INDUSTRIAL AND ENGINEERING CHEMISTRY
2470
(7) Ghosh and Basak, Petroleum (Chicago),11, 131 (1948). (8) Hamai, J . Chem. Soc. Japan, 62,516 (1941). (9) Hofer and Peebles, J . A m . Chem. Soc., 69,893 (1947). (10) Kummer, DeWitt, and Emmett, I b i d . , 70,3632 (1948). (11) Kummer, Podgurski, Spencer, and Emmett, Ibid., 73, 564 (1951). (12) Matsumura, Tarama, and Kodama, J . Soc. Chem. Ind. (Japan), 43,Suppl. Bdg., 175 (1940). (13) Taylor and Strother, J . Am. Chem. Soc., 56, 586 (1934).
Vol. 44, No, 101
(14) Travers, "The Experimental Study of Gases," p. 23, Lolidon, Maomillan Co., 1901. (15) Van Itterbeek and Dingenen, 2.phgsik. Chem., 50B,341 (1941). (16) Weller, Hofer, and Anderson, J . Am. Chem. Soc., 70, 799 (1948). RECEIVED for review October 11, 1951. ACCEPTEDM a y 21, 1952. Abstracts from the thesis of K. A. Kini for the Ph.D. degree of the University of Bombay, 1950. Presented by M. V. C. Sastri before the Section of Fuel, Gas, and Petroleum Chemistry, a t the XIIth International Congress of h r w and Applied Chemistry, New York, Beptemher 1961.
echanism o d e w Iopment
Plate Efficiencies FRANK 5. WEST', WALTER D. GILBERT2, AND TORU SHlMlZUa Universify of Washingfon, Seoffle, Wash.
T
HE purpose of this investigation was to help establish the mechanism of mass transfer between vapor and liquid on bubble plates. Theoretical relations for the mass transfer coefficients in the liquid and gas phases were tested for a limited number of systems using the simplest of all bubble plates, the sieve or perforated plate. Data were obtained on foam voids, on effective interfacial area, and on initial bubble size.
Values of K L have ordinarily been determined from the Miirphree plate efficiency based on liquid concentrations
(49 There is no general equation relating EOLto the mass transfer coefficient or number of transfer units, but under certain q w i x l conditions one of the two following equations may apply:
Basic Relations The eiirichment to be produced by an actual bubble plate can best be calculated from the Murphree plate efficiency which, however, depends upon the amount and kind of mixing of the liquor on the plate and of the vapor below the plate. The Murphree vapor point efficiency is essentially independent of such factors and therefore is the more basic relation. It has been related to the Murphree plate efficiency for various kinds of mixing by Lewis (12) and by Kirschbaum (9, 10). The Murphree point efficiency based on vapor concentrations is defined as
Equation 5 applies when there is no mixing of the liquid except in the vertical direction as the liquid flows across the plate. Equation 6 applies when the mixing is so complete that the liquor concentration is uniform across the entire plate (18). Both assunie the vapor composition to be essentially constant across the plate and up through the liquid, The latter condition is seldom met in practice, but it may be created experimentally to assist in determining K L by using either a pure vapor or else such a tremendous excess of gas that its composition does not (,hang? itppreciably during passage through the plate. By correlating experimental kca and k ~ data, u Walter mid SherIf the liquid flowing across the plate is completely mixed in the wood (18) derived a general relation for predicting point vertical direction so that y*npis constant, E@is related to the mass ciencies for bubble-cap plates based on Equations 2 and 3. ll'~ transfer coefficient (1, f4, 18) and to the number of transfer mas taken proportional to the effective liquid depth and inverwly units ( 3 ) by the equation proportional to the cube root of the slot width and the 0.68 power of the viscosity. KOallowance nay made for variations in cliffusivity or for the effect of gas rate Geister et al. ( 3 ) have presented additional empirical corielaK Qis related to the gas and liquid phase mass transfer coeffia Equations 2 and 3 for tions leading to values of kca and k ~ for cients by the equation one particular bubble-cap plate. The effect of gas and liquor rates and of liquor seal were shovn. Methods were sugyvted for allowing for the effect of different diffusivities. A more fundamental approach to the problem, as suggested b y The values of ka and of k~ may be determined experimentally from runs made under such conditions that KQ = k~ or K L = k ~ . Geddes ( I ) , is to study separately the factors which determine t h e bubble size, the time of contact, and the individual ka and kL The humidification of air with water has been used for the former values. I n the absence of such information Geddes suggested and the absorption or desorption of slightly soluble gases from that the bubble size might be estimated b y an equation similar water for the latter. to that for bubbles formed slowly a t an orifice involving a balance 1 Present address, Shell Development Co., Emeryville, Calif. between surface tension and buoyant forces. The time of contact 9 Present address, General Electric Co., Hanford Works, Hanford, Wash. was calculated from the liquor seal on a foam-free basis and a n 8 Present address, North American Aviation, Ino., Downey, Calif. (lfi-
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1952
empirical equation for the velocity of rise of individual gas bubbles through liquids. The effective liquid film coefficient was computed by Higbie’s equation (7) for unsteady state diffusion of a solute into a semi-infinite stagnant liquid layer k~ = 1.13
($)’’’
CLav
2471
a = 3- 6
foam, by
If preferable, koa and k ~ may a be evaluated directly by substituting te from Equation 9 into Equation 7 and multiplying through by Equation 10
(7)
ka = 2.394 ( D V E ) ~ / ’ J C , ~ / T ~ / ~
(11)
DL is the diffusivity of the solute, and t, is the time of diffusion
Empirical or theoretical correlations are needed for 3 / r .
corresponding t o the life of the liquid layer. The latter was estimated as the time required for a bubble t o rise a distance equal to its own diameter. The average total moles per cubic foot, C L ~has ~ , been introduced here to convert the units of k~ from feet per hour to pound moles per (hour)(square foot). The effective gas film coefficient was calculated from the equation for unsteady state diffusion into a rigid sphere of the gas for a time equal to the total time of contact of the bubbles. It now appears that the equations tentatively proposed by Geddes involve two large but partially compensating errors. Hornbeck (8) and Meredith (13) have shown that bubbles formed from single, round and a/,,-inch orifices increase greatly in size with increasing gas velocity and are 10 to 200 times the bubble volumes computed by Geddes’ method for practical operating velocities. Secondly, it has been observed that bubbles rising through a liquid are constantly changing shape, thus undergoing a high degree of internal mixing and rendering the assumption of stagnant spheres completely invalid. Thus, it seems likely that the equations suggested by Geddes predict too high interfacial areas and too low gas film coefficients. The excellent agreement found in Geddes’ examples must have been due to a fortuitous cancellation of errors.
