Problem Statement   

      This problem requires that a species DMc be added to DM and DP. The FEMLAB mixed steady-state expression for these conservation principles in the flow field is 

            DM:    

            DP:     

            DMc:     

where D denotes the diffusion coefficient (m2/s) for species mass transport, c is the concentration (mol/m3) and h (kg/m×s) is dynamic viscosity. Inside the catalyst pellet, the steady state mass conservation principle is 

            DMc:     

where Deff is the effective diffusion coefficient (m2/s), related to the porosity and tortuosity of the pellet, and k is the rate constant for the assumed second order reaction (m3/mol×s) creating the species mass. 

      The non-D Reynolds and Schmidt numbers are defined in FEMLAB terminology as

            ,

where w is the diameter of the pellet and vo is the inflow velocity. The corresponding non-D forms for the conservation principles are 

            DM:  

            DP: 

            DMc:     

            DMc:   

       In FEMLAB nomenclature, the BCs for the symmetric half-domain flowfield simulation are shown in Figure 1a, while the BCs for the mass transport are given in Figure 1b. For the flowfield, the word symmetry specifies  and no-slip specifies u = 0. For mass transport, symmetry corresponds to the Robin BC  while convection >> diffusion implies that the BC is , which must be evaluated.

 

 

 Figure 1. Pellet problem BCs, a) flowfield, b) mass transport. 

Setting-up the problem in FEMLAB 

This problem requires you to select two modes, the Incompressible Navier-Stokes and the convection and conduction mode from the Chemical Engineering module. It is required to set the axis and grid based on the given geometry as shown in the following table 

Axis

 

Grid

 

X min

-0.001

X spacing

0.001

X max

0.003

Extra X

0.0009

Y min

-0.001

Y spacing

0.001

Y max

0.007

Extra Y

0.0021 0.0039

 The base case data specification is:

Parameter

Value

ro (density)

0.66 kg/m3

mu (dynamic viscosity)

2.6e-5 kg/ms

D (diffusion coeffcient)

1e-5 m2/s

Deff (effective diffusion coeffcient)

1e-6 m2/s

k (rate constant)

100 m3/mol×s

vo (inlet velocity)

0.1 m/s

c1o ( inlet concentration)

1.3 mol/m3