method of optimizing motor and bit performance for maximum rop

6
June 2009, Volume 48, No. 6 1 Method of Optimizing Motor and Bit Performance for Maximum ROP H.R. MOTAHHARI, G. HARELAND, R. NYGAARD* University of Calgary B. BOND Departure Energy Services Inc. *currently with Missouri University of Science and Technology PEER REVIEWED PAPER PUBLISHED AS A TECHNOLOGY BRIEF (“REVIEW AND PUBLICATION PROCESS” CAN BE FOUND ON OUR WEBSITE) Introduction Positive Displacement Motors (PDMs) have gained widespread use in vertical, directional and horizontal drilling applications. In directional and horizontal mode, bent housing PDMs are used to manipulate well trajectory (inclination and azimuth) to inter- sect bottomhole targets. Slide drilling occurs when the bend in the PDM is oriented in a certain direction. During slide drilling, the drill string does not rotate. In slide drilling mode, bit rotation is generated only from the motor as drilling fluid is pumped through the drill string. Drilling in this mode can significantly reduce ROP and increase well costs. Accordingly, overall performance of bit and motor combinations can have an extremely significant im- pact on drilling costs. In comparison to using a simple approach like mechanical specific energy (MSE) which is a relative ‘local’ value as a function of instantaneous operating parameters like WOB and RPM only (1) , the approach herein can do a global bit run optimization in the pre-planning and follow-up phases, which include bit selection and detailed design parameters, bit wear throughout the bit run as a function of operating parameters and motor selection and performance. MSE does not consider any of these parameters and is not an overall ‘global’ ROP or $/m opti- mization tool. In a PDM, the power section converts hydraulic energy of mud flow into mechanical rotary power – the reverse action of the Moineau pump principle (2) . Each PDM has a helical rotor assem- bled inside a helical stator. The rotor has one less spiral or lobe than the stator, which results in a continuous seal line between the two. Likewise, the length of helical pitch for the stator is greater than the rotor, which forms cavity spaces between them. These cavities move along the power section from the inlet to outlet by rotating the rotor. Mud flow fills the cavity connected to the inlet and extends it by the pressure applied on the rotor body until the next cavity connects to the inlet. This process forces the rotor to ro- tate eccentrically inside the stator. Motor performance is, therefore, controlled by the combination of the rotor/stator lobe configuration and the motor stage number. Increasing the number of rotor lobes produces higher output torque from the motor and lower rotational speed. By increasing the motor stage number, motor output torque will be higher. The minimum mud flow rate is set to ensure effec- tive hole cleaning, which determines the lower limit of motor RPM for a given PDM lobe configuration. The second limitation is the pump horsepower which limits the total frictional losses combined with the flowrate. The maximum available torque and rotary speed for normal drilling operations with a mud motor is, therefore, lim- ited to an operational window. Within these restrictions, the motor and its operating parameters should be selected wisely in conjunc- tion with the bit and its optimal performance. Samuel (3) studied the optimization of drilling operations with PDMs and rollercone and natural diamond bits. These studies de- termined optimum WOB and mud flow rate for the motor by bal- ancing the WOB with the net thrust force on the bearing section of the motor to extend the life of the transmission section and to maximize ROP. One factor not considered in this model is the bit wear effect on the performance of the PDM and bit. Also, the ROP is estimated as the instantaneous ROP. If bit wear is included in the analysis, the ROP averaged over the entire section has to be studied, not only the instantaneous ROP. Abstract Downhole motors are widely used to drill vertical, directional and horizontal wells in conjunction with Polycrystalline Diamond Compact (PDC) bits. When a bent housing Positive Displacement Motor (PDM) is oriented for slide drilling to manipulate a well’s trajectory, the drill string does not rotate. Consequently, the rate of penetration (ROP) typically decreases. It is therefore impor- tant to optimize bottomhole assembly (BHA) performance in conjunction with PDC drill bits. This paper discusses how motor performance data, coupled with an ROP model, can predict the optimal weight-on-bit (WOB) required to derive maximum ROP for a given section of a hole to be drilled. This approach solves the ROP model and determines the ideal WOB with respect to any restrictions that PDM performance equations apply on it. Bit wear is included in the ROP model and an analysis is performed to optimize a given interval of wellbore. The optimization ap- proach is illustrated with two examples for different formation types and one field case comparing the performance of two mo- tors with PDC bits. The optimum WOB, maximum average ROP and differential pressure values are the outputs from the analysis. This analytical approach can be used to determine the optimum PDM/PDC bit combination to achieve maximum ROP through a wide range of operational conditions.

