ABSTRACT SOLUTE DISPERSION AND ADSORPTION IN LIQUID-SOLID CHROMATOGRAPHIC COLUMNS by Yale S. Finkle This research project was a continuation of previous work which had the overall objective of developing a reli- able scale-up procedure for liquid—solid chromatographic columns. The purpose of this study was to evaluate and analyze values for equilibrium constants and mass transfer coefficients at various flow rates of a solute passing through a bed packed with an adsorbing material. It was assumed that the axial dispersed, plug flow model, with ad- sorption occurring, described the unsteady state chroma- tography process. The pulse injection and response technique was used to calculate equilibrium constants and mass transfer coeffici- ents. The axial dispersion coefficients were estimated from data of previous research in this area. Actual calculations were made from analyses of solute concentration versus time curves at two positions in the bed which was packed with irregularly shaped particles of a synthetic molecular sieve. A dilute aqueous solution of sodium chloride was used as the solute so that caufintrations could be measured by elec- trolytic conductance. The results of the work indicated that an equilibrium condition existed between the solute in the fluid phase and Yale S. Finkle the solute on the packing surface. It was also found that the controlling factor in the adsorption process was mass transfer through the liquid-film resistance. SOLUTE DISPERSION AND ADSORPTION IN LIQUID-SOLID CHROMATOGRAPHIC COLUMNS BY Yale S. Finkle A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Chemical Engineering 1968 G qmm L~£j-6¥ ACKNOWLEDGMENTS The author gratefully acknowledges the Upjohn Company for financial support of this work. Sincere appreciation is also extended to Dr. Martin C. Hawley for his guidance through the entire course of this project. ii TABLE OF ACKNOWLEDGMENTS . . . LIST OF TABLES . . . . . LIST OF FIGURES . . . . . INTRODUCTION . . . . . . PREVIOUS WORK . . . . . THEORY . . . . . . . . . Model of Dispersion Experimental Method APPARATUS AND PROCEDURE . The Flow System . Conductivity Cells Tracer Injection System Tracer Solution . . Packing Material . Measuring and Recording Liquid Level Control Determination of Void Fraction Packing Procedure . End Effects . . . . Run Procedure . . . Analysis of Concentration-Time Distributions CONTENTS Apparatus iii Page ii vi 10 14 14 16 16 18 18 18 21 23 27 28 30 31 TABLE OF CONTENTS (Cont.) RESULTS AND DISCUSSION . . . . . . . . . . . . Calculation Calculation Calculation Calculation Correlation of Void Fraction . . . . . . of Dispersion Coefficients . of Equilibrium Constants . . of Mass Transfer Coefficients of Mass Transfer Data . . . . Discussion of Mass Transfer Data . . . . Discussion of Errors in EXperimental Pro- cedure and Data Analysis . . . . . . CONCLUSIONS . . RECOMMENDATIONS FOR FUTURE WORK . . . . . . . . APPENDIX A . . . APPENDIX B . . NOMENCLATURE .. . BIBLIOGRAPHY iv Page 34 34 34 39 44 46 49 55 58 59 6O 65 67 69 Table II. III. IV. V. VI. VII. VIII. LIST OF TABLES Void fraction data (Runs 3—14) . Void fraction data (Runs 15-38) Data for runs 3-14 (6 - 0.4470) Data for runs 15-38 (e = 0.4454) Data from this work used for mass correlation . . . . . Data of Al-Khudayri . . . Data of Resnick and White Data of Hurt . . . . . transfer Page 35 36 40 41 48 51 52 54 LIST OF FIGURES Figure Page 1. Diagram of adsorbing bed . . . . . . . . . . . 6 2. Incremental length of bed . . . . . . . . . . 7 3. The arrangement of A104 and Si04 tetrahedra which yield open cavities in some zeolites . 11 4. Tetrahedral arrangement of truncated octa- hedra in zeolite type X . . . . . . . . . . 13 5. Model of the structure of zeolite type X based on packed oxygen atoms . . . . . . . . . . . 13 6. Schematic diagram of flow system . . . . . . . 15 7 Conductivity cell . . . . . . . . . . . . . . 17 8. Specific conductance of sodium chloride at 25°C 19 9 . Schematic of electrical circuit for conductivity measurements 0 O O O O I O O O O O O O O O O 20 10. Schematic of rectifying amplifying circuit . . 22 11. Diagram of fritted glass joint . . . . . . . . 26 12. Diagram of method employed for packing main section of column . . . . . . . . . . . . . . 29 13. Typical concentration—time curves for cells 1 and 2 . . . . . . . . . . . . . . . . 32 14. Hawley's and Gentile's data correlated by a plot of 4 MU/Dv gs. D/DV . . . . . . . . . . 38 15. Equilibrium constants at various flow rates . 43 16. Mass transfer coefficients at various flow rates 45 '17. Correlated mass transfer data . . . . . . . . 47 vi INTRODUCTION Liquid-solid chromatography has long been used as an analytical tool in the laboratory, and it is this use that we naturally associate with it. However, there has been an ever increasing use of liquid-solid chromatography as a separational technique and this has presented the problem of scaling—up an optimized laboratory column for industrial purposes. At present, the general scale-up procedure for chroma- tographic columns is to first optimize a small laboratory column with respect to the pressure drop and time required to effect the separation and then to increase the cross sectional area of the column in proportion to the amount of material to be separated. This method of scale-up is not always precise and it would be highly desirable to determine exactly what factors in the chromatographic process actu— ally influence the scale-up procedure. In an effort to reach this goal, a detailed study of the liquid—solid chromatography process has been undertaken. PREVIOUS WORK The liquid—solid chromatography process can be visual- ized in the following manner. Consider a packed bed with a solvent running continuously through it. At some initial time zero a "pulse" containing the two components to be separated is injected uniformly into the bed. As the sol— vent carries the pulse through the bed, the components will separate from each other due to the difference in adsorp- tivities of the components upon the packing material. The length of the packed column needed to produce a particular separation depends upon the amount and relative difference in the adsorptivities of the components involved. The chromatography process can be considered as a fluid flow process superimposed upon an adsorption—desorption process. Hawley1 began the study of chromatographic separations by theoretically showing how the fluid flow and adsorption processes could be separated. Once this was accomplished, the fluid flow process wassmudied separately by employing inert, spherical, glass beads as the column padking. For this study the axial, dispersed, plug flow model was used to describe flow through the column packed with beads of uni— form size.1 Since the scale-up procedure of taking the optimized laboratory column for a particular separation and increasing 3 its diameter in prOportion to the amount of material to be passed through the column was frequently unsuccessful, it was decided1 to study the fluid flow process by determining which variables could cause the axial diffusivity to be a function of column diameter. The pulse injection technique for determining the axial dispersion coefficients was used since it is the same in- jection technique used in liquid-solid chromatography. Aris2 has shown that when the aforementioned technique is employed, the axial dispersion coefficient can be determined from the following equation. 