Water separation under varied pressure

A method for substantially separating water from a liquid mixture including water, the method comprising:

• directing a flow of a carrier gas through in at least one direct-contact packed-bed humidifier;
• directly contacting the carrier gas flow with the liquid mixture in the direct-contact packed-bed humidifier to humidify the carrier gas with water evaporated from the liquid mixture, producing a humidified gas flow;
• compressing the humidified gas flow;
• directing the compressed humidified gas flow through at least one dehumidifying heat exchanger;
• dehumidifying the compressed humidified gas flow in the dehumidifying heat exchanger to condense water from the compressed humidified gas flow, wherein the absolute pressure in the dehumidifying heat exchanger as the water is condensed is at least 10% greater than the absolute pressure in the direct-contact packed-bed humidifier as the water is evaporated, and wherein the dehumidifying heat exchanger is substantially thermally separated from the direct-contact packed-bed humidifier such that thermal energy is conducted from the dehumidifying heat exchanger to the direct-contact packed-bed humidifier primarily via mass flow of the carrier gas and the liquid mixture rather than via a heat transfer driven by a temperature difference;
• recirculating the dehumidified gas flow from the dehumidifying heat exchanger back through the direct-contact packed-bed humidifier, where the dehumidified gas is reused as the carrier gas, in a closed loop;
• expanding the dehumidified gas flow to decrease its pressure as the dehumidified gas flow is recirculated from the dehumidifying heat exchanger to the direct-contact packed-bed humidifier, also allowing for extraction of work from the expansion process;
• and
• collecting the water condensed in the dehumidifying heat exchanger.