Method and system for controlling vibrations in borehole equipment.

This invention relates to a method and system for controlling vibrations in borehole equipment comprising a string of tubulars and an associated drive system.

Numerous vibrations may occur in borehole equipment during well drilling or oil production operations. If the equipment includes a rotary drill string torsional and longitudinal vibrations may be induced by alternating slip-stick motions of the drill string alongside the borehole wall, by fluctuating bit-rock interaction forces and by pressure pulses in the drilling fluid generated by the mud pumps.

In various situations it is required to damp these vibrations in order to reduce shock loads to the equipment but in some situations it may be required to enhance these loads, for example to create a resonance jar for freeing a stuck drill pipe.

Various concepts are known in the art for damping or enhancing vibrations in borehole equipment.

US patent 4,535,972 discloses a system to control vertical movements of a drill string with the aid of a hydraulic cylinder connected between the travelling block and the top of the drill string. Although the known system is designed to maintain weight on bit within desired limits it is not operated as a feedback controlled vibration damper.

SPE paper 18049 "Torque feedback used to cure slip-stick motion" presented by G.W. Halsey et al. of the Rogaland Research Institute at the October, 1988 SPE conference in Houston (USA) describes a system that adapts the value of the speed of the rotary drive of a drilling assembly based on measurement of the torque at the rotary table. The known system is able to perform a rotary speed correction proportional to minus the measured torque.

However, measurement of torque at the rotary table during actual drilling operations is inconvenient and prone to failures, as it involves equipment, such as strain gauges, that is sensitive to vibrations and shockloads.

The present invention aims to avoid this drawback of the known system by providing a method for controlling vibrations in borehole equipment, the equipment including an elongate body extending into a borehole formed in an earth formation and an associated drive system for driving said elongate body, the method comprising controlling the energy flow through the driving motor to be between selected limits when the drive system drives the elongate body, which energy flow is definable as the product of an across-variable and a through-variable, by measuring fluctuations in said motor in at least one of said variables and adjusting at least the other of said variables in response to the measured fluctuations in said at least one of said variables.

The method according to the invention is based on the insight that vibrations in a physical system can be expressed as variations of the energy flow through the system, and that this energy flow can always be expressed in terms of two variables, such as voltage times current, pressure times flowrate, linear velocity times force, torque times angular velocity, or generally speaking "across-variable" times "through-variable".

Furthermore, in accordance with the invention there is provided a method for controlling vibrations in borehole equipment, the equipment including an elongate body extending into a borehole formed in an earth formation and an associated drive system for driving said elongate body, the method comprising controlling the energy flow through the driving motor to be between selected limits when the drive system drives the elongate body, which energy flow is definable as the product of an across-variable and a through-variable, by measuring fluctuations of the angular velocity of any of the rotating parts and adjusting of the torque delivered by the driving motor in response to the measured angular velocity.

In addition, in accordance with the invention there is provided a method for controlling vibrations in borehole equipment, the equipment being a drilling assembly comprising a rotary drill string connected at its upper end to a rotary drive and an associated drive system for driving the drill string, which drill string extends into a borehole formed in an earth formation, the method comprising damping torsional vibrations in the drilling assembly by maintaining the energy flow delivered by the rotary drive to the drill string between selected limits when the drive system drives the drill string, which energy flow is definable as the product of an across-variable and a through-variable, by measuring fluctuations in at least one of said variables and adjusting at least the other of said variables in response to the measured fluctuations in said at least one of said variables, wherein the drill string is driven by a diesel engine and wherein the energy flow in the drill string is controlled by connecting a feedback controlled electric or hydraulic motor-generator to the drive shaft of the engine by means of a differential.

Based on the insight of the present invention various vibrations in borehole equipment can be controlled in an accurate manner.

For example, if the borehole equipment is a drilling assembly comprising a rotary drill string which is connected at its upper end to a rotary drive, torsional vibrations in the assembly can be damped by maintaining the energy flow delivered by the rotary drive to the drill string between selected limits. In other words vibrations propagating in upward direction through the drill string are transferred into the rotary drive and further into its power supply instead of being reflected back at the upper end of the drill string.

