DRILL STRING AXIAL VIBRATION ATTENUATOR
The drill string axial vibration attenuator (10) is installed in the bottom hole assembly (BHA) of a drill string to attenuate axial and torsional vibrations of the drill string. The vibration attenuator (10) includes a massive elongate stabilizer (14) installed in a sealed chamber (12) that is, in turn, rigidly installed within the BHA of the drill string. Clearance between the inner wall of the chamber (12) and the stabilizer (14) is provided to preclude frictional interference therebetween. The stabilizer mass (14) is supported from below by a compression spring (18) and a shock absorber or damper (24) at the top to allow movement of the mass (14). The stabilizer (14) substantially reduces or eliminates axial and coupled torsional vibration of the drill string when the mass of the stabilizer (14), the rate of the spring, and the damper stiffness are properly configured.
The present invention relates generally to earth boring and drilling equipment, and particularly to a drill string axial vibration attenuator for damping or attenuating undesired axial motion in a drill string during drilling operations.
BACKGROUND ARTThe problem of drill string vibration has been recognized as one of the prime causes of deterioration in drilling performance. These vibrations may be lateral, torsional, or axial. Field observations have indicated that drill strings can exhibit severe vibrations that may become even more severe at the bottom-hole assembly (BHA), which comprises the drill collars, stabilizers, and the drill bit, and may also include other logging tools and instruments.
This application is directed to axial and torsional drill stem vibrations, and means for reducing or eliminating such axial and torsional vibrations. As the drill bit is penetrating the underlying formation during the drilling operation, the normal reaction force or weight-on-bit (WOB) may become excessive and fluctuate, resulting in axial vibration in the drill string. This is known as “bit-bounce.” Excessive axial vibration or bit-bounce may result in reduction of the rate of penetration (ROP) of the drill bit and/or damage to the drill bit, adverse effects upon telemetry tools and data conveyed to the surface, and fatigue of the drill pipes that form the drill stem. All of these factors result in decreased efficiency in the drilling process and increased costs of operation due to the need to replace various components more frequently than would be the case without such axial drill string vibrations.
Excessive torsional vibrations may eventually result in limit cycles where the BHA rotary speeds are bounded between zero and two or possibly even three times the designated rotary table (rotary drive for the drill stem) speed. At its extreme, this phenomenon is known as “stick-slip” where the rotational velocity of the drill bit is momentarily decreased to zero as it sticks at the bottom of the down hole, then slips and accelerates beyond the prescribed rotary table speed. This “stick-slip” phenomenon is also detrimental to the drill pipes and string, the drill bit, logging tools, and to the entire drilling operation.
Thus, a drill string axial vibration attenuator solving the aforementioned problems is desired.
DISCLOSURE OF INVENTIONThe drill string axial vibration attenuator comprises a massive, elongate stabilizer installed concentrically within a sealed internal chamber of the drill collar (DC) or BHA of a drill string, the chamber being rigidly secured concentrically within the DC or BHA. Drilling fluid or “mud” is routed around the sealed stabilizer chamber between the outer wall of the chamber and the inner wall of the drill string pipe. The stabilizer is supported within its chamber by a compression spring at its lower end and by a shock absorber or damper extending between the upper end of the stabilizer and the drill string structure. Clearance is provided around the stabilizer to preclude contact with the surrounding wall of the sealed chamber.
The mass of the suspended stabilizer, the spring rate of the supporting compression spring, and/or the stiffness of the damper may be adjusted or configured according to the needs of the system. The spring and damper rates may be linear or nonlinear. The stiffness, mass, and/or damping values for the assembly are selected after considering the drill bit type, type of geological formation, DC and/or BHA mass, and/or other drill string parameters. Axial vibrations of the drill string are dissipated due to the damping forces that arise from the relative velocity between the stabilizer mass and the DC and/or the BHA of the drill string. This provides two beneficial effects, namely, (1) resonant and off-resonance forced vibrations are attenuated; and (2) vibration instabilities caused by modulation of cutting force amplitudes are suppressed.
Torsional vibrations may also be attenuated by rotating or spinning the stabilizer within its chamber. A mathematical analysis of the various relevant parameters is also provided herein.
