A mathematical model for the dynamic performance of gas separation with high flux, asymmetric hollow fibre membranes was developed considering the permeate pressure build-up inside the fibre bore and cross flow pattern with respect to the membrane skin. The solution technique provides reliable examination of pressure and concentration profiles along the permeator length (both residue/permeate streams) with minimal effort. The proposed simulation model and scheme were validated with experimental data of gas separation from literature. The model and solution technique were applied to investigate dynamic performance of several membrane module configurations for methane recovery from biogas (landfill gas or digester gas), considering biogas as a mixture of CO2, N2 and CH4. Recycle ratio plays a crucial role, and optimum recycle ratio vital for the retentate recycle to permeate and permeate recycle to feed operation was found. From the concept of two recycle operations, complexities involved in the design and operation of continuous membrane column were simplified. Membrane permselectivity required for a targeted separation to produce pipeline quality natural gas by methane-selective or nitrogen-selective membranes was calculated.