CA2009654A1 - Method of predicting drill bit performance - Google Patents

Abstract

ABSTRACT OF THE DISCLOSURE
A method is disclosed for predicting the per-formance of a drill bit. By using a generalized model, with bit description, operating conditions and rock prop-erties as inputs, the rate of penetration and duration for the bit can be predicted. Further, model is based on the-oretical considerations of single-cutter rock interaction and can include a variable for cutter wear.

Description

2~)096S4 PATENT

Hareland, et al.

"METHOD OF PREDICTING DRILL BIT PERFORMANCE"
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Background of the Invention 1. Field of the Invention The present invention relates to a method of predicting drill bit performance and, more particularly, to such a method that can predict the performance of dif-15 ferent configurations of drill bits.

2. Setting of the Invention -, Two classes of drill bits are normally used in the petroleum exploration industry: drag bits and rol-20 ler-cone bits. Drag bits have gained in popularity in recent years because of their increased use with high speed downhole motors. Drag bits seem to have longer bit life, due to better cutter wear characteristics. Also, unlike rollerrcone bits, they do not have bearings which 25 fail easily and shorten bit life. To assist in selecting a bit to use in a particular location, the anticipated drilling performance of a bit is desired. One usually wants to know how fast a particular bit will penetrate a particular type of formation and how long will the bit : . , : ,: , .,,,: . .
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2~109654 effectively penetrate before wearing out. Several arti-cles that describe drag bit modeling are:

Appl, F. C. and Rowley, D. S., "Analysis of the Cutting 5 Action of a Single Diamond," Soc. of Petr. Engrs. J. (Sep-tember 1968), 269-280.

Peterson, J. L.: "Diamond Drilling Model Verified in Field and Laboratory Tests," Journal of Petr. Tech. (Feb-10 ruary 1976), 213-223.

Warren, T. M. and Sinor, L. A.: "Drag Bit Performance Modeling," SPE Paper No. 15618, Presented at SPE Annual Technical Conference and Exhibition, New Orleans, LA
15 (October 1986).

The geometrical correlations were derived from Perry, R. H. and Chilt~n, C. H.: Chemical Enqineers' Handbook, Fifth Edition, McGraw Hill, New York, NY (1973), Page 2-7.
Attempts to predict drilling performance for drag bits have been made by various investigators.
Natural diamond bit predictive models were first developed by Appl and Rowley in 1968 and by Peterson in 1976. Appl and Rowley assumed a plastic Coulomb rock failure with 25 Mohr circle failure criteria and the energy required to remove the rock was obtained from the mechanical energy applied to the bit. Peterson used a static loading condi-tion and an equivalent blade concept, both of which are inapplicable to normal drilling situations. In fact, - ,. ~, ~, .

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Peterson's equivalent blade concept has been found to be impractical and difficult to adapt for natural diamond bits and other bits that do not have blades.
A polycrystalline diamond compact (PDC) perform-5 ance model was developed by Warren and Sinor. The modelis a weight-on-bit (WOB) model, i.e., the penetration rate is an input and WOB is the output. The model requires detailed descriptions of cutter geometry and cutter place-ment on the bit face. Therefore, it can be time consuming 10 to run. The model is useful for detailed bit-design stu-dies, such as single-cutter wear profile, bit balance and vibration, etc. Further, there are no known models that can accurately predict Geoset-type bits. There is a need for a simple, universal model that with few inputs can 15 provide accurate and useful bit performance information.

SummarY of the Invention The present invention has been developed to overcome the foregoing deficiencies and meet the above 20 described needs. Specifically, the present invention pro-vides a method for predicting the drilling performance of a drill bit without the need for a detailed description of the bit such as the bit geometry and arrangements for the purposes of bit design, selection and operation. Lithol-25 ogy coefficients are used to describe the type of rock inwhich the modeled drill bit is to be evaluated, and selected optimal bit conditions, such as WOB and RPM are used to place boundaries on the modeling process. Once the above lithological coefficients are obtained, the rate - . i - i . , :
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of penetration (ROP) and duration of a bit run can be cal-culated from the equation described hereinafter.
This invention describes a new approach to model mathematically the drilling performance of full-hole and 5 core drag bits -- natural diamond bits (NDB), polycrystal-line diamond compact bits (PDC), and Geoset bits. With this new method, the drilling performance of any drag bit, i.e., bits without rotating cones, whether new or worn, can be predicted given the bit description, operating con-10 ditions and rock properties.
The model can be used both for drilling preplan-ning and also for parametric studies to determine effects on penetration rate of bit and operating parameters. This optimization approach based on model sensitivity analysis 15 has not been utilized for drag bit design and operation before. The model is based on theoretical considerations of single-cutter rock interaction, together with empirical calibration factors to account for considerations not ame-nable to theoretical treatment. Significant features 20 incorporated in the model include "equivalent bit radius,"
"dynamic cutter action," and "lithology coefficients."

