(28 McMullen A. K., Miyauchi, T., Vermeulen, T., Univ. dalifornia Radiation Lab., Rept. UCRL-3911-Suppl. (1958). (29) Matsuyama, T., Chem. Eng. (Japan) 14, 249 (1950). (30) Miyauchi, T., Univ. California Radiation Lab., Rept. UCRL-3911 (AuPust 1957). (31) Miyauchi,‘ T.,-unpubliihed manuscript. (32) Vyauchi, T., McMullen, A. K., Vermeulen, T., Univ. California Radiation Lab., Rept. UCRL-9112 (1960). (33) Nagata, S., Eguchi, W.. Kasai, H., Morino, I.,’ Chem. Eng. (Japan) 21, 784 (1957). (34) Oldshue, J. Y . , Rushton, J. H., Chem. Eng. Progr. 48, 297 (1952). (35) Otake, T . , Kunugida, E., Chem. Eng. (Japan) 22, 144 (1958). (36) Otake, T., Kunugida, E., Kawabe, A , , Ihid., 23, 81 (1959). (37) Prausnitz, J. M., A.Z.Ch.E. J . 4, 14M (1958). (38) Reman, G. H., “Joint Symposium on Scaling-Up Problems,” p. 35, Inst. Chem. Eng.: London, 1957. (39) Reman, G. H.: Olney, R. B., Chem. Eng. Progr. 51, 141 (1958). (40) Scheibel: E. G., A.I.Ch.E. J . 2, 74 (1956). (41) Sege, G., LYoodfield, F. W., Chem. Eng. Progr. Symp. Ser., No. 13, 50, 39 (1954). (42) Sherwood, T. K., Pigford, R. L., “Absorption and Extraction,” 2nd ed., Chap. 5 . McGraw-Hill, New York, 1952.
(43) Sleicher, C. A,, Jr., A.Z.Ch.E. J . 5 , 145 (1959). (44) Thornton, J. D., Chem. Eng. Prog~.Symp. Ser., No. 13, 50, 179 (1954). (45 V‘an Deemter, J. J., Zuiderweg, F. J., Klinkenberg, A,, dhem. Eng. Sci. 5 , 271 (1956). (46) Vermeulen, T., Lane, A. L., Lehman, H. R., Rubin, B., Univ. California Radiation Lab., Repts. UCRL-2983, UCRL718 (revised), in press. (47) Vogt, H. G., Geankoplis, C. J., Znd. Eng. Chem. 45, 2119 (1953) : 46. 1763 119541. (48) Wkhner,’J. F., ’Wilhklm, R. H., Chem. Eng. Sci. 6 , 89 (1956). (49) Wicke, E., Travinski, H., Chem. Zng. Tech. 25, 114 (1953). (50) Yagi, S..Miyauchi, T., Chem. Eng. (Japan) 17, 382 (1953); 19, 507 (1955). (51) Young. E. F., Chem. Eng. 64, 241 (February 1957). RECEIVED for review March 8, 1960 ACCEPTED February 2 5 , 1963 Studies conducted in Lawrence Radiation Laboratory under asupices of the U. S. Atomic Energy Commission. Part of the work of T. Miyauchi was done under a fellowship from the Japan Atomic Energy Commission. Computations made in the Universitv of California Computer Center.
LIQUID-PHASE MASS TRANSFER A T LOW REYNOLDS NUMBERS J.
E. W I L L I A M S O N ,
K .
E . B A Z A I R E , A N D C. J . G E A N K O P L I S
The Ohio State University, Columbus 10, Ohio Liquid-phase mass transfer coefficients were obtained for packed beds of benzoic acid spheres and water ) of 0.08 to 120. All previous data were obtained with granular solids in the Reynolds number ( N ” R ~range or modified spheres. The previous correlation for J’ of Gaffney and Drew extended down to N ” R of ~ 0.8, with considerable scatter of the data and uncertainty of the slope of the line in the range of N ” R below ~ 50. The present data confirm the exponent on the Schmidt number in J’ of 0.58 for liquids. The data check those of Goffney and Drew and McCune and Wilhelm above a N ” R of ~ 0.8. Equations are proposed for the entire liquid range.
