None.
Embodiments of the invention relate to systems and methods for determining whirl attributes of a rotating drill string, which may be used in hydrocarbon drilling operations.
Hydrocarbon reservoirs are developed with drilling operations using a drill bit associated with a drill string rotated from the surface or using a downhole motor, or both using a downhole motor and also rotating the string from the surface. A bottom hole assembly (BHA) at the end of the drill string may include components such as drill collars, stabilizers, drilling motors and logging tools, and measuring tools. A BHA is also capable of telemetering various drilling and geological parameters to the surface facilities.
Resistance encountered by the drill string in a wellbore during drilling causes significant wear on the drill string, especially the drill bit and the BHA. Understanding how the geometry of the wellbore affects resistance on the drill string and the BHA and managing the dynamic conditions that lead potentially to failure of downhole equipment is important for enhancing efficiency and minimizing costs for drilling wells. Various conditions referred to as drilling dysfunctions that may lead to component failure include excessive torque, shocks, bit bounce, induced vibrations, bit whirl, stick-slip, among others. These conditions must be rapidly detected so that mitigation efforts are undertaken as quickly as possible, since some dysfunctions can quickly lead to tool failures.
One common observed dysfunction includes whirl, which often causes failures in the BHA and damages the drill bit. Whirl refers to a lateral vibration where the rotational axis of the bit does not align with the center of the borehole, and the bit center performs additional rotations around the borehole. Three distinct whirl forms include: (1) backward whirl where the drill string rotates clockwise and the center of the drill string rotates counter-clockwise around the borehole; (2) forward whirl where both drill string and drill-pipe center rotate clockwise but with different rotational speeds; and (3) chaotic whirl where the drill-pipe center does not follow a particular direction but moves in a random and highly unstable fashion.
Tri-axial accelerometers used in the drilling industry measure three orthogonal accelerations related to shock and vibration during drilling operations. The magnitudes of the acceleration data provide a qualitative evaluation of the extent of the drill string vibration. The acceleration data combined with other information may produce a qualitative drilling risk index.
However, prior approaches for quantifying whirl require estimations based on frequency domain computations. This use of the whirl frequency rather than only time domain fails to provide robust results. For example, signal noise may introduce additional peaks in the frequency spectrum and thus limit ability to make accurate determinations of whirl frequency.
Therefore, a need exists for systems and methods to provide reliable determinations of drill string whirl attributes, such as magnitude, orientation and velocity.
For one embodiment, a method of determining a whirl attribute of a drill string includes estimating centers of rotation on the drill string based on acceleration sensed per revolution for each of the centers being estimated. The method includes determining the whirl attribute from information provided by the centers of rotation. The whirl attribute output includes at least one of magnitude, orientation, velocity and type of whirl.
In one embodiment, a system for determining a whirl attribute of a drill string includes a drilling rig coupled to the drill string extending into a borehole and a sensor disposed on the drill string to detect acceleration. A processor couples to receive data from the sensor and is configured to determine the whirl attribute by estimating centers of rotation on the drill string based on the data per revolution for each of the centers being estimated. The processor derives from the centers of rotation at least one of magnitude, orientation, velocity and type of whirl.
The foregoing and other objects, features, and advantages of the disclosure will be apparent from the following description of embodiments as illustrated in the accompanying drawings, in which reference characters refer to the same parts throughout the various views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating principles of the disclosure:
Embodiments of the invention relate to methods and systems for outputting at least one drill string whirl attribute, such as magnitude, orientation, velocity and type, without requiring determination of whirl frequency. Transforming acceleration data into drill string motions provides a path of one point along the drill string. Fitting these motions throughout one complete revolution of the drill string to a revolution ellipse, for example, provides revolution ellipse centers defining centers of rotation for each revolution fitted. A whirl ellipse, for example, derives from another fitting using a plurality of the revolution ellipse centers. Coefficients from the whirl ellipse and/or vector direction of the centers provide at least one whirl attribute for output. While described with respect to drilling, the output may apply to other rotating equipment problems as well and may be used in any application for proactive detection of temporal events in automated systems to aid in avoiding failures.
