Journal of Energy Resources Technology Volume 130 issue 4 2008.pdf

8/10/2019 Journal of Energy Resources Technology Volume 130 issue 4 2008.pdf

1/12

David W. Raymond

Sandia National Laboratories,Albuquerque, NM 87185

M. A. ElsayedUniversity of Louisiana at Lafayette,

Lafayette, LA 70504

Yarom Polsky

Scott S. Kuszmaul

Sandia National Laboratories,

Albuquerque, NM 87185

Laboratory Simulation of Drill BitDynamics Using a Model-BasedServohydraulic Controller

Drilling costs are significantly influenced by bit performance when drilling in offshore

formations. Retrieving and replacing damaged downhole tools is an extraordinarily ex-pensive and time-intensive process, easily costing several hundred thousand dollars ofoffshore rig time plus the cost of damaged components. Dynamic behavior of the drillstring can be particularly problematic when drilling high strength rock, where the risk ofbit failure increases dramatically. Many of these dysfunctions arise due to the interactionbetween the forces developed at the bit-rock interface and the modes of vibration of thedrill string. Although existing testing facilities are adequate for characterizing bit per-

formance in various formations and operating conditions, they lack the necessary drillstring attributes to characterize the interaction between the bit and the bottom holeassembly (BHA). A facility that includes drill string compliance and yet allows real-rock/bit interaction would provide an advanced practical understanding of the influence ofdrill string dynamics on bit life and performance. Such a facility can be used to developnew bit designs and cutter materials, qualify downhole component reliability, and thusmitigate the harmful effects of vibration. It can also serve as a platform for investigating

process-related parameters, which influence drilling performance and bit-induced vibra-tion to develop improved practices for drilling operators. The development of an ad-vanced laboratory simulation capability is being pursued to allow the dynamic propertiesof a BHA to be reproduced in the laboratory. This simulated BHA is used to support anactual drill bit while conducting drilling tests in representative rocks in the laboratory.The advanced system can be used to model the response of more complex representationsof a drill string with multiple modes of vibration. Application of the system to fielddrilling data is also addressed. DOI: 10.1115/1.3000142

The Drill Bit Vibration Problem

The drilling industry has developed comprehensive test facili-

ties to characterize bit performance for the challenging environ-

ments encountered downhole. These facilities have resulted in im-

proved understanding of the physical interaction between the bit

cutting elements, the rock, and even wellbore hydraulics. These

laboratory-based characterizations have given birth to high perfor-

mance bits that can effectively drill soft to hard rock formations

under precisely controlled operating conditions.

However, field drilling conditions can result in downhole con-

ditions that are drastically different from the preferred operating

conditions typically encountered in the laboratory. The bit can

interact in a complex way with the constraints of the formation

and the bottom hole assembly, resulting in a range of vibration

modes being excited in the drill string. In harder formations, these

vibrations can cause cutter damage and even complete failure of

the bit cutting structure. This bit damage is often accompanied by

significant economic losses due to the nonproductive time in-

curred while tripping out of the hole to replace the bit. The vibra-

tion problem becomes especially frequent in deeper and harderformations. Hence, drill bit dynamics are limiting factors in the

use of high performance bits and related tools for drilling hard

rock formations.

The phenomena of drill string vibrations and their effect on

drilling performance have been the subject of extensive analytical

and field investigation for almost 50 years. The development ofanalytical representations of drill string axial and torsional vibra-

tions to identify critical modes was initially pursued by research-ers 1,2. Over the years, drill string vibration models were ex-panded to include numerous additional physical behaviors

including lateral vibrations whirl and mode coupling 35.Many other researchers developed models designed to quantifyvibrational instability regimes arising from coupling of rock/bitinteraction and vibration of the drill string 68.