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Page 1: Method of Optimizing Motor and Bit Performance for Maximum ROP

June 2009, Volume 48, No. 6 1

Method of Optimizing Motor and Bit Performance for Maximum ROP

H.R. MOTAHHARI, G. HARelAnd, R. nyGAARd*

University of Calgary

B. BOnd departure energy Services Inc.

*currently with Missouri University of Science and Technology

PEER REVIEWED PAPER PUBLISHED AS A TEcHnoLogy BRIEf (“REVIEW AnD PUBLIcATIon PRocESS” cAn BE foUnD on oUR WEBSITE)

IntroductionPositive Displacement Motors (PDMs) have gained widespread

use in vertical, directional and horizontal drilling applications. In directional and horizontal mode, bent housing PDMs are used to manipulate well trajectory (inclination and azimuth) to inter-sect bottomhole targets. Slide drilling occurs when the bend in the PDM is oriented in a certain direction. During slide drilling, the drill string does not rotate. In slide drilling mode, bit rotation is generated only from the motor as drilling fluid is pumped through the drill string. Drilling in this mode can significantly reduce ROP and increase well costs. Accordingly, overall performance of bit and motor combinations can have an extremely significant im-pact on drilling costs. In comparison to using a simple approach like mechanical specific energy (MSE) which is a relative ‘local’ value as a function of instantaneous operating parameters like WOB and RPM only(1), the approach herein can do a global bit run

optimization in the pre-planning and follow-up phases, which include bit selection and detailed design parameters, bit wear throughout the bit run as a function of operating parameters and motor selection and performance. MSE does not consider any of these parameters and is not an overall ‘global’ ROP or $/m opti-mization tool.

In a PDM, the power section converts hydraulic energy of mud flow into mechanical rotary power – the reverse action of the Moineau pump principle(2). Each PDM has a helical rotor assem-bled inside a helical stator. The rotor has one less spiral or lobe than the stator, which results in a continuous seal line between the two. Likewise, the length of helical pitch for the stator is greater than the rotor, which forms cavity spaces between them. These cavities move along the power section from the inlet to outlet by rotating the rotor. Mud flow fills the cavity connected to the inlet and extends it by the pressure applied on the rotor body until the next cavity connects to the inlet. This process forces the rotor to ro-tate eccentrically inside the stator. Motor performance is, therefore, controlled by the combination of the rotor/stator lobe configuration and the motor stage number. Increasing the number of rotor lobes produces higher output torque from the motor and lower rotational speed. By increasing the motor stage number, motor output torque will be higher. The minimum mud flow rate is set to ensure effec-tive hole cleaning, which determines the lower limit of motor RPM for a given PDM lobe configuration. The second limitation is the pump horsepower which limits the total frictional losses combined with the flowrate. The maximum available torque and rotary speed for normal drilling operations with a mud motor is, therefore, lim-ited to an operational window. Within these restrictions, the motor and its operating parameters should be selected wisely in conjunc-tion with the bit and its optimal performance.

Samuel(3) studied the optimization of drilling operations with PDMs and rollercone and natural diamond bits. These studies de-termined optimum WOB and mud flow rate for the motor by bal-ancing the WOB with the net thrust force on the bearing section of the motor to extend the life of the transmission section and to maximize ROP. One factor not considered in this model is the bit wear effect on the performance of the PDM and bit. Also, the ROP is estimated as the instantaneous ROP. If bit wear is included in the analysis, the ROP averaged over the entire section has to be studied, not only the instantaneous ROP.

