Batch pressure-driven membrane separation with closed-flow loop and reservoir

A method for batch pressure-driven membrane separation, comprising:

• a) pumping a feed of at least one of (i) a source liquid including a solvent with a dissolved impurity and (ii) a retentate of the source liquid into a substantially closed loop through a liquid-separation module, wherein the liquid-separation module comprises a membrane that passes at least partially purified solvent as filtrate to a permeate side of the membrane while diverting at least a portion of the impurity in a retentate on a retentate side of the membrane;
• b) extracting the purified solvent from the permeate side of the membrane;
• c) pumping the retentate as feed component from the liquid-separation module to or through a pressurized reservoir with a variable volume for the feed component;
• d) recirculating the retentate as feed component via steps (a)-(e) and reducing the volume for the feed in the pressurized reservoir, in the conduits and in the liquid-separation module and increasing the pressure applied to the feed in the reservoir over time to balance against an increasing difference in osmotic pressure across the membrane as the feed increases in osmotic pressure;
• and
• e) after a plurality of iterations through the above steps, discharging a concentrated impurity stream from the liquid-separation module and supplying new source liquid to the substantially closed loop.