A sludge digester including a vessel and floating cover. The vessel includes a sidewall and an interior volume configured to receive and contain sludge. According to one embodiment, the cover comprises a frame structure that is constructed and arranged to form a skirt member formed at a periphery of the cover and extending downwardly into the vessel, and a continuous ballast ring attached to a lower portion of the skirt member and configured to form a trough member with an interior surface of the skirt member. The sludge digester may also include a guide system coupled to the sidewall and the skirt member and configured to allow vertical displacement of the cover with change in volume of at least one of a gas and a sludge contained in the vessel beneath the cover.