AbstractDownhole motors are widely used to drill vertical, directional

and horizontal wells in conjunction with Polycrystalline Diamond Compact (PDC) bits. When a bent housing Positive Displacement Motor (PDM) is oriented for slide drilling to manipulate a well’s trajectory, the drill string does not rotate. Consequently, the rate of penetration (ROP) typically decreases. It is therefore impor-tant to optimize bottomhole assembly (BHA) performance in conjunction with PDC drill bits. This paper discusses how motor performance data, coupled with an ROP model, can predict the optimal weight-on-bit (WOB) required to derive maximum ROP for a given section of a hole to be drilled. This approach solves the ROP model and determines the ideal WOB with respect to any restrictions that PDM performance equations apply on it. Bit wear is included in the ROP model and an analysis is performed to optimize a given interval of wellbore. The optimization ap-proach is illustrated with two examples for different formation types and one field case comparing the performance of two mo-tors with PDC bits. The optimum WOB, maximum average ROP and differential pressure values are the outputs from the analysis. This analytical approach can be used to determine the optimum PDM/PDC bit combination to achieve maximum ROP through a wide range of operational conditions.

Page 2: Method of Optimizing Motor and Bit Performance for Maximum ROP

2 Journal of Canadian Petroleum Technology

Mud Motor Performance

Output parameters of a mud motor are output torque and rotary speed which are controlled by the mud flow rate (Q) and differen-tial pressure across the motor. For an ideal motor, the rotary speed is a function of the motor geometry and mud flow rate. The actual rotary speed of the motor is decreased by the slip flow through the seal line. Slip flow is a function of motor geometry and differential pressure across the motor(1). Equation (1) states the relationship for the actual motor rotary speed.

RPMQ Q

qslip=

0 .................................................................................... (1)

The q0 is called unit displacement of the mud volume required to revolve the rotor one revolution and is a function of motor ge-ometry and lobe number. Also, the output torque of the motor is a function of geometry and differential pressure(2). Generally, torque is a linear function of the motor differential pressure as shown in Equation (2). The constant, k, is called motor torque slope property.

T k P= .∆ ............................................................................................... (2)

Bit Performance

The ROP model for PDC bit performance used in this study is a based on the approach introduced by Hareland et al.(4) The general form of ROP equation for 100 percent efficient bit cleaning is:

ROP WG RPM WOB

DfB

=

.

. ..

γ α

σ ............................................................... (3)

The term G is a coefficient determined by the bit and blade ge-ometry. The term Wf is the wear function calibrating ROP values for a worn bit and is estimated by Equation (4) as a function of cumulative bit wear at the depth of drilling. The cumulative bit wear is assumed to be a function of applied WOB, RPM and rock strength values at depth of drilling. The bit wear coefficient, Ca is a property of the bit(5).

WBG

f = −

1

8∆

ω

................................................................................... (4)

where

∆BG C RPMWOB

xaC

C

i=

. . . .1

2

1000 1000σ

ii

n

=∑

1 ........................................... (5)

The torque required for a new bit to drill is assumed to be a function of applied WOB and rock properties, as in the following equation:

T k WOBn T= . β......................................................................................... (6)

The required torque for a worn bit changes with bit wear as:

T T RBG

w n t

Rp

= +

. .1

8∆

...................................................................... (7)

The Rt is usually a negative number and the Rp is usually in the range of 0.8 to 1.0.

Technical ApproachTo optimize the drilling operation while using a mud motor, the

operational parameters should be selected according to motor ca-pabilities and the bit operational drilling parameters. The method developed establishes the optimum constant WOB required to achieve the maximum average ROP when drilling a given forma-tion interval with a specific bit and motor combination. The av-erage ROP is defined as the ratio of the total length drilled to the time elapsed. The mud flow rate is assumed to be fixed; therefore, the RPM output of the motor is limited. To determine optimum drilling parameters, the ROP model and the motor performance equations are used to simulate the drilling operation and estimate average ROP for different WOB values over a practical range. Op-timum WOB is defined as the value that yields the highest average ROP.

