Applying an Efficient Approach for Modeling and Optimization of Membrane Gas Separation Processes Using Maxwell-Stefan Theory

The Maxwell-Stefan theory (M-S) provides a comprehensive framework for mass transfer that can be applied for describing multicomponent diffusion in microporous materials, e.g., zeolites and metal-organic frameworks (MOFs), see e.g., Krishna (1990). M-S theory has been applied successfully to model membrane separation processes, cf. Krishna (2014), relying on principles that can accurately estimate competitive adsorption equilibria, such as the Ideal Adsorbed Solution Theory (IAST) by Myers & Prausnitz (1965). In this work, we incorporate IAST to solve transient mass balances of membrane processes with an efficient strategy developed by Fechtner & Kienle (2018) for chromatographic separations modeling. To render accurate & efficient computations of the required M-S mass transfer fluxes, we apply analytical expressions for partial derivatives of adsorbed concentrations w.r.t. fluid concentrations developed by Rubiera Landa et al. (2013). We implement this efficient approach in three types of membrane process models of increasing detail to analyze propane/propylene separations on thin-layered membranes made of zeolitic imidazolate frameworks (ZIFs). In the first model, we consider only the thin-layered membrane. The second model considers a “batch” process, which includes mass balances around membrane, permeate & retentate compartments. The last more-detailed model considers a spatially-distributed asymmetric hollow-fiber membrane system, with flux estimations obtained from the less-detailed models. Robustness & efficiency of the proposed M-S/IAST calculation approach are tested with an optimization study using the more-detailed model, where we apply a genetic algorithm to identify process operation variables (i.e., decision variables) that yield optimal performance for this hydrocarbon separation example.