Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127 Received for review: 2023-05-31
© 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME Received revised form: 2023-10-31
DOI:10.5545/sv-jme.2023.662 Original Scientific Paper Accepted for publication: 2023-11-20
*Corr. Author’s Address: State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,  
Southwest Petroleum University, China, 202122000793@stu.swpu.edu.cn
116
Research on the Adaptability of Packers  
for Integrated String Fracturing Operations  
in Low Porosity and Low Permeability Reservoirs
Wan, Z.Y . – Yu, H. – Xiao, Y . – Zhao, Z.Y . – Lian, Z.H. – Chen, F.X.
Zhiyong Wan
1,*
 – Hao Yu
1
 – Yong Xiao
2
 – Zhaoyang Zhao
1
 – Zhanghua Lian
1
 – Fangxin Chen
1
1 
Southwest Petroleum University, State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, China 
2 
Chengdu North Petroleum Exploration and Development Technology Co, Ltd, China
To study the failure of conventional packers in the fracturing and stimulation of low-porosity and low-permeability reservoirs and reduce 
the failure accidents of packers in the fracturing process, a suitable integrated string packers was selected in the process of fracturing and 
stimulation in an oilfield in the Middle East as a case study. Three different well types have been established. The wellbore temperature 
distribution and the axial force of the string can be calculated under the conditions of various wellhead pressures and different displacement, 
and it is found that the temperature at the bottom of the well can reach 130 °C, and the maximum axial force at the wellhead is 500 kN. 
At the same time, the applicability of retrievable tubing testing squeeze (RTTS) and hydraulic-set retrievable (RH) packer in different working 
conditions was evaluated, and it was found that only RTTS packers can meet the needs of the oil field. According to the calculated temperature 
field and axial force distribution, the stress on different components of the packer under different working conditions is established during the 
fracturing-stimulation operation. In the worst working conditions, the maximum stress of the packer occurs at the lower part of the central pipe, 
reaching 303.83 MPa, which is in a safe state. The contact stress on rubber rings can reach 30 MPa, indicating that the sealing performance 
can meet the requirements of on-site use. The temperature and axial force data calculated by the model provide a theoretical basis for safe 
well control. At the same time, through model evaluation, it was found that the RTTS packer can be suitable for the fracturing and stimulation 
needs of the oilfield. The research methods and achievements in the article provide theoretical guidance for evaluating the applicability of 
packers in the fracturing and stimulation process of low porosity and low permeability reservoirs.
Keywords: low porosity and low permeability reservoirs, integrated pipe string, packer rubber ring, acid fracturing, finite element 
simulation
Highlights
• 	 Established a practical applicability evaluation model for three types of well types used in a Middle Eastern oil field.
• 	 Based on the results obtained from the adaptability evaluation model of the packer, combined with the finite element method 
to calculate the stress distribution of key components on the packer, it is found that the upper central pipe of the packer is a 
weak structure.
• 	 Combined with the contact pressure and contact length obtained by finite element calculation, the sealing performance of the 
rubber ring under extreme conditions was evaluated, and the adaptability evaluation model of the rubber ring of the packer 
was established.
0  INTRODUCTION
In recent years, with the improvement of mining 
technology, more low-porosity and low-permeability 
reservoirs have been developed. In order to activate 
the reservoir and increase production, it is necessary 
to use acid fracturing technology [1]. However, the 
reservoir is characterized by high crustal stress, easy 
leakage, interlayer interaction, strong formation 
heterogeneity, relatively developed fractures, and great 
difficulty in oil testing and reservoir reconstruction. 
The conventional operation of lowering the string 
multiple times cannot meet the requirements of oil and 
gas well testing and acidizing stimulation operations 
[2]. Therefore, in the process of acid fracturing 
operation, the perforation-fracturing-completion 
triple integrated string operation is adopted, which 
has reliable tool function and stable performance, 
reducing the number of frequently lowered strings 
and damage to the reservoir [3]. It can also improve 
construction efficiency, save the cost of exploration 
and development, avoid the secondary pollution of 
the formation by the well control fluid to the greatest 
extent, meet the needs of environmental protection, 
fracturing displacement and efficient construction [4], 
and can solve the problem of out-of-control wellhead 
during the installation of blowout preventers, to 
reduce well control risks, construction risks and 
operating costs [5]. To realize the perforation-
fracturing-completion operations once, the design 
of the integrated string is more stringent. There are 
still defects, such as insufficient understanding in the 
design, which seriously restricts the development of 

