A device and method are provided for mitigating annular pressure buildup in a wellbore casing annulus of an oil or gas well. The device includes a tubular member including an outer side, a chamber secured around the outer side, the chamber having at least one flexible portion for varying the internal volume of the chamber, at least one reservoir capable of supplying a gas, and a pressure compensator connecting the reservoir and the chamber. The reservoir is able to feed the chamber volume with the gas via the pressure compensator.