INDUSTRIAL AND ENGINEERING CHEMISTRY
1124
average fraction of voidagr in thr path of fluid srgregating from zone 1 to zone 2 fluid viscositv. absolutr. lb. mass ’(ft.)isec.) “a function bf” Carman’s shape factor for securing the specific surface of nonsuherical oarticles. enuals (~.3 6 ~ ) ’3’ Vn2j 3 , A , by Leva (8) fluid density, lb. niass//cu. ft. true (not hulk) particle density, lb. niassjcu. ft. I
_
I
L I T E R A T U R E CITED
Blake, F. C., Trans. Am. Inst. Chem. Engrs., 14, 415 (1922) Brownell, L. E., arid Katz. D . L., Chem. Eng. Progress, 43, 537-48 (1947).
Burke, S.P., wid P l u n i n w . IT. R . , I m . Ex:. C m x , 20, 1196 (1928). Cnrman, I?. C., 7’rana. f i i s t . (‘hem, Brig. (1,ondon). 15, Pa1.t 1 . 15O-iiB (1937,.
Mass an
Vol. 41, No. 6
( 6 ) Chilton, T. El., and Colhuin, A. P., IXD.ENG.CHEW,23, 8, 9139 (1931). Furnas, C. C., Bur. U i n e s Bull. 307 (1929). Koeeny, Ber. Wien A k a d . , 136a, 271 (1927). Leva, M . , Chem. Eng. Progress, 43, 649-54 (1947). Leva, M., and Grummer, M.. Ibid.. 43, 633-8 (1947). Ibid., 43, 713 (1947). Leva, M., Grummer, M., et al.. Ibid., 44, 511 (1948). Ibid., 44, 619 (1948). Oman. A. O., and Watson, X. M., S a t l . Petivleum S e w s , 36, 44, Sect. 2, R795-802 (Nov. 1, 1944). (14) Parent, J . D., Yagol, S . .and Steinel, C . S., Chem. Eng. [’?ogress, 43, 429-37 (19473” (15) Rose, H. E., I n s t . Mech. Eng. Proc., 153, War Emergency Issue SO. 5 . 141-61 (194S’I. (16) Sullivan,’ R.R., and Hertel. K. L..J . Applied Phys., 11, 761-5 (1940); 12, 503-8 (1941); 13, 725--30 (1942). (17) Wilhelm, R. H., and Kwauk. >I.. Chem. Eng. Progress, 44, 2011s (1948). R X C E I V L DFebruary 7 . 1944
Transfer
T h i s paper deals w i t h mass t r a n s f e r between a n upward s t r e a m of l i q u i d and solid particles i n consolidated a n d in expanded, fluidized beds. T h e solid particles in question were 2 - n a p h t h o l a n d t h e l i q u i d was water. It is believed t h a t t h e mass t r a n s f e r results are applicable equally well t o heat t r a n s f e r u n d e r s i m i l a r physical circumstances. Mass transfer i s a componemt m e c h a n i s m in l i q u i d phase c a t a l y t i c processes, in leaching a n d adsorption operations, and in exchange processes such as occur in resin columns. T h e experimental t e c h n i q u e involved p a r t i a l dissolution of spherical and flake-shaped particles of d i f f i c u l t l y soluble 2 - n a p h t h o l in a r i s i n g stream of water. A precise anal y t i c a l t e c h n i q u e was developed f o r measuring t h e s m a l l concentrations o f 2 - n a p h t h o l in t h e e x i t s t r e a m i n v o l v i n g dye f o r m a t i o n a n d c o l o r i m e t r i c analysis. T h e measured variables were water flow rate, e x i t concentration, water temperature, p a r t i c l e a n d bed characteristics, a n d pressure drop. F r o m these d a t a c o r r e l a t i n g variables i n c l u d -
i n g J factor, Reynolds n u m b e r , f r i c t i o n factor, a n d d r a g coefficient were interrelated. T h e range of experimentat a n d correlative variables is: particleshape, modified spheres a n d flakes; p a r t i c l e size, 3/16, and i n c h modified spheres, 8- t o I O - and 14- t o 18-mesh flakes (UsS. standard sieves) a n d mixed sizes; Reynolds n u m b e r , 14 t o 1755 in fixed beds; degree o f expansion in fluidized beds, 36q6 voids in consolidated state t o i n f i n i t e expansion as represented b y a single suspended particle; S c h m i d t group, 1200 t o 1500; bed diameter, 4 inches; a n d consolidated bed depth, 5 t o 24 inches. T h e correlated results concerning mass t r a n s f e r a n d f r i c t i o n in fixed and fluidized beds are discussed a n d compared. T h e i m p o r t a n c e o f f r a c t i o n void a n d t h e effect of n o n u n i f o r m i t y o f flow p a t t e r n as u n i f y i n g relationships f o r mass t r a n s f e r in fixed a n d f l u i d ized bed a n d f o r single particles are discussed. Mass transfer per unit pressure d r o p in fixed a n d fluidized beds is also considered.