Brief Description of the Drawings Figure la is a three part illustration of a 25 natural diamond bit cutter geometry.
Figure lb is a three part illustration of a Geoset bit cutter geometry.
Figure lc is a three part illustration of a polycrystalline compact diamond (PDC) cutter geometry.

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Figure 2 is an illustration with explanatory equations o~ the dynamic cutting action of a single cutter.
Figure 3 is an illustration with explanatory 5 equations of the volume of rock material removed per cutter per revolution of a drill bit.
Figure 4 is a graphical representation of how penetration rate is not linearly dependent upon RPM.
Figure 5 is a graphical representation of pene-10 tration rate versus RPM for different weight on bit forthe bit used in Figure 4.
Figure 6 is an illustration of a cutter's con-figurational changes because of wear.
Figure 7 is an illustration with explanatory 15 equations of the volume of rock not removed due to cutter wear.
Figure 8 is a graphical representation and com-parison between actual and calculated ROP versus RPM
thr~ugh shale for a bit.
Figure 9 is a graphical representation and com-parison between actual and calculated ROP versus WOB
through limestone for a bit.
Figure 10 is a graphical representation and com-parison between actual and calculated ROP versus WOB
25 through shale for a bit.
Figure 11 is a graphical representation and com-parison between actual and calculated ROP versus WOB
through shale for a bit.

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Figure 12 is a graphical representation and com-parison between actual and calculated ROP versus WOB
through limestone for a worn bit.
Figure 13 is a graphical representation of the 5 predicted model results sensitivity to changes in operat-ing parameters.
Figure 14 is a graphical representation of the predicted model results sensitivity to changes in bit parameters.
Figure 15 is a graphical representation and com-parison of the actual and calculated ROP for a bit without wear correction.
Figure 16 is a graphical representation and com-parison of the actual and calculated ROP for a bit with 15 wear correction.

Detailed DescriPtion of the Preferred Embodiments The present invention provides a method of mod-eling any configuration of drill bit and from the model 20 predicting the rate of penetration and duration for a given lithology and operating conditions. The present model is based on physical phenomena with empirical cor-rection coefficients from lab and/or field data. The - basic assumptions of the model are that for a particular 25 group of drag bits, all cutters are roughly the same aver-age geometry, and are equally loaded. significant con-cepts described below include (1) equivalent bit radius, (2~ dynamic cutter loading, and (3) lithology coeffi-cients.

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2(~096S4 Figure l shows three typical cutter geometries;
one for natural diamond bits (la), one for Geoset bits (lb) and one for polycrystalline compact diamond bits (lc). The following discussion concentrates on the 5 natural diamond bit model, although, as shown later, it can be modified for other drag bit types.
The dynamic rock penetration criterion is used, i.e., the cutter projected (contact) area with the rock is half of Peterson's area (see Fig. 2). This represents 10 dynamic (moving) cutting action as opposed to Peterson's static action. In general, the projected area is given by Ap = ~ech (l) where Ap = projected (contact) area of each cutter, ac = rock compressive strength, and Wmech = mechanical loading per cutter diamond, i.e., applied weight-on-bit less the pump-off force, divided by the number of diamonds.

From basic geometry, the projected dynamic cut-ting area for a natural diamond type cutter given by Ap = 2 [2 ~ (2 ~ P) ] = ~2(dSP-P2) = 2 ' (2) .- ~ - . .. . .
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assuming dsp p2, as will be generally applicable, where ds = diamond (stone) cutter diameter, and S P = diamond cutter penetration Combining Equations 1 and 2 to eliminate Ap, the diamond .
penetration, P, is obtained such that p = 2Wmech (3) Using P again, an equation is obtained for Av, the area being compressed in front of a cutter, as shown in Figure 3, such that d Av = (2S)2 x c03 1(1-(2 x P/d5))~(dg x P~P2)1/2(dg/2~P) (4) To avoid complications associated with detailed description of each cutter location on the bit face, an assumption is made that all cutters can be visualized as located at an "equivalent radius" and thus each cutter does equal work, which is an average. Therefore, all cut-ters travel an effective distance 2~Re per revolution.
Equivalent radius, Re is defined in Fig. 3 such that .

