Integrated carbon capture and conversion for production of syngas

A gas capture and conversion system, comprising:

• a flue gas feed, the flue gas containing nitrogen and carbon dioxide;
• a methane gas feed;
• an adsorption column fluidly coupled to the flue gas feed and to the methane gas feed, the adsorption column comprising an adsorbent having an affinity for the carbon dioxide contained in the flue gas;
• a vent fluidly coupling the adsorption column to the atmosphere, the vent exhausting the nitrogen contained in the flue gas;
• a reactor fluidly coupled to the adsorption column via a reactor line;
• and
• wherein supplying methane gas to the adsorption column increases a partial pressure of the methane gas and results in a reduction of a partial pressure of the carbon dioxide contained in the flue gas causing the carbon dioxide to be desorbed from the adsorbent to create a mixture of the carbon dioxide gas and the methane gas that is supplied to the reactor via the reactor line.