A previously reported approach (E.I. Bozhenko and S.V. Bozhenko Gas Sep Purif (1993) 7 123) and software for simulation of multicomponent membrane gas separation processes are further developed for two-stage processes with permeate recycling. The described method was successfully applied to the design and optimization of a membrane device manufactured by the CLIMBI Company, Moscow, Russia, for storage of museum relics in controlled gas media at the Hermitage in St. Petersburg, Russia.