2.2.   Particle model

of 6:7

· 105

m2=kg.

research of this process. To solve the reaction–diffusion equation inside the catalyst pellet, a pore structure model and a diffusion model are needed. Often used pore structure models are the micro- and macro pore model of Wakao and Smith (1962), the random pore model of Johnson (1965), the grain model of Szekely and Evans (1971). More recently, a more detailed and realistic three-dimensional pore network model has been proposed by Rieckmann and Keil (1999). The diffusion fluxes are usually mod- elled with the dusty gas model, Maxwell–Stefan model, Wilke and Wilke-Bosanquet models (Solsvik and Jakobsen, 2013). One may refer to the works of Solsvik and Jakobsen (2012a) for a detailed summary of different diffusion models. For catalyst pellet con- taining bi-modal pore size distribution, the micro- and macro pore model of Wakao and Smith (1962) with the Wilke formular can  be a good option for practical reaction engineering calculations (Hegedus, 1980).

2. Mathematical modeling

2.1. Reaction kinetics

In this work, the micro- and macro pore model of Wakao and Smith (1964, 1962) was applied which was specifically    developed

Fig. 1.  Triangle reaction network for n-butane oxidation (Wellauer et al., 1986).

Table 1

Kinetic parameters for partial oxidation of n-butane taken from Guettel and Turek (2010).

The triangle (three-reaction) network as shown in Fig. 1 was used in this work which includes the main reaction of n-butane to maleic  anhydride,  total  oxidation  of  n-butane  to  carbon  oxides

(CO2    and  CO)  and  consecutive  MAN  oxidation  to  CO2    and   CO

Y.  Dong et al. / Chemical Engineering Science 142 (2016)   299–309 301

for catalyst pellets containing bi-modal pore structure. In this model, the pore structure of the catalyst pellets is described by four parameters: mean macro-pore diameter dM, mean micro-pore

Table 3

Properties of  the catalyst pellet  (Guettel and Turek,   2010).

Property Symbol Value Unit

diameter dm, macro-pore porosity εM  and micro-pore porosity  εm.           

The specific surface area (surface per catalyst weight) Sg and pellet density ρpellet are directly related to the pore structure and can be evaluated as follows (Hegedus,  1980):

ρpellet  ¼ ρsolidð1— εtotalÞ;     εtotal  ¼ εM þεm ð9Þ

Combining Eqs. (8) and (9), one   obtains:

In the model of Wakao and Smith (1964, 1962), both Knudsen diffusion and molecular diffusion are considered and the effective diffusivity of each species is expressed   as

ε2    1þ3εM Þ

where Deff ;i is the effective diffusivity of each species, λpellet is the effective thermal conductivity of the pellet, ζ is the  dimensionless

radial cylindrical coordinate of the pellet. In this study, the con- servation equations were only solved along the radial coordinate

Deff ¼ DM ε2

mð

1— εM

Dm