Portions of a feed liquid are passed through respective condensers and liquid-liquid heat exchangers. The feed liquid is then heated and injected into a first feed-liquid containment chamber, where vapor from the feed is passed through a first gas-permeable membrane and directed into a first condenser, where the vapor is cooled by the feed liquid passing through the first condenser and condenses as it cools to produce a first liquid permeate. The first liquid permeate is passed through the first liquid-liquid heat exchanger where the first liquid permeate is cooled by the feed liquid passing therethrough. After the vapor is removed from the feed liquid in the first feed-liquid containment chamber, the remaining feed liquid from the first feed-liquid containment chamber is injected into a second feed-liquid containment chamber, where the process is repeated. The first liquid permeate from the first liquid liquid-liquid heat exchanger is combined with the second liquid permeate from the second condenser to form a combined liquid permeate; and the combined liquid permeate is passed through the second liquid-liquid heat exchanger where the combined liquid permeate is cooled by the feed liquid passing therethrough.