Drilling system control for reducing stick-slip by calculating and reducing energy of upgoing rotational waves in a drillstring

A non-transitory computer readable medium storing a computer program comprising code which, when run on a computer, causes the computer to perform a method for controlling a drilling system comprising a drive system, drillstring and drill bit, wherein the drive system rotates the drillstring during a drilling process to drill a borehole through an earth formation in a manner that reduces stick-slip, the method comprising:

• receiving a desired rotation speed v0 of the drive system to rotate the drillstring;
• receiving property measurements of the drilling system and deriving therefrom a rotation speed vup of upgoing rotational waves of the drillstring associated with upgoing rotational energy in the drillstring;
• determining an actual rotation speed v of the drive system to rotate the drillstring by:
• representing energy in the drillstring as a mathematical expression comprising a sum of rotational energy produced by the drive system and downgoing rotational energy vdown caused by the upgoing rotational waves that are reflected at an upper end of the drillstring into downgoing rotational waves, wherein the rotational energy produced by the drive system is a function of v and v0, and wherein the downgoing rotational energy caused by the upgoing rotational waves is a function of v and vup;
• optimizing the mathematical expression, the optimized mathematical expression expressing v in terms of v0 and vdown, and
• controlling the drive system to rotate the drillstring at v,
• wherein the energy in the drillstring is proportional to the mathematical expression comprising
• (
• v
• -
• v
• 0
• )
• 2
• +
• λ
• ⁢
• v
• down
• 2
• where λ is a coefficient of relative weight ranging between zero and one.

A drilling system comprising:

• a drillstring;
• a drill bit coupled to the drillstring;
• a drive system comprising a top drive, the drive system being configured to rotate the drillstring to drill a borehole through an earth formation in a manner that reduces stick-slip;
• one or more sensors configured to measure properties of the drilling system;
• and
• a built-in control system for the top drive configured to:
• receive a desired rotation speed v0 of the drive system to rotate the drillstring;
• receive the property measurements of the drilling system and deriving therefrom a rotation speed vup of upgoing rotational waves of the drillstring associated with upgoing rotational energy in the drillstring, wherein vup is derived from surface measured properties comprising:
• rotational speed of the drillstring and a torque T in the drillstring;
• determine an actual rotation speed v of the drive system to rotate the drillstring by:
• representing energy in the drillstring as a mathematical expression comprising a sum of rotational energy produced by the drive system and downgoing rotational energy caused by the upgoing rotational waves that are reflected at an upper end of the drillstring into downgoing rotational waves, wherein the rotational energy produced by the drive system is a function of v and v0, and wherein the downgoing rotational energy caused by the upgoing rotational waves is a function of v and vup;
• and
• optimizing the mathematical expression, the optimized mathematical expression expressing v in terms of v0 and vup;
• and
• control the drive system to rotate the drillstring at v.