The disclosure provides a formation fluid pumping method and pump, and a wellbore system that in one example includes wellbore surface equipment connected to a downhole tool including a formation fluid container having a fluid input port and a fluid output port, and a moveable piston inside the formation fluid container having two fluid chambers positioned to alternately pump a quantity of formation fluid in the formation fluid container from the fluid input port to the fluid output port. The wellbore system further includes a mechanical piston actuator having a rotary portion attached to the formation fluid container and a linear portion attached to the moveable piston, and a brushless direct current motor coupled to the rotary portion of the mechanical piston actuator and controlled to alternately rotate the rotary portion of the mechanical piston actuator in opposite directions to pump the quantity of formation fluid.