determination of optimal well trajectory during drilling and production

8/20/2019 Determination of Optimal Well Trajectory During Drilling and Production

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Determination of optimal well trajectory during drilling and production

based on borehole stability

M.R. Zare-Reisabadi n, A. Kaffash, S.R. Shadizadeh

Ahwaz Faculty of Petroleum Engineering, Petroleum University of Technology, Abadan, Iran

a r t i c l e i n f o

Article history:

Received 2 August 2011

Received in revised form12 April 2012

Accepted 24 July 2012Available online 23 August 2012

Keywords:

Wellbore stability

Optimal wellbore trajectory

Maximum drawdown pressure

Mogi–Coulomb failure criterion

Sand production

a b s t r a c t

Several studies have been done about borehole stability and optimized wellbore direction. However,

the majority of them focused on stability during drilling, and there are only a few studies concerns with

stability during drilling and production and its problems such as sanding simultaneously. This paperpresents an analytical model that estimates collapse pressure in stability analysis during drilling and in

addition determines maximum drawdown pressure to prevent sand production, using the Mogi–

Coulomb failure criterion. The results show that in different in-situ stress regimes, the inclination and

azimuth have a significant role in wellbore stability during both drilling and production. Furthermore,

the results show that the optimum direction for wellbore stability during drilling is also the best

direction for stability of a production well. The analytical model is applied to field data in order to verify

the applicability of the developed model.

& 2012 Elsevier Ltd. All rights reserved.

1. Introduction

In recent years, drilling of complicated well trajectory has beenincreased. Multilateral wells, and horizontal and highly deviated

boreholes are drilled frequently. Therefore, borehole stability

becomes more important. When a well is drilled, the surrounding

rock must support the load previously burdened by the removed

material, stresses near the borehole would be redistributed and

causes stress concentration that may lead to formation failure [1–3].

Borehole stability is mainly affected by in situ stresses, pore pressure

and rock strength. During drilling, there are two different pressures:

initial formation pressure and mud pressure, whereas in production

condition, a pore pressure distribution exists around the wellbore.

Therefore, stress distribution around the borehole in production and

drilling conditions would be different. Numerous works have been

done on wellbore stability during drilling and production, sepa-

rately. But a few studies have been done to determine the optimumwell trajectory considering drilling and production problems simul-

taneously in different in-situ stress regimes. The wellbore inclina-

tion and azimuth have remarkable effect on sanding potential onset.

Therefore to decrease sand production risk, considering of produc-

tion problems is required in optimum well trajectory planning of

new wells.

In stability analysis during drilling, Al-Ajmi and Zimmerman

[1,2] developed a 3-D analytical model to study the behavior of

the collapse pressure under the different in-situ stress regimes

and different trajectory in drilling conditions. Last and Mclean [4]

show that the highly deviated wells are most stable than thevertical in an over thrust region by conventional stability analysis.

Moos et al. [5] put forward a method to optimize well trajectories.

Hassan et al. [6] used logs and core’s data, and they evaluated the

stability of wellbores with different angle of deviation. Awal et al.

[7] found that respect to the in-situ stress regimes, the optimal

wellbore trajectory can be vertical, directional or horizontal.

Russell et al. [8] analyzed stability of the Tullich field wells and

concluded the boreholes are drilled parallel to maximum hor-

izontal stress have minimum risk of instability. Recently, Al-Ajmi

and Zimmerman [9,10] developed the Mogi–Coulomb failure

criterion, according to polyaxial failure data of the variety of

rocks. They concluded that Mohr–Coulomb failure criterion is

conservative in estimating of collapse pressure during drilling and

using Mogi–Coulomb failure criterion can minimize the conser-vative nature of the mud pressure predictions. Zhang et al. [11]

considered stability of wells during drilling of shale formations.

They investigated the effect of well trajectory in a normal stress

regime by using Mohr–Coulomb failure criterion. Zhang et al. [12]

used the five strength criteria, with parameters determined based

on the triaxial compression test data, to analyze wellbore stability

of both vertical and inclined boreholes.

