bha dynamics paper spe-173154-ms

SPE/IADC-173154-MS

Fully-Coupled Nonlinear 3-D Time-Domain Simulation of Drilling Dysfunctions Using a Multi-Body Dynamics Approach Dr. Andrew S. Elliott, SPE, MSC Software Mark Hutchinson, SPE, Leader Drilling International Copyright 2015, SPE/IADC Drilling Conference and Exhibition This paper was prepared for presentation at the SPE/IADC Drilling Conference and Exhibition held in London, United Kingdom, 17–19 March 2015. This paper was selected for presentation by an SPE/IADC program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers or the International Association of Drilling Contractors and are subject to correction by the author(s). The material does not neces-sarily reflect any position of the Society of Petroleum Engineers or the International Association of Drilling Contractors, its officers, or members. Electronic reproduction, distribution, or stor-age of any part of this paper without the written consent of the Society of Petroleum Engineers or the International Association of Drilling Contractors is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE/IADC copyright.

Abstract Traditional finite element (FE) methods used to analyze drill string dynamics are linear and operate in the frequency domain. They can address only one type of drilling problem at a time (e.g. bit-bounce, stick-slip or bending) and cannot account for coupled motions or aperiodic responses. While attempts have been made to more completely examine fully-coupled and three-dimensional bottom-hole-assembly (BHA) responses using non-linear FE methods, those efforts have proven computa-tionally problematic for long drill strings and even for some more complex short duration simulations. Using a multi-body dynamics (MBD) approach, drill string components are modeled in a physically intuitive manner. All nonlinear geometric and inertial effects are properly accounted for, without restrictions on angular displacements or angular rates. Modern commercial MBD codes run on typical engineering workstations and are much faster than FE simulations which are often two to three orders of magnitude slower for drill string models. The computational efficiency of MBD also enables parametric variations and sensitivity studies of BHA configuration and surface drilling controls that can help the driller optimize drilling performance and avoid dysfunctions. Multi-body simulations are performed in the time-domain. Input parameters such as hole diameter, well trajectory, bit wear, wall stiffness, contact damping and friction, as well as operating parameters like hookload, drive torque and flow rates, can also be defined as a function of depth. Some model input and parameters may be uncertain. In such situations the efficient parametric variation capability of the MBD codes can be used to “tune” the model to match whatever surface and downhole data are available, including magnitudes, phases and frequency content. MBD models can be extensively instrumented to predict the response along the entire length of the drill string with a very low computational cost and which can be visualized versus time. Such displays, together with graphical animations of drill string motions, provide a more complete picture than is available from other analytical approaches of what is physically hap-pening downhole. Loads computed by the MBD simulations can be applied to more detailed FE models of drill string com-ponents to predict stress and fatigue. These physical insights enable drilling engineers to make better assessments of BHA design choices, and ultimately enable manufacturers to design better drilling tools. Results of MBD modeling are presented that provide insights on an actual drilling dysfunction and downhole failure. Robust and efficient MBD-based drill string modeling and simulation that reliably predict the dynamic response of the drill string and BHA prior to tripping into a well, combined with the ability to update those predictions as measured data are re-ceived from both surface and downhole, can improve bit life, reduce string failures, facilitate improvements to BHA designs and improve overall drilling performance with a significant reduction in drilling costs. Ultimately, because of its very fast solution speeds, MBD-based analysis could become a key component of drilling automation.

