R S T MFTHOD DO 80 1 = 1 , 1 0 C ( I ) = WW( 1 )+WW(2 ) * Z ( I ) +WW ( 3 ) * Z (I )**2+WW( 4 ) * Z ( I ) * *3+KW ( 5 ) * Z (1 ) * * 4 0 ( 1 ) = D0 ( 1) +DC (2 )*Z ( I ) •»00( 3 ) * Z ( I ) * * 2 + DC( 4 ) * Z ( I ) * *3+DD( 5 ) * Z ( I ) * * 4 "80 O C C P K I ) = W W ( 2 ) + 2 * W W ( 3 ) * Z ( I ) + 3 * W W ( 4 ) * Z ( I ) * *2+4*WW( 5 )*Z (I ) * * 3 F L U X ( 1 ) = 0 . 5 * ( F W * ( W INT + W 0 U T ) - F K * ( D I N T * D 0 U T ) ) F L L X ( 2 ) = F W * h I N T - F K * D C U T F L U X ( 3 ) = F W * W 0 L T - F K * D I N T C S U E R O L T INE E B L S T F ; U N S M O C T F E C C O N C . IN TWO P H A S E S A R E USED IB = 1  C A L L E e L S T F ( F L U X , F W , F K , C M W , C M D , O L O U P , I R U N , F A K D A , A E M , Z « MI N T , W O U T , D I 1 N T , D C U T ) C S U B R O U T I N E E B L S T F ; SMCCTHED C C N C . IN TWO P H A S E S ARE U S E D IB=2 C A L L E E L S T F ( F L U X , F W , F K , C D , OLDUP , I R U N , F A K C A , A E M , Z , W I N T , W O U T , D I N T , D 1 0 U T )  C S T A R T T O C A L C U L A T E E ' S BY T H E T H I R D METHOD C S U B T C l T I N E E B F L U X C A L L E B F L U X ( I R U N , Z , FW , F K , C , 0 , F L U X , O C C P 1 .CiLOUP » 1 F O R M A T ( 1 0 F 8 . 6 ) 2 F ( ! P M A T ( 2 I 1 0 , L 1 ) 3 F O P M A T t I 3 , 3 F 7 . 2 , 4 F 9 . 7 , 2 1 3 ) 4 FORMAT ( 1 H 1 / 4 X , ' C O N T I N U O U S P H A S E C O N C E N T R A T I O N P R O F I L E * M X , 3 8 ! » » ' I ) 51 F O R M A T ! / 3 X , « D E G R E E PF P O L Y N O M I A L = ' , I 3 / 3 X , • SUM OF S Q U A R E S 1 = ' , G 1 5 . 6 / 3 X , • P A R A M E T E R S ' / 3 X , 5 G 1 5 . 6 ) 5 F O R M A T ( / / / 3 X , ' V A L U E S OF Z V A L U E S OF CC F I T T E D V A L U E S OF CC l R F S I D U A L S ' / 3 X , 6 2 ( ' * ' I ) 6 F O R M A T ! IX , 3 G 1 5 . 6, 5 X , G 1 5 . 6) 7 F O R M A T ( 1 H I / 4 X , ' O I S P F R S E O P H A S E C O N C E N T R A T I O N PROF 1 1 E ' / 4 X , 3 7 ( ' * ' ) ) 8 F C R M A T ! / / / 3 X , • V A L U E S OF Z V A L U E S OF CD F I T T E D V A L U E S OF CO 1 R E S I D U A L S ' / 3 X , 62 ( I) 9 F C R M A T I 6 X » 1 3 ) 11 F O R M A T ! 1 5 X , I 2 , 4 X , F 1 0 . 6 , 1 X , F 1 0 . 5 ) 14 FORMAT ( I H i , 30 X , 'RUN NO ' , I 4 / 3 0 X , ' W A I E R S U P E R F I C I A L V E L O C I T Y = ' , 1 F 6 . 3 , 4 X , ' C U . F T . / ( H R . S U . F T . ) ' / 3 0 X , ' MIRK S U P E R F I C I A L V E L O C I T Y =_•_ ? , F 6 . 3 . 4 X , ' C U . F T . / ( H R . S Q . F T . ) • / 3 0 X , ' H A C C O N . IN I N L E T WATER P H A S E = 3 ' , F 8 . t , ? X , ' L B - M C L F / ( C U . F T . ) ' , / 3 0 X . ' M A C C O N . IN O U T L E T WATER P H A S E = 4 ' , F 8 . 