Journal of Petroleum Science and Engineering 133 (2015) 328–334
Contents lists available at ScienceDirect
Journal of Petroleum Science and Engineering
journal homepage: www.elsevier.com/locate/petrol
Worn pipes collapse strength: Experimental and numerical study
N.M. Moreira Junior a,b, A.A. Carrasquila b, A. Figueiredo c, C.E. da Fonseca a,n
a
b
c
Petrobras, Brazil
North Fluminense State University, Brazil
Vallourec do Brasil, Brazil
art ic l e i nf o
a b s t r a c t
Article history:
Received 13 March 2015
Received in revised form
17 June 2015
Accepted 22 June 2015
Available online 23 June 2015
After drilling an oil or gas well the open well-bore is usually cased with steel pipes, which must be
properly designed to support all predicted loads (pressures) along its service life. Such casing can be
subject to material loss after deployed. One of the reasons for material loss comes from that the well-bore
is drilled deeper with rotating drill pipes after casing installation. The interaction between the rotating
drill-pipes and casing inner wall leads to the casing wear, which can significantly reduce the wall
thickness at particular regions. Casing designers usually assume evenly distributed inner casing wear.
Under this assumption the remaining wall is constant and the predictive burst and collapse strength
equations presented by standards are applied, but resulting in much lower strength values than the real
case.
Few authors studied the pipe remaining strength under more realistic wear assumptions. Kuryama
et al. presented an analytical formulation based on pipes with circular cross-section and an equivalent
wall thickness eccentricity to simulate material loss over an angular section. Sakakibara et al. presented a
model for collapse strength prediction of worn pipes with initial geometric imperfection (cross-section
ovalization) and constant pipe wall loss within a given angular section. None of them combined real
initial (ovalization and eccentricity) and produced (casing wear) geometric imperfections. This paper
presents the full scale experimental set up and results for thin and thick walled intact and worn pipes
under applied external hydrostatic pressure. The test procedure included pipes’ geometry mapping and
wear production to match real conditions. The specimens were collapsed and numerical analysis based
on finite element analysis and an analytical model were carried out to simulate physical conditions. The
numerical results were then extended to a broad range of pipes with different geometries and steel
grades representative of drilling well applications. As expected, one developed model developed predicts
really well thin walled pipes, but not for thicker ones.
& 2015 Elsevier B.V. All rights reserved.
Keywords:
Worn pipes
Collapse
Experimental
Numerical
1. Introduction
After drilling an oil or gas well the open well-bore is usually
cased with steel pipes, which can have from hundreds to thousands meters of length. The pipes are installed together through
threaded connections and are subject to a harsh downhole environment. A proper casing design has to address possible chemical reactions or mechanical interactions leading to pipe wall
material loss (as corrosion and erosion), and the remaining pipe
wall thickness must support all predicted loads (pressures) along
the well life. If the material is properly designed, corrosion rate can
be neglected.
Usually the well-bore is drilled deeper with rotating drill pipes
inside steel casing after it is installed. The interaction between the
n
Corresponding author.
E-mail address: cefonseca@petrobras.com.br (C.E. da Fonseca).
http://dx.doi.org/10.1016/j.petrol.2015.06.024
0920-4105/& 2015 Elsevier B.V. All rights reserved.
rotating drill-pipes and casing inner wall can lead to the so-called
casing wear, which can significantly reduce the wall thickness at
particular regions. Assessing properly the strength of the worn
pipe can be the key to achieve a feasible technical and economical
well design. Casing designers usually assume evenly distributed
inner casing wear. Under this assumption the remaining wall
thickness is constant and equal to minimum remaining wall.
Predictive burst and collapse strength equations presented by API
5C3 (API BULL, 1994) or ISO TR 10400 (ISO TR, 2007) are applied.
Assuming the remaining wall thickness as the lowermost possible
results in the lowermost strength values.
