A system for distilling water is disclosed. The system comprises a heat source, and a plurality of open-cycle adsorption stages, each stage comprising a plurality of beds and an evaporator and a condenser between a first bed and a second bed, wherein each bed comprises at least two vapor valves, a plurality of hollow tubes, a plurality of channels adapted for transferring water vapor to and from at least one of the condenser or the evaporator, a thermally conductive water vapor adsorbent, and wherein each vapor valve connects a bed to either the condenser or the evaporator.