Within the project HylyPure, a process for the separation of hydrogen from a mixture with methane has been developed at the Institute of Chemical, Environmental, and Biological Engineering. This enables the usage of the natural gas grid for the transport of hydrogen. The HylyPure process includes gas permeation and pressure swing adsorption steps and a test facility for both steps was developed at TU Wien. For further optimizations of the process, a solution to efficiently simulate large parameters sets and complex flow sheets is required. An algorithm for the simulation of gas permeation was developed and published at the institute some years ago, but does not fulfill all the current needs. This thesis presents VECGP, an updated and enhanced algorithm based on the finite difference method. VECGP not only ensures stable calculations for a wide range of gas permeation cases, but also significantly improves performance and is able to solve multi component systems and cases with high recovery rates efficiently. A new object oriented and modular implementation allows easy expansion and re-usage of code while simultaneously improving user-friendliness. Besides evaluating the mass transfer through membrane modules, VECGP also provides pressure drop and energy balance calculation and allows inclusion of real gas properties based on the best currently available models. The core feature set is validated against the existing algorithm and has successfully been used to simulate complex multi-stage processes.