A method and a system for treating seawater to facilitate secondary recovery of petroleum from a location below a body of saline water by flooding a permeable stratum with the treated water. The system utilizes a spirally-wound cross flow semipermeable membrane cartridge incorporating a three layer membrane arrangement preferably having nanofiltration characteristics which facilitates treatment of open ocean water by a single pass without any chemical or mechanical pretreatment to result in a liquid stream of desired character that can have greater ionic strength than the input seawater, e.g. at least about 18,000 ppm of chloride ion and less than 50 ppm of sulfate ion. This surprising objective is obtained even at high operating temperatures, e.g. as high as about 70° C., through the combination of the construction of the feed spacer and the nanofiltration character of the three layer membrane arrangement.