SCALE-UP OF FIXED BEDS USING NAPHTHALENE PACKING Thesis for the 099m cf M. S. MICHIGAN STATE UNIVERSITY Richard Thomas Baum: I958 " 0v 0 O1”...“.c'.-.~.w‘ “'~..W "uo'v LIBRAR Y MichiganSuw University SCALELUP OP FIXED BEDS USINGrllPHIHLLENEIRACKIEG; m, Richard Thomas Bourne A THESIS Summitted to the Obllege of Engineering Michigan State University of Agriculture and Applied Science in partial fulfillment of the requirements for the degree of‘ MASTER OF SCIENCE Department of Chemical Engineering 1958 ACKNOWLEDGEMENTS The author wishes to express sincere thanks to Dr. Randall W. Ludt for his continued strong interest in-this investigation, his wise guidance of the research and for the gift of his vacation time for the convenience of the author. The author also wishes to thank Dr. 0. had Gurnham and Dr. Rich- ard A. Zeleny for their helpful suggestions. Acknowledgement is also due William clippinger for help in fabri- cation and design of parts of the apparatus and the Reynolds Aluminum (lemony for the gift of the aluminum tubing for the reactor towers. ABSTRACT -‘ The problem under study in this thesis was the scale-up of packed beds. The particular approach to scale-upswas the use of similarity; type calculations to predict conditions and then to verify these pre- dicted conditions with experimental data. The method of obtaining data for these correlations was to operate three size towers packed with balls of a size such that the ratio of the diameter of the ball to the diameter of the tower was nearly con- stant. The system used was vaporization of spherical balls of naph- thalene into a stream of heated air. The packing depth, air rate and the thickness of insulation on the outside of the towers were varied so that the three towers all=had nearly similar conditions of temper- ature distribution and final concentration. The data taken were used to calculate values of the mass transfer coefficient, the mess transibr factor and moles vaporized per unit time. These calculated values were plotted against the conventional variables, mass velocity and Reynolds numbers The mjor findings in this investigatbn were correlations of moles vaporized per unit time at equal mass velocities and equal Reynolds numbers. In addition values of the mass transfer coefficient were cor- related at’different and equal velocities. To illustrate the approxi- mate agreement of the data of this investigator with that of others a plot of the mass transfer factor against modified Reynolds numberrwas [‘I‘ll‘ll‘l‘ llll I, made. The use of these plots along with the calculations served to illustrate the possibility of scale—up by the similarity approach; TABLE OF CONTENTS Acknowledgments — - i _ ___=_ - __ 1 Abstract _— - — w _ _ 2 Table of Contents _ _ _ 4 I. Introduction. _ __ 5‘ Il. Historical Background 8 III. Apparatus and Supplies _ 11 TV. Procedure _ 25 .V. Derivations and Correlating Relationships _ 28 v1. Data_ a _ __ as Vll. Calculated Results __ 118 Will. Nomenclature __ 55 . SIX. Discussion: —A 55 X. Conclusion. —- ‘ - 57 Appendix —~ — 59 List of References 71 INTRODUCTIGIZ Statement of Problem A problem which has plagued the chemical industry as long as mod- els of equipment have been used has been the problem of scale-up.9 The term scale—up has referred to the process of designing commerical sized equipment using the data obtained in a model unit. The partioa ular phase of scale-up studied in this investigation was the scale-up of packed beds. Application of the system to the General Problem The rate of reaction in a catalytic reaction has been shown to be governed by one or more of the five steps:19 1. Diffusion of reactants in to the surface of the catalyst. 2. Adsorption of the reactants on the surface. 5. Chemical reaction on the catalyst surface. 4. Desorption.of products. 5. Diffusion of products out to the main gas streanu In addition step one or five has been shown to have two divisions, dif- fusion to the surface and diffusion into the pores of a porous particle. The use of the system of naphthalene vaporization to simulate a catalytic bed did not allow each of the possible controlling steps to be studied. It was suspected that the controlling step in naphthalene vaporization was diffusion of the naphthalene out into the main gas streamn If either chemical reaction or diffusion were found to be the controlling step similarity calculations could have been made. The choice of a diffusion controlled process for this first experimental application of similarity to reactor scale—up had the advantage of the availability of data correlated by different methods. Similarity Approach The principle of similarity has been used for years in other inp dustries such as the boat and aircraft building industries.10 The use of similarity for chemical reaction which dated back to Damkohler5 has not been completely exploited; Similarity has offered advantages over direct calculations using relationships such as the Peclet. number which has been usually expres- sed as a function of the Reynolds number. For equal Reynolds numbers the values of the Peclet number for large and small equipment have been shown to be the same. The similarity approach, because ratios were used, has allowed the value of the Peclet number to be cancelled out at equal Reynolds numbers. This has eliminated any errors of Peclet number determination. The similarity approach has been criticized7 because all the coup ditions of similarity have not been always maintained in calculations for transferring small peices of equipment to larger ones. Similarity and the use of “partial similarity', have been justified by considerimg the factors which made up the similarity ratio. For example, in fluid *See Nomenclature II ‘IIII-Ill' ill... ' flow calculations the Reynolds number has been used extensively for correlations. The Reynolds number has been derived as the ratio of. the kinetic energy term divided by the viscosity term. Because the Reynolds number correlated the fluid flow data so well the kinetic and viscosity forces seemingly were the important forces involved. The li'roude'.I number could have been used for correlation but this number included gravitational forces. The Proude number correlated weir data where gravity is important but it did not correlate fluid flow in pipes. If in scale-up of fluid flow the Proude ratio was not equal to one but the Reynolds ratio was, this might be called 'partial similarity“. Because the Reynolds number has included the important forces dissimilarity of the Proude group has caused very little dis- similarity in scale-up. ‘See Nomenclature HISTORICAL BACKGROUND Previous WOrk. The references in the literature to packed beds studies were quite numerous. Many of the variables have been studied such as radial temp perature profile, radial velocity distribution and fluid properties