Introduction
The drilling pipe used in slim-borehole drilling performs well
due to its lower cost and higher efficiency (Zhang et al., 2015). Due to it being the most fragile
component of the whole driving pipe string (Zhou, 2009), the joint thread has
attracted many researchers' interest to improve its sealing quality (Li et al., 2014) and
connection stress, which are the key characteristics and areas of research
emphasis with regard to the drilling pipe (Gong, 1995).
Structure of the drilling pipe.
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Many studies have been conducted on the joint thread according to American Petroleum Institute
(API) standards (American Petroleum Institute, 1995). Tafreshi and
Dover (1993) analysed threaded connections using a finite-element method (FEM) to find the
greatest concentration of stress under the action of axial loading. However, the
contact stress was not reported. They optimized the shape of the teeth of
the threaded connection according to the load distribution. Baryshnikov
and Baragetti (2001) determined the load bearing percentage of each tooth to
calculate allowable loads for API drill string threaded connections under
conditions of bending and axial and combined loading. Griffin et al. (2004) analysed the
stresses in a specific drill pipe connection under axial loading via FEM.
Shahani and Sharifi (2009) built a model contact between mating surfaces of the
threads and analysed this by using ABAQUS 6.6 standard code. The contact pressure on
the contact surfaces and the effect of preload on the stress concentration factor and were investigated. Santus et al. (2009) compared the torsional
strength between two assembling techniques for connection of an aluminium drill pipe to a steel
tool joint. Zhang et al. (2010) studied the taper trapezium joint threads
of a drilling rod with a large hole. An improvement scheme for dual taper and cylinder
seal has been proposed which has successfully tackled the problem of stress
concentration. A double-sealing shoulder was used by Li et al. (2011) to develop a
73 mm diameter directly connected drill pipe without friction welding. The
angular clearance was enlarged, which can satisfy the logging tool and drill-out tool. Zhu et al. (2013) established a drill pipe thread FEM to aid failure analysis and to study solutions in a horizontal-direction drilling project. An XT-M joint developed by Grant Prideco has reached a
high level of technology. Its torsional capability is 70 % higher than the
API's, whose joint airtight capacity can reach 15 000 psi (Zhuang et al., 2015).
The contact model of the drill pipe has been analysed, and
different specifications of the thread have been designed, but these
connections are used in a large-sized oil well. Few studies have been
conducted with regard to modelling the correlation between the contact stress and tightness.
At present, most of the drill pipes which are widely
used in API standard are more than 89 mm in diameter (Shi et al., 2014; Wang et al., 2010). API seldom performs research on small-diameter drill
pipes, as these are unable to meet the requirements of slim-borehole drilling.
In this paper, a 68 mm diameter drilling pipe and its joint are developed.
On the basis of Lame's theory, we create a contact model of the joint thread under different axial force, makeup torque, and pressure difference between inner and outer pipe, which provides a good reference for judging the quality of sealing of the joint thread. The analysis software
ANSYS\Workbench is applied to stimulate the distribution of contact stress and
sealing. A premium condition for drilling has been proposed, which provides a
good theoretical basis for slim-borehole drilling.
Model of the tool joint
Structure of the drilling pipe
Based on the requirements of a slim-borehole drill, the drill pipe is
designed as shown in Fig. 1. The drill pipe consists of pin joint 3, box joint 1 and drilling pipe body 2. The joint
is connected to the pipe body by friction welding. The joints are connected to the pipe body by friction welding and stress-relieving annealing. The concentricity between the joints and pipe body is no greater than 0.4 mm. There is a flat surface
inside and outside the welding position, whose faults are eliminated. The
connector is the cone threaded joint, with a 1 : 30 thread taper and
equilateral trapezoid thread. The overall quenching hardness can be equal to
the hardness of HRC30-35. The sealing cone concentricity of the respective
internal and external threads is no greater than 0.02 mm. The end portion of
the incomplete thread is cut off.
Basic model of the joint for stress analysis.
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Theoretical foundation and assumptions
The thread is the most fragile but important component in the pipe.
According to the theory of thread sealing, the thread's sealing is realized
through the interference fit between the thread's teeth. The sealing quality is
mainly influenced by the stress of the connection of the joint thread, which has
a close relationship between axial load, makeup torque, and the pressure
difference between inner and outer pipe.
The projection of the drill pipe joints at one certain point in the
radial direction is a thick-walled cylinder. Based on the analysis method
of Lame's stress, as shown in Fig. 2, the radial stress and circumferential
stress of some certain point under mud pressure within the drill pipe are
expressed as
σr=R12⋅PiR22-R12⋅1-R22R2σt=R12⋅PiR22-R12⋅1+R22R2.