The simulated depth interval is divided into smaller segments (sub-intervals) which are all individually simulated as depth steps, thus, giving more realistic ROP results. The depth steps are typi-cally between 0.2 and 1.0 metre. Within these smaller depth seg-ments, the drilling parameters including WOB, RPM and bit wear and formation rock strength is assumed to be constant.

Using the ROP outputs for the smaller segments, the average bit run ROP is defined as:

ROP

x

tavg

ii

n

ii

n= =

=

∑1

1 ....................................................................................... (8)

where ti is the drilling time for the i th segment and is calculated by applying Equation (3), knowing overall bit wear in the sub-in-terval, operational parameters and its length.

The average ROP values reported for the drilling interval can be plotted on a contour plot as a function of WOB and RPM. This plot, which we call a ROP map, is an informative representation of the overall bit performance through the entire interval drilled.

The simulation of drilling operation for a fixed WOB in the ith

segment is done as: 1. Estimation of the total drilling torque and the mud pressure

drop through it, from Equations (6), (7) and (2).2. Motor RPM estimation knowing the functionality of mud slip

flow through the motor and the pressure drop, from Equation (1).

3. Calculation of ROP and drilling time of the sub-interval, from Equations (3) and (4).

4. Evaluation of the applicable bit wear grade in the next sub-interval, from Equation (7).

In the context of this paper, it is assumed that the drill string is not rotated from the surface. Therefore, the mud motor is the only energy and torque source to the bit and total drilling torque ap-plies to it.

Sample ApplicationsExample 1: Drilling of a limestone formation and effect of drilling interval length on optimum results

In this example, the method is utilized to compare the drilling performance of two different motors used with the same PDC bit. A 2,000 ft interval of a limestone formation (constant rock strength of 26,000 psi) is to be drilled with an 8½ in PDC bit.

Page 3: Method of Optimizing Motor and Bit Performance for Maximum ROP

June 2009, Volume 48, No. 6 3

The laboratory drilling data(6) analysis shows that the values for parameters G and kT [Equations (2) and (3)] are 3.93 × 10-3 and 6 × 10-3, respectively, for this bit and lithology. The bit wear coeffi-cient is assumed to be equal to 4.9 × 10-8.

Two different 6½ in motors are evaluated and their properties are given in Table 1. Motor 1 is a high torque motor with a 7:8 lobe configuration, and motor 2 is a 4:5 high RPM motor which pro-vides moderate torque values. The slip flow function for these mo-tors is found to be in the form of the following equation:

Q q a b Pslip = 0. .exp( . )∆ ......................................................................... (10)

The method is used to simulate drilling operations for three dif-ferent mud flow rates of 300, 450 and 600 gpm through the motors. Figure 1 shows the general ROP map for different combinations of WOB and RPM values, applied constantly on the specified PDC

bit to drill the interval. It is clear that the average ROP to drill this interval is most sensitive to high WOB values. In other words, one can apply a combination of high WOB and low RPM values to drill as fast as possible in normal drilling operations. However, the WOB and RPM values can not be selected arbitrarily while drilling with mud motor, as shown later. The blue region in the upper right-hand side corner of the map indicated those combina-tions of RPM and WOB values which lead to incomplete drilling operations because the bit wears completely out. Figure 2 shows the result of the drilling operation simulation for both motors for three different mud flow rates. It includes an optimum WOB value for each motor, as well as the average ROP value. Clearly, motor 1 is able to drill the interval with higher average ROP values in comparison to motor 2. However, the optimum WOB values for motor 1 are significantly greater than those for motor 2. For ex-ample, in the case of a mud flow rate of 600 gpm, motor 1 drills the interval in an average ROP of 24.4 ft/hr by applying 20,000 lbf WOB, whereas, the average ROP and optimum WOB for motor 2 is 15.3 ft/hr and 10,500 lbf. The maximum approachable ROP is 24.4 ft/hr by motor 1 applying a WOB of 20,000 lbs. Motor 2 can drill with an average ROP of 15.3 ft/hr applying a WOB of 10,500 lbs. As shown in Figure 2, the optimum WOB values for both mo-tors decrease as mud flow rate increases. This can be explained by considering the RPM provided by the motor to the bit. Since an increase of mud flow rate results in higher bit RPM, the optimum WOB should be reduced to ensure drilling of the complete interval is achieved with a single PDC bit run. The initial differential pres-sure through the motors is reported in Table 2. Due to constant rock strength values for the formation, fixed WOB and gradual in-crease of the bit wear, the ROP and drilling torque decrease by the depth drilled. Therefore, the maximum differential pressure occurs in the beginning of the drilling operation.

