THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING MASS TRANSFER BETWEEN ISOBUTANOL AND WATER IN CONCURRENT FLOW THROUGH A PACKED COLUMN James A. Leacock A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1960 March, 1960 IP-425

ACKNOWLEDGMENTS The author wishes to express his appreciation of all the assistance given him over the course of this work, especially that of Professor Stuart W. Churchill, his committee chairman, and Professors L. 0. Case, K. F. Gordon, D. R. Mason and R. R. White, members of the committee. The Union Carbide Chemicals Company very generously donated the large amount of isobutanol required for the study. Dr. George Clark, Dr. Bruce Bray and John Chen offered many workable suggestions. Finally, the author wishes to express his appreciation to the Industry Program of the College of Engineering for their work in reproducing this thesis,

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS........................................... ii LIST OF TABLES.................................................. v LIST OF FIGURES.............................................. vi NOMENCLATURE.....i...................................... vviii ABSTRACT..................................................... x I. INTRODUCTION.......................................... II, RATIONALIZATION FOR CORRELATION OF DATA.................. 3 III. EXPERIMENTAL PROGRAM................................ 6 A. Introduction...................................... 6 B. Experimental Equipment............................ 7 C. Experimental Conditions............................... 11 D. Experimental Procedure................................ 12 IV. RESULTS OF THE VARIABLE COLUMN LENGTH EXPERIMENT.......... 16 V. THE CONTRIBUTION OF THE RECEIVER TO TOTAL TRANSFER....... 22 A. Estimating the Receiver Effect Experimentally........ 23 1. Experimental................................... 24 2. Experimental Results............................. 25 3. Procedure for Estimation of Internal Column Phase Indices of Reraction..................... 34 B. Discussion......................................... 40 VI. THE INDIVIDUAL PHASE TRANSFER COEFFICIENTS................44 VII. DISCUSSION OF RESULTS.................................. 46 VIII. CONCLUSIONS............................................55 APPENDIX A. ORIGINAL VARIABLE COLUMN LENGTH DATA.............. 56 APPENDIX B. VARIABLE COLUMN LENGTH DATA CORRECTED TO NOMINAL FLOW RATES..................................... 63 iii

TABLE OF CONTENThS CONT'D APPENDIX C. ORIGIINIAL RECEIVER EFFECT EXPERIMEINTAL DATA... APPENDIX D. CALCULATION OF TBE PRA.SE TRANSFER COEFFICIENITS..... APPENDIX E. REFRACTIVE INDEX CALIBRATION WATERA D ISOBUTANOL... BIBLIOGRAPHY......................... Page 70 79 91 95 iv

LIST OF TABLES Table Page I Scheme of Nominal Flow Rate Variation for Experimental Runs.................................................. 13 II Summary - Estimation of Internal Column Refractive Indices..................... 35 III Calculation of Water Phase Transfer Coefficients........ 82 IV Calculation of Isobutanol Phase Transfer Coefficients.,. 85 V Incremental Water Phase Transfer Coefficients........... 88 VI Incremental Isobutanol Phase Transfer Coefficients...... 89 VII Summary of Average Individual Phase Transfer Coefficients................................................ 90 VIII Index of Refraction - Weight Fraction Calibration for the Water - Isobutanol System........................ 92 v

LIST OF FIGURES Figure Page 1 Schematic Diagram of Equipment.......................... 8 2 Column Inlet Flange and Column and Receiver Assembly.... 9 3 Procedure for Correcting Data to Nominal Flow Rates.... 17 4 Water Phase Data Corrected to Nominal Alcohol Rates, 4-Inch Column.......................................... 18 5 Water Phase Data Corrected to Nominal Alcohol Rates, 6-Inch Column.......................................... 19 6 Alcohol Phase Data Corrected to Nominal Alcohol Rates, 2-Inch and 6-Inch Columns.......................... 20 7 Water Phase Data, 1-Inch Column, Corrected to Nominal Isobutanol Rates.................................. 26 8 Isobutanol Phase Data, 1-Inch Column, Corrected to Nominal Isobutanol Rates............................... 27 9 Inlet vs. Outlet Water Phase Refractive Indices, 1-Inch Column......................................... 30 10 Inlet vs. Outlet Water Phase Refractive Indices, 1-Inch Column..................51....... 31 11 Inlet vs. Outlet Isobutanol Phase Refractive Indices, 1-Inch Column.......................... 32 12 Inlet vs. Outlet Isobutanol Phase Refractive Indices, 1-Inch Column,........................................ 33 13 Receiver Effect Estimation Curves, Water Phase.......... 36 14 Receiver Effect Estimation Curves, Water Phase......... 37 15 Receiver Effect Estimation Curves, Isobutanol Phase.*... 38 16 Receiver Effect Estimation Curves, Isobutanol Phase..... 39 17 Incremental Water Phase Transfer Coefficients.......... 48 18 Incremental Isobutanol Phase Transfer Coefficients...... 49 vi

LIST OF FIGURES CONT'D Figure Page 19 Averaged Water Phase Transfer Coefficients.............. 51 20 Averaged Isobutanol Phase Transfer Coefficients......... 52 21 Equal Area Calculation of Water Phase Transfer Coefficient............................................ 83 22 Equal Area Calculation of an Isobutanol Transfer Coefficient.......................................... 87 23 Index of Refraction Calibration for Water Phase,........ 93 24 Index of Refraction Calibration for Isobutanol Phase.... 94 vii

NOMENCLATURE a interfacial area for mass transfer, area per unit column volume Ca - molal concentration of component a in the P phase, moles per unit volume C - molal concentration of a in the saturated P phase, moles per unit volume Capi - molal concentration of a at the interface of the P phase, moles per unit volume H - total height of packing, unit length - local transfer coefficient for the component a in the P phase, unit length per time k local transfer coefficient for the component a in the P phase, reciprocal time k - mean transfer coefficient for the component a in the P phase, reciprocal time L moles of water-rich phase flowing, moles per time Lo - inlet moles of water-rich phase, moles per time L - mass of water-rich phase flowing, mass per time N - number of moles of component a transferring per unit time, per unit area S - cross-section of empty column, area V - moles of isobutanol-rich phase flowing, moles per time V - inlet flow of the isobutanol-rich phase, moles per time V - mass of isobutanol-rich phase flowing, mass per time VR - unit volume of empty column - mole fraction of component a in the L phase - mass fraction of component in the L phase viii * * Vlll

y - mole fraction of component a in the V phase Ya - mass fraction of component a in the V phase Z - internal height in the column, length Subscripts A - denotes f - denotes L denotes o - denotes V - denotes W - denotes isobutanol component a final condition the water-rich phase an initial condition the isobutanol-rich phase water component ix

I. INTRODUCTION Industrial liquid-liquid extraction is ordinarily carried out in countercurrent packed or spray columns or in equipment of the mixersettler type. Countercurrent columns allow continuous contacting of the liquid phases but the throughput of this type of column is seriously limited by the low flow rates obtainable using fluid density as the driving force. Mixer-settler equipment is bulky and expensive and is inefficient unless care is taken in the mixing and. settling. In this study, mass transfer between two liquid phases is investigated with the two phases flowing coricurrently through a packed bed. The packed bed serves the purpose of dispersing the two phases, thus creating a very large interfacial area for mass transfer. Since the flow rates of the two phases are restricted only by the allowable pressure drop across the bed, large mass rates per unit cross sectional area can be handled. The phases leaving the column can be expected to approach equilibrium compositions as the length of the column is increased, i.e., the process becomes equivalent to a single equilibrium stage. A multistage operation can be simulated by a number of concurrent units operated in series, with the flow of extract and raffinate being countercurrent from unit to unit. Most commercial applications of liquid extraction involve two relatively immiscible solvents and a distributed solute. The mass transfer process then involves three components, two transferring in one direction and the third in the opposite direction. Colburn and Welsh(l) suggested for fundamental investigations of mass transfer between liquid phases that -1 -

-2 - the solute be eliminated and transfer limited to two relatively immiscible solvents into one another. When the system is thus restricted, evaluation of the individual phase mass transfer coefficients is possible. This scheme has been used in numerous studies of mass transfer coefficients in countercurrent packed and spray columns and other special types of contacting equipment. Investigations of two component liquid systems in countercurrent packed columns include that of Colburn and Welsh with isobutanol-water; Laddha and Smith(5) with isobutyraldehydewater and 3 pentanol-water: Gayler and Pratt(2) with ethyl-acetate-water; Smith and Beckman with methyl isobutyl carbinol-water and methyl ethyl ketone-water. The isobutanol-water system was utilized by Ruby and Elgin(7) and Heertjes, Holve and Talsma(4) in investigating transfer in countercurrent spray columns and by Gordon and Sherwood(3) and Lewis(6) in special transfer cells. No mention has been found in the literature of any investigations of mass transfer, in liquid systems, in a packed bed with concurrent flow, with either two or three components. The isobutanol-water system was chosen for this investigation because of the prior work with other types of flow and because of experimental and analytical convenience. Transfer was investigated as a function of bed height and individual phase flow rates, in upward flow through a column packed with glass beads. Only one column diameter (2 inch) and one bead size (3 mm) were utilized.

II. RATIONALIZATION FOR THE CORRELATION OF DATA The steady state transfer of a component a between two liquid phases is generally taken to be proportional to a transfer coefficient times the concentration difference of a between the bulk and the interface of either of the phases, Na = kav(Cav - Ci) = kaL(CaLi - CaL) (1) where Na = the rate of transfer of a, moles per unit time per unit area for transfer, CaL, CaV = the bulk concentration of a in the L and V phases, moles per unit volume. C A, Ca the concentration of a at the interface of the L and V Li i phases, moles per unit volume, k L k = the individual phase mass transfer coefficients of the atl aV component a in the L and V phases, unit length per unit time. Interfacialconcentrations are difficult if not impossible to measure. Therefore, the interface is assumed to be in static equilibrium, Ca = mCaL (2) where m is usually some function of temperature, pressure and concentration. If the system under consideration is only two component, Equation (2) is completely determined at any given temperature and pressure. These concentrations will be those of the mutually saturated phases, C and C aV aL -35 -

-4 - For the system isobutanol-water, the equation for transfer, Equation (1),, can be written (where L becomes the water-rich phase and V the isobutanol-rich phase) for water transferring, NW kw(CW-CW)= W-kWL(CWL C-WL) (5) and for isobutanol transferring, -N = kV(CA-C) = -kAC L-(C AL (4) The rate of transfer of the component a can be equated to the rate of longitudinal transport of component a in the two phases, d(Lxa) -d(Vya) N = = - -(5) adVR adVR where L, V = the number of moles flowing in the L and V phases per unit time, x, y = the mole fraction of a in the L and V phases, a = the interfacial area for mass transfer per unit column volume, VR = unit volume of the column without packing. For example, the rate of transfer of water into the isobutanolrich phase can be written, d(VYw) - k * -cv) (6) aSdZ where V = the number of moles flowing in the isobutanol-rich phase per unit time, SdZ = the unit volume of the column, S = the cross section of the empty column, Z = the unit height of column, C = the static equilibrium concentration of water in isobutanol, WV

The interfacial area for mass transfer between the liquid phases in a packed column is extremely difficult to measure directly or even to estimate. However, it can be grouped and measured in combination with the phase transfer coefficient as (ka), i.e., as a volumetric coefficient k' Theinal form of the transfer equation to be used to represent the data is then, for example, for water transferring, From an an expression for ) = kV(C V-C) (7) overall and a component material balance around the column, L or V can be derived. Since dL = -dV or (vy01), - vyc, = LXce - (Lxcxo and L + V = Lo + V there results (Vya)o + (L)o - xa(Lo + Vo) V = -. (8) (ya - X) From Equation (8), it is seen that once the xc( and yc are known as a function of height in the column, Equation (7) is completely determined, and the phase transfer coefficients k? can be computed as a function of height. ap

III. EXPERIMENTAL PROGRAM A. Introduction As implied in the preceding section, the experimental problem is to determine phase concentrations as a function of height in the packed columno Internal sampling or analysis of the phases as they rise in the column would be the preferred solution of the problem, but were ruled out as experimentally unfeasible. Instead, the outlet phase streams of a series of columns of different packed heights were sampled and analysed. Sampling the outlet streams is in itself a difficult problem due to the necessity of separating them. The separation was accomplished with a receiver-settler placed on the top of the column. This posed the problem of estimating the amount of transfer which takes place in the outlet tube and settler, The experimental work then took on two aspects: (1) Determining the receiver outlet concentrations with a series of columns of different packed heights as a function of the individual phase flow rates, and (2) estimating the mass transfer which takes place in the outlet tube and receiver as a function of the phase flow rates and the receiver outlet concentrations. This latter transfer will be called the receiver "end effect." What follows treats in detail the first aspect, determining receiver outlet concentrations for the various column lengths. The end effect is treated separately in a subsequent section. -6 -

B. Experimental Equipment The equipment used to carry out the determination of the receiver outlet phase concentrations of the various column lengths is shown in a schematic diagram in Figure 1, the main fixtures of which are (1) the feed reservoirs, (2) the proportioning pumps for the feed streams, (3) the column inlet packing gland, (4) the glass column with packing, (5') the receiver-settler. The feed reservoirs were four foot long sections of 100 mm diameter Pyrex glass tubing, dished at the bottom and fitted with a glass ball joint. A side arm riser of 10 mm diameter glass tubing was attached to this to facilitate reading the liquid level in the larger tubes. Behind the side arm riser was placed a meter stick, and flow rates were determined by reading the height of the liquid level in the riser before the pumps were turned on and after they were turned off. The pumps used to move the isobutanol and water to the column were Milton Roy proportioning pumps of approximately 5.5 gals/hr capacity. They were of stainless steel construction. A brass ball and spring check valve was fitted into the pump outlets to neutralize the head of liquid in the reservoirs so that the feed came through the pump only on the forward stroke of the plunger. The feed pulses were then successfully dampened by placing 1000 ml Pyrex round-bottom flasks in the outlet lines as partially air-filled surge vessels. The column inlet packing gland was turned out of aluminum bar stock. As indicated in Figure 2, the alcohol and water feed lines led

-FEED I IO I IILTON ROY TEMPERATURE Figure 1. Schematic Flow Diagram of Equipment.

