Fig. 2.  Graphic illustration of the simulation  set-up.

Momentum balance:

In the first part of this section, the obtained reactor profiles and pellet profiles simulated are discussed. A reference case was defined  with  the   pellet   pore   structure   parameters   set   to: εM ¼ εm ¼ 0:25,  dM ¼ 100 nm,  dm ¼ 1 nm.  The  operational  para-

meters of the reactor are summarized in Table   5.

Fig. 3 shows the typical velocity field and temperature profile inside  the  fixed-bed  for  n-butane  oxidation.  The  flow  field pre-

Continuity equation:

∇ · .ρf u. ¼ 0 ð25Þ

Eq. (24) is the extended-Brinkman equation which is recom- mended for use of calculating velocity fields in fixed-bed reactors instead of using the conventional plug-flow assumption (Hunt and Tien, 1988). The reactor wall effects on the flow in fixed-bed reactors, especially with small reactor diameter to particle dia- meter ratio (dR =dp), is included in the Brinkman equation by introducing the radial function of the porosity εbedðrÞ. The radial porosity function  used in this  work is as follows (Tsotsas,   2010):

dicted by the extended Brinkmann equation together with the radial porosity profile and Ergun correlation shows maximum values in the near-wall region and zero value at the wall (Marín et al., 2010). This is caused by the high porosity of the random packing in the vicinity of the wall and no-slip boundary condition applied at the wall. Detailed flow calculations, instead of using conventional plug-flow assumption, are important in this  study due to the strong interconnection between the flow and the   heat

and mass transport. This coupling is described by the ‘λr  model’ of

Winterberg et al. (2000) applied in this work. For a strong exo- thermic reaction in wall-cooled fixed-bed reactors with low dR =dp ratio, the accurate prediction of the hot spot temperature is of vital

importance  (Anastasov,  2002).  This  is  the  reason  why  a     two-

Table 4

Boundary conditions  applied  to the  reactor model.

a ¼

0

— 1;    b ¼ 6:0 ð27Þ

z ¼ 0; 8 r : ci  ¼ ci;0 T ¼ T 0

.!u .     u0

The porosity of a  cylindrical packing  in a  infinite bed  ε0  is   calcu-

.   . ¼

lated according to Zou (1996) to be 0.32. The inertia resistance in the bed is described by the Ergun hydraulic permeability KE as (Marín et al.,  2012):

The  set  of  effective  heat  and  mass  transport  parameters  were

Operational parameters used in this work.

calculated  following  the  work  of  Winterberg  et  al.  (2000)   and

 uðr ¼ 0Þf  R    r  D 29

ð  —  Þ  AB ð   Þ

Parameter Symbol