Packings wall effect

Dispersion in packed tubes with wall effects was part of the CFD study by Magnico (2003), for N — 5.96 and N — 7.8, so the author was able to focus on mass transfer mechanisms near the tube wall. After establishing a steady-state flow, a Lagrangian approach was used in which particles were followed along the trajectories, with molecular diffusion suppressed, to single out the connection between flow and radial mass transport. The results showed the ratio of longitudinal to transverse dispersion coefficients to be smaller than in the literature, which may have been connected to the wall effects. The flow structure near the wall was probed by the tracer technique, and it was observed that there was a boundary layer near the wall of width about Jp/4 (at Ret — 7) in which there was no radial velocity component, so that mass transfer across the layer... 

The major directions of changing porosity in DRP are schematically shown in Figure 9.22 [3,61], As a starting point, one can use the porosity of DRP of monospheres s0 = 0.36-0.42. Values of >s0 increase with particles anisotropy, roughness, and internal porosity, and also with the influence of wall effects at K> 0.1, and DIH > 0.05. Values of < (J are characteristic for polydis-perse particles when denser zones with ordered or unidirectional packings are formed, and also under forced densification and deformation of particles, correspondingly. 

Wall effect. In a packed bed, the particles will not pack as closely in the region near the wall as in the centre of the bed, so that the actual resistance to flow in a bed of small diameter is less than it would be in an infinite container for the same flowrate per unit area of bed cross-section. A correction factor fw for this effect has been determined experimentally by Coulson(15). This takes the form ... 

Wall effects are neglected and the bed is supposed to be uniformly packed. 

Fig. 1.6. Schematic illustration of loci of the wall effect where EOF decays in the case of charged tube wall and uncharged packing particles.

Wall Effect—When particulate matter is packed into a cylinder or column, the voids along the wall will be greater than in the body of the bed. Furnas" (1929) examined the nature of these voids for a circular container, and obtained the relation for the wall voids,... 

When the diameter of the particles is very small in comparison with the diameter of the container, the wall effect may be appreciable. The method of accounting for the difference in packing voids with regard to flow of fluids is discussed in Chapter 13. 

Huber and Hiltbrunner (185) showed that when the column to packing diameter ratio (DjJDp) is smaller than 10, the effect of lateral mixing is so large that only a strong maldistribution can decrease column efficiency (but note also that this range of DjJDp is uncommon in practice because of wall effects, Sec. 9.2.4). However, when DjJDp is greater than 30, the lateral mixing becomes too small to counteract the influence of maldistribution, and the effect of variations in L/V ratio dominates. 

In small columns, the wetted wall contributes to mass transfer. This problem can be overcome by keeping the ratio of column to packing diameter above 10 (Sec. 9.2.4). For cases where wall effects are significant, Wu and Chen (167) recommend applying the following safety factor. 

Use a column to packing diameter ratio of at least 10 alternatively, correct HETP for wall effects using Eq. (9.38). 

Example 4.6 Entropy production in a packed duct flow Fluid flow and the wall-to-fluid heat transfer in a packed duct are of interest in fixed bed chemical reactors, packed separation columns, heat exchangers, and some heat storage systems. In this analysis, we take into account the wall effect on the velocity profile in the calculation of entropy production in a packed duct with the top wall heated and the bottom wall cooled (Figure 4.7). We assume... 

Wall Effects. In the above discnssion, we have assnmed that the reaction is homogeneous (i.e., no catalytic reaction at the walls of the reaction bnlb). The fact that the data give first-order kinetics is not a proof that wall effects are absent. This point can be checked by packing a reaction bnlb with glass spheres or thin-walled tnbes and repeating the mea-snrements under conditions where the surface-to-volume ratio is increased by a factor of 10 to 100. This will not be done in this experiment, but the system chosen for study must be free from serious wall effects or it may not be possible to discnss the experimental results in terms of the theory of nnimolecular reactions. 

---