A remedial method for repairing a damaged cement sheath, especially for use in wells in which fluids with a pH lower than 6 are injected, stored or extracted, comprises placing an acid swellable composition adjacent to the cement sheath. In the event of cement-matrix failure, or bonding failure between the cement/casing interface or the cement/borehole-wall interface, the composition may be injected into or adjacent to the cement sheath so that the material swells when contacted by acid gases, including carbon dioxide and hydrogen sulfide. The swelling seals voids in the cement matrix, or along the bonding interfaces, thereby restoring zonal isolation.