A positive displacement pump for pumping fluids from a downhole formation to the earth's surface is provided. The pump first comprises a plunger. The plunger is reciprocated axially within the wellbore by a linear actuator, such as a submersible electrical pump, in order to form an upstroke and a downstroke. A pump inlet is disposed near the bottom end of the plunger, while a pump outlet is disposed near the top end of the plunger. The pump is configured such that it is able to pump a first volume of fluid upward within the wellbore during the pump's upstroke, and a second volume of fluid upward within the wellbore during the pump's downstroke. Thus, the pump is "double-acting."