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PDC Bits : All comes from the cutter rock interactionLaurent Gerbaud, Stephane Menand, Hedi Sellami

To cite this version:Laurent Gerbaud, Stephane Menand, Hedi Sellami. PDC Bits : All comes from the cutter rock interac-tion. IADC/SPE Drilling Conference, Feb 2006, Miami, United States. pp.1, 2006, <10.2118/98988-MS>. <hal-00585922>

Copyright 2006, IADC/SPE Drilling Conference

This paper was prepared for presentation at the IADC/SPE Drilling Conference held in Miami,Florida, U.S.A., 21–23 February 2006.

This paper was selected for presentation by an IADC/SPE Program Committee followingreview of information contained in a proposal submitted by the author(s). Contents of thepaper, as presented, have not been reviewed by the International Association of DrillingContractors or Society of Petroleum Engineers and are subject to correction by the author(s).The material, as presented, does not necessarily reflect any position of the IADC, SPE, theirofficers, or members. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the International Association of DrillingContractors and Society of Petroleum Engineers is prohibited. Permission to reproduce in printis restricted to an abstract of not more than 300 words; illustrations may not be copied. Theabstract must contain conspicuous acknowledgment of where and by whom the paper waspresented. Write Librarian, SPE, P.O. Box 833836, Richardson, TX 75083-3836, U.S.A.,fax 1.972.952.9435.

AbstractPDC drill bit performances in hard rock has been greatlyimproved during the last decades by innovations in PDC wear,impact resistance and better vibrations understanding. The bitdesign is generally done by balancing the bit, distributinguniform wear along the profile and achieving high drillabilityand steerability. To obtain required drilling performances,drill bit designer adjust features such as profile shape, gageand mainly cutter characteristics (shape, type and orientation).Cutter rock interaction model became a critical feature in thedesign process. But previously used models considered onlythree forces on a cutter based on the cutter-rock contact area :drag force, normal force and side force. Such models are nolonger valid with the introduction of PDC cutters with chamferand special shape.

This paper presents a new cutter rock interactionmodel including some several improvements. It is based onthe presence of a build-up edge of crushed materials on thecutting face often described in the literature. In addition, thechamfer, which significantly affects bit Rate Of Penetration(ROP), is taken into account (shape and size). Forces appliedon the back of the cutter and due to the rock deformation andback flow of crushed materials are considered in the model.Finally, results of numerous single cutter tests (underatmospheric and confining pressure) are presented andcompared to the new cutter rock interaction model predictions.An analysis of the influence of the PDC characteristics (shape,size, chamfer, back and side rake angles, ….) is presented.The model has been applied to optimize the cutting efficiencyand bit steerability and some design rules are given tominimize the specific energy and maximize the rate ofpenetration. Finally, full scale laboratory drilling tests andfield results indicate that the use of accurate cutter rockinteraction model can help the drill bit designer to find the bestdrill bit for a specific application. Standard laboratory fullscale drilling procedures have been developed. The tests haveshown that drillability, stability, steerability and wear can be

improved and controlled by acting on the cuttercharacteristics, cutter setup, trimmer characteristics and gagetype.

IntroductionSince their introduction in the 1970’s, PDC drill bitperformances increase continuously by improving PDCtechnology1, cutting structure2,3, dynamic stability4,5,hydraulic6 and steerability7 to drill more and more smoothlyand rapidly. Now, with the development of surface anddownhole drilling parameters measurements, real timeperformance analysis8 become the key of the future drillingperformance improvement. Real time performance analysisallows to optimize the drilling parameters9 to reach theoptimum ROP while post analysis helps the driller to choosethe best bit adapted to a specific application.

What is common with the major part of all theprevious topics ? The cutter rock interaction process. Indeed,to estimate the bit drillability versus the nature of formationsto be drilled, to calculate the imbalance force for stabilization,to determine the bit steerability, we need to know what are theelementary cutter forces and how you can handle them.Furthermore, to optimize the drilling parameters in order toincrease the ROP, you need to know the real drill bit responsewhich is a direct function of the cutter rock interaction.

