Correspondence Comment on “Calcium Bisulfite Oxidation Rate in the Wet Limestone-Gypsum Flue Gas Desulfurization Process” Received for review October 3, 2000. Accepted May 10, 2001.
SIR: In a recent issue of Environ. Sci. Technol., Lancia and Musmarra (1) reported their experimental results on calcium bisulfite oxidation rate in the wet limestone-gypsum flue gas desulfurization process. They considered that the kinetics of bisulfite oxidation in the presence of MnSO4 as catalyst follow a parallel reaction mechanism, in which the overall reaction rate can be calculated as the sum between the uncatalyzed reaction rate and the catalyzed reaction rate:
r ) ru + r c
(1)
where ru is the “uncatalyzed” reaction rate derived previously by Lancia et al. (2) on the basis of the experimental data in the absence of catalyst: 3/2 ru ) kuCHSO 3
(2)
TABLE 1. Experimental and Calculated Values of r under Different Experimental Conditions r × 103 (mol/m3 s)
no.
CMn2+ (mol/m3)
CHSO3(mol/m3)
EVa
CVb
CVc
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.018 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.088 0.088 0.51 1.33 4.17 9.0 13.1 35.0 0.11 0.18 0.21 0.33 0.69 2.60 5.10 7.60 16.50 28.90 38.14
3.1 3.8 3.46 3.1 5.13 6.2 6.39 13.4 7.59 6.62 7.27 7.87 8.2 9.61 10.9 13.1 15.5 17.0 17.6
2.99 2.99 3.53 4.09 5.24 6.48 7.28 10.24 7.68 7.79 7.84 7.99 8.32 9.33 10.16 10.81 12.49 14.18 15.22
2.61 2.61 2.64 2.76 3.43 5.27 7.16 22.48 7.25 7.26 7.26 7.27 7.31 7.65 8.36 9.26 13.68 22.16 29.86
a Experimental values. values using eq 4.
b
Calculated values using eq 6. c Calculated
where ku is the kinetic constant equal to 0.96 × 10-4 m3/2 mol-1/2 s-1 at 45 °C and CHSO3- is the concentration of HSO3in aqueous solution (mol/m3). In eq 1, rc is the “catalyzed” reaction rate derived from data under experimental conditions in the presence of Mn2+ as catalyst:
rc ) kcCMn2+
(3)
where kc equals 0.145 s-1, and CMn2+ is the concentration of Mn2+ in aqueous solution (mol/m3). Substituting eqs 2 and 3 into eq 1, r is further expressed as 3/2 r ) kuCHSO - + kcCMn2+ 3
(4)
Through analysis on experimental data in ref 1, we think that the hypothesis of parallel reaction is reasonable. But it is also found out that the agreement between the calculated values of r using eq 4 and the experimental values of r is not good enough. The main reason is because the uncatalyzed reaction rate, ru, is directly calculated using eq 2. If eq 5 is used in place of eq 2 for calculating ru, there would be a much better agreement between calculated and experimental values of r. On the basis of experimental data given in ref 1, eq 5 1/2 ru ) k′uCHSO 3
(5)
was developed with k′u ) 1.29 × 10-3 mol1/2 m-3/2 s-1. Substituting eqs 3 and 5 into eq 1, the other equation (eq 6) for calculating r can be obtained: 1/2 r ) ku′CHSO - + kcCMn2+ 3
(6)
Table 1 gives the experimental values of r and values calculated using both eq 6 and eq 4. It is easy to make out 3270
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FIGURE 1. Reaction rate versus HSO3- concentration. (O) CMn2+ ) 0.018 mol/m3; (4) CMn2+ ) 0.05 mol/mn3; (-) eq 4; (- ‚ -) eq 6. that the calculated values using eq 6 are much closer to the experimental values than those using eq 4. For the sake of clear comparison, in the original figure given in ref 1, the curves based on eq 6 are also illustrated, as shown in Figure 1. It can be seen from Figure 1 that the points of experimental data are much closer to the curves based on eq 6 than to those based on eq 4. In addition, further discussion can be done from the other angle. Because rc does not change with CHSO3-, for a fixed value of CMn2+, rc can be regarded as a constant. Through calculating the differences between the experimental values of r relative to different CHSO3- and rc relative to a fixed value of CMn2+, r - rc, the relationship curve of r - rc versus CHSO3is illustrated in Figure 2, in which CMn2+ for calculation of rc is equal to 0.05 mol/m3. For the curve in Figure 2, it can be found out that when CHSO3- increases, the slopes of the tangent lines of points on the curve will decrease, i.e., the values of d(r - rc)/dCHSO3- will decrease. Since ru ) r - rc, the values of dru/dCHSO3- should also decrease when CHSO3- increases. Hence, only the function, ru ) f(CHSO3-), the dru/dCHSO3- of which decrease with increasing CHSO3-, would be reasonable. 10.1021/es001732u CCC: $20.00
2001 American Chemical Society Published on Web 06/26/2001
FIGURE 2. Relationship curve of r - rc vs CHSO3- with CMn2+ ) 0.05 mol/m3 for calculation of rc. Examine eqs 2 and 5, respectively. For eq 2, the derivative of ru with respect to CHSO3- is
dru 3 ) k C1/2 dCHSO3- 2 u HSO3
(7)
the values of dru/dCHSO3- decrease when CHSO3- increases. Therefore, eq 5 could be thought to be a reasonable equation that can correctly describe the trend of experimental data. The discussion above indicates that eq 5 is more suitable for calculating ru than eq 2. As a result, the overall reaction rates calculated using eq 6 are much more consistent with the experimental values than those calculated using eq 4. Although it is difficult to give the theoretical explanation on above cases by means of mechanism analysis, it is certain that eqs 2 and 5 are corresponding to different reaction machanisms, respectively. Therefore, for the reaction system with Mn2+ as catalyst in ref 1, it would be the best if we determine the equation for calculation of ru with both the order and the kinetic constant using the data obtained from the experiments in which the catalyst is used.
Literature Cited (1) Lancia, A.; Musmarra, D. Environ. Sci. Technol. 1999, 33, 19311935. (2) Lancia, A.; Musmarra, D.; Pepe, F. Chem. Eng. Sci. 1996, 16, 3889-3896.
Yu Liu,* Qingyu Li, and Anmin Yan
Similarly, for eq 5
dru 1 1 ) k′ dCHSO3- 2 uC1/2
(8)
HSO3-
It is clear that, for eq 7, the higher the CHSO3- is, the higher the value of dru/dCHSO3- is. But for eq 8 derived from eq 5,
Department of Electric Power Environmental Protection Henan Electric Power Research Institute No. 85 South Songshan Road Zhengzhou 450052, Henan Province People’s Republic of China ES001732U
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