A method and apparatus for the removal of free, emulsified, or dissolved water from liquids of low volatility, such as oil, is shown. The liquid of low volatility is removed by contacting the fluid stream of concern with one side of a semi-permeable membrane. The membrane divides a separation chamber into a feed side into which the stream of fluid is fed, and a permeate side from which the water is removed. The permeate side of the chamber is maintained at a low partial pressure of water through presence of vacuum, or by use of a sweep gas.