In stability analysis during production, Wiprut and Zoback

[13,14] obtain the full stress tensor in Visund field and used it to

determine the optimal stable trajectory for wellbore stability and

sand production; they just investigated one specific case in strike

slip stress regime. Ewy et al. [15] used hollow cylinder and

Contents lists available at SciVerse ScienceDirect

journal homepage: www.elsevier.com/locate/ijrmms

International Journal of Rock Mechanics & Mining Sciences

1365-1609/$ - see front matter & 2012 Elsevier Ltd. All rights reserved.

http://dx.doi.org/10.1016/j.ijrmms.2012.07.018

n Corresponding author. Tel.: þ98 913 2543709; fax: þ98 611 5556962.E-mail address: [email protected] (M.R. Zare-Reisabadi).

International Journal of Rock Mechanics & Mining Sciences 56 (2012) 77–87

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2/11

modified Lade failure criterion to obtain maximum drawdown

during production before well collapsed. Palmer et al. [16]

prepared a stress based model for shear failure around the

perforation and an open hole wellbore according to Mohr–

Coulomb failure criterion, which measure strength of rock with

TWC (Thick Walled Cylinder strength) laboratory core tests. This

model was conservative in prediction of bottom hole pressure.

They conclude that observed drawdown is two times predicted

value, as a rule of thumb. Oluyemi and Oyeneyin [17] developed anew time coupled analytical failure model according to Hoek–

Brown failure criterion to analysis sanding potential prediction.

They concluded that Hoek–Brown failure criterion can help to

overcome the inherent problems in Mohr–Coulomb criterion and

performs better in sanding onset prediction. Khaksar et al. [18]

presented a Geomechanical study for hole stability and sanding

potential in Malay Basin field. They only investigate the Normal

stress regime case.

Recently, Al-Ajmi and Zimmerman [9] developed 3-D Mogi–

Coulomb failure criterion. This failure criterion has been justified

by experimental evidence from triaxial tests as well as polyaxial

tests. They applied this failure criterion to analyze stability of

vertical and deviated wells during drilling. Based on their study,

the Mogi–Coulomb criterion leads to the best prediction of

required mud weight to prevent borehole collapse. In this paper,

Mogi–Coulomb failure criterion is used to model: (1) the opti-

mum well trajectory during drilling and production operations

simultaneously, (2) collapse pressure during drilling operation

and (3) maximum pressure drawdown during production opera-

tion, (4) finally the developed model was applied to the field data

of two different region and applicability of model was verified.

2. Methodology

Assuming that the formation behaves like brittle rock, stability

analysis in drilling or production condition, required to compare

principal stress around the borehole with an appropriate failure

criterion to see if conditions for a wellbore collapse will be

fulfilled or not. Using the stress transformation equations, the

virgin formation stresses expressed in Cartesian wellbore coordi-

nate becomes [19]:

s x ¼ ðsH cos2 aþsh sin2 aÞ cos2 iþsv sin2 i, s y ¼ ðsH sin2 aþsh cos2 aÞ

s z ¼ ðsH cos2 aþsh sin2 aÞ sin2 iþsv cos2 i, t xy ¼ 0:5ðshsH Þ sin2a cos i

t xz ¼0:5ðsH cos2 aþsh sin2 asvÞ sin2i, t yz ¼0:5ðshsH Þ sin2a sin ið1Þ

where i is inclination and a is the azimuth angle due to themaximum horizontal stress (sH ) direction, and sH and sh are themaximum and minimum horizontal in situ stresses. It is easier to

express stresses in a cylindrical system (r , y

and z ). Based on

linear elasticity, maximum stresses, occur in the wellbore wall.

Therefore, failure is expected to initiate at the borehole wall. The

total stress component assuming plane strain condition in drilling

situation, at the borehole wall becomes [19]:

sr ¼ pw, sy ¼ ðs x þs yÞ22ðs x2s yÞ cos2y4t xy sin2y pws z ¼s z 2n½2ðs x2s yÞ cos2y4t xy sin2y, ty z ¼ 2ðt yz cosy2t xz sinyÞ

ð2Þwhere, y is the angular position around the wellbore circumfer-

ence and n is Poisson’s ratio.In production conditions, well pressure is lower than forma-

tion pressure and this cause that formation around the borehole

shrinks and hence tangential and axial stress decrease. This

reduction is proportional to drawdown pressure. Assuming linear

poroelasticity, total stresses at the borehole wall become [15]:

sr ¼ pwsy ¼s x þs y22ðs x2s yÞ cos2y4t xy sin2y pw þb0ð pw2 p f Þ

s z ¼s z 2n 2ðs x2s yÞ cos2y4t xy sin2y þb0ð pw2 p f Þ

ty z ¼ 2ðt yz cosy2t xz sinyÞ ð3Þ

b0 ¼ 12n

1n b ð4Þ

where pw is wellbore flowing pressure, p f is current average

reservoir pressure, and b is Biot’s poroelastic constant. Usually

radial stress is minimum principal stress, and maximum and

intermediate principal stress determined by following equation

[20]:

s1,2 ¼ 0:5ðsy þs z Þ7 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðsy þs z Þ2 þ4t2y z

q ð5Þ

To predict shear failure, various failure criteria have been

developed, among which Mohr–Coulomb is much referred and

used in practice. But it is usually conservative in predicting shear

failure, because it does not consider the effect of intermediate

principal stress. Recently, Al-Ajmi and Zimmerman [9] developed

the three-dimensional Mogi–Coulomb failure criterion. Based on

the Al-Ajmi and Zimmerman [10] study, the Mogi–Coulombcriterion leads to the best prediction of required mud weight to

prevent borehole collapse. According to this criterion:

tMogi ¼aþb s01 þs03

2

ð6Þ

toct ¼ 13

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðs01s03Þ2 þðs01s02Þ2 þðs02s03Þ2

q ð7Þ

where a and b are coefficients that can be determined according

to Mohr–Coulomb strength parameters:

a¼ 2 ffiffiffi

2p

3 s0 cosj, b¼

2 ffiffiffi

2p

3 sinj ð8Þ

when toct4tMogi, shear failure happens and critical bottom holepressure can be determined.

Regarding the fact that radial, tangential and axial stresses are

functions of wellbore pressure, P w, the principal stresses are

therefore also functions of well pressure. Moreover, when apply-

ing these principal stresses in different failure criteria, effective

principal stresses must be used, i.e., wellbore pressure subtracted

from the principal stresses. So an iterative loop should be applied

to obtain critical bottom hole pressure. In this study, a computer

program is developed to obtain the critical bottom hole pressure

that causes the wellbore collapse and determines the best well-

bore trajectory. This program using several input parameters,

including: in situ stresses (vertical stress, maximum and mini-

mum horizontal stresses), rock strength parameters (cohesion,

friction angle and Poison ratio), well inclination and azimuth,

initial formation pressure and Biot’s poroelastic constant. Indrilling situation wellbore pressure increase from initial forma-

tion pressure to minimum horizontal pressure to determine

minimum pressure that prevents wellbore collapse. In production

condition wellbore pressure decrease from initial formation

pressure until the condition for wellbore collapse satisfied. This

pressure is named critical bottom hole flowing pressure (CBHFP ).

Maximum sand free drawdown (MSFDD) could be determined by

following equation:

MSFDD¼ Currentreservoirformationpressure2CBHFP ð9ÞThese analyses have been done for different well inclination

(i¼01 to i¼901) and azimuth (a¼01 to a¼1801) in several cases of in-situ stress regimes. Based on the results the optimum wellbore

trajectory which has maximum stability in both drilling and

M.R. Zare-Reisabadi et al. / International Journal of Rock Mechanics & Mining Sciences 56 (2012) 77–87 78


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production condition could be determined regarding different

in-situ stress regimes.

3. Results and discussion

Table 1 shows five cases of different stress regimes and the

input parameters for mechanical stability analysis for a well in

drilling condition. According to these data minimum bottom holepressure that mud weight must be provided to prevent well

collapse determined. Furthermore, optimum well trajectory that

indicates the best stable drilling direction for stability obtained

for each case.

Case 1. indicates a normal stress regime. Fig. 1 shows the 3-D

plot of collapse pressure as a function of inclination and wellbore

azimuth for Case 1. The vertical axis is collapse pressure in psi,

and horizontal axes indicate wellbore inclination and azimuth.

It reveals the collapse pressure of a vertical borehole is less than

the horizontal borehole, so the vertical boreholes are more stable

than the horizontal boreholes and almost all the deviated wells.

It is also obvious that drilling in the direction of minimum

horizontal stress (where a¼

901), regardless of the inclination, is

better to avoid borehole collapse. So drilling parallel to the

minimum horizontal stress direction is the most stable state in

this case. Moreover, it shows that the collapse pressure is highly

sensitive to the inclination in all direction or azimuth.

In Case 2, the formation is in the boundary between normal

fault and strike-slip regimes. Fig. 2 shows that, the horizontal

boreholes are more stable than the vertical or all deviated bore-

holes in all directions. In addition, it is obvious that the risk of

borehole instability decreases with increasing the inclination

angle. The optimum drilling azimuth is still parallel to the

minimum horizontal stress. Therefore, a horizontal borehole that

is drilled in the minimum horizontal stress direction is the

best one.