While abondent literature deals with PDC bit design,there is no progress in the cutter rock interactionunderstanding and modeling since many years. It is generallyassumed both in analytical10,11 and empirical12 models, that themagnitude of the cutting force acting on a cutter, while cuttinga groove in a rock sample, is proportional to the cut surfacearea. This modeling gives good results with sharp cutter (15°back rake angle) but when you change back rake angle or usechamfered cutters, theoretical results do not fit withexperimental results13 and give higher cutter forces whenincrease back rake angle compared to experimental results.Although the importance of chamfer and back face cutter havebeen outlined in some recent papers1,2, no modelling of theseeffects on the cutting forces have been done. To improve PDCbit performance and design, it is now very important to takeinto account this phenomena.

The new cutter rock interaction model presented in thispaper consider the effect of side and back rake angle byintroducing a build-up edge of crushed materials on the cuttingface. The use of crushed materials provided a better forceestimation . Chamfer size and shape effects are also modeledas well as rock deformation on the back cutter.

New cutter-rock interaction model has been applied to

IADC/SPE 98988

PDC Bits : All Comes From the Cutter Rock InteractionL.Gerbaud, S.Menand, H.Sellami, Ecole des Mines de Paris

2 IADC/SPE 98988

drill bit design. Full scale laboratory drilling tests and fieldtrials show significant improvements in bit drillability byoptimizing cutting efficiency playing on cutter shape andcutter orientation. At the end of this paper, several designconcepts and features including energy minimization,balancing and steerability are presented.

Cutter Rock Interaction ModelConsider a cylindrical chamfered PDC cutting a groove on thesurface of a rock sample at constant depth of cut. The cutterinclination is defined by the back rake angle ωc and the siderake angle ωs. During the cutting process, a force is applied onthe rock by the cutter in order to create a chip and to maintaina constant depth of cut (Figure 1). Previous models10,11,12

considered only one force applied on the cutting face. Such amodel is no longer valid with the introduction of PDC cutterswith a chamfered geometry, which significantly affects bitROP and WOB/TOB relationship. Furthermore, laboratorytests13 have found that the orientation of PDC cutter relative torock surface (back rake and side rake angle) play a significantrole in the determination of cutting forces; the previousmodels highly overestimate the effects of these angles. In thenew cutter rock interaction model, the total force acting on thePDC cutter is divided here into three groups (Figure 2): forcesacting on the cutting face surface denote Fc, forces acting onthe chamfer surface denote Fch and forces acting on the backcutter surface denote Fb:

bchc FFFF ++= (1)

Cutting face force. Generally considered as the pure cuttingforce, the cutting face force is used for destroying the rock.Previously, it was generally assumed in literature10,11,12 that thehorizontal (in the direction of the cutter velocity) and vertical(normal to the rock surface) forces were proportional to thecross-section area A of the cut :

ARF

ARF

eqcfc

n

eqc

c

**)tan(

*

ωθ +=

= (2)

Where the constant Req is defined as the intrinsic specificenergy or rock equivalent strength and θf is the rock-cutterfriction angle at the rock-cutter interface. Laboratoryobservations show the presence of a build-up edge of crushedmaterials on the cutting face which controls the flow of failedmaterial. The new cutting force model takes into account thisphenomena by introducing this crushed material14. As shownon Figure 3, the model considers that the force applied by thecutting face is transferred to the rock through the build-upedge of a crushed material. The direct consequence is aconstant single chip failure plane independent of PDCorientation and characterized by Ψ angle. Back and side rakeangles affect the cutting face force only trough the frictionalcontact between the build up of crushed material and the rocksurface. By considering that cutter width is large compared tothe depth of the cut and using a Morh-Coulomb criteria, thecutting face force can be expressed by equations 3 :

AkF

AkF

cfc

n

cc

c

*))tan(*)tan((*

*))tan(*)'tan(*1(*

0

0

ωθσωφσ

+=

+= (3)

where k is the ratio between the horizontal contact surface ofthe crushed zone and the product A*tan(ωc), σ0 is thehydrostatic stress in the crushed material and ϕ’ the frictionangle between the crushed rock and the virgin rock.σ0 is obtained by chip equilibrum (figure 3) and defined by :

