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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