Over the years, many field investigations measuring drill string

vibrations at the surface have also been conducted 9,10. Moreinvolved efforts have also been completed using downhole instru-ments to measure vibration near the drill bit in order to validatevibration models11. Unfortunately, field testing does not neces-sarily provide the most efficient venue for providing the experi-mental data to corroborate the massive amount of study that hasbeen devoted to understanding the influence of vibration on drill-

ing. In particular, field investigation tends to be very expensivebecause of the high operating costs associated with drilling a holethat can be many miles deep. Moreover, the environment presents

many uncontrolled variables such as lithological uncertainty asso-ciated with the complex geologies encountered as well as otherunknowns associated with the application. What is desirable is tosomehow shrink the multiple thousands of feet of drill string andother BHA components into a laboratory-scale rig in order to pro-vide a more controllable environment in which to study the mul-tiple modes of vibration and their impact on the drilling process.This capability does not currently exist. Consequently, present daybits are not dynamically robust enough for the impact conditionsthey encounter in the field, simply because they have not beenproven for these loads in their development process. Given thecomplex nature of bit cutting structures in use throughout theindustry, a laboratory simulation capability is needed to reproduce

Contributed by the Petroleum Division of ASME for publication in the JOURNAL OF

ENERGY RESOURCES TECHNOLOGY. Manuscript received June 18, 2008; final manu-

script received September 5, 2008; published online November 24, 2008. Review

conducted by John Rogers Smith. Paper presented at the 26th International Confer-ence on Offshore Mechanics and Arctic Engineering OMAE2007, San Diego, CA,June 1015, 2007.

Journal of Energy Resources Technology DECEMBER 2008, Vol. 130 / 043103-1Copyright 2008 by ASME

wnloaded From: http://energyresources.asmedigitalcollection.asme.org/ on 11/23/2013 Terms of Use: http://asme.org/terms


2/12

the dynamic behavior of field drill strings in the laboratory. It isthe purpose of this work to outline the critical elements requiredto develop this capability as well as to report a series of proof-of-concept experiments that have been performed to demonstrate itsviability.

Laboratory SimulationObjectives.The purpose of this drilling simulation is to repre-

sent the dynamic motion of the drill string in a controlled labora-tory setting accurately reflecting field drilling conditions so thatthe bit response may be monitored, characterized, and improvedbefore committing the bit and drilling tools to expensive fielddrilling operations. Ideally, one desires to simulate the propertiesof any drill string in the laboratory and evaluate the response of acandidate bit in a representative rock sample. This approach, il-lustrated in Fig. 1, would allow a bit to drill the formation andrespond as if it is drilling at depth. There are several motivationsfor development of this capability. It will allow the drilling indus-try to 1 develop an advanced practical understanding of the in-fluence of drill string dynamics on bit performance and life thatwill be used to improve and optimize bit designs, 2 identify de-

ficiencies in drill bit material properties and designs as represen-tative impact loadings that occur in the field can be reproduced inthe laboratory, 3 validate development of hardware and method-ologies that can be used to introduce stability to the drilling pro-cess to eliminate drill string dynamic dysfunctions, and 4use thecapability as a proving ground to determine best practices to prop-

erly handle dynamic dysfunctions when they occur.

The dynamic range where the complications occur must be

identified for these drill string representations to be meaningful.

Drill strings vary dramatically in their properties depending on

their geometry, depth, well profile, and surface support. Conse-

quently, drill string modes of vibration exist in broad ranges. Za-mudio 12 showed fundamental modes of vibration in the sub-hertz level to tens of hertz for a 7200 ft model of a drill string.

Jogi et al.11 measured vibrations below 100 Hz for a relativelyshallow depth. Wise et al. 13 measured similar vibrations usinga downhole diagnostics tool. These vibrations are observed at the

bit in the longitudinal, rotational, and lateral axes. The present

work addresses modes of vibration up to 100 Hz. The larger fre-

quency modes will typically have smaller amplitudes and accord-

ingly less energy. To accurately reflect reality, vibration modesshould be included in all axes. However, for the purposes of thispaper, the scope is limited to the representation of the axial modeof the drill string. If a realistic simulation can be accomplished in

the laboratory, obtaining these objectives will be of significantbenefit to the drilling industry.

Mechanical Analog Versus Model-Based Control. To under-

stand how a drill bit specified for a given drill string applicationwill respond in a particular formation requires a capability to re-produce a broad range of drill string attributes. The properties of afield drill string can be simulated in the laboratory using either a

mechanical analog or model-based control. These two approachesare illustrated schematically in Fig. 2. In the mechanical analogapproach, drill string vibration is introduced using a mechanicalsystem that has a dynamic response simulating simplistic models

of a drill string, for example, a single degree of freedom spring-mass-damper, or a system of spring-mass-dampers, that replicatesthe dynamic response of the desired system in narrow frequencybands.