6 , 2 X , ' L B - M O L E / I C U . F T . ) ' , / 3 0 X , • H A C C O N . IN INLET MIBK P H A S E = 5 ' , F 8 . 6 , 2 X , ' L B - M O L E / ( C U . F T . ) ' , / 3 0 X , ' H A C C O N . IN O U T L E T MIBK P H A S t = fc',F8.6,?X,'LB-MOLE/(CU.FT.)'/?OX,'AVERAGE HOLDUP =' 7 . F 6 . 3 . 4 X , * * » / 3 0 X, ' A VERA, f. F_ D I S T R I B U T I O N C O E F F = ' , F 8 . 5 , 2 X / 3 0 X , ' T u 8 T A L N T ' I IN T H E T E S T " SECT ION = • , F 8. 5, 2 X / 3 0 X , ' A V E R A G E KDA IN THF TE S <5T S E C T I O N = ' , F 8 . 3 , 2 X , ' 1 / H R . V 3 0 X , ' A V E R A G F V A L U E OF E = ' , 1 F 8 . 3 , 7 X , ' S Q . F T . / H R . « / / / / ? . 0 X , ' S E C T I O N Z M C C CD 2 C C C P 1 DCCP2 NTU K OA F « / 1 9 X , 8 2 ! • - • ) ) 15 F O R M A T ! 1 9 X . I 5 , 3 X , 4 F 8 . 5 , 2 F 9 . 5 , F 8 . 3 , 2 F 8 . 3 ) 16 F O R M A T ! 1 9 X , S 2 ( ' - ' ) )  17 F O R M A T ( 1 H i , 3 X , ' N T U OF E A C H S E C T I O N OF THE T E S T S E C T I O N • / / 3 X , • S E C T I ION NO OF S T E p S I 7 F OF N T U ' / l 4 X , • C V C L E I N T F G R A T I O N ' / 5 X , 3 5 ( • - • 2 ) / > S T O P END 223 SURROUT I NE E B L S T F ( F LUX , F W » F K , C M W , CMO, 01 DUP, IRUN , AKK , E M, Z , W I NT , WOUT 1 , O I N T , O O U T ) C S U B R O U T I N E FOR T H E F I R S T METHOD OF C A L C U L A T I N G E P IMENS1 CN CMWI10 I . CCWI IO I , C M D ( 1 0 ) , FX1 ( 10 I . EX2 ( 10 ) . S ( 7 > , FLUX ( 3 ) ( 1 1 0 ) COMMON IB DO 9 9 I 1 = 1 , 3 W R I T E ( 6 , 1 1 ) I R U N , F W , F K , A K K , E M , W I N T , W O U T , D I N T , D O U T , O L D U P GO T O (91 , 9 ? , 9 3 ), II 91 W R I T E ( 6 , 1 4 ) F L U X ( I I )  GO T O 17 9 ? W R I T F ( 6 , 1 5 ) F L U X ( I I ) GO TO 17 9 3 W R I T E ( 6 , 1 6 ) F L U X ( I I I 17 I F U B . E Q . 2 ) W R T T E ( 6 , 1 8 » W R I T E ( 6 , 1 3 )  C 0 L M = 4 . 5 3 4 7 C F O D I F = A X I A L D I S P E R S I O N C O E F F I C I E N T EDO IF = 1 . 0 E = l . - O L D i J P / 1 0 0 . D?MI N = U 0 0 0 0 0 0 0 0 0 . E 0 1 F F = 1 0 0 0 0 .  7 AL P H A = 0 . 5 *{Fto *CtL M / ( C 0 0 I F * E ) + A K K * C O L M / F K 1 BE T4 = ( T K - E M * F W ) * A K K * C O L M * * 2 / ( k M * F x * E D D I F * E ) A H C = A L P H A * * ? • B E T A I F ( A B C . L T . O . O ) GO T C 10 DEI TA = F L U X ( I I ) * E M / ( F K - E M*F W J E IGN1= A L P H A ^ S Q ^ T I A t . P H A * * 2 + B E T A )  E I G N ? = A L P H A - S O R T ( A L P H A * * 2 • R E T A I I F ( E I G N 1 . G T . 3 7 . 0 . O R . F I G N 2 . G T . 3 7 . 0 ) GO TO 1 0 0 0 12 1 = 1 , 7 12 S ( I ) = 0 . 