wellbore strengthening analysis in single and multi

1. INTRODUCTION

Wellbore strengthening is a practical method for

reducing lost circulation while drilling formations with

narrow drilling mud weight windows. It increase the

wellbore's maximum sustainable pressure by bridging

drilling induced or natural fractures with lost circulation

material (Feng and Gray, 2016). To keep downhole

pressure within the mud-weight window, drilling fluids

and lost circulation material (LCM) are considered to

make wellbore-hydrodynamic pressure low enough to

evade downhole lost circulation but high sufficient to

avoid borehole instability or kicking( Feng et al., 2015).

These drilling fluids and additives cause in the formation

hoop stress enhancement ,called stress cage, which is a

near wellbore area of high stress induced by propping

open and sealing narrow fractures at the

wellbore/formation boundary (Alberty and McLean,

2004). All lost circulation materials are not same and

their type plays a role in terms of both plugging and

toughness to better endure displacement pressures. It

also has been confirmed that, mostly, combinations of

LCMs act more efficiently compared with the practice of

only one type in wellbore strengthening (Savari et al.,

2014). Some companies are produced a designer mud

which effectively increases fracture resistance while

drilling, which can be valuable in both shale and

sandstone.it acts by forming a stress cage, using particle

bridging and some type of fluid loss mud (Aston et al.,

2004). In recent years many deep fundamental studies

has been done, related to the lost circulation and

wellbore strengthening (Feng and Gray, 2017; Feng et

al., 2016). To better understanding of basics of the

process of Wellbore strengthening, the effects of several

parameters are still not fully understood, and a complete

parametric study for each type of formations is necessary

ARMA 19–A-230-ARMA

Wellbore Strengthening Analysis in single and multi

Fractures Models Using Finite Element and Analytical Methods, Case

Study: South Pars Gas Field

Farzad Mehrkhani

Department of Petroleum Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran,

Email:[email protected]; [email protected]

Arash Ebrahimabadi

Department of Mining, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran,

Email: [email protected]; [email protected]

Mohamad Reza Alaei

Department of Petroleum Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Email:[email protected]

Copyright 2019 ARMA, American Rock Mechanics Association

This paper was prepared for presentation at the 53rd US Rock Mechanics/Geomechanics Symposium held in New York, NY, USA, 23–26 June

2019. 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: Wellbore strengthening is an extensively-used method to reduce lost circulation in the petroleum drilling industry,

with adding Lost Circulation material to the drilling mud and bridging the fractures on the wellbore to increase maximum stable

pressure. In this study, the finite element and Kirsch analytical methods used to model the hoop stress distribution and its effective

factors, in one of South Pars gas field’s formations, based on Persian Gulf. Findings showed that the compressive stress, in the

single fracture model, is raised up to the degree of 30º in the fracture initiation state and it will be more in the bridging location

across the fracture faces. Furthermore, the hoop stress at the tip of the fracture tends to be tensile; moreover, the compressive stress

with higher wellbore pressure on the wellbore, before the area of 60º and after bridging the fracture, is greater than the compressive

stress with lower wellbore pressure on the wellbore wall and it will be reversed after the area of 60º. In the multi-fracture model, by

moving away from the first fracture, the compressive stress decreases around the 90º, due to the existence of second fracture and

the compression stress is raised by increasing the horizontal stress contrast.

Keywords: Wellbore strengthening, Kirsch analytical method, Finite element method (FEM), Hoop Stress, Fracture

Model

mailto:[email protected]

to improving field operations. There are plenty of

numerical models and analytical solutions which have

been developed in recent years for that reason.

(AlBahrani and Noynaert, 2016; Wang et al., 2007;

Mehrabian et al., 2015; Zhong et al., 2017;Salehi and

Nygaard, 2014; Kiran and Salehi,2016; Salehi and

Nygaard, 2011; Shahri et al., 2015; Zhang et al., 2016;

Zhang et al., 2017;Wang et al., 2018; Chellappah et al.,

2018; Feng et al., 2018; Wang, 2018 ); besides, some

research has been done for the usage of wellbore

strengthening methods for depleted reservoirs.(Shahri et

al., 2014). Besides, a set of analytical equations,

considered their advantages and disadvantages, are

developed for parametric analysis of typical wellbore

strengthening approaches. (Morita and Fuh, 2011). A

finite-element method is the most important numerical

technique, used today to model the wellbore

strengthening problems, has been developed to research

the effects of major parameters on the distribution of

near wellbore hoop stress and fracture width (Feng and

Gray, 2016; Arlanoglu et al., 2004; Towler, 2007). In

this research, the term hoop stress is generally used to

mean the circumferential stress at the wellbore wall. The

hoop or tangential stress around a wellbore wall is the

main factor in borehole stability and integrity analysis.

This research investigates different and effective

parameters of wellbore strengthening, related to the

formations of south pars gas field in Persian gulf and

numerical and analytical methods are used for this

purpose; besides, new numerical model with multi

fractures has been created to better understanding of

wellbore strengthening mechanism and related effective

parameters, to investigate of hoop stress around the

wellbore and the width of the fractures.

2. RESEARCH METHOD

The final goal of the wellbore strengthening is to

increase the maximum sustainable pressure in the well,

and numerical models in this study will determine that

hoop stress around the well and the fracture can be

efficiently altered and increased by changing the

important parameters in the wellbore strengthening;

Therefore, these analysis can provide very effective field

results to reduce fluid loss and increase the fracture

gradient in the well. These parameters consist of

horizontal stresses contrast, LCM bridge location, pore

pressure, the Young’s modulus and the Poisson’s ratio of

rock formation and pressure behind LCM bridge.

