Post on 18-Dec-2021
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:Farzmhe@gmail.com; Mehrkhani.fa@ppars.com
Arash Ebrahimabadi
Department of Mining, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran,
Email: Arash.xer@gmail.com; A.Ebrahimabadi@Qaemiau.ac.ir
Mohamad Reza Alaei
Department of Petroleum Engineering, Central Tehran Branch, Islamic Azad University, Tehran, Iran
Email:Eng.alaei@gmail.com
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
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
Pre Fracture StateSHmax=1.2Shmin
Pre Fracture StateSHmax=1.3Shmin
Pre Fracture StateSHmax=1.4Shmin
Pre Fracture StateSHmax=1.5Shmin
-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
Fracture StateSHmax=1.2Shmin
Fracture StateSHmax=1.3Shmin
Fracture StateSHmax=1.4Shmin
Fracture StateSHmax=1.5Shmin
-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
Fracture StateSHmax=1.2Shmin
Fracture StateSHmax=1.3Shmin
Fracture StateSHmax=1.4Shmin
Fracture StateSHmax=1.5Shmin
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.
Fig. 11. Hoop stress distribution on the wellbore wall with
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)
Fracture StateSHmax=1.4Shmin
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
Fig. 12. Hoop stress distribution on the wellbore wall with
different wellbore pressures, before fracture state, fracture
initiation state and after plugging, with SHmax=1.4*Shmin
and wellbore pressure 8,000 Psi.
Fig. 13. Hoop stress distribution on the wellbore wall with
different wellbore pressures, before fracture state, fracture
initiation state and after plugging, with SHmax=1.4*Shmin
and wellbore pressure 9,000 Psi.
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
Horizontal stress contrast. ( SHmax/ Shmin)
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.
Fig. 16. Comparing the Hoop stress distribution along the
fracture faces with different horizontal contrast, after fracture
initiation.
-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 90H
oo
p S
tres
s(P
si)
Angle(deg)
Pre Fracture StateSHmax=1.4Shminwellbore=8000
Fracture StateSHmax=1.4Shminwellbore=8000
After PluggingSHmax=1.4Shminwellbore=8000
-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=9000
Fracture StateSHmax=1.4Shminwellbore=9000
After PluggingSHmax=1.4Shminwellbore=9000
-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)
After PluggingSHmax=1.4Shminwellbore=9000
After PluggingSHmax=1.4Shminwellbore=8000
After PluggingSHmax=1.4Shminwellbore=10000
-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
Hoop Stress WithSH/Sh=1.2
Hoop Stress WithSH/Sh=1.3
Hoop Stress WithSH/Sh=1.4
Hoop Stress WithSH/Sh=1.5
-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
)
Distance From the Wellbore(Inch)
Hoop Stress WithSH/Sh=1
Hoop Stress WithSH/Sh=1.1
Hoop Stress WithSH/Sh=1.2
Hoop Stress WithSH/Sh=1.3
Hoop Stress WithSH/Sh=1.4
Hoop Stress WithSH/Sh=1.5
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.
Fig. 17. Comparing the Hoop stress distribution along the
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.
Fig. 18. Comparing the Hoop stress distribution along the
fracture faces, before and after bridging the fracture, with
SHmax=1.4*Shmin
Hoop stress on the wellbore wall for different
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
Hoop stress on the wellbore wall for different
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
)
Distance From the Wellbore(Inch)
Hoop Stress WithD4.5 SH/Sh=1
Hoop Stress WithD4.5 SH/Sh=1.1
Hoop Stress WithD4.5 SH/Sh=1.2
Hoop Stress WithD4.5 SH/Sh=1.3
Hoop Stress WithD4.5 SH/Sh=1.4
Hoop Stress WithD4.5 SH/Sh=1.5
-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)
Hoop Stress WithSH/Sh=1.4
Hoop Stress WithD4.5 SH/Sh=1.4
-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
Fracture StateSHmax=1.4Shmin
-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
)
Distance From the Wellbore(Inch)
Pore Pressure-1800(psi)
Pore Pressure-2000(psi)
Pore Pressure-2500(psi)
Pore Pressure-3000(psi)
Pore Pressure-3500(psi)
Pore Pressure-4500(psi)
Hoop stress on the wellbore wall for different
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
Fig. 21. Comparing the Hoop stress distribution along the
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
Fig. 22. Comparing the Hoop stress distribution along the
fracture faces, with wellbore pressure at 9,000 Psi,
