16
lADC/SPE IADCISPE 17192 A Method for Detecting In-Situ PDC Bit Dull and Lithology Change by E. Kuru and A.K. Wojtanowsicz, * Louisiana State U. SPE Members IADC Member I Copyright19S8, IADCLSPEDrillingConference This paper wss prepsred for prstsenlation61the 1988 lADC/SPE DrillingConferenceheld in Dallss, Texas, February 28-March 2, 19SS. This paper wse aelscled for prasentstlonby an IADCISPE ProgramCommitteefollowingreview of informationcontainedin an abstractsubmilledby !he aulhork}. Contents of the oaoer, 8s oreaented, have notbwn reviewedby the Societyof PetroleumEngineersor InternalionslAssociationof Drill. Ing Contrac{oraand are aubjtict” to correctionby the author(s),The maferialj as preseoied, does not necasa$zrily reflect any positionof the IADC or SPE, ita officers, or members. Papers presented at lADC/SPE maelinge are subjectto publicationreview by Editorial Committeesof the IADC snd SPE. Permissionto copy Is restrictedto an abstrsct-f not morethen 300 words.Illustrationsmay not be copied,The abstractshouldcontainconaplcu- ouaacknowledgmentofwhere and by whomthe papa ia presented.Write PublicationsManager, SPE, P.O. BoxS33S36, Richardson,TX 7548$2S3S. Telex, 730989 SPEDAL. ABSTRACT A mathematical diagnostic drilling model was derived from the balance of forces acting at the PDC bit cutter. The model combined the torque and the drilling rate equations, cutter’s geometry and rock properties. It was verified using the laboratory drilling data from several research reports as well aa the field drilling data collected by the authors. Based on the drilling odel, a new method wae developed for the in-situ measurements of the PDC bit condition and for the lithology change detection, In this technique, a diagnostic plot is made by correlat- ing two dimensionless groups containing measured values of torque, weight on bit, rotary speed and penetration rate. Several laboratory and field data (presented in the study) confirmed lineari~y of such a plot. The diagnostic plot is e.unique indicator of the bit-rock interaction and 5.:is independent from the bit opera- tional variab?.es. Moreover, the instantaneous wear of a PDC bit can be computed from coordinates of the straight line points. This method is feasible for a graphical use supplemented with a computer program. The technique waa further verified by comparing the predicted and the measured PDC bit wear from the MWD records in the Gulf Coast area. Also provided, were the examples of a correlation between rapid forma- tion changes and discontinuties in the diagnostic plots. The new method contributes to the PDC bit drilling theory. Its importance lies in the MWD software development for the purpose of the in-situ rock detec- tion and the PDC bit evaluation and control. INTRODUCTION Polycrystalline Diamond Compact (PDC) bits are a high-tech revival of the earliest bit types, drag bits. w using the state of the art materials, drag bita have been competitively reintroduced into the oil well ~rilling technology, Absence of moving parts and the high wear resistance of synthetic diamonds make a drag bit a long lasting bottomhole tool. The auccesa of th~ PDC’S in the petroleum dr~:$ing industry is well docu- mented in the literature. PDC bits are extremely senaitiv~ to formation properties and operating conditions. Recent studies on PDC drilling performance in the harsh f~v~~onment such as geothermal and hard rock drilling ‘ showed an average two-fold increaae of penetration rate afid bit life as compared to conventional bits, which resulted in coat reduction 10 to 15%. However, in the case where the PDC bit life waa reduced 50%, the coat savings were cut in half. Therefore there ia a very good reason to improve bit life in any potential appli. cation of PDC bits, in order to take advantage of chei] high penetration rates. Early detection of formation changes and appropriate adjustment of the operational variables are very important measures to save the bit. Such detection can be made possible with the instan- taneous drilling data acquisition (MWD) system. Development of the drilling data acquisition systems haa been in progress for many years in the petroleum industry. However, without having an appro- priate data proceaaing tool (a drilling model), some o~ the information will become invaluabl~2,1~:1&~$:1~ fel predictive models have been proposed. Ziaja 12 developed a mathematical model of a singl~ PDC cutter penetration assuming a circular cut snd an absence of cutters interaction. The model waa designe{ for a core bit. The single proportionality constant was used to up-scale from the single cutter load and penetration to the weight on bit and drilling rate. Data from one field run of a core bit was used to verify the model. Glowka’3 used experimental data from laboratory drilling in hard rocks and developed a power-function correlation between cutter penetration and atresa at the wearflat area. Hia analytical work also included derivation of the single cutter wear equation as a function of penetration per rotation and footage. He References and illustrations at end of paper 137

[Society of Petroleum Engineers SPE/IADC Drilling Conference - Dallas, Texas (1988-02-28)] SPE/IADC Drilling Conference - A Method for Detecting In-Situ PDC Bit Dull and Lithology

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lADC/SPEIADCISPE 17192

A Method for Detecting In-Situ PDC Bit Dulland Lithology Changeby E. Kuru and A.K. Wojtanowsicz, * Louisiana State U.

SPE Members

●IADC Member

I Copyright19S8, IADCLSPEDrillingConference

This paper wss prepsred for prstsenlation61 the 1988 lADC/SPE DrillingConference held in Dallss, Texas, February 28-March 2, 19SS.

This paper wse aelscled for prasentstlonby an IADCISPE ProgramCommitteefollowingreview of informationcontainedin an abstractsubmilledby!heaulhork}.Contentsofthe oaoer, 8s oreaented,have notbwn reviewedby the Societyof PetroleumEngineersor InternalionslAssociationof Drill.Ing Contrac{oraand are aubjtict”to correctionby the author(s),The maferialj as preseoied, does not necasa$zrilyreflect any positionof the IADC orSPE, ita officers,or members. Papers presentedat lADC/SPE maelinge are subjectto publicationreview by EditorialCommitteesof the IADC sndSPE. Permissiontocopy Is restrictedtoan abstrsct-f notmorethen300 words.Illustrationsmay notbe copied,The abstractshouldcontainconaplcu-ouaacknowledgmentofwhere and by whomthe papa ia presented.Write PublicationsManager, SPE, P.O. BoxS33S36, Richardson,TX 7548$2S3S.Telex, 730989 SPEDAL.

ABSTRACT

A mathematical diagnostic drilling model wasderived from the balance of forces acting at the PDCbit cutter. The model combined the torque and thedrilling rate equations, cutter’s geometry and rockproperties. It was verified using the laboratorydrilling data from several research reports as well aathe field drilling data collected by the authors.

Based on the drilling ❑odel, a new method waedeveloped for the in-situ measurements of the PDC bitcondition and for the lithology change detection, Inthis technique, a diagnostic plot is made by correlat-ing two dimensionless groups containing measured valuesof torque, weight on bit, rotary speed and penetrationrate. Several laboratory and field data (presented inthe study) confirmed lineari~y of such a plot. Thediagnostic plot is e.unique indicator of the bit-rockinteraction and 5.:is independent from the bit opera-tional variab?.es. Moreover, the instantaneous wear ofa PDC bit can be computed from coordinates of thestraight line points. This method is feasible for agraphical use supplemented with a computer program.

The technique waa further verified by comparingthe predicted and the measured PDC bit wear from theMWD records in the Gulf Coast area. Also provided,were the examples of a correlation between rapid forma-tion changes and discontinuties in the diagnosticplots.

