THE UNIVERSITY OF MI C H I G A N COLLEGE OF ENGINEERING Department of Chemical and Metallurgical Engineering Technical Report No. 1 EXPERIMENTAL AND THEORETICAL INVESTIGATION OF CONTINUOUS FLOW COLUMN CRYSTALLIZATION Joseph D. Henry, Jr. ORA Project 01730 sponsored by: NATIONAL SCIENCE FOUNDATION GRANT NO. GK-1913 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR October 1968

ACKNOWLEDGMENTS I wish to express my appreciation to the following individuals and organizations for their contributions to this research: Professor J. E. Powers, chairman of the doctoral committee, for his personal interest, guidance, and generous donation of time to the discussion of the problems which arose in the course of this investigation. Professor J. D. Goddard, committee member, for his perceptive discussion of several aspects of the mathematical model developed in the dissertation. Professor J. L. York and. R. H. Kadlec, committee members, for their assistance, criticism, and helpful suggestions. Professor E. A. Boettner, committee member, for his invaluable suggestions and help in confirming the results of the gas chromatographic analysis technique used in the course of this work; he willingly donated, much of his time and the services of his staffo Drs. R. Albertins and W. C. Gates, Jr. for their encouragement, assistance suggestions, and continued interest in this research. Mr. M. D. Danyi for his assistance and suggestions in experimentally evaluating the effect of the feed position on column performance. Mr. M. R. Player for his constructive criticism of several aspects of this work. The personnel of the shops of the Department of Chemical and. Metallurgical Engineering for their cooperation and assistance in constructing and maintaining the experimental equipmento ii

The National Science Foundation for traineeship support and. sponsorship of this research through grant GK-1913. Phillips Petroleum Company for donating the benzene and cyclohexane used. in this investigation. The Upjohn Company for the donation of the drive mechanism for the column crystallizer. Mr. T. G. Smith for his careful proofreading of the manuscript. The service units of the Office of Research Administration for their efficient and accurate production of this dissertation in its final form. My wife, Ruth Ann, for her encouragement, support, and assistance in the preparation of this thesis. iii

TABLE OF CONTENTS Page LIST OF TABLES vii LIST OF FIGURES viii NOMENCLATURE xi ABSTRACT xv Chapter I. INTRODUCTION 1 II. REVIEW OF LITERATURE 4 A. Description of the Process 4 1o Column configuration 6 2. Process flow in the Schildknecht column 6 B. Published. Reviews 9 C. Other Literature Related, to Column Crystallization 10 D. Experimental and. Theoretical Studies for Total Reflux Operation 11 E. Previous Investigations with Continuous Feed. and Product Draw-Off 15 1. End-fed. column 15 2. Center-fed column 16 F. Summary 19 III. THEORETICAL DEVELOPMENTS 20 A. Possible Mechanisms 20 B. Formulation of Model 22 1. Enriching section, (z>zF) 24 2. Stripping section, (z<zF) 27 3. Boundary conditions 28 4. Summary of assumptions 29 C. Simplification of the Model 29 1. Enriching section 30 2. Stripping section 54 3. Summary of the resulting model 355 D. Transport Equation Approach 36 E. Implementation of the Model 40 1. End compositions for the purification section 40 2. Column calculations 43 iv

TABLE OF CONTENTS (Continued.) Chapter Page F. Implications of the Model 44 G. Approximations 47 IV. EXPERIMENTAL INVESTIGATION 50 A. Description of Equipment 50 lo The column proper 50 2. Feed, and. product draw-off system54 30 Spiral drive mechanism55 4. Column environment 56 5* Refrigeration system 56 B. Operating Procedures 57 1. Start-up 57 2o Operation 58 35 Flow measurements 59 4. Temperature measurements 60 5. Sampling technique 60 6. Approach to steady state 61 7. Analytical method 64 C. Variables Investigated. 64 D. System to be Investigated. 65 E. Experimental Results 67 F. Reproducibility of the Data 67 V. INTERPRETATION OF RESULTS 68 A. Evaluation of the Model 68 1. Enriching section composition profile shape 69 2. Stripping section profile shape 71 3. Impurity associated with the crystal phase 77 4. Effect of feed composition 81 5. Column calculations with experimentally determined parameters 82 6. Mass transfer factors 88 7. Predictive column calculations 95 8. Effect of the enriching section product-crystal rate ratio, RE 97 B. Limits of Operation 101 1o Crystal rate 101 2. Overhead product-crystal rate ratio, RE 105 C. Error Analysis 105 D. Conclusions 105 VI. DISCUSSION OF CONTINUOUS FLOW COLUMN CRYSTALLIZATION 107 v

TABLE OF CONTENTS (Concluded.) Chapter Page A. Parameter Studies 107 1. Feed position 108 2. Enriching section product-crystal rate ratio, RE 108 35 The relation between continuous and total reflux operation 111 B. Production of Ultrapure Benzene 112 1. Multiple pass operation 114 2. Design example 115 VII. SUMMARY AND CONCLUSIONS 118 VIII. RECOMMENDATIONS FOR FUTURE INVESTIGATION 122 Appendix A. METHODS OF ANALYSIS 125 1o Determination of Cyclohexane Benzene Compositions 125 2. Analysis of Impurities in Phillips Pure Grade Benzene 128 B. CALIBRATIONS 129 C. EXPERIMENTAL DATA AND CALCULATED PARAMETERS 133 D. COMPUTER PROGRAM FOR COLUMN CALCULATIONS 138 E. TOTAL REFLUX DATA 144 1. Impurity Associated with the Crystal Phase 144 2. Total Reflux Mass Transfer Factor, rO 145 F. CALCULATION OF THE CHARACTERISTIC ROOTS OF EQUATION (13) 146 BIBLIOGRAPHY 148 vi

LIST OF TABLES Table Page Io Impurities in Phillips Pure Grade Benzene 66 IIo Comparison of Calculated and Experimental Values of the Shape Determining Group for the Stripping Section 76 IIIo Comparison of Experimental and Calculated Values of the Terminal Compositions 87 IV. Comparison of the Mass Transfer and Diffusion Groups Obtained from Total Reflux and Continuous Flow Data 92 V. Response of the Flame Detector to Benzene-Cyclohexane Mixtures 127 VI. Voltmeter Calibration 130 VIIo Locations of the Sample Taps in the Purification Section 131 VIII. Locations of the Thermocouples in the Column 131 IX. Experimental Data 134 Xo Parameters Calculated from the Composition Profiles 137 XIo Definitions of Computer Symbols 139 XII. Program Listing 141 XIIIo Typical Output 145 XIV. Ultimate Purity that can be Obtained by Column Crystallization of a 30,000 ppm Cyclohexane-Benzene Mixture with Total Reflux Operation 144 XV. Total Reflux Mass Transfer Factors 145 vii

LIST OF FIGURES Figure Page 1. Sections used, in a column crystallizero 5 2o Phillips end.-fed column crystallizer operated with feed and product draw-off. 7 3o Crystals and melt in countercurrent contact. 8 4. Typical free liquid. composition profile obtained by Albertins1 for total reflux operationr 14 5. Elemental description of columrn crystallizero 23 6. Relationship between internal and external streams. 26 7. Melting and freezing section modelso 41 80 Composition profile shapes predicted by the modelo 46 9. Schematic diagram of the column crystallizer used in this ine stigati on. 51 10. Photograph of the column crystallizer used in this investigationo 52 11. Feed. introduction assemblyo 5 12. Approach to steady state indicated by the enriching section product compositiono 62 13. Approach to steady state indicated by the enriching section composition profile. 65 14. Experimental confirmation of the three enriching section composition profile shapeso 70 15. Modified enriching section composition profiles. 72 16. Determination of Yp for Run 5o 73 17o Enriching and stripping section composition profiles, 74 viii

LIST OF FIGURES (Continued) Figure Page 18. Enriching and stripping section composition profiles. 75 19. Correlation of crystal phase impurity composition with the bottoms product composition. 79 20. Influence of feed composition on the impurity level in the enriching section0 83 21. Enriching section composition profiles for the purification of Phillips pure grade benzeneo 84 22. Comparison of experimental and calculated composition profiles. 86 23. Comparison of calculated and experimental values of the mass transfer factoro 91 24 Comparison of experimental and. calculated composition profiles. 96 25. Enriching section composition profiles for large values of enriching section product-crystal rate ratio. 99 26. Enriching section composition profile obtained at the onset of crystal plugging. 102 27. Influence of feed. position on the enriching section product composition. 109 28. The effect of the enriching section product-crystal rate ratio and product recovery on the enriching section product purity. 110 29. Comparison of the purity achieved, with continuous flow and. total reflux operation. 111 30. Chromatograms which confirm the purification of Phillips pure grade benzene by column crystallization. 113 31. Effect of the second pass feed. composition on the time required. to produce 2,000 gm of 3 ppm product. 116 532 Comparison of one pass and. two pass operation. 117 ix

LIST OF FIGURES (Concluded.) Figure Page 33. Typical cyclohexane-benzene chromatogram. 126 34. Calibration curve for the feed and bottoms pumps. 129 x

NOMENCLATURE A Cross-section area of column measured perpendicularly to flow of crystalliquid slurry, cm2 a Area available for interphase mass transfer per unit volume of column, cm/cm3 bl Collection of terms defined by Eq. (75b) b2 Collection of terms defined by Eq. (75c) b3 Collection of terms defined by Eq. (75d) C Internal crystal rate, gm/min C1 Constant in general solution of differential equation for enriching section C2 Constant in general solution of differential equation for enriching section C1 Constant in general solution of differential equation for stripping section C2 Constant in general solution of differential equation for stripping section C* Crystal rate corresponding to maximum value of the function defined by Eq. (24) D Coefficient of eddy diffusion, cm2/min e 2.71828 F Response factor defined by Eq. (86) K Liquid phase mass transfer coefficient, cm/min L Mass flow rate of free liquid, gm/min L' Mass flow rate of adhering liquid, gm/min E xi

NOMENCLATURE (Continued) L Mass flow rate of stripping section product, gm/min S XZ Length of purification section, cm MD Mass transfer rate of impurity due to axial dispersion, gm/min MK Mass transfer rate of impurity from the adhering liquid to free liquid, gm/min Summation index Qi Collection of terms defined by Eq. (lOa) Q2 Collection of terms defined by Eq. (lOb) Collection of terms defined by Eq. (20a) Collection of terms defined by Eq. (20b) r1 Characteristic root of Eq. (15) r2 Characteristic root of Eq. (13) rl Characteristic root given by Eq. (22) ro Characteristic root given by Eq. (22) R E Ratio of enriching section product rate to crystal rate, LE/C R Ratio of stripping section product rate to crystal rate, L /C S S X Parameter in Eq. (55) X Value of X for enriching section defined by Eq. (51) E X Value of X for total reflux operation, special case of Eq. (51) o XS Value of X for stripping section defined by Eq. (52) Y Free liquid impurity composition, ppm wt Y' Adhering liquid impurity composition, ppm wt YE Enriching section product composition, ppm wt YE xii

NOMENCLATURE (Continued) YF Feed composition, ppm wt Collection of terms defined by Eq. (7) Y Collection of terms defined by Eq. (7) Y Collection of terms defined by Eq. (18) Y Stripping section product composition, ppm wt S Y Free liquid composition inside the column at the feed point, ppm wt Y1 Free liquid composition at Noe 1 sample tap, ppm wt z Position in column measured from the freezing section, cm z Feed position, cm Greek Symbols a Ratio of the adhering liquid to crystal rates A Small increment e Impurity composition of crystal phase, ppm wt Volume fraction free liquid O Function defined by Eq. (55) p Free liquid density, gm/cm3 E Summation symbol |E Enriching section mass transfer factor defined by Eq. (4lb), cm E 4Y Enriching section mass transfer factor defined by Eq. (46b), cm E Stripping section mass transfer factor defined by Eq. (42b), cm S1 Stripping section mass transfer factor defined by Eq. (i7b), cm S xiii

NOMENCLATURE (Concluded) Subscripts max Denotes the maximum value of a function min Denotes the minimum value of a function xiv

ABSTRACT A theoretical and experimental investigation of the separation achieved in a column crystallizer which utilizes a spiral conveyor was conducted to determine the effect of variables associated. with continuous flow operation. A system which exhibits negligible solid. solubility was used. Several feed mixtures containing less than 31,000 ppm wt cyclohexane in benzene were employed. The principal variables evaluated in this study in a column of constant length were the feed position, internal crystal rate, and flow rates of terminal streams. A mathematical model was developed which considers the transfer of impurity by axial dispersion in the reflux liquid., washing of impurity from the adhering liquid which is associated with the crystal phase, and. the presence of impurity in the crystal phase due to either volumetric inclusion or slight solid solubility. The model was developed by employing a component material balance on an element of the reflux liquid and. a balance embracing all streams. Two forms of the model were obtained. In the first case the axial dispersion term was included in both balanceso The second form was obtained by including the axial dispersion term only in the material balance which includes all streams. This procedure is called the "transport equation approach" and has been applied previously by both Powers and Gates for column crystallizers operating with total refluxo This procedure considerably reduces the complexity of the final form of the model. A mathematical criterion..s established which defines the conditions under which the form obtained by the transport equation xv

approach is applicable. The experimental data are interpreted. with the form of the model d.eveloped, by the transport equation approach. This model satisfactorily predicts the influence of the variables associated with continuous flow operation on the terminal stream compositions and axial composition profiles. The slope of the enriching section composition profile is a measure of the separation power of the column. The slope is determined by the internal crystal rate, pure end. product rate, and the diffusional and mass transfer groupso The diffusional group is DpAnr where D is the axial diffusion coefficient, p is the liquid density, A is the column cross section area for flow, and. q is the volume fraction of the free liquid. The mass transfer group is a(a+l)/KaAp where K is the mass transfer coefficient between the adhering and. free liquid., a is the specific surface area for mass transfer, and a is the adhering liquidcrystal rate ratio. The diffusional and. mass transfer groups are assumed to be constant for fixed spiral agitation conditions. The values of the two groups obtained from continuous flow data are compared, with values obtained for the same agitation conditions from the total reflux data of Albertins. Axial dispersion was found to be the dominant mechanism which limits the separation for continuous flow operation. This finding is consistent with the previous work of Albertins. In fact, the dominance of the diffusional term is more pronounced for the continuous flow case due to an additional dependence of the slope of the enriching section composition profile on the flow rate of the pure end product. The diffusional group obtained, from the continuous flow xvi

data is in reasonable agreement with the value determined. from the total rem flux data, i.e., for continuous flow operation DpAq = 6 54 + 1o 94 gm-cm/min and. for total reflux operation the same term is 6.86 ~ 0.11 gm-cm/mino Total reflux data provide a more severe test of the contribution of the mass transfer term because of the increased, dominance of diffusion for the continuous flow caseo The mass transfer groups and their standard errors obtained. from continuous flow and. total reflux data differ markedly, i.e., a(a+l)/KaAp O. 410 ~ O.44 cm-min/gm and 0.910 ~ o08 cm-min/gm, respectively, The ultimate purity that can be achieved in a single column crystallizer is limited by the composition of the crystal phase, e. It was reasoned that c should be related to the mother liquor composition in the freezing sectiono The mother liquor composition is equal to the stripping section product composition if the freezing section is perfectly mixed. The values of c calculated from the enriching section composition profile data are well correlated by a linear dependence on the stripping section product composition, Y, i.e., c = 0,00142 Yoo The values of c ranged from 1 to 100 ppm wt C6H12o It is shown that YS is proportional to the feed composition when a very pure enriching section product is produced. Therefore the e(Y ) dependence implies that the purity which is attainable in a single pass is limited by the feed. composition. There is no limit, however, to the purity that can be achieved if multiple pass operation is employed. xvii

CHAPTER I INTRODUCTION The demand. for ultrapure materials for both laboratory and commercial applications has led. to the further development of many of the less common separation processes in recent years. Fractional solidification is an example of such a separation method. While fractional solidification has conventionally been carried out in staged crystallizer-solids recovery systems, the development of a crystallizer that can achieve several stages of separation in a single piece of equipment is relatively recent. This process which was patented by Arnold6 in 1951 is called column crystallization. Column crystallization is based. on the countercurrent contacting of the crystals and crystal melt. Two column configurations have evolved. An endfed. column which utilizes an oscillatory flow of the liquid phase to transport the crystals has been developed for commercial application by Phillips Petroleum Company. A center-fed. column which utilizes a spiral conveyor was developed by Schildknechto28 A variety of systems having phase diagrams of both the eutectic and solid solution type have been separated. by column crystallization. Systems of the former type are of primary concern in this dissertationo Most of the investigations of the Schildknecht column have been for total reflux operation. Powers27 suggested a model for the purification of systems with negligible solid solubility which included consideration of impurity transfer by axial dispersion and washing of the adhering liquid associated with the crystal phase. He subjected this model to a preliminary check with a compositio 1

2 profile calculated from an experimental axial temperature profile. Powers assumed that the crystal phase was free from the impurity. Albertins2 found in a later investigation where he measured the composition profile directly for the benzene-cyclohexane system that it was necessary to include the impurity associated with the crystal phase in his model, Both Powers' and Albertins' investigations were for total reflux operation. Very little work has been done to evaluate the continuous flow operation of a center-fed column. Schildknecht and Mass29 have separated solid solution systems by operating a column semicontinuously. Breiter7 used a continuous flow column to separate components of both solid solution and eutectic systems. Most of his work was with systems which form solid. solutions, Sea water was the only system with negligible solid. solubility which he investigated.. Only enough work was done with the sea water system to demonstrate the separation. Breiter did not propose a model to represent the separation of a eutectic system with continuous flow column crystallization. In view of the minimal information available for the separation of systems which exhibit negligible solid solubility (eutectic systems) by continuous flow column crystallization such a study is the goal of this dissertation. The primary aim of the investigation is to explain the effects of the variables specifically associated with continuous flow operation of a center-fed column crystallizer, that is, feed. position, terminal stream flow rates, etco A mathematical model which includes the transfer of impurity by axial dispersion, washing of impurity from the adhering liquid. and. the impurity associated. with the crystal phase is developed for the continuous flow case, Experimental data

5 obtained. with continuous flow operation of a center-fed. column are used. to evaluate the model. The benzene-cyclohexane system was chosen so that comparisons could be made with the continuous flow data of this investigation and the total reflux data of Albertinso

CHAPTER II REVIEW OF LITERATURE Due to the relatively complex mechanical arrangement of a column crystallizer a process description is presented prior to the discussion of previous investigations of column crystallization. This will facilitate the understanding of the later sections of this chapter. Ao DESCRIPTION OF THE PROCESS A column crystallizer is a device for carrying out countercurrent crystallization in a single piece of equipment. The process was patented. by Arnold6 in 1951. The major advantage of column crystallization is its capability to achieve separations equivalent to several stages in a single piece of equipment. A column crystallizer consists of three distinct sections which are illustrated in Figure lo Crystals are formed. in the freezing section and pass through the purification section countercurrent to the liquid phase which is produced by melting the crystals in the melting section. The liquid phase is continuous while the crystal phase is the discontinuous or disperse phase. The column can be operated at total reflux or with continuous feed and product draw-off, It is instructive to note the analogy of the process flows that occur in column crystallization and distillation~ The freezing section which produces the crystal phase is analogous to the reboiler of a distillation column. The 4

5 Enriching Section Product Hot Fluid Melting Section Feed Purification Section Refrigerant Freezing Section Stripping Section Product Figure 1. Sections used in a column crystallizer.