In the model-based control approach, motion of the drill stringcorresponding to a bit force is predicted using a computational

Fig. 1 Laboratory simulation of drilling dynamics

Fig. 2 Mechanical analog versus model-based control

043103-2 / Vol. 130, DECEMBER 2008 Transactions of the ASME



3/12


4/12

parameters. There are, however, numerous limitations to labora-tory simulation using a mechanical analog. The mechanical analogis a single point representation that is not amenable to emulatingthe varying properties of the drill string over time, such as the

increase in length and compliance as more pipes are inserted intothe hole. Mechanical analogs also tend to be very time consumingto exchange in the setup and have obvious cost implications withrespect to maintaining the hardware necessary for a large range ofcompliance conditions Furthermore, since the damping is inherentin the type of analog used, it is difficult to precisely control thelevel of damping present in the system. For these reasons, simu-lation of the drill string properties using model-based control isdesired.

Simulation by Model-Based Control

Approach.The intent of simulation using model-based controlis to reproduce the dynamic properties of potentially any drillstring without the limitations of a mechanical fixture, as describedabove. The approach is to computationally model the drill string

and allow real-rock-bit interaction to generate the forces to beused as input to this model and then predict, or prescribe, how thesystem should respond to these forces. It then becomes a matter ofenforcing the correct displacement at the interface between the bitand BHA using fast-acting actuators such that the bit feels as ifit is in the hole at depth. The drilling function is performed by anactual bit in a representative rock sample, yet the bit will behave

as though it were attached to a long flexible drill string specified atthe users discretion. A schematic of the approach is shown in Fig.

6.

The former drilling facility was modified and used to demon-

strate a prototype system using this approach. As in the mechani-cal analog, model-based control comprises two primary equip-

ment subsystems: a drilling simulator and a dynamics simulator.

The drilling simulator consists of the drill rig gantry with the

vertically traversing frame. The dynamics simulator supports the

drill bit and possibly a BHA tool in future implementations andproduces the dynamic compliance of the drill string at the bit

using fast-acting actuators that are controlled by a model of the

drill string. The vertically traversing frame is used to support the

dynamics simulator, analogous to how fixed-compliance was ac-

commodated in the mechanical analog.

System Development. To develop a competent simulation us-

ing model-based control requires attention to several areas. These

include simulation requirement definition, predictor development,

dynamics simulator development, servohydraulic system selec-tion, and controller development.

Each of these items will be addressed separately along with the

approach to implementation of these in a prototype system. These

topics are coupled and their appropriate integration results in a

system that meets the performance objectives.

Simulation Requirement Definition. The relationship between

Fig. 5 Effect of drill string dynamics on bit response and resulting rate ofpenetration

Fig. 6 Model-based control approach




5/12

the forces applied to a particular drill string and its displacementresponse must be understood to define performance requirements

for the system. In the context of Fig. 2, the frequency response

function FRF, G, of the drill string must be known, so its re-sponse can be predicted when it is subject to an arbitrary bit force.

The relationship could be determined from a computational modelconsisting of simple formulations or a complex representation of adrill string, depending on the fidelity of response required. Fielddata of representative configurations can also be evaluated to un-

derstand these requirements. The displacement response should becharacterized as a function of the bandwidth of the system. The

initial objective for a prototype system was to reproduce the re-sponse seen in the mechanical analog fixture. This required a peak

displacement of approximately 0.5 in. from static to 5 Hz.

Predictor Development. The drill string model is the driver inthe drilling dynamics simulator. When the bit encounters a reac-tive force from contact with the formation, the model predicts

how the drill string would respond to that force. It can be a com-putational model or any rule-based method that specifies the re-sponse based on input parameters.

