7
Ind. Eng. Chem. Fundam. 1985, 24, 7-11
in pronounced nonlinear behavior of the logarithm of the activity corrected diffusivity-viscosity product as a function of the mole fraction. (4) The logarithm of the quotient of the experimental (Fickian) diffusivity and the viscosity is a straight line if the logarithm of the Fickian diffusivity deviates from linearity to the same extent and in the same sense as the logarithm of the solution viscosity. Both the logarithm of the Fickian diffusivity and the logarithm of the viscosity were found to exhibit deviations of the same sign, over at least a portion of the composition range, in 14 of the 16 systems examined in this work. Acknowledgment The authors wish to thank the Natural Sciences and Engineering Council of Canada for the financial support of this work. Nomenclature ai= activity of component i D = experimental (Fick) mutual-diffusion coefficient D = activity-corrected mutual-diffusion coefficient, equal to DIP D o = limiting mutual-diffusion coefficient when xA 0 D” = limiting mutual-diffusion coefficient when xA 1 xi = mole fraction of component i; i = A, B
--
Greek Letters = activity correction factor (eq 2) 9 = absolute viscosity
P
Subscripts AD = refers to Asfour-Dullien A, B = refers to components of mixture LC = refers to Leffler-Cullinan V = refers to Vignes
Literature Cited Anderson, D. K.; Babb, A. L. J . Phys. Chem. 1961, 65, 1281. Asfour, A. A. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., Canada, 1979. Bell, T.; Wright, R. J . Phys. Chem. 1927, 37, 1885. Bdlack, D. L.; Anderson, D. K. J . Phys. Chem. 1964, 68,3790. Bourrely. J.; Chevalier, V. J . Chim. Phys. 1966, 65, 1961. Caklwell. C. S.; Bab, A. L. J . Phys. Chem. 1956, 60,51. Campbell. A. N.; Kartzmark, E. M.; Chatterjee, R. M. Can. J . Chem. 1966, 4 4 , 1183. Christian, S. D.; Naparko, E.; Affsprung, H. E. J . Phys. Chem. 1960, 6 4 , 442. Cullinan, H. T. Ind. Eng. Chem. Fundam 1966, 5 , 281. Cullinan, H. T. Can. J . Chem. Eng. 1967, 4 5 , 377. Cullinan, H. T.; Cusick, M. R. AIChE J . 19678, 73, 1171. Cullinan, H. T. Ind. Eng. Chem. Fundam. l966a, 7 , 177. Cullinan, H. T. Ind. Eng. Chem. Fundam. 1968b, 7 , 331. Doiezalek, F.; Schulze, 2. Phys. Chem. 1913, 83,45. Dullien. F. A. L. Ind. Eng. Chem. Fundam. 1971, 10, 41. Funk, E. W.; Prausnitz, J. M. Ind. Eng. Chem. 1970, 62(9),8. -1, R. K. Ph.D. Thesis, University of Waterloo, Waterloo, Ont., Canada, 1973. Glasstone, S.; Laidler. K. J.; Eyrlng, H. “Theory of Rate Processes”; McGrawHill: New York, 1941. Grunberg, L. Trans. Faraday SOC.1954, 5 0 , 1293. Harris. K. R.; Pua, C. K. N.; Dunlop, P. J. J . Phys. Chem. 1970, 7 4 , 3518. “International Crkical Tables”, Vol. 5; McGraw-Hill: New York, 1929; p 43. Kelly, C. M.; Wlrth, G. B.; Anderson, D. K. J . Phys. Chem. 1971 7 5 , 3293. Kulkarni, M. V.: Allen, G. F.; Lyons, P. A. J . Phys. Chem. 1965, 69, 2491. Leffler, J.; Cullinan, H. T. Ind. Eng. Chem. Fundam. 1970a, 9 , 84. Marsh, K. N. Trans. Faraday SOC. 19888, 6 4 , 894. Marsh, K. N. Trans. Faraday SOC. 1966b,6 4 , 883. McAiilster, R. A. AIChE. J . 1960, 6 , 427. McGlashan, M. L.; Wingrove, M. Trans. Faraday SOC.1956, 5 2 , 470. McGiashan, M. L.; Prue, J. E.: Sainsbury, I. E. J. Trans. Faraday Soc. 1954, 50, 1284. Mlller, L.; Carman, P. C. Trans. Faraday SOC. 1959, 55, 1831. Rao, R. M.; Sitapethy, R.; Anjaneyulu, N. S. R.; Raju, G. J. V.; Rao, C. V. J . Sci. Ind. Res. 1956, 75B, 556. Sannl, S. A.; Hutchison, H. P. J . Chem. Eng. Date 1973, 78,317. Scatchard, G.; Wood, S. E.; Mochel, J. M. J . Am. Chem. SOC. 1939, 6 1 , 3206. Vlgnes, A. Ind. Eng. Chem. Fundam. 1966, 5 , 189. Wang, J. L. H.; Boublikova, L.; Lu, B. C. Y. J . Appl. Chem. 1970, 20, 172.
