on the separability of catalyst activity and kinetic behavior

Chmicni Engineering Science, Vol. 44, No. 6, pp. 1275-1280, 1989. OOC9 25W/g9 $3.00+0.00 Printed in Great Britain. 0 1989 Pergamon Press pk

ON TEIE SEPARABILITY OF CATALYST ACTIVITY AND KINETIC BEHAVIOR

DAVID T. LYNCH+ and GERHARD EMIG Institut fiir Technische Chemie I der UniversitSt Erlangen-Nhmberg, EgerlandstraDe 3, 8520 Erlangen,

F.R.G.

(First received 21 December 1987; accepted for publication in revised $m-m 1 September 1988)

Abstract-The separability ofcatalyst activity and kinetic behavior is examined for several reaction systems described by elementary-step mechanisms. It is shown that separability is directly related to the form of the elementary steps in a mechanism. Three general types of mechanisms are described. Activity and kinetics are always separable for type 1 mechanisms. The converse is true for type 2 mechanisms provided that the reactant surface coverage is neither extremely high nor low. For type 3 mechanisms, the most commomy encountered type, separability of kinetics and activity results when one of the steps in the mechanism is rate- controlling (surface reaction, adsorption etc.), and, conversely, nonseparable behavior is the direct result of the lack of a single rate-controlling step. It is shown that previous reports of nonseparable behavior can be adequately described by using type 3 mechanisms. The use of nonseparable activity and kinetics for model discrimination based on structural differences between mechanisms is also discussed.

INTRODUCTION

Catalyst deactivation is an important phenomenon in the industrial usage of catalysts as well as in the fundamental examination of reaction kinetics. For a catalytic reaction to be industrially viable it is usually necessary to minimize any deactivation which occurs. This can typically be done through appropriate catalyst development. or through careful control of the feed and reactor operating conditions. If significant deactivation cannot be avoided, then catalyst regeneration procedures are necessary. Regeneration is often employed when deactivation occurs by coking or sintering, where the operating time between regener- ations can range from several months, for hydrocar- bon reforming on supported noble metal catalysts, to on the order of a minute (continuous regeneration) for the cracking of hydrocarbons using synthetic zeolites (Denny and Twigg, 1980). The various aspects of catalyst deactivation have recently been extensively reviewed (Hughes, 1984; Butt, 1984).

One of the steps in the systematic development of a catalyst is the determination of the reaction rate behavior as a function of expected operating conditions. This information is essential for proper scale- up in order to produce the eventual design of an industrial reactor. In addition, the rate behavior can be used to infer the detaiis of the sequence of elementary steps through which the overall reaction proceeds_ Information concerning the elementary-step mechanism can subsequently be used to produce improved catalysts. The occurrence of catalyst deactivation adds another level of complexity to the determination of intrinsic kinetic behavior in that it be- comes necessary to somehow adjust the rate data to compensate for any effects due to deactivation. This

To whom correspondence should be addressed. Per- manent address: Department of Chemical Engineering, IJni- versity of Alberta, Edmonton, Alberta, Canada T6G 2G6.

adjustment of rate data normally involves the quanti- tative specification of the catalyst activity. Following Szipe and Levenspiel (1971), it has been assumed in most recent studies [e.g. Agnew and Shankar (1986), Mukkavilli et al. (1986) and Pal et af. (L986)] that the activity, (I can be separated from the intrinsic rate behavior, ri, by expressing the overall rate, r, in the form

r = a(past history). r,(present conditions) (1)

rather than in the general nonseparable form

r= r(past history, present conditions). (2)

If the kinetics and activity are separable, then it is possible to study deactivation independently of reaction kinetics. However, it has been shown experimentally that the assumption of separability is not always valid (Bakshi and Gavalas, 1975; &al and Butt, 1981; Ltie and Tanger, 1987). Nonseparability can be accounted for by assuming the existence of a nonideal surface (Butt et al., 1978), or by describing the deactivation via a mechanism composed of elementary reaction steps coupled in some fashion to the mechanism of the main (desired) reaction (Corella and Asha, 1982). Nevertheless, the separability assumption has routinely been invoked, perhaps because of the generally held belief that it is valid for ideal (in the Langmuir sense) surfaces (Hughes, 1984; Butt, 1984).

