1

1. INTRODUCTION

Oil and gas industry is largely developing in more

challenging reservoirs such as shale oil and shale

gas. These reservoirs are known as tight reservoirs

due to very low permeability and matrix porosity

[1]. On one hand their huge amount of reserves

cannot be neglected and on the other hand

traditional recovery techniques looks inefficient.

For the purpose of maximum recovery, stimulation

operations such as hydraulic fracturing encountered

within horizontal drilling seem inevitable. All these

have led to a different set of challenges specifically

related to wellbore instability and regional

geomechanical problems.

For a successful geomechanical model we need

information about rock strength, pore pressure, in-

situ stresses and elastic properties of the rocks.

Besides, stress alteration around the borehole and in

a radius from the wellbore will occur while drilling

and production is in action. For such reasons, these

changes are needed to be predicted prior to the

drilling or stimulation operations. A good

geomechanical model which embraces anisotropic

formation elastic properties will result in an

accurate stress analysis and can simulate regional

geological hazards to prevent future financial

losses.

2. THEORY & BACKGROUND

Formations at depth exist under a state of

compressive in-situ stresses. When a well is drilled

through a formation a significant amount or rock

volume is removed which causes stress alteration.

As a result the surrounding rocks of the borehole

must compensate for the eliminated load. Stress

concentration around the borehole is the direct

result of this process, thus in case of weak

formations such as unsolicited sands or shales the

formation may fail. In anisotropic formations where

the rock strength differs in two or even three

ARMA 13-150

Stress Analysis and Wellbore Stability in Unconventional Reservoirs

Mehdi Ostadhassan1, Steve Benson

1 and Siavash Zamiran

2

1- Dept. of Petroleum Engineering, University of North Dakota, Grand Forks, ND 58202 USA 2- Dept. of Civil Engineering, Science and Research Branch, Islamic Azad University, Markazi, Iran

Copyright 2013 ARMA, American Rock Mechanics Association

This paper was prepared for presentation at the 47th US Rock Mechanics / Geomechanics Symposium held in San Francisco, CA, USA, 23-26

June 2013.

This paper was selected for presentation at the symposium by an ARMA Technical Program Committee based on a technical and critical review of the paper by a minimum of two technical reviewers. The material, as presented, does not necessarily reflect any position of ARMA, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of ARMA is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 200 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgement of where and by whom the paper was presented.

ABSTRACT: This study will provide insight to evaluate the potential risks involved with the alteration of in situ effective stresses

around the borehole and the risks involved with the reservoir pressure decline. We studied how years of production and reservoir

depletion may cause future major geological hazards in the area understudy. Wellbore instability and stress distribution analysis

around a vertical and horizontal borehole is also carried out in the Bakken Formation including elastic anisotropy of the layer. We

calculated the magnitude of maximum principal horizontal stress as a major input parameter through a new method. This study

shows the importance of geomechanical modeling in petroleum industry with the recent growth of drilling plans in unconventional

reservoirs as a novel source of energy where many of them are thin layered, anisotropic and naturally fractured. To improve

production in such reservoirs horizontal wells seem inevitable which should proceeded by further stimulation operations such as

hydraulic fracturing; All these require a good understanding of formation elastic properties such as Young’s modulus and Poisson’s

ratio, geomechanical response of the formation and stresses around the borehole. For this study, dynamic elastic properties were

collected through the Bakken Formation using advanced sonic logs. The interpretation of these data is significant in estimating the

rock strength, pore pressure, and in situ stresses. In the next step, the measured dynamic elastic moduli were converted to static

ones and were used as input into poroelasticity equations to calculate the magnitude of the horizontal principal stresses. The

direction of the maximum principal horizontal stress was determined to be N70E by analyzing fast shear azimuth (FSA) using

major fractures which have caused more than 2% shear anisotropy. Finally stress analysis and wellbore stability were performed

and compared in the current state of the reservoir stress state and after 5 years of production. The results approve the possible

occurrence of normal faulting in the region and existence of borehole breakouts after years of production.