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
117 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
special reservoir characteristics, such as low porosity 
and low permeability [6] and [7].
At present, the research on the design of the 
integrated string mainly focuses on the research on the 
failure of the thread seal [8] and [9], the construction 
process of the integrated operation string [10], and the 
design of the perforation-pressure test dual string. For 
harsh reservoir conditions, such as low porosity and 
low permeability, research on the use of perforating-
fracturing-completion triple-integrated operation 
strings is lacking. In conventional production 
operations, the string is often run in three times, 
which increases the risk of reservoir damage, and 
the wellhead needs to be lifted and lowered multiple 
times, which increases the risk of well control failure. 
Compared with the integrated operation string, the 
construction operation time is increased, as are the 
development costs of oil and gas reservoirs [11]. 
Therefore, this article focuses on three different 
well types developed in a Middle Eastern oil field 
with low porosity and low permeability reservoirs, 
namely vertical wells, deviated wells, and horizontal 
wells. Key components in the integrated perforation 
fracturing completion operation string used for special 
reservoir development include a numerical simulation 
model for wellbore string temperature and axial 
force during perforation and fracturing processes, 
as well as an evaluation model for the applicability 
of packers, which was established through software. 
The simulated temperature and axial force data were 
then combined with finite element analysis software. 
Conduct applicability analysis and research on key 
components of integrated operation string, provide 
theoretical basis and guidance for the failure research 
of key components of integrated operation string used 
in oil fields, and also provide theoretical basis for the 
design of integrated operation string and various safe 
construction operations.
1  INTEGRATED PIPE STRING STRUCTURE AND ANALYSIS OF 
ITS STRESS CONDITIONS
1.1  Structure and Working Principle of Key Components of 
Integrated Pipe String
At present, in the development process of some oil 
and gas fields, multiple lowering pipe strings are used 
[12]. The schematic diagram of the operation process 
is shown in Fig. 1.
First, the well-cleaning and scraping strings 
are lowered to clean the debris attached to the inner 
wall of the strings, and then the perforated strings 
are lowered for perforation operations, and finally 
the acid fracturing and well completion operations 
are performed. During this series of operations, it is 
necessary to open the wellhead several times to raise 
and lower the pipe string, increasing the risk of well 
control failure, but the integrated operation string can 
prevent it. Therefore, an oilfield in the Middle East 
actually uses the perforation-fracturing-completion 
triple integrated operation string, which consists 
of tubing, rupture disk (RD) cycle valve, rupture 
disk safety (RDS) valve, OMNI™ valve, packer, 
tubing conveyed perforation (TCP) gun and other 
components. The three different wellbore structures 
and integrated pipe strings used are shown in Fig. 2.
Fig. 1.  Schematic diagram of the operation process of repeatedly 
lowering the pipe column; a) hole structure, b) wiper string,  
c) scraper string, d) perforation string, and e) completion string
Fig. 2.  Schematic diagram of three types of wellbore structures 
and integrated pipe string structures; a) horizontal well,  
b) vertical well, and c) deviated well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
118 Wan, Z.Y. – Yu, H. – Xiao, Y. – Zhao, Z.Y. – Lian, Z.H. – Chen, F.X.
As a key component of the integrated string, the 
packer determines the sealing performance of the 
operating string during perforation and acid fracturing; 
therefore, an in-depth safety analysis is required. There 
are two packer selection schemes on site: the RTTS 
packer and the RH packer. The technical parameters 
and manufacturer of the packer are shown in Table 1 
The structural schematic diagrams of the two packers 
are shown in Fig. 3.
Fig. 3.  Structural schematic diagram of;  
a) RTTS packer, and b) RH packer
The RTTS packer is a suspension packer with 
a large diameter and can seal off two-way pressure. 
It consists of a slot transposition mechanism, slips, 
rubber ring and hydraulic anchoring mechanism. 
The hydraulic anchoring mechanism can prevent the 
lower part of the packer from being pushed out of 
the wellbore when the pressure is too high. It is also 
equipped with friction blocks and an automatic groove 
sleeve structure. Designed for formation testing, 
acidizing, and cementing plug well operations, the 
large diameter is used to pump a large amount of fluid 
under a small pressure drop and can pass through the 
tubing perforating gun. Its working principle is that 
when it is necessary to seal the annular space between 
the tubing and the production casing, the upper limit 
groove of the packer is rotated so that the upper 
structure of the packer can move axially within the 
allowable range of the limit. When the string applies 
a part of its own weight and axial displacement to 
the RTTS packer, the slips are stretched to fix the 
packer on the inner wall of the production casing, 
and then continue to apply its own weight and axial 
displacement until the rubber ring of the packer is 
fully supported and the annulus between the oil pipe 
and the production casing is completely sealed. 
The other type of packer planned to be selected 
on site is the hydraulic retrievable packer, which 
is a compact, sturdy, reliable, convenient to use, 
single column hydraulic retrievable packer that can 
be directly lifted up and released. It is suitable for 
applications such as deviated wells, multi packer 
completion. The envelope curves for the sealing 
performance of two types of packers are shown in Fig. 
4.
Fig. 4.  Envelope Curve of RTTS Packer and RH Packer
The packing capacity of the two packers selected 
on site can be obtained from Fig. 4. The red shape in 
the figure is the envelope curve of the RTTS packer, 
while the envelope curve of the RH packer is the 
blue shape, and the envelope of the RTTS packer 
completely encompasses the RH packer, indicating 
that the packing ability of the RTTS packer is better 
than that of the RH packer.
Table 1.  Manufacturer and technical characteristics of the packers
Packer 
type
Maximum outer 
diameter [mm]
Minimum inner 
diameter [mm]
Length  
[mm]
Working pressure 
[MPa]
Working 
temperature [°C]
Applicable tubing 
diameter [mm]
Manufacturer
RTTS 201 124 1450 25 to 100 20 to 150 177.8 GWDC
RH 213 137 1300 10 to 60 20 to 120 177.8 TechWest