The new method contributes to the PDC bit drillingtheory. Its importance lies in the MWD softwaredevelopment for the purpose of the in-situ rock detec-tion and the PDC bit evaluation and control.

INTRODUCTION

Polycrystalline Diamond Compact (PDC) bits are ahigh-tech revival of the earliest bit types, drag bits.

w using the state of the art materials, drag bita havebeen competitively reintroduced into the oil well~rilling technology, Absence of moving parts and the

high wear resistance of synthetic diamonds make a dragbit a long lasting bottomhole tool. The auccesa of th~PDC’S in the petroleum dr~:$ing industry is well docu-mented in the literature.

PDC bits are extremely senaitiv~ to formationproperties and operating conditions. Recent studieson PDC drilling performance in the harsh f~v~~onmentsuch as geothermal and hard rock drilling ‘ showedan average two-fold increaae of penetration rate afidbit life as compared to conventional bits, whichresulted in coat reduction 10 to 15%. However, in thecase where the PDC bit life waa reduced 50%, the coatsavings were cut in half. Therefore there ia a verygood reason to improve bit life in any potential appli.cation of PDC bits, in order to take advantage of chei]high penetration rates. Early detection of formationchanges and appropriate adjustment of the operationalvariables are very important measures to save the bit.Such detection can be made possible with the instan-taneous drilling data acquisition (MWD) system.

Development of the drilling data acquisitionsystems haa been in progress for many years in thepetroleum industry. However, without having an appro-priate data proceaaing tool (a drilling model), some o~the information will become invaluabl~2,1~:1&~$:1~ felpredictive models have been proposed.

Ziaja12

developed a mathematical model of a singl~PDC cutter penetration assuming a circular cut snd anabsence of cutters interaction. The model waa designe{for a core bit. The single proportionality constantwas used to up-scale from the single cutter load andpenetration to the weight on bit and drilling rate.Data from one field run of a core bit was used toverify the model.

Glowka’3 used experimental data from laboratorydrilling in hard rocks and developed a power-functioncorrelation between cutter penetration and atresa atthe wearflat area. Hia analytical work also includedderivation of the single cutter wear equation as afunction of penetration per rotation and footage. He

References and illustrations at end of paper 137

A METHOD FOR DETECTING IN-SITU PDC BIT DtIsed the model to analyze response of a single cutterto various input loada. He also analyzed distribution>f wear, penetration, end load acroas the bit face. He~ug~eated that the PDC bit performance should be calcu-lated by integrating performance of all individualcutters.

Warren and Sinor14,15

developed a computer program#hich rigorously calculated individual cutters perfor-mance baaed on observed drilling rate, cutter positionsnd its geometry. Wear and loads were calculated for!ach cutter, then they were suusnarizedand compared to~he observed values of bit weight and torque. To date,Lhe program has been successfully verified by using~xperimental full-scale drilling results. The programseems to be an effective simulator needed by the PDC>it manufacturers to investigate various bit designconfigurations.

,ape>~e approach presented here (and in the previous) aims to develop a mathematical model for the

purpose of optimum drilling programs and interpretationof drilling data. The model requires a small amount ofinput data regarding the bit’s geometry and its dullconditon. Such an approach calls for explicit expres-sions for all the drilling variables measured on therig site such as bit weight, rotary speed, drillingrate, torque, and the bit’s dull. An effort is made tosimplify the model as much as possible in order to makeits practical use more convenient without losing the~ccuracy of the model’s predictions,

Successful application of s drilling model is notonly a result of the model’s precision but it is alsodependent upon the quality of the input data. Accuracy~f drilling measurements, specifically regarding the

~~~~ ~~oefyndition, iS 10W. Recently, an effort hasto improve the bit dull evaluation. How-

ever, the quantitive measurement of bit dull is stillto be developed. Furthermore, there is no measurementof bit condition while drilling, which makes the veri-fication of drilling models unreliable,

The conventional drilling models consisted of thedrilling rate and the bit wear formulas. The measuredvariables included weight on bit, rotary speed, anddrilling rate. With the development of the MWD, thebit torque has become another important variableneasured st the bit, thus improving verification ofdrilling models. Ilecentlyi8theroller bit torque modelwas developed and studied, It was also provedexperimentally that drilling efficiency, as measured by

~~&~i~gdrilling energy, did not correlate with weightIt was concluded that the torque equat;on

should be eveloped from the balance of forces ratherthan ~om~d the specific energy concept.

In the authors’ opinion, the main controllingvariable in drilling is weight on bit (given constantbit dull). On one hand, bit weight controls the torquethrough the mechanisms of shear, friction, and rollingresistance (in case of roller bits), On the otherhand, the bit weight determines the level of stress atwhich the rock is destructed. Specific energy dependaupon this stress. Therefore for each weight-on-bitvalue, the drilling efficiency (measured by the energyoutput-input ratio) is different. Also, the bit dull-ing process changes stress under the bit cutting struc-ture which results in a change of drilling efficiency,Torque equation represents energy added to the drillingprocess, thus providing an important energy ~~lanceevaluation to the drilling model, Recently, simplerelations between bit weight, tooth penetration and

AND LITHOLOGY CHANGE MDC)SPE 17192

uearflat area were used together with the torque equa-tion to infer roller bit dull from the MWD measure-ments. This intereating concept was not supported byLhe actual measurements of bit dull. However, qualitaLive correlations between torque, drilling rate and bicondition were observed for roller bits,

Experimental studies of PDC bita13,21

showed thatthere was a strong correlation between the bit torque%nd the bit wear. It was suggested that rotary torquecould be used as a guide for selecting the bit weight,md rotary apeed for the beat penetration.

The approach used in this work i~6further developnent of the explicit model of PDC bit by using anexpression for PDC bit torque. The torque and drillinrate equations will then be combined to give a diag-nostic drilling model. Based on the model, a simpleprocedure will be developed for evaluation of aninstantaneous bit wear, as well as for detecting rapidchanges in lithology of formations drilled.

DIAGNOSTIC DRILLING MODEL AND ITS VERIFICATION

The model is derived from the analysis of forcesactive at the single cutter, aa shown in Figures 1 and2, The bit life, the drilling rate and the bit torqueequations are deduced from the static balance of forcefor a cutter moving through the rock at a constantvelocity. The assumptions made throughout the deriva-tion of the model are aa follows:

1.

2.

3.

4.

5.

6.

7.

Formation rock behavea plastically, i.e.rock deforms without losing its cohesion. Iothez words, rock resistance to pressing (orcutting) is proportional to the contact areaand it does not depend upon cutter’s penetration (vertical) or displacement (horizontal)

Bot~ X( le profile is predominantly parallelto $.$ ‘~? orofile as s result of the cutter

-,,,

-e LS a mechanical similitude betwee.]l.ecutter and the entire bit;_ ,.,

a) ‘he drilling rate is proportional to thcutter penetration with proportionalityconstant k

b) The norma13force acting on a singlecutter is proportional to the weight onbit with proportionality constant kl.

The cutting angle UC is ignored. i.e. cuttemoves in the direction perpendicular to itsstud axis.

Volumetric wear of a PDC cutter ia propor-tional to the friction work with proportion-ality constant k2.

Inadequate bottomhole cleaning results in anon-linear response of the drilling rate tothe rotary speed.

Friction at the cutter side surface isignored.

The assumption 1 is based on the fact that manyrocks exhibit ductile behavior at confining pressurescorr~~p~~ding to deptha usually reached during drill-ing. Triaxial compression experiments at rela-tively low confining pressures indicated that manysedimentary rocks can undergo deformations without

138

IADC/SPE 17192 E.KURU,

Losing cohesion.L- In general, the rock failure~echanisniis brittle at low confining pressures and it1s ductile at high confining pressures, with transitionFrom predominantly brittle to predominantly ductileBehavior. It ia alao known that the macroscopic mode~f rock failure is controlled by nominal effectiveItreas i.e. by the diff$g$$~e between confining Pres-Iure and pore preaaure. As the nominal effectiveltress increases with depth the rock deformation mode>ecomes more plastic. In addition, for soft and mediumioft formation (shales, carbonates), the angle ofinternal friction reduces at a higher confining stress,thus increasing the co~&ribution of cohesive resistanceLO the shear strength.

The simplified mechanical model of the assumednechanism of rock deformation ia shown in Figure 2.rhe simplification is supported by the ex~fr~F;~13iseasurementsof forces at a single cutter . .[t should be noted that the measurements were takenErom the laboratory drilling experiments performed atthe atmospheric conditions. The zone of force varia-tion (chipping) represents consecutive cycles of form-ing new fractures. It is expected that at the higherconfining pressure the amplitude of stress fluctuationsreduces even further, so it can be averaged by someconstant value as shown in Fig. 4. This value repre-sents rock resistance to cutting, or to pressing.

The assumptions 3 and 4 imply that bit behaviorcan be inferred from a single cutter behavior. Thoughconsnonlyl~~~~in bit modelling (except for oneresearch ), such an aasuniptionis quite contro-versial, specifically for PDC bits. Cutters placementmd the bit profile are, at present, subject to experi-