LEROY K. MC=GUNEIANDRICHARD W. WILMELM PRINCETON UNIVERSITY, PRINCETON, N
NOKG the many types of industrial processes that involve the interaction of solid particles with gas or liquid streams are catalytic reactions and catalyst regeneration, adsorption operations, exchange processes as in water treatment, and drying and dissolving or subliming. I n most cases the bed of solids is ‘,fixed” or confined in an immobile state within a particular apparatus. I n an increasing number of cases, the solids are not held immobile by mechanical restraints but are free t o move if the forces caused by a flowing stream 19ithin the bed so dictate. A bed of solids utilized in this unrestrained condition is properly called a fluidized bed, inasmuch as the solid phase behaves as a pseudoliquid and solids may be withdrawn from and added to the main body of the fluidized mass through pipes and valves much in the manner of a true liquid. I n either fixed or fluidized beds, mass transfer rate data are required for design purposes, particularly in processes in which external mass transfer is the prime rate variable. Mass transfer 1 Present address, E. I. du P o n t de Nrmours & Company, Ino., Wilmington, Del
J.
may also be an important fraction of the over-all resistance offered by several mechanisms in series or parallel, as can be the case in catalytic reactions. Mass transfer rates between gases and solid particles have been the subject of several publications. Gamson. Thodos, and Hougen (S),Wilke and Hougen (9),and Hurt (4)studied mass transfer between fixed beds of granular solids and floming gases. Resnick and Wiite ( 6 ) studied mass transfer between both fixed arid fluidized beds of solids and flowing gases. In each case experimental conditione Twre such that the process of mass transfer was steady state, or nearly so. Hougen and co-workers measured the rate of evaporation of water from wet porous granules during the constant rate drying period. Resnick, White, and Hurt measured the evaporation of naphthalene particles into various gases. KO previous work has been reported for mass transfer between liquids and beds of solid particles. The present paper presents the results of experiments on the rate of solution of 2-naphthol particles in watei \?lien in fixed
INDUSTRIAL AND ENGINEERING CHEMISTRY
June 1949
or fluidized beds. These experiments represent conditions in which the entire resistance to mass transfer may be assumed to reside in a film around the particle. THEORY
l n the analysis of the results of the experiments on dissolution
of 2-naphthol particles in water the following assumptions are made: The driving force for dissolution is the concentratlon difference across an effective film resistance surrounding the particle. Solute concentration adjacent to the solid is the saturation concentration. Dilute solutions are involved at all points and simplifying assiimptions may be made accordingly. The equations for computing liquid film coefficients and other derived variables for mass transfer and friction loss from the experimental data are well known and are reproduced here for local reference without derivation. The rate equation for dissolution is: G’FdC = kFaMACdV
(1)
With constant flow rate, uniformly distributed particles, and isothermal conditions, Equation 1 is integrated between inlet and outlet conditions of the bed. There is no limitation whether the bed of solids is fixed or fluidized. The following equation results: G’p(C2
- Ci) = kFaMACL,ifV
(2)
A convenient dimensionless parameter for relating the film coefficient, k F , to the physical pro erties of the li uid system is the J factor of Colburn ( 2 ) and 8hilton and Caburn (1). This parameter is defined as follows: (3) On the basis of the solution’s being dilute, the total flow rate of liquid and its molecular weight may be assumed that of the solvent alone. As a consequence the following equation may be written in terms of pound quantities:
(4) The modified Reynolds number by which flow conditions are defined and to which J factors are related is defined as follows :
1125
EXPERIMENTAL
Pellets and flakes of 2-naphthol were utilized as fixed and fluidized beds by placing them in glass columns 4 inches in diameter and subjecting them to a n upward stream of water. Restraining screens were used in the fixed bed experiments and a support screen only was used for the fluid beds. The rate of solution of the solids was computed from the measured water flow rate and 2-naphthol analysis of the effluent stream. Pressure drops were also measured in all experiments. The behavior of individual pellets was investigated in separate experiments.