2 1 2” - 02 '0‘ (1) Ul' LJ~2 ‘ H1 , where on2 = variance of concentration-time distribution at measuring point n(n = 1 or 2). ”n : mean time of concentration—time distribution at measuring point n(n = 1 or 2). D = dispersion coefficient U = interstitial velocity L = length of column between measuring points. The results of Hawley's study showed that in the absence of adsorption, the axial dispersion coefficient is independ- ent of the column diameter and length, that viscous finger- ing1 is not an important consideration in chromatographic columns up to six inches in diameter even when the mobility ratio is as high as 100, and that the axial dispersion coef- ficient is proportional to particle diameter. 4 Since the shape of the packing material is very ir- regular in chromatography, it was of interest to determine the effect of packing irregularity upon the dispersion co- efficient. Gentile4 studied the fluid flow process in the same manner as Hawley. However, where as Hawley used uni- form, spherical, glass beads as packing, Gentile used ir- regular glass particles obtained from crushing glass raschig rings. Gentile's results4 showed that for flow between one and one-hundred feet per hour and particle diameters of order of magnitude of 10'-3 inches, the diffusivity increases as the shape of packing material becomes more random. Up until Hawley began his study of dispersion in liquid- solid chromatographic columns, little effort had been fun- neled toward producing a suitable method for scaling-up chromatographic columns for industrial purposes. However, there was an extensive study, by many people, of axial dis- persion of fluids flowing through porous media. Many theor- etical models1 were developed to describe flow of fluids through packed beds. Correlations dealing with the promin- ent variables have been developed and are useful in the scale-up of chromatographic separations. The purpose of this research project is to study the entire chromatography process. That is, the fluid flow process occurring simultaneously with the adsorption pro- cess. Specificly, it is hoped that measurement and analyses of an equilibrium constant (if one exists for the system considered) and mass transfer coefficients obtained at 5 various flow rates will enable the determination of the best conditions under which the column should be operated. Ulti- mately, it is hOped that a scaled—up separation can be pre— dicted by simply knowing the mass transfer chracteristics and values of the equilibrium constants associated with the components to be separated and the packing employed for the separation. THEORY Basically, this research is simply a continuation of the work of Hawley and Gentile. The major difference being that the adsorption process was introduced into the experi— mental system by use of a packing which would hopefully simulate the adsorption-desorption phenomena. The first part of this section will deal with the mathe- matical model of the chromatography process. The theory and reasoning behind the experimental method will also be examined. Model of Dispersion in an Adsorbing Bed Consider a bed packed with an adsorptive material and having two concentration measuring devices located at X1 and X2 (Figure 1). Flow Figure 1. Diagram of adsorbing bed. Solvent is continually flowing through the bed with a volumetric flow rate W. A pulse of tracer is injected into the bed at some point prior to X1 and is allowed to flow through the bed past X2. Unsteady state adsorption is occurring in the bed along with solute dispersion. 7 The following assumptions are necessary: 1. The tracer is injected uniformaly across the bed. 2. The flow is uniform over the cross section of the bed. 3. The adsorption isotherm is linear. Let CA be the average concentration of component A of the tracer across a section of the column. Assume that the mass transfer by diSpersion is proportional to the axial concentration gradient 5;§.. The proportionality constant is termed the axial dispersion coefficient D, and is the sum of the molecular diffusivity and the eddy diffusivity. The equations describing the dispersion and adsorption in the packed bed are obtained by making a material balance on an incremental length of the packed bed as shown in Figure 2. X X + AX I I : Liquid : input >= lKXaAAX(CA - CAi)1i output OCA : j' OCA “DA Bi" >: solid : ”DA 3') I L Figure 2. Incremental length of bed. There are terms similar to the above which describe the input and output for components of the tracer other than A. A major assumption at this point, is that there are no inter- actions between the components of the tracer. For a two 8 component tracer, this would mean that component B would not effect the isotherm of A or vice versa. The equations resulting from the material balance on component A over the incremental length of the bed are as follows. Liquid Phase 5sz - 9255: ' D: (CA-CAi) = T15 5751: (2) Solid Phase a $57? (CA ' CA1) = 8:? (3) cAS = mcA1 (4) where: X = axial distance t = time W = volumetric flow rate D = axial diSpersion coefficient e = void fraction of bed A = cross sectional area of column KX = mass transfer coefficient a = solids transfer area per volume CA = concentration of component A in the tracer CAi = concentration of component A at the solid- liquid interface C = concentration of component A on the solid m = equilibrium constant defined by Equation (4). 9 Equation (4) represents assumption (3) on page 7. The boundary conditions for the above problem are: CA = 0 when t = 0 for x > X1 (5) at x = x1 CA = CAO(t) for t > 0 (6) at x = 00 C(t) = finite for t > 0. (7) A restriction on CAO(t) is that it must be a "hump" func- tion of time to represent a pulse input.1 The complete solution of Equations (2) through (7) for CA' CAS’ and CAi is not obtainable in closed form. However, Hawley1 has shown, by employing some formal mathematical properties of the LaPlace Transform, that the complete solu- tion is not necessary. Essentially, what happens is that the parameters of interest, Kx’ m, and D, are related to the differences in variances and mean times of concentration- time distributions at two positions in the bed. Hawley's results1 yield the following equations for an infinitely long bed in which both axial dispersion and adsorption are occurring. _ =E-A—I'J-+-1'—;€—AL (8) ”2 ”1 W mW _ _ 2 022 — 012 = EAL (1 W 6) -+ 2E-(DeA)3 X m a 3 18‘ W (9) [Lie—3.1.9.1.] emD D where: L = distance between measuring points H1 = mean time of concentration-time distribution at measuring point 1 10 u2 = mean time of concentration—time distribution at measuring point 2 01 - variance of concentration-time distribution at measuring point 1 2 . . . . . . 