Display omitted •Non-ideal mathematic model for hollow facilitated transport membrane module is established.•Pressure drop, concentration polarization and Joule-Thomson effect have significant influence on separation process.•Hollow facilitated transport membrane module with short fiber length, moderate packing fraction and high fiber inner diameter is promising for practical application. Membrane separation technology has been regarded as a promising alternative for carbon capture process due to its low consumption and low footprint. Facilitated transported membranes exhibit attractive CO2/N2 separation performance due to the existence of CO2-philic reactive carriers. However, the highly pressure and temperature dependent CO2 permeance of it, as well as non-ideal effect, make the simulation of carbon capture process based on simplifying model challenging. Herein, we established a rigorous model for hollow fiber facilitated transport membrane considering both non-ideal effect and variable permeance. This rigorous model was applied for post-combustion carbon capture, and compared with simple model which only considering variable permeance. It was found that rigorous model has a 44%-55% lower carbon capture capacity due to the declined driving force and permeance. Pressure loss accounts for the deviation at low stage cut (10%), while Joule-Thomson effect and concentration polarization effect become greater at high stage cut (20%). Thanks to the mild condition of post combustion flue gas, the impact of real gas behavior can be neglected. Moreover, the attractive configuration of hollow fiber facilitated transport membrane was found to be with relative short fiber length, moderate packing fraction and large fiber inner diameter.