~~~~~;~4~~5bit manufacturers. The most rigorousto the modelling of PKICbits ia, without

doubt, to measure the individual cutters position andorientation and to mathematically integrate the indi-vidual cutters performance across the bit face. Suchspproach considers the uniqiseneasof bit geometry (“bitfingerprint”) and it can effectively detect differencesbetween behavior of individual bits.

Field applications, however, call for standardiz-ationi.e. selecting features which are common in largegroupa of bits. The recent IADC classification of thefixed cutter b“ s geometry, using the three-by-threematrix aystern~i is a good example of generalizationmade at the expense of accuracy.

In addition, there ia already some experimentalevidence supporting the assumptions 3 and 4. Theproportionality between drilling rate and cutter pene-tration is not just a flat assumption but it can bededuced from experiments. The assumption 3A, regardin[bit weight W being linear function of cutter normalforce FN, and the theoretical expression Eq. A-25,showing linearity between cutter penetration h and thenormal force F can be written as

N

W-FN;

and h-FN

The example of experimental data supporting theoretira;relation h vs. FN is shown in Fig. 5. Moreover, thereis ❑assive laboratory and field data showing a linearrelationship between drilling rate and bit weight,similar to that shown in Fig. 6. Thus

R -w

,The three linear correlations above are simply equiva-1

!/DA.K.WOJTANOWICZ 3

lent to the linear relation between drilling rate and:utter penetration as

R-h

>r to the assumption 3B.

In view of the need for simplicity, the assump-~ions 3 and 4 are considered the very first attempt toFormulate an explicit ❑odel for PDC bits. Extensive~erification, sensitivity analysia, aa well as furtherdevelopment of the model still remains to be seen.

The assumption 5 regarding proportionality betwee?olumetric wear and the work of friction is conunonlynade when some grinding mechanism is involved. Speci-fically for PDC cutters, there is an additional evi-ience of the frictioexperimentally ahom9~1&~~~~;~~;&~~”t~t&sirill blanks waa much greater for dry cutting than for#et cutting. This fact implies that the basic cuttingnechanism for PDC cutters is shearjag action, and thatthe friction work predominantly contributes to cutterswear.