Throughout this research, the positive and negative

values of stress, respectively, mean tensile and

compressive stresses. There are several methods for

wellbore strengthening analysis, which in general

include the following:

2.1. Analytical Methods Fortunately, several analytical methods like Kirsch

equations have been developed in recent years to

calculate the hoop stress and fracture width around the

wellbore and they are valid only for circular holes.

Analytical methods have been used to validate numerical

models in this research, with different number of

elements around the borehole.

𝝈𝒓 =𝟏

𝟐(𝑺𝑯 + 𝑺𝒉) (𝟏 −

𝑹𝟐

𝒓𝟐) (1)

+𝟏

𝟐(𝑺𝑯 − 𝑺𝒉) (𝟏 − 𝟒

𝑹𝟐

𝒓𝟐+ 𝟑

𝑹𝟒

𝒓𝟒) 𝐜𝐨𝐬 𝟐𝜽 + ∆𝑷

𝑹𝟐

𝒓𝟐

𝝈𝜽 =𝟏

𝟐(𝑺𝑯 + 𝑺𝒉) (𝟏 −

𝑹𝟐

𝒓𝟐) (2)

−𝟏

𝟐(𝑺𝑯 − 𝑺𝒉) (𝟏 + 𝟑

𝑹𝟒

𝒓𝟒) 𝐜𝐨𝐬 𝟐𝜽 + ∆𝑷

𝑹𝟐

𝒓𝟐

𝝉𝒓𝜽 = −𝟏

𝟐(𝑺𝑯 + 𝑺𝒉) (𝟏 + 𝟐

𝑹𝟐

𝒓𝟐− 𝟑

𝑹𝟒

𝒓𝟒) 𝐬𝐢𝐧𝟐𝜽 (3)

where σr is the radial stress, σθ is the circumferential

stress τrθ is the tangential shear stress, R is the radius of

the hole, θ is the azimuth measured from the direction of

SH and ∆P is the difference between the fluid pressure in

the borehole and that in the formation (positive indicates

excess pressure in the borehole); SH and Sh refer to the

effective horizontal principal stresses

2.2. Numerical Methods Numerical methods are used to find the appropriate

response for the complex mechanical equations, with use

of different approximations. The method used in this

research is known as the finite element method. In this

technique, the object is divided into smaller components

called elements, which are connected altogether as

nodes. The advantage of the mentioned method is

considering the different boundary conditions and

obtaining an appropriate approximation to solve the

system’s equations. The ABAQUS finite-element

package, for numerical simulation studies, has been used

in this study.

It can offer powerful and complete solutions for both

routine and sophisticated engineering problems like linear and nonlinear models, in use of stress analysis,

around the wellbore. In this research, linear elastic

model with considering pore pressure, called pore-elastic

model are simulated by using finite element method

(FEM)

2.2.1. Numerical model with one fracture in

wellbore

Two-dimensional numerical model is developed with the

help of a plain strain element in ABAQUS and half of

the model is considered, because of the symmetry

boundary condition

Fig. 1. Half of the two–dimensional model of wellbore

geometry

In this model, reservoir rocks are supposed to follow

linear elastic law; furthermore, wellbore diameter is set

to 8.5 inches and the length and width of the half of the

model is 40.25 inches in figure. 1. The model is

considered as a vertical wellbore. The formation

minimum horizontal stress and maximum horizontal

stress are applied on the outer boundary of the half of the

wellbore. The fracture face is aligned with the X axis.

The displacement along the Y axis is set equal to zero to

create the effect of the plugging the fracture; besides, the

pore pressure is considered in the mentioned model;

plus, the wellbore pressure is applied to the inner wall of

the wellbore, as seen in figure. 2.

Fig. 2. Half of the two–dimensional model of wellbore with

boundary conditions

In the next step, for modeling, the pressure of the well is

applied into the surface of the fracture, the areas that are

blue represents compressive stress and areas that are red

represents tensile stresses. The negative amount of stress

in this study shows the compressive stress; while, the

positive amount of stress represents tensile stress.

In the second step, to show the bridging of the fracture,

plenty of nodes are fixed in the model and the

displacement constraint is used; besides, the pressure is

applied behind the assumed nodes, to simulate the pore

pressure. It is also assumed that pressure of the area

behind the fixed nodes , where represent the bridging of

the fracture, due to the exchange with the reservoir, will

be equal with the pore pressure. Location of the bridge

and length of the bridge is variable and can be changed

in the model; furthermore, the bridge is considered

incompressible and it runs an effective seal between the

wellbore pressure and fracture pressure.

It is important to define hard contact interaction along

the faces of the fracture to prevent overlapping of the

fracture faces after bleeding of the pressure inside the

fracture.

2.2.2. Assumptions and boundary conditions, used

two-dimensional model The structure mesh has been generated with four quad

elements and with eight quad elements. Hoop stress

distribution calculated by the numerical model, for

different number of elements around the half wellbore,

respectively with 60, 80,100,120,140 elements around

the half wellbore and it is compared with the Kirsch

equation.

As seen in figures. 3, 4. The hoop stress error between

the numerical method and analytical method of Kirsch,

with different type and number of elements around the

half wellbore.

The 8 node quad elements with 60, 80,100,120,140

elements around the half wellbore has the highest

accuracy and minimum error compared with the 4 node

quad elements with different elements around the half

wellbore and compared with the analytical method of

Kirsch. Although denser mesh increases the accuracy of

the numerical model, but the computational time of the

model will be increased dramatically; therefore, The 8

node quad element with 100 elements around the half

wellbore is selected and is used thorough the study.