I n predicting point efficiencies it will be convenient to substitute the equations for k~ and k~ into Equation 3 to obtain a gen-
It is proposed that point efficiencies be evaluated by Equations 2 and 3 with ZV,a, k ~ and , k~ being evaluated as follows: 1. ZV may be related to E, the fraction voids in the foam in a bubble plate, by the relation = Zi/(l
-
E)
(8)
where 2;is the liquor level in the absence of bubbles for a perforated plate or the liquor level in the absence of bubbles less the distance from the plate t o the middle of the bubble-cap slots for a bubble-cap plate. Empirical or theoretical correlations are needed for E . 2. k~ should be evaluated by Equation 7 , using a transient liquid film life, te, computed arbitrarily by the relation te = 2 r 4 V
w
Ilk
I
WET
\I
\I1
DRY
t
TEST SECTION 1
C 02-H2 0 MIXERMIXER
c02
H2°
THERM0
M-
4z:E
STEAM AIR
OR
u
u
HUMIDIFIER Flow Sheet of Experimental Apparatus
era1 expression for Ko, which may then be substituted into Equation 2 along with B=VCv,, and the relations for ZV and a to yield Equation 12 1 In 1 - EG
The right-hand term in the denominator represents the ratio of the mass transfer resistance of the liquid phase to that of the vapor phase. Any dimensionally consistent set of units can be used in Equation 12. Note that m is properly defined by
(9)
where V is the superficial gas velocity on the plate (so that V / e is the velocity of rise of the bubbles), and r is the effective bubble radius. This ignores the local upward displacement of the liquid with the gas bubbles. It assumes the gas to exert a negligible upward frictional drag on the liquid near the interface compared to the retarding drag exerted by the relatively stationary bulk of the liquid. Consistent results should be obtained even if Equation 9 should prove to be in error, provided that the true transient film life is directly pro ortional to that calculated by Equation 9. 3. ko should also &e evaluated by Equation 7, substituting D V for DL and CvOVfor C L ~ The ~ . transient film life, t,, would be the same for both phases since it re resents the time required for the gas-liquid interface t o be carriea around the bubble. The theory is simlar to that for liquid-liquid extraction from single drops (19). Such values of ko are not as sound theoretically as the corresponding values of k ~ .This results from the gas diffusivities being of the order of 1000- to 10,000-fold greater than the liquid dihsivities, so that a solute enetrates a gas layer 30- to 100-fold further than it will a liquidfayer in the same time interval. Thus the p s transient film is less likely t o behave like a semi-infinite solid than the corresponding liquid transient film over the same time interval. The k~ values so found should nevertheless be much better than those corresponding to rigid gas spheres, and they may prove t o be reasonable approximations t o the true values. 4. a, the effective interfacial area per volume of foam, is related to 3 / r , the effective interfacial area per volume of gas in the
BULB
VERFLOW
Figure 1.
Proposed Correlation
zv
-
m = :Y
Xp
- Yip - Zip
The present investigation was undertaken to test the validity of the proposed correlation. Perforated plates were used because of their known orifice areas as compared to the variable slot openings of bubble caps. Values of kaa were determined for the humidification of air with water a t the wet bulb temperature so that the gas phase should be controlling. Values of k ~ a were determined for the absorption of pure carbon dioxide gas by water and for the desorption of carbon dioxide from water by a great excess of air in order that the conditions for Equation 6 should be satisfied. The fraction voids in the foam was calculated from the initial clear liquid and final foam levels by means of Equation 8. Attempts were made t o determine the bubble radius, both by direct measurement of bubble size and by indirect calculation by substituting the experimental values of ~ G Uand of k ~ into a Equation 11.
Apparatus
A preliminary study was made using a 2-row, 14hole sieve plate test section (6),but most of the data were obtained with
INDUSTRIAL AND ENGINEERING CHEMISTRY
2472
a 10-row, 83-hole sieve plate test section ( 1 7 ) . The flow sheet for the larger apparatus is shown in Figure 1. It consisted of the test section and of systems for metering and processing the air and water supplies.
STATIC PRESSURE TAP
SIEVE PLATE 834/8" D. HOLES
-AIR
-
EXIT VALVE
I THERMOMETER
REGULATOR
CHAMQER
M ,,
BAFFLES 7
I--'
A
THERMOCOUPLE
AIR CHAMDER Figure 2.
Sieve Plate Test Section
Figure 2 shows the 83-hole test section, nhich consisted of a perforated plate, an air chamber below the plate, a column above the plate, and inlet and outlet water manifolds. The perforated plate was formed by drilling '/*-inch inside diameter holes on 3/pinch equilateral triangular centers in a '/g-inch thick brass plate measuring 3'/4 X 39/16 inches. A total of 95 holes were drilled in rows, alternating 9 and 10 holes. This number was reduced to 83 by plugging holes a t each corner after a fev preliminary runs showed excessive leakage of water into the air chamber a t these points. The perforated plate was soldered into and flush with the surface of a rectangular hole in a larger 1/2-inch thick brass base plate. Inlet and outlet brass water X 31/2 inch nianifolds were screwed to the base plate beneath slots milled through the base plate on either side of the pel forated plate itself. The plate was oriented so that the nater flox-ed across the plate normal to the r o m of holes. A Lucite air chamber was screwed to the base plate between the water manifolds and beneath the perforated plate to distribute the air to the holes and to permit observation of any leakage of water through the holes. The 3-inch deep chamber was filled with copper turnings to above the air inlet for more even distribution of the air. To minimize humidification in the air chamber, '/2-inch wide Lucite gutters m-ere glued to the four sides an inch below the plate to drain off the water which persisted in leaking through the holes near the perimeter of the plate at low gas rates. A 3/16-in~hdiameter horizontal stainless steel thermowell was inserted well above the copper turnings to measure the dry bulb temperature subsequent to any humidification taking place in the lower part of the chamber. The walls of the rectangular column above the sieve plate fitted into grooves milled into the base plate and partly filled with aquarium cement. The column consisted of 12 inches of Lucite for visibility surmounted by 18 inches of galvanized iron
VOl. 44, No. 10