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
119 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
1.2  Theoretical Analysis of the Failure of Key Components 
of Packers
As an important part of ensuring the sealing ability of 
the packer, the packer rubber ring needs to be analysed 
thoroughly. The rubber ring is made of rubber, which 
is a typical hyper-elastic body.[13] and [14] It is often 
described with the Mooney-Rivlin constitutive model, 
and its constitutive relation expression is:
 WCIC I  
10 10 12
33 ()() , (1)
where W is the density of strain energy [J/m
3
], C
10
 and 
C
01
 are the Mooney-Rivlin coefficients of the material 
[MPa], and I
1
 and I
2
 are the first and second strain 
tensor invariant, [1].
The relationship between shear modulus and 
elastic modulus is:
 
EC C
GC C





6
2
10 01
10 01
()
()
. (2)
According to the large deformation properties of 
rubber, the relationship between its elastic modulus E, 
shear modulus G and material constants is:
 
EC C
GC C





6
2
10 01
10 01
()
()
. (3)
According to the rubber compression test, due to 
E = 11.49 MPa, the simulation results are relatively 
close to the measured results, resulting in C
10 
= 1.879 
MPa and C
01 
= 0.038 MPa.
In acid fracturing operations, the fracturing fluid 
injected from the wellhead is regarded as a Newtonian 
fluid, and when it flows to the target layer, the 
calculation formula for pipe flow friction is:
 R
vd
e
t