However, as shown in the following, the existence of an energetically uniform (ideal) surface is not a suf- ficient condition for activity and kinetics to be separable. As a first step to illustrating this, it is necessary to define a quantity which can be used to quantitatively describe the interaction between the activity and kinetics for a system. Such a quantity, p, has been previously defined by Bakshi and Gavalas (1975):

ptc. T)= J-(c, T; poisoning level i)

r(c, T; poisoning level j) (3)

1275

1276 DAVID T. LYNCH and GERHARD EMIG

If the activity is only affected by the quantity of poison (fractional surface coverage), then from the combi- nation of eqs (1) and (3) it is seen that when a system is separable p will be a constant for any two levels of poisoning [the ri terms in eq. (1) cancel]. If p is not constant, but is instead a function of concentration

where

and temperature, then the activity and kinetics are nonseparable. For separable kinetics it is seen that p is just the ratio of the activities (usually denoted by a or s) at two different levels of poisoning. If poisoning level and

j in eq. (3) refers to the fresh catalyst, then p is in fact identical to the generalized form of the activity as defined by Szepe and Levenspiel (1971), where time and poisoning level are considered to be analogous.

(7)

a= ~K~CBI(K~I+K~IK~CB~-K~~K,CAI) (I+K,CAI+K,CB])*

__ (8)

This measure of separability is primarily intended for systems where the catalyst can be dehberately deactivated by the addition of measured quantities of an irreversibly adsorbed poison, with rate measurements performed subsequent to each addition of poison. The measurement of p would typically consist of determining the reaction rate for a fresh catalyst at several reactor concentration levels at a single temperature. These measurements would then be repeated using -a partially deactivated catalyst employing ex- actly the same concentration levels and temperature as for the fresh catalyst. Alternatively, a single concentration level could be chosen, and rate measurements made at several temperatures. For the rate measurements it is important that the reactor be operated iSothermally and in the absence of all concentration gradients. While a differential reactor could be used, a well-mixed gradientless reactor is normally a better choice. F&ther details concerning experimental equipment and strategies for the measurement of p have been given by Liiwe (1981).

with the restriction that @>4a due to the numerator and denominator of eq. (6) both changing sign when /? is reduced below 4a. For constant values of the rate constants (constant temperature) a and /3 only depend on the reactant concentrations.

It is.readily determined from eq. (6) that p asymptotically approaches either a value of (1 -8,)2 for small values of c( and /3, or a value of (1 - 0,) for large values of these two parameters. Physically, these two situations correspond to either the surface reaction being rate-controlling, or to adsorption of one (or both) of the reactants being the limiting step, respectively. Thus, when theie is a single rate-controlling step, upparenrly separable activity and kinetics can occur over a range of operating parameters with p approximately constant at a value of either (1 --tJ,,) or (1 - Hp). However, in the absence of a single rate- controlling step, p will vary within these two limits because it will be a function of the reactant concentrations and the reactor temperature. It is thus seen that the widely held belief that activity and kinetics are separable for energetically uniform (ideal) surfaces is, for this mechanism, only valid as a limiting situation.

DETERMINATION OF 0 FROM MECHANISMS

The determination of the form of p for a particular mechanism composed of elementary reaction steps can be readily determined from component balances for the various surface species. For example, for the bimolecular mechanism (mechanism 1)

A + %$A-S (Ml-I)

B + S=B-S (M l-2)

A-S + B-S -+C + 25 (Ml-3)

the steady-state surface species balances, for a constant fractional coverage of poison Q,, are given by

From an examination of several additional mechanisms it is possible to empirically generalize the pre- ceding result through the definition of three types of mechanisms.