Fig. 3. Hope stress for the 4 node quad element with different

elements around the half wellbore, compared with Kirsch

solution

Fig. 3. Hope stress error for the 8 node quad element with

different elements around the half wellbore, compared with

Kirsch solution

2.2.3. Numerical model with Multi fractures in

wellbore After the first fracture has been formed, some part of the

wellbore is still under tensile stress; as a result, further

fractures can be generated and propagated, in those

areas. In this model, four fractures are considered to

show the parameters affecting the hoop stress around the

wellbore and fracture geometry. All four fractures are

symmetrical. It is assumed that the second, third and

fourth fractures, relative to the initial fracture,

respectively have an angle of 90º, 180º and 270º.

The two fractures are in parallel with the minimum

horizontal stress and the two other fractures are in the

direction of maximum horizontal stress, as shown in

figure. 5.

Fig. 5. The two–dimensional model of wellbore with multi

fractures

To create a model, the wellbore is divided into four parts

which are connected by the tie constraint. However it

ought to be avoided to use the tie constraint along the

fractures to allow fracture faces move freely and hard

contact will be defend along them for the reason that

mentioned before. In first step, It is assumed that the

wellbore pressure is equal to the fractures pressure

before the bridging. In next step, the first fracture is

plugged and the affecting parameters in hoop stress and

fractures width will be considered.

It is crystal clear that the fracture in the 0º region is

considered as the first and the fracture in the 90º region

is considered as the second fracture and, in the same

way, the third and fourth fractures are defined

counterclockwise.

3. INPUT DATA

Table 1 show the date ,used for input model, related to

the one of the well, located on the south pars gas field in

Persian Gulf, and is used for 2D models simulation.

Row Parameter Values Units

1 Model length 80.5 inches

2 Model width 80.5 inches

3 Wellbore radius

(R) 4.25 inches

4 Young's modulus

(E)

1,360,000,

2,710,000

psi

5 Poisson's ratio (y) 0.24 , 0.48

6

Minimum

horizontal stress

(Shmin)

7005.32

psi

7

Maximum

horizontal stress

(SH)

1 -1.5 Sh psi

8 Wellbore pressure

(Pw) 9000 psi

9

Pressure in

fracture before

bridging (Pfo)

9000 psi

10

Pressure ahead of

bridge after

bridging (Pfa)

9000 psi

11

Pressure behind of

bridge after

bridging (Pfb)

1800- 4500 psi

12 Fracture length (a) 6 inches

13 Initial pore

pressure (Pp) 4500 psi

14 Permeability 120 mdarcy

15 Void ratio 0.07

16

LCM bridge

location away

from wellbore

0.75- 5.25 inches

4. RESULTS AND DISCUSSION

4.1. Model of one fracture on the wellbore wall

4.1.1. Hoop Stress on the wellbore wall By use of numerical model of finite element, the hoop

stress around the wellbore and along the fracture faces

are considered, by means of various parameters

Horizontal stress contrast. ( SHmax/ Shmin)

In this case, the hoop stress in the wellbore wall is

considered from 0º to 90º and the different horizontal

stresses are applied to the numerical model .The result

are compared in 3 category :before fracture initiation,

after fracture initiation and after bridging the fracture on

the wellbore wall.

The results are shown in figures. 6, 7, 8. When there is

no fracture in the wellbore wall, the hoop stresses around

30º is in the compression state. In this point, the

difference between horizontal stresses does not affect the

amount of tensile stress and all horizontal stresses pass

through this point as shown in figure. 6. It is assumed

that the maximum horizontal stress is considered along

the X axis.

By increasing the difference between the maximum and

minimum horizontal stresses, before the area of the angle

of 30º, the compressive stress will be declined and

tensile tress will be more. However, after the angle of

30º, the compressive stress will be raised by increasing

the difference between the maximum and minimum

horizontal stresses

Fig. 6. Hoop stress distribution on the wellbore wall before

fracture initiation for different stress anisotropy

After fracture propagation on the wellbore wall, as

shown in figure. 7. Hoop stress on the wellbore wall,

where is a place near the mouth of the fracture, put in

compressive stress. And, by increasing the difference

between the maximum and minimum horizontal stresses,

the compressive stress will be raised.

Fig. 7. Hoop stress distribution on the wellbore wall after

fracture initiation for different stress anisotropy

It is interesting to note that the compressive stress will

be increased, by raising the difference between the

maximum and minimum horizontal stresses, around the

wellbore wall among 0º and 20º.

As shown in figure. 8. The distribution of hoop stress

after bridging the fracture with the plugging location of

4.5 inches away from the wellbore wall.

Fig. 8. Hoop stress distribution on the wellbore wall after

bridging the fracture for different stress anisotropy

In this case, the hoop stress distribution in the wellbore

wall has the similar pattern compared with the situation

that the fracture was not plugged as shown in figure. 8.

Aimed at better investigation, the maximum horizontal

stress is considered to be 1.4 times larger than the

minimum horizontal stress and bridging location is 2.25

inches away from the wellbore wall.

As shown in figure. 9. The compressive stress, around

the wellbore wall among 0º and 30º, will be increased

when the fracture is created and when the fracture is

plugged; however, after the angle of 30º, the

compressive stress on the wellbore wall when the

fracture in not plugged is larger, compared with the

situation that the fracture is plugged.

-18,000.00

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess(

Psi

)

Angle(deg)

Pre Fracture StateSHmax=Shmin

Pre Fracture StateSHmax=1.1Shmin





-20,000.00

-18,000.00

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess

(Psi

) Angle(deg) Fracture StateSHmax=Shmin

Fracture StateSHmax=1.1Shmin





-20,000.00

-18,000.00

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess(

Psi

)

Angle(deg) Fracture StateSHmax=Shmin






Fig. 9. Hoop stress distribution on the wellbore wall before

and after bridging the fracture with SHmax=1.4*Shmin

Because, after bridging the fracture, the pressure of the

fluid behind the bridge is reduced and the fracture begins

to close.