These and other features of the present invention will become readily apparent upon further review of the following specification and drawings.
Similar reference characters denote corresponding features consistently throughout the attached drawings.
BEST MODES FOR CARRYING OUT THE INVENTIONThe drill string axial vibration attenuator, also referred to herein as the attenuator, is installed within a length of drill pipe in a drill string to greatly reduce or eliminate vibrations in and along the drill string during drilling operations. The attenuator is particularly configured to dampen or eliminate axial vibrations, but may be used for the reduction or elimination of torsional vibrations as well.
The stabilizer mass 14 is resiliently supported at its lower end 16 by a compression spring 18 that extends upward from within the lower end 20 of the chamber 12. The opposite, upper end 22 of the stabilizer mass 14 is connected to a shock absorber or damper 24 that extends downward from the upper end 26 of the chamber 12. The spring 18 may have a linear or constant spring rate, or alternatively, may have a nonlinear rate, e.g., having stiffer coils forming a portion of its length and lighter coils forming the remainder of the length. Similarly, the damper 24 may have a linear or nonlinear damping rate.
The chamber 12 has an inner wall or surface 28 defining an internal span or diameter that is larger than that of the stabilizer mass 14. Thus, the outer wall or surface 30 of the stabilizer mass 14 and the inner wall or surface 28 of the chamber 12 define a toroidal stabilizer mass clearance volume 32 therebetween. Thus, the stabilizer mass 14 is free of contact with the inner surface 28 of the chamber 12. The above-described structure enables the stabilizer mass 14 to move vertically, relative to the chamber 12, within the limits imposed by the spring 18 and damper 24. By selecting appropriate masses, spring rates, and damper rates according to the mass of the drill stem, or more appropriately, to the mass of the drill pipe or bottom hole assembly in which the attenuator 10 is installed, the attenuator 10 serves to reduce or eliminate vertical vibrations along the drill stem between the drill bit and the top drive at the surface.
However, the drill stem is also subject to torsional vibrations due to frictional drag at the drill bit and the relatively constant torque of the top drive. In extreme cases, the rotational velocity of the drill bit may be reduced to zero as the bit sticks in the substrate in which it is working, and then accelerate to two or three times the rotational speed of the top drive when the bit is released due to the energy stored in the drill string when the bit sticks and the inherent torsional elasticity of the elongate drill string. This phenomenon is known as “stick-slip” in the drilling industry.
The additional mass of the stabilizer 14 disposed within the drill pipe can serve to reduce or eliminate such torsional vibrations, even if the stabilizer mass 14 is restricted from rotational movement within the chamber 12, e.g., by the damper 24 serving as a rotationally rigid link between the stabilizer mass 14 and the chamber 12. However, it may be desired to provide for rotational movement of the stabilizer mass 14 relative to the chamber 12, adjusting the direction and speed of the rotation in accordance with any torsional vibration that may occur along the drill stem. This may be accomplished by installing a drive motor 34 at some convenient location between the structure of the chamber 12 and the stabilizer mass 14, e.g., affixing the motor 34 to the upper portion 26 of the chamber 12 and connecting the motor 34 to the damper 24 to selectively rotate the damper 24. Alternatively, the motor 34 might be combined structurally with the damper 24. In any event, appropriate power input to the motor 34 rotates or torsionally oscillates the stabilizer mass 14 accordingly to dampen or eliminate torsional vibrations during drilling operations.
Before proceeding further with a description of the attenuator 10, and particularly the various graphs and charts provided to illustrate the various parameters involved and their effects on the efficiency of the attenuator 10, it is appropriate to provide tables listing the various parameters, terms and symbols used herein and their definitions. The values shown in the right hand columns are purely exemplary, and may be adjusted as required.
