THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING COCURRENT FLOW OF IMMISCIBLE LIQUIDS IN PACKED BEDS Robert G. Rigg A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1963 May, 1963 IP-617

ACKNOWLEDGEMENTS The author is indebted to many people who rendered assistance during the course of the doctoral program. Thanks are due particularly to: Professor S. W. Churchill, chairman of the doctoral committee, for his guidance, assistance, and helpful suggestions during the course of this work. Professors Eo F, Brater, M. Ro Tek, G. Bo Williams, and J. L. York, committee members, for their suggestions and constructive criticism. Dr. R. P. Larkins, who constructed much of the experimental apparatus used here. Mr. James A. Craig for his generous assistance in various phases of the computer programming. The shop personnel of the Chemical and Metallurgical Engineering Department for their assistance in equipment construction and the Computing Center at The University of Michigan for their donation of computing time. The National Science Foundation for financial aid in the form of fellowships. The Phillips Petroleum Company for their donation of isooctane. The Union Carbide Chemicals Company for their donation of isobutanol. The Industry Program of the College of Engineering for their cooperation and assistance in the preparation of the final form of this dissertation. Last, but certainly not least, my wife, Veronica, for her help in preparation of the manuscript and for her patience and understanding during the course of my work. ii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTSo. o................o o o o o o o......... ii LIST OF TABLES o o o o. o o o o o o o. o o o.o o o.o o o............. v LIST OF FIGURES o............ oo........................... Vii LIST OF APPENDICESo o......o..o 0...... o.....o ooo o...o....... xi NOMENCLATURE o..O o o o........... o... o o. o o o o. o o o o....... o xii ABSTRACTO o o o o. o oo oo. 9 o o o... o ooo o o o. o o o... 6 o.6 a a. o. o. o. o o X Io INTRODUCTION o o o... o. o. o..o..o o. o..o. o.. oo. o o. o o.. o o 1 IIo LITERATURE REVIEW o o. o o....o....o....o.... oo............ 4 1o Single-Phase Flow in Packed Beds....o........... o.. 4 2o Two-Phase Flow in Open Pipeso,..o....... o.. oo...... 7 201 Gas-Liquid Flowo o..o..... o o o o oo.......... o 7 2o2 Liquid=Liquid Flowo,......... o.... o..........o 9 30 Countercurrent Flow in Packed Beds ooo.............. o 10 40 Cocurrent Flow in Packed Beds.oo............. o...o 12 50 Drop Breakup and Interfacial Area o oo..o o... ooooooooo 14 III. THEORY OF SINGLE-PHASE FLOW IN PACKED BEDSo.oooo... oooooo ooo 16 IVo EXPERIMENTAL PROGRAMo o o.oo o o.o o...... o.... o....o...... oo o 21 lo Introduction.......o. o.................. o.... o.... o 21 20 Experimental Apparatus oo...o o..o.. o.......o...... 21 30 Photographic Equipmento o...............o.... o.o 29 40 Operating Procedures..o o....o.........ooooo...o.....o 30 5o Photographic Techniques....oo....................... 35 60 Properties of Systems Studied..o...................... o 36 601 Packing Propertieso o o o o o o... o...... oo... o 37 6o2 Fluid Properties o o..oo.....o.. ooo.......o.... 38 Vo EXPERIMENTAL RESULTSo o. o.. o o o o o. o o o o oo.... oo..... o 42 lo Generalo. 0........0..... 6...6......6.....6,..0..06 42 2o Data Processing, 6...o......................... o 46 30 Pressure -- -':t.o..OOOOOOOO. O o o o O o. o. o o. o o o 48 iv

TABLE OF CONTENTS (CONT'D) Page 31o Single-Phase Pressure Gradient................. 48 3,2 Two-Phase Pressure Gradient,..............,,, 52 4~ Phase Holdup...................o.................... 70 50 Drop Sizes OOOOOO.....oooooo......................ooo 75 VIo CORRELATION OF DATA.............., o.. o o o o o o o o o o 91 1o Phase Holdup Correlation o....o....o.o......ooo...oo 91 2. Pressure Gradient Correlation,0..,.....,,,,,, 0 0.... 10C 2,1 Separation of Otatic and Frictional Pressure Gradients........0000000000000.....................000000000000000000000 100 2,2 Correlation of Frictional Pressure Gradient,..o 103 3. Drop Size Correlation.oo,...o o..oo..,o....oo....... 114 3,1 Effect of Velocityo....,,..o......,o.,,,..... 116 3.2 Effect of Packing Diameter,0...00..0 0.. 0..... 116 3.3 Effect of Fluid Properties.,....... o...o... 116 3.4 Summaryo... o.......... o o o o o o o....... o o o o o o o o 120 VIIo CONCLUSIONS..c..........,o o................ o o o........ 125 VIIIo RECOMMENDATIONS FOR FUTURE STUDYo....o. ~ oo.o..... o.o. 127 LITERATURE CITED.o,. o..... o.......... o..o.o.. o oooo...... 128 APPENDICES o o o o o o............o o o o o o..... o...... o o..oooo..... o o o o o c o o o o o 134 V

LIST OF TABLES Table Page I Properties of Packing Materials..........ooo..o..... 40 II Physical Properties of Fluids......................... 41 III Coding of Data Runs.................................... 49 IV Values of Ergun Equation Constants.................... 50 V Time Dependence of Phase Holdup........................ 71 VI Reproducibility of Drop Size Measurements............. 85 VII Results of Phase Holdup Correlation..............o...... 99 VIII Results of PRATI0 Correlation....................... 110 IX Results of Drop Size Correlation...................... 122 Appendix B I Values of Constants for Viscosity Curves.,............. 138 Appendix C I Water Flow through Bed of 0.501 Inch Spheres........... 141 II Isobutanol Flow through Bed of 0.501 Inch Spheres...... 141 III Water Flow through Bed of 0.340 Inch Spheres........... 141 IV Isobutanol Flow through Bed of 0.340 Inch Spheres...... 142 V Water Flow through Bed of 0.164 Inch Spheres........... 142 VI Isobutanol Flow through Bed of 0.164 Inch Spheres...... 142 VII Water Flow through Bed of 0.164 Inch Spheres........... 143 VIII Isooctane Flow through Bed of 0.164 Inch Spheres....... 143 IX Water Flow through Bed of 0.340 Inch Spheres........... 144 X Isooctane Flow through Bed of 0.340 Inch Spheres....... 144 vi

LIST OF TABLES(CONT'D) Appendix D Page I Isobutanol-Water Flow through. Bed of 0o501 Inch Spheres..................,......... 146 II Isobutanol-Water Flow through Bed of 00340 Inch Sphereso eo o o o. o o.. o o o o o o o. 147 III Isobutanol-Water Flow through Bed of 0.164 Inch Spheres.,..... o..... o. o.......... o o. 1448 IV Isooctane-Water Flow through Bed of 0.164 Inch Spheres.oooO o. o o o o..o o. o o o.. 149 V Isooctane-Water Flow through Bed of 0.340 Inch Spheres.....OOOO...ooo OOOOOOOCOCOOOOOOOOOO 150 J VI Isooctane-Alkaterge "C"-Water Flow through Bed of 0 340 Inch Spheres o o............................. 151 Appendix E I Isobutanol-Water Flow through Bed of 0.501 Inch SphereS o....... OO. o.........o o o o o o 15 II Isobutanol=Water Flow through Bed of 0.340 Inch Spher es...............OO.................................OOOO 154 III Isobutanol-Water Flow through Bed of 0.164 Inch Spheres.......o................................... 155 IV IsooctaneAWater Flow through Bed of 00164 Inch Spheres.....S.OO.OOO.....O.......O..OO.OOOUOQOO......5. V Isooctane-Water Flow through Bed of 0.340 Inch SphereSOOOOooo o.oo o o. oo. oo.o..... o. o o. oo.oo. o 157 VI Isooctane-Alkaterge "C"-Water Flow through Bed of 0.340 Inch Spheres............... o.....,........ 157 vii

LIST OF FIGURES Figure Page 1 Test Section Dimensions (Not to Scale)...........oo. 23 2 Schematic Diagram of Experimental Apparatus.....o... 25 3 Schematic Diagram of Pressure Manifold System....... 28 4 Arrangement of Photographic Equipment (Top View).... 31 5 Photograph of Typical Packing Particles.............. 39 6 Appearance of "Slug Flow" Patterno......o........... 45 7 Fit of Single-Phase Data to Ergun Type Equation...... 51 8 Comparison of Single-Phase Data with Ergun Equation,, 53 9a Total Pressure Gradient in the System Isobutanol -Water-00501 Inch Spheres................ooooo........ 55 9b Total Pressure Gradient in the System Isobutanol -Water-00501 Inch Spheres........................... 56 9c Total Pressure Gradient in the System Isobutanol -Water-0o501 Inch Spheres, 0.......,ooooo..o,,0 0o0O. 57 lOa Total Pressure Gradient in the System Isobutanol -Water-0340 Inch Spheres.......o.............o,,... 59 10b Total Pressure Gradient in the System Isobutanol -Water-00340 Inch Spheres.....oooo............00 0.00 60 lla Total Pressure Gradient in the System Isobutanol -Water-00164 Inch Spheres 00o,,o0.........00....00.... 61 lib Total Pressure Gradient in the System Isobutanol -Water-00164 Inch Sphereso......oo...oo.......ooo.... 62 12a Total Pressure Gradient in the System Isooctane -Water-00164 Inch Sphereso...0,,.......00...0.. 0000 63 12b Total Pressure Gradient in the System Isooctane -Water-00164 Inch Sphereso o o ooo o oo............. o 64 viii

LIST OF FIGURES (CONT'D) Figure Page 13a Total Pressure Gradient in the System Isooctane -Water-0.340 Inch Spheres........................5.... 13b Total Pressure Gradient in the System Isooctane -Water-0.340 Inch Spheres.......................... 66 14a Total Pressure Gradient in the System Isooctane -Alkaterge "C" -Water-0.340 Inch Spheres............ 67 14b Total Pressure Gradient in the System Isooctane -Alkaterge "C" -Water-0.340 Inch Spheres............. 68 15 Time Dependence of Phase Holdup...................... 73 16 Isobutanol Phase Holdup in the System Isobutanol -Water-0.501 Inch Spheres............................ 76 17 Isobutanol Phase Holdup in the System Isobutanol -Water-0.340 Inch Spheres............................ 77 18 Isobutanol Phase Holdup in the System Isobutanol -Water-0.164 Inch Spheres........................... 78 19 Isooctane Phase Holdup in the System Isooctane -Water-0.340 Inch Spheres........................... 79 20 Isooctane Phase Holdup in the System IsooctaneAlkaterge "C" -Water-0.340 Inch Spheres.............. 80 21 Photograph of Flowing Water-Isobutanol Mixture in Bed of 0.501 Inch Spheres.............................. 82 22 Photograph of Flowing Water-Isobutanol Mixture in Bed of 0.340 Inch Spheres................................ 82 23 Photograph of Flowing Water-Isobutanol Mixture in Bed of 0.164 Inch Spheres................................. 83 24 Photograph of Flowing Isooctane-Water Mixture in Bed of 0.164 Inch Spheres............................. 83 25 Drop Size Distribution Photographs 7, 8, 9, 10, 17, 18................................................... 87 26 Drop Size Distribution Photographs 99, 101........... 88 ix

LIST OF FIGURES (CONT'D) Figure Page 27 Drop Size Distribution Photographs 151, 152.......... 89 28 Drop Size Distribution Photographs 157,158> 183, 184.......g............................ 90 29 Phase Holdup in the System Isobutanol -Water-0.501 Inch Spheres.................................. 94 30 Phase Holdup in the System Isobutanol -Water-0.340 Inch Spheres....................................... 95 31 Phase Holdup in the System Isobutanol -Water-0.164 Inch Spheres......................... 96 32 Phase Holdup in the System Isooctane-Water-0.340 Inch Spheres...............................0 97 33 Phase Holdup in the System Isooctane-Alkaterage "C" -Water-0.340 Inch Spheres........................... 98 34 Dependence of PRATIO on Phase Holdup in the System Isobutanol -Water-0.164 Inch Spheres.........,...... 108 3D3a Comparison of Predicted and Measured PRATIO.......... 112 35b Comparison of Predicted and Measured PRATIO With Exclusion of Surfactant Data...........*...,..... 113 35c Comparison of Predicted and Measured PRATIO with Corrected Surfactant Data........................ 115 36 Effect of Velocity on Sauter Mean Drop Diameter...... 117 37 Effect of Velocity on Sauter Mean Drop Diameter...... 118 38 Effect of Packing Diameter on Sauter Mean Drop Diameter........................................... 119 39 Effect of Interfacial Tension on Sauter Mean Drop Diame ter 0.............................................0 121 40 Correlation of Drop Size Data........................ 124 A-1 Rotameter Correction Factor......................... 136 B-l Liquid Viscosity Data................................ 139 x.

LIST OF APPENDICES Appendix Page A Density Correction Factor for Rotameters,......o.. 135 B Physical Properties of Liquids.................... 1.37 C Tables of Processed Single-Phase Data,............ 140 D Tables of Processed Two-Phase Data..........,....... 145 E Tables of Processed Drop Size Data...........o....... 152 F Estimation of Interfacial Tension Effect............. 158 G Table of Two-Phase Pressure Drop Correlation Parameters.....................0.....o,. 0 o.. 160 H Supplementary Bibliography........................ 166 xi

NOMENCLATURE A Cross sectional area of porous medium A, A, Al Empirical constants a Empirical constant B. B 8 B1 Empirical constants b Empirical constant C1 Empirical constant c, c, cl Empirical constants D Diameter of packed bed D1 Empirical constant Dc Diameter of capillary channel in packed bed Dp Diameter of packing particle d Diameter of a sphere di Diameter of individual drop d32 Sauter mean diameter F Friction factor defined by Equation (39) g Acceleration due to gravity gc Gravitational conversion constant H Liquid holdup i Counting index K Permeability K Time constant Kg K2 Empirical constants Ko Ki Relative permeabilities of oil and water phases, respectively kl, k2 Empirical constants xii

In Logarithm to base e L Liquid flowrate L Length of capillary channel L Thickness of porous medium m Slope of holdup data line Equations (15) and (16) N Number of capillary channels N Number of droplets in a given photograph P Pressure dP dP Pressure gradient dL _P Pressure drop per length of bed, L L f(7)TP Two phase pressure drop, Equation (10) (-) Pressure drop for gas flowing alone, Equation (10) AL g o(2) Pressure drop for liquid flowing alone, Equation (10) PRATIO Ratio of two phase pressure gradient due to friction to predicted frictional pressure gradient PI Weight per cent isobutanol in water phase, Equation (B-2) Pw Weight per cent water in isobutanol phase, Equation (B-l) Q Volumetric flowrate R Fluid flowrate R1 Ratio of scale fluid density to metering fluid density R2 Ratio of float density to scale fluid density R32 Ratio of volume to surface area for Sauter mean sphere RT Ratio of volume to surface area for total population of drops r Radius of sphere xiii

r Empirical constant Re Reynolds number Rem Modified Reynolds number defined by Equation (40) RI Phase holdup of non-wetting phase RIf Value of RI as time oo S Particle surface area per volume of packed space Sv Particle surface area per volume of packing particle s Empirical constant T Absolute temperature, ~R t Temperature, ~C t Time U Superficial liquid velocity Ucg UD Superficial velocities of continuous and discontinuous phases, respectively u Velocity V Interstitial velocity V Terminal drop velocity 0 Vs Slip velocity VT Volume of test section, see Equation (36) Vw Volume of overflow water from test section, see Equation (36) v Specific volume - P W Mass flowrate of fluid wf Frictional work ws Shaft work We Weber number X Discontinuous phase holdup xiv

X Ratio of (I) to (2)g XT Total phase holdup Z Distance along test section Greek Symbols a Empirical constant B Ek~Empirical constant A Denotes a difference 5f Frictional pressure gradient 6fp Predicted frictional pressure ~rd- ient e Porosity M- Viscosity p Density pf Continuous phase density PI Isobutanol phase density, Equation (B-l) pw Water phase density, Equation (B-2) a Interfacial tension 0$g ~ Functional relationship defined by Equation (10) Subscripts 1 Upstream position 2 Downstream position m Mean o Organic phase o Oil phase w W n- Water phase I Isobutanol phase f Refers to frictional contribution xv

ABSTRACT The purpose of the research reported in this thesis was to investigate the upward cocurrent flow of immiscible liquids in packed beds, Manometers were used to measure the pressure difference over segments of a vertical 4 inch ID by 82 inch long Lucite tube packed with one of three different sized glass spheres. Phase holdup measurements were obtained by trapping the contents of the test section. Flash photographs taken through the wall of the column allowed direct measurement of drop sizes near the wall. The three liquid pairs: isobutanol-water, isooctane-water, and isooctane-Alkaterge "C"-water were passed through beds of 0,501 inch, 0o340 inch, and 0.164 inch diameter glass spheres, Individual phase flowrates of approximately 0.65 gpm to 15 gpm were investigated over a complete range of flow ratios. Experimental measurements indicate that steady state phase holdup can be approximated by assuming no slip velocity between phaseso A more precise estimate of phase holdup can be obtained by an equation of the form: RI = ( U )a Uo + Uw where RI represents phase holdup and UO and Uw are the individual phase volumetric flowrates divided by the cross sectional area of the empty test sectiono The constant a has been evaluated for each system, studiedo I.n addition a limited amount of transient phase holdup data are presented, xvi

The manometric data indicate that immiscible liquids flowing in a packed bed cannot be treated simply as if they comprised a single liquid phase with averaged physical propertieso The data do however deviate from the "single-phase" prediction in a systematic mannero Measured two-phase pressure gradients are in all cases greater than the "single-phase" prediction. The measured values approach the "single-phase" curve asymptotically at both extremes of flow ratio and pass through a maximum at a flow ratio of approximately 75 volume per cent of the nonwetting phase. These data were correlated in terms of a parameters PRATIO' which is the ratio of frictional pressure gradient (total pressure gradient less pressure gradient due to gravity) to that predicted by means of the "single-phase" assumption, PRATI is then a measure of the degree of phase interactiono Values of PRATI as great as 10 were observed, A correlation of PRATIo with the independent experimental variables is presented. The pressure gradient in the entrance section was found in all cases to be less than that in the interior of the test section. Phase interaction is attributable to surface energy effects. That is, during the formation of a dispersion by means of flow through a packed bed, energy is converted from pressure energy to surface energyo A sample calculation shows that surface energy effects are indeed an important contributor to pressure losso The addition of a surfactant was found to have less effect on pressure drop than would be indicated by its effect on statically measured interfacial tensiono Sauter-mean drop diameters were computed and used to characterize interfacial area, Dispersed-phase drop diameters were found to be xvii

directly proportional to packing diameter for the systems studiedo In addition they were found to decrease exponentially with total mixture velocity. The effect of fluid properties on drop diameter was not fully ascertained, but an increase in interfacial tension causes an increase in drop diametero In addition drop diameters were found to exhibit a Gaussian (normal) distribution in all cases. xviii

I, INTRODUCTION In recent years a great deal of interest has developed in the field of multi-phase flow, A large number of papers on this subject have been published but they have been concerned almost exclusively with the problems of gas-liquid flow in open pipes, fluidization of solids, and counter-current flow in packed beds. A recent investigation of liquid-liquid extraction in a cocurrent flow system(45)performed at the University of Michigan has created a desire for information about the cocurrent flow of immiscible liquids in packed beds. The mass transfer investigation indicated a linear increase in mass transfer coefficients with velocity over the range of variables studied. As a result, any application of cocurrent liquid-liquid extraction would be limited only by fluid flow considerationso It is therefore desirable to be able to predict pressure gradient, phase holdup, and the amount of interfacial area produced in liquidliquid flow in a packed bed, This information will not only provide design information for cocurrent extraction systems, but provides insight into the general problem of cocurrent two-phase flowo It is the purpost of this study to investigate the cocurrent flow of immiscible liquids in packed beds, to determine the important physical variables and their effect on pressure gradient, phase holdup (the fraction of the void spaces occupied by the dispersed phase) and dispersed phase drop sizes, and if possible to present generalized correlations for predicting these functions, A search of the periodical literature has shown that no work of this type has been undertaken to dateo -1

-2A preliminary investigation indicates that the following variables could all have some effect on the three dependent variables, i eo, pressure drop, phase holdup, and drop size: (1) Flow rate of each liquid phase (2) Ratio of flowrates of the two liquid phases (3) Direction of flow (vertically upward, vertically downward, horizontal, inclined, etc.).(4) Fluid properties of each phase (viscosity, density, interfacial tension) ( Entrance or mixing arrangement (6) Packing shape (spheres, Raschig rings, Berl saddles, etc.) (7) Packing size (8) Packing material (determines wettability of packing) (9) Column size (10) Possibly others such as pH of solutions, packing orientation, etc. Because of the large number of independent variables involved in such systems, it is necessary to limit the scope of the problem so that it can be adequately investigated in a reasonable length of timeo As a result the present investigation was limited to one column size, one entrance arrangement, one flow direction, one packing shape, one packing material, three packing sizes, and three liquid-liquid systemso The liquid-liquid systems however, were chosen so as to give a relatively wide range of the physical properties, density, viscosity, and interfacial tension.

-3In attempting to correlate the data obtained from the above systems, it was decided to draw as much as possible from the single phase correlations for flow in packed beds and the correlations proposed for other two-phase flow systems. It is hoped that by this technique the results of this investigation can be made more general and can have a wider range of applicability.

II. LITERATURE REVIEW An exhaustive search of the periodical literature has shown that to date no information on the cocurrent flow of immiscible liquids in packed beds has been published. There are, however, in the literature a large number of articles of value to the present problem. The more important of these articles are reviewed here. A supplementary bibliography is presented in Appendix H without comment. This supplementary bibliography contains articles which are not directly applicable to the present problem, but which are of interest to the worker in the general area of liquid-liquid or gas-liquid flow. 1. Single-Phase Flow in Packed Beds The first significant contribution to the study t flow in packed beds, other than D'Arcy's law, was due to Blake,(4) who by dimensional analysis and analogy with flow in open pipes obtained the dimenAPfDp DpVp sionless correlating groups LV2 an the latter of which is the Reynolds number. Substituting e for V, where U is the superficial velocity and V is the actual interstitial velocity, and E for Dp, where S = area of particle surface he proposed that the following volume of packed space unique relationship exists for turbulent flow: ZLPfE 3 Vp _ = F (~) (1) LU2pS S (27) Furnas(27) presented the most comprehensive collection of data, but only proposed the simple correlation - =AR (2) L

-5where R = fluid flowrate, and A and B are constants for a given packing and fluid. Following Blake's lead, several authors since have attempted to correlate packed bed flow data using some form of Reynolds number and friction factor.(8,9,11,13,18,46,47) Chilton and Colburn(l8) proposed a two-range correlation with a different friction factor for the viscous and turbulent ranges. Carman(l3) pointed out that for spheres the S in Blake's equation is given by S = 6(1-) (3) Dp Substituting this in Blake's equation, he showed that in the turbulent range the dependence of pressure drop on porosity is given by -AP 1-e f a (4) L c3 Starting with the Kozeny equation and employing the above technique he found that in the viscous range the dependence of pressure drop on porosity would be given by -Pf (1-)(5) L c3 Leva(46'47) correlated a great deal of data from the literature by the friction factor-Reynolds number method with a separate equation for the viscous, transition, and turbulent flow regimes. He also included the effect of packing roughness. Brownell and Katz(829) assumed the Fanning friction factor relationship to be absolute and suggested a modified Reynolds number and modified friction factor to force their data to fit the Fanning relationship.

-6Morcom(56) proposed the following functional relationship based on dimensional analysis: -PfSgpD3 DUp -Ltp F(DUP) = F(Re) (6) L 2. Assuming the function F to be of the form F(Re) = a Re + p Re2, (7) he developed the two term correlating equation for all ranges of flow: -if Dp - = a + p Re (8) L [iU He found, however, that the constants a and 3 were functions of the bed Ergun and Orning, (24,25) using an idealized physical model derived a two term equation very similar to that of Morcom but which includes the effect of porosity on pressure drop. Their final equation was -APf (1-e) 2 PU 1-e U2p gc = k -- + k2 (9) L c3 DJ 3 p 3 Dp The constants kl and k2 have physical significance but were evaluated empiricallyo This equation is developed and discussed in detail in the section "Theory of Single Phase Flow in Packed Bedso" Fahien and Schriver(26) recently attempted to modify the Ergun equation to better account for wide variations in porosity and also to better fit data in the transition regiono

-7Ranz(60) proposed that pressure drop in packed beds was merely an additive property of the pressure drop for flow past a single particle. A major problem, however, arises in deciding what velocity to use for the computation of drag coefficients. His results indicate order of magnitude agreement with packed bed data. Most authors to date have assumed that packing size, packing shape, and porosity are sufficient to determine the permeability of a packed bed to a given fluid. Martin,(53) however, showed that particle orientation is also a factor in determining permeability. By packing beds of spheres in regular patterns he experimentally showed that beds with equal porosities but different packing arrangements produce different permeabilities. Benenati and Brosilow(2) pointed out that even with a "random" packing of spheres point porosity varies considerably with distance from the wall of a circular container. 2. Two-Phase Flow in Open Pipes Since most of the investigations of two-phase flow have been carried out in open pipes a brief review of the results and methods of attack of these investigations is presented here. (Since so little literature is available on cocurrent flow in packed beds it is extremely helpful to draw on the open pipe literature in analyzing results and drawing conclusions.) 2.1 Gas-Liquid Flow A tremendous amount of data on gas-liquid flow in open pipes has been published but only four basic methods of analysis have been

-8used. The most satisfying but at the same time the most difficult approach is the analytical one. Due to the difficulty of application only two relatively simple flow regimes have been attacked by this method. Calvert and Williams(12) and Anderson and Mantzouranis(l) have presented theoretical analyses of annular flow in vertical pipes. Street(7^) theoretically analyzed the "slug flow" regime. The second basic approach to the problem of pressure drop and phase holdup in two-phase flow was first developed by Martinelli, Lockhart, et al. (51,5455) By treating each phase of the two-phase system as if it were flowing by itself, and by drawing on single-phase pressure-drop correlations, they proposed a four regime empirical correlation of the following form: (A TP / g = (X). (10) where LAPf (L )Tp = Two-phase frictional pressure gradient U Tf ( ) = frictional pressure gradient due to gas flowing alone g APf /ZAPf X = ratio of single-phase pressure gradients - (- ) / Although the correlag deal of scter in the d, th i Although the correlation left a great deal of scatter in the data, this approach has been widely used. Hoogendoorn(37) and Chenoweth and Martin(l7) have pointed out limitations of the Martinelli-Lockhart approach and have presented improved correlations for high gas densities. Chisolm and Laird(l9) added a correction for pipe roughness to the Martinelli-Lockhart approach. Recently Hughmark and Pressburg(38) pointed out that total mass

-9velocity appears to be an important variable in the interaction of two phaseso In a series of articles Govier and co-workers(6s753031,,32) treated a two-phase gas-liquid system as a single phase and presented plots of friction factor versus liquid Reynolds number with a parameter of gas-liquid ratio. Other authors who have applied the same general technique are Brigham and co-workers(5) and Bertuzzi and co-workers.(3) Recently a general dimensional analysis was applied to twophase flow by Roso(63) He found, however, after correlating a tremendous amount of data, that only four of his original nine dimensionless groups had a significant effect on pressure dropo 2.2 Liquid-Liquid Flow Recently some interest has developed in the flow of immiscible liquids in open pipe, with particular application to the reduction of pressure gradients by injection of water into crude oil pipelineso Gemmell and Epstein(29) and Charles and Redberger(l6) have applied numerical analysis to the horizontal, stratified flow of oil-water mixtures but found only moderate agreement between theory and experimento Experimental investigations of horizontal oil-water flow in pipes by Charles, Govier and Hodgson,(l5) Russell and Charles,(64) and Russell, Hodgson and Govier(65) have not resulted in a satisfactory correlation but have indicated some interesting resultso Reduction of pressure gradient by as much as a factor of 10 has been observed. Flow patterns similar to those for gas-liquid flow have been observed.

-10In the vertical flow of oil-water mixtures in open pipes, Govier, Sullivan and Wood(33) observed the following flow patterns for increasing oil rate at constant water rate: drops of oil in water, slugs of oil in water, froth, drops of water in oil. They also observed that frictional pressure drop is independent of the oil viscosity as long as water is the continuous phase. Brown and Govier(6) felt that frictional pressure drop was approximately equal to that of the continuous fluid. flowing alone at the mixture velocity. They also found that at a constant superficial oil velocity the slip velocity is approximately constanto Cengel, et alo(14) treated dispersions of organic solvents in water as single-phase fluids and calculated pseudo viscosities for the mixtureso They found that at low velocities the viscosities tended to increase. 30 Countercurrent Flow in Packed Beds Since pressure drop in countercurrent flow is important only with respect to loading and flooding, no discussion of the literature on this subject will be presented hereo It is interesting to note, however, that White(77) found that any wall effect on pressure drop was negligible when Dtower > 6 dpacking This section will, therefore, be devoted to a review of the literature on phase holdup in countercurrent flow in packed towerso Jesser and Elgin(40) first postulated a simple expression for liquid holdup in a gas-liquid packed tower of the form H bL (11)

-11where H = liquid holdup L = liquid flowrate b = constant dependent only on area of packing s = constant dependent only on shape of packingo Gayler and Pratt(28) first observed different types of holdup. Wicks and Beckman(78) noted three types of holdup: permanent, free and totalo They also noted that channelling of the dispersed phase occurred for Dtower < 6 dpacking From dimensional analysis they derived the following expression for total holdup for a given system: XT = A(UD)r + Bl(UD)(UC) (12) Markas and Beckman(52) noted a hysteresis effect on permanent holdup and modified Equation (12) to XT = Al + Bl(UC) + Cl(UD) + Dl(UC)(UD) (13) More recently Johnson and Lavergne(41) applied Bernoulli's equation to each phase separately and obtained the following expression for dispersed phase holdup in packed towers: X3 = Al UCL ( X_) + B. (14) UD 15 uDlo5 1-X where Al, B' are r are empirical constants for a given system.

