1267
Ind. Eng. Chem. Res. 1989,28, 1267
Response to Comments on "Simulation and Optimization of an Industrial Ammonia Reactor" Sir: We thank Dr. Krishna for his valuable comments. Of course the Maxwell-Stefan diffusion equation (Kubota et al., 1969) is the more rigorous equation for the estimation of the diffusivities in multicomponent systems. However, our experience in modeling similar-type industrial reactors (single reversible reaction) has shown that the simple Wilke-type equation is adequate (Elnashaie and Alhabdan, 1988; Elnashaie et al., 1986). The use of the Maxwell-Stefan equation for a single reaction does not introduce any more difficulties to the modeling problem. However, for multiple reactions, the use of the Maxwell-Stefan equation complicates the modeling problem considerably since it dictates the use of a full dusty gas model for the simulation of the diffusion with chemical reaction in porous catalyst pellets. This problem is being investigated for multiple reversible reactions for the steam reforming of methane (Soliman et al., 1988; Elnashaie et al., 1989); the primary results show that it may be possible to model industrial steam reformers using the simple Wilke equation. In order to illustrate our argument for the ammonia case, recalculation has been done for the simulation of the ammonia reactor using the heterogeneous model with three internal collocation points and the Maxwell-Stefan equation for the prediction of diffusion coefficients:
Table I. Heterogeneous Model convsn temp, "C Bed I, Outlet 0.1578 507.000 expt Wilke 0.1604 506.470 Maxwell-Stefen 0.1577 504.400
eff factor, v 0.490 44 0.477 25
Bed 11, Outlet expt Wilke Maxwell-Stefan
0.2555 0.2517 0.2494
502.000 504.148 504.525
0.584 49 0.557 39
Bed 111, Outlet expt Wilke Maxwell-Stefan
0.3091 0.3126 0.3103
455.000 462.105 462.125
Table 11. Effective Diffusion Coefficient' N2 H2 T = 504.4000 OC 0.001 183 0.001 957 Wilke Maxwell-Stefan 0.000 815 0.003 183
0.773 05 0.748 80
NH3 0.001 049 0.000 922
T = 504.5250 "C Wilke Maxwell-Stefan
0.001 041 0.000 771
0.001 934 0.003 012
0.001 055 0.OOO 872
T = 462.1250 OC Wilke Maxwell-Stefan
0.000 875 0.000677
0.001 749 0.002 643
0.000 967 0.000 765
In m2/h. Pressure = 226.0 atm.
zi =
Ni N1 + N2 + N3
i = 1-3
however, since the use of the Maxwell-Stefan equation for single reactions does not add any complication to the model and to its solution algorithm, we agree to include it in the model instead of the simplified Wilke equation. Registry No. NH3, 7664-41-7.
Literature Cited instead of the simplified Wilke equation
j+i
to check the effect of implementation of the MaxwellStefan equation on the results. The results are shown in Tables I and 11. Although the effective diffusivity of hydrogen predicted by the Maxwell-Stefan equation is higher than that of the Wilke equation (Table 11), the opposite is true for nitrogen and ammonia-and the final result is that the simulation results are almost the same (Table I), and there is no significant difference between the results of the two equations, especially at the outlets of the second and third beds. However, a 2 "C difference is observed at the outlet of the first bed, and at this point, the simplified Wilke equation gives better temperature prediction than the MaxwellStefan equation, but the conversion of the latter almost coincides with the experimental results. The Kubota equation gives a slightly lower effectiveness factor along the reactor length. From the shown results, it seems that the simplified equation of Wilke is quite satisfactory;
0888-5885/89/2628-1267$01.50/0
Elnashaie, S. S. E. H.; Alhabdan, F. Mathematical Modelling & Computer Simulation of Industrial Water Gas Shift Converter. J. Math. Comput. Model. 1988, in press. Elnashaie, S. S.; Abashar, M. E.; Al-Ubaid, A. S. Simulation and Optimization of an Industrial Ammonia Reactor. Ind. Eng. Chem. Res. 1988,27, 2015-2023. Elnashaie, S. S. E. H.; Elahwany, A.; ELshishini, S. S. Digital Simulation and Optimization of an Industrial Shift Converter for the Production of Hydrogen. I-Reactor Modelling and Simulation. Proceedings of the IASTED, International conference for modelling and simulation, Cario, Egypt, 1986. Elnashaie, S. S. E. H.; Adris, A,; Soliman, M.; Al-Ubaid, A. S. Parametric Investigation for Industrial Steam Reformers. 1989, unpublished results. Kubota, H.; Yamanaka, Y.; Dalla lana, I. G. Effective Diffusivity of Multicomponent Gaseous Reaction Systems. Application to Catalyst Effectiveness Factor. J. Chem. Eng. Jpn. 1969,2, 71-75. Soliman, M.; Elnashaie, S. S. E. H.; Al-Ubaid, A. S.; Adris, A. Simulation of Steam Reformers for Methane. Chem. Eng. Sci. 1988, 43. 1801-1806.
S. S . E. H. Elnashaie Chemical Engineering Department College of Engineering King Saud University P.O. Box 800 Riyadh 11421, Saudi Arabia
0 1989 American Chemical Society