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Al = A2 = 2 AB

where AB is the bit-face area.
Areas Al and A2 are defined such that they remove the same rock volume.
Mathematically, 2~ Re = ~RB~ where RB is the radius of the bit face, giving -Re RB~ ~ ~
or (6) R~ = DB/(2 ~) for full hole bits.

15 For core bits, the applicable equation is Re = ~ ~(Do + Di ' (7 where Do~ Di are outer and inner diameters of the core bit.
The same approach can be used to define applica-ble equivalent radius for bits with unusual cutter dis-tributions or bit face profiles.
Summing the volume removed for all diamondsgives VD = volume removed per revolution in the form ::
D ~ 2~Re Nc Av (8) _ g _ . ~ - :, ,,, . . . , -:- ~ ~ . .. . . . .
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where Nc = number of cutters.
To obtain the rate of penetration ~ROP) in ft/hr, the volume, VD is divided by the bit face area, and appropriate units correction is applied. For full-hole 5 bits, ROP = 14.14(Dl) (Nc ~ RPM Av) . (9) 10 Substitutin~ for Av and P, N RPM ds 1 4W
ROP = 14 .14 ( c D [ Ncd2n~c ( 10 ) :.

2Wmech 4Wmech 1/2 ds 2Wmech _ ( - ) (2 Ncnacds ]

20 For core bits, lDo + D2i (D2 _ Di2~ s v (11) Di is bit inner diameter in the case of a core bit, and equals zero for full bits. Do is the outer diam-eter. Notice that for Di = ~ Equation 11 defaults to Equation 9 with Do = DB.

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Experience from lab and field studies shows that the behavior of the bit penetrating the rock is not line-arly dependent on RPM as ideally predicted by Equations 9 to ll. This is shown to be so in Figure 4. A correction 5 factor, therefore, is introduced to model phenomena not modeled theoretically. Such phenomena cause deviations from theory and include effects such as rock strain rate and bit cleaning (hydraulics). At this time, these effects are not accounted for rigorously in the model as 10 they are not amenable to accurate theoretical description.
The mechanical weight-on-bit (WOB) empirical correction is also incorporated in the model depending on cutter geom-etry and lithology (see Figure 5).
The "lithology total correction factor," COR =
15 a/(RPMb x WOBC), has the same set of a,b,c coefficients for each cutter geometry describing a particular drag-bit group (NDB, PDC, Geoset, etc.). These coefficients are developed from lab or field drill-off tests using non-li-near regression analysis. The theoretical ROP from 20 Equation 9-11 is then multiplied by the lithology coeffi-cient, COR, to obtain the model prediction of ROP.
As an example, for natural diamond bits, only one set of a, b, c coefficients is needed to describe the performance for one lithology, because all cutters are 25 assumed to be spherical. The same principle applies to Geoset and PDC bits. Although the present invention dis-closure concentrates on diamond-bit modeling, equations developed for Geoset and PDC bits are included as part of the invention.

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Other drag bits can be treated in the same manner. The projected area and the area in front of the cutter are calculated depending only on cutter geometry.
Referring to Fig. lc, for PDC bits Ap = Sin(~)[(2 ) cos (1 ~ cos(~)d ) (cos(~) co~2 )l/2(2c P (G)] (12) Av = cos(a) cos(~)[(2C)2 cos 1 (1 ~ cosP(~)d )~(co~

co~2(~)) (2 cos(~))] (13) where ~ = cutter backrake angle a = cutter siderake angle dc = diameter of cutter.

~5 From Figure lb, for Geoset bits, Ap = 2 x L x Tan (~) x P (14) -~

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Av = p2 (Tan~)) (15) where ~ = cutter included angle.
L = Geoset cutter length.
It should be noted that for Geoset cutters, siderake and backrake angles are easily introduced depend- -ing on the bit specifics. Also, it is possible that side-rake and backrake angles may affect the a, b, c coefficients for both Geoset and PDC bits. However, such additional consideration does not appear to apply to natural diamond bits.
In order to support actual drilling operations including progressive bit wear, the rock uniaxial compres-sive strength, rock abrasiveness coefficient, the proper-tie~ of the cutter compact material, as well as operating conditions are used in calculating the cutter volume removed by wear. As the cutter volume removed is calcu-lated, the new penetration rate is modified accordingly based on the new projected area and rock volume removed per cutter. This concept is illustrated in Figure 6. As the cutter becomes worn, the following wear equation results:

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VD = ~ CA x RPM x WOB x ~c x ABR ~ (16) ... n refers to footage drilled.