))²(sin*)tan()cos(*)(sin(*))tan(*)tan(1()tan(*)²(cos)cos(*)(sin(*0

0 ψϕθψψϕθϕψψψ

σ+−−

++=

ff

bPC

(4)where Co is rock cohesion, ϕ the rock internal friction angleand Pb the mud pressure.ϕ’ is defined by15 :

)tan(*2

)'tan( ϕπϕ = (5)

Chamfer force. Present on the PDC cylindrical tip, thechamfer was introduced to avoid diamond chipping whendrilling hard formations. Although all PDC cutters arechamfered, the chamfer forces are rarely considered inliterature. Two different mechanisms take place at the chamferwith respect to the depth of cut. If the depth of cut is greaterthan the chamfer height, crushed rock is trapped between thecutting face and the rock and additional forces are generated inthe same way than for the cutting face crushed material. Asshown on the figure 4, the chamfer forces are the results of theadditional friction surface on the bottom of the groove and canbe expressed by :

chch

n

chch

c

AF

AF

*

*)'tan(*

0

0

σϕσ

=

= (6)

where Ach is the chamfer surface area projection on ahorizontal plane.

Now, if depth of cut is lower than chamfer height, thechamfer becomes the cutting face with higher back rake angleand the chamfer forces are the cutting face forces. Forexample, at 45° chamfer angle and 15° back rake angle, thereal back rake angle for small depth of cut becomes 60°.

Back cutter forces. In addition to the cutting face forces andthe chamfer forces, it has been shown16 using an elasto plasticrock behaviour model that some deformation appeared on theback of the cutter during the cutting process (figure 5) andthus applied additional forces on the cutter. Furthermore,laboratory observations have shown that a part of the crushedmaterial is driven on the back of the cutter. As shown on thefigure 6, the stresses on the back of the cutter vary linearlyfrom the hydrostatic pressure σ0 in the crushed rock zone atthe tip of the cutter to 0 at the repression end point with anangle α which is assumed to be a rock property.

IADC/SPE 98988 3

The back cutter forces can be expressed by :

),,(*

),,(*

1

0

db

cb

n

db

c

dfFF

dfF

ωαωασ

=

= (7)

where d is the depth of cut and ωd the relief angle.

wear forces. When drilling hard and abrasive formations,PDC cutter is wearing and a wear surface parallel to the rocksurface appear on the cutter. Additional forces are generated atthe wearflat area-rock surface contact. As wearflat appears,back cutter forces and chamfer forces disappear. Wear forcescan be expressed by :

ff

n

ff

c

AF

AF

*

**

0

0

σ

µσ

=

= (8)

where Af is the wearflat area and µ is the interfacial frictionangle between wearflat and rock.

Experimental dataExtensive series of single cutter experiments were carried atthe Ecole des Mines de Paris under atmospheric as well asmud pressure conditions. All the cutting tests were performedat constant cutting speed under imposed depth of cut d. Testswere carried out with sharp and chamfered cutters of diameter8, 13 and 19 mm.

Experimental setup. The tests were conducted on a linearsingle cutter test-stand (figure 7) for atmospheric test and in adrilling cell (figure 8) for confinement tests. During each test,the forces are recorded in 3 directions and the operatingparameters are controlled.

Experimental procedure. The test procedure consists inmaking groove at constant depth of cut on the planned surfaceof the rock sample. The tests were carried out in three steps :

- move up the cutter to tangent the cutting edge with thefree surface of the rock sample,

- adjust the depth of cut with respect to the tangencypoint,

- cut the groove at constant velocity of 25 cm/min andrecord the cutting forces

Rock materials. Most of the cutting tests were carried out inVosges Sandstone (compressive strength = 36 MPa, Cohesion= 10 MPa, internal friction angle = 35°) which is anhomogeneous and medium strength rock. The cutting processis dominated by ductile failure and brittle failure is negligible.Additional tests were carried out in Buxy limestone which is aharder rock (Compressive strength = 85 MPa).