Prior to the installation of the attenuator 10 in the BHA of the drill string, the torsional equation of motion is given as:
J{umlaut over (φ)}+CT{dot over (φ)}+KTφ=Td−TOB (1)
where
Td=KT·ωd·t. (2)
The axial equation of motion is given as:
mDC{umlaut over (x)}d=W0−WOB. (3)
The depth of cut per revolution per blade is given as:
dn(t)=xd(t)−xd(t−tn). (4)
The total depth of cut is given as:
d=n·dn (5)
where tn is the instantaneous time delay obtained by solving the equation:
φ(t)−φ(t−tn)=2π/n. (6)
The WOB and the TOB both have cutting and friction components:
WOB=Wc+Wf; (7)
TOB=Tc+Tf. (8)
The expressions for the cutting components are given as:
The friction components are given as:
When the drill bit loses contact with the formation during bit bounce, the depth of cut, d, is negative and the friction components vanish.
By substituting Equations (10) and (12) into equation (1), we have:
By substituting Equation (9) and (11) into Equation (3) we have:
With reference to equation (14), the coefficient of xd represents the stiffness of the formation that can be expressed as:
kc=a·ξ·ε·n. (15)
mf·{umlaut over (x)}f+cf({dot over (x)}f−{dot over (x)}DC)+kf·(xf−xd)=0 (16)
Hence the axial equation of motion of the BHA after adding the stabilizer mass is given as:
mdxd+a·ξ·ε·n·xd(t)=F0−Wf+a·ξ·ε·n·xd(t−tn)+cf({dot over (x)}f−{dot over (x)}d)+kf·(xf−xd). (17)
The modeling can be enhanced into a finite element model (FEM) by considering both the torsional and axial flexibility of the BHA and the drill pipe. If the displacement vector of the element is denoted by Wi=[xi φi xi+1φi+1]T, and if the moduli of elasticity and rigidity of the element are denoted by Ei and Gi, respectively, the element flexibility matrix Ki is given as:
where Ai and Ii are the element cross-sectional area and moment area of inertia, respectively.
As an example, if a 200-meter long BHA is discretized into 20 elements equal in length and if a 1000-meter drill pipe is added to the FEM, 10 additional elements (also equal in length) are appended, providing a drill string having 62 degrees of freedom.
Many drilling operations utilize a roller cone drill bit that has different dynamics than its PDC counterpart, but nevertheless the coupling between the axial and torsional modes still exists. The WOB in the case of a roller cone drill bit is given by:
The formation surface elevation, s, is given as:
s=s0·sin bφ. (20)
The torque-on-bit (TOB) is given as:
where a Stribeck friction model is expressed as:
In this case, the depth of cut, d, is given as:
The rate of penetration (ROP) is defined as:
ROP=c1·F0·√{square root over (ωd)}+c2. (24)
The description and exemplary values of the parameters for the PDC and roller cone drill bit cases are listed in tables 1 and 2, respectively, further above.
Equations 13 and 14 (or 16 and 17, after adding the attenuator) represent a system of delay differential equations (DDEs) that can be expressed in a state-space model with a time delay τ either constant or variable as:
{dot over (x)}(t)=A0·x(t)+A1·(t−τ)+B·u(t). (25)
The characteristic equation is a quasi-polynomial in the form of:
|s·I−A0−A1·e−τ·s| (26)
The presence of the term e−τ·s leads to a theoretical infinite number of complex solutions for a continuous system. Here, the Chebyshev Spectral Method is presented as a numerical method to solve DDEs of a discrete system that will have a finite number of roots, since a closed form solution is virtually impossible to obtain. In the present system, the quasi-polynomial is solved using the approach developed by Breda et al. to discretize the solution operator. The solution operator is the operator transforming an initial condition φ onto the solution segment at a later timepoint specified by a parameter h, in the following sense.
We define the solution operator of the DDE in equation (25) to be the operator transforming an initial condition φ to the solution segment at timepoint h. This operator is denoted by T(h):C([−τ, 0], n)→C([−τ, 0], n). The solution operator applied to φ, i.e., (T(h)φ)(θ)=: ψ(θ), is the solution segment of (2.1) with initial condition φ=φ=at timepoint h. More precisely, ψ(θ):=(T (h)φ)(θ)=x(h+θ), θ∈└−τ, 0┘, where x(t) is the solution of Equation (25) with initial condition φ=φ.
