Doraiswamy, L. K.

Kulkarni, B. D.

Ravikumar, V.

English

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INFLUENCE OF CATALYST DEACTIVATION ON THE NATURE OF
THE STEADY STATE SOLUTIONS FOR REACTIONS ON CATALYTIC
SURFACES†
V. Ravikumara; B. D. Kulkarnia; L. K. Doraiswamya
a National Chemical Laboratory, Pune, India
To cite this Article Ravikumar, V. , Kulkarni, B. D. and Doraiswamy, L. K.(1982) 'INFLUENCE OF CATALYST
DEACTIVATION ON THE NATURE OF THE STEADY STATE SOLUTIONS FOR REACTIONS ON CATALYTIC
SURFACES†', Chemical Engineering Communications, 17: 1, 305 — 312
To link to this Article: DOI: 10.1080/00986448208911634
URL: http://dx.doi.org/10.1080/00986448208911634
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Chem. Eng. Commun. Vol. 17. pp. 305-312 
0098-W5/82/17014305$06.50/0 
0 Gordon and Breach. Science Publishers. Inc.. 1982 
Printed in the U.S.A. 
INFLUENCE O F  CATALYST DEACTIVATION ON 
THE NATURE O F  THE STEADY STATE 
SOLUTIONS FOR REACTIONS ON 
CATALYTIC SURFACESt 
V. RAVl KUMAR, B.D. KULKARNI and L.K. DORAISWAMY 
Narional Chemical Laborarory 
Pune 411 008, India 
(Received January 6. 1982; in final form May 11. 1982) 
INTRODUCTION 
Multistep catalytic reactions are known to exhibit multiplicity behaviour even in the 
absence of heat and mass transfer effects. Clearly, this is attributable to kinetic rea- 
sons, and a number of recent studies (Belyaev er at., 1973; Sheintuch and Schmitz, 
1977; Eigenberger, 1978; Ivanov et a!., 1980; Pikios and Luss, 1977) have analyzed 
the multiplicity and stability behaviour of different reaction mechanisms. In all these 
studies the underlying assumption has been that the total number of active centers on 
the surface of the catalyst remains unchanged during the progress of the reaction. In 
the event, however, when the reaction is accompanied by a loss of a certain number 
of sites, due to irreversible adsorption of impurities present in the feed stream or ad- 
sorption of the reactant itself, then the assumption of constant number of sites on the 
surface of catalyst is difficult to justify. 
In the present investigation we consider the reaction mechanism in which reactant 
A, forms a surface complex AS, reactant Bm reacts with this complex to give another 
complex ABS, and the two complexes react with each other to give the final product. 
I t  may be represented as 
p AS + q ABS 2 ApqBq + (p  + q)S [I] 
We shall analyze the consequences of this mechanism in the presence of effects that 
lead to a loss in the number of active centers. In the event when the rate of catalyst 
deactivation (or rate of loss of active centers) is sufficiently small in comparison with 
the rates of the other processes, the problem essentially reduces to one of obtaining 
first the behaviour of the system ignoring catalyst deactivation (i.e. at constant number 
t NCL Communication Number 2703. 
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306 V.R. KUMAR, B.D. KULKARNl AND L.K. DORAISWAMY 
of active centers) and then investigating change in the total number of sites with the 
progress of reaction (time). I t  is this case of slow deactivation that is considered here. 
The reaction Scheme I with appropriate values of the parameters (n = 2, m = 1, 
p = I, q = 2) represents the case of oxidation of ammonia. (Il'chenko et a/., 1974; 
1975) and is interesting in that both the impact (step 2) and the interaction (step 3) 
mechanisms are simultaneously operative. Besides, the reaction involves a competitive- 
parallel reaction network with respect to the intermediates AS and ABS. 
THEORY 
The conservation equations with respect to the intermediate species can be written as: 
d(AS) 
-- 
dr - k l p ~ ( S ) ~  - k-](AS)" - k z p ~ ( A S ) ~  + k-z(ABS)'" - k>(AS)P(ABS)'I ( I )  
Also at any instant of time the following equation representing conservation of active 
centers should hold: 
L(r) = (S) + (AS) + (ABS) (3) 
Equations (1)-(2) can be expressed in dimensionless form in terms of surface coverages 
x and y of the two intermediate species: 
dx - 
-- 
dB a ~ ( l  - x - y)" - a2xn - a3xm + a4ym - XPYV (4) 
where the parameters al-a4 are defined as follows: 
I t  is interesting to note that the parameters al-a4 depend on the total number of 
centers present at any instant and therefore vary with the progress of reaction. How- 
ever, in view of the slower deactivation process considered, the rate of their change is 
sufficiently slow to justify the assumption of constancy for that instant. 
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CATALYST DEACTIVATION 307 
RESULTS AND DISCUSSION 
The steady state solutions to Eqs. (4) and (5) have been obtained for the specific case 
of n = 2, rn = 1, p = 1 and q = 2. These stoichiometric coefficients typically corre- 
spond to the case of ammonia oxidation. No experimental data to precisely estimate 
the parameters (at-ad) is available. However for real catalytic reactions the parameters 