In Case 3, the formation is in the strike-slip regimes. It is

obvious from Fig. 3 that a horizontal well is the most stable one.

As Fig. 3 depicts, in this case drilling in the direction of maximum

horizontal stress, regardless of the inclination, need the lowesthydrostatic pressure to avoid borehole collapse (opposite of the

before cases) in drilling condition. As Al-Ajmi and Zimmerman

[1,2] and Wirput and Zoback [13,14] mentioned, in this case, the

most stable orientation is a wellbore drilled horizontally in the

direction of the maximum horizontal stress. Contrary to Case 1, in

Case 3 the collapse pressure is not sensitive to inclination in all

directions. In the direction of minimum horizontal stress, sensi-

tivity is low. But the collapse pressure is highly sensitive to

inclination in the direction of maximum horizontal stress.

Case 4. reveals a formation which is in the boundary between

strike-slip and reverse fault regimes. Fig. 4 shows that a horizon-

tal borehole which, is drilled parallel to the maximum horizontal

stress is the best trajectory. Here also the risk of boreholeinstability decreases with increasing the borehole inclination.

When the intermediate principal in situ stress is equal to the

maximum in situ stress (sH ¼sv, NF–SS stress regime) the bestazimuth is 901, and gradually decreases to be 01 when the

intermediate in-situ stress reaches the minimum in situ stress

(sh¼sv, SS–RF stress regime).Finally Case 5 indicates a formation in the reverse fault

regimes with anisotropic horizontal stresses. Fig. 5 shows that

the optimum drilling inclination is close to the horizontal well.

In this case, the optimum drilling direction is parallel to the

maximum principal in situ stress.

As mentioned before, wellbore trajectory should be optimized

considering both drilling and production conditions. Previous

studies such as Al-Ajmi and Zimmerman [1,2] only focused onstability during drilling. Wirput and Zoback [13,14] obtain the full

stress tensor in Visund field and used it to analyze wellbore

stability during drilling and production. Their study confined just

to the strike-slip regime, but our study presents the optimum

trajectory during drilling and production simultaneously in different

Table 1

Input data for stability analysis in different stress regimes.

Case Stress

regime

Depth

(ft)

sv

(psi/ft)

sH

(psi/ft)

sh

(psi/ft)

P f

(psi/ft)

n S 0

(psi)

j

degree

1 NF 6000 1 0.9 0.8 0.44 0.35 900 35

2 NF –SS 6000 0.9 0.9 0.8 0.44 0.35 900 35

3 SS 6000 0.85 1 0.8 0.44 0.35 900 35

4 SS –RF 6000 0.85 1.1 0.85 0.44 0.35 900 35

5 RF 6000 0.85 1.1 0.9 0.44 0.35 900 35

0 20 40

60 80

100 120

140 160

180

01020

3040

5060

7080

90

2700

2750

2800

2850

2900

2950

3000

3050

3100

3150

A z imu t h(degree )

Inc linat ion( degr ee)

P w ( p s i )

Fig. 1. Collapse pressure for various wellbore trajectories in NF stress regime (Case 1).



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case of in-situ stress regimes. In addition, the new 3-D failure

criterion (Mogi–Coulomb) was used for sand production prediction

for first time. Table 2 shows input parameters of five different cases

for mechanical stability analysis during the production conditions in

a sandstone formation. By using developed program and input data,maximum sand free drawdown pressure (MSFDD) is determined.

Furthermore, optimum wellbore trajectory that indicates the best

direction for stability of a production well obtained for each case.

Fig. 6 shows the 3-D plot of MSFDD pressure of the wells with

different inclination and azimuth in Case 1. It is concluded that

the MSFDD pressure of a vertical borehole is greater than the

horizontal borehole, so the vertical boreholes have less potential

for sanding than the horizontal boreholes and almost all the

deviated wells. In this case, the best drilling trajectory is a well

with i ¼401 and a¼901. It is also obvious that, drilling parallel tothe minimum horizontal stress direction is the best trajectory in

this case. In addition, it shows that the MSFDD pressure or

sanding potential is highly sensitive to the inclination in all

direction or azimuth.