02 = variance of concentration-time distribution at measuring point 2. Experimental Method Since this project was a continuation of work started at Michigan State University, it was decided that the most efficient method of attacking the problem would be to employ the same general experimental apparatus and procedure as was used by Hawley1 and Gentile‘. Thus the pulse tracer input method utilizing two measuring points in the column was employed. As was done previously, a dilute solution of sodium chloride was used as the tracer along with distilled water as the solvent. It was desirable to find a type of packing which would introduce or simulate the adsorption phenomena in the experi- mental system. A synthetic zeolite (type "132X") made by Linde Division of Union Carbide appeared to fit the neces- sary requirements. Type "13-X" is a member of a group of zeolites which are complex alumino-silicate compounds hav- ing the important characteristic of Openness of the [(Al, Si)02]n framework5 (Figure 3). This is the charac- teristic which makes possible their use as ion exchangers and selective adsorbants or "molecular sieves". ll Figure 3. The arrangement of A10 and 8104 tetrahedra which yield 0pm cam“; on in some zeolites 12 The framework of the X type zeolite consists of octahedra joined at the octahedral faces by hexagonal prisms (Figure 4). The corresponding structure of oxygen atoms is shown in Figure 5. The cations in type X zeolite can occupy three types of positions.6 Type 1. in the center of the hexagonal prism, 16 sites per unit cell Type 2. on the six membered rings, the unjoined hex- agonal faces, 32 sites per unit cell Type 3. on the walls of the channels, 48 sites per unit cell. Type “13-X" is the sodium form of type X zeolite and con- tains 86 cations per unit cell distributed in the three different sites. The void spaces in the zeolite structure consist of elliptical cavities 13 R in length, entered by apertures of distorted, chair-shaped, 12-membered rings which have a free diameter of 8 £6. The overall structure, as shown in Figure 5, is that of a densely packed structure of oxygen atoms which surrounds relatively large interstitial voids. Zeolite type "13-X" was chosen for use in this research project in hopes that its structure and properties would simulate an adsorption process. Due to the relatively large cavities along with the ion exchange property of the zeolite, it was thought that the soidum ions would diffuse on and into the packing particles and exchange with the zeo- lite cations. This process would simulate the adsorption- desorption phenomena by slowing the flow of sodium ions through the column. 13 Figure %. Tetrahedral arrangement of truncated octahedra in zeolite type X. Figure 5 Model of the structure of zeolite type X.based on PaCked oxygen atoms. The three types of cation sites are shown. APPARATUS AND PROCEDURE The principle equipment required for this experimenta- tion consisted of one-half inch diameter glass pipe for the column, conductivity cells and automatic recorder for measuring tracer concentration-time curves at two points in the column, a manometer for measuring pressure drops through the packed bed, and a photoelectric amplifier system for maintaining a constant liquid level above the packing. The Flow System (Figure 6) The column was composed of various lengths of glass, pyrex pipe with flanged ends. In all cases, the inside diameter of the pipe was one-half inch. The main section of the column, which was placed between the two conductiv- ity cells, was 18 inches long and had two extending side arms located three inches from each end. The side arms were 8 mm. in diameter and two inches long. A three—inch length of pipe was placed below the bottom conductivity cell and a 12—inch length of pipe was located above the first cell. The tracer injection mechanism (see below) was located above the 12-inch length and below the six- inch uppermost section of the column. The solvent feed line and the outlet line were made of 1/4-inch diameter copper tubing. The outlet line began at the bottom of the column and was extended upward so that 14 To amplifier 15 Nitrogen pressure Brass tOp section Syringe (i r—I '1_J Pressure gauge Six-inch glass section 4—inch brass section Solenoid valve Solvent feed To drain ‘_— Microm- eter i valve Globe valve x Figure 6. ‘__u__ 12-inch .tracer lass To amplifier LnjeCtlo+ gection tube \\ LIN w) Photo- . ‘ cell i/jj iTo recorder Cell 1! - ' K/jj; ,,Water ‘x/ . /)—m:; (h 18-inch P////’ Fritte glass glass ,//// joint section ::::: % 1/4 H ////’ Tygon .//;7 ///// tubing Manom- ///// ‘ eter ::::: Side arm gim— ConductivT '::;E; liTo recorder it cell 2 ‘ r y §;//V 3-inch glass ngZ section \ ' Brass bottom Mercury section Schematic diagram of flow system. 16 its end was near the level of the packing. Both a globe valve and a micrometer valve were located in the outlet line. The globe valve served to facilitate rapid on—off control of flow, while the micrometer valve was used to help set a desired flow rate. The solvent (water) feed line was connected directly into the tracer injection mount- ing. The distilled water was stored in a 12 gallon, resin- coated, steel tank. It was fed to the column by subject- ing the storage tank to nitrogen pressure. Nitrogen was also used to pressurize the column when fast flow rates were desired. Conductivity Cells (Figure 7) The two conductivity cells were identical to those designed and used by Hawleyl. The cells were machined from plexiglass to specifications indicated in Figure 7. The wire was No. 25 platinum wire. Tracer Injection System (Figure 6) The tracer was injected into the column yig_a 10 m1. Luer-Lok Syringe. The syringe receptacle extended from a four-inch long brass fitting located between the 18—inch and 12-inch long glass sections. The mounting which received the syringe was stainless steel and extended two inches outward from the column. A small (between two and five mm. in diameter) stainless steel 17 Plexiglass ———————————— Wire 'f 1" ., l Wire ——| —————— ll— 1:— _ __ __ _ - 1 165/8" P—l/M—‘I 1 1‘ Figure 7. Conductivity cell 18 tube joined the syringe mounting (Figure 6) from the inside of the brass section and extended approximately eight inches down the center of the 12-inch glass pipe section. Thus, the tracer could be introduced into the column four inches above the first conductivity cell. Tracer Solution The tracer was a 2 gram/liter aqueous solution of sodium chloride. Sodium chloride was used because its con- centrations can be readily determined by electrolytic con- ductance. However, it must be remembered that a dilute solution of sodium chloride is necessary to insure that conductance is proportional to the concentration. Figure 8 shows that the specific conductance of sodium chloride is proportional to its concentration over the range 0 to 2,000 parts per million (29/1). The value of the molecular diffusivity Dv for a 0.5 molar solution of sodium chloride at 30°C is 1.84 x 10-5 cmz/sec.7. Packing Material As mentioned previously, zeolite type "13eX" was used as packing. The zeolite was crushed in a mortar and pestle and screened to obtain the particles between 60 and 80 mesh. Measuring and Recording Appartus Figure 9 shows a diagram of the circuit designed by Hawley1 to measure and record tracer concentrations as a function of time at the two conductivity cells. Actually the circuit is measuring conductance, but as shown in 19 .0mm um mUHHoHno Edwoom mo mocmuosocoo UHMHommm .w musmflm 4‘ . _ _ L _ . coma OONH oow oov COAHHHE Hem munmm Q ‘\ 0 .UCH mucmESHDmcH HMHHumDUCH wn ponmmwum muma * _ soqmoxorm go spuesnoqq u: eoueionpuoo orgroads H AAJ N L m A v 44 20 Hmvuoumm L. _ HmHMHuomm paw HmHMHHmE¢ A\I//I\y Houmaaflomo oaosm .mucoEmHSmmmE mufl>flu05Usoo How “HDUHHU HMUHHuome mo oaymfimnom .m musmflm my, / / / auoaam 21 Figure 8 for the tracer involved, the concentration is pro- portional to the conductivity. The circuit was designed so that the voltage across resistor R would be proportional to the