Apparatus. The fixed bed apparatus is pictured in Figure 1. Water was supplied from the main through a constant head tank to the suction side of the pump. The pump discharged through either of two rotameters capable of metering with a minimum accuracy of 5% at the lowest flow rates and 1 or 2% a t higher rates, and having a combined range of 0 to 55 gallons per minute. A by-pass to the sewer was also located at the discharge side of the pump to facilitate flow control. The metered liquid flowed past a calibrated thermometer and then into a calming section of standard brass pipe 12 X 4 inches in diameter. This section, filled with inert spheres approximately s/16 inch in diameter, was installed to ensure a uniform velocit front into the test section. The test section consisted of a conical flanged, Pyrex pipe 4 inches in inside diameter, held in place by a pair of metal companion flanges a t each end. The bottom flange of the bottom pair and the top flange of the top pair of flanges were fitted with 30-mesh retaining screens and equipped with pressure taps at the periphery of each screen. The bed of solids was held rigidly in place by the screens. Surmounting the test section was a straight piece of 4-inch standard brass pipe 6 inches long, reduced to 2 inches. The liquid was eventually discharged through a combination ditching and sampling line. The total inventory volume of the piping above the test section was kept a t a minimum. The 6-inch length of large pipe in the takeoff section was considered necessary in order not to disturb the flow in the test section, and the reduction in diameter from 4 to 2 inches was made to provide mixing of the exit solvent The test section was made available for filling by loosening the top flange and removing the entire take-off section. Test sections of various lengths were installed to investigate the effect of bed height and obtain optimum experimental conditions for each of the particle sizes studied; 5-, IO-, and 24-inch sections were used. The pump was an all-bronze centrifugal type operating at 3500 r.r.m., with a capacity of 100 gallons per minute at 100-foot head. A 1 pipe and fittings were of standard red or yellow brass. For the fluidized bed experiments the apparatus was altered t o provide a 7-foot Pyrex test section and the retaining screen was removed from the top flange. The column was charged with solids
E
Pressure drop relationships for fked beds are defined through the modified friction factor:
I n fluid beds the hcight, L, has been taken (8) as L, in the calculation of f’ La is defined as:
La = L (1 -
e)
Figure 1.
K,
= ---
(8) (9)
A. E. C. D.
E.
F.
Mass Transfer Apparatus
W a t e r supply Constant-head t a n k Centrifugal p u m p , capacity 100gallons per minute By-pass t o sewer Rotameter, 0 t o 5 gallons per m i n u t e Rotameter, 5 t o 50 gallons per m i n u t e
