Ind. Eng. Chem. Fundam. 1900, 19, 21-26
ti = empirical constants in eq 1 tl,t2 = values of time used in eq 7 u = deviation of C, from its final steady-state value, g-mol/cm3 micropore volume w = E,,u, g-mol/cm3 pellet volume x = mole fraction corresponding to y o yi, yo = deviations from their final steady states of the concentrations of sorbate in the gas streams flowing into and out of the sorption vessel, g-mol/cm3 Yo' = dY,/dt z = dimensionless distance from the closed end of the zeolite pellet Greek Letters em = macropore porosity of a pellet, cm3macropore volume/ cm3 pellet volume E,, = micropore porosity of a pellet, cm3micropore volume/cm3 pellet volume { = first argument of the Jacobian 0 function, e4 t) = Yo/M t)',~'' = dv/dt and d2q/dt2,respectively 0 ({,q) = the fourth Jacobian 0 function (see Rainville, 1960) Ai = correction factor for the tortuoisty and diameter variations of macropores kn = the nth moment of the response to an ideal pulse input 5 = dummy variable in eq A7, s1j2 T * , '7 = time constants for the sorption vessel (see Kelly and Fuller, 1980) I,L = c,(aG/aC,)~ (g-mol sorbed/pellet volume)/(g-mol in gas/gas volume) Subscripts
21
i = inflow = outflow
0
Superscripts a = approximate t = true t = error - = the final steady-state value of a variable Literature Cited Anderssen, A. S., White, E. T., Chem. Eng. Sci., 25, 1015 (1970). Jeffreson, C. P., Chem. Eng. Sci., 25, 1319 (1970). Kelly, J. F., Ph.D. Thesis, McGill University, Montreal, 1975,copies available from the National Library of Canada, Ottawa. Kelly. J. F., Fuller, 0. M.. Ind. €no. Chem. Fundam.. Drecedina article in this issue, 1980. Kubin, M., Collect. Czech. Chem. Commun ., 30, 1 104 (1965). Kucera, E., J. Cbromafogr., 19,237 (1965). Ralnville, E. D., "Special Functions", Macmillan, New York, 1960. Ramachandran, P. A., Smith, J. M., Ind. Eng. Cbem. Fundam., 11, 148 (1978). Rony, P. R., Funk, J. F., J . Cbromafogr. Sci.. 9, 215 (1971). Ruthven, D. M., Derrah, R. I., Can. J . Chem. Eng., 50, 743 (1972). Sater, V. E., Levenspiel, O., Ind. Eng. Chem. Fundam., 5, 86 (1966). Wakao, N., Tanaka, K., J . Chem. Eng. Jpn., 8, 338 (1973). Youngquist, G.R., Allen, J. L., Eisenberg, J.. Ind. Eng. Chem. Prod. Res. Dev., 10, 308 (1971).
Received for review October 27, 1978 Accepted September 13, 1979 The authors gratefully acknowledge the support of the National Research Council of Canada, the J. W. McConnell Foundation, and Mrs. R. B. Fuller. We acknowledge with pleasure the suggestions and criticisms of Professors J. Grace and H. de Lasa and Mr. N. Nguyen-Dinh.
Gas Holdup and Bubble Diameters in Pressurized Gas-Liquid Stirred Vessels 1.Srldhar and Owen E. Potter" Depaltment of Chemical Engineering, Monash University, Clayton, Victoria, 3 168 Australia
The effect of system pressure on gas holdup has been experimentally determined in a stirred gas-liquid reactor. The effect of increased gas density is to increase gas holdup. The contribution of the power supplied through the gas stream to the total power dissipated in the stirred vessel increases as the pressure increases, other things being equal. Bubble diameters decrease as pressure is increased. Measurements at varying pressures (and hence varying gas kinetic energies) but at constant gas volumetric flow rate and temperature were used to study the effect of kinetic energy on the characteristics of the gas-liquid dispersion. The data were correlated by a simple modification of Calderbank's equations. The equations presented reduce to Calderbank's equation at atmospheric pressure. The fact that the same correction factors enter in the equations for interfacial area, gas hoklup, and bubble diameters lends confidence to the recommended equations. Since data were obtained with one small vessel only, caution is required in scaling up to larger vessels.
Introduction Gas-liquid mass transfer and reacting systems constitute an important processing tool. Knowledge of the surface area of gas-liquid dispersions of holdup of gas in the dispersion and of mean bubble diameter and mass transfer rates are of fundamental importance. Such systems may comprise bubble-towers without agitation other than by the bubble-stream or agitated vessels where the liquid is circulated throughout the vessel by the agitator with or without turbulence depending on the degree of agitation. 00 19-7874/80/10 19-0021$0 1 .OO/O
Holdup, bubble diameter and surface area are related a=-
6H
DBM While there has been ample experimentation at atmospheric pressure, determinations of the above properties in pressurized agitated systems have not been made, so that the available models all involve extrapolation from atmospheric pressure operation to pressurized operation. The most notable feature of pressurized operation is that 0 1980 American
Chemical Society
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Ind. Eng. Chem. Fundam., Vol. 19, No. 1, 1980
the kinetic energy of the inlet gas increases as the density increases with pressure. Furthermore, the inlet gases may be saturated with the vapor of the reaction medium and a t higher temperatures this can lead to further increase in gas density. This paper presents the first data on gas holdup in agitated sparged vessels operated above atmospheric pressure. It is shown that a suitably modified version of the holdup equation developed by Calderbank (1958) represents the data adequately. Agreement with the latter work is good a t atmospheric pressure. In a two-phase system where the continuous phase remains in place, Le., no net flow in or out of the system, the holdup is related to gas rate and bubble rise velocity
For sieve plates, when V, that