-12The most satisfying correlation from a theoretical view point is that of Sitaramayya and Laddha(71) which relates holdup to slip velocity or the relative velocity between the dispersed phase and the continuous phase. In a countercurrent packed tower the slip velocity Vs is given by V UD U (15) s eX e(1-X) ( The authors assumed Vs = Vo (-X) (16) where V0 is a limiting mean droplet velocity, rearranged Equation (15) and plotted (UD + X UC) versus X(liX)o Their data produced a straight 1-X line through the origin with a slope m, which was found to be a given function of the fluid properties and the packing propertiesO 4. Cocurrent Flow in Packed Beds A search of the periodical literature revealed only two articles which dealt with cocurrent flow in packed beds and in both cases the sys~ tems studied were gas-liquid. Dodds, et al (22) presented pressure-drop data on gas-liquid flow in packed beds but did not attempt a general correlation. Their data are limited to rather low pressure drops. Larkins(44) covered a much wider range of flowrates and was able to correlate his data plus some industrial data fairly well by the Martinelli-Lockhart approach. Although no literature is available on cocurrent liquid-liquid flow in packed beds, several articles have been written on cocurrent flow of liquids in porous mediao An excellent review of this work can be found in a book by Scheidegger (66) Brownell and Katz(1O) proposed a Reynolds

-13number-friction factor correlation with a different form of the two correlating groups for the wetting and non-wetting phases. The more widely accepted approach, however, is that presented by Leverett.(48) Beginning with D'Arcy's law which defines permeability of a medium as K = S (17) -APf he defined an effective permeability for each phase as Ko Q~oL = oil permeability (18) AAPf and Kw = Iwl = water permeability (19) w AAPf where Q = volumetric flowrate p = viscosity A = cross sectional area /Lf= frictional pressure gradient L The relative permeabilities Ko KO and K = -W were found to be funcK K tions of water saturation or water holdup only. It was observed, however, that K + K' was sometimes less than unity. This was attributed to the Jamin effect or the situation where droplets of oil (non-wetting phase) are lodged in apertures in the medium through which they cannot pass until the pressure gradient is increased.

-145o Drop Breakup and Interfacial Area Almost all investigations of interfacial area to date have been performed in mixer-settler type equipment due to the ease of making measurementso The results of these studies, however, aid in understanding the drop sizes obtained in other types of equipmento Hinze(35) describes several types of drop breakup and attempts to establish a theoretical basis for predicting stable drop sizeso He points out that viscous stresses and dynamic pressures cause deformation and, as a result, splitting in liquid-liquid systems. Surface tension forces tend to counteract deformation. He states that a critical Weber number exists above which breakup will occur. He defines the Weber number as We = DP2 (20) where D = drop size. The value of the critical Weber number depends on the breakup mechanism. Mugele(57) used a force balance to determine the critical Weber number for a drop exposed to the drag of a continuous medium. Several authors(20,23,42,62,69,70) have presented highly empirical correlations for stable drop sizes in agitated mixtureso The only consistency among their results is that the mean drop diameter is inversely proportional to the first power of the impeller speedo Shinnar(69) even found a variation in this exponent depending on whether the agitation is causing breakup of drops or merely preventing coalescence of existing drops. Levich(49) in a review of Russian work on the subject implied that very little is known about drop breakup due to turbulence and that only

-15the simpler cases of breakup due to laminar drag forces have been even reasonably well covered. Another group of authors proposed dimensional analysis as a tool for attacking this problem.(6174^75) Rodger, Trice, and Rushton(61) found the interfacial area produced in an agitated liquid-liquid mixture to be proportional to the 0.36 power of the Weber number. They also found the effect of the relative viscosity of the two liquids to be small, but observed an exponential increase of interfacial area with Ap/pf, where pf is the continuous phase density. Only three investigations of drop sizes in flow equipment have been found in the literature. Sleicher(72) studied maximum drop sizes in cocurrent turbulent flow in a pipe and found the maximum drop size to be independent of the inlet drop size as long as inlet drops are not too small. Weaver, Lapidus, and Elgin(76) in an investigation of liquid spray towers photographically observed a Gaussian distribution of drop sizes. On the other hand Lewis, Jones, and Pratt(50) found a non-Gaussian distribution when fairly uniform droplets were allowed to flow countercurrently to the continuous phase in a packed bed. They, however, did agree with Sleicher that the inlet drop size has little effect on the outlet size.

III. THEORY OF SINGLE-PHASE FLOW IN PACKED BEDS Before attempting to study two-phase flow in packed beds a sound understanding of the theory of single-phase flow in packed beds is necessary. From a theoretical view point the most satisfying approach to single-phase flow in packed beds is that of Ergun and Orning.(25) In this section a development of their flow equation will be presented along with a discussion of its strong and weak points. To begin, assume that a packed bed is equivalent to a number of parallel, equal sized capillary tubes such that the internal surface area of the tubes is. equal to the surface area of the packing and that the total internal volume of the tubes is equal to the void volume of the packed bed. The well known Poiseuille equation for flow in capillary tubes is then applicable: dPf 2g=2(21) dL gc 32pV/Dc where Dc = diameter of the channel. In a capillary the kinetic energy losses due to entrance and exit effects occur only once. However in a packed bed the number of times these kinetic energy losses occur is statistically related to the number of particles per unit length. As a result a term accounting for these kinetic energy losses must be added to Equation (21). Equation (21) then becomes -dPfg = 322V/D. + P pv2/Dc (22) dL 2 where the factor P accounts for the number of times the kinetic losses occur. In addition the stream lines frequently converge and diverge in -16

a packed bed so a correction factor must be included in the viscous term of Equation (22): d- g = 32 aCV/D2 + (_)pV2/D (23) dL 2 Equation (23) is of limited value in its present form since the channel diameter Dc and the actual interstitial velocity V are unknown. The mean pore velocity given by U, where U is the mean superficial velocity (the velocity if no packing were present) may be substituted for V. In reality V varies from point to point along the bed as the area available for flow contracts and expandso The expression U is, however, the best approximation available for V at the present time. To eliminate Dc recall the original assumption that the internal surface area of the capillary tubes is equal to the surface area of the packing. If the capillaries are assumed to be cylindrical, the specific surface, Sv, of the packing (the surface area of the packing per unit volume of packing material) is given by the following equation: Sv = NLiDC/Lt(D2/4)(1 ) (24) where N = the number of capillaries in the bed and D = the diameter of the packed bed. The second original assumption (that the internal volume ofl the capillary tubes is equal to the void volume of the packed bed) yields the following relationship: NMDC/4 = iD2e/4 (25)

-18Elimination of N between Equation (24) and (25) gives the following expression for DC in terms of measureable bed parameters: Dc 4 = - 1 (26) 1-e Sv Substitution of Equation (26) and the expression V = (27) C into Equation (23) yields dPf ( IU + c p 2 (28) - 2- 3'SU + 3PSvU2 ~~dL E8 ~3 It is interesting to note here that tne dependence of pressure gradient on porosity given by Equation (28) is the same as that proposed by Carman and observed by several experimental workers. It has been common practice in recent years to replace Sv, the specific surface area, in Equation (28) with an equivalent diameter for any shape particle. This diameter Dp is derived from the relations for spheres. For a sphere Sv is given by 4 ir2 3 6 Sv =4~ =r d.(29) - jr3 r d The equivalent diameter for any particle is, therefore, defined as D 6 (30) P Sv Substitution of Equation (30) into Equation (28) gives dPf (1-E) 2 u 6 1-E pU2 (31).g.. D3 P- 3,, E3 D~ 8 c3 Do

-19In its present form the flow equation is completely general. If now, however, only constant density fluids are considered, Equation (31) can be integrated to give - fgc = 72 a + (32) L p e D2 8 ~3Dp In order to apply Equation (32) to an actual calculation the so-called constants a and P. must be evaluated. This can be accomplished by fitting experimental data to the above equation but it would be preferable to obtain at least an approximate value for these numbers from theoretical considerations. The correction factor a in the viscous energy term represents the ratio of actual viscous energy losses to that predicted for a fluid flowing at velocity V through a capillary of length L. However the method by which V has been evaluated causes it to be a numerical measure of only the component of velocity parallel to the axis of the bed. The velocity which should be used to measure viscous losses is that parallel to the walls of the channel. If the bed is assumed to be composed of spherical particles, the ratio of actual path length to bed length would be given by the ratio of one half the circumference of a particle to its diameter or. At the same time, however, the ratio of the velocity parallel to the surface of the particle to the component of velocity parallel to the axis of the bed is given by the same number. The value derived for c 2 is, therefore, (2) or approximately 2.47. Since the kinetic energy term of Equation (32) is not dependent on the length of the bed but merely the number of contractions in the flow

-20path per unit of channel diameter, the same reasoning cannot be applied there. It does, however, follow that the velocity to be used in this term is the same as that used in the viscous energy term. Since velocity appears to the second power the correction factor. must be squared before putting it in the equation. The simplest assumption concerning the number of times the flow path contracts is that it contracts once for each channel diameter of length along the bed. Making the proposed substitutions in Equation (32) yields 2 2 Lf = 72() (1-) U 6(())2 1- pU gc = 7T2(") i- ^ () | (33) L 2 82 DP or L gc = 177 (1E)2I L + 1.85 -L pU2 (54) L c3 D In actual practice the two constants are replaced by experimentally evaluated constants kI and k2, respectively. Ergun(24) evaluated the constants kl and k2 for a great deal of data and obtained the following results: kl = 150 k2 = 1.75 It is very satisfying to note how closely the experimental numbers agree with the predicted ones. The form of Ergun's equation which is most widely used and which will be used here is g= kl (1-E)2 IU + k2 (1- pU L E3 D c3 Dp

IVo EXPERIMENTAL PROGRAM 1. Introduction Due to the lack of knowledge in the area of two-phase flow, any investigation of this subject must be based on a sound experimental program. In addition, due to the complete lack of data on cocurrent flow of immiscible liquids in packed beds, an experimental investigation of this subject must be largely exploratory in natureo As a result even the most carefully designed experimental program would probably not solve all the problems associated with this subjecto Therefore the experimental program must be explained in detail so that workers with further interest in this area need not repeat work unnecessarily, As pointed out in the introduction, a large number of independent variables may possibly effect the flow characteristics of immiscible liquids in packed beds. The number of these variables actually studied must of necessity be limited. This section describes in detail the experimental equipment and operating procedures used to study these variables and also describes the manner of selection and ranges of variables studiedo 2. Experimental Apparatus The main piece of experimental apparatus used in the present study was the test section which consisted of an 82-inch long 4-inch ID transparent Lucite tube with Lucite flanges attached at each endo The tube actually consisted of two sections of tube joined at the center by a 1-1/2 inch lap joint supported by a two-section 4-inchLucite collar held in place by steel wire. The flanges enabled the test section to be -21

-22mounted vertically between two 4-inch, flanged quick-closing valveso Since the purpose of the valves was to.trap the contents of the test section during a run, a system of weights and pulleys was provided to close the valves simultaneously and as rapidly as possibleo The valve handles were connected by steel cables through a system of pulleys to a single weight which could be dropped thus actuating the valves simultaneously. In order to obtain accurate holdup measurements the packed portion of the column had to extend as close as possible to the valve disks. Therefore retaining screens were placed inside the valves and the valves themselves were filled with packingo A detailed drawing of the lower valve connection is shown in Figure 1o In order to measure pressure drop in the test section, four holes were drilled and tapped along the length of the tubeo In these were placed 1/8 inch pipe to 3/16 inch copper tubing connectors which were in turn connected to a manometer manifold system by means of 3/16 inch copper tubing. The 3/16 inch size was used to minimize errors caused by the two-phase mixture being drawn into the manometer lead lineso An additional pressure tap was placed just below the valve disk in the lower quick-closing valve to measure pressure drop in the entrance section. To prevent the packing particles from plugging the pressure taps, four small holes were drilled in the end of each 1/8 inch pipe connector. Two copper wires, crossed at right angles, were then inserted in the holes. This kept packing particles out of the pressure tap without introducing a capillary pressure error sometimes caused by placing fine wire screens over the openings,

-23 - Inside diameter of column = 3.96 in. Cross sectional area = 0.08553 ft.2 Total volume between valve disks = 0.629 ft.3 Packed volume = 0.615 ft.3 Length of packed section = 86.25 in. Distance between taps 1 and 2 = 11.09 in. Distance from entrance to packed section to tap 2 = 7.09 in. Distance between taps 2 and 3 = 24.00 in. ) \ Distance between taps 3 and 4 = 24.06 in. Distance between taps 4 and 5 = 24.00 in. RETAINING SCREEN RUBBER G AS K ETS. V ^ PRESSURE PERFORATED\ \ TAPS ALUMINUM SUPPORT PLATE VALVE HANDLE QUICK CLOSING VALVE VALVE DISC RETAINING SCREEN Figure 1. Test Section Dimensions (Not to Scale).

-24Complete test section dimensions and pressure tap locations are given in Figure 1. To facilitate the description of the flow system associated with the test section, consider the system in operation. A schematic flow diagram is shown in Figure 2. All lines unless otherwise stipulated were 1-1/2 inch galvanized pipe. The two liquids were picked up from their respective 200 gallon storage tanks and pumped to separate rotameter systems. A recycle line to the storage tank with a manual control valve was provided for each liquid system. The water pump was a 5 hp. turbine pump while the organic liquid pump was a 3 hp. centrifugal pump. Water inlets were provided in both systems for flushing and filling purposes. Two Fischer & Porter rotameters were used in each liquid system to measure flowrates. A large rotameter of approximately 20 gpm maximum capacity and a smaller rotameter of approximately 8 gpm maximum capacity were used in series in each system. The large meter in the water system was a Fischer & Porter Model 10A1735 rotameter with a size 8 tube and an SVP-87 float, while the small meter was a Fischer & Porter Model 10A1735 rotameter with a size 6 tube and an SVP-67 float. The large meter in the organic liquid system was a Fischer & Porter Model 10A17355 rotameter with a size B8 tube and a BNSVT853 float, while the smaller meter was a Fischer & Porter Model 10A1735 rotameter with a size B6 tube and a BSVT-64 float. The piping was arranged so that the liquids could flow through both rotameters in series, the large rotameter only, or neither rotametero Line pressures could be monitored by the gauges shown in Figure 2.

-25QUICK CLOSING f VALVE CHECK TA K LDRAI N / I _: VALVE T SECTN I \L _~\ /I I..:;*:.;'*.I TEST SECTCIO, SURGEL \ I P'OR.:ATE STO /~ G TANK -T' C — CAMERA \ T X — 1ROTAMETE VALVE THERMOCOUP LIQIDSTRA WTER SESP RATIN Figure 2. Schematic Diagram of Experimental Apparatus. SEPARATING [} CALIBRATION I ------ TANK DRAINS 200 GALLON LIQUID STORAGE WATER STORAGE TANK TANK FLUSHING 3 HP WATER SUPPLY DRAIN.4 PUMP!"S* Figure 2. Schematic Diagram of Experimental Apparatus.

-26After leaving the rotameter systems the liquids flowed through filters, past calibration drains, through check valves and came together in a 2 inch crosso The filters consisted merely of a copper wire screen placed in a tee in the line with a small amount of glass wool over the screen. The sidearm in the tee enabled the glass.wool to be changed periodically. An immersion type copper-constantan thermocouple was used to measure the temperature at the inlet to the test section. It was mounted in a 1-1/2 inch length of 1/4 inch stainless steel tubing and mounted directly through the wall of the 2 inch cross. A commercial temperature indicator was used to obtain temperature readingso During normal operation the liquid mixture flowed out through one arm of the 2 inch cross, through the lower 4 inch quick-closing valve and into the test section. The effluent mixture from the test section flowed through a 1-1/2 inch line and entered an opening half way up the wall of a 140 gallon separating tank. A glass window in the front of the separating tank allowed visual observation of the position of the interface between the two liquids. The separated liquids then flowed by gravity, through 2 inch lines, back to their respective storage tankso The position of the liquid interface was maintained approximately midway in the tank by adjusting the flowrate of the heavier liquid. In order to eliminate the possibility of a water hammer when the quick-closing valves were actuated, a by-pass for the flowing liquids was provided through the fourth arm of the 2 inch cross located at the entrance to the test sectiono A 2 inch line led from the cross, through

-27a check valve and into a surge drum. Before each run the surge drum was pressurized with air to a pressure at least 10 psi greater than that expected at the entrance to the test section. This kept the check valve in the by-pass line closed. When the quick-closing valves were actuated the check valve in the by-pass line was forced open and the liquid mixture began to fill the surge tank. The drain valve on the surge tank was then opened and the liquid mixture drained into the separating tanko If for some reason the drain valve were not opened and the pressure in the surge tank continued to build up, a relief valve set for 100 psig was provided to dump the system into the separating tanko As mentioned previously, all piping was galvanized but the storage and separating tanks were constructed of ordinary carbon steel sheet. To prevent corrosion and thereby contamination of the liquids these tanks were painted inside and out with DuPont Imlar Vinyl Chemical Resistant Paint. Pressure drop measurements were obtained by means of a dual, well-type manometer manufactured by the Meriam Instrument Company with a 40 inch range and a maximum operating pressure of 350 psigo One manometer tube was filled with mercury while the other was filled with a manometer fluid provided by the King Engineering Company; this fluid had a specific gravity of lo750 at 20~C relative to water at 4~Co The manifold system shown schematically in Figure 3 enabled either the high or low range manometer to be connected across any two pressure taps in the system. The numbered circles in Figure 3 correspond to the numbered pressure taps in Figure 2. An Ashcroft laboratory test

-28-'(>-TEST GAUGE ALL VALVES ARE HOKE BLUNT POINT NEEDLE VALVES HIGH RANGE MANOMETER LOW RANGE MANOMETER TO PRESSURE TAP5 TO PRESSURE TAP 4-) TO PRESSURE, TAD 3 HIGH PRESSURE LOW TO PRESSUR TAP MANIFOLD PRESSURE MANIFOLD Ii TO PRESSURE TAP 2TO PRESSURE TAP I FLUSHING7 LIQUID SUPPLY TO SURGE TANK 1J 90PSIG L -- AIR SUPPLY Figure 3. Schematic Diagram of Pressure Manifold System.

-29gauge with a range of 0 to 100 psig was connected to the manifold system so that static pressure at any point in the test section could be obtainedo A supply of flushing liquid taken directly from the water pump discharge, the highest pressure location in the system, was providedo As a result during operation the manometer lines were always filled with the water phaseo In addition the building air supply at a supply pressure of approximately 90 psig was connected to the manifold systemo The manifold system could, therefore, be used to fill and meter the pressure in the surge tanko Connections for this purpose are shown in Figure 35 The system was constructed entirely of 1/8 inch brass pipe and 35/16 inch copper tubing. All valves were Hoke blunt point needle valveso 3. Photographic Equipment To measure the dispersed phase drop sizes during a run, flash photographs of the flowing system were taken through. the wall of the test section. The camera used for this purpose used a 50 mm Argus lens with an adjustable focus and having f/2o8 to f/22 stopso The resulting magnification was approximately 2o9Xo A ground glass focusing plate mounted in the film holder allowed the droplet images to be focused on the film without a trial and error procedure. The film used was Kodak Contrast Process Ortho 4" x 5" cut film. This is a fine grained orthochromatic film used for high contrast applications. The film was exposed by means of a high intensity light flash from a General Electric FT 220 flashtube powered by the discharge of a 76 microfarad capacitor initially charged to 2250 volts.

-30The camera was positioned approximately 24 inches from the bed entrance as shown in Figure 2. The relative positions of camera, flashtube, and test section are shown in Figure 4. Arrangement a, using transmitted light, is the preferred arrangement since it eliminates distortion due to reflection. This arrangement was used with the largest packing size. For smaller sizes, however, the light produced by this arrangement was too diffuse to adequately expose the film, so arrangement b was used. 4o Operating Procedures Before starting actual operation the four rotameters were calibrated by passing water through them and weighing the water collected in a given time. The calibration curves agreed substantially with those provided by the manufacturer. For use with liquids of density different from that of water, rotameter correction factor curves supplied by the manufacturer were used. These correction factors were checked by the direct weighing method for at least three points for each liquid and were found to be quite accurate. A plot of this correction factor for meters calibrated with water and using a stainless steel float is given in Appendix A. As was mentioned earlier the porosity of the packed bed is an important variable in the present investigation. In order to accurately measure porosity and to assure a reproducible packing arrangement the following procedure was used in packing the test section: (1) The bottom of the test section was sealed by means of a rubber gasket and an aluminum plate bolted to the bottom plastic flange. The test section was then placed in an

FLASH TUBE - CAMERA TEST SECTION (a) Transmitted Light TEST SECTION, CAMERA \\~,\\\ -FLASH TUBE (b) Reflected Light Figure 4. Arrangement of Photographic Equipment (Top View)

-32upright position on the floor, the pressure taps were sealed off, and the test section filled with water to the uppermost pressure tapo An overflow line from this tap led to a graduated cylindero (2) Packing was slowly poured into the test section and the overflow water collected. The column was intermittently tapped with a rubber hammer to ensure adequate settling of the particles. This method of packing eliminated further settling during operation. (3) The following expression was then used to compute porosity: v=1- (36) VT where Vw = volume of overflow water collected VT = total volume of test section between the lower flange and the uppermost pressure tap. (4) The porosity was independently measured by weighing the amount of packing introduced into the test sectiono By using the density of the packing material an equation similar to Equation (35) could be used to compute porosity. The two values for porosity agreed within 2% in all cases. (5) Since it was originally assumed that capillary pressure may have some effect on pressure drop, the test section was next allowed to drain slowly ("-1/2 hour) through the lowest pressure tap to determine permanent holdupo The

-33permanent holdup was in all cases less than 2o65% of the total void volume indicating that capillary pressure is not an important variableo (6) The quick-closing valves were then filled with packing to the retaining screen, the plate removed from the bottom of the test section, and the test section bolted in placeo The pressure taps were connected and the equipment was ready for operationo In order to eliminate possible errors in the constants of the Ergun equation from influencing the results of the present study, singlephase pressure-drop measurements were made for each packingo The procedure used in these runs was essentially the same as that used in the twophase runs which is described below, The procedure used in a typical two-phase run was approximately as followso The drain valve from the surge tank was closed and the surge tank pressurized with airo The quick-closing valves were opened and the two liquid pumps started. The flows were adjusted to the desired levels by means of the recycle valves and the valves adjacent to the rotameters. The manometer lead lines were then flushed by introducing flushing liquid into the pressure manifolds and then opening the valves to the pressure taps one at a timeo The flushing liquid supply was then turned off and pressure taps 2 and 3 connected across the appropriate manometer. When a constant reading was obtained, the valves leading to the manometer were closed and the pressure tap lead lines reflushed, This ensured that the lead lines were filled with the aqueous phaseo Pressure taps 2 and. 3 were

-34again opened and a reading taken. Taps 4 and 5 were then connected to the manometer and a reading was taken. A second reading was then taken between taps 2 and 3 and this process continued until both readings were constant. Readings were then taken for the pressure difference between taps 3 and 4 and taps 1 and 2o All valves leading to pressure taps and manometers were then closed and the inlet temperature was recordedo Comments regarding the flow pattern were noted at that timeo The procedure for measuring phase holdup was then started by dropping the weight which actuated the quick-closing valveso As soon as the valves were closed the drain valve from the surge tank was opened and the pumps were turned off. The two liquid phases were then allowed to separate in the test sectiono One of two methods was then used to measure phase holdupo If a readily discernible interface formed between the two phases the distance from the interface to the lower flange was measuredo Since the total volume contained between the two valve disks and the porosity in the packed section are known, the fraction of the void spaces occupied by the discontinuous phase could be computedo If no clear interface formed (eogo. in the case of very small packing) a more time consuming method of obtaining holdup data was required. The test section was allowed to drain slowly through the sample tap located at pressure tap 2 as shown in Figure 2. The volume of the more dense phase contained in the column was measured and used to compute the phase hold.up. A few runs were made to measure the time dependence of phase holdupo In these runs no pressure drop measurements were made. The flow of one

-35phase was established and allowed to completely fill the test sectiono The flow of the second phase was then established. After a short time the quick-closing valves were closed and the holdup measured. A series of such runs over varying lengths of time provided data on the time dependence of holdup. 5o Photographic Techniques Following completion of the pressure drop and phase holdup runs for a given system a series of photographs at various velocities and flow ratios was taken. Photographs could not be taken during the runs themselves because of a lack of space. The desired flowrates were established and a film holder placed in the camera. Since the open lens technique of flash photography was used (the camera lens was open at all times) the protecting shield was not removed from the film holder until just a few seconds prior to triggering the flashtubeo Normal room light intensity was not great enough to expose the film. The intense light emitted by the flashtube was required to expose the filmo At least two photographs were taken at each set of flow rates. The film was then developed for 5 minutes at 68 F in Kodak D-ll developer, rinsed for 30 seconds, placed in Kodak Acid Fix for 10 minutes, rinsed for 30 seconds, placed in Kodak Hypo Clearing Agent for 2 minutes, rinsed for 10 minutes and dried. Drop sizes were then measured directly from the negatives with the help of a comparator which produced a 10X enlarged image on a ground glass screen. This resulted in an overall magnification of approximately 30Xo Drop diameters parallel to the axis of the test section were measured

-36using one of two triangular templates; one graduated in tenths of an inch to a maximum of 1.5 inches, the other graduated in hundredths of an inch to a maximum of 0.5 inches. Only diameters parallel to the axis of the cylindrical test section were measured, because the curvature of the walls of the test section produced a slight distortion perpendicular to the axis. All drops in reasonable focus were measured. The number of drops counted per photograph ranged from as few as 11 to as many as 2835 In order to obtain actual drop sizes it was necessary to calibrate both the camera and the comparator. This was accomplished by photographing a sphere of known diameter and measuring its diameter on the negative and on the comparator image of the negativeo The camera magnification was 2o94X while the comparator magnification was 10OOXo 6. Properties of Systems Studied A single packing shape was used in this study in order to isolate the effect of packing size on pressure drop, phase holdup, and drop size. Spheres were chosen because of their simple geometry and their lack of any particle orientation effecto For the same reason as mentioned above a single packing material was selected. Glass was used with the hope of being able to observe flow patterns in the bed more closely than with opaque materials. Spheres were selected from commercially available sizes to give a wide range without introducing a wall effect. Fluid pairs were also selected to give a wide range of physical properties. In all cases water was one of the fluids; isobutanol, isooctane, and isooctane with a surfactant added were used as the second phase.

-37The systems used in this investigation were: (1) Saturated solutions of water and isobutanol on 0.501 inch spheres. (2) Saturated solutions of water and isobutanol on 0.340 inch spheres. (3) Saturated solutions of water and isobutanol on 0,164 inch spheres. (4) Water and isooctane on 0.164 inch sphereso (5) Water and isooctane on 0.o40 inch sphereso (6) Water and isooctane with Alkaterge "C" (a surfactant) added on 0.340 inch spheres. 6o1 Packing Properties The two larger sizes of glass spheres were made of flint crystal glass and were obtained from the Peltier Glass Company of Ottawa, Illinoiso The small glass spheres are called 3M Brand Spherical Impact Media IM0406(S) and were obtained from the Minnesota Mining & Manufacturing Companyo The characteristic diameter of each size of spheres was obtained by two different methods. Fifty spheres of each size were selected at random and the diameter of each sphere was measured five times in random directions by means of a micrometer. An arithmetic mean diameter was computed from these measurements. The total volume of the fifty spheres was next determined by water displacement. The mean particle diameter was computed from this volumetric measurement based on the assumption of a perfectly spherical shapeo The glass density, which was required to compute porosity by the direct weighing method, was computed by dividing the

-38weight of the fifty spheres by the volume determined by the water displacement method. The two values of diameter and the value of density are presented in Table I along with the two values determined for porosity. Since the column had to be repacked with the medium sized packing in order to make the isooctane-water runs, two values of porosity are presented in Table I. The first was that used for the water-isobutanol runs and the second for the water-isooctane and water-isooctane-Alkaterge "C" runs. Figure 5 shows samples of the three packings usedo 6.2 Fluid Properties The solutions used in the runs involving water and isobutanol were prepared by circulating tap water and commercial grade isobutanol through the experimental equipment for a period of about 4 hours. The isobutanol was used as received from the Union Carbide Chemicals Companyo To prevent the formation of a stable emulsion, the water phase was acidified to 0001 N HClo This small concentration of acid was found not to affect the physical properties of either phaseo The isooctane used in this investigation was Pure Grade Isooctane and was obtained from the Phillips Petroleum Companyo It contained a minimum of 99 mole per cent 2, 2, 4-Trimethyl Pentane. The interfacial tension of the isooetane-water system was reduced for the final set of runs by preparing a 0.009 volume per cent solution of Alkaterge "C" in isooctane, Alkaterge "C" is an organic-soluble surfactant supplied by the Commercial Solvents Company of Terre Haute, Indianao The physical properties of all fluids used in this investigation are presented in Table II. Literature values were used when available.

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Fif Photog-raph of Typical Packing Particles.

-40Those values which were not available in the literature were measured in the Sohma Precision Laboratory. In addition the literature values of physical properties were checked experimentally and found to be in good agreement in all cases. Viscosity was measured by means of an Ostwald viscometer, density by means of a precision hydrometer, and interfacial tension by means of a ring type tensiometero Since viscosity is a strong function of temperature, all viscosity data were fitted with curves of the form log10 k = A + B (37) where T = absolute temperature. These equations could then be used to compute the liquid viscosities for any run. Plots of viscosities as functions of temperature plus all equations used to compute the data in Table II are presented in Appendix Bo TABLE I PROPERTIES OF PACKING MATERIALS Diameter Diameter Packed Packed by direct by water Glass porosity porosity measure- displace- density by direct by water ment (in.) ment (in.) (gms/in3) weighing displacement 0.501 0.502 40o57 0.400 0.339 0.34o 40 89 0,383 0.379 0.382(a) 0O377(a) 0.165 0.163 47o98 0.337 0 345 (a) These values were obtained when the test section was repacked for isooctane-water runs.

TABLE II PHYSICAL PROPERTIES OF FLUIDS Interfacial Tension against saturated Density @75~F Viscosity at water solution at Fluid Composition (gms/cc) 75~F (cpO) 75~F (dynes/cm.) Water o 0998(36) 0.915(43) Water saturated with isobutanol 8.4 wto. isobutanol(68) 0.987(59) 1.30(L) Isobutanol saturated with water 83.5 wt.% isobutanol(68) 0.832(59) 3.10(L) 2.1(39) Isooctane 99 mole % min. 2, 2, 4-Trimethyl Pentane 0.692(36) 0 478(L) 49 5(34) Isooctane with 0.009 vol. %(L) Alkaterge "C" Alkaterge "C" o 692(36) 0 478(L) 16.0(L) Superscripts indicate number of reference which is source of data. (L) numbers indicated thus were measured in the laboratory.

