A mathematical model of a membrane with a thin, oriented, and selective MFI layer, which also includes contributions from defects, pore blockages, support layer, and external mass transfer, was formulated based on the Maxwell-Stefan equations. It was validated using reported (Kim et al., Angew Chemie Int Ed, 2018, 57:480–485; Jeon et al., Nature, 2017, 543:690–694) para/ortho-xylene separation data from five MFI membranes. The diffusivities of the xylenes were considered to be the same for all membranes, while the thickness and the density of defects and pore blockage were treated as unique properties of each membrane, and their contributions were estimated by fitting the model to the corresponding separation data. The effects of these properties and the role of permeate pressure on the separation performance were subsequently analyzed. The proposed modeling, parameter estimation, and analysis framework allow one to quantitatively interpret the variation of separation performance, to understand separation bottlenecks, and to provide guidance for designing membranes with desired performance.
Bibliographical noteFunding Information:
This material is based upon work supported by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office Award Number DE‐EE0007888. J Liu is also supported by the International Postdoctoral Exchange Fellowship Program by the Office of the China Postdoctoral Council (grant number 20180066). Nomenclature viscous flow parameter concentration, mol.m , diffusivity, m .s activation energy, J.mol index for the external mass transfer resistance multicomponent mass transfer coefficient, m.s adsorption constant, Pa molecular weight, g.mol number of component molar flux, mol.m .s pressure, Pa adsorption loading, mol.kg gas constant, J·K ·mol temperature, K , molar fraction coordinate through the membrane, m Δ enthalpy change of adsorption, J·mol Δ entropy change of adsorption, J·K ·mol Abbreviation SF separation factor pX para‐xylene oX ortho‐xylene IAST ideal adsorption solution theory Greek letter the fraction of pore blockage thickness, m density, kg/m adsorption loading fraction chemical potential spreading pressure, Pa Γ thermodynamic factor porosity tortuosity P permeance binary mass transfer coefficient, m.s Ξ a correction factor to the mass‐transfer coefficient Ψ a transformation of mass‐transfer coefficient Subscripts bulk phase defect external transport in the boundary layer component index gas‐membrane interface Knudsen diffusion MFI layer; the index for membrane index for measured data in membrane separation support saturation property total A surface area of adsorbent B 0 c −3 D Đ 2 −1 E a −1 I k −1 K −1 M −1 n N −2 −1 p q −1 R −1 −1 T x y z ads H −1 ads S −1 −1 α δ ρ 3 θ μ π ε τ κ −1 b d ET i, j, k I Kn m n s sat t
© 2021 American Institute of Chemical Engineers
- membrane modeling
- membrane property estimation
- separation data analysis
- xylene separation