ef- fects. The particular problem of scale-upsof packed beds has not re- ceived its share of attention. The first application of the principle of similarity to scale-up. of chemical reaction processes was made by Damkohler.5 Previouslyfthe uses made of similarity were, for example, in fluid flow using the friction factor concept. Dankohler derived dimensionless numbers using the vector form.of the basic equations for the conservation of mass, energy and momentum. By dividing through any one of these equations hy am one quantity a group of dimensionless numbers was formed. An exmple of this was shown by taking the equation for conservation of momentum» and dividing through by‘the viscosity term. The kinetic energy term divided by the viscosity term formed the well knowntReynolds number. Damkohler's approach to scale-up was to take the dimensionless groups derived as described above and show that ratios of some:of these groups for two sizes of beds were equal to one for similarity between the model and the scaled up reactor. He derived relationships for the case more chemical reaction controlled the reaction rate and the rates of heat: transfer through the inside film.of the reactor controlled the heat transferred through the reactor wall. 8 A continuation of the type of work done by Damkohler was made by Johnstone.9 He derived relationships in a.menner similar to Damkohler. Johnstone extended the work to cover the case where diffusion to the surface of the peeking controlled the rate of reaction. He also in- troduced the Arrhenius equation into the chemical reaction controlled relationships. This equation caused no significant change in the re- lationships controlled by chemical reactions Neither Johnstone or Damkohler presented experimental data to justify their calculations. An experimental study of scale-up was made by Hurt.7 He intro- duced the concept of the 3.3.11. (height of a reactor unit) and no.0. (height of a catalytic unit). His treatment had certain limitationsflg In order to use his concept he has shown that the surface processes must be first order; otherwise the linear driving force required can- not'represent the kinetics of the surface steps. Also the reversible reaction rate had to be negligible for Burt's work to apply. Much of the work on fixed bed systems has been applied to a pro- cess in which the rate was controlled by diffusion. To correlate the diffusion data the concept of the mass transfer factor 3d and the heat. transfer factor 3h suggested by solbum‘.‘ and Chilton. and Colburnz has been.used extensively. In this work the investigator only planned to use the 5d concept to show the approximate agreement of the data with that of other investigators. . In the calculations of the 5d numbers many investigators have as- sumed that the temperature of the surface film.on the naphthalene was the same as the bulk gas temperature. The work done by Shulman;6 I . Ill. . Ii"! all. , |l allll'lll ... IIIIINII I. showed that 5d was affected by varied bulk gas temperatures. He;found a decrease in 3d with an increase in bulk gas temperature. His 3d values all correlated to one line when using the following approximate equation: P 3- 0.6% (t — ta) + Po 8 . The Ps value was intended to represent the partial pressure at the actual surface temperature. In the work done by. Bar-ilan and Resinck1 the particle size ap- peared as a parameter in correlation of j d against modified Reynolds number for small spherical particles. For pellets of 0.41 and 0.82 centimeters one line correlated the data. For small particles Resinck and White15 and Hurt7 also observed that particle diameter was a p arameter. Accuracy of Previous Work A problem of variation in the void space of freshly packed colums has been recognized for some time. A number of'investigators have dis- 12,18,11 cussed the effect of packed bed variations on accuracy. Peclet number has been shown to be a function of void space for 81% of the ‘ ' 18 bed radius. The last 19% is affected by wall effect. The velocity at the bed's center for one set of conditions was found to be 65% of 17 the maximum on the velocity profile. One of these authors, Levan gave the reproducability as 1 10%. His material balances ranged from 95 to 111%. This served to illustrate the inherent problem of repro— ducability using packed beds. 10 APPARATUS AND SUPPLIES Apparatus The air for this series of experiments was furnished by a Nash: I-brtor air pump equipped with a seven and one half horsepower motor and a Reeves variable speed control. The air was heated by passing it through an approximately two and one half foot sectiontof the one and one quarter inch inlet pipe. This section was covered with as- bestos then wound with twenty two feet 'of Chromel-A wire with; 0.641 ohms per foot resistance. The pipe and heater. were insulated with standard magnesia insulation. At a given air rate the temperature of the air was regulated with a manually controlled Powerstat‘. The heater was located on: the inlet line just before the maintower to decrease cooling of the air between the heater and packed tower. The main towers were made from aluminum tubing. The outside dia- meters of the pipe used for the towers were six, three, and one and one half inches. These diameters were referred to as the size of the tower although the exact inside diameters were used for calculations. Sections of the pipe cut for towers were made longer thanthe actual packed section and an adjustable packing support was used to adjust the height of the packed section. One of two types of packing supports was used to adjust the bed height. The support for the two larger towers was interchanged by bolting a screen of the correct diameter on the top. platform. 11 Telescopic legs on this support allowed an adjustment for bed height. The packing support for the small tower was made from brass tubing having an outside diameter equal to the inside diameter of the alumia. num towers Sections of this tubing were cut to three eights inch lengths. A circle of fine screen was glued to the top-ring of tubing to support the packing beads. The construction of the face plates to hold the towers in place was designed so that all three towers could use the same plates. The plates were made from two inch maple stock. To the top of the top. plate and the bottom of the bottom plate was screwed a floor flange. These flanges permitted the one and one quarter inch pipe to be at-‘r tached directly to the wooden plates. The plates were grooved to a depth of approximately three sixteenth of an inch and to a width of the tower wall. Separate concentric grooves were made for each of the three sizes of towers. The material of construction, wood, which. was selected for the face plates was chosen ‘to minimize the heat con» ducted down to the bed from the top heater. The two face plates were held against the ends of the tower with one quarter inch rods threaded to the correct length for each individual tower. Consideration was given to the problem of flow distributionof the gas entering the bottom of the beds. In the larger towers a sec- tion' of pipe was left unpty below the bedsto allow the incoming air to expand from the one and one quarter inch pipe to the tower size. In the three inch tower a height of at least a foot was provided. In; the six inch tower nearly a foot of empty pipe in additionto four A inches of glass wool was used to obtain uniform distribution. 