GREEKLETTERS = intensity per unit wavelength, einsteins/cm*/sec 0 = angular spherical coordinate, radians A = wavelength, mg p = absorption coefficient, cm-' p = radial spherical coordinate, cm @' = angular spherical coordinate, radians 4 = quantum efficisncy, moles reacted/einsteins absorbed N
literature Cited
Baxendale, J. H., and Bridge, N. K., J . Phys. Chem. 59, 783 (1955). Harris, P. R., M. S. Thesis, Northwestern University, Evanston, Ill.. 1964.
Harris, P. R., Ph.D. Thesis, Michigan State University, East Lansing, Mich. 1967. Hatchard, C. G., Parker, C. A., Proc. Roy. Soc. 235A, 518 (1956). Jacob, S. M., Dranoff, J. S., A.1.Ch.E. Symposium on Photoreactor Design, Dallas, 1966. Lee, J., Seliger, H. H., J . Chem. Phys. 40, 519 (1964). Parker, C. A., Proc. Roy. SOC.220A, 104 (1953). Parker, C. A., Trans. Faraday SOC.,50, 1213 (1954). Parker, C. A,, Hatchard C. G., J . Phys. Chem. 63, 22 (1959). Wegner, E. E. and Adamson, A. W., J . Amer. Chem. SOC.88, 394 (1966). RECEIVED for review February 20, 1969 ACCEPTED July 8, 1970
Separation of T w o Immiscible Liquids in a Hydrocyclone Kenneth A. Burrillland Donald R. Woods Chemical Engineering Department, McMaster University Hamilton, Ont., Canada
The separation of a mixture of carbon tetrachloride in water was studied in a 2-in. diam glass hydrocyclone. The work first considered the effect of oil/water ratio and pressure d r o p across a mixing valve on the volume/surface diameter of the oil/water mixture. A linear relation between valve pressure d r o p and the volume/surface diameter was found. Oil/water ratio h a d no statistically significant effect. Secondly, the effect of Feed drop size distribution, feed oil/water ratio, and volume split on the separation efficiency of the cyclone was studied. Ranges of the variables were: Feed drop size, 15Op 12 300p; volumetric oil/water ratio, 0.135 to 0.210; volume split
xi
0 0 -1
0 0 -1 -1 1 1
-1 1 1 1 0 0 1 1 -1 -1 0 0 0 0 0 0 -2 2 0 0
-1 1 1 -1 0
-1 1 -1
1 -1 1 0 0 2 -2 0 0
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12 A13 A14 A15 A16 A17 A18 A19 A20
0 1
0
0 0 0 0 2 -2
-1 -1 1 0
0 -2 +2 0 0 0 0 0 0
1
0 1 -1 1 -1 0 0 0 0 -2 2 0 0 0 0
Mixing valve pressure drop and feed concentration ranges were selected to give the best photographic results for the drop size measurements. ‘The range of volume split was selected so that the optimum separation occurred whether or not coalescence existed within the hydrocyclone. That is, if all the drops coalesced so that pure carbon tetrachloride left in the underflow, then for 145, heavy fluid. in the feed, 14% of the total flow should leave through the underflow. If no coalescence occurred, then the underflow should represent the concentration of heavy fluid plus the interstitial volume of water. In sizing the hydrocyclone, there was uncertainty as to the value of (Dp)5,,to use. For clarification of the feed, the value of (D,,)70should be close to the smallest drop size encountered in the feed. Hence, a value for of less than 100 microns was desired. Secondly, the cyclone was operated without an air core. All correlations and predicting equations for are for cyclones with an air core. The cyclone was therefore designed to yield a (Dp)511 of 5 5 from ~ existing correlations. The objective of the study was to identify the most significant operating variables so that, subject to the economic constraints of the hydrocyclone operation, an operator could most readily improve the cyclone separation. Hence, the range of variables was as wide as deemed feasible; they were not restricted to just the locale of the maximum separation efficiency. Samples of the overflow and underflow streams were taken directly. The overflow was analyzed for carbon tetrachloride by extraction with hexane, and measurements of the extract refractive index with a dipping refractometer. The underflow was analyzed using turbidimetric titration (Siggia and Hanna, 1949). Since the feed liquids were mutually insoluble, the measured concentrations were, in effect, the immiscible contaminant concentrations. Because volume split was measured using underflow and overflow tanks, the separation efficiency, 7, could be found directly. Photographs also were taken of the overflow drop-size distribution. Total mass balances were checked for the runs. The volume split was changed by altering the underflow valve
only with the overflow valve being kept open for all runs. Care was taken to ensure that there was not an air core in the hydrocyclone and that no syphoning took place through the overflow pipework. Results and Discussion
Effect of Oil Concentration and Valve Setting on Drop Size Distribution. T o interpret successfully the influence of operating variables on hydrocyclone behavior requires a knowledge of the feed drop size distribution. For the system used, the drop size distributions generated from the mixing valve were log-normal. Figure 2 is a partial summary of typical data. A maximum of 500 t o 2000 drops were counted per distribution and the correction of Gwyn et al. (1965) was made before each average volume to surface diameter was calculated. All measured drops were spherical so the general shapefactor equation for the volume to surface diameter simplified to:
Since the Gwyn correction could be applied to lognormal distributions only a chi-square test, with a weighting procedure recommended by Kottler (1950), was performed and indicated that the distributions were lognormally distributed and the correction prodedure was justified. For the set of drop size distribution data deviating most from an ideal log-normal distribution, the calculated value of x L was 6.241 whereas the 9 5 7 confidence limit value for 12 degrees of freedom was 21.03. Qualitatively, the effect of increasing the pressure drop (or increasing the turbulence) a t the mixing valve, for a fixed feed concentration, is shown in Figure 2. When the pressure drop increased, the dispersion became more uniform. For the largest pressure drop used in this work a knee-bend distribution resulted, apparently a composite of two distributions. The existence of this tends to substantiate the concept of a maximum stable drop-size for a given degree of turbulence (Sleicher 1962). (However, for the range of variables studied, the knee-bend distribution 1000VA LVE
INCREASING PRESSURE
$
--E
P
n
I
(3
s
fj 100.. I-
5
n n 0
a
a
I 50 99 9
‘O0.0,
NUMBER OF DROPS SMALLER THAN Dp , (%)
Figure 2. Effect of mixing valve pressure drop on feed drop size distribution (oil/water ratio constant)
Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 4,1970 547
could be approximated by a single log-normal distribution to within a 95% statistical confidence level.) The experimental results are shown in Table IV. The values of were calculated from the total volume and area contribution over each size increment. If the distributions had been precisely log-normally distributed rather than statistically acceptable a t the 95% confidence level, then the values of the volume/ Surface diameter could be calculated from the relationship
+ 2.5 ln2g
In < D,>il = In < D,>
(3)
Table V is a comparison among the volume/surface average drop sizes as calculated from Equation 2, and corrected following the procedure of Gwyn et al. (1965) and from Equation 3. The relatively large discrepancy between the corrected summation and prediction of Equation 3 indicates the importance of the tails of the distribution in determining the volume and surface contributions. A second order polynomial that included interaction terms was used to correlate the data statistically. For a 95% confidence level, the result, in uncoded form, is 32 324.64 - 1.69 x I with a multiple regression coefficient calculated to be 0.7427. The table value is 0.576, a t 95% confidence level, and the variance is 0.4823 with the calculated t value of 3.50 as compared with a table value of 2.228 a t the 95% confidence level. A significant linear relationship between < D,> 32 and mixing
Table IV. Statistical Experiment Design for T w o Independent Variables at Five Levels and Resulting Volume/Surface Diameter Vol/Surface Av Calcd from Eq. 3,
Measured Values Run
1 2 3 4 5 6
7 8 9 10 11 12
, P
Go, P
94 79 97 73 76 78 84 80 68 113 93 90
1.92 1.95 2.20 2.22 2.34 2.00 1.88 1.82 1.84 1.98 1.89 1.88
?>,
valve pressure drop thus existed. Data and the correlation are given in Figure 3. These results indicated that the feed oil concentration and the interaction terms were not statistically significant a t the 95% confidence level. This negligible effect of oil concentration substantiates the conclusions of Holland et al. (1960) who found that the interfacial area generated by an orifice was proportional to the volume fraction of dispersed phase to the 0.9 power or < D,> l 2 varied as the volume fraction dispersed phase to the 0.1 power. The Effect of the Operating Variables on Separation Efficiency and Effluent Compositions. For purposes of evaluating the overall influence of the three operating variables, the cyclone separation efficiency defined by Equation 1 was used. However, from an operating point of view, the use of the cyclone as a clarifier may dictate that the composition of only one stream is important, and the overall separation efficiency may be of no interest. The results of this work are discussed using both criteria. OPERATING VARIABLESA N D SEPARATION EFFICIENCY. The experimental results are given in Table VI. Again, with a second order polynomial, the significant correlation, in coded form for a 95% confidence limit, is i~ = 79.45 - 2.94 yl - 4.42 x2 - 8.84 xg. The efficiency is given in per cent and the multiple correlation coefficient is 0.959. The variable, yl, is the coded Sauter mean diameter of the feed. The tabulated multiple correlation coefficient a t the 95% confidence limit is 0.615. All t tests were performed a t the 95% confidence level. The effects of these variables on the separation efficiency are shown in Figures 4-6. From these relationships, the order of importance of the variables is the volume split, the feed concentrations, and the drop size distribution as characterized by the pressure drop across the mixing valve based on the correlation obtained in the first part of this paper.