Received for review November 21, 1983 Revised manuscript received April 16, 1984 Accepted May 11, 1984
SO2 Absorption into NaOH and Na,SO, Aqueous Solutionst ChungShlh Chang’ and Gary T. Rochelle Department of Chemical Engineering, The Universtty of Texas at Austin, Austin, Texas 78712
The chemical absorption of sulfur dioxide into aqueous sodium sulfite and sodium hydroxide solutions is modeled by simultaneous mass transfer and multiple instantaneous reversible reactions. Experiments on the absorption of dilute sulfur dioxide into aqueous sodium hydroxide solutions were carried out in a stirred vessel with a plane gas-liquid interface. An approximation method based on film theory is used to estimate surface renewal theory solutions for mass transfer enhancement factors. Predictions by the present model are compared with those by a previous irreversible model over a wMe range of SO2 partial pressure in the gas phase.
Scope Because of its relevance to pollution abatement, SO2 absorption into NaOH or N@03 solution has been studied by several investigators. Goettler (1967) investigated the simultaneous absorption of SO2 and C02 into NaOH solution flowing over a single sphere. The absorption rates were modeled by film theory with the assumption that
* Acurex Corporation, P.O. Box 13109,Research Triangle Park, NC 27709.
Presented at the AIChE 88th National Meeting, Philadelphia, June 8-12,1980. 01984313/85/1024-0007$01.50/0
dissolved sulfur dioxide and hydroxide ion participate in a two-step instantaneous irreversible reaction and two reaction planes are formed within the liquid phase. Hikita et al. (1972) derived the solution of the penetration theory using the model of two reaction planes. Onda et al. (1971) studied the behavior of reaction plane movement by absorbing sulfur dioxide into agar gel containing sodium hydroxide or sodium sulfite solution. The experimental results for the sulfur dioxide-sodium hydroxide system were found to agree with penetration theory based on the two-reaction-plane model. Hikita et a1 (1977) measured the absorption rate of pure sulfur dioxide into aqueous sodium bisulfite, sodium hydroxide, and sodium sulfite 0 1985 American Chemical Society
8
Ind. Eng. Chem. Fundam., Vol. 24,
No. 1, 1985
solutions in a liquid jet column. The absorption rates obtained with no interfacial turbulence were in good agreement with the theoretical prediction based on penetration theory. The two-reaction-plane model used by previous investigators neglects the reversible hydrolysis of the absorbed sulfur dioxide. Most previous studies used either pure or concentrated sulfur dioxide in the gas phase under which the sulfur dioxide hydrolysis reaction is highly depressed (Teramoto et al., 1978). However, the sulfur dioxide concentration in stack gas SOz scrubbers is normally very low (lOO-4OOOppm) and under these conditions the sulfur dioxide hydrolysis reaction can have a significant effect on the absorption rate. This paper develops an approximation of surface renewal theory with instantaneous, reversible chemical reactions representative of SO2 absorption into NaOH or NaZSO3solution. The theory is tested by experimental absorption of SO2 at low partial pressure in a well-stirred vessel. These results are of direct interest to SOz absorption into CaC03/CaS03 slurries where the mass transfer is frequently limited by liquid-phase diffusion. Further applications of this approach are given by Chang and Rochelle (1982b) and Chan and Rochelle (1983). Chemical Absorption Mechanism When dilute sulfur dioxide is absorbed into aqueous alkaline solutions, the following three reactions should be considered. SOz + H 2 0 * H+ + HS03-
(1)
+ SO:-
(2)
H+ + OH- s HzO
(3)
HS03- ~t H+
The values of the three equilibrium constants for reactions 1, 2, and 3 are designated as Kal, Ka2,and Ka3 and are given, respectively, as at 25 "C and infinite dilution. Reaction 1is very fast, with a forward rate constant estimated to be 3.4 X lo6 (s)-l (Eigen et al., 1961). Reactions 2 and 3 are even faster than reaction 1 since they are proton transfer reactions. Therefore, the absorption of sulfur dioxide into aqueous alkaline solutions can be regarded as a process of gas absorption accompanied by multiple instantaneous reversible reactions in the liquid phase. The differential equations describing the diffusion of all species in the liquid phase, based on surface renewal theory and total-component material balance (Olander, 19601, can