The fracture tends to close and the compression stress

will be raised near the fracture mouth, between 0º and

30º; besides, the tensile stress will be declined; however,

after the angle of 30º and after bridging, the compressive

stress will be declined and the tensile stress will be

increased compared with the fracture initiation step

without bridging, as seen in figure. 9.

After bridging, the compressive stress is increased

around the fracture, which tends to close; however, the

other fractures can be propagated after the angle of 30º

because the compressive stress will be decreased.

Hoop stress on the wellbore wall for different

bridging locations

As seen in figure. 10. The hoop stress in the wellbore

wall before and after bridging the fracture and when the

bridging location is near the wellbore wall, with the

plugging location of 0.75 inches away from the wellbore

wall, compressive stress will be increased dramatically.

When the bridging location is far from the wellbore wall,

the amount of the compressive stress, will be declined,

compared with the fracture initiation state, near the

fracture mouth. For example, with the bridging location

of 5.25 inches away from the wellbore, there is no

significant change of hoop stress, compared with

fracture initiation state.

Fig. 10. Hoop stress distribution on the wellbore wall with

different bridging locations, compared with the fracture

initiation state, with SHmax=1.4*Shmin

It should be noted that the compressive stress is higher

than elsewhere in the bridging area.

The best place for bridging fracture is near the wellbore

wall, because of the significant increase in compressive

stress, as seen in figure. 10. Hoop stress on the wellbore wall for different

wellbore pressures

In this case, it is assumed that drilling mud

penetrates inside the fracture and wellbore pressure

will be declined, as seen in figure. 11., with pressure

approximately 8000 Psi and its effect on hoop stress,

on the wellbore wall, will be considered as well as

by increasing the pressure to 10,000 Psi;

furthermore, the LCM bridge is 5.25 inches away

from the wellbore wall after bridging the fracture.

As seen in figures. 11, 12, 13. Respectively, the

hoop stress distribution, when the wellbore pressure

is 8,000, 9,000, 10,000 psi. There is no significant

change in the hoop stress before and after bridging

the fracture, with the bridging location of 4.5 inches

away from the wellbore wall, because of the increase

of distance away from the bridging location to

wellbore wall.


different wellbore pressures, before fracture state, fracture

initiation state and after plugging, with SHmax=1.4*Shmin

and wellbore pressure 10,000 Psi.

-15,300.00

-14,300.00

-13,300.00

-12,300.00

-11,300.00

-10,300.00

-9,300.00

-8,300.00 0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess(

Psi

)

Angle(deg)


Bridge-2.25in-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90Fracture StateSHmax=1.4Shmin

Bridge-0.75in

Bridge-2.25in

Bridge-3.75in

Bridge-5.25in

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess(

Psi

)

Angle(deg)

Pre Fracture StateSHmax=1.4Shminwellbore=10000

Fracture StateSHmax=1.4Shminwellbore=10000

After PluggingSHmax=1.4Shminwellbore=10000









As shown in figure. 14., the compressive stress with

higher wellbore pressure, before the angle of 60º and

after bridging the fracture, is greater than the

compressive stress with lower wellbore pressure and it

will be reversed after the angle of 60º.

Fig. 14. Comparing he Hoop stress distribution on the

wellbore wall with different wellbore pressures, after

plugging, with SHmax=1.4*Shmin

4.1.2. Hoop Stress along fracture faces


By increasing the compressive stress, the fracture

tends to close; therefore, it will be very important in

wellbore strengthening to increase the compressive

hoop stress along fracture faces. Figures. 15, 16 and

17; respectively, indicate the hoop stress along

fracture faces, before fracture state, fracture

initiation state and after plugging, for different

horizontal contrast. As can be seen in figure. 15. The

horizontal axis represents the length of the fracture,

before creating a fracture according, by increasing

the difference between the maximum and minimum

horizontal stresses, the compressive stress is

declined near the fracture mouth and the

compressive stress is increased, By increasing the

distance from the wellbore along the fracture faces.

Fig. 15. Comparing the Hoop stress distribution along the

fracture faces with different horizontal contrast, before

fracture initiation.

As shown in figure. 16., after fracture initiation, the

hoop stress along the fracture faces is compressive

however; the hoop stress is tensile at the tip of the

fracture. It also shows that, by increasing the difference

between the maximum and minimum horizontal stresses,

there is little effect on the hoop stress along the fracture

faces.


fracture faces with different horizontal contrast, after fracture

initiation.

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-8,000.00

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0.00

0 9 18 27 36 45 54 63 72 81 90H

oo

p S

tres

s(P

si)

Angle(deg)




-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess(

Psi

)

Angle(deg)




-16,000

-15,000

-14,000

-13,000

-12,000

-11,000

-10,000

-9,000

-8,000

-7,000

0 9 18 27 36 45 54 63 72 81 90

Ho

op

Str

ess

(Psi

)

Angle(deg)




-8000

-7000

-6000

-5000

-4000

-3000

-2000

-1000

0

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)

Distance From the Wellbore(Inch)

Hoop Stress WithSH/Sh=1

Hoop Stress WithSH/Sh=1.1





-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

2,000.00

4,000.00

6,000.00

8,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess

(Psi

)


Hoop Stress WithSH/Sh=1






As shown in figure. 17., after bridging the fracture, it

also shows that, by increasing the difference a the

maximum and minimum horizontal stresses, there is

little effect on the hoop stress along the fracture faces;

however, the compressive stress is increased

dramatically at the bridging location of 4.5 inches away

from the wellbore wall.


fracture faces with different horizontal contrast, after bridging

the fracture.