P
212.1 223.2 293.9 220.2 274.3 195.3 230.5 199.6 162.0 304.0 226.1 220.0
K
320
300..
280-
260-
Table V. Values for the Volume/Surface Average
Run
1 2 3 4 n
6 n
1
8 9 10 11 12
548
Vol/Surface Av (8 Vol/Z Surface) < D p > I?, P
193.5 203.8 254.8 187.3 241.7 176.0 197.7 188.4 153.4 266.8 205.7 208.1
Corrected Vol/Surface Av Gwyn et 01. Correction
u, P
212.1 223.2 293.9 220.2 274.3 195.3 230.5 199.6 157.8 304.0 226.1 220.0
Ix 240-
a
0
Calcd from Equation 3
lJr
220-
:
P
272
LEAST SQUARES REGRESSION LINE
e
200-
460 460 226
e 1606
172 241
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
2'0 2 '0
4'0 4 '0
6'0
.
Id0
MIXING VALVE PRESSURE DROP (mm. Hg.)
Figure 3. Effect of mixing valve pressure drop on volume/surface diameter < D,> i~
Table VI. Cyclone Outlet Sample Compositions for all Trials and Calculated Efficiencies ComDositions Water YI
O h
Vol
in Overflow
Pressure Profiles
y i in Underflow
Trial
(1)
(2)
(1)
(2)
Calcd Efficiency, 7 Yo
Feed
m m Hg Overflow
A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 All A12 A13 A14 A15 A16 A17 A18 A19 A20
100.0 94.40 96.70 96.00 96.80 96.56 94.05 99.36 96.84 99.68 96.49 96.48 99.38 94.56 99.94 94.67 97.60 96.32 96.93 97.28
99.68 94.37 96.90 96.10 97.60 96.50 94.17 99.36 96.54 99.53 96.18 96.47 99.32 94.30 99.94 94.33 97.76 96.02 96.71 96.96
17.02 14.31 19.80 20.50 17.80 17.83 18.90 22.42 14.87 14.67 17.20 18.27 20.95 16.32 23.80 16.35 13.29 21.41 16.53 17.00
17.58 14.28 19.95 20.43 18.35 17.58 17.90 21.30 14.62 15.47 17.23 18.02 20.08 15.89 23.75 16.60 13.21 21.90 17.12 17.32
95.66 67.58 79.55 70.85 80.60 76.76 65.41 91.69 75.90 94.99 75.74 76.46 91.96 69.89 94.16 64.54 84.25 74.05 78.63 80.35
310 315 315 320 315 315 320 310 315 310 315 315 315 320 310 325 315 330 315 310
103 122 111 124 116 116 124 103 120 109 118 116 115 120 98 126 115 116 116 111
I
I
I
Underflow
176 203 183 199 190
190 204 174 199 181 196 190 170 199 170 208 190 198 194 190
I
'
O
0
1
90-
z
I
>:
1
701 LARGE DROPS 295p 265p I
SMALL DROPS
235p I
205p I
I+ I
Figure 4. Effect of feed drop size distribution on cyclone efficiency Data a t zero levels for CO and OF/UF. Efficiencies for d r o p
+
1 levels were determined by averaging efficiencies size a t -1 and to give zero levels for CO and OFIUF. Coded levels of pressure d r o p used to give the coded d r o p size level.
V E uLL
REGRESSION LINE
80..
b
F 70..