Some available computational modeling approaches for a pre-

dictor include transfer function representations, finite elementanalysis methods, wave propagation formulations, and normalmode analysis. With selection of a reasonable time increment fornumerical integration in these models, desktop computers can pre-

dict future displacements very quickly enabling real-time updating

of the actuator controllers. The complexity of the model utilized isprimarily limited by the computational ability to provide a solu-tion in time to update the controller. The appropriate level of

spatial discretization necessary to reasonably reflect the vibra-tional behavior of the drill string can be determined through sen-sitivity analysis, which can also be utilized to optimize time dis-

cretization for control purposes. Preliminary work in this areaindicates that fairly simplistic representations can be used to cap-ture the dominant modes of vibration. A normal mode solution hasbeen incorporated for a predictor and is presented in further detail

later in this paper.Field data can also be used as a predictive driver. This would

allow vibrations encountered in production drilling operations tobe reproduced. Using measurements of bit forces and the resulting

response, the systems identification method could be used to de-

velop frequency response functions for the drill string. Systemsidentification is a linear regression technique used in controlstheory. It allows a representative model of the system to be devel-

oped by assuming a model order and using regression analysis tosolve for the algebraic coefficients in the model. The order of thesystem is verified by reducing the least squares error between fitand actual data in the regression analysis.

In a real drill string, the relationship between input and outputvariables can easily manifest itself as a nonlinear relationship. Theversatility of the model-based control approach is that it allows

the predictor to be chosen to represent any user-specified drillstring and then addresses the ensuing response using the physicalsimulation.

Dynamics Simulator Development. To simulate the dynamic re-sponse on a particular axis of a drill string requires that the labo-ratory system be configured with actuators that can produce dy-namic displacements on that axis with amplitudes mandated bythe predictor. The development of the dynamics simulator mustaddress the mechanical design of the drilling equipment, the con-figuration of the actuators to produce the required dynamic re-sponse, the rock containment system, and the sensors used tomonitor the mechanical response of the system. The mechanicaldesign of the prototype system was a modification to the drillingsystem described above with the fixed-compliance system re-moved. To achieve the required system response, the dynamicmass of the top drive system had to be reduced by decoupling it

from the load head. The top drive sits on a 12 in. wide structural

steel channel and is supported by two 8 in. channels. The 8 in.wide channels were slotted to allow for relative motion of the topdrive system. This reduced the effective mass of the system andallowed axial motion of a lighter mass to be introduced. The sys-tem could have been configured with a lighter top drive to extendthe frequency response, but the complexity of the system wouldhave required a large system rebuild. As shown in Fig. 7, theactuators are configured within the load path between the topdrive beam and the vertically traversing beams to enforce therequired displacement of the bit relative to the rock.

Figure 6 shows a measurement sensor at the interface betweenthe bit and the dynamics simulator. It measures both the reactionforce transmitted from the bit and the displacement response. Theforce measurements are inputed to the predictor to determine therequired response of the drilling system to the drilling load. In theprototype system, the measurement sensor is integral to the actua-tors described below. The actuators feature an integral strain-gauge based load cell and an embedded displacement sensor lin-ear variable differential transformer LVDT. The measureddisplacement can be used as input to the controller to assess theaccuracy of the response relative to predictor requirements.

The rock sample must be properly restrained so that is does nothave any additional compliance that feeds back into the responseof the bit. In the drilling facility, the rock is clamped at its base ona structural steel pallet that is clamped in place against an over-

head plate. If pressurized containment is used, then the seal fric-tion on the drill string must be accounted for in the dynamicresponse of the simulator.

Servohydraulic System Selection. The appropriate motive forcetechnology must be identified to motivate the dynamics simulatorwith a bandwidth consistent with the output of the predictor. Ser-vohydraulic actuators are the only motive-force technology avail-able to accommodate the forces and displacement-bandwidth ap-plicable to this problem 16. However, these motions are subjectto the additional overhead in mass and friction imposed by themechanical system that supports the bit and top drive. Hence, theactuators must be selected to be an integral part of the overallsystem. The actuators have both static and dynamic force require-ments since they operate in series with the load path.

Servohydraulic actuators powered by a 30 hp hydraulic power

unit were chosen for the prototype system. They are typically usedfor modal excitation analysis on large structures. They are com-pact and easily integrated into the drilling fixture, as shown in Fig.7, to accomplish the dynamics simulation. These specific actuators

produce 1000 lb across a dynamic range of static to 100 Hz. Theactuator force and displacement capability versus bandwidth isshown in Fig. 8. The actuators are able to reproduce any transientsignal that lies beneath these envelopes.