Few authors studied the pipe remaining strength under more
realistic wear assumptions. Some authors developed analytical
models to account the wear at inner wall to evaluate the burst
strength (Wu and Zhang, 2005; Shen and Beck, 2012), or to evaluate the stress concentration of plain dents due to mechanical
damages in steel pipes subjected to internal pressure (Pinheiro,
2006). Regarding to the remaining collapse strength for worn
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
329
Fig. 1. Sketches of wear mechanism and casing cross-sectional worn geometry: (a) rotating drill-string connection (tool joint) causing a wear groove located only at one side
of inner wall; (b) pipe circular cross-section with outer radius ro and inner radius ri . The circle representing the inner wall presents an offset t w , which is chosen to match an
equivalent geometry of the worn area (modified from Kuriyama et al., 1992). Dashed line represents the real casing wear and (c) constant wear geometry of thickness tmin for
a given circular sector (modified from Sakakibara et al., 2008).
pipes, Kuriyama et al. (1992) presented an analytical formulation
based on pipes with perfectly circular cross-section and an
equivalent wall thickness eccentricity to simulate material loss
over an angular section (Fig. 1(b)). Sakakibara et al. (2008) presented a model for collapse strength prediction of worn pipes with
initial geometric imperfection (cross-section ovalization) and
constant pipe wall loss within a given angular (1-(c)). Though the
latter presents good match with experimental results, the produced wear does not match the geometry usually produced by
rotary pipes inside casings.
To accurately predict collapse strength of worn pipes, the initial
(cross section ovalization and wall thickness eccentricity) and resulting (casing wear) geometrical imperfections must be included
in any analysis. This paper presents the full scale experimental set
up and results for thin and thick walled, intact and worn pipes,
under applied external hydrostatic pressure. The test procedure
included pipe geometry mapping, before and after producing
wear, to account both initial and produced (wear) geometrical
imperfections. Casing wear was produced to match real conditions. The specimens were collapsed and numerical analysis based
on finite element analysis and model developed by Sakakibara
et al. (2008) were carried out to simulate physical conditions. The
numerical results were then extended to a broad range of pipes
with different geometries and steel grades representative of drilling well applications.
Table 2
Typical material properties for both pipes (which are different steel grades). The
values inside parentheses are in psi.
Specimen series
E - MPa (psi)
7
3 10 (207,532)
3 107 (207,532)
80
90
so - MPa (psi)
ν
1070 (155,215)
1002 (145,455)
0.29
0.29
effect of material loss and collapse mechanism (elastic versus
“plastic” collapse). With full-scale geometry it was possible to
build a representative damage at the inner pipe wall.
The samples prepared from pipe type 1 were called series 80,
and from pipe type 2 series 90 respectively. Samples were prepared long enough to avoid end effects during collapse tests.1
Samples geometry (do, t ) were gathered before and after machining (to produce worn pipes). The geometrical data were
gathered from measurements over 12 equally spaced cross sections spanned by 200 mm, called sections A till L, depicted at
Fig. 2. Typical values are presented in Tables 3 and 4 before machining, and Table 5 for intact (non-machined) samples. These
data are representative of the collapsed cross sections during tests.
The initial ovalization was evaluated by Eq. (1) below, where
⎛ ⎞
⎛ ⎞
D = max ⎜do ⎟ and d = min ⎜do ⎟ represent the maximum and minido ∈ : ⎝ ⎠
do ∈ : ⎝ ⎠
mum measured outside diameter at a given cross-section :
{:≔A , B… , L}:
D−d
× 100%
D+d
2. Material and methods
▵=
2.1. Full scale samples preparation
It is important to remember that geometry mapping was done
before and after machined (see Fig. 3). Herein the pipes’ types
1 and 2 were sampled and labeled according machined (label 83
and 93 respectively) or non-machined (84 and 94 respectively).
The machined samples from pipe type 1 (namely 83-1, 83-2, and
83-3) were prepared in order to present maximum wall thickness
reduction of 20%. The machined samples from pipe type 2 (namely
The full scale physical tests were addressed to collapse specimens prepared from two-representative pipe configurations:
(i) representing thick pipes (with do/t = 13.5, herein called type 1),
and (ii) representing thin pipes (with do/t = 20.3, type 2). Both
configurations are usual for oil and gas industry (Table 1). Intact
and worn samples were prepared making possible to compare the
Table 1
Nominal geometry of chosen pipes to evaluate hydrostatic collapse loads (measures
in parentheses are in inches).
Pipe type/specimen series
do -mm (in.)
t-mm (in.)
do/t
1-80
273 (103/4 )
245 (95/8)
20.24 (0.797)
13.5
11.99 (0.472)
20.3
2-90
(1)
1
The samples dimensions criteria to collapse tests were followed as recommended by ISO 10400 (ISO TR, 2007). According to these recommendations,
the samples prepared for tests shall have a minimum length in relation to the outer
diameter of the sample. For pipes with outer diameter lower or equal than 95/8 in.,
the sample shall have a length of at least 8 times its diameter. For pipes with
outside diameter of 103/4 in. or larger, the ratio is at least 7 times the outer diameter. These limits are established for the purpose of eliminating the influence of
the ends in the collapse strength. Small samples present higher stiffness and
therefore are not representative of collapse strength values. From Fig. 2 it is possible to see that the length is at least 10 times the outside diameter.