LOW FEED OIL CONC. 6oi0.\3 0." 50 -2 -I
0.17
HIGH FEED OIL CONC 0.!9 0.21
0 +I LEVEL OF FEED OIL CONCENTRATION
+2
Figure 5 . Effect of oil/water ratio on cyclone efficiency Second order effects were not statistically significant. This correlation shows that for the range of volume splits 4 / 1 to 811 a linear correlation is significant even though for a wider range of volume splits, as shown in Figure 7, a linear correlation is not satisfactory. However, the efficiency for a given volume split can be theoretically estimated from a simple mass balance if all the dispersed phase is thrown to the cyclone wall. For convenience of comparison, these efficiencies are calculated a t the 14.6 vol % oil concentration, the zero level, and are plotted on Figure 7 for the two conditions: complete coalescence and no coalescence for constant interstitial volumes of 15% and 30% If complete coalescence occurred within the hydrocyclone, the maximum efficiency would occur a t a volume split of 85.4114.6 = 5.811. If no coalescence occurred within the hydrocyclone, then the interstices of the drop size distribution leaving in the underflow would be filled with water. For extremely dense random spherical packing,
Data o t zero levels for 1 P and OF/UF Feed oil concentration in volume fraction
for powder compaction purposes, Norman (1968) predicts that the packing density for uG = 1.82 is 80.85.Hence. the interstitial volume is 19.2%. The data are not available for loose random packing of spheres nor for deformable fluid drops. In laboratory tests with emulsions, fluid dispersions that had an interstitial volume as low as 4% vol/ vol could be synthesized. The water concentrations in the underflow were in the range 10 to 2 0 7 , Assuming an interstitial volume of 15% by volume, as might be obtained for tightly packed deformable drops, the maximum efficiency would occur a t a volume split of 83.3/ 16.7 or 5.011 for a corresponding separation efficiency of 97.8%;. For the same interstitial volume, the other separation efficiencies are calculated on the basis of a simple overall mass balance. Ind. Eng. Chem. Process Des. Develop., Vol. 9 , No. 4, 1970
549
15% whereas the optimum separation occurred when the interstitial volume approximated that for a loose random packing of about 30%. The data also suggest that no coalescence occurred within the hydrocyclone. OPERATING VARIABLES A N D EFFLUENT CONTAMINATION. If feed clarification is considered, the above simple mass balance also allows overflow oil concentrations to be calculated. Results are shown in Figures 8-10 for constant 15% interstitial volume in the underflow. The data in Figure 8 show that the drop size distribution does have a slight influence on the overflow oil concentration, contrary to the prediction of the model. This is simply because increased pressure drop (increased turbulence) across the
'""I
LARGE UNDERFLOW 4/ I 511
6/1
SMALL UNDERFLOW 7/ I 811
OVERFLOW OIL CONCENTRATION
r-----l 'r
Figure 6. Effect of volume split on cyclone efficiency
4t
-2
-I
0
+I
0
+2
LEVEL OF MIXING VALVE PRESSURE DROP (OTHER VARIABLES AT THE ZERO LEVEL)
I 50
WITH 15% INTERSTITIAL VOLUME
t
40
?
Figure 8. Observed and predicted overflow oil concentrations for changes in mixing valve pressure drop
OVERFLOW OIL CONCENTRATION
%
%
Y
%
x
LEVELS OF VOLUME SPLIT
6-
Figure 7. Calculated separation efficiencies 5-
For a loose packing of a dispersion interstitial volumes of 3 0 9 might be expected. These calculated efficiencies together with the experimental data are shown in Figure 7 . For volume splits less than that for the optimum separation all behavior is independent of the interstitial volume as all the heavy oil leaves in the underflow. This, of course, assumes that there was sufficient centrifugal force to throw all the drops to the cyclone wall. If the centrifugal force had not been sufficient, then all the curves would be shifted to the right. Part of the curve calculated from the assumption that the centrifugal force was sufficient t o send 8 0 5 of the volume of dispersed oil to the cyclone wall is shown on Figure 7. From these data one can conclude that there was sufficient centrifugal force available to achieve separation. During hindered discharge when the volume split was greater than the optimum, the drops were densely packed and deformed to offer an interstitial volume of about 550
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
8
4-
w
3
$ 3 -
2-
I O
/
/ I
-2
-I
I
0
I
+I
I
I
+2
LEVEL OF FEE0 OIL CONCENTRATION (OTHER VARIABLES AT THE ZERO LEVEL)
Figure 9. Observed and predicted overflow oil concentration for changes in feed oil concent rat ion
OVERFLOW OIL CONCENTRATION
i
101 001
1
1
1