12 In the one and one half inch tower no provision was made because the expansienzwas only from.the one and one quarter inch pipe to the one and one half inch pipe. Apparatus was designed for measuring temperature and pressure drop from the bottom to the top of the packed section of the beds. The pressure measurements were made with brass tubing of approximately three thirtyaseconds of an inch inside diameter. Both the top and bottom tubes were bent so that the gas flowed parallel to the.open. face of the tube. The opening of the top probe was fixed at a height of three fourths of an inch from.the top of the tower while the bottan probe was free to slide either up or down to measure the gas pressure at the bed's center just below the entrance to the bottom of the bed. The free sliding of the brass rod was accomplished by welding a short length of tube into a hole drilled in the bottom.elbow. The inside diameter of the inserted tube was selected so that the fit with the probe tube was a firm slip fit. The outer leads from.the pressure taps were connected to a water filled U;tube manometer. The temper- ature measurements were made using iron-conttantan thermocouples fit- ted into the same size tubing as was used for the pressure measure- ments. The locations and mechanics of the temperature tubes were the same as for the pressure probes. The tip of the thermocouples pro- truded one quarter of an inch from.the open end of the brass tubing. Thought was given to minimizing the error caused by conduction of heat along the temperature probe. In every case at least five inches of the end of the temperature probes were in contact with the heated gas. 13 The temperature difference along this length of the probe seldom.was more than two or three degrees. This small temperature difference allowed very little heat to be conducted along the probe because of the small temperature driving force thus practically eliminating the conduction error in the temperature readings. Thermocouples were located on the side of the tower at positions at the top, middle, and bottom of the packed section on each side of a sheet of asbestos.. The intention was to use this temperature drop» to determine the heat loss. For convenience a commen cold junction. and a selector panel of four single polo double throw switches were used. The potentials for the temperatures were read on a Leeds and Northrup potentiometer. In;most of the investigations the air used in packed bed studies was dried first. This was not done in this investigation. In.the Rash pump.the air was continuously in contact with cold running water. The water served to drop the saturationtpoint of the air to the tem- perature of the cold water or below. As long as the temperatures in. the tower or saturator did not approach the dew point of the water vapor in the air no problem.from the undried air was encountered. An illustration that the water condensation was detected was found by an inspection of run 140. In this run a relatively large increase in. weight of the second saturator was noticed. Calculations showed that the increase in weight of saturator number one was also abnormally high. 14 They indicated that the dew point had been reached and water had cone densed out in the saturators. The ease in detecting the effect of the water seemed to justify not drying the air but warned of the possible danger of 'wet air". To remove a sample of the gas for analysis a one quarter inch pipe was threaded into the wall of the one and one quarter inch outlet pipe. A small cock was screwed to the one quarter inch sample pipe. In order to insure that an ample amount of gas passed out the sample cook, a valve was installed in the main exhaust line. The main exhaust line discharged through the window. A heater made in a manner similar to the inlet heater covered the first six inches of the exhaust line. This heater was necessary to keep the naph— thalene fromzcrystallizing out before a sample was taken. The tempera ature was raised enough so that crystallization would not take place any time before the gas reached the packed saturator bed. of 2. 3. 5. 6. 7. 8. 9. 10. 11. 12. 15. 1h. 15. 16. Figures one through six were included to aid in the discription equipment. The following list is a key to Figure 1. Key to Apparatus Sketch Precision wet meter. Air pump-Nash Hytor with Reeves Drive (Vi-horsepower motor). Fischer-Porter rotameter tube 5A-60A, Float D9-1559 or Fischer-Porter rotameter tube 7A-60, Float (custom.made). Inlet heater; 22 ft. chromel-A wire with 0.6Al ohms per foot coiled on pipe and covered with insulation. ’Piping 1%” galvanized iron pipe. Manometer- filled with water. Powerstats. Potentiometer. Iron-Constantan used for all thermocouples #20 wire. ,Outlet heater is the same type wire as inlet heater. Manemeter clean out type filled with water. Selector switch panel (four double throw switches). Towers 6','§' or lfi’ outside diameter aluminum tubing. Saturators lg' alumimm tubing. Thermometer. . Thermometer. 16. amass, \SQQ .\ NMMoQ | CU @ 8 fl e i w t 3 : let @8 a e o 3 he 4 4 E @ e a @ L. \ o b a h .m Q x \KU \< 0 Q. 3 Q\ Q 0 m\ k m. ; 19 tower m inch half themeusim twith 3e W Pigu'e 38R 5 838. 3883 so...“ 8&3 3.. Si poo-cosh O i is... .‘l. Ill‘l'nl. .4 caper.— 20 88R fl 8:3 Boss? oofi HE B» 5? Shannon .m .33.... 21. SUPPLIES The naphthalene for this investigation was from the Barrett Divi- son of Allied Chemical Corporation. The moth bills were listed as ' active ingredient 100%. 22 PROCEDURE Preparation of Naphthalene Spheres The preparation of the naphthalene spheres for the runs required a tedious series of steps. For the one half inch diameter balls the crude moth balls with molding marks were ball milled for approximately one hour. The cutting action was between the moth balls themselves and between the moth balls and the well. No grinding balls or rods were added. When.the machined balls were removed from the mill the ones that were not broken were nearly round but rough and about three forths inches in diameter. A small number of the machined balls, ap- proximately thirty, were put into a wire basket. 