Every DDE can be rewritten as a partial differential equation (PDE) by introducing an additional memory-dimension. If the original DDE is represented as:
then the equivalent PDE can be written as a boundary value problem as:
for the unknown u∈C(┌0, ∞┐×[−τ, 0],2). Let φ∈C([−τ, 0], n) be given. Then if x(t) is the solution to equation (26), and if u(t, θ) is a solution to equation (28), then:
u(t,θ)=x(t+θ),θ∈[−τ,0],t≧0. (29)
Let A correspond to the differentiation operator in θ-direction with the domain of functions fulfilling the boundary conditions in equation (28), that is:
Hence the problem is reduced to an abstract Cauchy-problem in the form:
The differentiation operator, A, of the abstract Cauchy-problem is expressed in terms of the solution operator of the DDE, T, as:
The eigenvalues of the operator A are the eigenvalues of the DDE. It is now required to discretize A and compute the eigenvalues of the corresponding finite-dimensional linear operator An that represents the eigenvalues of the system with the time-delay incorporated.
For a given natural number, N, the Chebyshev nodes over the interval [−τ, 0] are defined as:
The Chebyshev differentiation matrix, DN, is obtained utilizing the Chebyshev nodes as:
Thus, AN can now be evaluated as:
where m is the number of degrees of freedom of the original state space of the continuous DDE.
At a certain operating point there exists a minimum stability speed of the top drive of the rotary table, below which the system becomes unstable due to increased time delay due to the cutting action of the blades of the PDC drill bit. It is well known that time delay resembles negative damping that destabilizes a system. Hence, the BHA will be more susceptible to bit bounce when the speed of the top drive is lowered. In drilling operations, there are several reasons as to why the top drive speed is decreased. Logging-while-drilling (LWD) or measurement-while-drilling (MWD) operations usually require lower penetration rates in order to obtain accurate data of the well. Another reason is the power limitation on the motor driving the rotary table, since the torque load on the driving motor increases as the friction at the drill bit increases and puts a limit on the maximum rotary speed. Even during normal operation, with increasing torque on bit (TOB), the rotary speed of the drill bit would be oscillating around the mean value of the top drive speed, and when its speed falls significantly, the time delay between the cutting actions of the individual blades will increase. Moreover, the addition of new sections of drill pipe requires that the drilling action be temporarily paused, bringing the rotary table to a complete stop and then restarting and passing through low RPM ranges that are susceptible to bit bounce.
One of the methods for stabilizing the system is by adding additional mass to the BHA in order to suppress bit bounce. This can be done by either increasing the BHA length, which is referred to as the “unsprung mass” case, or by attaching attenuator units comprising a mass sprung on one or more springs and dampers, generally as shown schematically in
Consider a case where the top drive speed decreases to 105 RPM. Bit bounce vibrations will be seen, as shown clearly in the graph of
Since numerical integration of the dynamic equations of motion is very time-consuming, and thus a relatively small number of possible solutions can be scanned through trial and error, the Chebyshev-based discretization spectral method was implemented in order to find values of the attenuator mass, spring stiffness, and damping that achieve overall system stability. By applying equation (35) above one can obtain a characteristic matrix AN, in which the eigenvalues determine the stability. The system is stable if, and only if, all eigenvalues have negative real values. Hence, the computational time is reduced, and thousands of possible solutions can be scanned in just a matter of minutes.
The validity of the Chebyshev method is verified by numerical integration of the equations of motion under the same conditions. Consider a case when the equivalent soil stiffness is 67 MPa and the top drive speed is 80 RPM. Without the attenuator 10, the system is unstable, as can be seen in
Another advantage of the Chebyshev method is that it can be implemented to obtain or predict an operating point stability chart.
In contrast,
In order to demonstrate robustness, consider a universal attenuator with a natural frequency of 30 rad/s and a damping ratio of 0.3 to be fitted upon any BHA that utilizes either a PDC or roller cone drill bit.