G. H. 1. J.
K. L.
Thermometer 12-inch c a l m i n g section Glass test section Pressure tapped flanges Manometers Discharge a n d sampling line, e x i t t e m p e r a t u r e station
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
1126
Vol. 41, No. 6
A 25-ml. samale of B n a ~ h t h o lsolution was diluted with 50'ml. of 95% ethyl alcohol and made alkaline b y the addition of 1 ml. of 3 N sodium hydroxide solution. One milliliter Lb,) PS a, a, A, v. of the diazonium salt, a large excess for all 2Inch Inch Sa. Ft. Cu. F t . C u . Ft. ' l/ainch 0.251 0.121 1.374^X 1 0 - 3 4.792 X 10-8 79.55 naphthol concentrations encountered, was then J/lainch 0.189 0.081 0.7793 X 10-3 2.046 x 10-0 79.05 added and coupling took place immediately. '/sinch 0.1286 0.071 0.3442 X 10-3 0.6004 X 10-e 80.04 The dye remained in solution because of the relatively high concentration of ethyl alcohd, which is a n excellent solvent Table I I. Characteristics of Flaked Particles 1 2 3 4 5 6 7 8 for the dye. A small portion Nominal Av. ThickAv. Vol., Av. Length, Av. Area, Av. Length, DP, ps, Lb./ of the resultant solution was Size ness, Ft. Cu. Ft. Ft, Sq. Ft. Ft. Ft. Cu. Ft. stored for approximately 1 hour in a stoppered test tube 2.362 X 10-8 15.56 X 10-8 8.115 X 10-8 20.84 X 10-6 8.986 X 10-3 6.778 X 1 0 - 8 77.98 8-10 mesh 14-18 mesh 2 . 0 8 5 X 10-3 3.797 X 10-8 4.267 X 10-87.201 X 10-6 5.118 X 10-8 4.107 X 10-8 78.27 to allow time for destruction Figures in columns 3,4, 5, a n d 8 were determined by measurement of water displacement. Figures in columns 2, of the excess diazonium salt. 6, a n d 7 were determined b y micrometer measurement. This sample was then diluted 50 t o 1 in two steps with95yo alcohol and analyzed for per Gent transmittance in a Fischer electrophotometer equipped with a pair of microcells 5 mm. in inthrough a blind tee a t the top. The solids were discharged a t the side dianleter and a. wide-band filter peaking at 480 millimicrons. conclusion of the run by increasing the water velocity sufficiently A calibration curve for the instrument was prepared by determinato carry the solids out the discharge line. The high capacity of the tion of per cent transmittance of 2-naphthol solutions of several pump was specified for this purpose. known concentrations. The concentration of the unknown 2Materials. T a p water was chosen as the experimental liquid naphthol solutions was determined from this calibration curve. because of its availability. 2-Naphthol was selected as the The solutions do not follow Beer's law, presumably because of experimental solid on the basis of low solubility and precise the excess diazonium salt; the amount of this excess varied analysis of the resulting dilute solutions, high purity and stability, with different concentrations of %naphthol. The method gave ready availability a t low cost, amenability to pelleting without consistent results. Four different batches of diazonium salt lubricants or other foreign substances, and high density relative and 28 individually prepared 2-naphthol standards were used in t o water. 2-Saphthol of high purity was purchased in flake calibrating the colorimeter. The calibration data fell on a form. smooth curve and the least precise point showed a deviation of T o provide accurately sized solid particles of uniform characonly 2.3% from the concentration as determined by the best teristics, the 2-naphthol was pelleted into modified ball shapes in curve through the experimental points. At 50 to 1 dilution of the an F. J. Stokes Machine Company Eureka single-punch tablet prepared samples, concentrations from 0.0 to 0.140 gram of 2machine. No lubricating or binding agents were used in the pelnaphthol per 100 ml. of water covered a range of 65 to 14% leting operation. Three sets of punches and dies were used which produced uniform, rugged pellets l / 8 , 3/le, and 1/4 inch in transmittance, thus providing adequate sensitivity. nominal diameter, respectively. The average diameter was acSolubility. Accurate values of solubility of 2-naphthol are curate and consistent to within 0.001 inch and the average density essential for a proper calculation of the rate constant for mass remained constant within 1.5y0. diffusion. Values in the literature were found t o be in disagreement with each other to an extent greater than could be The characteristics of the pellets taken singly are given in tolerated. Therefore solubilities a t different temperatures were Table 1. determined in this work. Standard procedures were used and I n order to extend the range of particle size and shape, a portion it was determined that, within the particle size range studied, of the distilled flake 2-naphthol was screened on U. S. standard size has no effect on solubility. The results, which are in agreescale sieves for 8- to 10- and 14- to 18-mesh fractions. These ment with those listed by Seidell(7), are given in Table 111. flakes had approximately the same surface appearance as the ballshaped pellets. The average thickness for each of the two sizes The data fall on a straight line when plotted as logl0C" us. was determined by micrometer nieasuiement of 200 particles in 1/T. The equation of the most probable line, determined by the each size range. The average volume per particle was determined