-9 - BOTTOM FLASK 16 MESH SS. SCREE RUBBER TUBINGCOPPER WIRE 1/2 ID. GLASS TUBE BEADS - RUBBER GASKET -16 MESH SS. SCREEN. 1/4" PIPE THREAD FOR FEED INLET. Figure 2. Column Inlet Flange and Column and Receiver Assembly.

-10 - separately to either side of the base of the flange, went as far into the base as the middle and then, still separately, made a right angle turn to go up through the remainder of the flange to the bottom of the column. The flange and column connection was made pressure tight by a bolted compression fitting with a hard rubber gasket 2" O.D x 3/4" I.D. x 1/4" The column was 1/2" I.D. Pyrex gauge glass cut to the desired height. To keep the packing in place while handling the column, the bottom of the column was closed with a piece of 16 gauge stainless steel screen, the screen being held to the glass by a black, de Kotinsky-type cement which was insoluble in isobutanol. The packing was made up of fairly uniform 3 mm glass spheres. Of the various receivers that were tried, a round bottom flask with a short hooked side arm at its equator, as shown in Figure 2, was found to be the most satisfactory. Two different sizes, a 200 ml and a 500 ml, were used. The level of the phases in the receiver were controlled manually by adjusting the flow of the water phase through a stopcock in an outlet at the base of the flask. The alcohol phase then overflowed through an outlet in the neck of the flask. The water and alcohol phase samples were taken off in 1 oz. screw cap bottles at these two points. The inlet feed streams were kept at a fairly constant temperature by using a crude coil-in-box type constant temperature bath on each feed line. The temperature of the bath was maintained manually by adjusting the proportions of hot and cold tap water which made up the cooling water of the bath.

-11 - Copper tubing, 1/4" diameter, was used throughout the equipment for the flow lines. All the valves in the equipment were either brass Hoke toggle valves or brass Hoke needle valves. The receiver was attached to the column by a piece of rubber tubing, tightened down to the column and receiver side arm ends by copper wire. C. Experimental Conditions A column diameter of 1/2" was chosen so that fairly high mass velocities could be attained without using unreasonable amounts of isobutanol. Commercial grade isobutanol was used as received and was obtained from the Carbon and Carbide Chemicals Company. Its index of refraction was 1.39382, which agrees substantially with values published in other studies. Distilled water was used for the water phase. It was necessary to acidify the water to 0.0001 N HC1 in order to avoid incurring an emulsion. The phases separated very quickly when the water was acidified. Bed heights of 1", 2", 4" and 6" were used. A temperature of 25~C + 0.5~C was maintained throughout the work. The inlet streams were always the pure components. The flow rates of the inlet phases were determined by convenient percentages of the total plunger stroke of the proportioning pumps. The water rate was varied in five steps from approximately 35700 to 20,000 gms/hr, and the isobutanol rate also in five steps from approximately 2,200 to 16,600 gms/hr. The highest flow rates corresponded to about 5/6 of the total stroke and the lowest about 1/10. The flow rates corresponded to 6,000 to 52,000 lbs/(hr)(ft)2 in the water phase and 3,500 to 27,000 lbs/ (hr)(ft)2 in the isobutanol phase.

-12 - D. Experimental Procedure The four columns, with wire screens cemented in place at the bottom, were filled with glass beads until there was no looseness apparent when the tubes were shaken. After a column was filled with beads, a stainless steel screen was placed on the top and held in place by a piece of rubber tubing, the same rubber tubing which served to connect the column with the receiver side arm. A column was made up only once and was stored in distilled water when not in use. This was an attempt to avoid variations in the packing arrangement of each column. The porosity of the columns ranged from 0.36 for the 1" column to 0.34 for the 6" column. The receiver was placed on the top of the column and was adjusted to a position held during all the runs by means of three marks on the equator of the flask which indicated when the receiver was in a level position. In this way, the phases always entered the receiver in the same way. The interface between the separated phases was adjusted to the marks on the flask equator and was held there by adjusting the flow of the water phase leaving the receiver. This eliminated variations in phase residence time and interfacial area. For a given bed height, the experimental data were obtained in the following manner. With one of the receivers in place, a water flow rate was fixed, and receiver outlet phase samples were taken for a series of isobutanol flow rates, with each isobutanol rate being a separate run. The water flow rate was then changed and receiver outlet phase samples were taken varying the alcohol rates again. This was continued for a

-13 - number of water rates. The second receiver was then put in place and the procedure repeated with appropriate flow rates. In general, the larger receiver was used to handle the higher flow rates and the smaller receiver the lower flow rates. Some flow rates were established in both receivers for purposes of comparison. The pump stroke settings were not finely adjusted after the initial coarse setting. Each flow rate corresponded to a certain pump stroke length. Since the flow rates could be reproduced within 5% with the coarse setting, no further adjustment was made. The data obtained were ultimately adjusted graphically to nominal flow rates (those which minimized the adjustment). The system of nominal flow rates used to obtain the variable column length data is indicated in Table I. TABLE I SCHEME OF NOMINAL FLOW RATE VARIATION-APPROXIMATE FLOW RATES IN lbs/(hr)(ft)2 Large Receiver Small Receiver Water Isobutanol Water Isobutanol 12,000 13,000 18,000 6,800 19,000 13,000 27,000 3,500 18,000 27,000 12,000 3,500 19,000 6,800 13,000 13,000 25,0 1000 16,000 6 13,000 6,800 19,ooo 19,000 6,800 27,000 3,500 32,000 27,000 19,000 13,000 6,800

-14 - Sampling from the two phases took place at their outlets in the neck and bottom of the receiver and consisted of filling one 1 oz. screw cap bottle with the water phase and another with the alcohol phase. When the receiver and column were in place, the inlet line constant temperature baths at the correct temperature and the pumps set for the desired water and isobutanol rates, the liquid levels of the feed reservoirs were read, and the pumps were started. After the phases filled the receiver, the water phase level was set at the marks at the receiver equator by adjusting the flow through the stopcock in the water outlet line. After this level was steady, the system was allowed to come to steady state before any samples were taken. This waiting time corresponded to the approximate time it would take the phases to replace themselves 7 to 10 times in the receiver. This time was estimated by taking a series of samples from the large receiver when both the water and isobutanol flow rates were fairly low. It turned out that after a replacement of about 4 times, there was no change in the outlet phase compositions. The replacement time of 7-10 was used, however, as a conservative estimate. After the samples were taken, the pumps were turned off and the liquid levels of the feed reservoirs again read, The exact flow rates were obtained from calibration curves of height of liquid in the reservoir vs, weight, the difference in the two readings being the weight of the liquid pumped. The time of the run was determined with a stop watch. The phase samples were analysed for composition by measuring the refractive index with a Bausch and Lomb Precision Refractometer. The refractive index of a sample could be determined easily within + 0.00005

-15 -units. Calibration curves for phase composition in weight percent of water vs. index of refraction are presented in Figures 23 and 24 in Appendix E. The addition of the small amount of HC1 to the distilled water did not change the index of refraction readings for a given composition nor the values of the equilibrium compositions.

IV. RESULTS OF THE VARIABLE COLUMN LENGTH EXPERIMENT The original data obtained with the four column heights 1", 2", 4" and 6", with the inlet feeds being pure components, are tabulated in Appendix A. The data consist of inlet phase flow rates and indices of refraction of the receiver outlet phases (water-rich and isobutanol-rich). The flow rates obtained by the coarse pump adjustment were usually very close to the nominal rates tabulated in Table I. Small deviations were handled by the following procedure. A plot of outlet phase index of refraction vs. alcohol inlet rate at the fixed inlet water rate was first made. This plot established the dependence of the index of refraction of the outlet phase on inlet alcohol rate (at the constant inlet water rate) and was used to adjust the index of refraction of the outlet phase (water-rich or isobutanol-rich) to what it would have been if the inlet alcohol rate had been the nominal rate included in Table I. This procedure, which is illustrated graphically in Figure 3, retained the identity of the data points which cross-plotting would not do. When the adjustment of the receiver outlet indices of refraction was carried out for the alcohol rate, the adjusted points were plotted against water rate at the nominal alcohol rates. Examples of these plots are shown as Figures 4, 5 and 6. Outlet water phase refractive indices from a 4" and a 6" column are shown in Figures4 and 5 respectively. Outlet isobutanol phase refractive indices are shown for a 2" and a 6" column

1.3390 LU -r a. Iw ILJ 0 Lo LU 0 z LL. 0 0 z Q 1.3380 1.3370 1.3360 1.3350 1.3340 I X-CORRECTED DATA POINTS / -ORIGINAL DATA POINTS i i i i i i ~ I i i -i-i I FI 30 2000 4000 6000 8000 10000 120( ALCOHOL INLET RATE, Gms/Hr Figure 3. Procedure for Correcting Data to Nominal Flow Rates.

x w z w cr I LL CO 4 J w 0. LJ cn w I aw _J I-. 0 ILr 0 1.3410 1.3400 1.3390 1.3380 1.3370 _______WATER PHASE REFRACTIVE INDEX VS. WATER RATE CONSTANT ALCOHOL RATES 0 A FOR 4" COLUMN 0 0 - A i J O E I ~ 4 I X t x, X ALCOHOL RATES A -16600 gms/hr. 0-12000 * 0 - 8,000 X - 4,200.. * 2 00 1.3360 1.3350 3000 5000 7000 9000 11000 13000 15000 17000 19000 WATER RATE gms/h. Corrected to Nominal Alcohol Rates, 4-Inch Column. Figure 4. Water Phase Data

1.3420 -- I QV0 -aX - 0 ALCOHOL 'i.. RATES...... 16600 12000 8000 4200 2200 Gr/Hr If x w Ca z W 1.3410 I u LL w i 1.3400 (n I a. ct: w: 1.3390 I — -J I — 0 c- 1.3380 w LJ w 1.3370 V -- -"-a ------- Y ---------- -V ---- --- - v -------- " ' ~ 0 0 X x 0 13 El 8 0 x ~ X x II mX I I',o i 3000 5000 7000 9000 11000 13000 15000 17000 19000 21000 WATER RATE, Gms/Hr Data Corrected to Nominal Alcohol Rates, 6-Inch Column. Figure 5. Water Phase

1.3940 x I w Z 1.3930 Vw 0 I- 2" COLUMN W 0 o [ 0 < 1.3890 - -2200 WATERNOMINAL ISOBUTANOL RATES gm/hr Figure 1.39006. Alcohol Phase Data Corrected to Nominal Alcohol Rate -Inch and 6-Inch Colns _ —_ 8000 1.3890 ~ --- 0 ~ — 2200 ~ ------------------------------- WAL IATES gm/hr

-21 -in Figure 6. The points on these plots were then adjusted to the nominal water rates, These doubly adjusted data points are tabulated in Appendix B for the various column lengths used, with the weight fractions corresponding to the index of refraction readings added. Figures 4 and 5 show that the outlet indices of refraction of the water phase are sharply separated as functions of the inlet flow rates. However, Figure 6 shows that those of the alcohol phase do not vary nearly as much with flow rate. At a given bed height and at a constant water rate, the degree of saturation of the isobutanol phase is practically insensitive to the alcohol rate. An idea of the reproducibility of the data is also given by Figures 4, 5 and 6. All duplicate data points (except those from different receivers during the same column run) were obtained in completely independent runs, that is, on different days, with a re-setting up of the column and receiver. It would appear then, that the data are fairly well reproducible.