equations. Therefore, there are no analytical solutions for these differential equations. However, an approximate analytical solution can be obtained from surface renewal theory by replacing all the diffusivity ratios in the exact solution based on film theory by their square roots (Goettler, 1967; Hikita et al., 1977; Chang and Rochelle, 1982a; Chang, 1979). The general solutions of the film theory material balance equations are Dso2[S02]+ DH~O,-[HSO~-] + DSO,Z-[SO~~-] =b 1+ ~ bz (6) D,+[H+] - D~so,-[HS03-]- 2Dso,*-[S032-]Do,-[OH-] = b3x
+ b4
(7)
Concentrations of all the species are subject to the equilibrium relations of reactions 1, 2, and 3. The boundary conditions are: at x = 0 [SO21 = [So~li d[HS03-] d[S032-] d[H+I - 2Ds0,2-DH+- dx - DHS03dx dx d [OH-] DOH-=0 dx atx=6 [OH-] = [OH-],, [S032-]= [S032-]o The SO2 absorption rate is given by
"I,=
([SOzli - [SOZI,)
(8)
where 4 is the mass transfer enhancement factor. Solution of eq 6 and 7 with appropriate boundary conditions followed by substitution for diffusivity ratios by their square roots gives the approximate enhancement factor from surface renewal theory C$,=l+
[
The values of [HSO3-Iiand are related to [H+Iiand [S021iby the equilibrium relations [HSO,-li = Kc1[SO2li/[H+li [SO3'-Ii = KclKcz[S021i/[H+Ii2 where KeltKcz,and Kc3are the effective equilibrium constants of reactions 1,2, and 3 expressed in concentration units. Furthermore, the value of [H+Iican be obtained from the following equation, derived from eq 6 and 7 by substituting the boundary conditions and equilibrium relations
Furthermore, the chemical equilibrium relations of reactions 1, 2, and 3 also apply a t all points in liquid phase. Substitution of the equilibrium relations into eq 4 and 5 results in two nonlinear second-order partial differential
Experimental Apparatus and Procedures Experiments on the absorption of sulfur dioxide by aqueous sodium hydroxide solutions were carried out in an agitated vessel with an unbroken gas-liquid interface, used by Chang and Rochelle (1981) in a previous work. The absorber uses continuous flow for both gas and liquid
Ind. Eng. Chem. Fundam., Vol. 24,
Table 11. Effective Diffusivities at 25 OC and Infinite Dilution ion D X lo6, cm2/s
Table I. Parameters for the Estimation of Activity Coefficient at 25 O C C3j
H+ OHHSOc SO?-
6.0 3.0 4.5 4.5
c,
9.31 5.25 1.33 0.958 1.16 2.122 1.33 1.18
H+ OHHSOc
0.4 0.3 0.0 0.0
so:-
phases and is suitable for steady-state operation. Sulfur dioxide diluted by nitrogen was fed into the stirred vessel at constant flow rate. Sufficient sodium chloride (0.5 M) was added to the aqueous sodium hydroxide solutions to eliminate any effect of the electric potential gradient on the diffusivities of ionic species (Vinograd and McBain, 1941). All the experimental runs were performed at about atmospheric pressure and 25 f 1"C. The sulfur dioxide partial pressure of the outlet gas stream was measured by a pulsed fluorescent SO2analyzer (Thermoelectron Model 40). At steady state, samples of the outlet liquid were acidified by HC1 and oxidized by hydrogen peroxide. Total sulfate concentration was determined by an ion chromatograph. The sulfur dioxide absorption rate, N , was calculated from the liquid phase material balance. The enhancement factor, 4, was calculated from the equations
SO2 NaOH NaHS03 Na2S03
I
h
t-u 0.4
0.6
1
08
I
[SO,]iXIOJ
'
(12)
kloA([S02li - [SOZIO)
The values of k A and kl"A were 1.4 X gmol/atm-s and 2.5 X lo4 i / s , respectively. Physical Properties. The physical solubility of sulfur dioxide in water was obtained from the following equation based on the measurement of Rabe and Harris (1963).
[SOdi = H ~ s o ,
H = exp(2851.1/T - 9.3795)
(13)
since the equilibrium constants of reactions 1,2, and 3 are in thermodynamic activities, an appropriate activity coefficient must be incorporated with the concentration of each component to estimate the effective equilibrium constants in concentration units needed for eq 10. For example
Individual ion activity coefficients at 25 "C were calculated by a modified Davies equation (Epstein, 1975) log y j = 0.512nr
' I .
-I1/2
1
+ 0.312C3j1"2 + CdjI
1
1
IO
1
I2
1
,
1.4
1
(M)
Figure 1. Comparison of surface renewal theory with experimental data for S02/N2-NaOH system a t 25 OC.