In Case 2, formation is in the boundary between normal fault

and strike-slip regimes. Fig. 7 shows that horizontal boreholes

have less potential for sand production than the vertical or all

deviated boreholes in all directions. Also, it is obvious that the risk

of sanding onset decreases with increasing the inclination angle.A horizontal borehole which is drilled in the minimum horizontal

stress direction is the best one. On the other hand, the tolerance

between maximum and minimum MSFDD in all directions is less

than 200 psi. Therefore, MSFDD pressure is not sensitive to

inclination and azimuth in all directions.

Case 3. depicts a formation in the strike-slip regime. It is obvious

from Fig. 8 that the horizontal boreholes have less potential for

sand production than the vertical and deviated boreholes in all

directions. As Fig. 8 shows, in this case the best direction is a

horizontal borehole close to the maximum horizontal stress

direction same as Wirput and Zoback [13,14] studies. Contrary

to Case 2, in Case 3 the MSFDD pressure is sensitive to inclination

and azimuth in all directions. In the direction of minimum

020

4060

80100

120140

160180 0

1020

3040

5060

7080

90

2740

2750

2760

2770

2780

2790

2800

2810

2820

2830

I n c l i n a t i o n (

d e g r e e ) Az i m u t h( d e g r e e )

P w ( P s i )

Fig. 2. Collapse pressure for various wellbore trajectories in NF –SS stress regime (Case 2).

0 20

40 60

80 100

120 140

160 180

010

2030

4050

6070

8090

2650

2700

2750

2800

2850

2900

2950

3000

3050

3100

3150

A z imu t h(degree )I nc l i nat i o n( d e g r e e )

P w ( p s i )

Fig. 3. Collapse pressure for various wellbore trajectories in SS stress regime (Case 3).



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horizontal stress sensitivity is low. But the MSFDD pressure is highly

sensitive to inclination in the direction of maximum horizontal stress.

In Case 4, formation is in the boundary between strike-slip and

reverse fault regimes. It is concluded from Fig. 9 that the optimum

well pattern is a horizontal boreholes drilled parallel to the maximum

horizontal stress direction. Here also the risk of sanding potential

decreases with increasing the borehole inclination.

Finally Case 5 indicate a formation in the reverse fault regimes

with anisotropic horizontal stresses. Fig. 10 shows in the produc-

tion situation the highly inclined wells are more stable than the

vertical ones. In this case, the optimum direction is parallel to the

maximum principal in situ stress, sH and the largest MSFDDpressure is associated with 601 deviated borehole.

Regarding Table 3 comparing these five cases reveal that the

optimum wellbore trajectory to prevent shear failure is the same for

both drilling and production condition. For example, in Case 1, wells

are drilled near to vertical are more stable than horizontal ones. Also

in this case, drilling in the direction of minimum horizontal stress

provide the maximum safe mud window for drilling situation and

maximum safe drawdown for production condition.

Principal stresses difference, plays a key role in shear failure of

the rocks. In all cases, the best drilling direction in point of stability

is perpendicular to the plane which there is minimum difference

between principal stresses. For example in NF regime (sv¼s1,sH ¼s2, sh¼s3) a vertical well (in NF regime vertical well directionwill be perpendicular to the s 2–s 3 plane) will be more stable than

0 20

4060

80 100

120 140

160 180

010

2030

4050

6070

8090

2700

2800

2900

3000

3100

3200

3300

3400

3500

A z i m u t h( d e g r

e e )

I n c l i n a t i o n ( d e g r e e )

P w ( p s i )

Fig. 4. Collapse pressure for various wellbore trajectories in SS –RF stress regime (Case 4).

0 20

40 60

80 100

120 140

160 180

010

2030

4050

6070

8090

2800

2900

3000

3100

3200

3300

3400

3500

A z im u t h(de g ree )

I nc l i nat i o n( d e g r e e )

P w ( p s i )

Fig. 5. Collapse pressure for various wellbore trajectories in RF stress regime (Case 5).

Table 2

Input data for sanding onset analysis in different stress regime.

Case Stress

regime

sv(psi)

sH (psi)

sh(psi)

P f (psi)

n S 0(psi)

jdegree

b0

1 NF 4095 3600 3150 2025 0.2 1000 35 0.8

2 NF –SS 3600 3600 3150 2025 0.2 1000 35 0.8

3 SS 3600 4095 3150 2025 0.2 1000 3 5 0.8

4 SS –RF 3600 4095 3600 2025 0.2 1000 35 0.8

5 RF 3150 4095 3600 2025 0.2 1000 3 5 0.8



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Fig. 6. MSFDD pressure for various wellbore trajectories in NF stress regime (Case 1).

