e PergamonInt. J. Rock Mech. Min. Sci. Vol. 35, No. 4/5, pp. 578-580, Paper No. 109, 1998

© 1998 Elsevier Science Ltd. All rights reservedPrinted in Great Britain

PH: S0148-9062(98)00125-9 ISBN: 0080433332 ISSN: 0148-9062/98 $19.00 + 0.00

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Evaluation of Drilling Parameters of a PDCBitD. NGUYEN MINHtH.GEOFFROYtJ. BERGUEStc. PUTOTt

Paper No. 10911Full paper on enclosed CD-ROM

INTRODUCTION

Polycrystalline Diamond Compact drill bits are known to be more efficient than traditional roller cone bits,specifically in soft rocks. However, their sensitivity to wear, namely in hard or abrasive formations, has still lim­ited their development. A better understanding of bit performance has to take into account bit-rock interactionof the worn tool. In normal drilling conditions, e.g. under assumption of a steady motion, and avoiding excessiveheating, a worn cutter exhibits a wear flat which can dissipate up to 50% of the energy for drilling by frictionalcontact. Although many studies have dealt with this subject, the frictional mechanism generated by wear on cut­ters has still been overlooked. The present analysis of the global drilling parameters takes into account recentadvances on the subject. In the following, the term "bit profile" means a curve in a fixed meridional plane whereall the cutters centers are supposed to pass through.

FRICTIONAL MECHANISM ON A WORN CUTTER

We assume that cutting by a worn cutter involves two independent mechanisms: "pure cutting" on the cuttingface and a frictional mechanism on the wear flat. Cutting is generally considered as a yield load mechanism andhorizontal cutting force as equivalent to a "specific energy" times the cross-sectional area of the cut (Detournay,1992). For the other mechanism, we use a friction law we have recently stated, based on an elastoplastic in­terpretation of experimental studies (Geoffroy, 1996). This law appears as a relationship between the normalapplied pressure on the wear flat (In, and the subsequent dip angle rt. of the wear flat into the rock surface.Simplified forms are used herein, depending if limit load occurs (a) or strain hardening (b):

(In = (Jo(1- exp(-rt./rt.o)) (a)

(In = (Jo(1 + Port. - exp(-rt./rt.o)) (b)

WEAR LAW

It is necessary to describe wear flat orientation and quantitative wear evolution. We admit with other authors(Glowka, 1987), that wear develops tangentially to the rock wall, e.g., practically tangentially to the bit profile,as supported by experimental data. A quantitative wear law is generally proposed which relates the volumetricwear of a cutter per unit cutting length d Vw/d£ to the total normal force Fn , and wear flat surface Aw (Glowka,1987):

dVw/d£ = C*.Fn/A~ O:C;;m:C;;1, C*: wear constant (2)

We shall use a somewhat modified law, considering that wear mainly result from action of the tangential stresses(]if/Aw ) , and that cutting forces only have a secondary effect. Moreover, evolution of wear can be described interms of thickness variation d~, normally to the wear flat. A linear relationship is then used:

tNow working in LGM-ENTPE, rue Maurice Audin, 69518 Valux-en-Ve1in, FrancetLMS-Ecole Polytechnique, 91128 Palaiseau, France.§IFP, 3-4 Avenue Bois Preau, 92506 Rueil-Malmaison, France.IIConference Reference: FRA-827-2

578

NARMS '98 579

1,8

1,6-- RlS=l

1,4

1,2......... RlS>l

.!d --- RlS<l

~ 0,8 I

\-- RlS=l0,6

0,4 \-0- RlS>1 I0,2 [-0- RlS<l I

0,5 1,5 2 2,5 3,5 4

r(in.)

Fig.!. Intrinsic wear distribution on elliptic bit profiles (eccentricity RjS).

d~

d.e1 F[CAw

C: wear constant (3)

which lends to form (1) when m = 0, and can be extended if necessary to a non linear form.

BIT WEAR EVOLUTION

The wear model and friction forces developed by the rotating bit on cutters wear flats, allow for determiningwear evolution of the PDC bit. The frictional forces result from angle rx defined as:

(4)

where n----> is the unit external normal to bit profile, and T----> is the unit tangent to the helicoIdal trajectory of acutter passing through the bit profile. On the other hand, law (3), with d.e expressed in terms of bit rotation fre­quency N and ordinate y of the cutter on bit profile lends to expression of an intrinsic wear rate (in case of nohardening):

d~/(2nf.lN 0"0 dt) = y(1- exp(-rx(b,y)/rxO)) (5)

This quantity, for a given rock, depends on bit profile and on bit penetration per revolution b, but not on thecutter distribution on the bit profile.

GLOBAL FORCES ON BIT

Forces on individual cutters, resulting from cutting and friction mechanisms are now determined as functionof the cutter position and bit advance, and summed up into the global forces applied to the bit, (T) and (WOB),which share themselves into components relative to each mechanism. Under the assumption of a constantspecific energy for all cutters, it is known that global cutting parameters (Tt and (WOBt are simply pro­portional to the cross-sectional area removed per revolution, i.e., to Rb, where R is the profile radius(Detournay, 1992).

This is not the case for frictional forces (Tf and (WoBf, which depend on cutter wear flat distribution, andon their evolution as drilling proceeds.

NUMERICAL EXAMPLES AND CONCLUSION

For illustration, some simple bit geometries are considered and evolution of wear and drilling parameters arecompared. Parameters are chosen using some experimental and numerical results from literature. Figure 1 showsfor three different elliptic bit profiles, and two different bit penetration per revolution b, the "intrinsic wear rate"vs distance to the bit axis. It can be seen that sharper bits ("bullet nose"), exhibit less wear, and that maximal

580 NARMS '98

wear is more centred towards the axis. If advance per revolution b is lower, wear distribution decreases andmaximum wear is shifted towards bit axis.

The model allows to obtain some results observed on tests laboratory (Warren, 1989 and Glowka, 1987).For example, it is shown that the shape of the drill bit controls the cutters wear. Moreover, for a worn bit,

the relationship between (T) and (WOB) is sensitive to the ROP contrary to the sharp bit.

Key words-wear, drilling, PDC bit, worn bit, rock cutting, friction mechanism, specific energy, torque, rate ofpenetration, weight on bit

REFERENCES

Detournay, E. and Defourny, P., International Journal of Rock Mechanics and Mining Sciences, 1992,29(1), 13-23.Geoffroy, R., Etude de I'interaction roche-outil de forage: influence de I'usure sur les parametres de coupe, These de l'Ecole Polytechnique,

France, 1996.Glowka, D. A., Development of a method for predicting the performance and wear of PDC drill bits, Sandia Report 86-1745, Sandia

national laboratories, 1987.Sinor, A. and Warren, T. M., SPE Drilling Engineering, 1989, (I), 128-137.