Interpreting gas sorption isotherms in glassy polymers using a Bayesian framework: A view on parameter uncertainty propagation into mixture sorption predictions

Abstract

Investigation of mixed-gas sorption is necessary for robust design and optimization of membrane-based processes. While sorption models for glassy polymers are well-established, they often deviate from observed mixture data. In doing so, however, parameters of these models are typically estimated via traditional least-squares optimization methods, and so parametric uncertainty is often ignored in mixture sorption predictions. As an alternative, we use Bayesian Inference (BI) to estimate probability distributions for sorption models' parameters and thus provide statistically meaningful mixture sorption forecasts that reflect parameter uncertainty rigorously. To this end, we exploit molecular sorption simulations, combining Grand Canonical Monte Carlo (GCMC) and Equilibrium Molecular Dynamics (EMD), to focus on two different glassy polymer systems (i.e., single- and mixed-gas sorption of CO2/CH4 in a fluorinated polyimide and CH4/H2 in a polymer of intrinsic microporosity) and three popular mixture sorption models (the Dual-Mode Sorption model, Non-Equilibrium Thermodynamics for Glassy Polymers model, and the Ideal Adsorbed Solution Theory) to demonstrate the benefits of this technique for uncertainty quantification and propagation in membrane applications. We show that observed sorption data at typical working pressures (e.g., 0−25atm) are often insufficient to accurately estimate model parameters, and consequently, these models often fail to represent observed mixture data adequately. Furthermore, we show that sorption data (e.g., high-pressure data), able to capture intrinsic isotherm nonlinearities of sorption models, are critical to considerably improve parameter inference from collective model-data fits and thus accurately predict mixture sorption.