MOSHE BAR-ILANl and WILLIAM RESNICK2 Israel Institute of Technology, Haifa, Israel
Gas Phase Mass Transfer in Fixed Beds at Low Reynolds Numbers Important design information for a number of unit operations
A
KNOWLEDGE of the mass transfer rates between a bed of packed solids and a fluid flowing through it is required in many chemical operations. This information is indispensable in such diverse applications as drying, absorption, reaction between a solid and a liquid or 1 Present address, Consolidated Refineries, Ltd,, Haifa, Israel. 2 Present address, Research Department, Standard Oil Co. of Indiana, Whiting, Ind.
4. Solution of liquids contained in porous particles into other liquids (73) 5 . Mass transfer in a solid-gas reaction (27).
gas, extraction, and various other exchange processes. Previous studies on mass transfer in packed beds were undertaken by several methods :
Because of the interrelationships between heat and mass transfer, information can be obtained concerning the mass transfer characteristics of a porous bed by measuring the equivalent heat transfer. The heat and mass transfer factors, Jh and Jd,developed by Chilton
1. Sublimation of solids into gases (75, 20)
2. Evaporation of liquids from porous particles into gases (70, 74,22, 24) 3. Solution of solids into liquids (5, 7,8, 79)
I
0 .I
JD
OR JH
o,or
-
0.00
Figure 1.
I
I
1
1
1
1
1
-
0.00494
I
1
l
1
1
,
1
I
I
I
I
I l l ,
I
I
I
I
I l l
Comparison of previous mass transfer and heat transfer data with experimental data in fixed beds
Spheres and cylinders; 2. McCune and Wilhelm. Haugen, others. Pellets and cylinders; 3.McCune and Wilhelm. Flakes; 4. Dryden, others. Pellets; 5. Authors. Pellets; 6. Authors. Granules; 7. Evans and Gerald. Granules; 8. Satterfleld and Resnick. Spheres; 9. L6f and Howley. Granules; 10. Eichhorn and White. Spheres; 1 1. Grootenhuis, others. Spheres
1. Chu, others.
VOL. 49,
NO. 2
FEBRUARY 1957
313
and Colburn (7, 3) were almost numerically equal (9,27). Heat transfer measurements in beds of porous solids have been made (4, 6, 70, 72,78, 27) and can be converted into equivalent mass transfer factors. Many of these data are presented in Figure 1 in which Jdis plotted us. D,G/p(1 a). This plot shows wide discrepancies among the results of the various investigators. The major discrepancy is the presence of the particle diameter as a parameter in the work of Lof and Hawley (78), Eichhorn and White ( 6 ) , and Grootenhuis, Mackworth, and Saunders (72),all of whom measured heat transfer characteristics of granular beds, and the absence of a particle diameter effect in the results of other investigators (2, 8, 70, 73, 79, 24). Resnick and White (20) and Hurt (75) measured mass transfer in porous beds by sublimation of solids into gases and also found that the particle diameter appeared as a parameter. Some doubt exists as to the numerical accuracy of the results of Resnick and White due to the close approach to the saturation conditions obtained in the gases exiting from the bed. Hurt did not present sufficient information on the particle and bed properties to permit an accurate calculation of the mass transfer factor. However, the existence of particle diameter as a parameter for their results appears to be well established by their data.
-
Previous Work
Gas Phase Mass Transfer. Gamson, and others (70) and Wilke and Hougen (24)studied the rate of evaporation of
water from spherical and cylindrical pellets into gas streams. Shallow beds were used and as a result there exists the possibility of large entrance and exit effects. The Reynolds number ranged from 50 to 4000. Taecker and Hougen (22)extended this work using Raschig rings, partition rings, and Berl saddles. They determined J h and converted this to equivalent J d values by the use of the ratio J h / J d = 1.076. The Reynolds number ranged from 70 to 20,000 with most measurements made between 250 to 3000. Hurt (75), Resnick and White (20), and Chu, Kalil, and Wetteroth (2) vaporized naphthalene into air streams and measured the rates of evaporation. Hurt also measured rates of adsorption and desorption of water from air. Resnick and White obtained conditions near the saturation in the gas leaving the bed with the resultant possibilities of magnification of experimental errors. Because Hurt reported incomplete bed characteristics, his data were recalculated using bed data as obtained by Resnick and White. Chu and others vaporized naphthalene from naphthalenecoated Celite cylinders and lead shot in their fixed bed measurements. Bed heights were adjusted so that the exit gases were not saturated over 90%. As a result, very small bed heights were necessary when the smaller particles were used. Particle diameters ranged from 0.18 to 1.4 cm. ( 2 ) and the particles ranged from 0.04 to 1.0 cm. (75,20). The Reynolds number were from 7 to 670 (75), 0.8 to 25 (ZO),and 50 to 2000 ( 2 ) . Mass Transfer in Liquid Phase. McCune and Wilhelm (79) measured
mass transfer rates of 2-naphthol Fellets and flakes into water streams. They used ample bed heights, had adequate knowledge of the geometric area of the particles, and worked at conditions sufficiently removed from saturation. The Reynolds number range was from 14 to 1765. They obtained one line (Figure 1) which correlated all their data for pelleted material and a second line €or the two flake sizes used. Gaffney and Drew (8) carried out a study similar to that of McCune and Wilhelm in benzene-salicylic acid, n-butyl alcohol-succinic acid, and acetone-succinic acid systems using pelleted particles. The Reynolds number range was from 1 to 800. Hobson and Thodos (73) passed water through a bed of Celite spheres which had been soaked with a saturated solution of water-isobutyl alcohol or water-methyl ethyl ketone. Measurements were made of the variation of effluent concentration with time. Transfer rates were calculated at a zero time. Evans and Gerald (7) measured mass transfer rates by passing water through beds of granules o€ benzoic acids at low Reynolds numbers. Heat Transfer in Gas Phase. Lof and Hawley (78) determined the value of the coefficient of heat transfer between heated air and beds of loose grax7el by unsteady state heat transfer measurements, They reported a volumctric heat transfer coefficient as a function of air mass velocity and particle diameter. The present authors recalculated these data to a J h factor and have assumed a value of 0.8 for the sphericity of the particles. On this basis the value of u, square feet/cubic feet of bed, was cal-
Q2?