have been reported for mass transfer of gases in packed beds of solids. In recent years, mass transfer with liquids in lobv velocity regions has assumed a greater importance because of the use of ion exchange and chromatography in packed beds. Relatively few d a t a have been obtained for liquids. particularly in the low Reynolds number regions, and no data for liquids have been obtained using beds of true spheres. Gaffney and Drew ( 4 ) made a complete study of the effect of Schmidt number and varied it from 150 to 1300 for liquids. They found the exponent of A’sc in the J’ factor to be 0.58 and not 2 / 3 as for gases. using modified spheres in the . V ” R ~ range of 0.8 to 1500. Below a .Y”R~of 50, there was considerable uncertainty of J’ because of scatter of the data. They stated that the data of Hobson and Thodos (6) for liquids should not be considered because of uncertain extrapolations. McCune and Wilhelm (8) used modified spheres of 2-naphrange of 40 to tho1 and obtained data for liquids for a S’’R~ 5000. Dryden, Strang, and PVithrow (2) used modified spheres of 2-naphthol and benzoic acid in water in a ,V’‘R~ range of 0.004 to 7. Different lines were obtained for the two solutes using the 0.58 exponent for N s c . Evans and Gerald ( 3 ) obtained data for liquids with granules of benzoic acid. However, it was necessary to obtain the ANY D A T A
126
I&EC FUNDAMENTALS
surface area by the indirect method of measuring the permeability of the bed. In the present work, mass transfer coefficients of benzoic acid spheres to water were obtained in packed beds. Data obtained in the ‘V‘‘R~region of 0.08 to 120 were correlated and compared with data from the literature. Equations are presented for calculating the J ’ factors. Experimental
T h e process flow diagram is shown in Figure 1. All previous investigators (2, 4>8) used modified spheres made by pelletizing powder. T h e pellets consisted of a short cylindrical section with hemispherical caps. I n this rvork? true spheres were made by casting. Figure 2 shows the two halves of the copper mold for casting the spheres. T h e sphere mold was made by cutting approximate hemispheres about 0.115 inch deep in each of the two matching plates. Steel ball bearings 0.250 inch in diameter \yere inserted in the holes of one plate, and the two plates were clamped together. T h e plates were pressed slowly together several times using a pressure of 200,000 p.s.i. to form 0.250-inch holes. While still clamped together. holes were drilled for steel taper pins
to allow precise alignment of the plates when reassembled. After separating the pla.tes, channels lvere drilled to and from the holes for pouring molten benzoic acid, and then the plates were nickel plated. H a r d , glossy white 'benzoic acid spheres were produced? as shown in Figure 3. T h e diameter of 20 spheres for series I runs was measured in 10 different directions. T h e maximum of any one of the 200 measurements was 0.2533 inch, and the minimum was 0.2452 inch. T h e average sphere diameter was 0.2484 inch. with the maximum average diameter of a single sphere being 0.2496 inch and the minimum 0.2468 inch. The average diameter of the spheres after a series of mass transfer runs was 0.236 inch, or a decrease of 5% in diameter. For calculations, the avlerage diameter of 0.242 inch was used. For series I1 runs! the average was 0.2505 inch before the runs and 0.2444 inch after th.e runs, or a decrease of 2.4y0 in diameter. For calculations. the average of 0.2475 inch was used. T h e average void fr,action of the bed was determined as 0.431 for series I and 0.441 for series I1 by counting the number of spheres in a 2.00-inch packed height and calculating the void fraction. I n making R run, the flow was downflow and the outlet fluid rate was determined by timing several weighed samples. T h e total outlet flow was coniposited and analyzed by titration with 0.01O.V N a O H solution. All samples were collected under nitrogen and titrated under nitrogen to prevent contamination by ( 2 0 1 . .4 mixture of phenol red and bromothymol blue was used as the indicator. This gave a sharp end point in the 7.2 to 7.4 p H range.
Figure 1.
A. Storage of distilled water 6 . Throttle valve C. Overflow constant-head tank D. Flow control valve E , F, G. Rotameters H. Glass tower (2.625-inch inner diometer) with packed bed K. Packed bed of benzoic acid spheres 2.00 inches high I. Bed of 6-mm. glass beads 2.0 inches high above and below bed of benzoic acid spheres
Results and Calculationls
All of the mass transfrr runs were made with the inlet water concmtration of benzoic acid a t zero. T h e mass transfer coefficient can be calcuhted by Equation 1 : L(C2 - C,)
=
Process flow diagram
T h e J factor is defined as:
(1)
kLa,X(AC)I,
If C1 = 0 and b = CJC,, then T h e J' factor of Gaffney and Drew ( J ) is: k 0.53 J' = 2 L
(5)
Table 1. Run
KO. 1-1 1-2 1-3 1-4 1-5 1-6 1-7 1-8
1-9 1-10 1-11 1-12 1-1 3 11-1 11-2 11-3 11-4 11-5 11-6 11-7 11-8 11-9 11-10 11-11
Tpm,b.,
c.