330
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
Table 4
Typical geometric values for samples series 90 (prior machining), in mm, with
⎛⎞
⎛⎞
max ⎜⎟ and min ⎜⎟ representing the maximum and minimum outside diameter and
()∈ : ⎝⎠
()∈ : ⎝⎠
wall thickness at section : . The sections presented are the ones where the collapse
occurred.
Fig. 2. Pipe geometry mapping sketch. In the left cross-sections labeled from A to L
spanned by 200 mm where diameter and wall-thickness measurements were
gathered. In the right the cross-section locations from where outside diameter and
wall thickness were measured, with shaded area representing the worn region.
Table 3
Typical geometric values for samples series 80 (prior machining), in mm, with
⎛⎞
⎛⎞
max ⎜⎟ and min ⎜⎟ representing the maximum and minimum outside diameter and
()∈ : ⎝⎠
()∈ : ⎝⎠
wall thickness at section : . The sections presented are the ones where the collapse
occurred.
Sample 83-1
F
G
H
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
275.0
275.44
275.14
⎛ ⎞
min ⎜do ⎟
do∈ : ⎝ ⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
274.49
274.44
274.412
0.093
21.99
0.182
21.40
0.186
21.39
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
20.29
20.26
20.57
Sample 83-2
G
H
I
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
275.4
274.9
275.4
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
274.2
274.1
274.6
0.218
20.99
0.146
20.96
0.145
21.14
20.56
20.69
20.31
Sample 93-1
H
I
J
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
246.93
246.52
246.77
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
246.07
246.11
246.04
0.17
13.26
0.08
13.40
0.15
13.38
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
11.84
11.79
11.89
Sample 93-2
F
G
H
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
246.14
246.53
246.46
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
245.94
245.81
245.93
0.049
12.77
0.146
12.93
0.108
13.05
12.14
12.30
12.30
do∈ : ⎝
do∈ : ⎝
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
93-1, 93-2, and 93-3) were prepared to present maximum wall
thickness reduction of 30% . The worn geometry was mapped to
guarantee the maximum wall thickness in accordance with the
plan.
inside a cap attached to the chamber body by bolts, as shown in
Fig. 5. It is possible to see that the pipe ends located inside the caps
were free to rotate under applied external pressure, but not for
applied internal pressure.
Rubber and metal seal rings are inserted over the pipe end
which is outside the chamber. A ring is screwed behind the rings
completing the sealing mechanism. Inner pipe side is subject to
atmospheric pressure at all times.
The collapse test consisted of slowly pressure increase to avoid
pressure waves inside the chamber. The tests’ sequence was to test
first two intact and then two machined samples. If the results
presented great difference, a third sample could be prepared and
tested. The pipe collapse is defined as the sudden change of its
cross sectional shape. After the pipe collapse, the shape change
results in volume increase between the pipe specimen and the
pressure chamber, which leads to a sharp system pressure drop.
The collapse pressure is then defined as the maximum pressure
during the test, which occurs exactly before the pressure drop.
2.2. Steel grade properties
2.4. Numerical model
The nominal yield strength so (according to Iso, 2011) of pipes
type 1 and 2 are 965 MPa (140 ksi) and 861 MPa (125 ksi) respectively. But tensile tests for both pipes were conducted based
on ASTM (2007) procedures, and values for Young Modulus E,
yield strength so and Poisson ratio ν, and plastic deformation were
obtained once numerical analysis using finite element method
were done using isotropic hardening. Typical values for elastic
properties are presented in Table 2 and characteristic stress–strain
curve is presented in Fig. 4. Yield stress was obtained following
specifications of Iso (2011).
Numerical models were built using the commercial software
Abaqus v.6.1014 based on the finite element analysis. The geometry was sketched based on the geometric mapping of the
samples, considering actual external diameter, wall thickness, and
constant initial ovalization overall length. Initial ovalization was
taken as geometric average of ovalization values presented in Tables 3–5. For each tested sample one model was built representing
its geometric and material properties.