V. THE CONTRIBUTION OF THE RECEIVER TO TOTAL TRANSFER The resultsof the experiment with the various column lengths show the variation in mass transfer that takes place in the system consisting of the packed bed plus the receiver. Pure components were fed at various rates in this experiment. The portion of the total transfer that takes place in the receiver is difficult to assess directly and will be discussed at some length in this section. The conclusion arrived at, however, is simply that the contribution of the receiver to the total transfer is not significant, and hence, the variable column length data may be treated as if the receiver outlet phase compositions were column outlet phase compositions. Qualitative support for the reasonableness of this conclusion can be drawn from the low mass transfer coefficients that are obtained in countercurrent spray and packed column experiments relative to those obtained at the higher rates of flow possible in concurrent flow through a packed bed. An additional factor in the concurrent case is that the two phases leave the column and enter the receiver at nearly equal velocities, and that the dispersed isobutanol phase is coalescing rapidly. The quantitative support gathered in this section for the assumption of negligible receiver transfer relative to column transfer can be summarized in the following three points, which will be discussed at the end of the section. 1. No receiver transfer could be detected in experiments in which the transfer in a column plus receiver was measured as a function of inlet flow rates and inlet phase compositions. -22 -

-23 - 2. The receiver outlet indices of refraction appear to extrapolate to the pure component index of refraction at zero bed height. 3. Outlet phase compositions were found to be independent of the size of receiver in experiments in which the flow rates for the two receivers overlapped. A. Estimating the Receiver Effect Experimentally —The Method The end effect of the receiver could be determined directly if it were possible to reproduce the physical condition of the dispersed phases entering the receiver side arm from the column without incurring any mass transfer in the process. It then would be a simple matter to vary the composition of the inlet streams to the receiver and produce plots of the outlet phase composition as a function of inlet phase composition. These plots would then define the transfer occurring in the receiver. Since it is impossible to disperse the phases without incurring some unknown amount of mass transfer, it was decided to determine the effect of inlet phase composition and flow rates on the receiver outlet phase compositions of a 1" column. A 1/2" I.D. column with one inch of packing was chosen for these experiments because this height of packing was about the minimum which would create a dispersion, at all flow rates, of the phases. Now, if it is assumed that the phase transfer coefficients, kW and kAL, are independent of height in the column, i.e., the phases are uniformly dispersed along the length of the column, then this 1" column

-24 - plus the receiver in place on top of it, can be equated to the last inch of packing plus the receiver of the 2", 4" and 6" columns. Then, in effect, by subtracting the transfer which takes place in the 1" column plus receiver from the total transfer of the 2", 4" and 6" columns, it is possible to estimate the compositions of the phases entering the last inch of these latter columns. In other words, with the results of this experiment with the 1" column, an attempt is made to estimate graphically the phase compositions entering the last inch of packing of the 2"11, 4" and 6" columns that produced the receiver outlet phase compositions measured in the variable column length experiment. These phase compositions are then estimates of the internal column compositions. For a given inlet flow rate condition, the internal phase compositions can be plotted against height of column, since their values are known at 0', 1", 5" and 5" of column packing. A superposition of these plots on similar plots of receiver outlet compositions at 1", 2", "4 and 6" of column will yield the receiver effect, i.e., the difference between the curves. 1. Experimental The equipment used to study the effect of inlet phase compositions and flow rates on the receiver outlet phase compositions was the same as that described previously for the variable column length experiment. It was decided that three compositions of each phase would be run making a total of nine combinations of inlet phase compositions. These compositions were roughly 0, 40 and 80 percent of the saturation compositions of the phases. About 15 gallons of a phase were needed to run through a complete

-25 - set of flow rates. The 45 gallons needed for the three runs using a particular inlet phase composition were mixed at one time in a 55 gallon, 316 stainless steel drum and stored for future use in 5 gallon carboys. The feed reservoirs were filled directly from the carboys, using compressed air, and thus the feed system was completely closed to air, eliminating possible concentration changes of the feed during the long period needed to run all the required flow rates. The nominal flow rates at which these experiments were run were those tabulated in Table I. The experimental procedure used was the same as that used in the variable column length experiments. 2. Experimental Results The original data obtained in this experiment are tabulated in Appendix C. They are based on the feed calibration obtained for pure components and must be multiplied by the density ratio corresponding to the various inlet phase compositions in order to obtain true weights of solution flowing in gms. per hour of the solution in question. These data were then treated in exactly the same manner as in the variable column length experiment. The refractive indices were first plotted against isobutanol rate at constant water rates and then replotted against water rate choosing refractive indices at constant alcohol rates as in Table I. This was done for each combination of water phase and isobutanol phase inlet compositions. Examples of the indices of refraction of the receiver outlet phases corrected to the nominal isobintanol rates are shown as Figures 7 and 8. In Figure 7, the indices of refraction of the receiver outlet water phase are shown plotted against the inlet water rate, the inlet

80so % SATURATED INLET WATER, REFRACTIVE INDEX - 1.33870 x0 0 + x x x + + _I V _ _ _ _ _ _ _ _ _ _ _ _ _ _ I 0 v O I v NOMINAL ISOBUTANOL RATES 0 - 16600 gr/hr X - 12000, w I LJ I-f w -- w I z 0 o cr LU w LL 0 X w 0 z 1.3380 1.3370 1.3360 1.3350 + -- 8000, V - 4200 0 - 2200,, 80 % SATURATED INLET ISOBUTANOL, REFRACTIVE INDEX -1.38955 0 X 0 0 +X X X x + + + + V + V 0V 0. I h) 0'~ I 1.3340 1.3330 3000 5000 7000 9000 11000 13000 15000 17000 19000 21000 WATER RATE, gm/hr. 1-Inch column, Corrected Figure 7. Water Phase Data, to Nominal~ Isobutanol Rates.

1.3940 1.3930 x w 0 z I LL w rr: w LJ U) Q. 0 I 0 LU -J I 0 1.3920 1.3910 1.3900 0 % SATURATED INLET ISOBUTANOL-INDEX OF REFRACTION, 139380 X | 40 % SATURATED INLET ISOBUTANOL-INDEX OF REFRACTION, 1.39198 xxvp -- ALCOHOL RATES 16600 Gm/Hr.- t 12000 I s-,. 8000.t is- i s, 4200 2200 -1 80% SATURATED INLET ISOBUTANOL —INDEX OF REFRACTION, 1.38955 IVJ _ _ __ _____ " _____ ^_____ J______ 1.3890 3000 5000 7000 9000 11000 13000 15000 17000 19000 21000 WATER RATE, CALIBRATION BASIS, Gm/ Hr Figure 8. Isobutanol Phase Data, 1-Inch Column, Corrected to Nominal Isobutanol Rates.

-28 - isobutanol phase being approximately 80o saturated with water. The top set of points are for a water inlet saturation of approximately 80% and the lower set for a water inlet of 0% saturation. In Figure 8, the outlet isobutanol phase refractive indices are plotted against the water rate, with the inlet water phase being 40% saturated with isobutanol. Three inlet isobutanol phase compositions, 0%, 40% and 80% saturated with water, are shown. The secondary parameter in these two plots is the nominal inlet flow rate of the isobutanol phase. It is interesting to note that the receiver outlet composition (refractive index) of the isobutanol phase is quite insensitive to the alcohol rate, and to some degree of the water rate. The plots in Figures 7 and 8 (outlet refractive index vs. actual water rate, parameters-inlet phase saturation, actual alcohol rate) are based on the inlet rates of the phases of various percentages of saturation. These plots, therefore, cannot be used directly to construct column inlet vs. receiver outlet compositions for comparison with receiver outlet compositions from the variable column length experiment. These latter data are plotted on a basis of pure inlet components. Therefore, to effect the comparison, the column inlet vs. receiver outlet composition plots must also be constructed on a basis of pure inlet components, i.e., if a pure water phase started out at Lo gms/hr and a pure alcohol phase started out at V gms/hr, what would their respective flow rates L and V1 be at a point in the column where their respective saturations were, say, 40 and 80 percent? These are found by a component material balance, t I I Lo =-LX +VY' VL = L'X + V'YW o A A

-29 - where Xa, Ya are mass fractions of component a in the L and V streams, L, V' are actual mass rates at the point in the column being considered, L1, V' are the mass rates of pure components that are equivalent o o to L and V' when their compositions reach Xa and Ya, and are nominal rates found in Table I. Indices of refraction of the receiver outlet phase can then be!! found for the L and V is computed as above on plots such as Figures 7 and 8. These indices of refraction constitute an estimation of the outlet phase refractive index, when the inlet phases are of a certain percentage of saturation and have total component flow rates L and Vo. Examples of these plots are shown as Figures 9-12. These plots are the goal of the experiment. Aside from their intended use in the receiver end effect problem, these plots also have the additional property of purporting to show the effect of the concentration of one phase on the amount of mass transfer that takes place into the other phase. It is seen from the data that the composition of the water phase apparently has very little influence on the transfer of water into the isobutanol phase. On the other hand, the more water present in the isobutanol phase, the more isobutanol transferred to the water phase. This is especially true at higher flow rates. However, the region of respective saturation of the phases in Figures 9-12, where this effect is most pronounced, never have to be considered when the receiver effect is estimated. In order for the effect of saturation

-30 - 1.3410 1.3400 -- 40 % I / i x — o % / 1.3390. - ~// /8 / / 4 ALCOHOL RATE / / 16600 Gr/Hr I '/ a 1.3380 i / 4w I-l. / i 3 / // > Io / / ' </ 1.3370 / / ALCOHOL RATE L 1.3 /3/0 1.3360 II - '/ ii I — / / ~ ALCOHOL IRATE._ 1.3350 / /4200 Gr/Hr - / / / i 1.3320 ----------------------- - 1.3340 4 4,/ / o 1.332o 1.3320 1.3340 1.3360 1.3380 1.3400 1.3420 1.3440 INLET WATER PHASE REFRACTIVE INDEX Figure 9. Inlet vs. Outlet Water Phase Refractive Indices, 1lInch Column.

-31 - 1.3410 1.3400 1.3 l imoouu ur/Hr - / / i 1.3390... VV. rnr. 1.3380 - -------- x V LJ/ r 1.3370 -- -------- ALCOHOL RATE-t --- / 8000 Gr/Hr W I / / / u 1.3360 IL.J / / / / I L 1.3320 / o INLET WATER PHASE REFRACTIVE INDEX 1"3340 -Inch Column.. 10 i 1.3330 ' -------------------— i4____0___ 1.3320 1.3340 1.3360 1.3380 1.3400 1.3420 1.3440 INLET WATER PHASE REFRACTIVE INDEX Figure 10. Inlet vs. Outlet Water Phase Refractive Indices, 1-Inch Column.

-32 - 1. w T 1.3925 - IJ / -I o WATER RATE / -J o 11300 Gr/Hr 1.3915 -- x Z~ 4 1.3905 00 ' I / -WATER RATE < 20000 Gr/Hr ~0I.w 1.3895, — 13875 - I-1 I - e: ~ ~ 4 -J 1.3875 L_______ 1.3875 1.3885 1.3895 1.3905 1.3915 1.3925 INLET REFRACTIVE INDEX ALCOHOL PHASE Figure 11. Inlet vs. Outlet Isobutanol Phase Refractive Indices, 1-Inch Column. 1.3935

1.3945 I | ALCOHOL RATE 8000 Gr/Hr WATER SATURATION v - 80 %. 1.3935 - 0 40 % 8 Ix -- o % X 1.3925 1 8 | WATER RATE X AOH P /. I s I/ o // 1.3915 --- 0 Z / / 0 // / _ W 1.390885 - 0 / 7 I"-. -- WATERI /. l // I20000 ' I /7w 1.3875 - ----- - 1.3875 1.3885 1.3895 1.3905 1.3915 1.3925 INLET REFRACTIVE INDEX ALCOHOL PHASE Figure 12. Inlet vs. Outlet Isobutanol Phase Refractive Indices, 1-Inch Column. 1.3935

-34 - to be significant (considering the scatter in the variable column length experiment) the alcohol phase must be highly saturated with water while the water phase must be relatively pure. Since the variable column length data has been taken with the inlet phases being pure components, this situation never exists in the column. As a matter of fact, in the variable column length experiment, the water phase becomes saturated far more quickly than the isobutanol phase, therefore keeping the concentration effect of the isobutanol phase not particulary significant (see Figure 9). 3. Procedure for Estimation of Internal Column Phase Indices of Refraction From plots such as those shown in Figures 9-12 it is possible, t t under the assumption that the phase transfer coefficients kAL and kWV are independent of height (uniform dispersion with height), to estimate how much mass transfer took place in the receiver and last inch of packing of the 2", 4" and 6" columns, thereby estimating internal column compositions at 0", 1", 3" and 5" of bed height. For example, consider the water phase under the column flow conditions of 20,000 gms/hr pure inlet water and 16,600 gms/hr pure inlet isobutanol. At a bed height of 6", the receiver outlet water phase had a refractive index of 1.3411 (cf. Appendix B). Now, taking this as the refractive index of the water phase at the receiver outlet, as in Figure 9, the refractive index of the inlet water phase to a 1" column plus receiver is estimated to be 1.3409. This is then assumed to be the refractive index of the water phase leaving the fifth inch of packing in the 6" bed. The procedure is repeated for the

-35 - 4"1 column and a refractive index of the water phase is estimated for the third inch of packing and again for the 2" column. It is to be remembered that the level of saturation of the alcohol phase should be taken into account when estimating these water phase refractive indices. A summary of the values obtained for this example is given in Table II below and plotted as the 16,600 gms/hr alcohol rate parameter of Figure 13. Where duplicate data points were available for the various column lengths, the arithmetic average was taken. TABLE II SUMMARY —ESTIMATION OF INTERNAL COLUMN REFRACTIVE INDICES OF TE WATER PHASE —INLET FEED RATES: WATER - 20,000 gms/hr, ISOBUTANOL - 16,600 gms/hr. total height receiver outlet height of est. internal of bed ref. index est. ref. index 6" 1.34109 5" 1.3409 4" 1.34007 3" 1.3391 2" 1.33793 1" 1.3358 1" 1.33595 0"o 1.33245 The plots shown in Figures 13-16 are representative of this procedure for both the water phase (Figures 13, 14) and the isobutanol phase (Figures 15, 16)o These plots include both the original refractive indices of the receiver outlet with the various columns (the dots) and the estimated internal refractive indices (the x's). If there is a significant receiver effect, a curve through the internal refractive indices should lie

x C3 z w I — LL w cr w C,) 0: a. cr w -J I 1.3420 1.3400 1.3380 1.3360 1.3340 1.3320 WATER RATE 20000 Gr/Hr SATURATED WATER PHASE - ---- — 1 ALCOHOL 16600 Gr/Hr 1 s ALCOHOL 8000 Gr/Hr l / 7- = - ALCOHOL 4200 Gr/Hr / A / 777./ / / / / \/ / 7/ /- -ESTIMATED INTERNAL REFRACTIVE INDEX - RECEIVER OUTLET REFRACTIVE INDEX / /__ ____ ^l I 1 0 I 2 3 4 5 6 HEIGHT OF COLUMN, INCHES Figure 13. Receiver Effect Estimation Curves, Water Phase.