method of least squares, is: by measurement of the water displacement of groups of 100 to 200 particles each, three groups for each size. Water absorption by loglo (100 C*) = 5.8833 -_1195.81/T0 IC, (10) the material was determined and found to be negligible, as was loss of material by solution during the period of the measurement. All solubilities were calculc ted using this equation. It was assumed for the purpose of area determination that the Diffusion Coefficient. Tn evaluate the Schmidt group the average particle was a squaIe prism and, knowing the average diffusivity of 2-naphthol in water must be known. S o values thickness and average volume per particle, an average particle length was calculated. An average area was then readily calculated, when the dimensions of the particle were laown. I n determining the flake particle diameter, DP,for use in the Reynolds number, an average particle length was determined by micromTable 1 1 1 . Solubility of 2-Naphthol i n Water eter measurement. The average D P was then calculated as the t , c. C", Gram/100 M I . arithmetic mean of the three dimensions assuming, again, a square prismatic configuration. The DP arrived at by this method Authors 3 1 25 0,0928 23.20 0,0680 was slightly lower ( 3 to 5%) than the arithmetic mean of the 1G.24 0 0526 mesh openings in the particular sieves involved. 15.55 0 0501 Table I.
't-
Characteristics of Pelleted Particles
1
The pertinent physical measurements for flake 2-naphthol are presented in Table 11. Analysis. The solubility of 2-naphthol in water is of the order of 0.5 gram per liter and it was desirable t o analyze with precision solutions between this low-valued upper limit of concentration and zero concentration. A colorimetric method of analysis was developed, utilizing the coupling reaction between 2-naphthol and benzene diazonium chloride and producing a water-insoluble orange-red azo dye. The accuracy of the method was ~ 2 . 0 % .
12.5 28.1 29..5
Seidell
Table IV. t,
0,044 0.074 0,0876
Diffusion Coefficient for 2-Naphthol in Water
c.
21.0 18.15 15.45
CO
G./lOd M1. 0.0643
Co = initial cell concentration.
0.0522 0.0354
sq. cm.jnay DR 0.7731 0.7490 0.7104
June 1949
INDUSTRIAL AND ENGINEERING CHEMISTRY
1127
were found in the literature and this property was therefore measured. The method used was that of McBain and Lui (6),using a diffusion cell with a Pyrex fritted diffusion membrane of porosit F. as designated by the manufacturer, the 6ormng Glass Works. The cell was calibrated using 0.4 N hydrochloric acid, the diffusion coefficient for which is known (6) with high accuracy. The diffusion determinations were made a t several different temperatures with test solutions that were a t or near the saturation concentration. Thus diffusion took place from a saturated solution into fresh solvent through the membrane, a set of conditions very similar to those in the liquid film surrounding the particles. The diffusion data are compiled in Table IV. Experimental Technique. FIXEDBED. In fixed bed experiments the test section was firmly packed with particles in accordance with a standardized procedure. With the top section of the apparatus in place, the bed was held firmly between the upper and lower retaining screens, thus preventing particle motion within the bed. Water from the pump was by- assed to the sewer until its temperature ha$ stabilized and was then directed through the test section a t the desired flow rate. No attempt was made t o control water temperature a t any arbitrarily selected value, though temperature constancy during any one run was important. After 4 to 5 minutes' operation, temperature conditionn within the test section had stabilized and sampling was started; 500-ml. samples of liquid from the discharge line were slowly collected over a period of about 30 seconds and generally six such samples were obtained for each run a t constant velocity. When analyzed for 2-naphthol these provided a minimum of six concentration determinations for each run. Fraction void for each type of packing was determined in a separate apparatus consisting of an 11.5-inch piece of standard Pinch pipe mounted vertically and sealed a t the bottom except for a needle valve. The void volume of the empty pipe as compared to its void volume when packed with solids was measured by filling with water. The volume of water required to fill the packed apparatus was used in computing the fraction void. This procedure was used in preference to drainage experiments. Three different column lengths were used to determine the effect, if any, of bed height on the mass transfer rate constant and to avoid concentration extremes in the effluent liquid. Slight decrease in pressure drop was noted as each run progressed, due t o particle diameter shrinkage, and an average of the several readings was used for calculation purposes. The pellet surface, originally smooth and free of cracks or pits, remained substantially unchanged during the mass transfer runs. A maximum diameter shrinkage of 2% was allowed before the pellets were replaced in the column and it was observed that the diameter shrinkage was uniform within the bed and over the entire surface of the pellets. FLUIDIBED BED. The experimental procedure for fluidized beds was similar to that for fixed beds.