normally lie within the range of (0-2). The parameters are thus arbitrarily chosen 
within this range for purpose of elucidation. For the values of the rate parameters 
used (a l -a)  only a unique steady state exists, and the stability of the steady state solu- 
tion obtained using the linear stability analysis indicates that it is a stable solution. As 
a result of loss of active centres this steady state solution would alter, and several 
steady state solutions are generated corresponding t o  different values of L (and hence 
of the parameters at-a,). For each of the solutions the linear stability analysis was 
carried out to check the stability. The steady state values of x and y are presented in 
Figure 1 for the corresponding value of L. The nature of the steady state solution is 
always stable for this case. 
For ease of comparison and to help generalize the influence of loss of active centers 
FIGURE I Dimensionless concentration of adsorbed intermediates and reaction rate per site (F) as a 
function of total number of active centers (Mechanism I).  
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308 V.R. KUMAR, B.D.  KULKARNI A N D  L.K. DORAISWAMY 
on the nature of the steady state solutions, solutions have also been obtained for 
another reaction mechanism: 
Two subcases are analyzed for this reaction mechanism. In one i t  is assumed that the 
reaction occurs on a homogeneous surface, while in the other surface heterogeneity is 
accounted for through the variation of activation energy with surface coverage of one 
of the components (say [BS]) in a manner similar to that treated by Pikios and Luss 
(1977). The rate constant for the third step in the latter case is thus taken as: 
where E! is the activation energy when y = 0 and (Y is the coefficient of surface hetero- 
geneity. The results for these two cases (also presented as x and y against the corre- 
sponding value of L)  are shown in Figures 2 and 3. The nature of the steady state so- 
20  SITE DENSITY, ( ~ , / c r n ' )  2 50 
O.e 
- 
0.6 -0410 '11  x C' - 
- 
- 
- 
- 
- - 
0 . 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  0 
20 6 0  100 1 4 0  180 220 250 
L ( t )  
FIGURE 2 Dimensionless concentration of absorbed intermediates and reaction rate per site (3 as a 
function o f  total number of aclivc centers (Mechanism I 1  with surface heterogeneity taken into account). 
~ ' ~ ' 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1  
- n o m n p r q r l .  
k; exp [ -E~ /RT]  -150 
- 
4 = 1 4  
1 
- - 
----- 
- a, 0 0 . 8 4  x L-' 
- 
- o2 ~ 0 . 0 7  X L-' - 
- - 
1.0 
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CATALYST DEACTIVATION 
2 0  SITE DENSITY, (LI/cm2) 2 0 0  
I .O 1 I I I I I I I 1.0 
- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
- 
2 0  
FIGURE 3 Dimensionless concentration o f  adsorbed intermediates and reaction rate per site (T) as a 
function o f  total number o f  active centers (Mechanism 11). 
lutions [using linear stability analysis] when unstable is also indicated on the respective 
curves in Figure 2. In Figure 3 the nature of steady state solutions are, however, al- 
ways stable. 
Of greater importance than the coverage of species A and B with respect to L is the 
variation of the reaction rate. For  mechanism I and I1 [step Il l]  this can be written as 
with the rate constant appropriately defined for each case. A plot of r vs L is domi- 
nated by the value of Lpq and shows a monotonical increase of r with L. In most 
cases the coverages x and y tend to  level off, thus masking any possible maximum in 
the rate. 
It would be instructive to redefine the rate as 
and plot it as a function of L site density ( ~ l / c m ' )  as shown in Figures 1 to  4. The 
plots shown in these figures can be explained as follows. 
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310 V.R. KUMAR, B.D. KULKARNl AND L.K. DORAISWAMY 
20 SITE DENSITY, ( L ~ / c ~ ~ )  
FIGURE 4 Dimensionless concentration of adsorbed intermediates and reaction rale per site (3 as a 
function of  total number o f  active centers (Mechanism I 1  with step 2 irreversible). 
On a surface of unit area with (L = L I )  number of sites (site density ~ l / c m ' )  this 
rate f(=r/Lpq) can be interpreted as the rate one would obtain if all sites except one 
are frozen. The variation of i: with LI in Figures 1-4 indicates that such a rate is a 
function of the environment (site density) and only for a specific site density, one can 
expect a maximum of 7. The rate i:[based on rhs of Eq. (9)] can also be interpreted as 
the extent of interaction among the adsorbed species leading to product formation on 
a site and hence a measure of its activity. The plot of Fvs Ll therefore indicates the 
variation of activity of the site in relation to the packing site density on the surface. 
An optimum site density is seen to exist for each of the cases shown in Figures 1-4 
and for a uniform distribution of sites on the surface, this corresponds to an optimum 
