Chm,rcal Engmrering S<ience, Vol. 44. No. 10, pp 2191 2195. 1989. ooo9 X09)89 s3.00+0.00 Printed m Great Brlram $’ 1989 Psrgamon Press plc

THE EFFICACY OF CONCENTRATION FORCING

RAJIV YADAV and ROBERT G. RINKER’ Department of Chemical and Nuclear Engineering, University of California, Santa 3arbara. CA 93106,

U.S.A.

(Received 22 July 1988; accepted 7 February 1989)

Abstract-Concentration forcing research is largely inspired by expectations of improving reactor productivity beyond that attainable under any (including optimal) steady state. Are these expectations reasonable and are they well-grounded? In a recent paper, Nowobilski and Takoudis (1986, Chem. Engng Cmmnrn. 40, 249-264) suggest otherwise. In their opinion the optimal steady-state productivity cannot he exceeded by periodic forcing of catalytic reactors. However, a survey of the literature reveals that, in several studies (including OUT own), production rates higher than those of the optimal steady state have been obtained through forced feed cycling of catalytic reactors. In this paper, using such cases as evidence, we contend that improving reactor productivity over the optimal steady state through concentration forcing is not an elusive goal. From reports in the literature, it appears that it has already been realized by several researchers, including ourselves.

INTRODUCTION

In the last two decades forced periodic operation of heterogeneous catalytic reactors has emerged as a plausible means of improving reactor performance. Although the literature is replete with reports on improvement of productivity or selectivity in cycled reactors, questions concerning the true efficacy of such reactor behavior have been raised. Most notably, in a recent paper, Nowobilski and Takoudis (1986) directly address the question of attainability of global im- provements in periodically operated reactors. After simulating models for three prominent cases of im- provement reported in the literature, these authors conclude that production rate improvements over the optimal steady state are not achievable by periodic forcing of the reactor in these cases. They also survey some previously reported experimental findings and conclude that there is no evidence which confirms an improvement in reactor production rate over the best or optimum steady state. To some extent Nowobilski and Takoudis are correct, and since the number of reported instances of productivity improvement over the optimum steady state is not large, one might even find their assertions persuasive. It is only recently that reported experimentation in this area has begun to flourish.

In the concluding section of their paper, however, Nowobilski and Takoudis claim that “The physical

impossibility (emphasis added) of increased rates of reaction when perturbing optimal steady-state con- ditions may be the reason for the inability of improved behavior. This would suggest that any rate improve- ment observed by researchers to date might be a

favorable averaging of a spectrum of steady states, outproducing less favorable base steady states.” Thus they suggest that, in general, periodic operation of reactors for improving productivity is futile and any

‘Author to whom correspondence should be addressed.

improvements in reactor performance a mere chimera. Although their questions are valid, we feel that such conclusions are neither justified nor tenable. For example, why should it be physically impossible to increase rates of reaction beyond the optimum steady state? Transient reactor operation is a phenomenon quite different from steady-state reactor operation and one should not be a barrier for the other. Similarly, to imply that all transient reactor operation is just some kind of an average of steady states is neither consistent with our present understanding of catalytic reactors nor is it borne out by facts. If averaging a spectrum of steady states could represent periodically forced reac- tors, one would expect that rate models which predict steady-state reactor behavior would perform equally well under transient conditions. Many researchers have shown that this is not the case. Particular reference to concentration forcing papers by Thullie et al. (1987a) and Chiao and Rinker (1989) can be cited.

For the preceding reasons, even though Nowobilski and Takoudis’s paper is an excellent and timely cri- tique of periodically forced reactors, their assertion that the optimum steady state represents some kind of an upper bound for all reactor productivities is unjusti- fied. In this paper we dispel the notion that period- ically forced reactors can never yield production rate improvements over the optimal steady state. This is accomplished by citing examples of improvement over the optimum steady state from published literature. In the absence of any a priori proof, this is a reasonable course of action.

Questions about the efficacy of periodic operation stem largely from a confusion related to the per- formance criteria used to evaluate cycled reactors. Hence, the first part of this paper is devoted to outlining the correct performance criteria that must be used to compare the performance of cycled reactors to that of steady-state reactors. A final word concerning terminology is in order. Since we are only focusing on

2191

2192 RAW YADAV and

forced oscillations in feed concentration, the terms concentration forcing, forced cycling, periodic forcing, and periodic operation are used interchangeably and must be construed to be synonymous.