, (4)
where R
e
 is the pipe flow friction; ρ is the fluid 
density [kg/m³], v
t 
the fluid velocity, [m/s], d the 
inner diameter of the pipe column [m], and μ the fluid 
viscosity, [kg/(s·m)].
When the Reynolds number R
e
 of the acid fluid 
in the wellbore is less than 2000, the flow state of 
the acid fluid in the wellbore is a laminar flow state. 
At this time, the hydraulic friction coefficient of the 
fracturing fluid in the wellbore in the pipeline is [15]:
 f
R
e
=
64
. (5)
When the Reynolds number R
e
 of the acid fluid 
in the wellbore is greater or equal to 2000, it is in a 
turbulent state. At this time, the hydraulic friction 
coefficient of the fracturing fluid in the wellbore in the 
pipeline is:
 f
R
e
=
0 079
02 5
.
.
.
 (6)
However, when the fluid flows to the bottom of 
the well in the annular space, it will be subjected to 
friction along the way to reduce the pump pressure. 
The formula for calculating the friction loss of the 
fluid along the way is:
 Pf
Lv
gd
t


2
2
, (7)
where ΔP is the frictional loss along the way [kg/m²], 
L is the length of the pipeline along the route [m], and 
g is the gravitational acceleration [m/s²].
When the fluid reaches the bottom of the well, 
since the temperature of the injected fluid at the 
wellhead is much lower than the temperature of the 
downhole formation, the temperature of the wellbore 
will change during the acid fracturing operation, 
resulting in thermal expansion and contraction.
The temperature effect expression is [16]:
 
T
aT   , (8)
where ε
T
 is the thermal expansion elongation per unit 
length [m/m = 1], the expansion coefficient [m/°C] 
and ΔT the temperature difference [°C].
In the process of acid fracturing, it is often 
necessary to suppress the pressure of the wellbore, and 
the pressure mainly acts on the inner wall of the string, 
which will cause the axial deformation of the string. 
At the same time, in order to protect the downhole 
tools, such as packers, from failure, it is necessary to 
apply pressure to the annulus by squeezing the string 
from outside to inside will result in a reduction in the 
diameter of the string and an axial elongation.
The pressure inside the tubing consists of two 
parts: pump pressure and the hydrostatic column 
pressure of the liquid inside the tubing.
 PP gh
ipi
  , (9)
where P
i
 is the pressure inside the tubing [MPa], P
p
 
is the surface pump pressure [MPa], and ρ
i
 the fluid 
density inside the casing [kg/m³].
The external pressure of the pipeline is mainly 
the static liquid column pressure of the annular liquid, 
which is P
o
 = ρ
o
gh, where ρ
o
 is the density of liquid in 
the annular space [17] and [18].
The total axial deformation of the oil pipe under 
the combined action of internal and external pressures 
is:

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
120 Wan, Z.Y. – Yu, H. – Xiao, Y. – Zhao, Z.Y. – Lian, Z.H. – Chen, F.X.
 l
v
E
PR P
R
dh
H
oi
 



2
1
0
2
2
, (10)
where d
o
 is the outer diameter of the oil pipe [m], 
d
i
 the inner diameter of the oil pipe [m] where  
R = d
o 
/ d
i
, H the depth of pipe string [m], and ν 
Poisson’s ratio.
When the axial load on the string in the wellbore 
exceeds a certain critical value, the string will lose its 
stable state and buckle, causing the string to shrink, 
shorten, bend, and deform, and increase the friction 
between the string and the wellbore. The axial 
deformation of the packer will cause the seal failure 
of the packer and even the plastic failure of the string.
Then the true axial force of the tubing cross 
section at any well depth is F
a
, and the equivalent 
axial force F
e
 is:
 FFPA PA
ea oo ii
  , (11)
where A
o
 is the outer circular area of the column cross-
section [mm²], and A
i
 is the internal circular area of 
the pipe column cross-section [mm²].
The critical value of helical buckling deformation 
of the pipe column is [19]:
 FE Iq
helm
= 55 5
2
3
., (12)
where F
hel
 is the critical buckling load [kN], q
m
 is the 
line floating weight of the oil pipe [kN/m] and EI is 
the bending stiffness of the oil pipe [kN·m²].
When the pipe column is in a helical buckling 
state, the bending stress on the pipe column σ
m
 is:
 