(1)

K,[A](1--8,--8,--8,)--8,--KjIeAeg=0 (4)

K2[B](1 -Qep-eA-8S)-8s-K 88 =o (5) 32 A B

where K,=kJk_,, K,=k,/k_z, K,,=k3/k_, and K,, = k,/k_.. Solving for OA and B, from eqs (4) and (5) results in p being given by

@a ODP # 0) p = 8,0,(@, = 0)

(2)

A mechanism is type 1 if in each steady-state surface species balance equation, the sums of the powers for the surface species concentrations (including the empty site concentration) are identical for each term in a particular balance equation. This does not imply that the sums must be identical between equations. Activity and kinetics are separable for type 1 mechanisms independent of parameter values. Many Eley-Rideal mechanisms are of this type. A mechanism is type 2 if any surface species occupies more than one active site. Kinetics and activity are inherently nonseparable for a type 2 mechanism. Apparently separable behavior only occurs when the surface coverage of adsorbed reactants is very high or very low due to p asymptotically approaching a limiting value. A mechanism of this type has-been examined by Petersen and Pacheco (1984).

On the separability of catalyst activity and kinetic behavior 1277

(3) All other mechanisms are type 3. Activity and kinetics are effectively separable for type 3 mechanisms when,, for the entire range of operating conditions considered, there is a single rate-controlling step in the mechanism (surface reaction, adsorption etc.). Nonseparability is a direct consequence of the lack of such a step. The vast majority of mechanisms are type 3. Also included in this group are reaction systems where products can be produced by two or more foutes (e.g. parallel Eley-Rideal and Langmuir-Hinshelwood reaction steps).

When examining mechanisms, all surface species must be considered, even species which do not take part in any reactions, but only interact with the surface through adsorption and desorption processes. This classification indicates an approach which can be used to explain reports of nonseparable behavior which have appeared in the literature. This will be illustrated by examples using data from two detailed experimental studies of nonseparability (Bakshi and GaGalas, 1975; &al and Butt, 1981).

Example 1 Bakshi and Gavalas (1975) examined the de-

hydration of methanol on silica-alumina and made measurements of p for a variety of conditions by using a fresh and a poisoned catalyst (n-butylamine was used as the poison). Their data [from Bakshi (1975)] is shown in Fig. 1, where it is seen that, for a constant methanol concentration, p decreases as the water concentration is increased (squares), and that, for a constant water concentration, p is approximately independent of the methanol concentration (circles).

Bakshi and Gavalas (1975) did not propose a mechanism for methanol dehydration. Instead, they empirically described their data by using a rate function of the form

r= k,K, ,/CCH,OHl

~+K,&zH,oH]+-K,[~,O] (9)

The variation in p was accounted for by using two different sets of values for the rate constants in eq. (9). However, it is also possible to account for variations in p without changing the values of rateconstants for the fresh and the poisoned catalysts, but instead by utilizing a reaction mechanism which intrinsically gives rise tp nonseparability. For example, KnSzinger et al. (1973) examined several mechanisms for this reaction, &e of which is as follows (mechanism 2):

CH,OH(g)+A+B=CH,O-A+H-B (M2- 1)

CH,OH(g) + E%=CH,OH-B (M2-2)

CH,O-A+CH,OH-B+(CH,),O(g)+OH-A+B (M2-3)

OH-A + H-B + H,O-A + B (M2-4)

H,O(g) + A=+H,O-A (M2-5)

1.6 3-

0

L 1.5 c rT 1.2 z e Ei

0.9

- 0.6 s z

a.3

0.0

0.60

0.55 a

0.50

0.45

CHzO1, or ECHJOHl x 0.1, mol/m

Fig. 1. Reaction rates and p for methanol dehydration on fresh and poisoned silica-alumina (open symbols =fresh catalyst; solid symbols = partially poisoned catalyst; circles =[HzO] = l.l(r1.24 mol/m with varying methanol concentration; squares = [CH,OH] = 10.2 mol/m3 with varying water concentration; 170C reaction temperature; model predictions using K 1 = 6.5 m3/mol, K, = 0.24 m/mol, k, = 0.011 mol/h g-cat, K, , = 11, K, = 5 m3/mol, tip = 0.63).

