Anode/cathode feed high pressure electrolysis system

One embodiment of a method of operating an electrochemical cell system (32) comprises: flowing supply water to an anode electrode (75) of an electrolysis cell, applying a first current density to the electrolysis cell, electrolyzing the supply water at the anode (14) electrode (77) wherein hydrogen ions and a first portion water (22) migrate to a cathode electrode (75) of the electrolysis cell (32), collecting the first portion of water (22) in a chamber (108) in fluid communication with the cathode electrode (75), monitoring a first portion water (22) level in the chamber (108), when the first portion water (22) level attains a first selected level, decreasing the supply water flow to the anode electrode (77) a sufficient amount to draw the first portion water (22) from the chamber (108) to the anode electrode (77), and electrolyzing the first portion water (22).