Likewise, the radial stress and circumferential stress under the mud
pressure outside the drill pipe are
σr=R22⋅PeR22-R12⋅1-R12R2σt=R22⋅PeR22-R12⋅1+R12R2.
According to Lame's theory, the radial displacement at any point with a
radius of R can be expressed as
u=1-μE⋅RR12Pi-R22PeR22-R12+1+μE⋅R12R22Pi-PeRR22-R12.
Force diagram of thread A.
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Contact mechanical model
Makeup torque influenced by the axial force
A drilling string formed by a pipe connection will be influenced by different
axial forces when in use – for example, gravity, drilling
pressure, and friction between the pipe and the borehole wall. The force diagram of the
screw thread is shown in Fig. 3. Thread A, intercepted from the box
connector, is selected to make a mechanical analysis. Due to the spiral
structure, the axial force will be decomposed, resulting in the box
connector thread being subjected to, for example, the action of tangential forces and friction of the
threaded surface.
Force analysis on a section of box thread A, and according to the
balance of force conditions, can be expressed as
f=μ⋅N=μ⋅Ffsinβ+FbcosβFfcosβ+Fbsinβ=f.
To finish the above formulas, the tangential force Ff can be obtained
because of the axial force,
Ff=μcosβ+sinβcosβ-μsinβ⋅Fb=K⋅Fb.
From the analysis of Eq. (5), we can see that the axial force of the threads
has a direct impact on the makeup torque, and there is a linear
correspondence between them. The connector thread's contact surface's
friction coefficient is about 0.08 and the thread angle is 3∘,
which allows the contact surface to produce self-locking, and there
will be no relative slide due to the axial tension for the drill pile. The
effect that axial force produces is similar to the effect of makeup torque;
the analysis of the thread contact force under the action of axial force can
be converted to the analysis of makeup torque, and subsequent analysis of
torque contains the influence factors of axial force.
Contact mechanical model of the joint
The drill pipe thread is a taper thread, and the inner radius of the box
joint is smaller than the outer radius of the pipe body for the radial
joints at a certain point (such as tolerance or machining error), and the surface
contact pressure is generated at the contact interface. A schematic diagram
of the connection between the box and the pin joint is shown in Fig. 4.
Let Ra be the inner diameter of a pin joint, Rb the outside diameter
of a pin joint (which is also the inner diameter of a box joint), and Rc the
outside diameter of a box joint, and the external pressure can be described
as Pe = 0. According to Eq. (3), the radial displacement of the inner
surface of the box connector is expressed as
u1=Rb⋅PbE⋅Rb2+Rc2Rc2-Rb2+μ.
According to Eq. (3), the inner drilling mud pressure Pi = 0, and the
radial displacement of the outer surface of the joint is
u2=Rb⋅PbE⋅Ra2+Rb2Ra2-Rb2+μ.
Because the increment of the inner diameter of the joint and the reduction
of the outer diameter of the joint is equal to the original tolerance value,
the existing constraint is
u1+u2=δ.
By combining Eqs. (6)–(8), the surface contact pressure between the pin and the
box joint can be obtained by simplifying:
Pb=EδRb2-Ra2Rc2-Rb22Rb3Rc2-Ra2.
Connection diagram of the box and the pin joint.
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The circumferential stress model of joint
When fastening the screw, radial contact pressure is generated in external
threads. From Eq. (2), the maximum axial stress occurred in the inner wall,
and according to Lame's theory, the axial force and the circumferential
stress generated by fastening the pin joint external thread can be expressed
as
R1=RaR2=Rbσt1⋅max=-Rb2⋅PbRb2-Ra21+Ra2Ra2=2Rb2⋅PbRb2-Ra2.
A negative sign of the circumferential stress is compressive stress. For the
box joint, contact pressure is uniform internal stress. From Eq. (1), the
maximum circumferential stress is on the inner wall; according to Lame's theory, the axial force and the circumferential stress generated by
fastening the box joint internal thread can be expressed as
R1=RaR2=Rbσt2⋅max=-Rb2⋅PbRc2-Rb21+Rc2Rb2=Rc2+Rb2Rb2-Ra2⋅Pb.
By inserting Eq. (9) into Eq. (11), the circumferential stress generated in the box
joint internal thread can be obtained:
σt2max=EδRb2-Ra2Rb2+Rc22Rb3Rc2-Ra2.
In the above formula, σt2 is the axial stress of the thread on
the box joint that is produced (Pa).