separation of sites. The conclusion of highest activity being realized for a specified 
separation of sites is known for certain specific cases [see Froment and Bischoff (l979)] 
and is generally proved here for the most common mechanisms. 
Besides the important result of the activity exhibiting a maximum, the decay of the 
catalyst or more specifically the loss of active centers also aduces certain other features 
to the system depending on the reaction mechanism. For example, as evidenced in 
Figure 2, the nature of the steady state solution changes from unique stable steady 
state to unique unstable state that eventually changes back to stable steady state on 
further loss of sites. In the unique unstable region Pikios and Luss (1977) have pre- 
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CATALYST DEACTIVATION 31 1 
dicted limit cycle behaviour. A qualitative change in the phase plane plot is therefore 
possible. 
Figure 3 shows another interesting feature where, for the parameters values studied, 
multiplicity of steady states is indicated within a certain range of L values. Only the 
two stable solutions are shown in the figure, and it is seen that on reducing L the di- 
mensionless rate follows the curve AB. At L = L, there is a sudden drop in the rate 
and on further loss of sites the rate moves along the curve CD. An interesting variation 
of this case is shown in Figure 4 where at L = L, the rate drops to zero. The specific 
case assumes the second step in the reaction mechanism I 1  to be irreversible. For this 
case i t  can be easily shown that one of the steady states always corresponds to .r = 0, 
y = 1 where the rate has a zero value. At L = L, the rate therefore jumps from one 
steady state solution to the other where no reaction can proceed. As a consequence, 
even when as many as LC centers are still left on the surface, the reaction is extinguished. 
Clearly this is possible only if the second step is irreversible. For even a small value of 
the reverse rate constant the picture shown in Figure 3 holds. 
CONCLUSIONS 
To sum up, the present paper analyzes the most common types of reaction mechanisms 
to illustrate the influence of loss of active centers on the nature of steady state solu- 
tions. Using suitable examples it is shown that 
( I )  the loss of active centers might induce a qualitative change in the phase plane 
plot, 
(2) there can exist a minimum value of the number of active centers on the surface 
below which no reaction can progress. and 
(3) there exists an optimum site density on the surface of the catalyst that would 
lead to largest interactions among the surface adsorbed species. 
NOTATION 
A, B = reactant and product species 
AS, BS, ABS = adsorbed species 
0 1 ,  0 2 ,  0 3 ,  a4 = parameters defined in Eq. 6 
I 3  = activation energy for the third step when y = 0 
k ~ ,  k - I ,  k2, k-2, k3 = rate constants of mechanistic steps 
k! = Arrhenius parameter for the third reaction step 
L = total number of active sites 
L I = site density on the surface 
n, m, p, q = stoichiometric coefficients 
PA, PB = partial pressure of reactant species 
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312 V.R. KUMAR, B.D.  KULKARNI A N D  L.K. DORAISWAMY 
Greek letters 
= reaction rate defined in Eq. (8) 
= modified reaction rate defined in Eq. (9) 
= active site 
= time parameter 
= dimensionless concentration of adsorbed species 
= dimensionless time 
= coefficient of surface heterogeneity 
LITERATURE CITED 
Belyaev. V.D.. Slinko, M.M.. Timoshenko, V.I.. and Slinko. M.G.. "Appearance of  Auto-fluctuations in 
the Oxidation of  Hydrogen on  Nickel". Kiner. Karol.. 14, 810 (1973). 
Eigenberger. G. .  "Kinetic Instabilities in Heterogenously Catalyzed Reactions". Chem. Eng. Sci.. 33, 1255 
(1973). 
Froment. G.F.. and BischofC. K.B.. Chemical Reocror-Analysis ondDesign. John Wiley and Sons. N.Y.. 
192 (1979). 
Il'chenko. N.I.. and Golodets. G.I.. "Catalytic Oxidation of Ammonia". J. Coral.. 39, 57 (1975). 
Il'chenko. N.I.. and Golodets. G.I.. "Selecrion of Catalysts for Selective Oxidation of Ammonia and Or- 
ganic Substances". Karol. Karol.. 11, 3 (1974). 
Ivanov. E.A.. Chumakov. G.A.. Slinko. M.G.. Bruns. D.D. ,and Luss. D.. "Isothermal Sustained Oscilla- 
tions due to the Influence of Adsorbed Species on  the Catalytic Reaction Rate", Chem. Eng. Sc i .  
35, 795 (1980). 
Pikios. G.A.. and Luss. D.. "Isothermal Oscillations on  Catalytic Surfaces", Chem. Eng. Sci.. 32, 191 
(1977). 
Sheintuch. M.. and Schmitz. R.A., "Oscillations in Catalytic Reactions". Carol. Rev. Sri. Eng.. 15, 107 
(1977). 
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Influence of catalyst deactivation on the nature of the steady state solutions for reactions on catalytic surfaces

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Influence of catalyst deactivation on the nature of the steady state solutions for reactions on catalytic surfaces

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