Experimental program. In order to demonstrate the goodrelation between experimental data and the new cutter rockinteraction model, numerous single cutter tests were done withdifferent experimental setup. Tests have been done in order toassess and analyse separately the different forces listed before.During each test, the three force components were recorded atat a sampling rate of 500 Hz. Figure 9 shows an example of

experimental results where we can observe the cutting processalong time. For each force component, an average value of themaximum force is obtained, corresponding to the cuttingremoval.

For the cutting face force and the presence of the build upedge of crushed rock, tests were carried out with sharp cutterand different back and side rake.

For the chamfer forces, comparison were made betweensharp and chamfer cutter under the same conditions (constantorientation, same rock, same experimental device, same testprocedure).

Finally, to observe the back cutter forces, tests werecarried out at constant back rake angle with different reliefangle.

Analysis of experimental results. The assumption regardingthe presence of a build up edge of crushed rock between thecutter face and the rock chipping is demonstrated by thelaboratory experiments and the numerical simulations. If weconsider previous cutter rock interaction models, the normaland tangential forces are overestimated when back rake angleis increased over 20°. The new cutter rock interaction modelgives a good relation with experimental results whenincreasing back rake angle with sharp cutter (Figure 10).Indeed, the introduction of a build up edge of crushed rockreduces the impact of the back rake angle. The forcescorresponding to the chipping action remain independant frombake rake angle. The additional force is due to the frictionbetween the crushed zone and the groove. With the sameassumption, figure 11 shows the theoretical and experimentalevolutions of the normal force as a function of side rake angleat 1.5 mm depth of cut during an assymetric cut (distance toadjacent groove equal to 6 mm). Forces increase with a goodaccuracy between expriments and theory. The lateral forceincreases slowly with respect to the side rake increase (Figure12).

Figure 13 shows the normal force evolution versus depthof cut for sharp and chamfered PDC cutters. We can observethat normal chamfer force represent 40% of the total normalforces at 2 mm depth of cut but more than 50 % at smallerdepth of cut. Force recording (Figure 14) during single cuttertests at very low depth of cut (0.15 mm) shows no differencebetween sharp cutter with 60° back rake angle and chamferedcutter with 15° back rake angle and 45° chamfered angle.These observations validate the major influence of thechamfer on the total forces and the importance of depth of cutin the chamfer.

During special single cutter tests using pre existing holebefore the groove to be cut17 (no contact between the cutterand the bottom of the groove cut), rock cutter friction anglewas estimated to 10°. When considering the normal forceversus the tangential force for a sharp cutter (figure 15), weobtained an experimental rock cutter friction angle greater andequal to 20°. So, we consider that the additional force isgenerated at the back cutter face. For a 13 mm PDC diameterwith 15° back rake angle and 10° friction angle we obtainedan α angle, which is a rock characteristic, equal to 11°. Thisconclusion was verified using various cutting tests; the backcutter force increase while reducing the relief angle.

4 IADC/SPE 98988

PDC Bit DesignCutter layout of a PDC bit is one of the most importantfeatures in PDC bit design. Indeed, cutter layout acts directlyon bit drillability, wear of cutters over the bit face, bit stabilityand bit steerability. The development of the new cutter rockinteraction model described in this paper allows significantadvancements in all these topics.

ROP improvement. Let consider the drilling strength ζ as theratio between the normal cutting force and the cross sectionarea :

AFn=ζ (9)

Theoretical model and results of PDC cutter tests (figure 16)show that the drilling strength has a minimum function ofdistance to adjacent pre-existing cuts18. This minimum is alsoa function of the depth of cut. When applying this concept tothe PDC bit, major improvement can be made and optimizedPDC bit cutter layout can be chosen with regard to ROP.

Full scale drilling bench tests (figure 17) were conductedin order to demonstrate the cutter layout importance in bitdrillability. Special PDC bits have been designed for thesetests (Figure 18). Figure 19 shows that at low ROP, the highcutters density bit drills faster than the low cutters density bitbecause lateral distance between PDC needs to be small. Athigher ROP, the low cutters density bit drills faster, which iscoherent with drilling strength optimization.

