Packed beds relative contributions

Most adsorbers are designed to operate with relatively small pressure drop relatively large particles are used, and the velocity is typically low to allow equilibration of the fluid with the adsorbent. That typically means short, fat packed beds rather than long, thin ones. Generally, pipes, valves, and fittings contribute as much to the flow restriction as the pressure drop in the adsorbent bed. 

For relatively large particles and runs at high velocity, the contribution of fluid-to-particle mass transfer (5f) to the second moment is usually small for gaseous systems (Schneider and Smith, 1968). Small contribution of fluid-to-particle mass transfer can be corrected by using correlations for kt in packed beds. First, dr is calculated, and from Eq. (6-29), d(f + did are obtained. By plotting dd + dui of the same system for different particle sizes versus the square of the particle radius, a linear relation is expected, and from the slope, the intraparticle diffusivity can be obtained. A typical example of this type of plot is shown in Fig. 6.4. 

This equation passes through a minimum which, for a small molecule and a well packed column, is found to occur at a value for h of about 2. For a conventional 4.6 mm i.d. column filled with a 5 micron reversed-phase packing in methanol/water mixtures the flow-rate of this minimum is about 0.5 ml/min, and v of the order 3—5. The A term describes the contribution to dispersion due to tortuous flow through a packed bed, and is a measure of how well the column is packed. The B term describes the effects of axial diffusion (in the direction of flow) on dispersion at normal flow-rates the influence of this term is relatively unimportant. The C term is concerned with the effects of slow equilibration between the mobile and stationary regions due to, for instance, the diffusion of solute into and out of the particle and the kinetics of adsorption and desorption. For a well packed column and a small solute A < I, B 2 and C S 0.1. 

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