m
out
out in
M
W
Fr
rr


2
2
44
()
, (13)
where σ
m
 is the bending stress when the pipe string 
undergoes helical buckling [MPa], M is the bending 
moment at the central pipe when the pipe column 
undergoes helical buckling [N/mm], and W is the 
bending section coefficient of a circular section 
[mm
3
].
By calculating the stress on the string and 
comparing it with the yield strength of its material, 
if it is less than the yield strength, it means that the 
pipe string is still in a safe state. Although the average 
stress on the integrated pipe string can be evaluated 
and calculated by Eq. (13), the pipe string is not 
regular, and it is impossible to accurately calculate the 
force on the upper part of the packer with an analytical 
formula, and only the finite element method can be 
used for simulation.
2  TEMPERATURE AND AXIAL FORCE ANALYSIS OF 
INTEGRATED PIPE STRING
According to the data provided by the Halfaya 
Oilfield in Iraq [20], the average porosity of the B1, 
B2, and B3 sub-member of the Sadi Formation is 
17.5 %, 19.3 %, and 13.6 %, respectively, and the 
average permeability is 0.13 mD, 0.2 9 mD, and 5.11 
mD, respectively. It belongs to a low porosity, ultra-
low permeability carbonate reservoir, with a wellbore 
temperature of 25 ℃, a fracturing fluid density of 1200 
kg/m³, a wellhead injection pressure of 30 MPa to 50 
MPa, and a displacement of 3 m³/min to 5 m³/min, 
The data on the wellbore structure and the integrated 
string structure used are summarized in Table 2, The 
geological structure of the Halfaya Oilfield is shown 
in Fig. 5.
X1 to X3 wells are three typical well types 
developed in an oil field in Middle East. The obtained 
data were used to establish an integrated string 
temperature and axial force analysis model using 
software, and the temperature, axial force, axial safety 
factor, and packer applicability were calculated for 
different layers of the wellbore structure.
2.1  Analysis of Temperature Field Calculation Results for 
Integrated Pipe String
Since the higher the wellhead pumping pressure and 
displacement, the larger the volume of the pumped 
fluid, the more intense the downhole string cooling, so 
the analysis and calculation of the temperature of the 
three wellbore structures when the wellhead pumping 
pressure is 50 MPa and the pumping displacement is 5 
m³/min The field distribution diagram is shown in Fig. 
6. It is found that during the acid fracturing process, 
the temperature of the tubing string at all levels in 
the wellbore increases to varying degrees compared 
Table 2.  Summary of well bore structure and integrated pipe string structure data used
Number Well type
Well depth 
[m]
Intermediate casing diameter 
[mm]
Production casing diameter 
[mm]
Tubing diameter 
[mm]
Packer depth 
[m]
X1 Vertical 4000 381.0 254.0 177.80 2100
X2 Deviated 2500 / 254.0 177.80 2200
X3 Horizontal 3750 342.9 247.65 177.80 1900