1128
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
.IO
,
’
,
1
I
I
I
I / I ,
100
loo0
Figure 3.
I Factor for Fixed Beds
The test section was Pyrex pipe 7 feet by 4 inches in inside diamet,er with 110 top restraining screen. A weighed amount of solids was charged through a blind t,ee at, t,he top of the column, which was partially filled with water to prevent particle breakage. The amount of solids charged ivas the minimum required to ensure nieasurable concentrations in the exit stream while at the same t,ime allowing t,he maximum amount of bed expansion. For each particle size t,he initial velocity run nTas made with the bed still in a consolidat,ed state. All subsequent velocities were sufficient to fluidize the bed t o various degrees of expansion. Sampling procedure and analyses Twre the same as in fixed bed runs. Bed height, pressure drop, liquid temperature, and fiow rate were noted. Because of t,he considerable liquid holdup in the 7-foot column, an appropriate time lag was introduced before sampling after each change in velocity between different runs. Operation of the apparat,us \vas very st.ahle. Pressure drop remained constant duriug each run. Bed height in the expanded state Fas sensitive t o flow rate and because the latter was precisely controllable the bed height also was stable. With modified ball-shaped pellets there was always a vory sharp inferface between the top of the bed and the clear liquid above. The 8- to 10- and 14- to 18-mesh flake material, because it contained a range of particle sizes, had a more diffuse interface but t’he bed height was still readily clctermined. With mixtures of part,icle sizes, the smaller particles were always a t the top of tho bed. When the size difference was clearly defined, there was a distinguishable dividiiig line between each size, even at high values of fraction void. Considerable motion of a seemingly random nature was imparted to the particles, particularly at the higher velocities. Particles were observed to travel up and then down almost the entire length of the bed. Other particles rcmained relatively stationary for some time. At high degrees of expansion there was observed to be a greater population of pellets a t the n-all than in the center of the column. With t,he onset of fluidization each particle arranged itself in the liquid stream in such a manner as t,opresent the maximum resistance to flow-the fialces were horizontal and the “belt” around the ballRhaped pellets was also horizontal. X o evi-
vs. Modified Reynolds
Number
&e
Figure 2. Mass Transfer Coefficients for Fixed Beds vs. Modified Reynolds Number
Vol. 41, No. 6
dericc~of forccs or renotions kiet\veeri particles was noted except when a ball-shaped pellet, approached another pellet from directly above. .hi instanr before thr expected collision the two particles
formed a doublet pair and neatly inverted, the original top pellet beconling the bottom pellet,. The bottom pellet then cont,inued its course downward. SINGLE PARTICLES. In order to simulate conditions exist,ingin a bcd a t infinite expansion, experiments were performed with accura.telyn-eighedsinglepelletsatvelocities justhigh enoughto keepthe pellet suspended in the column. This condition was stable arid runs of approximately 50 minutes’ duration mere made n-ithout altmation in the velocity. During all but averysmallfractionof the total run time, the pellet assumed a position very close t o the column wall at a distance of 50 to 200 cm. above the bottom retaining screen. Similar runs with single pellets were also made at, lonw velocit,ies ivith t,he pellet resting on the bottom retaining screen. These single pellets were recovered from the column by discharging them out the top into a cloth trap. They were desiccated for 24 hours and weighed once again to determine thc weight, loss.