1.3420 x z I (r -L. LL LH I mL a.f;Q x 1.3400 1.3380 1.3360 WATER RATE 11300 Gr/Hr SATURATED WATER PHASE..-, ---s ^ ALCOHOL 16600 Gr/Hr - - ----— ALCOHOL 8000 Gr/Hr /-,/ A 0t0,,,,0, / / / / / / >/ / / ', j'1,'-I / - > '- ESTIMATED INTERNAL REFRACTIVE INDEX / / - RECEIVER OUTLET REFRACTIVE INDEX 1/// I / / I" i/./:1:,,,,/ ^i I 1.3340 1.3320 0 I 2 3 4 5 6 HEIGHT OF COLUMN, INCHES Figure 14. Receiver Effect Estimation Curves, Water Phase.

a 1.3915 o \. 0 z 1.3905 - 0 w WATER 20000 Gr/Hr N ___ ____9 ---------------------- - __ ____ u. 1.3895 z 1.3885 1.3875 0 2 3 4 5 6 7 HEIGHT OF COLUMN, INCHES Figure 15. Receiver Effect Estimation Curves, Isobutanol Phase.

1.3935 1.3925 w Un M) I X- 1.3915 _J 1 0 0 U, Z 1.3905 0 U1Lw cr L. 1.3895 0 x w z 1.3885 1.3875 NSNo% NN NI __ _ ___0 _______________N_____ _ N N N N N WATER RATE 11300 Gr/Hr ALCOHOL RATE 8000 Gr/Hr I I-1 I 0 0 I 2 3 4 5 7 8 HEIGHT OF COLUMN, INCHES Figure 16. Receiver Effect Estimation Curves, Isobutanol Phase.

nearer the less saturated end. of the refractive index scale than a curve through the receiver outlet points, i.e., a positive amount of transfer should be taking place in the receiver. Therefore, Figures 13-16 yield an estimate of the transfer which occurred. in the receiver with total bed heights of i", 2", 4" and 6". B. Discussion The three points mentioned in the introduction to this section as summarizing the support for the assumption of negligible receiver transfer will now be discussed in detail, taking into consideration the relevance for the first point of the experimental work discussed above. 1. By considering Figures 13 and 14 for the water phase, it is apparent that, with the exception of the highest flow rates run, 20,000 gms/hr water and. 6,600 gms/hr isobutanol, the procedure described in Section A, above, yields an estimate of a negative amount of transfer taking place in the receiver for the 2", 4" and 6" columns. This is indicated by the curves through the internal refractive indices (the xts) lying above those drawn through the receiver outlet indices or, toward more saturated water solutions. Those of the highest flow rates are essentially coincident, indicating an estimate of zero transfer in the receiver at this condition. In the plots for the isobutanol phase, Figures 15 and 16, the curves are essentially coincident regardless of flow rate. These curves bear out the assertion that the receiver effect is not large enough to constitute a significant proportion of the total mass transfer incurred in the column packing and the receiver.

-41 - Now, the method of estimation is based on the assumption of uniform dispersion along the column length, making the first inch physically equivalent to any other. This condition should be most closely approached at the highest flow rates run, i.e., at 20,000 gms/hr water and 16,6)00 gms/hr alcohol. Therefore, at these rates, the method of estimation should come closest to estimating the true receiver effect. Moreover, the receiver effect at these rates should be greatest, due to the turbulence in the receiver side arm. However, it is at these rates that the receiver effect is estimated to be zero. At lower flow rates, the first inch is probably not equivalent to later ones and the receiver effect correspondingly is estimated to be negative. Since the turbulence of the phases entering the receiver at these lower rates is much reduced, the receiver effect is probably reduced also. And since the transfer in the receiver can not be detected when it should be greatest, it seems safe to conclude that it is negligible at all conditions. At all flow rates, the internal refractive indices of the alcohol phase appear to coincide with those of the receiver outlet, thus showing that for the alcohol phase also, the receiver-effect can not be detected, In both the experiment of this section and that of varying the column length, the outlet phase compositions of the alcohol phase were relatively insensitive to flow rates. Because of this, the same reasoning applied to the water phase can be applied to the alcohol phase. In other words, the experiment varying the inlet phase compositions shows that the effect of the receiver on outlet phase compositions

-42 - is small enough so that the experiment can detect a difference in transfer taking place in the first inch of packing of a column as compared with the last inch. Therefore, unless the first inch of packing is completely ineffective in causing mass transfer, the receiver effect cannot constitute any significant proportion of the total transfer. 2. Further indirect evidence can be cited to support this conclusion. As Figures 13-16 shows the receiver outlet refractive indices, in every case, can be extrapolated without difficulty to the refractive index of the pure component (water or isobutanol) and never to that of finite saturation. Though this extrapolation cannot be used in any quantitative sense, it indicates qualitatively that the receiver outlet phases of the one inch column, where the driving force for mass transfer is greatest, does not contain a very significant contribution from the receiver. Since the effect does not appear significant for the one inch column, it follows that for the remaining columns, where it should be diminishing, it will also remain small. 3. The third point in support of negligible receiver effect is that receiver size did not appear to affect receiver outlet phase concentrations. The outlet phase compositions vary continuously over the entire range of flow rates and coincide in the region where the receivers overlap, as seen in Figures 3-5. Since the phases certainly separate under different conditions and have different residence times in the two receivers, the effect on the outlet compositions should be different. If this effect were large, then the difference should be detected. Since it is not, the effect must not be significemt.

There is no absolute estimate of the receiver effect in any of the forgoing points supporting the assertion that it is negligible. It is nevertheless clear, however, that all evidence points to the conclusion that there will be little difference in choosing to call the receiver outlet compositions equivalent to the corresponding column outlet compositions. With this assumption, the data from the variable column length experiment can be treated as internal phase compositions, from which the!! individual phase transfer coefficients kA and kV can be derived. This is the subject of the following section.

VI. THE INDIVIDUAL PHASE TRANSFER COEFFICIENTS The individual phase transfer coefficients can be calculated from the data obtained in the variable column length experiment (and tabulated in Appendix B) provided that the following two assumptions are made. (1) The transfer in the receiver is negligible, and (2) the internal compositions at any height are the same as the outlet compositions from a packed column of the same height. The data obtained are incremental in nature and the transfer coefficients cannot be obtained directly from the differential model, Equation (5). There are several ways of processing the data in order to obtain phase transfer coefficients k. On the one hand, if the phase transfer coefficient is considered independent of height in the column, Z, then Equation (5) can be integrated explicitly. For example, for water transferring into the isobutanol-rich phase, there results, (vYW)f '(VyW) -( (v)o ) W f(* IkWV SH (9) (Vy) V WV where H is the total length of the column, S is the empty cross-section of the column, VyW is the moles of water flowing in the isobutanol-rich phase at any point in the column, kWV is the mean transfer coefficient for the column, (hr.)-l The left hand integral can be evaluated graphically using the values of VyW and (CV - CW) calculated from the data. This procedure gives an

-45 - average phase coefficient for the entire length of the column. On the other hand, a more satisfactory procedure, in that it indicates the variation and consistency of the coefficients with height, is to derive differential rates from the incremental data. The calculation of phase coefficients from Equation (5) can proceed in two ways. 1. Substituting differences for the differentials in this equation, the incremental rates of mass transfer, A(Vyw)/AZ, can be smoothed graphically with respect to Z on an equal area plot (A(Vyw)/AZ vs. Z). The smoothed (differential) rates of mass transfer are then plotted against the driving force. From Equation (5) it can be seen that the slope of a curve through these points is the transfer coefficient at the driving force where the slope is measured. A straight line through the origin gives a mean coefficient for the entire column. 2. A far more critical approach involves the calculation of incremental coefficients, k, from Equation (10) below, for example, for the coefficient for water transferring into the isobutanol-rich phase, A(VYW) _ * k~ss cV WV mean (10) successful only if the variation in this quantity is moderate. Therefore, in so far as the choice of a mean AC is arbitrary, this procedure yields a completely unbiased estimate of the coefficients k over the increment of column. For convenience in later discussion, the resulting coefficients will be referred to as integral, equal area and incremental.

VII. DISCUSSION OF RESULTS The data from the variable column length experiment were treated both by the equal area and the incremental procedures. A few selected conditions were treated by the integral method. Sample calculations for all three procedures may be found in Appendix D. It was found that the number of increments of column length used were not sufficient to enable accurate graphical differentiation of the data. This was especially true of the data for water transferring into the alcohol phase. In this case, some of the coefficients derived by the equal area procedure were quite inconsistent by comparison with those obtained by the incremental or integral methods. For the case of isobutanol transferring into the water-rich phase, the situation was better, and the equal area method usually gave coefficients in agreement with coefficients calculated by the other methods. Since the incremental coefficients were more consistent as well as independent of any datasmoothing bias, they were utilized in subsequent correlations. They are tabulated in their entirety in Tables V, VI and VII, Appendix D. The incremental coefficients for isobutanol transferring into the waterrich phase, kAW, are tabulated in Table V. Those for water transferring into the isobutanol-rich phase, kWV, in Table VI. The sample calculations and these tables are expressed in the mixed units obtained in the experiment. A sunmmary of these coefficients, in units of lbs/(hr)(ft), is presented in Table VII. The coefficients in this table were obtained by taking an arithmetic average of the incremental coefficients with respect to height,

-47 - The incremental coefficients for the water phase are seen in Table V to be essentially constant with respect to column height, although the coefficient for the first inch is almost always a little lower than those for the succeeding incrementso This is further illustrated in Figure 17 for a few selected inlet flow conditions. The low first inch coefficients would be expected due to insufficient mixing and are in agreement with the results of the end effect experiment, where it was found that a one inch column accounted for too little transfer in the last inch of the 2", 4" and 6" columns, The alcohol phase coefficients, at least at the higher flow rates, seem to increase with increasing bed height. This increase is usually about 70% of the coefficient of the first inch, which is strikingly greater than the increase of the coefficients in the water phase. At lower flow rates, the incremental coefficients, though somewhat erratic, are more nearly invariant with bed heighto This is illustrated in Figure 18, where the coefficients are plotted for two water rates, each with a high and a low inlet isobutanol rate. The behavior of the incremental phase coefficients taken together is curiouso For one coefficient to increase with increasing bed height while the other coefficient remains relatively constant, indicates that the effect is not just one of increasing the interfacial area for transfero Since the effect cannot be attributed with certainty to composition effects or to height, use of the incremental coefficients in other situations is subject to considerable uncertainty. Hence, average coefficients k were computed and are those given in Table VIIo These up(

-8-h 16 14 1 2 C LEN C,) L I0 8 6 LEGEND- WATER ISOBUTANOL RATES, gr/hr *- 20000 16600 i *- 15500 16600 is_ _ _ _ _ _ _ _ _ *- 11300 12000 i X- 7200 8000 - 3700 42001 -MEAN COEFFICIENTS _kAL - El 4 2 0 0 I 2 3 4 5 6 HEIGHT OF BED,. INCHES Figure 17. Incremental Water Phase Transfer Coefficients.

8 7 6 c I. (f) K 'I3 5 4 3 2 0 LEGEND WATER ISOBUTANOL RATES, gr/hr V - 20000 16600 0 - 20000 8000 X - 11300 16600 *- 11300 4200 — EAN COEFFICIENTS kv 0 I 2 3 4 5 6 HEIGHT OF BED, INCHES F igure 18. Figur 18.Incremental Isobutanol Phase Transf er Coeff icients.

-50 - values are shown plotted in Figures 19 and 20. The water phase coefficients are shown in Figure 19 and those of the alcohol phase are shown in Figure 20. It is seen that their behavior is very regular, and that the average coefficients are functions of the flow rates of both phases. Using a bivariate, least squares regression procedure with an equation of the type y = Axnx1, (after taking logarithms) adequate representations for the dependence of the phase coefficients on the phase flow rates were obtained. For the water phase coefficient the equation is kAL =.00069(L0)7 (V).8 (11) and for the alcohol phase, the equation is k = 0.00056(L)4 (V) 98 (12) where kk has units of (hr)1 and Lo andVo have units of Ibs/hr.ft. The standard errors of the powers are 0.05 and 0.04 for Equation (11) and 0.06 and 0.05 for Equation (12). The coefficients of determination of the regression equations are 0.97 and 0.97 respectively, which are very respectable values for mass transfer data. From Equation (11), it is seen that the water phase coefficient is influenced equally by the water and isobutanol flow rates and that the effect diminishes with increasing flow rate. From Equation (12), the isobutanol phase coefficient is much less affected by the water rate than the isobutanol rate, the coefficient increasing very nearly with the first power of the alcohol rate while increasing only with the square root of the water rate. Data for countercurrent flow follow much the same behavior.

36 32 28 'I NCX '0 -l -4 _ -. 24 20 16 12 8 4 0 WATER RATE V 32000 lbs /hr. ft - 25000,, 0- 18000,, -X- 12000 -- 0- 6000 THE DASHED LINES REPRESENT REGRESSION EQUATION THROUGH PREDICTED POINTS. / '____ o - 0] / / I/ /;- _r' /_ 1x xt.00r9-o 01 -01 0.00 - _ _ 2000 6000 10000 14000 18000 22000 26000 30000 INLET ISOBUTANOL RATE, Ibs/hr-ft2 Averaged Water Phase Transfer Coefficients. Figure 19.

