A self-adaptive cement system includes cement, water and at least one additive that reacts or/and expands in contact with oil and gas. Several chemical products have been identified including rubber alkylstyrene, polynorbornene, resins such precrosslinked substituted vinyl acrylate copolymers and diatomaceous earth. These additives have the effect of making the cement self-healing in the event of physical failure or damage such as micro-annuli. The self healing property is produced by the contact with subterranean hydrocarbon fluids, the potential repair mechanism is thus activated if and when needed in case of start of loss of zonal isolation. In another embodiment, the expansion is deliberately induced by pumping a hydrocarbon fluid in the vicinity of the set cement.