2

different directions, failure could be more

complicated. In general, failures could be

categorized under three main classes as shown in

Figure 1[2]:

1. Formation breakdown or unintended

hydraulic fracturing that will result in loss of

drilling fluid circulation, Figure 1(a).

2. Hole enlargement due to brittle rock fracture

or rupture, Figure 1(b).

3. Hole size reduction which can happen

because of ductile yield of the rock, Figure

1(a).

Fig 1. Three main classes of wellbore failure.

2.1. Wellbore Stability Influencing Parameters

To obtain a good prediction of wellbore stability

and geomechanical behavior of the reservoir, we

should try to recognize the governing parameters

and various possible conditions occurring around

the borehole when the formation is drilled [3].

There is a comprehensive list of factors encountered

in wellbore stability analysis and geomechanical

modeling, but the major ones that are controllable,

predictable and measurable are: rock strength,

stiffness, permeability, temperature, pore pressure

and concentration (Figure 2).

Fig 2. Major factors changing around the borehole.

2.2. In-Situ Stress Calculation (Principal Stresses)

Formation stresses play an important role in

geophysical prospecting and development of oil and

gas reservoirs. Both the direction and magnitude of

these stresses are required in (a) planning for

borehole stability, (b) hydraulic fracturing for

enhanced production, and (c) selective perforation

for sand control. The formation stress state is

characterized by the magnitude and direction of the

three principal stresses, one vertical and two

horizontal. Consequently, formations could be

either normally stressed or tectonically stressed [4].

In a normally stressed formation the maximum

principal stress is the vertical effective stress ( ),

equal to the overburden stress. Total vertical stress

is defined as the sum of the weight of the rock

matrix. It is described as the vertical effective stress

plus the pressure exerted by the fluids in the pore

spaces that overlie the depth of interest [5] as

presented in Eq. (1):

(1)

where is the total vertical stress at depth ,

is the density at depth Z below the surface and

is the acceleration due to the gravity. Eq. (1) can

also be rearranged in the form of Eq. (2):

(2)

In such condition the other two principal in-situ

stresses ( , ) are in the horizontal plane. In

tectonically stressed regions which may contain

active faults, salt domes or severe folding and

fracturing, the principal in-situ stresses are not

necessarily oriented in vertical or horizontal

directions that have led into structural deformations,

thus their magnitudes are usually different and more

complicated to be estimated, comparing to the

normally stressed regions.

To calculate minimum principal horizontal stress

anisotropic poroelasticity equation, Eq. (3) can be

used [6]:

(3)

The anisotropic dynamic elastic parameters (

, , and ) are measured by advanced

sonic log [7] and then the values are transformed to

static ones to better represent the formation

geomechanical characteristics. Wang correlation [8,

3

9] for soft rock is applied to measured data to

transform dynamic values into static ones, Eq. (4):

(4)

Calculating the minimum principal horizontal and

overburden stress’s magnitude as a function of depth

will be used as input to evaluate the magnitude of the

maximum horizontal principal stress [10]. To perform

this task acoustoelastic parameter AE in terms of the far-

field shear moduli C55 and C66 is defined as Eq.(5):

(5)

In the above equation it has been assumed that the

effects of permeability on the shear moduli (C55 &

C66) are similar and negligible [11].

Once the acoustoelastic parameter (AE) has been

determined for a given lithology interval (shale units and

middle member separately), we can calculate the

maximum horizontal principal stress magnitude ( )

as a function of depth from the following equation:

(6)

Where C55 and C44 denote the fast and slow dipole

shear moduli. These values are measured from the

fast and slow shear wave velocities with respect to

the formation density. C66 is similarly shear

modulus from Stoneley shear wave and is

calculated from Stoneley wave velocity and

formation density [12].