When the drill pipe is subjected to the pressure of the internal mud
pressure Pi, the combined body of the pin joint and the box joint is
subjected to the outward expansion force, thereby causing the
circumferential stress. According to Lame's theory, using the
circumferential stress on the outer surface of the joint and the
circumferential stress on the inner surface of the box joint to individually calculate the surface contact pressure Pc, which is caused by
internal pressure between box joint and a pin joint mating surface, the
corresponding force is equal in magnitude and opposite in direction; thus
σti=Ra2⋅PiRc2-Ra21+Rc2Rb2σte=Rb2⋅PcRc2-Rb21+Rc2Rb2σti=σte.
To complete Eq. (13), the contact pressure can be obtained under the action of mud
pressure in the drill pipe,
Pc=Ra2Rb2⋅Rb2-Rc2Rc2-Ra2⋅Pi.
Model and criterion of the sealing joint
The circumferential stress obtained from the above analysis is superimposed; it is expressed as tensile stress when the outcome is positive. The
following conditions must be satisfied in order to avoid leaking from drill pipe joints. Firstly, a rational stress distribution must be on the
joints, which means that the sum of the axial force, makeup torque, and the
contact pressure caused by the difference between the mud in the inner and
outer pipe must be larger than the difference between the inner and outer pipe.
Secondly, the stress distribution must be kept balanced to ensure a larger
sealing area. Therefore, the relationship can be expressed as
Pb+Pc≥|Pi-Pe|.
Material properties.
Component
Materials
Young's
Poisson's
Tensile
Yield
Hardness
modulus
ratio
strength
strength
(HB)
(N mm-2)
(MPa)
(MPa)
Box joint
42CrMo4
205 000
0.3
1080
930
217
Pin joint
42CrMo4
205 000
0.3
1080
930
217
Finite-element model (L – left shoulder; M – middle screw; R – right shoulder).
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Finite-element analysis
Material properties of joints
Material properties given in Table 1 are linear and isotropic as modal analysis
ignores nonlinearities. Young's modulus and density for a modal analysis must
be specified.
Finite-element modelling
A parametric 3-D model can be a better choice to comprehensively reflect the
situation of the joint. Considering the smaller thread's lead angle and that the
main research emphasis of this paper focuses on the relationship of the helical tooth's
strain and the sealing quality, the influence of the thread's
lead angle can be ignored when modelling, which makes it possible to
establish a 2-D model to simulate the joint.
In this paper, the contact interference is applied to simulate the makeup
state. Friction torque of each tooth buckle can be obtained through multiplying the contact pressure on the interference surface by the distance between the contact surface and the pipe centre. The equivalent makeup torque can be obtained by
integrating all the friction torques of the buckle on the teeth. The value
of the tooth interference of threads can be calculated on the basis of the
number of turns on the buckle, as well as thread taper, pitch, tooth type angle and
other parameters. Based on the API's common method of calculating the radial
movement δr, the pin buckle to box buckle can be expressed as
follows:
δr=0.5T×ΔL=0.5T⋅n⋅P=0.5T×θ360×P.
Interferences of contact surfaces.
Addendum
Bearing
Guide
Shoulder
surface
surface
surface
Interference (mm)
0.0100
0.0025
0.0025
0.6000
Element selection and meshing
Solid structural steel defined as 42CrMo4 is used for modelling of different
components, i.e. the box joint, pin box and drilling pipe body. For both the
box joint and pin box, “manual contact region” contact elements are used;
therefore, both of the threaded surfaces are of the same element type.
Two-dimensional “manual contact region” contact elements, in combination
with the command CONTACT for pin joint surface and TARGET for the box joint surface are used
between the box joint and pin joint surface to simulate contact distribution.
Body-sizing meshing is used throughout in the regions of the high-stress
distribution box, i.e. box joint faces and pin joint faces. Front areas
of the model are meshed first and then the same meshing pattern of meshed
area is swept over the volumes. The command “Refinement” is used for the
meshing with 3 × amplification. The FEM of the
joint thread fitting is shown in Fig. 5.
Boundary conditions and loading
In order to eliminate the boundary effect in simulation, the pipe length in the model should be 2 times longer than the length of the drill pipe end to the thread disappearing point. The equivalent torque and
axial force are applied by setting the contact interference or applying a preload.
