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Application of rock strength in drilling evalutionR. Nygaard University of Calgary, G. Hareland University of Calgary, University of Calgary

Copyright 2007, Society of Petroleum Engineers

This paper was prepared for presentation at the 2007 SPE Latin American and CaribbeanPetroleum Engineering Conference held in Buenos Aires, Argentina, 1518 April 2007.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSP E meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than300 words; illustrations may not be copied. The abstract must contain conspicuous

acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P .O.Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435.

Abst ractDifferent sources can be used to develop rock strength

information along the wellbore. Such strength information is

important when assessing the stability of the wellbore,

selecting mud weights and designing casing programs.However, there are other areas, especially in drilling, where

rock strength information is applicable, but still underutilized.

A methodology is developed to estimate drilling time and

bit wear before drilling if rock strength is known. To estimatedrilling time and bit wear, effects of other parameters like

drilling parameters, well bore size and drilling bit design has

to be normalized. This methodology has been used to estimate

drilling time and estimate bit wear and further evaluate drilling

performance while drilling.After drilling the additional information has been used to

conduct a post analysis and transfer knowledge from well to

well. The advantage of this methodology is it eliminates theeffect of geological variability when comparing performance

between wells and fields.

IntroductionDifferent sources can be used to develop rock strengthinformation along the wellbore. Such strength information is

important when selecting mudweight and assessing the

stability of the wellbore, selecting mud weights and designingcasing programs. Strength information is also used for

completion and hydraulic stimulation design. However, there

are other areas, especially in drilling, where rock strength

information is applicable, but still underutilized. To obtain the

rock strength along the well bore, logs, rock mechanical tests

or even drilling data can be used. In this paper we address howto obtain this rock strength and some areas where rock

strength has been provided to give valuable information for

drilling purposes.

Rock strength calculationsThe rock mechanical parameter that is most important

when conducting drilling analysis is unconfined compressiverock strength (UCS)

1. The UCS can be determined from Mohr

Coulomb failure criteria. The Mohr-Coulomb failure criterion

in terms of peak loads is given as:

tan'' hSUCSvS += (1)

Where Sv is vertical effective stress, Sh is horizontal effective

stress, and is failure angle. Effective stresses are defined thedifference between total stresses and pore pressure.

ppv

Sv

S =' (2)

Svis the total stress, pp is the pore pressure.

There are several methods to obtain UCS along the wellbore. In most cases, the availability of data determines whichmethods to choose. Different methods for obtaining UCS are

described below.

Rock Mechanical laboratory testingRock mechanical laboratory testing on preserved core samples

are the most accurate method for calculating rock strength

Rock mechanical tests are conducted on cylindrical rock

samples in a triaxial laboratory cell2. The triaxial cell can

control and monitor the confining stress, vertical load and pore

pressure. The vertical and horizontal strain (i.e. normalized

deformation) of the rock sample is also recorded. First are the

samples consolidated with isotropic confining stress. It meansthat the sample is loaded when vertical and horizontal stress is

kept equal. After consolidation, in the shear phase, the verticastress is increased until the sample reach peak strength. To

obtain a failure criterion for a specific core depth severa

triaxial tests are conducted with different consolidation

stresses. Figure 1 shows the shear phase results, in the vertica

effective stress vs. horizontal effective stress space, of 3 North

Sea sandstone triaxial tests3. The tests had confining stresses

of 2, 5 and 10 MPa. In the shear phase the horizontal stress is

kept constant while the vertical stress is increased. The Mohr

Coulomb failure criterion calculates the UCS to be 76 MPaFigure 2 shows the shear phase of 3 North Sea shale triaxia

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tests with confining stresses of 5, 10, 15 MPa. Low

permeability materials like shale are tested undrained (i.e. porepressure valve is closed). The change in pore pressure during

the shear phase will also change the effective horizontal stress

since the total horizontal stress is kept constant. The Mohr

Coulomb failure criterion gives UCS equal to 8 MPa for the

shale. The disadvantage with using triaxial tests results for

drilling applications is the lack of available core material fortesting and that testing is time consuming. Therefore triaxial

tests are more often used to calibrate rock strength to otherinformation sources like petrophysical properties or well logs.