2.3. Stress Distribution around the wellbore

To evaluate the stress distribution around the wellbore,

plain strain condition is taken into account. The

complete solution for stress distribution around the

borehole and deeper in the formation are presented in

Eqs. [7-11] [13]:

2 4

H h H hr 2 4

2 2

2 2

(1 ) (1 32 2

3 )cos 2

w w

w ww

R R

r r

R RP

r r

(7)

2 4

H h H h

2 4

2

2

(1 ) (1 3 )2 2

cos 2

w w

ww

R R

r r

RP

r

(8)

2

H h 22 ( ) cos 2w

z v fr

R

r (9)

4 2

H h

4 2(1 3 2 )sin 2

2

w wr

R R

r r

(10)

0rz z (11)

Where Rw is the well radius, is the pressure exerted

on the wellbore wall by the drilling fluid, is

formation Poisson’s Ratio then , , and

are radial, tangential, axial and shear stresses

respectively. is the angle measured relative to the

direction of maximum principal horizontal stress.

2.4. Horizontal Principal Stress Orientation

Various methods have been discussed in the

literature for estimating the direction of maximum

principal horizontal stress [14]. The most reliable

way to determine stress orientation is to identify

features (either geological features or wellbore

failures) which their orientation is controlled by the

direction of the in-situ stresses. Other methods that

rely on the observing if the effect of the stresses on

the rock properties such as using oriented core have

been found to be less reliable and subject to

influence by factors other than the in-situ stresses.

Methods that are the most reliable to identify the

orientation of the principal horizontal stresses are as

follows:

Using wellbore failure or elongations.

Analyzing seismic anisotropy.

Utilizing advanced sonic logs (sonic

scanner) -using the fast shear azimuth

(FSA).

Wellbore failure can consist of breakouts or induced

fractures. Breakouts normally occur in a vertical

well at the azimuth of , and drilling-induced

tensile fractures occur 90° to breakouts parallel to

the azimuth of . By detecting such features,

direction of principal horizontal stresses would be

found with high accuracy.

Acquiring multicomponent seismic survey (source

and receiver) can be helpful to detect the shear

splitting phenomenon which indicates azimuthal

anisotropy within the formation. Azimuthal

anisotropy originates from shear splitting due to the

presence of structural elements such as bedding

planes or joints and fractures (Figure 3) [15].

Advanced sonic logs which are enhanced by

mounted dipole sources and receivers are designed

in such a way to allow computation of the velocity

and orientation propagation of fast and slow shear

dipole modes [17]. In such configuration the fast

shear wave propagation azimuth is recognized to be

in the direction of .

4

Fig 3. Shear wave splitting and advanced sonic logging tool

placement in a vertical well (courtesy of Schlumberger).

2.5. Failure Criterion

A failure criterion should be chosen to predict

wellbore stability conditions in any geomechanical

model. Mohr-Coulomb is a conventional and widely

used failure criterion so far used by the industry for

geomechanical modeling [18]. Mohr-Coulomb

failure model in a linear elastic formation with

horizontal in-situ stresses and drilling fluid exerting

pressure on the borehole wall ( is given by

following equations:

(12)

(13)

Where is the maximum stress and is the

minimum stress, likewise and C are the friction

angle and cohesion respectively. In the case of r=Rw

in Eqs. [7-10], the largest stress difference can be

achieved and Mohr-Coulomb criterion can be

written as:

(14)

and are tangential and radial stresses

respectively.

3. METHODOLOGY

3.1. Preliminary Analysis

Sonic Scanner log (Mark of Schlumberger) was

acquired through the Bakken Formation in a

producing horizontal well (Figure 5) which was

drilled 5 years ago in Williston Basin, North Dakota

(Figure 4). The Bakken Formation is primarily a

shaly unit which is aged late Devonian to early

Mississippian. The Bakken Formation consists of

three members: upper shale member, middle clastic

and carbonate member and lower shale member

[19]. Regarding low porosity and permeability of

this formation, along with the presence of fractures,

this layer is categorized as a unconventional,

naturally fractured reservoir. As a result in order to

enhance the production from this tight formation,

stimulation plans should be performed in a

horizontal section of every well in the Bakken

Formation; Therefore a comprehensive

geomechanical numerical modeling and wellbore

stability analysis is necessary for success in such

operations. Previous studies show that the middle

member which is the producing section of the

Bakken can be considered isotropic for

geomechanical study [20].