Bit Stability. There are two design principles to improve bitstability : anti-whirl PDC bit design and global balanced PDCbit design. Anti-whirl PDC5 bit design consists in generating aresultant radial force directed toward a specific low frictionportion of the bit. The negative effect of this technology isenergy loss du to additional friction on the gage pad.

The global balanced PDC bit principle1 is different. PDCcutters are arranged so that the resultant radial force andbending moments are minimized. Resultant radial forcecontributes to bit lateral motion and whirl. Bending momentscontribute also to bit lateral motion and also to bit tilt motionwhich have an effect on bit stability and directional control. APDC bit with both radial force and bending moment balancedis more stable. The new PDC-rock interaction model allows toachieve this goal.

Bit directional control. The bit directional behaviour iscontrolled by the main following characteristics : the bitsterrability and the walk angle7. The bit design for a specificdirectional application must also take into account thedircetional system used, that plays a major role in thedeviation process.

The bit steerability corresponds to the ability of the bit,submitted to lateral and axial forces, to initiate a lateraldeviation. Bit steerability is defined19 by the ratio of the lateraldrillability (Dlat) over the axial drillability (Dax). PDC bits sidecutting capabilities become essential to increase bitsteerability. Steerable PDC bits are generally chosen for “pushthe bit” rotary steerable systems (RSS), although low steerable

PDC bits are prefered for “point the bit“ RSS. The walk angleis the angle measured in a plane perpendicular to the bit axis,between the direction of the side force applied to the bit andthe direction and the direction of the lateral displacement ofthe bit7.

Another critical factor in directional system deviationcontrol is the bit tilt. The bit tilt is defined as the anglebetween the bit axis of rotation and the tangent of thewellpath, and is mainly controlled by the directional system :rotary bottom hole assembly, steerable assembly or RSS. Thedirectional behaviour of the drilling system is then a complexcoupling between bit directional responsiveness andmechanical behaviour of the directional system (side force andbit tilt effects), while having in mind a possible rock-formation effect20 (interbedded or laminated formations).

Whatever the directional system used to deviate thewellbore, one need to estimate the bit steerability and the walkangle of the PDC bits. The cutter rock interaction model isthen critical, as it enables to evaluate within the PDC bitperformance evaluation software, the bit directionalresponsiveness in any type of rock formation.

Field ApplicationsThe new cutter rock interaction model described in this paperhave provided several improvements in term of drillingperformances. For example, in a slim hole project in Gabon2, aspecial bit has been designed incorporating these designprinciples. The newly designed bit drilled successfully 671 mat an average ROP of 11 m/h whereas previous bit drilled thesame length at an average ROP of 4.3 m/h. In this case, thePDC bit performance improvement was obtained by theutilisation of the minimum energy concept and betterstabilisation. Another application concerned the design and therun of PDC bits having left, rigth or neutral directionaltendencies. This application provided a new classification ofPDC bits according to their steerability19.

Conclusions.Cutter rock interaction is very important in drill bit design dueto its great effect on ROP, stability and bit steerability. A newcutter rock interaction model was developped for taking intoaccount the new evolution in PDC technologies and the recentexperimental observations.

The build up edge of crushed material modeling provides agood evaluation of back and side rake effect on PDC forces.

The chamfer modeling allows direct estimation of thechamfer shape and size on the PDC forces.

The introduction of the back cutter forces provides a goodevaluation of the cutter forces and add more optimizationpossibilities.

The innovations incoporated into this model and describedin this paper provide a number of benefits in terms of ROPimprovement, bit stability, bit wear and bit directional control.

