A method and system for treating a hydrocarbon-bearing reservoir with a DOWS system includes forming a first and a second DOWS system wells that fluidly communicate with both a first and second hydrocarbon-bearing formation. The first well has an upflowing DOWS unit and the second well has a downflowing DOWS unit. The DOWS units separate production fluid into a water-rich fluid and a hydrocarbon-rich fluid that passes to the surface. Both wells have an injection zone and a production zone. The DOWS system is operated such that water-rich fluid from the first DOWS well is introduced into the first hydrocarbon-bearing formation, water-rich fluid from the second DOWS well is introduced into the second hydrocarbon-bearing formation, production fluid from the second hydrocarbon-bearing formation is introduced into the first DOWS well, and production fluid from the first hydrocarbon-bearing formation is introduced into the second DOWS well.