Fig 4. Map of the study area, state of ND- The black arrow

points to the well location and red polygons shows different

fields.

Figure 6 represents the corresponding set of

conventional logs through the Bakken Formation in

the well. The logs include gamma ray (first track),

Density log (second track), compressional wave

velocity (third track) and fast and slow shear wave

velocities (fourth track, blue and red curves

respectively) plus the layers’ tops (first column)

picked on the logs. This formation can be easily

identified from the overlaying Lodgepole Formation

and the underlying Three Forks Formation from its

very distinct high gamma ray response. Likewise

the upper and lower shale members can be

distinguished from the middle member with their

higher gamma ray signature.

5

Fig 5. Top) General overview of well trajectory, Bottom) A

closer look at the kick of point (KOP) and horizontal section

of the well in Middle Bakken (MB).

Fig 6. Set of conventional logs through the Bakken Formation,

gamma ray log (first track), Density log (second track),

compressional wave velocity (third track) and fast-slow shear

wave velocities (fourth track, blue and red curves respectively)

with layers’ tops.

3.2. Stress Analysis (Magnitude & Orientation)

In order to calculate horizontal principal stresses,

C44, C55 and C66 should be calculated from the slow

shear, fast shear and Stoneley wave velocities

respectively including formation density. The

measurements are shown in Figure 7. First column

denotes the formation tops, the first, track blue and

red curve are representing C55 and C44 respectively

and the second track represents C66.

Fig 7. Three shear moduli measured through the Bakken

Formation.

Anisotropic minimum and maximum principal

horizontal stress which means to take the effect of

elastic properties of the formation in horizontal and

vertical direction into consideration is calculated by

Eqs. (3) and (6), and are displayed in the following

figure. The black star in figure 8 shows the

measured pore pressure in Middle Bakken (MB)

from DST (drill stem test).

Fig 8. Anisotropic horizontal principal stresses and

overburden stress through the Bakken Formation- The black

star shows the DST measurement.

6

It’s worth mentioning that in order to estimate the

stress magnitudes in shale which is considered as a

vertical transverse isotropic (VTI) medium with the

latest described methodology, it is necessary to take

the anisotropic characteristic of shale into

consideration to obtaine more accurate results.

Vertical transverse isotropy can be quantified in the

manner of having isotropic planes either in the

horizontal or vertical direction with the axis of

rotational symmetry normal to the plane of isotropy

[16]. In this regard the horizontally aligned clay

particles are known to be the main source of

anisotropy in shales resulting in transverse isotropy

causing a difference between elastic properties in

horizontal and vertical directions.

Clay minerals show a huge impact on the difference

between Stoneley shear modulus C66 and the dipole

shear moduli C44 or C55. Generally, shear modulus

C66 in the isotropic plane of shale (parallel to the

clay minerals surfaces) is larger than shear modulus

C44 or C55 in the orthogonal planes. In such

condition, we need to reduce the measured C66 by

40% before inputting it together with the shear

moduli C44 and C55 for stress magnitude estimation

[10] to calculate stress specifically in the upper and

lower members of the Bakken Formation.

The direction of maximum principal horizontal

stress is found to be N65E by counting and

detecting the orientation of fractures that have

caused slowness or time based anisotropy greater

than 2% shear anisotropy. The results are plotted in

a rose diagram showing the orientation of fracture

planes with their frequency (Figure 9). These

fractures are believed to be tensile and along the

maximum principal horizontal stress which will be

discussed in the further sections. As previously

illustrated where shear splitting takes place, fast

shear azimuth (FSA) which is along the natural

fractures can be utilized to determine the orientation

of the maximum principal horizontal stress. Fast

shear wave is polarized along the fracture planes

and propagates with higher velocity comparing to

the slow shear wave which polarizes across the

fracture planes. The FSA is obtained through a

mathematical procedure known as Alford rotation

[21] by assigning fast and slow shear wave arrivals

on the right orthogonal receivers of the logging tool.

