Ind. Eng. Chem. Process Des. Dev. 1988, 25,838-839
838
(Sridharan and Sharma, 1976; Alvarez-Fuster et al., 1980), the reduction in rate from the irreversible case is simply the ratio in the outlet gas phase from a differential reactor, YCO2IYCo2jr.
Notation
[CHA], = CHA concentration at equilibrium, M [CHA], = CHA concentration at beginning of measurement, M [C*It = C* concentration at equilibrium, M [C*], = C* concentration at beginning of measurement, M F = total amount of COz reacted during t , kgmol H* = solubility in solution of C02, 1.0417 M/MPa Keq = 8070 f 800, M-5/2 P = pressure in the reactor, MPa Q = inert gas flow during reaction, m3/s Q, = inert gas flow during purge, m3/s R = 0.00831, m3 MPa/(kgmol.K) T = temperature, K t = total time for equilibrium measurement, s t , = reaction time to change [CHA], s t = purge time to establish equilibrium, s S = volume of solution, m3 xi = moles C 0 2 inlet/moles Nzinlet
x, = moles C 0 2 outlet/(moles N2 + toluene outlet) yco2 = equilibriummole fraction of C02in the outlet gas phase yco2,ir= mole fraction of COz in the gas phase if the carbamation reaction was assumed to be irreversible Registry No. COz, 124-38-9;CHA, 108-91-8;cyclohexylcarbamic acid, 4363-89-7. Literature Cited Alvarez-Fuster, C.; Midoux, N.; Laurent. A.; Charpentier, J. C. Chem. Eng. Sci., 1980, 35, 1717. Alvarez-Fuster. C.;Mloux, N.; Laurent, A.; Charpentier, J. C. Chem. Eng. Sei. 1981, 36, 1513. BarIos, T. M.; Satterfleld, C. N. AIChE. J . 1986, In press. Mahajani, V. C.; Sharma, M. M. Chem. Eng. Sei. 1979, 34, 1425. Mldoux, N.; Morsi, B. I.; Purwasasmlta, M.; Laurent, A,; Charpentier, J. C. Chem. Eng. Sci.. 1984, 39, 781. Morsi, B. I.; Laurent, A.; Midoux, N.; Charpentier, J. C. Chem. Eng. Sci. 1980, 35, 1467. Sridharan, K.; Sharma, M. M. Chem. Eng. Sci. 1978, 3 1 , 767.
Department of Chemical Engineering Thomas M. Bartos Massachusetts Institute of Charles N. Satterfield* Technology Cambridge, Massachusetts 02139 Receiued for reuiew June 28, 1985 Accepted February 4, 1986
Bubble Formation in Molten NaNO, The size of a single bubble formed from carbon and Pyrex glass nozzles in molten NaN03 can be estimated from empirical equations presented for aqueous systems by use of the outer diameter of these nozzles because of the nonwettability of these nozzles by molten NaNO,.
Molten salts have recently been used as reaction media for gas-liquid reactions, so knowledge about bubble behavior in molten salts is significant. Irrespective of the characteristics of the nozzles used, the behavior of bubble swarms in gas bubble columns can be correlated by use of the physical properties of molten salts and operating conditions (Sada et al., 1984). In the region of a single bubble, however, the behavior of the individual bubble may be affected by the wettability of the nozzle material with molten salts. The present work was undertaken to study the behavior of a single bubble in molten salts.
Results and Discussion
Figure 1 shows the bubble size in water plotted against the gas flow rate. At very low gas flow rate, the bubble diameter is determined by the balance between the surface tension and the buoyancy force.
For the constant-frequency region a t higher flow rates, Davidson and Amick (1956) presented the following empirical equation.
Experimental Section
i) ] 0.5
A transparent Pyrex glass column of 7.3 cm inside diameter and 95 cm in height was used (Sada et al., 1984). It was equipped with a polished glass window to allow flashlight photography of bubbles leaving a nozzle set at a height of 32 cm. The bubble size was measured from the photographs, and the equivalent diameters of individual bubbles were calculated by dB = ( a 2 b ) 1 / 3
dB = 054[ p(
0.289
(3)
For the intermediate region, Mersman (1962) presented eq 4.
(1)
(4)
where a and b are the maximum and the minimum diameters of the individual bubbles, respectively. The molten salt used was NaNO,. The salt was transferred to the column and melted a t a desired temperature in an electric furnace. The nozzles were made of carbon and Pyrex glass. To obtain a basis for comparison, measurements for water were made in the same apparatus with carbon and Teflon nozzles. Bubbles were formed under constant gas flow conditions.