20 0 I0 10 --- - 6~ ~ ~ ~~~ ----------— ] ~ - - *8 6 - - '"o- --------...... — e.... ---0 2000 6000 10000 14000 18000 2200C INLET WATER RATE, lb/hr-ft2 ) 26000 30000 34000 Figure 20. Averaged Isobutanol Phase Transfer Coefficients.

A comparison of the numerical values of the phase transfer coefficients obtained in concurrent flow with those obtained by Colburn and Welsh in countercurrent flow immediately indicate the possible advantages of c6ncurrent flow. In countercurrent flow, the flow rates were restricted to 500-1,350 lbs/hr.ft2 for the continuous water phase and to 250-2,090 lbs/hr.ft2 for the discontinuous isobutanol phase. The transfer coefficients obtained, k, ranged from approximately 3 to 30 (hr) 1 for the water phase and from 6 to 70 (hr)-1 for the isobutanol phaseo For the range of flow rates studied in concurrent flow (6,000 to 52,000 lbs/hr<,ft2 for the water phase and. 5,500 to 27,000 lbs/hr.ft2 for the isobutanol phase) the phase coefficients ranged from 230 to 3,400 (hr)-1 ~-l for the water phase and from 110 to 1770 (hr)-1 for the isobutanol phase. The flow rates are much higher in the concurrent work than were allowable in the countercurrent work and the phase coefficients for the concurrent case are correspondingly much larger. From Equations (11) and (12) and from the plots of the coefficients, Figures 19 and 20, it would appear that the coefficients will continue to increase with increasing flow rate. Also, if Equations (11) and (12) are used to predict the concurrent transfer coefficients for flow rates used in the countercurrent work, the values are of comparable magnitude, For example, for a water rate of 1,350 lbs/hr.ft2 and an isobutanol rate of 2,090 lbs/hr.ft2, the transfer coefficients are 40 (hr)"l for the water phase and 35 (hr)"l for the isobutanol phase, as compared with coefficients of 30 and 70 (hr)'1 respectively obtained. in the countercurrent work. Therefore, the concurrent column, operating at very low phase flow rates with poor dispersion

-54 - still gives approximately the same coefficients as a countercurrent column operating at optimum flow rates. At higher flow rates the concurrent coefficients are much greater while the countercurrent column becomes inoperative due to flooding. It is possible to calculate numbers for the transfer coefficients for water in the water-rich phase and for isobutanol in the isobutanolrich phase. It is, however, not apparent that these coefficients have any utility, especially as they behave ambiguously as the bulk of one phase approaches equilibrium, while the other phase differs substantially from equilibrium, with the rate of transfer across the phase interface remaining finite. This anomalous behavior is apparent from an inspection of Equation (3), for taken literally, it shows that as the water phase becomes saturated, the rate of transfer of water, NW, should become very small if the transfer coefficient kWL remains relatively constant. However, it is known that water will transfer into the isobutanol-rich phase until this phase becomes saturated, regardless of the concentration driving force in the water-rich phase. Therefore, in this situation, the coefficient for water is the water-rich phase must increase appreciably. For example, for inlet flow rates of 20,000 gms/hr water and 16,600 gms/hr isobutanol, the incremental coefficients of water in the water-rich phase, kL * S, and kWL for the column increments are: 0-1 in 1-2 in 2-4 in 4-6 in kWL * S 6.7 10.0 16.3 54.5 liters/hr,in WL 2,070 3,090 5,040 16,800 hr 1

VIII. CONCLUSIONS Several conclusions may be stated: (1) Concurrent flow through a packed bed affords an effective means for obtaining high mass transfer coefficients in liquid systems. The coefficients for both phases increase as the flow rates of the phases are increased. The average column phase transfer coefficients can be expressed as a power function of both phase flow rates, koD = AL1Vm (2) The incremental phase transfer coefficients for the water phase are essentially independent of height in the column, excluding the first inch of bed, where the coefficient was generally a little lower than for succeeding increments. (3) The incremental coefficients of the isobutanol phase appear to increase somewhat with bed height at higher flow rates, while at lower flow rates they can be considered constant. The increase is usually about 70o over the value of the coefficient of the first inch. -55 -

APPEN$D(T A ORIGINAL VARIABIE COLUIN LENGTH DATA

APPENDIX A TABLE A-1 ORIGINAL DATA FOR 1 INCH COLUMN Water Phase Isobutanol Phase Sample Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction gms/hr Refraction Size I.. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 50 31 32 33 34 35 20,025 19,950 20,025 19,950 20,025 19,950 20,025 19,950 15,600 15,600 15,600 15,600 11,300 11,350 11,350 11,300 11,300 11,300 11,300 11, 350 11,300 11,300 11,350 11,350 7,200 7,200 7,200 7,200 7,520 7,175 7,175 3,675 3,675 3,675 3,675 1.33608 1.33578 1.33485 1.33489 1.33428 1.33415 1.33354 1.33349 1.33614 1.33472 1.33417 1.33332 1.33595 1.33535 1.33495 1.33504 1.33503 1.33440 1.33433 1.33453 1.33440 1.33444 1.33329 1.33323 1.33578 1.33498 1.33472 1.33466 1.33491 1.33349 1.33323 1.33569 1.33492 1.33423 1.33375 16,400 16,530 11,870 11, 700 7,830 7,710 4,125 4,100 16,590 12, 030 7,920 4,225 16,475 16,550 12,025 11,900 11,950 7,875 7,850 8,050 8,000 7,800 4,125 2,140 16,560 11,480 7,860 7,900 7,880 4,000 2,240 11,975 8,o6o 4,360 2,230 1.39289 1.39295 1.39505 1.39298 1.39292 1.39293 1.39280 1.39293 1.39307 1.39309 1.39292 1.39293 1.39323 1.39332 1.39331 1.39326 1.39322 1.39319 1.39325 1.39316 1.39310 1.39311 1.39316 1.39280 1.39341 1.39341 1.39328 1.39316 1.39331 1.39320 1.39310 1.39344 1.39340 1.39326 1.39310 L L L L L L L L L L L L L L L L L L L L L L S S L L L L L S S S S S S -57 -

TABLE A-2 ORIGINAL DATA FOR 2 INCH COLUMN Water Phase Isobutanol Phase Sample Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction gms/hr Refraction Size _~ ~ ~ ~ ~ ~~'.........._...._._..1,4_ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 20,000 19,980 19,980 20,000 20,000 19,980 19,980 20,000 15,300 15,300 15,300 15,300 15,500 11,075 11,075 11,375 11,375 11,075 11,075 11,075 11,375 11,075 11,300 11,190 11,300 11,350 11,350 11,190 11,190 11,350 7,200 7,430 7,430 7,200 7,200 1.33807 1.33780 1.33685 1.33705 1.33585 1.33589 1.33471 1.33465 1.33852 1.33743 1.33614 1.33479 1.33484 1.33877 1.33850 1.33817 1.33717 1.33742 1.33746 1.33633 1.33624 1.33608 1.33611 1.33601 1.33620 1.33608 1.33446 1.33453 1.33381 1.33341 1.33887 1.33897 1.33827 1.33829 1.33720 16,68o 16,620 11,920 11,870 8,190 7,800 4,250 4,100 16,700 12,030 7,950 4,225 4,180 16,625 16,600 16,550 12,000 11,975 12,075 7,925 7,875 7,950 8,075 8,070 7,950 7,960 4,200 4,275 2,200 2,275 16,575 16,625 12,060 12,160 8,o60 1.39216 1.39202 1.39220 1.39217 1.39229 1.39202 1.39189 1.39213 1.39210 1.39226 1.39213 1.39194 1.39174 1.39256 1.39268 1.39277 1.39280 1.39259 1.39274 1.39259 1.39268 1.39256 1.39268 1.39280 1.59246 1.39271 1.39250 1.39276 1.39251 1.39298 1.39286 1.39301 1.39280 1.39273 1.39262 L L L L L L L L L L L L L L L L L L L L L L L S S S S S S S L L L L L

-59 - TABLE A-2 CONT'D Water Phase Isobutanol Phas:e Sample Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction I gms/hr Refraction Size -.....I I........ 36 37 38 39 40 41 42 43 44 45 46 47 7,430 7,200 7,200 7,200 3,650 3,620 3,650 3,620 3,620 3,650 3,650 3,620 1.33727 1.33711 1.33533 1.33401 1.33795 1.33817 1.33704 1.33743 1.33634 1.33608 1.33472 1.33472 8,o40 8,100 4,125 2,180 12,100 11,960 8,020 7,940 4,220 4,400 2,165 2,280 1.39259 1.39262 1.39247 1.39249 1.39341 1.39337 1.39324 1.39322 1.39297 1.39299 1.39292 1.39290 L S S S S S S S S S S S

-60 - TABLE A-3 ORIGINAL DATA FOR 4 INCH COLUMN Water Phase Isobutanol Phase Sample I Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 19,500 19,960 19,960 19,300 19,350 19.960 19,960 19,500 15,480 15,480 15,450 15,390 10,725 11,250 11,250 10,600 11,000 11,250 11,600 11,400 11,400 12,325 11,400 11,100 6,680 6,800 6,940 7,100 8,500 9,350 7,100 7,100 8,880 4,400 3,640 3,640 4,400 3,640 5,180 3,640 4,460 1.34013 1.34001 1.33935 1.33929 1.33813 1.33813 1.33638 1.33636 1.34015 1.33929 1.33624 1.33816 1. 3445 1.34029 1.33974 1.33994 1.33883 1.33882 1.33855 1.33849 1.33650 1.33662 1.33466 1.33467 1.34070 1.34029 1.33955 1.33971 1.33893 1.33720 1.33810 1.33585 1.33488 1.34061 1.34051 1.33981 1.33994 1.33871 1.33798 1.33665 1.33633 16,6oo00 16,530 11,800 11,900 7,860 7,830 4,075 4,075 16,620 12,000 4,050 7,710 16,200 16,550 11,900 11,925 7,850 7,950 7,770 7,680 4,075 4,075 2,150 2,050 16,660 11,960 7,780 7,950 7,850 4,075 4,275 2,140 2,185 12,000 12,240 7,920 7,620 4,140 4,060 2,080 2,060 1.39057 1.39038 1.39039 1.39077 1.39068 1.39050 1.39017 1.39042 1.39098 1.39117 1.39098 1.39110 1.39153 1.39159 1.39129 1.39141 1.39129 1.39105 1.39135 1.39115 1.39108 1.39113 1.39145 1.39147 1.39207 1.39198 1.39177 1.39095 1.39159 1.39129 1.39077 1.39086 1.39129 1.39237 1.39280 1.39238 1.39210 1.39180 1.39189 1.39171 1.39189 L L L L L L L L L L L L L L L L L L S S S S S S L L L S S S S S S S S S S S S S S

-61 - TABLE A-4 ORIGINAL DATA 6 INCH COLUMN Water Phase Isobutanol Phase...I Flow Rate Index of I Flow Rate Inex of I Receiver Sample gms/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 15 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 19,600 19,600 19,960 20,000 19,600 19,960 20,000 19,960 20,000 19,600 15,200 15,200 15,200 15,200 11,000 11,325 11,000 11,325 11,325 11,000 11,325 11,325 11,000 11,300 11,500 11,000 11,250 11,500 11,500 11,000 7,000 7,000 7,000 6,950 6,950 1.54109 1.54058 1.34058 1.54058 1.55961 1.55952 1.33938 1.33762 1.33766 1.33752 1.34099 1.34064 1.33955 1.33768 1.34102 1.34095 1.34072 1.34077 1.34063 1.34000 1.34013 1.33984 1.34019 1.33987 1.33975 1.33834 1.33791 1.33794 1.33556 1.33586 1.34109 1.34099 1.34061 1.34058 1.33897 16,700 11,870 12,200 11,730 7,920 7,800 7,800 4,100 4,150 4,025 16,500 11,820 7,440 3,950 16,400 16,575 11,550 12,000 12,325 7,450 7,700 7,575 7,560 7,900 7,900 4,050 4,200 4,225 2,150 1,960 16,460 11,800 7,640 7,575 3,975 1.38922 1.38932 1.38941 1.38925 1.38935 1.58956 1.38932 1.38940 1.38928 1.38946 1.38992 1.38970 1.38977 1.38973 1.39038 1.59041 1.39028 1.39005 1.59045 1.39016 1.38973 1.59038 1.38989 1.39008 1.39025 1.39007 1.59042 1.59020 1.39026 1.39016 1.59099 1.39086 1.39039 1.39038 1.39031 L L L L L L L L L L L L L L L L L L L L L L S L S S S S S S L L L S S

TABLE A-4 CONT'D Sample Flow Rate gms/hr Index of Refraction I Flow Rate I gms/hr Index of Refraction I Receiver | Size 56 57 38 59 40 41 42 43 44 7,250 6,950 3,400 3,400 3,740 3,740 3,400 3,400 3,740 1.33865 1.33643 1.34109 1.34096 1.34096 1.34006 1.34038 1.33821 1.33804 4,150 1,920 11,800 7,500 8,080 4,180 3,800 1.960 2,000 1.39065 1.39047 1.39220 1.39141 1.39156 1.39080 1.39068 1.39091 1.39084 S S S S S S S S S

