Gradient in packed beds

The pressure gradient in packed bed flow is generated by the upward flow of gas relative to the solids in the standpipe. The Ergun equation [Equation (8.25)] provides the relationship between gas flow and pressure gradient in a packed bed. 

Both criteria for extraparticle gradients contain observables and can be calculated based on experimental observations of reaction rates. For heat and mass transfer coefficients in packed beds various correlations exist in terms of dimensionless numbers. In Table 1 the most appropriate ones for laboratory reactors are given [5, 7, 30, 31]. Values of k( and h for gases in laboratory systems range between O.l-lOms-1 and 100-1000JK-1s-1 m-2, respectively. In the case of monoliths, other correlations should be used because of the different geometry [32-34],... 

In packed bed reactors the solid catalyst is held stationary by plates at the top and bottom of the bed. In contrast, in fluidized bed reactors, the catalyst bed is relatively loosely packed, and there is no plate at the top. Rapid fluid flow from the bottom raises the bed and ensures good mixing, leading to insignificant temperature or concentration gradients. However, due to high fluid velocity some catalyst carryover is common. 

In addition to these pressure drop models, models to represent spreading of liquid in packed beds because of spatial variation in flow resistance are needed. In a randomly packed bed, the void fraction is not uniform. This implies that some flow channels formed within a packed bed offer less resistance to flow than other channels of equal cross-sectional area. Liquid will tend to move toward channels of lower resistance, leading to higher liquid hold-up in such channels. Thus, even if the initial liquid distribution is uniform, inherent random spatial variation of the bed leads to non-uniform liquid flow. Yin et al. (2000) assumed that the dispersion coefficient for liquid phase volume fraction is linearly proportional to the adverse gradient of... 

Due to the forced aeration, oxygen supply in packed bed bioreactors is usually not a problem, even if quite low aeration rates are used [138]. In contrast, temperature control can be difficult, especially in packed beds above 15 cm diameter and lacking internal heat transfer plates. In such bioreactors, the main heat transfer mechanisms are axial convection and evaporation, and radial temperature gradients are negUgible except close to the bioreactor wall. The dynamics of convective cooHng mean that axial temperature gradients are established and temperatures over 20 °C higher than the inlet air temperature... 

First check that the solids are moving in packed bed flow. We do this by comparing the actual pressure gradient with the pressure gradient for fluidization. 

Since the actual pressure gradient is well below that for fluidized flow, the standpipe is operating in packed bed flow. 

---