Chmicni Engineering Science, Vol. 44, No. 6, pp. 1275-1280,
Printed in Great Britain.
ON
1989.
0
TEIE SEPARABILITY
OF CATALYST
KINETIC
BEHAVIOR
DAVID
T. LYNCH+
and GERHARD
Institut fiir Technische Chemie I der UniversitSt Erlangen-Nhmberg,
ACTIVITY
OOC9 25W’/g9
$3.00+0.00
1989 Pergamon Press pk
AND
EMIG
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 ratecontrolling (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 regenerations can range from several months, for hydrocarbon 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 scaleup 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 becomes necessary to somehow adjust the rate data to
compensate for any effects due to deactivation. This
‘To
adjustment of rate data normally involves the quantitative 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)
rather than in the general nonseparable
r= r(past
(1)
form
history, present conditions).
(2)
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;
If
the
Butt,
1984).
However, as shown in the following, the existence of
an energetically uniform (ideal) surface is not a sufficient 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):
whom correspondence should be addressed. Per-
manent address: Department of Chemical Engineering, IJniversity of Alberta, Edmonton, Alberta, Canada T6G 2G6.
1275
ptc. T)=
J-(c, T; poisoning
level i)
r(c,
level j)’
T;
poisoning
(3)
DAVID
1276
T. LYNCH
If the activity is only affected by the quantity of poison
(fractional
surface coverage), then from the combination 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
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
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.
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 exactly 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).
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
and GERHARD
where
(7)
and
__
a=~K~CBI(K~I+K~IK~CB~-K~~K,CAI)
(I+K,CAI+K,CB])*
(1) A mechanism
K2[B](1
-Qep-eA-8S)-8s-K
8 B =o
32 8‘
A
(5)
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)
is type 1 if in each steady-state
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).
surface
the steady-state surface species balances, for a constant fractional coverage of poison Q,, are given by
(4)
(8)
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 /3only 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 ratecontrolling
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.
From an examination of several additional mechanisms it is possible to empirically generalize the preceding result through the definition of three types of
mechanisms.
(Ml-3)
K,[A](1--8,--8,--8,)--8,--KjIeAeg=0
EMIG
(2)
On the separability
of catalyst
(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).
activity
and kinetic
behavior
1277
1.6
30
L
c
1.5
rT
1.2
e
0.9
z
Ei
s-
z
0.6
a.3
0.0
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).
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
and poisoned silica-alumina (open symbols =fresh
fresh
symbols = partially poisoned catalyst; circles
mol/m’ with varying
methanol
concentration;
squares = [CH,OH]
= 10.2 mol/m3 with varying
water concentration; 170°C 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).
catalyst;
Example
1
Bakshi and Gavalas
(1975) examined
the dehydration 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
(9)
~+K,&zH,oH]+-K,[~,O]’
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):
(M2- 1)
CH,OH(g)+A+B=CH,O-A+H-B
CH,OH(g)
=[HzO]
solid
= l.l(r1.24
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 @CH,O5 CH,OH
where QcnXOis determined from the solution
OcHIO= &, due to the assumptions)
(10)
of (note
Kt CCH,OHl
Gi,O
1+KsCHzOl
+(K,,
- l)K,[CH,OH]
- 1
I
(M2-2)
+ E%=CH,OH-B
CH,O-A+CH,OH-B+(CH,),O(g)+OH-A+B
(M2-3)
OH-A
+ H-B + H,O-A
H,O(g)
+ A=+H,O-A
+ B
(M2-4)
(M2-5)
(11)
1278
DAVID T. LYNCH and GERHARD
subsequently
with SCH,OH
CHsOH
where K 1, K,
=
found from
1 + K, [CH,OH]
and K,,
are as in mechanism
23
(12)
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 Zbonded benzene complex
(Kehoe and Butt, 1972),
according to the steps (mechanism 3)
H,(g)+
22
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. 1b 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 (M23) 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 purpose 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.
S+C,H,-S
(M3-1)
C,H,-S-+C,H,-S
(M3-2)
C,H,(g)+
EMIG
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 context of the classification system employed herein, this
21
20
19
0.16
b
-i=--.._
0.12
%---._
0.08
a.04
0.00
2.20
2.25
2.90
2.35
(Temperature)-’
2.40
x 1000,
2.45
2.60
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
Q,/R=42OOK,
K’$=lO-‘torr-‘,
K; =3.5x
10-h
torr-‘,
k; = 10” mol/s g-cat,
E,/R=4500
K, K;*
QJR = Q 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) proposed an alternate mechanism for the hydrogenation
of benizene on nickel given by (mechanism 4)
C,H,(g)
(M4- 1)
+ S+C,H,-S
(M4-2)
H2(g) + 2S=2H-S
H-S+C,H,,.-S-+&H,+,-Si-S
(n=O,
H-S+C,H,1-S+C6H,2(g)+2S.
1, 2, 3, 4)
(M4-3)
(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,
‘=(l
.,k
f&k,
+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
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?,
where Bs is determined
O%,
L &W’H,
-Q,jl
(15)
from the solution
of
+lIJK~P”~}+K,P,(l-~O,)=O
(16)
found from
A
B
:
K/R
ki
Ki
QiIR
r
K,=K;eQ’IRT,
K~=K;~Q~IRT,
k,=k”,emE’IRT
and K,, = KO,, eCQ1pEJ)‘RT. The values of the parameters were estimated using nonlinear regression,
and the predictions from eqs (15j(17)
are shown iq
Fig. 2 as solid’lines. 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-ofthe-art of kinetic model development
leaves a great
deal to be desired (Berty, 1988).
CONCLUSIONS
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 mechIt
anisms.
This will primarily
surface is approximately
be useful when the catalyst
energetically
uniform,
and
to fixed levels,
at each level.
NOTATION
a
Kij
where
activity
Acknowlrdgrmenf-The
sponsorship of this work by the
Alexander van Humboldt-Stiftung
(research fellowship for
D.T.L.) ix grAtefully acknowledged.
k_i
+~,~,+C~31(1-~,)
with 8, subsequently
when the catalyst can be deactivated
with constant
1279
ri
;
T
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
parameters [eqs (6)-(S)]
I> B
fractional surface coverage
of reactant A
0,
(mechanism 1)
fractional surface coverage of reactant B or
8,
benzene (mechanism 4)
fractional
surface
coverage
of hydrogen
0,
(mechanism 4)
fractional surface coverage
of poison (all
0,
mechanisms)
0 CHlO
fractional
surface coverage
of methoxide
radicals on acid sites (mechanism 2)
fractional surface coverage of methanol on
5CH,OH
basic sites (mechanism 2)
fractional surface coverage of hydrogen on
5H
basic sites (mechanism 2)
measure of separability
P
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