Ind. Eng. Chem. Res. 2002, 41, 131
131
CORRESPONDENCE Comments on “Analysis of Equilibrium Acid Distribution in the System of Citric Acid-Water-(Triisooctylamine + Methyl Isobutyl Ketone) Using a Quasi-Physical Approximation” Paul H. Salim Department of Coiled Tubing Research & Engineering, BJ Services Company, 6620 36th Street S.E., Calgary, Alberta, Canada T2C 2G4
Sir: In the paper published in Ind. Eng. Chem. Res. by Wiratni et al.,1 the authors presented three alternative mathematical models of equilibrium acid distribution in the reactive extraction system studied. The authors stated that model II, although less accurate than model III, was important because of its simplicity. Using model II’s constants at various temperatures presented in Table 2 from Wiratni et al.,1 I obtained a very poor data fit, especially at 329 K (with an average of absolute relative error of 72.30%) and at 338 K (with 116.81% error). Therefore, constants for model II needed to be refitted, not with the linear regression as the authors chose but with the nonlinear least-squares method2 because of the nature of formulated model II. An objective function (F) that would be minimized over N sets of experimental data at an isotherm was N
F)
∑ i)1
(
(CA,tot(M)/CA(W))icalc (CA,tot(M)/CA(W))i
)
Table 1. Model II’s New Constants at Various Temperatures T, K
Kf
KTi
φ
η
301 320 329 338
0.01337 0.01283 0.00996 0.01208
1.93347 4.23115 2.35963 4.04891
0.15701 0.26393 0.21322 0.26505
0.95901 1.20206 0.98136 1.18997
Table 2. Comparison of Fit between This Work and Wiratni et al.1 % AAEa
% AAEa
T, K this work Wiratni et al. T, K this work Wiratni et al. 301 320
6.86 14.94
19.56 15.74
329 338
10.81 12.84
72.30 116.81
(M)/ a % AAE ) percent average of absolute relative error of C A,tot CA(W).
2
-1
(1)
where
(CA,tot(M)/CA(W))calc ) a + b(CTi,tot)c(CA(W))d The function F would be minimum if dF(a,b,c,d) ) 0 and d2F(a,b,c,d) > 0. Four nonlinear equations were generated, and four constants (i.e., a-d) were iteratively solved. Model II’s constants were then calculated as follows and tabulated in Table 1: Figure 1. Data fitting on model II at 301 K: ([) experimental data (Wiratni et al.1); (- - -) model II (Wiratni et al.1); (s) model II (this work).
Kf ) a
(2)
η)c
(3)
wider range than up to 20 as achieved by Wiratni et al.1
φ)1+d
(4)
Literature Cited
KTi ) b/Kfφ
(5)
Model II’s constants generated in this work give a better fit to experimental data than those generated in the original work, as shown in Table 2. Moreover, Figure 1 shows that the new constants fit well the data at 301 K with CTi,tot/CA(W) values up to 63, which is at a much
(1) Wiratni; Tyoso, B. W.; Sediawan, W. B. Analysis of Equilibrium Acid Distribution in the System of Citric Acid-Water(Triisooctylamine + Methyl Isobutyl Ketone) Using a QuasiPhysical Approximation. Ind. Eng. Chem. Res. 2001, 40, 668-673. (2) Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1992; pp 681-688.
IE010556A
10.1021/ie010556a CCC: $22.00 © 2002 American Chemical Society Published on Web 11/07/2001