If the drill string is driven by an electric motor, the motor current can be selected as said through-variable, whereas the motor voltage can be selected as said across-variable.

If the drill string is driven by a hydraulic motor, the flowrate in the motor may be selected as said through-variable, whereas the fluid pressure in the motor may be selected as said across-variable.

If the drill string is driven by a diesel engine, the energy flow in the drill string may be controlled by connecting a feedback controlled electric or hydraulic motor-generator to the drive shaft of the engine by means of a differential.

With any kind of electric, hydraulic or mechanical rotary drive the angular velocity in a rotating part of the assembly may be selected as said across-variable and the torque delivered by the rotary drive as said through-variable, while the energy flow through the assembly may be maintained between selected limits by measuring fluctuations of said angular velocity and by inducing the torque delivered by the rotary drive to fluctuate in response to the measured velocity fluctuations.

The invention will be described in more detail with reference to the accompanying drawings, in which: <ul id="ul0001" list-style="none"><li>Figure 1 is a schematic representation of a rotary drilling assembly equipped with a system according to the invention which serves to control torsional vibrations;</li><li>Figure 2 shows an electronic circuit for use in the system of Figure 1;</li><li>Figure 3 shows schematically a rotary drilling assembly equipped with another embodiment of a system according to the invention for controlling torsional vibrations;</li><li>Figure 4 shows an electronic circuit for use in the system of Figure 3;</li><li>Figure 5 shows a detail of an electronic circuit for use in a system according to the invention; and</li><li>Figure 6 shows yet another embodiment of a system according to the invention for controlling torsional vibrations.</li></ul>

Figure 1 illustrates schematically a rotary drill string drive comprising a rotary table R having a mass moment of inertia J_t, a gearbox G having a gear reduction 1:n, and an electric shunt motor M having a mass moment of inertia J_r, which motor is equipped with a vibration control system according to the invention.

The control system includes a subtractor S to compare the actual rotary speed Ω with the nominal rotary speed Ω_r and a feed back loop L1 which uses fluctuations in the motor voltage V as input across-variable and the system controls the motor current I in such a manner that the torque T delivered by the motor varies in a predetermined manner in response to fluctuations in the rotary speed Ω of the motor such that the energy flow through the drill string is controlled so as to stay between selected limits.

A characteristic of the shunt motor is that T is proportional to I, and that Ω is proportional to V.

In Figure 1 T_p represents the drill pipe torque.

The relationship between the measured across-variable V and the controlled through-variable I in the active damping system of Figure 1, such that their product V.I remains between selected limits is defined with the aid of a feedback function. The feedback function strongly influences the amount of damping of the system. It is possible to optimize the damping characteristics of the system by using an appropriate feedback function. This feedback function can be derived from the following sequence of calculations.

The torsional impedance Z of the drive system can be defined as the ratio of torque T at the motor shaft and the resulting rotary speed Ω of the motor:<maths id="math0001" num="(1)"><math display="block"><mrow><mtext>Z = </mtext><mfrac><mrow><mtext>T</mtext></mrow><mrow><mtext>Ω</mtext></mrow></mfrac></mrow></math><img file="EP0443689B1_D0001.tif" /></maths> If the torque T delivered by the electric motor is made dependent on the angular velocity Ω using a complex feedback function F₁(β) = - T/Ω, the torsional impedance at the motor shaft is<maths id="math0002" num="(2)"><math display="block"><mrow><mtext>Z = - F₁(β)</mtext></mrow></math><img file="EP0443689B1_D0002.tif" /></maths> where β = frequency of the changes of the variables.

Alternatively, one can make the angular velocity Ω dependent on the torque T using a complex feedback function F₂(β) = - Ω/T.

