Methods and systems are provided for flowing exhaust through a second cooler, arranged downstream of a first cooler and upstream of an intake in an exhaust gas recirculation passage, and extracting condensate for water injection from condensate in cooled exhaust gas exiting the second cooler. In one example, a method may include adjusting the amount of exhaust gas flowing through the second cooler based on an amount of water stored at a water storage tank of a water injection system and engine operating conditions. Further, the method may include selectively flowing exhaust gas from the second cooler to a location upstream or downstream of a compressor in response to engine operating conditions.