Controller Development. The development of the overall sys-tem must also address the development of the controllers thatdrive the actuators in the dynamics simulator to produce the re-sponse mandated by the predictor. The actuators must accelerate

Fig. 7 Dynamics simulator for model-based control

Journal of Energy Resources Technology DECEMBER 2008, Vol. 130 / 043103-5



6/12

the mass of the top drive and also drive the bit against the rock inresponse to the required model dynamics. The actuators are oper-ated in stroke-control mode, since a displacement is enforcedbased on the output from the predictor. The approach to integratethe controller that drives the dynamic simulator was to have a

system run in parallel completely autonomous from the drillingfunction performed by the drilling simulator. This is synonymouswith how drilling takes place in the field, i.e., the drill stringresponds based on its dynamics properties regardless of how thedrilling system is controlled. This autonomous system samples theforce measurements from the measurement sensor, sends them to

the predictor, transmits the predicted command to the controller,

and the controller sends a command signal to the actuators.

System Configuration. The basic system configuration con-

sists of the servohydraulic actuators with the companion analog

controller that drives the spool valve on the actuator, and the

desktop computer equipped with software that is used for data

acquisition and control. A data acquisition card is used to monitor

the force and displacement measurements from the embedded sen-

sors on the actuators. The software application monitors the forces

from the load cell, inputs these to the predictor model, and then

uses the predicted displacement values to output a voltage to drivethe displacement of the actuators in stroke-control mode. A sam-

pling rate of 5000 Hz is used resulting in a solution time average

of 200 ms/step. The output signal is sent to the analog controllers,

which in turn control the response of the actuators. The voltage to

drive the actuators to get the required displacement must be speci-

fied. Hence, a transfer function is required for the actuators so

they can input the proper control signal to achieve the desired

response. Testing was conducted to characterize the frequency re-sponse of the actuators when they are used to drive inertial masses

that represent the dynamic mass of the top drive.

Some dynamic mass must be moved to accomplish the simula-

tion. This mass includes the top drive, rotating drill string, bit, and

other components comprising the dynamics simulator. The

displacement-bandwidth relationship for the overall system is a

function of this mass. Too much dynamic mass in the system willlimit the ability to meet the requirements for the simulation.

Testing was also conducted to characterize the frequency re-

sponse of the actuators when they act against an elastic founda-

tion. As the bit enters the rock, it is decelerated by the rock pen-

etration reaction. The bit is driven by the actuators, which are in

stroke-control mode, so the actuator force must be large enough to

allow the bit to penetrate the rock in accordance with model pre-

dictions.

Overall System Transfer Function. Shake testing was con-ducted on weights representing the dynamics simulator to develop

a transfer function for the overall system that can be used to

control the actuators. A typical displacement-time history response

is shown in Fig. 9. A chirp input signal was provided to the ac-

tuator controller and the response of the system was observed.

This information was used to develop a transfer function for thedynamic simulator when motivated by the servohydraulic system.

For a 212 lb mass, the response of the system starts to fall off after

about 8 Hz.

A transfer function for the displacement of the servohydraulic

actuators as a function of driving voltage was derived using sys-

Fig. 8 Force capacity and displacement response for servohy-draulic actuators used in simulation 17

Fig. 9 Input voltagetopto actuator controller and actuator displacement responsebottom




7/12

tems identification. The resulting function is shown in Fig. 10.

This was derived from the data in Fig. 9 for 04 s before thesystem response starts to drop off corresponding to a frequencyrange of 010 Hz.

However, the inverse of this transfer function is needed to getthe actual driving voltage applied to the actuator to enforce thecorrect displacement response. The block diagram shown in Fig.11 is used to produce the inverse of the transfer function in Fig.10. This system is inputed into the controller software to controlthe actuators in stroke-control mode.

Proof-of-Concept Demonstration

With the exception of the predictor, the other components of the

system have been prepared for a simulation. A transfer functionfor the drilling facility equipped with the mechanical analog canbe characterized to develop a predictor, or drill string driver, for aproof-of-concept demonstration using the model-based control ap-proach.

Predictor for the Mechanical Analog. A model for this systemi.e., a frequency response functionwas derived by impacting theend of the drill string when the mechanical analog was in placewith an instrumented hammer. Time histories of the impact forceon the hammer and the resulting displacement of the bit are mea-sured. A FRF is derived by taking the ratio of these two quantitiesin the frequency domain. This is shown by the solid lines in Fig.12.

