Casing/Tubing design manual october 2005 Chevron
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The curve labeled “Recommended” in Figure 3-4 is a plot of the formula:
(
)
[
σσ
yy
T=− −|. .
38
1 0000238 378
]
, (3-6)
where
σ
y
|
38
is the yield strength at 37.8°C and is temperature in degrees
Celsius. If temperature is given in degrees Fahrenheit, the corresponding formula
is:
T
(
)
[
σσ
yy
T=− −|.
100
1 000043 100
]
, (3-7)
where
σ
y
|
100
is the yield strength at 100°F.
3.10.2 Young’s Modulus
Figure 3-5 illustrates the affect of temperature on Young’s modulus from several
sources. Temperature degradation of Young’s modulus becomes significant
beyond 200°F.
0.82
0.87
0.92
0.97
1.02
0 200 400 600 800
Temperature, Deg F
Modulus Degredation Factor
Recommended
Kattus [1973]
Leslie [1981]
Figure 3-5. Affect of Temperature on Young’s Modulus of Carbon Steel
The curve labeled “Recommended” in Figure 3-5 is a plot of the formula:
(
)
[
]
EE T=− −|. .
93
1 0000139 933
, (3-8)
3-18 Casing/Tubing Design Manual
October 2005
where is Young’s modulus at 93.3°C (= 206,800 MPa) and is
temperature in degrees Celsius. If temperature is given in degrees Fahrenheit,
the corresponding formula is:
E|
93
T
(
)
[
]
EE T=− −|.
200
1 000025 200
, (3-9)
where
is Young’s modulus at 200°F (= 30x10E|
200
6
psi).
3.10.3 Poisson’s Ratio
Figure 3-6 illustrates the affect of temperature on Poisson’s ratio
7
. Temperature
has only a minor affect on this variable.
1
1.01
1.02
1.03
1.04
1.05
0 100 200 300 400 500 600
Temperature, Deg F
Degredation Factor
Figure 3-6. Affect of Temperature on Poisson’s Ratio of Carbon Steel
The curve in Figure 3-6 is a plot of the formula:
[
]
µµ
=+|.
0
1 0000044T
, (3-10)
where
µ
|
0
is Young’s modulus at 0°C (= 0.3) and
T
is temperature in degrees
Celsius. If temperature is given in degrees Fahrenheit, the corresponding formula
is:
(
)
[
]
µµ
=+ −|.
32
1 000008 32T
, (3-11)
where
µ
|
32
is Young’s modulus at 32°F (= 0.3).
7
The Poisson’s ratio dependence was obtained by combining the affect of temperature on
Young’s modulus, E, and shear modulus, G
, τηρουγη τηε φορµυλα µ
= E/2G -
1[Leslie, 1981].
Casing/Tubing Design Manual 3-19
October 2005
3.10.4 Coefficient of Thermal Expansion
Figure 3-7 illustrates the affect of temperature on the coefficient of thermal
expansion.
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
-200 0 200 400 600 800
Temperature, Deg F
Coefficient Degredation Factor
Figure 3-7. Affect of Temperature on the Coefficient of Thermal Expansion of
Carbon Steel
The curve in Figure 3-7 is a plot of the formula:
()
[]
()
[]
α
=
+−≤
+−≥
⎧
⎨
⎪
⎩
⎪
aTT
aTT
|. .,
|. .,
93
93
1 000164 933 933
1 000036 933 933
.
.
, (3-12)
where
α
|
93
is the coefficient of thermal expansion at 93.3°C (= 14x10
-6
m/m-°C)
and
is temperature in degrees Celsius. If temperature is given in degrees
Fahrenheit, the corresponding formula is:
T
()
[]
()
[]
α
=
+−≤
+−≥
⎧
⎨
⎪
⎩
⎪
aTT
aT
|. ,
|. ,
200
200
1 000091 200 200
1 000020 200 200
T
, (3-13)
where
α
|
200
is the coefficient of thermal expansion at 200°F (= 7.8x10
-6
in/in-°F).
3-20 Casing/Tubing Design Manual
October 2005
3.11 References
1. Bull. 5C3, Bulletin on Formulas and Calculations for Casing, Tubing, Drill
Pipe and Line Pipe Properties, latest edition, API, Washington DC.
2. SPEC. 5CT, Specification for Casing and Tubing, latest edition, API,
Washington DC.