'The basket was low- ered into a pail of boiling water and agitated in the water for about ten seconds. The agitation was continued after the removal from.the water until the surface of the balls solidified. The short time in the boiling water melted only the surface of the balls. The cooled balls were screened on a one half inch screen with the sizes saved both plus and minus the one half inch value. A further selection was made by comparing the naphthalene with the one half inch diameter glass balls. An average diameter was determined by measuring a number of balls and averaging the values. The second size, the one forth inch balls, were made in two ways. with both methods of production the sizes sared were between the one forth inch and the 0.187 inch screens. 25 The first way was the method used for one half inch balls. The second. method was somewhat like one used by a former worker.1 In the present. investigation about forty grams of naphthalene were melted in two liters of water. After agitation the mixture was allowed to cool slowly to below the melting point of naphthalene. Many of the droplets of naphthalene retained their spherical shape. It was interesting to note that the size and shape of the vessel used appeared to influence the balls size distribution. The production by this method was very' slow because the number of one forth inch spheres found was quite limited. The third size, the one eighth inch spheres, were obtained in rel- atively good yield by melting the naphthalene in water. The sizes saved were between a 0.158 and 0.095 inch size screens. An average diameter for both groups of screened balls was taken as the average of the two screen sizes between which the fraction of balls was saved. Standardization of Rotameters The metering of air was done with either of two rotameters. The first had a capacity of twelve to forty-five cubic feet of air per unnute. To standardize this meter carbon dioxide was fed into the air stream at a weighed rate. Farther down stream the gas was analyzed hr percent carbon dioxide. From.this information the meter was calibrated. The second rotameter, with a capacity of two to twelve cubic feet of air per minute, was calibrated using three wet gas meters in-par- allel. This calibration was not made directly. A rotameter with a 24 slightly lower range was first calibrated with the wet meters. From the lower range rotameter the meter on the experimental unit was cali- brated. Analysis Method A number of analysis methods have been used by other investiga- tors for the amount of naphthalene vaporized into a gas stream. Among“ these methods were such ways as weighing the packed tower before and after the air was passed through.16 Another method was to pass the air over a bed of naphthalene and weigh the same amount of naphthalene; vaporized to saturate the air.1 A more refined but expensive method was the use of a Bookman DU spectrophotometer.1 For this investiga- tion the method decided upon was a modification of the saturator’nmthod. The difference in principle for this saturator was that condensa- tion rather than vaporization usually took place. 'The choice of comp densation or vaporization was dependent on the concentration of naphe thalene in the inlet gas and the saturator temperature. A saturator used in preliminary work was a tube packed with glass wool and cooled with an ice jacket. The results were not very reliable because of temperature variation and "wet air'. For these reasons a modified ap- proach was used. A tube packed with naphthalene and cooled by room; temperature was used to obtain the data. The temperature of the bed was usually lower than the saturation temperature of the sample of gas. 25 This caused the naphthalene to crystallize out in the saturator. Hav- ing the bed packed with naphthalene helped to seed out crystals thus prevented supersaturation of the gas. The temperature and pressure of the gas leaving the saturator were recorded. This informatioh along 8 smelt with the vapor pressure from.the International Critical Tables, of sample and the change in weight of the saturator allowed the concen- tration of the sample.to be calculated. To check for supersaturation a second saturator was set in series and the weight and temperature chedh- ed each time a run was made. As a safeguard to prevent naphthalene from crystallizing out in the inlet tube to the saturator, a heater was located at the top of the packed tower on the exhaust line. Ekpertlental Procedure With the equipment as described and the analysis columns in place the actual experimental runs were begun. The first runs were made using the six inch diameter tube. In order to reduce errors in.measuring bed‘ height and entrance effects the naphthalene balls were spaced with glass beads. These beads were nearly the same size and shape as the naphthalene spheres. A bed dilution method was previously used hyr‘ Bar-ilan.1 Three balls of glass to each ball of naphthalene were used in all three towers. The naphthalene and glass were added alternatelyy to prevent the lighter naphthalene from.rolling to the outside of the tube. The balls were added in approximately ten portions of each. After the complete addition the side of the tower was tapped to give a more compact bed. Before the bed was packed the air was heated to the 26 correct temperature. This required from one to two hours. Both the heater and air were then shut off and the bed packed as described. The air and heater were then turned on and the bed allowed to assume a constant temperature distribution. This took up to ten minutes. At a specified time the sample petcock was turned on and a sample of gas removed. Usually a sample of two cubic feet was removed over a period of about five minutes. The pro-weighed saturators were then removed and a second set of saturators were put in place. The second sample was taken in the same manner. After the saturators were shut off they were left in place while the temperature distribution across the in- sulation was read. Beth sets of saturators were weighed after comp pletion of the run. Runs were made over a range of velocities at the same bed depth and temperature conditions. After completing this series, runs were made to obtain similar conditions in the three inch‘ and one and one half inch tower. 27 DERIVATTONS AND CORRELATING RELATIONSHIPS kg Correlations (Reynolds number greater than 550) Derivations Basic eguation. (1.) jd-kgMgPfl {-17%}; 2/5.o.989 52%;- Assumptions:. 1 The above equation Page 987, Hougen and Watson. Reynolds number greater than 350. Rearrangement. (2.) kg - 0.989 (M) "“1 __cg__ (P2!) 2/5 ( 1"») Pt (’flt) Ratio of kg; .59 (5-) - (.221 (92. Lt; 2/3 ':§:7( (91 A P t2 Efii'g Assumptionsz' a. Viscosity constant. b. Diffusity constant. c. Pressure factor equal to total pressure. d. Same mean molecular weight. 28 Simplification. 1c .41 .59 (4.) 