δns=δr⋅cosαδnl=δr⋅sin14.5∘δnd=δr⋅sin14.5∘-Δ
Through the above formulas, the amount of interference of the thread of each
surface can be calculated by setting the offset to define the size of the
contact between the unit and the target unit in ANSYS in a real constant
offset, which is the value of the force. Using the software, the axial tension and internal
pressure can be simulated in the form of uniform force, which can be loaded directly onto the threaded model. In the three
different mating connector states, including finger-tight, tight state
machine and state interference, the tension and the pressure of 0–300 kN are
respectively loaded onto a pair of mating threaded joints per 50 kN.
The stress distribution and air tightness are studied according to the preceding model.
The 68 mm diameter drill pipe is mainly used in the well with the maximum
depth of 2000–2500 m. The maximum axial tension and compression load
is calculated at about 300 kN on account of its weight and length of the l strings, which are selected as the parameters used. In addition, the data are
collected with a gradient of 50 kN to better reflect stress.
Results and analysis
Pipe joints and its connection states
There are 12 screw threads on the joint. Three different basic states
will exist during tightening of the pipe joints. As shown in Fig. 6, for
connection state A, the makeup torque is relatively small, resulting in a
certain gap existing in the thread shoulder. In connection state B, the
thread shoulders are in contact with each other but with no pressure
generated. In connection state C, the thread should also be in contact and the pressure can be very large. The three different states
can represent three different practical situations to describe the joint's
strength and tightness.
Stress distribution of pipe joints
Tensile force will be exerted on the pipe while dealing with problems, while
pressure will be exerted on the pipe during drilling. Based on
experience with simulation and real practice, for the pipe 68 mm diameter, the maximum tensile stress is 250 kN, and the maximum pressure is 150 kN. Therefore, there are
corresponding changes under three different connection states,
with the force changes in the range of 150–250 kN. The selection of a pipe can
be determined on the basis of the changes.
Connection states of the joints.
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Joint stress and strain under allowable tensile force: (a) joint
stress in state A, (b) joint strain in state A,
(c) joint stress in state B, (d) joint strain in
state B, (e) joint stress in state C and (f) joint strain
in state C.
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Joint state under allowable tensile force
When the axial tension reaches 250 kN in the joint's finger-tight connection
state, the maximum contact stress of the thread reaches 11.43 MPa. The left
sealing surface contact stress reaches 397.24 MPa when the drill machine is
in a state that is tight but under interference. The left sealing surface contact stress
reaches 397.24 MPa when the drill machine is in an interference state. In Fig. 7,
it is shown that, with the increase in torque on the buckle, contact stress
between the pin and the box connectors will correspondingly increase.
Joint state under allowable yield force
When axial tension reaches 150 kN in the joint's finger-tight connection
state, as shown in Fig. 8, the maximum contact stress of the thread reaches
6.13 MPa. The left sealing surface contact stress reaches 488.6 MPa when the
drill machine is in a state that is tight but under interference. The left sealing
surface contact stress reaches 931.6 MPa when the drill machine is in an
interference state. Similarly, it is shown that, with the increase in torque
on the buckle, contact stress between the pin and the box connectors will
also correspondingly increase.
Stress change principle with three different connection types
As shown in Fig. 9, in comparison with the influence axial load, the
influence of the connection type is more obvious. This shows that the
makeup torque is the key factor that determines the sealing quality and
joint strength. When the thread is in a finger-tight state, the thread
engagement is unstable, especially when tensile force is exerted. When
the machine changes gradually to the interference state from the tight
state, the contact stress is larger on both ends of the shoulder but the
contact stress in the middle of each thread is generally relatively stable.
Joint stress and strain under allowable tension force: (a) joint
stress in state A, (b) joint strain in state A,
(c) joint stress in state B, (d) joint strain in
state B, (e) joint stress in state C and (f) joint strain
in state C.
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Stress change principle with different connection types: (a) tension
stress in state A, (b) tensile stress in state A,
(c) tension stress in state B, (d) tensile stress in
state B, (e) tension stress in state C and (f) tensile
stress in state C.
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When the drill bit is in connection mode A, too much strain will
generate on the thread, resulting in structural damage after axial tension
reaches 251 kN. When in mode B, the contact stress for each part of the
joint is always within the stress limits, but with the increase in the
makeup torque, the contact stress of the sealing surface will further
increase. When in mode C, and the stress exceeds 150 kN, the local stress
will exceed the yield limit. The joints' carrying capacity will decrease during the
loading process because the initial stress is too large, which causes the
bearing capacity of the joint on the axial pressure to be less than the axial
tension. At the same time, the thread will produce plastic strain, affecting the
airtightness. In addition, the overall strength of the joints will also
decrease under the dynamic loading.
