A method for recovering crude oil from a reservoir that is penetrated by at least one injection well and at least one production well wherein the reservoir comprises a first carbonate rock layer and a second carbonate rock layer each having crude oil and a resident water present within the pore space thereof, the method comprising: isolating the second rock layer from direct hydraulic communication with the injection well; and injecting an injection water having a total-dissolved-solids (TDS) content lower than the TDS content of the resident water from the injection well into the first rock layer thereby forming a sulfate enriched aqueous displacement fluid through dissolution of water-soluble sulfate minerals from the first rock layer into the injection water wherein the displacement fluid flows through the first rock layer and from the first rock layer into and through the second rock layer thereby displacing oil towards the production well.