where A and B represent acid and basic sites, respectively. To simplify the analysis, the following assumptions are made: steps (M2-2) and (M2-5) are at equilibrium; steps (M2-3) and (M2-4) are irreversible; step (M2-4) is very fast relative to steps (M2-3) and (M2-1); all A sites are energetically uniform (also true for B sites); the total number of sites of type A is equal to that of type B; and the poison (n-butylamine) only affects the type A sites. Using these assumptions in conjunction with surface species balance equations gives the rate of formation of ether:

r=k @ 3 5 CH,O CH,OH (10)

where QcnXO is determined from the solution of (note OcHIO = &, due to the assumptions)

Gi,O Kt CCH,OHl 1+KsCHzOl

+(K,, - l)K,[CH,OH] - 1 I

(11)


with SCH,OH subsequently found from 23

CHsOH = 1 + K, [CH,OH] (12)

where K 1, K, and K,, are as in mechanism 1, and K,=k,/k_,.

Values of the parameters were estimated by nonlinear regression using the rate data in Fig. la, and the model predictions are shown in Fig. la as solid (water concentration varied) and dashed lines (methanol varied). It is seen in Fig. 1 b that this simplified model, using a single set of parameter values, can adequately describe the experimentally observed values of p. This is possible because mechanism 2 is a type 3 mechanism, which for the chosen parameter values has a shift in the rate-controlling step from surface reaction (M2- 3) to adsorption (M2-1) as the water concentration (and thus the fractional coverage of water on the A sites) is varied.

While even better agreement with the rate data would be possibIy by relaxing one or more of the assumptions (with more parameters needed), this is not warranted given the accuracy of the data (see p values for methanol variation). In addition, the pur- pose of this example is not so much to describe methanol dehydration kinetics as to illustrate that nonseparability can be readily described by use of an elementary-step mechanism employing only a single set of values for the kinetic parameters.

Example 2 &al and Butt (1981) examined the hydrogenation

of benzene on a supported nickel catalyst_ Their data [from &al (1981)] is shown in Fig. 2a, where for the sake of consistency the form of the axes is the same as that used by &al and Butt (1981). In Fig. 2b it is seen that p increases as the tempemture increases (benzene pressure is constant; hydrogen pressure is approximately constant). &al and Butt found that their rate data was adequately described by a rat& function of the form

(13)

This was derived from a mechanism in which it was assumed that an Elcy-Ridcal type reaction occurs involving a gas-phase hydrogen molecule and a Z- bonded benzene complex (Kehoe and Butt, 1972), according to the steps (mechanism 3)

C,H,(g)+ S+C,H,-S (M3-1)

H,(g)+ C,H,-S-+C,H,-S (M3-2)

H,(g)+C,HB-S-+C,H,o-S (M3-3)

HZ(g)+Cl,H,.-Sj~,H,,(g)+S. (M3-4)

In order to describe the reaction rates at the three levels of activity, three different sets of parameter values were used (12 parameters in total). Three sets of parameter values were necessary because, in the con- text of the classification system employed herein, this

22

21

20

19 0.16

0.12

0.08

a.04

0.00

-i=--.._ b

%---._

2.20 2.25 2.90 2.35 2.40 2.45 2.60

(Temperature)- x 1000, K-

Fig. 2. Reaction rates and p for benzene hydrogenation on fresh and poisoned (two levels) supported nickel [triangles =fresh catalyst; squares =16% activity; circles =6%

activity; average reactant pressures: P, = 38 tom, P,, = 817, 770 and 721 torr for fresh, 16% and 6% catalysts, respectively (rates in mol/s g-cat); model. predictions using K; =3.5x 10-h torr-, Q,/R=42OOK, K$=lO-torr-, QJR = Q K k; = 10 mol/s g-cat, E,/R=4500 K, K;*

=6000, 8,(16%)=0.68, 0,(6%)=0,81].

mechanism is type 1, and variations in p due to operating conditions can never be described by this mechanism when onIy a single set of parameters is used. Thus, the observation of nonconstant values of p leads to the conclusion that mechanism 3 is not consistent with the data in Fig. 2.