To illustrate how the length of drilling interval can affect the optimization results, a 3,000 ft interval of the same limestone for-mation is simulated using the same motors and PDC bit. Figure 3 shows the simulation’s results, including the optimum WOB and optimized average ROP for each motor in different mud flow rates. Similar to the previous results for the 2,000 ft interval, motor 1 drills the interval faster than motor 2 due to its lower output RPM values. These lower RPM values, combined with higher op-timum WOB values, make it possible for motor 1 to perform in a high average ROP area seen in the lower right hand corner of the ROP map (Figure 1). Comparison of the results of Figures 2 and

TABle 1: Performance properties of the considered motors.

Motor q0 k a b

1 4.132 10.698 1.3891 0.0033 2 2.012 5.77 2.423 0.0029

RP

M

WOB (lbf)

300

250

200

150

100

50

00 0.5 1 1.5 2 2.5

Average ROP (ft/hr)

x104

FIGURE 1: ROP map for drilling operation of 2,000 ft limestone interval.

0

5,000

10,000

15,000

20,000

25,000

250 300 350 400 450 500 550 600 650

Mud Flowrate (gpm)

Op

tim

um W

OB

(lb

f)

0

5

10

15

20

25

30 Op

timized

Averag

e RO

P (ft/hr)

Motor 1 WOBMotor 2 WOBMotor 1 ROPMotor 2 ROP

FIGURE 2: Optimum WOB and optimized average ROP values for 2,000 ft limestone interval.

TABle 2: Maximum motor differential pressure values for different simulation cases.

Motor 1 Motor 2

Mud Flowrate (gpm) 600 450 300 600 450 3002,000 ft limestone 164.8 228.3 369.9 134.5 181.9 286.82,000 ft Shale 258.3 335.2 523.7 256.4 338.8 478.93,000 ft limestone 98.1 144.8 228.3 77.7 119.6 181.92,000 ft Shale, Modified Bit 138.3 182.8 258.3 149.0 175.5 256.45,790 ft Field Case 397.5 523.7 765.2 394.5 507.2 795.1

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

250 300 350 400 450 500 550 600 650

Mud Flowrate (gpm)

Op

tim

um W

OB

(lb

f)

0

1

2

3

4

5

6

7

8

9

10 Op

timized

Averag

e RO

P (ft/hr)

MOTOR 1 WOBMOTOR 2 WOBMOTOR 1 ROPMOTOR 2 ROP

FIGURE 3: Optimum WOB and optimized average ROP values for 3,000 ft limestone interval.

Page 4: Method of Optimizing Motor and Bit Performance for Maximum ROP

4 Journal of Canadian Petroleum Technology

3 reveals that optimum WOB and optimized ROP values for a 3,000 ft interval are lower than those for a 2,000 ft interval.