N
r
No. 1, 1985 9
J
(15)
where nj is the charge on the jth ion, I represents the ionic strength, and C, and C, are the characteristic parameters for each ion species. Table I lists the values of those two parameters on a molar concentration basis. The activity coefficient of the hydrated sulfur dioxide was estimated by Harned and Owen (1958) log yso, = 0.0761 (16) The liquid phase diffusivity, Da, of sulfur dioxide in water was taken as 2.00 X lo4 cm2/s at 30 "C (Peaceman, 1951). The value of DSOeat 25 "C was predicted by correcting for the temperature and viscosity of water according to the Stokes-Einstein relation. Because the sodium hydroxide solutions contained 0.5 M NaC1, the effective diffusivities of all the ionic species
were assumed to be equal to their true diffusivities as determined from equivalent ionic conductances R T A+" D, = -
Nj(FU)
where Fa is the Faraday number and A," is the equivalent ionic conductance. The values of A,O for H+, OH-, HS03and SO?- at 25 "C and infinite dilution are given in Landolt-Bornstein (1960). The diffusivities used in the model calculations are listed in Table 11. Only the ratios of diffusivities were used for the estimation of mass transfer enhancement factors. It was assumed that these diffusivity ratios were independent of temperature and viscosity. Results and Discussion Experimental results for the absorption of dilute sulfur dioxide into aqueous sodium hydroxide solutions are shown in Figure 1as a plot of mass transfer enhancement factor vs. NaOH concentration. The data are in good agreement with the approximate surface renewal theory. Hikita et al. (1977) conducted a series of experiments with pure sulfur dioxide as a gas phase and concentrated NaOH or Na.+3O3 solutions as liquid phases with a laminar liquid jet. Because no excess sodium salt was added to liquid phase, the ionic diffusivities were affected by the electric potential developed by the diffusing ions. However, Figures 2 and 3 show that the present model can fit their experimental data if sodium salt diffusivities were used as the average effective diffusivities of the diffusing ions. For example, the average effective diffusivity of aqueous sodium hydroxide can be calculated from the work of Vinograd and McBain (1941).
The values of those average diffusivities used in the model calculation are listed in Table 11. Hikita et al. (1972) proposed a model using a two-step instantaneous reaction which considered the following
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Ind. Eng.
Chem. Fundam., Vol.
24, No. 1, 1985
a [(-.S,j~ Figure 2. Comparison of approximate surface renewal theory with Hikita's data (1977) for pure S02-NaOH solution.
Figure 4. Schematic diagram of concentration profiles for the absorption of sulfur dioxide into aqueous sodium hydroxide solutions: > 0.05 atm; (b) P~o,
--
' O m
-L
005 O !
[so;l, $0,!
Figure 3. Comparison of approximate surface renewal theory with Hikita's data (1977) for pure S02-Na2S03solution.
c W
reactions to occur irreversibly 8s sulfur dioxide is absorbed into aqueous alkaline solutions
SO2 + SO-: HS03- + OH-
-
2HS03-
(18)
S032- + H20 t 19) Reaction 19 is not important when sulfite ion is present in significant amount in liquid bulk; only reaction 18 proceeds irreversibly at a single reaction plane. When hydroxide ion is the major alkaline species in the liquid bulk, two reaction planes are formed within the liquid. Reaction 18 and reaction 19 take place irreversibly at the first and the second reaction planes, respectively. The main differences between Hikita's model and the present model are the reversible feature of reaction 1 in our work and the role of hydrogen ion in the absorption mechanism. The concentration profiles of important species predicted by our reversible model are shown in figures 4 and 5 for SO2-NaZSO3and S02-NaOH systems, respectively. It can be seen that, when the SO, partial pressure in the gas phase is high (Pso, >> 0.05 atm), the hydrogen ion concentration is negligible throughout the system relative to the concentrations of the other species. Therefore, the reversibility of reaction 1 is not important, but when SOz partial pressure in the gas phase is much less than 0.05 atm, the hydrogen ion concentration is comparable to the concentrations of SO2 and HS03- near the gas-liquid interface. Therefore, the reversible SO2 hydrolysis reaction has a significant effect on the sulfur dioxide absorption rate. Figure 6 compares the mass transfer enhancement factors predicted for the S02-Na2S03system by film theory with reversible reactions 1, 2, and 3, by approximate surface removal theory with reversible reactions 1, 2 and 3, and by penetration theory with irreversible reactions 18 and 19. With a constant ratio of [SO?-],, to [SO,], at 4.7, Hikita's irreversible model predicts a mass transfer enhancement factor which is independent of sulfur dioxide partial pressure. However, the present reversible model shows that the mass transfer enhancement factor increases
(A)
Fo, >> 0.05 A T M
Figure 5. Schematic diagram of concentration profiles for the absorption of sulfur dioxide into aqueous sodium sulfite solutions: (a) PSO,>> 0.05 atm; (b) PSo, >> 0.05 atm; (b) Pso,