22.2 22.2 22.3 22.3 22.3 22.4 24.6 24.6 22.5 22.5 23.0 22.9 22,8 24.3 25.2 25.4 23.2 23.7 23.3 23.3 23.5 23.5 23 :4 22 , '7
L> Lb./Sq. Ft.-Sec. 1.382 0.512 0.869 0.712 0.187 0.0940 0 . C814 1.581 0.440 0,564 0,232 0.165 0.138 0.00595 0.00183 0,00439 0.00305 0.00107 0.0730 0.0126 0,0371 0.0186 0.0239 0.1264
(4)
Experimental Mass Transfer Data "Re
43.6 16.1 27.4 22.6 5.90 2.98 2.71 52.7 14.00 17.9 7.65 5.30 4.44 0.201 0.0629 0.152 0.1004 0,0357 2.41 0.415 1.230 0.615 0.791 4.11
N"R~ 101.4 37.4 63.7 52.3 13.7 6.88 6.28 122.5 32.4 41.5 17.8 12.3 10.3 0,453 0.143 0.344 0,227 0.081 5.46 0.941 2.79 1.40 1.79 9.31
C'Z,
J 0.216 0.357 0.274 0.326 0.770 1.115 1.200 0.205 0,455 0,350 0.592 0.690 1.103 7.35 11.70 10.13 11.40 23.28 1.551 4.89 2.29 3.66 3.00 0.980 ~
~~~
VOL
Grams/ Liter 0.150 0.244 0.190 0,225 0.501 0.718 0.904 0.175 0,330 0,256 0.437 0.501 0.755 2.805 3,244 3.208 3,006 3.256 1.029 2,267 1.418 1.950 1.705 0.672
J' 0.117 0.194 0.149 0.177 0.418 0.605 0.663 0.113 0.248 0.191 0.325 0.378 0,605 4.02 6.41 5.56 6.22 12.91 0.843 2.67 1.25 2.01 1.64 0.531
2
~~~~~
NO. 2 M A Y 1 9 6 3
127
~~
Figure 2. suheres
Metal mold
Figure
for costing
T h e solubility data for benzoic acid given by Steele and Geankoplis ( 9 ) and the Schmidt number data of others were used (7,9). T h e final calculated results are given in Table I. T h e average void fractions used in recalculating the d a t a of other investigators were 0.36 for McCune and Wilhelm (8), 0.51 for Gaffney and Drew (4, 0.36 for Dryden, Strang, and Withrow ( Z ) , and 0.39 for Hougen and coworkers (5, 70). Discussion
I n Figure 4 the
J factor data of this work are plotted
us.
3.
Benzoic acid sphere
T h e equation relating the variables in the N'n. range of
0.035 to 55 is: J = 2.50 ( J V ' ~ ~ ) - O . ~ ~
(5)
This means k, is proportional to Lo." in this region. T h e d a t a of McCune and Wilhelm (8)correspond closely to those of this work. T h e line of Haugen and coworkers for gases is 10 to 25% above the data for liquids. In several runs a t N t n , of 0.1 to 0.5, the values of J were below the line shown in Figure 4 and a n apparent peak was found. Later it was found that the peak was erroneous, and
Nfn,. For the straight portion of the line, the mean deviation of the data poinrs Of this work is 15.8%.
Figure 4.
Plot of J vs. N ' R ~
1 . Doto of this work, liquids 2. Dato of McCvne and Wilhelm (81. liquids 3. Line of Bar-ilon and Rernick (11. gases 4. Line of Hovgen and coworkers (5, 101, gores 128
l&EC FUNDAMENTALS
1 . Dato of this work, liquids 2. Line of Goffney and Drew I41 and McCune and Wilhelm (81. liquids 3. A. Benzoic acid .. Line of Druden. Strano. and Withrow (21. . . . liauidr: , downflow. B. 2-naphthol dawnflow. C. 2-naphthol vptlow 4. Line of Hougen and coworkers ( 5 , 101. gores ~~~
~
~
, ~ ~_. . ~
----\3 -
4
’ ’
’
Nomenclature a,,,
b C’1
CI C’? CZ C’s Cs
D D,
JP J’
= sq. ft. surface a r e a i c u . ft. volume of bed = C,/Cs = C‘2/C’s = inlet concentration, grams/liter = inlet concentration, lb./lb. =
= = = = = = = =
outlet concentration, gramsiliter outlet concentration, lb./lb. saturation solubility, gramsiliter saturation solubility, lb./lb. molecular diffusivity, sq. ft./sec. Darticle diameter. ft. ik,/L)(:vsr)2’3
(k,/L)(,V),,OJ*
mass transfer coefficient, lb. solute,!sa ft.-sec.-AC 7-;--, Lk r I . liquid flow. lb./sq. ft empty column cross section-sec.
