Mass transfer coefficient diffusion-limited regime

Closure. After completing this chapter, the reader should be able to define and describe molecular diffusion and how it varies with temperature and pressure, the molar flux, bulk flow, the mass transfer coefficient, the Sherwood and Schmidt numbers, and the correlations for the mass transfer coefficient. The reader should be able to choose the appropriate correlation and calculate the mass transfer coefficient, the molar flux, and the rate of reaction. The reader should be able to describe the regimes and conditions under which mass transfer-limited reactions occur and when reaction rate limited reactions occur and to make calculations of the rates of reaction and mass transfer for each case. One of die most imponant areas for the reader apply the knowledge of this (and other chapters) is in their ability to ask and answer "What if. , questions. Finally, the reader should be able to describe the shrinking core model and apply it to catalyst regeneration and pharmacokinetics. 

If the rate of chemical reaction is much faster than the rate of mass transfer via diffusion, then A 1 and tanh A -> 1. Hence, the mass transfer enhancement factor Sh -> A in the diffusion-limited regime via equation (24-24) or (24-26). The final form for the liquid-phase mass transfer coefficient of component j in the diffusion-limited regime is... 

Karabelas et al." reviewed many of the published correlations for fixed-bed coefficients and proposed different correlations to be used depending on the flow regime that is, at low Reynolds number the effects of molecular diffusion and natural convection must be considered. Kato et al. reviewed mass transfer coefficients in fixed and fluid beds and observed considerable deviations from established correlations in both the literature and their own data for Re < 10. In some cases it appeared that the limiting Sherwood number could be less than 2 for gas-particle transfer. They suggested that for small Re and Sc i the concentration boundary layers of the individual particles in a fixed bed would overlap considerably. They proposed two correlations for different flow regimes which also inclutted a particle diameter to bed height term. 

Zeolite membranes, due to their microporous nature and hence the low diffusivity coefficients, could work under mass transfer limited regime due to the high thickness of the zeolite layer. When the membrane acts as a reactant distributor the mass transfer should help to obtain the desired reactant profile in the reactor. In a catalytic zeohte membrane reactor, when the intrinsic reaction rate is higher than the diffusion rate, the mass transfer becomes a limiting factor for the conversion. 

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