12,- ($1) (G 2) - 81 ( p2 ) (Eff) Assumptions: This simplification was justified for small Changes in total pressure. An increase in total pressure causes an increase in density. Carrel ating Rel ati onship Six to three inch diameter tower (5.) Tsi- (3%:1; - .47 <4) kga (131)0‘41 (G $59 0 I 2 u g (up?) (-5—) . .59 . u (D 2 ) (G2 ) ’59 (If?) 05") (6.) k a (D1 ReZ; .59 g (npa (3.1 k (8.) 52 -o.709 for Re2 ,2 R01 EggCorrelationz (Reynolds numbers less than 550) Derivations Basic equation. J D G ‘0051 k (9.) d-1.82< ) a gun: (I‘m/5 ( ) 9' (pDv ) Assumptions: Same as fhr equation (1). Rearran " 1 “m ‘ "5 (10.) 1‘ =1.82( G .ksmpt (/4. )2/5 g (%g G (pDv ) Ratio of k5: . 0.51 0.1.9 (110)1kiEEE_'( 1) P1 P2)2/5 ‘ s1 (ifs ’ (96313 1513 (T) Assumptions: Same as for equation (5). Simplification. .51 k e- as Assumptions: .49 ESE-3 Same as equation (4). correlating Relationships (Reynolds numbers less than 550) Six to three inch diameter tower. (12.) -< r51 (62) '49 2?: (23:) W) . .49.19 «my 51L?) (D 13%;; (GET) .49 .119 (15.) . D 1 Re?) ”52— R61) (14.) £5127 - 0.47‘ for equal Reynolds numbers 3 Six inch to one end one half inch diameter tower, .3?— 0.51% DP2 k (160) 1%— . 0.252 for equal Reynolds numbers , (using equation 15) Three inch to one and one half inch diameter tower. a7.) D 1 . 0.112 . . 5:2 .2 l (18.) kg - 0.494 , for equal Reynolds numbers . g1 (using equation. 13) 51 Ehual Velocity Correlations (Reynolds numbers less than 550) Derivations General. Us lbs. of gas passing through the tower Min. w. A (cross-sectional) x u ft.5 x p lbs. 5 min. fte (19.) "I A up we lb. moles of naphthalene vaporized min. Ratio of W. 1&- " .2. 32 P2 T1 A]. 111 p1 - D22 4 1r G '1‘ T D12 1-1.3- (15'1‘) 51 Basic equation. (21.) W8 kg ”A?“ Ratio of w (22.) :g . ngG‘Z QAPMQ E161 VIAlez Evaluation of 6;- . ‘57 surface is proportional to D2 ball. ball is proportional to D3 unit volume 5 19333232 is proportional to 1 unit volume ‘17" (25.) (2-41.” 1 5-1 ”p2 Evaluation of V . V1 . ‘ 2 V is proportional to Dt (21+. ) T2 . T (ITI— Sinplification of ratio. (.25) '12- kgzgzfif’z 031(1) ”342 31 L11191 Combination of (25) and (17). ;_2-_"_'_2-“ L2 4P2 Du (”tag 23-11; AP]. Dpz Dtl ) . (Dt: )2 (”ID z51' assumed concentrations equal-values were corrected to equal concentrations.) 33 Rearrangementggives (26) kg; c121. AP 2 . kgl 01-113 513'“:2 pm pl Cemhine (26) and (12)i then:shmpli§y 1.51 (27) ‘_£_1 D > ‘ ‘ L2 p2) Assumptions: 8.. 62 I Gi beAPl .APZ db.p1- 132 as Reynolds number less than 550 Combine ('22) and (121 3.122.123: ' (29) w lac . 1°; - Assumptions: a. . 32 a G1 d.. usvalues; b. Dig . 2 corrected to equal 41? 64 0‘0. D - o. A .0. L 2 1". ' 5h Qbrrel ating Relationship Three inch to one and one half inch tower —Ill 0.546 (from use of equation (27)) L2 " . -- s — a If 1.1 - 1.7'I thenba" 4-64 Equal Velbcity Correlation_s__ (Reynolds number greater than 350) Derivations - Combine (4) and (26) then simplify- , (50) .21 D . - L2 (5:; Assumptions: 8:.“ G1 I 32 504?]. IAPZ 1.41 d. p1 - re s. Reynolds number greater than 350 . Combine (25) and (4). _ _ . l.4l 2 .59 "IF-231443.213 ease ‘rd‘él 4.0- - ‘ - Emu -- (32) .311“ . , w l Assumptions: a. same as equation (29) except- b.D .o.h7 J51. _12. 1;; 1f- 1:13- 55 correlating Relationship 811 inch to three inch diameter tower J4 . 0.54-4- (from use of equation (50)) L 2 , - - If L2 I 12' thanLl III 4.1}. Equal Reynolds number Correlations —(any Reynolds number) Derivations Cbmbine either_(4) or (12) with (26) and 31111151111 1 (35) L D ——2 F92 - 1'1 Dp1 Assumptions: (equations used) Combine either (28) or (51) d with (35) and simplify 2 1'1 Dpz Dtl Assumptions: a. equations used b. equal Reynolds number' Correlating Using (55) and (54)the following was obtained. Relationships pwer pair LL L1 if 5-1.. 1%;- 6' 2.97' L98 6' to 5* 12' 5.645 1.87 2.78i 5.72 6' to l%’ 12' DATA TABLE I GAS ANALrsIs mm Run; Change in Weight (grams) First Sample Second Sample Average Exit Temperature (°B) First Sample Second Sample- Sat Sat Sat. Sank sen-.11 3.1.112 Sat.£1 sank Six Inch Diameter Tower la .106 .008 .095 .018 26.8 25.9 29.2 24.4 2a .125 .026 .107 .011 22. 5 20.6 25.8 20.6 5a .079 .005 .070 .025 50.5 50.0 55.5 50.0 4a .095 .002 .080 .001 28.5 27.5 28.9 28.0 5a .089 .004 .096 .005 27.9 27.5 28.5 27.5 6a .092 .002 .092 .005 28. 5 28.0 28.71 28.4 mree Inch. Diameter Tower lb .067 .011 .026 .045” 29.6 29.0 55.6 29.0 2b .060 .002 .044 .014 51.7 52.0 55.5 52.0 5b .050 -.006 .081 .007 24.2 24.5 26.5,» 25.0 4b .075 .005 .066 .015 25.8 25.5 28.4 25.8 5b .121 .002 .129 .001 29.2 29.0 29.5 29.0 6b; .091 .000 .092 .000 29.4 29.0 29.4 29.0 “lb .125 .002 .128 .000 26.7 26.5 27.1 26.5 IABLE I continued Run Change in weight (grams) Average EXit Temperature (°G) First Sample Second Sample First Sample Second Sample. Sat. Sat. Sat. Sat. Sat. Sat. Sat. Sat One and One Half Inch Diameter Tower 10 .067 -.001 .016 .019 .27.5 27.5 50.5 27.5 2c .085 .005 .011 .015 26.6 26.0 29.4 26.5 5a .060 .005 .045 .022 28.5 28.0 50.4 28.5 46 .072 .005 .040 .021 28.6 28.0 51.5 28.0 50 .064 .057 .041 .012 28.4 28.4 29.0 29.0 6c .145 -.012 .090 .014 26.0 25.8 28.8 26.0 7G .142 .004 .122 .011 26.4 25.5 28.5 25.5 8c« .117 .002 .117 .011 26.4 26.0 28.4 26.5 90 .051 .004 -.006 .016 27.5 26.5 29.4 27.0 100 .075 .012 - - 50.9 29.0 - - 116. .054 .001 .048 .005 28.6 28.5 50.0 28.5 126 .081 .002 .049 .002 29.8 29.5 50.6 50.5 15c .066 .008 .070 .021 28.1 28.5 28.5 28.5 14c .147 .075 .146 .054 25.1 24.7 25.8 25.4 59 TABLE I continued Total Sample #1 ’ Mole Fraction 222%” 3151233" ampl.°§§°e“’“§:3.1. #2 (mm 112.1 Gas . Six Inch Diameter Tower la 756.6 2.46 0.000478 0.000470 2a 754. 2 2. 58 0.000495 0.000479 5a 740.8 2.21 0.000481 0.000508 4a 759.1 2.25 0.000492 0.000454 5a 740.4 2.25 0.000470 0.000505 6a 740.0 2.25 0.000489 0.000490 Three Inch Diameter Tower 1b 742.9 2.21 0.000419 0.000560 2b 741.5 2.22 0.000455 0.000422 5b 741.6 2.24 0.000550 0 - 48 740.2 2.24 ' 0.000582 0.000595 55 758.9 2.24 0.000605 0.000652 60 741.7 2.21 0.000500 0.000505 7b 759.6 2.24 0.000571 0.000591 TABLE I continued Run Total Sample #1 A Hole baction; 2:23?" 3:331? Samplflfimwéizpl. 70 (mm Hg.) Gas 10 741.5 cm and ogfzfialf Inc}! mmgtSSoggg” 0.000252 20 757.2 2.24 0.000428 0.000218 5:: 745.2 2.25 0.000572 0.000547 4c 741.9 2.25 0.000417 0.000562 5c 740.2 1.11 0.000617 0.000465 60 745.1 2.24 0.000650 0.000480 70; 742.9 2.24 0.000620 ' 0.000588 80 741.0 2.25 0.000541 .- 90 741.8 2.25 0.000256 - 106 745.9 2.24 0.000470 - 110 745.1 1.12 0.000545 0.000525 12¢ 741.0 2.76 0/000414 0.000575 156 742.9 1.10 0.000625 0.000667 146 741.4 2.24 0.000607 0.000742 41. DATA TABLE II PACKED TOWER DATA Run Active Pressure Bed Air Void Insulation: Area Drop Depth. Rate Fraction At No. (ft.2) (cm 320) (111.) (ft.5/min.) Egg? fiyers Six Inch Diemeter Tower . la 5.72 5.8 12 59.5 0.40 6.7 5 2a 5.72 7.6 12 45.0 0.40 8.9 5 5a 5.72 0.6 12 9.1 0.40 7.8 5 4a 5.72 7.2 12 56.2 0.40 6.6 5 5a 5.72 1.7 12 12.1 0.40 8.5 4 6a 5.72 5.0 12 21.0 0.40 7.2 5 Three Inch Diameter Tower lb .659 10.7 4.5 ' 11.2 0.58 6.8 5 2b .659 10.8 4.5 11.2 0.58 5.6 5 5b .659 12.4 4.5 12.2 0.58 9.5 5 4b .659 10.1 4.5 10.2 0.58 8.1 5 5b 1.04 2.7 7.1 11.5 0.58 4.4 7 6b .878 9.9 6.0 9.0 0.58 7.0 7 7b .878 2.4 6.0 4.5 0.58 4.1 7. TABLE II continued Run; Active Pressure Bed Air Void At No. Area Drop . Depth Rate. Fraction. One of Layer Layers 2 - . 