353
Ind. Eng. Chem. Process Des. Dev. 1982, 21 353-355 I
i
Conclusions In the absence of catalyst the oxidation reaction is kinetically controlled and it is first order in O2 and first order with respect to mercaptide. The reaction shifts from the kinetically controlled,regime to the diffusion controlled regime in the presence of activated carbon particles.
5*ot
t
L.01
3*0t
E,
\
-
m:3*0;
P
a -
2
2.0
01
a* 1 . 0 00
/-
,' 0.1 4 '
0.2
0.4
0.3
0.5
Acknowledgment One of the authors (S.K.P.) wishes to thank the University Grants Commission for financial support. 0.6
[Bo] x103, mole /cm'
Figure 3. Effect of concentration of mercaptide on the rate of absorption at 32 O C : speed of agitation = 1400 rpm; partial pressure of O2 = 0.953 atm; ionic strength = 1.0 g-ion/L.
0.10
f
c
I
Literature Cited 0
f U
Nomenclature a = effective interfacial area per unit volume of the liquid, cm2/cm3 [A*] = solubility of the solute gas in the solution, mol/cm3 [Bo]= concentration of the nonvolatile reactant, mol/cm3 k2 = second-order rate constant, cm3/mol s k L = liquid-side mass transfer coefficient, cm/s kSL = solid-liquid mass transfer coefficient, cm/s m = order of the reaction with respect to the solute gas n = order of the reaction with respect to the nonvolatile reactant RAa = rate of absorption of the solute gas per unit volume of the liquid, mol/cm3 s
0.04
Bird, A. J. private communication, Johnson Matthey Research Centre, Blount's Court, Sonning Common, Reading, England, 1976. Chandrasekaran, K.; Sharma, M. M. Chem. Eng. Scl. 1977, 32, 669. Danckwerts, P. V. "Gas-Liquid Reactions"; McOraw-Hill: New York, 1970. Evans, E.; Leigh, D. private communication, Engelhard, Gioucestershire,E n g land, 1981. Gislon, A.; Quiqerez, J. M.; L'Orcher, G. (to Compagnie Francaise de Raffinage), U S . Patent 2823173, Feb 11, 1958. Mashelkar, R. A.; Sharma, M. M. I. Chem. E . Symp. Ser. No. 28 1968, 10. Moulthrop, B. L. (to Socony-Vacuum Oil Co., Inc.), U.S. Patent 2651 595, Sept 8, 1953. Siedeil, A. "Solubllltles of Inorganic and Metal Organic Compounds"; D. Van Nostrand: New York, 1940. Siggia, S.; Hanna, J. G. "Quantitative Organic Analysis Via Functional Groups"; Wlley: New York, 1978. Slesser, C. 0. M.; Allen, W. T.; Cuming. A. R.; Fawlowsky, U.; Shllds, J. In "Chemical Reaction Engineering", Proceedings of the Fourth European Symposium, Brussels, supplement to Chemical Engineerlng Science, 1968; p 41. Wallace, T. J.; Schriesheim, A.; Jonassen, H. B. Chem. Ind. (London) 1963,
, -
00
0.1
0.2
0.3
[Bo] x lo3, mole
0.4
0.5
/cm3
Figure 4. Effect of concentration of mercaptide on the rate of absorption in the pressure of carbon as catalyst at 32 O C : speed of agitation = 1400 rpm; partial pressure of O2 = 0.953 atm; ionic strength = 1.0 g-ion/L; loading of carbon = 0.1% w/w;average particle size = 1.7 X lo4 cm.
80% when the activated carbon loading (carbon A) was varied from 0.02590w/w to 0.2% w/w. These conditions are comparable to those employed in our work. Thus the observed increase in RAa with catalyst loading appears to be essentially due to the increase in the value of kLa.
734.
Wallace, T. J.; Schriesheim, A.; Hurwitz, H.; Glaser, M. B. Ind. Eng. Chem. Process D e s . Dev. 1964, 3, 237.
Department of Chemical Technology Subodh K. Pal University of Bombay Man Mohan Sharma* Matunga, Bombay 400019, India Received for review August 24, 1981 Accepted December 31, 1981
Mass Transfer Characteristics of Multiple Impeller Agitated Gas-Liquid Contactors The effect of superficial gas velocity, V,, on a and kLa for a multiple impeller agitated contactor was investigated. It was observed that a and kLa values were independent of V, and varied linearly wkh impeller speed. It appears that a and k,a values obtained from single impeller are representative of multiple impeller contactors, under
otherwise uniform conditions.