0 10 20 30

40 50 60

70 80 90

100 110 120 130

140 150 160

170 180

0

10

20

30

4050

60

70

80

90

1380

1400

1420

1440

1460

1480

1500

1520

1540

A z i m u t h( D e g

r e e )

I n c l i n a t i o n ( D e g r e e )

M S F D D ( P s i )

Fig. 7. MSFDD pressure for various wellbore trajectories in NF –SS stress regime (Case 2).

020

4060

80100

120140

160180

0

10

20

30

40

50

60

70

80

90

200

400

600

800

1000

1200

1400

1600

A z i m u t h( D e g

r e e )


M S F D D ( P s i )

Fig. 8. MSFDD pressure for various wellbore trajectories in SS stress regime (Case 3).



7/11

the horizontal one, as the presented model predict. In addition, in

this regime, drilling of a deviated well in sh direction will cause astress difference of (s1–s2) whereas it will be higher value (s1–s3)when a deviated well is drilled in direction of sH . Therefore, drillingparallel to sh will be better than sH direction, as the model predict.

4. Field case study

The developed analytical model will be applied to the two

deviated wells in Ahwaz oilfield for stability analysis during

drilling and also stability analysis during production will be run

in Malay Basin field, offshore Malaysia for a horizontal well. Wells

AZ - A and AZ -B are two deviated wells with same drilling condi-

tions that produce oil from Bangestan reservoir in Ahwaz oilfield

(one of southern Iranian field in the Middle East). Based on a

resultant Geomechanical model by Zare et al., data in Table 4 was

used to do stability analysis during drilling in Ahwaz oilfield. The

direction of maximum horizontal stress in this region is N–S to

N201E. As Figs. 11 and 12 show, well AZ - A and AZ -B are in same

condition except of the well trajectory. Well AZ - A was drilled at

351

deviation in a direction of N 301

whilst Well AZ -B is drilled at

020

4060

80100

120140

160180

0

10

20

30

40

50

60

70

80

90

400

600

800

1000

1200

1400

1600

1800

A z i m u t h( D e

g r e e )


M S F D D ( P

s i )

Fig. 9. MSFDD pressure for various wellbore trajectories in SS –RF stress regime (Case 4).

020

4060

80100

120140

160180

0

10

20

30

40

50

60

70

80

90

200

400

600

800

1000

1200

1400

1600

A z i m u t h( D e g r

e e )


M S F D D ( P s i )

Fig. 10. MSFDD pressure for various wellbore trajectories in RF stress regime (Case 5).

Table 3

Optimum wellbore trajectory in different cases for drilling and production condition.

Cases 1 2 3 4 5

Optimum trajectory in drilling

condition

Close to vertical wells,

parallel to sh

Horizontal wells

parallel to sh

Horizontal wells,

parallel to sH

Horizontal wells,

parallel to sH

Highly deviated wells

parallel to sH Optimum trajectory in

production condition

Close to vertical wells,

parallel to sh

Horizontal wells,

parallel to sh

Horizontal wells,

parallel to sH

Horizontal wells,

parallel to sH

Highly deviated wells

parallel to sH



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301 deviation in a direction of N901E. Therefore, the well AZ - A has

a drilling direction (a) in the range of around 101–301 from themaximum horizontal stress. But well AZ -B has a drilling direction

in the range of 701–90

1 [21] (see SPE 136989 for more details).

Fig. 13 shows the collapse pressure of the well with different

inclination and azimuth in Ahwaz oilfield by using data in Table 4

(is same as Case 5 and Fig. 5). It is obvious from Fig. 13 that well

AZ - A has been drilled in the optimum drilling direction (close to

Table 4

Input data for case studies.

Well Stress regime Depth (ft) C (psi) m u (deg) b rv (psi/ft) r H (psi/ft) rh (psi/ft) Po (psi/ft) I (deg) a (deg)

AZ- A RF 11,152 1100 0.29 43 – 1.03 1.2 1.1 0.46 35 30

AZ-B RF 11,152 1100 0.29 43 – 1.03 1.2 1.1 0.46 30 90

AA NF 6,760 1500 0.25 35 1 1 0.93 0.9 0.433 90 190

Fig. 11. Trajectory of well AZ - A.