The impedance at the rotary table is:<maths id="math0003" num="(3)"><math display="block"><mrow><msub><mrow><mtext>Z</mtext></mrow><mrow><mtext>rt</mtext></mrow></msub><msub><mrow><mtext> = iβJ</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><msub><mrow><mtext> + n² (iβJ</mtext></mrow><mrow><mtext>r</mtext></mrow></msub><mtext> + Z)</mtext></mrow></math><img file="EP0443689B1_D0003.tif" /></maths> where i = imaginary unit √-1

The equivalent rotary table inertia J_t′ is defined as<maths id="math0004" num="(4)"><math display="block"><mrow><msub><mrow><mtext>J</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><msub><mrow><mtext>′ = J</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><msub><mrow><mtext> + n² J</mtext></mrow><mrow><mtext>r</mtext></mrow></msub></mrow></math><img file="EP0443689B1_D0004.tif" /></maths>

From equations (2) through (4) it follows:<maths id="math0005" num="(5)"><math display="block"><mrow><msub><mrow><mtext>Z</mtext></mrow><mrow><mtext>rt</mtext></mrow></msub><msub><mrow><mtext> = iβJ</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><mtext>′ - n²F₁(β)</mtext></mrow></math><img file="EP0443689B1_D0005.tif" /></maths>

Z_rt is given a pre-selected value α in order to damp out torsional vibrations. For the required feedback function it follows:<maths id="math0006" num="(6)"><math display="block"><mrow><msub><mrow><mtext>F₁(β) = (- α + iβJ</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><mtext>′)/n²</mtext></mrow></math><img file="EP0443689B1_D0006.tif" /></maths>

This function is the desired feedback function for the frequency range in which the vibrations tend to occur. For the very low frequencies, in particular for the static component of the speed, it is desirable that the drive behaves as the conventional stiff drive, i.e. α must become very large for enabling the driller to slowly vary the rotary speed of the drilling assembly without the static component of the speed becoming dependent of the (static component of the) torque. This can be achieved by replacing α in the above equation (6) by<maths id="math0007" num=""><math display="block"><mrow><mfrac><mrow><mtext>iβσ + 1</mtext></mrow><mrow><mtext>iβσ</mtext></mrow></mfrac><mtext> α</mtext></mrow></math><img file="EP0443689B1_D0007.tif" /></maths> wherein σ is a time-constant.

This impedance becomes infinite if the frequency approaches zero, or approaches α for high frequencies. The turnover frequency, i.e. the frequency at which the absolute value of the impedance has increased to α√2, lies at f = 1/2πσ.

Substitution of the above impedance expression in equation (6) yields the new feedback function:<maths id="math0008" num="(7)"><math display="block"><mrow><mtext>F₁(β) = (-α - </mtext><mfrac><mrow><mtext>α</mtext></mrow><mrow><mtext>iβσ</mtext></mrow></mfrac><msub><mrow><mtext> + iβJ</mtext></mrow><mrow><mtext>t</mtext></mrow></msub><mtext>′)/n²</mtext></mrow></math><img file="EP0443689B1_D0008.tif" /></maths>

A suitable electronic circuit for varying the motor current I and motor torque T in response to measured fluctuations in angular velocity Ω of the top of the drill string in accordance with the above feedback function F₁(β) is shown in Figure 2.

The circuit of Figure 2 comprises three operational amplifiers A1, A2 and A3 respectively, each amplifier having a first and a second input; two capacitors C1 and C2 respectively; and seven resistors R1, R2, R3, R4, R5, R6 and R7 respectively. An input 1 of the circuit is connected via R1 to the first input of A1, which first input is connected via R2 and C2 to the output of A1. The output of A1 is via R3 connected to the first input of A2. The input 1 of the circuit is also connected via R7 and C1 to the first input of A2, which first input is connected via R4 to the output of A2. The output of A2 is via R5 connected to the first input of A3, said first input being connected via R6 to the output of A3 and to an output 2 of the circuit. The second input of each amplifier is connected to earth.

During normal use of the circuit shown in Fig. 2 a motor current feedback signal is delivered at the output 2 of the circuit to the motor M in response to a variation in the output signal of a tachometer at the motor shaft, which output signal is proportional to the motor voltage and which is delivered at the input 1 of the circuit.