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Introduction Systems modeling (SM), multi-body dynamics (MBD) and finite element (FE) methods are three common computational approaches to analyzing the dynamic response of a drill string. Each makes different assumptions and has various levels of complexity, and each has differing computational requirements. When comparing the amount of work the analyst and the program must do to solve for the response of a complex and grossly nonlinear mechanical system like a rotating drill string in a borehole, the MBD approach falls somewhere between nonlinear FE and pure SM. It is important to note that this ordering is not indicative of the relative accuracy of the approaches. Commercial SM codes like Easy5® and Matlab® require the analyst to make many simplifying assumptions about forces and motions that are appropriate for describing the dynamic behaviors of the drill string. SM string models most often contain less detail than is required for understanding complex working drill string components, such as drill bits and under-reamers, and may have trouble capturing the critically important contact and friction effects. SM, however, is usually not computa-tionally burdensome and such reduced models can easily be incorporated into real-time solutions. FE codes like Nastran® and Abaqus® construct their models automatically from a given geometry and thus reduce the re-quirements on the analyst, but they produce large models that require a tremendous amount of processing power and usually solve very slowly. Time-based FE simulations of entire drill strings run extremely slowly, especially when using nonlinear methods. Frequency-based FE solutions run considerably more quickly than time-based FE simulations, but are restricted to linear applications which rarely occur while drilling. Even frequency-based solutions of entire drill strings are computation-ally very demanding. Currently, when processing time is not critical, both frequency-based and time-based dynamic FE methods are used during well-planning for bottom-hole assembly (BHA) designs, and forensically after downhole failures. Manufacturers also use static FE modeling to help develop mechanical designs for individual downhole drilling tools and drill bits. The various frequency-based FE modeling tools used by the drilling industry to predict drill string behavior each make dif-ferent assumptions and often produce widely dissimilar results for nominally the same downhole drilling condition.(1) Such frequency-based FE models fail to account for the strong nonlinearities of contact and friction, and cannot predict aperiodic responses such as when helical waves of varying propagating velocity travel up the BHA and across stabilizers. Neither can frequency-based FE modeling account for the crucial axial-torsional-bending coupling that occurs when the drill string is under high compression or in high tension, nor can it correctly model cases when different types of dynamic response occur simultaneously, e.g. lateral bending during fully developed stick-slip. As a result, such frequency-based FE models and “crit-ical speeds” analyses are seldom used for real-time decision-making. Instead the oil companies and directional drillers rely more upon the driller’s experience and whatever surface and downhole measurements are available to react to downhole drill-ing dysfunctions.(2) In comparison to FE methods, models from MBD codes like Adams® or Dads® contain a moderate degree of structural complexity and solve the full system equations without having to resort to a reduced modal approach. MBD analyses can account more effectively for significant nonlinear dynamic phenomena like the intermittent rubbing contact against a bore-hole wall with both friction and stiction. The MBD approach also includes the ability to virtually instrument the drill string at as many locations as desired with customizable sensors, and can track both internal structural loads as well as externally ap-plied loads. MBD solution speeds using a typical engineering workstation can approach real-time, depending on the length of drill string being modeled, wellbore trajectory and nature of the drilling event being simulated. As a point of reference, MBD solution speeds are typically two to three orders of magnitude faster than equivalent FE models. The MBD solution speed enables the analyst to look at dozens of different BHA configurations and hundreds of combinations of drilling controls in a reasonable time frame, thereby supporting parametric sensitivity analyses for drilling optimization. This capability can also be used to determine improved estimates for uncertain input parameters like hole size, bit wear and formation characteristics. So instead of just answering how one BHA configuration will perform in a particular well under one specific set of control parameters, we can now reasonably discuss various BHA designs, comparative component performance, overall drilling robustness and drilling performance over a much wider range of conditions. Most MBD codes include the ability to directly incorporate FE models of specific components and to couple SM models of controls systems, hydraulics or external actuators right into the simulation (3). An example of the former might be when a detailed locally compliant response is need to accurately estimate fatigue life. An example of the latter could be the dynamic performance of the top-drive system. In both the automotive and aerospace industries, MBD modeling and simulation are habitually employed throughout the pre-liminary and detailed design cycles. The ability to accurately and reliably predict prototype performance through simulation

