A method for purifying a liquid is described. A liquid feed is fed to a feed chamber. A carrier gas is fed through the liquid feed in the feed chamber to form a humidified carrier gas. A coolant is fed to a coolant chamber. The coolant chamber is separated from the feed chamber by a permeate gap chamber. The permeate gap chamber is separated from the feed chamber by a membrane that allows vapor to pass while blocking liquid flow across the membrane. The coolant chamber is separated from the permeate gap chamber by a thermally conductive plate. At least a portion of the vapor from the feed chamber that transported through the membrane is condensed by the coolant in the coolant chamber and the thermally conductive plate to form a first distillate. At least a portion of the humidified carrier gas is condensed to form a second distillate.