Ind. Eng. Chem. Res. 1997, 36, 5037-5038
5037
CORRESPONDENCE Comments on “Design of Entrained-Flow and Moving-, Packed-, and Fluidized-Bed Sorption Systems: Grain-Model Kinetics for Hot Coal-Gas Desulfurization with Limestone” Yan Cao,* Zhong Tang, Zheng Zhou, and Jianmin Zhang Institute of Coal Chemistry, Chinese Academy of Sciences, P.O. Box 165, Taiyuan, Shanxi 030001, People’s Republic of China
Sir: The purpose of this letter is to point out some errors of facts in the recent paper by L. A. Fenouil and S. Lynn (1996). In the section Moving-Bed Design we find that the design equations which were derived by the original authors gave incorrect results on movingbed behaviors. For example, we cannot obtain the same results as expressed in their Figure 3 and Figure 4 on the basis of the same calculation conditions and design equations. After careful analyses, we find that the assumptions on their design of the moving bed and the basic reactor design equation were correct, but errors resulted from the incorrect derivation of the basic design equation in Appendix (A) Derivation of the Design Equations for Moving Bed. The authors made some mistakes in derivations, so they obtained incorrect design equations results. Equation A.1 should be corrected as
uG
dC dX + (1 - )Fs )0 dz dt
(1)
Equation A.17 should be derived from eq A.8 and not from eq A.6 as pointed out by the original authors. One of the main mistakes resulted from incorrect derivations from eq A.17 to eq A.21. Equation A.21 should be corrected as follows:
[(
dZ ) Pe′
)(
)
2
(
)
1 Sh′ - 1 A 1 1 - Yeq- /3 3 3 Sh′ A -1 A A -1 2 A 1 Y - /3 3 dA (2) Da′ eq A -1
(
)]
Other main mistakes resulted from incorrect derivations from eq A.21 to eq A.30. Below we will give the corrective derivations on the basis of the corrective eq 2 mentioned above as follows:
[
]
2 Yeq- /3
]
(
)
A-1 1 A2 + A + 1 ln + Ain - 1 2 Ain2 + Ain + 1 2Ain + 1 2A + 1 x3 arctan - arctan x3 x3
( ) Yeq Y
1/3
,
Ain )
(
)]
S0888-5885(97)00836-1 CCC: $14.00
)]
( ) Yeq Yin
(8)
1/3
(
(9)
)
(10)
y - yin (11) yout - yin
(
(1 - Xout) + (Xout - Xin) Y ) Yin ) 1 - Xout, at Z ) 0
(6)
)
Here
Yeq ) 1 - Xeq ) (5)
(Ain3 - 1)A3
[ ( )
[ ( )
(4)
(A3 - 1)Ain3
) () (
) () (
(7)
A-1 1 A2 + A + 1 ln Ain - 1 2 Ain2 + Ain + 1 2Ain + 1 2A + 1 x3 arctan - arctan x3 x3
I2(A) ) ln
Y ) 1 - X ) (1 - Xout) + (Xout - Xin)
1
(
(
)( )]
Z ) z/R
I(A) ) I1(A) + (-Yeq- /3)I2(A)
K(A) ) ln
[(
3 A3 - 1 Ain Ain3 - 1 A3
I1(A) ) ln
(3)
where
[
with
A)
Pe′ 1 Z) J(A) K(A) I(A) 3 Sh′ Da′
J(A) ) ln
Figure 1. Gas-phase concentration profile of H2S in a countercurrent moving bed of limestone particles.
)
yeq - yin (12) yout - yin
for countercurrent flow (13)
(
Y ) 1 - X ) (1 - Xin) - (Xout - Xin) © 1997 American Chemical Society
y - yin yout - yin
)
(14)
5038 Ind. Eng. Chem. Res., Vol. 36, No. 11, 1997
Figure 2. Gas-phase concentration profile of H2S in a cocurrent moving bed of limestone particles.
Yeq ) 1 - Xeq ) (1 - Xin) - (Xout - Xin)
Y ) Yin ) 1 - Xin, at Z ) 0
(
Figure 3. Gas-phase concentration profile of H2S in a countercurrent moving bed of limestone particles.
)
yeq - yin yout - yin (15)
for cocurrent flow (16)
(Symbols used above are all the same as those in the original paper.) Equations 3-16 are the design equations of a moving bed for the grain model, and for the unreacted shrinking core model Pe′′, Sh′′, and Da′′ should be replaced by Pe′, Sh′, and Da′, respectively. The six dimensionless numbers mentioned above are the same as those in the original paper. Because of their incorrect derivation of eq A.1, their results on the behaviors of not only the countercurrent and cocurrent moving beds but also the simplified packed bed were wrong. Following, we will give our calculation results on the basis of our derivation of eq 4 as shown in the following four figures. Among them, Figures 1 and 2 are calculation results based on the same conditions as those of Figures 3 and 4 in their original paper in order to supply accurate calculation comparisions. Figures 3 and 4 in this paper give calculation results on other conditions.
Figure 4. Gas-phase concentration profile of H2S in a cocurrent moving bed of limestone particles.
Literature Cited Beyer, W. H. Standard Mathematical Tables, 26th ed.; CRC Press: Boca Raton, FL, 1981. Fenouil, L. A.; Lynn, S. Design of Entrained-Flow and Moving-, Packed-, and Fluidized-Bed Sorption Systems: Grain-Model Kinetics for Hot Coal-Gas Desulfurization with Limestone. Ind. Eng. Chem. Res. 1996, 35, 1024-1043. Tan Haoqiang et al. FORTRAN Language, 1st ed.; Qinghua University Press, 1995.
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