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A set of experiments for CO 2 separation from CO 2 -N 2 mixture by absorption into water by means of a gas-liquid membrane contacting process is modelled using the mass continuity equation by combining process conditions, membrane and fluids properties, and module geometric characteristics. The general case of non-constant concentration of the diffusing component in the shell side (Case B) is used, which entails an integro-differential boundary condition at the lumen-wall. The computational method is compared with existing literature data in terms of the logarithmic averaged overall and lumen Sherwood numbers revalidating the superiority of the counter-current to the co-current mode of operation, while offering a theoretical prediction of the limited behaviour of the latter as a function of the equilibrium coefficient. The elaborate model is then applied in order to assess the extent of membrane wetting due to liquid penetration into the pores in terms of the resistance-in-series model by comparing with the experimental results derived in a commercial cross-flow membrane module under the counter-current mode of operation. It is revealed that the assumption of shell-side constant concentration (Case A) underestimates the wetting leading to a false estimation of the extent of liquid penetration into membrane pores. For Case B, a wetting-pattern appears showing a correlation of an increasing shell-side liquid flow rate with a decreasing wetting parameter and, thus, relatively less contribution of the liquid-filled membrane resistance to the overall membrane resistance with increasing liquid loading.