The drilling system with fixed-compliance acts like a simpleharmonic oscillator. Accordingly, system-specific values of stiff-

ness, mass, and damping can be expected to form a reasonablecharacterization damping was derived by logarithmic decrement.However, when this is done, there is a poor agreement betweenthe predicted and measured frequency response functions. Thesystem has extra apparent stiffness in the response of the drillstring due to the stiction between the bearings and guide shaftsthroughout the system. Using an artificially higher stiffness e.g.,5500 lb / in. results in a better fit, as shown in Fig. 12. This fre-

quency response function1 / 5500 / 0.0007562s2 +0.01s + 1 will

be used to generate results for comparison to the mechanical ana-

log system.

Implementation.The foregoing developments are used to con-

duct a model-based control simulation using the frequency re-

sponse function shown in Fig. 12 as a predictive driver. To dem-onstrate that a model-based control simulation approach can beused to reproduce drill bit dynamics, a proof-of-concept demon-stration was conducted in a static load frame prior to integrating it

into the drilling function. This required that the actuators be re-configured. One of the actuators was used to generate a WOBforce profile by loading it against a rigid frame. This force wasmeasured, the FRF was used to predict the response of the drill

string, the voltage to produce this response was determined andsent to the actuator, the response of that actuator was monitored,and a comparison was made to the predicted value from the

model. This was done using the controller software and incorpo-rated the previous control system characterizations. The approachis shown in Fig. 13. The only difference from an actual drillingsimulation is that the bit force was generated using a secondary

actuator as opposed to actually drilling and using bit forces. Thisallowed the response of the system to be evaluated against aknown input.

The predicted response and the error in the measured response

of the actuators are compared for a bit force in the form of a chirpin Fig. 14. Favorable results are obtained with the measured re-

sponse following the driver with an error of less than 0.010 in.over the response range. This is for an open loop control algo-rithm, i.e., there is no real-time comparison between the displace-

ment results from the servohydraulic actuator and the predictor tocorrect the input to the dynamics simulator. More accurate resultscould be obtained with feedback control. Nevertheless, based onthis success, the proof-of-concept demonstration advanced to a

drilling system configuration.

Drilling Tests.The drilling test follows the same approach usedin Fig. 13 only instead of forcing the system with another actua-

tor; an actual drilling test was conducted. This approach allowedthe fixed-compliance drilling results to be reproduced for a proof-of-concept verification. The displacement response of the bit andits corresponding fast Fourier transform FFT are shown in Fig.

15. The drilling conditions are 275 lb WOB at 135 rpm in SierraWhite Granite. The dominant mode of vibration at 5 Hz is clearlyevident. This response compares favorably with the measured

transfer function for the mechanical analog shown in Fig. 12. Notethat there are some other frequencies with weak amplitude thatcome into play. These other frequencies with small amplitude maybe due to the excitation of other modes of vibration in the system

e.g., structural vibration modes. This simulation has established

Fig. 10 Transfer function for the servohydraulic actuator de-rived using systems identification

Fig. 11 Block diagram to determine control voltage for a given displacement




8/12

Fig. 12 Transfer function for the mechanical analog bold lines represent measured data; dashedlines are fit

Fig. 13 Implementation of the simulator to produce a given response for a drill string

Fig. 14 Agreement between the predicted and measured displacements for the proof-of-conceptdemonstration




9/12

the viability of model-based control as an advanced means ofstudying drill bit dynamics. Unlike the previous approach, model-based control is not limited to simple modes of vibration, dampinginherent in the mechanical analog, or single point design con-straints. This approach can be used to more thoroughly evaluatebit, drill string, and rock interactions. The method is now appliedto more advanced representations of a drill string.

Advanced Drill String Representation

Normal Modes Model. A drill string model that is common inthe literature 12 is a normal mode characterization of a drillstring comprised of 7200 ft of 4-1 / 2 in. diameter drill pipe and

780 ft of 6-1 / 2 in. diameter drill collar. The properties of the rigsupporting this drill string are also modeled at the top of the drill

Fig. 16 Dominant modes from the normal mode model used in predictor

Fig. 15 Bit response for the proof-of-concept drilling test in the time andfrequency domain




10/12

string. The normal mode model was prepared by discretizing thissystem into a series of spring mass elements. The traveling block,

swivel, and kelly are represented by a mass of 22,600 lb, and thedrawworks cable with spring stiffness of 52,500 lb/ in. The

