I n d . Eng. Chem. Res. 1988,27, 2191-2192
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CORRESPONDENCE Comments on “Production Rate Improvement in Plug-Flow Reactors with Concentration Forcing” Sir: Our research group has been interested in the studies of Thullie et al. (1987) because they sometimes contradict results we have obtained with similar models, but in a mixed rather than in a plug-flow reactor system. Although we concur with their premise that models for periodically forced reactors must employ kinetic models based on dynamic observations rather than steady-state ones, the above paper chooses an absurd set of assumptions so that their premise is not satisfactorily demonstrated. Thullie et al.’s model (eq 1and 5) neglects surface capacitance, but assuming plug flow and infinitely fast mass transfer, they force the relaxation time of the reactor system to be zero. Thus, they have a model which oscillates between steady states even as the period approaches zero and so is quasi-stationary for all periods. A numerical solution of eq 5-7 is not necessary, and eq 11 results by inspection. All Thullie et al. are doing is comparing periodic operation with quasi-steady-state operation. Moreover, eq lb, assuming their phenomenological steps are elementary, postulates two-body adsorption on the surface (an even less likely event than a gas-phase, three-body collision because one body does not translate). We know of no such observation. Of course, the assumptions lead to a convenient form of nonlinearity, but should such a model be used to demonstrate a premise? Furthermore, the authors provide no justification of the realism of magnitudes chosen for K ~ K, p , and M in their models. We argue that the formulation used by Thullie et al. (eq 1) is actually a steady-state one. There is much evidence
for catalytic storage of species which seem not to be involved in reactions proceeding at steady state but may be consumed during transient operation (Jain et al., 1982; Biloen et al., 1983; Winslow and Bell, 1985; Shanks and Bailey, 1987). To allow for this requires at least a further material balance and the addition of a transport term to eq IC.Li et al. (1985a,b)were forced to use such a model expansion to successfully model resonance in NH, synthesis. Literature Cited Biloen, P.; Helle, J. N.; van den Berg, F. G. A.; Sachtler, W. M. H. J. Catal. 1983,81,450-463. Jain, A. K.; Huddns, - 1982, - . R. R.: Silveston, P. L. Can. J. Chem. Ene. 60,809-811. Li, C.; Hudgins, R. R.; Silveston, P. L. Can. J . Chem. Eng. 1985a, 63,795-802. Li, C:; Hudgins, R. R.; Silveston, P. L. Can. J . Chem. Eng. 1985b, 63,803-809. Shanks, B. H.; Bailey, J. E. AIChE J . 1987,33,1971-1976. Thullie, J.; Chiao, L.; Rinker, R. G. Ind. Eng. Chem. Res. 1987,26, 945-947. Winslow, P.;Bell, A. T. J. Catal. 1985,91, 142-154.
Peter L. Silveston, Robert R. Hudgins* Department of Chemical Engineering University of Waterloo Waterloo, Ontario, Canada NZL 3G1
Response to Comments on “Production Rate Improvement in Plug-Flow Reactors with Concentration Forcing” Sir: The purpose of our paper, (Thielle et al., 1987), referred to by Silveston and Hudgins in their letter, was to drive home a point that has generality and to use an uncomplicated, arbitrary example to accomplish this purpose. Obviously, Silveston and Hudgins are offended by our choice of an example system, but they do agree with the important point made in the paper, namely, that steady-state kinetics can give misleading results under concentration forcing conditions, even at invariant cycling. If one reads the paper carefully, he or she readily finds (as did the referees) that we clearly state the limitations of the example system and reemphasize its limitations in the Conclusions section. In real systems, one would generally not observe a concentration profile jumping back and forth almost discontinuously as shown in Figures 1and 2 because there would be molecular dispersion, surface capacitance effecb, non-zero mass-transfer resistance, etc. We purposely wanted to avoid these complications. 0888-5885/88/2627-2191$01.50/0
Nevertheless, the point made in the paper would still generally apply if part or all of the complications of a real system were brought into the picture. Silveston and Hudgins are incorrect in thinking that the two models in our paper “force the relaxation time of the reactor system to be zero.” Under our assumptions, the relaxation time of the pseudohomogeneous system is determined by the kinetics of the reaction. The reaction is not infinitely fast, although fast enough to essentially keep up with the forced concentration oscillations in the fluid phase. Thus, the relaxation time cannot be zero. Silveston and Hudgins incorrectly claim that both models (I and 11)operate in the quasi-steady-state (QSS) regime for all cycle times, wherein the time-averaged reaction rates would simply be the weighted average of two states which are quasi-steady. If their claim were correct, enhancements over the optimal steady state (OSS) such as those shown in Figure 4 would be impossible and Figure 0 1988 American Chemical Society
