Absorption determined by mass transfer in the liquid is described well with the Graetz-Lévèque equation adapted from heat transfer. The influence of a chemical reaction on the mass transfer was simulated with a numerical model and tested on the absorption of CO2 in a hydroxide solution. Absorption determined by mass transfer in the gas phase and the pores of the membrane was also analysed experimentally and numerically. It was found that the gas phase concentration profile is established at a very short distance from the entrance of the fibre. This results in a constant Sherwood number along the fibre. A module coated with a very thin silicone rubber layer showed absorption rates comparable to the uncoated membranes. If absorption liquids are used which wet the membranes, resulting in leaky membranes, such a coating can enlarge the application of microporous hollow fibre membrane module.