0 (ft. ) (01111120) (111.) (ft.5/min.) (1") One and One Half Inch Diameter Tower I 10 .097 5.7 107 Zea 0011’? " 3 2c .097” 4.1 1.7 2.6 0.47 4.4 5 5a .097 1.4 1.7 2.0 0.47 4.2 5 1‘07 .097 5.0 1.7 2.2 Ooh? A05 5 50: .097 0.2 1.7 .49 0.47 4.1 5 6:: .171 5.1 5.0 2.0 0.47 4.6 5 7e .171- 9.5 5.0 2.0 0.47 4.2 5 8a. .171 4.5 5.0 2.0 0.47,: 6.2 5 9c .0427 0.6 .75 2.0 0.47 6.2 5 100?. .0857 1.5, 1.57 2.0 0.47 6.2 5 0 11.: .171 0.9 .75 2.0 0.47 6.2 5 12¢ .171 17.8 5.0 4.0 0.47 - 0 15¢ .097 0.8 1.7 1.0 0.47 4.2 5 146 .097 0.6 1.7 .85 2.24 - 9 *Pure naphthalene 45 TABLE II continued Run Column Temperature First Sample Gas 72:? 42%;: “2229 4:22:22?" ”W _ - (mm 115'.) (#/ft.51 Six Inch Diameter Tower ‘ . la 121.0 117.1 5.9 760 (Assumed) 0.0685 2a 120.9 117.0 5.9 753.2 0.0678 5a 120.5 115.1 5.4 758.4 0.0685 4a 120.8 116.8 4.0 764.5 0.0689 5a 120.5 115.0 5.5 766.5 0.0690 60. 120.6 115.5 5.5 766.8 0.0691 Three Inch Diameter Tower lb 120.2 117.0 5.2 ' 759.6 0.0685 2b 119.9 117.0 2.9 748.4 0.0674 5b 120.8 117.5 5.5 747.4 0.0674 48 120.8 117.7 5.1 745.7 0.0672 50 120.4 114.8 5.6 756.9 0.0682 6b 120.6 116.1 4.5 772.9 0.0696 7b 119.7 114.8 4.9 760.1 0.0685 TABLE II continued Run Column Temperature . First Sample Gas Inlet Outlet Change Total Pressure Desslty (°r) (0:0 (°r) Main Tower ( mm Hg.) rt. One and One Half Inch Diameter Tower. ' 1e 120.2 117.8 2.4 756.1 0.0681 2o 119.4 116.7 2.7 742.2 0.0689 5s 119.5 117.4 2.1 754.9 0.0680 4o 119.2 116.9 2.5 750.5 0.0676 5e 120.4 110.2 10.2 742.8 0.0669 6c 120.0 114.6 5.4 760.0 0.0685 7c' 120.8 116.1 4.7 758.5 0.0685 8o 120.2 115.8 4.4 , 754.1 0.0679 90' 120.8 119.6 1.2 755.7 0.0679 10o 121.5 119.5 2.2 759.9 0.0685 11¢ 120.2 118.2 2.0 752.8 0.0679 12o 119.1 115.5 5.6 774.7 0.0694 15o 118.9 114.5 4.4 749.4 0.0674 14o 120.5 117.5 5.0 744.0 0.0670 TABLE II continued Run: Average Vapor Partial At A le Column Pressure Pressure of Average (m 38o) T . at Naphthalene Temp. (3'3 Average Temp. Exit Main Fraction:- . (mm Hg.) Tower of Sat. (mm Hg.) Six Inch Diameter Tower 1a 48.4 .70 . 565 .519 .496 23 48.5 .70 ~37) ~53} 390 5a 47.6 .65 .408 .628 .414 4a: 48.2 .69 .526 .545 .477 5'- 47.6 .55 ~57} .574 .455 6a 47.7 .66 .575 .568 .449 Three Inch Diameter To'wer lh~ 48.1 .69 .518 .461, .515. 2b 48.0 .68 .526 .479 .445 51: 48.4 .70 .262 .571 .558 «a 48.5 .71 .289 -"°7 55? 50 47.5 .65 .468 .720 . 568 6b 48.0 .68 .589 .572 .461 7b 48.5 .647 .442 .691 .576 TABLE II continued Run Average vapor Partial At le Column; Pressure Pressure of Average Temp. at Naphthalene Temp. (mm Hg.) (00) Average Temp. Ekit Main Erection. ' - (mm Hg.) . Tower of Sat. One and me Half Inch Diameter Tower 13 1'8.“ .70 e287 .1110 0545 2e 47.8 .67 .518 .475 .497 5C 118.0 .68 e280 Ola-2 e528 4o 47.8 .67 .515 .467 .498 5. 46.2 .59 .458 .776 .505 60 47.5 .65 .479 .757 $58 70; 48.0 .68 .470 .691 .401 80 A7e8 .67 .1119 e625 e226 90 1.9.0 .74 0195 0261 0641} 103' #900 .71} .357 0482 0544 110 48.4 .70 .408 .585 .467 120 4754 .65 .521 .495 .472 130 “7.9 .67 0469 e768 e390 ‘ 14o 48.5 .70 .502 -717 J98 mum's TABLE 111 Calculated Results Run Superficial Modified Reynolds l‘gx105 1x105 3 lass Numbers (#mole ) holes ‘1 Velocity (min.ft.2) 01088 Cir.) (m2) 1* fiTl-e) 0“ m Hg' A L 3:“ at) 0.1 Six Inch Diameter Tower 0 1a 858 778 1502 2.42 . 4.47 4.25 .0714 2a 1000 907 1517 2.96 5.59 5.0 .0741 5a 198 180 500 .670 1.05 1.15 .0965 4a 787 714 1199 2.57 4.22 4.04 .0766 5a 266 241 405 .841 1.56 1.40 .0826 6a 462 419 702 1.47 2.46 2.51 .0815 Three Inch Diameter Tower lb 980 417 672 5.50 1.12 1.17 .0851 2b 960 408 660 5.88 1.14 1.52 .0896 51: 1048 445 720 5.06 1.12 1.29 .0657 4b 871 570 598 2.51 .918 .961 .0716 51) 586 164 255 1.71 .650 .642 .111 6b 758 522 521 2.56 1.057 1.0 .0877 7b 594' 167 271. 1.89 .625 .625 .119 '17} is FY corrected to equal concentration and pressure driving force. TABLE III continued 4*“ ”1:3?“ ““1312?” ($5.325 , 1:12? 4 Velocity (min.ft.2) 01033 Inhibiftfi) A}: “fig-e ) (m m Hg. ) _p____Yau:;ized' (I) (v ) lo 971 0118231 One 1587f Inch ””33; To”T251 .274 .118 2o 889 187 555 5.57 .259 .274 .144 5e 694 146 277 5.45 .176 .201 .118 4c 755 159 502 4.44 .214 .252 .146. 5e- 167 55.1 66.6 2.57" .0702 .084 .562 _ 6o 697 146 277 4.89 .299 .299 .169 70 695 146 277 4.26 .295 .279 .148 8e 691 145 275 5.50 .254 .248 .125 9c 697 146 277 4.45 .122 .166 .155 100 698 147 279 4.79 .225 .192 .165 11c. 690 145 275 5.19 .255 .226 .110 120 1414 297 564 4.94 .599 .460 .085 15a 545 72.5 157 5.84 .145 .155 .524 14a. 285 59.4 115 5.56 .150 .121 .280 TABLE IV kg Correlations Tower Ball Reynolds kgxlO5 Exp. Cale. % Size Number fig 1‘32 Difference L111. ) (1110) g]- .151 Six to Three Inch Diameter Tower 6 514 550 1.21 5 241 550 5.0 .404 .47 -l5.4 6 514 250 .90 5 241 250 2.40 .375 .47 -20.2 Six to One and One Half Inch Diameter Tower 6 .514 500 1.06 15 .119 500 5.4 .196 .252 -15.5 6 .514 200 .75 1% .119 200 4.75 .154 .252 -55.6 Three Inch to One and One Half Inch Diameter Tower 3 .241 500 2.70 1% e119 500 5.4 0% 0,494 +1.21 5 .241 200 2.05 1% .119 200 4.75 .452 .494 -12.6 TABLE'V Ehual Velocity Correlation. Tower Bed Mass w x105 '5), Cale. ‘% Velocitg wl (In.) (Ins)iyhr ft.) ffiples O10H8 :?3 5/' Difference Min. . Read from. Corrected é/w pr Graph for Bed 'O/V Height ' Three Inch to One and One Half Inch Diameter Tower (Reynolds number less than 550) 5 4.5 1000 1.28 1.52 1 1 1% 1.7 1000 .285 .285 4.65 4.0 15.7 5 4.5. 900 1.19 1.25 l 1% 1.7 900 .265 .265 4.64 4.0 16.0 Six Inch to Three Inch Diameter waer (Reynolds number greater than 550) 6 12 1000 5.0 5.0 l l. 6 12 900 4.50 4.50 . 1- l 5 4.5 900 1.19 1.09 4.15 4.0 5.25 51 TABLE VI Correlttion at Banal Reynolds Number Tower Bed Reynolds w x105 'll ' Gale. ‘ Number 5/w (111.) (In.) 2:53.010118 or "62' Difference Read from. Corrected 5‘5 or Graph for Bed //" w I Be ggt i/w Six Inch with Three Inch Diameter Tower 6 12 200 1.21 1.21 . 1 l 5 6 200 . 75 .685 1.77 1.87 -5.55 6 12 500 1.78 1.78 1 l 5 6 500 .95 .891 2.09 1.87 +6.41 Six Inch to One and One Half Inch Diameter Tower 6 12 500 1.78 1.78 l l 1% 5 500 .47 4.55 4.09 5.72 +9.94 6 12 200 1.21 1.21 l 1 1%- 5 200 .545 .52 5.78 5.72 +1.62 6 12 150 .95 .95 l. 1_ 1% 5 150 0 e28 .26 50 58 5072 ‘5076 Three to One and One Half Inch Diameter T0wer 5 6 500 .95 .95 . 1 1 1% 5 500 .47 .47 2.02 1.98 +1.02 5 6 200 .75 .75 1 1 1% 5 200 . 545 . 545 2.12 1.98 +7.07 5 5 150 .60 .60 1 1 ~ 1% 5 150 .28 .28. 