As seen in figure. 18. The hoop stress along the fracture

in two cases is compared, after fracture propagation and

after fracture bridging, with the bridging location of 4.5

inches away from the wellbore wall. As shown in

figure. 18. It is clear that the bridging fracture increases

the amount of the compressive hoop stress on bridging

location; therefore, the fracture will be open harder at

bridging location.


fracture faces, before and after bridging the fracture, with

SHmax=1.4*Shmin


bridging locations

As seen in figure.19. The amount of hoop stress for

different bridging locations along the fracture faces

surfaces. When the bridging location is very close to the

fracture mouth, with the bridging location of 0.75 inches

away from the wellbore wall, a significant increase in

the amount of compressive stress is observed and the

compressive stress on bridging location along the

fracture surface will be less, by increasing the bridging

distance from the wellbore wall. When the bridge is at

the end of the fracture, there is almost no increase in the

compressive stress, compared with the fracture initiation

state, with the bridging location of 5.25 inches away

from the wellbore wall. As shown in figure. 19. It is

crystal clear that the best place for bridging location is

near the fracture mouth. This is one of the most

important issues in LCM design and to optimize the

bridging location in wellbore strengthening.

Fig. 19. Hoop stress distribution along the fracture faces, with

different bridging locations


pore pressures

In this case, the bridge is considered Impermeable and

consequently prevents pressure communication across

the bridge; besides, it is also assumed that the pressure

behind the LCM bridge will drop to pore pressure as the

fluid leak off.as shown in figure. 20. The pressure

behind the LCM bridge, defined as pore pressure, varies

from 1,800 to 4,500 Psi, with the bridging location of 4.5

inches away from the wellbore wall. The more pressure

behind the LCM bridge results the less compressive

stress in bridging location; nonetheless, the tensile stress

will be more at the tip of the fracture.

Fig. 20. Hoop stress distribution along the fracture faces, with

different pore pressures

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

2,000.00

4,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)


Hoop Stress WithD4.5 SH/Sh=1

Hoop Stress WithD4.5 SH/Sh=1.1





-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)




-30,000.00

-25,000.00

-20,000.00

-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)

Distance From the Wellbore(Inch

Bridge-0.75in

Bridge-2.25in

Bridge-3in

Bridge-3.75in

Bridge-4.5in

Bridge-5.25in


-18,000.00

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

2,000.00

4,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)


Pore Pressure-1800(psi)







wellbore pressures

In this case, the effects of different pore pressures in the

wellbore on Hoop stress along fracture faces are

analyzed.

As seen in figures. 21, 22, 23. By increasing wellbore

pressure, the compressive stress will be more on

bridging location, after plugging the fracture; besides,

the tensile stress is increased at the tip of the fracture.

The mentioned figures show the same trend for hoop

stress along fracture faces for different wellbore

pressures; respectively, before fracture initiation,

fracture initiation state and after bridging fracture, with

SHmax=1.4*Shmin


fracture faces, with wellbore pressure at 8,000 Psi,

respectively , before fracture initiation , fracture initiation state

and after bridging fracture, with SHmax=1.4*Shmin









But as it was said before, after bridging fracture, the

compressive stress will be more on bridging location

when the wellbore pressure is higher


fracture faces, with different wellbore pressure, after bridging

fracture, with SHmax=1.4*Shmin

As shown in Figure. 24., comparing the hoop stress

distribution along the fracture face, with different

wellbore pressure. The compressive stress will be more

on bridging location with wellbore pressure at 10,000

Psi; respectively, fracture initiation state and after

bridging fracture; furthermore, the tensile stress will be

more at the fracture tip compared with less wellbore

pressures.

4.1.3. Fracture width Understanding about fracture width on the wellbore is a

key factor to design the LCM sizes in wellbore

strengthening. In this section the important parameters

which can affect on Fracture width will be considered.

As shown in figures. 24, 25. The vertical displacement to

the direction of the Y-axis, respectively, on fracture

initiation state and after bridging the fracture, with the

bridging location of 4.5 inches away from the wellbore

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)


In Frac Pre FractureStateSHmax=1.4Shminwellbore=8000

In Frac AfterPluggingSHmax=1.4Shminwellbore=8000

In Frac FractureStateSHmax=1.4Shminwellbore=8000

-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)





-20,000.00

-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

15,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)





-20,000.00

-15,000.00

-10,000.00

-5,000.00

0.00

5,000.00

10,000.00

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Ho

op

Str

ess(

Psi

)





wall. The vertical displacement along the Y-axis or

fracture width before bridging the fracture (fracture

initiation state) is larger than the fracture width on the

bridging the fracture state. It is note that the minus sign

means the fracture opening displacement is opposite to

the direction of the Y-axis.

Fig. 25. vertical distribution in the ABAQUS model on

fracture initiation state

Fig. 26. vertical distribution in the ABAQUS model after

bridging the fracture


As shown in figures. 27, 28. The fracture width for

different horizontal stress contrast; respectively, in

fracture initiation state and after bridging the

fracture, with the bridging location of 4.5 inches

away from the wellbore wall. The fracture width will

be increased by increasing the horizontal stress

contrast which is more in the vicinity of fracture

mouth.

Fig. 27. fracture width distribution for horizontal stress

contrast in fracture initiation state

Fig. 28. fracture width distribution for horizontal stress

contrast after bridging the fracture, with the bridging location

of 4.5 inches away from the wellbore wall.

As shown in figure. 28. There is not any increase of the

fracture width before the bridging location of 4.5 inches

away from the wellbore wall, compared with the fracture

width in fracture initiation state; furthermore, increasing

the horizontal stress contrast have much effect in the

fracture width behind the LCM bridge.

As shown in figure. 29. The fracture width, with

SHmax=1.4*Shmin, in fracture initiation state are

compared with the fracture width after bridging of 4.5

inches away from the wellbore wall, with

SHmax=1.4*Shmin.As seen, the fracture width behind

the bridging location is smaller than the fracture width in

initiation state which indicates that fracture tend to close

after bridging in wellbore strengthening.