Figure 4.
Fixed Bed Mass Transfer Data
June 1949
Figure 5.
INDUSTRIAL AND ENGINEERING CHEMISTRY
IYRe
Modified Friction Factor for Fixed Beds vs. Reynolds Number RESULTS
Range of Variables. Measurements in fixed and fluidized beds included the following variables: exit concentration, water temperature, water flow rate, pressure drop, bed depth, and particle and bed characteristics. Computed variables derived from these measurements included k ~ J ,, N ' R ~f,', K ~ Pand , Kap. Single particle experiments were also conducted and for these weight loss in place of liquid concentration changes was measured. The range of major dependent variables was as follows: Fixed Bed Particle diameter, 1/14 inch to 14-18 mesh Particle shape, modified sphere and flake Bed depth, 5 to 24 inches Modified Reynolds number, 14 to 1755 Temperature, 13Oto 18' C. Schmidt number, 1250 to 1500 Fluidized Bed Particle size and shape as above Bed characteristics, uniform and niixed bed& Fraction void, 0.50 to 0.95 Modified Reynolds number, 6.8 to 670 Temperature, 16.1Oto 18.6' C . Schmidt number, 1200 to 1326 Single Particles Particle diameter, ' / I to 1,'s inch Particle shape, modified spheres Mode of operation, at rest to fully wspended Reynolds number, 31 t o 990 Temperature, 14.5Oto 18.4' C. Schmidt number, 1210 to 1420
1129
There appears to be no significant effect of particle size or shape when the data are plotted in this manner, even though a wide range was investigated. The two equations for J are the most probable lines as determined by the method of least squares for the data on the spherical pellets. The data on the 8- to 10- and 14- to 18-mesh flakes fall so close as to be well within the accuracy of determination of their physical characteristics. Three different bed heights were investigated and no effect on either Icp or J was noted. COMPARISON WITH PREVIOUS FIXEDBED Mass TRANSFER DATA. KO previous data for fixed bed mass transfer in solid-liquid systems are available in the literature. The most extensive work on solidgas systems is that OF Hougen and his co-workers (3, 9), who found that the experimental results from ten different particle sizes at temperatures ranging from 80" to 160" F. over a range of N ' R ~ from 45 to 3800 could be successfully correlated by means of J factors. Hougen and co-workers evapoModified rated water from porous particles into a gas stream during the constant rate drying period. The Schmidt number for the air-water mixtures used in their experiments varied from 0.61 to 0.62. The data are represented in Figure 4. Inasmuch as the Schmidt number for the present solid-liquid investigation ranged from 1200 to 1500 as compared with the above solid-gas range of 0.61 to 0.62, the solid-liquid data repre-
--.
80 60
---czi o
$
-kF
.
lV4" PELLETS -
6-10
~
MESH
a 16181
"
30
20
IO
IO
Figure 6.
100
Mass Transfer Coefficients for Fluidized Beds vs. Modified Reynolds N u m b e r
Fixed Beds. All experimental data and computed results are compiled in Table V. MASS TRANSFER DATA. Mass transfer coefficients plotted in Figure 2 as log,,(kr us. loglo N ' R ~are ) straight lines, a separate line for each particle size. k~ is a function of (N'~J0.60. A more general and proper form of displaying k~ is through the dimensionless J factor, which takes into account system characteristics and their variation with temperature. Figure 3 presents this factor as loglo J us. log,, i V ' ~ e . A single smooth curve is obtained. However, for convenience in use, the data may be represented by two straight lines: For l V ' ~below B 120:
J = 1.625 ( N ' R ~--O*5o7 ) For
iL"R6
(11)
above 120:
J
=
Figure 7.