to prevent excessive entrainment. The walls were held between the base plate and a similar brass top plate by tie rods at each corner. The top plate had tn-o 1-inch outlets, one containing a baffled thermometer chamber and the other a valve to regulate the pressure in the column so as to produce an air velocity of approximately 33 feet per second through the thermometer chamber regardless of the air rate. The baffles were necessary to prevent drops of water from reaching the ITet and dry bulb thermometers in the thermometer chamber. The top was removed for the desorption runs. The interior of the column was divided by two 10-inch Lucite baffles into an inlet water chamber, the bubble chamber proper, and an outlet chamber, as indicated in Figure 1. The foam was confined by the baffles to the middle section above the perforated plate and therefore should be representative of a much larger perforated plate. The baffles could be moved up or down to leave more or less room for the water to flow into and out of the perforated plate section. Injection of dyes in the bubble chamber showed that the water circulated from the walls along the surface of the plate ton-ard its center, up the middle portion of the plate, out to the -n-alls, and d o m the walls to the surface of the plate again. This flow resulted in a higher head of nater near the wall and particularly in the corners, rather than in the center, and accounted for the greater leakage a t these positions. To reduce this circulation the corner holes were plugged, and four 4-inch high corner baffles xere glued to the adjustable main baffles as indicated in Figure 2. All baffles and wdls were placed so that their distance to the closest holes were identical to the distance bet17 een adjacent holes, leaving an effective plate area of 0.077 square foot. The water processing and metering equipment consisted of a steam injection heater controlled by an automatic temperature controller, a constant head tank, and an orifice meter. Additional apparatus for saturating the water with carbon d i o d e was provided for the desorption runs. Gas from a carbon d i o d e cylinder was metered through a limiting orifice and injected into the water at a point below a mixing section, consisting of 5 feet of I/4-inch pipe. The resulting mixture was dischaiged into the constant head tank through a short open section packed ~ i t h 1/4-inch Raschig rings to remove excess carbon dioxide, as indicated in Figure 1. Water from the constant head tank paised through the orifice meter into the inlet water chamber, across the plate, through the outlet water chamber, and out an inverted L-shaped leveling leg. The air conditioning system consisted of an air pressure rcgulator, an orifice meter, and either an electric heater or a humidifier. The heater for the humidification runs was a section of insulated pipe wound n-ith Nichrome wire. It was replaced by a humidifier located just before the test section for presaturating the air in the desorption runs. The humidifier was a 55-gallon drum, into the bottom of which air was bubbled through 1001/3inch holes in a section of 1-inch pipe. Water at the same temperature as that of the sieve plate continually flowed through the humidifier, maintaining the level in the tank a t approximately 2 feet. Steam was also injected through a limiting orifice into the air stream prior to the humidifier to heat and partially humidify the air. The a-row, 19-hole test section used in the preliminary study ( 5 ) v a s similar t o the 83-hole test section in most essential details. The perforated plate contained 191/8-inch holes drilled in two rows on S/&ch equilateral triangular centers. Baffles spaced 0.75 inch apart were used to separate the bubble chamber from inlet and outlet water chambers. The walls of the test section were only 14 inches high, so that relatively low gas rates had to be used to prevent excessive entrainment. The brass air chamber inch deep and had no provision for below the plate was only preventing or correcting for humidification of the air by the water leaking through the plate.
October 1952
INDUSTRIAL AND ENGINEERING CHEMISTRY Procedure
Preliminary gas film runs were made, humidifying air with water using the 19-hole plate. Most of the efficiencies observed were above 99%, but these have not been reported here since it became evident that a large amount of humidification must have been taking place in the brass air chamber below the plate. Many of the holes did not even operate at the lower air rates, and experience with the larger plate suggests that there must have been much leakage of water back through certain holes even when all holes were operating. The humidification runs made with the 83-hole plate minimized and corrected for humidification in the Lucite air chamber and should be reliable. Metered air was heated to a wet bulb temperature approximately equal to room temperature. The valve on the air exit on the top plate was regulated to give a static pressure in the tower of 1 inch of water, sufficient to give a flow of 33 feet per second past the wet and dry bulb thermometers in the baffled thermometer chamber. Entrained droplets occasionally got past the baffles a t the highest air rates. This was indicated by slight but rapid dips in the dry bulb readings, which then returned to normal without the wet bulb having been affected. Readings were avoided during such "dips." The inlet water temperature was also controlled a t room temperature to eliminate liquid film resistances and heat losses to the surroundings. The water rate was adjusted so that a very small quantity dripped from the outlet leveling tube, thus ensuring a constant water level throughout a run. The water level on the plate was regulated by pivoting the leveling leg about a union. The baffles within the tower were raised as far as possible without too many bubbles leaking beneath the baffles into the water chambers. After operating conditions had been established, the inlet air, outlet wet and dry bulb, and inlet and outlet water temperatures were measured every 5 minutes until the difference between the wet and dry bulb readings was constant for three consecutive readings. The latter temperatures were read on 0.02" C. thermometers with reading lenses. The water and foam heights were also measured a t frequent intervals during each run. Preliminary liquid film runs were made absorbing pure carbon dioxide gas in water using the 19-hole plate. In this case the water leaking into the brass air chamber may even have been beneficial, in that it would have helped complete the humidification of the inlet gas which was begun in a crude water-seal saturator. So much carbon dioxide was discharged that it was necessary to vent it to a fume hood to avoid excessive errors in the analysis of the liquor produced. Otherwise the procedure was similar to although not identical with that de'scribed below for the desorption runs. The final liquid film runs were made, desorbing carbon dioxide from water by air in the 83-hole plate. The air was heated and partially humidified by injection of live steam and was then bubbled through 2 feet of water a t 22.4"C. in the humidifier before entering the air chamber. Other tap water a t 22.4' C. was saturated with carbon dioxide and was metered to the plate. The outlet baffle had to be lowered quite close to the plate to prevent too many bubbles from being swept out of the foam chamber a t the high water rates used. The same sweeping action of the water permitted the inlet baffle to be raised about '/z inch off the plate. Even so the level of water in the inlet chamber had to be maintained '/8 to inch above the desired liquid level to offset the head loss caused by flow under the baffle. After running at steady conditions for 30 minutes, samples of the inlet and outlet liquor were taken at four consecutive 5minute intervals and were analyzed for carbon dioxide content. To determine the equilibrium carbon dioxide and bicarbonate content of the inlet water, a water sample was taken from the humidifier a t the end of each day of operation. The inlet and outlet water and inlet air temperaures, the clear liquid level, and the foam height were noted a t each sampling.
