Title of Invention

METHOD OF DETERMINING DRILL STRING STIFFNESS

Abstract

The present invention relates to a method for determining the rotational stiffness of a drill string for drilling of a borehole in an earth formation, the drill string having a bottom hole assembly (BHA) and an upper end driven by a rotational drive system. The method comprises the steps of determining the time derivative of the drill string torque drilling of the borehole at a selected time when stick-slip of the BHA occurs, determining the nominal rotational speed of the drill string at an upper part thereof and at said selected time, and determining the rotational stiffness of the drill string from a selected relationship between said time derivative of, the drill string torque and said nominal rotational speed at the upper part of the drill string.

Full Text

METHOD.OF DETERMINING DRILL STRING STIFFNESS The present invention relates" to a method"«and system for determining the rotational stiffness of a drill string for drilling a borehole into an earth formation. During rotary drilling the drill string, and in particular the lower part -thereof which is termed the bottom hole assembly (BHA), can be subjected to undesired rotational vibrations also referred to as oscillations. The magnitude and frequency of such rotational vibrations depend on parameters such as the length and stiffness of the drill string, the number and positions of the drill string stabilisers, the shape of the borehole, and the weight of the BHA. Stick-slip is a mode of rotational vibration which is particularly undesirable as it leads to a reduced penetration rate of the drill bit and to enhanced wear and damage to the -drill string. During stick-slip the movement of the drill string is characterised by repeated cycles of deceleration and acceleration whereby in each cycle the drill bit comes to a halt and subsequently accelerates to a speed significantly higher than the nominal speed of the rotary table. EP-A-0443689 discloses a system for controlling drill string vibrations, which varies the -rotary speed gradually in response to rotational.vibrations of the string-so as to damp the vibrations. The drill string is driven by. a drive system which in mos-t cases includes 3 rotary table driven by an electric motor, or by a top drive driven by an electric motor. The control system operates on the principle of controlling the energy flow through the drive system and can be represented by a combination of a rotational spring'and a rotational damper associated with the drive system, to obtain optimal damping, the spring constant of the spring and the damping constant of damper are to he tuned to optimal values. It will be understood that the rotational stiffness of the drill string plays an important role in tuning to such optimal values. However, the actual rotational stiffness of the drill string is generally unknown as it changes during the drilling process due to, for example, the drill string being extended as the borehole becomes deeper. It is therefore an object of the invention to provide a method and a system for determining the rotational stiffness of a drill string for drilling of a borehole in an earth formation. In accordance with the invention there is provided a method of determining the rotational stiffness of a drill string for drilling of a borehole in an earth formation, the drill string having a bottom hole assembly (BHA) and an upper end driven by a rotational drive system, the method comprising the steps of: determining the time derivative of the drill string torque during drilling of the borehole at a selected time when stick-slip of the BHA occurs; determining the nominal rotational speed of the drill string at an upper part thereof at said selected time; and ' determinina the rotational stiffness of the drill string from a selected .relationship between said time derivative of the drill string' torque and said nominal rotational speed at the upper part of the drill string. The drill string torque is a linear function of the rotational stiffness of the drill string and the twist of the drill string. Consequently the time derivative of the drill string torque is linearly dependent on the drill string stiffness and the instantaneous speed difference between the BHA and the upper part of the drill string. During stick-slip the speed of the BHA varies between zero"and a magnitude of about twice the -nominal speedsof the upper part of the drill string. Therefore the amplitude of the' speed-variation of the BHA has a magnitude of about the nominal speed of the upper part of the string. Thus, by suitably selecting the relationship between the time derivative of the torque and the nominal rotational speed at the upper part of the string, the rotational stiffness can be determined. It was found that a sine-wave suitably fits the speed of the BHA as a function of time. Therefore, in a preferred embodiment of the method of the invention said selected relationship is: torque; oscillation. Preferably the time derivative of the drill string torque 'at said selected time is ■■at a maximum so that said - Alternatively the time derivative of the drill string torque at said selected time is at a minimum so that said selected relationship is: The system according to .. - means for determining the time derivative of the drill' string torque during drilling of the borehole at- a' selected time when stick-slip of the EHA occurs; means for determining the nominal rotational speed of the-drill string at an upper end part thereof at said selected time; and means for determining the rotational stiffness of the drill string from a selected relationship between said time derivative of the drill string torque and said nominal rotational speed. In order to further improve tuning of the spring constant and the damping constant of the control system it is preferred that the actual magnitude of the rotational moment of inertia of the BHA is taken into account/ which moment of inertia is determined from the rotational stiffness of the drill string using the The invention will.be described hereinafter in more detail and by way of example, with reference to the accompanying drawings in which: t Fig. 1 schematically shows a drill string and rotational drive system used in applying the method and system of the invention; and Fig. 2 schematically shows rotational velocity fluctuations of the BHA of the drill, string of. Fig. 1, as ■ a function of time. Referring to Fig. 1 there is shown a schematic i embodiment of a drill string 1 having .a lower part 3 forming a bottom hole assembly (BHA) and an upper end 5 driven by a rotational drive system 7. The BHA 3 has moment of inertia Jx, the drill string. 