CORRESPONDENCE
Kinetic Models for Consecutive Heterogeneous Reactions n the subject paper [IND.ENG. CHEM.57 (lo), 18 (1965)],
I a slight error crept into the treatment of our results a t 575' F.
In the Thaller-Thodos paper [A.I.Ch.E. J . 6 (3), 369-72 (1960)], it was concluded that with continual temperature decrease from 600' to 550' F., the controlling desorption step disappears completely (kH = a ) in favor of a surface-reaction controlling mechanism. Ford and Perlmutter [Chern. Eng. Sei. 19, 371-8 (1964)] essentially substantiated these results and concluded that a dual step controls in the range 550' to 700' F. at 1 atm., while at 800' F., the mechanism switches back to the one that controls at 550' F. ( k H = m ) . If k H in Equation 6 of our paper is set equal to infinity, suggesting that only a single step controls, Equation 3 is obtained. When we use data at 575' F. and Equation 3, a nonlinear least squares analysis gives:
L,kE
0.11194 = 0.39290 LkH A w KA
These represent the best set of parameters a t 575' F. The corresponding calculated rates are (replacing that part of Table I11 of our paper) :
Temp., F.
575
1
Rates, Lb. Moles Alcohol/Hr.-Lb. CatalyJt Pressure, Atm.
x lo2, Measured
1 .OO 3.00 5.00 7.00 9.60
2.27 2.77 2.55 2.17 1.83
?'At
x lo2,
Calcd.
2.2669 2,7798 2.5024 2.1890 1 ,8544
0.1378 0.3521 1.8675 0,8778 1 ,3306 Av.
0.9131
I t is difficult, if not impossible, for a computer to handle 4 m in Equation 6 and therefore, the nonlinear search technique, which produced the results at 575' F. in our paper (page 22), was in error. However, a t 600' F., two steps control, and the reported results a t this temperature reflect valid numbers for the parameters. Our objective function, Equation 8, was indeed polymodal and no allowance was made for large k H or k R values in our grid search, linear search, radial search, and perturbation search techniques. In short, a "global" minimum squared error was not obtained a t 575' F. One has to look at asymptotic solutions, k H = co or k8 = w ,
kH
as separate routines in the nonlinear search for kinetic param eters in Equation 6 or in Equation 12. We would like to acknowledge the assistance of Dr. Stein Kolbe, Central Institute for Industrial Research, BlindernOslo 3, Norway, for bringing this error to our attention and for his calculations. BURTONDAVIDSON Kutgers, The State University New Brunswick, N . J. M. J. SHAH IBM Corp. San Jose, Calif.
ERRATA DIMENSIONLESS GROUPS [IND.ENG.CHEM.58 (3), 56 (1966)] In Table 11, under the listing for Thermal Conductivity having the exponent -1, the following addition should be made : Parameter Thermal conductivity
1 1
Sg;-
korh
~
!
D:l:n~
ML/Te3
1 b g i t 1i x-2/3
j
1
-'/q
+l -
~
Groub
J2 T3 FIl,L7, R1
PREDICTING GAS DIFFUSIVITIES [IND. ENG. CHEM.58 ( S ) , 23 (1966)] In Table 111, columns headed ANDRd HBS CH-OT' OT-CH GILLb ARN MOD-HBS' SL-BDh should be changed to GILL'' ANDR' ARNi HBS MOD-HBS' CH-OT' SL-BDk OT-CHg MOLECULAR TRANSPORT IN MEMBRANES [IND.ENG.CHEM.58 (6), 21, 27 (19GG)] In Figure 3, the water flux for the lower, left-hand curve should be F = 10. In Figure 12b, the references should read: Reid and Breton (726) Lonsdale (97) VOL.
sa
NO.
a
AUGUST 1 9 6 6
a3