Figure 2.
Flow sheet of equipment-analysis
by saturators
1 . Pressure reducing valve; 2. Pressure gage; 3. Valve; 4. Dryers; 5. Copper coil; 6. Oriflce; 7. Reactor; 8. Saturator; 9. Gas meter;
3 14
10. Constant temperature box; 1 1. Manometer
INDUSTRIAL A N D ENGINEERING CHEMISTRY
culated to be 157, 105, 60.6, and 38.9 for their nominal sizes of a/*, */2, 1, and ll/z inch particles, respectively. The Reynolds number range was from 37 to 350. I n order to compare Jh with J d it was assumed for these and the following data that Jh was numerically equal to Jd.
Eichhorn and White ( 6 ) and Grootenhuis, Mackworth, and Saunders (72) carried out steady state measurements by two widely differing procedures. Eichhorn and White passed air through beds of spherical plastic particles which were heated continuously by dielectric heating. Particle diameters ranged from 0.01 to 0.084 cm. and the Reynolds number range was from 1 to 18. Grootenhuis and others passed air through porous metal plates which were heated continuously by radiation. The particle diameter range was from 0.00404 to 0.04 cm., and the Reynolds number ranged from 2.5 to 180. I n general, from the brief review, the data until now available for mass transfer in the liquid phase and for heat transfer appear to be more reliable than those available from the measurement of mass transfer in the gas phase. I n the present investigation, an attempt was made to eliminate the causes of inaccuracy for the gas phase mass transfer measurements and to establish, by reliable data, the effect of particle diameter on the mass transfer factor. Mass transfer characteristics were determined by measuring the rate a t which naphthalene particles in a fixed bed vaporized into air passed through the bed. For a high bed height which would minimize entrance and exit effects with the close approach to saturation normally obtained with high bed heights, it was necessary to use a dilute bed. The bulk of the bed consisted of inert material of size and shape similar to that of the naphthalene particles which were used as the active vaporizing material. Geometric area of the active material was accurately known. Analytical methods used were quick and resulted in a negligible change in active area in the bed during the time of the run. Hence, the present results are probably free of the various objections which can be raised with previous measurements of mass transfer in the gas phase.
Figure 3.
Flow sheet of equipment-analysis
by spectrophotometer
1. Pressure reducing valve; 2. Pressure gage; 3. Valve; 4. Dryers; 5. Coppercoil; 6. Orifice; 7. Reactor; 8. Clamps; 9. Sample cell; 10. Constant temperature box; 1 1 . Manometer
structed of 1-inch wood, was covered with '/pinch Celotex for insulation purposes. The internal dimensions were 200 X 90 X 90 cm. I t was equipped with doors and a window. Air within the thermostat was circulated internally by a fan which drew air from the top of the box through a duct and discharged it a t the bottom. The thermosensitive element was a J-tube which operated a sensitive electronic relay which, in turn, activated the heating elements. The temperature variations a t any one point were no greater than = ! ~ 0 . 0 5 C.~ and the maximum temperature variation from top to bottom of the box was no greater
than 0.15' C. All runs were made a t a temperature of 30.5" C. The reaction air was passed through a coil in the thermostat duct in order to bring it to the thermostat temperature and was then metered through a calibrated orifice before entering the column containing the bed. After passing through the bed, the air was taken for analysis. Figures 2 and 3 show the diagrams if analysis was by the saturator method or the ultraviolet absorption characteristics of the air sample, respectively. I n the analysis by the saturator technique, either part or all of the air passed through the saturators which saturated the air with naphtha-
8. 3
Description of Apparatus
Flow sheets of the equipment are shown in Figures 2 and 3. Air taken from the laboratory supply line was reduced in pressure to approximateIy 10 pounds per square inch gage. The air rate to the porous bed was adjusted by either a needle valve or a diaphragm valve and then admitted to two drying columns filled with silica gel before entering the constant temperature box. The constant temperature box, con-
3
Ip Figure 4.