The assumption 6 draws from several laboratory ac

~~~~~ ~Rs~~~&sja~~Yi~g3= linear effect of rotaryIt also implies thatsingle cutter penetration is inti?pendentfrom itslinear velocity, when bottomhole cleaning is suffi-cient. In the full scale tests, however, the effect crotary apeed on drilling rate was often nonlinear.Such discrepancy was usually attributed to poor holecleanin~ in field operations as compared to the lfibor:tory testao

The assumption 7 is supported by the laboratoryexperiments which revealed thst side forces ~~e gu~hfrange of less than 10% of the thrust forces,the frictional drag, resulting from the side forces,became insignificant.

The equilibrium of forces for the typical PDCcutter geometry (Fig. 1) defines the components of th(normal and the tangential forces considered in themodel. The normal force is a distributed force acres:cutting surface area and the wearflat. It’s distribu.tion is simplified using the mechanical analog shown :Fig. 2. Plastic behavior of rock under the PDC cuttelis assumed. Rock behaves in such a way that itaelastic limit eauala plastic yield and, when it isexceeded, the rock deforms continuouslyunder the actitof the PDC cutter until a new balance is reached. Tht

balance of all interacting forces between the rock antthe cutter is shown in Fig. 7A. For small values ofcutting depth, the cutting angle ac becomes negligibhTherefore the friction forces induced, due to thepresence of the cuttingshown in Fig. 7B.

The horizontal andequation can be written

‘N = FcsinO’ + ‘fccosa +

FT = Fccoso!- Ffcsina +

where

angle, will be eliminated as

the vertical forces balanceby using Figs. 1 and 5A as

Fwcosac+ ‘fwainac

Ffwcosa - Fwsinac

(1)

(2)

139

.

4 A METHOD FOR DETECTING IN-SITU PDC BIT DULL AND LITHOLOGY CRANGE IADC/SPE 17192

Fc = RCA= ; Ffc

=pFc = p RCA=(3) Cl =? fl(r) n(r) rdr (12)

oFw =RA ;

pw ‘fw= p RPAW

and it representa bit design features.

‘orsmall valuea of cutting depth (h S 0.1 in.) the It ia seen from Eq. (11) that, for a constantralueof the cutting angle ac is very small. After weight on bit, torque is solely the function of the,gnoringac, and introducing (3) into (1) and into (2), wear flat area. Equ. (11) indicates that, as the wearleohcain: increasea, the torque should reduce which ia supported

by t<z laboratory experiments - Figs. 8 and 9.FN = RcAc[sina + p cosd] + R A

pw(4)

Field data collected for this research from thePDC drilling in the Gulf Cost area furthe. support thelinear correlation cf torque vs. wear as shown in Fig.

‘T= RCACICOSU - p sinu] + p RPAW (5) 10$ However, all the field data from aeven wells

analyzed here consistently showed low sensitivity of

‘hehorizontal force at the cutter, FH, is related totorque to bit weight, as compared to the laboratorydata and as expected from Eq. (11).

.hetangential force asTheoretically, in homogeneous rock, the torque an

‘H= FT COSf)-l = FT (6) the penetration rate should both respond to the bit

weight similarly. In real drilling conditions howeverlecausethe side rake angle ~ is aa small as 5 deg. correlation between drilling rate and torque is much

stronger than correlation between each of them and theThe cutting area Ac, can be calculated using Eq. weight on bit. This henomenon ia well documented in

:4)aa; the recent researchobserved in p.eviou~~~~~iso ‘as ‘ualitati’vely

‘N~ ‘$

Ac =pw-—

Rc(sinu + p Cosa) Rc<ainff+ p Cosa) (7) Eq. (11) indicatea that, though absolute value oftorque for the worn bit ia smaller than that for thenew bit, its sensitivity to the bit weig>t (slope)

substituting(6) and (7) into (5) gives should not change. This is not quite supported bylaboratory experiments, (compare Figs. 8 and 9), and

2 not observed in the field. The most likely reason

‘H=F1-Mtga-2-(p+tg a)RA

NV+tg@ p+tgu pw(8) might be an unequal distribution of the bit weight

acroas the bit face, resulting from uneven distributicof cutters wear. Modelling of these effects requires

To convert Eq. (S) into the bit torque equation, an individual - cutter approach, which makes the model:he density of cutters placement is considered as a quite complex.!unctionof bit radius, n(r), and the torque is

In the authors opinion, for practical purposes,

1-the torque insensitivity to the bit weight can he

‘b =‘tga~FNn(r)rdr~+tgff o compensated by introducing the drilling rate ?nto Eq.

(11). This provides another measured variable, provi[a high level of correlation with the torque and the b]wear. The concept employed here is improve determina.

-2- (p+ tga)2R ~An(r)r dr tion of a non-measured variable (bit wear) by using al(9)p+tga p. w the four other measured variables (W, N, Tb, R). ‘l’hi!

will reduce a scatter of data caused by factors notconsidered by the model.

The explicit form of Eq. (9) require. somemowledge of load distribution and wear distribution The wearflat area Aw in Eq. (11) can be written ihcross the bit face. Let us asslumethat the load is a function of drilling rate, rotary speed, wear, andwenly distributed along bit radius and that the work weight on bit by using the drilling rate equations]erformedby cutters is different at each radius[unbalancedbit design), and it is represented by

given in the Appendix - Eqs. (A-28) and (A-29):

Eunction fl(r): Aw=[W- +1 / (Rpkl) (13:

i(r) = # = CONST.; and Aw(r) = Awfl(r) (lo)‘GIUDN

b By introducing (13) into (11), dividing both sid(by (w/db), and by standarization, we obtain

\fter substituting (10) into (9) and integrating, the>it torque becomes

‘D=E1+E2FD(14:

Fb = W $~p-+ut;gj) - Aw 2- ‘p + ‘g a)2 CIRPwhere

(11)b

p+tga

#here constant Cl is

..-

.

140

.knt-lcnw 17109 F KImfl. Aklll A K U01TANINJTI?7 K

.-V, -*LI .r. .A. “...”..”, .x. ” . . . ...”.?” -....””-”-

48 irl(l- p tg a) - Cl ~[2 - (p + tg a)z]

.

significant data scatter observed, however the linear

‘1 =trend was dominant in all plots made. The values of

~kl(p+tga) the linear correlation coefficientwere 0.6624 and0.69608 for the new bit and for the used bit, respec-

(15) tively. The linear trends for the new and the wornbits (the straight line in Fig. 15) are close; thus

12 C1[2 - (p + tg a)2] Rst providing additional evidence that the diagnostic plotT vs. FD does not depend upon anything but rock pro-

‘2= ~k1KG1(p+t8a) (W/db)stN~t $!p rtiea.

(16)

‘D= (12 *

st)/[uD(w~) (&)a]St(17)

Eq. (14) constitutes,a diagnostic drilling model.[t indicates a linear relationship between the dimen-sionless groups TD and FD while drilling a homogeneousEormation. The llnearity of Eq. (14) was verified,lsing results obtained in laboratory drilling tests astell as the field drilling data.

The ex nsive study on the PDC drilling by Hibbsmd Sogoia~f included results from the full scalekilling test conducted at the University of Tulsa.l’hesedata were analyzed here, using the diagnostic?lOt T VS F’ .

“!!

The results obtained for various bit:Ypes !/riddx ferent rocks confirmed thij,linearityofLhe plot. The example plot for the 8 4-in. bit runin Carthage marble is shown in Fig. 11.

