CO2 removal from binary mixture gaseous streams using hollow fibers membrane module under physical absorption (water) has been investigated. The impact of the gas composition on the mass transfer efficiency was experimentally investigated with a CO2/CH4 mixture of varying composition (2 = 10 − 90%), covering a wide range of process: natural gas sweetening (5-10 % CO2), post-combustion carbon capture (10-15 % CO2), for biogas upgrading to biomethane (35-50 % CO2), ... As expected, the absorbed CO2 flux is increasing with the CO2 partial pressure. Yet the absorbed CO2 flow is multiplied by a factor up to 15 between a 10 and a 90 % inlet CO2 molar fraction, while applying a factor 9 to the inlet flow parameters. This underlines the existence of a non-trivial behavior. Highlights-Absorption of a binary gas mixture was modelled in cross-flow HFMMs-CO2 absorption ratio is divided by up to a factor 15 in the presence of CH4-Resistance-in-series has to be adapted to describe HFMM mass transfer-Transition zone equations are implemented without fitted parameter-The model predicts mass transfer over a wide range of gas composition and flow rate