The worn geometry assumption was based on one inner
mandrel with 5.5 in. intersecting the original pipe along the full
sample length. This consideration leads to a reduced wall thickness section in the cross sectional plane equal to approximately
36°. So the geometry were sketched applying material loss within
36° in the cross sectional using a cosine law. Considering the two
symmetry planes of this problem (x – y and x – z as depicted in
Fig. 6), it was possible to reduce the model size by one quarter of
original sample dimensions. The worn area was thus constructed
do∈ : ⎝
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
2.3. Pressure test procedure
The samples were collapsed under hydrostatic pressure in
pressure chambers as depicted in Fig. 5. The pipe specimen free
span subject to hydrostatic external pressure was a little bit
smaller than the total specimen length. Pipe ends were located
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
331
Table 5
⎛⎞
⎛⎞
Data from intact pipes in mm, with max ⎜⎟ and min ⎜⎟ representing the maximum
()∈ : ⎝⎠
()∈ : ⎝⎠
and minimum outside diameter and wall thickness at section : : (a) pipe type 1;
(b) and (c) pipe type 2. The sections presented are the ones where the collapse
occurred.
(a)
Sample 84-1
G
H
I
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
275.26
275.21
275.17
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
274.46
273.45
274.45
0.146
21.55
0.321
21.80
0.129
21.62
20.22
20.07
20.44
E
F
G
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
246.17
246.29
246.27
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
246.10
246.15
245.93
0.028
13.33
0.077
13.15
0.069
13.28
11.73
11.85
11.88
E
F
G
⎛ ⎞
max ⎜do ⎟
do∈ : ⎝ ⎠
246.33
246.29
246.76
⎛ ⎞
min ⎜do ⎟
⎠
▵ (%)
⎛ ⎞
max ⎜t ⎟
t∈ : ⎝ ⎠
246.12
246.06
245.17
0.042
13.03
0.046
13.18
0.119
12.87
11.97
12.02
12.43
do∈ : ⎝
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
(b)
Sample 94-1
do∈ : ⎝
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
(c)
Sample 94-2
do∈ : ⎝
⎛ ⎞
min ⎜t ⎟
t∈ : ⎝ ⎠
Fig. 3. Worn sample after machining.
as 18° only, being located at the x – z plane. Also the x – z plane
⎛ ⎞
contains the maximum measured outside diameter (D = max ⎜do ⎟),
do ∈ : ⎝ ⎠
⎛ ⎞
while the x – y plane contains the minimum one (d = min ⎜do ⎟) of
do ∈ : ⎝ ⎠
each sample, as presented in Tables 3–5. The pipe ends boundary
conditions were set to be rotation free. The samples ends outside
the pressure chamber were not simulated.
A three dimensional quadrilateral element was used to build
Fig. 4. Stress–strain characteristic curve. The yield stress so is very close to ultimate
stress su, being possible to use an elastic-perfect plastic material to represent it.
the mesh. This quadrilateral element has eight nodes, with linear
interpolation function and reduced integration (C3D8R). Mesh
with two, three, four, and five elements at the wall thickness were
built. In the longitudinal direction, 160 were always used (remember that only half length was simulated). In circumferential
direction, 40 and 50 elements were tested. After some simulations,
the minimum requested number of elements along wall thickness
332
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
Fig. 5. On top: sketch of pressure chamber with pipe specimen. On bottom: pictures from seal mechanism. Pipe specimen free span subject to hydrostatic pressure is a little
bit smaller than the total specimen length. Pipe ends are located inside a cap attached to the chamber body by bolts. The ends located inside the cap are free to rotate under
applied external pressure, but not for applied internal pressure. Seal rings are located between the chamber body and the cap.
Fig. 6. Worn pipe model. On the top left the two symmetry planes defining the model and in the right the central cross-section meshing with worn area. In the bottom left
and right, inelastic stress for model A-II and model H-V respectively. Applied pressure is lower than collapse pressure in both cases.
(radial axis), circumference (hoop axis), and z-axis were 3, 40 and
160 respectively. Numerical results with only two elements in wall
thickness were considerable higher then others. These results also
presented good correlation to test results (and are presented in the
next section). The collapse pressure was achieved under static
analysis arc-length methodology (Riks, 1979) to assess the bifurcation point under static load. Besides the overall collapsed pipe
geometry was closely recovered, the post-buckling behavior was
not the focus of this study.
After choosing external diameter, wall thickness, initial ovalization, and logarithmic stress–strain inelastic curve for both materials, one simple computational code in Python1.6 was written to
build the model for all simulations. One example of the final model
in the x – y plane view is presented in Fig. 6, including principal
axis and worn area.
