Modeling for Multi-component Gas Permeation with Orthogonal Collocation and Arc-Length Continuation

Many chemical engineering programs teach gas permeation because of its important applications in the oil and gas industry. In fact, it is considered a good replacement for classical separation techniques such as cryogenic technologies, PSA, physical and chemical absorption etc. Gas permeation module modeling can play an important role in both simulation and design of permeation units. In fact, the simulation allows the prediction of the separation performance of gas permeation modules as well as the selection of optimal operating parameters, stage cut θ and pressure ratio γ. On the other hand, the design provides useful data such as the module area. Here, we present the theoretical background of this unit operation, and the modeling of a single-stage gas permeation module used to separate multicomponent gas mixtures for the following flow patterns: (1) perfect mixing, (2) one-side mixing, (3) cross flow, (4) co-current flow, (4) counter-current flow. Our numerical simulation methodology is based on Chebyshev orthogonal collocation and arc-length continuation techniques. We apply the proposed methodology to two industrially important systems, which are described in reference (Shindo et al. in Sep Sci Technol 20:445–459, 1985. https://doi.org/10.1080/01496398508060692): (1) separation of NH₃, H₂, and N₂ gaseous mixture by means of a polyethylene membrane. Such a gas mixture arises in the Haber process. (2) Separation of H₂, CH₄, CO, N₂, and CO₂ mixture through a microporous glass membrane. This mixture is important in the partial oxidation of fuels with air and in the steam gasification of biomass. Whenever possible, our results are benchmarked against data obtained from the open literature or predicted using the software Aspen-Plus^®. Furthermore, we performed sensitivity analyses where we vary either the stage cut θ or the pressure ratio γ in order to investigate the effect of these parameters on both the permeate and retentate compositions as well as on the surface area of the permeation module. Finally, we provide useful tips and computer coding to readers who wish to investigate similar gas permeation problems using our new methodology.