Slowness and time based shear anisotropy can be

defined with the following equations respectively,

Eqs. (15) and (16):

(15)

(16)

Where DT is the wave slowness (µs/ft) and TT is the

travel-time for the arriving fast and slow shear

waves at each receiver spacing on the sonic scanner

tool.

Fig 9. Rose diagram of natural fractures that have caused more

than 2% anisotropy- frequency and fracture plane orientation

are shown.

3.3. Stress Polygons

Stress polygons estimate the range of possible stress

states at any given depth and pore pressure while

that stress in the crust is limited by the frictional

strength of faults favoring normal, strike-slip, and

thrust faulting [22]. For these set of diagrams the

following conditions may exist:

line is the lower limit of

possible stress states.

Lines bounding the composite polygon on

its upper and left sides are thresholds of

failure.

Stress states to the left and above those lines

cannot exist in the natural state.

Different stress polygons apply for differing

depths, pore pressures, and friction

coefficients.

We created stress polygons in Middle Bakken (MB)

at a specific depth for two different stress states

conditions: initial reservoir condition and after 5

years of production when reservoir pressure is

7

declined. This analysis was performed in order to

improve our understanding about the possibility of

the occurrence of any geomechanical hazards in the

region such as: faulting, subsidence and induced

earthquakes specifically after reservoir depletion

when a major decline in reservoir pore pressure has

taken place.

To predict limiting stress differences at any specific

depth and in order to create the stress polygons the

following conditions should be satisfied [23]:

Normal faulting

(17)

Strike slip faulting

(18)

Reverse faulting

(19)

Where and are the principal stresses, Pp is

pore pressure and is the friction angle. The stress

polygons are created under elastic Mohr-Coulomb

failure criterion assumptions in the horizontal

section where the depth of the well is 10311ft TVD

(Figure 5). Table 1 represents the input values for

generating the stress polygons:

Table 1.Input parameters used for stress polygons in the MB.

PR

UCS

(MPa)

Initial

reservoir PP

(psi)

PP (after

production)

(psi)

M B 0.24 63.11 37.3 5800 4900

From Eqs. [17-19] we recognize that pore pressure

and depth (expressed in term of overburden stress,

Sv) are the main governing parameters for such

analysis; Pore pressure was obtained from reservoir

simulation and history matching after 5 years of

production (Figure 10). In addition it was assumed

that the formation shows elastic behavior. This

means that Hook’s Law is the governing relation on

the rock and also the contributing corresponding

parameters such as Poisson’s Ratio, Young’s

Modulus, compressive strength and friction angle

are independent of the processes followed by

reservoir depletion.

Fig 10. Current reservoir pressure obtained from reservoir

simulation.

Figure 11 is the stress polygon created for initial

reservoir stress state. Failure occurrences width in

degrees as a function of compressive strength of the

rock are shown in red contours. The solid black

lines outline the polygon that defines the limits of

Mohr-Coulomb failure for frictional equilibrium of

pre-existing faults in the region. It should be

mentioned that these limits are independent of any

criteria related to the wellbore. These limits are only

dependent on pore pressure, vertical stress (depth)

and the value of sliding friction. Therefore if the

stress state lies inside of this polygon then the

strength of the crust does not allow a larger stress

difference between the greatest and least principal

stresses to occur. The dashed lines separate the

three triangular regions reflecting normal faulting

(NF), strike-slip faulting (SS), and reverse faulting

(RF) stress conditions.

Fig 6. Stress polygon for initial reservoir condition.

8

The red contours in Figure 11 separate the

permissible stress states based on breakout

occurrences for a series of rock strengths. As it can

be found from Figure 11, reservoir stress state

(σhmin=55Mpa and σHmax=60Mpa) lays below the reservoir

rock compressive strength and in the normal fault

region. Figure 11 illustrated that for the presented

range of rock strengths, red contours delimit that

only strike-slip or reverse faulting stress regimes are

consistent with the observations which are even

beyond the principal stresses of the depth

understudy.