0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000


fracture width infrac SH/Sh=1

fracture width infrac SH/Sh=1.1





0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6


Fracture Width WithD4.5 SH/Sh=1

Fracture Width WithD4.5 SH/Sh=1.1





Fig. 29. Comparing the fracture width after bridging of 4.5

inches away from the wellbore wall, with SHmax=1.4*Shmin

It is noted that the fracture width in front of the bridging

location is decreased; comparing the decrease of fracture

width in initiation fracture state. As seen in figure. 29.

The decrease in fracture width is bigger in behind the

bridging.

LCM bridge location

As shown in figure. 30. The fracture width before and

after bridging the fracture with different LCM bridge

location. When the bridging location is near the fracture

mouth; for example, the fracture width after bridging of

0.75 inches away from the wellbore wall; then, the

fracture width is smaller, on the contrary, When the

bridging location is far from the fracture mouth; for

example, the fracture width after bridging of 5.25 inches

away from the wellbore wall, the change of the facture

width, compared with fracture initiation state is very low

and the two curves are placed almost on each other.

because the purpose of the wellbore strengthening is to

prevent the opening and propagating of the fracture on

the wellbore, as seen in figure. 30. The best place for

bridging fracture is near the wellbore wall.

Fig. 30. Comparing the fracture width with different LCM

Bridge location in fracture initiation sate and after bridging,

with SHmax=1.4*Shmin

Young’s modulus

Young's modulus has a very important affect

thorough the fracture width.as seen in figure. 31.

Larger Young’s modulus creates a smaller width for

the fracture. Furthermore, the fracture with a smaller

Young’s modulus after bridging with LCM has a

much larger width decrease comparing a fracture

with larger Young’s modulus. Besides, the width

decrease is more behind the bridging location.

Therefore, this indicates that Young's modulus has a

great factor on wellbore strengthening to optimize

the LCM size.

Fig. 31. Comparing the fracture width with different Young’s

modulus in fracture initiation sate and after bridging, with

SHmax=1.4*Shmin

Poisson’s ratio

As shown in figure. 32. The fracture width with

different Poisson’s ratio, with the bridging location

of 4.5 inches away from the wellbore wall.

Fig. 32. Comparing the fracture width with different Poisson’s

ratio in fracture initiation state and after bridging, with

SHmax=1.4*Shmin

Poisson's ratio has less effect on fracture width, in

comparison with Young's modulus, in fracture initiation

state and after bridging; besides, as seen in figure. 32.

Larger Poisson's ratio creates a smaller width for the

fracture.

0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

ture

Wid

th(I

nch

)


Hoop Stress in fracSH/Sh=1.4


0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

ture

Wid

th(I

nch

)


Bridge-0.75in

Bridge-1.5in

Bridge-2.25in

Bridge-3in

Bridge-3.75in

Bridge-4.5in

Bridge-5.25in

Hoop Stress infrac SH/Sh=1.4

0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6Frac

ture

Wid

th(I

nch

) Distance From the Wellbore(Inch)

Hoop Stress in fracSH/Sh=1.4y=1,356,102.8

Hoop Stress in fracSH/Sh=1.4y=2,712,205.6

Hoop Stress WithD4.5 SH/Sh=1.4y=1,356,102.8

Hoop Stress WithD4.5 SH/Sh=1.4y=2,712,205.6

0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

ture

Wid

th(I

nch

)


Hoop Stress in fracSH/Sh=1.4 p=0.24

Hoop Stress in fracSH/Sh=1.4 p=0.48

Hoop Stress WithD4.5 SH/Sh=1.4p=0.24

Hoop Stress WithD4.5 SH/Sh=1.4p=0.48

Impact of different pore pressures behind the

bridging location

The pressure behind the LCM bridge can be equal to

the pore pressure, with impermeable bridge as well

as the wellbore pressure with permeable bridge. As

shown in figure. 33. The fracture width for different

pore pressures which varies from 1800 to 4500 Psi,

behind the LCM bridge. It is clear that smaller pore

pressures create a smaller width for the fracture,

behind the LCM bridge; in fact, this means that the

drilling operations will be more efficient when the

LCM bridge is more impermeable.

Fig. 33. Comparing the fracture width with different pore

pressures behind the LCM bridge with SHmax=1.4*Shmin

Impact of different wellbore pressures

As seen in figure. 34. Larger wellbore pressure creates a

larger width for the fracture in fracture initiation state

and after bridging; besides, smaller wellbore pressure

creates a smaller width for the fracture.

Fig. 34. Comparing the fracture width with different wellbore

pressures ahead of the LCM bridge with SHmax=1.4*Shmin

As shown in figure. 34. It is noted that the decrease of

the fracture width is larger behind the LCM bridge

comparing the decrease of the fracture ahead of the LCM

bridge, with bridging location of 4.5 inches away from

the wellbore. 4.2. Model of Multi fractures on the wellbore wall

4.2.1. Hoop Stress on the wellbore wall

As shown in figure. 35. The hoop stress distribution with

multi fracture on the wellbore wall. The two fractures

are considered in the direction of minimum horizontal

stress (Shmin), closed after simulation. The two other

fractures assumed to be parallel to the maximum

horizontal stress (SHmax) which are considered in the

model, which are called the first and third fracture.

Fig. 35. Hoop stress distribution with multi fractures on the

wellbore wall The fracture width will be larger in the direction of

maximum horizontal stress by increasing the Degree of

Anisotropy. As it was said, in this section, it is supposed

that the second, third and fourth fractures, relative to the

initial fracture, respectively have an angle of 90º, 180º

and 270º.

