Abstract: This invention is directed to a method and system for extracting a solute from a fluid or a dense gas using a porous membrane. The invention includes providing a porous membrane having opposite sides in a module under pressure, with the membrane serving as a barrier interface between a fluid and a dense gas. The dense gas is introduced into the module on one side of the membrane and the fluid is introduced on the opposite side of the membrane. At least one of the fluid and dense gas contains a solute to be extracted, and the other one of the fluid and dense gas serves as an extracting medium. The dense gas has a density of at least about 0.5 g/cc and is essentially immiscible in the fluid so as to provide two phases. The process is conducted with the pressure on both sides of the membrane in the module being essentially the same, and the solute is extracted across the membrane as driven by the concentration gradient of the solute across the membrane.