V. EXPERIMENTAL RESULTS 1. General This section of the thesis presents the experimental results obtained from the preceding experimental program. Observations and a discussion of the results are presented but no attempt at correlation is included. That subject is treated in the following sectiono Use of the experimental apparatus and systems presented in the previous section limits further selection of independent variables to the flowrates of the individual phaseso Since the research was largely exploratory, an attempt was made to cover as wide a range of these variables as possible. An upper limit was imposed by the capacity and developable head of the pumps. A lower limit was imposed by the range of the rotameters and the sensitivity of the manometers. This lower limit, however, was not a serious limitation because in this flow range frictional pressure drop becomes very small relative to static pressure drop. Approximately 40 runs were performed on each system in an attempt to blanket the ranges of available flowrateso In addition, approximately 10 of these runs were repeated to see if the results were reproducible. No attempt was made to evaluate reproducibility numerically but these additional points are included in the data plots for examination. In examining the data for internal consistency it should be remembered that each data point stands alone, ioe. it does not depend on the data points preceding it. Recall that following each run the quick-closing valves are closed and the flows shut offo For each succeeding run the flows of the two phases must be reestablished. -42

-43In addition to the numerical data presented later in this section, visual observations of flow patterns were recordedo Although no correlateable effect of flow pattern on pressure drop, phase holdup, or drop size, was observed, descriptions of these flow patterns are included for comparison purposeso Three flow patterns or "modes" of flow were observed during this investigation. In the "bubble flow" regime small droplets of the dispersed phase were distinctly observable in the continuous phaseo A second flow pattern "homogeneous flow" occurred only at high flow rateso In this pattern no distinct droplets could be observed, but the liquid mixture in the test section had a "milky" appearanceo However, when the quick-closing valves were actuated, the "milky" appearance quickly disappeared and small droplets could be observed in the test sectiono In addition analysis of enlarged photographs of "homogeneous flow" showed very small droplets to be presento In light of these two observations "homogeneous flow" can be considered merely an extension of'bubble flow" to very small drop sizes. Although no distinct boundaries of the "homogeneous flow" regime were obtained, it seems to occur at high total flowrate, small packing diameter, and low interfacial tension. These are precisely the conditions expected to produce very small dropletso The third flow pattern is by far the most difficult to describe. "Slug flow" has been observed and described a number of times in the literature, but only Larkins(44) has used the term to describe the flow pattern observed here. "Slug flow" as observed here is best described by considering the test section to be initially in "bubble flow" (see

-44Figure 6a). A "slug" or volume of fluid in "homogeneous flow" approximately 4 to 6 inches thick next appears at the entrance to the test section (Figure 6b)o As the "slug" moves up through the bed, its shape becomes very irregular and very elongated (Figure 6c)o In most cases the "slug" seemed to disappear approximately 3 to 5 feet from the entrance to the bed, but in some cases it continued the full length of the columno The separation of the "slugs" varied but on the average was approximately one foot. Although again no definite boundaries for the "slug flow" regime could be obtained, it seemed to occur most often at high flow rates and at flow ratios in the vicinity of 75% organic phase. During the course of the experiments it was extremely difficult to determine which of the phases was continuouso Since in all cases the water phase preferentially wetted the glass packing, it was to be expected that the water phase would be continuous. This was indeed observed at low ratios of organic phase to water phaseo However as the flowrate of organic phase was increased, the "slug flow" and "homogeneous flow" regimes developed and visual observation was of little valueo Observation of the settling process following the closing of the quick-closing valves, however, did give an indication as to which phase was continuouso At low flow ratios of organic phase to water phase, droplets of the discontinuous phase could be seen rising in the continuous phase. The organic phase (in all cases the lighter phase) was therefore discontinuouso However for very high flow ratios of organic phase to water phase, droplets of the discontinuous phase were seen to fall in the continuous phase, indicating that the water phase was discontinuous. The flow ratios for runs in which

0 IL 9 Q ~~~~~~~~~~~~~~~~0 08 D p 0~~~~~~~~~~~~~~~~~~~C 0 q 9 0 1) O 9~~~~~~~~~~~~~~~~~~~~~~~~~~~~0, 0 0 j o 0b( Q e 0. C) 9 0 0 0 0" 0 o 0 90 D ^ tl 0 o,~~~~~09 I, 0 C)'I ~oo Q 0Q a 00* o~~~ ~ ~ ~~~~ ~~~~~~~~~~~~~;0 p l0 9 ^1 ~ 0 00g0.) 09 9 Q 0 09 ~ 00G 0 ^ 0 <1 Q o o ^ A yj /*", 1' 09 0 p\ 0 0 oo^ ^ c^^^ ^.^00 S 00 0 0 5^ 0,~~~~~~~~~~~~~ Q 0% 00 <Q^^^ (a) (b) (C) Column Init ially Slug CAp..pears Slug Becomes New Su in "Bubble Flow" Irregular For Figure 6. Appearance of "Slug Flow" Pattern.

-46this was observed were in all cases greater than approximately 75% organic phase. 2. Data Processing In order to save a great deal of work the raw data were processed on an IBM 7090 digital computer at The University of Michigan Computing Center. For the single-phase runs the following items of data were punched on IBM cards. One card was used for each run. (1) a five digit code number (2) the uncorrected flowrate taken from the rotameter, gpm (3) temperature, ~F (4-11) four manometer readings for the pressure differences between successive pressure taps and four code numbers (0 or 1) indicating which manometer (low range or high range) was used; the manometer readings were punched directly as inches of manometer fluid. A card preceding each set of single-phase data gave all information which applied to the entire set, such as physical properties, packing diameter, etc. The digital computer then computed and applied the rotameter correction factor, computed the liquid viscosity, computed actual pressure drops, averaged the latter three pressure drops, corrected this for static pressure drop, and computed the parameters necessary for evaluation of the constants in the Ergun equation~ It then evaluated these constants for each data set by a least squares technique. The computer then printed the results in tabular form as shown in Appendix Co The number

-47of digits reported in the data tables does not indicate the significance of the data. The tables were automatically printed by the computer and the numbers have not been rounded off. For each two-phase run the following items of data were punched on an IBM card: (1) a five digit code number (2-3) the uncorrected flowrates of each phase taken from the rotameters, gpm (4) temperature, ~F (5-12) four manometer readings in inches of manometer fluid and four code numbers (0 or 1) indicating which manometer was used (13) either the height of the liquid interface above the lower plastic flange in inches or the volume of the water phase drained from the column in cc. Two cards preceding each data set contained all information which applied to the entire set. The following information was automatically computed: corrected flow rates; total pressure gradients (The pressure due to the fluid in the manometer lead lines was added to the manometer reading to obtain the difference in total pressures between the two pressure taps. The pressure gradient was then computed.); the average of the three pressure gradients inside the column; and the discontinuous phase holdupo (See Appendix D) The five digit code number mentioned previously, which identifies each run, consists of three partso The first three digits are the number of the run itself. All runs, both single-phase and two-phase, were numbered consecutively. The fourth digit is an alphabetic character

-48indicatin.i the fluid used in addition to water (I = isobutanol, 0 = isooctane, W = water - used only for single-phase water runs). The fifth digit is also an alphabetic character indicating the flow pattern (B bubble flow, H = homogeneous flow, S = slug flow, 0 = single-phase run)o Table III serves as a guide to the extensive data tables found in the appendices. 3o Pressure Gradient 3,l Single-Phase Pressure Gradient Single-phase pressure gradient data were obtained for two reasons: (i) to check the reliability and accuracy of the experimental techniques used; (2) to evaluate kL and k2 in Ergun's equation precisely~ To evaluate k1 and k2 Equation (35) was rearranged to give - AEPfg ~D2 e3 Dk UD U -L U ( = kl + k2 (- (38) If k1 and k2 are indeed constants, a plot of 12lt - APf gD 3 D p U ( )- ) —-- versus will give a straight L IU (1_-)2 (l -e) line with intercept kl and slope k2. The Pf here is the frictional 1 2 L pressure gradient only. The static pressure gradient due to the vertical position of the column must be subtracted from the total pressure gradient before it is used in this equation. To save space define,APf gc D2 e3 F = (L - ) (39) L kU (I-()2 and Rem (40) I,-

-49TABLE III CODING OF DATA RUNS Inclusive Run Numbers Systems Involved 1-20, 45-51 Single-phase runs on 0.501-in. spheres 21-44, 52-87 Water-isobutanol on 0.501-in. spheres 88-113 Single-phase runs on 0.340-in. spheres 114-195 Water-isobutanol on 0.340-in, spheres 196-217, 286-305 Single-phase runs on 0.164-ino spheres 218-285 Water-isobutanol on 0.164-in. spheres 306-350 Water-isooctane on 0.164-ino spheres 351-371 Single-phase runs on 0.340-in, spheres 372-430 Water-isooctane on 0.340-ino spheres 431-470 Water-isooctane-Alkaterge "C" on 0.340-in. spheres The data for all single-phase runs were processed as described earlier and the results are presented in Tables I - X, Appendix Co All the data for a given packing size were used to evaluate kl and k2 by a least squares technique, i.e. the sum of squares of (F-kl-k2'Rem) was minimized by differentiating with respect to kl and k2 and equating the resulting derivatives to Oo These two equations were then solved for kl and k2. Since a significant effect of column length on pressure drop was not noted, the average of the three pressure drops measured inside the test section was used in this correlation. The values of these constants are presented in Table IVo

-50TABLE IV VALUES OF ERGUN EQUATION CONSTANTS Packing kl k2 0,501-in, spheres 315 1,16 0,340-in, spheres 254, 349(a) 1.52, 1.19(a) 0,164-ino spheres 210 1,28 Ergun Values 150 1.75 (a) These values were obtained when the test section was repacked. An examination of Table IV shows a much greater variation in kl than k2, This is understandable since all data were taken for Rem > 20, For Rem - 100 the contributions of the viscous and kinetic terms to the frictional pressure gradient are approximately equal, For Rem A 0.15 viscous effects account for 99.8% of the frictional pressure gradiento As a result most of the data fall in the region where kinetic losses are dominant, so the coefficient of the viscous term is less well known, The values given in Table IV are however those which best fit the data. In this thesis the values of kl and k2 presented in Table IV are used in place of the Ergun values unless otherwise noted, Figure 7 is an example of the type of plot used to evaluate kl and k2o It'snould be noted that the data for both fluids fall on one line. For this reason the variation in the values of kL and k2 presented in Table IV are believed to be due to bed variations only. That is, kl and k2 are not functions of either velocity or fluid propertieso

2400 PACKING DIAMETER = 0.340 INCHES 0 WATER SATURATED WITH ISOBUTANOL 0 ISOBUTANOL SATURATED WITH WATER 2000 0 ~L 1600 I u* L \J1 o~~~~~~~~~~~~~~~~~~~~ o 1t 1200 0~ 00 U. 800 400 k,= intercept 254 0 0 200 400 600 800 1000 1200 1400 Rem= DP Up Figure 7. Fit of Single-Phase Data to Ergun Type Equation.

-52In order to evaluate the accuracy and reliability of the experimental techniques used here, all of the single-phase data were compared with the Ergun equation, Figure 8 illustrates this comparison. A logarithmic plot is used to cover a wider range of variables. The solid line in Figure 8 is Equation (35) with k = 150 and k2 = 175. The single-phase data at large values of Rem are lower than those predicted by the Ergun equation. An examination of the data Ergun used to evaluate kl and k2 (24) however, shows the same effect. It is very possible, therefore, that some phenomenon other than those accounted for in the Ergun equation occurs at high values of Rem, 302 Two-Phase Pressure Gradient Before two-phase pressure-gradient measurements could be recorded, steady state operation had to be achieved. The procedure described in the section on experimental apparatus showed that a varying length of time was required to reach steady state, This time varied from about 10 minutes at high flowrates to as much as 35 minutes for low flowrateso The two-phase pressure-gradient results in Tables I - VI, Appendix D. were all obtained at steady state, With the system water-isobutanol-0,501-ino spheres an attempt was made to determine whether a hysteresis effect existed. Flowrates of the two phases were established and steady state pressure gradient data were recorded, One of the flowrates was then drastically changed and after a length of time returned to its initial setting. In all cases the pressure gradient returned to its steady state value within 30 minuteso

-55100,000...........' l o 0.501 IN. SPHERES l 0.340 IN. SPHERES A 0.164 IN. SPHERES SOLID POINTS ARE ISOBUTANOL OPEN POINTS ARE WATER WATER-ISOCTANE SINGLE PHASE DATA ARE OMITTED FOR CLARITY 10,000 - SOLID LINE IS EQUATION 35 / cm a 0 KINETIC CONTRIBUTION A /A 00..,.,,,...../, I.,-, I I I a I I. a j I00o X o ioo 10 100 1000 10,000 Rem -DDUp en S (I-)E Figure 8. Comparison of Single-Phase Data with Ergun Equation.

-54For most runs four valuse of total pressure gradient were meased the entrance pressure gradient and three pressure gradients inside the test section. These values are presented in Appendix D with. the arithmetic average of the three inside pressure gradientso An examination of Appendix D shows the variation of pressure gradient with column length to be insignificant, as a result the average values were used in all graphs and correlationso Plots of average total pressure gradient as a function of water phase flowrate with parameters of organic phase flowrate are presented in Figures 9-1.4o The total'pressure gradient is composed of a static gradient plus a frictional gradient. However in a system involving two fluid phases there is some question as to the value to be.used for the static gradient (as discussed on pages 100-103)o For this reason the total pressure gradient (a measure value) rather than the pressure gradient due to friction (a derived value) is plotted. in Figures 9-14o Figure 9a shows only average pressure gradiento Figure 9b, on the other han.d includes an. indication of the flow patterns observed, Consider, for instance, the line representing an isobutanol flowrate of 5~78 gpm in Figure 9bo The point at water phase flowrate =0 gpm is, a single-phase point. As the water phase flowrate is increased a point exhibiting slug flow is observed followed by points exhibiting bubble, homogeneous slug, homogeneous, and homogeneous flow, respectively. Despite apparent randomness in. flow pattern. the data follows a smooth curveo To save space in Figures 10-14 the type of information presented in Figures 9a and 9b will be presented in only one grapho Originally it was presumed that pressure gradients for the cocurrent flow of immiscible liquids in packed beds could be correlated, by the Ergun equation [Equation (35) ] if the proper mean values of density and viscosity and the total velocity were used. Figure 9c presents a comparison of the

-551.2 I.0 1.0 - 0.9 0 L0.3 cn, 0.PARAMETER = ISOBUTANOL 0.2 -O. 0 -— STATIC PRESSURE GRADIENT FOR ISOBUTANOL PHASE 0.3 PARAMETER ISOBUTANOL PHASE FLOWRATE,GPM 0.2 0. 0 J I 0 5 10 I5 WATER PHASE FLOWRATE,GP PM Figure 9a. Total Pressure Gradient in the System Isobutanol -Water-O.501 Inch S.heres.

1.6 1.5 0 BUBBLE FLOW 4 - A HOMOGENEOUS FLOW o SLUGGING FLOW V SINGLE PHASE FLOW 1.3 PARAMETER a ISOBUTANOL PHASE FLOWRATE, GPM I.9 /01 I'A U.o' I w 0.5 0.4.-*~STATIC PRESSURE GRADIENT FOR.3- ISOBUTANOL 0 5 10 15 20 WATER PHASE FLOWRATE,GPM Figure 9b. Total Pressure Gradient in the System Isobutanol -Water-O.501 Inch Spheres.

-571.2 Ir / I / II / \ / / / < 0.6 - / / /. / // / //0 / r-// /f / DL0.5L/ / /i Re / 0. / // / 0.7/ // 0.8A / / O0.6 WATER PHAS FOR THIS POINT zM / ~ ( 1080 O.I/ - 0.4 PARAMETER= ISOBUTANOL.3E PA PHASE FLOWRATE,G PM TWO PHASE DATA LINE ERGUN EQUATION, 0.2 -(kl= 150, k2= 1.75) ERGUN TYPE EQUATION, (k,:315, k2= I.1 6) 0.1 0 5 10 15 WATER PHASE FLOWRATE,GPM Figure 9c. Total Pressure Gradient in the System Isobutanol -Water-0.501 Inch Spheres.

-58two-phase pressure-gradient data, the total pressure gradient predicted by the Ergun equation (k1 = 150, k2 = 1o75), and the total pressure gradient predicted by an Ergun type equation with k1 and k2 evaluated experimentally. The following mean values were used in the Ergun and Ergun type equations: Uw4w + Uo~o m Uw + UO where U = individual phase superficial velocity and the subscripts indicate the water phase and the organic phase, and P = Uw + Up (42) m Uw + UO Pm = ^+v The static pressure gradient was computed using p m In Figures 10-14 the comparison between actual two-phase pressure gradient and the Ergun type equation is presented as Figures 10b-14bo The pressure-gradient data presented in this section are all total pressure gradients. The separation of these pressure gradients into static and frictional components is discussed in detail in the next section. Even though the data plots show that two-phase mixture does not behave as a single-phase fluid (ioeo, a single-phase equation cannot be used), they do point up some interesting resultso The data approach the "singlephase" curves at both extremes of flow ratio. This means at extremes of flow ratio the two-phase mixture behaves as a single-phase fluid with respect to pressure gradient. However at intermediate flow ratios the actual pressure gradient, is considerably greater than that predicted by the "single-ph ase" assumption. An examination of the data plots shows that this difference increases with the interfacial tension of the system

-59o BUBBLE FLOW A HOMOGENEOUS FLOW 2.0 - D SLUGGING FLOW / SINGLE PHASE FLOW PARAMETER ISOBUTANOL PHASE FLOWRATE, GPM 1.8 0.4', - ir / 1.2 VGRADIENT FOR 05 10 15 w a.. -I 0.8 I1 0 0.-Water-0.340 Inch Spheres. 0.2 STATIC PRESSURE 0.2 GRADIENT FOR ISOBUTANOL PHASE 0 5 10 15 WATER PHASE' FLOWRATE, GPM Figure 10a. Total Pressure Gradient in the System Isobutanol -Water-0.340 Inch Spheres.

-601.8 t,/ C/ // 1.6 / L 1.2 _' O A/' 0.8 C,) FOR THIS POINT 0r a'.... = 583 0.6 1,/ 0.4 PARAMETER - ISOBUTANOL PHASE FLOWRATE,GPM TWO PHASE DATA LINE 0.2 ---- ERGUN TYPE EQUATION (k,= 254, k2= 1.52) 0 I I 0 5 10 WATER PHASE FLOWRATE, GPM Figure lOb. Total Pressure Gradient in the System Isobutanol-Water -0.340 Inch Spheres.

-613.0 5.0 Ea. 2.0 4 w w I- 1.0! 0 CIPARAMETER ISOBUTANOL PHASE FLOWRATE, GPMGPM 0 1 1 1 --- 0 0 2 3 4 5 WATER PHASE FLOWRATE, GPM Figure lla. Total Pressure Gradient in the System Isobutanol -Water-O.164 Inch Spheres.

-62I I i PARAMETER = ISOBUTANOL PHASE FLOWRATE, GPM TWO PHASE DATA LINE ---- ERGUN TYPE EQUATION 3.0 (k,= 210, k2 1.28) CL 0 2.0 CO) a-.I6t Inch Spheres. WATE^.^.'FOR THIS POINT Figure llb. Total Pressure Gradient in the System Isobutanol -Water -0.164 Inch Spheres.

-632.5^2.0 A4.80 0 0 I W PHASE SLORAE GPM 0| / O O ~ P 1.0! PARAMETER= ISO OCTANE PHASE _.. WT PH FLOWRATE, GPM Cr: I 0 I2456 WATER PHASE FLOWRATE, GPM 0.5 e ~ ~ ~ ~ ~~~~~~FORTPV ~~J STTICPRESUR

-640 0 1.5 / / a 11./ // I-Cl~~.-ob, / / /0 5O /1 /w~ ~/ 100, s 1.0 / o 0 / 0.5 X, / 0.5 PARAMETER = ISOOCTANE PHASE FLOWRATE, GPM TWO PHASE DATA LINE -— ERGUN TYPE EQUATION ( k,- 210,k^ 1.28 ) 0 - 0 2 3 4 5 6 WATER PHASE FLOWRATE, GPM Figure 12b. Total Pressure Gradient in the System Isooctane-Water -0.164 Inch Spheres.

-65I PARAMETER =I I ISOOCTANE PHASE ULi~. ~FLOWRATE GPM 2.02 4 6 8 12 az 0 1.0 I II I. I I WATER PHASE FLOWRATE, GPM Figure 13a. Total Pressure Gradient in the System Isooctane -Water-0.340 Inch Spheres. cn ~ IOCAE PRMTE SOTN HS W ~ ~ PHS QL ~ ~ ~ ~ ~ ~ ~ ~ ~ LORTP 0 - r ~ ~ ~ 68 01

-66PARAMETER - ISOOCTANE PHASE FLOWRATE, GPM TWO PHASE DATA LINE --- ERGUN TYPE EQUATION ( k,= 349, k2 1.19) 1.5 a1.0 / w 1.0.5 (r) 0. FOR THIS POINT 0 2 4 6 8 10 12 WAT ER PHASE FLOWRATE, GPM Figure 13b. Total Pressure Gradient in the System Isooctane -Water O.340 Inch Spheres. -0.340 Inch Spheres.

-672.0 I 10.8 1.5 ILI - \,,J \i a 1' \ ^ on r Ur.I 0 /, 0 BUBBLE FLOW cr' 1f/ V SINGLE PHASE FLOW 0 \$~~~ ~~PARAMETER = ISOOCTANE PHASE FLOWRATE, GPM STATIC PRESSURE GRADIENT FOR ISOOCTANE PHASE 0 I 2 3 4 5 6 WATER PHASE FLOWRATE, GPM Figure 14a. Total Pressure Gradient in the System Isooctane-Alkaterge "C" -Water-0.340 Inch Spheres.

-681.5 PARAMETER- ISOOCTANE PHASE FLOWRATE, GPM TWO-PHASE DATA LINE ---- - ERGUN TYPE EQUATION (k, 349, kC1.19) LL bJ /.a. Cl) 0&~~~~ ^ y —-— ^FOR THIS POINT =678 I- -— IE 0 I 2 3 4 5 6 WATER PHASE FLOWRATE, GPM Figure l4b. Total Pressure Gradient in the System Isooctane-Alkaterge "C" -Water-0.340 Inch Spheres.

-69and decreases as the packing size increases. This phenomenon may be similar to the Jamin effect observed in two-phase flow in porous media(48 66) The Jamin effect concerns the situation where droplets of the dispersed phase which are too large to pass through the openings in the packing must be stretched or broken in order to allow flow to continue. This conversion of energy is observed as increased pressure drop. The maximum difference between.the actual and predicted pressure drops occurs at mixture compositions of 70 - 80 volume per cent of non-wetting phaseo This observation together with the visual observation of flow patterns and settling patterns indicates that a phase reversal may take place at mixture compositions of 70 - 80 volume per cent of the non-wetting phase, i.e. the non-wetting phase may become continuous at this concentration. This point will be discussed further in the section on data correlation. A comparison of Figures 13 and 14 points out an interesting result Since the interfacial tension for the system with the surfactant (Alkaterge "C") present is lower than that without it, one might expect the pressure drop to be considerably reduced by addition of the surfactant. In reality, however, this does not happen. A possible reason for this is as follows: During a static interfacial tension measurement (such as with the use of a ring tensiometer) the surfactant concentrates at the interface causing a reduction in measured interfacial tension, In a highly dispersed state, however, this high concentration at the interface cannot occur, because of the large ratio of surface area to volume. As

-70a result the effective interfacial tension during flow is not the same as the statically measured interfacial tensiono This means that any flow data taken with a surfactant present is of questionable significance o As was mentioned before, the entrance pressure drop was measured in addition to the pressure drop inside the test sectionO An examination of Appendix D shows that in all cases including single-phase flow the entrance pressure drop is less than the average test section drop. Ordinarily the reverse would be expected. This effect is probably associated with the inlet configuration and merits separate study. Because of this observation only internal pressure drops were used in correlation work. 4. Phase Holdup The term "phase holdup" ordinarily means the fraction of the void volume of the test section which is occupied by the discontinuous phaseO The difficulty encountered in defining which phase was discontinuous required that here "phase holdup" be used to indicate the fraction of the void volume of the test section which was occupied by the nonwetting phase (in all cases the organic phase). The length of time required to establish or re-establish, operating holdup is an important consideration in any commercial application of cocurrent liquid-liquid extraction. A series of runs was performed to establish this time dependence. These results are presented in Table Vo Figure 15 shows the results of Part A graphicallyo Since the data appeared to follow an exponential decay curve, the following treatment

-71TABLE V TIME DEPENDENCE OF PHASE HOLDUP A. Isobutanol-Water-O,501 Inch Spheres (Runs 79 - 87) Water Flowrate = 4.67 gpm, Isobutanol Flowrate = 4.34 gpm Time (min.) Isobutanol Phase Holdup 0,0 0,0 0.25 0.16 0.50 0.38 1.0o0 o 43 2.00 Oo43 4.00 0.46 Oo0 1o00 0.25 0,73 0.50 0.57 1.00 o047 2.00 0,45 Bo Isobutanol-Water-0,340 Inch Spheres (Runs 173 - 195) Water Flowrate = 4.67 gpm, Isobutanol Flowrate 4.34 gpm Time (min.o) Isobutanol Phase Holdup 0.0 0,0 0.25 0o26 0.50 o040 1,00 0,44 2,00 Oo43 4.00 046 0O0 1,00 0,25 0o82 0,33 0,64 0.50 o048 lo00 0o47 2,00 0o47

-72TABLE V (CONT D) Water Flowrate = 1.54 gpm, Isobutanol Flowrate =1.45 gpm Time (min.) Isobutanol Phase Holdup 0.0 0.0 0.50 0.21 0.75 0.31 1.00 0.37 2.00 0.37 4.00 0.38 10.00 0.42 0.0 1.00 0.75 0.81 1.00 o.62 1.50 0 44 2.00 0.43 4.00 0.43 C. Isobutanol-Water-0.164 Inch Spheres (Runs 251 - 255) Water Flowrate = 1.54 gpm\, Isobutanol Flowrate = 1.45 gpm Time (min.) Isobutanol Phase Holdup 0.0 1o00 0.75 0.91 1.00 0.62 1.50 0.38 2.00 0.38 4.00 0.38

-731.0. ISOBUTANOL- WATER - 0.501 INCH SPHERES 0L. WATER FLOWRATE 4.67 GPM o 0.8\ ISOBUTANOL FLOWRATE a 4.34 GPM -I 0 rI ---- EXPONENTIAL DECAY CURVES UjI \ --- SLUG DISPLACEMENT CURVES Cn I 0.6 -,_.- _.___._. 0.4 C, -! 0.2 0 I 2 3 4 5 TIME, MIN. Figure 15. Time Dependence of Phase Holdup.

-74was used. The dotted lines in Figure 15 are exponential decay curves defined by t ARI = RIf e e (43) where RI = isobutanol phase holdup RIf = value of RI as t — oo ARI = |RI - RIfI t = time, mino K = time-constant, mino For the curves in Figure 15, K was chosen as the minimum time required to refill the column to a holdup of RIf, or total void volume of test section x RIf K =(44 flowrate of missing phase For the upper curve in Figure 15 where isobutanol is being replaced with water K = 0.22 mino For the lower curve K = 00195 mino Figure 15 indicates that the time dependence of holdup can be loosely approximated by an exponential decay curveo It seems likely that some other value of K would give a better fit of the experimental data. It would, however, have little physical significanceo If the second phase were assumed to displace the first phase as a slug, a linear change in holdup with time would occur. Curves of this type (called slug displacement curves) are included in Figure 15 for comparison purposeso It should be noted that this is not nearly as good an approximation of the data as the exponential decay curves.

-75The steady state values of phase holdup (in all cases organic phase holdup) are presented in Tables I - VI, Appendix D, along with the pressure-drop data. Zero values of holdup in the tables indicate that holdup was not measured for those runs. The holdup data are presented graphically in Figures 16 - 20. Reproducibility is again indicated by the presence of duplicated points on the graphs. 5. Drop Sizes In any application of the results of this thesis to cocurrent liquid-liquid extraction, quantitative information about the amount of interfacial area produced would be desirable. The interfacial area produced in a given system determines, to a great extent, the rate of mass transfer from one phase to the other. To a lesser extent it is also important to know how this area is distributed between small drops and large drops in the liquid mixture. A number of methods have been used to present information of this type, e.og an equivalent drop diameter, surface area per unit volume of discontinuous phase, surface area per unit volume of mixture, etc. Since in the present case phase holdup is a known quantity and since interfacial area was determined by measuring drop diameters, data on interfacial area is presented as an equivalent drop diametero A number of equivalent drop sizes have also been proposed, e.go the arithmetic average diameter, the median diameter (that diameter such that half of the total population of drops are larger than it), the Saut'er mean diameter, etc. By far the most important in mass transfer

-760.9 0.8 - 0.7 0.6 a 0.5 _ 0 I 0.4 0 I0 WATER FLOWRATE = 0.655 GPM 0.2 6 of' =3. 19 V " o " 4.69 ~ " " =6.19 ~ II " = IO. 85 0.I 0 2 4 6 8 10 12 14 ISOBUTANOL PHASE FLOWRATE, GPM Figure 16. Isobutanol Phase Holdup in the System Isobutanol -Water-0.501 Inch Spheres.

-770.9, I9II - 0 0.8 0.7 0.6 D 0.5 _J I 0 2 4 6 8 rmC ~I0 WATER FLOWRATE0.655 GPM 0 Figure 17 3 P H i. 54Isobutao -Water-.340 Inch Spheres. 0.2 a of to a L\ " II ~ 3. 19 V " "i so. 69 is u-=6.19 0 1 Is a S.. 70,,,, =12.9 0 2 4 6 8 I0 12 14 ISOBUTANOL PHASE FLOWRATEGPM Inch Slpheres.

-780.9 0.8 0.7 0.5 w (L) I 0.4 0 C) 0.3 SOBUTANOL PHASE TER FLOWRATE. 655 GPM Figure 18. Isobutanol Phase Holdup in the System Isobutanol -Water-0.164 Inch Sph ~ " ( " 2.37 " Z~ "I': =3.19 0.I V " ",, 4.69 0 I 2 3 4 5 6 7 I SOBUTANOKI PHASE FLOWRATE, GPM Figure 18. Isobutanol Phase Holdup in the System Isobutanol -Water-O.164 Inch Spheres.

-79o0.9 0.8 0.7 0.5 I Io: o / 2/ 3 4 I~_) 0.2/ 0 WATER FLOWRATE - 0.65 GPM E] " > " a 1.53 \,,,. u = * 3. 17 0.1I V,' = 6.15 " 0 I 2 3 4 5 6 7 ISOOCTANE PHASE FLOWRATE,GPM Figure 19. Isooctane Phase Holdup in the System Isooctane -Water-0.340 Inch Spheres.