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
121 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
with the wellhead. However, due to the injection of 
fracturing fluid into the wellhead, the temperature 
near the oil pipe is lower at the same depth, and the 
farther layers are closer to the formation temperature. 
Additionally, due to the role of the integrated string 
packer, temperature faults occur at the packer, as 
shown in Table 3.
Table 3.  Temperature statistics at the upper and lower packers
Number Well type Packer depth [m] Upper [°C] Lower [°C]
X1 Vertical 2100 38.5 27.3
X2 Deviated 2200 33.2 26.7
X3 Horizontal 1900 31.9 25.8
Fig. 5.  Sadi formation information comprehensive histogram
         a)                                                                             b)                                                                           c)
Fig. 6.  Temperature distribution curve with depth in wellbore; a) X1 vertical well, b) X2 deviated well, and c) X3 horizontal well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
122 Wan, Z.Y. – Yu, H. – Xiao, Y. – Zhao, Z.Y. – Lian, Z.H. – Chen, F.X.
2.2 Analysis of Axial Force Calculation Results for 
Integrated Pipe String
Because the axial force of the integrated pipe column 
directly determines the safety status of the pipe 
column during service, attention needs to be paid to it, 
so the axial force distribution curve of the integrated 
string under different displacement and pump 
pressure conditions is obtained through software 
simulation calculation, as shown in Fig. 7, it is found 
that the axial force of the string at the wellhead is 
axial tension, while the axial compression force is 
generated at the bottom of the well, and the position 
where the axial force is 0 appears at the packer. Due 
         a)                                                                             b)                                                                           c)
Fig. 7.  Distribution curve of axial force in Wellbore with depth; a) X1 vertical well, b) X2 veviated well, c) X3 horizontal well
         a)                                                                             b)                                                                           c)
Fig. 8.  Distribution curve of axial safety factor in Wellbore with depth; a) X1 vertical well, b) X2 deviated well, c) X3 horizontal well
         a)                                                                             b)                                                                           c)
Fig. 9.  Load distribution of RTTS packers under different working conditions and well shapes;  
a) X1 vertical well, b) X2 deviated well, c) X3 horizontal well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
123 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
slip cones, slips, and tubing. When the RTTS packer 
is in normal operation, pressure is applied downwards 
from the connectors, and squeezed after the slip 
pressure cone stretches the slips, it bites on the inner 
wall of the casing to fix the packer and then continues 
to exert axial pressure on the joint to squeeze and 
deform the rubber ring to seal the inner wall of the 
casing, so that the centre pipe and the annulus between 
the casing can maintain a certain pressure difference 
between the upper and lower sides, so as to avoid the 
temperature effect caused by the temperature decrease 
during the acid fracturing process, which will cause 
the axial displacement of the integrated pipe string.
a)                                                    b) 
Fig. 11.  Finite Element Mechanical Model of RTTS Packer;  
a) solid model, and b) finite elements model; (1 connector, 2 and 4 
rubber ring, 3 spacer ring, 5 slip cone, 6 slip, and 7 casing)
to the cold contraction of the pipe string during the 
acid fracturing process, the normal packer prevents 
the displacement of the string. In order to intuitively 
judge the safety state of the string, the axial safety 
factors of each well type are summarized in Fig. 8 It 
is found that the axial safety factors of all pipe strings 
are greater than 1, indicating that the pipe strings are 
in a safe state and there will be no phenomenon of 
plastic tensile fracture.
Through model calculation, the evaluation 
diagrams of load and envelope curves of RTTS packer 
and RH packer are shown in Figs. 9 and 10. It is found 
that the RTTS packer is applicable in all working 
conditions, and the RH packer cannot be applied in 
most cases due to its weak packer capability.
3  STRESS ANALYSIS OF INTEGRATED STRING PACKER