THE CORRECT PERFORMANCE CRITERIA

Unfortunately the published literature on concen- tration forcing suffers from a diversity of performance criteria. A very common tendency has been to com- pare cycled reactor production rates to those of a steady-state reactor operating at the average feed concentrations of the cycled reactor (henceforth re- ferred to as the “average steady state”). For example Unni et al. (1973) in studying the effect of cycling on the rate of SO, oxidation, used such an average steady state to compare their cycling results and concluded that reactor performance can be improved. This prac- tice is widespread as is evidenced by other reports such as Cutlip (1979), Schadlich et al. (19831, Lynch (1983) etc. Obviously, such criteria should not be used if one is interested in illustrating the superiority of periodic operation over all steady states, including the opti- mum steady state. If steady-state operation can be improved by simply modifying the feed composition there would be no need to resort to concentration forcing. As Bailey (1973) cogently asks, “If feeding larger reactant concentrations gives larger conver- sions, why not use the most concentrated reactant available all the time, for example?” and in a more mathematical vein, “If the periodic control may as- sume any value in a set U of admissible controls, why should the competing steady state processes be re- stricted to those with control values in a proper subset of U?” Although Bailey goes on to say that process improvement over the average steady state through cycling might well be desirable in situations where “the average amount of raw materials or energy available is fixed by the neighboring processes,” such cases clearly would not be justified when compared to the optimum steady state. Also, if steady-state oper- ating parameters are constrained by the environment, there is no reason to always assume a flexibility with regard to periodic operation.

Thus, it is clear that utility of improvements over the average steady state is limited, and comparison of cyclic operation with any steady state other than the optimum or best steady state at the same operating pressure and temperature would generally be mislead- ing and often counterproductive. It is somewhat cur- ious that the notion of reactor performance improve- ment over the average steady state has persisted in the literature. In fact, in a recent review, Silveston (1987) raises this question of performance criteria, but strangely enough he rules both criteria, that of com- parison with the average steady state and that of comparison with the optimum steady state, equally valid. In our opinion, which is also shared by Nowobilski and Takoudis, the true test of periodic operation for almost all reaction systems would be one that involves a comparison with the optimum steady

ROBERT G. RINKER

state. Every reaction, however many components it may involve, has one feed composition which yields the highest production rate of the desirable product for some temperature and pressure, and for a particu- lar reactor geometry and size (or catalyst loading). If this production rate is called R,,,, in general, only those periodic processes would be preferred which give time-averaged production rates larger than R,,,.

Since we are only looking at concentration forcing, variations in temperature and pressure are not consid- ered. If, for some pressure and temperature where R,,,

is the highest rate attainable, we can obtain an even higher rate by cyclic operation at the same tempera- ture and pressure, and for the same reactor geometry and size (or catalyst loading), we would have proved our hypothesis+ven though higher rates may be obtainable at some other pressure and temperature or for some other reactor geometry and size (or catalyst loading). Our quest, then, is for such periodic pro- cesses. To do this, we consider two.areas: computer simulations and experimental studies.

EXPERIMENTAL STUDIES

The most telling evidence for production rate en- hancement over the optimum steady state comes from forced cycling experiments on ammonia synthesis. Three different groups in Canada, France and the U.S.A. have reported production rates higher than the optimum steady state during forced cycling of this reaction.

In Canada, Jain et al. (1983) studied forced compo- sition cycling of the ammonia synthesis reaction in a gradientless reactor at 2.38 MPa total pressure and at 633 and 673 K over a triply promoted iron catalyst. To compare their cycling results, they also measured the actual steady-state “reaction profile” (i.e. a plot of reaction rate vs the feed mole fraction of one compo- nent, in this case hydrogen). These authors found that, for both 633 and 673K and for some cycling par- ameters studied by them, the time-averaged reaction rate under cycling conditions was higher than any

Maximum Rates Under

- - - - Steady-state

- - - Cycling

I I t I I 0.0 0.2 0.4 0.6 0.8 1 .c

yi2(Balance N2)

Fig. 1. Steady-state and cycling rate maxima vs feed compo- sition. [For the ammonia synthesis reaction see Fig. 9 in Jain

et uf. (1983).]