The field verification was made using data fromseven wells drilled with PDC’S in the Gulf Coast area.[n two of these wells the drilling data were provided>y the MWD. In the other wells the drilling processias monitored at the surface. Five variables (drillingrate, weight on bit, rotary speed, torque, and drillingiepth) were recorded for each one foot interval Figs.12 and 13 show typical examples of drilling logs made>y plotting bit weight, torque, and drilling raterersus depth. In both figures, bit weight correlatesrery well with torque, though a significant fluctuation>f dats can be noticed. However, drilliug rate in?ig. 12 indicates no correlation with torque and bit~eight, unlike Fig. 13, where this correlation is good.rhe reason is that the drilling rate record in Fig. 12#as made from the surface measurements, and it was?lotted against bottomhole measurements of torque and>it weight. On the other hand, all data in Fig. 13 arefrom the NWD bottomhole record, and the drilling ratecorrelation is good. This comparison stresses theimportance of having a consistent bottomhole drillingiata for proper interpretation.

The two-step procedure was followed, to improvethe quality of the data snd hence the interpretationtechnique. At first, the logs of all drilling vari-ables involved depth, were prepared by using MWD data(Fig. 13). The logs were smoothed, to eliminate the~oise (or scatter), by following the general trend of?ach curve. Care was taken to correlate the character-istic points of the logs as shown in Fig. 13. Thereadinga of drilling variables were made, using thesmoothing curves. Then, they were used to calculatethe dimensionless groups, TD and FD, and to make plots.

Ten plots were made using early dats from variousPDC bit runs (sharp bits). Typical examples of theplots are ahown in Figs, 14 and 15. There was still a

DEVELOPMENT OF THE MWD DATA INTEkDETATION METHOD

The concept of the method is based on the diag-nostic drilling model - 13q.(14). In this equation,the dimensionless groups TD and F are functions of thfour measured drilling variables ybit weight, rotaryapeed, drilling rate, and torque) and one non-measuredvariable - bit wear (function Up). At the same time,the mechanical properties of drilled rock and the PDCbit geometry are exclusively combined in constanta El,and E . These constants represent the straight lineinter~ept and the slope, respectively. That simplymeans that, at least theoretically, for the same bitand the same formation there will be only one straight

line ‘D ‘s” ‘D’and it will be iridependentfrom the bi

wear.

The interpretation procedure is as follows:

1. Calculate dimensionless values of T and F byusing equation (16), Bit wear fu~nc;n,F#in;sTequal to unity for the new bit.values can be estimated by using the d~tapfrom t!initial period of drilling.

2. Mske a plot TD vs. FD. Verify linearity of theplot and draw the straight line. The position andirection of this line (Eformation drilled.

3.

~, E2) represent the

Use a continous record ’ofthe MWD to detect anychanges of the straight line’s trend. A con-sistent change in direction will indicate forma-tion change.

4. Use the straight line data to infer instantaneousvalue of the bit wear as follows:A. Calculate instantaneous value of TD using Eq

(16).B, Enter the straight line plot (TD vs F ) with

the calculated TD value [or use Eq. (?4)] andetermine corresponding FD value.

c. Solve Eq. (17) for U .D. Solve Eqs, (A-22b), ~A-22d) for w which is a

instantaneous bit wear,

The above algorithm is a general outline of the dataprocessing procedure, to be followed by a computationdevice installed on-line with the MWD data acquisitioncenter. Further analytical developments are beyond thscope of this paper. However, the most important issuhere is whether practical applications of the methodwill provide meaningful results.

Detection of Formation Changes

The MWD drilling data from the investigated wellswere collected above and below the transition depths awhich a distinctive change in lithology was present.Then, the diagnostic plot was msde and a change of thestraight line trend was sought and correlated with thetransition depth.

Examples of the lithology change detection usingthe method are shown in Figs. 16, 17, 18, and 19. Thedata from well No. 1 were used in analysis. There wex

141

6 A METHOD FOR DETECTING IN-SITU PDC BIT

two PDC bit runs in this well, The first one was aPD-11 9..875in. bit. The bit was run from 3100 ft. to5138 ft. Formation was primarily shale, layered withsand. The sequence of sands and shslea was carefullyanalyzed using the dual induction resistivity logs.The analysis showed that there was a rapid lithologychange at depth 3893 ft. - Fig. 16. The dimensionlessplot (TD VS F ) within the hole section from 3880 to

R3910 ft. is s own in Figure 17. The distinctive changeof slope indicated that there was a transition fromshale to sand at the same depth of 3893 ft. It wasfurther detected that the sand layer was about 9 ft.thick.

The second run was also with the PD-11, 9.875-inPDC bit. Fig. 18 shows the logging data, and Fig, 19shows the diagnostic plot for the well section from8009 ft to 8027 ft. The change of slope was even moreaPparent than for the previous case. The lithologychange was clearly detected at depth 8021 ft. The sandlayer thickness was about 6 ft.

Bit Wear Verification

In field drilling, there are only two measurementsof the bit wear: initial (wO) and final after the bithas been pulled out. Therefore, the verificationmethod haa to consider these limitations. The methodused in this research included plotting the diagnosticstraight line (TD vs FD) from the early record ofdrilling with new bit, Then the measurement of thebita final wear waa used together with the drillingdata, rec~rded just before the bit was pulled out ofthe well, to calculate several values of TD and FD.New pointa (TD, FD) were added to the plot. Thesepoints were associated w.th the worn bit. Theoreti-cally, for the same rock, these points should fall onthe new bit straight line. Therefore the deviation ofthe worn-bit pointa from this l~ne indicates anintegrity of the diagnostic model.

The field drilling data collected in this workincluded detailed information about the bit type,manufacturer and the final bit dull. In two cases; bitdull conditions were reported by using the latest IADCfixed cutter bit dull code, together with the picturesof the dulled bit. In all other cases, the bit dullwas assessed according to the bit vendors’ standards.

Example of the worn bit and its dull evaluation isahown in Fig. 20. A 9.875-in RP19 bit was run in wellNo. 3 from 6209 ft. to 10276 ft. The bit dull wasgraded 2, both for the inner and the outer rows, by ,Susing the IADC dull grading code.

Initially, the dimensionleas plot of TD vs FD for,the new bit was prepared in Fig. 14. Then, using the~measured finsl wear, the value of wear function, U wascalculated. ?Several TD and F values were calcula ed,using the same U

!!Rvalue and t e drilling record for the