3.1  Establishment of Finite Element Model for RTTS 
Packer
According to the model established in the second 
section, the analysis shows that only the RTTS packer 
is suitable for the use of the integrated string in this 
oilfield; therefore, based on the actual use of the 
integrated string structure in an oilfield in Middle East, 
a static 2D axisymmetric finite element mechanical 
simulation of the RTTS packer is established using 
ABAQUS. In the finite element model, the number 
of finite elements is 17,207, the number of nodes are 
18455, including 16.837 quadrilateral finite elements 
(CAX4R), 370 triangular finite elements (CAX3), the 
size of the casing finite elements is 10 mm, the size of 
the centre pipe is 10 mm, and the other components 
are 1 mm. The model and its finite elements model 
are shown in Fig. 11. In the figure, the RTTS packer is 
mainly composed of connectors, rubber ring, spacers, 
         a)                                                                             b)                                                                           c)
Fig. 10.  Load distribution of well completion packers under different working conditions and well shapes;  
a) X1 vertical well, b) X2 deviated well, c) X3 horizontal well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
124 Wan, Z.Y. – Yu, H. – Xiao, Y. – Zhao, Z.Y. – Lian, Z.H. – Chen, F.X.
The RTTS packer mainly uses two materials: 
steel and rubber. The Poisson’s ratio of the steel is 
0.3, the elastic modulus is 2.1×10
5
 MPa, the yield 
strength is 758.6 MPa, and the tensile strength is 862 
MPa. Comprising propylene-polytetrafluoroethylene 
material, high temperature resistance, high pressure, 
reliable sealing performance, compressive strength up 
to 60 MPa, the rubber ring and the end protection ring 
are vulcanized into one, prevent shoulder protrusions 
on the rubber ring, improve the pressure resistance of 
the rubber ring, and are used for the rubber material 
of the rubber ring Mooney-Rivlin constitutive model, 
in which parameters C
10 
= 1.879 MPa, C
0 1
= 0.038 
MPa, and temperature and axial force data obtained 
by software simulation are attached to the packer. 
The force situation of the packer from running into 
fracturing operation is simplified into four steps: the 
stage of fixed constraint, the stage of applying gravity, 
the stage of applying setting force, and the stage of 
applying internal and external pressure and axial 
force. The whole load and boundary a summary of the 
conditions imposed is shown in Fig. 12. In the fixed 
constraint stage, the slips are in a fixed state during 
the entire stress process, so fixed constraints are 
applied to the lower part of the slips, and secondly, in 
the gravity application stage, after the slips are fixed, 
the gravity of the entire string is applied to the packer. 
Then apply the upper axial force on the joint in the 
stage of applying the setting force, and finally apply 
the lower axial force and the internal and external 
pressure in the model in the stage of applying the 
internal and external pressure and axial force, which 
were simulated in Section 2 and are affected by the 
temperature difference; the applied load is shown in 
Table 4.
3.2  Finite Element Analysis Results of RTTS Packer
Through the finite element calculation of the 
established model, the stress distribution image of the 
three wells under different acid fracturing conditions 
are shown in Fig. 13. 
Analysis of the worst acid fracturing conditions 
in the field, when the wellhead pressure is 50 MPa and 
the displacement is 5 m³/min, the maximum stress on 
the packer does not exceed 400 MPa, which is much 
smaller than the yield strength of the RTTS packer, 
indicating that at this time it is in the safe state, the 
maximum stress value appears in the lower part of the 
Table 4.  Summary of the stress situation during the setting stage of RTTS packer
Well number
Axial force F1  
[kN]
Axial force F2  
[kN]
Internal pressure Pin  
[MPa]
Upper external pressure 
Pout1 [MPa]
Lower external pressure  
Pout2 [MPa]
X1 100 84.28 61.98 19.59 61.98
X2 100 106.87 64.18 27.98 64.14
X3 100 103.77 50.38 18.64 50.34
F
1
F
1
F
2
P
out2
P
out1
P
in
P
in
Step 1 Step 2 Step 3
F
G
F
G
F
G
                                          a)                                         b)                                            c)                                         d)
Fig. 12.  Schematic diagram of constraints and forces during the setting stage of RTTS packer;  
a) fixed constraints, b) apply gravity, c) apply sealing force, and d) apply pressure and axial force