Figure 12 depicts the stress changes at the borehole

wall and in a radius from the wellbore in the

reservoir initial stress conditions. Top left is the

radial stress, top right is hoop stress, lower right is

tangential stress and lower left shows the stress

variations at the borehole wall where the red and

blue curves represents the maximum and minimum

tensile stresses. It’s been realized that tensile stress

which is the main source of tensile fractures seems

to be lower than the critical stress (red line on top of

the plot). This can interpreted as we do not expect

to see any evidence of tensile fracture occurrence

around the borehole wall. This is consistent with the

outcomes obtained from the stress polygon study

which approved no tensile fractures could exist in

the initial reservoir pore pressure and stress state.

Fig 7. Stress variation round the borehole wall for initial

reservoir conditions, top left) radial stress, top right) tangential

stress, lower right) hoop stress and lower left) all of the

aforesaid stresses at the bore hole wall, the values are in Mpa.

Figure 13 displays the stress polygon created for the

reservoir in the horizontal section after 5 years of

production. The main phenomenon of the plot is the

noticeable shift of red contours which represent a

range of breakout width with respect to the rock

strength to the lower left part of the polygon. As a

result the rock strength in the new conditions

mainly covers the possible strike slip (SS) and

normal (N) fault area of the plot. This stress

analysis leads us to the fact that the occurrence of

breakout seems to be more likely for lower rock

strengths. This is concluded from the bound of red

contours laying below the new stress state of the

reservoir (σhmin=58Mpa and σHmax=58Mpa).

Fig 8. Stress polygon of the depth understudy after 5 years of

production with a decrease in pore pressure.

Comparing the reservoir rock strength which was

estimated to be around 63Mpa and the new stress

state conditions after producing from the reservoir,

it’s understood that rock strength sits below the new

reservoir stress conditions and in the normal fault

triangle of the plot. This means that producing from

the reservoir makes the new stress conditions to

exceed the reservoir rock strength. This feature will

finally lead into fault reactivation or new normal

faulting in the area understudy.

The following figure represents the horizontal

section of the well and also the required rock

strength around the borehole required for breakouts

to initiate. From Figure 14 it’s concluded that no

breakout may exist at the initial reservoir condition

in any direction around the borehole.

9

Fig 9. No breakout exists around the borehole with required

compressive strength at initial reservoir pr4ssure and stress.

Figure 15 depicts the stress variations at the

borehole wall and a radius from the wellbore wall

after reservoir pressure decline due to the

production. Top left is radial stress, Top right is

hoop stress, lower right is tangential stress and

lower left represents the stress variations at the

borehole wall for all of the above mentioned

stresses.

Fig 10. Stress variation round the borehole after 5 yrs of

production, top left) radial stress, top right) hoop stress, lower

right) tangential stress and lower left) all of the above stresses

at the bore hole wall, the values are in Mpa.

From previous figure (lower left), It’s realized that

the tensile stress (orange curve) is exceeded the

critical stress of the reservoir at the borehole wall.

This phenomenon will have a huge impact on the

stability of the wellbore thus resulting in failures

such as shear or tensile fractures and breakouts. The

existence of these failures will be discussed in the

following section. The possible breakout region is

marked by black ovals in Figure 16 along with the

required compressive strength (C0) diagram as

shown in colored scale. A more precise look at

Figure 16, the azimuthal direction of minimum

principal horizontal stress (S3) can be understood

from the breakouts presence around the borehole.

Considering the final outcome of the wellbore stress

analysis from 5 years producing from the reservoir,

it can be concluded that the detected fractures to

study the orientation of the maximum principal

horizontal stress are tensile and occurring at the

borehole wall or deeper in the formation. It should

be notified that these fractures exist due to reservoir

stress alteration along the reservoir depletion.