To demonstrate the effectiveness and advantages of the attenuator over standard or conventional shock absorbers, consider a case where the soil formation is not sufficiently hard to induce bit bounce vibrations at a given top drive spin speed, and hence no axial vibration suppression device is needed. Equation 36 below represents a simplified model of a standard shock absorber with stiffness kabs and damping cabs. Four simulations are conducted, including (i), original BHA, (ii) tuned absorber, (iii) mistuned absorber, and (iv) with the attenuator 10. The equivalent rock formation stiffness is 150 MN/m, and the top drive speed is 150 RPM, at which there is no bit bounce at steady-state speed. Adding an attenuator of mass ratio 0.15, natural frequency of 30 rad/s, and damping ratio of 0.3, or a tuned shock absorber with stiffness value of 2e4 N/m and damping value of 30e3 N.s/m, does not affect the stability of the system, as shown in
Now consider the case when drilling into a harder formation of equivalent rock formation stiffness of 170 MN/m with the same top drive spin speed of 150 RPM. In this case, severe bit bounce and torsional vibrations occur that nearly force the system into stick-slip. As shown in
Finally, consider an absorber with a natural frequency of 30 rad/s and a damping ratio of 0.3 that may be fitted to any BHA using either a PDC or roller cone drill bit.
In conclusion, a passive proof mass damper or attenuator serves to mitigate or fully suppress harmful axial vibrations in a drill string BHA. Simulation studies indicate that the sprung mass of the attenuator effectively mitigates (and can in some cases completely suppress) bit bounce, and that the value of the sprung mass is much less than the corresponding unsprung mass required to yield the same effect. This permits the driller to operate the top drive with minimal spin speed, thus conserving power and operational costs. Moreover, the spring and damper of the attenuator can be fine-tuned in order to minimize the sprung mass. The robustness of the attenuator is illustrated herein for a wide range of operating conditions for both PDC and roller cone drill bit models, as well as in comparison to a standard shock absorber conventionally used for such purposes. One, two, or more such attenuators may be installed in the drill string, particularly in the BHA of the drill string. Furthermore, the Chebyshev-based discretization spectral method has been applied in order to predict system stability by estimating eigenvalues and to estimate stabilizing attenuator parameters in a very time efficient manner, instead of the time-consuming trial and error process performed using numerical integration. Verification of the Chebyshev method DDE solver has been confirmed by comparison with the numerical integration of the equations of motion utilizing both a lumped model and FEM.
It is to be understood that the present invention is not limited to the embodiments described above, but encompasses any and all embodiments within the scope of the following claims.
Claims
1. A drill string axial vibration attenuator, comprising:
- an elongate sealed chamber adapted for being immovably affixed within a pipe of a drill string; and
- an elongate stabilizer mass resiliently supported within the sealed chamber.
2. The drill string axial vibration attenuator according to claim 1, wherein:
- the chamber is adapted for being disposed concentrically within one of the pipes of the drill string, the chamber having an outer surface and an inner surface, the chamber outer surface and the inner surface of the pipe defining a toroidal passage therebetween; and
- the stabilizer mass is disposed concentrically within the sealed chamber, the stabilizer mass having an outer surface, the stabilizer mass outer surface and the chamber inner surface defining a toroidal stabilizer mass clearance volume therebetween, the stabilizer mass being free of contact with the inner surface of the chamber.
3. The drill string axial vibration attenuator according to claim 1, wherein the chamber has a lower end and an upper end opposite the lower end and the stabilizer mass has a lower end and an upper end opposite the lower end, the attenuator further comprising:
- a compression spring disposed between the lower end of the chamber and the lower end of the stabilizer mass; and
- a damper disposed between the upper end of the chamber and the upper end of the stabilizer mass.
4. The drill string axial vibration attenuator according to claim 3, wherein the compression spring is selected from the group consisting of springs having linear spring rates and springs having nonlinear spring rates.
5. The drill string axial vibration attenuator according to claim 3, wherein the damper is selected from the group consisting of dampers having linear damper rates and dampers having nonlinear damper rates.
6. The drill string axial vibration attenuator according to claim 1, wherein the stabilizer mass is rotationally stationary relative to the chamber.
7. The drill string axial vibration attenuator according to claim 1, further comprising a motor communicating with the stabilizer mass, the motor selectively rotating the stabilizer mass.