Dimensions of reactors VOL. 49, NO. 2
FEBRUARY 1957
315
lene. Upon leaving the constant temperature box the air was metered by a calibrated American Meter Co. dry meter. If the analysis was by ultraviolet absorption measurement, part of the air passed through an absorption cell after leaving the porous bed. Measurement of the ultraviolet absorption characteristics of the air-naphthalene sample in the cell permitted the determination of the concentration of naphthalene in the air. Pressure measurements were made a t suitable points in the equipment. Essential dimensions of the reactors used are shown in Figure 4. In reactors I, 11, and 111, the bed was supported on fritted porous glass disks. In reactor I V the bed was supported on a glass disk perforated with holes, 1 mm. in diameter. Connections between the reactors and the remainder of the equipment were made of ground glass joints and Tygon tubing. Analytical Procedure
Air analysis for naphthalene by the saturators technique (2, 20) consists of passing air through a saturator or series of saturators with sufficient naphthalene surface to ensure saturation of the air leaving the saturators. The loss ofweight in the saturators, air quantity, vapor pressure of the naphthalene, and air pressure permit the calculation of the partial pressure of the naphthalene present in the air entering the saturator train. The major drawback of this procedure is that the passage of a relatively large amount of air through the saturators is required if a reasonable degree of accuracy is to be attained in the final result. The spectrophotometric method used for analysis of the air-naphthalene mixture overcame this drawback. In this method the absorption characteristics of the air-naphthalene mixture for ultraviolet light (2750 A. wave length) were measured with a Beckman D U spectrophotometer. A slit width of 1.0 mm. was used in all the measurements. An absorption cell with a 10-cm. light path was specially constructed to permit easy purging of residual gas by the fresh gas to be analyzed. This analysis procedure was quicker and easier to perform than the saturator technique. Since air requirements were small the run could be of shorter duration than that required by the saturator technique. As a result,
Table I. Particles
Granules Pellets
3 16
there was no danger of depleting active bed surface during a run.
I
I
Material Used
Two particle shapes were used in the present research in determining the mass transfer characteristics of fixed beds. One shape was spherical and the other, cylindrical. The naphthalene used was supplied by British Drug House, in technical grade and melting point of 80.0' C. The spherical material was prepared by heating a mixture of approximately 0.5 liter of water and 20 grams of naphthalene with vigorous agitation. When the temperature of the mixture rose above the melting point of the naphthalene, the naphthalene dispersed through the water as spherical drops. When 2 to 3 liters of cold water were added to the mixture, the naphthalene solidified quickly and retained its spherical shape. The maximum particle diameter obtained by this procedure was about 1 mm. However, this diameter was obtained only in small quantities. After drying, the granules were separated into two fractions: 20- to 30- and 30- to 40-mesh U. S. sieve series. T ~ v osizes of naphthalene pellets were prepared by compressing naphthalene powder with about 27, stearic acid as a binder in a pharmaceutical tableting machine. The nominal dimensions \vere 0.4 X 0.4 cm. and 0.95 X 0.68 cm. Figure 5 presents the dimensions of the pellets in greater detail. The inert materials, bvhich were used to dilute the bed, were similar in size and shape to the vaporizing material. In granular naphthalene, the inert material consisted of the correct size fractions of either polystyrene spheres or silica sand which had the rough edges removed prior to fluidization. In pellets, the inert material consisted of identically sized pellets of talc, prepared in the same dies used for the corresponding naphthalene pellets. The surface area of the granular material was determined with the aid of permeability measurements by the use of the Kozeny equation (77). The surface area of the pellets was determined by direct measurement and calculation from geometric considerations. Results are presented in Table I. The ~7aporpressure of the naphthalene was determined by passing a known volume of air through the saturators and
Properties of Particles
Nominal Size 20-30 mesh 30-40 mesh 4 x 4 9 . 5 X 6.8
INDUSTRIAL A N D ENGINEERING CHEMISTRY
SV Sq. Cm./G.
123 158 12.8 6.4
D,
=
6/Su
Cm. 0 . Q48 0.037 0.41 0.82
Figure
5.
Dimensions of pellets Pellets, Cm.
~ _ . _ _ _ _ _ _ _
4 X 4 a. b.
0.386 0.292
C.
0.388
h.
0.047 0.422
r.
9 . 5 X 6.8 0.635 0.445 0.952 0.095 1 .25
determining the loss in weight of the saturators. The vapor pressure of the naphthalene was then calculated according " to
a W,7r
ps =
M,,nr,
The vapor pressure obtained by this meanswas0.142mm. mercuryat30.5'C. This value is about 2% lower than that obtained from the I.C.T. equation (16) for the vapor pressure of naphthalene. Experimental Bracedure
The bed was made u p of a mixture of inert material and naphthalene. 'The results of preliminary exploratory runs were used to determine the approximate amount of naphthalene required to keep the exit gas composition reasonably removed from saturation conditions, In granules, the amount of active surface in the bed was determined in preparing the bed by weighing the naphthalene added to the reactor to lrithin k0.001 gram. In pellets, the amount of naphthalene surface was determined by counting the number of active pellets added. The bed was made up to a total height of 8 to 15 cm. by adding inert material which was weighed to d=l gram. The reactor was gently agitated until the bed appeared to be homogeneous, and then placed in the constant temperature box until thermal equilibrium was established. If analysis was to be by saturators, the saturators were weighed to 0.001 gram and inserted into the system. At the beginning of the run a suitable air rate was established and the following data recorded: air rate, pressure in the reactor, saturators, and air meter, barometric pressure, and temperature in the constant temperature box. For air rates up to 45 liters per minute, the entire quantity of air was passed through the saturator train. .4t higher rates it
Table 11.