3. Results and discussions
3.1. Full scale tests and numerical simulation
All the samples were subjected to hydrostatic external pressure
and the collapse pressures are presented in Table 6. During tests
one sample did not collapse and the test was canceled because the
applied pressure was close to chamber limits. Also in Table 6 results from numerical simulation and comparison with real collapse
pressures are presented. As can be noticed that the numerical simulation is capable of evaluating really well the collapse pressure
once the geometry and material properties are fully mapped. But
during fabrication both pipe geometry and material properties
present variation. For oil and gas upstream activities the tolerances
described by API (2005) are widely accepted. To develop models
for pipes in which the geometry and material behavior were not
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
Table 6
Collapse pressure test and numerical results. Values in parenthesis are in psi.
Sample
Test - MPa (psi)
Model - MPa (psi)
error (%)
84-1
83-1
83-2
94-1
94-2
93-1
93-2
151.1 (21,929)
121.8 (17,666)
123.9 (17,970)
64.7 (9384)
64.1 (9296)
42.0 (6092)
39.9 (5800)
151.5 (21,982)
115.8 (16,795)
123.7 (17,949)
63.5 (9207)
64.7 (9390)
43.5 (6313)
40.9 (5930)
0.24
4.93
0.11
1.88
1.01
3.62
2.24
gathered, some assumptions based on API (2005) were adopted.
The experimental tests were used to choose a geometry approach
and minimal mesh to accurately represent the problem, and these
approaches were used as basis to build geometry and mesh for a
broad number of pipes. The geometry and material properties for
all samples presented values above minimal limit values established by API (2005). It is worth to notice the well behavior for the
yield stress in all tested samples. Other properties as Poisson's
ratio and elastic modulus are very consistent with general steel
knowledge. The adopted values from now on are 0.29 and
207.5 GPa.
3.2. Parametric study
The models to perform the parametric study were built for a
wide range for do/t ratio, based on real pipes usually applied in the
industry with well established geometric and materials properties.
Table 7 presents main geometrical and material properties chosen
to build these models. Ovalization was established as 0.18%, as per
data used in series 90 tests.
The models were named with capital letter (A to H). For each
geometric and material combination five models were built
varying the final wall thickness, simulating different worn pipe
conditions. The models representing the new pipe were labeled as
A-I, B-I, etc. The most critical models were built with 40% of
maximum wall thickness loss, and were named as A-V, B-V, etc.
The other three models per chosen pipe presented 10%, 20%, and
30% of maximum wall thickness loss, totalizing 45 numerical results for collapse pressure of new and worn pipe for three different
steel grades and do/t ratio. Table 8 summarizes the collapse pressures results for each combination (models A to I) based on the
maximum wall thickness loss (0% up to 40%) and yield strength.
The easiest analysis is to compare the residual collapse strength
for each model based on the original collapse strength for a new
pipe (without any worn or defect). Such analysis can be seen in
Fig. 7, where the results from Table 8 were plotted together and in
the Y-axis a normalization result was applied, presenting the remaining collapse pressure normalized by the original collapse
pressure of the intact respectively pipe. For higher steel grades
(higher yield stress represented by models from A to G) just one
model presented a different behavior for de-rated collapse
Table 7
Model main properties for parametric study.
Model
so (MPa)
do/t
Δo
A
B
C
D
E
F
G
H
I
1002
1070
1002
1070
1002
1002
1070
517
517
11.19
13.49
13.49
16.00
16.00
17.66
20.39
11.19
20.39
0.18
0.18
0.18
0.18
0.18
0.18
0.18
0.18
0.18
333
Table 8
Numerical collapse pressure for different models (values in MPa).
Model I - 0% wear II - 10%
wear
III - 20%
wear
IV - 30%
wear
V - 40% wear
A
B
C
D
E
F
G
H
I
145.1
114.4
109.2
75.8
81.3
57.2
40.6
97.8
33.9
124.1
92.7
88.7
65.9
63.6
48.6
35.3
88.3
29.6
108.1
79.8
76.8
54.2
51.8
42.3
29.1
79.0
25.6
190.9
151.5
141.2
98.8
97.2
75.3
52.2
133.2
48.5
168.5
130.6
122.3
88.1
91.8
68.9
46.1
107.9
39.9
strength (model A) and all others suggest a linear relationship
between de-rated collapse pressure and remaining wall thickness
of the pipes. For the lowest steel grades (models H and I) the
answers seem to be slightly different from the linear pattern
presented by high steel grades models. It can be justified by the
larger inelastic deformation observed prior to the external applied
pressure reach the collapse pressure, once the material has lower
yield stress. This is true especially for model I, which also presents
larger do/t ratio. Also in Fig. 7 is possible to see an exponential
defining a lower boundary (dashed line).