worn bit just be ore the bit was pulled out. Thepointa corresponding to the late performance of theworn bit were plotted on the same graph, to checkwhether they fall on the straight line. As it is seenfrom Fig. 14, these points were reasonably close to thestraight line.

The second example waa from the 9.875-in PDC bitrun from 6538 ft. to 8325 ft in well No. 2. The dullof this bit was also graded 2, but close examination 01the bit condition, and information from the bit manu-facturer, indicated that in their ayatem the total weal

LL AND LITHOLOGY CHANGE IADC/SPE 17192

was considered 0.5 of compact face. Therefore, thesame wear in the IADC system would be 1 instead of 2.

As in the first case,‘he ‘alues ‘f ‘D and ‘D’corresponding to the final wear, were calculated and

plotted on the diagnostic graph. Figure 15 shows thefinal points being fairly close to the new-bit straighline.

DISCUSSION

The limited data from the field indicate that theresolution of the method and the sensitivity of alldrilling variables are low. For example, the flatshape of diagnostic plots (TD vs FD) makes them verysensitive to the vertical scatter of the experimentaldata. The plots were made from the typical drillingprocess, in which both weight-on-bit and rotary apeedwere held constant by a driller. The possible sourceof variation was: (1) instability inherent in the MWDmeasurements and; (2) irregularity of slacking-off hooload to maintain steady weight on bit; and (3) forma-tion heterogeneity. The diagnostic plots analysed inthis research were based on typical in-situ fluctua-tion of drilling variables. It ia expected that thediagnostic plots will improve if the drilling datainclude significant (deliberately made) changes in bitweight and rotary speed.

Another source of error associated with practicalapplication of the method, is the drilling modelitself. Basically, the model simplifies the actualdrilling process in two ways: (1) by using linearrelationships throughout the model; and (2) by infer-ring bit behavior from the single cutter behavior.

Numerous studies with sharp and worn PDC cuttersindicated a linear relationship between penetratingforce and penetration rate, in the rock chippingregime. The extrapolation of the linear trend showednon-zero penetrating force at zero depth of cut, Thisthreshold force was found to increase in magnitude witcutter wear and uniaxial compressive strength.

Response of torque t. weight on bit is alsolinear. Torque is determined by weight on bit exclu-sively for the new bit; the torque value is entirelycontrolled by cutting force. As the bit weara out, tbtorque increases, even at the constant drilling rate.The torque increase is caused by two factora:(1) increase of rock cutting force, and (2) sliding

:::::i?n ‘n ‘he ‘ear ‘lst area” ‘owever’ ain@e Cutteshowed that the cutting forces were almost the

ssme for sharp and dull cutters, for the equal depthsof cut. Thus, it is more likely that the increase oftorque, at the same drilling rate, primarily resultsfrom higher frictional drag between rock and wear flatarea. Since frictional drag is directly proportionalto normal force, and normal force is proportional towearflat area, then t.,elinearity between torque andbit weight is theoretically justified.

The assumption on mechanical similitude betweensingle cutter behavior and the entire bit has beenalready discussed. One more aspect, however, needs tobe pointed out: bit dull definition. In the singlecutter model, the dull is fully defined by the flat-crested cutter wear. Consequently, function UD, in thdiagnostic model, implies some average flat-crestedwear across the entire bit. In the practical applica-tions, the value of the bit wear (w or x), calculatedusing the method proposed here, is defined exclusivelyby this method. It ia meaningful because it represent.

142

reductionof bit performance due to drilling. However,it can hardly be compared to the measured bit dull,rhich alao accounta for broken or lost cutters. It}eema that a more specific procedure for evaluation of:he PDC bit dull must be developed. Such a proceduretill precisely comply with the diagnostic drillingoodel.

CONCLUSIONS

1.

). .

).

i.

i.

In the abaence of any direct measurements of PDCbit wear at the hole bottom, the proposed methodgives the only available option for instantaneouscontrol of drilling parameters to prevent earlybit failure.

Analysia of the field drilling data showed apotential ior this method to detect rapid forma-tion changea, and to asseas bit condition whiledrilling ahead. The latter application, however,requires more precise definition of the bit dull,as well as an analysis of the method’s resolution,

The method has been derived from the simplifiedPDC drilling model, namely the two explicit equa-tions for drilling rate and torque. The diag-nostic model, Eq. (14), constitutes a singlelinear relation between two dimensionless groupscontaining four measured drilling variables. Themodel allows simultaneous analysis of ever fluctu-ating values of these variables, at any particularinstant of time.

The method constitutes a theoretical basis fordevelopment of a software, necessary to make fulluae of the MWD data for the optimized drillingcontrol.

Further developments include: 1. Introducing PDCbit geometry in the diagnostic model; 2. Defininga composite bit dull and its measurement;3. Experimental determination of the ❑ethodaccuracy and its resolution; and 4. Development 04the MWD software.

fOMENCIATURR

4C =

4W =

4wd =

9 =

B1, B2 =

‘b =

dc =

‘1’ ‘2 =

Fc =

‘D =

‘fc =

Cutting area, in.2

Cutter wearflat area, in.2

Dimensionless cutter wearflat area, unitless

Rotary speed exponent, unitless

Constants representing rock bit Interaction,unitless

Bit Diameter, in.

Cutter Diameter, in.

Constants in diagnostic drilling model, Eq.(14), d-leas

Cutting force lbfs.

Dimensionless drilling rate group.

Friction force e fective on the cutting5

surface area, 10 lbfa.

‘fw

‘H

‘N

‘T

‘1

‘1

‘2

h

I

K

kl

‘2

‘3

n(r)

N

NSt

r

R

‘b

! Rc

RP

RSt

‘b

‘D

Tr

‘D

w

wo

wSt

w

x

a

ac

Friction3force effective on the wear flatarea, 10 lbfs.

Horizontal force at the cutter, 103 lbfs.

Normal force at the cutter, 1000 lbfs.

Tangential force, 103 lbfa.

Function defining the distribution of thelo~,dat acroas PDC bit face

Unit conversion constant, 0.7589* 60/hr. min

Unit conversion constant, 3.8637, unitleas.

Cutting depth, in.

Cutters Interference Constant, unit

Drlllability constant, ft/(103 lbf)

Proportionality constant between we:bit and n~ ~al force, unitless.

ess.

ght on

Cutter wear constant, sq. in (103 lbf):

Proportionality constant between penetrationrate and cutting depth, unitless.

Cutters density, unities

Rotary speed, l/rein

Standard Rotary speed, l/rein

radius, in

Drilling Rate, ft./hr.

Bit radius, in.

Rock resistance to shearing, lbs x 103/sq.in.

Rock resistance to pressingin.

Standard Penetration Rate, :

Bit torque, ft. lb.

dimensionless torque group

lbs X 103/sq.

t/hr.

Single cutter torque, in-lbs