7200 ft drill pipe section is modeled using 19 lumped mass com-

ponents with a mass of 5600 lb and a stiffness of 28,000 lb / in.The interface between the drill pipe and drill collar is modeled

using a mass of 7720 lb and a stiffness of 28,000 lb / in. The drillcollar section is modeled using seven lumped mass components

with a mass of 9800 lb each and a stiffness of 700,000 lb / in.Rayleigh damping is used to apply uniform damping through-

out the model. The assumption of proportional damping is com-monly used in structural applications and facilitates diagonaliza-tion of the system of equations. It is also standard in manycommercial finite element modal analysis software programs. Thisnormal mode model has been implemented into the model-basedcontrol systems as a predictive driver. Zamudio 12indicated that

the response of the system is dominated by the six most compliant

modes in the system. This reduced system, shown in Fig. 16, is

used as a predictor.

Drilling Tests. Drilling tests were conducted with this normal

modes model using the 3-1 / 4 in. diameter bit shown in the inset

of Fig. 3 in a sample of Sierra White Granite. A snapshot of the

drilling record results obtained at a nominal WOB of approxi-

mately 500 lb at 120 rpm is shown in Fig. 17. The look and feel

of an actual field drilling record are clearly evident and in stark

contrast with typical laboratory drilling records. The cyclic nature

of the drilling is dominated by the lowest mode of the system. The

total force on the system does not exceed the combined static and

dynamic force limitations of the servohydraulic system, i.e., the

system is not force limited when the bit impacts the rock. The

displacement response of the bit is shown in Fig. 18 where the

FFT magnitude is also shown. The bit response is dominated by

Fig. 17 Drilling record from the model-based control simulation using the normal mode predictor

Fig. 18 Bit response with the normal mode predictor in the time and fre-quency domain




11/12

the fundamental mode of vibration, despite applying a 1 / 10 scalefactor to this mode. The second mode is slightly apparent in theFFT. The higher modes have significantly greater stiffness result-ing in low amplitudes of vibration contributed to the bit response.The higher frequency modes will be reproduced provided theiramplitude is consistent with the capabilities of the system. Themagnitude of the frequency response function from the normalmodes model is shown in Fig. 19. It also shows that the system isdominated by the more compliant low frequency modes. Thesimilarity between the FFT of Fig. 18 and the frequency responsefunction in Fig. 19 attests to the success of the implementation ofthe advanced drill string representation using the model-basedcontroller.

Summary and Conclusions

This research has shown that bit/drill string dynamics can bereproduced in the laboratory using real-rock-bit interaction andphysical implementations of a drill strings dynamic response. Amechanical analog has been effective at demonstrating the neces-sity of addressing integrated bit, drill string, formation, and oper-ating parameter specifications. Simulation using model-based con-trol has been demonstrated to be capable of reproducing realisticdrill bit dynamics in the laboratory and has exceeded the capabili-ties realized by simulations using simple mechanical analogs.

Both approaches can be used to address the effect of rock type, bitdesign, and drill string properties on the stability of the drillingprocess.

A favorable response has been obtained using an open loopcontrol system in the model-based controller. Implementation of afeedback control system will allow the bit response to closelytrack the displacement predicted by the drill string model. Feed-back control is more important for producing faster responsetimes characteristic of greater frequencies in the drill string modesof vibration.

The scope of this paper is limited to the axial mode of the drillstring. This same approach could be extended to all coordinateaxes. Future work with a model-based controller should address

the interaction of these multiple modes of vibration, the influenceof confining pressure on the rock sample, and the nonlinear re-sponse of the drill string. The model-based control approach couldalso be used to allow the frequency response function of the drillstring to be adjusted to simulate drilling at extended depths.

Acknowledgment

This work was sponsored by the Department of Energy Geo-thermal Technology Program. Sandia National Laboratories is a

multiprogram laboratory operated by Sandia Corporation, a Lock-heed Martin Company, for the United States Department of En-ergy under Contract No. DE-AC04-94AL85000. The authors areindebted to the efforts of our Sandia colleagues for their engineer-ing and laboratory contributions in making this work possible:Doug Drumheller, Jim Grossman, Elton Wright, Jeff Greving,Charles Hickox, Doug Blankenship, and Keith Barrett. Specialthanks to Terry Dunlap at Xcite Systems, Milford, OH, for hissupport in configuring the servohydraulic system.