reciprocal of the cell resistance Rc’ and is given by E = IR (10) where I = v/(RC + R) (11) If Rc is much larger than R, then E = VR/RC (12) However, since both V and R are constant, E is pro- portional to l/RC. The voltage source was a variable frequency audio oscil- lator. The A.C. voltage across R was amplified, recti— fied, and measured with a Sargent Multi-Range Recorder. A diagram of the rectifying-amplifying circuit is shown in Figure 10. Liquid Level Control To make the operation of the experimental system as automatic as possible, a liquid level control device was desirable. In previous work114, the liquid level above the packing was controlled by the manual manipulation of valves. A photoelectric—amplifier system connected to a solenoid valve located in the solvent feed line was used as the liquid level control. The system was purchased from Worner Elec— tronic Devices Inc. and consisted of a Model 66-T Amplifier, 22 umummg s xqmfl o > m.o .uflsouflo msH>MHHmEm msflmmfluomu mo UHumesom .OH musmflm I Hmouoomu @— Ma + Hmouoowfi. N _ _ .3... _ >oom+ _ FIIIIIIII _ 23 a Model 36 Exciter Lamp, and a Model 26 Photocell. The solenoid was a Hoke two way normally closed valve. This solenoid valve permitted flow only when energized. The control system functioned in the following manner. The photoelectric cell (see Figure 6) was activated by the falling meniscus of the water (i.e. it interrupted the light beam through the column) and in turn opened the solenoid valve allowing solvent to enter the column and raise the level of the meniscus only slightly to above the photo- electric cell. Once the level of the meniscus passed above the photo cell, the light from the exciter lamp was trans- mitted through the water and activated the photo cell which closed the solenoid valve. This process was constantly re- peated and thus kept the liquid level at the photo cell position. Determination of Void Fraction The void fraction of the packed bed was calculated using the Blake-Kosney relationships: 150V0LH 3 .__E————— : (13) e 2 2 (1 E) Ach d(eff) where d = effective diameter of packing particles, (eff) feet V0 = superficial velocity of liquid through bed, ft/hr u = viscosity of flowing liquid, lb/ft-hr 24 AP = pressure drop across packed bed, lb/ft2 L = length of packed bed across which AP is measured, feet 6 = void fraction of bed 9C = gravitational constant, (lb mass sec2)/ (lb force ft). To determine the void fraction using Equation 13 it was necessary to measure the pressure drop through the bed and its correSponding superficial velocity. Once this was known, 6 could be found by trial and error. Since the packing was composed of irregular particles, it was necessary to define an effective particle diameter as the diameter a sphere would need to possess the same sur- face area as the irregular particle.4 Therefore, a bed of Spheres having diameters equal to the effective diameter would have the same total surface area as the bed of ir- regular particles. The value for the effective diameter used in this work was the same value that Gentile used.4 This value was 0.00497 inch. Although Gentile used a dif- ferent packing material, the effective diameters of the two packings were assumed to be nearly equal since both materials had been screened into the same size range (60-80 mesh). The pressure drOp versus flow rate measurements had to be made in the same bed as the experimental runs since the void fraction of the bed depended upon the manner in which the irregular particles arranged themselves. Each time the column was packed, it would possess a different void fraction because the particles would pack differently. 25 In order to accomplish the above, two side arms (see Figure 6) were extended from the column section between the two conductivity cells. A fritted glass joint was attached to each extended arm and then the glass joints were con- nected to a manometer using 1/4-inch Tygon tubing. -Mercury was the measuring fluid used in the manometer. The rest of the pressure measuring system (Tygon tubing and manometer) contained water only. The fritted glass joints (see Figure 11) enabled the extended arms and one chamber of the glass joints to be filled with packing. The fritted glass per- mitted flow of liquid through the pressure measuring system, while preventing any movement of the packing material. Before any pressure drOp measurements were taken, water was allowed to flow through the column for several hours. It was hOped that this would completely set the particles in the bed so that there would be no further rearrangement. Measurements were made by simply setting a certain flow rate, waiting for the manometer to come to equilibrium and then reading the corresponding pressure drop. Runs were made on two separate days to insure the void fraction re- mained constant. Once the pressure drop studies were com- pleted, the manometer was taken out of the system by clamp- ing the Tygon tubing leads. Experimental adsorption runs could now be made. 26 Fritted glass Right chamber Left ch mber <——————— —-——————D To Extendea To Tygon arm tubing h——~1" 1F 2"————III—1" —» Figure 11. (Diagram of fritted glass joint. 27 Packing Procedure It was extremely important for the correct operation of the experimental system, that there was absolutely no air entrapped in the packed column. Therefore, much care was taken in packing the column. The best general approach to the packing problem was to start with the bottom brass section (see Figure 6) by filling it with water and then to add the packing and let it settle. Before the packing was introduced into the column, it was slurried with water to remove air from the surface of the particles. A small piece of cotton cloth was placed 'in the bottom of the brass section to restrict the peeking while allowing the flow of solvent. The three inch sec- tion was now added and packed in the same manner. A con- ductivity cell was then placed on top of the three inch section and the main (18-inch) section was fastened into place. A small amount of water was added to the main sec- tion and a packing support was allowed to settle into place on top of the conductivity cell. The packing supports were pieces of cotton cloth glued to a stainless steel rim which was just under 1/2 inch in diameter and one—sixteenth of an inch thick. The conductivity cells should contain only water. Care must be taken to keep the cells free of air bubbles and packing particles. In order to obtain a uniformly packed bed in the main section of the column, the packing was dropped down the 28 column while water was slowly flowing upward. This method enabled the small, light particles to be carried out of the column with the rising water. A diagram of the set-up used for the above procedure is shown in Figure 12. To fill the extended arm and glass joint with packing, the end of the glass joint was disconnected from the tubing leads to the manometer. Packing was then carried into the arm and left chamber of the joint by the flowing water. After the main section was packed, the column was con- tinually tapped in an effort to settle the packing in a permanent arrangement. If this was not done now, the packing would settle once the column was in operation and would leave a space under the top conductivity cell. Once the tapping was completed, the top cell was added and the 12-inch section was fastened into place. 