Example 2: Drilling of a shale formation and effect of the bit wear coefficient on optimum results

In this example, the drilling operation of a 2,000 ft interval of a shale formation (σ = 8,000 psi) with an 8½ in PDC bit is simulated to determine the optimum WOB value. The laboratory drilling data(6) analysis shows that drilling coefficients for this set of bit and rock are:kT = 0.173G = 9.146Ca = 1.6 × 10-7

The same motors used in the previous example are considered. The simulation is done for three mud flow rates: 300, 450 and 600

gpm. An ROP map is generated to illustrate the sensitivity of av-erage ROP value of this operation to WOB and RPM, shown in Figure 4. The map indicates that higher ROP for this operation can be achieved by using a combination of high to moderate RPM and low to moderate WOB values. Figure 5 shows the results of the drilling operation simulation for both motors in three different mud flow rates for this interval. Similar to the previous example for the limestone interval, the optimum WOB values of motor 1 are higher than motor 2. Also, the optimum WOB values for both motors de-crease by increasing the mud flow rate. In contrast to the results for the limestone interval, the optimized average ROP value increases with mud flow rate as a result of the higher sensitivity of ROP to RPM values. Interestingly, motor 2, despite the lower optimum WOB values, drills the formation faster than motor 1. This perfor-mance is the result of the higher output RPM for motor 2 in com-parison to motor 1, given the fixed mud flow rates. Similar to the previous example, the maximum differential pressure through the motors occurs at the beginning of the interval, which is reported in Table 2. Since motor 2 can drill at higher average ROP values with lower WOB, and differential pressure values are similar for both motors, it can be concluded that the use of motor 2 in this specific interval is a better choice than motor 1.

To illustrate the effect of bit parameters on optimization results, the drilling of a 2,000 ft shale interval with a different PDC bit is simulated. The wear rate of the new bit is assumed to be two times greater than that of the previous bit simulated (Ca = 3.2 × 10-7). The simulation is done using the same mud motors, and optimum WOB and optimized average ROP values are estimated (Figure 6). Sim-ilar to the results of the previous bit, the performance of motor 2 is better than motor 1. Motor 2 drills the interval faster than motor 1; however, the optimum WOB values are smaller. In spite of this similarity, it can be observed by comparison of Figures 5 and 6, that drilling with the less wear resistant bit should be done less ag-gressively. This indicates that optimum WOB values are lower in

RP

M

WOB (lbs)

300

250

200

150

100

50

0.5 1 1.5 2 2.5

Average ROP (ft/hr)

x104

FIGURE 4: ROP map for drilling operation of 2,000 ft shale interval.

0

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

18,000

20,000

250 300 350 400 450 500 550 600 650

Mud Flowrate (gpm)

Op

tim

um W

OB

(lb

f)

50

52

54

56

58

60

62

64

66 Op

timized

Averag

e RO

P (ft/hr)

MOTOR 1 WOBMOTOR 2 WOBMOTOR 1 ROPMOTOR 2 ROP

FIGURE 5: Optimum WOB and optimized average ROP values for 2,000 ft shale interval.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

10,000

250 300 350 400 450 500 550 600 650

Mud Flowrate (gpm)

Op

tim

um W

OB

(lb

f)

29

31

33

35 Op

timized

Averag

e RO

P (ft/hr)

MOTOR 1 WOBMOTOR 2 WOBMOTOR 1 ROPMOTOR 2 ROP

FIGURE 6: Optimum WOB and optimized average ROP values for 2,000 ft shale interval with modified bit.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

0 20,000 40,000 60,000 80,000 100,000 120,000

Rock Strength (psi)

Dep

th (f

t)

FIGURE 7: Rock strength values of the 5,790 ft field case interval versus depth.

Page 5: Method of Optimizing Motor and Bit Performance for Maximum ROP

June 2009, Volume 48, No. 6 5

this case to ensure that a complete drilling operation of the interval occurs with a single bit run.

Example 3: Field Illustration

To demonstrate the method applicability to actual field data, a sonic generated strength log for a 5,790 ft interval is used as the input for the simulation. It is intended to drill the interval with the previously described motors. Figure 7 contains rock strength values of the interval versus depth. As shown in the ROP map of the interval in Figure 8, the higher average ROP values are more likely achievable in the region of high WOB and less RPM value. The performance of the motors are simulated and optimized for three different mud flow rates of 300, 450 and 600 gpm, plotted in Figure 9. Similar to the limestone formation example, motor 1 performs better and drills the interval faster. However, motor 1 re-quires higher WOB values to be applied than motor 2. Also, the optimum WOB and optimized average ROP values for both mo-tors decrease as the mud flow rate increases. The initial differential pressure values through the motors are reported in Table 2.

