A process for separating vapors, for example for separating water from ethanol, uses a gas separation membrane unit. Permeate from the membrane unit is compressed and may be used for example as heating steam for distillation. The membrane unit may have two or more stages. Permeate from a stage may be condensed and used for example as fermentation make up water, compressed and fed to the permeate from an upstream stage or heating steam, or fed to another membrane stage for further dewatering. The gas separation membrane unit may be used to remove water from a fermentation broth that has been partially dewatered, for example by one or more of a distillation column or molecular sieve.