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
125 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
centre pipe, and the rubber ring is greatly deformed, 
completely sealing the annulus between the pipe 
strings, and achieving a complete seal, indicating that 
the RTTS packer can meet the actual requirements 
of the site. However, in order to achieve the purpose 
of eliminating potential safety hazards in actual 
operation, it is recommended to increase the wall 
thickness of the lower part of the central tube.
As a key component for sealing in the packer, 
the rubber ring can be evaluated for its sealing 
performance using the Mises stress and contact 
pressure on the rubber ring. Therefore, the Mises 
distribution image and contact pressure distribution 
image were obtained through a finite analysis model, 
as shown in Figs 14 and 15, respectively. From the 
Mises distribution image, it is found that in the worst 
working conditions of each well, the maximum 
stress on the rubber ring has reached 60 MPa, but the 
material of the rubber ring is a special type of rubber, 
it still does not break under the stress state. The reason 
for the possible failure of the upper rubber ring is the 
failure of the seal; the contact pressure of the rubber 
ring in contact with the outer wall is 0 MPa. As shown 
in Fig. 16, the distribution shows that the maximum 
a)                                                         b)                                                         c) 
Fig. 13.  Stress distribution image of RTTS packer under acid fracturing conditions; 
a) X1 vertical well, b) X2 deviated well, and c) X3 horizontal well, (1 central tube, 2 rubber ring, 3 slip, and 4 casing)
a)                                                                                  b)                                                                c)                  
Fig. 14.  Mises stress distribution image in RTTS packer rubber ring; a) X1 vertical well, b) X2 deviated well, and c) X3 horizontal well
a)                                                                b)                                                              c)                
Fig. 15. Contact stress distribution image of RTTS packer rubber ring; a) X1 vertical well, b) X2 deviated well, and c) X3 horizontal well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
126 Wan, Z.Y. – Yu, H. – Xiao, Y. – Zhao, Z.Y. – Lian, Z.H. – Chen, F.X.
principal logarithmic strain of the upper rubber ring 
is greater than that of the lower rubber ring, but the 
material of the rubber ring is rubber. In the case of 
such a large strain, it can still work safely, but the 
extrusion part of the upper joint can be optimized in 
the design. The structure makes the deformation of 
the upper and lower joints similar, unifies the service 
life of the packer rubber ring, and facilitates the 
replacement of the rubber ring at the same time.
The contact pressure distribution curve of the 
contact part between the packer rubber ring and the 
outer wall casing is extracted, as shown in Fig. 17; 
the contact pressure on the rubber ring reaches about 
30 MPa, indicating that the rubber ring can still 
maintain good performance under the worst working 
conditions. The sealing performance is excellent, and 
the contact pressure of the upper rubber ring is larger 
than that of the lower rubber ring, but it can fully meet 
the requirements of the integrated string packer in the 
oil field.
Fig. 17.  Contact pressure distribution curve of the contact part of 
the rubber ring
4  CONCLUSIONS
(1)  Based on the dimensions and production data 
of three different wellbore structures provided 
on site, a multi-factor analysis model for the 
wellbore was established. The temperature, axial 
force of the tubing, and safety factor distribution 
of each part of the wellbore were calculated for 
three different wellbore types in a middle eastern 
oilfield. The analysed data provides a theoretical 
basis for on-site well control.
(2)  According to the finite element model of the 
mechanical distribution of the packer structure 
during acid fracturing established in this article, 
this model can simulate the stress distribution of 
various components in the packer under various 
working conditions during the acid fracturing 
process after the packer is set, and then evaluate 
the adaptability of the packer. It provides a 
reliable theoretical basis for the safety evaluation 
of the packer in the safe production of oil and gas 
fields.
(3)  The three types of wells studied in the article 
can all meet the needs of safety production using 
RTTS packers. However, the use of completion 
packers can lead to insufficient sealing capacity 
and safety production hazards. Therefore, using 
RTTS packers in integrated pipe strings is 
recommended.
(4)  Through a large number of finite element 
calculations and analyses, the packer can 
withstand the wellhead displacement of 5 m³/min 
and wellhead pressure of 50 MPa, which is the 
worst production condition on site. At this time, 
the maximum stress of the packer appears on 
the centre pipe of the packer, so special attention 
should be paid in the production process, and 
the contact pressure on the rubber ring reaches 
30MPa without sealing contact failure.
(5)  In the process of fracturing bottom layer 
stimulation, when the normal temperature 
fracturing fluid injected at the wellhead reaches 
the target formation, it causes the downhole 
string to cool down, causing the axial tension 
of the string to reach 500 kN due to thermal 
expansion. In order to reduce the axial tension of 
wellhead equipment and prevent accidents such 
as wellhead falling, adding expansion joints in 
the string is recommended.
a)                                                               b)                                                               c)                 
Fig. 16.  Strain distribution image of RTTS packer rubber ring; a) X1 vertical well, b) X2 deviated well, and c) X3 horizontal well

Strojniški vestnik - Journal of Mechanical Engineering 70(2024)3-4, 116-127
127 Research on the Adaptability of Packers for Integrated String Fracturing Operations in Low Porosity and Low Permeability Reservoirs  
5  ACKNOWLEDGEMENTS
This work was supported by the Sichuan 
Province Science and Technology Program (No. 
2023NSFSC0427).
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