A method and system for increasing oil production from an oil well producing a mixture of oil, water, gas, and/or solids through a wellbore penetrating an oil-bearing formation containing an oil-bearing zone and a selected injection zone, by separating from the mixture of oil, water, gas, and/or solids in the oil well at least a portion of the gas to produce a first separated gas and a first portion of an oil-enriched mixture; directing the first portion of the oil-enriched mixture through a bypass passageway having an outlet in fluid communication with a surface so that the first portion of the oil-enriched mixture bypasses a turbine in the oil well; driving the turbine with the first separated gas; driving a compressor in the oil well with the turbine; separating from the first separated gas in the oil well at least a portion of the gas to produce a second separated gas and a second portion of an oil-enriched mixture; compressing with the compressor the second separated gas to a pressure greater than a pressure in the selected injection zone to produce a compressed gas; injecting the compressed gas into the selected injection zone; and recovering at least a major portion of the first portion of the oil-enriched mixture and the second portion of the oil-enriched mixture.