1 "has torsion stiffness k2, and the drive system 7 has moment of - ■»-inertia J2. In the schematic embodiment of Fig. 1 the moment of inertia of the part of the drill string between the BHA 3 and the drive system 7 has been lumped to both ends of the string, i.e. to J, and J3 . The drive system 7 includes an electric motor 11 and a rotary table 12 driven by the electric motor 11, and is connected to an electronic control system (not shown) for damping rotational vibrations of the drill string 1 by absorbing rotational, vibration energy thereof. The damping action of the control system is simulated by a torsion spring 15 and a rotational damper 17 located between the electric motor 11 and rotary table. The spring 15 has spring constant kf and the rotational damper 17 has damping constant Cj . The control system has to be tuned so as to select optimum values for the parameters kj and cjt which optimal values depend on the drill string parameters k2andJl , The procedure of selecting such optimum values, is not an object of the present invention. Rather it is an object of the invention to determine the actual magnitudes of k2andJl in order to be able to tune the control system optimally. It will*be understood that the magnitudes of k2andJ} change as drilling proceeds due to, for example, the drill string being extended as the borehole is deepened, or the BHA being changed. In Fig. 2 is shown a diagram in which line 19 represents the rotational speed of the BHA as a function . of time during stick-slip, and. line 21 represents a sine-wave .approximation of the speed of the BHA. The speed of The control system can how be tuned in dependence on the values of the parameters k2 and Jx . -If necessary accuracy of the above procedure can be enhanced by determining any harmonics in the signal representing the drill string oscillation and taking such harmnnics into account in the above equations. WE CLAIM 1. A method of determining the: -rotational stiffness of a drill string for drilling of a borehole in an earth formation, the drill string having a bottom hole assembly (BHA) and an upper end driven by a rotational drive -system, the method comprising the steps of: determining the time derivative of the drill string torque during drilling of the borehole at a selected time when stick-slip of the BHA occurs; determining the nominal rotational speed of the drill string at an upper part thereof at said selected time; and determining the rotational stiffness of the drill string from a selected relationship between said time derivative of the drill string torque and said nominal rotational speed at the upper part of the drill string. 2. The method of claim 1, wherein said selected 3. The method of claim 2, wherein at said selected time the time derivative of the drill string torque is at a maximum, and said selected relationship is: 4. The method of claim 2, wherein at said selected time the time derivative of the drill string torque is at a minimum, and said selected relationship is: 5. The method of any one of claims 2-4, wherein the parameter Ac/ is selected to be: 6. The method of any one of claims 1-5, wherein the rotational drive sysxem includes- a rotary table and a . motor driving the rotary table, and wherein the time derivative of the drill string torque is determined from the equation of motion of the drive system: 7. The method of claim 6, wherein the motor is an electric motor and wherein Trand Qrare determined from the current and voltage supplied to the electric motor. 8. The method of any one of claims 1-7, further comprising the steps of determining the rotational .moment of inertia of the BHA from the rotational stiffness of the drill string, and from the relationship: 9. A system for determining the rotational stiffness of a drill string for drilling of a borehole in an earth formation, the drill string having a bottom hole assembly (BHA) and an upper end driven by a rotational drive system, the system comprising: means for determining the time derivative of the drill string torque during drilling of the borehole at a selected time when stick-slip.of the BHA occurs; means for determining the nominal rotational speed of the drill string at an upper end part thereof at said selected time; and means for determining the rotational stiffness of the drill string from a selected relationship between said time derivative of the drill string torque and said nominal rotational speed. 10. The method substantially as described hereinbefore with reference to the drawings. 11. The system substantially as described hereinbefore with reference to the drawings-

Documents:

in-pct-2001-329-che-abstract.pdf

in-pct-2001-329-che-claims duplicate.pdf

in-pct-2001-329-che-claims original.pdf

in-pct-2001-329-che-correspondance others.pdf

in-pct-2001-329-che-correspondance po.pdf

in-pct-2001-329-che-description complete duplicate.pdf

in-pct-2001-329-che-description complete original.pdf

in-pct-2001-329-che-drawings.pdf

in-pct-2001-329-che-form 1.pdf

in-pct-2001-329-che-form 26.pdf

in-pct-2001-329-che-form 3.pdf

in-pct-2001-329-che-form 5.pdf

in-pct-2001-329-che-other documents.pdf

in-pct-2001-329-che-pct.pdf