NomenclatureGs frequency response function for the drill string

in./lbHs transfer function for the actuator in./v

References1 Bailey, J., and Finnie, I., 1960, An Analytical Study of Drill-String Vibra-

tion, ASME J. Eng. Ind., 82, 122128.2 Dareing, D. W., and Livesay, B. J., 1968, Longitudinal and Angular Drill-

String Vibrations With Damping, ASME J. Eng. Ind., November, pp. 671

679.3 Elsayed, M. A., and Dareing, D. W., 1994, Coupling of Longitudinal and

Torsional Vibrations of a Drillstring, Dev. Theor. Appl. Mech., 17, pp. 128

139.4 Christoforou, A., and Yigit, A., 1997, Dynamic Modeling of Rotating Drill-

strings With Borehole Interactions, J. Sound Vib., 206, pp. 243260.

5 Leine, R. I., Van Campen, D. H., and Keultjes, W. J. G., 2002, Stick-SlipWhirl Interaction in Drillstring Dynamics, ASME J. Vibr. Acoust., 124, pp.

209220.

Fig. 19 Magnitude of the normal mode model transfer function




12/12

6 Dareing, D., Tlusty, J., and Zamudio, C., 1990, Self-Excited Vibrations In-duced by Drag Bits, ASME J. Energy Resour. Technol., 112, pp. 5461.

7 Elsayed, M. A., Wells, E. L., Dareing, D. W., and Nagirimadugu, K., 1994,Effect of Process Damping on Longitudinal Vibrations in Drillstrings,

ASME J. Energy Resour. Technol., 116, pp. 129135.8 Abbassian, F., and Dunayevsky, V. A., 1998, Application of Stability Ap-

proach to Torsional and Lateral Bit Dynamics, SPE Drill. Completion, 132,pp. 99107.

9 Finnie, I., and Bailey, J. J., 1960, An Experimental Study of Drill-StringVibration, ASME J. Eng. Ind., 82, pp. 129135.

10 Van Diver, J. K., Nicholson, J. W., and Shyu, R. J., 1990, Case Studies of theBending Vibration and Whirling Motion of Drill Collars, SPEDE, 5, pp.

282290.11 Jogi, P. N., Macpherson, J. D., and Neubert, M., 2002, Field Verification of

Model-Derived Natural Frequencies of a Drill String, ASME J. Energy Re-sour. Technol., 124, pp. 154162.12 Zamudio, C. A., Tlusty, J. L., and Dareing, D. W., 1987, Self-Excited Vibra-

tions in Drillstrings, 62nd Annual Conference, Dallas, TX, SPE Technical

Paper No. 16661, pp. 117123.

13 Wise, J. L., Finger, J. T., Mansure, A. J., Knudsen, S. D., Jacobson, R. D., and

Grossman, J. W., 2003, Hard-Rock Drilling Performance of a Conventional

PDC Drag Bit Operated With, and Without, Benefit of Real-Time Downhole

Diagnostics, Transactions, Geothermal Resources Council Annual Meeting,

Morelia, Mexico, October.

14 Elsayed, M. A., and Raymond, D. W., 2000, Measurement and Analysis of

Chatter in a Compliant Model of a Drillstring Equipped With a PDC Bit,

Proceedings of ASME ETCE Conference, New Orleans, LA, February.

15 Elsayed, M. A., and Raymond, D. W., 2002, Analysis of Coupling Between

Axial and Torsional Vibration in a Compliant Model of a Drillstring Equipped

With a PDC Bit, Proceedings of ASME ETCE Conference, Houston, TX,

February.

16 Dorf, R. C., and Bishop, R. H., 1998, Modern Control Systems, 8th ed.,

Addison-Wesley, Menlo Park, CA, p. 56, Fig 2.19.

17 Xcite Systems Corporation, 2000, Xcite 100 Field Test Series Product Speci-

fication, Milford, OH, 45150.


Date post:	02-Jun-2018
Category:	Documents
Upload:	chio2590
View:	217 times
Download:	0 times

Journal of Energy Resources Technology Volume 130 issue 4 2008.pdf

Documents