The solid and broken curves in Figure 1 are calculated from (3) and (4) by use of the inner diameter of the carbon nozzle and agree well with the experimental points. The bubble diameter in molten NaN03,however, is expressible by (3) and (4) by use of the outer diameter of the carbon nozzles, as shown in Figure 2. Figure 3 compares the bubble formation in molten NaN03 (carbon nozzle) and water (carbon and Teflon nozzles). From a carbon nozzle, which is wetted by water, the bubbles in water were formed
0196-4305/86/1125-0838$01.50/0
0 1986 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 25, No. 3, 1986 839 I "
'
'
"
' ' 1
'
I
Davidson 8 Amick Merman
E
h
dm 0 2.95 0 2.80
doui,mm 5.00 carbon 5.40 Teflon
4
-,$,Y/
b',e ,*!'A
ne
0
0
10
1
2.95 7.95 2.70 12.85
IO
1
Gas flow rate q , cmVsec
Gas flow rate q , cmVsec
Figure I. Bubble diameter in water (20"C): carbon nozzle, 2.95
Figure 4. Effect of outer diameter on bubble size: NaN03, 400 "C,
mm i.d., 5.00 mm 0.d.; Teflon nozzle, 2.80 mm i.d., 5.40 mm 0.d.
carbon nozzle.
Davidson 8 Amick
q tcm31sec3
Gas flow rate
Figure 2. Bubble diameter in molten NaN03 (400 OC): carbon nozzle, 2.95 mm i.d., 7.95 mm 0.d.
by water. The bubble diameter in water with the Teflon nozzle, as Figure 1shows, agrees with the curves calculated from (3) and (4) by use of the outer diameter, as is to be expected. The wettability of a solid by a liquid can be expressed by the contact angle between them. For water and Teflon, the angle is about 110", while for a eutectic of Na2C03-K2C03-Li2C03and graphite under a C02 atmosphere, the only reported example involving a molten salt, the angle is similarly high, 85" (Moiseev and Stepanov, 1967). Therefore, the size of a single bubble in molten salts, which usually do not wet carbon, can be estimated from (3) and (4) by use of the outer diameter of the nozzle and may be simulated by the water-Teflon system. Figure 4 shows the variation of the bubble diameter with the outer diameter of the nozzles. Up to a nozzle diameter of 7.95 mm, the bubble diameter agrees with the calculated curves, but above this diameter, it does not increase. Bubble diameters with Pyrex glass nozzles also behaved similarly. It is difficult to determine the maximum bubble size with an increase in the outer diameter in nonwettable systems, because it also depends on the inner diameter.
Nomenclature a = major axis of bubble, cm b = minor axis of bubble, cm d = diameter of nozzle, cm dB = diameter of initial bubble, cm g = gravitational constant, cm s - ~ q = gas flow rate, cm3 s-l
Greek Letters y = surface tension, g s - ~ pG = gas density, g cm-3 pL = liquid density, g cm-3 f
carbon, 7440-44-0. Registry No. NaN03, 7631-99-4;
Literature Cited
j
(C)
Figure 3. Bubble formation from nozzles: (a) water-carbon nozzle, 1.00 mm i.d., 5.00 mm o.d., q = 1.6 cm3/s, 20 "C;(b) NaN03-carbon nozzle, 1.00 mm i.d., 5.00 mm o.d., q = 7.6 cm3/s, 400 "C; (c) water-Teflon nozzle, 2.80 mm i.d., 5.40 mm o.d., q = 2.3 cm3/s, 20
"C. a t the inner surface of the nozzle; but in molten NaN03, the bubbles made contact with the outside surface of the nozzle. This may be caused by the nonwettability of carbon by the molten salt, because bubbles were similarly formed in water from a Teflon nozzle, which is not wetted
Davidson, L.; Amick, E. H., Jr. AZChE J. 1956, 2. 337-342. Mersman, A. V. D. I. Forshungsheft 1962, 491, 1-44. Moiseev, G. K.; Stepanov, G. K. "Electrochemistry of Molten and Solid Electrolytes";Consultants Bureau: New York, 1967; Vol. 5, pp 101-109. Sada, E.: Katoh. S.; Yoshii, H.; Yamanishi. T.; Nakanishi, A. Znd. Eng. Chem. Process Des. Dev. 1984, 2 3 , 151-154.
To whom all correspondence should be addressed.
Chemical Engineering Department Kyoto University Kyoto 606, Japan
Eizo Sada* Shigeo Katoh Hidehumi Yoshii Takayuki Tanaka
Received for review April 16,1985 Accepted November 13,1985
