Fundamental Insights into Intracrystalline Diffusional Influences on Mixture Separations in Fixed Bed Adsorbers

This article has the objective of elucidating the variety of factors that quantify influences of intracrystalline diffusion on mixture separations in fixed bed devices packed with microporous crystalline adsorbents such as metal-organic frameworks (MOFs) and zeolites. Such diffusional influences may act either synergistically or anti-synergistically to the mixture adsorption equilibrium, providing the ratio of the diffusivities Đ₁/Đ₂ ≫1. Experimental data on transient mixture uptake inside single crystals display overshoots in the loadings of the more mobile guest species; this overshoot can be quantitatively captured by use of the Maxwell–Stefan (M-S) diffusion formulation that takes proper account of thermodynamic coupling influences; if such thermodynamic influences are ignored, as is done in the Linear Driving Force (LDF) model, overshoots are not realizable. The use of the M-S formulation to simulate transient breakthroughs in fixed bed adsorbers provides a quantitative match with experiments; the match is significantly poorer if thermodynamic coupling effects are ignored. For a fixed bed of length L, packed with adsorbent particles of radius r_c and operating with an interstitial gas velocity, v, the diffusional influences are quantified by two separate parameters: (a) diffusional time constant, Đ₁/r_c², and gas–particle contact time L/v. The transient breakthroughs are uniquely dependent on the product (Đ₁/r_c²)­(L/v); this result is of practical importance for scaling up from small scale laboratory units to large scale industrial units that use different particle sizes, bed dimensions, and gas velocities.