A method includes producing a first blended low salinity injection water for injection into at least one injection well that penetrates a first region of an oil-bearing reservoir and producing a second blended low salinity injection water for injection into at least one injection well that penetrates a second region of an oil-bearing reservoir. The reservoir rock of the first and second regions has first and second rock compositions, respectively, that present different risks of formation damage. The first and second blended low salinity injection waters comprise variable amounts of nanofiltration permeate and reverse osmosis permeate. The compositions of the first and second blended low salinity injection waters are maintained within first and second predetermined operating envelopes, respectively, that balance improving enhanced oil recovery from the first and second regions while reducing formation damage upon injecting the first and second blended low salinity injection waters into the oil-bearing reservoir.