In a recent study, ZrnEeviC and RuGi: (1988) pro- posed an alternate mechanism for the hydrogenation of benizene on nickel given by (mechanism 4)

C,H,(g) + S+C,H,-S (M4- 1)

H2(g) + 2S=2H-S (M4-2)

H-S+C,H,,.-S-+&H,+,-Si-S (n=O, 1, 2, 3, 4) (M4-3)

H-S+C,H,1-S+C6H,2(g)+2S. (M4-4)

By assuming that the surface reaction between adsorbed benzene and adsorbed hydrogen is rate-controlling [step (M4-3) with n =0] they arrived at the rate function

k,K, .,k f&k, =(l +K,P,+,/K,P,,)2

(14)

which gave the best description of their data. While discrimination between rival mechanisms is normally based on statistical considerations, qualitative support for mechanism 4 was provided by the authors by observing the variation of activity with respect to time during continuous poisoning of the catalyst (constant

On the separability of catalyst activity and kinetic behavior 1279

concentration of poison in the reactor feed stream). From the development for mechanism 1, it is clear that if the assumption of a single rate-controlling step is removed, then mechanism 4 should be capable of describing the variation of p with respect to temperature shown in Fig. 2b because this mechanism is type 3. This would provide additional support for mechanism 4 over mechanism 3. If it is assumed that the surface is energetically uniform, with step (M4-2) at equilibrium, and with only adsorbed hydrogen and benzene present on the surface in appreciable quantities [step (M4-3) with n=O is much slower than the n > 0 steps], then the rate of benzene hydrogenation is given by

r=k,tY,t?, (15) where Bs is determined from the solution of

O%, L &WH, -Q,jl +~,~,+C~31(1-~,)

+lIJK~P~}+K,P,(l-~O,)=O (16)

with 8, subsequently found from

where K,=K;eQIRT, K~=K;~Q~IRT, k,=k,emEIRT and K,, = KO,, eCQ1 pEJ)RT. The values of the parameters were estimated using nonlinear regression, and the predictions from eqs (15j(17) are shown iq Fig. 2 as solidlines. It is seen that excellent agreement is possible and that temperature-dependent values of p are predicted. Thus, it is possible to discriminate between mechanisms 3 and 4 based on the structural characteristics of the mechanisms (type 1. vs type 3) instead of based on the more commonly employed statistical considerations. The possibility of this type of structural model discrimination should be considered when planning experiments for examining reaction rate behavior, because the current state-of- the-art of kinetic model development leaves a great deal to be desired (Berty, 1988).

CONCLUSIONS

It has b&en shown that even for energetically uniform (ideal) surfaces the routine assumption of separability of kinetics and activity should be re-examined. In particular, complete separability is only guaranteed for a very restricted class of mechanisms (type 1). Nonseparable behavior for other classes of mechanisms is due to an adsorbing (nondissociative) species requiring more than a single catalyst site (type 2), or to the lack of a single rate-limiting process (type 3). Previous reports of nonseparability (Bakshi and Gavalas, 1975; &al and Butt, 1981) can be quantitatively described using type 3 mechanisms. While nonseparable behavior will normally complicate the analysis of kinetic data, this type of behavior can be used to advantage for discriminating among potential mechanisms. This will primarily be useful when the catalyst surface is approximately energetically uniform, and

when the catalyst can be deactivated to fixed levels, with constant activity at each level.

Acknowlrdgrmenf-The sponsorship of this work by the Alexander van Humboldt-Stiftung (research fellowship for D.T.L.) ix grAtefully acknowledged.

a A

B

: K/R ki

k_i Ki

Kij

QiIR r ri

; T

NOTATION

catalyst activity reactant species (mechanism l), or acid site (mechanism 2) reactant species (mechanism l), or basic site (mechanism 2) bulk-phase concentration product species activation energy adsorption, or surface reaction, rate constant desorption rate constant ratio of adsorption to desorption rate constant ratio of surface rate constant to desorption rate constant heat of adsorption overall rate of reaction intrinsic rate of reaction cata1ys.t activity catalyst site for adsorption bulk-phase temperature

Greek letters I> B parameters [eqs (6)-(S)] 0, fractional surface coverage of reactant A

(mechanism 1) 8, fractional surface coverage of reactant B or

benzene (mechanism 4)

0, fractional surface coverage of hydrogen (mechanism 4)

0, fractional surface coverage of poison (all mechanisms)

0 CHlO fractional surface coverage of methoxide radicals on acid sites (mechanism 2)

5 CH,OH fractional surface coverage of methanol on basic sites (mechanism 2)

5H fractional surface coverage of hydrogen on basic sites (mechanism 2)

P measure of separability

REFERENCES

Agnew, J. B. and Shankar, H. S., 1986, Catalyst deactivation in acetylene hydrochlorination. Ind. Engng Chem. Prod. Res. Dev. 25, 19-22.

