Rotational continuous circulation system

A method for providing continuous circulation into a drill pipe string with a rotational continuous circulation system, the method including:

• drilling a subterranean well by rotating a downhole stand of the drill pipe string with a rig drive, where a downhole connector end of a circulation sub is connected to the downhole stand of the drill pipe string, and delivering a drilling mud through the drill pipe string by way of the rig drive, where the circulation sub has:
• an internal bore extending along a central axis;
• an uphole body that is a tubular member with an uphole internal bore, the uphole body having a first outer diameter along an uphole length of the uphole body and having a reduced outer diameter along a downhole length of the uphole body;
• a downhole body that is a tubular member with a downhole internal bore, an uphole portion of the downhole body circumscribing a downhole portion of the uphole body;
• at least one check valve located within a sidewall of the uphole body and operable to selectively allow fluid to flow into the uphole internal bore through the at least one check valve;
• and
• a sleeve assembly circumscribing the reduced outer diameter of the uphole body;
• setting the drill pipe string on slips;
• diverting the drilling mud to a side-entry port of the sleeve assembly, the side-entry port providing a fluid flow path from an exterior of the sleeve assembly to the at least one check valve;
• closing a central valve located within the uphole internal bore to prevent a flow of fluids past the central valve within the uphole internal bore;
• disengaging the drill pipe string from the rig drive;
• rotating the drill pipe string, the uphole body, and the downhole body about the central axis with a rotary table, free of relative rotation between the uphole body and the downhole body, where the uphole body and the downhole body rotate independently from the sleeve assembly;
• stopping rotation of the rotary table and securing an uphole connector end of the circulation sub to an uphole stand of the drill pipe string, where the uphole stand of the drill pipe string is secured to a subsequent circulation sub;
• opening the central valve to allow the flow of fluids past the central valve within the uphole internal bore and delivering the drilling mud through the drill pipe string by way of the rig drive;
• picking the drill pipe string off of the slips;
• and
• resuming the drilling of the subterranean well by rotating the uphole stand of the drill pipe string with the rig drive.