2473
Carbon dioxide was determined by adding a liquid sample to a known excess of 0.05 N sodium hydroxide containing a large excess of barium chloride and back titrating, after standing for 10 minutes with frequent agitation, with 0.05 N hydrochloric acid to the phenolphthalein end point. The concentrations found were corrected for the combined bicarbonate content of the inlet water. The flasks were flushed out with carbon dioxide-free air before adding the reagents and during the titration. The initial clear liquid level, 26,was taken as the level in the water chambers on either side of the foam chamber in the humidification runs where the water flow was very small. I n the desorption runs, ZI was taken as the liquid level in the corner sections cut off from the foam chamber by the corner baffles. I n the absorption runs with the 19-hole plate, the inlet water chamber level was used since it was possible t o raise the baffle on the inlet side some distance without bubbles working back beneath the baffle against the water current. The height of foam between the baffles in the bubble chamber, ZV, was determined in three ways: 1. Four photographs, such as those shown in Figure 7 , were made during a run a t an exposure of 1 / 1 ~second. ~ ~ Successive pictures showed that the foam level fluctuated widely with occasional large bubbles bridging across between the baffles in the 2-row plate. It was necessary to average the levels from four photographs for each run to obtain a reasonable average. 2. The levels were observed under the illumination of a General Radio Type 631 Strobotac flashing 1000 times a minute. This seemed to eliminate most of the fluctuations and permitted direct measurement of the levels. 3. The levels were observed and measured under ordinary illumination; the fluctuations were averaged out by eye.
All three methods were used in the preliminary investigation with the average of the results being reported. Methods 2 and 3 generally agreed within 0.1 inch during the absorption runs, while the average of the photographic levels was liable to be off by 0.2 to 0.5 inch. Visual observation only was used with the IO-row plate where a few photographs showed no sign of bridging over of bubbles. Attempts were made to determine the initial bubble size on the 2-row plate by measuring the rate of bubble formation a t each hole stroboscopically. Extremely constant air pressure was needed for these measurements, since it was impossible t o use the stroboscope with any accuracy when the air rate fluctuated slightly. Each hole was observed in turn while varying the frequency of the stroboscopic light until a stationary bubble appeared just above the hole. This usually occurred at 15 to 20 flashes per second. Higher multiples of these frequencies also stopped the bubbles, but the bubbles were less clear and seemed t o be jumping around more. Efforts to check submultiples of the stroboscopic frequencies were hampered by the Strobotac's lower limit of 10 flashes per second. Photographs taken at extremely low flow rates such that only one or two holes were operating revealed the same picture as seen by the Strobotac at what was believed to be the proper frequency. At normal gas rates the bubbles followed too irregular paths to permit stroboscopic observation after breaking away from the holes. At high gas rates and particularly at high gas and water rates, individual bubbles became very difficult to distinguish even a t the holes, because of bubble interaction between holes. This was accentuated a t the still higher ga? rates used in the 10-row plate t o such a degree that no reliable frequencies could be obtained.
Methods of Calculation The efficiencies, transfer units, mass transfer coefficients, voids, and effective interfacial areas per volume of gas in the foam along with the pertinent experimental data have been calculated and are tabulated in Tables I, 11, and 111.
INDUSTRIAL AND ENGINEERING CHEMISTRY
2414
Vol. 44, No. 10
found from the equivalent of Equation 11. The diffusivity of water vapor in air a t an estimated average temperature of 28" C. was 0.987 square 12 Z i , tib ta. tw. GO ~ n . 0 c'. 0 C. C. EG KGU NG e 3/r foot per hour corrected from the 0' C. data (16). 139.4 2 . 9 4 5 0.667 23.085 21.660 0.9474 117.3 23.26 2.00 48.8 The diffusivities of carbon dioxide in water at 0.735 150.2 2.419 25.580 23.310 0.9110 168.9 23.26 1.06 48.8 22.4' C. for the large plate and at 12.0' C. for the 0.704 12%1 2.888 0.9443 153.2 2.00 46.4 23.115 21,740 29.86 small plate were taken as 7.37 and 5.4 X 0.750 147.6 26.635 21.880 0.8536 196.3 1.920 29.86 0.87 50.8 0.800 160.1 27.685 21,480 0.7882 228.3 1.552 29.86 0.50 50.8 square foot per hour, respectively, corrected from 0.650 140.7 25.160 22,440 0.9150 212.7 2.465 44.95 2.00 54.4 151.5 1.00 53.5 27.215 22.300 0.8425 249.3 1.848 0.750 44.96 20" C. data (15). 0.846 148.1 257.1 1 550 28.690 21.980 0.7877 44.95 0.50 53.6 As a further test of the proposed method, the 130.2 2.570 0.765 241.0 23.920 21.480 0.9235 66.40 2.00 53.4 foam heights and bubble-cap efficiencies of 134.9 54.9 26.160 21,760 0.8671 268.0 2.018 0,833 66.40 1.00 140.3 0.704 0.9084 25.305 22.190 2 5 2 . 3 2.390 2.00 57.3 59.42 Gerster et al. (S) were utilized in Equations 2, 5 , 0 778 157.8 27.090 22,210 0.8610 59.42 1.00 312.6 1.973 57.3 8, and 11 to yield values of voids and of effective 0.738 147.3 0.8685 194.7 2.029 30.04 1.00 26.230 22,100 53.5 0.867 119.3 26.225 21.620 0.8379 135.6 1.820 23.31 0.50 50.0 3 / r for bubble-cap plates. The results are given 0.714 152.1 25,180 21,710 0 . 8 5 7 8 200.7 1.951 30.04 1.00 46.1 i n Table IV. In calculating ZV and Zi it was as158.3 0.7892 226.1 1.568 0 . 8 0 0 27.795 21,660 30.04 0.50 50.8 0.750 139.9 24.262 21.440 158.9 2.277 23.26 1.00 0.8974 48.9 sumed that only the space above the middle of 139 0 25.630 21.440 0.8317 165.8 1.782 0.833 23.26 0.60 46.3 the slots (1.31 inches above the plate) contained 0.791 169 9 0.50 51.4 0.7628 190.1 1.439 37.90 28.800 21.780 bubbles, and the voids are therefore based on this a G is based o n c'ross-sectional area of 0.077 square foot. restricted volume. The gas and liquid molar veb t i is corrected for radiationlosses; see text. locities, G and L, were based on the "net active cross-sectional area of tray" of 0.67 square foot. Table II. Carbon Dioxide Desorption Data and Results for The complete data were obtained from American the 83-Hole Plate Documelitation Institute Documents 2702 and 2703. The diffu(Inlet air a n d water temperature approximately 22.4' C . cross-sectional sivity for water in air was assumed to be the same as above, while area of bubble chamber, 0.077 &.re foot. inlet liquor cb;lcentration corrected for bicarbonate = about 0.00061 mdle fraction; and equilibrium conthat for oxygen in \m,ter at 31" C. was taken as 10.3 X l0-6square centration corrected for bicarbonate = negligible) foot per hour, as suggested by Gerster. The 60-gallon-per-minute G L 12 Zi EOL K L ~ KLUZV L 3/r humidification runs were omitted because the EQ values were 2.00 0.8403 0.750 148.5 68.14 444.0 3802 2336 so high that the slightest error in their values would have thrown 142.3 1417 0.800 68.14 434.6 1.00 0.7653 3390 170.4 51.37 443.1 2.00 2305 0.733 0,8388 3688 off the correlations materially. 0.767 169.2 00.92 437.6 1.00 0.7483 3675 1301
Table 1.