Bakshi, K. R. and Gavalas, G. R., 1975, Effects of nonseparable kinetics in alcohol dehydration over poisoned silica-alumina. A.I.Ch.E. J. 21, 494-500.

Bakshi, K. R., 1975, Characterization of acid-base catalysts and its application to catalyst-poisoning. Ph.D. thesis, California Institute of Technology.

Berty, 1. M., 1988, The state of kinetic model development. Chem. Engng Prog. 84(2), 61-67.

Butt, J. B., Wachter, C. K. and Billimoria, R. M., 1978, On the separability of catalytic deactivation kinetics. Chem. Enyng Sci. 33, 1321 1329.


Butt, J. B., 1984, Catalyst deactivation and regeneration, in Catalysis: Science and Technology (Edited by J. R. Anderson and M. Boudart), Vol. 6, pp. l-63.. Springer, Heidelberg.

Corella, J. and As&a, J. M., 1982, Kinetic equations of mechanistic type with nonseparable variables for catalyst deactivation by coke. Models and data analysis methods. Ind. Engng Chem. Process Des. Dev. 21, 55-61.

Denny, P. J. and Twig& M. V., 1980, Factors determining the life of industrial heterogeneous catalysts. Stud. Surf: Sci. Catal. 6, 577-599.

Hughes, R., 19X4, Deactioation of Catalysts. Academic Press, London.

Kehoe, J. P. G. and Butt, J. B., 1972, Kinetics of benzene hydrogenation by supported nickel at low temperature. J. appl. Chem. Biotechnol. 22, 23-30.

KnGzinger, H., Kochloefl, K. and Meye, W., 1973, Kinetics of the bimolecular ether formation from alcohols over alumina. J. Catal. 28, 69-75.

LBwe, A., 1981, Strategies of kinetic experiments with de- caying catalysts. Ger. them. Engng 4, 106112.

Ltiwe, A. and Tanger, U.. 1987, Catalyst deactivation studies by means of a concentration-controlled recycle reactor. Stud. Surf: Sci. Cutui. 34, 439450.

Mukkavilli, S., Wittmann, C. V. and Taviarides, L. L., 1986, Carbon deactivation of Fischer-Tropsch ruthenium catalyst. Ind. Engng Chem. Process Des. Dev. 25, 487494.

onal, 1. and Butt, J. fl., 1981, Kinetic separability of catalyst poisoning. Stud. Surf Sci. Caral. 7(B), 149&1491.

&al, I., 1981, Kinetic separability and structure sensitivity of poisoning processes. Ph.D. thesis, Northwestern Univer- sity.

Pal, A. K., Rhowmick, M. and Srivastava, R. D., 1986, Deactivation kinetics of platinum-rhenium re-forming catalyst accompanying the dehydrogenation of methyl- cyclohexane. Ind. Engng Chem. Process Des. Dev. 25, 236-241.

Petersen, E. E. and Pacheco, M. A., 1984, Fundamental deactivation data from laboratory reactors. Am. &em. Sot. Symp. Ser. 237, 363 374.

SzBpe, S. and Levenspiel, O., 1971, Catalyst deactivation, in Proceedings of the 4th European Symposium on Chemical Reaction Engineering), pp. 265-276. Pergamon Press, Oxford.

Zrncevi&, S. and RubiC, D., 1988, Verification of the kinetic model for benzene hydrogenation by poisoning experi- ment. Chem. Enyng Sci. 43, 763-767.

on the separability of catalyst activity and kinetic behavior

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