Abstract: A positive-displacement pump includes multiple pumping elements, each pumping element having a pressure vessel with a first and a second chamber and a separating member disposed between the first and second chambers. The first chambers and the second chambers are hydraulically connected to receive and discharge fluid, wherein the separating members move within the pressure vessels in response to pressure differential between the first and second chambers. A valve assembly having suction and discharge valves communicates with the first chambers. The suction and discharge valves are operable to permit fluid to alternately flow into and out of the first chambers. A hydraulic drive alternately supplies hydraulic fluid to and withdraws hydraulic fluid from the second chambers such that the fluid discharged from the first chambers is free of pulsation.