Rock strength from logsThe use of sonic velocity logs to determine elastic properties

of rock is well established. There is published several

correlations between rock strength and sonic travel time5-7.

Sonic travel time measured on cores can be correlated with

unconfined compressive strength derived from failure criteria8.

The failure criteria were established from triaxial compressivetests on sandstone and shale cores. The sonic vs UCS were

analyzed using Equation 37

3)(

00.1

21

kUCSktk c

+=

(3)

Where tc is travel time (s/ft), UCS is unconfinedcompressive strength (MPa) and k1, k2, k3 are experimentalconstants. In Figure 5 the shale and sandstone data are plotted

with a best curve fit for the sandstones, shales and both

lithologies combined. The best fit experimental constants for

equation 9 are given in Table 1. When sonic logs are available

these data can give a continuous strength profile along thewellbore as shown in Figure 5. However, in situation where

very limited information exists the same approach can be

applied by using average seismic travel times for eachformation (Figure 6). In Figure 6, UCS derived from triaxial

tests is also included. The mach between the rock mechanical

tests and the velocity trend is good. However this approach

will only give indicative results since there are no strengthvariations within the specific formations.

Neutron density logs can also be used for deriving rock

strength from logs. Porosity information can be obtained along

the wellbore from Neutron density logs. Figure 7 shows that

there is a good correlation between UCS and porosity forsandstones3. So if Neutron logs are available they can be used

in similar fashion as sonic logs to obtain rock strength

Rock strength from cuttingsAnother approach to overcome the time-consuming triaxial

testing is to conduct rock mechanical tests on small cuttingsamples9. The rock mechanical tests are performed on a few

mm-sized rock samples (cuttings) by a small spike, which is

indented into the sample. When deformation occurs in the

sample without increase in vertical load the critical transitionforce (CTF) is reached. CTF is correlated to UCS (unconfined

rock strength) derived from triaxial laboratory tests. One

example of cuttings derived rock strength log is given on

Figure 78-9.

Rock strength from ROP modelsThe use of drilling data to predict rock strength has been

developed based on Rate of penetration (ROP) models10-12

And specific ROP models have been developed for specific bi

types like rollercone, poly crystalline compact bits (PDC) andnatural diamond bits (NDB)10,11,13. The ROP models needs to

include all the parameters that influence ROP, such asoperational drilling parameters (e.g. WOB, RPM, flow rate

mudweight and type), bit types and wear and the rock

formation properties. The rock formation properties that are

included are lithology, abrasiveness, pore pressure and rock

strength. For a previous drilled well all the above mentionedinformation is recorded except the rock strength. The data

from a previous drilled well is used to generate a rock strength

by the inversion of a bit specific rate of penetration models

The effects of operating parameters, bit design and weardrilling hydraulics, mud rheology and pore pressure are

normalized model. The inverted rate of penetration provides

then a calibrated measure of the rocks strength under actua

drilling conditions and simultaneously determines the wearcharacteristics of the bits used in drilling the relevant sections

This wear character is an evaluation of the bits performance

while drilling various formation types and under a variety o

operating conditions and includes, detailed bit geometry andits resistance to wear.

Figure 9 shows an example of two ROP model based rock

strength logs from the North Sea. The two logs correlates well

The ROP model based rock strength is also included in Figure5 and 8. In Figure 5 it is good mach between the sonic rock

strength and the ROP model based rock strength. Also the

mach is good between the ROP model based rock strength and

cuttings based rock strength in Figure 8. So, several sourcescan create similar rock strength logs which make it possible toobtain strength information in most cases. However, meter by

meter based logs and more than one reference will give the

best predictions. Therefore it is preferable to use the either logbased or drilling based methods for obtaining rock strength

logs.

Appl ication of rock strength in dri ll ing simulationWhen planning a new well section it is valuable to know inadvance the total drilling time, to be able to predict bit wear

and further recommend optimized drilling parameters

Therefore a detailed analysis was initiated of a 12 inch

section in the North Sea. The section was planned through theHordaland and Rogaland shale formations which caps mos

reservoirs in the North Sea.