6 melting section is similar to a condenser; like the condenser it is the source of reflux liquid. Finally the purification section which includes an enriching and stripping section is similar to a packed. tower distillation column. The hydrodynamics of the crystal slurry transport, however, are similar to the two phase flow that occurs in a pulsed liquid-liquid extraction column. 1. Column Configuration Following Arnold.'s invention, both end-fed and center-fed. column crystallizers evolved. The former has largely been developed by Phillips Petroleum Company. The end-fed column is primarily used for large scale applications such as the separation of p-xylene from its isomers. Figure 2 shows a typical process arrangement for the end-fed column. Findlay,11 McKay,19 Thomas,32 and Weedman34 have described the construction, operation and performance of the Phillips column. The crystal phase is conveyed by the action of a reciprocating piston. The center-fed column shown in Figure 1 was developed by Schildknecht.28 The crystals are conveyed in this column by a spiral which is both rotated. and oscillated. Due to the fact that the Schildknecht column was used. in this study a detailed. discussion of its mechanical design is presented in Chapter IV. 2. Process Flow in the Schildknecht Column As Figure 1 illustrates, the column consists of two concentric tubes with a spiral conveyor in the annular space between them. Crystals are formed in the freezing section and are transported through the column. In the case of a sys

7 Scraped Surface Chiller Feed Refrigerant / Filter Mother Liquor Purification Section [o, Heater Melting Section Pulse Piston — High-Melting Product Figure 2. Phillips end-fed column crystallizer operated with feed and product draw-off. tem of the eutectic type the crystals are below their melting point in the purification section, i.e., they are stable until they are melted..-The crystals are melted. at the top of the column and a portion of the liquid is returned, as countercurrent reflux. Most of the liquid, movement is countercurrent to the rising crystals, but due to drag effects a small portion of the liquid stream rises with the crystals. This stream is called the adhering liquid and is continually contacted with countercurrent free liquid of lower impurity content. Rather than attempting to describe the complex hydrodynamic situation which occurs due to

8 the oscillation of the crystal-liquid slurry, the adhering liquid associated with the crystal phase is conceived as a distinct liquid phase. This is an idealization because the free and adhering liquids are in fact one phase. This approach facilitates visualization of the washing process and will be used in Chapter III to develop the model for the purification section. Figure 3 illustrates the movement of the phases in the purification section and. shows the adhering liquid as an idealized distinct phase. Free Liquid Purification Section ^Sec/ton Adhering Liquid Crystal Figure 3. Crystals and. melt in countercurrent contact. The freezing section is an integral part of the column. The action of the spiral provides the advantage of scraped, surface heat exchange. Refrigerant is pumped through the jacket of the freezing section. Crystals are transported to the purification section by the action of the spiral. The purification section is immediately above the freezing section. Feed introduction divides the purification section into an enriching section above the feed point and a stripping section below. The crystals and adhering

9 liquid are transported. countercurrent to liquid reflux of lower impurity contento The mass transfer between the countercurrent streams is enhanced by both rotation and. oscillation of the spiral conveyor. The oscillation of the spiral conveyor also promotes axial dispersion of the impurity in a direction which opposes the separation. Consequently the conveyor agitation level must be chosen to strike a balance between increased mass transfer and axial dispersiono The melting section which is located. directly above the purification section contains a heat sourceo The heater can be an electrical heater or a jacket around. the column through which a heating fluid is circulated. B. PUBLISHED REVIEWS Several reviews of column crystallization which have appeared in the literature are summarized below. The yearly reviews of Palermo, 25 while they are comprehensive, contain little information specific to-column crystallization and. therefore they are not discussed hereo Albertins, Gates, and. Powers4 have reviewed, the design, operation, and the effect of the variables in column crystallization. They compared. the Schildknecht and. Phillips columns. Their thorough review of the systems that have been purified. by column crystallization includes a summary of feed. and product compositions that resulted. for the various terminal stream flow rates that have been reported. Binary and multicomponent mixtures of both the eutectic and solid. solution type have been separated. These mixtures include aromatic and aliphatic hydrocarbons, aqueous systems, and. fatty acidso These authors also summarized the effect of variables on column performance.

10 Those variables affecting agitation of the crystal slurry have a critical effect on the performance of both the Schildknecht and. Phillips columns. There appears to be an optimum level of agitation for both columns, that is, frequency and amplitude of oscillation of the spiral for the Schild.knechtioflumn and. piston displacement and. frequency for the Phillips column, They also summarized several mathematical models for the Schildknecht column; however, with the exception of Powers' determination of the axial temperature profile and. comparison with theory, the models were not subjected. to a test with an experimental composition profile. Gates14 has evaluated several possible models for total reflux operation of the Schildknecht column. The mathematical analysis of column crystallization by previous investigators will be discussed in more detail in later sectionso Co OTHER LITERATURE RELATED TO COLUMN CRYSTALLIZATION Considerable work on crystallization has been reported, by the Office of Saline Water. Sherwood and. Brian35 have investigated the washing of brine from a static bed of ice crystals. They found. that their data could. be explained by a plug flow-axial dispersion model. Moulton and Hendrickson23 found. that the salt associated. with ice crystals was proportional to the initial salt concentration in the feedo Due to the fact that they also found that the final mother liquor composition was proportional to the feed. composition, the impurity associated with the crystal phase was equivalently proportional to the final mother liquor composition. There is also considerable information in the extraction literature that

11 is pertinent to column crystallization. No attempt is made to present a review here. Albertins1 summarized the literature of pulsed. liquid-liquid extraction and discussed the similarities with column crystallization, Thehydrodynamics of a pulsed, extraction column are similar to the pulsing action provided by the spiral in a column crystallizer. The effects of axial dispersion are similar in both processes. Do EXPERIMENTAL AND THEORETICAL STUDIES FOR TOTAL REFLUX OPERATION Most of the experimental results that have been compared with theoretical models were obtained at total reflux. This is particularly true of the Schildknecht column. Powers27 and Yagi35 have each postulated models for the column crystallizer. Powers proposed. a differential countercurrent contacting approach. He distinguished. between the mechanism of purification for eutectic and solid. solution systems. Only the model for the eutectic system is discussed here. The model which includes mass transfer between the adhering and. free liquid. and axial dispersion in the free liquid. is based, on the transport equation approach, This approach involves neglecting the axial dispersion term in the component material balance on an element of free liquid in the purification section. The diffusion term is retained., however, in the material balance which includes all streams in the purification section. The words "transport equation approach" as used in the remainder of this dissertation imply the assumption described above. The crystal phase was assumed to be pure, i.e,, any inclusion or occlusion of impurity was neglected. The model was in

12 qualitative agreement with data obtained for the purification of azobenzene with a Schildknecht column. The purification section temperature profile that was used for this comparison did not provide a basis for checking the assumption that the crystal phase was pure. Powers neglected all heat transfer effects, i.e., he assumed that all internal stream flow rates were independent of position in the purification section. This is a reasonable assumption for a nearly adiabatic column where refreezing of liquid on the subcooled crystals leaving the freezing section is not significant. Refreezing is not an important consideration in the Schildknecht column due to the small axial temperature gradients that are common to production of ultrapure materials. Yagi developed a model for the end-fed column that applies for purification of eutectic systems with batch operation. He neglected impurity in the crystal phase as well as axial dispersion in the liquid phase. He apparently recognized the importance of refreezing of the reflux liquid in the Phillips column due to the large axial temperature gradient that exists. Although he included an energy balance in his analysis, he did not include the term corresponding to the refreezing effect. Albertins2 studied the separation of the eutectic system benzene-cyclohexane in a Schildknecht column crystallizer operated at total reflux. His investigation included both theoretical and experimental considerations. In fact, his results obtained at total reflux are extended, to the continuous draw-off case in this thesis. Albertins' experimental data are based on the measurement of the axial composition profile in the column. These data provided the first test of the

13 assumption that the crystal phase is pure for the separation of a eutectic system~ This was achieved, by sampling the composition profile and analyzing the samples with a calibrated gas chromatograph. The original theory of Powers predicted. that the free liquid composition profile should be exponential if the crystal phase were pure. Figure 4 shows a typical composition profile obtained. by Albertins. It is readily apparent that the profile is not exponential in the upper half of the purification section. Albertins explained. this deviation from the exponential profile by the existence of a constant impurity level in the crystal phases Albertins also evaluated the influence of the major operating variables0 He found, that it is necessary to provide sufficient agitation to keep the phases well fluidized. This condition is necessary to obtain a good separationo Oscillation frequencies of 140 to 290 osc/min were required at an amplitude of 1 mm and. a spiral rotation rate of 59 RPM. At these levels of agitation the column plugged at a crystal rate of 5.4 gm/mino The column operated, smoothly at crystal rates below 5.4 gm/min. The charge composition had no effect on the separation other than that explained, by material balance considerations. Albertins used a plug flow-axial dispersion model to explain his data. This model also included. a constant impurity level. in the crystal phase. Although he considered mass transfer between the adhering and free liquid., he concluded that only axial disersion played a role in th in the mass transfer mechanism. As pointed out by Gates,13 Albertins neglected the impurity in the crystal phase when he considered, the axial dispersion-mass transfer model

14 0 Experimental Data Charge Composition 10,000 ppm wt. C6 H12 Crystal Rate = 2.5 gm/min 10,000 Spiral Agitation: 59 rpm _ ^~- ~290 osc/min. 1 mm Amplitude \0 Iooo000 r i \ >r \0 100 10 0 10 20 30 40 50 Z, cm Figure 4. Typical free liquid composition profile obtained by Albertinsl for total reflux operation.

15 (which he included. in his axial dispersion-plug flow model) in order to reach this conclusion. Gatesl4 performed. a thorough study of the models for the separation of both solid solutions and. eutectic systems at total reflux. In both cases he compared. his models with experimental data. He found for the case of eutectic systems that when the mass transfer mechanism is considered simultaneously with effects of a constant impurity level in the crystal phase, both the axial dispersion and the mass transfer between the adhering and. free liquid are significant effects, but that axial dispersion is the larger effects The detailed mathematics of Gates? model for eutectic systems are not presented here; his model is a special case of the model that is developed in Chapter III for the continuous draw-off case. E. PREVIOUS INVESTIGATIONS WITH CONTINUOUS FEED AND PRODUCT DRAW-OFF Both the end-fed. and center-fed column crystallizers have been operated. continuously. Most of the studies were experimental, and little effort was made to compare the experimental data with a mathematical model. These investigations are summarized. in -this section together with theoretical models that have been presented for continuous flow operation* 1. End-Fed Column The basis for the commercial application of the end-fed column is the ability to operate it continuously. The major commercial application has been the purification of xylenes.20 Most of the investigations of the endfed column have been pilot plant studies, e.g., McKay and Goard21 fed column have been pilot plant studies, e g., McKay and Goard described

16 the separation of xylenes methyl-vinyl-pyridine, methyl-ethylpyridine, organic esters, and food. stuffs such as beero One major difference between the performance of the end-fed. and centerfed. columns is the fact that there appears to be a composition discontinuity in the end-fed column when eutectic systems are purified. McKay and his coworkers22 measured the axial composition profile for the separation of xylenes and. found that the p-xylene composition was constant throughout most of the purification section and. increased, sharply in the vicinity of the crystal meltero All of the enrichment occurred in a 2 in. region near the melting section. The fraction of solids also increased sharply in this region. These results confirm the occurrence of significant refreezing of the reflux liquid on the crystal phase. No attempt was made in these investigations to incorporate the refreezing concept into a mathematical model that could be used to predict the performance of an end-fed column crystallizer. Player26 recently developed a mathematical model that included refreezing considerations. While there are no experimental data in the public domain which could be used, to check his model (McKay's profile data mentioned above did not include the internal flow rates), it did predict qualitatively the existence of a discontinuity in the region near the melting section. 2. Center-Fed. Column In order to obtain quantities of material larger than could be obtained, with total reflux operation, Schildknecht and Mass29 operated a center-fed column semicontinuously. They fed. ard. removed. products at periodic intervalsO

17 Diphenyl, azobenzene, and sea water have been purified by this technique~ Typical feed. and product quantities are 10 ml and. 5 ml respectively, added and withdrawn at 20 minute intervalso In a later investigation Breiter7 purified azobenzene-stilbene, caprolactam, and sea water with fully continuous operation0 The bulk of the work was done on the former two systems which form solid. solutions with their impuritieso Only enough work was done with the sea water system (the only eutectic system investigated) to demonstrate the separation0 A typical separation for a solid solution system is described, below0a A 50:50 mixture of azobenzene-stilbene was fed. to a column 70 cm long at a rate of 132 gm/hro The melting section product was 96.2 mol % azobenzene and the freezing section product was 13 mol % azobenzene. The product recovery was 491, and the column was operated. with a reflux ratio of 15. Breiter used, a model completely analogous to the McCabe-Thiele procedure for binary distillation to interpret his data. The above separation required 13o5 ideal stages which corresponds to a HETP of 4,7 cm. Schildknecht and Breiter have mad.e no attempt to use the differential countercurrent contacting approach that was suggested earlier by Powers.27 It is interesting to note that Breiter has found. that he can obtain purer products with fully continuous operation than with periodic operation. Thus even for laboratory separations continuous draw-off is the most desirable mode of operation if more than a few milliliters of product are required. Anikin5 suggested using the mathematical model already developed for packed fractionating columns8 because the physiocochemical processes which

18 occur in both processes are similar. Axial dispersion in the liquid phase was neglected. It is this author's opinion that this is the chief deficiency of Anikin's model. He did not evaluate his model experimentally. The Benzole Producersl617 have operated a bench scale Schildknecht column for purification of benzene. They are currently designing a pilot plant that will have a capacity of 30 gal/hro They hope to apply the center-fed column to the large scale production of benzeneo They are not currently interested in producing ultrapure. benzene, thus, they are using very low reflux rates. In fact, in some cases quantities of enriching section product were withdrawn that exceeded the internal crystal rate. Such operating conditions correspond. to cocurrent flow of the free liquid and. crystal phases in the enriching section as opposed. to conventional countercurrent operation of the column crystallizero They have demonstrated with countercurrent operation that benzene with as little as 10 ppm impurities can be produced from a 10,000 ppm feed.o They made no attempt to model the system nor did they obtain axial composition profile data that are essential to the thorough evaluation of a mod.elo The Benzole Producers have indicated that the Schildknecht column may find application for large scale production of benzene. Recently Newton Chambers Engineering Ltd.. have announced. that a crystallization process based, on the Schildknecht column is being developed,24 Powers4 presented a model for the purification of eutectic systems with continuous feed and product draw-off that is similar to his model for total reflux operation. He assumed that the mass transfer factor (defined later) is the same for both total reflux and. continuous operation. As will be

19 shown in Chapter III this is not the case. Powers did. not subject his model to an experimental check. Danyi, Henry, and Powers10 have recently reported the production of ultrapure benzene (< 10 ppm impurities) with a center-fed column operating continuously4 They found that for such operations the length of the stripping section should be minimized and. that it is sometimes desirable to use multipass operationo Further details of this work are presented in Chapter VIo F0 SUMMARY There is a need to develop a model for the continuous draw-off case0 While center-fed. columns have been operated. continuously, data do not exist for the purification of eutectic systems that could. be used. to evaluate a model for such an operation~ In view of the potential large scale application of the center-fed column, an experimental and. theoretical study of the continuous flow case would be especially timelyo It is also apparent that the continuous mode of operation will find increased, application in the laboratory0

CHAPTER III THEORETICAL DEVELOPMENTS A mathematical model is developed for a center-fed column crystallizer operating with continuous feed and product draw-off. Considerations are limited to the purification of simple eutectic systems in regions below the eutectic composition. Various mechanisms that might influence the separation are discussed. A model is developed which includes those parameters which are believed to be important. The implementation of the model by a numerical technique is also summarized. The implications of the model are discussed, i.e., predictions are made concerning various aspects of the performance of a continuous flow column. A. POSSIBLE MECHANISMS In the case of purification of systems with negligible solid solubility a high degree of separation occurs in the freezing section. The crystals formed in the freezing section are relatively pure, but the adhering liquid associated with them is impure due to the rejection of impurities from the crystal phase during the freezing process. The purification section provides a means of reducing the impurity content of the adhering liquid. This is accomplished by washing the adhering liquid with purer reflux liquid (henceforth called free liquid) that is formed in the melting section. Figure 3 of Chapter II illustrates the movement of the phases in the purification section with the adhering liquid idealized as a distinct phase. It is convenient to think of the adhering liquid as a distinct phase and 20

21 consider the washing as an interfacial mass transfer process. The driving force for mass transfer is the difference in composition between the adhering and. free liquid. This continual washing establishes an axial composition gradient in the purification section. Axial dispersion in the free liquid. acts to oppose the separation. The axial dispersion is driven by the axial composition gradient and is sensitive to hydrodynamic conditions in the column. It is possible for impurities to be associated. with the crystals. This can be caused. by either volumetric liquid inclusions or by the trapping of impurities on the irregular surface of the crystals. Also solid solubility may occur in the ppm range. The washing process mentioned above very likely has little or no effect on the level of impurity associated with the crystal phase. Consequently the crystal composition is essentially constant in the purification section. An axial temperature gradient is established. in the purification section as a result of the progressive concentration of the impurity toward. the freezing section. The crystals entering the purification section are at a temperature below their melting point. In an adiabatic column the crystals would exchange this sensible heat with the liquid by refreezing an appropriate quantity of the liquid. The axial temperature gradients are sufficiently small, so that refreezing of this type is negligible, for example, the largest axial temperature drop between the top and. bottom of the purification section encountered in this study was 8~C which would correspond to a 10% increase in the crystal rate in the purification section. Most of the axial temperature gradient occurs in the region near the freezing section below the first sample

22 tap. Hence any small increase in the crystal rate due to refreezing occurs below the region where the composition profile is sampled. Therefore any heat transfer effects can be neglected, i.e., the internal crystal and liquid flow rates can be considered constant in both the enriching and stripping sections. Both Albertins2 and Gatesl4 concluded that heat effects could be neglected for columns operated at total reflux. The mathematical model that is developed below includes the following considerations: Mass transfer of the impurity from the adhering to free liquid. Mass transfer of impurity in the free liquid by axial dispersion. A constant level of impurity in the crystal phase resulting from volumetric inclusion or other phenomena. Constant internal flow rates. B. FORMULATION OF MODEL Mathematical models for both the enriching and stripping sections are presented below. A separate derivation is not presented for the total reflux case, because it is a special case of the continuous flow model. Much of the devel2 1a G opment that follows is based on the earlier work of Albertins and Gates.14 The model that Gates employed to analyze Albertins' data is the total reflux analog of the model that is developed by the transport equation approach for the continuous flow case in a later section of this chapter. It is possible to operate the enriching section of a column crystallizer with either countercurrent or cocurrent flow. Countercurrent flow is the

23 normal case where free liquid. is generated. in the melting section which is used to wash the adhering liquid. The model is developed here specifically for the countercurrent case, but the differential equations that result are equally applicable to'cocurrent flow. The application of this model to the cocurrent case will be discussed in a later section of this chapter. The process flows illustrated in Figure 3 are further idealized in Figure 5 which shows the internal flows in relation to a differential element of the purification section. The flows are denoted by L, L', and C which represent the mass flow rates of the free liquid, adhering liquid, and crystals respectively. The compositions Y, Y', e represent the weight fraction of impurity (cyclohexane in this study) of the free liquid, adhering liquid and crystal phase respectively. L.Y MD Y' CE l., T l_ Z+AZ — MK L,Y MD IY' C,E MD=-D PA7 dZ MK= K AP(Y'-Y)AZ Figure 5. Elemental description of column crystallizer. The impurity is transported by bulk flow, axial dispersion and. mass transfer. The bulk flow is represented by LY, L'Y', and CE. The expression repre

24 senting the rate of axial dispersion, MD, is assumed to be of the form of Fick's Law as presented in Eq. (1). dY MD = -DpAr d (1) dz D:.is the effective diffusivity which includes the contributions of molecular diffusion, Taylor diffusion and backmixing; p is the free liquid density; A is the area through which liquid and crystals flow; and T is the volume fraction of free liquid in the purification section. The rate of mass transfer between the adhering and free liquid, MK, is assumed to be proportional to the difference in composition of the adhering and free liquid as shown in Eq. (2). MK = KaAp(Y'-Y)Az (2) K is the mass transfer coefficient; a is the interfacial area between the adhering and free liquid per unit volume; and z is the axial position in the column measured from the freezing section. The internal flow rates L, L', C; and the factors A, K, a, p, D, r are assumed to be independent of the position in the column. A material balance on a differential element of the free liquid yields Eq. (3). dY d2Y L d + KaAp(Y'-Y) + DpA dz 2 = 0 ( This expression is general for both the enriching and stripping section. Another relation between y and. Y' is needed before Eq. (3) can be solved. 1. Enriching Section, (z>ZF) A material balance on the enriching section as shown in envelope I in

25 Figure 6 yields a second relation between Y and Y' which is given in Eq. (4). d.Y Ce + L'Y' - LY - DpA. = LEYE (4) dz where LE and. YE are the pure end product rate and composition. An overall balance about envelope I gives Eq. (5). L = L' + C - LE (5) Equations (3), (4), and (5) can be combined to give the following differential equation which relates the impurity content of the free liquid, to the position in the enriching section: DqL,' day LL' d+ +(LL p+ DpA)>- + (C-LE)Y = Cc - LEYE (6) Ka dz K~aAp dz Equation (6) is a linear second. order ordinary differential equation. Inspection of this equation shows that its particular solution is given by Eq. (7). Yp = (Cc-LEYE)/(CLE) (7) It- was assumed throughout the course of this investigation that the flow rate of adhering liquid is proportional to the crystal rate as described by Eq. (8)o L = - oc (8) Using this expression the homogeneous part of Eq, (6) becomes, d2Y [KaAp + (+l-RE)C dY _ (1-RE)Ka 2 + - + Y = 0 (9) dz aC DpAr ~ d.z Dra where RE = LE/Co The definitions (10a) and (lOb) are introduced, to simplify further manipulations. KaAp + (a+l-RE)C (la) C C DpATr

26 LE:,YE I \ I I ENRICHING SECTION l T I I I I \ L STRIPPING II SECTION _ _ ______ _ - - --- --- LS 1YS FYFigure 6. Re nshp b n i l ad e l stms. Figure 6. Relationship between internal and. external streams.

