Batch Pressure-Driven Membrane Separation with Closed-Flow Loop and Reservoir

A feed of at least one of (a) a source liquid including a solvent with a dissolved impurity and (b) a retentate of the source liquid is pumped in a substantially closed loop through a liquid-separation module. The liquid-separation module includes a membrane that passes at least partially purified solvent to a permeate side of the membrane while diverting the impurity in a retentate on the retentate side of the membrane. The purified solvent is extracted from the permeate side of the membrane; and the retentate from the liquid-separation module is pumped to or through a pressurized reservoir with a variable volume for the feed component and recirculated as a component of the feed. Over time, the volume for the feed is reduced and the pressure applied to the feed in the reservoir is increased to balance against an increasing difference in osmotic pressure across the membrane.