Membrane oxygenators or artificial lungs have become a reliable and live saving clinical technique. To limit side effects on blood platelet parameters the high extrinsic surface introduced by the hollow fiber membrane packing has to be decreased. This adjustment must be accompanied with an improvement of gas exchange performance to guarantee sufficient blood gas transfer. Computational fluid dynamics (CFD) provides a spatial and temporal resolution of the membrane oxygenation process and enables systematic optimization of artificial lungs. In scope of this research a new CFD approach to examine the gas exchange performance of oxygenators was developed. Blood and sweep gas flow in the fiber packing as well as blood gas exchange through the membrane between blood and sweep fluid are fully resolved and simulated. The results were compared to in vitro experiments comprising determination of blood side pressure loss and CO2 exchange performance of a prototype membrane module. While flow simulations were conducted for the complete prototype module, gas exchange simulations were limited to a representative fiber packing segment. The presented simulation approach provides a basis for the design of future artificial lungs.