The present disclosure is described below with reference to block diagrams and operational illustrations of methods and devices. It is understood that each block of diagrams or operational illustrations, and combinations of blocks in the diagrams or operational illustrations, can be implemented by means of analog or digital hardware and computer program instructions. For the purposes of this disclosure a computer readable medium (or computer-readable storage medium/media) stores computer data, which data can include computer program code (or computer-executable instructions) that is executable by a computer, in machine readable form.
The BHA Dynamic Sub 114 acquires data including tri-axial acceleration data from respective sensors. Any data acquired with the BHA Dynamic Sub 114 may be transmitted to the drilling rig facilities 101 through drill string telemetry or through mud-pulse telemetry as time series data. The drill string may also contain associated sensors, for example mid-string dynamic subs 110, acquiring data utilized in some embodiments for determining drill string whirl attributes, and these instrumented subs can also send signals representing these measurements up the drill string where they are recorded on or near the drilling rig.
where P(x, y, z, t) is a position vector in a global stationary coordinate frame referenced at the center of the drill string, a(x, y, z, t) is an acceleration vector in a global stationary coordinate frame referenced at the center of the drill string, and t is the travel time of the drill string motion.
For one embodiment, the solution to equation 1 can be written in a double integral form as:
P(x,y,z,t+dt)=∫∫a(x,y,z,t)dt2 (2)
where dt is the time interval the drill string moves from P(x, y, z, t) to P(x, y, z, t+dt). If dt is small and typically equal to the data sample rate in the range of 0.01 to 0.0025 sec, the a(x,y,z,t) vector can be approximated to be constant within a small time interval. Equation 2 becomes:
P(x,y,z,t+dt)=P(x,y,z,t)+v(x,y,z,t)δt+a(x,y,z,t)δt̂2, (3)
where v(x,y,z,t)=Σa(x,y,z,t)dt, and δt is the time interval the drill string moves from P(x, y, z, t) to P(x, y, z ,t+dt). The drill string positions can be continuously determined using equation 3.
Since low frequency noise in the acceleration data may lead to slow drifting of positions calculated using equation 3, some embodiments solve equation 1 through a numerical optimization to calculate drill string position. An objective function for the drill string position is thus constructed from equation 1 and is:
where D(P) is a damping function such that D(P) increases significantly when |P|>Rp (i.e., drill string position is outside of the wellbore) given Rp is the radius of the drill string where the sensor is mounted and λ is a constant scaler to control the relative importance of the data misfit (first term) and the damping function. An example form of D(p) is:
A search for the correct drill string position that satisfies the acceleration data utilizes an iterative search on P to find the P that minimizes the objective function J(P) of equation 4. While one implementation uses a linearized quasi-Newton method to perform the iterative search, other exemplary suitable search methods include steepest descent or Monte Carlo.
In general, the recorded acceleration data include both the earth's gravitational and centripetal accelerations. Both accelerations should be accounted for before applying equation 3. Difficulty in obtaining exact locations and orientations of the downhole tri-axial accelerometers at a particular instance of time because of buckling and bending of the drill string make estimates for the exact gravitational and centripetal accelerations as a position of drilling depth challenging. A simple, but effective method to correct both gravitational and centripetal accelerations includes approximating both corrections by a local running mean of the acceleration data. After removing the local running mean, the acceleration data yield the measurements due to the vibration only.
where ar, at and az are radial, tangential and axial accelerations in a local moving coordinate frame; ax, ay and az are the corresponding accelerations in a global stationary coordinate frame; θ is the rotational angle (See
A conventional approach to estimate the rotational angle θ uses the vector dot product between acceleration vectors ax and ar. A better and more accurate method uses downhole RPM measurements to compute θ as:
θ=ωδt (7)
where ω is angular velocity of downhole RPM at a particular instance of time, and where δt is the time interval the drill string moves from P(x, y, z, t) to P(x, y, z ,t+dt).
