Ind. Eng. Chem. Process Des. Dev. 1984, 23, 181-182'
375 "C and 6.9 MPa, Figure 2 at 375 "C and 3.55 MPa, and Figure 3 for 6.9 MPa and at either 330 or 350 "C, where XPBzis the fraction of entering PBz reacted. Associated with each line is the calculated first-order rate constant in units of g-mol of PBz/(h g of cat.) X lo4. At 6.9 MPa total pressure and 375 "C the hydrogen sulfide decreased the hydrogenation rate by a factor of 2 and ammonia decreased it by a factor of 7. A mixture of H2Sand NH3 behaved like NH3 alone. At 3.55 MPa and 375 "C the NH3-H2S mixture caused over a threefold decrease compared to that with H2Salone. At 330 "C and 6.9 MPa the mixture of NH3 and H2S decreased the hydrogenation rate more than tenfold below that with H2S alone. No products other than propylcyclohexane, such as propylcyclohexene,were observed. Possible dealkylated products such as benzene or cyclohexane also were not found. Slight traces of ethylbenzene and ethylcyclohexane were noted. From the studies in the presence of H2Sand NH3 at 7 MPa, an activation energy for the hydrogenation reaction was calculated to be 146 kJ/mol. The inhibiting effect of H2S on the catalytic hydrogenation of propylbenzene is consistent with some other studies and with our earlier study of the reaction network in the catalytic hydrodenitrogenation of quinoline. There we found that addition of H2S substantially increased the hydrogenolysis reactions in the overall network but moderately inhibited hydrogenation reactions (Satterfield and Giiltekin, 1981). H2Shas also been found to inhibit butene hydrogenation in the HDS of thiophene (Satterfield and Roberts, 1968; Lee and Butt, 1977). In some cases reported by others H2S did not affect hydrogenation rates. Elsewhere (Yang and Satterfield, 1984),we explain these seemingly contradictory observations by postulating that those sites active for hydrogen-
181
ation-dehydrogenation reactions are sulfur vacancies associated with the molybdenum atom that are easily poisoned by nitrogen bases. The adsorption of H2S results in less sulfur vacancies but the number of vacancies is also determined by the initial sulfiding treatment. The poisoning effect of NH3 is dramatically shown by the presesnt results. Registry No. H2S,7783-06-4; NH,, 7664-41-7; Ni, 7440-02-0; Mo, 7439-98-7; propylbenzene, 103-65-1.
Literature Cited Gates, B. C.; Katzer, J. R.; Schuit, G. C. A. "Chemistry of Catalytic Processes"; McGraw-Hili: New York, 1979. Goudriaan, F. Thesis, Twente University of Technology, Enschede, The Netherlands, 1974. Gukekin, S. Ph.D.. Thesis, MIT, Cambridge, MA, 1980. Lee, H. C.; Butt, J. 8.J . Catal. 1977, 40, 320. McIivried, H. G. Ind. Eng. Chem. ProcessDes. D e v . 1971, IO, 125. Satterfield, C. N.; Cocchetto, J. F. Ind. Eng. Chem. Process Des. Dev. 1981. 20, 53. Satterfield, C. N.; GuRekin, S. Ind. Eng. Chem. Process D e s . Dev. 1981, 20, 62. Satterfield, C. N.; Roberts, G. W. AIChE J . 1968, 14, 159. Shih, S. S.;Katzer, J. R.; Kwant. H.; Stiles, A. 8. Am. Chem. SOC. Div. Pet. Chem. Prepr. 1977, 22, 919. Sonnemans, J.; Mars, P. J . Catal. 1974, 34, 215. Yang, S. H.; Satterfield, C. N. Ind. Eng. Chem. Process Des. Dev. 1984. Yang, S. H.; Satterfield, C. N. J. Catal. 1983, 8 1 , 168.
University of Petroleum and Minerals Dhahran, Saudi Arabia
Selahattin Giiltekin Syed A. Ali
Department of Chemical Charles N. Satterfield* Engineering Massachusetts Institute of Technology Cambridge, Massachusetts 02139 Received for review February 3, 1983 Accepted June 13, 1983
CORRESPONDENCE Solution to Homogeneous Diffusion Mass Transport Equatlon Sir: The solutions to homogeneous solid phase diffusional mass transport equations frequently involve numerical components (Tien and Thodos, 1965; Colwell and Dranoff, 1971; Kawazoe and Suzuki, 1975; Mathews and Weber, 1976; Coughlin et al., 1978). The paper by Mathews and Weber (1976) incorporated an analytical solution in time but a numerical solution for distance travelled within the particle. An alternative solution was reported by McKay et al. (1984) which gave an analytical solution for time and distance. Part of the solution is presented in more detail in this note since comments as to the procedures involved have been made. In this note we would like to indicate in more detail how result (30) in our paper (McKay et al., 1984) has been derived. In particular, what we want to show is that J1x{(l
+ x)B(a(l + x ) ) - (1- x)B(a(l - x ) ) ) dx =
4
2
K ( X ) - + -(xZ 3x3 3x3
+
- i)e+
"( 6 ) 3
2-
erf ( X ) (2d)
Changing the integration variable to a(1- x ) and a(1- x ) , respectively, in the first and second terms, the left hand side of (1)becomes
K(2a) (1) L 1 2 a X ( X - a ) B ( X )dX
where
a3
0198-4305/84/1123-0181$01.50/0
0
0 1983 American Chemical Society
(3)
182
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 1, 1984
Consider
Ci E J2aXB(X) d X
JzaX e-x2 dX
From (2b) and (2c) 7$/2
I = -erf 2
(2a) + d J e ~ * ' Xerf (X) dX Using the results (7) and (11) in (3), we get for the
Integrating by parts ,lJZ
I = -(1 2
+ 4a2)erf (2a) - J0
2a
X2e-x2dX
Integrating again by parts yields the final result
Consider next
using (2d) Q.E.D. Literature Cited
J = JZaX2B(X) dX From (2b)
J = J2a{Xe-X2+ d l 2 X 2erf (X){dX = 0
1 -(1 - e-4a2) T ~ / ~ Jerf~(X) ~ dX X ~(9) 2
+
Integrating by parts 1 2
J = -(1 -
+ 8a37r1/2 -erf 3
(2a) -
2 -J 3 0
2a
X3 e-xz d X (10)
Integrating again by parts
Colwell, C. J.: Dranoff, J. S. Ind. Eng. Chem. Fundam. 1971, 70, 65. Coughlin, R. W.; DRI, P.; Jere, E. H. J. Co//oid Interface Sci. 1978, 6 3 , 410. Kawazoe, K.; Suzukl, M. Chem. Eng. J. Jpn. 1975, 8 , 379. Mathews, A. P.; Weber, W. J., Jr. AIChESymp. Ser. No. 766 1976, 73, 91. McKay, G.; Allen, S. J.; McConvey, I. F.; Walters, H. R. J. Ind. Eng. Chem. Process Des. Dev. 1984 article in this issue. Tien, C.: Thodos, G. AIChE J. 1965, 11, 845.
Department of Chemical Engineering The Queen's University of Belfast Belfast, B T 9 5DL, Northern Ireland Department of Applied Mathematics and Theoretical Physics The QueenS University of Belfast Belfast, BT9 5DL, Northern Ireland
Gordon McKay*
H. R. James Walters