2.14 1.98 +8.07” 52 A, a Dp - pt I 5’ on sift-FF NSc a p I Pf~ - r, . Pha- - PB - 2n - P n2 T s V" - NOMENCLATURE cross-sectional area of column. diameter of particle» diameter of tower. diffusivity of vapor in gas. superficial mass velocity. mass transfer factor. mass transfer coefficent. packed bed height. molecular weight of nontransferred material. molecular weight of transferred material. mean molecular weight. Schmidt number A Dvp density' pressure faothrs Peclet number 22.! Pressure driving force. Do Vapor pressure of naphthalene at saturation. vapor pressure of’naphthalene at a partial pressure less than saturation; Absolute temperature (9K). total volume of packed section. NOMENCLATURE continued molar volume yield (moles) (min. ) yield corrected to equal concentration and pressure deriving force. air rate é lbs. 3 min. void fraction- surface per volume of bed viscosity 54 DISCUSSION jd Correlations The values of 3d calculated for all of the runs were plotted as a function of the modified Reynolds humber (Figure 6) and as a function: of modified Reynolds number corrected for void fraction (Figure 7). The purpose of the 3d plots was to show the agreement of‘the data—with; the data of other investigators. In order to compare the data to that of other investigators the plot made by Bar-ihan13 for 3d values against modified Reynolds number corrected for void fraction was re- produced on Figure 8. Bar-ihan included the work of several investi- gators. The portion of these reproduced curves was for jd values be- tween Reynolds numbers of one hundred to two thousand. Shulman's16 curves for 3d with and without the values corrected for bulk gas tem- perature were also reproduced. At a Reynolds number equal to two thousand Shulman's data showed practically no correction for temperature while at Reynolds number equal to one hundred the correction for 3d was about 0.2. Shulman's curve corrected for temperature gave the largest value of 3d and did not show a transition point. The curve of McCune and Nilhelm gave the lowest values of 3d. Vhlues from the present investigation fell be- tween the maxinum of Shulman and the minimum of McCune and Wilhelm. The present investigation showed a transition point in the 3d line 14 such as presented by Hougen and Watson. These lines did however have different slopes. The transition point as reported by Hougen and Watson. _ w T + A 9 if, 9 4.. Q. .0 9 .-1.. L— .5” e 4 . I iv 1 was at a Reynolds number of 550 while in this investigation the value was determined to be about 500. The difference in slopes of the work of this investigator from that of Hougen and Watson could have been partially due to the difference in temperature or particle size at which the data was taken. The comparison of the data of this investigation with that of to other investigations in general show fairly good agreement; The degee of disagreement among nearly all investigations seemed to indicate that the 3d correlation itself was not adequate or that all the factors influencing and explaining the different jd lines were not understood. kg Carrelations The next step toward similarity calculations was the k correla- 8 tion. All the values of k8 were plotted against modified Reynolds numbers. The advantage of similarity kg correlations over 3d corre- lations was that in scaling up on: the same side of the 550 Reynolds number the constants in the relationships cancelled each other out. Similarity also eliminated error in the determination: of some of these constants. For instance Shulmanm'correlated his data with:. Ja-(ksmr..)2/5. 0 ~56 ( G )(i-TDT) 1'1” 43:71.2); Hougen and Watson correlated with: “3 (pDv ) jd'i—Jk ”up (”I ) 2/5. 1.82( 0)"°51 57%) (Reynolds number less than 550) - 3d . kg Mm pr (1“ ) 2/5 -0.989, (ml) -,11 G? (pDv ) (;/A) (Reynolds number greater than 550) ’ The different lines on their plots reflect this diSagreement. The relationships derived in the derivations section were done as- suming Bougen and Watson's relationships. The results of these deriva- tions gave the following’relationships for kg. Egg-(221.; 0‘51 (G2 “"9 1 (D (\1 (Regnoldsplalumber less than 550) zg1 (Dp2 01) (Reynolds number greater.than 550) These relationships were used to check the agreement of the experimen— tal kg with kg calculated assuming Ho'ugen and Watson's 3d relationships. The results of the k correlations between the three and six inch: 8 diameter towers for Reynolds numbers less than 550 (Table IV) showed differences of -15.4% and -20.2% between calculated'and experimental. The scale—up in “through put” bf the larger tower was approximately twice that of the smaller tower. The correlations were shown in Table IV for scale-up .of one and one half inch to the six inch diameter tower. The increase in "through put' was four times. The difference between the calculated andexper- imental results were -15.5% and -55.6%. This increase in per cent difference may have been due to the doubled scale-up. The last scale-up made at Reynolds numbers less than 550 was from the one and one half inch to the three inch diameter tower. This like the first scale-up was only two fold. At Reynolds number of 500 the difference was only 1.11% but at 200 the difference was -12.6%. Hougen and Natson's relationships for the determinations of k8 have not fit the experimental data obtained in this investigation. By using the form of the equations derived from.Hougen and Watson’s Jd re- lationship with the best data, values for the coefficient of the Roy- nolds number have been obtained...I For the range above a Reynolds number of 550 the experimental coefficient has been found to be 0.75 as compared to Hougen and Watson’s value of .59. For the range below a Reynolds number of 550 the experimental coefficient has been found to be 0.565 as compared to 0.49. The comparison indicated that Hougen and Watson's6 coefficients did not adequately fit the system used in this investigation; For this reason before scale-up of a new system the exponents which core relate relationships should be checked for the specific system used. Correlations at Ehual Velocities The principle of similarity as applied to packed beds required certain conditions of the tower to be similar for scale—up. One of the conditions required was temperature similarity. *See derivations, 5:70 With temperature similarity the fraction of heat lost thr0ugh the walls of the towers should be the same for any two towers. The temper- ature and the concentration were interdependent. For example, if the final concentration were less, then less heat left the tower as latent heat of sublimation. In the derivations the ratios driving force and concentration;oo- curred. If they had been equal for all runs no correction would have been necessary. A correction was made, however, to compensate for the differences of both driving force and concentration. The two correc- tions opposed each other thus the overall correction was small in most cases. This indicated that the concentration.similarity tended to cor- rect