This paper analyses the real behaviour of the fluid in the channels of a three-end membrane module. The commonly accepted mathematical model of membrane separation of gas mixtures in such modules assumes a plug flow of fluid through the feed channel and perfect mixing in the permeate channel. This article discusses the admissibility of accepting such an assumption regarding the fluid behaviour in the permeate channel. Throughout analysis of the values of the Péclet number criterion, it has been demonstrated that in the industrial processes of membrane gas separation, the necessary conditions for the perfect mixing in the permeate channel are not met. Then, CFD simulations were performed in order to establish the real fluid behaviour in this channel. It was proved that in the permeate channel the fluid movement corresponds to the plug flow, with the concentration differences at both ends of the module being insignificant. In view of the observations made, the admissibility of concentration stability assumptions in the mathematical models for the permeate channel was discussed.