The system includes a first reactor configured to discharge CO2 depleted process gas. The first reactor having a first and a second portion of particulate sorbent material having captured CO2. A second reactor is arranged to receive the first portion of particulate sorbent material and is configured to release CO2 from the particulate sorbent material by decarbonation, return the first portion of particulate sorbent material to the first reactor, and discharge a CO2 rich gas stream. A third reactor is arranged to receive the second portion of particulate sorbent material and is configured to supply water to the second portion of particulate sorbent material to hydrate at least a part of a remaining portion of calcium oxide of the second portion of particulate sorbent material to form calcium hydroxide, and return the second portion of particulate sorbent material to the first reactor.