23.82 24.17 31.14 30.85 45.60 45.60 46.08
Humidification Data and Results for the 83-Hole Plate
439.3 442.1 434.8 439.5 061.5 375.6
2.00 1.00 2.00 1.00 1.00 1.00
0.8143 0.7497 0.8266 0.7493 0.6724 0.7945
279.5
1.00
0.8290
1926 1324 2038 1296 1153 1452 1335
3654 3531 3797 3891 3456 4360 4069
0.692 0.778 0.712 0.750 0.750 0.780 0.750
219.1 206.3 208.3 208.9 169.2 197.5 227.5
The point efficiencies for the humidification were talculated by Equation 14, which is essentially identical with E ~ tion 1 for water at the >yet bulb temperature Eo =
wtP tl tw
(14)
Discussion of Results Figure 3 shows how the number of transfer units in humidification, N U , is affected by the gas rate and the initial clear liquid level, Zi,on the 83-hole plate. NU increases with Zi hut by much less than the first power of Zi predicted by Walt'er and Sherwood's equation (18) and by Geddes' method ( 1 ) . This is due to the voids content of the foam decreasing with increasing 21so as to affect ZV, the IC's, and the interfacial area. N o is ~relativelY ~ -independent of gas velocity but goes through a minimum. Figure 4 for carbon dioxide absorption and desorpbion shom how K L u Z ~ or LNL vary with the gas rate and the initial liquid level on the two perforated plates. The effect of liquid level is the same as for humidification and for the same reason. The effect of gas rate is different for the two plates, perhaps because of the different order of flow rates involved. The values increase almost directly with gas rate for the small plate but only slightly with gas rate for the large plate. Figure 5 shows how the voids in the foam vary with gas rate and initial liquid level on the perforated plates. For the large plate the voids range from about 0.67 to 0.87, generally increasing with gas rat,e. The lower initial liquid levels are more effective per unit volume in that they produce foams with higher voids.
The inlet air temperature, !I, in the chamber below. the perforated plate was obtained by correcting the thermowell temperature for radiation to its surroundings which were a t 20' to 30' C. lower temperatures. An emissivity of 0.4 was assumed for the thermowell. The gas velocity past the thermowell was so low that the corrections amounted t o 1.0' to 1.5" C. The inlet wet bulb temperature was assumed equal t o the outlet wet bulb temperature, since the inlet water flow was small and very near the wet bulb temperature. The EOL efficiencies were calculated by Equation 4. The equilibrium concentrations were determined experimenTable 111. Carbon Dioxide Absorption Data and Rasults for t h s 19-Hole Plate tally for the desorption runs Water but were calculated from the Active T;mp., Bubb? Gn La 12 Zi 104 Z ~ L Holes C. EOL KLa KmZv e 3/r 3/rb Rate literature ( 1 1 ) , correcting for 0 . 7 6 8 151 106 14.8 0,370 1104 400.7 7.21 683.2 1.0 3.40 11 12.2 0 , 6 0 7 169 112 15.0 the experimental bicarbonate 7 . 1 5 695.5 1.7 3 59 12 10.6 0,378 1169 422.9 0 . 5 4 8 172 119 15.6 0 , 4 3 3 1139 523.4 7 . 1 5 686.8 2 . 3 4 . 0 5 1 4 1 1 . 1 11,39 6 9 3 , 0 l,o 3,54 18 concentration in the absorp0 , 7 8 6 131 116 17.8 0.392 1138 445.9 12.8 0 . 6 3 6 170 118 18.6 1520 593.6 0.467 tion rum. 11.39 7 0 6 . 8 1 . 7 4.17 18 12.2 0 , 5 7 0 184 117 18.2 0,509 1626 728.0 11.1 0.792 154 113 20.2 The transfer units, mass 15.03 702.2 11.47 711.9 21..30 4.81 4.56 19 11.1 1670 666.4 0,484 0 . 6 3 2 184 108 17.7 0,534 2022 783.5 14.92 683.2 1.7 5.02 19 11.1 transfer coefficients, and voids 14,92 683,2 2,x 5,49 19 11.1 0.585 2158 962.3 0 . 5 7 0 202 112 19.6 in the foam were calculated by a Rased on cross-sectional area of 0.0195 square foot for plate. Equations 2,6, and 8. The inb Based o n flow r a t e and stroboscopic bubble rate. Bubbles per second based o n the apparent stroboscopic frequency. terfacial areas per volume of gas in the foam, 3 / r , were __.__ -~ ._ C
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1952
2475
ul
t 3 z W a
xz c a L
0 0
za SMALL PLATE IO
0
GFigure 3.
20 G-
LB.MOLES AIR / (HR.)(SQ.FT.)
Effect of Gas Rate on Na at Various Initial Clear Liquid Levels for the 83-Hole Perforated Plate
Figure 4.
30
40
50
60
70
L B MOLES AIR/(HWSQ F T )
Effect of Gas Rate on KLaZv or LNL at Various Initial Clear Liquid Levels for Perforated Plates See Fieure 5 lor definition ot symbols
2 a
06-;F"
LEVEL
4
05
05 ___~_ t
SMALL PLATE ~
W
I 04
17 20
83 HOLE PLATE I9.HOLE PLATE YUMID DESORB GO2 HUMID ABSORB GO2
o
X
A
0
23
h
b
V
0
0
h
P
6
G - LO MOLES AIR / ( H R I Q FT)
Figure 5.
Effect of Gas Rate on Fraction Voids in Foam on Perforated Plates
-0
10
20 G
Figure 6.
