Instrumented saver sub for stick-slip vibration mitigation

A method for mitigating stick-slip vibrations of a drill string using a saver sub, comprising:

• matching, by a spring of the saver sub that comprises a shape-memory material, an adjustable spring constant to an impedance of a top drive to a first drill string impedance of the drill string in a first drill string configuration;
• dampening, by a damper of the saver sub that comprises a magnetorheological (MR) fluid and an adjustable dampening constant, the stick-slip vibrations in the first drill string configuration;
• detecting, by a controller of the saver sub, an identified change of the drill string from the first drill string configuration to a second drill string configuration having a second drill string impedance;
• and
• reconfiguring, by the controller, the adjustable spring constant to substantially match the second drill string impedance and the adjustable dampening constant to absorb the stick-slip vibrations of the drill string in the second drill string configuration.

A drilling rig apparatus, comprising:

• a drill string comprising a plurality of drill pipe sections;
• a top drive configured to impart a rotation on the drill string during drilling operations;
• and
• a saver sub comprising:
• a spring comprising a shape-memory material, the shape-memory material comprising an adjustable spring constant configured in a first spring constant to match an impedance of the top drive to a first drill string impedance of the drill string with the plurality of drill pipe sections;
• a damper comprising a magnetorheological (MR) fluid, the MR fluid comprising an adjustable damping constant configured in a first damping constant to absorb stick-slip vibrations of the drill string with the plurality of drill pipe sections;
• and
• a controller configured to receive an input identifying a second spring constant and a second damping constant corresponding to an addition of a drill pipe to the plurality of drill pipe sections,
• wherein the controller is further configured to translate the second spring constant to a current for the shape-memory material to substantially match the impedance of the top drive to a second drill string impedance of the drill string with the addition of the drill pipe, and translate the second damping constant to an electromagnetic (EM) field value for the MR fluid to absorb the stick-slip vibrations of the drill string with the addition of the drill pipe.