SPE/IADC-173154-MS 3

has eliminated much of the significant cost and time associated with protracted iterative physical testing. Once virtual proto-typing is complete, however, some physical testing is still required to validate operating limits and performance. During this phase, the MBD models are re-used and extended to included test hardware and instrumentation, and also to design appropri-ate test procedures that ensure the acquisition of useful test data. Experience from the automotive and aerospace industries has also shown that when system-level modeling does not include control effects and realistic inputs, then a solution devised to mitigate one type of problem in one component or sub-system can often have undesirable and unexpected effects elsewhere in the system(4). The drilling industry has similar experiences whereby mitigating certain downhole dysfunctions has indeed improved local instantaneous rates of penetration but has inad-vertently contributed to drill bit or drill string component failures with a net loss of overall progress rate. This is where MBD-based analyses, which include the entire BHA and all the coupled and aperiodic nonlinearities that occur while drilling, can provide a better understanding of drilling tool and drill string responses to drilling controls. Multi-Body Dynamics Modeling of a BHA As noted above, MBD methods, which do not necessitate using a modal approach, automatically account for the nonlinear structural couplings inherent in a rotating drill string, and also include all the nonlinear contact and friction forces that occur along the drill string. The comparatively fast speed of MBD solutions facilitates multiple model and operational variations to be run in a reasonable amount of time to gain a better understanding of how the drill string responds to various surface con-trol settings as well as to the dynamic behavior of a top-drive, rotary steering tool, mud motor, shock-sub or other active drill-ing component, when such are used. The following examples illustrate these MBD capabilities. Structural Coupling Example Being long and skinny structures, large sections of drill string are most often modeled using linear beam elements based upon Euler-Bernoulli beam theory, with uncoupled bending, torsion and axial responses. Such an approach fails when a beam is subjected to high axial loads, either in tension near the surface or in compression in the lower BHA. MBD codes can effi-ciently solve for nonlinear (Timoshenko) beams with axial-bending coupling included.

Figure 1. BHA Behavior for 45klbf (left) and 60klbf (right) with Axial-Bending Coupling Figure 1 above shows two example MBD simulations of a BHA with different weights-on-bit applied when drilling ahead in a vertical hole. The viewing angle is inclined to show the entire BHA. We can see the dynamic effects of increasing the

45 Klbf 60 Klbf


weight-on-bit from 45klbf (achieving a penetration rate of 50fph) on the left side, compared to 60klbf weight-on-bit (achiev-ing a penetration rate of 65fph) on the right side. On the left side, with less axial force, the BHA remains mainly in the center of the vertical borehole. On the right side, in-creasing the weight-on-bit moves the tension-compression neutral point up the string, and places more of the BHA into com-pression. This axial compression, combined with the drilling torque and high periodic bending loads from the bent motor, presses the drill string outward against the borehole wall. Friction in the BHA-wall contact initiates a backwards orbiting motion, further pushing the string against the wall. The result is the continuous generation of traveling helical waves propa-gating up the string. The waves are generated at a frequency that depends on the drilling torque and drill string rotation speed, but propagate up-string at a wave velocity that varies locally with axial load and local formation friction characteristics and also depends on the local drill string structural properties,. Note that the axial and torsional loads resulting from these traveling waves are asynchronous to the drill string rotation and pass at frequencies that are unrelated to any of the inherent linear mode frequencies of the various sections of the drill string. Non-Linear Example In Figure 2 we see the predicted lateral (North-South) displacement at the 16in string stabilizer approximately 40ft behind the bit in a vertical 17.5in borehole, which is just visible as the magenta-colored component above in Figure 1. The blue line shown below is for the lower weight-on-bit case on the left of Figure 1 and shows an unremarkable steady re-sponse at the BHA rotation frequency. The red line, however, for the higher weight-on-bit case on the right side of Figure 1, shows a much lower and unsteady frequency including multiple wall strikes. This kind of response is typically chaotic.

Figure 2. String Stabilizer Displacement for 45klbf (blue) and 60klbf (red) Weight-on-Bit Depending on exactly where and how the BHA is instrumented, and depending on how the signals are filtered, it might not be possible to identify this change in downhole response, even with continuous high frequency data being transmitted to sur-face from downhole.(8) The MBD simulation, however, clearly shows the change and can be used to determine good instru-mentation locations and to identify a dynamic “signature” for this event for the purpose of downhole detection.


