A pressure driven pumping system includes a piston disposed within a first bore of a housing to separate a process chamber from a working chamber. A rod member coupled to the separating member extends into a reduced pressure chamber. The piston has a first face exposed to the process chamber and a second face exposed to the working chamber. The second face has an effective area less than an effective area of the first face. The housing may be placed in seawater at a selected depth. The process chamber can be in fluid communication with a well to pass well fluid into the process chamber at well pressure to move the piston, to discharge seawater from the seawater chamber. The working fluid, typically seawater in a subsea application, is pumped into the working chamber to move the piston, which discharges well fluid from the process chamber.