Run
No.
Reactor Number
Actke Area, Sq.Cm.
Experimental and Calculated Results Analysis by Spectrophotometer
Pressure in Reactor, Mm. of Hg
Mass Velocity
x 104
G./Sec. Sq. Cm.
c,
x 103 G./Liter
I/I,
c/c,
Jd
N R ~
e
NI;,
Pellets, 9.5 X 6.8 la 2a 3a 4a 5a 6a 7a 8a 9a 10a lla 12a 13a 14a 15a 16a 17s 18a 19a 20a 21a 22a 23a 24a 25a 26a 27a 28a
1 1 1 1 1 1 1 1 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
211.5 141 211.5 141 141 141 141 141 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423 423
758 758 758 758 758 758 758 758 759 762 760 761 761 767 764 762 763 765 766 770 772 780 785 787 797 795 809 805
lb 2b 3b 4b 5b 6b 7b 8b 9b 10b llb 12b 13b 14b 15b 16b 17b 18b 19b 20b 2lb 22b 23b 24b 25b
1 1 1 1 1 1 1 1
190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190 190
758 758 758 758 758 758 758 758 759 759 759 760 762 763 765 767 781 770 772 787 795 796 796 805 814
.
1.41 2.11 2.60 3.27 7.92 14.6 19.0 30.0 45.6 61.4 62.1 76.1 76.1 76.1 87.7 112 117 146 148 182 205 257 298 316 343 360 398 398
0.652 0.650 0.623 0.650 0.686 0.731 0.754 0.786 0.664 0,685 0.680 0.691 0.685 0.695 0.701 0.696 0.730 0.706 0.725 0.735 0.745 0.751 0.759 0.745 0.760 0.749 0.763 0.760
1.43 2.37 5.64 4.50 8.07 11.4 16.1 20.3 27.8 42.7 69.0 86.5 87.6 108 147 178 178 208 234 316 316 357 357 398 439
0.671 0.653 0.634 0,642 0.646 0.654 0.664 0.673 0.683 0.705 0.742 0.751 0.765 0.775 0.795 0.805 0.797 0.814 0.821 0.827 0.832 0.840 0.846 0.854 0.865
0.961 0.961 0.961 0.961 0.961 0.961 0.961 0.961 0.959 0.957 0.958 0.956 0.956 0.955 0.953 0.953 0.952 0.952 0.951 0.946 0.943 0.933 0.928 0.926 0.914 0.916 0.900 0.905
0.883 0.891 0.976 0.891 0.782 0.650 0.587 0.526 0.840 0.783 0.799 0.758 0.788 0.754 0.731 0.751 0.687 0.724 0.672 0.647 0.624 0.607 0.596 0.629 0.601 0.622 0.593 0.506
0.631 0.977 0.996 0.977 0.672 0,463 0.39 0.33 0.27 0.225 0.236 0.209 0.229 0.206 0.194 0.205 0.166 0.189 0.164 0.153 0.143 0.137 0.133 0.146 0.136 0.143 0.133 0.104
0.63 0.94 1.16 1.46 3.52 6.53 8.48 13.7 20.4 27.4 27.6 33.9 33.9 33.9 39.2 50.1 52.2 65.3 66.1 81.0 91.5 115 133 141 154 162 173 173
0.468 0.468 0.468 0,468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.968 0.468 0.468 0.468 0.468
1.78 1.86 2.18 2.74 6.62 12.3 16.0 25.9 38.3 51.4 52.0 63.7 63.7 63.7 73.6 94.4 98.1 123 124 152 172 216 250 266 289 804 325 325
0.831 0.880 0.939 0.914 0.906 0.875 0.845 0.811 0.786 0.724 0.613 0.596 0.558 0.530 0.480 0.476 0.479 0.429 0.416 0.414 0.399 0.379 0.364 0.338 0.322
0.584 0.726 0.915 0.804 0.775 0.681 0.610 0.545 0.515 0.422 0.320 0.298 0.268 0.248 0.215 0.211 0.214 0.183 0.176 0.174 0.166 0.156 0.148 0.135 0.127
0.39 0.65 1.54 1.23 2.21 3.13 4.40 5.59 7.60 11.8 18.8 23.6 23.9 29.6 40.3 48.8 48.8 56.7 63.9 86.4 86.4 97.4 97.4 109 120
0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402
0.65 1.09 2.58 2.06 3.70 5.24 7.35 9.34 12.7 19.8 31.4 39.4 39.9 49.5 67.4 81.5 81.5 94.9 107 144 144 163 163 182 201