001 01
05
I
I
5
IO
I , , , ,
50
,
,
I
, , , , ,
500 1000
100
iV’Re
Figure 6. Plot of J’e vs.
”’Re
I . This work 2. Gaffney and Drew ( 4 ) 3. McCune and Wilhelm (8) 4.
=
5000 10000
%E
Dryden, Strong, and Withrow (2): A. Benzoic acid downflow. 2-naphthol downflow. C. 2-naphtha1 upflow
6.
= D,L/p
lV“xc = D,L/ep -vsc = P PD X = packed bed length, ft. e = void fraction P = viscosity. lb./ft.-sec. p = density, lb./cu. ft. literrrture Cited
sufficient time to reach steady state had not been used. Such a peak had been found ( I ) for gases for upflow (Figure 4 ) . This peak ivould be expected for upflow and is probably- due to natural convection effects in laminar flow, as discussed in detail by others (7: 2). Dryden and co\zorkers (2) found different effects of natural convection on up- and doivnflo\v runs a t ver)- lo\\-Reynolds numbers. I n Figure 5: the J ’ factors using -Vs,0.5* are plotted versus the - V ” R ~values. T h e data of this work check very closely those of Gaffney and Drew ( 4 ) and McCune and \t‘ilhelm (8). T h e data of this work also confirm the line to be used at values of *Y’’ne below 50> since the data of Gaffney and Dreiv ( 4 ) scattered considerabl). in this region. T h e line for gases is about 1 0 0 n higher than that for liquids. Hence, it appears that using the 0.58 power on the Schmidt number corre!ateq only the liquid data. T h e data for Dryden and coworkers (2) in Figure 5 are about 407; above the line of Gaffney and Drew
(1) Bar-Ilan, hfoshe, Resnick, \Villiam. Ind. Eng. C em. 49, 313 (1957). Dryden, C. E., Strang, D. A,, IVithrow, A. E., Chem. Eng. Proqr. 49, 191 (1953). (3) Evans, G. C.. Grrald. C. F., Ibid.. 49, 135 (1953). (4) Gaffney, B. .J., DreLv. T. B., Znd. En?. Chem. 42, 1120 (1950). (5) Gamson, B. L$T.> Thodos, George, Houyen, 0. A , Trans. A.1.Ch.E. 39, 1 (1943). ( 6 ) Hobson, Mark, Thodos: George, Chem. Eng. Prop. 47, 370
(2)
(1951). (7)’ Linion,
IV, H.. Sherwood, T. K.. Ibzd., 46, 258 (1950). (8) McCune. L. I(..\\’ilhelm, R. H., Ind. En?. Chem. 41, 1124 /I040) ”i’ \ A ’
(9) Steele, I,. R.. Geankoplis, C. J . . A.1.Ch.E. J . 5 , 178 (1959). (10) IVilkr, C . R., Hougrn. 0. A , , Trans. ‘4.I.Ch.E. 41, 445 (1 345).
RECEIVED for review August 31, 1962 A C C E P T E D February 25, 1963 Work supported by Procter and Gamble Co. and Esso Research and Enqineering Co.
(4). T h e recommended equations to use for liquids for the entire Reynolds number range are Equation 6, based on data of this ivork primarily: and Eqiuation 7 > based on data of Gaffne)and Dreiv (4) and h)fcCune and \Vilhelm (8): J’ J’
= 2.40 (.V”n,)-0.86
= 0.442 ( - V ’ ’ ~ ~ ) - 0 . 3 ~
N ” R 0.08 ~ to 125
(6)
I Y ’ ’ R125 ~ to 5000
(7)
For the values of , V S R e below 0.08, the data are inconclusive and extrapolations are hai:ardous. More experimental data are needed in this region. I t is expected that a series of lines would be obtained for different geometries, solubilities, and Grashof numbers. I n Figure 6: the data are plotted as J‘e us. ‘V’’R~. This method of correlation \vas used by Dryden and coworkers (2) and brings their data closer to those of Gaffney and Drew ( J ) . Holvever. the data of thir; work and of McCune and Wilhelm (8) are separated from those of Gaffney and Drew by 15 to 30y0. Hence, it is recommended that Figure 5 be used.
Correction
MASS TRANSFER AND CHEMICAL REACT I O N I N A TURBULENT BOUNDARY LAYER I n this article b>-\V. R . Vieth, J. H. Porter, and T. K. Sherivood [IND.ENG.CHEM.FUSD.~MEST.ALS 2 , 1 (1963)], thrre are two typographical errors in the equations on page 2. Equation 3 should read (final!!.)
Equation 12 should read (hnally) ,p =
- Dbl ~
Yo
VOL. 2
NO. 2
MAY 1963
129