Dimensionless cutter wear function, unitless

Weight on bit; weight on bit, lbf x 103

Threshold weight-on bit, lbs x 103

Standard weight on bit (4000 lbs/in at bitdiameter)

Dimensionless linear cutter wear, unitleas.

Linear cutter wear, in.

Back rake angle, degrees.

Cutting angle, degrees.

143

8 AMRTHOD FOR DETECTING IN-SITU PDC BIT DULL AND LITHOLOGY CHANGE IADC/SPE 17192

= Side rake angle, degrees. 9. Glowka, D. A.: “Implications of Thermal WearPhenomena for PDC Bit Design and Operation,” Pape

= Coefficient of friction between cutter SPE, 14222 Presented at the 60th Annual Tecl,.licalsurface and rock unitleas. Conference and Exhibition of the SPE, Laa Vegaa,

NV, (September 22-25, 1985).CKNOWLEDGEMENTS

10. Caraon, C. C. and Lin, Y. T,: “Geothermal WellThe authora wish to expreaa their appreciation to Costs and Their Senaitivities to Changes in Drill

rofessor A. T. Bourgoyne of LSU for hia help in ing and Completion Operation,” Proc. Intl. Conf.dlecting field data. Geothermal Drilling and Completion Technique,

Report SAND81-0036C, Sandia National LaboratoriesAn appreciation is given to Mr. Bill Cortlang and Albuquerque, NM (Jan. 1981) 8-1-8-26.

r. Rick Graff of The Temeco Oil Company, and to theeraomel of Tenneco Real Time Data Center in 11. Lin, Y. T.: !!TheImpact of Bit per~~rmance on

afayette. Geothermal Well Coat,” Trana. Geothefial Res.Council (Oct. 1981) 5, 153-56.

We would also like to thank Mr. L, E. Hibbs, Jr.or hia assistance in providing Laboratory data. 12. Zi.aja,M. B.: “Mathematical Model of the Poly-

crystalline Diamond Bit Drilling Process and ItsThe financial support from the Ministry of Educa- Practical Application,” Paper SPE 14217, Preaente

ion of Turkey, is greatly acknowledged. at the 60th Amual Technical Conference andExhibition of SPE, Las Vegas, NV (September 22-25

EFERENCES: 1985).

Cerkovnik, J,: “Design, Application and Future of 13. Glowka, D. A,: “The Use of Single-Cutter Data InPolycryatalline Diamond Compact Cutters in the the Analyais of PDC Bit Designa,” Paper SPE 15619Rocky Mountaina,” paper SPE 10893 presented at the Presented at the 61at annual Technical ConferenceRocky Mountains Regional Meeting of the SPE, and Exhibition of the SPE, New Orleans, LA (Oct.Billinga, MT, (May 19-21, 1982). 5-8, 1986).

. Ofenbacher, L. A., McDermaid, J. D., and 14. Warren, T. M. and Sinor, A.: “Drag Bit Perfor-Patteraon, C. R.: “PDC Bita Find Applications In mance Modeling,” Paper SPE 15618, Presented at thOklahoma Drilling,” paper IADC/SPE 11389 presented 61st Annual Technical Conferences and Exhibitionat the IADC/SPE 1983 Drilling conference, New of the SPE, New Orleans, (October 5-8, 1986).Orleans, LA, (Feb. 20-23, 1983).

15. Sinor, L. A., and Warren, T. M.: “Drag Bit WearMoore, S. O., Lynch, B. W., Talbot, K. T.: “A Model,” Paper SPE 16699, Presented at the 62ndCase History of Polycrystalline Diamond Compact Annual Technical Conference and Exhibition of theBlt Performance in the Tuacoolosa Trend,” paper SPE, Dallas, TX (September 27-30, 1987).SPE 11944 presented at the 58th Annual TechnicalConference and Exhibition of the SPE, San 16. Wojtanowicz, A. K. and Kuru, E.: “Dynamic Drill-Franciaco, CA, (Oct. 5-8, 1983). ing Strategy for PDC Bits,” Paper SPE/IADC 16118,

Presented at the 1987 SPE/IADC Drilling. Balkenbush, R. T.: “Application of PDC bits in Conference, New Orleans, LA (March 15-18, 1987).

the Kuparuk Field, Alaska,” paper SPE 11946,presented at the 58th Annual Technical Conference 17. Clark, D. A., Coolidge, R. B., Kelety, J. T., andand Exhibition of the SPE, San Franciaco, CA, Kerr, J.: “Application of the New IADC Dull(Oct. 5-8, 1983). Grading System for Fixed Cutter Bits,” Paper SPE

Arceneaux, M. A.,16145, Presented at the 1987 SPE/IADC Drilling

and Fielder, J. L.: “Field Conference, New Orleans, LA, (March 15-18, 1987).Experience with PDC Bita in North Texas,” PaperIADC/SPE 11390, Presented at the IADC/SPE 1983 18. Hibbs, L. E., Jr., and Flom, D. G.: “DiamondDrilling Conference, New Orleans, IA, (Feb. 20-23, Compact Cutter Studies for Geothermal Bit Design,1983). Paper presented at the ASNE 1977 Energy Technical

Conference and Exhibition, Houston, TX (SeptemberPateraon, A. W., and Shute, J. P.: “Experience 18-20, 1977).with Polycrystalline Diamond Compact Bits in theNorthern North Sea,” Paper EUR 339, Presented at 19. Warren, T. M.: “Factors Affecting Torque for athe European Petroleum Conference, London, Roller Cone Bit,” Journal of Petroleum TechEngland, (Oct. 25-28, 1982). nology,

(Sept., 1984), V. 36, pp. 1500-1508.. Fox, J. P., and Wood, J. E.,: “Pl)CBits Find

Application in San Joaquin Valley,” Paper SPE, 20. Burgess, T. M. and Leaao, W. G. Jr.: “Meaauring12790, Presented at the California Regional Meet- the Wear of Milled Tooth Bits Using NWD Torque aning, Long Beach, CA, (April 11-13, 1984). Weight on Bit,” Paper SPE/IADC 13475, Presented a

the SPE/IADC Drilling Conference, New Orleans, LA‘. Preslar, P. L., and ticDermaid,J. D.,: “PDC Bit (March 6-8, 1985).

Provea Effective at South Graham Deeae Sand Unit,”Paper SPE 11945, Presented at the 58th Annual 21. Hibba, L. E., Jr. and Sogoian, G. C.: “WearTechnical Conference and Exhibition, San Mechanisms for Polycryatalline Diamond Compacts aFranciaco, CA, (October 5-8, 1983). Utilized for Drilling in Geothermal Environments,

Report SAND82-7213, Sandia National Laboratoriea,Albuquerque, NM (May 1983).

.

!2.

!3 .

!4.

!5.

!6.

!7.

!8.

!9 .

10.

11.

12.

33.

34.

35.

Rock Sampl& Under Hydrostatic Pressure,” Trans.ASME (1957) 79, 695.

Chestham, J. B, Jr. and Gnirk, P. i.: “TheMechanics of Rock Failure Associated with Drillingat Depth,” Proc, 8th Symp. Rock Flech.,Univ. ofMinnesoty (October, 1958), pp. 410-439.

Gray, K. E.: “Some Rock Mechanics Aspects ofPetroleum Engineering,” Proc. 8th Symp. RockHech., Univ. of Minnesota (October, 1958), pp.405-433.

Handin, J., Hager, R. V. Jr., Friedmsn, M. andGeather, J. N.: “Experimental Deformation ofSedimentary Rocks Under Confining Pressing Tests,”Bull., AAPG (May, 1963) Vol. 27, 717.

Garner, E. N., Podio, A., Gaziin, C.: “Experi-mental Study of Crater Farmation in Limestone atElevated Pressures,u Journal of petroleum Tech-

- (December, 1963), Vol. 15, 1356.

Podio, A., and Gray, K, Z.: “Single-Blow BitToothImpact Tests on Saturated Rocks Under ConfiningPressure: I. Zero Pore Prenaure,” Society ofPetroleum Engineers Journal, (September, 1965),Vol. 5, No. 3, pp. 211-224.

Yang, J. H., and Gray, K. E.: “Single-Blow Bit-Tooth Impact Tests on Saturated Rocks Under Con-fining Pressure: 11. Elevated Pore Pressure,”~, (December, 1967), Vol. 7, No. 4, pp. 389-408.

Myers, G. M. and Gray, K. E.: “Rock FailureDuring Tooth Impact and Dynsmic Filtration,” SPEJ(June, 1968), Vol. 8, No. 2, pp. 163-173. —

Winters, W. J., and Warren, T. M.: “Roller Bit3iodelWith Rock Ductility and Cone Offset,” PaperSPE 16696, Preaente6 at the 62nd Annual TechnicalConference and Exhibition of the SPE, Dallaa, TX(September 27-30, 1987).

