Casing/Tubing design manual october 2005 Chevron

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Segment Attribute Symbol Metric English

External pressure at bottom

35.07 MPa 5,087 psi

Effective weight

28.77 kg/m 19.33 lb/ft

Average temperature

ave

49.3°C 120.7°F

3 Internal area

1.938x10

30.04 in

External area

2.483x10

38.48 in

Moment of inertia

1.918x10

46.07 in

Axial force at bottom

109.82 kN 24,687 lb

Effective force at bottom

308.99 kN 69,458 lb

Internal pressure at bottom

36.54 MPa 5,299 psi

External pressure at bottom

36.54 MPa 5,299 psi

Effective weight

32.05 kg/m 21.54 lb/ft

Average temperature

ave

57.7°C 135.9°F

4 Internal area

1.938x10

30.04 in

External area

2.483x10

38.48 in

Moment of inertia

1.918x10

46.07 in

Axial force at bottom

-279.81 kN -62,899 lb

Effective force at bottom

46.49 kN 10,451 lb

Internal pressure at bottom

54.92 MPa 7,966 psi

External pressure at bottom

56.01 MPa 8,123 psi

Effective weight

29.08 kg/m 19.54 lb/ft

Average temperature

ave

67.8°C 154.1°F

5 Internal area

1.882x10

29.18 in

External area

2.483x10

38.48 in

Moment of inertia

2.088x10

50.16 in

Axial force at bottom

-378.9 kN -85,166 lb

Effective force at bottom

0 MN 0 lb

Internal pressure at bottom

57.84 MPa 8,390 psi

External pressure at bottom

59.10 MPa 8,571 psi

Effective weight

32.40 kg/m 21.78 lb/ft

Average temperature

ave

78.7°C 173.7°F

Casing/Tubing Design Manual 9-33

October 2005

In completing the table, the following formulas, listed in the order in which they

were used, were applied:

9.5.3.2 Internal Area

(

ADt

=−

)

(9-38)

9.5.3.3 External Area

= D

(9-39)

9.5.3.4 Moment of Inertia

()

[

]

IDDt=−−

(9-40)

9.5.3.5 Total Length of String

LLLL

TOT i

==++L

∑

123

(9-41)

9.5.3.6 Internal Pressure at Bottom of Section

() () ()

surf

∑

(9-42)

For the current example the calculation for Section 2 in metric units is,

()

MPa

0 980665 10 2037 1006 2037 750 3507=+ ⋅ + ⋅ =

−

and in English units is,

()

psi ft

ppg

psi

0 0051948 17 3300 17 2460 5087=+ ⋅ + ⋅ =.

9.5.3.7 External Pressure at Bottom of Section

() () ()

surf

∑

(9-43)

9.5.3.8 Axial Force at Bottom of the Bottom Section

() ()

(

)

(

)

FpAApA

pi o

=− − + −() A

(9-44)

9-34 Casing/Tubing Design Manual

October 2005

9.5.3.9 Axial Force at Bottom of the Section

() () ( ) ()() ()

()() ()

FF wL pAA

pA A

=+ + −

⎛

⎝

⎜

⎞

⎠

⎟

−−

⎛

⎝

⎜

⎞

⎠

⎟

(9-45)

where

is the section below section

j +1

For the current example, the calculation for Section 2 in metric units is,

()

109820 980665 4316 732 3507 1996 1938 10

3507 2 483 2 483 10 16116

=+ ⋅⋅+ −×

−−×=

......

.. . .

and in English units is,

()

(

)

()

24687 29 240 5087 3094 3004

5087 3848 3848 36227

=+⋅+ −

−−=

9.5.3.10 Effective Force

(

)

FF pApA

ez iioo

=− −

(9-46)

9.5.3.11 Effective Weight

(

)

ww A A

esiioo

=+ −

γγ

(9-47)

9.5.3.12 Collapse Conditions

The conditions during evacuation because of evacuation can now be calculated.

However, before completing this calculation, it is necessary to compute the

length changes, or in this instance potential length changes, associated with

altering the environment from the initial conditions to the collapse conditions. The

length changes are summarized in Table 9-16, where calculations proceed

according to the following formulas.