Forensic Analysis of a Motor Twist-Off When drilling the tangent section of a 17.5” wellbore using a tri-cone bit and a 9-5/8” steerable motor with a 1.2º bend, the mud motor twisted off, as shown in Figure 3, at an internal connection near the top of the motor.

Figure 3. Twisted Off Mud Motor The drill bit is one primary source of BHA excitations, as are a mud motor or rotary steerable system when they are deployed within the drilling assembly. There can also be additional active drilling tools, e.g. under-reamers, roller-reamers, shock-subs or dynamic drag friction reducers that contribute to the overall dynamic behavior of a drill string. Ultimately, it is the drilling rig’s surface drive that puts most of the energy into the drill string, and so its feedback and control system also has a signifi-cant effect on the overall dynamic drill string response. In order to reliably simulate the dynamic behavior of a drill string and thereby detect or even predict the onset of a drilling dysfunction, it is important not only to understand the “normal” operating characteristics of the drill bit and other active drill-ing tools, but also to understand their dynamic characteristics when they are subjected to extraordinary dynamic loading and when they fail.(5) Mud Motor Characterization under Dynamic Loads Motor manufacturers provide charts for their mud motor’s steady state performance (flow rate, pressure drop, rotation speed and torque output) over the intended normal operating range. Sometimes the stall torque is also provided. For an accurate dynamic analysis of a drill string dysfunction, a more detailed understanding is needed of how the rotation speed, differential pressure and torque are related under dynamic loading, especially closer to the motor stalling. Such infor-mation is not generally published or, perhaps, even not known. A typical MBD code could effectively include such motor characteristics in a number of ways, either by hooking to an exist-ing systems model of the motor, by translating the motor’s system equations into the MBD model language or, in the event that a company does not wish to divulge the characteristics of their motors, by co-simulating with a proprietary model of the motor. For the purposes of the forensics modeling example shown in this paper, the steady state motor characteristics provided by the manufacturer were extended artificially from the operating range to the stalled values using simple quadratic functions as shown below in Figure 4.


Figure 4. Normal Operating Range Extended for High Dynamic Loading Parameterization of 3/rev Tri-Cone Drill Bit Excitations The precise nature of the excitations generated by the drill bit during both normal drilling and when the bit fails was not measured. Had this information been available it could have been included in the MBD simulation for greater accuracy. In the absence of such information, we developed a parametrically-defined, non-sinusoidal 3/rev factor on both the axial and torsional drilling forces produced by a bit sub-model. That is, the axial drilling forces were computed assuming a perfect bit, and then were multiplied by this factor to simulate the effect of bit damage. Since the drilling torque produced by the bit sub-model depends directly upon the axial load, the bit torque varied similarly. The purely lateral bit forces generated by the bit were not modified.

Figure 5. Simulated 3/rev Axial and Torsional Bit Force Factor


The overlay factor is parametrically defined as a shaped force “bump” with independently variable magnitude and duration, but that still averages to 1.0 over a full bit revolution so that the nominal weight-on-bit and torque loads are maintained. Multiple cases were run with different amplitude and duration excitation characteristics to investigate the influence of a failed bit on the drill string dynamics. Dynamic Motor Response Exciting the “extended” motor response shown in Figure 4 above with the simulated 3/rev bit forces shown in Figure 5 pro-duced the mud motor speed variations shown below in Figure 6.

Figure 6. Mud Motor Speed Variation for Low (blue) & Severe (red) 3/rev Bit Forces The mud motor speed variation depends highly nonlinearly upon the amplitude of the 3/rev bit excitation. For low amplitude 3/rev loads from the bit (blue), the motor speed only varied around 5rpm, whereas for higher amplitude 3/rev loads (red), above some threshold value, the variation of the motor speed increased markedly to greater than 50rpm.


MWD Detection of a Failed Tri-Cone Bit Figure 7 shows the surface rotating at around 110rpm (green), together with fundamental axial vibrations (blue) and torsional vibrations (green) at 3 times the bit rotation speed (equal to the sum of the surface and motor rotation speeds), around 8.5Hz, that were detected by the MWD vibration sensors.