The length of all fractures is the same as 6 inches;

besides, the pressure inside the fractures is equal to the

wellbore pressure; furthermore, it is noted that the tips of

the fractures are affected by tensile stress and the

compressive stress will be increased by getting away

from the first and third fractures on the wellbore wall,

before the bridging of the fractures.

Impact of Horizontal stress contrast. ( SHmax/

Shmin)

As seen in figure. 36,37. The hoop stress distribution in

multi fracture model, before and after the bridging of the

first fracture, by moving away from the first fracture, the

compressive stress decreases around the 90º angle, due

to the existence of second fracture .The compression

stress is raised by increasing the horizontal stress

contrast.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Frac

ture

Wid

th(I

nch

)


dis-Pore Pressure-1800(psi)







0

0.02

0.04

0.06

0.08

0.1

0.12

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

tur

Wid

th(I

nch

)


In frac with 8000 PSI-Wellbore Pressure

In frac with 9000 PSI-Wellbore Pressure

In frac with 10000PSI-WellborePressureinfrac Plugging 8000PSI-WellborePressureinfrac Plugging 9000PSI-WellborePressureinfrac Plugging 10000PSI-WellborePressure

Fig. 36. Hoop stress distribution in multi fracture model,

before and after the bridging of the first fracture with

horizontal stress contrast

Fig. 37. Hoop stress distribution in multi fracture model,

before and after the bridging of the first fracture, with

SHmax=1.4*Shmin

As seen in figure. 38. The hoop stress distribution in

multi fracture model, compared with one fracture model

on the half of the wellbore, with LCM bridge of 4.5 inch

away from the wellbore, before and after bridging of the

fracture, for multi fracture model the first fracture will

be plugged and others are open. As seen in figure. 38.

The compressive hoop stress in one fracture model is

more than the Compressive hoop stress in multi fracture

model, before and after bridging the fracture.it is

interesting that there is a slight difference in the amount

of compressive hoop stress, before and after bridging of

the fracture in both models (the first fracture in multi

fracture model), due to the long distance of LCM bridge

from the wellbore.

Fig. 38. hoop stress distribution in multi fracture model,

compared with one fracture model on the half of the wellbore,

with LCM bridge of 4.5 inch away from the wellbore before

and after the bridging of the fracture

4.2.2. Fracture width

Impact of Horizontal stress contrast ( SHmax/

Shmin)

As seen in figure. 39. The first fracture on the model has

the larger width, compared with the third fracture width,

which will be increased by growing the horizontal stress

contrast, in the direction of maximum horizontal stress,

before bridging the first fracture and after simulation.

Two other fractures, which are in the direction of

minimum horizontal stress, are closed.

Fig. 39. Changes in width of first and third fracture, in multi

fracture model, in fracture initiation state

As seen in figure. 40. The widths of the fractures in the

multi fracture model, compared with the fracture width

in one fracture model in the half of the wellbore, in

fracture initiation state, with different horizontal stress

contrast. It is noted that the fracture width will be

increased by increasing the horizontal stress contrast in

fracture initiation state.

-9,000.00

-8,500.00

-8,000.00

-7,500.00

-7,000.00

-6,500.00

-6,000.00

-5,500.00

-5,000.00

-4,500.00

-4,000.00

0 9 18 27 36 45 54 63 72 81 90H

oo

p S

tres

s(P

si)

Angle(deg)

Hoop StressWellboreSH/Sh=1.2Hoop StressWellboreSH/Sh=1.3Hoop StressWellboreSH/Sh=1.4Hoop StressWellboreSH/Sh=1.2 PluggingHoop StressWellboreSH/Sh=1.3 PluggingHoop StressWellboreSH/Sh=1.4 Plugging

-16,000.00

-14,000.00

-12,000.00

-10,000.00

-8,000.00

-6,000.00

-4,000.00

-2,000.00

0.00

0 9 1827 3645 5463 7281 90

Ho

op

Str

ess(

Psi

)

Angle(deg)

Hoop Stress SingleWellbore SH/Sh=1.4

Hoop Stress MultiWellbore SH/Sh=1.4

Hoop Stress SingleWellbore SH/Sh=1.4Plugging

Hoop Stress MultiWellbore SH/Sh=1.4Plugging

0.0000000

0.0100000

0.0200000

0.0300000

0.0400000

0.0500000

0.0600000

0.0700000

0.0800000

0 0.75 1.5 2.25 3 3.75 4.5 5.25 6

Frac

tur

Wid

th(I

nch

)


Frac1 Width in fracSH/Sh=1.2


Frac1Width in fracSH/Sh=1.4




Fig. 40. Widths of the fractures in the multi fracture model,

compared with the fracture width in one fracture model in the

half of the wellbore, in fracture initiation state, with different


As can be seen in figure. 40. The width of the first

fracture in multi fracture model after simulation is larger,

compared with the model with one fracture in the half

the wellbore.

In the next step, the first fracture is bridged in the multi

fracture model, the third fracture is open and the second

and forth fracture is closed because of the compressive

stress, applied to their fracture faces.

As seen in figure. 41. The width of the first fracture in

the multi fracture model, with LCM bridge in 4.5 inch

away from the wellbore wall, in fracture initiation state

and after bridging the first fracture, with different


Fig. 41. Width of the first fracture in the multi fracture model,

with LCM bridge of 4.5 inch away from the wellbore wall, in

fracture initiation state and after bridging the first fracture,

with different horizontal stress contrast

As seen in figure. 41. The width of the first fracture is

decreased after bridging; besides, the fracture width is

raised by increasing the horizontal stress contrast, before

and after bridging. As shown in figure. 42. The width of

the third fracture in the multi fracture model, in fracture

initiation state and after bridging the first fracture, with

LCM bridge of 4.5 inch away from the wellbore wall,

with different horizontal stress contrast.