Table 9-16. Potential Length Changes Because of Evacuation

Segment Length Change Symbol Meters Inches

1 Temperature

0 0

Axial Force

0.008 0.3

Ballooning

0.104 4.1

Buckling

0 0

2 Temperature

0 0

Axial Force

0.015 0.6

Ballooning

0.246 9.7

Casing/Tubing Design Manual 9-35

October 2005

Segment Length Change Symbol Meters Inches

Buckling

0 0

3 Temperature

0 0

Axial Force

0 0

Ballooning

0.027 1.1

Buckling

0 0

4-5 Below Cement Top

9.5.3.13 Temperature Change

Above the cement top,

(

)

δαδ

LLT

te ave

(9-48)

where for steel,

= 1.24x10-5 m/m°C (6.9x10-6 in/in°F), and

(

)

ave

is the

difference in average temperatures between the initial conditions and the

condition of evacuation.

Below the cement top, temperature change is a local affect, with the force

generated by the local temperature change given by

FEL

−

(9-49)

9.5.3.14 Axial Force Change

Above the cement top,

= (9-50)

where

is the total of axial force changes because of shoulders below the

segment of the string in question.

Any force generated at shoulders below the cement top or at the casing shoe will

be absorbed locally and not transmitted to positions above or below the cement

top.

9-36 Casing/Tubing Design Manual

October 2005

9.5.3.15 Ballooning Change

Above the cement top,

(

)

(

)

δδ

pr pr

ave

=−

−

(9-51)

where the average pressure change is the change in average pressure over the

section.

Below the cement top, ballooning is a local effect, with the force generated by the

local pressure change given by:

(

)

(

)

[

]

δµπδδ

Fprp

pr i i o o

=− −2

(9-52)

9.5.3.16 Buckling Change

A check is made to ensure that buckling has occurred (in this example, only for

the section above the cement top), that is, is the effective force at the bottom of

the section negative? If not,

0 . If the effective force is negative, the length

change due to buckling is:

EIw

=−

(9-53)

One final correction may be necessary. If the neutral point is above the section,

that is, if

is greater than the length of the section, the above length

change must be adjusted to:

−Fw

δδ

bu bu

=−

⎛

⎝

⎜

⎞

⎠

⎟

2 (9-54)

There can be no buckling length change below the cement top.

When both ends of an uncemented tubular string are fixed, the calculation for

buckling change is iterative. First, it is necessary to determine if buckling occurs

by assuming that there is no buckling and then checking the effective force (as

generated by the other potential length changes) at the bottom of the segment. If

the effective force is negative, indicating buckling, the length change for buckling

may then be calculated using the current effective force. This will generate a

shortening because of the tube assuming a helical configuration. This shortening,

when now appended to the other length changes, will result in a new value of

effective force from which a new length change due to buckling can be

calculated. The process continues until suitable convergence has been achieved.

Casing/Tubing Design Manual 9-37

October 2005

For the current load condition the ballooning length change is positive. This

indicates a tendency for axial expansion, which is countered by the fixed ends

(wellhead and cement top) of the casing, thus rendering the true axial force at the

cement top negative (compression). The effective force, however, is positive

because of the large external pressure differential. Therefore, the length change

due to buckling is zero.

9.5.3.17 Incremental Axial Force

The incremental load generated above the cement top from the sum of all

potential length changes is the axial force necessary to affect a length change

equal in magnitude, but opposite in sign, to the potential length change. For a

single uncemented segment,

(

)

LEAA

TOT

TOT o i

=−

−

(9-55)

and for multiple uncemented segments,

()

EA A

TOT

=−

−

⎡

⎣

⎢

⎤

⎦

⎥

∑

(9-56)

where the summation extends over all uncemented segments.

The forces for the collapse load condition are summarized in Table 9-17 for the

uncemented interval and for two locations below the cement top. Comparing the

axial load at the bottom of the uncemented interval (Segment 3) and the local

axial force at the top of the cemented interval (Segment 4), note the jump in axial

load at the cement top. Immediately above the cement top, the ballooning affect

is distributed over the entire uncemented length of the string. Immediately below

the cement top, the entire ballooning affect must be absorbed locally.

