Dynamic behavior of unsteady-state membrane gas separation: Modelling of a closed-mode operation for a membrane module

Membrane gas separations under unsteady conditions provide various opportunities for enhancement of separation performance, particularly in niche applications. An original model describing the dynamics of a closed-mode operation in a cross-flow membrane module is developed for optimization of a pulsed-retentate separation technique. The closed-mode operation is a key step of a pulsed retentate process providing an improvement of separation performance compared to a conventional steady-state separation without productivity losses. The closed-mode operation results in the evolution of a composition profile in a membrane module over time under a constant transmembrane pressure while the feed is being continuously admitted, and a permeate is being evacuated with no retentate withdrawal. During this step the highest possible concentration gradient is realized inside the module between the feed inlet and retentate outlet. The developed model reflects the dynamics of establishing the composition profile under closed-mode operation, linking concentrations, coordinates, and time, which is essential for the optimization of the unsteady membrane separation, as well as for the initial period after either the start of the process or the change of conditions. An axial mixing effect is considered taking into account the deviations from a plug flow present in a real process. The mathematical model is verified through a dedicated experimental study of two binary mixtures separation (CO2/N-2, and CO2/CH4) employing experimental techniques based on periodic sampling for gas chromatography analysis and in-situ monitoring by mass spectrometry. The case of a more permeable impurity removal from a less permeable main component is considered. An analytical solution is provided for the membrane module with zero retentate flow.