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PVDF hollow fiber membranes were fabricated using Thermally Induced Phase Separation (TIPS) method. Gas-liquid interface is formed at the pore openings adjacent to the liquid. In the membrane contactor module, gas diffuses from the gas side across the membrane and reaches the gas liquid interface where gas is absorbed and then reacted in the presence of solvent such as aqueous sodium hydroxide or amine solutions. Nowadays, Monoethanol amine (MEA) and Diethanolamine (DEA) are the most commonly used solvents. In the present work potassium glycinate is used as an alternative liquid absorbent. A comprehensive two-dimensional mathematical model was developed for the transport of carbon dioxide-methane gas mixture through the in lab-made hollow fiber membrane contactor. Potassium glycinate is found to be a promising liquid absorbent. Model predictions were validated with experimental data. Results revealed that mass transfer rate generally increased with the absorbent concentration and that aqueous potassium glycinate solution performs better than MEA and DEA. The model equations were solved using COMSOL software package, model predictions were in good agreement with experimental data.