0.781 0.901 0.956 0.976 0.975 0.964 0.808 0.952 0.730 0.783 0.747 0.735 0.737 0.662 0.642 0.634
0.245 0.373 0.502 0.602 0.595 0.520 0.337 0.489 0.276 0.319 0.287 0.277 0.280 0.227 0.214 0.210
Pellets, 4 X 4
1
4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
0.961 0.961 0.961 0.961 0.961 0.961 0.961 0.961 0.960 0.959 0.959 0.950 0.956 0.955 0.951 0.950 0.933 0.946 0.944 0.926 0.916 0.915 0.915 0.905 0.895
Granules, 0.048 mm. IC
2c 3C
4c
5c 6c 7c 8c 9c 1oc llc 12c 13c 14c 15c 16c
3 3 3 3 3 3 1 3 1 1 1 1 1 1 1 1
71.6 71.6 71.6 71.6 71.6 71.6 295.0 71.6 295.0 298.5 298.5 298.5 298.5 298.5 298.5 298.5
760 760 760 760 760 760 772 760 774 775 780 783 786 790 802 808
7.9 19.3 30.6 47.6 67.8 90.5 119.8 121.2 80.4 169.1 219.5 296.0 275.0 315.5 425 485
0.685 0.649 0.630 0.624 0.634 0.630 0.677 0.630 0.705 0.688 0.699 0.705 0.710 0.736 0.745 0.749
0.960 0.960 0.960 0.960 0.960 0.960 0.945 0.960 0.955 0.954 0.947 0.932 0.926 0.924 0.910 0.904
0.205 0.503 0.796 1.24 1.76 2.35 3.10 3.14 4.11 4.39 5.69 6.39 7.14 8.17 11.0 12.6
0.362 0.362 0.362 0.362 0.362 0.362 0.408 0.362 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408
0.321 0.789 1.25 1.94 2.75 3.67 5.25 4.92 6.94 7.43 9.60 10.8 12.1 13.8 18.6 21.3
(Continued o n following page)
VOL. 49, NO. 2
FEBRUARY 1957
317
Table II.
Experimental and Calculated Results Analysis b y Spectrophotometer (Continued)
in
Mass Velocity x 104
Reactor Mm. of H g
Sq. Cm.
Pressure Run
Reactor
dctive Area,
No.
No.
Sq. Cm.
c, x 103 G./Liter
G./Sec.
I/I,
C/C,
Nd.
e
NRC
Jd
Granules, 0.037 mm. Id 2d 3d 4d 5d 6d 7d 8d 9d 10d lld 12d 13d 14d 15d 16d 17d 18d 19d
3 3 1 3 1 3 3 3 3 3 3 3 3 1 1 1 1 1 1
80.5 80.5 348.5 80.5 348.5 80.5 80.5 93.5 98.3 98.3 98.3 98.3 98.3 348.5 348.5 348.5 348.5 348.5 348.5
757 757 756 757 756 757 757 756 756 756 756 756 756 776 780 781 790 800 830
Table 111.
Run
No.
0.85 1.67 2.63 2.90 3.03 4.67 6.54 6.91 7.86 8.03 8.34 9.90 11.6 18.7 21.6 26.9 30.3 33.8 51.3
0.669 0.693 0.658 0.638 0.725 0.635 0.632 0.632 0.644 0.649 0.652 0.648 0.651 0.685 0.710 0.740 0.755 0.786 0.805
0.949 0.949 0.950 0.949 0.950 0.949 0.949 0.950 0.950 0.950 0.950 0.950 0.950 0.937 0.934 0.927 0.922 0.911 0.878
0.846 0.944 0.879 0.948 0.696 0.950 0.953 0.966 0.923 0.907 0.891 0.918 0.893 0.900 0.740 0.641 0.557 0.522 0.491
0.17 0.33 0.53 0.58 0.61 0.93 1.31 1.38 1.57 1.61 1.67 1.98 2.33 3.74 4.33 5.39 6.06 7.76 10.3
0.269 0.414 0.378 0.432 0.387 0.430 0.438 0.397 0.301 0,279 0.260 0.294 0.260 0.287 0.241 0.183 0.161 0.183 0.121
0.362 0.362 0.429 0.362 0.429 0.362 0.362 0.362 0.362 0.362 0.362 0.362 0.429 0.429 0.429 0.429 0.429 0.429 0.429
0.27 0.52 0.93 0.91 1.07 1.46 2.05 2.17 2.46 2.52 2.62 3.10 4.08 6.55 7.57 9.41 10.6 13.6 18.0
NRe
E
lVde
Experimental and Calculated Results Analysis b y Saturator Method
Pressure, Mm. HE. At In Reactor A t gas saturator meter h-o exit reactor
.
Active Area
Sq. Cm.
Air Saturator through Wt., Reactor, Loss, Liter G.
Mass Velocity x 104 G./Sec.
P/Ps
Sq. Cm.