-80Q9 0.8 - /Q D ^o 0.7 0.6 0. / / O / 2 36 0 0.5 L0 w 0.4 F0 C/) 0.3 - 0 WATER FLOWRATE z 0.651 GPM 0.2 - E of. 1.5 - A " =35.17 V " -s6.15 0.1 0 2 4 56 7 ISOOCTANE PHASE FLOWRATE,GPM Figure 20. Isobctane Phase Holdup in the System Is66ctane-Alkaterge "C" -Water-0.340 Inch Spheres.

-81is the Sauter mean diameter, since it is the diameter of a drop which has the same ratio of surface area to volume as the total population of measured drops. Let d32 be the Sauter mean diameter. Then the ratio of volume to surface area for a drop of this diameter is given by d3 ~b - d2 d32 R32 2 (45) 32 For the total population of measured drops this ratio is given by N N RT = N l (46) where N togethe total number of drops. Equating these two ratios gives N 3 Zd5 d52 N (47) Zd2 i=l Equation (47) defines the Sauter mean diameter as it is used here. This diameter together with the value for phase holdup enables the computation of interfacial area. Typical examples of the photographs taken in this research are shown in Figures 21 - 24. The drop diameters measured from each such photograph were divided into twenty size classes, the sizes of which depended on the over-all size range found in the photograph. The number of drops in each size class was then punched on an IBM card along with the photo number and the two rotameter readings. One card was used for each photograph. A group of cards giving the fluid properties, sizes associated

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-84with each size class, etc. was placed before each set of photo cardso Fluid linear velocities and Sauter mean diameters were then computed on the IBM 7090 for each photographo The results are presented in Tables I - VI, Appendix Eo The raw drop count data were omitted since they were quite lengthy and were not considered to be of particular value in raw formo Due to a clouding of the inside wall of the test section after a period of time, the photographing and counting of drops became rather difficult for the last two systems studiedo For this reason only two photographs from each system are included in the data tableso Up to this point the drop size data have been treated as if they were truly representative of the drop sizes in the interior of the packed bedo This is open to question since the photographs were all taken just inside the wall of the test sectiono Although there is no means of verification, it is believed that any wall effect on d32 is quite smallo The effects of packing diameter, velocity, and fluid properties on drop size would be expected to show the same trends at the center of the bed as at the wallo The absolute drop size may, however, change slightly with distance from the column wall, due to the velocity profile and the change in porosityo The reproducibility of the drop size data can best be illustrated by examining the results for photographs 7, 8, 9, 10, 17, 18, and 81 given in Table I, Appendix E and reproduced below in Table VI for convenienceo These data, taken over a two-week period show a maximum deviation of 5o7% from their meano

-85TABLE VI REPRODUCIBILITY OF DROP SIZE MEASUREMENTS Data Taken for System Isobutanol-Water-OO501 Inch Spheres Water Flowrate = 1.54 gpm, Isobutanol Flowrate - 1o45 gpm Photograph Number Sauter Mean Diameter (Microns) 7 875 8 921 9 868 10 931 17 884 18 932 81 963 In addition to mean drop sizes, drop size distributions were computed for each pair of identical photographs. For each such pair the cumulative number of drops below a certain drop diameter was computed. Percentages were then computed from these numbers. In all cases the drops were found to be approximately normally distributed. Several samples of drop distributions are plotted in Figures 25 - 28. In these figures the ordinate is a normal probability scale. As a result data which is normally distributed will appear as a straight line. Figure 28 shows the largest deviation from a normal distribution. The downward. concavity of the curve suggests that these data may better fit a log-normal distribution. (In a log-normal distribution the

-86logarithms of the drop diameter would be normally distributed ) However, when these data were plotted on log-normal probability paper they produced a curve which was concave upward. Therefore the true distribution is somewhere between the normal and log-normal distributions. It can however by approximated by a normal distributiono

-8799.99 I I I 99.9 TOTAL NO. DROPS * 648,,, 99- ISOBUTANOL-WATER-0.501 INCH SPHERES I- w z > 90 / 0 80 o 0 60 I 20 / Ll 10 I00 0.1 o.o 0 200 400 600 800 1000 1200 1400 1600 DROP DIAMETER, MICRONS Figure 25. Drop Size Distribution Photographs 7, 8, 9, 10, 17, 18.

-8899.9 - 9 9.9 99 z 90 > / Q: 90 80 / ) / 0 o: 40LL z 20- o L / 0 / cr Qaw 0 > / F- / -J /TOTAL NO. DROPS =447 2.0 in_ ISOBUTANOL - WATER -0. 340 INCH 1.0 -/ SPHERES 0 O.1 0.010 200 400 600 800 000 1200 1400 1600 1800 DROP DIAMETER,MICRONS Figure 26. Drop Size Distribution Photographs 99, 101.

-8999.99. I 99.9 99. - (i / J80 I0w 900 / / 0 60 m / 20 / TOTAL NO. DROPS =292 Wo 10-o _ ISOBUTANOL- WATER-0.164 INCH Q | / SPHERES LJd 0a L / _ /0 J 1.0 0 / o E / 0 0.1 o. 0.01 0 100 200 300 400 DROP DIAMETER, MICRONS Figure 27. Drop Size Distribution Photographs 151, 152.

-9099.99 - 99.9 TOTAL NO. DROPS 685 ISOOCTANE-WATER - 0.164 INCH SPHERES n: 99. w - 0 0 > 90. Z 00 0 80. L, 10. L-J 1.040110 0.I 0 400 800 1200 1600 DROP DIAMETER, MICRONS Figure 28. Drop Size Distribution Photographs 157, 158, 183, 184.

VI. CORRELATION OF DATA The data presented in the previous section are of little value as they stand except for qualitative purposes. Numerical predictions for systems other than those used here would not be possible. Therefore an attempt was made to develop a generalized method for correlating the data of the previous section. Due to the complexity of the system involved, an analytical approach held little hope for success, Therefore a somewhat empirical approach had to be used. The results of that attempt are presented here. In deriving these correlations, correlations of similar systems were utilized insofar as possible. In the case of pressure drops singlephase relationships were used as a starting point. Since it appeared that phase holdup has a strong effect on pressure drop, an attempt was first made to correlate the holdup datao 1. Phase Holdup Correlation One might assume that the organic phase holdup, RI, could be predicted by an equation of the form RI = U (48) Uw + Uo where Uo = organic phase superficial velocity Uw = water phase superficial velocity However due to the density difference between the two liquids, the less dense liquid rises with respect to the more dense liquid. This relative -91

-92velocity, ordinarily called the "slip velocity" can be computed by the following equation for cocurrent liquid flow in packed beds: UO Uw V E RI (1 - RI) where Uw and Uo are both measured in the same direction. For countercurrent flow the same equation applies, but one of the velocities is now negative. In countercurrent flow the slip velocity has been used quite successfully to correlate holdup data. That is, slip velocities were predicted and then Equation (49) was used to predict RIo In cocurrent flow, however, Uo and Uw are much larger than in countercurrent flowo As a result the slip velocity computed by Equation (49) is the difference between two large numbers and is therefore subject to a great deal of error. In the present study the slip velocities calculated from Equation (49) were, in many cases, of the same order of magnitude as the uncertainties in the data. As a result slip velocities are of little value in correlating holdup data in cocurrent liquid-liquid systems. The assumption of zero slip velocity was tested and found to be approximately true For the present data. The relative errors, however, were significant enough, particularly at low values of RI, to encourage a search for a more adequate correlation technique. Wicks and Beckman(78) and Markas and Beckman(52) successfully correlated holdup data in countercurrent liquid-liquid systems by equations of the form RI = AlD) + Bl(UD)(UC) (50)

-93where UD and UC are the dispersed and continuous phase superficial velocities and Al, Bl, r, and s are constants dependent on the system being studied. This form is obviously unsatisfactory for cocurrent flow because RI is unbounded for large values of either UD or UCO In reality RI has a maximum value of lo The following modified form of the velocity-power relationship was tested with the data from this investigations ~ a RI' ( UO ) (51) UO + Uw It should be noted that this equation satisfies the limiting conditions of RI 0 when Uo = 0 and RI =1 when U= 0 o (52) In addition it is quite simple in that only one empirical constant need be evaluated. The constant a was evaluated for each data set presented here by first rearranging Equation (51) to the following form: in RI = a ln(u + ) (53) 0 + Uw A least squares technique was then used to evaluate the constant ao Uo Figures 29 - 33 present plots of RI versus Uo + U on a log-log scale. The solid lines represent Equation (53) with a evaluated by the least squares technique. The dotted lines represent Equation (53) for a = 1; this is equivalent to an assumption of zero slip velocity.

-941.0 - -— NO SLIP VELOCITY LINE 0.5 0 I 0.2 / / a7 0 / / o / 0.1 0.08 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 FLOW RATIO= oU Uo*+ Uw Figure 29. Phase Holdup in the System Isobutanol -Water-0.501 Inch Spheres.

-951.0:, /0 0 -0.2 o /0/ z /0 E~~Li~~~~~~ I NE o / /e 0.1 0.2 0.5 1.0 o/o FLOW RATIO, U Figure 30. Phase Holdup in the System Isobutanol -Water-0.340 Inch Spheres.

-96I. /6 m // / / / 0 // / X 0.2 / |/ / -— IP VELOCITY LINE 0.02 - LLI _O. 0.05 - O NO SLIP VELOCITY LINE 0.02 - 0.1 0.2 0.5 1.0 Uo FLOW RATIO, Uo+ Uw Figure 31. Phase Holdup in the System Isobutanol -Water-0.164 Inch Spheres.

-*sar.qdS qouI O1e#'O-ja4^ -aueoos9 I maqss ayq UT dnpTOH ass-q'zE Aannie mn + O0'O IlVl M OM 0 z ~~~~~~~on ~ ~'1//'0'O 0 G0'0 G) 3NI'I A110I13A dllS ON 0 00 /-1 r -0/~~ o 0/-0 0/ -o 0/0 0/ / /

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-99The difference between the solid and dotted lines indicates the error involved in assuming no slip velocity. Table VII is a summary of the results of the least squares evaluation of a. Also included are correlation coefficients computed on the basis of Equation (53). These indicate a very good fit of the experimental data by Equation (51). The constant a is probably a function of packing shape, packing size, and physical properties but no correlation of a could be evaluated from the data presented here. Qualitatively, however, it appears that a is inversely proportional to the packing size and is an increasing function of density difference. An interesting future set of experiments would involve the evaluation of a for a large variety of packings and liquid systems. TABLE VII RESULTS OF PHASE HOLDUP CORRELATION Correlation System a Coefficient Isobutanol-Water-O.501 Inch Spheres 1.083 0.988 Isobutanol-Water-03540 Inch Spheres 1.102 o 994 Isobutanol-Water-O.164 Inch Spheres 1.269 0.977 Isooctane-WaterO-.340 Inch Spheres 1.204 0.988 Isooctane-Alkaterge "C" -Water0.340 Inch Spheres 1.256 0.995

1002. Pressure Gradient Correlation 2.1 Separation of Static and Frictional Pressure Gradients The two-phase pressure gradients reported in Appendix D are total pressure gradients in a vertical test section. To separate the effects of static head and frictional pressure losses Bernoulli's equation was applied to each phase individually. The approach presented here is substantially that of Hughmark and Pressburg.(38) Consider velocities and length, Z, taken in the upward direction in the test section. Bernoulli's equation applied across an element of length, AZ, then takes the form P2 Au2 f vdP + 2- + AZ + f + ws = (54) 2gc Pi where Pi, P2 = upstream and downstream pressures, respectively v = specific volume of fluid = 1/p Au = u2-ul = velocity difference AZ = Z2-Z1 = vertical length of element of test section wf = frictional energy loss per pound of fluid Ws = shaft work loss per pound of fluid Shaft work here includes that work performed by one liquid on the other liquid. Now let the subscript w represent the water phase and let the subscript o represent the organic phase. If each phase is considered to form a continuum, Equation (54) may be applied to each phase individually. Then the equations P2 2 Ww f VwdP + Ww P w + WAZ + WWwwf + Wwwsw = O (55) P1 ^O

-1.01and P2 2 Wo f vodP + Wo - +a + WoZ + W owo + Woso = (56) P1 2go apply across the element of length, AZ, where Ww, Wo = mass flow rates of water phase and organic phase, respectively. Since liquids are, for practical purposes, incompressible P2 p vdP = vAP (57) PI P In addition, if phase holdup is considered to be constant throughout the length of the test section AuW = auo = o (58) Equations (55) and (56), therefore, reduce to WW + WA a + Wwwfw + Wwwsw = 0 (59) PW and Wo -P + WoZ + Wowfo + Wowso = 0 (60) PO If Equations (59) and (60) are added and simplified the resulting equation is [W + w]AP + [Ww + Wo]AZ + [WWwfw + Wowfo] Pw Po + [Wwwsw + WoWso] = 0 (61) Since no shaft work is performed on the surroundings by the fluids in the test section Wwwsw + WoWso = 0 (62)

-102and, therefore ww W [ + -]AP + [Ww + Wo]AZ + [WWwfw + WWfo] = 0 (63) Pw Po Since AP = P2 - P1, and AZ = Z2 - Zl, Equation (63) can be rearranged to give P2 P [Ww + W] + [WWWfw + WoWfo] = 0 (64) Z2 - Zi [ w Wo] z[WW + W_] Pw Po Pw Po The first term in Equation (64) is the negative of the measured pressure gradient which is presented in Appendix D. The second term is considered to be the static contribution to the total pressure gradient while the third term represents frictional pressure losses. Equation (64) can be simplified to P - P2 = Pm + bf (65) Z2 - Z1 where [Ww + Wo] = PwUw + PU, = "mean" density m [Ww + W] Uw + U Pw Po Uw,Uo = superficial liquid velocities f [Wwwfw + WoWfo!. zf [z + o] Pw Po Equation (65) is the form commonly used to correlate two-phase pressure-drop data. Ordinarily, however, the mean density, Pm, is arbitrarily defined as Pm = w(l-RI) + PORI (66)

-103where RI is the phase holdup. The pm defined immediately below Equation (65) appears to have more theoretical justification than that defined by Equation (66) Values for Pm and 6f were computed for each run and are presented in Table I, Appendix G. In all cases the average of the three interior pressure gradients was used in the computation. 2,2 Correlation of Frictional Pressure Gradient In attempting to correlate frictional pressure-gradient data a method analogous to that used in porous media flow was usedo In twophase flow in porous media a "relative permeability" is computed for each phase by means of Equations (17) - (19), Section II-4. This in reality is inversely proportional to the ratio of actual frictional pressure gradient to the frictional gradient if that phase were flowing alone in the medium. This relative permeability is then correlated as a function of water "saturation" or water holdup. The presence of the kinetic energy term in the equation for packed bed flow complicates the situation somewhat. However, if a predicted frictional gradient based on the assumption that the two-phase mixture can be treated as a single phase is computed, the actual frictional pressure gradient can be related to this predicted one, The variation between these two pressure gradients can then be attributed entirely to interaction between the two phaseso For the present data the Ergun type equation was used with volumetric average properties to predict the "single-phase" frictional

-104pressure gradient: (1-~) 2 LmUm (2-) 9mU2 pgc = k (-) Um + k2 (l-e) PmUm (67) 6fp c 1k 2 2 (67) p p where fp = predicted frictional pressure gradient subscript m = mean value of variable The "mean" values used were UoJo + Uwiw Am = Uo + Uw (68) - Uo + Uw (69) m =Uo + Uw Um = Uo + Uw (70) The ratio of the actual frictional pressure gradient to the predicted frictional pressure gradient was then computed: 5f PRATIO = (71) fp Values of 5f 6bfp and PRATIO are presented for comparison in Appendix Go The values of PRATIO varied from approximately unity to as great as 10. A value of unity indicates the "single-phase" assumption to be correct while a value of 10 indicates a high degree of interaction between the phases. An attempt was next made to correlate PRATIO with the physical properties and flow properties of the system, In the past other authors have suggested a variety of mechanisms for phase interaction in two phase flow. Larkins(44) suggested that in gasliquid flow the increased pressure gradient is due to the compressibility

-105of the gaseous phase, i.e. irreversible compression work is performed on the gaseous phase. Cengel,(14) on the other hand, suggested that in the flow of liquid dispersions the increase in pressure gradier-t could be attributed to an increase in effective viscosity. Neither of these mechanisms provide an adequate explanation for the results observed here. Surface energy effects are probably the largest contributor to pressure loss due to phase interaction. First the energy required to form a dispersion in flow through a packed bed appears as a pressure loss. When coalescence occurs the energy stored as surface energy is not recovered as pressure but is primarily converted to thermal energy. Therefore each time two droplets coalesce and are redispersed, an irreversible energy conversion occurs, resulting in a pressure loss. An additional contributor to pressure losses due to surface energy effects is believed to be the Jamin effect, previously observed in flow in porous media,(48) If a droplet of dispersed phase is too large to pass through a given opening in the bed, it must either be broken or mishaped to allow passage. Either of these processes involves the creation of additional surface area and thus the conversion of energy. Appendix F is a sample calculation which indicates that surface energy effects are indeed important in liquid-liquid flow in packed beds. For the case considered, if the dispersion is assumed to be formed only once per foot of packing and that no coalescence, redispersion, or "stretching" (due to Jamin effect) occurs in that foot of packing, energy dissipation due to surface effects is approximately 12% of that due to viscous and kinetic

-106energy effects. The assumptions made here are extremely conservative, so that in reality surface energy effects would be much greater than 12% of the viscous and kinetic effects. Since no information on coalescence and redispersion rates is available, an empirical approach to the problem of correlation was used. The most important factors affecting surface energy effects are the interfacial tension, a, the phase holdup RI, and the droplet diameter, d32The droplet diameter is, in turn, a strong function of packing diameter, Dp, interfacial tension, a, and mean velocity, Umo The effect of interfacial tension on drop size, drop breakup, etc. is most commonly presented in terms of the dimensionless Weber number defined as We (72) g9c where u = velocity p = density d = droplet diameter a = interfacial tension gc = gravity conversion constant The Weber number is characteristic of the ratio of inertial forces to surface tension forces. A qualitative examination of the data in Appendix G shows that PRATIO indeed increases with a and decreases with total velocity and packing diameter. The following form of the Weber number was therefore selected for use here~ We - UP (73)

-107The substitution of packing diameter., Dp. for droplet diameter is fully justified since d is shown later in this section to be directly proportional to Dpo A simple power dependence of PRATICO on We was assumedo Since PRATIO should approach a minimum value of unity the following quantitative dependence was usedo PRATIO - 1 O(We)a (74) The use of the Weber number takes into account all of the important variables except phase holdup, RTo The dependence of PRATIO on RI is best illustrated by the data for the isobutanol-water-0o164 inch spheres system shown in Figure 34. For those runs for which RI was not measured, RI was computed from the correlation presented previouslyo The data in Figure 34 scatter a great deal due to the fact that each point represents a different total velocityo It can easily be seen, however, that PRATIO goes through a maximum in the vicinity of RI = 0o75. A possible explanation for this is that a phase reversal may take place at this point, i.e. the discontinuous organic phase becomes the continuous phase when it occupies more than 75% of the void volume of the test section. The most compact arrangement for packing spherical particles (hexagonal close packing) exhibits a void fraction of 25o95%o(67) This corresponds surprisingly well with the maximum in the PRATIO versus RI curveo It is therefore possible that as RI increases, the spherical droplets of organic phase become closer and closer together until at RI "0o75 no closer packing can exist. As RI is increased beyond this point the organic phase becomes continuouso This reduces the interfacial

ISOBUTANOL FLOW RATES I.5- A ^ 0 0.723 GPM I V 0 1.45 " I A 2.17 AA V 2.89 " ~ 1.4 * 4.34 " / * 5.05 " J A 5.79 " \ V 6.50 ".3 7. 39 " v I U~ I InchAA A 0 0 v V 8 0 AA IR.I 8 0 0El A 0 CLOSEST POSSIBLE PACKING OF UNIFORM A v SPHERICAL PARTICLES RI Figure Figure 34. Dependence of PRATIO on Phase Holdup in the System Isobutanol-Water-O.164 Inch Spheres.

-109area of the dispersion which in turn reduces the pressure losses due to surface effects. As RI approaches 1, the pressure drop approaches that for the pure organic phaseo Due to the shape of the PRATIO versus RI curve the following form for quantitatively predicting the dependence of PRATIO on RE was assumed: PRATIO 1 a( e- -cl (75) This is the form of the Gaussian distribution. curve which approximates the PRATIO versus RI curve. It does not satisfy the end. conditions of PRATIO 1 for RI = 0 and (76) PRATIO = 1 for RI = 1 for all values of co It d.oes, however, closely approximate these condi= tions. Combining Equations (74) and (75) gives the following expression for correlation purposes RATIO 1 + K(We)a eC(R- 1c (77) In order to evaluate the empirical constants K, a, c, and c1l Equation (77) was rearranged to the linear form ln(PRATIO 1) lnK + aln(We) c(RI~cl)2 or ln(PRATIO 1) = (lnK=ccl) + aln(We) cR2 + 2cclRI (78)

-110A least squares regression analysis was used on the IBM 7090 digital computer to evaluate the constants in Equation (78). A lack of sufficient data for RI > 0.75, however, prevented an ad.quate determination of c1o Therefore cl was, on the basis of the preceding arguments, arbitrarily chosen as 0.75. The regression analysis was then applied to ln(PRATIO - 1) = lnK + aln(We) - c(RI-0.75)2 (79) Since logarithms do not exist for negative numbers, values of PRATIO < 1 were omitted from the analysis. This results in a small unavoidable bias in the values of the constants. Values of RI were computed for those runs in which RI was not measured. The results of the correlation are presented in Table VIIIo TABLE VIII RESULTS OF PRATIO CORRELATION Constant Value Variance In K -03,2413 0o00555 K 0.723 a -0.624 0o000761 c 5.59 0o145 Correlation Coefficient Based on Equation (79) = 0.846 The variance is the squaref the standard deviaton of the stanumber and is thus an indication of how well the number is known,

-111The final form of the pressure drop correlation is thus RATIO = 1 + 0o723(We)0~624 e-=559(RI-075)2 (80) The use of four empirical constants was required by the shape of the PRATIO versus RI curveo No physical significance should be attributed to the values presented hereo Values of We, RI and PRATI predicted by Equation (80) are included in the table of processed data in Appendix Go Figure 35a represents a comparison of the measured values of PRATIO with those predicted by Equation (80), For those points with predicted PRATIo less than lo1, only every tenth point is plottedo At first appearance Figure 35a exhibits quite a bit of scattero It should be noted, however, that most of the points exhibiting wide scatter were obtained with the system isooctane-Alkaterge T"C'waterOo34-0 inch sphereso As was pointed out previously there is some question as to the significance of these datao The concentration of the surfactant at the interface during a static interfacial tension measurement causes a reduction in the measured interfacial tensiono On the other hand. there is no proof that this is the effective interfacial tension during dynamic flow conditions. Due to the very large ratio of surface area to volume in a dispersion, the concentration of surfactant at the interface is considerably less than that in a static interfacial tension measurement. The data of Figure 35a are replotted in Figure 35b with isooctaneAlkaterge "C"-water data omitted. This figure indicates a much better fit for Equation (80) than Figure 35ao If the addition of a surfactant has little or no effect on the dynamic interfacial tension, the values predicted by Equation (80) would not be correct for the isooctane-Alkaterge

-1129 / /O - U /-/ 0N/ 4- - o~~/ / / 4 \ / / 0/ ~a- ~ ~ 0' 2- VU~^7~2/ o. ISOBUTANOL-AWATER -0.340 INCH 3 0.340 INC/ SPHERES tI*.J / m^M^ o7 / A- ISOBUTANOL-WATER-0.150 INCH Av SPHERES I E S A 2031 A5 6 2 / A / - ISOOCTANE-WATER-0.64 INCH /2 ^ E/A A 0- ISOBUTANOL-WATER 0.340 INCH IFIigu/r 35a. CmaioofSPHERES i/. G~7 Z~ ISOBUTANOL WATER - 0. 164 INCH /.*'-/ SPHERES Al, z V / v- ISOOCTANE-WATER-O.GE CWATER164 INCH SPHERES ~ ISOOCTANE-ALKATERGE "C"-WATER0 0.340 INCH SPHERES, 0.3-34 0 6iA I NC 2 3 4 5 6 7 8 910 PRATIO PREDICTED BY EQUATION 80 Figure 35a. Comparison of Predicted and Measured PRATIO

-113 - 10 91 / 8 / 0 0/ 7- / / / 0/ / 0 / / I _ / / I o 5^/ / / 5 / v/ / +20% LINES U I G{// / o / S SO~ /S-. / * ISOBUTANOL-WATER- 0. 501 INCH 2-5 s 7 >^2V / SPHERES 0,/ /O3,^y / s SOBUTANOL-WATER- 0.340 INCH -~z 0/ / W / 0 / / X,07 7Vv / A I SOBUTANOL- WATER - 0. 164 INCH 2 0 /^ SPHERES |1 _~- / A V ISOOCTANE-WATER-0.164 INCH / ^ /0 V/ SPHERES lbJlQ^^ V/A 0 ISOOCTANE- WATER- 0.340 INCH A*^^~ ^~SPHERES PRATIO PREDICTED BY EQUATION 80 Figure 35b. Comparison of Predicted and Measured PRATIO with Exclusion of Surfactant Data.

-114"C"-water data. New predicted values of PRATIO were computed for this system by Equation (80) using the normal value of 49o5 dynes/cm for co These corrected values are plotted in Figure 35c along with the rest of the data from Figure 35ao The improvement in the correlation indicates that the apparent change in interfacial tension caused by addition of a surfactant is not the actual change in interfacial tension under all degrees of dispersion. An analysis of the data in Figure 355a shows that 8354% of the points fall within +20% of the predicted valueo If the data taken with Alkaterge present are neglected 89~9% of the data are within the +20% limits. Again neglecting the Alkaterge "C" runs 92o2% and 97 4% of the data fall within +25% and +40%, respectively, of the predicted value. Even with the inclusion of the Alkaterge'C' runs, 92~2% of the data fall within +40% of the predicted value. 3~ Drop Size Correlation As was pointed out in the review of the literature very little previous work has been performed on interfacial area measurements in packed bedso As a result a completely empirical approach to the problem of correlation was used here. The characteristic diameter used in the correlation was in all cases the Sauter mean diameter discussed in the previous sectiono Since no completely general correlation of drop sizes was found to be adequate, the effect of the individual experimental variables will be discussed separately.

-115IC o9 r / / 0 / V / ~ a./ / /0" vS/ V 6-o ISOBUTANOL-WATER-O. 14 INCH 2/ V2S / - ISOTAN -WATER -0.164 NCH - ISOOCTANE-WATER-0. INCH 5 ASP HE/ / 0'7 /00-0 I N - W 3 / ~cl~ 00/ // / 3 V / o / / WV, /' 20 % LINES O / OEI) - ISOBUTANOL - WATER-0501 INCH U ^ o/ E^ SPHERESV or) 0 C(ElS O PREDITED ~ ISOBUTANOL -WATER-Q0.1 INCH _J. / El / SPHERES 2 / VV El *- ISOBUTANOL-WATER-O. 34 INCH V/o/(~7 V 2/ V-ISOOCTANE-WATER-0.164 INCH a/ Q A/ SPHERES LS> ^ V / 0- ISOOCTANE-WATER-0.340 INCH / ^ L^- ~A SPHERES CZJa~, Ell 1El El- ISOOCTANE - ALKATERGE"C'-WATER /<11 t^^^ ~/ A El~l0.340 INCH SPHERES A El I 2 3 4 5 6 7 8 910 / PRATIO PREDICTED BY EQUATION 80 Figure 35c. Comparison of Predicted and Measured PRATIO with Corrected Surfactant Data.

-1163l1 Effect of Velocity Several methods were tried before the effect of velocity on drop size was finally obtained. Since the total energy input per volume of liquid mixture is proportional to the total velocity of the mixture, d32= K(Um)b (81) was tried as a correlating equation. This proved to be of little value but an equation of the following form d3 = Ke (82) showed a very good correlation for each individual systemo Plots of In d32 versus Um are presented in Figure 36 for the isobutanol-water systems. An equivalent plot for the system isooctane-waterL0o164 inch spheres appears in Figure 37~ 352 Effect of Packing Diameter As can be seen from Figure 36 packing diameter has a strong effect on drop sizeo A plot of drop diameter, d32, versus packing diameter, Dp. on a logarithmic scale shows that d32 is directly proportional to Dp (see Figure 38). Only one set of flow velocities and flow ratios is shown for each liquid system. 353 Effect of Fluid Properties Due to the small number of different fluid systems studied, the effect of fluid properties cannot be determined very wello It was felt, however, that the effect of interfacial tension on drop size was far greater than that of any of the other physical propertieso Therefore,

2000 ~~~~~20001 --------, I-O ISOB L- W R- INC ISPHE 0 ISOBUTANOL-WATER- 0.501 INCH SPHERES l ISOBUTANOL-WATER- 0.340 INCH SPHERES A ISOBUTANOL-WATER-0.164 INCH SPHERES 1000 900 - 800 700 C 2 600 z ~ O0 500 300- - 200 \ 100 - I 0 0.04 0.08 0.12 0.16 0.20 0.24 0.28 Um, FT./SEC. Figure 36. Effect of Velocity on Sauter Mean Drop Diameter.

200C 2000 --- --- I - -I I1 -- I I O ISOOCTANE-WATER-0.164 INCH SPHERES 1000 - 900 - 800- e coot - O 700- - 0 0~ 300 2 400- 300 100o I o I I I I 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Um, FT. /SEC. Figure 37. Effect of Velocity on Sauter Mean Drop Diameter.

-1193000 I I \ 2000 1000 (f) oo / z 0 O 500 / C 4 0 / -ISOBUTANOL- WATER ISOBUTANOL VELOCITY = 0 0.0377 FT/SEC 300i 6 WATER VELOCITY 0.0402 FT/SEC r-ISOOCTANE - WATER 200 ISOOCTANE VELOCITY: 0.0208 FT/SEC WATER VELOCITY 0.0170 FT/SEC 100 -I, I I I I I I I 0.1 0.2 0.3 0.4 05 0.7 1.0 Dp INCHES Figure 38. Effect of Packing Diameter on Sauter Mean Drop Diameter.

