Abstract: A method and system for lifting drilling mud from subsea to a drilling vessel, which uses a pump having a body with a chamber, and a bladder in the chamber. The bladder attaches to the body and defines water and mud sides in the chamber. A mud inlet valve allows mud into the mud side of the chamber; which moves the bladder into the water side and urges water in the water side from the chamber and through a water exit valve. Pressurized water enters the chamber through a water inlet valve, which in turn pushes the bladder and mud from the chamber through a mud exit valve. The bladder separates the mud and water as it reciprocates in the chamber. The travel of the bladder in the chamber is controlled to prevent damage from contact with the chamber.