27 Q = Ka (1- (l-b) Dra Equation (9) then becomes Eq. (11). dY d.Y dz2 + Q1 d + Q2Y = 0 (11) i^ ^1^ "^ = 0 (11) dz dz The complete solution of Eq. (6) is given by Eq. (12). Y = Yp + Cler + C2e (12) The roots rl and r2 must satisfy the following characteristic equation: r2 +Qr + Q 2 = 0 (13) The roots of this quadratic equation are given by Eq. (14). Q1i~i^ = Qi~ltd^Q^/Q2)1/2]/^ (14) ri,r2= Ql[-l+~(l -4Q2/Q) /2 (14) 2. Stripping Section, (z<zF) The development of a relation between Y and. Y' for the stripping section and its combination with Eq. (3) is completely analogous to the preceding development for the enriching section. A component material balance around. envelope II of Figure 6 yields Eq. (15). dY Ce + L'Y' - LY - DpAr d = - LSYS (15) An overall balance around the envelope gives Eq. (16). L = L' + C + LS (16) The differential equation describing the stripping section that results from combining Eqso (3), (15), and. (16) is given in Eq. (17).

28 D~L' dyY +LL' TKa d KaAp + DpA + (C+LS)Y = C + LSYS (17) The particular solution of this equation is given by Eq. (18). yp = (CE+LsYs)/(C+Ls) (18) The homogeneous part of Eq. (17) can be simplified to: d2Y - dY is2+~lZs; ~ = 0 (19) dzZ + Q1 dz+ 2Y = (19) where, - = KaAp + (++R)C (20a) ac DpAq Ka(l+Rc) - D (20b) RS = LS/C (20c) The complete solution of Eq. (17) is presented in Eq. (21). rlz' r2z Y = Yp + Ce + C2e (21) The roots Fr and. ~ are the characteristic roots given by Eq. (22). rlr2= Qi [-l+(1-4 2/)/2]/2 (22) 3. Boundary Conditions A boundary condition for both Eqs. (12) and (21) can be obtained. from the fact that the free liquid. composition is continuous across the feed point. This boundary condition is given in Eq. (25).*

29 z = ZF Y = Y (23) where YY is the composition of free liquid inside the column at the feed point (Y$ in general is not equal to YF). This condition applies to both the enriching and stripping section composition profiles. In fact it is this relation that couples Eqs. (12) and (21). In addition tothe above boundary condition the restriction that Y must be between zero and one if compositions are expressed in weight fractions or between 0 and 106 if compositions are expressed in ppm wt must be satisfied. This condition also applies to both Eqs. (12) and. (21). 4. Summary of Assumptions Prior to further discussion of the model, all of the assumptions included in its development are listed below: The column is assumed to be at steady state. All internal flow rates are constant; this is equivalent to neglecting all heat transfer effects. The.impurity level associated with the crystal phase, E, is constant. Radial variations in each phase are negligible. All transport properties are assumed. to be constant. The flow rate of adhering liquid is assumed to be proportional to the crystal rate. C. SIMPLIFICATION OF THE MODEL The model presented in the previous section can be simplified. Examina

30 tion of the roots of the characteristic equations leads to the elimination of one of the characteristic roots. The resulting first order model has a form that can be compared.withthe model that is developed by the transport equation approach in a later section of this chapter. This comparison will facilitate the interpretation of experimental data presented. in Chapter V. 1. Enriching Section The nature of the roots of Eq. (14) is governed by the magnitude and sign Q 2 of Q2/Q1 defined by EqO (24). Q- = (Ka/Dra)(l-RE) [aA + ( +l-RE) C (24) Qf acb.. DpAr It can be shown that Q2/Q1 has a maximum with respect to crystal rate. Differentiating Eq. (24) with respect to C at constant RE and. setting the result equal to zero yields: KQ1 ax 4 4(a+l-RE) The maximum occurs at a crystal rate of: - KaA (26) If one further examines Eq. (24) it is apparent that there is a family of curves (Qa2/Q1 versus C) corresponding to different values of RE. Each curve has a maximum described by Eq. (25). It is clear that the largest value of (Q2/Q~)max < 1/4, because O is greater than zero. Consequently both roots of

31 Eq. (14) are real and negative for continuous flow and. total reflux operation. The relative importance of the two roots rl, r2 (given by Eq. (14))depend on their relative magnitudes. The roots are given by Eqs. (27a) and (27b). rl = 1 -1+(1-4 Q) ] (27a) r2 = 2 [-1-(1-4 Q2/Q)12] (27b) The ratio of the magnitude of the two roots, r2/rl is a minimum when Q2/Q2 is a maximum. Therefore (r2/rl)min corresponds to total reflux operation (RE = 0). When this ratio is a minimum the contribution of C2e relative to Cle is maximized.. It is necessary to obtain numerical values of rl and. r2 in order to examine the relative contributions of the terms Ce and C2er2 in Eq. (12) The terms involving the axial diffusion coefficient, DpAr, and. the mass transfer coefficient' KaAp, must be known before the values of rl and r2 corresponding to (r2/rl)min can be calculated. The empirical results derived from the total reflux data of Albertinsl are used to determine the diffusional and mass transfer terms. The values of rl and r2 that correspond to the minimum ratio of r2/ri are -0.284 cm-1 and -0.676 cm'l, respectively. The details of these calculations are presented in Appendix F. Consequently er2z decays more rapidly rlz than e The term involving r2 cannot be neglected in Eq. (12) until the relative magnitudes of C1 and C2 are established. At this point the following boundary condition is applied. to the expression for the enriching section composition

32 profile (Eq. (12)): z = ZF, Y = Y (23) Utilizing the values of rl, r2 and the above boundary condition for a feed. position of 4.0 cm above the freezing section, Eq. (12) becomes: Y- - Yp = 0.321 C1 + 0.0669 C2 (28) The argument now proceed.s by making the hypothesis that the relative magnitudes of C1 and C2 are such that the term C2er2 is significant to the degree that its effect could be observed experimentally. It will be shown that such a hypothesis leads to a physically intractable result. In order to experimentally detect the presence of C2e, this term must be at least 10% of Cle at a position two sample taps above the feed point, consequently, it is assumed. that r226 r2erZ6 - 0.1 (29) Cle z where z6 (the subscript denotes the sample tap number) is the position of the second. sample tap above the feed. point (17.75 cm in this case). The values of rl and. r2 presented, above can now be used. to calculate the value of C2/C1 corresponding to the original hypothesis (Eq. (29)). The calculation yields C2/C1 = 103. Equation (12) must also account for the level of impurity in the free liquid in the upper portion of the enriching section, for example at the top sample tap, zl, whose position is 47 5 cm above the freezing section. Equa

33 tion (12) reduces to Eq. (30) when the values of zl, rl, r2 and C2 = 103 C1 are substituted. Y - Yp = C1/722,000 (30) It is convenient to establish the minimum value of C1 in order to check if the original hypothesis of the magnitude of the term involving C2 is consistent with the expression for the enriching section profile evaluated, at ZF (Eqo (28)). The magnitude of C1 is 722,000 (Y1-Yp). Examination of the experimental composition profile data (Appendix C) in view of Eq. (30) indicates that for many cases Ya < 722,000 (Yi-Yp) (31) This is an empirical observation, Consequently Y, is a conservative estimate of the minimum value of C1. The validity of the original hypothesis of Eq. (29) can now be checked. Using the value of C1 = Y. and the identity C2 = C2/C1 Y~ Eq. (28) becomes: Y, - Yp = 0.321 Y. + 0.0669 - Y. (32) Substituting C2/C1 = 103 into Eq. (32) and. rearranging gives Yo = -Yp/6.21. Inspection of the defining relation for Yp shows that it is positive in many caseso Consequently the above relation predicts that Y~ is negative which contradicts the restriction stated earlier that O<Y<106, Therefore the original hypothesis of' Eq. (2?) concerning the relative magnitude of C2e and Cle is not valido Th-;.;L:ition that Y must be greater than zero requires that

34 C2e.... < 0.1 (33) Cle Thus neglecting the term in Eq. (12) involving C2er2 is justified in view of the fact that its presence cannot be detected experimentally. It is recognized. that'the validity of neglecting this term is based on consideration of a special case, ioe., particular values of rl and. r2 were used. It is pointed out, however, that the values of rl and. r2 were chosen to maximize the contribution of the term involving r2, i.e., the values of rl and r2 corresponding to (r2/rl)min were used. Therefore it is valid to reduce the expression for the enriching section composition profile (Eq. (12)) as follows: Y = Yp + Cierlz (34) The constant C1 can be evaluated. by using the boundary condition presented. in Eq. (23). Finally, the free liquid composition profile in the enriching section can be represented by Eq. (35)Y-YP erlz-zF) (35) = er F zz5p) YOYp 2. Stripping Section The simplification of Eqo (21) to a form similar to Eq. (34) can be justified. by arguments similar to those presented. above. In this case the group 21 Q2 governs the nature of the characteristic roots rl and r2o Like the corresponding group for the enriching section (Q2Q i2)max is less than 1/4. Therefore l and. r2 are real and negativeo Also, arguments similar to those used. -- Z r2 Z 1 in the enriching section case justify neglecting Ce relative to Cle

55 Equation (21) therefore reduces to Eq. (56). Y = Yp + Ceerlz (36) = Q [-1+(1- Q2/Q)1] (37) Applying the boundary condition described by Eq. (23), Eq. (36) becomes: -p = el(ZF-z) (38) Y-Yp 3. Summary of the Resulting Model The final expressions for the composition profiles in the enriching and stripping section are now obtained by introducing the definitions of Q1, Q2, Q1, Q2, Yp and Yp. It is convenient to introduce two additional definitions: IE i/(39)'E =- l/ri (59) ^g ^ ~~- l/?~ ~(4o) The expressions for the two composition profiles now become: Enriching Section Y-(CE —LEYE )/CLE) -(ZF)/E (41a) Y,-'(C~-LEYE)/ (C-LE) where, 2 (4lb) E =KaAp + (C+l-RE)C _ 4(Ka/Da ((-RE) LacC DpAT J [KaAp (a+l-RE)C 2 \Strip g DpASe Stripping Section

36 Y- (Ce+LsYs) / (C+L) _ -(ZF-)/S (42a) Y-(Cc+LSYS)/(C+Ls) where, = 2 aAp (a+l+Rs)c] | 4(Ka/Drla)(l+RS) } (42b) aL C DpAq L i [KA + (U+l+R)C n C p.DpA It can be seen that the parameters WE and. pS determine the separation power of a continuous flow column crystallizer operating at specified conditions. Henceforth these parameters will be referred to as mass transfer factors. Equations (41a) and (42a) show that as the mass transfer factors rE and IS increase the slope of the axial composition decreases, ioeo, the separation decreases. Therefore the mass transfer factors are inverse measures of the separation power of the enriching and stripping section respectivelyo D. TRANSPORT EQUATION APPROACH Expressions for the enriching and stripping section composition profiles can also be obtained by employing the transport equation approach. This method utilizes the same mechanisms previously discussed, but; involves a mathematical simplification of the material balance on an element of free liquid, Eqo (3), in the purification sectiono Impurity transfer by axial diffusion is neglected dY in this balance. The diffusion term DpAr - is retained, however, in the mated.z rial balances, Eqs. (4) and (15). The transport equation approach was first used. by Furry, Jones and Onsager12 to model thermal diffusion columns and later applied by Powers27 to column crystallization.

37 Neglecting the diffusional term Eq. (3) becomes: L d + KaAp(Y'-Y) = 0 (43) dz This relation can be combined. with Eqs. (4) and (15) to obtain a first order, ordinary differential equation, describing the enriching and stripping sections. Enriching Section LL') dY (KA + DpAIj -dz + (C-LE)Y = CE LEYE (44) KaAp dz Stripping Section (LLA + ( (KA + DPA d + (C+L)Y = CE + LSYS (45) These equations are readily solved by applying the following boundary condition to each. z = ZF' Y = Y (23) Enriching Section Y-(C -LEYE)/(C-LE) -(z-z)/6a y_-(CE-LEYE)/(C-LE) = e I, - =-mE p A],- [ a(a+i)C2 (cLEC] C-LE L Pr' KaAp KaAp (46b) Stripping Section Y- (Ce+LsYs)/ (C+Ls) e (ZF-z)/ (47a) Y-(Ce+LSYS)/(C+Ls) e

38 1_ f_, Q:(a+l)C,, g = 1r LDpAl + + (47b)'S C+LS KaAp KaApj (47b) It is instructive to compare the expressions for the composition profiles listed above that were developed, by the transport equation approach with the correspond.ing relations that were developed in the previous section without neglecting the diffusional term in Eq. (3) as subsequently simplified by consideration of limiting cases. Comparison of Eqs. (46) and (47) with Eqs. (41) and. (42) developed earlier show that both procedures result in enriching and stripping section profiles of the same form. The mass transfer factors for the enriching and. stripping section profiles are different, however, i.e., IfE + BE (48) and. xr4 $ (49) These parameters can be related by further manipulation. The square root terms in Eqs. (4lb) and (42b) are expanded in aTaylor series as follows: l.-4X' = - 2 1 (2n-2) X n (50) n n "'(n-l)' where, XE = (Ka/Dric)(l-RE)/ + Dp^Ar (51) XS (Ka/Da)(l+RS K (+l+R) C2 (52) Rearrangement of Eqs. (41b ) using the above relations yields: Rearrangement. of Eqs. (4lb) and (42b) using the above relations yields:

39 = /(XE) (53) S - *s/e(xs (54) where, 0 (2n-2)' n-1 o(X) = 1 + X + 2X2 + 5X +... = nl n xn (55) The mass transfer factors,:E and. *S, predicted by the original model are related to those predicted by the transport equation approach by the correction factors (XE) and 6(Xs). The mass transfer factors obtained by the transport equation approach become the same as those predicted by the original model when XE and XS are small, for example, XE < 0.1, Xs < 0.1 (56) 9(XE) = 6(XS) " 1 therefore, (57) S *S (58) A demonstration that XE and Xs are less than 0.1 requires calculation of these parameters from their defining expressions (Eqs. (51) and (52)). The validity of the approximation of Eq. (56) and the limitations involved with calculating lU XE and XS are discussed in Chapter V. Gates4 assumed that X0 < 0.1 (the subscript O refers to total reflux operation) when he analyzed the total reflux data of Albertins.l As shown above this is equivalent to using the transport

40 equation approach. Finally, one mathematical peculiarity of the expression for the enriching section profile (Eqs. (46)) is noted. When RE = 1 (LE = C) Eqs. (46a) and. (46b) reduce to 1 = 1 which prevents its application. If Eqs. (46) are rederived setting LE = C the following relation results: KLEYE-Ca ) Y = Y - (Z-ZF) (2C2 (59) KaAp + DA It can be seen that in this special case the free liquid composition is linear with position z. E. IMPLEMENTATION OF THE MODEL Models have been developed for the enriching and stripping sections, but before they can be utilized for column calculations the free liquid compositions at both ends of the purification section (z = o and z = O) must be related to the terminal compositions YE and. YS. Once this is achieved an iterative procedure is presented that can be used to perform column calculations. 1. End Compositions for the Purification Section The relationships between the compositions at the ends of the purification section and. the terminal compositions are established, by modeling the melting and freezing sections. Both sections are assumed. to be perfectly mixed as illustrated in Figure 7. The enriching section can be operated either countercurrently or cocurrently. The direction of the free liquid flow is determined by the

41 Melting LE YE Section LYM LY' CE _ y __ Purification F, Section Freezing L., Section LsYs Figure 7. Melting and Freezing section models.

42 relative magnitudes of overhead. product draw-off rate and. the mass flow rates of the crystal phase and. adhering liquido The following two relations determine whether the flow in the enriching section is countercurrent or cocurrent: Counter current Flow LE < L' + C (60) Cocurrent Flow LE > L' + C (61) Countercurrent operation is the normal mode, i.e., the purpose of the enriching section is to wash impurities from the adhering liquid which requires generation of a countercurrent free liquid stream, L, in the melting section. For countercurrent operation the composition at the top of the enriching section, z = c, is the same as the terminal composition YE because both streams are outputs from a perfect mixer; therefore for conventional countercurrent operation: z =- Y = YE (62) The cocurrent case is more complicated. With this type of operation the direction of free liquid, is the opposite of that shown in Figure 7. This stream is now an input to the perfectly mixed melting section, and. in general Y + YE at the top of the purification section. It is noted that there is minimal separation occurring in the enriching section with cocurrent operation, because a portion of the feed stream passes cocurrently up the column with the dY crystals and adhering liquid. It is therefore reasonable to assume - = 0 at dz z = o This condition can be combined with Eqs. (4) and (43) to obtain the following relation for cocurrent operation:

43 z = Y LEYE-C= (63) LE -C The composition of the free liquid at the bottom of the stripping section, YO, can be related to the bottoms product composition YSo Due to the perfect mixing conditions that are assumed in the freezing section Y' = YSo Also it is reasonable to neglect impurity transfer by the crystal phase at the bottom of the purification section, ioeo, LSYS >> CEo Equations (15), (18), (36), and (40) can be combined, utilizing the above conditions that prevail at the bottom of the stripping section to obtain the following relation between YO and YS: Y _ L'+Ls DpAT LS/r(Ls+C) YS L'+Ls+C-DpAri/' The dependence of YO on YS therefore depends on the ratio pDAq/rso It can be shown that when axial diffusion is the dominarnt mechanism determining *I that Eq. (64) reduces to YO/YS 1o Consequently the following relation will be used to facilitate column calculations: z = 0, Y = (65) It is shown in Chapter V that.ilumn calculati-os. sing this relation are in good agreement with experimental datao 2o Column Calculations The following parameters are specified bef;re calculations are started: F, YF, LS, C,,- and zpF Also 4E S and E are specified either from experi mental data or from correlati;n.;.btained frcn;i tW:E:f appropriate experimental

44 data. The terminal compositions YE, YS, and the composition profile Y(z) can then be calculated by the following iterative procedure * Assume YEo * Calculate YS from the overall material balance, FYF = LEYE + LSYS (66) e Calculate Y(1 from the mathematical model for the enriching section. Calculate Yc2 from the stripping section model. Increment YE and. repeat the calculations until Y,1 A Y2 i e., until a convergence criterion is satisfied.. This matching procedure satisfies the requirement that Y be continuous across the feed point. Calculate the composition profile Y(z) from the converged. values of Y$ and YS. A Fortran IV program has been written which implements the above procere. The program listing, definition of symbols and typical output are presented. in Appendix D. F, IMPLICATIONS OF THE MODEL The mathematical model developed earlier for the enriching and stripping section (see Eqs. (41a) and (42a)) can be used to predict the performance of a center-fed. column crystallizer. Equations (41a) and. (42a) when solved simultaneously will predict the influence of product draw-off rates (LE and. LS), feed. position (zF), and the internal crystal rate on the purity of the overhead product (YE). Such predictions require a knowledge of AE' KS' and c or

45 equivalently Ka, Dr, o, and. c from experimental data on the particular system of interest. The results of Albertins'1 study for total reflux operation were used. to estimate the above parameters. The iterative column calculation procedure can then be used to make the predictive calculations. Examination of Eq. (41a) indicates that the in(Y-Yp) should. decrease linearly with the position z in the enriching section. Recalling Eq. (7), Yp is defined. as follows: Ce-LEYE (7) YP = C-LE The important property of Yp is that it can change sign depending on the relative magnitudes of the amount of impurity transported by the crystal phase, Ce, and. the amount of impurity in the overhead product LEYE. When Yp is positive, zero, and negative the enriching section composition profile (lnY vs z) is respectively concave upward, linear, and concave downward. Figure 8a illustrates these three distinct enriching section profile shapes. Similarly Eq. (42a) shows that ln(Y-Yp) should also decrease linearly with the position in the stripping section. In this case however Yp is always positive as indicated by Eq. (18). Yp = (Ce+LsYs)/(C+Ls) (18) Due to the relative large magnitude of Yp the free liquid. composition in the stripping section can decay rapidly to Yp and then remain essentially constant until the feed position is reached. This effect is particularly noticeable when the feed. position, ZF, is well above the freezing section. Figure 8b qualitatively illustrates the flat portion of the stripping section profile

mY^^Yp<0 In Y \0 \ Z (a) Enriching Section Composition Profiles tn Y ZF Z - (b) Comparison of Stripping and Enriching Section Composition Profiles Figure 8. Composition profile shapes predicted by the model.