30
- LB.MOLES
40
50
60
70
GAS/(HRJ(SQ.FTJ
Effect of Gas Rate on Interfacial Area for Perforated Plates See rieure 5 for definition of symbols
For the small plate with its lower gas velocities, the voids are generally lower. The voids for air humidification have been included here, since they are not affected by leakage through the small plate. The air bubbles gave essentially the same fraction voids as the more dense carbon dioxide bubbles. Figure 6 shows how the effective interfacial area per cubic foot of gas in the foam, 3 / r , is affected by the gas rate and the mass transfer system used. The humidification data are nearly independent of gas velocity and are essentially independent of liquid level. The average value of 3 / r is 145 square feet per cubic foot with an average deviation of &7%, corresponding to a deviation in ka of about & l l % . The desorption data show 3 / r to be essentially independent of liquid level but to decrease with increase in gas rate approaching the humidification values a t the higher gas rates. The effective areas for carbon dioxide adsorption on the small plate are intermediate between the other two sets and show more dependence on initial liquid level. The effective interfacial areas in Figure 6 are of the same general order of magnitude regardless of whether the transfer involves the gas film resistance or the liquid film resistance. This suggests that the proposed correlation is basically sound. The humidification data in Figure 6 indicate effective bubble diameters of the order of 0.50 inch, as compared to the center-torenter hole spacing of 0.375 inch. This indicates that adjacent bubbles must have been in different stages of growth a t any moment (this was known t o be the case for the 19-hole plate where
adjacent holes even had somewhat different stroboscopic frequencies of bubbling). The stroboscopic frequencies of 15 to 20 flashes per second, which gave the clearest images of the bubbles on the small plate, correfipond to initial bubbles diameters of the order of 0.65 inch. The bubbles themselves, although never very clear under stroboscopic light, did not look quite this large as compared to the hole and baffle spacings. If the actual bubble rate had been twice the apparent stroboscopic frequency, the initial bubble diameters would have been approximately 0.5 inch. The bubbles were stopped a t twice the apparent frequencies but were not so clear. The apparent frequencies may represent the frequencies of emission of pairs of bubbles, one a little behind the other but disproportionately further ahead of the first bubble in the following pair Such bubble-pair emission has been reported by Meredith ( I S ) for certain gas rates from a single orifice where the bubbles could be followed stroboscopically for some distance. However, in the absence of definite proof of pair emission in the present observations, the apparent stroboscopic frequencies have been used in calculating 3 / r for Table I11 and Figure 6. The velocities of rise, V / E and , the effective bubble sizes on the bubble plates are entirely different from those obtained for a stream of gas bubbles from a single I/s-inch orifice hole a t similar mifice velscities, The sixe of bubbles from the single orifice
2476 Table IV. GQ
INDUSTRIAL AND ENGINEERING CHEMISTRY Humidification and Oxygen Desorption on a Bubble-Cap Plate (3) LQ
12 Zib
KLa
ec
3 / ~
HCMIDIFICATIOX 17.0 22.1 26.8 33.5 39.8 37.8 32.4 24.4 32.2 32.4
746 746 746 746 746
3.6 3.6 3.6 3.6 3.e
168.1 155.9 132.7 157.4 180.0
0,393 0.441 0.499 0.499 0.516 0.481 0.481 0.441 0.462 0.462
134.7 137.1 129.3 138.6 136.0 143.4 143.0 146.0 146.7 147.6
DEJORPTIOS 7.35 414 3.29 1276 0.298 192.7 15.16 414 3.29 170.5 1698 0.366 19.28 414 3.29 1718 0.401 154.0 27.56 414 3.19 116. 7 1448 0.458 7.81 829 3.59 203.0 1450 0.308 14.7 181.4 829 3.59 1842 0.369 19.72 829 3.59 160.0 1890 0,420 27.04 139.5 829 3.59 2012 0.463 1243 1485 7.36 3.89 0 371 198 0 1243 1933 14.7 3.89 0 418 180 0 1243 19.28 3.89 2200 0 459 173 5 1243 3.89 2260 27.56 0 529 150 0 1422 7.35 1658 4.09 0 388 189 3 1688 0 800 163 7 1835 14.7 4.09 2216 1658 19.28 4.09 0 555 163 7 2430 28.0 4.09 0 650 145 8 1658 1551 2072 4.29 0 476 180 1 8.27 2072 0 533 195 9 2480 14.7 4.29 2620 2072 20.2 o ex7 163 4 4.29 2072 0 740 158 0 2924 4.29 28.0 a Based o n t h e “ n e t active cross-sectional area of t r a y ” of 0.67 square foot. b Based on liquid level in absence of bubbles above the middle of slots; equals t o t a l liquid level above t r a y less 1.31 inches. Based on all foam and bubbles being above middle of slots.
increases rapidly with flow rate up t o about 1.5 inches in diameter a t the highest orifice velocities used on the 83-hole perforated plate. This is 30 times the effective bubble volume on the plate. plate bubbles On the other hand the velocities of rise of the 1 0 - r o ~ increased with flow rate to as high as 9 feet per second, while the bubbles from a single orifice approximated 1 foot per second over a wide range of flow rates and bubble sizes (8). The differences are due presumably t o the tremendous turbulence eyisting on an active bubble plate as compared to that set up by a single stream of bubbles. In an effort to obtain further direct confirmation of the bubble sizes, the %row- plate photographs were re-examined under moderate magnification. Most of the pictures were too blurred or the bubbles too overlapping to show details, but there were a few exceptionally clear photographs such as those in Figure 7. The horizontal line across the foam chamber marks the surface of the water in the outlet water chamber. The clear pictures showed numerous sharply outlined, small bubbles, 0.05 to 0.15 inch in diameter, as well as a number of less clearly outlined bubbles up to 0.25 inch in diameter. I n addition, some eight or ten large light-colored patches approximately 0.5 inch in diameter can be distinguished, which may be the bubbles sought for but whose outlines are too irregular and blurred for certainty. Occasionally much larger light-colored patches up to over 1 inch in size are observed. It seems probable that some of the initial bubbles coalesce and that some break u p into smaller bubbles under the influence of the violent agitation on t,he plate. The smaller bubbles may well circulate around and around the plate with the liquor. If so, they would not affect the humidification appreciably because they would soon be saturated. I n the desorption runs, however, where the gas is a long way from equilibrium with the liquid, such small recirculating bubbles might appreciably increase the mass transfer and indicate too high effective interfacial areas. Small carbon dioxide bubbles, of course, would remain effective until they disappeared. Thus the difference observed in effective interfacial areas between humidification and absorption and desorption map be due to
Vol. 44, No. 10
the difference in reaction of the systems to the presence of small bubbles. In most commercial oDerations the nas and liauid would be fairly close to equilibrium, and the effect of such small bubbles would be slight. Accordingly, the effective areas determined from the humidification data are to be preferred for predicting plate efficiencies. As a further check on the validity of the proposed method the recalculated data of Gerster et al. ( 8 ) have been plotted in Figures 8 and 9. Figure 8 shows that the voids in the foam on a bubblecap plate are generally smaller than for sieve plates but increase rapidly with gas velocity. The liquid flow rate here affects the voids through its influence on the liquid level in absence of bubbles as presented in Table IV. Figure 9 shows h o v the effective interfacial area per cubic foot of gas in the foam on the bubble-cap plate is affected by gas rate and by the mass transfer system used. The humidification point,s are almost identical with those for the perforated plate. The avera.ge value of 3 / r is 140 with an average deviation of ~ t 3 . 6 7 0 , corresponding to a deviation of 5 5 . 5 % in koa. The similarity in effective bubble sizes despite the dissimilarity between the ‘/*-inch holes in the horizontal perforated plate and the vertical dots in the bubble caps suggests that orifice size and shape may be relatively unimportant in determining bubble size under conditions of high agitation on bubble plates. It must be admitted that the values found for 3 / r on the bubble-cap plate depend upon the arbitrary measurement of the initial liquid and foam levels from the center of the bubble-cap slots. If the measurements had been made from the bottom of the slots, 3 / r would have been calculated to be about 2.5% smaller. The oxygen desorption points are also similar to the carbon dioxide desorption points for the perforated plate. They are higher than the humidification points a t low gas velocities but approach the humidification points at higher velocities. The desorption points are sensitive to the method used for calculating KLa from plate efficiencies. Equation 5 for no mixing of the liquor was used here as it was by Gerster. Equation 6 for complete mixing of the liquor nould have given 25 to 85% higher Y
Figure 7.