-120a plot of drop diameter versus interfacial tension is presented in Figure 39 This indicates that drop size is approximately proportional to the 1/4 power of interfacial tension. This, of course, can not be used for correlation purposes since the effects of the other fluid. properties are neglected. 3.4 Summary In order to summarize the effects mentioned here, a correlating equation of the following form was postulatedo d2 = K'e Um (83) DP Values of K' and c' were evaluated for each data set by a least squares technique after rearranging Equation (83) to give In 2 i= n Kg - c'Um (84) In addition all of the isobutanol-water data were fitted to Equation (84). The results of this correlation are presented in Table IXo The correlation coefficients are based on Equation (84)o In an attempt to make Equation (83) as general as possible, the technique of dimensional analysis was applied to the data presented hereo The following experimental variables were considered to have a significant effect on drop size~ interfacial tension, a; packing diameter, Dp; mean superficial velocity, Um; mean density, Pm; dispersed phase viscosity, tdo The gravitational conversion constant, gc, must also be included to allow dimensional consistency. A dimensional analysis of these variables

-121\ ---— I — I, I,, I I I,I I'I- I I I I NOMINAL FLOWRATES WATER PHASE - 0.017 FT/SEC ORGANIC PHASE - 0.020 FT /SEC 3000 0 2000 0i~~~~~~~~~~~~~~O0 N5AO S 500 - 2 -n A ISOBUTANOL-WATER - 0.340 INCH SPHERES 300 ~~~~~300 ~ ~V ISOBUTANOL-WATER-0.164 INCH SPHERES 0 ISOOCTANE-WATER-0.340 INCH SPHERES 200 * ISOOCTANE-WATER- 0.164 INCH SPHERES Q ISOOCTANE-ALKATERGE UC"- WATER0.340 INCH SPHERES 100I I I I I I I II I, I 1.0 2.0 3.0 4.0 5.0 10 20 30 40 50 100 INTERFACIAL TENSION, DYNES / CM. Figure 39. Effect of Interfacial Tension on Sauter Mean Drop Diameter.

-122TABLE IX RESULTS OF DROP SIZE CORRELATION System Kf c, sec Correlation ft Coefficient Isobutanol-Water-O o 501 Inch Spheres 0.126 6088 Oo957 Isobutanol-Water-0.5 40 Inch Spheres Oo158 8090 Oo983 Isobutanol-Water-0O 164 Inch Spheres Oo148 8o80 Oo913 All Isobutanol-Water Data 0o141 80oo0 0 946 Isooctane -Water-o. 164 Inch Spheres Oo299 5.31 Oo926 gives the following functional relationship~ (d32 f( DpPmUm DpPmUm (85) fDp / = f ( -m r c gc or Dp ) = f(Re, We) (86) where Re = Reynolds number We T Weber number A functional relationship which satisfies the empirical requirements of Equation (83) is - = K e -c^ (87) DP

-123This equation was rearranged to ~d ~We lnD = n K' - "(Re) (88) Dp and Kg and c" were evaluated for all of the drop size data by a least squares technique. The resulting equation is We d32 = 0168 e 20~() (89) Dp The correlation coefficient based on Equation (88) is 0o961 Figure 40 d32 We is a plot of 2 versus We on log-log paper. The solid line Dp R represents Equation (89).

0.4 I I I I I I I 0.3 v I 0.2 v v 2V EQUATION 89 0.15 N VH VV2V _ l 2A 0.10 Q 0.08 E l" -c l0~o o -ISOBUTANOL-WATER -0.501 INCH SPHERES 2 3 - ISOBUTANOL- WATER - 0.340 INCH SPHERES 2 0 0.05 -ISOBUTANOL - WATER - 0.164 INCH SPHERES V -ISOOCTANE - WATER- 0.164 INCH SPHERES * -ISOOCTANE - WATER -0.340 INCH SPHERES * -ISOOCTANE - ALKATERGE C "- WATER-0. 340 INCH SPHERES 0.02 I I 0.0001 0.0005 0.001 0.005 0.01 0.05 0.10 We /Re Figure 40. Correlation of Drop Size Data.

VIIo CONCLUSIONS As a result of the investigation presented here, the following conclusions can be drawn: 1o Although the form of the Ergun equation is quite satisfactory, the empirical constants vary for different beds and must be experimentally determined to enable precise single phase pressure drop predictionso Variations in packing arrangement are believed to cause the variations in the constantso On the other hand the values of the empirical constants are not effected by fluid properties. 2o Three flow regimes have been observed in the cocurrent flow of immiscible liquids in packed beds. They are bubble flow, homogeneous flow, and slug flowo 3o A mixture of two immiscible liquids flowing cocurrently through a packed bed cannot be treated as a single phase except at the extremes of flow ratio. At intermediate flow ratios surface energy effects have a significant effect on pressure dropo 4o If PRAT O is defined as the ratio of the actual two-phase pressure gradient to that predicted using the assumption that the two-phase mixture behaves as a single phase, PRATIO exhibits a maximum at approximately 75% holdup of the non-wetting phase. Values of PRATrIO9 which is a measure of phase interaction, have been observed as high as 10 -125

-1265. A phase reversal is believed to occur at a non-wetting phase holdup of —75%o 6. PRATIO can be approximated by RATIO = 1 + 0o723(We)-00624e -559(RI075)2 (90) for the systems studied hereo This expression should be approximately true for other liquid-liquid systems in which water is the wetting phaseo 7o Phase holdup of the non-wetting phase, RI, can be loosely approximated by assuming no slip velocity. Relative errors due to this assumption can be minimized, particularly at low values of RI, by using RI -( U )a (91) where a must be evaluated experimentallyo 80 The dispersed phase takes the form of spherical dropletso These droplets exhibit a Gaussian distribution with respect to diameter. The Sauter mean drop diameter is directly proportional to the packing diameter. Its dependence on velocity can be expressed by d32 a ec (92) where Um = total mixture superficial velocity. The effect of fluid properties on drop size has not been determined, however, increasing interfacial tension increases the drop size noticeably.

VIIIo RECOMMENDATIONS FOR FUTURE STUDY Any investigation of an exploratory nature raises some questions which cannot be answered. in a reasonable length of timeo The following subjects are therefore suggested as possible areas for future research: lo Determine the effect of fluid properties on drop sizes. The photographic techniques described here should be adequate for this purposeo In addition the wall effect on drop size should be investigatedo A specially designed test section would be required for this studyo 2. Determine the effect of fluid properties on phase holdup and PRATIO more precisely. 30 Determine coalescence and redispersion frequencies for liquid-liquid flow in packed beds. High speed photography could probably be used for this purposeo From data of this type an estimate of actual energy consumption due to surface generation could be obtained. 4~ Determine the effect of packing material on dispersion formation. A material which is preferentially wetted by the organic phase could be used to increase the tendency for a continuous organic phaseo The suspected phase reversal should then occur at 25% organic phase holdupo -127

LITERATURE CITED 1. Anderson, Go Ho, and Bo Go Mantzouranis, "Two-Phase (Gas-Liquid) Flow Phenomena - I Pressure Drop and Holdup for Two Phase Flow in Vertical Tubes," Chem. Eng. Sci., 12, 109 (1960)o 2. Benenati, Ro Fo, and C. Bo Brosilow, "Void Fraction Distribution in Beds of Spheres," AIChE Jo. 8, 359 (1962). 3o Bertuzzi, A. F., Mo Ro Tek, and F, Ho Poettmann,'Simultaneous Flow of Liquid and Gas Through Horizontal Pipe,' Jo Pet. Techo, 8, January 17, 1956, 4, Blake, Fo C,, "The Resistance of Packing to Fluid Flow,' Trans. AIChE, 14, 415 (1922). 5. Brigham, W. Eo, Eo D, Holstein, and Ro Lo Huntington, "T'wo-Phase Cocurrent Flow of Liquids and Air Through Inclined Pipe," Petro Engo, 29, No. 12, D-39 (1957)o 6. Brown, Ro A. So, and Go W. Govier, "High-Speed Photography in the Study of Two-Phase Flow," Can. J. Chem. Engo., 39, 159 (1961) 7o Brown, Ro Ao S., Go Ao Sullivan, and Go Wo Govier, "The Upward Vertical Flow of Air-Water Mixtures-III Effect of Gas Phase Density on Flow Pattern, Holdup and Pressure Drop," Can. Jo Chemo Eng., 38, 62 (196o0) 80 Brownell, Lo E, H. So Dombrowski, and Co A. Dickey, "Pressure Drop Through Porous Media - IV New Data and Revised Correlation," Chem, Engo Prog, 46, 415 (1950)o 9. Brownell, Lo Eo. and Do Lo Katz, "Flow of Fluids Through Porous Media," Chem. Eng. Progo, 43, 537 (1947)o 10o Brownell, Lo Eo, and Do Lo Katz, "Flow of Fluids Through Porous Media - II Simultaneous Flow of Two Homogeneous Phases," Chem, Engo Prog., 43, 601 (1947)o 11. Burke, S, P., and W. B. Plummer, "Gas Flow Through Packed Columns," Indo Eng. Chem., 20, 1196 (1928), 12. Calvert, S., and Bo Williams, "Upward Cocurrent Annular Flow of Air and Water in Smooth Tubes," AIChE Jo, 1, 78 (1955)o 135 Carman, P. Co, "Fluid Flow Through Granular Beds," Trans. Instn. Chemo Engo (London), 15, 150 (1937). -128

-12914. Cengel, J. Ao, Ao A. Faruqui, J. W. Finnigan, Co Ho Wright, and J. Go Knudsen, "Laminar and Turbulent Flow of Unstable LiquidLiquid Emulsions," AIChE Jo., 8, 335 (1962)o 150 Charles, Mo Eo Go W. Govier, and Go W, Hodgson, "The Horizontal Pipeline Flow of Equal Density Oil-Water Mixtures, " Canr Jo Chemo Engo, 39, 27 (1961)o 16. Charles, Mo Eo, and Po Jo Redberger, "The Reduction of Pressure Gradients in Oil Pipelines by the Addition of Water~ Numerical Analysis of Stratified Flow," Can. J. Chemo Eng, 40,9 70 (1962). 17. Chenoweth, Jo Mo, and M. W. Martin, "Turbulent Two-Phase Flow9 Petro Refo. 34, NOo 10, 151 (1955)o 18o Chilton, To Ho, and Ao Po Colburn, "Pressure Drop in Packed Tubes," Indo Eng. Chemo, 23, 913 (1931)o 19o Chisolm, Do and Ao Do Ko Laird, "Two Phase Flow in Rough Tubes," Transo ASME, 80, 276 (1958)o 20. Church, J. M., and Ro Shinnar, "Stabilizing Liquid.Liquid Dispersions by Agitation," Indo Engo Chemo, 53, 479 (1961)o 21. Dixon, Jo Ao, "Binary Solutions of Saturated Hydrocarbons," Jo Chemo Eng. Data, 4, 289 (1959)o 22. Dodds, W So, Lo F. Stutzman, B. J. Sollami, and Ro Jo McCarter, "Pressure Drop and Liquid Holdup in Cocurrent Gas Absorption," AIChE J. 6, 390 (1960)o 235 Endoh, Ko, and Yo Oyama'"On the Size of Droplets Disintegrated in Liquid-Liquid Contacting Mixer," Sci, Papers Inst. Phys. Chemo Research (Tokyo, 52, 131 (1958). 24, Ergun, S., "Fluid Flow Thlrough Packed Columns," Chem. Eng. Prog., 48, 89 (1952)o 25. Ergun, S., and Ao Ao Orning,'Fluid Flow Through Randomly Packed Columns and Fluidized Beds" Ind.. Engo Chemo, 41, 1179 (1949). 26. Fahien, Ro W., and C0 Bo Schriver, "The Effect of Porosity and Transition Flow on Pressure Drop in Packed Beds, Paper presented at Denver Meeting AIChE (1962). 27. Furnas, C. Co, "Flow of Gases Through Beds of Broken Solids," UoSo Bur. Mines Bullo 307, (1929)

-13028~ Gayler, R., and Ho Ro C. Pratt, "Holdup and Pressure Drop in Packed Columns," Trans. Instn, Chemo Engo (London), 29, 110 (1951)o 29. Gemmell, Ao Ro, and N. Epstein, "Numerical Analysis of Stratified Laminar Flow of Two Immiscible Newtonian Liquids in a Circular Pipe," Cano Jo Chemo Eng., 40, 215 (1962). 30. Govier, Go W., and Mo Mo Omer, "The Horizontal Pipeline Flow of Air-Water Mixtures," Can. J. Chemo Engo, 40, 93 (1962). 31. Govier, G, W., Bo Ao Radford, and Jo So C. Dunn, "The Upwards Vertical Flow of Air-Water Mixtures," Cano J. Chemo Engo, 35, 59 (1957)o 32. Govier, Go Wo. and Wo L. Short, "The Upward Vertical Flow of AirWater Mixtures ~ III Effect of Tubing Diameter on Flow Pattern, Holdup and Pressure Drop," Can. J. Cherm Engo, 36, 195 (1958)o 33. Govier, Go Wo, Go Ao Sullivan, and Ro Ko Wood, "The Upward Vertical Flow of Oil Water Mixtures," Cano J. Chem. Engo, 39, 67 (1961)o 54, Hassan, Mo E., Ro Fo Nielsen, and J. Co Calhoun- "Effects of Pressure and Temperature on Oil-Water Interfacial Tensions for a Series of Hydrocarbons," J. Pet. Tech,, 5, 299 (1953)o 550 Hinze, J. Oo "Fundamentals of the Hydrodynamic Mechanism of Splitting in Dispersion Processes," AIChE J., 1, 289 (1955). 56o Hodgman, Co D., Edo, "Handbook of Chemistry and Physics,' 36th Edo, Cleveland, Chemical Rubber Publishing Co., 1954. 37. Hoogendoorn, C. Jo. "Gas-Liquid Flow in Horizontal Pipes," Chemo Engo Scio, 9, 205 (1959). 38. Hughmark, Go Ao, and B, So Pressburg, "Holdup and Pressure Drop with Gas-Liquid Flow in a Vertical Pipe," AIChE Jo, 79 677 (1961). 39o "International Critical Tables," Vol. IV, New York, McGraw-Hill, 1926, p. 436. 400 Jesser, Bo Wo., and Jo Co Elgin, "Studies of Liquid Holdup in Packed Towers," Trans. AIChE, 39, 277 (1943)O 41, Johnson, A, Io and Eo A, Lo Lavergne, "Holdup in Liquid-Liquid Extraction Columns," Cano Jo Chemo Engo, 39, 37 (1961)o 42. Kafarov, Vo Vo, and Bo Mo Babanov, "Phase-Contact Area of Immiscible Liquids During Agitation by Mechanical Stirrers," J. Appl. Chemo (UoSoSoR.), 32, 810 (1959),

-13143o Lange, No Ao Edo, "Handbook of Chemistry," 9th Edo, Sandusky, Ohio, Handbook Publishers, Inco, 1956. 44. Larkins, Ro P,, "Two-Phase Cocurrent Flow in Packed Beds," PhoDo Thesis, The University of Michigan, 1959o 45. Leacock, Jo, "Mass Transfer Between Isobutanol and Water in Cocurrent Flow Through a Packed Column," PhoDo Thesis, The University of Michigan, 19600 46. Leva, Mo, "Pressure Drop Through Packed Tubes," Chem. Eng. Progo, 439 549 (1947)o 47~ Leva, Mo Mo Weintraub, Mo Grummer, Mo Pollchik, and Ho Ho Storch, "Fluid Flow Through Packed and Fluidized Systems," UOSo Buro Mines Bullo 504, (1951)o 480 Leverett, Mo Co, "Flow of Oil-Water Mixtures Through Unconsolidated Sands," Transo AIME, 132, 149 (1939)o 49~ Levich, Vo Go, "Physicochemical Hydrodynamics," Englewood Cliffs, No Jo, Prentice-Hall, 1962, ppo 454-464o 50. Lewis, Jo B., Io Jones, and Ho Ro C. Pratt, "A Study of Droplet Behavior in Packed Columns," Trans Instno Chemo Engo (London), 29, 126 (1951). 51o Lockhart, Ro W., and Ro Co Martinelli, "Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes," Chemo Engo Progo, 45, 39 (1949)o 52~ Markas, So E,, and Ro Bo Beckman, "Radioisotope Technique for the Determination of Flow Characteristics in Liquid=Liquid Extraction Columns," AIChE Jo, 3, 223 (1957). 530 Martin, J. Jo F Wo Lo McCabe, and Co Co Monrad, "Pressure Drop Through Stacked Spheres, Effect of Orientation," Chemo Engo Prog., 479 91 (1951). 54o Martinelli, Ro Co, Jo Ao Putnam, and Ro Wo Lockhart, "Two-Phase, Two-Component Flow in the Viscous Region," Trans. AIChE, 42, 681 (1946). 55~ Martinelli, Ro Co, Lo Mo Ko Boelter, To Ho Mo Taylor, Eo Go Thomsen, and Eo Ho Morrin, "Isothermal Pressure Drop for Two'Phase, TwoComponent Flow in a Horizontal Pipe," Trans. ASME, 66, 139 (1944)o 56. Morcom, Ao Ro,, "Fluid Flow Through Granular Materials," Transo Instn. Chemo Engo (London), 24, 30 (1946)o

-13257. Mugele, Ro Ao.,'Maximum Stable Droplets in Dispersoids," AChE Jo 69 3 (1960),.9 58. Oman, Ao 0., and K, Mo Watson, Nat Pet. News Tech. Sect, N o 44, R795 (1944) 59. Perry, J. Ho, Ed. "Chemical Engineers' Handbook," 3rd. Edo, New York, McGraw-Hill, 1950, pp. 192-53 60 Ranz, W. E., "Friction and Transfer Coefficients for Single Particles and Packed Beds " Chemo Engo Prog., 48, 247 (1952)o 61. Rodger W. Ao., V. Go Trice, Jr., and J. Ho Rushton, "Effect of Fluid Motion on Interfacial Area of Dispersions " Chem. Eng. Prog. 52, 515 (1956). 62, Rodriguez, F,, L, C. Gratz, and Do Lo Engle, "Interfacial Area in Liquid-Liquid Mixing," AIChE Jo,, 7, 663 (1961)o 63 Ros, No C. Jo "Simultaneous Flow of Gas and Liquid as Encountered in Oil Wells," paper presented at AIChE Meeting, Tulsa, September 25-28, 1960o 64, Russell, To W. F.o and Mo Eo Charles, "The Effect of the Less Viscous Liquid in the Laminar Flow of Two Immiscible Liquids," Can. J. Chemo Eng., 37, 18 (1959)o 65, Russell, To W. Fo, Go W. Hodgson, and Go Wo Govier, "Horizontal Pipeline Flow of Mixtures of Oil and Water, Can. J. Chem. Eng.o 37, 9 (1959) 66. Scheidegger, A. Eo, "The Physics of Flow Through Porous Media, University of Toronto Press, Toronto, (1960). 67. Scott, Go Do "Packing of Spheres," Nature, 188, 908 (1960)o 68. Seidell, Ao "Solubilities of Organic Compounds," 3rd Edo, Vol. I, New York, Van Nostrand, 1941, po 268. 69. Shinnar, Ro "On the Behavior of Liquid Dispersions in Mixing Vessels,' J. Fluid Mech., 10, 259 (1961)o 70. Shinnar, Ro and Jo Mo Church, "Predicting Particle Size in Agitated Dispersions," Ind, Eng. Chem., 52, 253 (1960)o 71o Sitaramayya, To, and Go S. Laddha, "Holdup in Packed Liquid-Liquid Extraction Columns," Chemo Eng. Scio 13, 263 (1961). 72. Sleicher, C. Ao, JrO "Maximum Stable Drop Size in Turbulent Flow," Shell Development Company, Emeryville, Californiao

-133735 Street, JO Ro, "A Study of Vertical Gas-Liquid Slug Flow.9 PhoDo Thesis, The University of Michigan, 1962o 74. Trice, V. Go, Jro, and WO A. Rodger, "Light Transmittance as a Measure of Interfacial Area in Liquid-Liquid Dispersions," AIChE Jo, 2 205 (1956)o 75o Vermuelen, To. Go Mo Williams, and Go E, Langlois, "Interfacial Area in Liquid-Liquid and Gas Liquid Agitation, Chem. Engo Progo, 51, 85 (1955). 76. Weaver, R, Eo Co, Lo Lapidus, and Jo Co Elgin, "The Mechanics of Vertical Moving Liquid-Liquid Fluidized Systems: I Interphase Contacting of Droplets Passing Through a Second Quiescent Fluid," AIChE Jo, 5, 533 (1959). 77. White, Ao Mo, "Pressure Drop and Loading Velocities in Packed Towers," Trans. AIChE, 31, 390 (1935)o 780 Wicks, C. Eo, and R. B. Beckman,'Dispersed-Phase Holdup in Packed Countercurrent Liquid-Liquid Extraction Columns," AChE Jo 9 1, 426 (1955)o

APPEND ICES -134

APPENDIX A DENSITY CORRECTION FACTOR FOR ROTAMETERS A rotameter calibrated for a liquid of given density ordinarily must be recalibrated, when the density of the liquid is changed. Correction factors based on the orifice equation have been computed by the Fischer & Porter Company and are presented in Instruction Bulletin 10A9020 Revision lo The correction factor is a function of two dimensionless ratios A- the ratio of scale fluid density to metering fluid density and the ratio of float density to scale fluid density. The scale fluid is that originally used to calibrate the rotametero The metering fluid is that for which a corrected flowrate is desired. In the present investigation all floats were made of 316 stainless steel and all rotameters were calibrated with water. As a result 7 98 the latter ratio mentioned above was a constant given by R2 - 0.98 = 8000 The correction factor is plotted in Figure Ali for R2 = 8.00. This curve was fitted by a quadratic equation by a least squares techniqueo The resulting equation, which was used in the computer processing of data, is CF = 0.213 + 0.980 R1 - 0.1917 R12 (A-l) -135

-1361.30,,, ACTUAL VOLUMETRIC FLOWRATE = 1.20- INDICATED VOLUMETRIC FLOWRATE x CF FLOAT DENSITY 00 / 1.10 - / _ *1.0 SCALE FLUID DENSITY 1.00 0 0 I IL.90 - z 0 C: 0 ^.70~.CF 0.213+ 0. 980 RI - 0. 1917 R2.60 ~50.50 I -, I I I 0.4 0.6 0.8 1.0 1.2 1.4 1.6 SCALE FLUID DENSITY METERING FLUID DENSITY Figure A-1. Rotameter Correction Factor.

APPENDIX B PHYSICAL PROPERTIES OF LIQUIDS Some of the values of fluid properties extracted from the literature for use in this investigation were given in equation formo The following equations were used to compute the densities of saturated solutions of water and isobutanol at 750~F(59) pI = 0O8055 + 0.00224Pw - 00000129 p (isobutanol phase) (B1l) Pw = 0o998 - 0o00169 pi + 0o000038 p2 (water phase) (B-2) where p = density, gm/mlo o = weight per cent water I = weight per cent isobutanol Seidell(68) gives the concentration of the saturated solutions as Pw 1605 and PI = 8040 Substitution in the above equations yields PI = 0.832 gm/ml P = o 987 gm/ml These values were checked by means of precision hydrometers and found to be quite accurate Hassan, Nielsen, and Calhoun(34) present the following equation for the interfacial tension of water-isooctane at 1 atmo a 49o5 - 0o07 (t-25) (B-3) where a = interfacial tension, dynes/cmo t = temperature,'C -137

-138Viscosity as a function of temperature is presented in Figure B-l for all liquids used in this investigation plus pure isobutanol and n-octane for comparison purposes. Data points represent measured values of viscosity. The viscosity curves for all liquids used here were fitted by a least squares technique to the equation log1O = A + T (B-4) where. = viscosity, cp T = absolute temperature, OR Values of A and B are given in Table Io TABLE I VALUES OF CONSTANTS FOR VISCOSITY CURVES Liquid A B Water -3 043 1 608 x 103 Water saturated with isobutanol -3 450 l 906 x 103 Isobutanol saturated with water -3.512 2.142 x 103 Isooctane -1o609 0 690 x 103

-1391.4 6.0 1.3 Q MEASURED VALUES \A LITERATURE VALUES 1.2 1.1 _______ ______ - I.I -- 1.0 0.9 4.0 0.8 0 >5\ 0 00 o 0. 3.0 0.5 C -- 0.7-4 _ —----— 2.0 TEMPERATURE, OF Figure B-l. Liquid Viscosity Data.

APPENDIX C TABLES OF PROCESSED SINGLE-PHASE DATA The following symbols are used in this Appendix: A, B = constants in liquid viscosity Equation (37) CODE = code number D = packing diameter, inches DELFA. = average frictional pressure gradient in test section, psi/ft DPDL(1) = entrance total pressure gradient, psi/ft DPDL(2) = total pressure gradient in bottom section of column, psi/ft DPDL(3) = total pressure gradient in middle section of column, psi/ft DPDL(4) = total pressure gradient in top section of column, psi/ft DPDIA = average of DPDL(2), DPDL(3), and DPDL(4), psi/ft E = porosity F = dimensionless friction factor defined by Equation (39) GPM = liquid flowrate, gpm NO = number of runs in data set D pU REM = modified Reymonds number, D RHO = liquid specific gravity T = temperature, ~F (The number notation XoXXXE YY is equivalent to X.XXXUtOYY) -140

'i141TABLE I WATER FLOW THROUGH ED O 0.501 INCH BSPHE A- -.0303E 01 B-.16085E 04 RHO-.998 E..400 0D.501 NO- 16 CODE T GP DOPOL(L) DPDL(2) OPDL(3) UPDL(4) DPOLA DELFA REM F 001WO 63.0.651.4398.4351.4351.4351.4351.0027 101.47 317.35 002 C 63.0 1.522.0000.4438.4438.4438.4438.0114 237.27 569.98 0038C 64.0 2.354.4462.4533.4538.4543.4538.0214 371.83 701.4: 00480 66.5 3.165.4559.4681.4686.4683.4683.0359 517.05 905.48 005MO 68.5 3.926.4618.4844.4853.4867.4855.0530 658.71 11C7.44 006WO 69.5 4.657.4765.5051.5056.5071.5059.0735 791.79 1310.56 007W0 71.0 5.409.4839.5248.5256.5283.5262.0938 937.85 1469.11 008W0 72.0 6.150.4941.5383.5424.5492.5433.1109 1080.44 1547.69 0090C 75.0 6.881.5132.5730.5699.5784.5737.1413 1257.02 1833.1u 01OCC 77.0 8.654.5558.6361.6423.6483.6422.2098 1622.17 222v.67 011O 17.0 10.767.6234.7338.7473.7518.7443.3119 2018.33 2652.95 012WO 78.0 12.820.6866.8526.8624.8604.8585.426; 2434.22 3383.03 017WC 74.0. 14.833.0000 1.0235 1.0243 1.0212 1.0230.5906 2674.92 3508.01 018WC 74.0 16.826.0000 1.1713 1.1808 1.1599 1.1707.7382 3034.34 3865.63 019WG 74.0 18.850.0000 1.3418 1.3418 1.3259 1.3365.9040 3399.19 4225.83 020W0 74.0 20.813.0000 1.5237 1.5277 1.5055 1.519) 1.0865 3753.20 4599.74 TABLE II ISOBUTAHOL FLOW THROUGH BED OF 0.501 INCH SPHERES A- -.35123E 01 HB.21422E 04 RHO-.832 En.40C D0.501 NO- 7 CODE T GPM DPOL(l) OPOL(2) 0UP0(3) OPUL14) DPOLA OELFA REM F 04610 73.0 4.341.0000.4459.4458.4459.4458.0853 189.19 5J2.15 05110 74.0 4.341.0000.4446.4446.4446.4446.0841 192.49 503.51 04510 76.0 5.788.0000.4832.4847.4858.4846.1241 265.66 576.62 05010 74.0 5.788.0000-.4807.4813.4821.4813.1208 256.66 542.67 04710 73.0 7.235.0000.5661.5692.5675.5676.2071 315.31 731.22 048IC 73.0 9.794.0000.6577.6633.6646.6619.3014 426.8d 786.00 04910 73.0 12.633.0000.8148.8179..8230.8186.4581 550.58 926.23 TABLE III WATER FLOW THROUGH BED OF 0.340 INCH SPHERES A= -.34499E 01 8=.19057E 04 RHO-.987 E6.383 0=.340 NOD 13 CODE T GPH DPDL(1) DPDL(2) OPOL(3) DPDL(4) PDLA DELFA REM F 088WC 78.0.655.0000.4357.4357.4357.4357.008o 58.08 316.61 08980 78.0 1.543.0000.4555.4549.4552.4552.0275 136.72 452.7C 090Wo 80.0 2.369.4599.4803.4799.4800.4801.L524 216.43 518.18 091WC 80.0 3.186.4813.5141.5151.5151.5150.0873 291.03 716.53 092W0 81.0 3.952.5037.5503.5500.5510.5504.1227 366.49 824.19 0930W 81.0 4.688.5269.5902.5891.5909.5901.1624 434.74 919.48 0948C 82.0 5.444.5529.6391.6363.6384.6379.2103 512.47 104..51 095WC 82.0 6.190.5758.6905.6892.6915.6904.2627 582.70 1143.33 096WO0 83.0 6.926.6125.7473.7458.7497.74.76.3199 661.77 1263.01 09780 83.0 8.701.6969.9079.8979.9006.9021.4744 831.3J 1491.14 09880 80.0 10.848.8346 1.1922 1.1744 1.1945 1.1870.7594 990.98 1830.10 09980 79.0 12.905 1.0111 1.4516 1.4263 1.4561 1.4447 1.0170 1161.22 2029.62 100WO 80.0 14.942 1.1938 1.7474 1.7078 1.7428 1.7327 1.3053 1364.89 2283.52