A multiple impeller agitated contactor can be advantageously used for gas-liquid contacting because of favorable residence time distribution of the gas phase as compared to a single impeller agitated contactor of the same volume (Sullivan and Treybal, 1970). Further, the power consumption per unit volume decreases with an increase in number of impellers (Nienow and Lilly, 1979). Thus, a beneficial effect would accrue by using multiple impeller 0198-4305/82/1121-0353$01.25/0
agitated contactors. In this work, the values of the effective interfacial area, a, and the liquid-side mass transfer coefficient, kLa, were measured by the chemical method for different number of impellers, superficial gas velocities, and speeds of agitation. The theory of gas absorption accompanied by fast pseudo-zero-order reaction (absorption of oxygen from air in aqueous alkaline sodium dithionite solution) was used 0 1982 American Chemical Society
354
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 2, 1982
Table I. Mathematical Models for Multiple Impeller Agitated Gas-Liquid Contactor effective interfacial area
liquid-side mass transfer coefficient
plug flow model for gas phase
dxldh = -V[XI(l + X)]”2[B,]’/2 u = [SU(~DA~,H*P)”~]/G’ b.c: h = 0, X = X,; h = h,, X = X, d[B,]/dt = -cY(X, - X,) CY = G’Z/VT b.c: t = 0, [ B o ]= [BO]i;t = t g , [Bo] = [Bo]f
dX/dh = -0 [XI(1 + X ) ] p = kLaH*PS/G’ b.c: h = 0 , X = X e ; h = h,, X = X, d[B,]/dt = -cY(X,- X,) 01 = G‘Z/VT b.c: t = 0, [Bo] = [B,]i; t = t g , [Bo] = [B,]f
stirred tanks in series model for gas phase
Xn3 + Xnz(l - 2Xn-1) + 6’[B,] + xn-lz) =0
x,z + Xn(@- x n - l +
+ Xn(Xn-1
Wn-1 -
@ = kLaH*PV/G’;X,,
1)- xn-l= 0 = X e ; X n = ~=, X,
( V U / G ’ ) ( ~ D A ~ , H * P=)X,; ~ / ~ ; X ~ [Bolf = ~ = [Boli-CYtB(Xe-Xo) Xn=N, = x o d[B,]/dt = -cY(X,- X,) CY = G’Z/VT CY = G’Z/VT b.c: t = 0, [Bo] = [BO]i;t = t g , [ B o ]= [BO]f b.C: t = 0, [Bo] = [BO]i;t = t g , [Bo] = [Bolt fi =
to measure a; the theory of absorption accompanied by slow chemical reaction (absorption of lean carbon dioxide in sodium carbonate-sodium bicarbonate solution) was used for measuring kLa. The concentration of sodium dithionite used in the runs was less than 0.08 M so that the reaction is first order with respect to dithionite and zero order with respect to oxygen. A small quantity of tricresyl phosphate (1mL/6.28 L of the absorbent solution) was UBed in all the runs as an antifoamingagent. The details of the chemical methods are discussed elsewhere (Jhaveri and Sharma, 1968; Sharma and Mashelkar, 1968). Experimental Section The experimental setup consisted of a 20 cm i.d., 100 cm tall Perspex contactor with standard axial baffles and six-blade stainless steel disk turbines (diameter 10 cm) as impellers. The impellers were arranged such that the lowermost one was 10 cm from the vessel bottom and the others were spaced at intervals of 20 cm. A maximum of 3 impellers was used. The gas was introduced at the bottom of the contactor through two 0.4-cm orifices. The shaft was fixed at the bottom with a ball bearing and passed through a gland and stuffing box at the top. The speed of agitation was varied by a set of pulleys. Experiments were carried out essentially under atmospheric pressure in a semicontinuous manner. A batch of the absorbent solution of known volume and concentration was taken in the reactor. The gas with the fiesired composition was passed continuously for a known period of time and the final composition of the absorbent was determined by chemical analysis. Most experiments were carried out such that the average temperature was 29 “C and the maximum rise in temperature was 5 “ C . A minimum of 3 min was used for each run. Results and Discussion The experiments in this study were carried out in a semibatch manner, and hence the concentration of sodium dithionite in the reactor decreases with time. This results in an increase in the outlet partial pressure of oxygen from the reactor. These factors have to be accounted for in the model for the calculation of a and kLa. Hence, a simplified model assuming an average dithionite concentration during the run for the calculation of a and kLa is not justified. The contactor was modeled assuming the liquid phase to be completely backmixed (Geerlings, 1957). The gas phase was assumed to be backmixed for each impeller stage. However, for the sake of comparison, the model based on the assumption of plug flow for the gas phase was also used. Typically, the a values based on the stirred tanks in series model were about 5% higher than those
n
3 I
*-----0----0
-
Y
>
c1
Figure 2. Effect of impeller speed on the effective gas-liquid interfacial area and the liquid-side mass transfer coefficient.