47 relative to the profile in the enriching section. Both Figures 8a and. 8b represent profile shapes that were obtained by applying theory via the column calculation procedure presented. earlier. It is desirable to avoid, such a flat region in the stripping section profile, because this type of profile indicates that a portion of the column does not contribute to the separation. Column calculations show that the flat portion of the stripping profile can be eliminated by moving the feed. point closer to the freezing section, that is, by decreasing the length of the stripping section. A closer inspection of the mass transfer factor in the enriching section (yE) shows a strong dependence on the ratio of the overproduct draw-off rate Ei to internal crystal rate (RE). The mass transfer factor is a minimum (which corresponds to a maximum separation power) at total reflux and. increases as RR is increased. Due to the exponential dependence of the free liquid. comE position on tE, the separation that can be achieved in a column is extremely sensitive to RE, i.e., as RE increases YE increases. G. APPROXIMATIONS Finally, several approximations are introduced, that result from the relative magnitudes of the various parameters that are determined from the experimental data. These relations will be applied in Chapter V to facilitate analysis of the data. The terminal stream material balance (Eq. (66)) can be simplified when the column is operated such that a very pure overhead. product is obtained. In this case the amount of impurity leaving the column in the overhead. stream is

48 negligible compared. to that contained in the feed. and. bottoms streams, that is, LEYE < LSYS and. FYF. Under these conditions Eq. (66) reduces to Eq. (67). Ys - s YF (67) Ls The expression for Yp (Eq. (18)) which determines the shape of the stripping section composition profile can be obtained, in a form that facilitates the calculation of Yp from experimental parameters. The amount of impurity in the crystal phase is much smaller than that in the bottoms stream, i.e., CC << TSYso The relation for Yp becomes: Y = C (68) C+L If LS, C, and. YS are known from experiments, Yp can be calculated, but Eq. (68) is very sensitive to errors in LSo Equation (68) and the modified, terminal stream balance (Eq. (67)) can be combined to give: (69) YP C- +L which is less sensitive to experimental errors in LS. The equations developed earlier which relate the mass transfer factors E and r' to the operating parameters (see Eqs. (46b) and (47b)) can be comE S bined to yield an expression for tE in terms of'. Considerable simplificaE S tion results from neglecting the mass transfer terms in relation to the diffusional term. (C-LE) s = y c h -Lsi (70) This relation is only valid when axial diffusion is the dominant mechanism

49 determining the mass transfer factors. It can be used to calculate *S from experimental values of R' when experimental values of *S are not available. E S

CHAPTER IV EXPERIMENTAL INVESTIGATION The details of equipment construction, operating procedures, variables studied and. experimental data are discussed. in this chapter. Much of the experimental equipment and. procedure are common to the previous study of Albertins. His equipment was modified for use in this investigation. While the description of equipment presented. below is intended to be complete, many aspects of the fabrication, etc. are presented in more detail in Albertins' thesis. A. DESCRIPTION OF EQUIPMENT lo The Column Proper A center-fed column crystallizer of the Schildknecht type was used in this study. A sketch of the column and. pertinent dimensions are given in Figure 9. Figure 10 is a photograph of the column. The column was constructed from a 52 mm O.D. pyrex tube 70 cm long. A 1.1 cm O.D. stainless steel tube was placed. inside the glass tube to define the annulus which contained the stainless steel spiral. The spiral of lenticular cross section and 1 cm pitch was provided by Speciality Design Company.31 The area normal to the flow of the crystal slurry defined by two spiral turns, the stainless steel tube, and the glass tube was 0.6 cm2. Six copper-constantan thermocouples were mounted in 1/16 in. holes in the wall of the steel tube with epoxy resin. The seventh thermocouple is located in the freezing section. Eight sample taps were fused 50

51, —Auxiliary Heater uxiliary Heater No. 2 No. 1 1/2i Enriching Section i J, _ >Product Line Melting 383 " Slurry Level Section in Column Z' Cartridge Heater 5.5 -Thermocouple (lof7) I10 X 6.6Sample Tap o'- t (2 of 8) X 6.25 Purification 10 6.0 Section 6. x X-+6.0 50 10 6.25!! — {x L —-Glass Tube 74 7.5 (2.6 cm. I.D.) 10 1 _. _ — Spiral Conveyor x 4.0 10.5 Freezing; (4.5cm I.D.) Section 6.5 Glass Tube 8 J _ l'~-Jacket End-Section O- ring Seal Annular Plug Stripping Section lr u Product Line —- S.S. Tube (1.1 cm O.D.) Figure 9. Schematic diagram of the column crystallizer used in this investigation. l.

52 Figure 10. Photograph of the column crystallizer used in this investigation.

53 in the glass column. The taps consisted of.a l/4 in, glass sleeve which could hold a rubber septum; interior to the glass sleeve was a 1/32 ino pinhole that minimized communication of the column contents with the tap areao The freezing section was at the lower end. of the glass column as shown in Figure 9. It consisted of a glass jacket mounted, in two nylon rings. Methanol coolant was circulated through the jacket. All nylon-glass seals were formed, by neoprene O-rings. The annulus between the glass and steel tubes at the bottom of the column was closed with a nylon plugo In this case Viton O-rings, which are resistant to benzene, were used, for the glass-nylon and. nylon-steel seals. The melting section was defined. as that portion of the column occupied. by the internal heater. The melting section heater was a GoE. Calrod cartridge heater (240 ohms) mounted with its lower end. 2.5 cm above the top sample tap as shown in Figure 9. In addition to the internal melting section heater, two auxiliary heaters were placed above and, external to the melting section. Each consisted, of several turns of resistance wire wrapped, around. the glass column. Auxiliary heater No. 1 was used. to flush the gap between the melting section and. the overhead draw-off line. This procedure is described more fully in a later section of this chapter. The second auxiliary heater was used, to melt back any crystals that inadvertently got past the mel-ting sectionl and draw-off line in the case that insufficient power was supplied to the melting section heater or auxiliary heater No. 1,

54 2. Feed and Product Draw-Off System The installation of a feed and product draw-off system represented, the most significant modification of Albertins' equipment. Both the feed and bottoms product were transported and, controlled by proportioning pumps. Both pumps were coupled to the same drive. The stroke of each side of the pump could be adjusted for a flow rate range of 0.6 - 7.0 ml/min. The pump specification was Hills-McCanna UM2 Feed size 2(MLE)33 catalog No. 117147. The feed and product streams were pumped. through 1/8 in. copper lines equipped. with Swagelok fittings. It was necessary to place the pump above the liquid level in the column to prevent benzene from flowing through the pump on the open stroke due to the liquid head driving force. The pump stroke-flow relationship was linear. A calibration curve is presented in Appendix B. The feed. material was cooled, prior to introduction into the column. The feed cooler was a hairpin double pipe exchanger. The shell side was a 3/8 in. copper tube and the tube side was constructed of 15 ga stainless steel hypodermic tubing. Benzene was cooled on the tube side and methanol coolant was circulated. on the shell side. The exchanger was 3.8 ft long which provided sufficient area to allow the temperature of the benzene effluent to approach that of the coolant within 05~C. A thermocouple was installed in the benzene effluent line to measure the feed temperature. This was accomplished by soldering the thermocouple bead. in the wall of the hypodermic tubing. It was possible to introduce the feed at any of the sample taps. This was accomplished by terminating the 1/8 in. copper line from the feed cooler with a Swagelok plug. The plug was drilled and fitted with a 25 ga hypodermic

55 needle. This arrangement made it possible to simply plug in the feed. through any of the rubber septums in the various sample taps. Figure 11 shows the feed introduction assembly. Outer Glass Tube of 25podeGaumic ge Purification Section 25 Gauge Needle 1/8" Swagelok Plug LRubber Septum Figure 11. Feed introduction assembly. The bottoms product was withdrawn through a drain in the plug at the bottom of the column. As mentioned previously both the feed and bottoms streams were transported by the proportioning pump. Consequently the overhead product was allowed to trickle through the overhead line. The overhead product was removed through a 3/8 in. glass tube that was fused into the wall of the column. It was inclined. at 45~ to prevent build up of liquid above the draw-off point. The overhead. product flowed to a receiver through 3/8 in. I.D. teflon tubing. The bottoms product was collected. in a receiver at the level of the pump outlet. 3. Spiral Drive Mechanism The spiral was both rotated and oscillated by the drive mechanism shown in Figure 10. The power was provided by two 1/3 H.P. motors. It was possible

56 to vary the oscillation and rotational speed, independently from 0-440 cycles/ min using two ZERO-MAX variable speed reducers. The spiral was connected to the drive by a 2-1/2 in. long nylon coupling. 40 Column Environment The column itself was insulated on three sides with 1 in.o thick styrofoam, The front was left open so the interior of the column could. be observed. The entire column was placed in a constant temperature air bath shown in Figure 10l The temperature was controlled at 5.5~C, the melting point of benzene, The air bath was an insulated. plywood box equipped with a cooling coil. The front door of the box had a window that permitted. inspection of the column. 5. Refrigeration System Three levels of coolant were required. to operate the column crystallizer. These include the coolant to the freezing jacket, feed cooler, and the constant temperature air bath. The system consisted of a primary refrigerant bath that provided methanol coolant at -30~C and three secondary baths which were used. to control the secondary refrigerant (also methanol) by on-off control of the primary refrigerant pumps. The coolant temperatures to the freezing jacket and. feed, cooler were controlled. by Foxboro model 5041-15 on-off controllers. Since these were originally designed. for high temperature service, thermopiles were used, to obtain the necessary signals. The coolant to the air bath was controlled, by an American Instrument Company bimetallic thermoregulator.

57 B, OPERATING PROCEDURES 1. Start-Up The column was charged with 300 ml of the feed. material prior to beginning each run. When the feed composition was changed from run to run, the column, pump and lines were flushed. with the new feed material. The desired terminal flow rates were established by adjusting the stroke of each side of the proportioning pump, i.e., the feed and stripping section product rates were set. The terminal flow rates were determined by collecting and weighing the various streams. The remaining steps of the start-up procedure are listed below in the order in which they were performed: The coolant flow to the coil in the air bath that surrounds the column was turned. on. The air bath temperature was maintained at 5-5~C. The spiral rotation and. oscillation were started. The coolant to the freezing section was turned. on. The coolant temperature was decreased. from 2~C to the desired temperature at a rate of approximately 20~C/hr, This was done to avoid plugging of the freezing section.. The feed. and bottoms product pump was started. Coolant flow to the feed, cooler was initiated. In most cases the feed. temperature was controlled at a level 1-2~C above the freezing point of the feed. The crystals were allowed. to rise through the purification section to the melting section. At this point sufficient power was applied to the melting

58 section heater to cause the crystal slurry-liquid interface to equilibrate at a position near the top of the melting section heater. The column was operated with the crystal Interface in this position for approximately an hour prior to flushing the region above the melting section. As Figure 9 illustrates there is a 2 5 cm gap of liquid between the melting section and overhead. draw-off line. Note that crystals do not normally enter this region. Prior to start-up this gap contains liquid of feed. composition. In order to accelerate the rate at which the composition of this region approached the melting section composition, this gap was flushed. in the manner described, below. The melting section heater was turned off and. the crystal slurry was allowed. to rise to a position just below the overhead draw-off line. The interface was controlled. at this point for 15 min by adjusting the power to auxiliary heater No. 1. The No, 1 auxiliary heater was then turned. off and the melting resumed with the melting section heater to reestablish the position of the crystal-liquid. interface in the melting section. This procedure was employed, twice in the first few hours of each run. 2. Operation Once the crystal slurry position was reestablished after the flushing procedure, adjustments were made in the coolant temperature to the freezing section to achieve the desired crystal rate. Except during the first hour after start-up, it was not difficult to determine the power necessary to just melt the crystals entering the melting section, The temperatures of the coolants to the freezing section and feed. cooler

59 were controlled, at set points established by calibrated thermometers in the secondary refrigerant baths, The cold bath temperature was controlled at a set point established by a thermometer in the bath itself. No difficulty was experienced in controlling the various temperatures or the position crystal slurry interface as the column approached. steady state. 3. Flow Measurements As mentioned earlier the terminal stream flow rates were determined by collecting and. weighing the overhead. and bottoms products. These rates were constant within +10% during a run in the range 0.6 to 4 gm/mino An experiment was designed to check the overall material balance. The feed. material was placed. in a 100 ml graduated. cylinder and. the two product streams were returned. to the cylinder. If there are no leaks in the system, i. eo, if the overall material balance closes, the liquid level in the graduated cylinder should, remain constant. At an overhead rate of 2.15 gm/min and. a bottoms rate of 5301 gm/min the interface remained constant for 1 hr 15 min. Consequently, it is concluded that there were no leaks in the system and. that the overall material balance closed. The constant interface also implies that there was no appreciable moisture pickup by the productso The crystal rate was calculated from the power required to melt the crystals entering the melting section. The voltmeter used. for the crystal rate measurement was calibrated. by Mr. C. H. Eichhorn at the Electrical Measurements Laboratory of The University of Michigan. This procedure involves the assumption that the overhead. product is at its melting pointo An experiment

60 was performed. to check the validity of the assumption. It was not readily possible to install a permanent thermocouple in the column in the vicinity of the overhead. draw-off line, consequently, the following scheme was used. The spiral and the melting section heater were turned. off and, a thermocouple was pushed. into position through the overhead. line. The temperature was measured. in this manner several times. The overhead. product temperature was 7.5~C (2 0~C above its melting point) for a run where the crystal rate was 5.7 gm/ min, and. the overhead product rate 1.01 gm/min. Therefore the sensible heat provided by the melting section heater to the product stream is negligible (0.5%) compared, to latent heat required, to melt the crystals. 4. Temperature Measurements All thermocouple potentials were measured with a digital voltmeter (United Systems Corp., 40 m.v. full scale, 0.1% accuracy). The primary reference temperature was that of a vigorously stirred eight gallon bath. As recommended by Albertinsl the temperature of the benzene at the top sample tap which was at least 0.999 pure was used, as a secondary reference. This was also the case for this investigation for all runs where the temperature profiles were measured. Copper constantan thermocouples were used. in all cases. 5. Sampling Technique The overhead. and. bottoms products were sampled. periodically throughout each run. Since these samples were obtained external to the column, its operation was not disturbed, As will be described in the next section these samples were used. to verify the existence of steady state prior to taking the

61 composition profile samples. Albertins developed, a reliable profile sampling technique which was used in this study. After steady state was achieved. the spiral was stopped. and the power to all heaters was turned, off. The coolant to the freezing section was left on. The air bath door was opened and. a 0.5 ml sample was withdrawn from each sample tap with a separate syringe. The feed introduction assembly was removed from the septum (see Figure 11) before the free liquid at the feed. position was sampled. The order of sampling was from the top of the purification section to the bottom. Typically 90-100 sec were required to withdraw the eight samples. 6. Approach to Steady State Due to the fact that the mathematical model of the column crystallizer was restricted to steady state, it is essential to show that the column was at steady state. The overhead composition decreases with time until steady state is achieved. The column was considered to be at steady state when the overhead, product composition did not change with time. Figure 12 shows typical data of this type. This hypothesis was checked. by duplicate Runs 11 and. 13. In both runs the overhead product composition became constant after 7 hrso The internal composition profile was obtained, after 7 hrs in Run 11 and. 9.5 hrs in Run 135 No disturbances occurred during this 2. 5 hr period. As Figure 13 illustrates both experimental profiles can be represented satisfactorily by the one smoothed line,

62 10,000 F LAA A 1000 \ C 0 0 J~~ \t \O _LF YF LE C Run gm/min ppm C6H12 gm/min gm/min A 7 1:.98 28,000 0.68 1.46 I 1 2.74 28,000 0.80 1.94 O 18 3.74 30,225 2.91 5.47 -0 2 43 6 8 10 TIME, hr Figure 12. Approach to steady state indicated by the enriching section product composition.

63 100,000:-0 0 I 1 13 Run 2.74 2.83 F,gm/min 28,000 29,700 YF, ppm C6H12 -3 0.80 0.80 LE,gm/min v\ 1.94 1.99 C,gm/min 10,000 \ 77.0 9.5 Time of Sampling, hr 0,0000 N I 0 o) pZF 4.0cm E 1000 C0. o00 ^0 10 20 30 40 50 Z, cm Figure 13. Approach to steady state indicated by the enriching section composition profile.

64 7. Analytical Method. Analyses were made using an F & M Model 5750 gas chromatograph with flame ionization detectors. The analyses were reproducible within +3. The analytical method. for cyclohexane in benzene was confirmed independently by gas chromatographic and, mass spectrographic techniques by Prof. E. A. Boettner of the School of Public Health at The University of Michigan. Further details of the analytical method are presented, in Appendix A. C. VARIABLES INVESTIGATED The following variables associated with continuous draw-off operation were studied in this investigation: Terminal stream flow rates -Feed rate: 2.0 - 5.6 gm/min -Bottoms product: 0.48 - 3.6 gm/min -Overhead product: 0.30 - 3.3 gm/min Internal crystal rate: 1.46 - 6.95 gm/min * Feed composition: 1500, 10,000, 28,000 ppm wt C6H12 o Feed. position: 4.0, 23575, 29.75 cm above the freezing section The only variable associated with the continuous flow problem that was not studied was the state of the feed entering the column. In all cases a liquid feed, 1-2~C above its melting point was fed. to the column. The primary goal of this study was to determine the effect of parameters associated, with continuous flow operation, consequently many possible variables were not studied. The following variables were held. constant:

65 Length of the purification section of the column: 50 cm. Rate of rotation, frequency and amplitude of oscillation of the spiral: 59 rpm, 290 min 1 mm, respectively. Configuration and. length of the freezing section.. Coolant circulation rate to freezing section.. Amount and configuration of insulation. o The temperature of the air bath: 5.5~C. The size and nature of the individual crystals in the slurry inside the purification section were not investigated. Attempts to measure the size of the crystals in the purification section were not successful. Crystals were withdrawn from one of the sample taps but sufficient melting occurred in transferring them to the cold. stage of a microscope (in a chilled. container) to render the observations meaningless. Photographs were taken of the crystal liquid. slurry in the column by Mr. G. G. Davenport of the Office of Research Administration of The University of Michigan. The lighting conditions were such that high speed. (plus-X) film had. to be used.. The grain in the resulting enlarged. photographs was so coarse that individual crystals could not be distinguished. No further attempts were made to photograph the crystals. D. SYSTEM TO BE INVESTIGATED The benzene-cyclohexane system was chosen for this investigation because it affords many advantages. Chief among these is the fact that Albertins used this system; therefore it was possible to make comparisons with his results obtained. at total refluxo Benzene-cyclohexane has a phase diagram of the simple

66 eutectic type.33 The system is also amenable to straightforward, analyses by gas chromatographic techniques. Lastly, as mentioned. earlier, there is evid.ence that commercial incentives to purify benzene by column crystallization may exist. The starting material for preparing all feed materials was Phillips pure grade benzene. This material contained several impurities. An analysis is presented in Table I. The details of the identification and determination of the composition of the various impurities are discussed in Appendix A. Phillips 99.5 wt% cyclohexane -was ad.ded. to the benzene to obtain the 10,000 and. 28,000 ppm wt feed stocks. In all runs the cyclohexane content of the feed. was determined by the gas chromatography TABLE I IMPURITIES IN PHILLIPS PURE GRADE BENZENE Component ppm wt Cyclohexane 1500 Methylcyclopentane 1081 Toluene 475 Hexane 267 2-Methylpentane 215 3-Methylpent ane 218 Cyclopentane 151 Unidentified materials 139 Total impurity 4046

67 E, EXPERIMENTAL RESULTS The experimental data are tabulated, in Appendix C. The operating conditions, terminal compositions and composition profiles are shown for each run. The overhead, product-crystal rate ratio was varied from 0.1 to 1.69. Crystal rates ranging from 1o4 to 6.95 gm/min were employed. The column was inoperable due to plugging at crystal rates higher than 6.95 gm/mino F. REPRODUCIBILITY OF THE DATA The reproducibility of the composition profile data is demonstrated. by Figures 13 and. 20. The profiles for duplicate Runs 11 and. 13 given in Figure 15 can be represented by one smoothed line. A similar pair of runs (14 and. 15) are shown in Figure 20 of Chapter Vo An error analysis of the various experimental parameters is presented in Chapter V.

