A carbon capture system includes a Carbonator for adsorbing carbon dioxide with a carbon dioxide lean sorbent generating a carbon dioxide rich sorbent, a first Calciner for thermally decomposing a carbon dioxide rich sorbent into a carbon dioxide lean sorbent and carbon dioxide, a supply of raw material to be calcined into the first Calciner containing a carbon dioxide rich sorbent, a connection between the first Calciner and the Carbonator, a second Calciner for thermally decomposing a carbon dioxide rich sorbent into a carbon dioxide lean sorbent and carbon dioxide, a connection between the Carbonator and the second Calciner, and a connection between the second Calciner and the Carbonator.