Effect of Porosity Profile

In the following membranes with a low permeability will be focused on, i.e. reactors where simplified boundary conditions at the membrane wall can be applied. 

The analogy of these results to that in fixed-bed simulations without sidestream is pronounced and can be explained with the predominance of the bed friction-force term in the extended Navier-Stokes equation (Eq. (5.6)). HydrodynamicaUy developed flow is achieved after a distance of just about one particle diameter in the axial direction. However, the developed profile in a PBMR is characterized by a radial velocity different from zero. One can prove analytically that for reactive flow problems with negligible change in the physical properties (density, viscosity) the superficial radial velocity decreases linearly towards the core (Kiirten, 2003). In Fig. 5.17b the superficial radial velocities are compared. Using the radial porosity profile, smaller absolute values of the local superficial velocity are calcu- 

---

Figure 5.17 (a) Axial and (b) radial velocity profile at z/L = 0.5 in the PBMR - effect of porosity profile. 

Figure 5.18 Effect of porosity profile on the local oxygen concentration, (a) 2D oxygen profiles (b) radially averaged axial O2 profile. ID simulation with Temperature 600°C,...

Figure 5.19 Effect of porosity profile on the ethylene selectivity - Temperature 600°C, = 250kgs/m ...

---