CHAPTER V INTERPRETATION OF RESULTS Both the theory of column crystallization and the experimental investigation have been discussed in previous chapters0 Two forms of the mathematical model based. on the same mechanisms were developed in Chapter III, One form was obtained, by simplification of the second order model, and. the other form was obtained by employing the transport equation approach. The details of the experimental investigation were presented. in Chapter IV and. tables of data for each experimental run appear in Appendix C. The purposes of this chapter are threefold. First, the experimental results are used. to test the modelL Second., the limits of operation of the center-fed crystallizer are discussed. Third., an error analysis of the experimental parameters is presented~ A. EVALUATION OF THE MODEL The mathematical model is subjected to eight tests in this section0 The first seven tests treat the data that were obtained with the enriching section operating countercurrentlyo The eighth test considers the enriching section product-crystal rate ratio, RE, and includes a discussion of the cocurrent mode of operation. It was shown in Chapter III that the two forms of the model that were obtained differ only in the expressions used for the mass transfer factors (y and Ir', see Eqs. (53) and (54)) The first five tests presented below are concerned 68

69 with the parameters other than the mass transfer factors. Hence these tests d.o not distinguish between the two forms of the model, but rather illustrate other quantitative aspects of the theory. The discussion of the mass transfer factors, the sixth test, treats the two forms of the model. The seventh test considers the application of the correlations obtained from earlier tests to predictive column calculationso Finally, the eight test discusses the effects of the parameter, REo 1. Enriching Section Composition Profile Shape The first test compares the enriching section profile shapes that were predicted by the theory with the experimental profiles. It was shown in Chapter III that the enriching section composition profiles could. have three characteristic shapes. As shown in Figure 8a, Eq. (35) which describes the enriching section profile predicts that plots of the natural log of the free liquid composition (Y) versus the position in the column (z) can give profiles that are concave upward or downward or a straight line. The shape determining group, Yp, is the particular solution of the differential equation which describes the enriching section profile (Eq. (6)). The enriching section profile shape depend.s on the sign and magnitude of Yp (see discussion in Chapter III) which is governed by the relative magnitudes of Cc and LEYE as shown in Eq. (7). The results from three experimental runs which were d.esigned. to test this prediction are presented. in Figure 14. Comparison of these profiles with Figure 8a demonstrates that the theoretical development is qualitatively consistent with the shapes of the experimentally determined profiles,

70 100,000 10,000 1O:OOO IT 6 RE=0.782 - \[< RE= 0.466 N,000 — EPO~r \RE=0.354 100. F YF LE C Run gm/min ppm C6H12 gm/min gm/min 0 2 4.02 28,000 1.04 2.94 A 3 5.30 32,000 2.30 2.94 07 1.98 28,000.68 1.46 10 I I I I 1, 0 10 20 30 40 50 Z, cm Figure 14. Experimental confirmation of the three enriching section composition profile shapes.

71 Equation (55) also predicts that a semi-logarithmic plot of Y - Yp vs z should be linearo The modified composition profiles for Runs 2, 3, and 7 are presented in Figure 15. The profiles are linear for all three cases as predicted by the theoryo The values of Yp were chosen such that the modified profiles were linearo In Run 7 the raw data Y vs z (Figure 14) was linear indicating that Yp = 0. The values of Yp were chosen by assuming values and inspecting the resulting modified profile for linearityo This procedure was checked for Run 5 by performing a linear regression analysis for various assumed values of Yp on the ln(Y-Yp) vs z data. The composition profile for Run 5 is shown in Figure 21 and is of the convave downward typeo The value of Yp (-82 ppm) which corresponded. to the minimum sum squared deviation was chosen (see Figure 16). The value obtained by inspection as described. above was -80 ppm. Therefore the more tedious regression analysis method, was not used for the other runso The values of Yp for each run are given in Table X in Appendix C. 2o Stripping Section Profile Shape This test considers the stripping section profile shape. It was also shown in Chapter III that the stripping section composition profile has a characteristic shape. The expression for the stripping section profile (Eqo (38)) predicted. that the composition profile would. be flat as illustrated, by Figure 8b. The results of experiments designed. to test this prediction are present:ed in Figures 17 and. 18. These data confirm the existence of the flat or inactive region in the stripping section profileo Danyi participated in.

72 100,000 Run Yp,ppm wt.C6H12 0 2 54 A 3 -1070 I7 0 10,000 \ C)1 0 00 ~~10~ Z, cm Figure 15. Modified enriching section composition profiles.

73 0 0 C\J E.\ a i 0a CLo \. *~. 00~ 0 0>- 4-r (0 C- 00C uo toD a Noll^ Sn0 0 0 0 NOllVlA3] G3JVfnOS 1 nfS

74 _ F YF LE C Run gm/min ppm C6H12 gm/min gm/min 0 6 2.40 26,300 1.42 3.30 i 18 3.74 30,225 2.91 5.47 10,00072 rA N - Z-=23.75cm \ \ -1 t 2 ZF =23.75 cm -~I,000 \ 0 1 00 0 10 20 30 40 50 Z,cm Figure 17. Enriching and stripping section composition profiles.

75 F YF LE C Run gm/min ppm C6H12 gm/min gm/min 0 16 2.90 29,300 2.30 4.55 A 17 2.93 29,300 2.45 6.8 100,000,I ZF=29.75cn\\ 1,000 E >-I,000 100I I 0 10 20 30 40 50 Z,cm Figure 18. Enriching and stripping section composition profiles.

76 this experimental study. The shape determining group for the stripping section, Yp, is the particular solution of the differential equation which describes the stripping section composition profile (Eq. (17))o The values of Yp obtained, from the stripping section composition profiles (Yp is the composition where the profile becomes flat) are compared in Table II with those calculated from Eq. (69) which relates Yp to F, C, LS and. YSo TABLE II COMPARISON OF CALCULATED AND EXPERIMENTAL VALUES OF THE SHAPE DETERMINING GROUP FOR THE STRIPPING SECTION Run Yp, from Eq. (69) Yp, from Figs. 17 & 18 % error 6 14,750 13,200 11.7 16 16,500 15 300 24.1 17 11,800 12,200 3 3 18 17,940 15,000 19.6 In view of the experimental confirmation of the flat region in the stripping section profile, and. the reasonable agreement of the experimental and calculated, values of Yp, it is concluded that the model satisfactorily explains the shape of the stripping section profile. Difficulty was encoun.tered in selecting operating co ons that would. produce a non-flat profile in the stripping section. The relation for Yp

77 (Eq. (68)) can be rearranged to yield the following equation which suggests operating conditions that might give a stripping section profile with an appreciable negative slope: P/YS = LS/(C+LS) (71) The slope of the profile should increase as the value of Yp/YS decreases. Therefore in Runs 16, 17, 18 the column was operated with large crystal rates and. small bottoms product rates. Figures 17 and 18 demonstrate, however, that the stripping section profiles for these runs remained flat. This can be explained by noting that the stripping section mass transfer factor probably decreases when the crystal rate is increased (this can be seen by examining Eq. (47b) for the case when the diffusional term is dominant). A decrease in the stripping section mass transfer factor corresponds to a more rapid. exponential decay of the composition Y to Yp thus cancelling the effect of the decreased, value of YP/YS' T[he slight positive slope of the stripping section profile for Run 16 (Figur(e 18) is attributed t aslow sampling of the composition profile for this runo The longer sampling t.inme very like Iy allowed. some of the crystals to melt an. i Alute the liquid *;hat was wi:th.d.rawn frcan the lower sample taps (the upper sample taps wore sampled first)o 35 Impuri.y Associated with. the Crystal Phase The mathematical model includes the effect of impurity transport by the crystal phaseo It was arg.i d that impurities could be entrapped. in the crystal or on their irregular surti4acee The impurity associated with the crystal

78 phase, c, is assumed to be independent of position in the column. This assumption is tested. in this section with e values calculated from the experimental data. The impurity composition in the crystal phase, E, can be calculated from the values of Y obtained from the composition profile data. Rearrangement of P the expression which relates Y to e, C, and L (Eq. (7)) yields: Yp(C-LE)+LEYE (72) C The values of C calculated from Eq. (72) are tabulated in Table X of Appendix C. It is emphasized that these values were calculated from experimental values of Yp, C, and LE. In no case was the crystal composition, e, measured directly. Gates15 suggested. that E should increase when the mother liquor composition in the freezing section increases. Other parameters such as the agitation level are not considered because the spiral oscillation and rotation rates were held constant in this study. The mother liquor composition in the freezing section is assumed to be equal to the bottoms composition, YS. This is equivalent to assuming that the freezing section is perfectly mixed. Figure 19 illustrates that E does increase with Y. The E(Ys) dependence is linear. A least squares fit of the values of E and YS gives the following relation: = 0.00142 Y (73) Figure 19 reveals considerable scatter of the values of C calculated from Eq. (72) from the line predicted by Eq. (73). It is noted, however, that both c and. YS varied fifty-fold. Therefore the dependence described by Eq. (73) is considered to be significant. The coefficient of determination, which is interpreted

79 a- 100 - I —; I~| (=0.00142Ys LL Least CD O - Squares Fit Z E UJ 10C l 0 w 0/ o Continuous Flow Data - i; / Runs 1, 2,3,5,6,9,' 11,13,14 a 15 ~<~ |' A a Total Reflux Data Sr Run 19 ~oI-.I -o ——, 1000 10,000 100,000 BOTTOMS PRODUCT COMPOSITION Ys, ppm wt. C6H12 Figure 19. Correlation of crystal phase impurity composition with the bottoms product composition.

80 as the fraction of the systematic variation of e that is explained by Eq. (73), is 0.986. Correlating expressions which assumed that E was proportional to 0.9 1.1 YS YS, etc. did. not give significantly better correlations. The data of Run 7 was excluded from the final correlation because the value of c contradicted the trend that c increases when YS increases (see Table X). The data from Runs 16, 17, 18 are excluded. from the correlation due to the minimal number of point compositions in the enriching section profile which could. be used to determine Yp (or equivalently e). The linear e(YS) dependence has been found, by other investigators. Moulton and Hendrickson23 found. a linear dependence of the crystal phase composition on the mother liquor composition for the crystallization of ice from sea wat-er. A linear dependence is consistent with the occurrence of volumetric liquid inclusions, but it does not rule out the possibility of slight solid. solubility in the ppm range. The validity of the assumption that c is independent of position in the purification section is implied. by the correlation of c with YS, The expression used to calculate E from Yp (Eq. (72)) is based on this assumption. The three enriching section composition profile shapes presented in Figure 14 are further indications of the validity of the constant c hypothesis. The fact that c decreases with YS leads to an interesting consequence. For a given feed or charge composition, E would be largest when the column is operated at total reflux, because YS is largest due to the concentration of impurities in the freezing section. When the column is operated continuously the impurity level in the freezing section is reduced due to the removal of

81 impurities in the bottoms stream. Thus it is possible to produce purer materials with continuous draw-off of product (when RE is sufficiently small) than can be produced with total reflux operation. This effect is illustrated by the following experimental results: at a feed. composition of 28,000 ppm wt C6H12, RE = 0.354, and. zF = 4.0 cm (Run 2);the overhead product composition, YE, was 57 ppm wt CeH12; the ultimate purity that could be achieved. with total reflux operation is approximately 100 ppm wt C6H12 (see Appendix E). The E(YS) dependence also implies a restriction on the ultimate purity that can be achieved with a continuous flow column crystallizer for a particular feed composition. The simplified form of the terminal stream balance, Eq. (67) is employed. The minimum value of YS occurs when the stripping section is flushed, with feed. material or when the enriching section is operated at conditions approaching total reflux, i.e., - = 1. Equation (67) therefore suggests Ls that (YS)min = YF' Therefore the equation below gives the minimum level of impurity associated with the crystal phase that can be attained. Emin = 0.00142 YF (74) The ultimate purity that can be achieved in a column crystallizer, emin' would occur when the washing of the adhering liquid is complete. 4. Effect of Feed Composition Three feed compositions were used in this investigation: 1500, 10,000, and 28,000 ppm C6H12. The experiments show that the feed composition has the following two effects:

82. Increasing YF increases YS and in turn E as suggested by Eqs. (69) and. (72). * The impurity composition in other streams are related. to YF by material balance considerations. The separation factor 4E is independent of feed. composition. This condition was implied, in Chapter III by the assumption that the transport properties are constant. Figure 20 shows that for comparable operating conditions, with the exception of the feed. composition, the composition profiles are parallel. This is equivalent to 4E being the same for both feed. compositions. Composition profiles for the lowest feed. composition that was used. (1500 ppm C6H12) are given in Figure 21. The feed stock for these runs was Phillips pure grade benzene, It can be seen that very pure materials were obtained. The production of ultrapure benzene is discussed. in more detail in Chapter VI. 5. Column Calculations with Experimentally Determined. Parameters A further test of the model is accomplished by comparing experimental profiles with those calculated using experimental values of the mass transfer factor,*E, and crystal phase composition, o. The iterative calculation procedure described. in Chapter III has been used. to calculate the terminal compositions and. composition profiles for the experimental runs. The appropriate operating parameters, 0 ZF, F, YF, LS and C were specified for each run. In addition experimental values of the enriching section mass transfer factor, f &and the crystal composition,e,were used in the calculations. Experimental values of the stripping section mass trans

83 F YF LE C 0 Run gm/min ppm C6H12 gm/min gm/min 0 I 4.18 28,000.68 2.60 10,000 \ 14 2.61 10,400.74 2.94 \ 15 Duplication of Run 14 0 ~ \ \ I I_ \ \ I 3 \ \ \ E ZF~4.0cm', - F \ 0 0 01 0 ]oo t S X I 0 A 0 15 l l l, 1 0 10 20 30 40 50 Z,cm Figure 20. Influence of feed composition on the impurity level in the enriching section.

84 10 \ Run F,gm/min LE,gm/min. C,gm/min 1000 _ 0 5 5.76 2.23 2.60 A 9 3.50 0.30 2.94 YF =1500 ppm C6HI2 | \ \ Feed Material: Phillips Pure \ Grade Benzene 100 -ZF=4.0 cm 1 A I \II I I I Z.C)m I0 0 10 20 30 40 50 Z, cm Figure 21. Enriching section composition profiles for the purification of Phillips pure grade benzene.

85 fer factors could. not be obtained because the composition profiles in this section were essentially flat, i.e., the slope could not be measured. Therefore the values of *S were calculated from *E It is assumed that the results of the transport equation approach are applicable in order to relate *S to E y i.e,, E == ~ E and. S =' The following relation that was developed. in ChapE E S S ter III is employed: (C -LE) (70) *s = E (C+L)) The calculations were facilitated. by the computer program described. in Appendix D. Figure 22 compares the calculated, profiles with two sets of experimental data. It is concluded that the mathematical model satisfactorily explains the form of the experimental data. The calculations also reflect the internal consistency of the flow rate, profile, and terminal composition data. It is emphasized that these calculations are not completely predictive, because experimental values were used for $E and E which are strictly dependent variables once d ZF, F, YF, LS, and C are specified. Table III compares the experimental values of the terminal compositions YE and YS with the values calculated by the above procedure. The reasonable agreement again illustrates the consistency of the data. Further, it experimentally confirms the validity of the end conditions that were specified in Chapter III, i.e., z = Y = YE (62) z = O, Y = YS (65)

86 100,000 ZF=4.0cm \O. I 0,00 100^- c s - Run 0 0 2 Values of o' and E 10 10 20 30 40 50 Z,cm Figure 22. Comparison of experimental and calculated composition profiles.

87 TABLE III COMPARISON OF EXPERIMENTAL AND CALCULATED VALUES OF THE TERMINAL COMPOSITIONS Run YE, Experimental YE, Calculated YS, Experimental YS, Calculated - - - - ----- ppm wt C6H12 -- -. — ------ 2 60 57 37,000 37,800 3 370 440 37,000 56,200 5 16 21 2,090 2,460 6 101 111 72,000 64,300 7 300 403 43,400 41,800 9 1 1 2,140 1,640 11 62 69 39,600 39,000 13 55 58 41,200 41,400 14 29 28 14,200 14, 500 15 29 28 14,300 14,000 16 65 80 186,000 165,000 17 84 84 225,000 180,000 18 107 105 153,000 136,000

88 These conditions were used. in the column calculations discussed above. 6. Mass Transfer Factors The only difference between the two forms of the model developed in Chapter III is the expressions that represent the mass transfer factors (see Eqs. (41b), (42b), (46b), and (47b)). The purpose of this section is to correlate the experimental mass transfer factors with an appropriate mathematical expression developed earlier. It was shown earlier that the mass transfer factors which result from the transport equation approach can be related to the more complicated expressions which result from the original form of the model that includes the axial diffusion term in the free liquid material balance. The mass transfer factors derived by the two approaches differ by a factor e(X) as shown in Eqs. (53) and (54). The experimental mass transfer factors will be correlated by assuming that e(X) - 1. Using this approximation, the mass transfer factors developed by the two methods become identical, i.e., IE = /E and. = S. Thus the simpler expressions, 4', can be used. If a satisfactory correlation of the data is obtained, by this method, no attempt will be made to fit the data with the more complicated, expressions for r (Eqs. (4lb) and. (42b)). Experimental values of Er and. *0 can be obtained by measuring the slope of the modified composition profiles, e.g., the slope of ln(Y-Yp) vs z is the negative reciprocal of IrE (see Eq. (59)). Total reflux mass transfer factors, 4r, are available from Albertins' data. Only experimental values of are 0aaailable for -t~he continuous drawoff case. The stripping secEion mass ransE available for the continuous draw-off case. The stripping section mass trans

89 fer factor A' could not be determined due to the flat region that occurred in the experimental profiles. Hence only experimental values of 4E and. 0 are correlated. It is important to reemphasize the assumption that the parameters Dr, Ka, etc., are assumed. to be constant for fixed spiral agitation conditions. This assumption implies that the mass transfer factor data for different feed. compositions, feed positions, terminal stream flow rates and. internal crystal rates can be correlated by single values of Dvi, Ka, etc., for either total reflux or continuous flow operation. Consequently the expression that relates 7 to C and LE (Eq. (46b)) can be transformed to Eq. (75a) which suggests that a multiple linear eression analysis of the experimental data will yield the correlation constants: = blX1 + b2X2 + b3X3 (75a) where. bl = DpAr (75b) b2 = a(a+l)/KaAp (75c) b3 = - a/KaAp (75d) X1 = 1/(C-LE) (75e) X2 = C /(C-LE) (75f) Xs = CLE/(C-LE) (75g) Note that the expression for 0' for total reflux operation is a special case of the above equations, that is, when LE = 0 the total reflux separation factor becomes:

90 0 = blX1 + b2X2 (76) It is emphasized that the constants bl, b2, and. b3 have physical significance. They are determined. by the physical parameters of the system (see Eqs. (75b), (75c) and (75d)). Albertins'l total reflux data T0 vs C are tabulated in Appendix E. These data were obtained with the same spiral rotation speed, oscillation frequency and amplitude as employed. in the present study. A regression analysis of his data employing Eq. (76) yields the following expression: t. = 6.862/C +.o9096 C (77) where C and *T are expressed in gm/min and cm, respectively. Gates13 obtained the same constants by correlating Albertins' data with the following expression: C = bl + b2 C2 (78) Utilizing Eqso (75b) and (75c) the following relations are evident: DpAr = 6.862 gm-cm/min (79) a(a+l)/KaAp = 0.9096 cm-min/gm (80) Equation (77) predicts the experimental values with a maximum deviation of 5.5%. The accuracy of the correlation is considered to be excellent and implies that using *0 rather than O (or equivalently taking e(X ) to be one) is consistent with the data. A regression analysis of the *E data obtained in this investigation resulted in the following expression:

91 6. 538 +0.4102 C2 0.4185 CLE (8 *E =(C-LE) (C-LE) (C-LE) The experimental values of *E are given in Table X. The data of Runs 9 and 10a were excluded from the correlation due to uncertainties in the experimental values of the crystal and overhead product rates C and. LE. Runs 16, 17, and 18 were deleted due to the minimal number of data points that were obtained. in the enriching section profile. In these runs a larger number of the sample taps were below the feed. point. The calculated values of the mass transfer factors are in reasonable agreement with the experimental values. Figure 23 compares the experimental 2O o Continuous Flow, 1 E A 25 Calculated Values From Eq.77 0 E 7 S A Total Reflux, 0 / 20 Calculated Values From Eq.81 - 105 o I0 < 5 0 5 10 15 20 25 EXPERIMENTAL P', cm Figure 23. Comparison of calculated. and experimental values of the mass transfer factor. and calculated, values. As mentioned. earlier the maximum error between the

