Negligible mass and thermal dispersion

The simplest manifestation of the nonisothermal nature of a packed bed is the presence of temperature gradients at the reactor scales (axially over the bed length L and radially across its 

Mears [68] derived criteria for negligible axial mass and heat transfer effects in nonisothermal reactors with uniform wall temperature (so that the rate deviates 5% from the one observed from a plug-flow model), extending the results from Young and Finlayson [139]. In terms of the bed length to particle diameter ratio, it writes as 

Under isothermal conditions, the criterion includes previous results for negligible axial mass dispersion [128, 140]. In terms of the observed conversion, the criterion can be written as [128, 140] 

Concerning the radial heat dispersion, the criterion for negligible interparticle thermal resistance (applicable at the hot spot) is given by [128]  

If this assumption is reasonable, it is common to use an overall heat transfer coefficient U, combining the individual resistances. Compared with axial interparficular effects, radial heat transfer at the hot spot is more significant. Moreover, axial and radial mass transfer effects are also less important in experimental reactors. A more generic statement of Equation 3.102 is based on the scaling from (3.87)  

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