Figure 7. Axial & Torsional Bit Vibrations (8.5Hz) Detected by the MWD Tool Rotating @110rpm Subsequently, when the surface rotation speed was reduced to around 55rpm, the axial and torsional vibration frequencies detected by the MWD vibration sensors were reduced to 7.1Hz as shown in Figure 8. Again, this reflects 3/rev of the bit ro-tation speed, equal to the sum of the surface and motor rotation speeds. Note also the 14.2Hz 6/rev harmonic in the axial re-sponse, and the fundamental BHA rotation frequency of 0.9Hz shown in the lateral vibrations.

Figure 8. Axial & Torsional Bit Vibrations (7.1Hz) Detected by the MWD Tool Rotating @55rpm

8.5Hz = 3/rev

7.1Hz

0.9Hz

14.2Hz

10 seconds

Formatted: Font: Times New Roman

Formatted: No underline


MBD Simulated BHA Response The BHA configuration, well path and drilling conditions for the surface rotation speed of 55rpm shown in Figure 8 were built into an MBD model of the BHA. The simulated BHA rotation speed response at the location of the MWD sensor in the non-magnetic drill collar, and its FFT, are presented below in Figure 9.

Figure 9. Simulated BHA Rotation Speed & Frequencies for Surface Rotation @55rpm

We can see in Figure 9 that the MBD simulated response captures very well the same frequencies as the MWD sensor in Figure 8, however the predicted peak-to-peak rotation speed variation at 6.9Hz shown in Figure 9 is only 15 rpm, as opposed to around 100 rpm peak-to-peak at 7.1Hz measured by the MWD tool (Figure 8, green). Note that the MBD simulation also reasonably predicts a large 1/rev component at 0.9Hz associated with the bent motor that is seen in the MWD data (Figure 8, red), as well as the 6/rev component at 13.8Hz which we can see in the MWD axial vibration data at 14.2Hz (Figure 8, blue). A likely explanation for the difference in the variation in rotation speed between the measured data and the MBD simulation is that the MWD rotation and vibration sensors are mounted on a centralized chassis located within a long flexible tube that is fixed to the drill collar at one end preventing any axial movement, but which leaves the chassis and tube able to flex torsion-ally and laterally within the drill collar. No information is readily available about the frequency response characteristics of the sensors or what filtering was applied to those signals. Clearly, more details about the MWD sensors’ mounting are needed to characterize the influence of the mounting structure on the data. Note that it is common in MBD-based analyses to actually build the instrumentation mount-ing hardware and signal conditioning into the model itself, so that simulation outputs and test data can be directly compared. Twisting and Bending Moments at Top of Motor Figure 10, below, compares the predicted twisting moment at the top of the bent motor where it connects to the string stabi-lizer early in the simulation when the 3/rev excitation is smaller (blue), to that later in the simulation when the 3/rev response is fully developed (red). Note that the magnitude of the underlying moment variation at 0.9Hz (1/rev at string rotation speed), which is caused by reactions between the formation and the rotating 1.2° motor bend in a straight hole, remains rela-tively constant at around 0.6kft-lbf (blue) for both scenarios, both without and with the fully developed 3/rev component. The 6.9Hz 3/rev component (red) adds around 4.5kft-lbf variation to the 1/rev component.

13.8Hz Bit 6/rev

6.9 Hz Bit 3/rev

0.9 Hz BHA1/rev


Figure 10. Torsional Load Variation at the Top of the Mud-Motor

Unlike the twisting moment shown in Figure 10 above, the lateral bending moments at the same location, shown below in Figure 11, are completely dominated by the 0.9Hz (1/rev) deflections caused by the motor bend and do not show any similar large increase when the 3/rev excitation is added (red) to the bending moment without the 3/rev excitation (blue).