92 predicted and experimental values for the total reflux case was 5.5%. The errors were larger for the continuous flow case. The average error between the predicted and experimental values of the enriching section mass transfer factors was 17%. The uncertainity in the experimental values of Er used. in the correlation was 12%. The correlation results indicate that axial diffusion is the dominant effect in determining the mass transfer factor. The relative contribution of the mass transfer terms was determined for each run by calculating the magnitude of all three terms with Eq. (81). The average contribution of the second two terms in Eq. (81) to E1 was 18%. The maximum contribution of the mass transfer terms was 29% in the case of Run 1. Table IV compares the values of the constants obtained from the continTABLE IV COMPARISON OF THE MASS TRANSFER AND DIFFUSION GROUPS OBTAINED FROM TOTAL REFLUX AND CONTINUOUS FLOW DATA Total Reflux Continuous Flow Data Group Data of Albertins of this Study b = DpA, gm-cm 6.862 +.1134 6.538 + 1.936 mmin b2 = a(a+l)/KaAp, cm-m 0.9096+.0770. 4102+ 0.4439 gm cm-min b3 = -a/KaAp, g -m -O.4185+ O.4192 gm uous draw-off and total reflux data. In both cases the diffusional term DpArl

93 is dominant and. the agreement between the values obtained, from the two sets of data is satisfactory. Also the mass transfer terms obtained from the continuous flow data b2 and b3 have the signs that are suggested, by the theory (see Eqs. (75c) and (75d)). These constants, however, differmarkedly. It is also noted that the standard errors of b2 and. b3 given in Table IV for the continuous draw-off case are large. These errors coupled with the dominance of the diffusional term illustrate the insensitivity of the continuous flow data to the mass transfer terms b2 and b3. This insensitivity of the continuous flow data relative to the total reflux data can be explained by rearranging the expression for ~E (Eq. (46b)) and comparing it with the corresponding relation for. CLE {DPA1+ KaAp [(a+l)c2LE (82) o = C + aAp (8 It can now be seen that the dependence of TE on the overhead product rate, LE, dampens the sensitivity of the continuous flow data to the mass transfer effect. Therefore it is evident that the total reflux data provides a more severe test than continuous flow data of the relative importance of the diffusional and mass transfer terms. It must be remembered, that the mass transfer factor data have been correlated using the expressions that result from the transport equation approach, that is, O(Xo) and e(XE) were assumed to be one. A direct check of this hypothesis would require a calculation of X0 and XE from the constants obtained

94 from the above correlations. Comparison of the defining relation for XE (Eq. (51), X0 is a special case of this equation for RE = 0) with the definitions of bl, b2, and b3 (Eqs. (75b), (75c), and (75d)) reveals that a must be separated from the constants in order to calculate XE or X0, i.e., a must be known individually. The adhering liquid-crystal rate ratioo, cannot be obtained from the total reflux data. It is grouped with the parameters KaAp as shown in Eq. (80). In principle a can be obtained from the correlation constants obtained from the continuous flow data, i.e., combination of Eqs. (75c) and (75d) yields: a: -(b + (84) Unfortunately the standard errors of b2 and. b3 given in Table IV do not permit the application of this relation. Therefore a cannot be obtained from either the total reflux or continuous flow data. Consequently XE or X0 cannot be calculated or equivalently the validity of the approximation e(X) = 1 cannot be directly determined. The justification for using the mass transfer factors obtained by the transport equation approach is the excellent correlation of the total reflux data mentioned above. The approximation, O(X) = 1, should be even more accurate for the enriching section, because XE < XO. In view of the above considerations it is concluded that the model summarized in Eqs. (46) and (47) provides a satisfactory representation of the experimental data. Henceforth in this dissertation all discussions that refer to the "model" will be in reference to the expressions that result from the transport equation approach.

95 7. Predictive Column Calculations The model is subjected to its severest test in this section. The correlations developed, in the earlier section of this chapter are used in conjunction with the model to perform column calculations. The results are compared with experimental datao The composition profiles and. terminal compositions are calculated by the iterative procedure presented. in Chapter III by specifying only the column operating conditions: K2, ZF F, YF, LS and Co The mass transfer factors and the crystal compositions can be calculated from the correlations developed earlier. The enriching section mass transfer factor is related. to the flow rates by Eq. (81). 6.538 0.4102 C2 Oo.4185 CLE + _(81) E (C-LE) (C-LE) (C-LE) The stripping section mass transfer factor is calculated. using the same constants in conjunction with Eq. (47b) as shown in Eq. (86)., 6.538 0.4102 C2 O.4185 CLs (85) *S (C+LS) (C+L) (C+Ls) Finally, the impurity composition of the crystals E is given by Eq. (73), E 0o 00142 YS (72) It is emphasized that these relations are peculiar to the benzene-cyclohexane systems and the spiral agitation conditions employed in this study. Figure 24 compares experimental data with composition profiles calculated

96 100XpOO — Run 02 A 3 0 7 _ \l/- Calculated, Using Predicted I\\/ VValues of ^' and E AL E 10,000- n 0 A A c _ O ZZ F:4.0cm 0 _ uoo- o 100100 0 00 10 20 30 40 50 Z,cm Figure 24. Comparison of experimental and calculated composition profiles.

97 by this method. The deviation between the calculated and experimental values of the point compositions for Run 3 (one of the worst cases) are as large as 200%. Errors of this magnitude can be explained by errors in the predicted. values of *Eo It was mentioned above that the values of rE predicted by Eq. (81) show an average error from the experimental values of 17o% It is further noted that the calculated values of WE enter the calculation in an exponential term (see Eq. (46)) which magnifies the error and thus results in the discrepancy between calculated. and experimental values of the point compositionso While the point compositions calculated from the model are in considerable error the predictive calculations do qualitatively predict the influence of variables. 8. Effect of the Enriching Section Product-Crystal Rate Ratio, RE As pointed. out in Chapter III the separation that is achieved. in a column crystallizer decreases with increasing RE. Experimental data are presented in this section which illustrate this effect. The operation of the enriching section with cocurrent flow is also discussed. The effect of RE is illustrated by Runs 2, 3 and 7 shown earlier on Figure 14. The relative position of the enriching section composition profiles indicate that increasing RE decreases the separation. The enriching section product composition, YE, for Run 2 was 60 ppm wt C6H12 for a value of RE of 0.354. The corresponding product composition for Run 3, where RE was 00782, was 570 ppm wt CiHi2o The bottoms product rate was approximately the same for each run (see Table IX of Appendix C)o The increase of YE with RE, which is

98 exponential when YE > e, occurs due to the exponential dependence of the free liquid composition on the enriching section mass transfer factor. The column calculations presented in the previous section demonstrate that the model predicts the influence of RE. When RE is further increased, the separation continues to decrease as shown in Figure 25. In Run 10A RE is 0.99. The enriching section profile is observed. to have a small slope which corresponds to a large value of 4E. In the limit when RE is one, the composition profile in the enriching section is described by Eq. (59) which predicts a linear relationship between Y and z. The mass transfer factor increases sharply as RE approaches one. The individual flow rates LE and C are only known within 10%, consequently the true value of RE is between 0.8 and 1.2. The sensitivity of E' to RE can be demonstrated for the crystal rate employed in Run 10A by calculating values of 4E for RE = 0.8 and 0.99. Equation (81) which relates *E to C and LE gives 4 = 11.0 cm for RE =0.8 and. = 197.0 cm for RE = 0.99. In view of this range of possible enriching mass transfer factors there is no justification to assume that RE = 1.0 for Run 10A in order to test Eq. (59). When RE is greater than one, the flow in the enriching section can be cocurrent depending on the magnitude of the adhering liquid rate (see Eqso (60) and: (61)). Run lOb was obtained with RE = 1.69 and a feed composition of 26,400 ppm wt C6H12. The overhead product composition YE was 12,400 ppm wt CeH12. The corresponding value calculated from the model using the end. condition for cocurrent operation given by Eq. (63) was 11,870 ppm.

99 100,000 N E 10,000 ZF -4. \.ZF 4.Ocm 0 1,000 - F YF LE C Run gm/min ppm C6H12 gm/min gm/min - O IOA 5.3 26,400 3.30 3.33 A IOB 5.3 26,400 3.30 1.95 RE 0.99 A 1.69 100 1 1 0 10 20 30 40 50 Z,cm Figure 25. Enriching section composition profiles for large values of enriching section product-crystal rate ratio.

100 The overhead. product purity obtained, for cocurrent operation of the enriching section is compatible with the purity obtained. by dilution of the portion of the feed that rises through the enriching section with the crystals from the melting section. This can be illustrated, by a simple calculation. In Run lOb 5.3 gm/min of 26,400 ppm C6H12 feed. was fed to the column, but due to the fact that LE was greater:.than C, 1.35 gm/min of feed. passed cocurrently up the column with 1.95 gm/min of crystals. These streams were combined. in the melting section to give an overhead, product rate of 353 gm/min. Now if it is assumed. that the portion of the feed. and. the crystals are transported through the enriching section without interacting, i. e, with no separation in this section, the overhead, product composition YE can be calculated. by considering only the dilution effect of melting the pure crystals in the melting section. Such a calculation gives YE = 10,800 ppm wt C6H12. The experimental results and calculations for Run lOb are summarized as follows: The experimental enriching section product composition is 12,400 ppm wt C6H12. * The value of YE calculated. with the model using the end. condition for cocurrent flow is 11,870 ppm wt C6H12.. The value of YE calculated considering only the dilution in the melting section is 10,800 ppm wt C6H12o The purity that was obtained in Run lOb can be explained by the dilution effeet alone. Consequently, it is apparent that the purification section of the column crystallizer does not contribute to the separation when the enriching

101 section is operated with cocurrent flow. Thus this mode of operation is not of further interest and the cocurrent enriching section model is not discussed. further. Bo LIMITS OF OPERATION The limits of operation of the center-fed. column crystallizer are considered in this section. The internal crystal rate, and the ratio of overhead. product rate to crystal rate are discussed, relative to the operability of the column. 1. Crystal Rate The capacity of a column crystallizer is determined, by the maximum crystal rate that can be achieved. The experimental results discussed below show that the column plugs and. becomes inoperable at a crystal rate higher than 6.95 gm/mino At this crystal rate cavities started to form in the freezing section indicating the onset of plugging. When the crystal rate was increased beyond. 6.95 gm/min the column plugged. Albertins found that with total reflux operation the same column plugged. at a crystal rate of 5.4 gm/min. According to Albertins3 the spiral may have been binding slightly with the glass wall in the lower region of the column. Other than this effect which may have limited, the crystal rate which he obtained, no attempt is mad.e to explain the differences in the observed plugging crystal rates, The experimental results deviated, from the mathematical model when the plugging crystal rate was approached. Figure 26 shows an enriching section composition profile for a crystal rate of 6095 gm/min. It can be seen that

102 100,000 0 Run 8 Fgm/min 2.86 YF,ppm C6H12 28,000 LE, gm/min 1.49 C,gm/min 6.95 10,000 -' ---- Expected Profile E 1,000 0ZF 4.Ocm 100 \ \ to I I I 0 10 20 30 40 50 Z, cm Figure 26. Enriching section composition profile obtained at the onset of crystal plugging.

103 the profile deviates from any of the three characteristic profile shapes discussed earlier. The dashed line indicates the profile shape that would be expected for the value RE =:. 21 which was-used in this run. At crystal rates below the plugging level no such deviation was observed, for example, in Run 17 (Figure 18) when the crystal rate was 6.8 gm/min the enriching section profile was consistent with the model. 2. Overhead Product-Crystal Rate Ratio, RE The column was found to be operable for all the values of RE that were used (RE was varied from 0.1 to 1.69). This range of RE embraces both countercurrent and cocurrent operation of the enriching section. There were no observable differences in the nature of the fluidized crystal liquid slurry in the purification section over the range of RE studied. Co ERROR ANALYSIS The results of an error analysis of the various experimental parameters that were determined in this study are presented below: o The point compositions canbe in error as much as 8%. This includes errors in the analytical method (3%) and the effect of back diffusion while the profile is being sampled (5%).1 The maximum uncertainity in the position of the syringe tip during sampling was 0.5 cm. This could occur if the hypodermic needle were deflected by the spiral. o The terminal stream flow rates (F, LE, and LS) are known within + 10%. The magnitude of this error s eobtained by repeated, measurement of the flow rates during each rIlno

104 The terminal stream material balance, Eq. (64), closes within + 10%. This was established. by comparing calculated and experimental values of the feed composition. The internal crystal rate in the purification section is known within 15%. This error is based on a consideration of refreezing of crystals due to the axial temperature gradient, errors in reading the voltmeter which was used. to determine the power input to the melting section (this was the basis for determining the crystal rate), and the heat gain to the purification section from the surroundings. The mass transfer factors,, are obtained, from the negative reciprocal of the slopes of the enriching section composition profiles. Multiple values of 4' were calculated for Run 2 by using all possible combinations of the experimental point compositions to calculate the slopes. The values of |' were found to flu +12% around the mean value. The procedure used to estimate the error associated. with measuring the internal crystal rates requires clarification. The estimate was made for a crystal rate of 2.6 gm/mino The percentage error that results increases as the magnitude of the crystal rate decreases. Only four of the experimental runs employed crystal rates below this level. Possible refreezing on the crystals due to the axial temperature drop in the purification section (4o9~C) was estimated as 6% of the 2.6 gm/min crystal rate. The error in reading the voltmeter could have been as much as 0.5 volt; this corresponds to a + 3% of the crystal rate. The heat gain of the purification section was determined by Albertinsl for total reflux operation. He found that the heat gain in the

105 purification section corresponded to a decrease in the crystal rate of 0.48 gm/mino This provides a conservative estimate for continuous flow operation because the temperature difference with the surroundings is larger for total reflux operation. For a crystal rate of 2.6 gm/min this heat gain would decrease the crystal rate 18%. The errors due to refreezing and heat gain tend to cancel one another. Therefore the net uncertainity in the measured crystal rate is 15%. D. CONCLUSIONS On the basis of the comparisons in earlier sections of this chapter of the experimental data with the mathematical model it is concluded that the form of the model developed by the transport equation approach (Eqs. (46) and (47)) is consistent with the experimental data. It provides a satisfactory explanation of the influence of the variables that were studied in this investigationo The model breaks down as the plugging crystal rate is approached. The concept that the level of impurity in the crystals is independent of position in the purification section was subjected to more tests than could. be applied with total reflux, The variable profile shapes that occur in the enriching section, the E(Ys) dependence, and the fact that purer material can be obtained with continuous draw-off (for small values of RE) than with total reflux operation all support the constant c hypothesiso Finally the internal flow rates were assumed to be constant in the mathematical analysis, The crystal rate was only measured at one position (the melting section), ie., the validity of the assumption of constant flow rates

io6 was not verified by direct experiments. The error analysis presented above which considers the heat effects in the purification section shows that the crystal should. not vary more than 15%. This in conjunction with the linearity of the modified enriching section composition profiles (Figure 15) justifies the assumption of constant internal crystal rate, i.e., the constant slope, 2 14 -l/, implies that the crystal rate is constant. Both Albertins and Gates foundm that their data for total reflux operation were consistent with this assumption.

CHAPTER VI DISCUSSION OF CONTINUOUS FLOW COLUMN CRYSTALLIZATION This chapter discusses continuous flow column crystallization in view of the theoretical and. experimental results that were compared. in the previous chapter. The mathematical model is used to predict the influence of some of the variables in ranges that were not evaluated experimentally. Also the application of continuous flow column crystallization to the production of ultrapure benzene is discussed. All of the calculations presented in this chapter are based on the model derived from the transport equation approach (Eqs. (46) and. (47)). The mass transfer factors \r and *S are calculated using the correlations given by Eqs. E S (81) and (85). The impurity level in the crystal phase, e, is represented by Eq. (73). All column calculations were performed using the iterative procedure described in Chapter III which is implemented by the computer program given in Appendix Do A, PARAMETER STUDIES The influence of the feed position, feed. rate, enriching section productcrystal rat.^e ratio and product recovery are discussed in this section. No at+,tempt is made to exhaust all the possible combinations of the parameters. The intent' is to illustrate the effect of these variables rather than map the enti:re region of interesto 1.07

108 1. Feed. Position The separation that is achieved. in a column is a function of the feed position. It was demonstrated both theoretically and experimentally in Chapters IV and. V that a flat portion can exist in the stripping section composition profile (see Figures 17 and 18). A flat region of this type corresponds to inefficient utilization of the purification section. The flat region of the profile can be eliminated. by decreasing the length of the stripping section. Figure 27 illustrates the effect of feed position on the enriching section product composition for fixed feed composition, YF, crystal rate, C, and. terminal stream flow rate, F, LE, and LS. There is a feed position which corresponds to a maximum product purity. The plot of the composition of the free liquid at the feed. point, YO, vs zF shown on the same figure illustrates that the maximum separation that is achieved occurs when there is a feed match, i. eo, Y( = YF' 2. Enriching Section Product-Crystal Rate Ratio, RE Figure 28 illustrates that the product purity reaches a limiting value as RE is decreased. When RE is decreased. to a value where YE = E (complete washing), a further decrease does not effect the product purity. Decreasing RE beyond this point decreases the mass transfer factor,' but does not necessarily increase the enriching section product purity. As mentioned. in Chapter III the washing process d.oes not reduce the level of impurity associated with crystal phase. Consequently in applications where maximum purity is

109 -Calculated 2200 | C =2.4 gm/min 40,000 F = 2.0 gm/min LE = 1.9 gm/min 2000 35,000 o 1800 30,000 t \F 8 \0 /YF =28,000 o a- 0. w 1600- \ - 25,000 - 1400- \ I / -20,000 1200o -I I I 1 =15,000 0 10 20 30 ZF cm Figure 27. Influence of feed position on the enriching section product composition.

110 desired, RE should be chosen so that YE is just equal to e, i.e., so there is not a flat region in the enriching section composition profile. Figure 28 also illustrates that the product purity decreases as the 200'- Calculated YF 28,000ppm C6H12 ZF = 4.0cm C = 4.0 gm/min c 160 I / J~ |LE /F'0.66 /l a~,120( a L /F= 0.500 wb E >" 80} / LE /F =.333 0.2.4.6.8 i. LE/C Figure 28. The effect of the enriching section product-crystal rate ratio and product recovery on the enriching section product purity. recovery, LE/F, is increased. The crystal phase composition, c, increases when the recovery is increased. This can be explained by Eq. (67) in Chapter III which shows that for a given feed. composition YS is determined by the value of F/LS which is uniquely determined by the value of LE/F. Also, it was shown in Chapter V that c is determined by YS (see Eq. (73)). Note that the maximum

111 value of RE which corresponds to YE = c (the break point in the curves on Figure 28) increases as the recovery is decreased.. 3. The Relation Between Continuous and Total Reflux Operation The expressions for the enriching and stipping section composition profiles each reduce to the expression for the composition profile for total reflux operation when RE and RS are zero and Y( is replaced by the free liquid composition at z = 0, Yo. Figure 29 shows the effect of the feed rate on the 240O -- Calculated YF =28,000ppm C6H 12 N 200 ZF =4.0 cm C =4.0gm/min (nID~~~ LEL/Ls= 2.0!60 80 ota Reflux, F 0 1 2 3 4 5 F, gm/min Figure 29. Comparison of the purity achieved with continuous flow and total reflux operation.