Note that the controlled as well as the measured variables are expressed in voltages. These voltages serve as information carriers, and should not be confused with the variables defining the energy flow which is to be controlled.

Figure 3 illustrates schematically a rotary string drive comprising a rotary table or drive R having a mass moment of inertia J_t, a gearbox G having a gear reduction 1:n, and an electric shunt motor M having a mass moment of inertia J_r, which motor is equipped with a vibration control system according to the invention.

The control system includes a subtractor S to compare the actual rotary speed Ω with the nominal rotary speed Ω_r and a feed back loop L2 which uses fluctuations in the measured motor current I as input through-variable and the system controls the motor voltage V such that the product V.I, or in other words the electrical energy flow through the motor, stays between selected limits.

Again the relationship between the measured through-variable I and the controlled across-variable V such that their product remains between selected limits is defined with the aid of a feedback function F₂ which is the reciprocal of F₁.

A suitable electronic circuit for varying the motor voltage V in response to measured fluctuations in the rotor current I in accordance with the feedback function F₂ is shown in Figure 4.

The circuit of Figure 4 comprises two operational amplifiers A4 and A5 respectively, each amplifier having a first and a second input; two capacitors C3 and C4 respectively; and four resistors R8, R9, R10 and R11 respectively. An input 3 of the circuit is via R8 connected to the first input of A4. The output of A4 is connected to an output 4 of the circuit, via C3 to the first input of A4, and via R11 to the first input of A5. The first input of A5 is via C4 and R10 connected to the output of A5, which output is via R9 connected to the first input of A4.

During normal use of the circuit shown in Fig. 4 a motor voltage feedback signal is delivered at the output 4 of the circuit to the motor M in response to a signal representing variations in the motor current delivered at the input 3 of the circuit. The motor voltage feedback signal is supplied to the subtractor S shown in Fig. 3.

In case the electric motor driving the rotary table is a DC shunt motor there is a simple relationship between motor current and torque, and between motor voltage and rotational speed. For other motor types, such as a series or compound motor, the relationship is more complex because both torque and rotational speed are functions of squares and cross products of motor current and motor voltage.

A suitable electronic circuit for determining motor torque T from motor current I, motor voltage V and motor speed Ω is shown in Fig. 5. The circuit comprises a multiplier M1 having a first input 8 and a second input 9, a multiplier M2 having a first input 10 and a second input 11, and an operational amplifier A6. The output of M1 is connected to a first input of A6, and the output of M2 is connected to a second input of A6. The output of A6 is connected to a first input of M2.

During normal use of the circuit shown in Fig. 5 a signal representing the motor voltage V is applied to the first input 8 of M1, a signal representing the motor current I is applied to the second input 9 of M1, and a signal representing the motor speed Ω is applied to the first input 10 of M2. The circuit adjusts itself in a manner that at the output of the amplifier A6 a signal representing the torque T is obtained, because V.I = T.Ω.

A suitable control system for use in conjunction with said other motor types (e.g a series or compound motor) is shown in Fig. 6, which control system comprises a multiplier M3 having a first input 12 and a second input 13, a multiplier M4 having a first input 14 and a second input 15, an operational amplifier A7, a feedback loop L3 having a feedback function F₃, a power drive D and a subtractor S which compares the actual motor rotary speed Ω with the nominal motor rotary speed Ω_r. The first input 11 of M3 is connected to the output of L3, and the second input 13 of M3 is connected to the output of a conventional tachometer (not shown) at the rotary shaft of the motor M. The output of M3 is connected to an input of A7. The first input 14 of M4 is connected to a first output 16 of D, and the second input 15 of M4 is connected to a second output 17 of D. The output of M4 is connected to another input of A7. The output of A7 is connected to an input 18 of power drive D.

During normal use of the control system shown in Fig. 6 a signal representing motor voltage is delivered by power drive D at its output 16, and a signal representing motor current is delivered by power drive D at its output 17. A signal representing motor speed is delivered by the tachometer to input 13 of M3. The system adjusts itself in a manner that a signal representing the motor torque is delivered at the input 12 of M3. The feedback function F₃ may be realised using the circuit with reference to Fig. 2.