PlanFirst, rock strength from a reference well had to be

established to be able to analyze drilling time, bit wear and

optimized parameters. The rock strength was based on a

previous drilled vertical 12 section in the area. Therecorded drilling data (ROP, WOB, RPM, Flow rate) is

reported in Figure 10. The section was drilled from 1755m

down to 2730m with two IADC 437 Roller cone bits. The tota

drilling time was 44 hours. The average ROP was 27 m/h. The

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ROP model rock strength was calculated from the drilling

data. The reference rock strength log represents the rockstrength along the reference well path. The well path for the

planned well hit the Rogaland formation at different depth

which can be seen by comparing formation tops on Figure 9

and 10. Figure 10 shows the formation tops along the planned

well path of the new well. This reference rock strength had to

be shifted approximately 50m to mach the new well. Theprocedure assumes geological continuity and homogeneity i.e.

the lithological properties of the individual formations will bebroadly similar in the offsets and planned well. For deviated

wells this process is more complex since the reference well

path (at the inclination of the offset well) has first to be plotted

against true vertical depth. Then the formation tops had to be

adjusted for the new well site before it can be transposed along

the new well path. In most instances due to the complexity ofgeological structures this may not be an exact representation

of the strengths along the new well path but a fair

approximation, except for an area with any major structuralchanges. However, in this area there exists detailed geologic

information and the rock strength for the planned well given in

Figure 10 based on the reference well should be a close

approximation to the actual rock strength log for the new well.

When the rock strength log is established for the new wellsimulations based on ROP models can predict drilling time, bit

wear and optimized parameters. The simulations performed on

the rock strength log were done in a commercial availabledrilling simulator14. The effect of any number of drilling

parameters and operating conditions, within known limitations

of operational parameters and the rig, are then evaluated. Theperformance of several bits can be evaluated to enable

selection of the best bit and the corresponding optimal set of

parameters to use while running the bit. Multiple scenarioswere evaluated with variations in:

WOB/RPM combinations. Changes in operating parameters as a function of

rock strength variations.

Bottom-hole assembly configurations. Bit hydraulics Bit types, impregnated, NDB, PDC, and roller

cone

This approach ensures that an optimal solution isobtained.

Based on the performed simulation a set of recommended

parameters on WOB, RPM and Flow rate was determined for

a specific PDC bit. The PDC bit wear was prognosed to be anaverage of 1.2. The simulated bit wear of 1.2 is equivalent to

an IADC reported bit wear on the rig of 1-1 or 1-2 (inner-outerwear on cutters). The total drilling time for the new sectionwas prognosed to be 22 hours and with an average ROP of

40m/h. The prognosed drilling plan for the new well improves

the drilling compared to the reference well. This prognosis

(Figure 10) with the selected PDC bit and recommended

parameters was sent to the rig.

Follow upThe drilling progress was continually evaluated during

drilling. During this phase updates were conducted daily orseveral times a day to verify the predictions or if needed,

modify the model predictions. The effects the actual drillingprogress had on the predicted performance, bit wear condition

and drilling time prognosis where evaluated and informed

back to the drilling operation. Practically speaking, Figure 10

was updated with the actual ROP, WOB, RPM and Flow rates

as the drilling went on. The bit wear and rock strength werere-simulated based on this actual information and included as

well. The information on Figure 10 provided to be a goodcommon picture of the situation in discussions between the rig

and the office. In Figure 11 the final update plot are shownwhere the prognosis of the well are overlaid with the actual

outcome of the section. The rock strength log from the

reference well is slightly higher than the actual well but the

correlation is good. Also the drilling time prognosed was sameas the actual. Average simulated bit wear was slightly less

than reported and prognosed. The reason for less bit wear is

the small reduction rock strength and reduced RPM. The

overall result shows a very good mach between the prognosis

and the actual outcome.This example shows that rock strength can be a very

valuable tool for developing drilling prognosis. The quality o

the prognosis will be determined on the lithologicahomogeneity and on the availability of data for constructing

the rock strength log.