Fig 11. Black ovals on the right diagram mark the region of

possible breakouts around the borehole with required rock

compressive strength (C0) after reservoir depletion.

3.4. Stability Analysis

The following figures are representing the stability

status of the wellbore at the specific depth of

10311ft- the horizontal section- which are created

under elasto-plastic Mohr-Coulomb failure criterion

assumptions. Comparing figures 17, wellbore

stability plot for the initial stress conditions and

figure 18, the stability plot after 5 years of

production, we can realize that shear failures will be

possible in the second state of reservoir stress

condition. After 5 years of production and pore

pressure reduction breakouts or non-radial shear

10

planes can occur under specific mud weight and

rock compressive strength. The black circle denotes

the reservoir stress condition and the red counters

are indicating the breakouts.

Fig 12. Fraction of wellbore circumference mode as a function

of mud weight and compressive strength of initial reservoir

condition, circle indicates reservoir stress conditions.

Fig 13. Fraction of wellbore circumference failed in difference

mode as a function of mud weight and compressive strength

after 5 years of production, circle indicates reservoir stress

conditions.

4. SUMMARY

A full geomechanical modeling and stress variation

analysis around the wellbore was performed in a

horizontal well in Williston Basin, ND in Middle

Bakken which is considered to be an

unconventional reservoir. This procedure includes

stress polygons and stability plots generation to

study the possibility of future faulting or breakouts

existence in the study area and at borehole wall.

Results showed the possibility of wellbore non-

radial shear failures also known as breakouts after 5

years of production from the reservoir. This was

found to be due to the reduction in reservoir pore

pressure. Initial reservoir pressure was measured

through DST and current pore pressure was

predicted by reservoir simulation and history

matching. In addition the stress polygons are

showing the possibility of normal faulting after the

production. This means in order to prevent future

hazards reservoir pressure should be maintained by

injection.

Orientation and magnitude of anisotropic horizontal

principal stresses were carried out. The magnitude

of anisotropic minimum horizontal principal stress

was calculated through poroelasticity relations and

the magnitude of maximum principal horizontal

stress was found through measurement of three

shear moduli of the formation. The direction of

maximum principal horizontal stress was found to

be N70E from the direction of fast shear azimuth

(FSA). The direction of fast shear azimuth was

attained by analyzing existing tensile fractures

around the borehole that have caused shear

anisotropy more than 2%. Three shear moduli of the

formation were measured by acquiring advanced

sonic logs.

5. ACKNOWLEGEMENT

The authors would like to thank the following sponsors

for their financial support: US DOE through contract of

DE-FC26-08NT0005643, North Dakota Industrial

Commission together with four industrial sponsors

(Encore Acquisition Company, Hess Corporation,

Marathon Oil Company, and Whiting Petroleum

Corporation) under contract NDIC-G15-031 and North

Dakota Department of Commerce through UND’s

Petroleum Research and Education and Entrepreneurship

Center of Excellence (PREEC). The authors would like

to express special appreciation to Baker-Hughes for

providing us with the software.

REFERENCE

1. National Petroleum Council, “Unconventional Oil,”

Working Document of the NPC North American

Resource Development Study, Paper #1–6, September

15, 2011.

2. McLean, M. R., 1987. Wellbore Stability Analysis.

PhD Thesis, University of London. LTK.

3. Dusseault, M. B., 1994. Analysis of borehole

stability. Computer Methods and Advances in

Geomechanics Balkema: 125-137.

4. Finkbeiner, T., Zoback, M., Flemings, P. et al. 2001.

Stress, Pore Pressure, and Dynamically Constrained

Hydrocarbon Columns in the South Eugene Island

11

330 Field, Northern Gulf of Mexico. Am. Assoc. Pet.

Geol. Bull. 85 (6): 1007-1031.

5. Sayers. M., 2006. An introduction to velocity-based

pore pressure estimation. TLE December 2006, 1496-

1500.