-142TABLE ZV ISOBUTANOL FLOW THROUGH BED OF 0.340 INCH SPHERES As -.35123E 01 8u.21422E 04 RHO-.832 E=.383 D=.340 NO- 13 CU0DE GPM DPOL(l) OPODL2) DPOL(3) DPDL(4) DPDLA DELFA REM F 10110 72.0 3.617.0000.5062.5046.5C73.5060.1455 102.25 386.12 10210 73.0 2.894.0000.4690.4664.4679.4678.1073 83.24 361.99 10310 73.0 2.170.0000.4323.4322.4323.4323.0717 62.43 322.84 10410 74.0.723.0000.3836.3837.0000.3836.0231 21.17 317.77 10510 76.0 1.447.0000.4056.4057.0000.4057.0451 43.83 32).94 10610 73.5 4.341.4649.5544.5520.5541.5535.1930 125.94 436.04 10710 74.0 5.053.4918.6088.6049.6102.6080.2475 147.88 486.66 81810 74.0 5.788.0000.6722.6633.6736.6697.3092 169.38 530.84 10910 74.0 6.500.5663.7390.7265.7445.7367.3762 190.23 515.07 11010 75.0 7.390.6080.8171.8017.8175.8121.4516 220.05 617.78 11110 78.0 9.794.7639 1.1376 1.1199 1.1558 1.1378.7773 307.02 844.62 11210 79.0 12.187.9255 1.3970 1.3696 1.4175 1.3947 1.0342 388.59 918.63 11310 79.0 14.436 1.1238 1.6973 1.6533 1.7019 1.6842 1.3231 463.27 992.67 TABLE V WATER FLOW THROUGH BED OF 0.164 INCH SPHERES A= -.34499E 01 8.19057E 04 RHO=.987 E=.337 D=.164 NO= 11 COOE T GPM DP PDL(l) DPDL2) UPOL(3) DPDL(4) DPDLA DELFA REM F 196WO 73.0.655.0000.4690.4675.4717.4694.0418 24.15 205.51 197WC 77.0 1.543.4918.5461.5431.5558.5483.1207 6..45 268.28 198W0 78.0 2.369.5454.6439.6356.6636.6477.2200 94.26 323.41 199W0 81.0 3.186.6086.7624.7465.7879.7656.3379 132.62 386.42 2000W 81.0 3.952.6811.8960.8852.9222.9012.4735 164.51 436.48 2010O 84.0 4.688.7630 1.0579 1.0405 1.0761 1.0582.6305 204.07 512.4C 202WO 85.0 5.444.8435 1.2127 1.1880 1.2286 1.2098.7821 240.52 555.46 203WO 85.0 6.190.9300 1.3606 1.3355 1.3833 1.3598.9321 273.48 582.24 204WO 85.0 6.926 1.0358 1.5426 1.5058 1.5745 1.5409 1.1133 306.0C 621.49 205WO 86.0 8.701 1.3011 2.0204 1.9620 2.0546 2.0123 1.5847 390.1) 714.69 2060W 86.0 10.848 1.7424 2.7030 2.6293 2.7372 2.6898 2.2622 486.39 818.28 TABLE VI ISOBUTANOL FLOW THROUGH BED OF 0.164 INCH SPHERES A= -.35123E 01 8=.21422E 04 RHO-.832 E=.337 D=.164 NO= 11 CODE r GPM DPDL(l) DPDL(2) DPDL(3) DPDL(4) DPDLA DELFA REM F 20710 83.0.723.0000.4855.4799.4869.4841.1236 11.0U 271.58 20810 75.0 1.447.4783.5992.5939.6040.5990.2385 19.34 228.78 20910 75.0 2.170.5633.7431.7396.7569.7465.3860 29.01 246.83 21010 76.0 2.894.6334.8933.8859.9243.9012.5401 39.35 263.77 21110 76.0 3.617.7243 1.0716 1.0632 1.1103 1.C817.7212 49.19 281.48 21210 76.0 4.341.8093 1.2354 1.2107 1.2923 1.2461.8856 59.02 288.06 21310 76.0 5.053.9046 1.4288 1.4036 1.4971 1.4432 1.0827 68.11 302.50 21410 76.0 5.788 1.0179 1.6382 1.5966 1.7132 1.6493 1.2888 78.70 314.4J 21510 77.0 6.500 1.1551 1.8498 1.8C31 1.9476 1.8668 1.5063 89.91 332.84 21610 77.0 7.390 1.3190 2.1228 2.0550 2.2252 2.1344 1.7738 102.23 344.73 21710 77.0 8.570 1.5996 2.5620 2.4817 2.6985 2.5807 2.2202 118.55 372.08

-143 - TABLE VII WATER FLOW TEROUGE BED OF 0.164 INCH SPERES A- -.30430E 01 Bs.16085E 04 RHO-.998 En.337 Ds.164 NO 12 CODE T GPM DPDL(1) OPOL(2) DPOL(3) OPDL(4) DPDLA DELFA REM F 286W0 71.0.651.0000.4704.4704.4732.4713.0389 33.44 265.60 287WO 71.0 1.532.0000.5322.5347.5438.5369.1045 78.72 303.08 2880W 70.0 2.354.5191.6225.6261.6524.6337.2012 119.33 375.17 289WO 70.0 3.165.5676.7189.7250.7739.7393.3068 160.46 425.40 2900W 70.0 3.926.6249.8397.8441.9171.8670.4346 199.05 485.71 291WO 70.0 4.657.6866.9553.9653 1.0917 1.0041.5717 236.11 538.66 2920W 70.0 5.409.7262 1.0917 1.1014 1.2281 1.1404.7080 274.20 574.42 293W0 70.0 6.150.7894 1.3191 1.3282 1.4555 1.3676.9351 311.77 667.28 294W0 69.0 6.881.8541 1.4827 1.4756 1.6146 1.5243 1.0919 344.26 687.20 2950W 70.0 8.654 1.0920 1.9442 1.9178 2.0124 1.9581 1.5257 438.71 773.69 2960W 70.0 10.767 1.4656 2.5921 2.5414 2.7058 2.6131 2.1807 545.85 888.77 297WO 70.0 9.715 1.3180 2.2966 2.2466 2.3421 2.2951 1.8627 492.54 841.33 TABLE VIII ISO0CTAmE FLOW THROUGH BED OF 0.164 INCH SPHERES A= -.16086E 01 8=.68994E 03 RHO=.692 E=.337 0=.164 NO= 8 CODE T GPM DPDL(1) DPDL(2) OPDL(3) OPDL(4) OPDLA DELFA REM F 29800 66.0 3.193.0000.5180.5029.5139.5116.2117 218.21 565.78 29900 67.0 3.991.0000.5899.5828.6035.5921.2922 274.32 628.27 30000 67.0 4.789.0000.7488.7439.7596.7508.4509 329.19 807.93 30100 68.0 5.575.0000.8438.8401.8696.8512.5513 385.40 853.40 30200 68.0 6.386.0000 1.0008.9994 1.0690 1.0230.7232 441.43 977.37 30300 69.0 7.171.0000 1.4782 1.3849 1.4782 1.4471 1.1472 498.59 1388.A1 30400 64.0 9.455.0000 2.1147 1.9972 2.0920 2.0680 1.7681 638.82 1577.07 30500 65.0 10.806.0000 2.5921 2.5641 2.7513 2.6358 2.3360 734.31 1833.70

-144TABLE IX WATER FLOW THROUGE BED OF 0.340 INCH SPHEES A= -.30430E 01 8-.16085E 04 RHO..998 E-.384 D-.340 NO. 14 CODE T GPM DPDL(l) DPDL(2) DPDL(3) DPDL(4) DPDLA DELFA REM F 351WO 64.0 1.532.0000.4596.4595.4596.4596.0271 160.02 528.28 3520W 63.5 2.354.0000.4800.4798.4806.4801.0477 244.13 600.71 353W0 63.0 3.165.0000.5098.5083.5139.5107.0782 326.06 727.63 354W0 62.5 3.926.4941.5478.5448.5506.5477.1153 401.75 858.73 355WO 63.0 4.657.5294.5859.5834.5872.5855.1531 479.81 967.50 356W0 62.5 5.409.5529.6293.6234.6279.6269.1944 553.43 1051.18 357W0 68.0 6.150.5823.6537.6505.6469.6504.2180 677.50 1115.68 358W0 68.0 6.881.6087.7013.6938.6985.6979.2654 758.05 1214.36 359W0 69.5 8.644.6734.8329.8238.8289.8285.3961 971.36 1471.60 360WO 71.0 10.777.7615 1.0644 1.0402 1.0349 1.0465.6141 1235.27 1866.22 361WO 72.0 12.820.9025 1.2622 1.2375 1.2281 1.2426.8102 1488.86 2097.10 362W0 73.0_ 14.823 1.0494 1.5237 1.5096 1.5009 1.5114 1.0790 1744.13 2447.20 363WO 73.5 16.826 1.2110 1.8192 1.7817 1.7737 1.7915 1.3591 1992.75 2733.39 364WO 74.0 18.850 1.4108 2.1261 2.0652 2.0693 2.0869 1.6544 2246.92 2989.53 TABLE X ISOdCTANE FLOW THROUGH BED OF 0.340 INCH SPHERES A= -.16086E 01 8=.68994E 03 RHOs.692 E-.384 0=.340 NO= 7 CODE T GPM DPDL(l) DPDL(2) DPDL(3) DPUL(4) DPDLA DELFA REM F 36500 77.0 7.171.0000.5916.5912.5916.5914.2916 1163.43 2718.39 36600 77.0 6.386.0000.5451.5448.5451.5450.2452 1035.93 2567.04 36700 77.0 8.154.0000.6632.6654.6816.6701.3702 1322.81 3035.51 36800 77.5 10.8Q6.0000.8452.8455.8587.8498.5500 1757.95 3411.83 36900 78.0 13.446.0000 1.0462 1.0447 1.0462 1.0457.7459 2193.47 3729.03 37000 78.0 15.927.0000 1.3191 1.3168 1.3191 1.3183 1.0185 2598.11 4298.76 37100 78.0 18.420.0000 1.5532 1.5504 1.5532 1.5523 1.2524 3004.75 4570.86

APPENDIX D TABLES OF PROCESSED TWO-PHASE DATA The following symbols are used in this Appendix:.CODE = code number DPDL(1) = entrance total pressure gradient, psi/ft DPDL(2) = total pressure gradient in bottom section of column, psi/ft DPDL(3) = total pressure gradient in middle section of column, psi/ft DPDL(4) = total pressure gradient in top section of column, psi/ft DPDLA = average of DPDL(2), DPDL(3), and DPDL(4), psi/ft GPM = liquid flowrate, gpm INT TENS = interfacial tension, dynes/cm LOG VIS = logarithm to base 10 of viscosity; viscosity in cp PACK DIA = packing diameter, inches RHO = liquid specific gravity RI = organic phase holdup RUNS = number of runs in data set T = temperature, ~F VOIDAGE porosity (The number notation XoXXXE YY is equivalent to XoXXXlOY) -145

TABLE I ISOBUTABOL-WATER FLOW THROUGH BED OF 0.501 INCH SPHERES SUBSCRIPT (W) = WATER PHASE SUBSCRIPT (0) = ORGANIC PHASE LOG VIS(W) = -.34499E 01 +.19057E 04/T RHO(W) =.987 LOG VIS(O) = -.35123E 01 +.21422E 04/T RHO(O) =.832 VOIDAGE =.400 PACK DIA =.501 INT TENS = 2.100 RUNS = 51 CODE T GPM(W) GPM(O) DPOL(l) DPDL(2) DPDL(3) DPUL(4) DPOLA KI 0211B 74.0.655.723.0000.4316.4316.4316.4316.0000 02218 76.0.655 1.447.0000.4329.4329.4329.4329.0)3C 02318 75.0.655 2.170.0000.4334.4334.4334.4334.7179 02418 79.0 1.543 1.447.0000.4431.4414.0000.4407.3917 025IB1 7.5 1.543 2.894.0000.4662.4696.4697.4685.611C 02618 77.5 1.543 4.341.0000.5089.5170.5213.5158.7234 02718 70.0 1.543 5.788.0000.5820.5816.5847.5827.1613 0281H 72.5 1.543 9.794.7273.7349.7341.7355.7348.8906 0291H 74.0 1.543 12.187.7079.8313.8976.8809.8699.83J1 0301H 75.0 3.186 1.447.0000.4910.4874.4869.4885.2355 03118 74.5 3.186 2.894.4709.5241.5266.5275.5261.4383 03218 76.0 3.186 4.341.4933.5723.5816.582..5786.5589 03318 76.0 3.186 5.788.5260.6517.6654.6701.6644.6357 034IS 77.0 3.186 9.794.7466.9015.9168.8974.9053.7070 035IH 77.0 3.186 12.633.0000 1.0693 1.0859 1.0420 1.0657.7344 03618 66.0 4.688 1.447.4843.5392.5390.5379.5387.1152 03718 69.0 4.688 2.894.5007.5778.5843.5875.5832.3342 038IH 70.0 4.688 4.341.5499.6439.6407.6453.6433.463C 039IH 74.0 4.688 5.788.5976.7321.7416.7473.7433.5370 0401H 75.0 4.688 7.034.6483.8382.8578.8526.8495.6138 0411H 75.0 4.688 9.794.6840 1.0147.9497.9920.9855.6823 04218 74.0 4.688 2.894.0000.5654.5678.5682.5671.35C6 04318 75.0 4.688 2.894.0000.5682.5774.5840.5765.3451 04418 75.0 3.186 1.447.0000.4835.4840.4855.4843.2519 0521U 79.0 4.688 4.341.5424.6288.6324.6346.6319.4657 0531U 79.0 4.688 4.341.5439.6267.6331.6371.6323.4548 0541U 80.0 4.688 4.341.5320.6288.6365.6371.6341.4685 0551B 78.0 1.543.723.0000.4391.4391.4391.4391.241C 05618 78.0 1.543.723.0000.4391.4391.4391.4391.2332 05718 76.0 3.186.723.0000.4717.4716.4724.4719.1423 05816 75.0 3.186 1.447.0000.4902.4910.4917.4910.2574 05918 75.0 4.688 4.341.5529.6384.6401.6499.6398.4712 06018 76.0 6.190 1.447.5216.5533.5534.5527.5531.1642 06118 77.5 6.190.723.5231.5406.5417.5427.5417.0875 06218 79.0 6.190 2.894.5663.6446.6505.6522.6491.2903 06318 81.0 6.190 4.341.6050.7163.7272.7293.7243.3945 0641B 80.5 6.190 6.500.6372.8816.8949.8947.8904.5J69 06518 81.0 6.190 8.570.6855.9078.9497.9920.9498.5699 066IH 86.0 10.848.723.6527.8189.8234.8210.8211.0300 067IH 87.0 10.848 1.447.6647.8650.8701.8664.8672.093C 068IH 88.0 10.848 2.894.6647.9373.9338.9191.9301.2026 0691H 89.5 10.848 4.341.7481 1.0193 1.0178 1.0079 1.0150.2656 0701H 90.0 10.848 6.500.8212 1.2240 1.2221 1.1945 1.2135.3616 071IS 87.0 15.930 1.447.8838 1.2013 1.2039 1.1740 1.1931.0930 0721H 80.5 15.930 2.894.9702 1.3606 1.3696 1.3719 1.3674.1478 0731H 84.0 15.930 4.341 1.0418 1.5016 1.5126 1.4971 1.5038.2190 074IH 85.0 15.930 5.788.0000 1.6109 1.6C79 1.5949 1.6046.2602 075IS 86.5 1.543 5.788.0000.5813.5823.5836.5824.7974 07618 87.5 6.190 1.447.6050.5957.5946.5950.5951.1642 077IH 89.0 6.190 6.500.6542.8781.8880.8960.8874.5151 078IB 91.0 1.543 1.447.0000.4414.4411.4408.4411.4082

-147mis 10 I87e0ToL-WAm L7OW mw0U m8 OF 0.540 I08C 81P8888 SUBSCRIPT 1(W WATER PHASE SUOSCRIPT 101 ORGANIC PHASE LOG VISIW) * -.34499E 01 + *.9057E 04/T RHO(W).987 LOG VlilOQ ~ -.35123E 01 +.21422E 04/T RHD(O) ".832 VOIUAGGE.383 PACK 04 ~.340 INT TENS ~ 2*100 RUNS * 50 CODE T GPM()I GPM(O) PPDOL() DPOL2) DPDLI3) OPL(4) DPODL RI 11418 74.0.655.723,0000.437,4387.4387.4387.4029 11518 75.0.655 1,447,0000.4629.4624.4628.4627.6190 11618 74.0.655 2.894.4775.5592.5592.5627.5634.8104 1471S 74.5.655 4.341.5260.6479.6273,6329.6327.0000 1188H 76.0.655 6.500.6393.8258.8124,8227,8203.0000 11918 80.0 1.543.723.000O 4767.4762.4759.4763.2389 12018 79.5 1.543 1.447,4664.5007.4991.4994.4997.4111 1211H 79.0 4.688 4.341.7094,9624,9452.9328.9468.4658 12218 80.0 1.543 2.894.4977.5771.5757.5758.5762.6299 12316 80.0 1.543 4.341.5404.6887.6853.6866.6869,7119 1241S 73.5 1.543 6.500.6885.9277.9141.9401.9273.7229 12718 78.5 3.186.723.4918.5478.5461 40486.5475.1514 12818 80.0 3.186 1.447.5088.5781.5755.5775.5771.2635 12918 80.0 3.186 2.894.5559.6715,6640.6680,6678.4494 1301H 81.0 3.186 4.341.6214.8003.7973.4017.7998.5725 1311H 82.5 4.688 4.341.6900.9396.9202.9055.9218.4604 13418 75.5 4.688.723.5445.6402.6363.6397.6387.0994 1351i 77.0 4.688 1.447,5445,6853,6812,6849,6838.1978 1361H 78.5 4.688 2.894.5931.7913.7877.7930.7907.3564 1371H 76.0 4.688 4.341.6870.9578.9406.9328.9437.4713 14018 79.0 6.190.723.6125.7565.7520.7569.7551.0830 84118 80.0 6.190 1.447.6405.8012.802p.8072.8057.1541 14218 81.5 6.190 2.894.7124.9374.9336.9415.9375.2990 146I8 79.C 8.701.723.7347 1.0215 1.0019 1.0193 1.0142.0447 1471B 80.0 8.701 1.447.7735 1.0875 1.0632 1.0830 1.0779.1213 14818 81.0 8.701 2.894.8659.?33 1.2084.1.2331.2249.2416 1491H 73.0 8.738 4.341.9687 1.4448 1.4263 1.463) 1.4447.3291 l501H 74.5 8.70o 6.5Q0 1.1446 1,8065 1.7827 1.834 1.8092,4248 851H 75.0 4.488 4.341.6930.9965.9877 1,0079.9960.4686 1521H 77.0 12.905.723 1.0343 1.5372 1.4944 1.5267 1.5174.0447 1531H 77.5 12.905 1.447 1,0782 l.6268 1.6C11 1.6336 1.6235.o057 854iH 78.0 12.905 2.894 1.2147 1.8202 1.7736 1.8202 1.847.1732 15518 79.0.655 1.447,0000.4628.4026.46Z4.4626.6)81 1561H 79.0 1.543 9.794.8593 1,3037 1.2902 1.3151 1.3030.8049 15718 80.5 3.186.723,0000,5550.5506.5530.5529.1404 85818 79.5 4.688 6.500.8122 1.2696 1.2675 1.2923 1.2764.6025 l5915 80.0 6.190 6.500.9210 1.4288 1.4195 1.4516 1.4333.5205 16018 80.5 8.701 1.447.7630 1.0875 1.0632 1.0830 1.0779.1158 1611S 81.0 6.190 9.794 1.2296 1.9977 1.9938 2.0318 2.0077.6381 1621H 81.0 6.190 4.341.7678 1,1171 1.1086 1.tl94 1.1150.4057 16315 81.0 4.688 9.794 1.0984 1,8043 1.7895 1.8247 1.8062.7037 16415 74.0 3.186 6.500.7502 1.1694 1.1812 1.1831 1.1779.6983 16515 74.0 3.186 9.794.0000 1.6Z22 1.5625 1.5881 1.5910.7283 14618 75.0 4,688 1.447.5642.6949.6901.6922.6924.1978 1671H 76,0 1.543 12.187 l,0940 1.6518 1.6306 1.6655 1.6493.8705 1681H 77.5 1.543 9.794.9017 1.3219 1.3083 1.3264 1.3189.7776 16918 79.0 6.190 6.500.9389 1,4357 8.4263 1.4539 1,4386.5123 17018 79.0 4.688 6.500.8242 1.2673 1.2675 1.2923 1.2757.5943 1711U 80.0 3.186 2.894.5514.6818.6784.6818.6807.4521 17218 81.5 4.688 4.341.6855.9738.9731.9806.9748.4113

-148TABLE III ISOBUTANOL-WATER LOW THROUGH BED 0 0.164 INCH SPHEE SUBSCRIPT (W) I WATER PHASE SUBSCRIPT (0) * ORGANIC PHASE LOG VIS(W) * -.34499E 01 +.19057E 04/T RHO(nW).987 LOG VIS(O) - -.35123E 01 +.21422E 04/T RHO(O) -.832 VOIDAGE *.337 PACK DIA 8.164 INT TENS * 2.100 RUNS * 63 CODE T GPMIW) GPM(O) DPOL() DPOL(2) UPDL3) DPDLI4) UPDLA RI 2181B 79.0.655.723.5067.5946.5891.6061.5968.4200 2191B 80.0.655 1.447.5886.7789.7781.8189.7920.6452 2201B 80.0.655 2.894.7869 1.2923 1.2932 1.4061 1.3295.8188 2211S 75.0.655 4.341.9464 1.7588 1.8349 2.0773 1.8903.8297 2221H 76.0.655 6.500 1.2803 2.1114 2.1299 2.4306 2.2238.8623 2231H 80.0.655 7.390 1.4913 2.4527 2.4023 2.6803 2.5118.9165 2241H 82.0 1.543.723.5499.6784.6695.6931.6803.2544 22518 82.0 1.543 1.447.6214.8340.8193.8588.8314.3657 22618 82.0 1.543 2.894.8122 1.2696 1.2448 1.3378 1.2840.6180 22718 83.0 1.543 4.341 1.0090 1.7815 1.7554 1.8611 1.7994.7130 22815 70.0 1.543 5.r88 1.4617 2.7258 2.7428 2.8168 2.7618.7266.22915 76.0 1.543 5.053.0000 2.3390 2.3342 2.5210 2.3981.7703 23018 75.0 3.186.723.6796.9510.9383.9851.9582.000C 23118 75.0 3.186 1.447.7601 1.0989 1.0791 1.1444 1.1075.00oO 2321H 76.0 3.186 2.894.9419 1.4925 1.4763 1.5881 1.5193.4010 2331H 77.0 3.186 4.341 1.2236 2.0614 2.0278 2.1683 2.0858.5583 2341S 78.0 3.186 5.788 1.5848 2.7940 2.7428 2.9647 2.8338.6615 2351H 79.0 4.688.723.8480 1.2354 1.1994 1.2696 1.2348.000j 2361H 75.0 4.688 1.447.9184 1.4061 1.3809 1.4516 1.4129.0000 2371H 76.0 4.688 2.170 1.0299 1.5995 1.5512 1.6564 1.6023.2052 2381H 76.0 4.688 2.894 1.1610 1.8338 1.7781 1.9180 1.8433.2761 2391H 77.0 4.688 4.341 1.4427 2.3959 2.3569 2.5438 2.4322.4281 24018 79.0 2.369.723.0000.7941.7767.8099.7936.0000 24118 8C.0 2.369 1.447.6870.9510.9383.9851.9582.2436 24218 80.0 2.369 2.170.7705 1.1103 1.0972 1.1444 1.1173.3793 2431H 81.0 2.369 2.894.8629 1.3151 1.3015 1.3606 1.3257.4986 2441H 81.0 2.369 4.341 1.0880 1.8611 1.8235 1.9408 1.8152.6343 2451S 82.0 2.369 5.788 1.4371 2.5665 2.5271 2.7030 2.5989.7320 24618 74.0.655.723.5096.6026.5926.5999.5983.3955 24718 75.0 2.369.723.0000.7982.7836.8106.7975.0000 2481H 75.0 4.688.723.0000 1.2422 1.2153 1.2696 1.2424.000J 24915 75.0 3.186 5.788 1.6095 2.7713 2.7655 2.9419 2.8262.6723 25015 75.0 1.543 5.053.0000 2.3162 2.2888 2.4186 2.3412.7863 2561U 75.0.655 2.894.0000 1.2923 1.2902 1.3833 1.3219.000 2571U 75.0 1.543 2.894.0000 1.2923 1.2902 1.3378 1.3368.0000 2581U 76.0 1.543 4.341.0000 1.9294 1.9143 2.0204 1.9547.0003 2591U 77.0.655 4.341.0000 1.6677 1.7781 1.9408 1.7956.0000 2601H 71.0 2.369 5.053.0000 2.4414 2.4023 2.5665 2.4711.0000 2611S 71.0 2.369 5.788.0000 2.7258 2.6747 2.9078 2.7694.0000 26215 72.0 1.543 4.686.0000 2.1114 2.0845 2.2138 2.1366.0000 2631 5 75.0 1.543 5.788.0000 2.7258 2.6974 2.8851 2.7694.0000 26418 77.0.655 2.170.0000 1.0761 1.0745 1.1103 1.3870.0000 26518 77.0.655 3.617.0000 1.7019 1.6646 1.7929 1.7198.0003 2661S 77.0.655 5.053.0000 1.7701 1.7668 1.8953 1.8107.0000 2671S 78.0.655 5.788.0000 1.7929 1.7441 1.8611 1.7994.0000 26818 78.0 1.109.723.0000.6343.6310.6605.6419.0000 26918 82.0 1.109 1.447.0000.8134.8069.8258.8154.0000 27018 82.0 1.109 2.170.0000 1.0306 1.0178 1.0648 1.0377.0000 27118 82.0 1.109 2.894.0000 1.2923 1.2788 1.3424 1.3045.0000 27218 82.0 1.109 3.617.0000 1.5767 1.5625 1.6564 1.5985.0000 2731S 83.0 1.109 4.341.0000 1.8725 1.8916 2.0204 1.9282.0000 2741S 83.0 1.109 5.053.0000 2.1228 2.1640 2.2821 2.1896.0000 27515 84.0 1.109 5.788.0000 2.2252 2.3032 2.5096 2.3450.000. 27615 84.0 1.109 6.500.0000 2.3162 2.4136 2.6575 2.4625.000C 27718 85.0 1.966.723.0000.7417.7300.7562.7426.0000 27818 85.0 1.966 1.447.0000.8878.8660.9029.8856.0000 27918 85.5 1.966 2.170.0000 1.0534 1.0291 1.0716 1.0514.0000 28018 86.0 1.966 2.894.0000 1.2696 1.2448 1.3378 1.2840.0O0O 28118 86.0 1.966 3.6i7.0000 1.5540 1.5171 1.6109 1.5607.0000 28215 86.0 1.966 4.341.0000 1.8611 1.8349 1.9749 1.8903.0000 2831S 86.0 1.966 5.053.0000 2.2366 2.2094 2.3845 2.2768.0000 28415 87.0 1.966 5.788.OOU0 2.6120 2.5839 2.8054 2.6671.0000 2851S 87.0 1.966 6.500.0000 2.8396 2.8449 3.0898 2.9248.0000

-149ISOOcTA-IWATm FLOW THOGH B) 0.16 IHCB SPE mR SUBSCRIPT (WI) WATER PHASE SUBSCRIPT (0) * ORGANIC PHASE LOG VIS(W) * -.30430E 01 + *16085E 04/T RHO(WI *.998 LOG VIS(O) * -.16086E 01 +.68994E 03/T RHO(O) *.692 VOIDAGE *.337 PACK DIA *.164 INT TENS * 49.500 RUNS * 45 CODE T GPM(W) GPM(O) DPDL(I) DPDL) DPDL(3) DPUL(4) OPDLA RI 30608 54.0.651 *798.7321 1.1144 1.0787 1.1144 1.1025.0000 3070B 56.0.651 1.596.8350 1.4100 1.3395 1.4100 1.3865.0000 30808 56.0.651 2.395.9701 1.8419 1.7704 1.8419 1.8181.0000 30908 58.0.651 3.193 1.0788 2.2057 2.1786 2.2284 2.2042.0000 31008 60.0 1.532.798.7380 1.1144 1.0334 1.0690 1.0723.0000 31108 61.0 1.532 1.596.8497 1.3418 1.2488 1.3191 1.3032.0000 31208 62.0 1.532 2.395.9642 1.6146 1.5209 1.5691 1.5682.0000 31308 62.0 1.532 3.193 1.1082 1.9329 1.7931 1.8874 1.8711.0000 31408 63.0 1.532 3.991 1.2434 2.2966 2.2012 2.2511 2.2497.0000 31508 73.0 1.532 3.991.0000 2.2511 2.1332 2.2284 2.2043.0000 31608 75.0 1.532 4.789.0000 2.6149 2.4507 2.5239 2.5298.0000 31708 76.0 2.354.798.7468 1.1372 1.0561 1.0803 1.0912.0000 31808 77.0 2.354 1.596.8497 1.3191 1.2261 1.2509 1.2653.0000 31908 78.0 2.354 2.395.9701 1.5464 1.4075 1.4555 1.4698.0000 32008 70Qn 2.354 3.193 1.1023 1.8647 1.7024 1.7510 1.7727.OOOC 32108 79.0 2.354 3.991 1.2434 2.1375 2.0198 2.0693 2.0755.0000 32208 80.0 2.354 4.789.0000 2.4785 2.3373 2.3875 2.4011.0000 32308 81.0 3.165.798.7703 1.1599 1.1127 1.1372 1.1366.0000 32408 81.0 3.165 1.596.8673 1.3418 1.2715 1.2963 1.3032.0000 32508 69.0 3.165 2.395.9966 1.6601 1.5436 1.5919 1.5985.0000 32606 73.0 3.165 3.193 1.1347 1.8874 1.7931 1.8647 1.8484.0000 32708 74,0 3.165 3.991 1.2698 2.1602 2.0879 2.1375 2.1285.0000 32808 75.0 3.165 4.789.OOQO 2.4557 2.3827 2.4330 2.4238.0000 32908 77.0 3.926.798.8232 1.2281 1.2C35 1.2281 1.2199.0000 33008 78.0 3.926 1.596.9172 1.4100 1.3395 1.3873 1.3789.0000 33108 78.0 3.926 2.39'5 1.0171 1.6146 1.5436 1.5919 1.5834.0000 33208 78.5 3.926 3.193 1.1670 1.8647 1.7817 1.8306 1.8256.0000 33308 79.0 3.926 3.991 1.3109 2.1375 2.0765 2.1375 2.1172.0000 33408 80.0 3.926 4.789.0000 2.4557 2.3600 2.4557 2.4238.0000 33508 80.5 4.657.798.8643 1.2850 1.2375 1.2963 1.2729.0000 33608 81.0 4.657 1.596.9495 1.4668 1.4075 1.4555 1.4433.0000 33708 81.0 4.657 2.395 1.0788 614 1.6116 1.6487 1.6439.0000 33808 82.0 4.657 3.193 1.1934 1.9215 1.8498 1.9101 1.8938.0000 33908 82.0 4.657 3.991.0000 2.2057 2.1105 2.1829 2.1664.0000 34008 82.0 6.150.798.9642 1.5237 1.4756 1.5350 1.5114.0000 34108 83.0 6.150 1.596 1.0759 1.7169 1.6570 1.7283 1.7007.0000 34208 83.5 6.150 2.395 1.1993 1.9215 1.8611 1.9215 1.9014.0000 34308 84.0 6.150 3.193 1.3462 2.1716 2.0879 2.1602 2.1399.0000 34408 83.0.651 2.395.0000 1.7737 1.7024 1.7283 1.7348.0000 34508 84.5 1.532 3.991.0000 2.2739 2.2466 2.2511 2.2572.0000 34608 85.0 2.354.798.0000 1.1599 1.1127 1.1372 1.1366.0000 147nfR Rs-O 3 15 2.395.0000 1.5464 1.4983 1.5237 1.5228.0000 34A08 86.0 3.926 3,991.0000 2.1375 2.0425 2.0693 2.0831.0000 34908 86.0 4.657,798,0000 1.2622 1.2148 1.2622 1.2464.0000 3fsoDR A^.f 6.15 1.596.0000 OQQ 75 1.6343 1.6828 1.6742.0000

