Method and apparatus for reducing stick-slip

A method of drilling a borehole, the method comprising:

• rotating a drill string with a drilling mechanism so as to rotate a drill bit at a lower end of said drill string;
• and
• in response to detection of stick-slip oscillations of said drill string, wherein said stick- slip oscillations comprise torsional waves propagating along said drill string, damping said stick- slip oscillations, for every length of said drill string, using a PI controller to control said drilling mechanism, which PI controller has been tuned so that said drilling mechanism absorbs most torsional energy from said drill string at a frequency that is approximately at a frequency of said stick-slip oscillations;
• and
• calculating an I-term of said PI controller using a value of estimated period of said stick slip oscillations and on a value of effective inertia of said drilling mechanism, wherein the calculating the I-term does not use a value of the length of said drill string and a value of a speed of the torsional waves, whereby said drilling mechanism has a frequency dependent reflection coefficient of said torsional waves, which reflection coefficient is substantially at a minimum at or near said frequency of stick-slip oscillations.

A drilling mechanism for use in drilling a borehole, the drilling mechanism comprising:

• an electronic controller having:
• a PI controller and
• memory storing computer executable instructions that when executed cause said electronic controller to:
• damp stick-slip oscillations, for every length of a drill string, using said drilling mechanism at a top of said drill string, wherein said stick- slip oscillations comprise torsional waves propagating along said drill string;
• control speed of rotation of said drilling mechanism using said PI controller and to:
• tune said PI controller so that said drilling mechanism absorbs most torsional energy from said drill string at a frequency that is approximately at a frequency of said stick-slip oscillations;
• and
• calculate an I-term of said PI controller using a value of an estimated period of said stick slip oscillations and a value of an effective inertia of said drilling mechanism, but not using a value of the length of said drill string and a value of a speed of the torsional waves in the calculation of the I-term, whereby said drilling mechanism has a frequency dependent reflection coefficient of said torsional waves, which reflection coefficient is substantially at a minimum at or near said frequency of stick-slip oscillations.

An electronic controller for use with a drilling mechanism for drilling a borehole, the electronic controller comprising:

• a PI controller;
• and
• memory storing computer executable instructions that when executed cause said electronic controller to:
• damp stick-slip oscillations, for every length of a drill string, using said drilling mechanism at a top of said drill string, wherein said stick-slip oscillations comprise torsional waves propagating along said drill string;
• control speed of rotation of said drilling mechanism using said PI controller;
• and to:
• tune said PI controller so that said drilling mechanism absorbs most torsional energy from said drill string at a frequency that is approximately a frequency of said stick-slip oscillations;
• and
• calculate an I-term of said PI controller using a value of an estimated period of said stick slip oscillations and a value of an effective inertia of said drilling mechanism, but not using a value of the length of said drill string and a value of a speed of the torsional waves in the calculation of the I- term, whereby said drilling mechanism has a frequency dependent reflection coefficient of said torsional waves, which reflection coefficient is substantially at a minimum at or near said frequency of stick-slip oscillations.

A method of upgrading a drilling mechanism, the method comprising:

• uploading computer executable instructions to an electronic controller to be used on a drilling rig, which electronic controller is for controlling operation of said drilling mechanism;
• wherein said computer executable instructions comprise instructions for:
• damping stick-slip oscillations, for every length of a drill string, using said drilling mechanism at a top of said drill string;
• controlling speed of rotation of said drilling mechanism using a PI controller;
• and
• tuning said PI controller so that said drilling mechanism absorbs most torsional energy from said drill string at a frequency that is approximately a frequency of said stick-slip oscillations;
• wherein said stick-slip oscillations comprise torsional waves propagating along said drill string, and wherein the tuning comprises a step of calculating an I-term of said PI controller which uses a value of an estimated period of said stick slip oscillations and a value of an effective inertia of said drilling mechanism, but which step of calculating the I-term does not used a value of the length of said drill string and a value of a speed of the torsional waves, whereby said drilling mechanism has a frequency dependent reflection coefficient of said torsional waves, which reflection coefficient is substantially at a minimum at or near said frequency of stick- slip oscillations.