1
1
1
% I
-2
-I
I
0
I
+I
'
1
'
10
I
1
1
'
50
1
1
'
'
90
1
'
1
I
99
999
CUMULATIVE NUMBER OF DROPS LESS THAN SIZE D p %
I
c2
LEVELS OF VOLUME SPLIT
Figure 1 1 . Drop size distributions for feed and overflow
(OTHER VARIABLES AT THE ZERO L E V E L )
Figure 10. Observed and predicted overflow drop size distribution mixing valve produces a more uniform drop size distribution. hence a larger underflow interstitial volume and a larger oil flow to the overflow. The model does not show the change in mixing valve pressure drop on interstitial volume since in the model the interstitital volume was assumed constant a t 15'.(. Agreement is excellent between the theory and the observed overflow oil concentrat,ions for Figures 9 and 10. SEPARATION EFFICIENCY AND DROPSIZEDISTRIBUTION. The relative unimportance of the feed drop size distribution on separation efficiency suggested by the statistical correlation is both deceptive and important. This lack of importance may be understood by considering the overflow drop size distribution. The cyclone in this study was partially operated under a condition of hindered discharge. Therefore, the volume split and the feed oil concentration are the most important variables. Feed drop size distributions are unimportant for hindered discharge operation since more oil is centrifugally sent to the cyclone walls than can be removed from the underflow. This condition of hindered discharge coupled with large /, < 11.> of the feed drop size distributions compared with ( D h ) ~tneans #, that the simple mass balance model can be used to interpret the results, and therefore allows the cyclone separation mechanism to be probed. For the zero level operation conditions only, photographs were taken of the drop size distribution in the overflow. A mathematical model used to calculate this distribution theoretically from the feed drop size distribution provides some insight into what could have been occurring in the cyclone. To obtain the excellent agreement between the observed and calculated distributions as shown in Figure 11, assumptions were made about the short circuit flow (that portion of the feed distribution that passes directly t o the overflow). and the efficiency of' separation of each segment of the distribution. N o coalescence appears to occur arid hindered discharge operation occurs at the 6 1 volume
split for the zero level conditions. Hindered discharge operation represents conditions where the feed dispersion has been separated so that it rests along the cone wall yet portions of it leave in the overflow owing t o limited underflow discharge. This type of operation is employed when excessive light phase contamination of the underflow cannot be tolerated although heavy phase contamination of overflow is allowed. Photographs were taken of dye traces injected into the feed for single phase water studies. These suggested that some short circuit flow existed. Calculations with 0 to 15'-< of the total feed drop size distribution going directly to the overflow seem reasonable based on thb observations of Kelsall (1953). For the efficiency of separation versus drop size. the correlation used was that of Yoshioka and Hotta (1955). This correlation expressed the fraction of drops separated into the underflow region as a function of the ratio of ,. the drop diameter to the 50% diameter ( D , J ) ~ ,Values -,,, are almost impossible to obtain experimentally of (ZJ,) for liquid-liquid systems because of coalescence of the dispersion in the separated streams. For liquid-solid systems for hydrocyclones operating with air cores, semitheoretical estimates for yield values of 5 5 p , whereas the empirical correlation of Dahlstrom (1949) gives a value of log. However, since the present work considers cycloiies depends operated without an air core, and since (DP)-,,! on the velocity profiles, it is only fortuitous if the values of (D,])-,,! required by this present work are in this range. A simple mass balance over the cyclone was made for the drops and for the concentration of carbon tetrachloride in the overflow. Different values of (Dp).,tl(range 10 t o 6 0 ~ ) and . interstitial volumes in underflow' (range 10 to 20";) were taken for no short circuit flow. Table V I 1 shows qualitatively the results. The distribution was relatively insensitive to the interstitial volume but wab very sensitive to the valve of (LIP);,,. Excellent agreement between observed and predicted = 25g and for l F , distributions was obtained for (D,q)50 interstitial volume as is shown in Figure 11. The surprising result is that excellent agreement f o r both drop size distribution and contamination w;is (;I)t
