attempt is made to apply Equation 1, proposed by Dakshinamurty et al. (1971) for the prediction of bed porosities in gasliquid fluidized beds comprised of glass beads and balls and lead shot in a circular channel, and in annular channels containing beds of glass balls and beads and rockwool shot. When the bed porosity data (Rao, 1970) of systems 1-3 (Table I) are predicted through Equation 1, there is good agreement between experimental and calculated data with an average % dev of 3.7 when the constant in Equation 1 was changed from 2.65 to 2.85. Further, the bed porosity data (Subbaraju, 1970) for systems 4-9 (Table I) in annular channels could be predicted with the above equation satisfactorily with an average % dev of 5.6, when the constant in Equation 1 was changed from 2.65 to 2.85. It is evident from the above that Equation 1, with a slight alteration in the value of the constant, could predict the bed porosity data satisfactorily both in circular and annular channels containing different beds operating under different ranges of both liquid and gas superficial velocities.
u t = terminal velocity of the particle, cm/sec E = bed porosity (fraction bed volume occupied by gas and
liquid) surface tension, dynes/cm pt = viscosity of the liquid, poise NRef= Reynolds number based on particle terminal velocity u =
literature Cited
Dakshinamurty, P., Subrahmanyain, V., Rao, J. Nageswara, Ind. Eng. Chem. Process Des. Develop., Vol. 10 ( 3 ) (1971). Ostergaard, K., Chem. Eng. Sci., 20, 165 (1965). Subbaraju, R. V., 11Tech thesis, “Ionic Mass Transfer in GasLiquid Fludizied Beds,” Andhra Uniu., Waltair, India (1970). Rao, K. Veerabhadra, MTech thesis, Pressure,,Drop and HoldUp Studies in Gas-Liquid Fludized Beds, Andhra Univ., Waltair, India (1970).
P. DAKSHINAMGRTY1 K. VEERBBHADRA RAO R. V. SUBBARAJU V. SUBRAHMXNYAM Department of Chemical Engineering Andhra University Waltair, I n d i a
Nomenclature 1
D , = equivalent diameter of the annulus u,= average superficial gas velocity, cm/sec u, = average superficial liquid velocity, cm/sec
To whom correspondence should be addressed. RECEIVED for review September 2, 1971 ACCEPTED December 6, 1971
CORRESPONDENCE
Controlling Mechbnisms in the Catalytic Vapor-Phase Ethylation of Aniline SIR: We would like to point out that the rate expressions presented by Goyal and Doraiswamy (1970) are not consistent with their kinetic analysis. We will show below that what they present as reaction rate expressions for individual reactions in their proposed mechanism are instead linear combinations of all five reaction rates. ~ h conc~usions ~ i concern~ ing magnitudes of rate constants, controlling resistances, and applicability of Hougen-Watson models are not justified. Consider the following kinetic scheme which they propose:
A +E+M+W
This is not so. The rate of production Ri of t h e j t h species is given by
R,
vijri
= i
where r i is the rate of the ith reaction and vi, is the stoichiometric coefficiellt Of the jth species in the ith ‘eaction* Therefore
RA
=
-rl - r j
(6)
(1)
RD
=
r2 - r4
(7)
=
-rl - ra - r3
(8)
M+E+D
+W
(2)
RE
E+O
+W
(3)
R M = r1 - rp
(4)
Ro
D-.M+O A +O+M
(5) As was correctly pointed Out, only three of the above reactions are independent. The stoichiometries of Reactions 4 and 5 are related to the stoichiometries of Reactions 1-3 by
= r3
RW = r1
r4
r4
(9)
- rj
(10)
+ +
(11)
r3
r2
Goyal and Doraiswamy claim that T I = - -
(4) = (3) - (2) r2
=
-
However, Goyal and Doraiswamy incorrectly imply t h a t the rates of Reactions 4 and 5 are similarly related tt, the rates of Reactions 1-3:
r4 = rg - r2
r6 = r1 - r3
+
+ + r5
rq =
Ro + R -M -8
Ro
RM
-
8
3Ro 8 ~
4 - -
4
RE 8
RE - ___ 8
+ Rnr4 + R8E -
(12)
-
Ind. Eng. Chem. Process Des. Develop., Vol. 11, No. 2, 1972
(15) 319
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 =
=
Rj W vij
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 The 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
f,
aniline S,S-diethylaniline ethanol N-ethylaniline = ethylene = rate of i t h reaction = rate of ith independent reaction \\-hen dependent, reactioiis are eliminated = rate of production of j t h species = water = 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%)