The efficacy of concentration forcing 2193

steady-state rate. Their results are illustrated in Fig. I which shows both the steady-state and forced-cycling production rates vs the inlet mole fraction of hy- drogen. It is clear from Fig. 1 that as much as a 30% improvement in the production rate of ammonia over the optimum steady-state was observed by Jain et al.

In France, Rambeau et al. (1982) and Rambeau and Amariglio (1981) have studied ammonia synthesis over osmium powder and ruthenium powder, respect- ively, using a cyclic procedure. Over osmium powder the authors report, and here we quote, “the best average rate obtained is between 5 and 50 times higher than the best steady-state rate, depending on the temperature in the range of 25&4OO”C.” Similarly, over ruthenium powder, the authors report that “the average rate of production is eight times higher than the best steady-state rate of production.”

Finally, in the U.S.A., Chiao et al. (1987) have studied the ammonia synthesis reaction over a pro- moted iron catalyst in a fixed-bed reactor under concentration forcing conditions at 703 K and 4.14 MPa. These authors use a production rate en- hancement factor + to compare their cycling results with their steady-state results. This factor is defined as

cyclic production rate (time-averaged) *= .

optimum steady,state production rate (1)

Thus, a value of $ > 1 would indicate an improvement in production rate over the optimum steady-state rate. Both steady-state and cycling results of these authors are succinctly represented by Fig. 2 which is also a

I.10

+- 1.05 i s E 8 L%

1.00 r E

0.85

+ , -

0.

o Steady State

A Mixture Cycling

I I

20 0.30 0.40

Average Feed Composition, y,!., 2 .

Fig. 2. Comparison, at 703 K and 4.14 MPa, of exper- imental production rate enhancement at steady state with mixture cycling (0.40, 0.20) as a function of average feed composition. The maximum point at $ = 1 on the steady- state curve corresponds to the OSS with y L, =0.30. The cycle time for the cycling curve is T = 30 s and the maximum point corresponds to y&,=0.36 with y =0.8 and $ = 1.08. The dashed line connectmg the cycling data points is not a model fit. [For the ammonia synthesis reaction see Fig. 11 in Chiao

et al. (1987).]

dramatic illustration of production rate increases over the optimum steady state. As much as an 8% improve- ment in production rate over the optimum steady state was observed by these authors through mixture cycling.

It is evident, then, that time-averaged production rates exceeding the highest or optimum steady-state production rates can be realized through concentra- tion forcing, at least for the case of ammonia synthesis. Since the ammonia synthesis reaction falls into the broad category of heterogeneously catalyzed reactions one can expect that production rate improvements via concentration forcing over the optimum steady-state are possible, in principle, for other heterogeneously catalyzed reactions. There is nothing insurmountable about the optimum steady state as the above studies show.

Further experimental evidence for production rate improvement over the optimal steady state comes from the experimental work of El Masry (1985). El Masry studied the Claus reaction under both steady-state and forced-cycling conditions over a bauxite catalyst in a differential reactor. The results of some of his experiments are shown in Fig. 3 where both the steady-state and time-averaged production rates under cycling conditions are plotted vs the mole fraction of hydrogen sulfide. From Fig. 3 it is again apparent that concentration forcing can yield time- averaged production rates which are significantly higher than the highest production rate under steady- state conditions.

In a recent study, Prairie and Bailey (1987) have shown that forced cycling of ethylene hydrogenation on Pt-AI,O, in a CSTR can result in time-averaged

production rates as much as 31% higher than the maximum steady-state rate. Pertinent results from this study are shown in Fig. 4. These authors also make the key point that the “observed rate improvement is clearly due to surface dynamics and is not a result of the favourable averaging of a spectrum of steady states. The latter has been speculated to be the cause of rate enhancement by forced composition cycling (Nowobilski and Takoudis).” A similar point was also

0.7 -_ F

- - - Cycling Rate Curve

w - ss Rate Curve 0, 0.6

f z 0.5

z 0.4 II

.s 0.3

5 a” 0.2

u 0.1

f-

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole Fraction of b-l+

Fig. 3. Steady-state and cycling rate curve [For the Claus reaction see Fig. 7 in El Masry (1985).]