APPENJDIX B VARIABLE COLTJN LENGTH DATA CORRECTED TO NOMINAL FLOW RATES -653 -

APPENDIX B TABLE B-1 FLOW RATE CORRECTED DATA FOR 1 INCH COLUMN Water Phase Isobutanol Phase Lo Index of Wt. Fr. V0 Index of Wt. Fr. No. | gms/hr Refraction H20 gms/hr Refraction H20 I l- I,.... 1 20,000 1.33608.9650 16,6oo 1.59289.0335 2 20,000 1.3580.9678 16,oo000 1.39295.0315 3 20,000 1.33488.9760 12,000 1.59305.0280 4 20,000 1.33490.9758 12,000 1.39298.0300 5 20,000 1.33425.9818 8,000 1.39292.0330 6 20,000 1.33420..9824 8,000 1.39293.0330 7 20,000 1.33352.9890 4,200 1.39280.0370 8 20,000 1.33350.9893 4,200 1.39290.0335 9 15,500 1.33610.9648 16,600 1.39307.0275 10 15,500 1.33472.9775 12,000 1.39309.0275 11 15,500 1.33420.9824 8,000 1.39292.0330 12 15,500 1.33332.9910 4,200 1.39293.0330 13 11,300 1.33595.9663 16,6oo 1.39323.0215 14 11,300 1.33535.9717 16,600 1.39332.0180 15 11,300 1.33495.9753 12,000 1.39331.0180 16 11,300 1.33504.9745 12,000 1.39326.0205 17 11,300 1.33503.9747 12,000 1.39322.0220 18 11,300 1.33440.9805 8,000 1.39319.0230 19 11,300 1.33433.9810 8,000 1.39325.0205 20 11,300 1.33450.9795 8,000 1.39316.0240 21 11,300 1.33440.9805 8,000 1.39310.0260 22 11,300 1.33444.9800 8,000 1.39311.0260 23 11,300 1.33335.9907 4,200 1.39316.0240 24 11,300 1.33325.9917 2,200 1.39280.0370 25 7,200 1.33578.9680 16,600 1.39341.0145 26 7,200 1.33505.9745 12,000 1;39341.0145 27 7,200 1.33475.9772 8,000 1.39328.0195 28 7,200 1.33470.9776 8,000 1.39316.0240 29 7,200 1.33490.9758 8,000 1.39331.0180 30 7,200 1.33352.9890 4,200 1.39320.0225 31 7,200 1.33320.9922 2,200 1.39310.0260 32 3,700 1.33569.9687 12,000 1.39344.0140 33 3,700 1.33490.9758 8,000 1.39340.0150 34 3,700 1.33415.9828 4,200 1.39326.0200 35 3,700 1.33370.9873 2,200 1.39310.0260

-65 - TABLE B-2 FLOW RATE CORRECTED DATA FOR 2 INCH COLUMN Water Phase Isobutanol Phase No. Lo Index of Wt. Fr. Index of Wt. Fr. gms/hr Refraction H20 gms/hr Refraction H20 1 20,000 1.33805.9467 16,600 1.39216.0585 2 20,000 1.33780.9490 16,600 1.39202.0625 3 20,000 1.33690.9577 12,000 1.39220.0570 4 20,000 1.33710.9557 12,000 1.39217.0580 5 20,000 1.33580.9677 8,000 1.39229.0545 6 20,000 1.33593.9665 8,000oo 1.39202.0625 7 20,000 1.33470.9777 4,200 1.39189.0665 8 20,000 1.33468.9778 4,200 1.39213.0595 9 15,500 1.33848.9427 16,600 1.39210.0605 10 15,500 1.33740.9529 12,000 1.39226.0555 11 15,500 1.33614.9645 8,000 1.39213.0595 12 15,500 1.33479.9768 4,200 1.39194.0650 13 15,500 1.33484.9765 4,200 1.39174.0710 14 11,300 1.33870.9405 16,6oo 1.39256.0455 15 11,300 1.33845.9429 16,600 1.39268.o415 16 11,300 1.33825.9448 16,600 1.39277.0380 17 11,300 1.33720.9548 12,000ooo 1.39280.0370 18 11,300 1.33738.9530 12,000 1.39259.0450 19 11,300 1.33740.9528 12,000 1.39274.0390 20 11,300 1.33630.9630 8,000 1.39259.0450 21 11,300 1.33630.9630 8,000 1.39268.0415 22 11,300 1.33610.9650 8,000 1.39256.0455 23 11,300 1.33610.9650 8,000 1.39268.o415 24 11,300 1.33610.9650 8,000 1.39280.0370 25 11,300 1.33620.9638 8,000 1.39246.0490 26 11,300 1.33612.9646 8,000 1.39271.o405 27 11,300 1.33446.9798 4,200 1.39250.0475 28 11,300 1.33453.9793 4,200 1.39276.0385 29 11,300 1.33381.9867 2,200 1.39251.o470 30 11,500 1.33340.9903 2,200 1.39298.0305 31 7,200 1.33887.7389 16,600 1.39286.0350 32 7,200 1.33900.9377 16,6oo 1.39301.0295 33 7,200 1.33825.9448 12,000 1.39280.0370 34 7,200 1.5533825.9448 12,000 1.39273.o4oo 35 7,200 1.33720.9548 8,000 1.39262.0435 36 7,200 1.33727.9540 8,000 1.39259.o450

-66 - TABLE B-2 CONT 'D Water Phase Isobutanol Phase No I L Index of Wt. Fr. I V Index of Wt. Fr..i gms/hr Refraction H20 I gms/hr Refraction HpO 37 7,200 38 7,200 39 7,200 40 3,700 41 3,700 42 3,700 43 3,700 44 3,700 45 3,700 46 3,700 47 3,700 1.33710 1.33535 1.33405 1.33794 1.33820 1.33705 1.33745 1.33630 1.33600 1.33475 1.33470 ~9557.9718.9838.9477.9453.9562.9525.9631.9657 ~9771.9776 8,000 1.39262 4,200 2,200 12,000 12,000 8,000 8,000 4,200 4,200 2,200 2,200 1.39247 1.39249 1.39341 1.39337 1.39324 1.39322 1.39297 1.39299 1.39292 1.39290.0435.0485.0480.0150.0o6o.0210.0215.0310.0300.0330.0335

TABLE B-3 FLOW RATE CORRECTED DATA FOR 4 INCH COLUMN Water Phase Isobutanol Phase No. LoIndex of Wt. Fr. V0 Index of Wt. Fr. gms/hr Refraction H20 gmns/hr Refraction H20 1 20,000 1.54010.9273 16,6oo 1.59057.1020 2 20,000 1.54005.9280 16,6oo 1.59058.1065 5 20,000 1.33940.9540 12,000 1.59059.1065 4 20,000 1.33930.9348 12,000 1.59077.0970 5 20,000 1.33820.9453 8,000 1.59068.0990 6 20,000 1.33820.9455 8,000 1.59050.1038 7 20,000 1.33643.9620 4,200 1.59017.1120 8 20,000 1.33643.9620 4,200 1.59040.lo6o 9 15,500 1.54015.9268 i6,6oo 1.59098.0915 10 15,500 1.33929.9550 12,000 1.59117 o0865 11 15,500 1.33825.9448 8,000 1.59110.0885 12 15,500 1.33635.9628 4,200 1.59098.0915 13 11,500 1.34o4o.9245 16,6oo 1.59155.0765 14 11,500 1.34030.9253 16,6oo 1.39159.0750 15 11,500 1.33977.9504 12,000 1.59129.0830 16 11,500 1.33990.9292 12,000 1.59141.0800 17 11,500 1.33885.9591 8,000 1.59129.0830 18 11,500 1.55882.9595 8,9000 1.59105.1038 19 11,500 1.33870.9405 8,000 1.59155.0818 20 11,500 i.3386o.9415 8.,000 1.59115.0870 21 11,500 1.33665.9600 4,200 1.59108 o0890 22 11,5300 1.55685.9580 4,200 1.59120.o86o 25 11,500 1.55470.9776 -2,~200 1.59145.0790 24 11,500 1.55475.9771 2,~200 1.59147.0785 25 7,,200 i.34065.9220 16,,6oo 1.59207.o6io 27,~200 1305.9258 12 000 1.59198.o64o 27 7,7200 1.55960.9520.8,000o 1.59177.0700 28 7,7200 1.55970.9510 8,000o 1.59095.0922 29 7,~200 1.55950.9548 8,9000 1.59170.0720 50 7,~200 1.55775.9495 4,9200 1.59150.0775 51 7,y200 1.55800.9472 4,200 1.59077.0970 52 7,200 1.33585.9674 200 1.59086 o0945 55 7,7200 1.55560.9695 2,1200 1.59145.0790 34 5,9700 1.34o65.9220 12,9000 1.59250.o475 55 5,~700 1.54047.9258 12,000 1.59280.0570 56 5,9700 1.55985.9298 8,000o 1.59258.0515 57 5,7700 1.34oo5.9278 8,~000 1.59220.0572 38 5,9700 1.55875.9400 4,9200 1.59180 o0690 59 5,700 1.33845.9428 4,9200 1.59200.o635 4o 5,700 1.55675.9590 2,200 1.59171.0715 41 5,9700 1.55675.9590 2,9200 1.59200.o635

-68 - TABLE B-4 FLOW RATE CORRECTED DATA FOR 6 INCH COLUMN Water Phase Isobutanol Phase L Index of Wt. Fr. I Vo Index of Wt. Fr. | gms/hr Refraction H20 gms/hr Refraction HO2 1 20,000 1.34109.9180 16,600 1.38922.1355 2 20,000 1.34058.9227 12,000 1.38932.1330 3 20,000 1.34038.9246 12,000 1.38941.1308 4 20,000 1.34045.9240 12,000 1.38925.1348 5 20,000 1.33960.9320 8,000 1.38935.1320 6 20,000 1.33937.9342 8,000 1.38956.1270 7 20,000 1.33945.9355 8,000 1.38928.1340 8 20,000 1.33768.9502 4,200 1.38940.1310 9 20,000 1.33768.9502 4,200 1.58928.1340 10 20,000 1.33765.9505 4,200 1.38946.1295 11 15,500 1.34099.9188 16,600 1.38992.1180 12 1, 500 1.34064.9221 12,000 1.38970.1235 13 15,500 1.33975.9306 8,000 1.38977.1220 14 15,500 1.33785.9485 4,200 1.38973.1230 15 11,300 1.34102.9185 16,600 1.39038.1065 16 11,300 1.34095.9192 16,600 1.39041.1060 17 11,300 1.34075.9212 12,000 1.39028.1095 18 11,300 1.34077.9210 12,000 1.39005.1150 19 11,300 1.34063.9222 12,000 1.39045.1050 20 11,300 1.34010.9273 8,000 1.39016.1120 21 11,300 1.34018.9265 8,000 1.38973.1230 22 11,300 1.34000.9283 8,000 1.39038.1065 23 11,300 1.34028.9255 8,000 1.38989.1190 24 11,300 1.33990.9292 8,000 1.59009.1140 25 11,300 1.33980.9300 8,000 1.39025.1100 26 11,300 1.33835.9438 4,200 1.39007.1140 27 11,300 1.33791.9480 4,200 1.39042.1055 28 11,300 1.33795.9476 4,200 1.59020.1110 29 11,300 1.33570.9685 2,200 1.39026.1095 30 11,300 1.33605.9653 2,200 1.39016.1120 31 7,200 1.34110.9177 16,600 1.39099.0910 32 7,200 1.34100.9188 12,000 1.39086.0945 33 7,200 1.34065.9220 8,000 1.39039.1065 34 7,200 1.34068.9218 8,000 1.39038.1065 35 7,200 1.33905.9373 4,200 1.39031.1085

-69 - TABLE B-4 CONT 'D Water Phase Isobutanol Phase No. Lo Index of Wt. Fr. Vo Index of Wt. Fr. gms/hr Refraction H20 gms/hr Refraction H20 36 37 38 39 40 41 42 44 44 7,200 7,200 3,700 3,700 3,700 3,700 3,700 3,700 3,700 1.33868 1.33680 1.3411o 1.34095 1.34095 1.34010 1.34040 1.33855 1.33835.9407.9585.9177.9192.9192.9273.9244.9420.9438 4,200 2,200 12,000 8,000 8, 000 4,200 4,200 2,200 2,200 1.39065 1.39047 1.39220 1.39141 1.39156 1.39080 1.39068 1.39090 1.39084.1000.1045.0570.o800.0760.0960 0990.0935.0950

APPENDIX C ORIGINAL RECEIVER EFFECT EXPERIMENTAL DATA -70 -

APPENDIX C TABLE C-1 ORIGINAL DATA: 1 INCH COLUMN, PURE WATER - 40% SATURATED ISOBUTANOL INLET INLET REFRACTIVE INDICES: WATER - 1.33245, ISOBUTANOL - 1.39195 Water Phase Isobutanol Phase Sample Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 7,100 7,100 7,100 11,150 11,150 11,150 15,200 15,200 15,200 15,200 7,220 19,600 19,600 19,600 19,600 11,350 11,350 11,350 7,350 7,350 7,350 3,800 3,800 3,800 3,800 1.33394 1.33456 1.33572 1.33504 1.33582 1.33407 1.33443 1.33342 1.33530 1.33613 1.33614 1.33588 1.33508 1.33420 1.33362 1.33375 1.33417 1.33303 1.33332 1.33383 1.33456 1.33537 1.33604 1.33404 1.33381 4,o60 7,660 11,880 11,880 16,625 8,000 8,000 4,175 12,000 16,550 16,550 16,550 11,870 7,800 4,200 4,200 7,920 2,130 2,130 4,175 8,100 8,100 12,000 4,000 2,120 1.39141 1.39148 1.59147 1.39147 1.39141 1.39146 1.39177 1.39123 1.39117 1.39117 1.39150 1.39104 1.39111 1.39106 1.39087 1.39120 1.39135 1.39126 1.39126 1.39129 1.39144 1.39153 1.39159 1.39150 1.39132 L L L L L L L L L L L L L L L S S S S S S S S S S

