97
Ind. Eng. Chem. Fundam. 1982, 21, 97
R = radius of spherical particle, cm t = process time, h T = catalyst temperature O R To= initial catalyst temperature, O R
alters both the apparent deactivation activation energy and preexponential factor. It is expected that external diffusion resistances will further modify the magnitudes of both deactivation parameters. Since the activation energy for deactivation is unchanged by increasing diffusion resistance for a first-order deactivation process, this suggests a means of distinguishing between first and higher orders of deactivation. Note, however, that the expressions for fouling rate obtained from eq 12 and 13 are independent of n and identical with eq 10 and loa, respectively. Nomenclature a = fractional catalyst activity AA = preexponential factor for primary reaction, h-' Ad = preexponential factor for deactivation, h-' Bim = mass Biot number = (K,.R/D,) DA = effective diffusivity of reactant mthin spherical particle, cm2/h E A = activation energy for primary reaction, cal/g-mol E d = activation energy for primary reaction, cal/g-mol FR = fouling rate, O F f h h = Thiele modulus, ( R / 3 ) (ki/DA)'I2 ki = intrinsic reactant ( R / 3 ) constant, h-l k d = deactivation rate constant, h-I K , = mass transfer coefficient, cm/s
Greek Letters
vot = time-dependent overall effectiveness factor time-dependent overall effectiveness factor 4 = dimensionless group = (3h) 4' = dimensionless group = 3h.a1/2 qo =
Literature Cited Chou, A.; Ray, W. H.; Arls, R. Trans. Inst. Chem. Eng. 1987, 45. T153. Krishnaswamy, S.; Kimell, J. R. AIChE J . 1981a, 2 7 , 120. Krlshnaswamy, S.; Klttrell, J. R. AIChEJ. WOlb, 2 7 , 125. Krlshnaswamy, S.; Klttrell, J. R. Ind. Eng. Chem. Process Des. Dev. 1979. 78, 399. Shah, Y. T.; Paraskos, J. A. Ind. Eng. Chem. Process Des. Dev. 1975, 14,
366. Gulf Research 8 Development Co.,Harmarville. PA.
Department of Chemical Engineering University of Massachusetts Amherst, Massachusetts 01003
S. Krishnaswamy* James R. Kittrell
Received for review February 5, 1981 Accepted September 8,1981
CORRESPONDENCE Comments on "A Simple Device for the Determination of Sphericity Factor" Sir: The short paper by Subramanian and Arunachalam
(IdEng. . Chem. Fundam. 1980 19,436) contains an error.
"=
The Ergun equation in the form used by these authors is not valid for vertical flow of a dense fluid, i.e. a liquid, without a correction for the gravitational potential of the fluid. For a fluid flowing downward, the correct expression is (using the nomenclature in the paper, and neglecting the inertial term)
_-hp = 150(1 - e)'pV L
4s2D,2gce3
[
150L(1 - t)'By
D,2t3g
]
11'
Note that for the special case of Hl = L, eq 5 reduces, correctly, to -AP = 0, and when this value is inserted into eq 1 we find V = 0, which is not correct since a granular bed just filled with a liquid will still drain, implying V # 0. On the other hand, the form of Ergun's equation valid for a dense fluid predich a definite value for V when AP = 0. Faculty of Engineering Science J. M. Beeckmans
- gp gc
If this equation is used in lieu of eq 2 in the paper, then the following expression is found
The University of Western Ontario London, Ontario, Canada N6A 5B9
Response to Comments on "A Simple Device for the Determination of Sphericity Factor" Sir: Professor Beeckmans is correct in his observations. The term L in the Pressure drop equation and hence the fador L/Hl in eq 4 should be deleted. However, the values of L/H1 in the present investigation were very low. The
0198-4313/82/1021-0097$01.25/0
results and the conclusions are not affected. P. Subramanian Vr. Arunachalam*
Department of Chemical Engineering Regional Engineering College Tiruchirapalli, 620015,India
0
1982 American Chemical Society