Bubbling on the 19-Hole Perforated Plate
effective areas. Since Gerster used three r o w of bubble caps with bubbling only in the two lanes of liquor betn-een the three rows. neither Equation 5 nor 6 is strictly applicable. Kirschbaum’s pool concept (9, I O ) , if applied to this case assuming four pools, m-ould have given effective areas 5 t o 1170 higher than for no mixing of liquor. Although liquor rate and liquid level have a pronounced influence on the fraction voids, they have little if any effect on the effective bubble size. This is shown best by Gerster’s desorption results in Figure 9 for which the liquor rate was varied fivefold. The points for the various liquor rates fall indiscriminantIy above, below, and on the correlating line, the variations apparently being due to random error. The liquor rate was not varied
2477
INDUSTRIAL AND ENGINEERING CHEMISTRY
October 1952
sufficiently in the perforated plate runs t o establish any trend with liquor rate, but it is significant that a t high gas rates the game effective bubble size was obtained for humidification a t negligible liquor flow as for desorption a t 440 pound moles per (hour)(square foot). Thus it appears that liquor rate affects the point efficiency significantly only through its effect on the initial clear liquid level and fraction voids.
Cv,, CL,,
m
Ea
0.0021 pound mole per cubic foot 3.14 pound moles per cubic foot = 3.1 by Equation 13 ( mvaries from 3.4 to 2.8 for a bubble as it increases from 9 to 28.5 mole yo composition while rising through the liquor of constant 9 mole % composition) = 86% predicted by Equation 12; this should also be the Murphree plate efficiency for the low liquor rate involved = =
2. Furfural extractive distillation of isobutane from 1butene a t 66.5 pounds per square inch gage pressure and 82 mole furfural in the liquor [ ( 6 ) , run IEBOA]. By similar computations: 0.7
V = 3470 Air rate having same superficial velocity = 8.7 Liquor rate = 30 E = 0.36 r = 0.0215 Zi = 0.433 Dv = 0.0464 DL = 0.71 x 10-4 Cvav = 0.0125 C L =~ 0.81 ~ m = 7.1 [based on true mole fractions including furfural ( d ) ] EQ (predicted) = 26%.
u)
0 0.6 0 5
z
0 0.5
b a LL U
0.4
:Id. w
0.3 0.2 0
IO G
Figure 8.
-
20
30
I
40
LB. MOLES AIR / (HRJ(SQ.FT3
Effect of Gas Rate on Fraction Voids in Foam on Bubble-Cap Plates From data of Gorster ef a/. (3)
As a further check on the theoretical validity of the proposed method, a few calculations have been made of the depth of solute penetration into effectively infinitely thick transient films for t i s encountered in this study. The velocities of rise of the bubbles ranged from about 3 t o 9 feet per second in the %hole perforated plate. Since the effective bubble size was essentially constant a t 0.5 inch, the times required to rise one diameter, t,, varied from about 0.014 to 0.004 second. Oxygen diffusing into a semiinfinite stagnant water layer for 0.01 second would deliver less than 1% of the dissolved solute deeper than 0.0007 inch and less than 15% deeper than 0.0003 inch. Water vapor diffusing into a semi-infinite stagnant air layer for 0.01 second would deliver less than 15% of the solute vapor deeper than 0.035 inch or one seventh of the radius of the gas bubble. It is a t least conceivable that the transient air film inside a bubble being pulled along by the water interface might be relatively stagnant to a depth of one seventh of the bubble radius. To illustrate the ultimate application of the proposed method, point efficiencies have been predicted for two systems (b, 6) which have been studied in plates of identical design to that represented by Figures 8 and 9. 1. Rectification of methanol-water with 9 mole % methanol in the liquor a t total reflux, 1 atmosphere total pressure and a slot velocity of 13.3 feet per second (2).
V
10,300 feet per hour, based on superficial area of 0.67 square foot Air rate in Figure 8 having the same superficial velocity = 26 pound moles er (hour)(square foot) Liquor rate = 0.9 galyon per minute e = 0.44, extrapolated from Figure 8 for the same superficial linear velocity in the absence of correlations for the effect of different physical properties 1’ = 0.0215 foot, from the humidification curve in Figure 9 in the absence of correlations showing the effect of different physical roperties = 0.233 foot, incgding the head above the wier by the Zi Francis wier formula for a suppressed wier DV = 1.185 square foot per hour by Sherwood’s method (16) D L = 2.2 X square foot per hour by Wilke’s method (WO), the diffusivity of methanol a t infinite dilution in water a t the boiling point of a 9 mole yo solution =
The above predictions were made to illustrate the application of the method in the absence of any knowledge as to how the different physical properties of the systems would actually affect E and the effective bubble diameter. The agreement with the observed efficiencies is not good. For 6 to 10 mole % methanol in water the observed efficiencies ranged from 56 to 70% (2). The predicted value could be reduced from 86% to about 65%, either by reducing E by 50% or by increasing T by 50%. It seems quite possible that the lower viscosity of the boiling solution should reduce the fraction voids. For the extractive distillation the observed point efficiency was 44y0 (6). The predicted value could be raised t o about 44% either by increasing the fraction voids by about 60% or by reducing T by about 35%. The density of the hydrocarbon vapor is about ten times that of the air used in obtaining the data plotted in Figures 8 and 9, and it may be that the linear velocity is not the proper basis for comparing fraction voids. I
I
I
2501
I
B 200 c’ IA 5
1
150
+ 0 18 G.P.M.
