A pump system for producing fluids from a reservoir using a wellbore having a vertical section with a casing defining an annulus, a transitional section and a horizontal section, and a production tubing having a vertical section and a horizontal section, wherein the system includes a completion with an isolation device in the annulus near the bottom of the vertical section, a gas/liquid separator for receiving produced fluids from the horizontal section, and a vertical lift pump; a continuous flow path from the terminus of the production tubing to the vertical section; a plurality of horizontal pumps in the horizontal section, each having an intake exposed to the reservoir and an outlet in the continuous flow path. The horizontal length of the production tubing is closed to the reservoir except through the horizontal pumps. A method of producing fluids includes isolating a vertical section of a wellbore from a horizontal section; isolating the production tubing from the reservoir; pumping fluid from the reservoir adjacent a toe segment into a production tubing toe segment and towards the heel segment; and pumping fluid from the reservoir adjacent a heel segment into the production tubing heel segment and towards the vertical section, and pumping fluid up the vertical section to the surface. Also disclosed is a diaphragm pump.