Figure 11. Bending Moment Variation at the Top of the Mud-Motor


We might reasonably conclude from these MBD simulation results that the onset of severe torsional and axial 3/rev excita-tions from a failing tri-cone bit resulted in a high-cycle torsional load at the top of the mud motor which, when combined with the large dynamic bending moments produced by the motor bend, resulted in the fatigue failure and twist-off of an in-ternal motor connection near that location, as shown in Figure 3. Note that instrumentation which monitored only the bend-ing moments would not give any indication of an impending fatigue failure. Further, the model also shows that this high amplitude 3/rev response occurs in both axial and torsional directions, and should be easily identifiable at any location along the BHA. Depending on the well path, well bore friction and mud proper-ties, this clear dysfunction signature could even propagate up to the surface. From a practical perspective, because this response is exactly synchronous with 3 times the bit rotation speed, downhole torque sensor measurements could be tightly filtered at that frequency to identify the damaging dysfunction, with an alarm threshold set to capture any significant increase in the signal. Improved Surface Detection of Drilling Dysfunctions Using MBD Simulation Previous experience with instrumented top-drives has shown

(6) it is sometimes possible to identify certain types of drilling dysfunctions from surface data. The MBD models used for this work include detailed structural models, with contacts and friction between the drill string and the well bore, but only for the 291m of the BHA. A low-resolution dynamically equivalent upper drill string is included in the models with appropriate uncoupled axial stiffness, torsional stiffness and inertia properties, but without any wall contacts or friction. The choice to concentrate on BHA dynamics was made for the purpose of understanding BHA dysfunctions when a mud motor had twisted off, and does not reflect any inherent limitation in the MBD code. Predicting drill string responses at an instrumented top drive from an MBD simulation would require a more detailed drill string model, including wellbore friction, extended from the top of the BHA to the surface. How much detail in the upper drill string is required to capture the important dynamics, and at what level of discretization, are not yet known. The authors note that for MBD simulations of drill strings, the largest computational cost is in the contact and friction algo-rithms, not the structural dynamics. Simulation run times should scale linearly with the number of string segments in contact with the well bore at any one time. Therefore even very long strings in vertical wells, where contact is isolated or intermit-tent, should run quickly. Long inclined or horizontal sections where most of the string is lying against the formation or cas-ing will run more slowly. Virtual Instrumentation and Visualization of Simulation Results Finding effective ways to visualize and understand the abundant response data available from a MBD simulation is non-trivial. Having too much data is a problem with which most drilling engineers are unfamiliar. We may sometimes need to look at the dynamic response of the entire BHA, or the entire drill string, at sampling rates up to 200Hz and in multiple di-mensions, to gain better physical insights into the salient physics. The standard multivariable strip-chart plot formats com-monly used in the industry are inadequate for this purpose. Interpreting large quantities of simulation data is a familiar problem in many other industries. Often, a graphical animation of the simulated response is very useful for understanding what is happening on the system level. Unfortunately, drill strings have extremely high aspect ratios, often greater than 1000:1, so even imaging the full response is challenging. Worse, looking at just a small piece of the string, or using unequal scaling in one dimension can give misleading impressions. In Figure 12 below, we see three snapshots of a simulation of the same drill string, at the same time in the same vertical hole.

• In the leftmost view, we have a true-scale, true-lateral view of the lower 100 feet of the string. In this view, no dy-namic response is visible at all.

• In the center view, the viewpoint is inclined 70° (to 20° from straight up), and we can now see the full 291m of BHA. The response appears to be a long wavelength lateral vibration mode.

• Only in the rightmost view, where the viewpoint is only 2° from vertical, can we begin to see the real character of the response, which has a helical shape with variable helix spacing.

• Finally, it is only by animating the response that we can see its true dynamic character, that of a helical traveling wave propagating up-string a varying speeds.


Figure 12. Three views of the same BHA response Another way to look at a BHA simulation output is to plot particular responses along the full length of the BHA at a specific time. For example, in Figure 13 we have a snapshot of both magnitude and orientation of the bending moment from the twist-off example, as a function of distance behind the bit at a single time. The marked locations are the bottom of the non-magnetic drill collars and the middle of the shock sub.