ConclusionsDrilling performance utilizing downhole motors is restricted by

motor specifications and operational parameters in such a manner that WOB and RPM cannot be selected arbitrarily to achieve op-timal bit run success, yet many drilling operations continue to do so.

The method introduced in this paper can be used to estimate fixed optimum WOB values to drill a specific formation interval. The examples presented in this paper, illustrate this application for fixed mud flow rates and predetermined properties of the bit and the mud motor.

It is shown that the bit wear coefficient, length of the interval and interval rock strength values affect the simulation results.

The method can be used to better select mud motor, PDC bits and estimate optimum WOB in the planning phase of a well drilling operation.

It is shown that the method can be applied to drilling intervals consisting of formations with variable rock strength values.

As a further application of the method, the drilling interval can be divided into smaller intervals and the optimum fixed WOB can be estimated for each of them in a manner such that overall average ROP is optimized. The method can be easily used by any ROP model, bit type and bit design.

nOMenClATUReα = ROP model WOB exponentβ = torque model WOB exponentγ = ROP model RPM exponentω = wear function exponentσ = unconfined rock strength (psi)∆P = differential pressure across the motor (psi)∆BG = total bit wear (out of 8)a, b = motor slip flow model coefficientsCa = bit wear coefficientC1, C2 = bit wear model exponentsDB = bit diameter (in.)G = ROP model coefficientk = motor torque slope (ft.lb/psi)kT = torque model constantQ = mud flow rate (gpm)Qslip = mud slip flow through the motor (gpm)q0 = motor unit displacement (gal/ rev.)ROP = bit rate of penetration (ft/hr)RPM = bit/motor rotary speed (rpm)Rt, Rp = worn bit torque model coefficientsti = drilling time of ith sub-intervalT = motor output torque (ft.lb)Tn = drilling torque of a new bit (ft.lb)Tw = drilling torque of a worn bit (ft.lb)Wf = wear functionWOB = applied weight-on-bit (lbf)xi = length of ith sub-interval

SI Metric Conversion Factors

ft × 3.048 E−01 = mft.lb × 1.355818 E+00 = N.mgpm × 6.309 E−05 = m3/seclbf × 4.448222 E+00 = Npsi × 6.894757 E+00 = kPa

ReFeRenCeS 1. DUPRIEST, F.E. and KEODERITz, W.L., Maximizing Drill Rates

with Real-Time Surveillance of Mechanical Specific Energy; paper SPE 92194 presented at the SPE/IADC Drilling Conference, Am-sterdam, Netherlands, 23-25 February 2005.

2. NELIK, L. and BRENNAN, J.R., Progressing Cavity Pumps and Mud Motors; Gulf Publishing Company, Houston, TX, 2005.

3. SAMUEL, R., Mathematical Modelling and Design Analysis of the Power Section of A Positive Displacement Motor (PDM); Ph.D. dis-sertation, University of Tulsa, Tulsa, OK, 1997.

4. HARELAND, G. and RAMPERSAD, P.R., Drag - Bit Model In-cluding Wear; paper SPE 26957 presented at the SPE Latin America/Caribbean Petroleum Engineering Conference, Buenos Aires, Argen-tina, 27-29 April 1994.

5. RAMPERSAD, P.R., HARELAND, G. and BOONyAPALUK, P., Drilling Optimization Using Drilling Data and Available Tech-nology; paper SPE 27034 presented SPE Latin America/Caribbean Petroleum Engineering Conference, Buenos Aires, Argentina, 27-29 April 1994.

6. WARREN, T.M. and ARMAGOST, W.K., Laboratory Drilling Per-formance of PDC Bits; SPE Drilling Engineering, Vol. 3, No. 2, pp. 125-135, June 1988.

