-
ð11Þ
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of the pellet, i.e. concentration and temperature gradient along the height of the pellet were neglected. This is because in the pseudo-
1 1 1
12Þ
heterogeneous model, the detailed particle geometry is not
DM ¼ DAB þDK;M ð
resolved in the calculation domain and thus only one effective coordinate can be taken for solving pellet equations. Also, the
concentration and temperature gradient between the outer sur-
Dm ¼ DAB þ DK ;m
where M and m stand for the macro-pore and micro-pore, respectively. The Knudsen diffusivity is calculated by
face of the pellet and the bulk gas were neglected. Solsvik and Jakobsen (2012b, 2012a) have found in their study that the viscous flow and pressure drop inside the pellet are very small and can be neglected. Hence, no convective term and momentum balance are
applied in the pellet equations. Eqs. (16) and (17) can be solved with the boundary conditions:
The molecular diffusivity is simplified to the binary diffusivity of each component in nitrogen since air is used as an oxidizer and is calculated by the Fuller equation as follows (Kleiber et al., 2010):
where δv is the so-called diffusion volume listed in Table 2.
The shape of the catalyst pellet studied in the present paper is cylindrical (d ¼ h ¼ 3 mm) and physical parameters of the catalyst were adapted from Guettel and Turek (2010). Due to the limited
published information on the available pore structure of this cat- alyst, parameters dM, dm, εM were estimated. The estimated phy- sical properties for the reference case are listed in Table 3.
The conservation equations applied for the catalyst pellet are: Mass balance:
A fixed-bed reactor was modeled applying a two-dimensional pseudo-heterogeneous model (Froment, 2011) including mass, heat and momentum balances in both axial and radial direction. The set-up of the simulation is illustrated in Fig. 2. The 3-D reactor was simplified to a 2-D rectangular geometry assuming rotational symmetry. All the simulations were carried out with Comsol Multiphysics 5.0s. The governing equations solved for the reactor at steady state are (Marín et al., 2012):
Mass balance:
∇ · ð — Di ∇ci þuci Þ ¼ — ð1— εbedÞavDeff;i
The dispersion coefficient matrix is expressed as:
Table 2
Diffusion volumes in the Fuller equation used in this work (Kleiber et al., 2010).
ρf Cpf u · ∇T — ∇ · ðλeff ∇T Þ ¼ — ð1— εbedÞavλpellet d ∂ζ
302 Y. Dong et al. / Chemical Engineering Science 142 (2016) 299–309
K2 ¼ 0:40 þ0:6 exp 230
ð35Þ
n ¼ 2 ð36Þ
The effective thermal conductivity of the fixed-bed without gas
flow λbed is calculated according to the model of Tsotsas (2010).
The conservation equations were solved with the boundary conditions listed in Table 4.
3. Results and discussion
3.1. Model prediction: reference case