5 where CA= wear coefficient for the cutter :
RPM/Re = relative cutter velocity -WOB/NS = Mechanical loading on each cutter 10 c = uniaxial compressive strength of the rock ABR = relative abrasiveness of formation The volume lost from the cutter is given in Figure 7, using Reference 4, as ~;.

VD = 2(Pw ds) (17) where Pw i5 the cutter penetration lost due to wear.
20 Transposing, .
- : Pw ~ --3-- (18) s The new projected area due to wear from Figure 6 is now : ~ given by .

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pw ~ ( 2 ) 2 (19) Total projected area with wear, Ap equals Apold + Apw (see Figure 6). Mathematically, Ap = 52 1 + 2 w (20) where P1 is the diamond penetration with wear (i.e., Pl =

w ) 2Ap Pl ~ds Pw (21) Similarly, the new area involved in the rock volume removal is given by Avl = Av Avw (22) where AVw = (2 ) x C09 1 (1 - (2 x dW)) - ((d x p _ p2)1/2 x (dS/2 ~Pw)) (23) .':;' " ''.: .'.... .. ,` ' `, : ~ ' `

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The new Av is given by AVl = (2S) x cos l (l - (2 x d )) - (dsx p _ p2)1/2 x (dS/2 ~ P~ Avw This is then input into the equation for volume removed per revolution, and a new ROP is calculated to 10 include cutter wear. The same procedure can be followed for PDC and Geoset bits. The difference again lies in the cutter geometry. Also, for Geoset and PDC cutters, wear coefficient, CA, is obtained from the following equation CA = f~Dm) = C'(Dm) (25) where C' = is a constant describing Dm~ and Dm = is micron size of diamond inside the polycrystalline compacts.
The volume of cutter removed, VD, is found from the equations describing the cutter geometry. The pene-tration rate is then back calculated for the cutter the same way as for natural diamond bits described earlier.
The projected area increases, decreasing the effective stress, and the area removing the rock volume decreases resulting in decreased ROP. This also means that because of the wear-flat, an initial WOB is required before the rock is penetrated. Viewed in another sense, the model . .
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provides a tool to predict how worn the diamonds are by performing WOB drill-off tests.
Using this wear model, one can predict how the bits will wear every foot while drilling different forma-5 tions under different operating conditions. The mosteffective bit can then be selected based on economics.

EXAMPLE APPLICATION
The model can give ROP predictions for different 10 lithologies and rock strengths (uniaxial compressive strength). This provides the capability of predicting penetration rate for any set of operating conditions, for-mation description and bit parameters. As an example, drill-off data from a 6-1/4" natural diamond bit were 15 used to determine applicable a, b, c coefficients. This set of coefficients was then applied to OTHER natural dia-mond bits with DIFFERENT design features. Refer to Table 1. The bits that were evaluated are listed in Table 2.
Typical results shown in Figures 8-11 indicate good match 20 between the present model and field data. Note that Figure 12 applies to a worn bit. The model, therefore, overpredicts the bit performance in this case, as expected.

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25 Parametric evaluations of operating variables and bit design features can be done as shown in Figures 13 and 14.
These figures show that the model can be used to study effects on ROP of changes in bit parameters and operating conditions. Given a set of conditions in the field, the . , :

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model can be used to study parameters that would optimizeROP. For example, Figure 13 shows that if other parame-ters are held constant, increase in applied weight-on-bit will increase the ROP significantly. On the other hand, S the mud weight does not show a high degree of sensitivity.
The same conclusions can be drawn for bit parameters, such as bit diameter, diamond size, etc., shown in Figure 14.
This application could be used to impact actual bit design to optimize the rate of penetration.
Figures 15 and 16 show the Geoset bit match between actual field data and model prediction without wear and including wear. Data from the first 50 ft of the well were used to generate the a, b, c coefficients. The corrected model was then used to predict drilling perform-15 ance befo~e the rest of the hole was drilled. The match with no wear correction is poor ~Figure 15). However, with wear correction (Figure 16), the actual field data -match the model predictions very well. The unmatched sec-tion at 4550 ft is due to a change in lithology from that 20 used to develop the a, b, c lithology coefficients.
The new mathematical model described herein has been programmed on the computer and has been used as fol-lows:

1. To optimize the operating parameters and bit selections and obtain the maximum ROP and minimum $/ft. The bit runs can be simulated before actually drilling the well and, therefore, can form an impor-tant part of overall well planning strategy.

. ~, - . - . . . . , . . . . . -. , ~ ~ -2~?096S~t 2. From Figures 13 and 14, the model can be used for parametric studies. The model has the capability to optimize bit design features by evaluating different bit parameters and their effects on ROP and $/ft.
The most suitable bit design for a particular situ-ation can then be selected.

