Methods and systems for greenhouse gas capture and sequestration

A method comprising:

• forming a mixture stream that is water-based by dissolving carbon dioxide in water;
• injecting the mixture stream into a solid subterranean formation, wherein the solid subterranean formation is a coal seam, wherein carbon dioxide is diluted to a concentration that does not cause the solid subterranean formation to swell, and the solid subterranean formation naturally absorbs carbon dioxide within the mixture stream gas over nitrogen and methane;
• wherein the methane within the solid subterranean formation moves along a pressure gradient across multiple axis of the solid subterranean formation;
• sequestering downhole carbon dioxide within connected fractures of the solid subterranean formation without swelling the solid subterranean formation;
• and
• capping the solid subterranean formation with a water head, wherein a pressure of the water head on the gas sequestration medium is maintained above a pressure of the carbon dioxide within the solid subterranean formation.