Significance of the radial porosity profile for the description of heat transport in wall-cooled packed beds

The influence of a radial porosity and velocity profile on the predicted temperature and concentration profiles in wall-cooled packed beds is studied, with and without an exothermic first-order chemical reaction, on the basis of literature correlations for the effective transport coefficients. Furthermore, values for the effective heat transport coefficients are obtained from ¿cold-flow¿ experiments by means of model fitting, with and without taking the radial velocity profile into account. The radial porosity and velocity profiles are approximately by step-function, which is referred to as the ¿two-region model¿. It is shown that the effective radial heat conductivity can be taken constant over the radius, despite the wall effect. Nevertheless, the influence of a radial superficial velocity profile can be significant through the convective term in the heat balance, especially for low tube-to-particle diameter ratios. The predicted NTU can increase the order of 20% for high values of the Reynolds number and up to 100% for low values. This is confirmed by the results obtained from the model fitting. In case of a first-order exothermic reaction, significantly higher values for the hot-spot temperatures are predicted, if a radial porosity and velocity profile is incorporated in the heat and mass balances. This is found to be mainly caused by the non-uniform distribution of active catalyst over the radius, due to the porosity profile.