2194 RASIV YADAV and ROBERT G. RINKER

Average Ethylene Feed Fractmn, X,

Fig. 4. Time-average reaction rate dependence on the time- average ethylene feed fraction for cyclic forcing at T= 180 s. Squares, experiment Ik triangles, experiment III; diamonds, steady-state intrinsic rates for 20% H, in the reactor feed- stream. [For ethylene hydrogenation see Fig. 9 in Prairie and

Bailey (1X37).]

made by Nappi et al. (1985). In a study of forced feed composition cycling of catalytic methanol synthesis, the authors found that the instantaneous rate of methanol formation during step-test experiments was as much as 40% higher than the maximum steady- state rate. The authors argue that, if the instantaneous rate maxima approached the steady-state maxima, it could be “seen as a sequence of brief steady states so that the rate of methanol formation will change with time following the rates observed at steady-state. Something more than this (emphasis added) must be happening to explain the 40% greater rate than predicted by rhe maximum in Fig. 2.”

What is the importance of all these experimental studies which demonstrate improvements in produc- tion rate aver the optimum steady stale through cycling? First of all, it is clear that concentration forcing merits attention as a possible means of increas- iqg reactor productivity beyond that obtained by operating the reactor under optimum steady-state conditions. Second, diverse reaction systems can be forced to yield higher production rates than the optimum steady-state rate. Finally both fixed-bed reactors and CSTR-type reactors can exhibit such behavior.

COMPUTER SIMIJI,ATl0NS

Some skeptics may well argue that experimental instances of production rate increases through con- centration forcing beyond the optimum steady-state production rate may well be experimental artifacts and that the evidence in favor of forced cycling is not enough to be convincing. One way of overcoming such objections is computer simulations of periodically forced reactors. It is somewhat interesting to note that such simulations are rather scarce, at least in the open literature. Moreover, most simulation studies of forced cycled reactors have relied on hypothetical reaction kinetics. Hence, in this paper, we discuss only

one simulation study showing time-averaged rates larger than the optimum steady-state rate.

In the study discussed, Thullie et al. (1987b) simu- lated a hypothetical reaction sequence in an iso- thermal fixed-bed reactor. They wrote down the com- plete balance equations for a one-dimensional, iso- thermal plug-flow reactor without axial mixing and solved those equations using the method of character- istics. They also defined an enhancement factor, I,+, which is the same as the one defined by Chiao et al. (1987) and given by eq. (1). Their simulations showed that, for nonlinear kinetics, a number of parameter values lead to values of i greater than 1. It must be recalled that a value of $ > 1 implies that the time- averaged production rate during cycling is higher than the production rate at optimum steady state.

CONCLUSIONS

The experimental studies and computer simulation discussed here support the view that there is a real possibility of obtaining time-averaged production rates during periodic operation of catalytic reactors which are higher than those obtained at the optimum steady state. It is indeed true that some of the opti- mism created by concentration forcing studies must be treated with caution because very often the per- formance criteria employed by researchers to evaluate cycling results tend to be misleading, as pointed out very effectively by Nowobilski and Takoudis. How- ever, there are an adequate number of unambiguous reports where results of concentration forcing have been compared to optimum steady-state results actually obtained under the same reactor operating conditions.

One final point deserves mention: forced cycling of catalytic reactors is an inherently complex phenom- enon. It entails a complicated interplay of reaction kinetics, reactor dynamics emanating from the volu- metric space time and the catalyst surface space time, frequency and amplitude of the forcing function, nature of concentration forcing, i.e. mixture cycling or pure component cycling, reactor configuration, i.e. completely mixed (CSTR) or plug-flow type, and the type of oscillation, i.e. square wave or sinusoidal, etc. At present, an understanding of how these factors interact to affect the reactor productivity is quite inadequate and somewhat rudimentary. It is justifi- able therefore to say that to make any a priori generalizations about periodically forced catalytic re- actors must await a greater understanding of the fundamental underlying processes. Meanwhile, if one is to take one’s cue from experimental and simulation studies, a strong case exists for improving reactor productivity through periodic oscillations of the feed composition or what is now also known as concentra- tion forcing or forced cycling.