-72 - TABLE C-2 ORIGINAL DATA: 1 INCH COLUMN, PURE WATER - 80o SATURATED ISOBUTANOL INLET INLET REFRACTIVE INDICES: WATER - 1.33245, ISOBUTANOL - 1.38955 Water Phase Isobutanol Phase Sa e Flow Rate Index of Flow Rate Index of Receiver gms /hr Refraction gms/hr Refraction Size 1 2 5 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,300 7,300 7,500 11,325 11,325 11,525 15,400 15,400 15,400 15,400 19,600 19,600 19,600 19,600 11,300 11,300 11,300 7,250 7,250 5,900 3,900 3,900 3,900 1.33517 1.33595 1.33669 1.33646 1.33556 1.33463 1.33466 1.55556 1.33562 1.33552 1.33640 1.33562 1.33459 1.33368 1.33359 1.33456 1.33315 1.33322 1.33404 1.33507 1.33598 1.33659 1.33453 1.33374 7,460 11,980 16,600 16,600 11,960 8,050 8,050 4,225 12,000 12,000 16,530 11,930 7,860 4,250 4,250 8,140 2,340 2,240 4,300 4,300 7,980 12,000 4,175 2,260 1.38919 1.38917 1.38922 1.38916 1.38913 1.38904 1.38892 1.38883 1.58890 1.38904 1.38895 1.38895 1.38889 1.38886 1.38897 1.38907 1.58890 1.38899 1. 38901 1.38901 1.38913 1.38925 1.38913 1.38911 L L L L L L L L L L L L L L S S S S S S S S S S

-73 - TABLE C-3 ORIGINAL DATA: 1 INCH COLUMN, 40% INLET REFRACTIVE INDICES: WATER SATURATED WATER-PURE ISOBUTANOL INLET - 1.33568, ISOBUTANOL - 1.39380 Water Phase Isobutanol Phase Flow Rate Index of Flow Rate Index of Receiver Sample gs/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,420 7,420 7,420 11,450 11,450 11,450 15,500 15,500 15,500 15,500 19,975 19,975 19,975 19,975 11,450 11,450 11,450 7,450 7,450 7,450 3,700 3,700 3,700 3,700 1.33675 1.33720 1.33762 1.33771 1.33701 1.33659 1.33659 1.33621 1.33698 1.33749 1.33727 1.33711 1.33662 1.33627 1.33614 1.33646 1.33601 1.33604 1.33633 1.33659 1.33711 1.33759 1.33669 1.33636 7,560 11,900 16,700 16,700 11,650 7,950 7,950 4,175 12,030 16,500 16,500 11,880 7,920 4,225 4,225 7,920 2,200 2,200 4,300 7,900 7,900 11,975 4,175 2,220 1.39325 1.39331 1.39331 1.39316 1.39319 1.39316 1.39301 1.39295 1.39307 1.39301 1.39277 1.39289 1.39287 1.39253 1.39316 1.39322 1.39307 1.39316 1.39319 1.39331 1.39331 1.39337 1.39325 1.39316 L L L L L L L L L L L L L L S S S S S S S S S S

TABLE C-4 ORIGINAL DATA: 1 INCH COLUMN, 40% SATURATED WATER - 40% SATURATED ISOBUTANOL INLET. INLET REFRACTIVE INDICES: WATER - 1.33568, ISOBUTANOL - 1.39195 Water Phase Isobutanol Phase Sample Flow Rate Index of Flow Rate Index of Receiver gms/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,550 7,550 7,550 11,550 11,550 11,550 15,700 15,700 15,700 15,700 19,950 19,950 19,950 19,950 11,350 11,350 11,350 7,400 7,400 7,400 3,700 3,700 3,700 3,700 1.33706 1.33750 1.33813 1.33797 1.33720 1.33662 1.33675 1.33617 1.33717 1.33788 1.33791 1.33724 1.33688 1.33617 1.33617 1.33677 1.33591 1.33607 1.33641 1.33691 1.33756 1.33807 1.33677 1.33633 7,500 12,000 16,600 16,600 11,900 7,900 7,900 4,175 12,000 16,600 16,600 12,000 7,920 4,200 4,200 7,830 2,300 2,500 4,200 7,880 7,880 11,975 4,175 2,260 1.39150 1.39153 1.39156 1.39132 1.39138 1.39138 1.39120 1.39120 1.39132 1.39123 1.39105 1.39108 1.39099 1.39102 1.39129 1.39144 1.59135 1.39141 1.39141 1.39150 1.39151 1.39153 1.39159 1.39147 L L L L L L L L L L L L L L S S S S S S S S S S

-75 - TABLE C-5 ORIGINAL DATA: 1 INCH COLUMN, 40% SATURATED WATER - 80o SATURATED ISOBUTANOL INLET. INLET REFRACTIVE INDICES: WATER - 1.33568, ISOBUTANOL - 1.38955 Water Phase Isobutanol Phase e Flow Rate Index of I Flow Rate Index of Receiver S gms/hr Refraction | gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 6,900 6,900 6,900 11,400 11,400 11,400 15,500 15,500 15,500 15,500 19,800 19,800 19,800 11,600 11,600 11,600 7,250 7,250 7,250 3,725 3,725 3,725 3,725 1.33730 1.33771 1.33829 1.33823 1.33740 1.33678 1.33678 1.33627 1.33737 1.33810 1.33775 1.33665 1.33624 1.33624 1.33672 1.33588 1.33604 1.33646 1.33724 1.33788 1.33788 1.33688 1.53627 7,860 11,980 16,750 16,750 11,925 8,000 8,000 4,525 12,000 16,620 12,800 8,o40 4,200 4,200 7,890 2,240 2,240 4,300 7,950 7,950 11,975 4,175 2,220 1.38934 1.38931 1.38934 1.38921 1.58927 1.38928 1.38913 1.58913 1.38917 1.38916 1.38907 1.38916 1.38910 1.38919 1.58925 1.38922 1.38923 1.38922 1.38922 1.38925 1.38939 1.38930 1.38932 L L L L L L L L L L L L L S S S S S S S S S S

TABLE C-6 ORIGINAL DATA: 1 INCH COLUMN, 80% SATURATED WATER-PURE ISOBUTANOL INLET INLET REFRACTIVE INDICES: WATER - 1.33870, ISOBUTANOL - 1.39380 Water Phase Isobutanol Phase Flow Rate Index of Flow Rate Index of Receiver Sample gs/r Refraction Size gms hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,075 7,075 7,075 11,400 11,400 11,400 15,700 15,700 15,700 15,700 20,250 20.250 20,250 20.250 11,500 11,500 11,500 7,300 7,300 7,300 3,550 3,550 3,550 3,550 1.33922 1.33955 1.33981 1.33961 1.33935 1.33913 1.33915 1.33897 1.33934 1.33971 1.33994 1.33955 1.33925 1.33874 1.33903 1.33903 1.33890 1.33893 1.33908 1.33919 1.33935 1.33958 1.33916 1.33903 7,980 11,920 16,550 16,550 11,925 8,000 8,000 4,200 11,900 16,600 16,600 12,000 8,220 4,230 4,230 8,070 2,180 2,180 4,275 7,960 7,960 12,000 4,200 2,200 1.39331 1.39325 1.39331 1.39322 1.39317 1.39319 1.39295 1.39280 1.39301 1.39301 1.39268 1.59265 1.39262 1.39274 1. 39295 1.39322 1.39280 1.39307 1.39298 1.59331 1.39331 1.39337 1.39325 1.39316 L L L L L L L L L L L L L L S S S S S S S S S S

-77 - TABLE C-7 ORIGINAL DATA: 1 INCH COLUMN, 80% SATURATED WATER - 40% SATURATED INLET. INLET REFRACTIVE INDICES: WATER - 1.33870, ISOBUTANOL - ISOBUTANOL 1.39195 Water Phase Isobutanol Phase Flow Rate Index of Flow Rate Index of Receiver amp gms/hr Refraction gms/hr Refraction Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,360 7,360 7,360 11,500 11,500 11,500 15,800 15,800 15,800 15,800 20,200 20,200 20,200 20,200 11,500 11,500 11,500 7,340 7,340 7,340 3,650 3,650 3,650 3,650 1.33932 1.33942 1.33948 1.33948 1.33930 1.33904 1.33906 1.33897 1.33947 1.33968 1.33987 1.33948 1.33925 1.33900 1.33900 1.33915 1.33884 1.33887 1.33903 1.33917 1.33945 1.33961 1.33917 1.33897 7,540 12,000 16,600 16,600 11,900 7,925 7,925 4,125 11,880 16,620 16,620 11,900 8,010 4,175 4,175 7,890 2,270 2,270 4,225 7,870 7,870 12,025 4,100 2,160 1.39142 1.39154 1.39165 1.39153 1.39153 1.39153 1.39141 1.39111 1.39117 1.39132 1.39108 1.39111 1.39105 1.39086 1.39117 1.39132 1.39117 1.39123 1.39129 1.39147 1.39153 1.39162 1.39141 1.39147 L L L L L L L L L L L L L L S S S S S S S S S S

-78 - TABLE C-8 ORIGINAL INLET. DATA: 1 INCH COLUMN, 80o SATURATED WATER - 80% SATURATED INLET REFRACTIVE INDICES: WATER - 1.33870, ISOBUTANOL - ISOBUTANOL 1.38955 Water Phase Isobutanol Phase Sample I Flow Rate Index of I Flow,Rate Index of I Receiver gms/hr Refraction gms/hr Refraction f Size 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 7,400 7,400 7,400 11,500 11,500 11,500 15,700 15,700 15,700 15,700 20,125 20,125 20,125 20,125 11,500 11,500 11,500 7,325 7,325 7,325 3,700 3,700 3,700 3,700 1.33922 1.33935 1.33961 1.33955 1.33928 1.33913 1.33916 1.33897 1.33929 1.33955 1.33961 1.33929 1.33897 1.33896 1.33903 1.33909 1.33884 1.33893 1.33890 1.33921 1.33938 1.33968 1.33909 1.33894 7,520 11,900 16,600 16,600 11,950 7,900 7,900 4,225 11,940 16,600 16,600 12,030 7,770 4,275 4,275 7,920 2,210 2,210 4,225 7,880 7,880 11,925 4,200 2,280 1.38931 1.38935 1.38937 1.38933 1.38933 1.38923 1.38907 1.38899 1.38916 1.38917 1.38916 1.38913 1.38922 1.38898 1.38904 1.38922 1.38904 1.38907 1.38919 1.38929 1.38922 1.38937 1.38925 1.38916 L L L L L L L L L L L L L L S S S S S S S S S S

APPENDIX D CALCULATION OF PHASE TRANSFER COEFFICIENTS -79 -

APPENDIX D CALCULATION OF PHASE TRANSFER COEFFICIENTS Regardless of the procedure used to compute the phase transfer coefficients kA and kWV, it is necessary to calculate, from the phase compositions tabulated in Appendix B, the following information for each phase, at each bed height and for each combination of flow rates (cf. Table I). For the water-rich phase; (1) the number of moles of isobutanol flowing - LxA (2) the molal concentration of isobutanol - CAL (3) the concentration driving force for the transfer of isobutanol (CAL CAL). For the isobutanol-rich phase; (1) the number of moles of water flowing - VyW (2) the molal concentration of water - CWV (3) the driving force for the transfer of water into the isobutanol (Cwv - CWV)* The tabulated mass fractions were first converted to mole fractions by the relation, W = XW/(O75676xW + 0.24524) Yw = YW/(O.75676YW + 0.24524) where xW, Yw = the mole fraction of water in the water-rich and isobutanolrich phases respectively and XW, YW = the mass fraction of water in the water-rich and isobutanol-rich phases respectively. Of course, xA and YA are found by (1.0 - xW) and (1.0 - yw). -80 -

The moles of a component, say water flowing in the alcohol phase, was computed using Equation (8) and multiplying by yW, or Lo - xW(Lo + Vo) V = - (YW - XW) and the moles of water equals VyW. The molal concentrations were computed using the relations CAL = XA/(0.0925 xA + 0.018 xW) and CWV = YW/(0 0925 YA + 0.018 y). The molal concentrations for the saturated phases were computed to be C = 1.10 gm moles/liter AL and WVt = 7.68 gm moles/liter. * * The values of LxA, VYW, CAL, CWV, (CAL CAL) and (Cw - CWV) were computed. for all the data points tabulated in Appendix B on the IBM 704. The execution time was approximately one minute. If there were duplicate values of LxAA Vywr ACALand ACWV at any flow condition, the arithmetic mean was used in subsequent computation. Two sets of sample calculations follow which are intended to exhibit some of the properties of the data, The first will concern computing transfer coefficients for the water phase and the second the alcohol phase. The water phase transfer coefficient kAL for the flow condition of 11,300 gms/hr water and 12,000 gms/hr isobutanol will be computed by the several methods discussed in Section VI, (1) by drawing an equal area through the differenced values of LXA, (2) by averaging the kAL 's computed