respectively , before fracture initiation , fracture initiation state
and after bridging fracture, with SHmax=1.4*Shmin
Fig. 23. Comparing the Hoop stress distribution along the
fracture faces, with wellbore pressure at 10,000 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
Fig. 24. Comparing the Hoop stress distribution along the
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
)
Distance From the Wellbore(Inch)
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
)
Distance From the Wellbore(Inch)
In Frac Pre FractureStateSHmax=1.4Shminwellbore=9000
In Frac FractureStateSHmax=1.4Shminwellbore=9000
In Frac AfterPluggingSHmax=1.4Shminwellbore=9000
-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
)
Distance From the Wellbore(Inch)
In Frac Pre FractureStateSHmax=1.4Shminwellbore=10000
In Frac AfterPluggingSHmax=1.4Shminwellbore=10000
In Frac FractureStateSHmax=1.4Shminwellbore=10000
-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)
In Frac AfterPluggingSHmax=1.4Shminwellbore=9000
In Frac AfterPluggingSHmax=1.4Shminwellbore=10000
In Frac AfterPluggingSHmax=1.4Shminwellbore=8000
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
Horizontal stress contrast. ( SHmax/ Shmin)
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
Distance From the Wellbore(Inch)
fracture width infrac SH/Sh=1
fracture width infrac SH/Sh=1.1
fracture width infrac SH/Sh=1.2
fracture width infrac SH/Sh=1.3
fracture width infrac SH/Sh=1.4
fracture width infrac SH/Sh=1.5
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
Distance From the Wellbore(Inch)
Fracture Width WithD4.5 SH/Sh=1
Fracture Width WithD4.5 SH/Sh=1.1
Fracture Width WithD4.5 SH/Sh=1.2
Fracture Width WithD4.5 SH/Sh=1.3
Fracture Width WithD4.5 SH/Sh=1.4
Fracture Width WithD4.5 SH/Sh=1.5
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
)
Distance From the Wellbore(Inch)
Hoop Stress in fracSH/Sh=1.4
Hoop Stress WithD4.5 SH/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
)
Distance From the Wellbore(Inch)
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
)
Distance From the Wellbore(Inch)
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
)
Distance From the Wellbore(Inch)
dis-Pore Pressure-1800(psi)
dis-Pore Pressure-2000(psi)
dis-Pore Pressure-2500(psi)
dis-Pore Pressure-3000(psi)
dis-Pore Pressure-3500(psi)
dis-Pore Pressure-4000(psi)
dis-Pore Pressure-4500(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
)
Distance From the Wellbore(Inch)
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
)
Distance From the Wellbore(Inch)
Frac1 Width in fracSH/Sh=1.2
Frac1 Width in fracSH/Sh=1.3
Frac1Width in fracSH/Sh=1.4
Frac3 Width in fracSH/Sh=1.2
Frac3 Width in fracSH/Sh=1.3
Frac3 Width 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
horizontal stress contrast
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
horizontal stress contrast
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
)
Distance From the Wellbore(Inch)
Frac Single Width infrac SH/Sh=1.2
Frac Single Width infrac SH/Sh=1.3
Frac Single Width infrac SH/Sh=1.4
Frac1 Width in fracSH/Sh=1.2
Frac1 Width in fracSH/Sh=1.3
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
)
Distance From the Wellbore(Inch)
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 Width in fracSH/Sh=1.2
Frac 3 WidthAfterPlugging Frac1in frac SH/Sh=1.2
Frac 3 Width in fracSH/Sh=1.3
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.
1. Arlanoglu, C., Y. Feng, E. Podnos, E. Becker, and K. E.
Gray. 2014. Finite Element Studies of Wellbore
Strengthening, In IADC/SPE Drilling Conference and
Exhibition, Society of Petroleum Engineers.
2. Albahrani, Hussain. 2016. An Analyzing Model of Stress-
Related Wellbore Strengthening Techniques, Society of
Petroleum Engineers.
3. Aston, M. S., M. W. Alberty, M. R. McLean, H. J. De Jong,
and K. Armagost. 2004. Drilling Fluids for Wellbore
Strengthening, IADC/SPE Drilling Conference.
4. Alberty, Mark W., and Michael R. McLean. 2004. A
physical model for stress cages, SPE Annual technical
conference and exhibition, Society of petroleum engineers.
5. Cook, John, Fred Growcock, Quan Guo, Mike Hodder, and
Eric van Oort. 2011. Stabilizing the Wellbore to Prevent Lost
Circulation, Oilfield Review.
6. Feng, Yongcun, and K. E. Gray. 2016. A Parametric Study
for Wellbore Strengthening, Journal of Natural Gas Science
Engineering.