'Another packing support was allowed to settle in place and enough padking was added to bring the top of the bed three inches above the first cell. The remaining sections of the column were added and the photo cell and light source were clamped into place about one inch above the top of the packed bed. End Effects End effects is a term used to denote the results of conditions at the end of column which tend to disrupt the flow pattern. Obviously, it is desirable to minimize end effects whenever possible. For this work, it was assumed tmfizend effects did not exist since there were at least 29 Water from flask Glass tube __7 Overflow for water and light packing particles o.__l Fritted Glass Tygon joint joint Mag/l. ‘ To manometer D Cell #2 1' 1 fi Extended arm <® \\\\‘E Figure 12. Diagram of method employed for padking main section of column. 30 three inches of packing above and below the first and second conductivity cells respectively. Run Procedure To begin a run, the desired flow rate was set by using the micrometer valve and nitrogen pressure. To Obtain low flow rates (0.00 to 2.00 ft/hr), the column was opened to the atmOSphere and the flow rate was controlled by the posi- tioning of the outlet tubing*. The outlet could be located anywhere between the top of the packing and the liquid level in the column. At low flow rates the micrometer valve was found to be insensitive to controlling the flow rate. The flow rate was measured by collecting liquid from the outlet tubing in a burette (calibrated in twentieths of a milliliter) over a known period of time. Once the desired flow rate was obtained, the liquid level was allowed to drop to the top of the packing and then a measured amount (pulse) of sodium chloride solution was injected, Eli syringe, into the column. The pulse was then allowed to enter the bed, the flow was stopped, solvent was carefully introduced to bring the liquid level back to photo cell height, and the flow was started again. As the tracer passed through the column, the conduc- tance versus time curves were recorded on a Sargeant Multi Range Recorder (catalog number S-72150). The two cells were *- A piece of three—eights inch diameter Tygon tubing was at- tached to the c0pper tubing outlet line so that the outlet fluid could be easily collected for flow rate measurements. 31 hooked into the measuring circuit by means of a two—way switch enabling transfer from one to the other. Before the pulse reached the conductivity cell, the recorder speed, range, and zero point were set. 'The zero point reading could be set by preference while pure solvent was passing through the cell. The range was set to give the maximum pen deflection without going off the chart. A resistance box was placed in the measuring circuit in place of the cells to determine what recorder ranges yielded scale readings prOportional to conductance. It was found over the extimated resistance span of the cells (one to 100,000 ohms), that only the ranges of 5, 25, and 50 mv. could be used. Thus, it was necessary to vary the concen- tration of the tracer solution to find the one which would yield the optimum output curves using only the aforementioned recorder ranges. Analysis of Concentration-Time Distributions Typical recorder output for both cells is shown in Figure 13. Referring back to Equations 8 and 9, it is seen that values are needed for U2: U1: 0:, and 0:. m / 00 (14) = Ct dt C dt “N f. f. and 2 oo 00 ON = f0 C(t - u)2 dt/fO c dt N = 1,2 (15) 32 .N 0cm H maamo How mm>nsu oEHu.MN coaumuucmocoo HMOHmmB .mH madman . mEHB . T; .9 .1 uotiexqueouoo 33 where the subscripts 1 and 2 refer to the upper and lower conductivity cells respectively. Equations 14 and 15 were solved numerically using Simp- son's Rule and time IBM 1800 Digital Computer. A copy of the Fortran program used to analyze the output curves can be found in Appendix A. The input data for the computer consisted of scale readings obtained from the recorder chart at equally spaced time increments. The actual input values were equal to the scale readings minus the zero point. These corrected scale readings could be used as values of C in Equations 14 and 15 because they were proportional to concentration. RESULTS AND DISCUSSION Calculation of Void Fraction The void fraction of the packed bed was determined as discussed in the previous section. Runs 3 through 14 were made in the same bed, while runs 15 through 38 were made after the column had been repacked. Tables I and II pre- sent the data used in the Blake-Kosney Relationship to calculate void fraction. The void fraction for runs 3 through 14 was found to be equal to 0.4770 and its value for runs 15 through 38 was 0.4544. To be certain that the void fraction of each bed remained constant, two sets of data were taken a day apart. FIOW'WaS maintained through the column during the one day interval. Calculation of Dispersion Coefficients To evaluate an equilibrium constant and a mass trans— fer coefficient at a given flow rate using Equations 8 and 9, it is necessary to know the value of the dispersion co— efficient at the flow rate in question. Since Hawley showed that an adsorption process occurring simultaneously with axial dispersion in a packed bed has no effect on the dis- persion coeffient, it was assumed that disperSion coeffici— ents evaluated in the inert beds of Hawley and Gentile could be used for this work. Hawley1 has reported that for flow in a pipe a log-log plot of D/DV versus dtU/Dv where 34 35 'Table I. Void fraction data (runs 3-14). Run gigging: Fiiyfiigte (glfiiin) in. Hg. in. Hg. Set 1 0.90 2.35 2.61 2 2.05 5.45 2.66 3 3.10 8.44 2.72 4 4.05 10.90 2.69 5 5.15 13.85 2.69 6 6.20 16.75 2.70 (VD/AP)ave = 2.68 (ml/min) in. Hg. Set 2 1.05 2.68 2.54 2 2.02 5.20 2.58- 3 3.05 8.26 2.68 4 4.10 11.25 2.75 5 5.06 13.70 2.71 6 6.28 17.60 2.80 (VD/AP)ave =' 2.69 (ml/min) in. Hg. 36 Table II. Void fraction data (runs 15-38). Pressure VOZEP Run Drop, AP Flow Rate (ml/min) . 7 ml/min . in. Hg. in. Hg. Set 1 1 0.70 2.08 2.98 2 1.86 5.45 2.93 3 2.95 8.64 2.94 4 3.65 10.90 2.99 (VG/AP)ave = 2.96 (ml/min) in. Hg. Set 2 1 1.50 4.34 2.90 2 2.55 7.50 2.94 3 3.32 9.75 2.94 4 4.07 11.95 2.94 (VG/AP)a = 2.94 (ml/min) in. Hg. V6 37 D - dispersion coefficient Dv - molecular diffusivity dt - tube diameter U - interstitial velocity should yield a straight line. It is logical to assume that a similar plot would correlate data for packed beds. Both Hawley and Gentile used the aforementioned plot to correlate their data. They replaced dt in the above relationships with four times the hydraulic radius, 4M. For a packed bed of spheres 4“ = 5 T‘s—2' d(eff) A plot of log D/DV versus log 4MU/Dv based upon both Hawley's and Gentile's data is seen in Figure 14. The value of the dispersion coefficient used in Equations 8 and 9 was determined from the equation describing the line best fitting Hawley's data (see Figure 14). The equation of this line was D = 9.0 DV (4MU/DV)1°°43. Gentile's data was taken in beds of irregular glass particles and as Figure 14 shows, the dispersion coeffici- ent was larger compared with the data taken in beds of glass spheres. Since this work involved packed beds of irregularly shaped (Appendix B) particles (60-80 mesh), it would seem logical that Gentile's dispersion data should be used for evaluations in this work. However, this was found not to be the case, and Hawley's data for spheres was used instead. 