ConclusionsComparable rock strength logs along the wellbore can becreated from different sources such as rock mechanical

laboratory testing, rock mechanical testing on cuttings, drilling

data, sonic or neutron density logs, or even average travetimes. The quality of the predictions will be highest for the

meter by meter based logs.

Strength logs can be a very valuable tool to use in

combinations with ROP models for conductiong drilling

analysis such as predicting drilling time, bit wear andrecommend optimum parameters.

NomenclatureMD =Shale/sand porosity ratio (dimensionless)

ct = Sonic Compressional Travel Time

(sec/ft)

Flow = Flow rate (L/minute)

k1, k2, k3 = Experimental constants

MD = Measured depth (m)

p = porosity (%)

pp = Pore pressure (MPa)RPM = Rotations per minute

ROP = Rate of penetration (m/h)

Sh = Horizontal effective stress (MPa)

Sv = Vertical total stress (MPa)

Sv = Vertical effective stress (MPa)

UCS = Unconfined compressive strength (MPa)

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WOB = Weight on bit (MPa)

References1. Goodman, R. 1989. Introduction to Rock Mechanics. John

Wiley & Sons, New York. P562.

2. Berre, T., Tunbridge, L. & Heg, K., 1995, Themeasurement of small strains and K0values in triaxial

tests on clay-shales, 8th Int. Congress on Rock Mech.,Tokyo, pp 1195-1199.

3. Nygaard, R., Bjorlykke, K., Heg., K. and Hareland, G.The effect of diagenesis on stress-strain behaviour andacoustic velocities in sandstones. 1st Canada-U.S. Rock

Mechanics Symposium, May 27-31, 2007, Vancouver,British Columbia, Canada.

4. Nygaard, R., Gutierrez., M. and Heg., K. Shear failure andShear fracturing in Shales and Mudrocks, Accepted in 1st

Canada-U.S. Rock Mechanics Symposium, May 27-31,2007, Vancouver British Columbia, Canada.

5. Kasi, A. Zekai, S. & Bahsa-Eldin, H., 1983. Relationshipbetween Sonic Puls Velocity and Uniaxial Compressive

Strengths of Rocks. Proc. Of the 24th U.S. Symp. On Rock.Mech. Texas A&M University, 20-23 June 1983, TX, US:

409-419.6. Tokle, K, Horsrud, P. & BratIi, R.K., 1986. Predicting

Uniaxial Compressive Strength From Log Parameters: 61stAnn.Tech. Conf. and Exh. of the Soc. of Petr. Eng., 5-8October 1986. Orleans, LA USA. SPE15645.

7. Onyia, E.C., 1988. Relationships between FormationStrength, Drilling Strength, and Electric Log Properties.63rd Ann. Tech. Conf. Houston October 2-5 1988, TX,USA. SPE 18166.

8. Hareland, G., Nygrd, R. Calculating unconfined rockstrength from drilling data, Accepted in 1st Canada-U.S.Rock Mechanics Symposium, May 27-31, 2007,

Vancouver, British Columbia, Canada.9. Zausa, F., Agip Spa; Civolani, L., Brignoli, M., Santarelli,

F.J., 1997. Real-Time Wellbore Stability Analysis at theRig-Site. SPE/IADC Drilling Conference, 4-6 March 1997.

Amsterdam Netherlands. SPE37670.10. Warren, T.M. 1987. Penetrationrate Performance of Roller

Cone Bits. SPE Drilling Engineering: 9-18.11. Hareland, G. & Hoberock, L.,1993. Use of Drilling

Paramters to Predict In-Situ Stress Bounds. SPE/IADCDrilling Conf. 23-25 February 1983, Amsterdam

Netherlands. SPE 25727.12. Rampersad. P.R., Hareland, G., & Boonyapaluk, P. Drilling

optimization Using Drilling Data and Available

Technology. 3rd Latin American/Caribean Petr. Eng. Conf.27-29 April 1994 Buenos Aires, Argentina. SPE 27034.