For some embodiments, transforming tri-axial accelerations into drill string motions includes the following three steps: (1) approximating the gravitational and centripetal accelerations by a local running mean of the acceleration data and removing the local running mean to yield the acceleration measurements due to the vibration only, (2) transforming the corrected acceleration data from a local rotating coordinate frame to a global stationary coordinate frame using equation 6, and (3) mapping the acceleration data into continuous drill string positions via equation 3. In some embodiments, transforming tri-axial accelerations into drill string motions includes an iterative search on P to find the P that minimizes the objective function J(P) of equation 4 and that is then mapped into continuous drill string positions.
Ax
2
+Bxy+Cy
2
+Dx+Ey+F=0, (8)
with an ellipse-specific constraint of:
4AC−B*B=1, (9)
where A, B, C, D, E, and F are the coefficients of the ellipse, and x and y are the coordinates of drill-string motion. The least-squares algorithm fits the drill string motions within a complete revolution to derive the coefficients of A, B, C, D, E and F. The coefficients of the ellipse, in turn, yield the major and minor axes, rotational angle, and center 404 of the revolution ellipse 402.
The whirl ellipse 520 provides whirl magnitude, orientation and velocity. Whirl orientation corresponds to rotational angle of the whirl ellipse 520 obtained from the coefficients set forth in the ellipse equations 8 and 9. For some embodiments, a whirl magnitude equation defines extent of the whirl as:
whirl magnitude=d/(R−r), (10)
where d (shown in
In some embodiments, the whirl magnitude is defined as the ratio between the drill string's kinetic energy for the whirl motion and of the normal rotation, in dB scale:
where Rwhirl is the radius of the whirl motion, calculated by the geometric average of the semi-major and semi-minor axis of the whirl ellipse 520: Rwhirl=√{square root over (ab)}/2 given a is major axis of the ellipse and b is minor axis of the ellipse; Ri and Ro are the inner and outer radius of the drill pipe where the acceleration sensor is mounted; ωwhirl is the angular velocity of the whirl motion determined by the ellipse centers 504A-E, with ωwhirl>0 corresponding to a whirl motion in the direction of the drilling rotation (forward whirl); and ωdrilling is the angular velocity of the drill string rotation.
In some embodiments, a whirl velocity equation defines the whirl cycles per unit of time by:
whirl ellipse perimeter/T, (12)
where T is the average of total travel time observed per revolution to restart the whirl ellipse, and the ellipse perimeter is approximated by:
π(a+b)(1+3h/(10+√{square root over (4−3h)})) (13)
where a is the major axis of the ellipse, b is the minor axis of the ellipse, and
h=(a−b)2/(a+b)2. (14)
A whirl determination step 701 includes fitting the centers to a closed curved shape, such as another ellipse referred to herein as a whirl ellipse, and outputting at least one whirl attribute upon determining magnitude, orientation, velocity and/or type of drill string whirl. Determining the magnitude, orientation and/or velocity of the drill string whirl utilizes coefficients derived from the whirl ellipse. Further, determining type of whirl, e.g., forward or backward, relies on vector direction of the centers determined in succession.
The processor may output to a user the whirl attribute on a display of the processor 103 or other remote location for monitoring drilling performance. In some embodiments, the output of the whirl attribute results in automatic or user controlled stopping and restarting of drilling, adjusting weight on bit, changing drill string rotation rate, drill bit replacement and/or adjusting drill string stiffness. Such mitigation efforts may continue based on feedback from the output of the whirl attribute until the output of the whirl attribute reaches an acceptable level to avoid or limit tool failures.
Although the systems and processes described herein have been described in detail, it should be understood that various changes, substitutions, and alterations can be made without departing from the spirit and scope of the invention as defined by the following claims. Those skilled in the art may be able to study the preferred embodiments and identify other ways to practice the invention that are not exactly as described herein. It is the intent of the inventors that variations and equivalents of the invention are within the scope of the claims while the description, abstract and drawings are not to be used to limit the scope of the invention. The invention is specifically intended to be as broad as the claims below and their equivalents.
This application is a non-provisional application which claims benefit under 35 USC §119(e) to U.S. Provisional Application Ser. No. 62/181,559 filed Jun. 18, 2015, entitled “CHARACTERIZATION OF WHIRL DRILLING DYSFUNCTION,” which is incorporated herein in its entirety.
Number | Date | Country | |
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62181559 | Jun 2015 | US |