38 000.0 00 O Q G) -.100.0 D/D ‘ V A A‘ KEY: I G) Irregular glass parti- cles d - 0.0049 in. eff A Glass spheres -,. 10.0 C dp - 0.00217 1n. Glass spheres A A d - 0.0071 in. 19(two cells) Glass spheres Equation of line is: A d 2 0.0071 in.) three cells D = 9.000 (4MU/D )1’043 v v : .1 ‘ 1.0 4MU/DV 10 .0 100 Figure 14. Hawley's and Gentile's data correlated by a plot of 4 MU/DV Kg, D/Dv° 39 A possible explanation for the fact that Gentile's data did not give good results in analyses concerned with this thesis is the difference in the type of packing used in this work compared to Gentile's work or that mass trans- fer may affect axial dispersion. It is quite possible that inherent characteristics of the packing such as surface roughness or surface porosity are the primary contributors to the dispersion for some substances while packing shape is the primary contributor for other substances. Figure 14 shows definitely that for glass particles, packing shape affects dispersion. However, this might not be true for substances other than glass (i.e. molecular sieve). Calculation of Equilibrium Constants The equilibrium constant for the adsorption process occurring in the experimental work of this thesis is calcu- lated using Equation 8 and the tabulated values are found in Tables III and IV. A plot of flow rate versus equilibrium constant is shown in Figure 15. The plot seems to confirm the idea that an equilibrium process is occurring. There is some scat- ter, but the error between the lowest and highest value for the equilibrium constant is approximately 15% and is con- sidered as good results for the type of experimental measure- ments employed in this study. The actual magnitude of the equilibrium constant was compared to the results of batch studies9, made by Barrer, 4O .HOHHm UmpommmSm on one omNmHmcm Dos HDQ cmxmu mum? UmumHSQmu Doc masm "muoz* mbHoo.o mmmao.ou embN.N omvw.o mm.mwm H.vmm.H Hmb.vm mma.oom Va meoo.o mamoo.ou am®H.N vmww.o hm.mom m.mvN.H mvH.bN www.mwfi mH ObHoo.o movHO.OI mbNH.N Hva.o vo.®mv H.wmm.H th.Hm mom.mmm NH Nbfioo.o mmmao.on wovv.m bmmm.o Nh.mmv m.NH>.H vHN.bH wmo.ovm HH momoo.o bmbmo.o wovH.N wmmN.H Nw.vwm w.®NN.H ©N0.m mom.wvH OH onwoo.o mbmao.o ommO.N hOhN.H wn.HNm m.NHm.H mam.m oam.HhH m mmmoo.o mbmoo.o mfivm.a mmam.fi oo.wmm m.hw®.a me.HH vmv.vmm m mmmoo.o vaflo.o owwH.N Hmm®.fi mH.omm on.mwm mmm.®H wOH.HNH v vmvoo.o wbHHo.o ommo.m Humm.a om.mmN NH.Nvm omm.m mmb.®m m H£\wum Q H£\um xx E H£\um D 00m H1 00m «1 «00m Mo «00m Mo cam .Aoevv.o n 0V eeum mean How meme .HHH magma 41 mvmoo.o Hmomo.o HHON.N boom.m Hw.bNH om.0Hm m.O®G.H mom.NN Hm Homoo.o wvbflo.o vvum.m Howv.m hm.¢mfi N©.Hmb m.mHo.v HHm.Hm om mmmoo.o wammo.o nonm.m mmvv.m bH.¢ON vm.mv® o.Hmm.m www.mv mm ommoo.o Hmmho.o Hmmm.m mmmw.m hm.mbfi mm.mmm ®.bbm.m omv.Hv mm vomoo.o hammo.o mumN.N mvmv.m mm.mbH vm.mm® ©.mmm.m mwm.ov hm moaoo.o Hmvoo.on momH.N bmom.o mb.HHw b.0Hv.N ¢O0.0®H owo.omm om omooo.o wmfloo.OI Hmbm.m momm.o v.mww.a N.vmv.v www.cmv mma.¢mm.fl on Nmooo.o wmaoo.ou oomm.m ounm.o m.mmm.m H.mmm.v wmb.mmm mvm.bvfi.m mm bHHoo.o mmmfio.0I H8ON.N mmmm.o wH.va m.om®.m Hom.vNH omn.mm® Hm ofiaoo.o wooao.ou wme.N womm.o om.bam b.wmv.m www.5m mvH.wom om mwmoo.o momfio.o mvmfi.m ovam.m om.mmH mm.oom m.b®m.v new.Hv ma mmmoo.o HmHNo.o vaN.N ovam.m om.m®H HH.vmm m.mom.m Nom.wm wH ommoo.o mwvmo.o mmhm.m mHmH.v mw.mHH mm.Hmm w.Hmm.H www.mH SH vbmoo.o Hmeo.o Hwom.m moHN.v HH.®NH ha.omm N.mwm.m www.mm ma vhmoo.o bmmmo.o HmmH.N moHN.v bb.¢0fi mm.me o.omv.H www.mfi ma H£\num Q H£\um xx E H£\pm D com a: 00m «1 «00m Mo «com mo :sm .Aemee.o n 0V wmume menu Hoe meme .>H magma 42 N L vbmoo.o meNo.o bva.N mem.m vm.mom mv.®©m m.vwo.w HHo.Hv mm ommoo.o mwmao.o mm®H.N hmoo.m ®S.NNH ow.mvm >.mmo.m bbN.ov hm vmhoo.o Hmovo.o mmwN.N oowv.m Ob.mbH mm.mmv w.®Nb.m www.mm mm emboo.o HmbNo.o ova.N ooov.m mv.bva mo.mmm o.me.m www.mm mm Hmwoo.o mmmvo.o mmmm.m wmmm.m wh.NvH m>.Nov «.mvm.m mmm.om on bmmoo.o moovo.o Hmhm.m vfimw.m mb.mmH mm.wov o.mvm.m va.om mm oomoo.o wwowo.o oth.N Hmom.m mu.hmH mH.mHv H.vmm.m abo.om mm H£\~um D H£\um xx E H£\um D 00m H1 00w «1 «00m Ho «00m Mo sum A.ucoov .>H magma 43 .mmumu 30am mDOHHm> um musmumcoo Esflunflafisvm .mH mHDmHh GO o.v o.m Awe\0ev O _ O.N mumu 30Hm d o.H . o om.Hl oo.NJ oe.m1 O 8.3 om.NJ ofmi queisuoa mnrxqrxrnba 44 employing molecular sieve (13-X) and a NaCl solution. Barrer, exhibited his results by plotting the nonlinear isotherm for the above mentioned system. A value for m was calculated from Barrer's data by finding the slope of a line drawn tangent to the isotherm curve at the concen- tration of the tracer solution used in this study (29/1). The lepe of the line was found to be about 0.05. However, Barrer's measurements were made with packing in the shape of pellets 1/16 of an inch in diameter and 1/4 of an inch long. Since the packing of this study was of different shape and much smaller than the pellets, it would have more surface area. It was calculated that the irregularly shaped particles used in this study had approximately 8.40 times as much surface area as the pellets used by Barrer. -This means that Barrer's value of m corrected for the packing shape of this work would be about (8.40)(0.05) = 0.420 com- pared to the experimental value of between 2.10 and 2.30. At this time the deviations in the above values for the equilibrium constant cannot be explained. Calculation of Mass Transfer Coefficients_ The values of the mass transfer coefficients for this study were calculated using both Equations 8 and 9 and axial dispersion coefficients from Figure 14. The results are tabulated in Tables III and IV. A plot of mass transfer coefficient versus flow rate is shown in Figure 16. The plot indicates a general trend 45 G)oo in)“: o.N _ .mmumu 30am mSOHHm> um mucmHOHmmmoo Hmwmcmug mumm 3oam o.H _ (a O .®H musmflm O O O CO N H )0 *v 201 x quarorggeoo Iagsu211 ssew 46 of the mass transfer coefficient to increase with increas— ing flow rate. The tabulated data reveals that flow rates less than one foot per hour yielded negative mass transfer coefficients. This is physically impossible and may posh sibly be explained by the fact that the values used for the dispersion coefficient in this flow range were taken from extrapolating the data shown in Figure 14. As can be seen in Figure 14, there is very little diSpersion data in the low flow range and thus no firm justification for the extrap- olation. The scatter of the data observed in Figure 16 can rea— sonably be blamed upon errors compiled during the actual run and the analysis of the data. These errors will be discussed in further detail later in this thesis. Correlation of Mass Transfer Data The mass transfer data of this study were compared to data collected by several other investigators using complete— ly different experimental systems. The data of this work, of Resnick and Whitelo, of Al-Khudayrill, and of Hurt12 is correlated on a plot of Re/l-e versus Sh/(Sc)1/3. The results of the correlation are shown in Figure 17, and the data used for the plot are tabulated in Table V. As can be seen, the data of Resnick and Whitelo, Hurt12, and Al—Khudayri11 tend to fit a straight line in the higher flow range. The data of this work, although taken at much slower flow rates, appears to fall on the extrapolated 47 .mumw Hmmmcmnu mom: UopmHmHHoo .hH musmflm . A.-.V\.mc o OOOH o.ooH 0.0H o.H OH. Ho. — q _ mDHSB E xoflsmmm 4 0303 menu O 9.39.2 4 #HSD O «mmx O we no 1H0. 