Lithium purification and conversion

A method of recovering lithium from a brine source, the method comprising:

• extracting lithium from the brine source using an ion withdrawal process to form a lithium extract;
• concentrating the lithium extract using a first membrane separation operation, having a first semi-permeable membrane to yield a preconcentrated stream and a permeate stream;
• and
• concentrating the preconcentrated stream using a second membrane separation operation, wherein the preconcentrated stream flows into a plurality of reactors in series, each containing a semi-permeable membrane separating the reactor into a first volume and a second volume, wherein the preconcentrated stream flows sequentially as a non-permeating stream into the first volume of each reactor, wherein the non-permeating stream exiting the plurality of reactors yields a lithium concentrate and wherein the second membrane operation yields a dilute brine stream that exits the second volume of at least one of the reactors, wherein the dilute brine stream is recycled into the first membrane separation operation, wherein the second membrane separation operation includes a permeating stream that flows sequentially in the second volume of the plurality of reactors, counter-current from the non-permeating stream, wherein the permeating stream yields the dilute brine stream, and wherein a portion of the non-permeating stream exiting the plurality of reactors is recycled into the permeating stream.