Chemical Engineering Journal 94 (2003) 19–28
Relationship between the kinetic parameters of different
catalyst deactivation models
A. Monzón
a,∗
, E. Romeo
a
, A. Borgna
b
a
Department of Chemical and Environmental Engineering, Faculty of Science, University of Zaragoza 50009, Zaragoza, Spain
b
INCAPE (FIQ-UNL-CONICET), Santiago del Estero 2654, 3000, Santa Fe, Argentina
Received 1 March 2002; accepted 12 December 2002
Abstract
This paper presents a mathematical relationship between the parameters of Levenspiel’s Deactivation Kinetic Model (LDKM) and those
of the Deactivation Models with Residual Activity (DMRA) and their evolution over time. This correlation provides an explanation for the
erroneous variation obtained in the kinetic parameters (deactivation order and deactivation function) over time when LDKM is used to fit
deactivation data having a certain level of residual activity, which frequently leads to systematic errors in estimating intrinsic parameters,
such as activation energies. The variations of the LDKM parameters cannot in fact be related to a physical phenomenon, but are only
a consequence of a mathematical artifact. The methodology developed in this work provides a valuable tool for the comparison and
discrimination between different models used in kinetic studies. The equations here presented are applied to analyze the deactivation by
fouling of Pt/Al
2
O
3
reforming catalysts during methyl cyclohexane dehydrogenation.
© 2003 Elsevier Science B.V. All rights reserved.
Keywords: Deactivation kinetic models; Residual activity; Variable deactivation order; Parameter estimation; Pt/Al
2
O
3
; Catalytic reforming; Fouling;
Methyl-cyclohexane dehydrogenation
1. Introduction
One of the main problems in the estimation and interpre-
tation of kinetic parameters lies in the choice of the most
suitable kinetic model. An inappropriate choice of kinetic
model can result in misleading conclusions about the mech-
anism involved in the reaction under consideration [1].
In this context, the Deactivation Kinetic Model proposed
by Szepe and Levenspiel, LDKM, [2], has been widely used
in the area of the kinetics of catalyst deactivation to calculate
the loss of catalytic activity, a, over reaction time.
-
da
dt
= ψ
d
(p
i
, T)a
d
(1)
The two kinetic parameters appearing in this model are
called “deactivation function”, ψ
d
, and “deactivation
order”, d, respectively. The deactivation order depends on
the mechanism involved in the deactivation process and, in
principle, d must be constant throughout the reaction. The
deactivation function takes into account the influence on the
∗
Corresponding author. Present address: Departmento de Ingenieria
Quimica y Tecnologias del Medio Ambiente, University of Zaragoza,
Zaragoza 50009, Spain. Tel.: +34-976-761157; fax: +34-976-762142.
E-mail address: amonzon@posta.unizar.es (A. Monz´ on).
deactivation rate of the operating conditions, i.e. reaction
temperature and concentration of reactants, products and
poisons. The explicit form of the deactivation function can
be of the pseudo-homogeneous type [2,3].
-
da
dt
= (k
d
p
m
A
)a
d
(2a)
or of the LHHW type, usually deduced from mechanistic
developments [4–9].
-
da
dt
=
k
d
p
m
A
(
1 +
∑
K
i
p
i
)
m
a
d
(2b)
This equation is usually used in its integrated form. Thus,
if the kinetic parameters d and ψ
d
can be considered as
constants, the integration of Eq. (1) leads to the following
expressions:
a = exp(-ψ
d
t); d = 1 (3a)
a =
1
(1 + (d - 1)ψ
d
t)
1/(d-1)
; d = 1 (3b)
The LDKM represented a significant advance in the develop-
ment of the kinetic modeling of catalyst deactivation, since
it was demonstrated that the majority of the empirical ki-
netic models previously proposed were particular cases of
1385-8947/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved.
doi:10.1016/S1385-8947(03)00002-0