0 m m s o w. e V O S o I -36 fl 8 421 d d < 4 Q Q r 4 3 .4 O Q 104 .<.q< O O O O O O 1 . _ ._ . _ 48 Table V. Data from this work used for mass transfer cor- relation. Run Re/(l-e) Sc Sh Sh/(Sc)173 3 0.03961 518.9 0.06843 0.00853 4 0.03349 0.08316 0.01037 9 0.02572 0.10894 0.01358 15 _0.08638 0.15022 0.01873 16 0.08638 0.10806 0.01347 17 0.08517 0.38706 0.01798 18 0.05998 0.12377 0.01543 19 0.05998 0.11081 0.01381 27 0.05116 0.37850 0.04720 28 0.04998 0.44262 0.05519 29 0.05024 0.22814 0.02845 30 0.05088 0.10151 0.01265 31 0.07571 0.17893 0.02231 32 0.08005 0.23740 0.02960 33 10.07983 0.23261 0.02900 34 0.07930 0.25530 0.03183 35 0.07098 0.15980 0.01992 36 0.07098 0.23761 0.02963 37 0.06168 0.09811 0.01223 38 0.06066 0.13461 0.01678 49 straight line fit of the higher flow rate data. Figure 17 indicates that the mass transfer coefficients evaluated in this study compare favorably to values calculated from com— pletely different experimental methods. Discussion of Mass Transfer Data A closer look into the methods used in obtaining the data in Figure 17 might help in determining the controlling mechanisms involved in the work of this thesis. Before the works of Al-Khudayrill, Resnick and Whitelo, and Hurt12 are discussed in more detail and conclusions made, it will be helpful to keep in mind a few facts concerning available mass transfer data. First of all, there are wide discrepancies between mass transfer correlations for low velocity flow of gases through packed bedsll. Also, Resnick and White11 found that discrepancies in correlations oc— curred between data taken with large particle sizes and data taken with small particle sizes, and the smaller the size the greater the deviations. This work involves evaluating mass transfer coefficients employing both slow flow rates and small particle sizes. The flow rates used in this work were, in fact, much slower than those used in any other work the author could locate. It would be fairly safe to say that little if any experimental work has been conducted in an at- tempt to evaluate mass transfer coefficients at flow rates as slow as those used in this work. It was also noted that 50 the particle size employed in this work was considerably smaller than sizes employed in other experimental work. Considering the above discussion, it could be expected that the mass transfer data of this work would be in dis— agreement with the majority of the other experimental work. Basically this is true11. However, Figure 17 indicates ex- perimental work which tends to agree with the work of this thesis. Al-Khudari11 was primarily interested in gathering mass transfer data for gas-solid systems with the gas film re- sistance controlling. He took precautions in his eXperimental work to minimize other resistances and to eliminate other effects which might be detrimental to the results. His padking consisted of aluminum balls coated with a metallic halide. The fluid passed through the packing was a mixture of ammonia and an inert gas. The ammonia formed a complex with the coating on the packing to insure adsorption was occurring. Data used in Figure 17 from Al-Khudayri's work are listed in Table VI. Resnick and white10 also measured mass transfer coef- ficients with the gas film resistance controlling by evapor- ating fixed and fluidized beds of naphthalene into air, hydro- gen, and carbon dioxide. The data they accumulated for fixed beds are shown in Table VII. Hurt12 decided to undertake a study of transfer rates to packed beds since at the time only a sparse amount of data was available in this area. He was primarily interested in 51 Table VI. Data of Al-Khudayri (11). System SC Re/(l-e) Sh/(SC);/3 Halide? 1.31 5.57 0.488 ammonia 2.22 0.340 7.85 0.613 4.09 0.375 7.10 0.278 9.25 0.716 13.73 1.108 17.33 0.795 25.45 1.374 31.45 1.340 52 mmH.o om.m . am wba.o mm.m mmo.w Ohm.o Imcmamzpnmmz mvw.o mb.mm Nco me.H oo.Hv Hhv.H mome.o Imcmamnunmmz How.o mm.» va.o mm.NH mhh.o mo.mH Hem 05>.o ob.mH mm.m voo.o ¢>.mm Hmm.o mmwo.o 10:0Hmnuzmmz Aomv\£m mIH\mm om omm\mEo UU\NEU m Eu Emummm E Q Q m .. U .AHH.OHV opens pom Evesmmm mo mama 9HH> magma 53 accurate experimental measurement of gas film H.T.U. and thus was careful to insure that the gas film resistance was controlling. He investigated three different systems one of which was the evaporation of naphthalene into air from naphthalene particles. The data is tabulated in Table VIII. Considering the preceding discussion along with Figure 17 it would seem entirely logical to conclude that the con- trolling mechanism in the work of this thesis is the liquid film resistance. The overall mass transfer process can be visualized as sodium ions from the dilute tracer slowly diffusing through the stagnant liquid film at the interface between the liquid and the packing and then instantaneously reacting (ion exchange) at the surface of the packing. This explanation would also give further credence to the conclu- sion, supported by the horizontal line fitting the data of Figure 15, that an equilibrium process was occurring. It must be remembered that these conclusions were made by assuming that a straight line extrapolation was correct for the correlated data of this work. Since there is no available data in the area between Re/(l-e) = 0.10 to 2.0, the straight line extrapolation was assumed to be correct. Results exhibited by Figure 16 also add validity to the above conclusions. If the liquid film resistance is the controlling factor in mass transfer, the mass transfer coefficient would certainly increase with a larger flow rate since the liquid film thickness decreases as flow rate in- creases. This phenomena was observed and is illustrated in Figure 16. 54 on.s see we wo.mH ham omH Ammxmam ma.om mam men 44.8 oe.o emm.e name eumv >>.o o.HH m.o OH.H m.om w.NH wh.H m.mv w.mm wm.m N.mHH o.mb mm.m «mm mes em.m owe com mo.m mmv.o Amumecaamov mh.H m.vm m.mH Hv.m o.mv m.wm 00.5 m.Hm N.bm Hm.h mmm omH AmumUCHamuv NO.NH wan own new am.om mace ohm om.m emo.o mm.m mem.o mom.o loadamnunmmz «\HAomv\£m wIH\mm mm om ommfian UO\NEU 0 MO Emummm a m o .ANH.HHV unsm mo muma .HHH> magma 55 Discussion of Errors in Experimental Procedure and Data Analysis Much theoretical work has been done in the area of pulse injection and response techniques. However, experi- mental work in this field is lacking tremendously and this is due, most likely, to the many experimental problems which can arise in work such as this. Rao and Hoelscher3 used this technique to study diSpersion and adsorption in gas-solid systems, but other than this, the author could locate no other work applying the pulse injection technique to systems where diSpersion and adsorption were occurring simultaneously. The most frequent problems arising in the actual exper- imental procedure of this work were those of injecting a pulse so that tailing on the output curves would be mini- mal, keeping a constant flow rate through the column during the span of an entire run, and trying to prevent the output curves from being deflected off the width of the chart paper. Many completed runs were discarded for one or more of the above listed reasons. For the vast majority of runs, the tails of both the first and second curves did not return to the base line at which the curves were started. This meant that before the runs could be analyzed a base line somewhere between these two points had to be chosen. It was later realized that the actual positioning of the base line could result in as much as a 50% change in value of the mass transfer coefficient. 