A two-dimensional mathematical model for CO₂/CH₄ separation through high-permeable hollow fiber DD3R zeolite membranes

High-permeable hollow fiber DD3R (HF-DD3R) zeolite membrane exhibits excellent CO₂ removal performance in natural gas upgrading. To facilitate its application, we have established a modified two-dimensional (2-D) mathematical model with distributed parameters to describe the CO₂/CH₄ separation process, where the distributed pressure drop, as well as the external resistances induced by concentration polarization (ECP) and lumen resistance (ELR) were explicitly considered. Compared to the classical one-dimensional (1-D) model with lumped parameters, the predicted CO₂ permeance by our model showed better agreement with the experimental data under the same conditions. The distributions of trans-membrane resistances were examined in terms of relative pressure drop (RPD), where the external resistances resulted in a remarkable loss of pressure drop (arrived to 42 %) in the high-permeable membrane with a membrane thickness of 0.5 μm, primarily attributed to the stronger bulk flow towards to the membrane surface. Furthermore, the external resistances significantly inhibited the CO₂ removal efficiency at different retentate CH₄ purity (X_{CH4, retentate}) for the membrane. The modeling results indicated a reduction in processing capacity per unit area by approximately 66 %, accomplished by a six-fold increase in CH₄ loss rate due to these resistances, when subjected to a feed pressure of 3.0 MPa and flowrate of 200 mL min⁻¹. Finally, the decreased passage area achieved by adjusting the membrane packing density and the module diameter could also promote the convection mass transfer in the shell side, leading to the improved CO₂ removal efficiency. The established 2-D mathematical model serves as a valuable tool for elucidating the CO₂/CH₄ separation behaviors in the high-permeable HF-DD3R zeolite membrane, guiding the design of high-quality membranes.