A well screen system for use in a wellbore has an elongate base pipe and a screen encircling the base pipe. The screen is configured to filter against passage of particulate into a center bore of the base pipe. The base pipe has a fluid impermeable portion exterior to the screen. A cover sleeve resides over the fluid impermeable portion of the base pipe. A drain tube with a fluid permeable sidewall resides exterior to the base pipe and screen, affixed to the cover sleeve. The drain tube is adapted to communicate fluid from the wellbore around the fluid impermeable portion to the screen.