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 (y(CO2)(in) = 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. In the meantime, a 2D numerical model describing the absorption of CO2 in a binary gas mixture, based on the internal module geometry and on a local description of the hydrodynamics was proposed. Its development showed that in order to capture the key phenomena, a proper description of mass transfer in transition zone (Knudsen number around 0.34) is mandatory. Implementing this description allowed the model to accurately describe mass transfer over a wide range of gas composition and flow rate, without relying on any fitted parameter.