Blowout preventer with reduced fluid volume

A system for operating a blowout preventer (BOP), the system comprising:

• a front piston positioned at least partially in a front chamber, wherein the front chamber comprises:
• a front volume on a front side of the front piston;
• and
• a back volume on a back side of the front piston;
• a back piston connected to the front piston, wherein the back piston is positioned at least partially in a back chamber, wherein the back chamber comprises:
• a front volume on a front side of the back piston;
• and
• a back volume on a back side of the back piston;
• a ram connected to the front piston;
• a first valve configured to:
• permit fluid flow from a tank to the back volume of the front chamber to push the front piston toward a closing position during a free closing stroke of the BOP;
• permit fluid flow from the tank to the back volumes of the front and back chambers to push the front and back pistons toward the closing positions during a shearing stroke of the BOP, which causes the ram to shear a tubular member;
• and
• permit fluid flow from the tank to the front volume of the front chamber to push the front piston toward an open position during an opening stroke of the BOP;
• a second valve configured to:
• permit fluid flow between the front and back volumes of the back chamber during the free closing stroke;
• prevent fluid flow between the front and back volumes of the back chamber during the shearing stroke;
• and
• permit fluid flow between the front and back volumes of the back chamber during the opening stroke;
• and
• a third valve configured to:
• cause the second valve to permit fluid flow between the front and back volumes of the back chamber during the free closing stroke in response to a pressure in the back volumes of the first and second chambers being less than a predetermined threshold;
• cause the second valve to prevent fluid flow between the front and back volumes of the back chamber during the shearing stroke in response to a pressure in the back volumes of the first and second chambers being greater than the predetermined threshold;
• and
• cause the second valve to permit fluid flow between the front and back volumes of the back chamber during the opening stroke in response to the pressure in the back volumes of the first and second chambers being less than the predetermined threshold.

A method for operating a blowout preventer (BOP), the method comprising:

• performing a free closing stroke with front and back pistons, wherein the front piston is positioned at least partially within a front chamber, wherein the back piston is positioned at least partially within a back chamber, and wherein performing the free closing stroke comprises:
• pumping fluid through a first valve and into a back volume of the front chamber to push the front piston toward a closing position;
• and
• actuating a second valve to permit fluid flow between front and back volumes of the back chamber, wherein the second valve is actuated by a third valve in response to a pressure in the back volumes of the front and back chambers being less than a predetermined threshold.