0.700 0.682 0.735 0,684 0.665 0.666 0.638 0.440 0.620 0.533 0.375 0.413 0.418 0.327
52.5 74.8 88.1 161.5 208.0 101.0 259.5 294.0 307.5 299.0 355.0 434.0 459.0 505.0
0.266 0.252 0.197 0.171 0.162 0.162 0.149 0.098 0.143 0.168 0.104 0.079 0.115 0.088
23.5 33.5 39.5 72.4 93.4 45.3 116.5 131.8 137.8 134.0 159.0 196.5 205.5 226.5
0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468 0.468
44.3 63.1 74.2 136.0 175.2 85.1 219.0 247.5 259.0 251.5 299.0 369.0 386.0 426.0
0.634 0.606 0.560 0.485 0.685 0.415 0.335 0.380 0.504 0.257 0.386 0.429 0.580 0.525 0.540 0.555
62.4 106.8 149.5 149.5 163.5 221 258 327 3 50 430 482 565 854 890 1130
0.333 0.312 0.269 0.218 0.252 0.264 0.200 0.236 0.154 0.147 0.120 0.139 0.118 0.105 0.109 0.113
13.8 17.1 23.6 33.1 33.1 36.1 48.9 56.9 72.4 77.1 95.0 107 125 189 197 250
0.402 0.402 0.402 0.402 0.402 0,402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402 0.402
23.0 28.6 39.4 55.4 55.4 60.3 81.6 95 121 129 159 179 209 316 329 418
82 97 143 184 2 73 320 328 491 600 1178 1395 1492
0.531 0,396 0.338 0.362 0.312 0.206 0.233 0.239 0.208 0.112 0.135 0.105
Jd
Pellets, 9.5 X 6.8 la 2a 3a 4a 5a 6a 7a 8a 9a 10a lla 12a 13a 14a
1 1 1 1 1 1 1 1
1 1 1 1 1 1
763 764 759 768 775 761 770 780 791 771 779 781 786 790
778 786 788 802 831 784 789 859 893 802 823 818 840 839
815 836 837 917 97 1 852 854 999 1029 879 928 922 967 957
282 2 82 423 423 423 423 423 423 423 282 282 423 282 282
471.0 893.1 721.3 925.4 516.0 120.4 787.4 838.3 1166 770.5 731.5 946.4 538.6 907.4
760 76 1 763 768 768 760 765 770 774 787 778 787 764 771 769 771
774 785 806 806 802 812 838 795 879 812 823 787 809 806 787
814 82 1 843 799 899 888 961 973 850 1059 904 926 867 908 908 959
190 190 190 190 190 127 127 127 285 127 254 254 95 95 95 95
515.0 616.8 612.8 684.4 692.8 487.3 684.3 468.4 498.5 918.2 420.0 767.4 578.5 658.0 1037.2 399.3
759 759 764 771 778 782 773 789 80 1 764 772 772
776 781 797 811 836 857 796 829 855 825 840 796
817 830 867 912 966 1018 86 1 93 1 984 979 1013 804
263.5 263.5 263.5 351 35 1 351 350 350 350 278 278 328
601.5 621.1 710.7 632.5 1084.3 735.0 723.0 520.6 538.4 813.1 963.0 516.4
0.1500 0.3030 0.2185 0.3475 0.2022 0.2898 0.5118 0.4067 0.5157 0.3730 0.4518 0.5610 0.3115 0.5925
Pellets, 4 X 4 lb 2b 3b 4b 5b 6b 7b 8b 9b 10b llb 12b 13b 14b 15b 16b
1 1
1 1 1 1
1 1 1 1 1 1 2 2 2 2
777
0.1896 0.2578 0.2822 0.3625 0.2485 0.2883 0.4452 0.3195 0.2663 0,6270 0.2532 0.4873 0.2655 0.3340 0.5160 0.1965
77.0
Granules, 0.048 mm. IC 2C 3c 4c 5c 6c 7c 8c 9c 1oc llc l2c
3 18
1 1 1 1 1
1 1 1 1 1 1 1
INDUSTRIAL A N D ENGINEERING CHEMISTRY
0.0852 0.1360 0.2158 0.1282 0.2675 0.2681 0.2214 0.1649 0.1979 0.1864 0.2045 0.0980
0.894 0.813 0.760 0.870 0.827 0.687 0.728 0.738 0.682 0,871 0.915 0.895
2.14 2.53 3.74 4.79 7.10 8.31 8.54 12.8 15.6 30.8 36.2 38.7
0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408 0.408
3.62 4.28 6.31 8.1 12.0 14.1 14.4 21.6 26.4 52.0 61.1 65.4
was necessary to bypass part of the air due to the high pressure drop encountered. After the completion of the run, the saturators were again weighed. The preliminary procedure of analysis by absorption was similar. During the run, part of the air exiting from the reactor was passed through the sample cell until the air in it was purged and replaced by the new sample. The cell was then sealed and the absorption characteristics measured on a Beckman DU spectrophotometer. The standard absorption cell against which the sample was compared was filled with dry, naphthalene-free air at atmospheric pressure. Several samples and measurements were taken a t each air velocity.
%E=
Figure 6.
Diameter Cm. Pellets 0 . 8 2
Chu, others.