Casing/Tubing Design Manual 3-21
October 2005
Casing/Tubing Design Manual 4-1
April 2007
4 Tube Performance Properties
4.1 Introduction ................................................................................................ 4-1
4.2 Collapse Strength....................................................................................... 4-1
4.2.1 Example Problem..................................................................................4-5
4.3 High Collapse Casing.................................................................................4-7
4.3.1 Example ................................................................................................ 4-8
4.4 Collapse Due to Non-Uniform Loading.......................................................4-9
4.5 Operational Considerations......................................................................4-11
4.6 The Thick Wall Alternative........................................................................ 4-12
4.7 Effect of Wear on Collapse Resistance....................................................4-12
4.8 Burst Strength..........................................................................................4-13
4.8.1 Example Problem................................................................................4-13
4.8.2 Effect of Wear on Burst Strength......................................................... 4-14
4.8.3 Effect of Temperature on Burst Strength............................................. 4-15
4.8.4 Burst Strength based on von Mises Initial Yield ..................................4-15
4.8.5 Burst Strength Based on Full Yield......................................................4-17
4.9 Tube Body Yield....................................................................................... 4-17
4.9.1 Example Problem................................................................................4-19
4.10 Tension/Compression Strength................................................................4-20
4.11 References...............................................................................................4-20
4.1 Introduction
Casing design consists of a comparison of the most reasonable load scenarios to
the resistance of the tube to those loads. Typical load scenarios will be covered
elsewhere. The purpose of this chapter is to list the recommended formulas for
determining the latter part of the problem, the resistance of the tube to casing
loading.
4.2 Collapse Strength
Collapse resistance (strength) of the tube cross section to instability is the
casing’s ability to resist an external pressure differential. Collapse performance of
tubes is based on these principles:
• The collapse performance of the connection is always assumed to
exceed that of the tube body.
• Collapse performance includes resistance to internal/external fluid
pressure and axial tension. Cross-sectional deformations due to non-
uniform loads, such as salt flow are treated separately.
4
4-2 Casing/Tubing Design Manual
April 2007
• The effect of bending on collapse resistance is treated as an equivalent
axial load, where the equivalent axial load is the maximum tensile
bending stress applied to the entire cross section.
• The deleterious effect of tensile axial loading on collapse resistance is
considered. The beneficial effect of compressive axial loading on
collapse is ignored. Compressive loads expected during the design
phase cannot be insured in actual field environments.
Collapse performance is calculated using the procedure recommended by the
American Petroleum Institute [API, latest edition]. Given the following input
variables:
• Internal pressure,
p
i
• Axial stress,
σ
z
• Tube outside diameter,
D
• Tube wall thickness,
t
• API or specified minimum yield stress of tube material,
σ
API
API standards present four formulas to define collapse strength (resistance) of
tubes by four types of collapse (see Figure 4-1) according to the range of tubular
OD-to-wall thickness ratio:
1. Elastic collapse 2. Transition collapse
3. Plastic collapse 4. Yield strength collapse
Table 4-1. API Elastic Collapse Pressure Formula
Grade D/t Range
H-40 42.64 and greater
J-K-55 37.21 and greater
N-L-80 31.02 and greater
C-90 29.18 and greater
C-95 28.36 and greater
P-110 26.22 and greater
Q-125 24.46 and greater
2
6
1
10*95.46
⎟
⎠
⎞
⎜
⎝
⎛
−
=
t
D
t
D
P
e
(4-1)
Table 4-2. API Transition Collapse Pressure Formula
Grade D/t Range F G
H-40 27.01 to 42.64 2.063 0.0325
J-K-55 25.01 to 37.21 1.989 0.036
N-L-80 22.47 to 31.02 1.998 0.0434
C-90 21.69 to 29.18 2.017 0.0466
C-95 21.33 to 28.36 2.029 0.0482
P-110 20.41 to 26.22 2.053 0.0515
Q-125 19.63 to 24.46 2.092 0.0565
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
⎟
⎠
⎞
⎜
⎝
⎛
= G
t
D
F
YP
Pt
(4-2)
Casing/Tubing Design Manual 4-3
April 2007
Table 4-3. API Plastic Collapse Pressure Formula
Grade D/t Range A B C
H-40 16.40 to 27.01 2.95 0.0465 754
J-K-55 14.81 to 25.01 2.991 0.0541 1206
N-L-80 13.38 to 22.47 3.071 0.0667 1955
C-90 13.01 to 21.69 3.106 0.0718 2254
C-95 12.85 to 21.33 3.124 0.0743 2404
P-110 12.44 to 20.41 3.181 0.0819 2852
Q-125 12.11 to 19.63 3.239 0.0895 3301
(4-3)
Table 4-4. API Yield Collapse Pressure Formula
Grade D/t Range
H-40 16.40 and less
J-K-55 14.81 and less
N-L-80 13.38 and less
C-90 13.01 and less
C-95 12.85 and less
P-110 12.44 and less
Q-125 12.11 and less
⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
−
=
2
1
2
t
D
t
D
YP
Pyp
(4-4)
Figure 4-1. API Collapse Pressure Curves for P-110 Grade Casing
The collapse performance of a tube will be reduced under axial tension and the
reduced collapse performance of a tube is calculated by the following procedure,
which must first be carried out in English units, and then, if desired, the final
answer may be converted to metric units:
4-4 Casing/Tubing Design Manual
April 2007
1. Compute a pseudo-yield stress to account for the presence of the axial
tension according to the formula:
σ
σ
σ
σ
σ
σ
py
z
API
z
API
API
=−
⎛
⎝
⎜
⎞
⎠
⎟
−
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
1
3
4
1
2
2
. (4-5)
2. Compute the empirical constants
A
,
B
, C ,
F
, and G :
Axx
x
py py
py
=+ +
−
−−
−
28762 010679 10 021301 10
053132 10
510
2
16
3
.. .