0.687
("E$)
(12)
J Factor for Fluidized Beds Reynolds N u m b e r
VI.
Modified
1130
INDUSTRIAL AND ENGINEERING CHEMISTRY
rc 0
L
Vol. 41, No. 6
June 1949
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
sent a severe test of the ChiltonColburn analogy using the Schmidt group t o the a/s power. An inspection of Figure 4, in which the gas and liquid systems are graphically compared, indicates that the Only serious differis in the ‘lope Of the two lines for higher values of Figure contains a @;raphical comparison of the authors’ data with those of Resnick and White (6) and Hurt ( 4 ) , both of whom evaporated naphthalene into flowing gas streams. H~~~ reported no data on per cent voids and Resnick and White have recalculated his data in the form of J factors, using the particle characteristics found in their own investigation. It is apparent that among all investigators two sets have found an effect of particle size and two others have not. This discrepancy remains to be resolved. PRESSURE DROP IN FIXED BEDS. Pressure drop datain the form of amodified friction factorReynolds number curve are preFigure 8. Fraction Vold sented in Figure 5. A comparilWodified Reynolds son with Figure 3 for comparable Number Beds for mass transfer experiments shows that pressure drop data scatter more than do mass transfer data. A similar observation was made by Hougen (3)and co-workers in gas-solid studies. I n the experiments of Figures 3 and 5 the beds were repacked between runs, and although the surface area within the bed could be calculated accurately, it is likely t h a t bed configuration changed somewhat, The scattering of the pressure drop data as compared to the mass transfer data indicates that pressure drop is very sensitive to configuration and mass transfer rate is less so. Fluidized Beds. All experimental data and computed results for fluidized beds of uniform particle sizes are presented in Table VI and for mixed sizes in Table VII. MASSTRANSFER DATA, The mass transfer coefficient, La, is related to Reynolds number in Figure 6. The data for the various particle sizes and shapes may be represented in part by a straight line with a variation as ( N ’ R ~ ) O . ~ ~ .The data passed through a maximum for runs carried t o high degrees of expansion. Figure 7 represents the data as J factor versus (N’RJ with the fraction void, E, indicated as a third parameter. On fluidization, J factors deviate from the fixed bed curve. The value of Reynolds number a t which the deviation commences is different for each particle size and agrees with the Reynolds number at which fluidization begins as indicated by pressure drop data. The trend of J away from the data for fixed beds continues as the bed further expands until the limit, as determined experimentally for single suspended spheres, is attained. The limiting line for single suspended flakes ( E = 1.0) was obtained by modest extrapolation of fraction Figure 9. void and mass transfer data. Particle size is a parameter in this plot, as expected because parti-
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cles of different size fluidize a t different Reynolds numbers. An effect of particle shape is also noted between spheres and flakes. Fluidized flakes oriented themselves horizontally. The effect of initial bed height on mass transfer during fluidization was studied and none was noted. From Figure 7 i t is evident that, a t a given velocity or Reynolds number, a fixed bed is a more effective instrument for mass transfer than the same bed in a fluidized condition. PRESSURE DROPAND FRACTION VOID IN FLUIDIZED BEDS. The observed data for variation of fraction void with Reynolds number are presented in Figure 8. These results, as well as pressure drop-fraction void-Reynolds number relations, are in quantitative agreement with the correlation of Wilhelm and Kwauk ( 8 ) for the fluidization of solids in liquids and are therefore not further treated here* GENERALIZATION OF FLUID BED RESULTS.It would be desirable to extend a t least to a limited degree present mass transfer data to systems with other liquid and solid characteristics than those here investigated. This may be done by the use of two relationships. The first is given in Figure 9, which is a plot of log J versus log N ’ R s / f ( = N ’ R ~ ~ / K Awith P ) separate lines for spheres , and granules. The second relationship is that relating K A ~KA,,, e, and N ’ R in ~ Figure 14 of Wilhelm and Kwauk (8). The following is a procedure for estimating the J os. N‘R