Figure 13 – Plots of Drill String Bending Moment (top) and Orientation (bottom)


In Figure 14 below, we have extended this approach by plotting the bending moment from the twist-off case on the vertical Z-axis, distance behind the bit along the X-axis, and adding four seconds of time along the third Y-axis. This allows us to see how the bending response changes while drilling.

Figure 14. 3-D Plot of String Bending Moment vs. Time and Position We again see the strong 1/rev (at string speed) variation in the moments, which peaks just above the string stabilizer. The secondary bending moment peak at ~180 feet behind the bit is associated with the shock-sub, which is much stiffer in bend-ing than the drill string components above and below it. A running animation of this plot, serving as a “sliding window” on the response, could give additional physical insights into the drilling dynamics and how they develop and change character over time. There are other possible ways to plot these kinds of results. For example, surface color could be separated from the Z-axis and used to plot a 4th dimension. When searching for response at particular frequencies, 2-D periodograms, which are a type of contour plot where the coloring represents the 3rd dimension, are often used in spectral analysis and can sometimes offer useful insights. Future Directions During this initial effort to apply multi-body dynamics (MBD) methods to drilling problems, a number of areas likely to pro-duce important results in future research were discovered. Two of these areas – accurate dynamic modeling of downhole motors and better modeling of downhole sensor systems, including mechanical mounting, frequency response characteristics and signal conditioning, have already been discussed above. Three other areas of probable value are listed here:


• Improved functional characterization of the forces generated at the bit-rock interface – In a system-level MBD mod-el of a working drill string, it is not required to have a highly detailed local model of the rock destruction mecha-nism. However, the simplified functional model used in this work can be improved to better handle off-nominal and off-axis drilling conditions as well as worn and damaged bit conditions.(7)

• Incorporation of realistic sub-systems models of the top-drive and hookload systems controlling both string rotation

speed and weight-on-bit. The simulations have shown that the dynamics in these two subsystems have a very strong effect on the overall string response. The existing model uses analog proportional-integral-derivative (PID) control-lers in both directions. Gains were tuned to get realistic-looking responses and robust computational performance. They do not correspond to any actual controls.

• Better characterization of the stiction/friction in the string-wall contacts, both against the formation and against cas-

ing, noting that these may also depend on the local drilling fluid properties and solids content. As mentioned, the MBD model is already set up to allow for varying these parameters as a function of depth.

Work continues to improve the user interface and make multi-body dynamics more accessible to the drilling engineering community, increase the computational speed, and further validate against different types of drilling dysfunctions. Conclusions

• A multi-body dynamics (MBD) simulation approach provides the drilling engineer with a capability to predict non-linear, highly-coupled and intermittent dynamic phenomena that commonly occur during drilling. Simulations can be used to help interpret drilling dysfunctions from downhole sensor measurements, and to predict the effectiveness of changes in drilling controls for mitigating such dysfunctions.

• When drilling a vertical hole with a bent motor, the bit and motor assembly will exhibit forward synchronous whirl.

Depending upon the weight-on-bit and motor torque, the BHA above the motor can contact the borehole wall and begin orbiting backwards, creating helical traveling waves propagating up the drill string at varying velocities. The non-magnetic drill collar, typically located directly above the mud motor, where these two dynamic phenomena meet, can experience chaotic motion and severe shocks.

• The simulations presented in this paper demonstrate how a progressive bit failure and the associated combination of

axial and torsional vibrations exceeded a threshold which changed the character of the drill string dynamics. This re-sulted in substantial high-cycle torsional loads that combined with a large variation in bending moment. This mech-anism ultimately resulted in a fatigue failure and twisting off of a mud motor at one of its internal connections.

• An effective method for the early detection of bit failures and potentially prevent twist-offs, sidetracks and fishing

trips would be to set an alarm threshold for torsional response filtered at a frequency that is the appropriate integer multiple of bit rotation speed (i.e. three/rev for tri-cone bits or the N/rev for PDC bits, where N is number of blades). This torque can be measured anywhere in the BHA.

