In current literature two main approaches are used for the simulation of membrane contactors. One route considers membrane modules only in 1D for process simulation applications, the other route focuses on 3D simulation of modules using Computational Fluid Dynamics to provide very detailed information about membrane mass transfer or geometrical influences on the module performance. A new CFD algorithm is introduced in the current work. It is capable of performing both 3D and 1D simulations using the same code -1D to be used in fast process simulation applications whereas the 3D method can be applied for fully resolved CFD applications. Using experimental results from pure gas permeation of a hollow fiber module, it was demonstrated that 1D and 3D simulations compare with less than 2% deviation on a global scale. Based on the 3D simulations, it was found that the arrangement of the fibers can lead to high velocity zones close to the module walls. It was demonstrated that the 1D CFD method performs well even for almost pure gases like CH4 at retentate side, by running simulations of a pilot scale biogas separation module in co- and counter-current configurations.