Cooling for bellows pump

A system for pumping treatment fluid into a well,

• comprising:
• a bellows pump configured to pump treatment fluid into the well, comprising:
• a power end comprising a piston;
• a fluid end having a chamber;
• and
• an expandable bellows, wherein the power end is configured to reciprocally expand and contract the bellows within the chamber based on movement of drive fluid by the piston;
• and
• a make-up system configured to maintain a controlled volume of the drive fluid between the piston and the bellows;
• wherein:
• the make-up system comprises a make-up fluid source fluidly coupled to the bellows and to at least one additional component of the system;
• the make-up system is configured to receive heat from the at least one additional component of the system via circulation of the drive fluid, and to discharge heat through the bellows via circulation of the drive fluid;
• further comprising a control system having one or more sensors configured to detect one or more parameters of the system;
• wherein the control system is configured to receive data from the one or more sensors, to evaluate the sensor data to determine a circulation protocol for circulating the drive fluid between the make-up system and the bellows, and responsive to determining a circulation protocol, to circulate the drive fluid between the make-up system and the bellows based on the circulation protocol;
• wherein the control system determines the circulation protocol based on temperature, prioritizing flow from whichever of the make-up fluid source or the at least one additional component has hotter drive fluid to the bellows.