Fig. 6 shows inelastic deformation for models A and H (bottom
left and right), with 10% and 40% wall thickness reduction respectively. Models with larger wall thickness loss and lower yield
stress presented larger inelastic deformation, always concentrated
in the worn area. The inelastic deformation can be cause of reduced remaining collapse strength.
Analyzing these results in logarithmic scale for remaining collapse pressure we can say that roughly speaking results are converging for a single curve and it is possible to assess one curve that
can satisfy all models with safety. Thus it is possible to establish
one simple model to evaluate collapse pressure for worn pipes
under external pressure, where the remaining collapse pressure
Pcw depicted in Fig. 7 can be expressed in terms of the intact and
remaining wall thickness of the pipe, to and tr, and the original
collapse pressure strength Pco as follows:
⎡
⎛ tr − to ⎞ ⎤
Pcw
= 0.9782 exp ⎢1.58 ⎜
⎟⎥
o
Pc
⎝ to ⎠ ⎦
⎣
(2)
Comparing the results from this study developed by Kuriyama
et al. (1992) one can see that it does not fit very well for thick
walled pipes (see Fig. 8), underestimating collapse pressure reduction compared to numerical analysis. For thin walled pipes it
fits well as expected.
4. Conclusions and remarks
The collapse strength de-ration as a function of increasing wall
thickness wear was studied and some analytical and numerical
models were analyzed. Among the few models developed to study
such problem, the two most suitable in our opinion are Kuriyama
et al. (1992) and Sakakibara et al. (2008). Both presented mechanical models to predict the remaining collapse pressure for
worn pipes. In the first case, pipes with circular were considered,
what can result in a much higher collapse pressure. The latter
represents really well collapse pressure for thin walled pipes with
worn area. But for thick walled pipes, where material non-linearity
appears due to plastic deformation, none of the models can represent well the remaining collapse pressure.
Full-scale tests were successfully performed and made possible
to evaluate the effects of worn casing. Numerical models based on
334
N.M. Moreira Junior et al. / Journal of Petroleum Science and Engineering 133 (2015) 328–334
Fig. 7. Comparative results among models (A to I).
loss). For larger do/t ratios and lower wall thickness loss these
results are very accurate.
Analyzing all models as the remaining collapse pressure based
on original collapse rate showed one consistent reduction in the
collapse pressure for a typical value of initial ovalization (0.18%).
These behaviors were well approximated by an exponential regression accounting with original (or nominal) wall thickness,
remaining wall thickness, and original collapse pressure rate. The
behavior seems to be compatible for all models despite the do/t
ratio and elasto-plastic properties (but we also have to recognize
the material elasto-plastic consistent behavior). The final equation
does not account for initial pipe ovalization and future studies
must be carried out to couple the geometric ovalization with worn
wall of pipes developed at different angular sections.
Fig. 8. Comparison between numerical results from this study and from Kuriyama
et al. (1992) (lines are results from present study).
finite element method were built considering an approximated
worn shape constant through full sample length. Initial ovalization
was applied in the middle of the model with the maximum observed value measured from each sample. The circumferential
affected area was kept constant as 10% of inner pipe area, corresponding to cross-sectional angle of 36°, based on drilling operations assumptions. With few elements with linear interpolation
were possible to have good prediction of collapse pressure. Also it
was possible to notice plastic deformation across the inner face of
the pipe in the worn area even before the pipe collapse, as shown
in Fig. 6. Using an external script developed in python, the models
building and simulation times were very attractive, making possible to simulate as many cases as planned, in order to perform the
parametric study.
The results from numerical model were compared to full scale
hydrostatic pressure collapse tests for new and worn tubular with
different do/t ratios and material properties. The results were
pretty accurate and then the pattern adopted to build these
models was applied to analyze several models with different do/t
ratios, elastic-plastic materials, and remaining wall thickness after
an abrasive effect. A parametric studied was carried out and
compared to Kuriyama et al. (1992), showing the latter overestimates the remaining collapse pressure for pipes with do/t < 16,
especially for lower remaining wall thickness (larger material
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