Fig. 42. Width of the third fracture in the multi fracture model,

in fracture initiation state and after bridging the first fracture,

with LCM bridge of 4.5 inch away from the wellbore wall,

with different horizontal stress contrast

The width of the third fracture is decreased after

bridging the first fracture; furthermore, the fracture

width, related to the third fracture, is raised by increasing

the horizontal stress contrast, before and after bridging

5. CONCLUSION

Hoop stress distribution on the wellbore wall and inside

the fracture, as well as the process of creating a fracture

and its propagation, is a complex subject, which still

remains unspecified in many aspects and many wellbore

strengthening operations are based on trial and error. The

purpose of this study was to investigate the behavior of

hoop stress on the wellbore wall as well as fracture

geometry, before and after fracture propagation and

fracture bridging, which are key factors in wellbore

strengthening. For this purpose, various parameters

which can affect on the fracture width and the hoop

stress on the wellbore wall, on the wellbore

strengthening, have been studied in detail.

The two-dimensional model, based on plain strain

elements with linear elastic state, has been used and then

this model has been extended to the two-dimensional

model with multi fracture, in ABAQUS software, based

on finite element method. These models have the capacity to simulate the hoop stress and fracture

geometry, with considering the parameters affecting

them, on the wellbore wall, before and after fracture

propagation and after bridging the fracture.

The most important results from the simulation of the

mentioned models, related to the wellbore strengthening,

in ABAQUS software are as follows:

The compressive stress will be more in the

bridging location across the fracture faces, with

the length of the fracture equal to 6 inches; for

instance, the compressive stress will be equal -

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

tur

Wid

th(I

nch

)


Frac Single Width infrac SH/Sh=1.2





Frac1Width in fracSH/Sh=1.4

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0

0.7

5

1.5

2.2

5 3

3.7

5

4.5

5.2

5 6

Frac

tur

Wid

th(I

nch

)


Frac 1 Width in fracSH/Sh=1.2

Frac 1 WidthPlugging in fracSH/Sh=1.2Frac 1Width in fracSH/Sh=1.3

Frac1 WidthPlugging in fracSH/Sh=1.3Frac 1Width in fracSH/Sh=1.4

Frac1 WidthPlugging in fracSH/Sh=1.4

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 0.75 1.5 2.25 3 3.75 4.5 5.25 6


Frac 3 WidthAfterPlugging Frac1in frac SH/Sh=1.2


Frac3 Width AfterPlugging Frac1 in fracSH/Sh=1.3

Frac 3Width in fracSH/Sh=1.4

Frac3 Width AfterPlugging Frac1 in fracSH/Sh=1.4

13,474 Psi, with bridging location of 4.5 inches

away from the wellbore , based on the input data

of the two-dimensional model with single

fracture on the half the wellbore; besides, the

amount of the tensile stress will be less at the tip

of the fracture, after bridging the fracture;

therefore, this will cause that the fracture with

LCM bridge becomes harder to open.

The compressive stress will be raised before the

area of the angle of 30º in the fracture initiation

state, with bridging location of 2.25 inches away

from the wellbore, based on the input data of the

two-dimensional model with single fracture on

the half the wellbore; besides, The compressive

stress will be declined after the area of the angle

of 30º after bridging the fracture.

The compressive stress is highest on the

bridging location; therefore, this will cause that

the fracture with LCM bridge becomes harder to

open and it is very important to predict and

determine the particle size of the LCM bridge;

therefore, the best place for bridging the fracture

is near the fracture mouth. When the bridging

location is near the wellbore wall, the

compressive stress will be increased

dramatically on the wellbore wall, with the two-

dimensional model with single fracture on the

half the wellbore. When the bridging location is

far from the wellbore wall, the amount of the

compressive stress will be declined on the

wellbore wall; besides, the amount of the tensile

stress will be reduced at the tip of the fracture

after bridging of the fracture.

The hoop stress distribution on the wellbore wall

and fracture faces will be changed after bridging

the fracture. The stress around the fracture

mouth tends to be compressive; while, the stress

at the tip of the fracture tends to be tensile;

besides, it is interesting that the tensile stress

will be less at the tip of the fracture after

bridging. The compressive hoop stress will be

less on the LCM bridge by increasing the

distance from the bridging plug to the fracture

mouth throughout the fracture.

The more pressure behind the LCM bridge (from

1800 to 4500 PSI) results the less compressive

stress in bridging location; however, the tensile

stress will be more at the tip of the fracture.

The fracture width will be increased by

increasing the horizontal stress contrast which is

more in the vicinity of fracture mouth.

Thorough the fracture width, Larger Young’s

modulus creates a smaller width for the fracture.

Furthermore, the fracture with a smaller

Young’s modulus after bridging with LCM has a

much larger width decrease comparing a fracture

with larger Young’s modulus. Poisson's ratio has

less effect on fracture width, in comparison with

Young's modulus, in fracture initiation state and

after bridging, Larger Poisson's ratio creates a

smaller width for the fracture.

Larger wellbore pressure creates a larger width

for the fracture in fracture initiation state and

after bridging it is noted that the decrease of the

fracture width is larger behind the LCM bridge

comparing the decrease of the fracture ahead of

the LCM bridge; besides, the compressive stress

with higher wellbore pressure on the wellbore,

before the angle of 60º and after bridging the

fracture, is greater than the compressive stress

with lower wellbore pressure on the wellbore

wall and it will be reversed after the angle of 60º

In multi fracture model, by moving away from

the first fracture, the compressive stress

decreases around the 90º, due to the existence of

second fracture .The compression stress is raised

by increasing the horizontal stress contrast,

before and after the bridging of the first fracture.

It is noted that the fracture width will be

increased by increasing the horizontal stress

contrast in fracture initiation state as well as

after bridging the fracture, in multi fracture

model.

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wellbore strengthening analysis in single and multi

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