This is very simple.
An eductor is a very simple design, that in this case the "liquid impulsor" is a solution of Calcium Chloride (that is liquid at least under -50°C) to "disolve" CH4 Clathrates releasing the gas that will pump up a column of mud and gas. Gas is separated from mud. Mud is filtered, mud is return to sea and liquids are separated by solvents of our design in an enriched CaCl2 brine that is pumped to the eductor and water that is returned to the sea.

This design is simpler, cheaper and less contaminating than current method used for obtaining Shle gas.