Design of membrane cascades for gas separation

Membrane cascade design with varying number of stages is systematically studied for a binary gas separation example. The constant separation factor (CSF) design strategy, with the same separation factor values for each stage in the cascade, was compared with the variable separation factor (VSF) strategy in which the separation factor values for each stage are optimized independently to minimize the energy consumption. Through enumeration and simulation of all feasible cascade configurations of interest, we identified the globally optimal configuration with the minimum energy usage. Interestingly, the same configuration is obtained as the globally optimal solution by the VSF as well as the CSF design methods. Moreover, irrespective of the design method used, the configuration has similar operating parameters at global optimality. Notably, the mixing losses due to the recycle stream are nearly absent under this condition, even though the possibility for losses was allowed in the simulation algorithm. Deviation in the number of stages in either direction from the one under global optimality leads to an increase in energy demand. When the number of stages in a cascade is reduced significantly below the global optimal value, the VSF design method with mixing losses is more likely to provide net lower energy consumption than the VSF design with the constraint of no mixing loss, whereas the CSF design method may not provide a feasible solution.