Dispersion of Mass and Heat in Fixed Bed Reactors

For packed beds, the axial Peclet number for mass PCm.ax = Wsdp/(EDax)j is defined based on the interstitial velocity (ratio of superficial velocity and porosity, Us/e) 

According to Eq. (4.10.123), the empty spaces of a packed bed with a gas flow can be regarded as ideal mixers, and each particle layer acts as one stirrer. Consequently, for a ratio of tube length to particle diameter of more than 40 (cascade with N = 40), a fixed bed can be regarded as an ideal plug flow reactor (Section 4.10.2.3). For liquids, similar consideration leads to a tube length of 160 particle diameters to reach almost plug flow behavior. 

which is by a factor of 5 higher than the value of Pem.ax- More details on dispersion of mass in packed beds may be found in Delgado (2006). 

Dispersion of heat can be described in a similar manner as dispersion of mass if we use an effective thermal conductivity in the axial and radial direction (kax, 2-rad)- The corresponding dimensionless Pedet numbers are Pch ad (= MsCpp oidp/Xrad) and Pch,ax (= WsCpPmoi p/ ax)- Note that the superficial fluid velocity, Us, and not the interstitial velocity, Ws/e, is used in the definition of Pejj, as the effective heat conduction (reflecting both the effective heat conduction in the gas and solid phase) is not limited to the empty space of the packed bed as in the case of dispersion of mass (see also differential equations of a fixed bed reactor in Section 4.10.7). As a rule of thumb, we can approximately use the same values for the Pedet number for dispersion of heat for high Rep numbers ( 100) as for the corresponding numbers for dispersion of mass, that is, Pe r d 10 and Pe 2. Details on the radial heat dispersion, which is important for wall-cooled reactors, are given in Section 4.10.7.3. 

As we will learn in Section 4.10.7.2, radial dispersion of heat is by far the most important dispersion effect in fixed bed reactors. Thus, Section 4.10.7.3 gives some more accurate equations to determine the effective radial heat conductivity XefF. 

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