8. A drill string axial vibration attenuator, comprising:
- an elongate sealed chamber adapted for being disposed concentrically within a pipe of a drill string, the chamber having an outer surface and an inner surface, the chamber outer surface and the inner surface of the pipe defining a toroidal passage therebetween, the chamber having an upper end and a lower end;
- a first resilient member extending downward within the chamber from the upper end;
- a second resilient member extending upward within the chamber from the lower end; and
- an elongate stabilizer mass disposed concentrically within the sealed chamber, the stabilizer mass being attached to and suspended between the first and second resilient members, the stabilizer mass having an outer surface, the stabilizer mass outer surface and the chamber inner surface defining a toroidal stabilizer clearance volume therebetween, the stabilizer being free of contact with the inner surface of the chamber.
9. The drill string axial vibration attenuator according to claim 8, wherein:
- the chamber is immovably affixed within one of the pipes of the drill string; and
- the stabilizer mass is resiliently supported within the sealed chamber.
10. The drill string axial vibration attenuator according to claim 8, wherein the stabilizer mass has a lower end and an upper end opposite the lower end, the attenuator further comprising;
- a compression spring disposed between the lower end of the chamber and the lower end of the stabilizer mass; and
- a damper disposed between the upper end of the chamber and the upper end of the stabilizer mass.
11. The drill string axial vibration attenuator according to claim 10, wherein the compression spring is selected from the group consisting of springs having linear spring rates and springs having nonlinear spring rates.
12. The drill string axial vibration attenuator according to claim 10, wherein the damper is selected from the group consisting of dampers having linear damper rates and dampers having nonlinear damper rates.
13. The drill string axial vibration attenuator according to claim 8, wherein the stabilizer mass is rotationally stationary relative to the chamber.
14. The drill string axial vibration attenuator according to claim 8, further comprising a motor communicating with the stabilizer mass, the motor selectively rotating the stabilizer mass.
15. A drill string with axial vibration attenuation, comprising:
- a plurality of elongate pipes connected end-to-end to define a drill string, the drill string having an upper end and a lower end;
- a drill bit mounted on the lower end of the drill string;
- a bottom hole assembly located in the lower end of the drill string; and
- at least one attenuator mounted in the bottom hole assembly, the attenuator having: an elongate sealed chamber mounted coaxially within the bottom hole assembly, the chamber being annularly spaced from the bottom hole assembly, the chamber having an upper end and a lower end; a vibration damper mounted at the upper end of the chamber; a spring mounted at the lower end of the chamber; and an elongate mass having an upper end attached to the damper and a lower end attached to the spring, the elongate mass being annularly spaced from the chamber and resiliently move upward and downward to counteract axial forces occurring during drilling operations, thereby preventing and reducing axial vibration of the drill string.
16. The drill string with axial vibration attenuation according to claim 15, wherein the chamber is immovably affixed within one of the pipes of the drill string.
17. The drill string with axial vibration attenuation according to claim 15, wherein:
- the chamber has an outer surface and an inner surface, the chamber outer surface and the inner surface of the pipe defining a toroidal passage therebetween; and
- the elongate mass is disposed concentrically within the chamber, the elongate mass having an outer surface, the elongate mass outer surface and the chamber inner surface defining a toroidal stabilizer clearance volume therebetween, the elongate mass being free of contact with the inner surface of the chamber.
18. The drill string with axial vibration attenuation according to claim 15, wherein:
- the spring is selected from the group consisting of springs having linear spring rates and spring having nonlinear spring rates; and
- the vibration damper is selected from the group consisting of vibration dampers having linear damper rates and vibration dampers having nonlinear damper rates.
19. The drill string with axial vibration attenuation according to claim 15, wherein the elongate mass is rotationally stationary relative to the chamber.
20. The drill string with axial vibration attenuation according to claim 15, further comprising a motor communicating with the elongate mass, the motor selectively rotating the elongate mass.
Type: Application
Filed: Jul 9, 2015
Publication Date: Jun 15, 2017
Inventors: AHMED SAEED (COLLEGE STATION, TX), ALAN B. PALAZZOLO (COLLEGE STATION, TX), SHEHAB AHMED (DOHA)
Application Number: 15/325,074