Modelling of gas interstitial velocity radial distribution over cross-section of a tube packed with granular catalyst bed; effects of granule shape and of lateral gas mixing

The previously presented [Ziółkowska, I., Ziółkowski, D., 1993. Modelling of gas interstitial velocity radial distribution over a cross-section of a tube packed with granular catalyst bed. Chemical Engineering Science 48, 3283–3292] mathematical model of gas flow field within a tube packed with a bed of spherical elements has been modernised. The modernisation consists in more rigorous treating of the radial gas dispersion within the bed voids in the fluid dynamic equations and in involving the formulae correlating the flow resistance in beds packed with various non-spherical elements (Raschig rings, cylinders) with their characteristics. The model solution relates the gas interstitial and superficial radial distributions with an empirical parameter—the local effective viscosity or corresponding Reynolds number, dependent on the geometric, aerodynamic and physical properties of the system which are usually known. The effective viscosity is associated with the kinetic energy dissipation due to the interface friction, the shear stresses in molecular and turbulent motion and the radial dispersion in the gas stream. Its knowledge makes possible the evaluation of the radial profiles of the gas interstitial velocity, as well as the dispersion coefficient, or corresponding Péclet number and the drag coefficient for individual element within the bed. The effective viscosity has been determined experimentally for beds of Raschig rings and cylinders by the method presented previously [Ziółkowska, I., Ziółkowski, D., 2001. Experimental analysis of isothermal gas flow field in tubes packed with spheres. Chemical Engineering and Processing 40, 221–233] and the results have been correlated with the system characteristics. Then the correlations have been used, according to the model, in evaluation of the radial distributions of the gas interstitial velocity, the radial dispersion coefficient and the drag coefficient for individual element within the bed.