Accurate Effective Diffusivities in Multicomponent Systems

Abstract

Mass transfer is an omnipresent phenomenon in the chemical and related industries for which effective diffusivities ((Formula presented.)) constitute a useful and simple mathematical tool, especially when dealing with multicomponent mixtures. Although several models have been published for (Formula presented.) they generally involve simplifying assumptions that severely restrict their use. The current work presents the derivation of accurate analytical equations for (Formula presented.), which take into account the nonideal behavior of multicomponent mixtures. Additionally, it is demonstrated that for an ideal mixture the new model reduces to the well-known equations of Bird et al., which are the exact analytical solution for ideal systems. The procedure for (Formula presented.) estimation is described in detail and exemplified with two chemical reactions: the liquid phase ethyl acetate synthesis and the high pressure gas phase methanol synthesis. Relative to the Bird et al. ideal equations the effective diffusivities calculated with the new model show differences up to 38% for ethyl acetate synthesis when using UNIFAC model to evaluate activity coefficients. For methanol synthesis, deviations from −23% to 22% are found using PC-SAFT equation of state (EoS) and from −49% to 24% when applying the Peng–Robinson EoS to estimate fugacity coefficients. Comparisons are also performed with the models by Wilke, Burghardt and Krupiczka, Kubota et al., and Kato et al. The worst results are achieved by the Wilke and Kubota et al. equations for the liquid phase and gas phase reactions, respectively. Furthermore, it is shown that substantial errors in effective diffusivity calculations may occur when deviations from the ideal behavior are unaccounted for. This can be avoided by adopting the new rigorous approach here presented.