3R_ o +%- 5 rs= -_ 8 4 8
73 =
However, if Equations 6-11 are substituted for Rj in the above expressions, the followirlg expressions result : 71
2
7-3
9 2
rj
2
(11417-3
(l/ti)rI
+
(3/s)r5
(1/8)r1
i
(5/8)r2
(1/4)r3
(3/s)r4
-
(l/s)rS
(1/I)r1
+
(1/~r2
(114)i-I
-
(1/4)r5
Nomenclature
(l/g)r3
A
=
D E 11 0 ri
= = =
(3/s)rl
-
(3;’8)r2
!1/8)r2
-
(l/,)rQ
(lj4)r3
-
(5/8)r4
-
(l/g)r*
+ (5/s)r3
Thus we see that Equations 12-16, which Goyal and Doraismamy used to relate their experimentally measured rates of change (Ro,RM, and R E ) to their kinetic model, result not in expressions for the individual reaction rates proposed in the model, but in complicated linear combinations of all five rates of the proposed reactions. Obviously, their conclusions, based on the above incorrect expressions, are not justified. Reactions 1-3 alone are sufficient to describe the stoichiometry of the reactioii network. However, if two sets of reactions are to provide a n equivalent kinetic description of a system, both must predict the same production rate for each species. Thus the reaction rate expressions of the independent Reactions 1-3 must be modified to include the rates of the eliminated Reactions 4 and 5 . Let f l , 72, and $3 be the rates of Reactions 1-3, respectively, when Reactions 4 and 5 are discarded. Then comparing
RA
=
-fi
Ru
=
Pa
RE
=
-71
Rx
=
Pi
Ro
= P3
Rw
=
-
Pa
-fa
Pi
+ + jip
Fl = r1 fa =
P3
+ rs
Pi =
=
literature Cited
Goyal, P., Doraiswamy, L. K., Ind. Eng. Chem. Process Des. Develop., 9, 26-38 (1970).
Daniel R. Schneider Robert G. Squires
Purdue Vniversity Lafayette, IIV 47907
CORRECTION The following corrections should be made to the paper, “Tests for Transport Limitations in Experimental Catalytic Reactors,” by David E. Mears which appeared in I&EC Process Design and Development, [lo (4), 541 (1971)]. In Equation 21, should appear instead of y in the numerator on the right-hand side of the criterion. I n Equation 26, the denominator on the right-hand side of the criterion should read:
rp - r4
-+
r3 rI - r3 T h e above set of equations can be solved for the modified reaction rates in terms of the experimentally measured , RE to give rates Ro, R M and P3
aniline S,S-diethylaniline ethanol N-ethylaniline = ethylene = rate of i t h reaction f , = rate of i t h independent reaction \\-hen dependent, reactioiis are eliminated R j = rate of production of j t h species W = water v i j = stoichiometric coefficient of j t h species in i t h reaction
- 73
with Equations 6-11, we find
320
Thus the data can be recalculated to give estimates of PI, and 73. These modified rates, as shown above, are linear combinations of the five elementary rates of the proposed reaction network.
( ~ s ) r 2
r4 2 (l/s)rl -
Ro
72,
+
(5/s)r1
+ + + + (1/2)r3+ + +
+ Ro + R E )
Pz = - l / z ( R ~
(16)
‘ / ~ ( RM Ro - R E )
Ind. Eng. Chem. Process Des. Develop., Vol. 1 1 , No. 2, 1972
(1
in which
+
2%)
