Tke dusty gas model is used to establish the effects of temperature and pressure gradients on catalyst pellet effectiveness factors for reaction systems in which species molecular weights and transport coefficients are indistinguishable and Lui = 0. For this class of reactions, the total molar flux of species i is shown to be expressible simply as Ni = -cDVxi in terms of the molar concentration, the Bosanquet diffusivity, and the mole fraction gradient. The effects of temperature and pressure gradients are reflected only in variations in molar concentration and dausivity. Furthermore, the temperature-pressure relationship is shown to be given by the thermal transpiration equation for a pure gas.
Typical numerical results are reported for first order reactions in spherical pellets under diffusive conditions ranging from the Knudsen through the bulk diffusion regimes.
The variation in diff usion regime is shown to be controlled by an additional parameter n, the Knudsen to bulk diffusion ratio. Comparisons are made with the classical Weisz-Hicks nonisothermal pellet solutions based on Ni = -De,JIci. For highly exothermic reactions, effectiveness factors are 18% lower in the Knudsen regime and 30% higher in the bulk diffusion regime than are the Weisz-Hicks values. For highly endothermic reactions with a significant diffusion limitation, the effectiveness factors are 30% lower than the Weisz-Hicks values.
The classical Damköehler relationship for pellet temperature rise is shown to apply in the Knudsen regime, with the maximum dimensionless center temperature given by (1 t p), where p is the heat of reaction parameter. This temperature is accompanied by a maximum dimensionless center pressure of (1+ /3)"'.
In the bulk diffusion regime, the maximum center temperature is shown to be increased by the additional term j3'/4. This additional temperature rise accounts for the 42% increased bulk diffusion effectiveness for highly exothermic reactions.