.
σσ
σ
Bx
py
=+
−
0 026233 0 50609 10
6
..
σ
Cx
x
py py
py
=− + −
+
−
−
46593 0030867 010483 10
036989 10
7
2
13
3
.. .
.
σσ
σ
F
x
B
A
B
A
B
A
B
A
B
A
B
A
B
A
py
=
+
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
+
−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
−
+
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
46 95 10
3
2
3
2
1
3
2
6
3
2
.
σ
G
FB
A
=
3. Compute the D/t boundary for each of the recognized collapse formulas:
() ()
D
t
AB
C
A
B
C
YP
py
py
⎛
⎝
⎜
⎞
⎠
⎟
=
−++
⎛
⎝
⎜
⎞
⎠
⎟
+−
+
⎛
⎝
⎜
⎞
⎠
⎟
28 2
2
2
σ
σ
(4-6)
()
()
D
t
AF
CBG
PT
py
py
⎛
⎝
⎜
⎞
⎠
⎟
=
−
+−
σ
σ
(4-7)
D
t
B
A
B
A
TE
⎛
⎝
⎜
⎞
⎠
⎟
=
+
2
3
(4-8)
Where the subscripts designate the respective collapse modes as yield (Y),
plastic (P), transition (T), and elastic (E). For example,
(
)
Dt
PT
/ is the D/t
boundary between the plastic and transition collapse formulas.
4. Compute the D/t of the current tube and determine the appropriate collapse
formula by comparing this value to the D/t formula boundaries of the previous
step.
5. According to the collapse mode, compute the collapse performance from one
of the following formulas:
Casing/Tubing Design Manual 4-5
April 2007
()
()
P
D
t
D
t
Ypy
=
−
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
2
1
2
σ
, Yield (4-9)
P
A
D
t
BC
Ppy
=−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
−
σ
, Plastic (4-10)
P
F
D
t
G
Tpy
=−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
σ
, Transition (4-11)
()()
P
x
D
t
D
t
E
=
−
46 95 10
1
6
2
.
, Elastic (4-12)
6. The result of the above calculation is a collapse pressure,
P
Collapse
. The
external pressure necessary to cause collapse with a non-zero internal
pressure is:
pP
D
t
p
o
Collapse
i
=+−
⎛
⎝
⎜
⎜
⎞
⎠
⎟
⎟
1
2
(4-13)
4.2.1 Example Problem
Given a tube of 244.48 mm (9-5/8 in.), 69.94 kg/m (47 lb/ft), N-80 casing in the
presence of 1,334 kN (300,000 lbs) tension and an internal pressure of
6.895x10
-3
MPa (1,000 psi), and compute the collapse resistance.
• The input variables are:
ppsi
i
=
1000
()
σ
z
psi=
−
=
300000
07854 9 625 8681
22104
22
.. .
Din
=
9625.
tin
=
0.472
σ
API
psi
=
80000
• The pseudo yield stress is:
σ
py
psi
=
66624
• The empirical constants are:
A
=
3026.
B
=
0 0600.
C
=
1555
F
=
1986.
G
=
00394.
4-6 Casing/Tubing Design Manual
April 2007
• The Dt/ boundaries are:
D
t
YP
⎛
⎝
⎜
⎞
⎠
⎟
= 1402.
D
t
PT
⎛
⎝
⎜
⎞
⎠
⎟
= 2367.
D
t
TE
⎛
⎝
⎜
⎞
⎠
⎟
=
3396.
• The D/t of the subject tube is 9.625/.472 = 20.39 and, therefore, because
this value falls between the yield/plastic and plastic/transition boundaries,
the plastic collapse formula governs.
• The collapse resistance in the absence of internal pressure is:
Ppsi
Collapse
=−
⎛
⎝
⎜
⎞
⎠
⎟
−=66624
3026
2039
00600 1555 4330
.
.
.
• With 1000 psi internal pressure the external pressure necessary to
collapse the tube is:
ppsi
o
=+−
⎛
⎝
⎜
⎞
⎠
⎟
=4330 1
2
2039
1000 5230
.
Note the following:
• If the axial force had been compressive instead of tensile, then the
pseudo-yield stress would have been set equal to the API-minimum yield
stress,
σ
API
. That is, the beneficial effect of axial compression raising
the yield stress would have been ignored.
• The API calculation procedure actually is quite specific concerning both
intermediate and final rounding of the results of calculations. Ignoring
these round-off procedures will only slightly affect the final answer.
Figure 4-2 presents the measured tube collapse pressure data from a JIP (DEA-
130), compared to the above tube-minimum tube-collapse strength (resistance)
by API standards.