Packed beds velocity distribution

Flow distribution in a packed bed received attention after Schwartz and Smith (1953) published their paper on the subject. Their main conclusion was that the velocity profile for gases flowing through a packed bed is not flat, but has a maximum value approximately one pellet diameter from the pipe wall. This maximum velocity can be 100 % higher than the velocity at the center. To even out the velocity profile to less than 20 % deviation, more than 30 particles must fit across the pipe diameter. 

The gas risers must have a sufficient flow area to avoid a high gas-phase pressure drop. In addition, these gas risers must be uniformly positioned to maintain proper gas distribution. The gas risers should be equipped w ith covers to deflect the liquid raining onto this collector plate and prevent it from entering the gas risers where the high gas velocity could cause entrainment. These gas riser covers must be kept a sufficient distance below the next packed bed to allow the gas phase to come to a uniform flow rate per square foot of column cross-sectional area before entering the next bed. 

Fig. 5.1.9 (a) MR measured propagators and es the velocity distribution narrows due to the (b) corresponding calculated RTDs for flow in a dispersion mechanisms of the porous media model packed bed reactor composed of 241- this effect is observed in the RTDs as a pm monodisperse beads in a 5-mm id circular narrowing of the time window during which column for observation times A ranging from spins will reside relative to the mean residence 20 to 300 ms. As the observation time increas- time as the conduit length is increased. 

MRM methods have been demonstrated to provide data on the advective transport in capillary, packed bed and VF bioreactors. The correspondence between the MR measured propagators and RTDs has been demonstrated. While the exact correspondence holds only in the case of invariant velocity distributions, scale dependent RTDs can be calculated from time dependent propagators. This provides a clear connection between MR propagators and the classic RTDs used broadly in chemical engineering to design and troubleshoot reactors, indicating the strong poten-... 

In chromatography the components of a mixture are separated as they pass through a column. The column contains a stationary phase which may be a packed bed of solid particles or a liquid with which the packing is impregnated. The mixture is carried through the column dissolved in a gas or liquid stream known as the mobile phase, eluent or carrier. Separation occurs because the differing distribution coefficients of the components of the mixture between the stationary and mobile phases result in differing velocities of travel. 

Experiments were also performed to compare the holdup and flow distribution in a bed, randomly packed with 3 mm spherical alumina particle, under the same flow conditions as was done for structured packing. However, it was evident that the successful operating conditions for structured packing were too severe for random packed bed, due to very high pressure drop. For very low liquid velocity ( 1 mm/s) and no gas flow, when the experiment was possible, the liquid distribution was poor as indicated by a low uniformity factor ( 40%). However, this information is insufficient to compare the distribution characteristics of structured and random packings. 

In this paper, we will consider only the dynamic aspects of this percolation problem, i.e., the stochastic distribution of velocities between the flow structures. To analyze a percolation process, it is useful to represent the scattering medium (i.e. the packed bed) by a lattice as depicted in Figure 2. The sites of the lattice correspond to the contact points between the particles whereas the bonds correspond to the pores connecting two neighbour contact points. The walls of these pores are delimited by the external surface of the particles. The percolation process is... 

Using the velocity and temperature gradients, we obtain the dimensionless entropy production for the empty bed (Figure 4.10). Comparison of Figures 4.9 and 4.10 indicates that outside the wall region, the distribution of the rate of entropy production is uniform in the packed bed, which is the thermodynamic optimality criterion. The profile of entropy production shows a typical S shape in the empty bed. 

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

The distribution of gas over all parallel channels in the monolith is not necessarily uniform [2,5,6]. It may be caused by a nonuniform inlet velocity over the cross-sectional area of the monolith, due to bows in the inlet tube or due to gradual or sudden changes of the tube diameter. Such effects become important, because the pressure loss over the monolith itself is small. Also, a nonuniformity of channel diameters could be a cause at the operative low Reynolds numbers, as was reported for packed beds [7]. A number of devices were proposed to ensure a uniform inlet velocity [5,8], which indeed increases the total pressure drop. 

Microscopic fluid distribution non-ideality is caused by fluid dynamic adhesion between the fluid and the adsorbent particle inside the microscopic channels of the packed bed. Adhesion results in a higher fluid velocity in the middle of the channel than at the channel walls (Fig. 2.9a). Solute molecules in the middle of the channel thus have a shorter retention time than those at the channel walls. 

Fig. 1 Numerical simulation of flow in a packed-bed reactor. Velocity quivers illustrate near-wall channeling, which affects residence time distributions, heat transfer, etc. (From Ref. l)...

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