RP

M

WOB (lbs)

300

250

200

150

100

50

0.5 1 1.5 2 2.5

Average ROP (ft/hr)

x104

FIGURE 8: ROP map for drilling operation of 5.790 ft field case interval.

0

5,000

10,000

15,000

20,000

25,000

30,000

250 300 350 400 450 500 550 600 650

Mud Flowrate (gpm)

Op

tim

um W

OB

(lb

f)

20

30

40

50

60

70

80

90

100

110

Op

timized

Averag

e RO

P (ft/hr)

MOTOR 1 WOBMOTOR 2 WOBMOTOR 1 ROPMOTOR 2 ROP

FIGURE 9: Optimum WOB and optimized average ROP values for 5.790 ft field case interval.

Page 6: Method of Optimizing Motor and Bit Performance for Maximum ROP

6 Journal of Canadian Petroleum Technology

Provenance—Original Petroleum Society manuscript, Method of Opti-mizing Motor and Bit Performance for Maximum ROP (2007-088TB), first presented at the 8th Canadian International Petroleum Conference (the 58th Annual Technical Meeting of the Petroleum Society), June 12-14, 2007, in Calgary, Alberta. Abstract submitted for review December 1, 2006; editorial comments sent to the author(s) March 12, 2009; revised manuscript received April 13, 2009; paper approved for pre-press April 13, 2009; final approval <Approved>.

Authors’ BiographiesHamed Reza Motahhari is a Ph.D. stu-dent in the Department of Chemical and Petroleum Engineering at the University of Calgary. His current research interests in-clude measurement and modelling of heavy oil and bitumen physical properties. He holds two B.Sc. degrees in mechanical en-gineering and petroleum engineering from the Sharif University of Technology, Iran (2006). He received his M.Sc. degree in pe-troleum engineering from the University

of Calgary (2008), where he worked on drilling optimization and PDC bit performance modelling. He is a member of SPE and the Petroleum Society.

Dr. Geir Hareland is a Professor in the Chemical and Petroleum Engineering De-partment and the NSERC/CAODC Chair in Drilling Engineering at the University of Calgary. He got his B.Sc. degree in me-chanical engineering from the University of Minnesota (1981), his M.Sc. degree in pe-troleum engineering from the University of Tulsa (1985) and his Ph.D. degree in me-chanical engineering from Oklahoma State University (1991). Dr. Hareland was an As-

sistant and Associate Professor at New Mexico Institute of Mining and Technology. He has consulted with various oil companies and was the founder of Drops Technology AS. Dr. Hareland’s research focuses on working closely with all aspects of the drilling industry including contractors, service companies and operators. His main research interests are centred on the various aspect of drilling engi-neering optimization with an emphasis on ‘engineering.’ The spe-cific research tasks include processes/factors affecting the actual drilling and trouble time it takes to drill an oil or gas well.

Dr. Runar Nygaard is an Assistant Pro-fessor in petroleum engineering in the Department of Geological Sciences and Engineering at Missouri University of Sci-ence and Technology. He got his B.Sc. and M.Sc. degrees in geosciences from the Uni-versity of Oslo (both 1996) and his Ph.D. in geomechanics from the same institution in 2004. Dr. Nygaard was the General Man-ager for Drops Technology AS. He also held a position as a Management Consul-

tant with McKinsey & Company until he started as a Research As-sociate at the University of Calgary, a position he held until he started at Missouri S&T in 2007. His research interests are in geo-mechanics applied to drilling, well design and long-term integrity of wells.

Bruce J. Bond is a Co-founder and Prin-ciple of Departure Energy Services Inc., a provider of directional drilling services and technology to the Canadian and inter-national petroleum industry. He currently works in Calgary, Alberta as Departure En-ergy’s Sales and Marketing Manager. Mr. Bond has been employed in the oilfield ser-vices sector for the past 30 years. His career includes over 20 years dedicated to direc-tional drilling, primarily with a large mul-

tinational corporations where he participated in the conception, development and testing of many new and emerging directional drilling and MWD technologies.