The mass transfer coefficient was calculated by N, k, = (2)
Jd
=
urn (3) G Nse213
Equation 2 can be expanded and rewritten
(4) By substituting Equation 4 into Equation 3 and taking the case where the air entering the bed is free of naphthalene (Pal= 0), the following expression is obtained : A J J = 3 In (1 (5) The ratio, p / j B , can be calculated from the saturator data by the equation
where W,, and w,, can be calculated by equations similar to Equation 1 and w, is an experimentally measured quantity. The procedure for determining the ratio j / p 8 from spectrophotometer data was based on the Lambert-Beer light absorption equation (7)
which can be put into the more convenient form c = -log I / I o k
0
Correlation
-- -- -- -
(8)
The constant, k, was determined by absorption measurements on air saturated with naphthalene and was found to equal 21 9 liters per gram. The value of c, was also known for air saturated with naphthalene and the ratio p/ps is equal to c/c,. Reynolds number for flow through porous beds can be expressed as
(10)
Since S,can be expressed as (1 - e ) s, = ___
' I
A
solid as defined by
- s,
0
V
(9)
6 D --
e)
0
D,is the effective diameter of a granular
The mass transfer factor, suggested by Chilton and Colburn (7), can be written as
-
Analytical Method Spectro. Saturator
0.41 Granules 0.048 0.037
Method of Calculation
s e A film
y
Mass transfer factor v5. Reynolds number, D, G/u ( 1
(11)
the Reynolds number can also be written GG(1 - e ) (12) N R= ~ w Gamson (70) proposed the use of a modified Reynolds number defined as
which can also be written
In calculating the Schmidt group, p / p D , , theviscosity and densityof air were used since the amount of naphthalene in the air has a negligible effect on these properties. The diffusivity as calculated by the Gilliland equation ( 7 7 ) was 0.0618 sq. cm. per second. The value of the Schmidt group was calculated to be
2.57. Experimental Data and Calculated Results
The experimental data and calculated results for all runs are presented in Tables I1 and 111. Table I1 presentsdata and calculated results forthe runs inwhich the gas analysis was determined by the spectrophotometric method and Table 111 gives the data and calculated results for analysis by the saturator technique. Figure 6 is a plot of Jd us. Nxe for all the data obtained. From this figure two facts are immediately obvious: 1. The particle diameter appears as a parameter for the granules but not for the pellets ; 2. A maximum in the J d factor ap-
pears at a Reynolds number of about one; for values of the Reynolds number greater than one, the Jd factor decreases with increase in Reynolds number. Reproducibility of the data by both methods of analysis is excellent. Discussion The departure from a straight line correlation obtained a t the extremely low Reynolds number can be partially explained by a free convection effect and back diffusion. Dryden, Strang, and Withrow ( 5 ) and Gaffney and Drew (8) reported anomalies in their data at low Reynolds numbers and differences in results for downflow as compared with upflow which they attributed to back diffusion and convection effects. Gaffney and Drew also reported visual evidence of downward streamers of concentrated solution and Winterkamp (25) observed strong free convection effects when he passed water through beds of slightly soluble dye pellets. An additional factor must be considered for these low Reynolds numbers for which case flow would definitely be laminar in nature. Von KQrmbn (23) has shown that for the case of laminar flow, since the eddy viscosity and eddy diffusivity would be negligible in comparison with p and D,.the exponent on the Schmidt number should be unity. This means that at decreasing flow rates the exponent on the Schmidt number of the Jd factor should change gradually from a value of for the case of fully developed turbulence to a value of one as laminar flow characteristics are reached. The existence of particle diameter as a parameter for the small particles in the correlation of J-factor versus Reynolds number confirms the results of Hurt (75) and Resnick and White (20) in mass transfer, and the results of Grootenhuis and others (72), Eichhorn and White ( 6 ) , and Lof and Hawley (78) in heat transfer. VOL. 49, NO. 2
FEBRUARY 1957
319
p,
N k E * E #(I-0
Figure
7.
0.82
Analytical Method Spectro. Saturator
0 0
0.41 Granules 0 , 0 4 8
V
0.037
n
0
w
v
Figure 7 is a plot of log J d versus log N R e for the value of .TB, above 1.5. The correlating curve of Chu, Kalil, and Wetteroth (2) is shown as a dashed line. The particle diameter still appears as a parameter for the smaller particles and the correlating curve of Chu and others provides a reasonable correlation for the pelleted material. Figure 1 shows a plot of the correlating curves for the previous data with data from the present investigation. In this plot the diameter appears as a parameter in the regularly shaped particles below a diameter of approximately 4 mm. and for irregularly shaped particles. Regularly shaped particles with a diameter above 4 mm. have single correlating curves providing satisfactory correlation. In all the cases cited the areas used were either geometric areas which were determined by direct measurement or