Today membrane technology is a well-established basic operation for gas separation in various fields of application, such as air separation or the recovery of gaseous substances in the chemical industry. Besides, it also plays an important role in the natural gas industry and the processing of gases from biological processes (biogas, landfill gas, etc.). The performance of membranes for gas separation depends on a large number of influencing variables, for example on the process conditions under which the separation process is to be carried out. For instance, different applications of gas membranes lead to variable process pressures and temperatures. The aim of the master thesis was the investigation and description of the membrane under variable process conditions and the development of a mathematical model to describe it.