An Improved Short-Cut Method for Effectiveness Factor Estimation
Francisco J. Valde
J. Obet Marroquı
n de la Rosa,
J. Alberto Ochoa-Tapia
Departamento de Ingenierı
a de Procesos e Hidra
n de Ciencias Ba
sicas e Ingenierı
noma Metropolitana-Iztapalapa, Apartado Postal 55-534, Me
xico D.F., 09340 Me
Instituto Mexicano del Petro
leo, Eje central La
rdenas 152, Me
xico D.F., 07730 Me
Two main short-cut methods for catalyst particle effectiveness factor (EF) estimation that use kinetics
linearization about surface and average concentration conditions have been recently considered in the literature.
The former produces simple computations with acceptable estimations for low Thiele modulus values, although
negative particle concentrations can be generated. The latter is intended to improve the particle concentration
profiles but at the expense of increased computations. The aim of this paper is to propose a hybrid method
that combines the advantages of the two approaches to obtain EF and concentration profile estimations that
are better than those of the individual ones. This is done by taking a kinetics linearization at an artificial
concentration condition resulting from a type of Crank
Nicholson scheme. From a simple error analysis, it
is shown that the resulting short-cut procedure displays enhanced convergence properties, which is corroborated
by means of numerical computations.
Some approaches have been proposed for short-cut computa-
tion of the catalyst particle effectiveness factor (EF). Wedel and
used perturbation series to derive a rational expression
for the EF as a function of the Thiele modulus. Haynes
proposed a modified Thiele modulus, obtained by either
differentiation or integration of kinetic expressions, yielding an
approximate EF based on a first-order kinetics expression.
Marroquı´n de la Rosa et al.
proposed a short-cut method by
departing from a kinetics first-order Taylor series expansion at
surface conditions (SCC). By incorporating the linear driving
Szukiewicz and Petrus
improved the surface
concentration-based EF estimation scheme and reported accept-
able results for small and moderate Thiele modulus values.
Although the use of the SCC approach
yields acceptable EF
estimation for relatively small Thiele modulus, significant errors
can be obtained for large Thiele modulus since the particle
concentration profile becomes very sharp. In fact, such errors
are caused by estimated concentration profiles with negative
values, which lead to overestimated EF values. To address this
problem, Ochoa-Tapia et al.