-150ISO'OTAXE-WATER FLOW THROUGH BED OF 0.40 INCH SPHERE SUBSCRIPT (WI) WATER PHASE SUBSCRIPT T0) a ORGANIC PHASE LOG VIS(S) - -.30430E 01.16085E 04/T RHO(W).998 LOG VIS(O). -.16086E 01 8.68994E 03/T RHO(O) *.692 VOIDAGE -.384 PACK DIA *.340 INT TENS * 49.500 RUNS - 59 CODE T GP(W GP) GPO(O DPDLIl) DPUPL2) PUPL3) DOPUOL4 OPLA RI 37208 69.5.651.798.0000.5234.5205.5193.5211.4834 37308 173.0.651 1.596.0000.5818.5773.5763.5785.6627 37408 74.0.651 3.193.0000.7664.7751.7719.7711.6923 37508 75.5.651 4.789.6293.8644.8633.8871.8716.7883 37605 76.0.651 6.386.6440.8811.9313.9439.9238.8063 37705 77.0.651 8.154.6822.9439.9767 1.0008.9738.0000 37808 78.0.651 10.806.7850 1.1599 1.1127 1.1372 1.1366.000 37908 79.0.651 13.446.9349 1.4100 1.3622 1.3645 1.3/89.0038008 81.0 1.532.798.0000.5302.5178.5207.5229.3239 38108 82.0 1.532 1.596.0000.5580.5530.5573.5561.4171 38208 82.0 1.532 3.193.0000.6850.6897.6768.6838.5102 38308 83.0 1.532 4.789.6175.8397.8496.8479.8457.6838 38405 84.0 1.532 6.386.6675.9553.9767 1.0008.9776.7473 38505 84.0 1.532 8.154.7380 1.0235 1.0561 1.0690 1.0495.0000 38605 84.0 1.532 10.806.8614 1.2395 1.2035 1.2281 1.2237.000O 38705 85.0 1.532 13.446.9966 1.5237 1.3962 1.4441 1.4547.0000 38808 86.0 2.354.798.0000.5329.5245.5261.5278.0000 38908 86.0 2.354 1.596.0000.5465.5367.5356.5396.03)3 39008 87.0 2.354 3.193.0000.6605.6518.6524.6549.00v0 39108 87.0 2.354 4.789.0000.8099.8116.8085.8100.0000 39205 68.0 2.354 6.386.7174 1.0235 1.0334 1.0576 1.0382.0000 39305 70.0 2.354 8.154.7938 1.1713 1.2035 1.2395 1.2047.OOj 3940S 71.0 2.354 10.806.9437 1.3532 1.3509 1.3645 1.3562.0000 39505 71.0 2.354 13.446 1.1082 1.6260 1.5890 1.6032 1.6060.00 39608 73.0 3.165.798.0000.5546.5503.5465.55J5.1532 39708 73.0 3.165 1.596.0000.5967.5909.5859.5911.2463 39808 74.0 3.165 3.193.0000.7108.6884.6917.6910.3888 39908 75.0 3.165 4.789.6616.8370.8347.8316.8344.4820 40008 76.0 3.165 6.386.7409 1.0235.9880 1.0008 1.0341.6245 40105 77.0 3.165 8.154.8291 1.1599 1.1808 1.1826 1.1744.0000 4020S 77.0 3.165 10.806.9731 1.4100 1.4075 1.4441 1.4205.000O 4030S 78.0 3.165 13.446 1.1435 1.6828 1.6457 1.6714 1.6666.0000 40408 78.5 4.657.798.0000.6049.6017.6008.6025.000C 40508 79.0 4.657 1.596.0000.64683.6383.6368.6411.0000 40608 77.0 4.657 3.193.6381.7610.7493.7474.7526.Z000 40708 80.0 4.657 4.789.0000.9103.8753.8778.8818.0000 40808 80.0 4.657 6.386.8085 1.0690 1.0447 1.0349 1.0495.0000 4090S 81.0 4.657 8.154.9055 1.2281 1.2035 1.2054 1.2123.300 4100S 81.0 4.657 10.806 1.0994 1.5123 1.5209 1.5464 1.5265.03OJ 41105 82.0 4.657 13.446 1.2874 1.8419 1.8384 1.8419 1.8408.0000 41208 82.0 6.150.798.0000.6945.6816.6795.6852.0840 41308 82.5 6.150 1.596.0000.7406.7277.7284.7322.1489 41408 83.0 6.150 3.193.0000.8601.8319.8329.8417.2632 41508 83.0 6.150 4.789.0000 1.0121.9767.9780.989;.3437 41608 83.5 6.150 6.386.0000 1.1713 1.1354 1.1372 1.1480.4411 41700 83.5 6.150 8.154.0000 1.3304 1.3055 1.2963 1.31J/.000J 4180S 74.0 6.150 10.806.0000 1.6828 1.6343 1.6714 1.6628.0000 41901 74.0 6.150 13.446.0000 2.0238 2.0085 2.0465 2.0263.0000 42008 74.0 8.644.798.0000.8985.8860.8871.8935.0000 42108 75.0 8.644 1.596.0000.9667.9427.9553.9549.0000 4320R 75.0 8.644 3.193.0000 1.1031 1.0674 1.0690 1.0198.0000 42308 75.0 8.644 4.789.0000 1.2622 1.2261 1.2281 1.2388.0000 42408 75.0 8.644 6.386.0000 1.4555 1.3962 1.4327 1.4281.000; 42508 75.0 8.644 8.154.0000 1.6601 1.5436 1.5919 1.5985.0000 4260S 75.0 8.644 10.806.0000 1.9783 1.9064 1.9556 1.9468.000 42708 75.5 12.820.798.0000 1.3418 1.3055 1.3191 1.3221.000 42808 75.5 12.820 1.596.0000 1.4100 1.3622 1.3873 1.3865.0000 42908 76.0 12.820 3.193.0000 1.5919 1.5436 1.5691 1.5682.0000 43008 76.0 12.820 4.789.0000 1.7965 1.7250 1.7624 1.7613.0000

-151TABLE VI ISOCTA3E-ALKATZOE "C" - WA FLW THROUH D OF 0.140 Io. M PHRS SUBSCRIPT (W) * WATER PHASE SUBSCRIPT (0) - ORGANIC PHASE LOG VIS(W) a -.30430E 01 +.16085E 04/T RHO(W) -.998 LOG VIS(O) * -.16086E 01 +.68994E 03/T RHO(O) *.692 VOIDAGE *.384 PACK DA *.340 INT TENS * 16.000 RUNS a 40 CODE T GPNIMW GPN(O) DPDL(1) OPDL(2) DPDL3) DPOL(4) DPDLA RI 43108 77.0.651.798.0000.4677.4676.4677.4677.4679 43208 78.0.651 1.596.0000.5234.5259.5248.5247.5893 43308 78.5.651 3.193.0000.7515.7575.7488.7526.7248 43408 80.0.651 4.789.0000 1.0235 1.0674 1.1144 1.0685.8673 43508 80.5.651 6.386.0000 1.4327 1.4529 1.4782 1.4546.0000 43608 80.5.651 8.154.0000 1.7510 1.8838 1.9556 1.8635.0000 43708 80.0 1.532.798.0000.4800.4798.4800.4799.2470 43808 80.0 1.532 1.596.0000.5193.5191.5193.5193.4016 43908 80.0 1.532 3.193.0000.6578.6491.6592.6554.5554 44008 81.0 1.532 4.789.0000.8628.8753.8778.8720.7177 44108 81.0 1.532 6.386.0000 1.1144 1.1127 1.1372 1.1215.7883 4420B 82.0 1.532 8.154.0000 1.4100 1.4529 1.4555 1.4394.0000 44308 82.0 2.354.798.0000.4962.4974.4976.4971.0000 44408 83.0 2.354 1.596.0000.5343.5340.5343.5342.0000 44508 83.0 2.354 3.193.0000.6469.6369.6388.6409.0000 4460B 83.5 2.354 4.789.0000.8085.7994.8044.8041.0000 44708 83.5 2.354 6.386.0000 1.0462 1.0447 1.0235 1.0382.0000 44808 84.0 2.354 8.154.0000 1.2509 1.2715 1.2850 1.2691.0000 44908 84.5 2.354 10.806.0000 1.6601 1.7250 1.7283 1.7044.0000 45008 85.0 3.165.798.0000.5234.5232.5234.5233.1292 451AR aS. 3.165 1.596.0000.5587.5530.5573.5563.2322 45208 85.0 3.165 3.193.0000.6673.6532.6578.6594.3790 45308 85.0 3.165 4.789.0000,8099.7981.8017.8032.5215 45408 85.0 3.165 6.386.0000 1.0008.9767 1.0008.9927.6274 45508 85.5 3.165 8.154.0000 1.2167 1.2035 1.2281 1.2161.0000 45608 85.5 3.165 10.806.0000 1.5919 1.6116 1.6373 1.6136.0000 45708 86.0 4.657.798.0000.5845.5760.5804.5803.0000 45808 86.0 4.657 1.596.0000.6307.&166.6171.6214.0000 45908 86.5 4.657 3.193.0000.7298.7141.7175.7205.0000 46008 87.0 4.657 4.789.0000.8871.8520.8644.8678.0000 4610B 87.0 4.657 6.386.0000 1.0576 1.0107 1.0235 1.0306.0000 46208 87.0 4.657 8.154.0000 1.2281 1.2035 1.2167 1.2161.0000 46308 87.0 4.657 10.806.0000 1.5691 1.5890 1.6146 1.5909.0000 46408 87.5 6.150.798.0000.6809.6721.6673.6734.0755 46508 88.0 6.150 1.596.0000.7393.7209.7243.7282.1454 46608 86.0 6.150 3.193.0000.8506.8333.8343.8394.2618 46708 86.5 6.150 4.789.0000 1.0008.9653.9780.9814.3493 46808 86.5 6.150 6.386.0000 1.1599 1.1241 1.1372 1.1404.4425 46908 86.5 6.150 8.154.0000 1.3532 1.3168 1.3418 1.3373.0000 47008 86.0 6.150 10.806.0000 1.6942 1.6570 1.6828 1.6780.0000

APPENDIX E TABLES OF PROCESSED DROP SIZE DATA The following symbols are used in this Appendixo CLASSES = the number of different size classifications used in analyzing the photographs CODE = photograph number DSAUT IN = Sauter mean diameter, inches DSAUT MIC = Sauter mean diameter, microns FPS = superficial liquid velocity-, ft/sec FPSTOT = sum of superficial velocities, ft/sec GPM liquid flowrate, gpm INT TENS interfacial tension, dynes/cm LOG VIS = logarithm to base 10 of liquid viscosity; viscosity in cp N number of drops counted in photograph PACK DIA packing diameter, inches PHOTOS = number of photographs in data set RHO liquid specific gravity VOIDAGE = porosity (The number notation X.XXXE YY is equivalent to X.XXX-1lO1) -152

-153TABLE I ISOBUTANOL-WATER FLOW THROUGH BED OF 0.501 INCH SPHERES SUBSCRIPT (W) = WATER PHASE SUBSCRIPT (0) - ORGANIC PHASE LOG VIS(W) a -.34499E 01 +.19057E 04/T RHO(W) =.987 LOG VIS(O) a -.35123E 01 +.21422E 04/T RHO(O) a.832 VOIDAGE =.400 PACK DIA -.501 INT TENS a 2.100 PHOTOS a 21 CLASSES 2 2 CODE GPM(W) GPM(O) FPS(W) FPS(O) FPSTOT DSAUT IN USAUT MIC N 007 1.543 1.447.04019.03769.07788.03444 874.79 102 008 1.543 1.447.04019.03769.07788.03627 921.25 85 009 1.543 1.447.04019.03769.07788.03419 868.32 114 010 1.543 1.447.04019.03769.07788.03666 931.14 99 017 1.543 1.447.04019.03769.07788.03482 884.38 107 018 1.543 1.447.04019.03769.07788.03667 931.53 141 081 1.543 1.447.04019.03769.07788.03792 963.14 45 078 3.186 1.447.08300.03769.12069.02724 691.83 38 082 3.186 1.447.08300.03769.12069.02782 706.65 49 079 4.688 1.447.12213.03769.15983.02053 521.35 13 083 4.688 1.447.12213.03769.15983.02155 547.33 48 084 6.190 1.447.16127.03769.19896.01659 421.29 32 080 6.190 1.447.16127.03769.19896.01294 328.73 18 085 8.701 1.447.22667.03769.26436.00836 212.33 11 086 1.543 2.894.04019.07539.11557.02860 726.38 41 096 1.543 2.894.04019.07539.11557.02767 702.94 79 087 1.543 4.341.04019.11308.15327.03041 772.29 33 097 1.543 4.341.04019.11308.15327.02170 551.28 24 089 3.186 2.894.08300.07539.15838.02290 581.54 66 090 4.688 2.894.12213.07539.19752.01906 484.14 56 093 3.186 4.341.08300.11308.19608.01859 472.12 27

-154TABLE II ISCBUTANOL-WATER FLOW THROUGH BED OF 0.40 INCH SPHERES SUBSCRIPT (W) - WATER PHASE SUBSCRIPT (0) - ORGANIC PHASE LOG VIS(W) = -.34499E 01 +.19057E 04/T RHO(W) =.987 LOG VIS(O) = -.35123E 01 +.21422E 04/T RHO(O) =.832 VOIDAGE a.383 PACK OIA =.340 INT TENS = 2.100 PHOTOS 30 CLASSES = 2 CODE GPM(W) GPM(O) FPS(W) FPS(O) FPSTOT DSAUT IN DSAUT MIC N 099.655.723.01707.01885.03592.04079 1035.97 232 101.655.723.01707.01885.03592.D4115 1045.15 215 100 1.543 1.447.04019.03769.07788.02688 682.85 195 118 1.543 1.447.04019.03769.07788.02784 707.08 162 102 1.543.723.04019.01885.05903.02980 756.87 242 103 1.543.723.04019.01885.05903.02911 739.32 205 110.655 1.447.01707.03769.05477.03344 849.30 91 111.655 1.447.01707.03769.05477.03607 916.28 76 123.655 2.894.01707.07539.09246.02602 660.96 116 124.655 2.894.01707.07539.09246.02714 689.44 105 104 3.186.723.08300.01885.10184.01992 505.91 154 105 3.186.723.08300.01885.10184.01999 507.78 169 106 4.688.723.12213.01885.14098.01348 342.40 94 107 4.688.723.12213.01885.14098.01392 353.50 139 108 6.190,723.16127.01885.18011.01180 299.72 98 109 6.190.723.16127.01885.18011.01135 288.19 130 112 3.186 1.447.08300.03769.12069.01872 475.53 122 113 3.186 1.447.08300.03769.12069.01883 478.22 128 114 4.688 1.447.12213.03769.15983.01298 329.82 77 115 4.688 1.447.12213.03769.15983.01365 346.73 143 116 6.190 1.447.16127.03769.19896.00998 253.58 108 117 6.190 1.447.16127.03769.19896.00948 240.88 112 119 3.186 2.894.08300.07539.15838.01380 350.56 169 120 3.186 2.894.08300.07539.15838.01385 351.71 128 121 1.543 2.894.04019.07539.11557.01907 484.38 149 122 1.543 2.894.04019.07539.11557.01858 471.96 138 125 1.543 4.341.04019.11308.15327.01284 326.19 124 126 1.543 4.341.04019.11308.15327.01183 300.58 75 127.655 4.341.01707.11308.13015.01419 360.36 150 128.655 4.341.01707.11308.13015.01654 420.11 122

-155TABLE III ISCBUTANOL-WATER FLOW THROUGH BED OF 0.164 INCH SPERES SUBSCRIPT (W) - WATER PHASE SUBSCRIPT (0) - ORGANIC PHASE LOG VIS(W) = -.34499E 01 +.19057E 04/T RHO(W) a.987 LOG VIS(O) a -.35123E 01 +.21422E 04/T RHO(O) *.832 VOIDAGE a.337 PACK DIA -.164 INT TENS * 2.100 PHOTOS - 26 CLASSES 2 2 CODE GPM(W) GPM(O) FPS(W) FPS(O) FPSTOT USAUT IN DSAUT MIC N 131.655.723.01707.01885.03592.01858 472.01 45 132.655.723.01707.01885.03592.01873 475.84 53 133 1.543.723.04019.01885.05903.01579 400.98 64 134 1.543.723.04019.01885.05903.01511 383.75 54 144 1.543 1.447.04019.03769.07788.01276 324.15 75 145.655 1.447.01707.03769.05477.01605 407.74 110 146.655 1.447.01707.03769.05477.01808 459.22 95 135 3.186.723.08300.01885.10184.01041 264.53 72 136 3.186.723.08300.01885.10184.01082 274.88 92 137 4.688.723.12213.01885.14098.00884 224.65 108 138 4.688.723.12213.01885.14098.00780 198.06 82 139 4.688 1.447.12213.03769.15983.00728 185.01 72 140 4.688 1.447.12213.03769.15983.00681 172.85 57 141 3.186 1.447.08300.03769.12069.00898 228.21 121 142 3.186 1.447.08300.03769.12069.00920 233.75 70 143 1.543 1.447.04019.03769.07788.01140 289.53 116 147.655 2.894.01707.07539.09246.00835 212.20 85 148.655 2.894.01707.07539.09246.00777 197.35 83 149 1.543 2.894.04019.07539.11557.00726 184.30 116 150 1.543 2.894.04019.07539.11557.00698 177.42 139 151 3.186 2.894.08300.07539.15838.00682 173.28 162 152 3.186 2.894.08300.07539.15838.00658 167.06 130 153 1.543 4.341.04019.11308.15327.00568 144.28 148 154 1.543 4.341.04019.11308.15327.00584 148.36 126 155.655 4.341.01707.11308.13015.00581 147.61 137 156.655 4.341.01707.11308.13015.00622 157.93 101

-156TABLE IV ISOOCTANE-WATER FLOW THROUGH BED OF O.164 INCH SPHERES SUBSCRIPT (W) = WATER PHASE SUBSCRIPT (0) = ORGANIC PHASE LOG VIS(W) = -.30430E 01 +.16085E 04/T RHO(W) -.998 LOG VIS(O) = -.16086E 01 +.68994E 03/T RHO(O) =.692 VOIDAGE =.337 PACK ODIA.164 INT TENS = 49.500 PHOTOS z 24 CLASSES = 1 CODE GP(W) GPM(O) FPS(W) FPS(O) FPSTOT DSAUT IN DSAUT MIC N 183... 51.798.01696.02079.03775.03861 980.63 90 184.651.798.01696.02079.03775.04021 1021.24 147 157...651.798.01696.02079.03775.04161 1056.86 283 158 _____. 798.01696.02079.03775.04175 1060.45 165 159....651 1.596.01696.04159.05855.03353 851.77 155 160.651 1.596.01696.04159.05855.03440 873.82 163 16.1. —_. —---— _..651 3.193.01696.08318.10014.02264 575.02 168 162.651. 3.193.01696.08318.10014.02515 638.88 160 163 1.532.798.03992.02079.06071.03699 939.42 158 164 1.532.798.03992.02079..06071.03807 966.90 131 166-,-. 1..-1532 1.596.03992.04159'.08151.03293 836.40 160 167 1.532 3.193.03992.08318.12310.02387 606.22 190 16 ___8..1.532 3.193.03992.08318.12310.02508 637.04 172 169.. 1.532 3.979.03992.10365.14357.02063 524.11 166 170_ -532_. 3,979.03992.10365...143_57.01970 500.31 137 A_71___________-16- 3..5__._.,798.08245.02079.10325.03274 831.70 134 172~. 3.165.798.08245.02079.10325.03217 817.00 131.1.._....._.. 3,165 1.596.08245.04159.12404.02775 704.91 126 174-__.__.__.3.165 1.596.08245.04159.12404.02713 689.12 119 175 __..3.165 3.193.08245..08318.16563.02071 526.14 101 U-.Z6-. 3.165_. 3.193.08245.08318.16563.02072 526.21 122 177 4.657.798.12133.02079.14212.02667 677.33 91 178 4.657.798.12133.02079.14212.02243 569.80 108 179__. 4.657 1.596.12133.04159.16292.02194 557.31 66

-157TABLE V ISOOCTAEE-WATER FLOW THROUGH BED OF 0.340 INCH SPHERES SUBSCRIPT (W) - WATER PHASE SUBSCRIPT (0) a ORGANIC PHASE LOG VIS(W) a -.30430E 01 +.16085E 04/T RHO(W) -.998 LOG VIS(O) - -.16086E 01 +.68994E 03/T RHO(O) -.692 VOIDAGE a.384 PACK DIA -.340 INT TENS - 49.500 PHOTOS - 2 CLASSES - L CODE GPM(W) GPM(O) FPS(W) FPS(O) FPSTOT DSAUT IN DSAUT MIC N 185.651.798.01696.02079.03775.09236 2346.01 39 186.651.798.01696.02079.03775.06959 1767.64 16 TABLE VI ISO6CTANE-ALKATERGE "C"-WATER FLOW THROUGH BED OF 0.40 INCH SPHERES SUBSCRIPT (W) a WATER PHASE SUBSCRIPT (0) a ORGANIC PHASE LOG VIS(W) - -.30430E 01 +.16085E 04/T RHO(W) -.998 LOG VIS(O) ~ -.16086E 01 +.68994E 03/T RHO(O) =.692 VOIDAGE a.384 PACK OIA a.340 INT TENS a 16.000 PHOTOS a 2 CLASSES = 1 CODE GPM(W) GPM(O) FPS(W) FPS(O) FPSTOT DSAUT IN DSAUT MIC N 209.651.798.01696.02079.03775.06067 1540.91 42 210.651.798.01696.02079.03775.05750 1460.52 30

APPENDIX F ESTIMATION OF INTERFACIAL TENSION EFFECT In order to decide whether interfacial tension can be neglected as a contributor to pressure drop, a comparison was made between the energy required to generate the interfacial area and the energy loss due to friction. Run 311 is used as an example. The conditions for this run were: Packing diameter = 0164 inches Porosity = 0o337 Water flowrate = lo53 gpm Isooetane flowrate = 160 gpm InSerfacial tenson =49 5 dynes/em The frictional pressure drop based on the'?single-phase r assumption (iLoe the mixture can be treated as a single-phase fluid with averaged physical properties) is 0.228 psi/ft of column length (Refer to Table I, Appendix G)o At a total flowrate of 3513 gpm, this pressure loss amounts to an energy loss of _. _ _psi gal 1 ft3 min in2 0.o2 x 3o13 -- x - x 60 x 144 1 ft min 7o48 gal hr ft2 825 ft lb/ft of column length hr The most conservative estimate that can be made concerning droplet formation is that the dispersed phase droplets are ormed. only once in one foot of packing and that no coalescence or redispersion -158

-159occurs. Based on this assumption the energy required to generate interfacial area can be computed as follows: drop size (Sauter mean diameter) = 0.033 in. (Table IV, Appendix E) surface area per 1.60 gal. of dispersed phase 1 ft3 6 in.= 5 1 ft2 1.60 gal x x x 12 511 ft2 7.48 gal 0.033 in. ft The term in brackets represents the ratio of surface area to volume for the dispersed phase. dynes -8 ft-lb surface energy = 511 ft2 x 49.5 m x 7.38 x 10 src9 dncm 75x dyne-cm x (30. 2 cm2 ft2 = 1.7 ft-lb/1.60 gal of dispersed phase rate of surface energy dissipation = 1.74 ft-lb x 1.60 gl x 60 min 1.60 gal min hr = 104 ft-lb/hr It should be noted that the surface energy dissipation rate amounts to approximately 12% of the frictional dissipation rate even with the conservative estimate of no coalescence and redispersion in one foot of packing. It should also be remembered that a certain amount of energy input is required to keep the dispersion from coalescing. It is obvious, therefore, that interfacial tension cannot be neglected in any correlation of two-phase pressure drop in packed beds,

APPENDIX G TABLE OF TWO-PHASE PRESSURE DROP CORRELATION PARAMETERS The following symbols are used in this Appendix: CODE = code number DELFA = 6f, average frictional pressure gradient, psi/ft DELFP = bfp, predicted frictional pressure gradient, psi/ft Pl-P2 DPDLA = 1 —-, average total pressure gradient, psi/ft ~~~1-ZPRAT PRAT = PRATIO = —, ratio of frictional pressure gradient bfp to predicted frictional pressure gradient PRATP = value of PRATIO predicted by Equation (80) RHOM = Pm, mean density RI = organic phase holdup WE = DpPmU Weber number a gc (The number notation XoXXXE YY is equivalent to X.XXXt0lOY) -160

-161CODE OPOLA RHOM OELFA DELFP PRAT WE RI PRATP 02118.4316.9057.0391.0162 2.4222.65693E 00.4974 1.6578 02218.4329.8803.0515.0294 1.7527.14844E 01.6673 1.5438 02318.4334.8679.0573.0456 1.2581.26442E 01.7179 1.3919 02418.44C7.9120.0456.0427 1.0680.31098E 01.3917 1.1738 02518.4685.8859.0846.0818 1.0341.66526E 01.611C 1.1989 02618.515e.8726.1376.1287 1.0692.11525E 02.7234 1.1567 02718.5827.8646.2081.1939 1.0730.17726E 02.7673 1.1200 0281F.7348.8531.3652.3906.9350.41836E 02.8906 1.0630 0291H.8699.8494.5019.5364.9357.61096E 02.8001 1.0548 0301H.4885.9386.0818.0810 1.0098.76865E 01.2355 1.0461 03118.5261.9132.1304.1310.9953.12880E 02.4383 1.0853 03218.5786.8976.1897.1874 1.0124.19402E 02.5589 1.0921 03318.6644.8870.2801.2532 1.1059.27254E 02.6357 1.0854 0341S.9053.8700.5283.4768 1.1079.55933E 02.7070 1.0581 0351F 1.C657.8632.6917.6746 1.0253.82416E 02.7344 1.0460 03618.5387.9504.1269.1321.9606.13650E 02.1752 1.0223 03718.5832.9278.1812.1907.9500.20351E 02.3342 1.0420 03811.6433.9125.2479.2585.9591.28382E 02.4630 1.0566 03911.7403.9014.3498.3291 1.0628.37742E 02.5370 1.0582 0401H.8495.8940.4622.3993 1.1574.46872E 02.6138 1.0591 0411h.9855.8822.6032.5802 1.0397.70600E 02.6823 1.0495 04218.5671.9278.1651.1856.8896.20351E 02.3506 1.0452 04318.5765.9278.1745.1846.9452.20351E 02.3451 1.0441 04418.4843.9386.0776.0810.9588.76865E 01.2519 1.0506 0521U.6319.9125.2365.2472.9571.28382E 02.4657 1.0571 0531U.6323.9125.2369.2472.9585.28382E 02.4548 1.0551 0541U.6341.9125.2387.2460.9704.28382E 02.4685 1.0575 05518.4391.9375.0329.0269 1.2212.18368E 01.2410 1.1162 05618.4391.9375.C329.0269 1.2212.18368E 01.2300 1.1091 05718.4719.9583.0567.0581.9753.55883E 01.1423 1.0314 05818.491C.9386.0843.0810 1.0410.76865E 01.2574 1.0522 05918.6398.9125.2444.2519.9702.28382E 02.4712 1.0580 06018.5531.9576.1382.18C1.7673.21312E 02.1642 1.0157 0611.5417.9708.1210.1483.8164.17706E 02.0875 1.0103 06218.6491.9376.2429.2452.9904.29523E 02.2903 1.0268 06318.7243.9231.3243.3183 1.0187.39062E 02.3945 1.0362 06418.8904.9076.4971.4465 1.1132.55770E 02.5C69 1.0423 06518.949e.8970.5611.5852.9588.74568E 02.5699 1.0409 0661F.8211.9773.3976.3643 1.0916.49933E 02.0497 1.0041 0671H.8672.9688.4474.4076 1.0978.55878E 02.0930 1.0053 068IH.9301.9544.5166.5009 1.0313.68766E 02.2026 1.0097 06911 1.C150.9427.6065.6015 1.0084.82983E 02.2656 1.0124 0701H 1.2135.9289.8110.7686 1.0552.10667E 03.3616 1.0169 0711S 1.1931.9741.7710.7801.9883.11222E 03.0930 1.0034 0721H 1.3674.9632.9500.9163 1.0368.13021E 03.1478 1.0046 0731H 1.5038.9538 1.0905 1.0461 1.0424.14953E 03.2190 1.0066 0741H 1.6046.9457 1.1948 1.1877 1.0060.17018E 03.2602 1.0077 07515.5824.8646.2077.1737 1.1958.17726E 02.7974 1.1187 07618.5951.9576.1802.1724 1.0454.21312E 02.1642 1.0157 077IH.8874.9076.4941.4339 1.1387.55770E 02.5151 1.0432 07818.4411.9120.0459.0386 1.1904.31098E 01.4082 1.1854 11418.4367.9057.0463.0347 1.3327.44582E 00.4029 1.6104 il1518.4627.8803.0813.0641 1.2676.10074E 01.6190 1.6538 11618.5604.8606.1874.1392 1.3462.28071E 01.8104 1.3720 11715.6327.8523.2634.2314 1.1382.55088E 01.8565 1.2340 1181I.8203.8462.4537.4005 1.1326.11218E 02.8996 1.1411 11918.4763.9375.0700.0576 1.2164.12465E 01.2389 1.1463 120CI.4997.9120.1046.0926 1.1293.21104E 01.4111 1.2388

