Synergistic and Antisynergistic Intracrystalline Diffusional Influences on Mixture Separations in Fixed-Bed Adsorbers

Separations of mixtures in fixed-bed adsorbers are influenced by factors such as (1) selectivity of adsorption, S_ads, (2) diffusional time constants, Đ_i/r_c², and (3) diffusion selectivity, Đ₁/Đ₂. In synergistic separations, intracrystalline diffusion of guest molecules serves to enhance the selectivities dictated by thermodynamics of mixture adsorption. In antisynergistic separations, intracrystalline diffusion serves to reverse the hierarchy of selectivities dictated by adsorption equilibrium. For both scenarios, the productivities of the desired product in fixed-bed operations are crucially dependent on diffusional time constants, Đ_i/r_c²; these need to be sufficiently low in order for diffusional influences to be effective. Also, the ratio Đ₁/Đ₂ should be large enough for manifestation of synergistic or antisynergistic influence. Both synergistic and antisynergistic separations have two common, distinguishing characteristics. Firstly, for transient uptake within crystals, the more mobile component attains supraequilibrium loadings during the initial stages of the transience. Such overshoots, signifying uphill diffusion, are engendered by the cross-coefficients Γ_ij(i ≠ j) of thermodynamic correction factors. Secondly, the component molar loadings, plotted in composition space, follow serpentine equilibration paths. If cross-coefficients are neglected, no overshoots in the loadings of the more mobile component are experienced, and the component loadings follow monotonous equilibration paths. The important takeaway message is that the modeling of mixture separations in fixed-bed adsorbers requires the use of the Maxwell–Stefan equations describing mixture diffusion employing chemical potential gradients as driving forces.