NomenclatureA = cross section area of the cut, mm²Ach = chamfer surface area on a horizontal plane, mm²Af = PDC wear flat area, mm²d = Depth Of Cut, mmF = Total force acting upon PDC, N

IADC/SPE 98988 5

Fb = Force acting upon the back cutter face, NFc = Force acting upon the cutter face, NFc = PDC Cutting force, NFch = Force acting upon the cutter chamfer, NFf = Force acting upon the PDC wear flat, NFl = PDC Lateral force, NFn = PDC Normal force, Nk = ratio between the projection of the crushed zone

on the surface parallel to the rock surface and cuttingarea

Req = Rock intrinsic specific energy, MPaROP = Rate Of Penetration, m/hRPDC = PDC radius, mmTOB = Torque On Bit, daN.mWOB = Weight On Bit, tonsα = repression angle, degreesφ = rock internal friction angle, degreesφ’ = friction angle between crushed rock and virgin

rock, degreesµ = interfacial friction angle between wear flat and

rock, degreesθf = Rock-cutter friction angle, degreesσ0 = hydrostatic stress into the crushed zone, Mpaτ0 = tangential stress into the crushed zone, MPaωc = Back rake angle, degreesωd = Relief angle, degreesωs = Side rake angle, degreesψ = chip failure angle, degreesζ = drilling strength, MPa

References1. Clayton R., Chen S., Lefort G., “New Bit Design, Cutter

Technology Extend PDC Applications to Hard Rock Drilling”,paper SPE/IADC 91840 presented at the 2005 SPE/IADCDrilling Conference, Amsterdam, Feb. 23-25

2. Gerbaud L., Sellami H., Lamine E., Sagot A., “New PDC BitDesigned Increased Penetration Rate in Slim Wells”, paper

3. Mensa-Wilmot G., Penrose B., ”Advanced Cutting StructureImproves PDC Bit Performance in Hard and AbrasiveEnvironments”, paper SPE 81167 presented at the 2003 LatinAmerican and Caribbean Petroleum Engineer Conference,Trinitad, April 27-30

4. Warren T.M., Brett J.F., Sinor L.A., “ Development of a WhirlResistant Bit”, SPE Drilling Engineering, 5 (1990) 267-274.

5. Weaver G.E., Clayton R.I., “A New PDC Cutting StructureImproves Bit Stabilization and Extends Application into HarderRock Types”, paper SPE/IADC 25734 presented at the 1993SPE/IADC Drilling Conference, Amsterdam, Feb 22-25

6. Watson G.R., Barton N.A., Hargrave G.K., “Using NewComputational Fluid Dynamics Techniques to Improve PDC BitPerformance”, paper SPE/IADC 37580 presented at the 1997SPE/IADC Drilling Conference, Amsterdam, March 4-6.

7. Menand S., Sellami H., Simon C., Besson A., Da Silva N., “HowBit Profile and Gages Affect the Well Trajectory”, paper SPE74459 presented at the 2002 IADC Drilling Conference, Dallas,Texas, Feb 26-28

8. Finger J.T., Mansure A.J., Knudsen S.D., Jacobson R.D.,“Development of a System for Diagnostic-While-Drilling(DWD)”, paper SPE/IADC 79884 presented at the 2003SPE/IADC Drilling Conference, Amsterdam, Feb 19-21

9. Dupriest F.E., Koederitz W.L., “Maximizing Drill Rates withReal-Time Surveillance of Mechanical Specific Energy”, paper

SPE/IADC 92194 presented at the 2005 SPE/IADC DrillingConference, Amsterdam, Feb 23-25

10. Sellami H., Fairhurst C., Deliac E., Delbast B., “The role of insitu rock stresses and mud pressure on the penetration rate ofPDC Bits”, presented at the 1989 International SymposiumRock at Great Depth, Pau, France, Vol. 2, pp. 769-777

11. Detournay E., Defourny P., “A phenomenological model for thedrilling action drag bits” International Journal of RockMechanism Mining Science, 1992, pp 13-23.

12. Glowka D.A., “Use of Single Cutter Data in the Analysis of PDCBit Designs: Part 1 – Development of a PDC cutting ForceModel”, SPE Journal of Petroleum Technology, 41 (1989), 797-849.

13. Coudyzer C., Richard T., “Influence of the back and side rakeangles in rock cutting”, paper AADE-05-NTCE-75 presented atthe 2005 AADE Technical Conference and Exhibition, Houston,April 5-7

14. Menand S., “ Analyse et validation d’un modèle decomportement directionnel des outils de forage monobloc petitdiamètre”, Phd thesis at Ecole des Mines de Paris, 2001.