56 The author found that the best results in analyzing the curves were obtained when the base line was chosen closer to its beginning value than to the value indicated by the tail of the curve. This meant that the tail of the curve had to be extrapolated downward to the chosen base line. To eliminate errors incurred by guessing at a correct base line value and then extrapolating, it is suggested that re- finements be made in the measuring system which might pos- sibly result in stronger input signals to the recorder. Possibly, all that is needed is a more sensitive recorder. Actually there were several other problems that sug- gested the replacement of the recorder with a more sophis- ticated model. First of all the chart speeds could be varied only by manually changing gears. Also, the lowest chart speed available made runs under 1/2 a foot per hour unreliable because the output curves had such wide spreads on the chart paper. Secondly, the range settings were ex- tremely hard to duplicate and this often resulted in output curves exceeding the width of the chart paper. As a matter of fact, several of the runs analyzed in this work were so done only after the top portions of the curves had been estimated and drawn in by hand. ‘The most difficulty encountered in this experimenta— tion was adjusting the flow rate and then keeping it con- stant. Many runs had to be discarded because of changes in the flow rate. This problem became predominant below flow rates of 1/2 foot per hour and both tabulated runs at 1/4 57 foot per hour were analyzed even though the flow rate varied over the duration of the run. Considering all the problems involved in the actual gathering and analyses of the data of the unsteady state experiments of this work, it would seem entirely reasonable to blame the scatter in the data (Figures 15 and 16) on a combination of many experimental factors. CONCLUSIONS An axial dispersed, plug flow model, with adsorption occurring, was used to describe the unsteady state chrom- atography process. Equilibrium constants and mass transfer coefficients were evaluated at various flow rates using the pulse injection and response technique. The variance between the highest and lowest values of the equilibrium constants evaluated at flow rates between 0.00 and 4.25 ft/hr was only 15%. The fact that these values were relatively constant indicates that the chromatography process, as simulated in this study, was occurring under equilibrium conditions. That is, the sodium ions in the fluid were in equilibrium with sodium ions on the packing surface. The mass transfer coefficients were evaluated over the same flow range as were the equilibrium constants and showed a strong tendency to increase with increasing flow rate. When correlated, the mass transfer coefficients of this study compare favorably with data taken with the gas film resist- ance controlling (gas-solid system). This led to the con- clusion that the adsorption occurring in this study was con- trolled by the liquid film resistance (liquid-solid system). Therefore, the adsorption phenomena can be visualized as the diffusion of tracer ions through a liquid film resistance with subsequent instantaneous adsorption at the packing sur- face. 58 RECOMMENDATIONS FOR FUTURE WORK The following are recommendations for further work that will be helpful in attaining an accurate and complete method of scaling-up chromatographic separations. 1. The third moment of the output curves, which can be mathematically related to the dispersion coefficient3, should be calculated and used to evaluate dispersion coef- ficients. This would eliminate the approximation method used in this work and certainly eliminate a possible cause of error. 2. A complete investigation should be made into end effects and their relation and importance to the chromato- graphic separation. 3. A system in which interparticle diffusion is a major factor should be investigated. Porous glass beads could possibly be used as a packing in this system. 4. Finally, an actual separation of two components should be predicted and then tested. 59 APPENDIX A 60 61 mnzoomm zH I Hume mom ezmsmmozH mzHe I e.¢aHmc o HBHmo Am.mv mama Av.onwv aezmom m z Am.mv mama n .H u x a on mHHmo mo mmmzoz I o o mmmzsz zsm I z o o.: Am.mv 64mm moz .H u H m on mzsm mo mmmzoz I moz o moz Am.mv gems AmHmv season a AH.mv weHms A\ .n. 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ZMDBmm H dfimd H H on APPENDIX B 65 Microphotograph of Packing Particles AP - Re - Sc — Sh - NOMENCLATURE cross sectional area, ft2 solids transfer area per volume, ftZ/ft3 concentration of component A in tracer, mol/vol concentration of component A in the tracer at the liquid-solid interface, mol/vol concentration of component A on the solid, (mol/vol solid) dispersion coefficient, ftz/hr molecular diffusivity, ftz/hr tube diameter, ft effective diameter, ft gravitational constant, (lb mass sec2)/(lb force ft) mass transfer coefficient, ft/hr length of bed between cells, ft hydraulic radius equilibrium constant (defined by equation 4) pressure drop through packed bed, lb/ft2 Reynolds number, dep/u Schmidt number, u/Dvp Sherwood number, dep/Dv time, hr interstitial velocity, ft/hr superficial velocity, ft/hr volumetric flow rate, ft3/hr axial distance 67 68 Greek Letters: e — void fraction u — viscosity of solvent, lb/ft—hr U1 — mean-time of concentration-time distribution at cell #1, hr U2 — mean-time of concentration-time distribution at cell #2, hr 01 - variance of concentration-time distribution at cell #1, hr2 2 . . . . . . 02 - variance of concentration-time distribution at cell #2, hr2 10. 11. 12. BIBLIOGRAPHY Hawley, M. C. "solute Dispersion in Liquid—Solid Chromato- graphic Columns." Ph.D. Dissertation, Michigan State University, East Lansing, 1964. Aris, R. "The Longitudinal Diffusion Coefficient in Flow Through a Tube with Stagnant Pockets," Chemi- cal Engineering Science, 9, 266, 1959. Chao, Raul and Hoelscher, H. E. "Simultaneous Axial Dispersion and Adsorption in a Packed Bed," A.I.Ch.E. Journal, 12, March 1966, pp. 271—278. Gentile, J. F. "The Effect of Particle Shape on Solute Dispersion in Liquid—Solid Chromatographic Columns." M.S. Thesis, Michigan State University, East Lansing, 1966. Cotton, Albert F. and Wilkinson, Geoffrey. Advanced Inorganic Chemistry. Second edition. New York: John Wiley & Sons, 1960. Breck, D. W. "Crystalline Molecular Sieves," Journal of Chemical Education, 41, December 1964, pp. 678- 689. International Critical Tables, McGraw-Hill Book Co., Inc., New York. Bird, R. B., Stewart, W. E., and Lightfoot, E. N. Trans- port Phenomena. New York: John Wiley & Sons, 1960. Barrer, R. M., and Walker, A. J. "Imbibition of Elec- lytes by Porous Crystals," Transactions of the Faraday Society, 60, 1964, pp. 171-83. Resnick, W., and White, R. R. "Mass Transfer in Sys- tems of Gas and Fluidized Solids," Chemical Engineer- ing Progress, 45, 377, 1949. Al—Khudayri, Tariq. “Mass Transfer Rates in Packed Beds." Ph.D. Dissertation, Michigan State University, East Lansing, 1960. Hurt, D. M. "Gas-Solid Interface Reactions," Industrial Engineering7Chemistry, 35, 522, 1943. 69 MICHIGAN STATE UNI 12 0 3 93 R YLB llll'lllIIIIl'Es 0 SIT 3056 468 VE