112 enriching section product composition. Total reflux operation corresponds to F = O. The continuous flow calculations (F j 0), however, do not predict the correct pure end. composition for total reflux operation when F is made arbitrarily small. This occurs because the end conditions (see Eqs. (62) and- (65)) for continuous flow operation do not apply for the total reflux case. The corresponding relation for total reflux is an initial condition, i.e,, the total mass of impurity initially charged. to the column must be equal to the sum of the masses of impurity in the melting section, purification section, and freezing section at steady state. B. PRODUCTION OF ULTRAPURE BENZENE It has been demonstrated in the previous chapter that it is possible to greatly reduce the cyclohexane content of benzene by column crystallization. Figure 21 illustrates that the cyclohexane content of Phillips pure grade benzene can be reduced three orders of magnitude. There are many other impurities besides cyclohexane in Phillips pure grade benzene (see Table I)o These impurities are identified on the chromatogram presented. in Figure 30. The chromatogram of the overhead. product for Run 9, also given in Figure 30, illustrates that all of these impurities were removed, to a level where they could. not be d.etected, by the gas chromatograph. The lower limit of detection of the chromatograph used. for this analysis, which was equipped with a non-polar Squalane packing, was less than 10 ppm for each of the impurities. The cyclohexane content of the Run 9 overhead. product was approximately 1 ppm as determined by a chromatograph equipped with a polar

113 auanlol a,' rF P0 C Z 3O 0 z R "J a ll \1 h O pal!J!uaPiun Cr 4-\ C4ON 0 H paipluapiun - o pa!U!puap!u n 5 1n0wo oluNluanows olu l0) auazua 08I auazuag 9UD 8u9dooAI3ojAq4i9u 0 II N auoxaH ~= =w w p\ a) r "pd auoDuadldjAqa/Iy- bo auoDUado1o3o U,- h pa!j!iuap!un paJ!N!uap!un - QNnOdlA0o NOIiVnN311V aNnod0 o NNOlVnN311V

114 Carbowax packing. It is apparent that column crystallization provides an effective means of reducing the impurity content of benzene. The benzene product purities obtained. by column crystallization are comparable to those of zone refined, benzene, e.g., zone refined benzene is commercially available8 containing ten, one hundred., and ten thousand ppm impurities. Column crystallization, however, provides a means of producing much larger quantities of very pure materials than can be obtained by zone refining techniques. The remainder of this chapter is devoted to discussion of operating conditions and methods that could. be used. to produce ultrapure benzene. 1. Multiple Pass Operation There is a limit to the purity that can be achieved in a column crystallizer with one pass operation. As discussed in Chapter V the minimum level of any impurity that can be obtained for a given feed composition is c in. The relAtion for emin (Eq. (74)) indicates that the minimum impurity level is determined by the feed composition, YF. With multipass operation the feed composition to the second and any subsequent passes is reduced, i.e., the pure product from the first pass becomes the feed to the second pass, etc. Therefore theoretically there is no limit to the purity that can be obtained by multiple pass operation. The same effect could be achieved for large scale applications by staging column crystallizers in series with the product from one column becoming the feed for the next. Another advantage of multiple pass over single pass operation is the fact that higher production rates can be achieved if sufficiently large quan

115 tities of product are required. This results from operating the first pass and. second pass at higher overhead product rates than could be achieved. with single pass operation. 2. Design Example An example is presented to illustrate the conditions under which there is a production time advantage of two pass over one pass operation. The discussion concerns the determination of operating conditions that will minimize the operating time of the existing laboratory column (described in Chapter IV) to produce benzene containing 3 ppm wt C6H12 from Phillips pure grade benzene. This purity was chosen because it can be attained by either single or two pass operation. The problem of determining the operating conditions was constrained, so that only the overhead product rate from the first pass and the quantity of final 3 ppm wt C6H12 product could be varied independently. The feed and crystal rates were set at 5 gm/min for each pass. The cyclohexane content of the feed to the first pass was 1500 ppm wt. Column calculations were performed for the first pass for a variety of overhead product rates. Similar calculations were done for the second pass for several feed compositions obtained from the first pass. The results of these calculations were used to determine the time required to produce various quantities of 3 ppm product by both one pass and two pass operation. The calculation of time required included, consideration of start up time (5 hr for each pass), and steady state running time for both passes. Figure 31

116'r Feed and Crystal Rate 30 5.0gm/min for both Passes IL 28 w0o 27 - 26 0 L (YF2)oPT MUM 75ppm 0 I'~ 25 I-I-I-,,,I 0 100 200 300 ppm wt. C6H12 FEED COMPOSITION TO SECOND PASS Figure 31. Effect of the second pass feed composition on the time required to produce 2,000 gm of 3 ppm product.

117 illustrates the effect of the feed composition to the second. pass on the processing time for the production of 2000 gm of 3 ppm product. The optimum (minimum production time) second pass feed. composition was 75 ppm which corresponds to a first pass enriching section product rate of 4.6 gm/min. Figure 32 compares one pass and two pass operation. It can be seen that two pass operation becomes advantageous when more than 2000 gm of 3 ppm product are required. The curve for two pass operation in Figure 32 represents the time required. for producing the various quantities of product with the optimum second. pass feed composition for each product weight shown. 40 1 Pass 2 Pass 30 Feed and Crystal Rate *- / 1 5.0gm/min for both I 2 Passes: 20 H / P1 2 Passes -^- Recommended 10 / 1 Pass Recommended.; 0 I =MM 0 1000 2000 3000 4000 5000 WEIGHT OF 3PPM WT. C6HI2 PRODUCT, GM Figure 3.2. Comparison of one pass and two pass operation.

CHAPTER VII SUMMARY AND CONCLUSIONS A theoretical and. experimental investigation of the component separation of a system of the simple eutectic type by column crystallization illustrated. the effects of the variables associated with continuous flow operation. Terminal composition and axial composition profile data were obtained. to study the column performance. The effects of the variables associated. with the continuous flow problem are satisfactorily explained by a mathematical mod.el which includes consideration of mass transfer by axial dispersion of impurity in the free liquid, mass transfer of impurity from the adhering liquid to free liquid, and. the presence of impurity associated. with the crystal phase which is assumed. to be constant throughout the purification section. The model was derived. using the transport equation assumption which greatly simplified. the final form of the expressions for the mass transfer factors (parameters which are an inverse measure of the separation power of the column). The mod.el satisfactorily explains the shape of the experimental composition profiles in both the enriching and stripping sections. The variable profile shape in the enriching section and the correlation of the impurity composition of the crystal phase, c, with the stripping section product composition, YS, are further justifications beyond Albertins'2investigation for total reflux operation that E is independent of position in the purification section. The E(YS) dependence implies that purer material can be obtained with continuous 118

119 flow than with total reflux operation (at low values of RE)O The interpretation of the mass transfer factors obtained, from both continuous flow and. total reflux data show that axial dispersion is the dominant mechanism determining the extent of separation, but that mass transfer between the adhering and. free liquids is significant. The average values of -"he diffusio; terms DpAr obtained from the continuous data flow of this study and total reflux data of Albertins are in excellent agreement. The values of the mass transfer terms, a(a+l)/KaAp, obtained from these two data sources differ by a factor of two (see Table IV), The deviation is explained by the relative insensitivity of the enriching section mass transfer factors to the mass transfer terms, i.e., the melting section product rate LE reduces the contribution of the mass transfer terms as shown by Eqso (82)and (83), The computer program developed, for column calculations can be used to predict the influence of variables associated with continuous flow operation. The agreement between calculated and. experimental compositions is excellent when experimental values of the mass transfer factors are used. When values of the mass transfer factors are calculated using the values of the diffusional and mass transfer groups (DpAi, a(a+l)/KaAp, and. a/KaAp) obtained from the correlation of I with C and LE given by Eqo (81), there is considerable discrepa:ncy between the calculated and. experimental composition. In Run 5, for e?:xample, some of the calculated point compositions were 200% less than the experimental values. This occurs due to the exponential nature of the model, ioe., its sernsitivity to relatively small errors in the predicted values of the mass transfer factors. The model does a reasonable job of prediceting

120 point compositions in view of the tremendous separations that are achieved.; the cyclohexane composition of the free liquid, was typically decreased, one to three orders of magnitude in'the enriching section. Both countercurrent and. cocurrent operation of the enriching section were investigated both experimentally and theoretically. Countercurrent operation is the conventional case in which reflux is provided to wash impurities from the adhering liquid. The calculated and. experimental results obtained for the cocurrent case indicate that the separation which is achieved can be explained by the dilution effect of melting the crystals in the melting section. Therefore it is apparent that-the.purification section does not contribute to the separation when the enriching section is operated. cocurrently. The experimental data demonstrate the capability of producing ultrapure benzene. The column crystallizer removed all of the impurities in Phillips pure grade benzene to a level comparable to cyclohexane. The separation that is achieved, is very sensitive to the enriching section product-crystal rate ratio, RE. There is no advantage, however, in operating a column with RE less than that value corresponding to YE = E (see Figure 28). The ultimate purity that can be achieved. is limited by impurities associated with the crystal phase. Calculations show that the separation is maximized when the feed position is such that there is a feed, match. In most cases with relative dilute feeds such as used. in this study the feed match will occur at a feed. position close to the freezing section. The capacity of the center-fed. column is limited by the maximum internal crystal rate that can be achieved. The column plugged and became inoperable

121 when the crystal rate was greater than 6.95 gm/min. The mathematical model breaks down when the plugging crystal rate is approached.

CHAPTER VIII RECOMMENDATIONS FOR FUTURE INVESTIGATION The results of this investigation as well as previous studies2'14 suggest several topics that may be profitable for future investigation. The experimental data of this and. Albertins' investigation indicate that the impurity associated, with the crystal phase can limit the separation obtained in a column crystallizer. While there is considerable evidence that the crystal phase composition is not affected by the washing that occurs in the purification section, experimental data do not exist that permit a positive identification of the mechanism by which the impurity becomes associated with the crystal phase. It is of interest to know whether the phenomena is caused by volumetric inclusion of impurity or by a slight solid. solubility in the ppm C6H12 range. One method of experimentally distinguishing between the two effects would be to determine the composition profile of two impurities (a second. impurity such as methylcyclopentane could. be added. to the feed.). C could then be calculated for each impurity from the composition profiles. Both impurities should be present in the feed. at the 30,000 ppm level to permit convenient analysis of the profile samples with a gas chromatograph. It has been shown that the impurity composition of the crystal phase, a, for cyclohexane is proportional to the cyclohexane composition of the stripping section product (see Eq. (73)). If the impurities in the crystals are due to volumetric inclusion then the proportionality constant in Eq. (73) should be the same for each impurityo If the proportionality constant for cyclohexane 122

123 is significantly larger than that for methylcyclopentane, the occurrence of solid solubility is likely, i.e., one would expect cyclohexane to have a higher solid, solubility than methylcyclopentane. Locating the freezing section at the top rather than at the bottom of the column should. have two desirable effects for systems where the specific gravity of the crystals exceeds that of the liquid (this is the case for cyclohexane-benzene). First, the crystal flux that can be achieved, is increased due to the effect of gravity, e.g., the Benzole Producers6 achieved higher fluxes for the C6H12-C6H6 system with the freezing section at the top of the column than were obtained in this investigation. Second, increasing the crystal flux also tends to minimize the effect of axial dispersion which opposes the separation. A limited experimental investigation utilizing a column with the freezing section at the top should be performed to determine whether the effects of the variables are the same as those demonstrated by the results of this study. The key to comparing the experimental data from each configuration is the assumption that the hydrodynamics of the crystalliquid movement are similar in both cases which must of course be determined experimentally. Before commercial scale column crystallizers could, be designed confidently, the effect of column size on the diffusional and mass transfer parameters (D, A, K, and a) must be determined. Also any volumetric inclusion that occurs is certainly a function of the configuration of the freezing section. These problems suggest a scale-up study.

124 It was shown in Chapter V thatit. is necessary to know the ratio of the adhering liquid. to crystal rate, a, to obtain a direct verification of the validity of the assumption that E(X) - 1 (see Eqs. (51) and. (53)) which would. directly prove that the transport equation approach applies. It was pointed. out also that a could. not be calculated. with any confidence from the correlation coefficients obtained. from the enriching section mass transfer factors. Therefore the only approach would. be to determine a experimentally. This is indeed. a difficult problem and. no approaches are obvious to the author. The mathematical model developed. for cocurrent operation of the enriching section included an assumed boundary condition, d.Y/dz = 0 at z = 4 which was based. on the concept that little separation occurs in the enriching section with cocurrent operation. The model predicts results that agree with experimental data. There is little incentive from a practical point of view to develop a more rigorous boundary condition because the enriching section would. seldom be operated. cocurrently. The question then is largely an academic one; can a rigorous boundary condition for the cocurrent case be obtained, from strictly diffusional considerations?

APPENDIX A METHODS OF ANALYSIS 1. DETERMINATION OF CYCLOHEXANE BENZENE COMPOSITIONS An F and M Research Gas Chromatograph, Model 5750, was used. to determine the cyclohexane-benzene compositions of the composition profile and terminal stream samples that were withdrawn from the column. The instrument was equipped, with a flame ionization detector. Benzene and. cyclohexane were separated with a column packed with a 10% solution of Carbowax 20M on a 40/45 mesh Chromosorb support phase. The column was constructed from 1/8 in. stainless steel tubing six feet in length. The carrier gas was Matheson prepurified nitrogen. Matheson dry air and. prepurified hydrogen were used. to support and. maintain the flame. The operating conditions for the chromatograph are presented. below: injection port temperature............................ 110~C column temperature,................................. 82~C detector temperature.................................. 220~C carrier gas rate (nitrogen)........................... 30 ml/min air rate...........................,......... 600 ml/min hydrogen rate................................ 40 ml/min The chromatograph heaters and. carrier gas were turned on at least three hours prior to the analysis. The flame was turned. on one hour in advance of the analysis. A Hamilton syringe, type 701, was used to introduce 0. 6 plml of liquid 125

126 sample into the injection port. The chromatogram was recorded with a Brown (Model 153X12-X-30) recorder which has a range of 0-2 millivolts and a response of one second. full scale. A typical benzene-cyclohexane chromatogram is shown in Figure 33. C6Hi2 C6H6 peak peak height height TIME — Figure 335. Typical cyclohexane-benzene chromatogram. The chromatograph was calibrated. using standard samples that were prepared by weighing and successive dilution. The response of the flame detector to cyclohexane and benzene is a function of the hydrogen, air, and carrier gas rates; the shape of the flame; and the injection port, column, and detector

127 temperatures. Consequently the response factor was calculated. from Eqo (86) with the peak height data from the chromatograms of the standard samples each time unknown samples were analyzed.. F _ (106 parts C6H6) (C6H12 peak height) (C6H12 attenuation) 86 (parts C6H12) (C6H6 peak height) (C6H6 attenuation) Table V gives the response factors calculated. from Eq. (86) for the standard. TABLE V RESPONSE OF THE FLAME DETECTOR TO BENZENE-CYCLOHEXANE MIXTURES Ratio of C6H12/C6H6, ppm Response Factor, F 162 1.97 1,459 1.94 6,997 2.02 30,900 o 96 55,858 2.00 samples. The fact that the response factors are constant + 35 illustrates that the response of the detector was linear. The reproducibility of the response factors indicates that the compositions of the unknown samples can be calculated from Eq. (86) within ~ 35% These results are comparable to those obtained, by Albertins for cyclohexane-benzene with the same chromatograph. The analytical method. for cyclohexane was confirmed. independently by Professor E. A. Boettner of the Public Health School of The University of Michigan by

128 both gas chromatographic and. mass spectrographic techniques. 2. ANALYSIS OF IMPURITIES IN PHILLIPS PURE GRADE BENZENE As mentioned in Chapter VI there are several impurities in Phillips pure grade benzene besides cyclohexane. An analysis of this material is given in Table I and. a chromatogram is shown inFigure 30. These impurities were identified. and, their compositions determined because the Phillips pure grade benzene was the starting material for preparing the feed. stocks used. in this investigation. Professor Boettner and his staff isolated most of the individual impurities with a gas chromatograph (Beckman GC-2A) equipped with a stream splitter upstream of the detector. The column was packed with Squalane on Chromosorb-P. Approximately 80% of each impurity exiting the column was diverted to a cold. trap. The impurities that were collected. in this manner were identified by comparing their mass spectra with the mass spectra of known compoundso An Associated. Electrical Industries, Ltd. (Type MS10) mass spectrometer was used.. Calibration standards were prepared. for the impurities that were identified and. the composition of the impurities in the Phillips pure grade benzene were d.etermined. with the same chromatograph that was used. to isolate the impurities. The results of this analysis are summarized in Table I of Chapter IV. The compositions of the impurities for the compounds that were not identified, were obtained from the peak area ratios.

APPENDIX B CALIBRATIONS Pertinent calibrations are summarized. in this section. The sample tap and thermocouple positions are also presented. Other column dimensions are given in Chapter IV. The feed pump described in Chapter IV was calibrated by determining the flow rate-stroke length curve. Figure 34 illustrates that the flow rate 0 Left Plunger. c - A Right Plunger E 4o' L2 t NeP. 5,- uj o I I 0 0.25 0.50 0.75 1.00 STROKE LENGTH INDICATED BY THE SCALE POSITION ON EACH PLUNGER, inches Figure 34. Calibration curve for the feed and bottoms pumps. stroke length response is linear. A scale which was machined on each plunger by the manufacturer was used. as an indication of stroke length. The zero 129

130 position on the scales did. not correspond. to a zero stroke length, consequently, Figure 34 does not have a zero intercept. This curve was used. to choose the stroke length for various flow rates, but the actual flow rates reported. in Appendix C were obtained, by collecting and. weighing products during the course of each experiment. The voltmeter used. to measure the power input to the internal melting section heater was calibrated. against a standard voltmeter (~ 0.1% accuracy) at the Electrical Measurements Laboratory of The University of Michigan. Table VI illustrates that the YEW voltmeter used. in this study is within ~ 0.3% of the standard voltmeter. TABLE VI VOLTMETER CALIBRATION YEW Voltmeter, volts Standard. Voltmeter, volts 10.0 10.00 20.0 20.04 30.0 o. 08 40. 40.08 5o.0 50.05 70. 69.99 The locations of the sample taps and thermocouples in the column are given in Tables VII and. VIII. The sample tap positions shown in Table VII are the

131 TABLE VII LOCATIONS OF THE SAMPLE TAPS IN THE PURIFICATION SECTION..Sample tap number Location in the purification section, Sample tap number. cm above the freezing section 1 47.5 2 42.0 5 36.o 4 29.75 5 23-75 6 17.75 7 11.5 8 4.0 TABLE VIII LOCATIONS OF THE THERMOCOUPLES IN THE COLUMN Location in the purification section, Thermocouple number cm above the freezing section 1 47.5 2 37.5 3 27.5 4 17.5 5 7.5 6 inside the freezing section 7 refrigerant in the jacket about the freezing section

132 values of the positions in the purification section that correspond, to the sample tap numbers given in Table IX of Appendix C. These sample tap and thermocouple positions are the same as those used by Albertinsl These measurements were checked at the beginning of this investigation.