,d kng Chem. Process Des. Develop , Vol. 9,No. 4, 1970
55 1
Nomenclature
Table VII. Qualitative Summary of Curve Fits for Various Values of ( D , ) 0 and of Interstitial Volume in Underflow Interstitial Volume
io, ) used p
10%
15%
20%
20 25 30
Poor Good Poor
Fair Excellent Fair
Poor Good Poor
tained assuming that no drops short circuited the cyclone despite the dye study indications that the continuous phase does short circuit. Also surprising is the sensitivity of the results to the values of More details are given by Burrill (1967). Conclusions
Log-normal distributions of drops result when a carbon tetrachloride-water system passes through a gate valve. When the pressure drop across the valve is increased, the dispersion becomes more uniform in diameter. At high pressure drops, knee-bend distributions result that tend to substantiate the concept of a maximum stable drop size for a given degree of turbulence. The linear relation between < D,> 12 and mixing valve pressure drop was found to be independent of oil concentration from 12 to 18 vol 5.Interactions between the variables were not significant a t the 95% confidence level. For the separation efficiency, volume split was the most important variable, followed by feed oil concentration and feed drop size distribution. The importance of volume split emphasizes that the hindered discharge mechanism is important. Also. if a cyclone is to be designed for different operating conditions, it should have valves on the outlet streams. Interactions between the variables were not significant a t the 9 5 7 confidence level. The data suggested that coalescence did not occur within the hydrocyclone. For a limited set of data, the exit drop size distribution can be predicted by assuming values for the interstitial volumes and for (D,) These calculations were sensitive to the (D,) ,"values but relatively insensitive to the interstitial volume values. Dye studies suggested that short circuit flow occurred although the calculations suggest that no short circuit flow of contaminant drops occurred. The ability to predict the location of the optimum separation without experimentation depends on our ability to estimate ahead of time the amount of coalescence and the interstitial volumes. For the hindered discharge regions of operation the interstitial volumes seemed to be about 15'5 volivol. This suggested that the droplets were densely packed and deformed because the calculated interstitial volumes for the log-normal distribution of rigid spheres is predicted by Norman to be 1gCc.However, a t the optimum separation the interstitial volume seemed to be about 3 0 5 . ,,).
552
Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 197:)
C CO D, n OF,U F IP Q
= feed oil concentration, volume per cent = feed oillwater ratio = particle diameter, microns
= number of drops in a given size D , = volume split = mixing valve pressure drop, mm Hg = volume flow rate, c.f.s. y = volume fraction light phase X' = statistical test chi-squared = micron c = standard deviation of the drop size distribution 7 = overall separation efficiency 8 = summation
SUBSCRIPTS 1 = hydrocyclone feed 2 = overflow 3 = underflow 32 = volume i surface of particle size distribution 50 = particle size appearing 50% in the overflow and 50% in the underflow G = geometric method of calculation i = index n = calculation based on a number-size distribution OTHER
= general symbol for average
Literature Cited
Burrill, K. A., M. Eng. Thesis, McMaster University. Hamilton, Ont., Canada, 1967. Dahlstrom, D. A., Mining Trans. 184, 331 (1949). Ellefson. R. R., M.Sc. Thesis, Northwestern University, Evanston, Ill., 1953. Gwyn, J. E., Crosby, E. J., Marshall, W. R., Ind. Eng. Chem. Fundam. 4,204-8 (1965). Holland, C . D.. McDonough, J. A., Tomme, 51;. J., A.I.Ch.E. J . 6, 615-18 (1960). Hunter, J. S...Chem. Eng. Progr. Symp. Ser. 56, (31), 10-26 (1960). Kelsall, D. F., Chem. Eng. Sei. 2, 254-72 (1953). Klein, F. G., M.Sc. Thesis, Northwestern University, Evanston, Illinois, 1951. Kottler, F., J . Franklin Inst. 250, 419-41 (1950). Norman, L. D.: Dept. of the Interior, Bureau of Mines, College Park, Md. 20740, private communication, 1968. Rietema, K., Chem. Eng. Sci. 15, 298-325 (1961). Siggia, S..Hanna. J. G., Anal. Chem. 21 (9), 1086-9 (1949). Simkin, D. J.: Olney, R. B., A.1.Ch.E. J . 2 (41, 54551 (1956). Sleicher, C. A., Jr., A.I.Ch.E. J . 8 (4), 471-7 (1962). Yoshioka, N.. Hotta, Y., Chem. Eng. J a p . 19, 632-40 (19553. RECEIVED for review March 3, 1969 ACCEPTED July 30, 1970 The authors thank the National Research Council of Canada for awarding a bursary to K. A . €3. and the Department of Chemical Engineering for financially supporting this work.