were determined by permeability measurements in the laminar flow region. If small protuberances were present on the surface of the particles neither one of these methods of determining surface area would be capable of detecting them or bringing them into account. Small protuberances would: however, be expected to affect mass transfer characteristics in the turbulent flow regime since surface roughness plays a role in determining flow characteristics in this region. They would also affect the calculated mass transfer factor since the area used in the calculation would be different from that actually available for mass transfer. The proportional effect of protuberances could be expected to be greater for the smaller particles and for the higher Reynolds numbers. As the laminar flow region is approached the affect of protuberances on the flow pattern should tend to disappear. Further work in this field should be attempted at extremely low Reynolds numbers and should aim for accurate and significant surface area measurements. The technique of dilute beds and continuous gas analysis used in the present work should
320
100
zoo
Mass transfer factor vs. modified Reynolds number,
Diameter Cm. Pellets
50
500
D, G / u ( 1
- e)
enable accurate transfer measurements to be made a t the l o ~ vReynolds number range. This investigation showed that for pelleted material of two different diameters, 0.41 and 0.82 cm., a single line correlated the Jd-factor with the modified Reynolds number. However, for small spherical particles the particle diameter appeared as a parameter in the correlation. These results, in general? confirm the resu!ts reported by previous investigators. Nomenclature A = cross-sectional area of column, sq. cm. = effective aarticle diameter (defined b; Equation 10) cm.‘ = diffusivity of vapor in gas, sq. cm.-sec.-l = superficial mass velocity, g. sec.-l cm.-2 = intensity of light entering cell = intensity of light leaving cell = molecular weight of nontransferred material = molecular weight of transferred material = moles of material transferred per unit time, g. moles/sec. = Reynolds number, D,G/p, dimensionless = modified Remolds number,
, dimensionless
(1: €)P Schmidt number, p / p D , , dimensionless = gas constant = active surface, sq. cm. = specific surface of solid, surface per unit volume of solid, cm.-l = surface per unit weight of solid, sq. cm. g.-l = absolute temperature, O K. = active area per unit volume of bed, cm.? = concentration of naphthalene in air, gram liter-’ = concentration of naphthalene in air at saturation conditions, gram liter-’ = mass transfer factor, dimensionless = heat transfer factor, dimensionless = coefficient in Lambert-Beer equation = mass transfer coefficient, g. molesec. -1-cm.-2-atm. -l = mean partial pressure of nontransferred material, atm. =
k
k.,
INDUSTRIAL AND ENGINEERING CHEMISTRY
partial pressure of transferred material, atm. 6, = vapor pressure of transferred material, atm. be?,, = log mean partial pressure driving force, atm. w,, = weight of naphthalene to saturare air at reactor exit pressure, g. am = weight loss of saturators, gram kVm, = weight of naphrhalene to saturate air at saturator exit pressure, gram 8 = time, sec. ,u = viscosity, gram cm.? sec.-l e = bed voidage, dimensionless p = density, gram cm. --3 =
Subscripts 1 = entrance to bcd 2 = exit from bed Literature Cited ( 1 ) Chilton, T. H., Colburn, A. P., IND. ENG.CHEM. 26, 1183 (1934). ( 2 ) Chu, J. D., Kalil, J., Wetteroth, W. A , , Chem. Eng. Progr. 49, 141 (1953). ( 3 ) Colburn. A. P., IND.ENG.CHEM.22. 967 (1930).
(4) Denton, W. H., “General Discussion on Heat Transfer,” Institute of Mechanical Engineers, p. 370 (1951). ( 5 ) Dryden, C. E., Strang, D. A . , With-
row, A . W.,Chem. Eng. Progr. 49,
191 11953). ( 6 ) Eichhorn, J.; White, R. R.., Zbzd., 48, Symposium Ser. No. 4, 11 (1 952). ( 7 ) Evans, G. C., Gerald, C. F., [bid., 49, 135 (1953).
(8) Gaffney, B. J., Drew, 7’. B., IRD.
ENG.CHEM.42. 1120 (1950).
( 9 ) Gamson, B. W., khern. Eng. Progi. 47, 19 (1951). (IO) Gamson, B. W., Thodos, G., Hougen,
0. A,
Trans. A m .
Inst.
Chem.
Engrs. 39, 1 ( 1 943). (11) Gilliland, E. R.,IND.EXG.CHFx 26, 681 (1932). (12) Grootenhuis, P., hlackworth, R. C.
A,. Saunders, D. A , , Proc. “General Discussion on Heat Transfer,” Institute of Mechanical Engineers,
p. 363 (1951). (13) Hobson, hl. E., Thodos. C., Chern. Eng. Progr. 45, 517 (1949). (14) Zbtd.. 47, 370 (1951). (15) Hurt, P. M., IND.ERG.CHEM. 35, 522 11943). (16) 1n;erna;ional Critical Tables, vol. 111, p. 208, McGraw-Hill, New York, 1928. (17) Kozeny, J., Sztrber. Akad. Wiss.
W i e n , M a t h . natur-w KI. Abt. Ila, 136, 271 (1927). (18) Lof, G. 0. G., Hawley, R. W., IXD. ENG.CHEM. 40, 1061 (1948). (19) McCune, L. K . , Wilhelm, R. H., Zbzd., 41, 1124 (1949). ( 2 0 ) Resnick, W., White, R . R., Chem. Eng. Progr. 45, 377 (1949).
(21) Satterfield, C. N., Resnick, H., 16zd., 50, 504 (1954). (22) Taecker, R. G., Hougen, 0. A , , Zbid., 45, 188 (1949). (23) Von KArmAn, Th., Trans. A m . Soc. Mech. Engrs. 61, 705 (1939). (24) Wilke, C. R., Hougen, 0. A., Trans. A m . Znst. Chem. Engrs. 41, 445 ( 1 945). (25) Winterkamp, F. H., M.S. thesis, Ohio State University (1950).
RECEIVED for review November 21, 1955 ACCEPTEDAugust 9, 1956