based on the plug flow model. kLa values differed by about 20 % . The values of a and kLa reported in this paper are based on the stirred tanks in series model, as this model appears to be more realistic. The mathematical equations are given in Table I. The differential equations were solved by the Runge-Kutta method and the algebraic equations were solved by using the Newton-Raphson technique. The effects of superficial gas velocity on a and kLa were studied at four different speeds of agitation. A typical plot of a and kLa vs. V , at 1080 rpm is shown in Figure 1. It can be seen that a and kLa are practically independent of
Ind. Eng. Chem. Process Des. Dev. 1982, 21, 355-356
355
[Bo]= concentration of the reactive species in the liquid phase, g-mol/cm3 DA = diffusivity of the solute gas in the liquid, cm2/s G’ = molar flowrate of inerts in the gas phase, g-mol/s h = height of the liquid column, cm h, = height of clear liquid, cm H* = Henry’s constant for the solute gas in the liquid, gmol/cm3 atm k~ = true liquid-side mass transfer coefficient, cm/s kl = first-order rate constant, s-l N = impeller speed, rpm N , = number of stages P = operating pressure, atm S = cross-sectional area of the column, cm2 t = time, s tB = batch time, s V = volume of each stage, cm3 of clear liquid VG= superficialgas velocity at the inlet of the contactor, cm/s VT = total volume of the reactor, cm3 of clear liquid X = mole ratio of the solute gas, moles of solute gas/mole of inert gas 2 = stoichiometric factor for the gas-liquid reaction
VG at 1080 rpm. Similar results were obtained at 255,530, and 730 rpm. The effect of impeller speed on a and kLa is shown in Figure 2. Values of a and kLa vary linearly with the impeller speed in the range studied in the present work (fitted by least squares criterion-correlation coefficient >0.95). The above results are in agreement with the earlier work on single stage contactors (Westerterp et al., 1963; Mehta and Sharma, 1971). The effect of VGon a and kLa depends on the hydrodynamic regime of operation. Above a certain speed of agitation, referred to as the critical speed of agitation, the effect of superficial velocity on a and kLa is negligible and below the critical speed of agitation, there will be a significant effect. Further, in the case of noncoalescing systems (as was the case in this investigation), the critical speed of agitation will be substantially lower than that in the case of coalescing systems. The speeds of agitation in this work were higher than the critical speed of agitation, and hence the insignificant effect of VG on a and kLa is quite reasonable (Westerterp et al., 1963; Mehta and Sharma, 1971). It can be seen from Figures 1 and 2 that a and kLa are not affected by the number of impellers for the geometry considered in the present work. This is an important observation, but this finding should be considered as tentative and further work should be carried out in, say, a 60 cm diameter contactor. It may be stressed that even in the case of the single stage contactors, there is need for data from contactors equal to or greater than 60 cm diameter. Conclusions In the range of variables studied in the present work, the following conclusions could be drawn for a multistage gas-liquid contactor: (1) superficial gas velocity has practically no effect on the values of a and kLa,above the critical speed of agitation; (2) kLa and a vary linearly with the impeller speed; and (3) it appears that the values of a and kLa obtained from single impeller contactors are representative of multiple impeller contactors, under otherwise uniform conditions. This should be considered as a preliminary finding. Nomenclature a = effective gas-liquid interfacial area cm2/cm3of clear liquid
Subscripts e = entrance f = final i = initial n = stage number o = outlet
Literature Cited Geeriin@, M. W. Ph.D. Thesis, Darmstadt, Germany, 1957. (See Westerterp et ai., 1963). Jhaveri, A. S.; Sharma, M. M. Chem. Eng. Sci. 1968, 23, 1. Mehta, V. D.; Sharma, M. M. Chem. €178.Sci. 1971, 26, 461. Nienow, A. W.; Liily, M. D. Bbtech. B h n g . 1979, 27. 2341. Sharma, M. M.; Mashekar, R. A., “MassTransfer with Chemical Reaction”, Pirie, J. M., Ed.; Proceedings of a Symposium presented at the Tripartite Chemical Engineering Conference, Montreal, Canada, 1968, Institution of Chemical Engineers, U.K., p 10. Sullivan, G. A.: Treybai, R. E. Chem. Eng. J . 1970. 7 , 302. Westerterp, K. R.; Van Dierendonck, L.; Dekraaa, J. A. Chem. €47. Sci. 1963, 78, 157.
Department of Chemical Technology University of Bombay Matunga, Bombay-400 019, India
K. A. Ramanarayanan M. M. Sharma*
Received for review June 15, 1981 Accepted November 16,1981
CORRESPONDENCE Comments on “Simple Conversion Relationships for Noncataiytlc Gas-Solid Reactions”
Sic En a recent paper (1980), Lee developed a simple conversion relationship for noncatalytic gas-solid reactions A(g) + bB(s) pP(g) + gG(s)in which the pore structure undergoes a change due to the reaction. The conversion relationship is a function of the physical parameters of the solid reactant system and is given by
where Z is the conversion, De is the effective diffusivity of the gaseous reactant in the solid reactant, k is the rate constant of surface reaction, y is the half-thickness of a parallel pore, to is the porosity of solid reactant at time zero, g is the stoichiometric coefficient, MG is the molecular weight of solid products G, Co is the concentration of reactant at the mouth of the pore, pG is the density of G, EG is the porosity of G, qavBis the average effectiveness factor, and y is the molal volume ratio defined by eq 4b in Lee. It is convenient to rewrite this equation as 22+EZ=Ft (2)
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1982 American Chemical Society