itself for small deviation of concentrations The next correlation (Figure 10) was for moles of naphthalene vaporized per minute (w) against superfical mass velocity. Because of lack of data to obtain an experimental slope one fairly reliable point was established from.three points of data for the three inch tower and the slope was taken as the same as the slope for the one and one half inch diameter tower data. The results of the equal velocity scale-up from.the one and one half inch diameter tower to the three inch diameter tower showed devi- ations of 15.7%.at 1000 mass velocity and 16.0% at 900 mass velocity. The scale-up here was four fold. The last correlation on basis of equal velocities was between the six and three inch diameter towers. Gas capacities were in a ratio of‘ one to four. Deviations were 7.0%rfor 1000 mass velocity and 5.25%.for 6) + v 4 o . .a 4 s 900. These results showed an improvement overkg correlations. The relationships of Hougen and Watson were used in the derivation of the 'calculated' results. Correlations at Equal Reynolds Number The data taken for correlation at equal Reynolds number were taken at bed height assuming the scale-up factor to be two between tower diameters. The actual measurements of the balls gave a slightly different value of the scale-up factor. The results of scale-up between the six inch and three inch dia- meter tower gave -5.55% difference at Reynolds number of 200 and 6,41% at 500. The scaledup from the one and one half to six inch diameter tower which was twice the scaleeup just described gave differences of 9.94%, 1.62% and 5.76% at Reynolds numbers of 500, 200 and 150 respectfully. The scale-up between the three and one and one half diameter tower gave per cant differences of 1.02, 7.07 and 8.07 for Reynolds number of 500, 200 and 150 respectfully. The variation in differences could have been due to error in the experimental slopes or due to the use of Rougen and Watson's slopes. 65 CONCLUSI 0N8 In summary, the following results were found in this investigation. First, the data was shown by comparison with the existing 3d plots to be within the range of the results of other investigators. Second, the correlations of tower performance made using 1: ratios derived wholly: 8 from the equation: of chgen and Watson-.6 were found to be in agreement with the experimental work within an. average of 16.8%. Third, results from the correlations of kg showed that Hengen and Watson's 3d equations do not fit all gaseous diffusion controlled systems. For a specific system the coefficients should be determined experimentally. Pmrth, using the similarity relationships that apply to a diffusion process ' and Beugen. and Vatsonih 3d equation, correlations were made between the three towers at equal'velocities and at equal Reynolds numbers. The equal velocity correlations between towers were found to have an average difference from the calculated values of 10.5%. {the equal Reynolds number correlations resulted in an average of 5. 45% difference between: the exPerimental and the calculated values. Fifth, the conclusions that were drawn from the results showed an indication. that the less the j d relationships were involved in the correlations the obser was the agreement of the calculated and the experimental results. Last, it. was concluded the similarity application has possibilities as an applied: to scaledup. 67 The author suggests that future work on the subject of similarity scale-up could follow two lines. 1. The naphthalene system.could be used again with the following improvements: ' (a.) Determine a more correct area of the naphthalene by having special screens made to give the ball size at most 1 0.05 inch tolerance. (b.) Use an instant method of gas analysis such as gas chroma- tography. (a.) Pass the gas downward through the packed bed so that high velocities would not disturb the bed. (d.) Dry the air before use. (a.) Automatically controlled temperature for the inlet air. 2. A new syotem, preferably a chemical reaction controlled one could be selected. This would allow more of the similarity relations to be used and eliminate the use of the id type equations. AEPENDIX Sample Calculations The following sample calculation.does not include calculations that are elementary. 1: '2/5 jd equation: (1.) 3‘1 'fiM Nae k (22:221.; where g ' Nh - G55 P ln Ps~Pn2 3 1’11. 5 Mn 9,. _s - Pn1 --(P,.Pn) Substitution of kg (P. )1 2/5 (2.) 3d . A P - P Nsc T fMEP—‘dnz .. Assumption: Inlet concentration of naphthalene - 0 Diffusivity 5/2 a- (5) DV 3 0.0045 1 1 4. 1 My»? hr 73% (Gilliland's equation p. 257'ém1th' ) i - 0.067 cm.2 (for the eonditionsfiof this: 80¢. investigation) Schmidt number fl. " 2067 DVD 3d sample 3d . 112 an? 2 1.93 1 g 5072 ft. 1951;:le MEI-0 a- - 0.0714 (using equation (2) rearranged) 69- ExPonent Determination. (Reynolds numbers greater than 550) Form of equation. . (6). k 2 I (Re ) a .EET’Bfi’('RT:’) 3 Data. Tower Re. kg x105 ' 6' 800 2.58 3' 400 5.5 Exponent (a) determination. 2.2g - 0.241 (800 a 5.5, 0.511; (1:66; a- 0.75 (Reynolds numbers less.than-§50 Form of equation.. s (15) same form as used above. Data. Tower Re kg x105 5' 170 1.85 I. 1%)" 85 3. & Exponent Determination. 1.8g - 0.112 £110 5. 0.2 l 5 g a - 0-565 I'Derivations and correlating relationships. 9. 10. 11. 12. 15. 14. 15. 16. 17. 18. 19. LIST OF REFERENCES Bar-ilan H., W. Rosnick, Ind. Eng. Chem., 22, 515 (1957). Chilton, T. H., A. P. Colburn, Ind. Eng. Chem., 3Q: 1185 (1954). Chu, J3 D., J. Kalil, W. A. Wetteroth, Chem. Eng. Prog. 49,141, (1955 . Colburn, A. P., Ind. 1mg. Chem. 2_2, 967 (1950). D?mkohler, cg. Translated by a. w. Ludt, z. Elektrochem, 3g, . 1956). - Hougen, C. A., K. M. Watson, Chemical Process Principles, Part III, p. 987, John Wiley and Sons,.Inc., New York (1947). Hurt, P. 11., Ind. mg. 0hem..55, 522 (1945). International Critical Tables, vol. III, p. 208, McGraw-Hill, New York, (1928). Johnstone, R. EL, Trans. Inst. Chem. Ehgrs. (london), 11. 129-56 (1939). Johnstone, R. EL, M. W. Wooldridge, 'Pilot.P1ants, Models, and scale-up Methods in Chemical Engineering, 1 ed., McGraw-Hill Book Company, Inc. New Tank (1957). Lava, 11., A.I.Ch.E J., .l_., 224 (1955). lynch, E. J., c. R. Wilke, A.I.0h.s. J., _1_, 9 (1955). licCune, L. K., R. H. Wilhelm, Ind Flag. Chem. 51, 1124 (1919). Perry, J. H., 'Chemical Engineers' Handbook,‘ 5 ed., p. 594, McGraw-Hill Book Company, Inc., New York (1950). Resnick, W., R. R. White, Chem. Eng. Progr., 45, 477 (1949. Shulman, H. 1... J. E. Margolis, A.I.Ch.E. J., 5. 157 (1957). Smith, J. 14.. c. E. Schwartz, Ind. Eng. Chem., 1+5, 1209 (1955). Smith, J. 11., a. w. Fabien, A.I.0h.E. J., _1, 28 (1955). Smith, J. M., 'Chemical Engineering Kinetics,“ 1 ed. McGraw—Hill Book Company,.Inc., New Yank (1956). 71. SITY LIBPAF'ES “11‘ f'dH'Zr-HGAN ST A TE UNIVER ‘l ‘14) 1‘ 5 ‘1 \‘ 3196 \" (1 LL 1