-162CODE DPDIA IHOM DELFA DELIP PRAT WE1 R PRATP 1211h.9468.9125.5514.5488 1.0047.19261E 02.4658 1.0727 12218.5762.8859.1923.1756 1.0953.45148E 01.6299 1.2604 12318.6869.8726.3088.2777 1.1117.78211E 01.7119 1.1987 1241S.9273.8617.5539.4843 1.1438.14433E 02.7229 1.1361 12718.5475.9583.1323.1276 1.0362.37925E 01.1514 1.0424 12818.5771.9386.1704.1728.9858.52164E 01.2635 1.0687 12918.6678.9132.2721.2795.9737.87407E 01.4494 1.1128 13011.7998.8976.4108.4028 1.0198.13167E 02.5725 1.1214 1311H.9218.9125.5264.5406.9737.19261E 02.4604 1.0714 134IB.6387.9663.2200.2192 1.0037.73274E 01.0994 1.0196 13518.6838.95C4.2719.2155.9871.92632E 01.1978 1.0328 136I1.7907.9278.3886.4024.9658.13811E 02.3564 1.0591 1371h.9437.9125.5484.5563.9857.19261t 02.4713 1.0739 14018.7551.9708.3345.3280 1.0196.12016E 02.0830 1.0127 1411B.8057.9576.3908.3945.9906.14464E 02.1541 1.0188 14218.9375.9376.5312.54C8.9823.20035E 02.2990 1.0357 1461B 1.C142.9751.5917.5695 1.0391.22425E 02.0447 1.0064 1471B 1.C779.9649.6598.6533 1.0099.25729E 02.1213 1.0105 1481e 1.224S.9483.8140.8359.9738.33011E 02.2416 1.0192 1491 1.4447.9354 1.0394 1.0642.9766.41196E 02.3291 1.0264 1501- 1.8092.9207 1.4103 1.4030 1.0052.55088E 02.4248 1.0328 15111.996C.9125.6007.5589 1.0747.19261E 02.4686 1.0733 1521I 1.5174.9788 1.C933 1.1285.9688.47073E 02.0447 1.0041 1531h 1.6205.9714 1.1996 1.2433.9648.51809E 02.0857 1.0052 1541- 1.8047.9586 1.3893 1.4878.9338.61957E 02.1732 1.0086 15518.4626.88C3.C811.0613 1.3234.10u74E 01.6381 1.6710 1561H 1.303C.8531.9333.8357 1.1169.28391t 02.8049 1.0881 15718.5529.9583.1376.1261 1.0912.37925E 01.1404 1.0394 1581B 1.2764.8969.8878.8020 1.1070.29072E 02.6025 1.0782 1591S 1.4333.9076 1.0400.9977 1.0425.37848E 02.5205 1.0558 16018 1.C779.9649.6598.6524 1.0113.25729E 02.1158 1.0101 1611S 2.0077.8920 1.6212 1.5096 1.0739.59019E 02.6381 1.0529 1621- 1.1150.9231.7150.7093 1.0081.26509E 02.4057 1.0482 1631S 1.8062.8822 1.4239 1.2640 1.1265.47912E 02.7037 1.0639 1641S 1.1779.e83C.7953.6463 1.2306.21450E 02.6983 1.1052 165IS 1.5910.8700 1.2140 1.0740 1.1303.37959E 02.7283 1.0746 16618.6924.9504.2806.2782 1.0086.92632E 01.1978 1.0328 1671F 1.6493.8494 1.2812 1.1795 1.0862.41462E 02.8705 1.0652 1681- 1.3189.8531.9492.8419 1.1274.28391E 02.7776 1.0892 16918 1.4386.9076 1.0453 1.0011 1.0442.37848E 02.5123 1.0546 17018 1.2757.8969.8870.8036 1.1038.29072E 02.5943 1.0771 1711U.6807.9132.285C.2795 1.0197.87407E 01.4521 1.1138 17218.9748.9125.5794.5429 1.0673.19261E 02.4713 1.0739 2181B.5968.9057.2044.1667 1.2261.21504E 00.4200 2.0261 21918.7920.88C3.4105.2971 1.3817.48592E 00.6452 2.0667 22018 1.3295.8606.9566.6013 1.5909.13540E 01.8188 1.5828 2211S 1.89C3.8523 1.5210 1.0140 1.5001.26572E 01.8297 1.3792 2221H 2.2238.8462 1.8571 1.6505 1.1252.54111E 01.8623 1.2349 2231 2.5118.8446 2.1458 1.8766 1.1434.68289E 01.9165 1.1867 22418.6803.9375.2741.2562 1.0698.60126E 00.2544 1.2516 22518.e374.912C.4422.4029 1.0975.10180E 01.3657 1.3131 22618 1.284C.8859.9002.7351 1.2246.21777E 01.6180 1.4036 22718 1.7994.8726 1.4213 1.1080 1.2827.37726E 01.7130 1.3133 228IS 2.7618.8646 2.3871 1.7501 1.3640.58025E 01.7266 1.2406 2291S 2.3981.8683 2.0218 1.4081 1.4359.47175E 01.7700 1.2740 2301B.9582.9583.5429.5280 1.0283.18293E 01.1175 1.0530 23118 1.1075.9386.7008.7191.9746.25161E 01.2283 1.0888 23211 1.519C.9132 1.1233 1.1295.9945.42161E 01.4010 1.1491 2331- 2.0858.8976 1.6969 1.5844 1.0710.63512E 01.5583 1.1858 2341S 2.8338.8870 2.4495 2.0841 1.1753.89213E 01.6615 1.1766

-163COOB PDEDLA RHOM DEB DELP PATWE RI PRAP 2351H 1.2348.9663.8161.8007 1.0192.35344E 01.0778 1.0263 236h4 1.4129.9504 1.0010 1.0458.9572.44681E 01.1599 1.0406 2371H 1.6023.9380 1.1959 1.2691.9423.55106E 01.2002 1.0460 2381H 1.8433.9278 1.4413 1.5135.9523.66619E 01.2761 1.0631 2391H 2.4322.9125 2.0368 2.0257 1.0055.92908E 01.4281 1.1008 24018.7936.9507.3816.3779 1.0097.11358E 01.1582 1.0943 24118.9582.9282.5560.5403 1.0290.168848 01.2436 1.1243 24218 1.1173.9129.7217.7194 1.0033.23498E 01.3793 1.1968 24311 1.3257.9018.9350.9026 1.0358.31199E 01.4986 1.2497 2441H 1.8752.8867 1.4909 1.3221 1.1277.49865E 01.6343 1.2462 2455I 2.5989.8770 2.2189 1.7780 1.2479.72883E 01.7320 1.2090 24618.5983.9057.2059.1789 1.1507.215048 00.3955 1.9346 24718.7975.9507.3855.3940.9784.11358E 01.1582 1.0943 2481H 1.2424.9663.8237.8254.9979.35344E 01.0778 1.0263 24915 2.8262.8870 2.4419 2.1370 1.1427.89213E 01.6723 1.1784 25015 2.3412.8683 1.9650 1.4226 1.3813.47175E 01.7863 1.2726 2561U 1.3219.8606.9490.6402 1.4825.135408 01.7718 1.5968 2571U 1.3068.8859.9229.7940 1.1623.21777E 01.5815 1.3795 2581U 1.9547.8726 1.5766 1.1898 1.3251.37726E 01.6798 1.3072 2591U 1.7956.8523 1.4262.9905 1.4399.26572E 01.8366 1.3768 2601H 2.4701.8815 2.0881 1.6994 1.2287.606538 01.6139 1.2117 2611S 2.7694.8770 2.3894 1.9639 1.2167.728838 01.6470 1.1973 26215 2.1366.8704 1.7595 1.35CO 1.3033.42171E 01.6969 1.2899 2631S 2.7694.8646 2.3948 1.6627 1.4403.58025E 01.7409 1.2412 26418 1.0870.8679.7109.4603 1.5444.86558E 00.7154 1.7859 2651B 1.7198.8558 1.3490.8009 1.6844.19512E 01.8095 1.4671 2661S 1.8107.8498 1.4425 1.1899 1.2123.34586E 01.8566 1.3128 2671S 1.7994.8478 1.4320 1.3937 1.0275.43955E 01.8727 1.2638 26818.6419.9258.2408.2170 1.1095.38829E 00.3074 1.4365 26918.8154.8993.4257.3445 1.2356.73374E 00.4857 1.5936 27018 1.0377.8844.6545.4957 1.3204.11880E 01.5922 1.5650 27118 1.3045.8749.9254.6598 1.4026.175108 01.6625 1.4884 27218 1.5985.8684 1.2223.8368 1.4607.24228E 01.7122 1.4129 27315 1.9282.8635 1.5540 1.0161 1.5294.32033E 01.7492 1.3497 2741S 2.1896.8599 1.8170 1.2141 1.4966.40781E 01.7774 1.2995 2751S 2.3450.8569 1.9737 1.4179 1.3920.50907E 01.8005 1.2582 276IS 2.4625.8546 2.0922 1.6399 1.2758.61798E 01.8188 1.2260 2771B.7426.9453.3330.3007 1.1076.854018 00.1889 1.1373 27818.8856.9213.4864.4509 1.0786.13403E 01.3365 1.2316 27918 1.0514.9057.6589.6110 1.0785.19354E 01.4411 1.2809 28018 1.2840.8947.8964.7825 1.1455.26393E 01.5179 1.2920 28118 1.5607.8866 1.1765.9700 1.2129.34519E 01.5765 1.2820 28215 1.8903.88C3 1.5089 1.1704 1.2892.43733E 01.6224 1.2629 28315 2.2768.8754 1.8975 1.3803 1.3747.53868E 01.6590 1.2414 28415 2.6671.8713 2.2896 1.5965 1.4341.65425E 01.6900 1.2195 285IS 2.9248.8680 2.5487 1.8304 1.3924.77702E 01.7151 1.1998 30608 1.1025.8295.7431.0857 8.6752.923088-02.4745 9.8011 30708 1.3865.7806 1.0482.1378 7.6049.20893E-01.6521 8.6595 30808 1.8181.7574 1.4899.2044 7.2884.37227E-01.7404 6.6325 30908 2.2042.7438 1.8819.2821 6.6718.58233E-01.7930 5.2188 31008 1.0723.8932.6852.1762 3.8884.25708E-01.2620 2.8755 31108 1.3032.8419.9384.2455 3.8225.43670E-01.4312 3.8904 312CB 1.5682.8114 1.2166.3277 3.7132.663048-01.5388 4.0637 31308 1.8711.7912 1.5283.4242 3.6024.93610E-01.6126 3.8524 31408 2.2497.7769 1.9130.5322 3.5944.12559E 00.6662 3.5371 31508 2.2043.7769 1.8676.5167 3.6147.12559E 00.6662 3.5371 31608 2.5298.7662 2.1979.6351 3.4604.162248 00.7068 3.2257 317CB 1.0912.9205.6923.2585 2.6788.484568-01.1796 1.7758 318CB 1.2653.8743.8865.3422 2.5903.72288E-01.3222 2.3392 31908 1.4698.8437 1.1042.4389 2.5157.10079E 00.4250 2.6770

-164-. DPDLA RHOM DELFA DELFP PRAT WE RI PRATP 32008 1.7727.8219 1.4166.5485 2.5825,.133978 00.5014 2.7941 32108 2.0755.8055 1.7265.6728 2.5661,.17182E 00,.5602 2.7741 32208 2.4011.7928 2.0576.8083 2.5456.21434E 00.6067 2.6853 32308 1.1366.9364.7309.3677 1.9875.77931E-01,.1349 1.4288 32408 1.3032.8954.9152.4688 1.9522.10756E 00.2551 1.7393 32508 1.5985.8662 1.2232.6088 2.0093.14187E 00.3489 1.9951 92608 1.8484.8443 1.4825.7277 2.0374.18084E 00.4227 2.1550 32708.._2.1285.8273 1.7700.8664 2.0430,.22449E 00.4820 2.2291 32808 2.4238.8138 2.0712 1.0180 2.0345.27281E 00.5304 2.2418 32908 1.2199.9463.8099.5035 1.6086.111928 00.1083 1.2838 33008 1.3789.9095.9848.6178 1.5941.14699E 00.2120 1.4742 33108 1.5834,.8821 1.2012.7475 1.6070.18673E 00.2972 1.6549 33208 1.8256.8608 1.4527.8889 1.6342.231158 00.3670 1.7943 33308 2.1172.8437 1.7516 1.0434 1.6786.28024E 00,.4248 1.8852 33408 2.4238.8299 2.0642 1.2096 1.7066.33400E 00.4731 1.9337 33508 1.2729.9532.8599.6338 1.3568.15033E 00.0905 1.2074 _133iQL._. 1.4433.9199 1.0447.7634 1.3684.19063E 00.1814 1.3338 33708 1.6439.8941 1.2565.9074 1.3847.23560E 00.2592 1.4636 33808 1.8938.8735 1.5153 1.0617 1.4272.28524E 00.3248 1.5757 33908 2.1664.8568 1.7951 1.2318 1.4573.33956E 00.3803 1.6609 34008 1.5114.9628 1.0942.9599 1.1399.24629E 00.0669 1.1276 34108 1.7007.9349 1.2956 1.1173 1.1596.297258E 00.1389 1.1911 34208 1.9014.9122 1.5061 1.2893 1.1682.352898 00.2039 1.2615 34308 2.1399.8934 1.7528 1.4743 1.1889.413208 00.2613 1.3303 34408 1.7348.7574 1.4066.1842 7.6344.37227E-01.7404 6.6325 __45a. 2.2572.7769 1.9206.5013 3.8313.12559E 00.6662 3.5371 34608 1.1366.9205.7378.2463 2.9950.48456E-01.1796 1.7758 34708 1.5228.8662 1.1474.5754 1.9943.14187E 00.3489 1.9951 34808 2.0831.8437 1.7175 1.0259 1.6740.28024E 00.4248 1.8852 34908 1.2464.9532.8334.6203 1.3436.15033E 00.0905 1.2074 35008 1.6742.9349 1.2691 1.1075 1.1459.297258 00.1389 1.1911 37208.5211.8295.1617.0187 8.6543.19137E-01,.4834 6.7373 37308.5785,.7806.2402,.0317 7.5762.43314E-01.6627 5.9131 37408.7711.7438.4488.0694 6.4653.12073E 00.6923 3.6547 37508.8716.7286.5559.1216 4.5705.23689E 00.7883 2.7615 376CS.9208.7203.6087.1887 3.2263.39179E 00.8080 2.2732 __17_QS.........9738.7146.6642.2799 2.3729.60861E 00.9117 1.8517 37808 1.1366.7094.8292.4506 1.8404.10230E 01.9320 1.5923 37908 1.3789.7061 1.0729.6606 1.6242.15416E 01.9447 1.4465 38008.5229.8932.1359.0386 3.5150.53297E-01.3239 2.6329 38108.5561.8419.1913.0566 3.3786.905348-01.4171 2.7418 38208..6838.7912.3410.1040 3.2782.19407E 00.5102 2.4584 38308.8457.7662.5137.1658 3.0985.33635E 00.6838 2.3925 38405.9776.7512.6521.2422 2.6923.51738E 00.7473 2.0907 38505 1.0495.7404,.7287,.3443 2.1162.763138 00.8127 1.8372 38605 1.2237.7300.9074.5314 1.7077.12209E 01.8524 1.6020 3870S...1.4547.7233 1.1412.7573 1.5070.17828E 01.8782 1.4598 38808,.5278.9205,.1290.0628 2.0544.10046E 00.1914 1.5301 38908.5396.8743.1608,.0855 1.8801.14987E 00.3360 1.9064 39008.6549.8219.2988.1416 2.1099.277748 00.5143 2.1789 39108.8100.7928.4665.2127 2.1928.44436E 00.6180 2.0880 3920S 1.0382.7744.7026.3077 2.2837.64973E 00,.6854 1.9244 3930S 1.2047.7605.8752.4197 2.0855.92244E 00.7369 1.7596 394CS 1.3562.7467 1.0326.6224 1.6590.14206E 01.7888 1.5759 3950S 1.6060.7376 1.2865.8651 1.4870.20228E 01.8235 1.4520 39608.5505,9364.1447.0984 1.4706.16157E 00.1532 1.3078 39708,5911.8954.2032.1260 1,6128.22300E 00.2463 1.4465 39808.6970,8443,3311.1916 1.7280.374918 00.3888 1.6432 39908.8344.8138.4818,2719 1.7722,56558E 00.4820 1.6906 40008 1.0041.7934.6603.3667 1.8005,794998 00,6245 1.7640

-165CODE DPAU RHQO DOHZM Dlb~ RM Vsw RI PRATP 4010S 1.1744.7776.8375.4890 1.7129.10943E 01.6738 1.6616 4020S 1.4205.7613 1.0907.7070 1.5427.16325E 01.7340 1.5317 4C30S 1.6666.7503 1.3415.9636 1.3923.22744E 01.7753 1.4314 4C408.6025.9532.1894.1674 1.1315.31166E 00.0989 1.1399 40508.6411.9199.2425.2029 1.1951.39521E 00.1932 1.2281 4C6C8.7526.8735.3741.2869 1.3037.59136E 00.3385 1.3895 4C708.eeie.8429.5226.3823 1.3671.82625E 00.4414 1.4783 40808 1.0495.8211.6938.4943 1.4036.10999E 01.5171 1.5031 409CS 1.2123.8032.8643.6347 1.3616.14482E 01.5804 1.4886 410CS 1.5265.7842 1.1868.8804 1.3480.20599E 01.6496 1.4353 4110S 1.84C8.7707 1.5068 1.1642 1.2942.27749E 01.6990 1.3769 41208.6852.9628.2680.2547 1.0524.51059E 00.0840 1.0921 413C8.7322.9349.3271.2984 1.0962.61625E 00.1489 1.1298 414C8.8417.8934.4545.3973 1.1440.85663E 00.2632 1.2118 41508.9890.8640.6146.5113 1.2020.11358E 01.3437 1.2654 416C8 1.148C.8421.7831.6395 1.2245.14536E 01.4411 1.3358 417C8 1.3107.8236.9539.7992 1.1936.18510E 01.5083 1.3552 41805 1.6628.803C 1.3149 1.0826 1.2146.25361E 01.5814 1.3451 4190S 2.0263.7880 1.6848 1.3957 1.2072.33243E 01.6355 1.3175 420C8.8405.9721.4693.4540 1.0337.95202E 00.0511 1.0486 42108.9549.95C3.5431.5112 1.0625.10946E 01.1067 1.0676 42208 1.0798.9155.6831.6388 1.0694.14089E 01.2065 1.1120 423C8 1.2388.8889.8537.7812 1.0927.17620E 01.2889 1.1547 424C8 1.4281.8680 1.0520.9383 1.1212.21537E 01.3568 1.1888 42508 1.5985.8495 1.2304 1.1294 1.0894.26330E 01.4189 1.2141 4260S 1.9468.8280 1.5880 1.4500 1.0952.34409E 01.4928 1.2311 427C8 1.3221.98C1.8975.8906 1.0077.19967E 01.0329 1.0265 42808 1.3865.9641.9687.9724.9962.22012E 01.0707 1.0335 42908 1.5682.9370 1.1622 1.1462 1.0140.26393E 01.1435 1.0505 430C8 1.7613.9148 1.3649 1.3355 1.0221.31161E 01.2085 1.0691 43108.4677.8295.1C83.0178 6.0696.59205E-01.4679 3.7037 43208.5247.78C6.1864.0311 6.0032.13400E 00.5893 3.1933 433C8.7526.7438.4303.0686 6.2697.37350E 00.7248 2.3319 43408 1.C685.7286.7527.1206 6.2394.73286E 00.8673 1.8128 43508 1.4546.7203 1.1425.1875 6.0938.12121E 01.8852 1.5789 43608 1.8635.7146 1.5538.2788 5.5731.188298 01.9080 1.4237 43708.4799.8932.0929.0389 2.3907.16489E 00.2470 1.5413 43808.5193.8419.1545.0571 2.7062.28009E 00.4016 1.8114 43908.6554.7912.3125.1046 2.9889.60040E 00.5554 1.8044 44008.672C.7662.5400.1664 3.2445.10406E 01.7177 1.7012 441C8 1.1215.7512.7960.2433 3.2720.16006E 01.7883 1.5347 44208 1.4394.74C4 1.1186.3451 3.2412.23609E 01.8055 1.4158 443C8.4971.9205.0982.0639 1.5365.31079E 00.1782 1.2410 444C8.5342.8743.1553.0864 1.7973.46365E 00.3205 1.4165 44508.6409.8219.2848.1430 1.9914.85926E 00.4998 1.5601 446C8.8041.7928.4606.2141 2.1514.13747E 01.6053 1.5273 447C8 1.0382.7744.7026.3001 2.3416.20101E 01.6743 1.4529 44808 1.2691.76C5.9396.4122 2.2794.285388 01.7272 1.3747 44908 1.7044.7467 1.3809.6143 2.2480.43951E 01.7808 1.2855 45008.5233.9364.1176.0935 1.2580.49984E 00.1292 1.1292 451C8.5563.e954.1684.1208 1.3940.68989E 00.2322 1.2036 45208.6594.8443.2936.1864 1.5751.11599E 01.3790 1.3053 45308.8032.8138.4506.2667 1.6895.17498E 01.5215 1.3809 454C8.9927.7934.6490.3617 1.7940.24595E 01.6274 1.3791 45508 1.2161.7776.8792.4839 1.8170.33856E 01.6624 1.3236 45608 1.6136.7613 1.2837.7013 1.8305.50505E 01.7243 1.2622 457C8.5803.9532.1673.1632 1.0250.96420E 00.0895 1.0645 45808.6214.9199.2229.1989 1.1207.12227E 01.1800 1.1037 45908.7205.8735.3420.28C9 1.2173.18295E G1.3231 1.1790 461GC 1.C306.8211.6748.4894 1.3790.34028E 01.5026 1.2392 46208 1.2161.8032.8681.6303 1.3773.44805E 01.5670 1.2352 463C8 1.5905.7842 1.2511.8755 1.4291.63727E 01.6376 1.2121 46408C.6734.9628.2562.2508 1.0219.157968 01.0755 1.0427 46508.7282.9349.3231.2944 1.0972.19065E 01.1454 1.0626 466CB.8394.8934.4523.3950 1.1450.26502E 01.2618 1.1039 467CB.9814.864C.6070.5084 1.1939.35137E 01.3493 1.1345 46808 1.14C4.8421.7755.6370 1.2175.449718 01.4425 1.1668 46908 1.3373.8236.9804.7965 1.2309.57264E 01.4937 1.1686 47008 1.678C.8030 1.3301 1.0701 1.2430.78460E 01.5679 1.1661

APPENDIX H SUPPLEMENTARY BIBLIOGRAPHY In addition to the works listed in the reference list, a number of recent articles of general interest to the worker in the field of liquid-liquid and gas-liquid two-phase flow have appeared in the literature. Although these articles are not directly applicable to the present problem they may be of assistance in attacking related problems. For this reason this appendix lists these references without comment for the benefit of workers in the field. This list is by no means complete but should serve as a starting point for future worko Drop Behavior in Liquid-Liquid Systems 1o Elzinga, E, R., Jr., and J. To Banchero, "Some Observations on the Mechanics of Drops in Liquid-Liquid Systems," AIChE J., 7, 394 (1961)o 2. Garner, F. H., and A. H. P. Skelland, "Some Factors Affecting Droplet Behavior in Liquid-Liquid System," Chemo Eng. Sci, 4, 149 (1955). 3. Gibbons, Jo H., Go Houghton, and J. Coull, "Effect of a Surface Active Agent on the Velocity of Rise of Benzene Drops in Water," AIChE J., 8, 274 (1962). 4. Hughes, R. R., and E. R. Gilliland, "The Mechanics of Drops," Heat Transfer and Fluid Mechanics Institute, 1951, 53 (1951). 5. Johnson, A. I., and Lo Braida, "The Velocity of Fall of Circulating and Oscillating Liquid Drops Through Quiescent Liquid Phases," Can. JO Chem. Eng., 35, 165 (1957)o 6. Klee, A. J., and R. E. Treybal, "Rate of Rise or Fall of Liquid Drops," AIChE J., 2, 444 (1956). -166

1677. Krishna, Po Mo, Do Venkateswarlu, and Go So R.o arasimhamurty, "Fall of Liquid Drops in Water. Terminal Velocities," J. Chemo Eng. Data, 4, 336 (1959). 80 Krishna, Po M., Do Venkateswarlu, and Go S. R. Narasimhamurty, "Fall of Liquid Drops in Water. Drag Coefficients, Peak Velocities, and Maximum Drop Sizes," J. Chemo Engo Data, 4, 340 (1959). 9. Licht, W,, and Go S. Ro Narasimhamurty, "Rate of Fall of Single Liquid Droplets," AIChE J., 1, 366 (1955)o 10, Madden, Ao Jo, and G. Lo Damerell, "Coalescence Frequencies in Agitated Liquid-Liquid Systems," AIChE Jo, 8, 233 (1962). 11o Satapathy, Ro, and Wo Smith, "The Motion of Single Immiscible Drops Through a Liquid," Jo Fluid Mecho, 13, 561 (1961). 12. Warshay, Mo. Eo Bogusz, Mo Johnson, and Ro C. Kintner, "Ultimate Velocity of Drops in Stationary Liquid Media," Can. J. Chem. Eng., 37, 29 (1959). Slip Velocities in Vertical Moving Systems 1o Beyaert, B.o 0, Lo Lapidus, and. J. Co Elgin, "Th.e Mechanics of Vertical Moving Liquid-Liquid Fluidized Systems o IEo Countercurrent Flow," AIChE J., 7, 46 (1961), 20 Lapidus, Lo, and Jo C. Elgin, "Mechanics of Vertical-Moving Fluid. ized Systems," AIChE Jo, 39 63 (1957)o 35 Price, Bo Go, Lo Lapidus, and Jo C. Elgin, "Mechanics of Vertical. Moving Fluidized Systems," AIChE Jo 59 93 (1959) 4. Quinn, Jo Ao, Lo Lapidus, and Jo Co Elgin, "The Mechanics of Moving Vertical Fluidized Systems~ Vo Cocurrent Cogravity Flow," A.IChE Jo, 7, 260 (1961), 5. Struve, Do L., Lo Lapid.us, and Jo C. Elgin, "The Mechanics of Moving Vertical Fluidized Systems o IIIo Application to Cocurrent Countergravity Flow," Cano J. Chem. Engo 36, 141 (1.958) Operating Characteristics and Flooding in Countercurrent Packed Columns 1. Bain, Wo Ao, Jro, and 0o Ao Hougen, "Flooding Velocities in Packed Columns," Transo AIChE, 40, 29 (1944).

-1682o Baker, T., To Ho Chilton, and. Ho Co Vernon, "The Course of Liquor Flow in Packed Towers," Trans. AIChE, 31, 296 (1935) 30 Bertetti, Jo W., "Theoretical Flooding Velocities in Packed Columns,' Trans. AIChE, 38, 1023 (1942)o 4. Eduljee, Ho Eo "Pressure Drop, Loading and Flooding in Irrigated Packed Towers," Brito Chemo Engo, 5, 330 (1.960)o 5. Elgin, Jo Co. and Fo Bo Weiss, "Liquid Holdup and. Flooding in Packed Towers " Indo Engo Chem., 31, 435 (1939)o 6. Fan, Lo, "Pressure Drop of Single Phase Flow Through Raschig Ring Type Tower Packings Effect of Hole Size," Can. J. Chemo Eng, 38, 138 (1960). 7o Frantz, To Fo, and. Ko Io Glass, "Pressure Drop and. Flooding Velocities for 1/4 Inch Berl Saddles," J. Ch.emo Engo Data, 7, 147 (1962). 80 Furnas, Co Co and F. Bellinger, "Operating Characteristics of Packed Columns," Trans. AIChE, 34, 251 (19358) 9o Gardner, Go C0 "Holdup and Pressure Drop for Water Irrigating'Non-Wettable Coke," Chemo Engo Sci.o, 5 101 (1956)o 10. Hillg So, "Channelling in Packed Columns," Chemo Engo ScSo, 1, 247 (1952)o 11o Hwa, Co S., and Ro Bo Beckman, "Radiological Study of Liquid Holdup and Flow Distribution in Packed Gas-Absorption Column.s AIChE J0 6, 359 (196o). 12. Lerner, Bo Jo, and C. S. Grove, Jr., "Critical Conditions of Two= Phase Flow in Packed Columns," Indo Eng. Chemo, 435 216 (1951)o 13o Lobo, W. Eo. L Friend, F. Hashmall, and Fo Zenz, "Limiting Capacity of Dumped Tower Packings," Trans0 AIChE, 41, 693 (1945)o 14. Piret, E. Lo, C. Ao Mann, and T. Wall, Jro. "Pressure Drop and Liquid Holdup in a Packed Tower," Ind. Eng. Chem.o 32, 861 (1940)o 15. Sakiadis, Bo Co0 and. Ao I. Johnson, "Generalized Correlation of Flooding Rates," Indo Engo Chem., 46, 1229 (1954). 16. Schoenborn, Eo Mo, and W. J. Dougherty, "Pressure Drop and. Flooding Velocity in Packed Towers with Viscous Liquids' Trans~ AIChE 40, 51 (1944). 17. Turner, G. Ao, and Go Fo Hewitt;, "The Amount of Liquid Held at the Point of Contact of Spheres and the Static Liquid. Holdup in Packed Beds," Trans. Instn. Chem. Engo (London, 357 529 (1959).

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IVERSITY OF MICHIGAN \I~II 111I111 - 1703 9015 03695 4306 j-o 1emet, A. Go, "Flow of Gas-Liquid Mixtures in Vertical Tubes," Indo Engo ChemO, 53, 151 (1961). 14. Nicklin, Do Jo, Jo O0 Wilkes, and. J. Fo Davidson, "Two-Phase Flow in Vertical'Tlbes" T rans. Instn. Chem. Eng. (London), 40, 61 (1962). 15. Reid., Ro C., Ao Bo Reynolds, Ao Jo Diglio, Io Spiewak, and Do Ho Kliptein, "Two-Phase Pressure Drops in Large-Diameter Pipes,t AIChE Jo, 3, 321 (1957). 16. Sobocinski, Do P., and Ro Lo Huntington, "Cocurrent Flow of Air, Gas-Oil, and Water in a Horizontal Pipe," Trans. ASME, 80, 252 (1958). 17. Vohr, J., "The Energy Equation for Two-Phase Flow," AIChE Jo, 8, 280 (1962)o 18o White, P. D., and Ro Lo Huntington, "Horizontal Co-Current TwoPhase Flow of Fluids in Pipe Lines," Petr. Eng., 27, No. 9, D_40 (1955). 19, Wicks, Moye, III, and Ao E. Dukler, "Entrainment and Pressure Drol in Cocurrent Gas-Liquid Flow: I. Air-Water in Horizontal Flow," AIChE Jo, 6, 463 (1960). 20. Zuber, N., "On the VariablesDensity Single Fluid Model for TwoPhase Flow," Jo Heat Transo, 82, 255 (1960)O