7. Feng, Yongcun, and K. E. Gray. 2017. Review of
Fundamental Studies on Lost Circulation and Wellbore
Strengthening, Journal of Petroleum Science and Engineering.
8. Feng, Y., C. Arlanoglu, E. Podnos, E. Becker, and K. E.
Gray. 2015. Finite-Element Studies of Hoop-Stress
Enhancement for Wellbore Strengthening, SPE Drilling &
Completion.
9. Feng, Yongcun, and K. E. Gray. 2017. Review of
fundamental studies on lost circulation and wellbore
strengthening. Journal of Petroleum Science and
Engineering 152: 511-522.
10. Feng, Yongcun, Xiaorong Li, and K. E. Gray. 2018.
Mudcake effects on wellbore stress and fracture initiation
pressure and implications for wellbore
strengthening. Petroleum Science15.2: 319-334.
11. Feng, Yongcun, John F. Jones, and K. E. Gray. 2016. A
Review on Fracture-Initiation and-Propagation Pressures for
Lost Circulation and Wellbore Strengthening, SPE Drilling &
Completion.
12. Kiran, Raj, and Saeed Salehi. 2017. Thermoporoelastic
Modeling of Time-Dependent Wellbore Strengthening and
Casing Smear.
13. Morita, Nobuo, and Giin-Fa Fuh. 2012. Parametric
Analysis of Wellbore-Strengthening Methods from Basic
Rock Mechanics, SPE Drilling & Completion.
14. Mehrabian, Amin, Dale E. Jamison, and Sorin Gabriel
Teodorescu. 2015. Teodorescu, G., Geomechanics of Lost
Circulation Events and Wellbore-Strengthening Operations.
15. Shahri, Mojtaba P., Trevor T. Oar, Reza Safari, Moji
Karimi, and Uno Mutlu. 2015. Advanced Semianalytical
Geomechanical Model for Wellbore-Strengthening
Applications, SPE Journal.
16. Salehi, Saeed, and Runar Nygaard. 2014. Full Fluid–Solid
Cohesive Finite-Element Model to Simulate Near Wellbore
Fractures.
17. Savari, Sharath, Donald L. Whiftill, Dale E. Jamison, and
Arunesh Kumar. 2014. A Method to Evaluate Lost
Circulation Materials - Investigation of Effective Wellbore
Strengthening Applications, IADC/SPE Drilling Conference
and Exhibition.
18. Salehi, Saeed, and Runar Nygaard. 2011. Evaluation of
New Drilling Approach for Widening Operational Window:
Implications for Wellbore Strengthening, SPE Production and
Operations Symposium.
19. Shahri, Mojtaba P., Trevor Oar, Reza Safari, Moji Karimi,
and Uno Mutlu. 2014. Advanced Geomechanical Analysis of
Wellbore Strengthening for Depleted Reservoir Drilling
Applications, IADC/SPE Drilling Conference and Exhibition,
Society of Petroleum Engineers.
20. Wang, Ze, Mingzheng Yang, and Yuanhang Chen. 2019.
Numerical modeling and analysis of induced thermal stress for
a non-isothermal wellbore strengthening process. Journal of
Petroleum Science and Engineering 175: 173-183.
21. Wang, Hong, Brian Francis Towler, and Mohamed Y.
Soliman. 2007. Near Wellbore Stress Analysis and Wellbore
Strengthening for Drilling Depleted Formations, In Rocky
Mountain Oil & Gas Technology Symposium, Society of
Petroleum Engineers.
22. Wang, Ze. 2018. Modeling and Analysis of Thermal
Effects on A Fractured Wellbore During Lost Circulation and
Wellbore Strengthening Processes.
23. Wang, Hong. 2007. Near Wellbore Stress Analysis for
Wellbore Strengthening.
24. Zhong, Ruizhi, Stefan Miska, Mengjiao Yu, Evren
Ozbayoglu, Jianguo Zhang, and Reza Majidi. 2017. A Leak
off Model for Critical Permeability in Wellbore Strengthening
Application, AADE National Technical Conference &
Exhibition.
25. Zhang, Jincai, Mark Alberty, and J. P. Blangy. 2016. A
Semi-Analytical Solution for Estimating the Fracture Width in
Wellbore Strengthening Applications, SPE Deepwater Drilling
and Completions Conference.
26. Zhong, Ruizhi, Stefan Miska, Mengjiao Yu, Evren
Ozbayoglu, and Nicholas Takach. 2018. An integrated fluid
flow and fracture mechanics model for wellbore
strengthening. Journal of Petroleum Science and
Engineering 167: 702-715.