13. DDS user manual. Drops Technology AS. 2006.

Tables and Figures

Table 1. Experimental constants for rock strength correlationbased on sonic logs.______________________________________________

k k k 21 2 3 r ______________________________________________Sandstone 0.0011 50 3.42 0.9Shale 0.0013 50 -2.66 0.9Combined 0.0012 50 0.22 0.9_____________________________________________

UCS=76 MPa

0

20

40

60

80

100

120

140

160

0 2 4 6 8 10 1

Horizontal stress (MPa)

Vertical

stress(MPa)

2

Figure 1. Results from rock mechanical tests on sandstoneUnconfined compressive strength is calculated to be 76 MPa.

UCS=8 MPa

0

5

10

15

20

25

3035

40

0 5 10 15 20

Horizontal effective stress (MPa)

Verticaleffectivestress(M

Pa)

5 MPa

10 MPa

15 MPa

Figure 2. Results from rock mechanical tests on shale

Unconfined compressive strength is calculated to be 8 MPa.

0

10

20

30

40

50

60

70

80

50 70 90 110 130 150 170 190

Sonic travel time (microsec/ft)

Unconfinedrockstrenght(MPa Sandstone

Shale

Sandstone

Shale

Oniya

Figure 4. Correlation of Unconfined compressive strength vssonic travel time for shale and sandstone.

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1000

1250

1500

1750

2000

2250

2500

2750

3000

0 25 50 75 100

Strength (MPa)

Depth(m)

Drillingstrength

Sonicstrength

Figure 5. Unconfined compressive strength calculated basedon sonic travel times and ROP model strength.

500

1000

1500

2000

2500

3000

0 5 10 15 20 25

UCS (MPa)

D

epth(m)

Average travel times

strength

UCS triaxial tests

Figure 6. Rock strength estimated based on seismic traveltimes.

UCS =137-34Ln(p)

R2=0.91

0

20

40

60

80

100

120

140

0 10 20 30

Porosity (%)

Verticalstressatfailure(MPa)

1350

1375

1400

14251450

1475

1500

1525

1550

1575

1600

1625

1650

1675

1700

1725

1750

0 25 50 75 100

Rock Strength (MPa)

Depth(m)

ROP

Cuttingstrength

Figure 8. Drilling data rock strength compared with rockstrength from rock mechanical tests done on drilling cuttings.

400

500

600

700

800

900

1000

1100

1200

1300

0 10 20 30 40 5

Rock Strength (MPa)

Depth(m)

0

Well 1

Well 2

Figure 9. Rock strength calculated based on ROP models.40

Figure 7. Correlation between strength from rock mechanicaltests and porosity.

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Figure 10. Drilling data for reference section.

Figure 11. Drilling prognosis of new section.

igure 11.F

0 5 10 15 20

WOB

[Ton]

1550

1650

1750

1850

1950

2050

2150

2250

2350

2450

2550

2650

2750

0 20 40 60 80

MD

ROP

[m/h]

100 125 150 175 200

RPM

2000 2500 3000 3500 4000

Flow

[lpm]

Formation Tops 0 1 2 3 4 0 10 20 30 4

Time

(hours)Avg . Bit Wear

Hordaland

Rogaland

0 2.5 5 7.5 10

WOB

[Ton]

1750

1850

1950

2050

2150

2250

2350

2450

2550

2650

0 20 40 60 80

MD

Rock Strength

[MPa]

100 125 150 175

RPM

3000 3250 3500 3750 4000 0 1 2 3 4

Avg. B it Wear

0 10 20

Time

(hours)Flow

[lpm]

Formation Tops

Hordaland

Rogaland

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Figure 12. Prognosis and actual results for the new well.

0 2.5 5 7.5 10

[Ton]

WOB

1750

1850

1950

2050

2150

2250

2350

2450

2550

2650

0 20 40 60 80 100

[Mpa]

MD

Rock Strength

100 125 150 175

RPM

3000 3250 3500 3750 4000

[lpm]

0 1 2 3 4

Avg . Bit Wear

0 10 20 30

Time

(hours)Flow

Formation Tops

Hordaland

Rogaland

Reported wear

Inner Cutter Wear - 1.0

Outer Cutter Wear - 1.0