Acknowiedgements~-Support for this work by the Division of Chemical Science (Office of Basic Energy Sciences) of the Department of Energy (U.S.A.) under grant number DE-FG03-84ER 13300 is gratefully acknowledged.

The efficacy of concentration forcing 2195

NOTATION

T T-A xi Yf,,

&*

time-averaged rate, pmol/s highest attainabIe production rate for a given temperature, pressure, reactor ge- ometry and size forcing period, s time-averaged average ethylene feed fraction time-averaged mole fraction of N, fed to the reactor mole fraction of hydrogen in feed

Greek letters Y cycle split, which is the fraction of the total

cycle time that the stream containing the

higher concentration of N, flows to the reactor cycle time, s production rate enhancement defined by eq. (1) dimensionless

REFERENCES

Bailey, .I. E., 1973, Periodic operation of chemical reactors: a review. Chem. Engng Commun. 4, 11 l-124.

Chiao, L. and Rinker, R. G., 1989, A kinetic study of ammonia synthesis: modeling high-pressure steady-state and forced-cycling behavior. Chem. Engng Sci. 44, 9-19.

Chiao, L., Zack, F. K., Rinker, R. G. and Thullie, J., 1987, Concentration forcing in ammonia synthesis: plug flow experiments at high temperature and pressure. Chem. Engng Commun. 49, 2733289.

Cutlip, M. B., 1979, Concentration forcing of catalytic surface rate processes. A.I.Ch.E. J. 25, 502-508.

El Masry, H. A., 1985, The Claus reaction: effect of forced feed composition cycling. Appf. Catni. 16, 301-313.

Jain, A. K., Hudgins, R. R. and Silveston, P. L., 1983, Influence of forced feed composition cycling on the rate of

ammonia synthesis over an industrial iron catalyst. Part I+ffect of cycling parameters and mean compo- sition Can. J. &em. Engng 61, 824-832.

Lynch, D. T., 1983, Modelling of resonant behavior during forced cycling of catalytic reactors. Can. J. &em. Engng 61, 183-188.

Nappi, A., Fabricino, L., Hudgins, R. R. and Silveston, P. L., 1985, Influence of forced feed composition cycling on catalytic methanol synthesis. Can. J. ckem. Engng 63, 963-970.

Nowobilski. P. J. and Takoudis, C. G., 1986, Periodic operation of chemical reactors: are global improvements attainable? Chem. Engng Commun. 40, 249-264.

Prairie, M. R. and Bailey, J. E., 1987, Experimenta and modelling investigations of steady-state and dynamic characteristics of ethylene hydrogenation on Pt/Al,O,. Chem. Engng Sci. 42,2085-2102.

Rambeau, G., Jorti, A. and Amariglio, H., 1982, Improve- ment of the catalytic performance of an osmium powder in ammonia synthesis by the use of a cyclic procedure. Appl. Coral. 3, 273-282.

Rambeau, G. and Amariglio, H., 1981, Improvement of the catalytic performance of a ruthenium powder in ammonia synthesis by the use of a cyclic procedure. Appl. Catal. I, 29 l-302.

Schadlich, K., Hogmann, U. and Hofmann, H., 1983, Period- ical operation of chemical processes and evaluation of conversion improvements. Chem. Engng Sci. 38, 1375-1384.

Silveston, P. L., 1987, Periodic operation of chemical reac- tors: a review of the experimental literature, in Reactions and Reaction Engineering (Edited by R. A. Mashelkar and R. Kumar), pp. 217-246. Indian Academy of Sciences, Bangalore.

Thullie, J., Chiao, L. and Rinker, R. G., 1987a, Production rate improvement in plug flow reactors with concentration forcing. Ind. Engng Chem. Res. 26, 945-947.

Thullie, J., Chiao, L. and Rinker, R. G., 1987b, Generalized treatment of concentration forcing in fixed-bed plug-flow reactors. Chem. Engng Sci. 42. 1095-1101.

Unni, M. P., Hudgins, R. R. and Silveston, P. L., 1973, Influence of cycling on the rate of oxidation of SOa over a vanadia catalyst. Can. J. cheer. Ergng 51, 623-629.