15. Kerisel J., “Cours de Mécanique des Sols”, Ecole National desPonts et Chaussées, Paris, p 272

16. Sellami H., “Simulation du travail d’un pic; modélisation de laphase de pénétration”, DEA Ecole des Mines de Paris, 1984.

17. Challamel N., Sellami H., “Application of yeld Design forUnderstanding Rock Cutting Mechanism”, paper presented atthe 1998 SPE/IRSM Eurock 98 conference, Trondheim, July 8-10.

18. Gerbaud L., “Optimisation de l’interaction PDC-Roche :application à la conception d’outils pour forage pétrolier en petitdiamètre”, Phd thesis at the Ecole des Mines de Paris, 1999.

19. Menand S., Sellami H., Simon C., “Classification of PDC bitsAccording to their Steerability”, paper SPE/IADC presented atthe 2003 Drilling Conference, Amsterdam, The Netherlands,Feb 19-21.

20. Boualleg R., Sellami H., Menand S., Simon C., “Effect ofFormations Anisotropy on Directional Tendencies of DrillingSystems”, paper SPE/IADC 98865 presented at the 2006Drilling Conference, Miami, Floride, Feb 21-23.

Metric Convertion Factorsft x 0.3048 = min. x 25.4 = mmlbf x 4.448 222 = Nft.lbf x 0.1355818 = daNm

6 IADC/SPE 98988

AB

C

Figure 1 : View of chip formation

Figure 2 : Idealization of forces acting upon PDC cutter

Figure 3 : build up edge of crushed material model

Figure 4 : Stress distribution within the chamfer zone

Figure 5 : rock deformation simulation under load with a PDC

Figure 6 : stress distribution upon the back cutter face

IADC/SPE 98988 7

Figure 7 : atmospheric single cutter test stand

Figure 8 : confinement single cutter test stand

Figure 9 : Experimental PDC forces during rock cutting

0

1000

2000

3000

4000

5000

0 10 20 30 40 50

Back rake angle (°)

Nor

mal

For

ce (N

)

experimental new model previous model

Figure 10 : PDC maximum normal force versus back rake angle

0

200

400

600

800

1000

1200

0 5 10 15 20 25 30 35

Side rake (°)

Nor

mal

For

ce (N

)

Experimental Theoretical

Figure 11 : PDC normal force versus side rack angle for asymetriccut

0

50

100

150

200

250

0 5 10 15 20 25 30 35

Side rake (°)

Late

ral F

orce

(N)

Experimental Theoretical

Figure 12 : PDC lateral force versus side rake angle forassymetric cut

8 IADC/SPE 98988

0

200

400

600

800

1000

0 0.5 1 1.5 2 2.5

Depth of cut (mm)

Nor

mal

For

ce (N

)

chamfered cutter sharp cutter

Figure 13 : Normal force on PDC versus depth of cut for sharpand chamfered cutter

020406080

100120140

0 5 10 15 20 25 30 35 40

time (s)

Fn (N

)

chamfer - Wc=15° sharp - Wc=60°

Figure 14 : Normal force evolution for sharp and chamfered cutterat depth of cut equal to 0.15 mm

0100200300400500600700800900

0 200 400 600 800 1000 1200 1400 1600

Fc (N)

Fn (N

)

Figure 15 : Evolution of the normal force versus the horizontalforce for a sharp cutter

0

20

40

60

80

100

120

0 2 4 6 8 10 12 14

lateral distance (mm)

Dri

lling

str

engt

h (M

Pa)

experimental Theoretical

Figure 16 : drilling strength versus lateral distance to pre-existingcut for chamfered PDC

Figure 17 : Full Scale Drilling Test stand

Figure 18 : Special bits designed for understanding PDC bitsperformances

IADC/SPE 98988 9

0

1

2

3

4

5

6

0 0.2 0.4 0.6 0.8 1 1.2 1.4

ROP (mm/rev)

WO

B (t

ons)

high density low density

Figure 19 : WOB versus ROP for low and high density bits