From the above description with reference to the figures it will be apparent that the energy flow in a physical system can be expressed in terms of a product of an across-variable times a through-variable. Active damping of vibrations requires control of at least one of the two variables based on measurements of the fluctuations in at least the other variable.

The following combinations of across- and through-variables are particularly suitable for use in a system according to the invention for controlling torsional vibrations in a drill string: <ul id="ul0002" list-style="none"><li>1) Adaptation of the torque delivered by an electric, mechanical or hydraulic rotary drive based on measurement of the angular velocity of any of the rotating parts at or in between the bit and the rotary drive such as the drillpipe, the rotary table, the gearbox, the drive shaft, etc.</li><li>2) Adaptation of the voltage supplied to an electric rotary drive based on measurement of the current flowing through the motor or vice versa.</li><li>3) Adaptation of the pressure to a hydraulic rotary drive based on measurement of the flowrate in the hydraulic motor or vice versa.</li></ul>

It is observed that adaptation of the variables can be performed in such a way that the active damping appears as a fluctuation in the energy consumption of the rotary drive. Another way to obtain the required adaptations is to use an additional device that can both store and generate energy. For example adaptations of the torque delivered to the rotary table by a diesel drive can be made with the aid of a feedback controlled electric motor/generator or a hydraulic motor/accumulator connected to the drive shaft by means of a differential.

It is furthermore observed that fluctuations in a variable can be measured indirectly by measuring the fluctuation in a derived variable. For example, fluctuations in velocity can be observed by measuring the displacement or the acceleration.

Furthermore, it is observed that control of a variable can also be achieved indirectly, for example the torque delivered by an electric motor can be controlled by controlling the motor current.

The concept of active damping of drill string vibrations as described above can be extended to include axial drill string vibrations. Damping of axial vibrations is of importance during drilling as well as during tripping or running of casing. For damping of axial vibrations use can be made of the system disclosed in US patent 4,535,972 to control the vertical movements of a drill string with the aid of a hydraulic cylinder connected between the travelling block and the drillpipe. Axial vibrations can also be actively damped by making use of heave compensating systems, which consist of a hydraulic system designed to compensate vertical motions of a vessel supporting a drilling rig. Another possible hydraulic device for active vibration damping consists of a telescopic part of drill string with an actively controlled variable extension. Such a device can be located in any part of the drill string, i.e. above or below the ground. Furthermore active damping of axial drill string vibrations can be obtained by feedback controlled operation of the hoisting gear. The damping system can act at the dead line anchor using a hydraulic device, or it can act at the drive of the winch or at the brake of the winch. The concept of active damping can also be applied to the running of sucker rods and use of sucker rods to drive plunger lift pumps. The following describes possible across- and through-variables for the feedback control systems to be used in such active axial vibration dampers: <ul id="ul0003" list-style="none"><li>1) Adaptation of the force supplied by the damping device (i.e. the hydraulic cylinder, the heave compensating system, the electric motor driving the winch etc.), based on measurement of the velocity of any of the drill string parts at or in between the bit and the damping device or vice versa.</li><li>2) Adaptation of the pressure to a hydraulic damping device based on measurement of the flowrate in that device or vice versa.</li><li>3) Adaptation of the voltage supplied to the electric motor driving the winch based on measurement of the current flowing through the motor or vice versa.</li></ul>

Another application of active damping systems can be in the damping of pressure pulses generated by pumps. This can be done by either controlling the drive of the pumps, or by using an additional device connected to the fluid system such as an actively controlled hydraulic cylinder. Active damping can now be achieved by adaptation of the flowrate in the fluid system, based on measurements of the pressure in the fluid system or vice versa.

Another way to use active damping is the complete opposite of the applications described above. Now the control system provides "negative damping" and reflects energy into the system rather than dissipating it. In this way the effect of tools such as resonance jars (downhole or at surface) could be drastically improved: By means of active, controlled, reflection of stress waves in the vibrating drill string a small resonance triggered by the resonance jar can be strongly amplified.