1050
HUMIDIFICATION
’ G
Figure 9.
I
I
-
I
I
LB. MOLES. A I R 1 (HR.)(SQ. FT.)
Effect of Gas Rate on Interfacial Area for Bubble-Cap Plates From data of Gerrter et a/. (3)
Before the present method can predict reliable efficiencies outside the range of Figures 5, 6, 8, and 9, correlations are needed for the effect of variable fluid properties and plate design on the fraction voids and effective bubble size. I n developing such correlations, the fraction voids can be studied independently of mass transfer, the theoretical approach presumably being related to that for fluidization. The effective bubble size can be obtained from plate efficiencies by the present method once the voids are known or can be predicted.
INDUSTRIAL AND ENGINEERING CHEMISTRY Conclusions The proposed method for predicting point efficiencies and utilizing Higbie’s equation for both the gas and liquid films appears to be sound. It reduces the empirical portion of the prediction to correlations for the effective bubble size and fraction of voids in the foam. These correlations will be independent of diffusivities and distribution coefficients, and therefore should be established more readily. The fraction voids in the foam varies quite differently with flow rate for the perforated and bubble-cap plates, being higher in the former but increasing more rapidly with flow rate in the latter, Insufficient data are available to show how the fraction voids varies with the physical properties of the gas and liquid. The humidification results indicate effective bubble diameters of approximately 0.5 inch a t all flow rates for both the perforated and bubble-cap plates. The agreement between the different types of plates is presumably coincitental, but it, mag indicate instead that orifice size and shape are relatively unimportant in determining bubble size under the conditions of violent agitation on a bubble plate. The desorption results for both types of plates indicate effective bubble diameters which are smaller a t low flow rates but which approach 0.5 inch, the humidification value, a t high flow rates. Much of the discrepancy a t low flow rates may be due to the many sniall bubbles observed in the photographs which can affect the desorption mass transfer materially but not the humidification results. I t is believed that the humidification effective sizes are closer to those which should be used for most commercial absorptions and distillations since these should be run near enough to equilibrium so as not to be affected greatly by small stray bubbles. Nomenclature
= interfacial bubble area, square feet per cubic foot of foam cav = conversion factor for converting IC’s from feet per hour to pound moles per (hour)(square foot), total pound moles per cubic foot D = diffusivity of solute, square feet per hour EG = Murphree point efficiency based on vapor concentrations EOL = Murphree plate efficiency based on liquid concentrations G = gas rate, pound moles per (hour)(square foot) I C = individual film mass transfer coefficient, pound moles per (hour)(square foot) K = over-all mass transfer coefficient, pound moles per (hour) (square foot) L = liquor rate, pound moles per (hour)(square foot) m = slope of appropriate section of the equilibrium line; see Eauation 13 hi = nimber of transfer units r = average bubble radius, feet ts = time of unsteady state diffusion; calculated as the time required for a bubble to rise a distance equal to its diameter, hour tl = temperature of air entering plate, O C. a
t2
t, Ti
x
zip zi
zp y,
yip
& Zi ZV AZ E
Vol. 44, No. 10
temperature of air leaving plate, O C. wet bulb temperature of air, C. superficial gas velocity based on active column cross section, feet per hour = mole fraction of solute in liquid = mole fract’ion of solute a t the liquid interface at some point = mole fraction of solute in liquid which would be in equilibrium with the vapor leaving the nth plate = mole fraction of solute in liquid at some point on the plat’e = rnolc fraction of solute in gas a t Borne point on the plate = mole irartion of solute a t gas interface a t some point on t’he plate = mole fraction of solute in gas which would be in equilibrium with solute in the liquid a t some poilit on the nth plate = initial liquid level above plate (or above middle of slots for bubble caps), feet = foam height above plate (or above middle of slots for bubble caps), feet = (ZV &), feet = fraction of voids in the foam in the bubbling section of a bubble plate = = =
O
Subscripts 0 = gas phase L = liquid phase n = nth plate Literature Cited (1) Geddes, R. L., Trans. Am. Inst. Chem. E n g r s . , 42,79 (1946). (2) Gerster, J. 9.Bonnett, , W.E., and Hess, Irwin, C h e m Eng. Progress, 47, 621 (1951). (3) Gerster, J. A., Colburn, A P., Bonnet, W. E., and Carmody, T W., Ibid., 45, 716 (1949). (4) Gerster, J. A., Mertes, T. S., and Colburn, A. P., IXD.EXG. CHEM.,39, 797 (1947). (5) Gilbert, W. D., M.S. thesis, University of Washington, 1949. (6) Grohse, E. W.,McCartney, R. F., Hauer, H. J., Gerster, J. A , , and Colburn, A. P., Chem. E n g . Progress, 45,726 (1949). ( 7 ) Higbie, Ralph, Trans. Am. Inst. Chem. Engrs., 3 1 , 3 6 5 (1935). ( 8 ) Hornbeck, R. D., B.S.thesis, University of Washington, 1949. (9) Kirschbaum, Emil, Forsch. Gebiete Ingenieurw., 5, 245 (1934). (10) Kirschbaum, Emil (translated by Wulfinghoff, M.), “Distillation and Rectification,” 1st English ed., pp. 276-300, New York, Chemical Publishing Co., Inc., 1948. (11) Lange, N. A., “Handbook of Chemistry,” 4th ed., p. 1079,
Sandusky, Ohio, Handbook Publishers, Inc., 1941. (12) Levis, W.J., Jr., IND. ENG.CHEM.,28,399 (1936). (13) Meredith, R. G., B.S.thesis, University of Washington, 1950. ENG.CHEM.,17, 747 (1925). (14) Murphree, E. V., IND. (15) Perry, J. H., “Chemical Engineers’ Handbook,” 2nd ed., p1169, New York, McGraw-Hill Book Co., 1941. ( l G ) Sherwood, T. K., “Absorption and Extraction,” 1st ed., pp. 18, 35, New York, hlcGraw-Hill Book Co., 1937. (17) Shimisu, Toru, M.S. thesis, Cniversity of Washington, 1951. (18) Walter, J. F., and Sherwood, T. K., IND.ENG.CHEM.,33, 493 /,
n” 1 \
,LZmL,.
(19) West, F. B., Robinson, P. A., Morgenthaler, A. C., Jr., Beck,. T. R., and McGregor, D. K., I b i d . , 43, 234 (1981). (20) xTiike, c. K., C,Lem. Eng. Progress, 45, 218 (1949). RECEIVED for review J u l y 28, 1951.
ACCEPTED May 29, 10.52.