6. Higgings, S., S. Goodwin, Q. Donald, A. Donald, T.

Bratton, and G. Tracy, 2008, Anisotropic stress

models improve completion design in the Baxter

shale, In Proceedings of SPE ATCE, Denver, 21-24

September 2008, SPE 115736.

7. Waters, G, R. Lewis and D. Bently, 2011. The effect

of mechanical properties anisotropy in the generation

of hydraulic fractures in organic shales. In

Proceedings of SPE ATCE, Denver, 30 Oct- 2 Nov

2011, SPE 146776.

8. Wang, Z., 2000. Dynamic vs. static properties of

reservoir rocks. In Wang, Z., A. Nur and A. Eds,

Seismic and acoustic velocities in reservoir rocks.

Volume 3: Recent developments, Published by SEG.

9. Chang, C., M. Zoback and A. Khaksar, 2006.

Empirical relations between rock strength and

physical properties in sedimentary rocks, J. Pet. Sc.

and Eng., 51, 223-237.

10. Sinha, B., J. Wang, S. Kisra, V. Pistre, T. Braton and

M. Sanders, 2008. Estimation of formation stresses

using borehole sonic data. Proceedings of 49th the

SPWLA, Edinburgh, Scotland, 25-28 May 2008.

11. Sinha, B., Vissapragada, B., Wendt, A., Kongslien,

M., Eser, H., Skomedal, E., Renile, L. and Pedersen,

E., 2007. Estimation of formation stresses using

radial variation of three shear moduli- a case study

from a high-pressure, high-temperature reservoir in

Norwegian continental shelf, In Proceedings of SPE

ATCE, Anaheim, 11-14 November, SPE 109842.

12. Sinha, B., B. Vissapragada, L. Renlie and S. Tysse,

2006. Radial profiling of the three formation shear

moduli and its application to well completions. J

Geophys.,71:6, E65-E77.

13. Fjar, A., R. Holt, A. Raaen, R. Risnes and P. Horsud,

1992, Petroleum related rock mechanics, Elsevier

Publishing.

14. Zoback, M., 2007, Reservoir Geomechanics,

Cambridge University Press, First edition.

15. Aki, K. and P. Richards, 2002, Quantitative

Sesimoloy, University Science Books, Second

edition.

16. Tsvankin, I. 2005. Seismic signatures and analysis of

reflection data in anisotropic media. 2nd

ed. Elsevier

Science.

17. Pistre, V., T. Kinoshita, T. Endo, K. Schilling,

J.Pabon, B.Sinha, B.,T.Plona, T. Ikegamiand D.

Johnson, 2005, A New modular wireline logging

sonic tool for measurement of 3D (Azimuthal, radial

and Axial) formation acoustic properties, In

Proceedings of SPWLA 46th

annual logging

symposium, New Orleans, June 26-29.

18. Jeager, J. and N. Cook, 2007. Fundamentals of rock

mechanics. 4th

ed. Blackwell Publishing.

19. Price, L. and LeFever, J., 1994, Dysfunctionalism in

Williston Basin: The Mid-Madison/Bakken

petroleum system, Bulletin of Canadian Petroleum

Geology, 42, 187-218.

20. Ostadhassan, M., Z. Zeng, H. Jabbari, Anisotropy

analysis in shales by acquiring advanced sonic data,

2012. In Proceedings of AAPG ACE, Long Beach,

22-25 April.

21. Alford, R., 1986, Shear data in the presence of

azimuthal anisotropy: Dilley, Texas presented at the

56th SEG annual meeting, Houston, 2-6 November,

expanded abstracts.

22. Zoback, M., C.A. Barton, M. Brudy, D.A. Castillo, T.

Finkbeiner, B.R. Grollimund, D.B. Moos, P. Peska,

C.D. Ward and D.J. Wiprut, 2003, Determination of

stress orientation and magnitude in deep wells,

International Journal of Rock Mechanics & Mining

Sciences, 40 (2003) 1049–1076.

23. Anderson E.M., 1951. The dynamics of faulting and

dyke formation with applications to Britain.

Edinburgh: Oliver and Boyd.