3. The model can be used to support total drilling system studies for penetration-rate, solids-control and hydraulics optimization. Economic impacts of the model can range in the thousands of dollars for one well, depending on operating conditions and expenses.

Major advantages of the new model are 1. The model is uncomplicated and straight forward.

2. Data requirements are standard, readily-available bit and drilling data.
3. Prediction for natural diamond bits have shown good agreement with lab and field data.

4. The model runs fast and is excellent for a drilling simulator, or as a stand-alone model.

5. Although at this time tested for natural diamond bits, the model can be generalized for other types of ~ ' .

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drag bits by incorporating the appropriate cutter geometric description in the model.

Whereby the present invention described in 5 relation of the examples and drawings attached hereto;
however, it should be understood that other and further modifications, apart from those shown or suggested herein, may be made within the scope and spirit of the present invention. --- - : ~ : .. . . . . .
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Claims (14)

What is Claimed is:

1. A method of predicting the rate of pene-tration for a drill bit comprising:
(a) determining for the drill bit a selected operating condition comprising revolutions per minute (RPM), weight on bit (WOB), and compres-sive strength of the material through which the drill bit is to drill;
(b) determining a geometry of the drill bit comprising drill bit diameter, number of cutters, face area, cutter dimensions, and equivalent cutter radius, (c) from the inputs of steps (a) and (b), determining the dynamic cutting area for the cutters;
and (d) from the inputs of steps (a), (b) and (c), determining the volume of material removed with each revolution (VD) divided by face area of the drill bit (DB) to generate a predicted rate of pene-tration (ROP).

2. The method of Claim 1 wherein the equiv-alent cutter radius is calculated from an equation equiv-alent to:

Re = DB / (2 ? ? ) wherein DB is the drill bit diameter for the full hole bits.

3. The method of Claim 1 wherein the equiv-alent cutter radius is calculated from an equation equiv-alent to:
RE = (1 / (2 ? ?)) / (Do2 + Di2)1/2 wherein Do is the outer drill bit diameter and Di is the inner drill bit diameter.

4. The method of Claim 1 wherein the dynamic cutting area for the cutter is calculated from an equation equivalent to: Areap = (.pi. dsP)/2 wherein ds is the cutter diameter and P is cutter penetration.

5. The method of Claim 4 wherein the cutter penetration is determined from an equation equivalent to:
P = 2 Wm / .pi. (ds .sigma.c) wherein Wm is the weight on bit less a pump-off force divided by the number of cutters, ds is the cutter diameter and .sigma.c is the rock compressive strength.

6. The method of Claim 1 wherein ROP is calcu-lated from an equation equivalent to:

wherein Nc = number of cutters RPM = revolutions per minute DB = drill bit diameter ds = cutter diameter Wm = mechanical loading per cutter oc = rock compressive strength

7. The method of Claim 1 wherein the ROP
determined in step (d) is multiplied by a lithology total correction factor (COR).

8. The method of Claim 7 wherein the COR is calculated using an equation equivalent to: COR = a/(RPMb ? WOBc) wherein constants a, b and c are lithology cor-rections dependent on cutter geometry and calculated from nonlinear regression analysis.

9. The method of Claim 1 wherein the cutter dimensions for polycrystalline diamond cutters include cutter backrake angle, cutter siderake angle and cutter diameter.

10. The method of Claim 1 wherein the cutter dimensions for Geoset-type cutters include cutter included angle and Geoset cutter length.

11. The method of Claim 1 wherein the calcu-lation of the volume of material removed with each revo-lution (VD) includes a depth dependent wear factor.

12. The method of Claim 11 wherein the wear factor is calculated from a wear coefficient for the cut-ters, relative cutter velocity and relative abrasiveness of the rock.

13. The method of Claim 12 wherein the volume of material removed (VD) with depth dependent wear factor is calculated utilizing an equation equivalent to:

wherein i, ... n = the footage drilled, CA = wear coefficient for the cutters, RPM/Re = relative cutter velocity, WOB/NC = mechanical loading on each cutter, .sigma.c = uniaxial rock compressive strength, and ABR = relative abrasiveness of rock.

14. The method of Claim 13 wherein the wear coefficient for cutters (CA) for polycrystalline diamond cutters (PDC) and Geoset-type cutters is calculated from an equation equivalent to:

CA = C' (Dm) wherein C' = wear constant describing Dm, and Dm = micron size of diamond within cutter.