Zeuch, D. H. and Finger, J. T.: “Rock BreakageMechanisms With a PDC Cutter,” Paper SPE 14219,Presented at the 60th Annual Technical Conferenceand Exhibition of the SPE, Las Vegas, NV(September 22-25, 1985),

Winters, W. J., and Doiron, H. H.: “The 1987 It&(Fixed Cutter Bit Classification System,” PaperSPE/IADC 16142, Presented at the 1987 SPE/IADCDrilling Conference, New Orleans, LA (March 15-18,1987).

Clark, D. A., and Walker, B. H.: “Comparison ofLaboratory and Field Data for a PDC Bit,” PaperSPE/IADC 13459, Presented at 1985 SPE/IADC Drill-ing Conference, New Orleana, LA (Harch 6-8, 1985),

Cheatham, C. A., Loeb, D. A.: “Effects of FieldWear on PDC Bit Performance,” Paper SPE/IADC13464, Presented at the 1985 SPE/IADC DrillingConference, New Orleans, LA (March 6-8, 1985).

Warren, T. M. and Armagoat, W. K.: “LaboratoryDrilling Performance of PDC Bits,” Paper SPE15617, Presented at the 61st Annual TechnicalConference and Exhibition of the Society of

145

Petroleum Engineers, New Orleans, LA (October 5-8,1986).

APPENDIX

DERIVATION OF TNT,WEAIO?LATAREA EQUATION

Shape 01 the cutter wearflat ia defined as anelypae. Elements of the elypae are defined in terms oPDC cutter terminology as follows:

2a = dc cosa

2b = dc(A-1

The distance, 2 ia ~efined as; (fig. 21b)

X2~=~d ‘-—

c Cosa 2(A-2

Cos c1

snd the distance t, (fig. 21b) is defined as

22t=a~l-—

b2

The dimensionless cutter wear ia defined as

(A-3

x-—w- dc COSU(A-4

The wear flat area (the shaded part of the elypse inFig. 21) is geometrically defined as follows:

Aw = ab Arc cos ~ - t!2 (A-5

By introducing (A-1), (A-2), (A-3), and (A-4) into(A-5) we obtain:

dc~Aw=—

2aina[~Arc coa~l - 4(w - W2)

- ~W - 5W2+8W3 - 4W4] (A-6

DERIVATION OF THE CUTTING AREA EQUATION

The model assumes that PDC cutters interact in

such a way that the cutter works always on the flatbottom.

The cuti,izgarea is modeled as a part of thecircle, Fig. 19. Perimeter equation for a segment ofcircle is:

p = J(2g)2 + f C* (A-7

Area of a segment of a circle is:

A=; [Pr - 2g(r-C)] (A-8

where r is the radius of the circle P and Q are definein Figure 19. Thus, using Figure 19, cutting area is:

(A-S

o A METHOD FOR DETECTING IN-SITU PDC E1’I

~here,x

cl=— comaX+h

c2=— C08U

)?O~ (X + h) < O,Liclc Cos(i (A-1O)

(x+h).—c1 = ‘c cosa

x.—C2 = ‘c cosa

For (x + h) > 0.5dc cosa (All)

‘2 = 4(:)2 - (> - C2)2 (A-12)

21 = J(>)2- (>- C*)2

P2 = 4(2J?2)2 + : C22

x h— —y = dc cosa + dc cosa

(A-13)

(A-14)

(A-15)

(A-16)

Finally, by introducing equation (A-1O) through[A-16) into equation (A-9), we obtain;

~or (x+h) > 0.5 dc cosa

,2

\c = KE.&+2- [JY +y - ~y- 5y2+8y3 - 4Y4

-~W+$#+ ~W-5W2+8W3-4W4

~or (x+h) < 0.5 dc cosa

d2

kc = cos~ C;sa c [J!@!?&.

43

52-24-w4+2w3-zw+& ~4-5y+y2

43

+24-y4+2y3 Ly.:2+;]

DERIVATIONOF WEAR FUNCTION, Un

(A-17)

The function A shows very small non-linearityflithcutting depth,ch, Fig. 23. It is assumed to be alinear function of the cutting depth within the cuttingiepth limit, O<h<O.l in. Maximum cutting depth is!stimated as 0.1 in. by asauming a maximum drillingrate of 100 ft/hr, minimum rotary speed of 40 rpm, andrive interfering blades. The function Ac is formulatedIs follows:

.

)ULL AND LITHOLOGY CNANGE IADC/SPE 17192

dASince Ac ia a linear function of h, -# becomes

dAconstant. Therefore L can be written as a functionof linear wear, x. T~~ functional relationship betweeh and x was calculated asauming average valuea ofnormal force, (300-800 lbf/cutter). The results areplotted in Figure 24. The relationship between h andcutter wear is then formulated as follows:

y(w) = ~ ‘w + 0.028 exp[-0,05 w]dc coaa (A-19

By taking firat derivatives of equation (A-17a)and (A-17b), the rate of chanRe of cuttinfiarea versuscutting depth is:

For h + x < 0,5dc coaa:

dAc_=+ [ 1‘$ -dh

(1 - If)y+ 24y2 - 16y3)

~y + y ~Y - 5Y2 + 8y3 - 4Y4J

For h + x ~ 0.5 dc cosa

dAc+ [ (s - 2Y)

r=

243 44 - 5y + y2

(-4y3+6y2-~+~)+ 1

+Y4 , 2Y3 - + $$2

(A-20a

(A-20b

Finally, using equations (A-20a), (A-20b) and (A-18),cutting area can be written as:

Ac =hb~ (A-21D

where;

b, - -: ‘c (A-22a

4(Y + ~) (y-52+8y3-4y4)UD =

(1 + 5y)4y-5y2+8y3-4y4-4y + ~ y2 [1-10y+24y2-16y3

(A-22b

for (x+h) < 0.5 dc cosa and,

b=+ (A-22c

352y2~3~&5y+y2~-y4+2y -p +4

‘D =

(5-2y)~-y4+2y3-~+~2~3 ~4-5y+y2[-4y3+6y2-~~]

(A-22ddA

A- = h (~) (A-18)

146

. .

ADC/SPE 17192 E.KURU. AND A.K.WOJTANOWICZ 11.—-,--- ----- —.—.–—‘or(x+h) ~ 0.5 dc cosu

ERIVATION OF PENETRATION RATE EQUATION

E( . 1 is wzittea 93:

FN = RcAc[Sinu + M cosa] + RApw

(A-23)

can be written as:c

‘NR Aw

‘c= Rc[aina + p co~ - Rc[sina + p cosa](A-24)

Combining (A-21), (A-22) and (A-24), cuttingepth, h, can be written as:

h= ~ ‘FN - ‘pAW]b Rc[aina + p coaa]

(A-25)

smuming the penetration rate ia proportional to theutting depth, the bit rotates at speed N, and theumber of interfering cutters is I, the drilling rates:

R= k3hNaI (A-26)

An assumption on linearity between bit weight andhe cutter’s normsl force, gives:

W = klFN (A-27)

y combining (A-27), (A-25) and (A-26), drilling ratequation is:

R = KG1[W - Wo]UDNa (A-28)

here

W. = G2A*Awdn*kl*I$

A = x d~/4(A-29)

A = Aw/Awd

A = tzwd/3.863703wdn

nd K is the drillability constant defined as:

k3 IK=

kl b Rc[sina + p cosa] (A-30)

. .-

uv6u.

#’.-H

d’

SS3141S oNlllncl

II

I

II

I

b“ o

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~

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EII.

~*2OUY

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z

10 - 0 CHAMPLAIN BLACK MARBLE0 WHITE DANBY MARBLE

o~o 5 20 25

OEP~H ( In. x ?0-3 )

Fig.5—cumum — sMlkfwmll wmqd0pul[d2um. 21).

8 34= STRATAPAXn BIT

CARTHAGE MARBLE

1-a 200 RPM (432 6PM)K 30

g*a

‘k

100 RPM (432 GPM1: 20

50 RPM (220 GPM1w

“0 -, /’:[432GpM)

o0 2 4 6 8 10

BIT WEIGHT (Lb. x 103)

m~--*hunmd w.tAWlUm.2l).

300

0 SHARP CUTTERS SIERRA WHITE0 OULLEO CUTT2RS GRANITE

(00 RPM250 -

2000 Psi315*C- !5° RAKE

Q 200 0

A:IA: 150 0

2 0$!o+ 100

50

0{/

() ~~o 400 800 [200 1600 i

BIT WEIGHT [Lbs.)D

400(

350(

300(

- 250C~

J,.

&

w 200C

sao1-

150C

1000

500

SHARP CUTTERSOULLEO CUTTERS

BEREA SANOSTONE

1250 PSI

60-175 RPM 0

/

~‘(,,,,/&

/’/’

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o0 4 a 12 16 20

WEIGHT ON BIT (Lbf. X 103)Fig.s-sJhu&8u&Wn01nwWHzAl$ummnilsma@~m

.

.

FTA. COMPLETE

M

B. SIMrLIFIED

WELL S 4 ----- ❑ WORN BIT

BIT DIAMETER: 9 % [n. — o NEW BIT

OEPTH IN, 5910 Ft.OEPTH OUT : 8586 Ft

0 2 4 0 0

WEIGHT ON Bil (Lbs. %103)

%.lO-SHutd POCMt-uM. K8QBm WmMti~Wh

1 r I Io 10 20 0 al 0.2 60 80

WEIGHT ON BIT ( Lbsx 103 ) TORQUE (Amps.x 103) ORILLING RATE (Ft. /Hr. 1

7.92

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:

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7.82

1 T L

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wEIGHT ON BITS ( LbsxlO% TORQUE ( Amps.x 103 ) ORILLING RATE ( F!. / Hr. )

*TS-WWV-MW93Z

0.90

I

BIT OIAMETER: 8‘~ In.

CARTHAGE MARBLEO.ao SHARP BIT (UD= 1)

0.70

0.60 [ 0 I~o 0.50 -

0.40 -

0.30 -

0.10 -

0.00 I 1 1 1 I I ! , I I I I 1 I

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