APPENDIX C EXPERIMENTAL DATA AND CALCULATED PARAMETERS The experimental data obtained, in this investigation are summarized in Table IX. The steady state terminal stream and internal crystal mass flow rates, terminal stream compositions, and. free liquid. composition profile are presented, for each experimental run. The purification section temperature profile was not measured for each runr, but is shown for those runs where it was obtainedo The parameters that were calculated from the free liquid. composition profile data are given in Table X, The shape determining group for the enriching section profile, Yp, was chosen so the modified composition profile, in(Y-Yp) vs z would be linear. The impurity associated. with the crystal phase, c, was calculated from the experimental values of Yp and their defining relation (Eqo (72))e The shape determining group for the stripping section profile (Yp) is the value of the free liquid composition in the flat region of the profile (Yp was obtained. only for the runs where zF > 4.0 cm). The enriching section mass transfer factor, t E, is the negative reciprocal of the slope of the mod. ified enriching section composition profile. The procedures used to calculate Yp, E Yp and dE were described. in Chapter Vo 133

134 00 K0 0 0 0 o N < -t N K"\ CM 0 00 00000000 0 000 00 0000000 I ll H- - CC 0 — 0 O J O - n - H Od — t CM - C- CU CM CM CU O/ - C\ OH C ON r4 k \,0 \ 0 ~0\ O-4 t- 0 rA OJ 0 r-I 0 r0 i oSK N O O\ \lD o or\ Hr- 0 r- CM H-4 3 t r \ co.O 0 0 n O o0 _~ o ~ ~ o o oo-000 o o o o l l co CM CM o, O O O. O 0 _ CJ C C\. r-I r A 1 6i 0 t O Q1 CC) ooO O O O _:o. C? CU 1sk -O C -\ 0 C 0 0 i O O O O (V N — I 0 - Dn o 0, C —!' —.\9 C CV CM K- \ _ O Kd t,-A r- — I r-l 0M - HE a O j 0 o E U a K F H r c- o X o tIr <U Di0CO(I t- 4 \ \ \'-I C ILSC O Nt L(a H CU H't; E- W O r Ch Cu \-0 o 0\ \n co aC\ O\ nM~~C t - H HH H C 00 04 <n ~~cu M rl- Mol<o O O r UD l l C0 rl W\ Kj\ H n C M n > oO O H-^ O N cmoj ojooo H o - c 0\c \ no0 0 o - oJ\-,, \ _ IJ r 0 OJ CMI xD O0 C -0 ON=1\ CO\ OJ j~d~idoi 8 \\ O LiN \'<D Or-4r-I — 0 I Wo 0 r-I M. O\ I0 0O C- il 0C t^ CM n C c00 0o \o0 n O i In n - 0 CO- r-i O O — 0 0H 0 O r\ CO t- iH\ -1 — 0C - n H - oo r,\ rQ)cl (U~~~ P CO O a H 0 -r-0 k r0 - o o P 0 i O K M-, H- ~ H h Pr to, - o CCoHP~ffrta O ti 0)0 o200 0 %0 oc.). O H Ho k Tj'd B bIFP c.) ^^! biD 0 *r4El Ce1 C5j rCH0.P-I, a

135 CM 14,, I I I o I I I h- ",. C cu -O o t I I I o0 H - CU o -- n I H - 0 - - L'- rN \ r-H \ C r-1 CI Od 0 0 0 r-'l L" 1\ 0 0 0 0t LC\ H K>CO K\IINCMOO\ LCKt-0 Lf OJ-0CM0 0 C co ra la oj d ir*\ CMi>-o irzt>-oojo o o o d.., i.~ i.'.. H- CM C MOO 0 r-H M \ o o o 0 o C LN\ ir\n L i O\ Ln OJ (XI ( -I OJ l'I rC\ LN H H-I WL\ iL\ cO n- o\ crt 0 — co >- CM OCOO OCh O NOCXOO rH1 K\ 0 HH-lict-J-H\K\Hc00 I III II t- K0N\ ClC OJ C O ON O LJ 0N 1n CI CU C C0,1 CU C CO r- rN- r- 1 rlIn o o Ln — o- O O O Pn LO O O O i \r \o j Ld \D c O ~ O O rl O\ o- F Li ~ 1 rH CM CO HHr r-H l C \ n OcO I J Ln~ ~ ~ d ~~~ ~t" 0...- Od -\ 0 yO0- C -ctLCNOH)O CU O CM CU M K(N K\ cO Ct I I r - ) - b-'-d' d iO O0 0 - O O LC L\ LN LF -c \O CJ 0 oV - 4 L O HCM OOO ONct z \0C C CM0 LCLUL OC LA L 4 O / H O CM O CM K\ I N\\O\ \O ct tO C OCr VI a0 -c- -t 0 i O Oc H O O C Uc LL n LAC L L c O O~, -A rd- cO M C O — d! r -. - HOO JH HC CO CM -_J H. r4 4 L o 0oco o r \,,ooo O \0. O cO OC r 1 cO O O 0 \0 r CJ -O.- C \CO O n CO ON rH r,, CM \ rH 0 O LC\ 0 CM 00 O -4AoY-&4 0o00 00000000 0 0 0 0 0 0 0 0 0 0' o-~ cu cC Cu L co n C* c*c CD c Ct -I N. -tJ C N N N O C\O r'-I Lr CU ~ COJ C~C C'W O C' CX) 0 0) vo ) 0o 0 C E o 0) oo) *r H. H- rd 0 0 *H W6 W- 0 P r-p l *H 0) CHCZ CH C) 0 - I ~ O.,-I.r- I C-) -ri $:I - t c O 0H OH V *rl w r!0 I I I I CO -P o 0E O 0 QP a. PO C 0 pr 0) 0a P4 O*S 0 0 0 0 0 0O E4 t H -V E- CO

136 Notes for Table IX (1) The gap above the melting section was not completely flushed. for this run. The enriching section product composition was 282 ppm wt CsH12. (2) Run 4 is not shown. The purpose of this run was to check the overall balance. A description of this experiment appears in Chapter IV. (3) There were two Runs 5 (5A and. 5B). Run 5A is denoted as Run 5 throughout the dissertation. The Run 5B composition profile data are not shown because the septum in the No. 4 sample tap failed. while the profile was being sampled, i.e., the column contents drained from the column. (4) Cavities were observed in the freezing section. When the crystal rate was increased, above 6.95 gm/min the column became plugged and was inoperable. (5) Run 12 is not shown because the benzene on the tube side of the feed cooler was frozen solid. before the column reached steady state. (6) This total reflux run was performed, to obtain a value of E for a moderate value of the mother liquor composition in the freezing section. The value of e and the mother liquor composition are 10 and. 11,700 ppm wt C 6H12 respectively.

137 TABLE X PARAMETERS CALCULATED FROM THE COMPOSITION PROFILES Run EP' cm (1).... __ __ —-." —---..ppm wt C6H12 -------—. E cm (1) 1 40 40 (1) - 3.22 2 54 57 - 4.42 3 -1070 57 - 15.82 5 - 82 2 - 20.41 6 100 100 13,200 4.62 7 0 140 11.56 09 0.9 - 6.47 11 61 63 - 5.53 13 50 52 - 5.81 14 27 28 - 3.53 15 27 28 - 3.53 16 108 86 13,300 1.94 17 90 88 12,200 1.80 18 90 105 15,000 1.46 (1)The value of c for Run 1 was taken as the value of Yp because the enriching section composition profile became flat at 40 ppm wt C6H12, See note (1) of Table IX.

APPENDIX D COMPUTER PROGRAM FOR COLUMN CALCULATIONS A Fortran IV program was written to implement the iterative procedure for column calculations summarized in Chapter III, The computer symbols are defined in Table XI. The program listing is presented in Table XII, and typical computer output for one column calculation is shown in Table XIII. Two options are available with respect to data inputc Simplified, inputoutput areused; the namelists FIXED and VARY include all of the required input data (see statements 5 and 6 of the program listing). Statements 23 and 24 allow the predicted values of the mass transfer factors to be used in the column calculations, i, eo 9 they override the mass transfer factors that are specified as datao If it is desired to specify the mass transfer factors directly (for example, when experimental data are available) statements 23 and 24 must be deleted. Similarly if it is desired to specify the impurity composition of the crystal phase rather than calculating it, statements 30 and 38 must be deleted.

139 TABLE XI DEFINITIONS OF COMPUTER SYMBOLS Program Thesis Des Description Symbol Symbol Physical Parameters A -Yp defined by Eq. (7) B Yp defined by Eq. (18) C C crystal rate, gm/min F F feed. rate, gm/min HE *f enriching section mass transfer factor, cm E HS' stripping section mass transfer factor, cm L oC length of purification section, cm LE LE enriching section product rate, gm/min LS LS stripping section product rate, gm/min RUN run number X E composition of crystal phase, ppm wt C6H12 Y Y free liquid composition, ppm wt C6H12 YFEED YF feed. composition, ppm wt C6H12 YO YE enriching section product composition, ppm wt C6H12 YPHI Y. free liquid composition at the feed point, ppm wt C6Hi2 YS YS stripping section product composition, ppm wt C6H12 Z z position above freezing section, cm ZFEED ZF feed. position, cm

140 TABLE XI (Concluded) Program Prym~ograml ~Description Symbol Artifical Parameters Associated, with Numerical Calculation Al defined, by statement 21 A2 defined by statement 22 A3 defined, by statement 31 B1 defined, by statement 25 B2 defined. by statement 26 Cl defined, by statement 45 DERIV slope of YO vs YO response; it is used. to calculate incremented. value of Yn, defined by statement 63 EPS1 convergence criterion for YO I subscript associated. with position in stripping section, z(I) ITER counter for iterations ITMAX maximum number of iterations J subscript associated with position in enriching section, z(J) PHI subscript used to specify feed position STEP initial incrementation of YE TEST 1 defined by statement 36 TEST 2 defined by statement 44 YE initial assumption for YO YFEW free liquid composition at feed point calculated. from stripping section model YFOLD free liquid. composition at feed point calculated. from enriching section model

141 TABLE XII PROGRAM LISTING FORTRAN IV G COMP ILER PR.F ILE 0001 INTEGER PHI, RUN 0002 REAL LS,LE,L 0003 DIMEINS ON Z(3) Y(8) 0004 OATA Z /.4.,11.5,17.75,23.75,29.75,36.,42.,47.5 / OCC5 NAMELIST/FiX J/LyYE, EPS1, STEP, ITMAX')00065 NAMEL IST/VAqRY/RUN,PHI, YFEED,HEHSX,CF, LS C(C7 01 FORMAT(' ITM X ITERATIONS NJ) CCNVERGENCE ) i008 62 FORMAT(' CPRE- AING CONDITIONS') 0009 o3 FURMAT(' CC L UMN PARAMETERS AN) TERMINAL COMPOS I TIONS ) Oul) 64 F-ORIAI' COPO1SITION PROFILE Y(8)...Y(1) ) 0 11 NAMEL I ST/CUT A/C1, TEST1, TE ST2 DERI V YFEWYFOLD 0012 NAMELI ST/CUrT 3/RUN 00 13 NAME LI ST/CUTC/L ZFFEED, YFEEDC, FtLELS 0014 NAIMELI ST/CUTJO/HE, HS, X, YO YPHI, YS 0015 NAMELIS T/CUTE/Y 0 lb REA) (5,FIXEJ) 0017 i01 ITER=0 0018 REAL) (5,V ARY,END=998) 0019 ZFEED=Z( PI ) 0020 LE = F -LS C021 Al = C- LE 0022 42 = C + LS 0023 HE=(6.53E/( C-LE ) )+(.4102*C*C./(C — E) )-( 0.41 85*C*LE/(C-LF) ) 0024 HS=(6.533/(C+LS))+(0.4102*C*C/(C+LS))+(.4185*C*LS/(C+LS)) 0025 81 = (L- ZFEED)/HE U026 32 =ZFFEC/HS 0027 102 YO = YE + STEP +.0001 0028 ITER = ITER + 1 CC29 YS = (F*YFEED - LE*YE)/LS 0030 X =.J0142*YS 0031 A3= C*X 0032 A (LL'~Y E -A3)/A1 0033 = (LS"YS + A3)/A2 0034 YFOLC= (Yt+A )/EXP(-B1 ) -A 0035 Y.FE W=( YS- ) *EXP( (-2) +B 0036 TESTI = YFCLD -YFFW 0037 YS = (F*YFEED - t E*YO)/LS 0038 X =.J0142*YS 0039 A3= C*X 0040 A = (LE*YO -A3)/A1 0041. = (LS*YS + A3)/A2 00.42 YFOLD=(YC+A) /EXP(-B1)-A 0043 YFEW=(YS-E)*X_-XP(-B2) + 6 0044 TEST2 = YFOLD -YFEW 0045 C1 = TEST2/YFOLD 0046 IF (AB3S(Cl).LT. EPSI) GO TO 106 0047 IF ( ITER.LT.. ITMAX) GO TO 105 0048 WRITE (:6,61) 0049 YPFI = (YFOLD +YFEW)/2. 00.50 DO 1035 I = 1,PH.I 0051 103 Y( I)-=B+( YS-B) EXP(-Z(I )/HS) 0052 DU 104 J - 1,8 0053 104 Y(J) = -A+ (YPHI+A) *EXP(- Z ( J).-Z FEED))/HE ) 0054 WRITE(6,CUTA) 0055' WRIT(l,CLTB)

142 TABLE XII (Concluded)..s _.... _._____ iTE_. 62 )__-___ 0057 WRITE(6 CUTC) 0..0 5.8......WR I TE_.1 6 31'__._6..._6 _ __ __.. 0059 WR.ITE(6,OUTD) CC60___ WR I ITE( 6. 4) u061 WRITE(6,OLTE ) 0.. 062..__ _ GO. TO.1.1.........________ 0063 105 OERIV = (TEST2 -TEST1)/(YO -YE) 0064 YE =2 O_-TEST2/DERIV _ 0065 STEP =STEP/2. 0066 GO TO 102 0.67 106 YPhI = (YFOLD +YFEW)/2..0068 DO.107 I.= 1, PHI __.. 0069 107 Y( I);=B+( YS-B)*EXP(-Z( I /HS 0070 DO 108 J = I, _ _ __0071 108 Y(J)= -A+(YP I +A)*EXP(-( Z(J-ZFEED)/HE) 0072 WRITE(6,CUTa) __ C.073 WRITE {(6,62) 0074 WR I T E 6, CL. TC) _ _ _.______ 0075 WRITE(6,63) UO 76 WRITE( 6,CUTD).._ _____ _0077 WRITE(6, 64) 00 78 ___ _ __ WRITE ( 6, CUTE) 0079 GO TO 1O1 00'80 998 CONTINUE____ 0081 END

143 HZ N m if ~4 - LA * * 0 ui, a ~ OO o m a 0 -0 It C~ U. C. * r1 0 ) -' o C' o 0' 0 4 o 0 0 OI to.I'0 "4 * Z N * >"4 oJ Q 0 I> * 0 * ~J * IZ CMW- 0 I0' 41rCI - 0 CI I- Q CM 03 03 ^ t4

APPENDIX E TOTAL REFLUX DATA Some of Albertins' experimental and calculated data were included in the previous chapters of this thesis. These data are tabulated, here for the convenience of the reader. The details of Albertins' investigation are available in his thesis. All of the data reported below is for the benzene-cyclohexane system and spiral agitation conditions of 59 rpm, 290 osc/min, and. 1 mm amplitude. These conditions are the same as those used in the continuous flow study of this thesis. 1. IMPURITY ASSOCIATED WITH THE CRYSTAL PHASE Albertins determined. E from the total reflux composition profile data. The values of C were chosen such that the modified composition profiles for total reflux operation, ln(Y-Yp) vs z, would be linear. Yp is equal to c for total reflux operation. Table XIV illustrates that the pure end composition TABLE XIV ULTIMATE PURITY THAT CAN BE OBTAINED BY COLUMN CRYSTALLIZATION OF A 30,000 PPM CYCLOHEXANE-BENZENE MIXTURE WITH TOTAL REFLUX OPERATION Crystal Rate, gm/min Pure End Composition, ppm wt C6H12 1.99 98 2.65 101 3592 106 4.35 105 144

145 (equivalently E) is independent of crystal rate at large values of the crystal rate. A composition of 100 ppm C6H12 corresponds to the ultimate purity that can be achieved by total reflux column crystallization of a 30,000 ppm C6H12 charge. The charge composition was reported as the nominal value (+5s). Consequently these total reflux data were obtained, for a charge composition that is comparable to the feed composition of 28,000 ppm for Run 2 of this study. 2. TOTAL REFLUX MASS TRANSFER FACTOR, *0 Albertins calculated the total reflux mass transfer factors from his modified. composition profile data. These values are tabulated in Table XV. They were used. in Chapter V to obtain the'K vs C correlation (Eq. (77)). TABLE XV TOTAL REFLUX MASS TRANSFER FACTORS Crystal Rate, gm/min.,t cm 0 75 10.00 0.79 9.28 0.90 8.65 1.02 7.71 1.20 6.88 1.95 5 00 2.54 5-12

APPENDIX F CALCULATION OF THE CHARACTERISTIC ROOTS OF EQUATION (13) The values of the characteristic roots rl and r2 of Eq. (13) which correspond. to the minimum ratio of r2/rl were used in Chapter III to show that the term C2 er2 in the expression for the free liquid composition profile (Eq. (12)) could. be neglected. relative to C1 e. The case corresponding to the minimum value of r2/rl was used. because it is the most conservative, r2z r1z i.e., the contribution of C2 e is maximized relative to C1 e. This occurs when Q2/Q2 is a maximum with respect to crystal rate and. for total reflux operation, RE = 0. For total reflux the relation for (Q2/Q)m (Eq. 25)) becomes: /2) - 1 (Q2/Q )max 4(a+l) (87) The value of Q1 which corresponds to (Q2/Q)max is given by Eq. (88). (Q1 )in = 2 D aAp (a+1)/2 (88) This expression can be simplified, further by introducing the correlation constants b, and. b2 obtained. from the total reflux mass transfer factor data. 1/2 2l-1)2 (Bl)min i 2 [ < (89) The characteristic roots for these values of Q1 and Q2/Q2 become: 146

147 2 Kl)m[- +(1 4 (Q2/;Q)max) rj (i / "Lm a I max)j (90) rl 2 max r2 = (Qm -1-(1-4(Q2/Q~)max) (91) The values of bl and. b2 are 6.862 gm-cm/min and 0.9096 cm-min/gm, respectively (see Table IV). The value of a was assumed. to be 0.2 for these calculations. The values of (Qm) mn and (Q2/Q) ma can be calculated from m-i n / max Eqs. (87) and. (89). (Q1)min = 0961 cm= (Q2/Q) max 0o8335 dimensionless The roots r2 and. r1 are now calculated from Eqs. (90) and (91): 1r Oo 2084 cm2 r = 0.676 cm

BIBLIOGRAPHY 1. Albertins, R., Ph.D. Dissertation, The University of Michigan, 1967. 2. Albertins, R., and J. E. Powers, accepted for publication in A.I.Ch.E.J. 3. Albertins, R., Sinclair Research Co., Harvey, Illinois, Personal'Communication, 1968. 4. Albertins, R., W. C. Gates, and J. E. Powers, in Fractional Solidification Vol. I (M. Zief and W. R. Wilcox, eds.) Marcel Dekker, Inc., New York (1967) pp. 343-367. 5. Anikin, A. G., Dokl. Akad. Nauk SSSR, 151 (5), 1139 (1963). 6. Arnold, P. M., U. S. Patent 2,540,977 (1951). 7. Breiter, J., Ph.D. Dissertation, Ruprecht-Karl-Universitat, Heidelberg, Germany, 1967. 8. Cohen, K. J., Chem. Phys., 8, 588 (1940). 9. Danyi, M. D., C. M. 690 Report, The University of Michigan, 1968. 10. Danyi, M. D., J. D. Henry, and J. E. Powers, in Fractional Solidification Voi. II (M. Zief, ed.) Marcel Dekker, Inc., New York (to be published in 1969). 11. Findlay, R. A., U. S. Patent 2,683, 178 (1954). 12. Furry, W. H., R. C. Jones, and L. Onsager, Phys. Rev., 55, 1083 (1939). 13. Gates, W. C., Ph.D. Dissertation, The University of Michigan, 1967. 14. Gates, W. C., and J. E. Powers, presented at the Symposium on Crystallization from the Melt, Preprint 37F, Second Joint A.I.Ch.E.-I.I.Q.P.R. Meeting, Tampa, Florida, 1968. 15. Gates, W. C., Texaco, Inc., Beacon, New York, Personal Communication, 1968. 16. Girling, G. W., and A. D. McPhee, Benzole Producers Ltd., Research Report 66-4, Watford, Herts, Britain, 1966. 17. Girling, G. W., A. D. McPhee, and M. H. Radley, Benzole Producers Ltd., Research Report 67-3, Watford, Herts, Britain, 1967. 148

149 BIBLIOGRAPHY (Concluded) 18. Hinton, J., Price List 37, James Hinton Co., Valpariso, Florida (1967). 19. McKay, D. L., U. S. Patent 2,823,242 (1958). 20. McKay, D. L., C. H. Dale, and. D. C. Tabler, presented at 59th National Meeting of the A.I.Ch.E., Preprint 8E, Columbus, Ohio (1966). 21. McKay, D. L., and H. W. Goard, CEP, 61 (11), 94 (1965). 22. McKay, D. L., G. H. Dale, and J. A. Weedman, IEC, 52 (3), 197 (1960). 23. Moulton, R. W., and. H. M. Hendrickson, Office of Saline Water, R and D Progress Report No. 10, U. S. Department of Interior (1956) p. 114. 24. Newton Chambers Ltd., Sheffield, Britain, Chem. Eng., 75 (16), 64 (1968). 25. Palermo, J. A., IEC, 58 (11), 67 (1966). 26. Player, M. R., Submitted to IEC, Manuscript No. 8-180 (1968). 27. Powers, J. E., in Symposium Uber Zonenschmelzen und Kolonnenkristallisiern (H. Schildkhecht, ed.) Kernforschungszentrum, Karlshrue, 57 (1963). 28. Schildknecht, H., Anal. Chem., 181, 254 (1961). 29. Schildknecht, H., and K. Mass, Die Warme, 69 (4), 121 (1963). 30. Sherwood, T. K., and P.L.T. Brian, Office of Saline Water, R and D Progress Report No. 96, U. S. Department of Interior (1964) pp. 7-16. 31. Speciality Design Co., Box 276, Ann Arbor, Michigan. 32. Thomas, R. W., U. S. Patent 2,854,494 (1958). 33. Timmermans, J., Physico-Chemical Constants of Binary Systems in Concentrated Solutions Vol. I, Interscience Publishers, Inc., New York (1959) p. 107. 34. Weedman, J. A., U. S. Patent 2,747,001 (1956). 355 Yagi, S., H. Inove, and H. Sakamoto, Kagaku Kogaku, 27 (6), 415 (1963).

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