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the maximum horizontal stress direction) but well AZ -B has been

drilled in the direction of minimum horizontal stress. Therefore it

is expected that well AZ - A be more stable with less drilling

problems than the well AZ -B. Refereeing to the drilling reports,

numerous cases of borehole instability, stuck pipe, and borehole

collapse have been stated while drilling well AZ -B. These pro-

blems caused highly increasing of drilling operation cost of this

well. However, well AZ - A has been drilled without any serious

problems which confirming the applicability and accuracy of

presented model.

Well AA is an open hole horizontal well in Malay Basin,

offshore Malaysia with sand/shale sequences. The local area is

located in a normal fault stress regime where maximum in-situ

stress is vertical stress. Regional stress data in the Malay Basin

field indicated that the direction of maximum horizontal stress

follows north–south or near north east–south west trend. Based

Fig. 12. Trajectory of well AZ -B.



10/11

on full scale Geomechanical study which was done by Khaksar

et al. [18], data in Table 4 was used to do stability analysis during

production for this area in sandstone interval.Fig. 14 shows the MSFDD pressure of the wells with different

inclination and azimuth in Malay Basin field (is same as Case 1

and Fig. 6). Fig. 14 indicates a MSFDD of 235 psi can be achieved

over the life of field condition for planned horizontal well AA in

sandstone section. Based on the model prediction, no sand

production will be occurred at the first stage of production and

no sand control would be needed. The maximum planned draw-

down in well AA is 200 psi and it is currently producing sand free,

confirming the accuracy of the sand production model [18].

5. Conclusions

In this study, we present an analytical model that estimates

collapse pressure in stability analysis during drilling and in

addition determines maximum drawdown pressure to prevent

sand production. The Mogi–Coulomb failure criterion was used to

analyze sand production for the first time. It was demonstratedthat optimum well trajectory to prevent wellbore collapse in

production condition is same as drilling condition.

It was shown that the best stable well trajectory in drilling and

production condition is highly affected by in-situ stress regimes

and the magnitude of in situ stresses. It was demonstrated that in

the case of the normal fault stress regime, drilling in the direction

of minimum horizontal stress, regardless of the inclination, is the

most stable direction for both drilling and production operations.

In strike-slip and reverse fault stress regime, drilling in the

direction of minimum horizontal stress is less stable than the

other directions. Drilling direction does not affect the horizontal

and highly deviated boreholes stability in the normal stress

regimes, but in the reverse and strike-slip regimes stability of

these wells both during drilling and production, is highly

0 20

40 60

80 100

120 140

160 180

010

2030

4050

6070

8090

5750

5800

5850

5900

5950

6000

6050

6100

6150

6200

A z i m u t h ( d e g

r e e )I n c l i n a t i o n ( d e g r e e )

P w ( p s i )

Well

AZ−B

Well

AZ−A

Fig. 13. Collapse pressure for various wellbore trajectories in in Ahwaz oilfield.

015

3045

6075

90105

120135

150165

180

0

15

30

45

60

75

90

200

400

600

800

1000

1200

1400

1600

A z i m u t h (

D e g r e e )

I nc l i nat i o n( D e g r e e )

X: 15

Y: 90

Z: 240

M

S F D D ( P s i )

Well

AA

Fig. 14. MSFDD pressure for various wellbore trajectories in Malay Basin field.



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sensitive to the drilling direction. Drilling a well near the vertical

direction is not always the most stable well trajectory. It is true

only in the normal stress regime.

The results also show that in reverse fault and strike slip stress

regimes, horizontal well provide a larger safe mud window in

drilling condition and larger MSFDD pressure in production mode.

References

[1] Al-Ajmi AM, Zimmerman RW. A new well path optimization model forincreased mechanical borehole stability. J. Petrol. Sci. Eng. 2009;69(1-2):53–62.

[2] Al-Ajmi AM, Zimmerman RW Stability analysis of deviated boreholes usingthe Mogi–Coulomb failure criterion, with application to some oil and gasreservoirs. In: proceedings of the IADC/SPE Asia Pacific drilling technologyconference. Bankok, Thailand; 13–15 November 2006. Paper SPE 104035.

[3] Mohiuddin MA, Khan K, Abdulraheem A, Al-Majed A, Awal MR. Analysis of wellbore instability in vertical, directional, and horizontal wells using fielddata. J. Petrol. Sci. Eng. 2007;55:83–92.