0 DO 4 1= I, 10 E X 1 1 I ) = E X P ( F I G N 1 * Z ( I ) ) :  E X 2 ( I ) = F X P ( E I G N 2 * Z ( I ) ) S U l = S ( l 1 + E X 1 U )*CMW( 1) S ( 2 I = S ( 2 ) + E X 1 ( I ) * * 2 S( 3 ) = S ( 3) + E X K I ) * E X ? ( I ) S ( 4 ) = S ( 4 ) * E X 1 U 1 S ( 5 ) = S ( 5 ) » E X 2 ( I ) * C M W ( N  S ( 6 ) = S ( 6 ) * E X 2 ( I ) * * 2 4 S ( 7 ) = S ( 7 ) + E X 2 ( I ) A1=S< 1) * S ( 6) - S ( 5) * S ( 3 ) + D F L T A * ( S ( 4 ) * S ( 6 ) - S ( 7 ) * S ( 3 ) ) A 2 = S ( 2 1 * S ( 6 ) - S ( 3 ) * * 2 A = A 1 / A 2 B = ( S ( 1 » * S ( 3 ) - S ( 5 ) * S ( 2 ) + 0 F L T A * ( S ( 4 ) * S ( 3 ) - S ( 7 ) » S ( 2 ) ) ) t ( S ( 3 ) * * 2 - S ( 6 ) * 1 S ( 2 ) ) 0 E L 2 = 0 . 0 0 0 5 1= I, 10 C C W U ) = A * E X 1 ( I) + B * E X 2 ( I ) - D E L T A 5 D E L 2 = D E L 2 * ( C M W ( I ) - C C W ( I ) ) * * 2 W R I T E ( 6 , 6 ) EDO I F , (CCW( 1 1 - 1 1 , 1 = 1 , 1 0 ) , D E L 2  I F ( 0 E L 2 . L T . D 2 M I N ) E D I F F = E D D I F I F ( D E L 2 . L T . D 2 M I N ) D 2MIN=DF L 2 10 E 0 D I F = E 0 D I F + 1 . 0 22k 1 F I E D D I F . L T . 6 1 . 0 ) GO TO 7 W M T F ( 6 , 8 ) FO I F F , 02 Ml N 9 9 C O N T I N U E 6 J L 1 ! ? . ^ T i 1 6 X , F5 .1 . 1 0 F « . 6, F 12^43 1 3 ' " F O R M A T ! 1 9 X , ' E • ,4X , • C l C 2 ~ C3 CA C 5 C b 1 C 7 C 8 C 9 C I O D F L 2 ' / 1 6 X . 1 0 5 ! ' * • ) ) 8 F O R M A T < / / 1 6 X , ' A X I A L D I S P E R S I O N C G E F F I C I E N T = » , F 4 . 1 / 1 6 X , • S U M OF SQU 1 A R E S =• , E 1 5 . 8 ) 11 FORMAT I 1 H 1 , • ' / / 3 0 X , ' R L ' N NO ' » I 4 / 3 0 X , ' WATER S U P E R F I C I A L 1_VF LOC H Y = • ,_F 8_. 3_,_2X, ' C U . F T . / ( HR . S O . FT ) » / 3 0 X , 'M I BK S U P E R F I C I AL 7 V F L 0 C 1 T Y = ' " J F 8 . 3 , ? x " , , C U . F T . 7 ( h R . S Q . F T ) ' / ? 0 X , ' C A P A C I T Y C O F F F I C I 3ENT = ' , F 8 . 3 , 2 X , « 1 / H R • / ? 0 X , ' A V E R A G E ' D I S T R I B U T I O N C O E F F 4 = ' f F 8 . 4 / 3 0 X , • H A C C O N . IN I NL FT WATER P H A S E = • , F R . 6 , 2 X , ' L B M O L F / ( C U . 5 F T . ) • / 3 0 X , ' H A C C O N . IN O U T L E T WATER P H A S F = ' , F 8 . 6 , 2 X , • L B M O L E / ( C U . F T 6 . ) • / 3 0 X , • H A C C O N . IN I N L E T MIBK P H A S F = • , F 8 . 6 , 2 X , ' I B M O L F / ( C U . F T . ) 7 ' / 3 0 X , ' H A C C C N . IN O U T I F T MlfiK P H A S F = 1 , F W . 6 , 2 X , ' L B^'Ol E / I C U . F T . ) ' / " * 8 3 0 X , « HOI D'lJP CF D I S P E R S E D PHASE =' , f 6 . 3 , 4 X , • % ' ) 14 F T R M A T ( 3 0 X , ' F L U X ( A V E OF TOP AN C BOTTOM) = * » F 8 . 6 » 7 X » ' I R M 0 L E / ( S Q ) . F 1 T . H R . ) • ) 15 F O R M A T ! 30X , T L U X ( TOP OF C O L U M N ) = ' , F 8 . fi , 2 X , • L B M O L F / < S Q . F 1T.HR.)