Disclosed are a method and a membrane module for the separation of oxygen from air during biomass gasification. The method comprises employing a membrane module as disclosed herein and using gas exiting the membrane module to heat incoming fresh air, more than 50% of heat energy contained in the gas exiting the membrane module being utilized to preheat the fresh air. The fresh air is further heated to a temperature of from 800° C. to 900° C. by directly feeding combustion gas or synthesis gas from the biomass gasification into a combustion space of the membrane module.