[4] Last NC, McLean MR. Assessing the impact of trajectory on wells drilled in anoverthrust region. J. Petrol. Tech. 1996;48:620–6.

[5] Moos D, Peska P, Zoback MD Predicting the stability of horizontal wells andmulti-laterals—rhe role of in situ stress and rock properties. In: proceedingsof the SPE international conference on horizontal well technology. Alberta,Canada; 1–4 November 1998. Paper SPE 50386.

[6] Hassan S, Klimentos T, Badri M, Sengul M, Zeid A Optimizing drillingperformance by wellbore stability evaluation and directional drilling prac-tices. In: proceedings of the IADC/SPE Middle East drilling conference. AbuDhabi; 8–10 November 1999. Paper SPE 57575.

[7] Awal MR, Khan MS, Mohiuddin MA, Abdulraheem A, Azeemuddin MA Newapproach to borehole trajectory optimisation for increased hole stability. In:proceedings of SPE Middle East oil show. Bahrain; 17–20 March 2001. PaperSPE 68092.

[8] Russell KA, Ayan C, Hart NJ, Rodriguez JM, Scholey H, Sugden C, et al.Predicting and preventing wellbore instability using the latest drilling andlogging technologies: Tullich field development, North Sea. In: proceedings of SPE annual technical conference and exhibition. Denver, Colorado; 5–8October 2003. Paper SPE 84269.

[9] Al-Ajmi AM, Zimmerman RW. Relationship between the parameters of theMogi and Coulomb failure criterion. Int. J. Rock Mech. Min. Sci. 2005;42(3):431–9.

[10] Al-Ajmi AM, Zimmerman RW. Stability analysis of vertical boreholes usingthe Mogi–Coulomb failure criterion. Int. J. Rock Mech. Min. Sci. 2006;43(8):1200–11.

[11] Zhang J, Yu M Maintaining the stability of deviated and horizontal wells:effects of mechanical, chemical and thermal on well designs. In: proceedingsof the SPE international oil & gas conference. China; 5–7 December 2006.Paper SPE 100202.

[12] Zhang L, Cao P, Radha KC. Evaluation of rock strength criteria for wellbore

stability analysis. Int. J. Rock Mech. Min. Sci. 2010;47:1304–16.[13] Wiprut D, Zoback M, Hassen T, Peska P. Constraining the full stress tensor

from observations of drilling-induced tensile fractures and leak-off tests:application to borehole stability and sand production on the Norwegianmargin. Int. J. Rock Mech. Min. Sci. 1997;34:365.

[14] Wiprut D, Zoback M, Hassen T, Peska P. Constraining the stress tensor in theVisund field, Norwegian North Sea: application to wellbore stability andproduction. Int. J. Rock Mech. Min. Sci. 1999;37:317–36.

[15] Ewy RT, Ray P, Bovberg CA, Norman PD. Open hole stability and sandingpredictions by 3D extrapolation from hole collapse test. SPE Drill. Complet.2001;16(4):243–51.

[16] Palmer I, Vaziri H, Wilson S, Moschovidis Z, Cameron J, Ispas I Prediction andmanaging sand production, a new strategy. In: proceedings of SPE annualtechnical conference exhibition. Denver, Colorado; 5–8 October 2003. PaperSPE 84499.

[17] Oluyemi GF, Oyeneyin MB. Analytical critical drawdown (CDD) failure modelfor real time sanding potential prediction based on Hoek and Brown failurecriterion. J. Petrol. Gas Eng. 2010;1(2):16–27.

[18] Khaksar A, Rahman K, Ghani J, Mangor H. Integrated geomechanical study forhole stability, sanding potential and completion selection: a case study fromSouth East Asia. In: proceedings of SPE annual technical conference andexhibition. Denver, Colorado; 21–24 September 2008. Paper SPE 115915.

[19] Hiramatsu Y, Oka Y. Determination of the stress in rock unaffected byboreholes or drifts from measured strains or deformations. Int. J. Rock Mech.Min. Sci. 1968;5(4):337–53.

[20] Brady BH, Brown ET. Rock mechanics for underground mining. 2nd ed.Dordrecht: Kluwer; 1999.

[21] Zare MR, Shadizadeh SR, Habibnia B Mechanical stability analysis of direc-tional wells: a case study in Ahwaz oilfield. In: proceedings of SPE annualtechnical conference and exhibition. Abuja, Nigeria; 31 July–7 August 2010.Paper SPE 136989.


determination of optimal well trajectory during drilling and production

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