• Drilling sensors located at a single BHA location are inadequate for characterizing certain types of dynamic drill

string motions. Synchronized sensors located at multiple appropriate locations along a drill string may be required.

• Because of the faster MBD solution speeds, as compared to nonlinear finite element methods, investigations of the performance of different BHA designs from multiple wells and under varying operating conditions are possible.

• The flexing of some probe-based MWD assemblies located inside long pressure barrels may exaggerate or attenuate

the measurements made. For proper model validation, the MWD sensor mounting structure, frequency response and signal conditioning can be included into the MBD model as an appropriate way to compare the predicted drill string response to measured data.

• Multi-body simulations can incorporate, when necessary, more detailed structural compliance of critical parts using

existing finite models for drill string components such as drill bits, mud motors, rotary steerables, under-reamers, roller-reamers, shock-subs and dynamic borehole friction reducers. The system controllers for top-drives, motor drives and drawworks are also easily incorporated into MBD-based models. With more detail about the internal de-sign of drilling tools, and by appropriately combining multi-body dynamics with finite element and systems models, potential vulnerabilities within BHA components can be identified and fatigue life can be more accurately estimated.


• The use of multi-body dynamics for virtual prototyping and testing of downhole drilling tools offers improved de-sign confidence, reductions in development cycles and less time and cost on expensive trials. Such cost savings have already been substantiated in the automotive and aerospace industries.(9)

• The insights into the physical drilling process that can be achieved through multi-body dynamics can yield improved

operating techniques, help avoid various costs associated with drilling dysfunctions, and enable higher efficiencies with better overall drilling performance. (6)(10)

Acknowledgements The authors would like to thank Perenco for giving permission to use their field data for the purpose of the simulation of a motor failure that is presented in this paper. References

1. Hanno Reckmann, MWD Failure Rates Due to Drilling Dynamics, SPE/IADC-127413, IADC/SPE Drilling Con-ference and Exhibition, February 2010, New Orleans, LA.

2. Dykstra, M.W et al., Experimental Evaluations of Drill Bit and Drill String Dynamics, SPE-28323, Annual Tech-nical Conference and Exhibition, September 1994, New Orleans, LA

3. Liu, C.S., Monkaba, V., Lee H., Alexander, T. and Subramanyam, V., Co-simulation of Visteon Driveline Torque Bias Controls, Visteon Corp. 2001 MDI North American Users’ Conference, Novi, MI.

4. Sellberg, R., A Holistic Approach to Heavy Truck Suspension Development, Hendrickson Truck Suspension Sys-tems. 2006 MSC Virtual Product Development Conference, Huntington Beach, CA.

5. Lesso, W., Testing the Combination of High Frequency Surface and Downhole Drilling Mechanics and Dynamics Data Under a Variety of Drilling Conditions, SPE/IADC-140347, SPE/IADC Drilling Conference and Exhibition, March 2011, Amsterdam, NED.

6. Macpherson J.D. et al., Application and Analysis of Simultaneous Near Bit and Surface Dynamics Measurements, SPE-74718, Drilling & Completions, Volume 16, Number 4, December 2001.

7. Endres, L.A., Computation Modeling of Drill Bits: A New Method for Reproducing Bottom Hole Geometry, Ph.D. dissertation, 2007, Univ. of California, San Diego, CA

8. Horne, J.H., Baliunas, S.L., A Prescription For Period Analysis Of Unevenly Sampled Time Series, Astrophysical Journal 302:757-763, 1986.

9. Ryback, H., Simulation Driven Design, IBM-MDTVISION. 2007 MSC EMEA Virtual Product Development Con-ference, Frankfurt, DEU.

10. Heisig, G, et al., Downhole Diagnosis of Drilling Dynamics Data Provides New Level Drilling Process Control to Driller, SPE-49206, SPE Annual Technical Conference & Exhibition, September 1998, New Orleans, LA

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