-82 - for the increments of the column and (3) by an integral average. The numbers pertinent to the calculations are given in Table III. TABLE III CALCULATION OF WATER PHASE TRANSFER COEFFICIENTS INLET FLOW RATES: WATER - 11,300 gms/hr ISOBUTANOL - 12,000 gms/hr Z LX A(LxA)/AZ ACALkA Ts (in.) gm. mo/hr A(LXA) gm. mohr. in gm.mol/lit. (ACAL)m lit/hr. in (ACAL)1 (in.. m.m.l.. i. t..A m.... 0 0 1.10.91 3.86 3.86.93 4.15 1 3.86.76 1.32 3.26 3.26.62 5.26 2 7.12.48 2.08 3.40 1.70.296 5.74 4 10.52.111 9.0.90.45.085 5.29 6 11.41.058 11.8 kAL * S = 5.25 kAL = 1,620 (hr) For method (1), the values of A(LxA)/AZ are plotted as in Figure 21a against the height of bed. An equal area curve is drawn through the rate rectangles. This ostensibly gives the rate of transfer of isobutanol into the water phase as a smooth function of height of packing. Now, since the driving force, (CAL - AL), is known at bed heights of 0", 2", 4" and 61, a plot such as Figure 21b can be drawn (the rate vs. driving force). The.-1 slope of the line through the points of this plot yields the quantity kAL S —! in the units liters/hr.in. assuming, of course, that the kA is a constant. From Figure 21b, it is seen that this is not entirely true for the equal area

5.,.c N,. 0 0 0 E w bJ 4 3 2 I 0 0 1 2 3 4 5 6 7 HEIGHT OF BED,INCHES (a) 5 c T %0 0) a E x6 -4 I 4 3 -..,OO -.00 -..O -A I I I 2 I 0 v 0.1.2.3.4.5.6.7.8.9 CAL- CAL,gm. moles/lit. (b) Equal Area Calculation of Water Coefficients. Figure 21. Phase Transfer

curve as drawn in Figure 21a, since the points are somewhat scattered. However, to a degree of approximation, a straight line is sufficient. A least squares line through the points and through the origin, yields a slope of 5.25. For method (2), the incremental coefficients, a mean driving force over the increment is needed, and this was taken as the arithmetic mean of the initial and final.LCAL of the increment in question. This corresponds to the column (ACAL)m in Table III. The rate of transfer in that increment, A(LxA)/AZ, is then divided by this mean driving force, yielding an average kAL * S for the increment of the bed in question. The _! values are then averaged once more, yielding a mean kAL * S for the entire composite column. In this case, it turns out that this mean is 5.25, the same value as that obtained in method (1). Method (2) has the advantage of presenting the incremental coefficients of the column, employing no data smoothing at any point in the treatment of the column data. From Table III, and also shown in Figure 17, the column of kAL * S values shows that the water phase coefficient is indeed quite constant throughout the composite column. For method (3), computing the integral average coefficient, a plot of 1/(CAL - CAL) vs LxA is constructed and integrated graphically. AL AL A This procedure gives a value of 5.8 to kA * S. AL The water phase data was generally very well-behaved and the difference in the methods of computing an average column coefficient was not significant. However, the incremental coefficients of method (2) gave a much better indication of the stability of the original data and of

-85 - any effect of the height of bed on the coefficients, This is brought out more clearly in the treatment of the alcohol phase data, which was far more erratic than the water phase data, and on inspection of the incremental coefficients of method (2) showed some tendency to vary with bed height. Very often method (1) failed even to approximate a transfer coefficient which would yield the correct amount of total transfer. This was probably due in part to the tendency of the isobutanol phase coefficient to increase with increasing bed height, but mostly to the impossibility of drawing a correct equal area curve through the too few rate rectangles that could be constructed from the data. As an illustration of this, a sample calculation for the alcohol phase transfer coefficient is presented for the flow condition of 11,300 gms/hro water and 8,000 gms/hr. isobutanol. The required numbers are given in Table IVo TABLE IV CALCULATION OF ISOBUTANOL PHASE TRANSFER COEFFICIENTS INLET FLOW RATES: WATER - 11,300 gms/hr ISOBTJTANOL - 8,000 gms/hr. z Vy A(Vyw)/ AZ t C * S (in.) gm.mo/hr. A(VyW) gm.mol/hrin gm.mol/lit. (ACWV)m lit/hr. in (ACwv) 0 0 7.68.13 10.58 10 58 7.14 1.48 1 10.58 6.61.151 8.32 8.32 6.19 1.34 2 18.90 5.76.174 18.39 9.20 4.82 1.91 4 37.29 3.89.258 14.18 7.09 3.02 2.35 6 51.47 2.16.463 kW * S = 1.89 kW= 580 (hr)

The corresponding plots of rate vs. bed height and the "equal area" smoothed rate vs. driving force are shown in Figures 22a and 22b. Drawing an equal area curve through the rate rectangles of Figure 22a, points on the rate vs. driving force plot, Figure 22b, are obtained which do approximate a straight line. This straight line, however, does not tend to the origin and, if only the straight portion is considered, the slope yields a kWV * S of 0.9, while an averaging of the incremental coefficients yields a value of 1.89. The integral averaging method yields a value of 1.91. Clearly, an ordinary smoothing of the rate rectangles, in this case, by an equal area curve, does not yield transfer coefficients consistent with the amdunt of mass transfer taking place. This was true for a great many of the calculations concerning the isobutanol phase coefficients. Due to the above situation, only the results of calculating the incremental coefficients for the variable column length data are presented. The incremental transfer coefficients for isobutanol transferring into water are tabulated in Table V, and those for water transferring into isobutanol are tabulated in Table VI.

-87 - I - (n E E nJ Hr 12 0 ----- 10 8 6 4 2 0 I 2 3 4 5 HEIGHT OF BED, INCHES (a) 6 7 8 c b. I HCJ 12 10 8 6 4 2 n K-~ - I- - 0, --- — w 0 I 2 3 4 5 6 7 8 Cwx~ Cwv, gm. moles/lit. (b)?2. Equal Area Calculation of an Isobutanol Transfer Coefficient. Figure

-88 - TABLE V INCREMENTAL WATER PHASE TRANSFER COEFFICIENTS r. liters ' Llet Flow Condition-gms/hr kAL * S for Bed Increment. litrEAL * SkAL -hr Ahr.in..AL k -hr water isobutanol 0-1 1-2 2-4 4-6 in. in. in. in. 20,000 16,600 10.5 9.5 9.4 13.5 11.0 3,400 12,000 7.0 8.2 8.o 8.5 8.0 2,480 8,000oo 4.9 4.8 6.4 5.7 5.7 1,750 4,200 2.9 3.6 351 3.3 3.2 990 15,500 16,600 8.6 9.3 6.4 7.8 7.7 2,390 12,000 5.0 8.2 5.2 7.9 6.6 2,030 8,000 3.8 5.1 4.3 5.5 4.7 1,460 4,200 1.8 3.4 2.2 3.1 2.6 810 11,300 16,6oo 5.3 7.8 5.1 - 5.8 1,810 12,000 4.2 5.3 5.4 5.3 5.3 1,620 8,000 3.1 3.4 3.9 4.0 3.7 1,160 4,200 1.4 2.2 2.1 2.1 2.0 620 2,200 1.2.5 1.0 1.1 1.0 310 7,200 16,600 3.5 5.9 3.2 - 4. 1,230 12,000 2.7 5.1 3.5 1.6 3.0 920 8,000oo 2.4 3.4 2.8 3.0 2.9 890 4,200 1.0 2.0 2.0 1.4 1.6 500 2,200.7.9.9.9.9 270 3,700 12,000 1.7 2.2 2.0 - 1.9 600 8,000 1.3 1.7 1.7 1.3 1.5 460 4,200.9 1.2 1.2 1.5 1.3 390 2,200.6.6.7.9 ~7 230

TABLE VI INCREMENTAL ISOBUTANOL PHASE TRANSFER COEFFIC IENTS Inlet Flow Condition-gms/hr | water isobutanol 0 * O.1 20,000 15,500 11,300 7,200 3,700 16,600 12,000 8,000 4,200 16,600 12,000 8,000 4,200 16,600 12,000 8,000 4,200 2,200 16,600 12,000 8,000 4,200 2,200 12,000 8,000 4,200 in. 4.3 2.7 2.1 1.2 3.6 2.6 2.1 1.1 2.5 1.9 1.5.8.7 1.8 1.3 1.3.7.4 1.3.9.7 _ for Bed 1-2 in. 4.6 3.2 1.9 1.1 5.4 3.2 2.1 1.5 3.2 2.1 1.3.7.0 2.5 2.5 1.7 1.0.4.1.4.4 - Increment 2-4 in. 5.4 3.6 2.2 1.2 3.6 2.4 1.4 0.6 3.3 2.9 1.9 1.0.5 2.5 1.7 1.2.7.4 1.5 1.3.8 liters,. -' -1 hr.in W * S kWV -hr 4-6 in. average 7.4 4.7 2.6 0.8 4.8 4.6 2.6 1.1 4.5 3.2 2.4 5.7 3.8 2.3 1.0 4.3 3.3 2.0 1.0 3.6 2.7 1.9 0.8 o.4 2.8 2.1 1.7.8.4 1.0 1.0.8 1,770 1,170 700 320 1,320 1,010 630 300 1,110 830 580 260 130 860 655 520 250 130 325 310 235.7.5 3.7 2.8 2.4.9.4 1.0 1.1 1.0 2,200. 4. 1.4.4.4 110

-90 - TABLE VII SUMMARY OF INDIVIDUAL PHASE TRANSFER COEFFICIENTS ilet Flow Condition lbs/hr.ft2 et Flow Codition t Water Phase Coefficient Isobutanol Coeffici Water Isobutanol -1 hk kAL hrk h 32,000 27,000 3,400 1,770 19,000 2,480 1,170 13,000 1,750 700 6,800 990 320 25,000 27,000 2,390 1,320 19,000 2,030 1,010 13,000 1,460 630 6,800 810 310 18,000 27,000 1,810 1,110 19,000 1,620 830 13,000 1,160 580 6,800 620 260 3,500 310 130 12,000 27,000 1,230 860 19,000 920 655 13,000 890 520 6,800 500 250 3,500 270 130 6,000oo 19,000 600 325 13,000 460 310 6,800 390 235 3,500 230 110

APPEND1IX E REFRACTIVE NIDEX CALIBRATION WATER AND ISOBUTANOL -91 -

APPENDIX E REFRACTIVE INDEX CALIBRATION WATER AND ISOBUTANOL The index of refraction - weight fraction calibration was determined by taking the refractive index of a sample of predetermined composition. The data obtained checked with that of Colburn and Welsh. ( Commercial grade isobutanol and distilled water acidified to 0.0001 N HC1 were used. The data are presented in Table VIII and are plotted in Figures 25 and 24. TABLE VIII INDEX OF REFRACTION - WEIGHT FRACTION CALIBRATION OF ISOBUTANOL - WATER AT 25~C. Index of Weight Fraction Sample No. Refraction Water 1 1.33245 1,0 2 1.33323,9922 3 1.33485,9761 4 1.33640.9623 5 1.33791.9482 6 1.33947.9335 7 1.34077.9210 8 1.34118.9170-sat. water 9 1.38795.1670-sat. isobutanol 10 1.38849.1536 11 1.38958.1266 12 1.39062.1009 13 1.39180.0692 14 1.39283.0363 15 1.39347.0124 16 1.39382 0.0 -92 -

0 U LL LU L*. LU 0 X Z 1.0.99.98.97.96.95.94.93.92 WEIGHT FRACTION WATER Figure 23. Index of Refraction Calibration for Water Phase.

I. z UL 1.3910 CLL 0 0 X 1.3900 1.3890 1.3880 0.02.04.06.08.10.12.14.16.18 WEIGHT FRACTION WATER Figure 24. Index of Refraction Calibration for Isobutanol Phase. I 0

BIBLIOGRAPHY 1. Colburn, A. P., and Welsh, D. G. "Experimental Study of Individual Transfer Resistances in Countercurrent Liquid-Liquid Extraction," Trans. Am. Inst. Chem. Engrs. 38, (1942) 179. 2. Gayler, R., and Pratt, H. R. C. "Individual Film Coefficients on an Area Basis for a Packed Column," Trans. Inst. Chem. Engrs. (London) 31, (1953) 78. 3. Gordon, K. F., and Sherwood, T. K. "Mass Transfer Between Two Liquid Phases," Chem. Eng. Prog. Symposium Ser. No. 10, 15, (1954). 4. Heertjes, P. M., Holve, W. A. and Talsma, H. "Mass Transfer Between Isobutanol and Water in a Spray-Column," Chem. Eng. Sci. 3, (1954) 122. 5. Laddha, G. S., and Smith, J. M. "Mass Transfer Resistances in LiquidLiquid Extraction," Chem. Eng. Progr. 46, (1950) 195. 6. Lewis, J. B. "The Mechanism of Mass Transfer of Solutes Across Liquid-Liquid Interfaces," Chem. Eng. Sci. 3, (1954) 3. 7. Ruby, C. L., and Elgin, J. C. "Mass Transfer Between Liquid Drops and a Continuous Liquid Phase in a Countercurrent Fluidized System," Chem. Eng. Progr. Symposium Ser. No. 16, 17, (1955). 8. Smith, G. C., and Beckman, R. B. "Individual Film Coefficients of Mass Transfer in Liquid-Liquid Extraction," A. I. Ch. E. Journal 4, (1958) 180. -95 -

UNIVERSITY OF MICHIGAN 3 9015 03466 6118