All in all, the interference fit between the threads significantly increases
the overall strength of the joint effect, but the contact pressure is not
always better. When taking the limitations of the material itself into
account, the following condition must be greater than the pressure difference
inside and outside the drill pipe, which additionally should remain stable
during operation.
Calculation of the premium makeup torque
The scale model
The law of thread stress changing in different axial loading is found through the model simulation mentioned above. It is concluded that
we can apparently get more data through simulation experiments through
increasing the number of teeth. Some errors exist between the
actual situation and the simulation. Therefore, the scale model shown in Fig. 10 is introduced again to calculate the makeup torque.
The scale model.
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Connection state under optimum makeup torque: (a) stress under
optimum makeup torque and (b) strain under optimum makeup torque.
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Model exposure settings, mesh, interference, etc. are set with reference
to the original model. The working environment is fairly complex during drilling.
A sudden increase in torque will probably occur if there is friction
between the drill pipe and the borehole wall or if faults occur. In this
case, the up-torque is too large, which will result in the initial contact
stress exceeding the limit, causing plastic deformation and affecting the
joint's airtightness. Therefore, the safety coefficient should be introduced to
provide a safe elastic stress range. In order to get the best deduction, the reference
value for the maximum contact stress safety factor is given as 620 MPa, whereby the amount of thread interference can be drawn in the radial direction.
Interferences of the contact surfaces are shown in Table 2. The values of interferences of the axial and the bearing surfaces can be
calculated through the radial values. Therefore, we can get the distribution of the
stress and strain under optimum makeup torque, which are shown in Fig. 11. We
can see the stress distribution has more uniform than aforementioned states, and
it must be kept balanced to ensure a larger sealing area.
Composition of the optimum makeup torque.
Items
Position
Friction
Centre
Torque
Total
force
distance
(N m-1)
torque
(kN)
(mm)
(N m-1)
Left shoulder
Contact surfaces
2.88
32.10
92.45
492.40
Left sealing surface
Contact surfaces
14.65
27.30
399.95
1st screw thread
Addendum
5.68
29.50
167.56
469.97
Dedendum
8.55
27.62
236.15
Bearing surface
2.32
28.56
66.26
2nd screw thread
Addendum
5.05
29.74
150.19
499.76
Dedendum
8.34
27.86
232.35
Bearing surface
4.07
28.80
117.22
3rd screw thread
Addendum
5.21
29.98
156.20
515.15
Dedendum
8.32
28.10
233.79
Bearing surface
4.31
29.04
125.16
4th screw thread
Addendum
5.18
30.22
156.54
526.60
Dedendum
8.45
28.34
239.47
Bearing surface
4.46
29.28
130.59
5th screw thread
Addendum
5.47
30.46
166.62
548.84
Dedendum
7.92
28.58
226.35
Bearing surface
5.28
29.52
155.87
Right sealing surface
Contact surfaces
2.79
30.70
85.65
267.94
Left shoulder
Contact surfaces
4.94
36.90
182.29
Total: 3320.66 Nm
The stress distribution is mostly influenced by torque, which determines the
stress magnitudes on different joint contact surfaces, affecting the
strength of the connection and sealing joints. The torque is obtained from
the values of friction force and centre distance in simulation, and it is
accumulated from three different components: the shoulder, sealing surface
and screw thread. As shown in Table 3, the makeup torque will reach
3320.66 N m-1 when in the premium state, where the torque
between the buckle teeth is 2560.32 N m-1, and the torque between
the sealing surface and the shoulder is 760.34 N m-1. The torque in each case takes up
77 and 23 % of the overall makeup torque, respectively, which means
that it plays a significant role in keeping the sealing quality of the pipe.
Conclusions
The connection type – A, B, and C – has a greater effect on the
contact stress than the axial loading's effect, which means the makeup
torque is the key factor that determines the joint's strength and its sealing quality.
The joints' double shoulders can significantly boost the thread's
overall stability because the shoulder reduces the phenomenon of stress
concentration and takes a part of axial force, which enhances the
thread's overall sealing quality and axial strength.
With the increase in the makeup torque, the maximum contact stress
gradually changes from the thread's teeth to the shoulders on both ends,
which enhances the overall sealing quality but weakens the structural
strength. Plastic deformation occurs on some of the thread, which
exceeds the allowable load.
When the makeup torque reaches up to 3320.66 Nm, the contact stress of
the sealing shoulder is greater than the pressure difference between the
inner and outer pipe. The even distribution of the joint thread's stress
contributes to the pipe joint's sealing and overall strength, which
provides a good reference for selecting the parameters of the drilling tool's makeup.