•) I 6 f j l f MA J_( 3 OX, ' F L U X (BO TTG V Of COLUMN) fiilL&j. 6 j» 2X , ' 1 BMQL F/ ( S O . F IT . H R . ) ' » 18 F C R M A T ( 3 0 X , • SMOOTHED V A L U E S OF C O N C . IN T H f TWO P H A S C S ARE U S E D ' / ) 9 9 9 K F T U R M ENC 225 S U B R O U T I N E E R F L U X l I R U N , Z , F W ,F K ,C , D , F L U X , OCCP1 » OLDUP ) C S U B R O U T I N E FOR THE TH IRD METHOD OF C A L C U L A T I N G E D I M E N S 1 C N C ( 1 0 ) , 0 ( 1 0 ) , Z ( 1 0 ) , F I U X ( 3 ) , A ( 3 , 1 0 ) , A A ( 3 , 1 0 ) , A E ( 3 , 1 0 ) , A C E ( 1 3 , 10) , T E ( 3 ) , D C C . P 1 ( 2 0 ) " C 11= HE IGHT OF T H E T E S T S E C T I O N H = 4 . 5 3 4 7 DC 10 1 = 1 , 3 T E ( I ) = 0 . 0 DO 2 0 J = l , 1 0 AI I , J ) = F W * C ( J ) - F K * 0 ( . J )  A A ( I, J )= A ( I, J ) - FLUX ( I ) A E E ( I , J ) = A A ( I , J ) * M / D C C P 1 ( J ) A E ( I , J ) = A E E ( I , J ) / ( 1 . 0 - O L D U P / 1 0 0 . 0 ) 2 0 T E ( I 1 =T E ( 1 1 + A E ( I , J ) 10 T F ( I ) = T E ( I ) / 1 0 . 0 DO 70 1 = 1 , 3  C T E ( I ) = A V E R A G E V A L U E OF E OF THE T E S T S E C T I O N W R I T E ( 6 , 1 ) I R U N , F W , F K , T E ( I ) GO T 0 ( 3 0 , 4 0 , 5 0 ) , I 30 W R I T E ( 6 , 2 ) F L U X ( I ) GO TO 6 0 40 HR I T F ( 6 , 3 ) FL DX ( I )  GO TO 6 0 5 0 W R I T C ( 6 , 4 ) F L U X ( I ) 6 0 W R I T E 1 6 . 5 ) W R I T E ( 6 , 6 ) ( ? ( J ) , C I J ) , D ( J ) , A ( I , J ) , A A ( I , J ) , D C C P 1 ( J ) , A E ( I , J ) , J = 1, 10 ) 7 0 W P I T E ( 6 , 7 ) I F 0 R M A T ( 1 H 1 , / / 3 0 X , ' R U N NO ' , I 4 / 3 0 X , ' W A T E R S U P E R F I C I A L V E L O C I T Y 1 ' , F 8 . 3 , 2 X , ' C U . F T . / ( H R . S O . F T . I » / 3 0 X , • M I B K S U P E R F I C I A L V E L O C I T Y 2 = ' , F 8 . 3 , 2 X , ' C U . F T . / ( H R . S Q . F T . ) • / 3 0 X , ' A V E R A G E A X I A L D I S P E R S I O N C O E F 3 F = ' , F R . 4 , 2 X , ' S Q . F T . / H R . ' ) 2 F O R M A T ! 3 0 X , ' F L U X ( A V E OF TOP AND BOTTOM) - • , F 9 . 6 , l X , ' L B M O L E / ( S O . F IT . HR . ) ' 1 3 F C R M A T ( 3 0 X , » F L U X ( T O P OF COLUMN) = ' , F 9 . 6 , IX, ' L B M O L E / ( S i ) .F 1 T . H R . ) i ) 4 F O R M A T ( 3 O X , ' F L U X ( B O T T O M OF C O L U M N ) = • »F 9 . 6 , I X , ' L B M O L E / ( S Q . F 1 T . H R . ) ' 1 5 F O R M A T ! / / 2 5 X , ' Z R CC CD . F W * C C - F K * C D F L U X - ( F W * C C - F K * C 101 DCCP1 E V 2 1 X , 77( ' - ' 1/1 6 FOR MA T( 1 9 X , 4 F 1 0 . 6 , 4 X , F 1 0 . 6 , 5 X , 2 F 1 0 . 4 )  7 FORMA T ( / 2 1 X , 7 7 ( • -• )1 R E T U R N END 

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