Table 9-17. Conditions during Evacuation

Segment Attribute Symbol Metric English

1 Axial force at bottom

210.56 kN 47,333 lb

Effective force at bottom

709.49 kN 159,488 lb

Internal pressure at

bottom

0 MPa 0 psi

External pressure at

bottom

20.09 MPa 2,914 psi

Effective weight

-7.42 kg/m -4.99 lb/ft

Average temperature

ave

31.4°C 88.5°F

2 Axial force at bottom

-94.34 kN -21,206 lb

Effective force at bottom

776.52 kN 174,555 lb

Internal pressure at

bottom

0 MPa 0 psi

9-38 Casing/Tubing Design Manual

October 2005

Segment Attribute Symbol Metric English

External pressure at

bottom

35.07 MPa 5,087 psi

Effective weight

-11.89 kg/m -7.99 lb/ft

Average temperature

ave

49.3°C 120.7°F

3 Axial force at bottom

-125.30 kN -28,166 lb

Effective force at bottom

781.84 kN 175751

Internal pressure at

bottom

0 MPa 0 psi

External pressure at

bottom

36.54 MPa 5,299 psi

Effective weight

-7.42 kg/m -4.99 lb/ft

Average temperature

ave

57.7°C 135.9°F

Cement

Top

Local axial force

-102.57 kN -23,057 lb

Local internal pressure

0 MPa 0 psi

Local external pressure

36.54 MPa 5,299 psi

Local temperature

ave

58.4°C 137.2°F

Bottom of

String

Local axial force

-696.10 kN -156,477 lb

Local internal pressure

0 MPa 0 psi

Local external pressure

57.85 MPa 8,390 psi

Local temperature

ave

80.2°C 176.4°F

Casing/Tubing Design Manual 9-39

October 2005

We are now in a position to compute safety factors associated with the collapse

load condition. See Table 9-18.

Table 9-18. Safety Factors during Evacuation

Segment Location Collapse Yield (von Mises) Joint Strength

1 Top

∞

4.73 5.9

Bottom 2.35 2.69 17.9

2 Top 1.04 1.46 17.7

Bottom 1.07 1.58 35.6

3 Top 1.34 1.70 39.8

Bottom 1.34 1.71 30.0

4 Cement top 1.34 1.70 36.6

5 Bottom of

string

1.09 1.29 5.9

The procedure for calculating collapse safety factor is lengthy, but demonstrated

in detail in Chapter 4 – Tube Performance Properties. At each location, the

differential collapse pressure and axial load applicable to evacuation are applied

to the string section under consideration.

The von Mises safety factor determines closeness to yield, taking into account all

stresses, and entails comparing a multi-dimensional equivalent stress to the

uniaxial yield stress. In the presence of bending, the effective stress is given by,

() ()()

σσσσσ σσσσσσσσ

θθθ

e r zb r rzb zb

=+++ − − +− +

(9-57)

where,

(

)

ii oo

ioio

pr pr

pprr

rr r

−

22 2

(9-57)

(

)

−

pr p r

pprr

rr r

ii oo

ioio

22 2

(9-58)

zzazb

(9-60)

the last relation differentiating the two components of the axial stress.

In the presence of bending because of buckling or a deviated wellbore, it is

uncertain whether the highest effective stress will occur at the inner or outer

radius. Therefore, both locations must be checked by successively setting

and r . Further, it is usually not immediately clear whether adding or

subtracting the bending stress will result in the highest effective stress, so both

the inner and outer longitudinal fibers of the bent tube must be checked by

adding and subtracting the bending stress. These four possibilities correspond to

separate effective stress calculations at the most compressed (due to bending)

circumferential position on the inner radius, the most compressed position on the

outer radius, the most extended position on the inner radius, and the most

extended position on the outer radius.

i o

9-40 Casing/Tubing Design Manual

October 2005

In the absence of bending,

0 , eliminating separate checks on the

compressed and extended surfaces of the tube. Further, it may be proved (see

Appendix B – Casing Design Software) that the maximum value of the equivalent

stress occurs at the inner radius. With no bending, only one check at the inner

radius is required.

The joint strength safety factor is determined based on the ultimate strength of

the connection. Joint strength is given by the formula:

Joint Strength (Casing) =

(Joint Efficiency)) (A

- A

).(9-59)

9.5.3.18 Burst Conditions

A check similar to that detailed above can also be performed for the burst (tubing

leak) load condition, including the changes in axial force, when the state changes

from the initial conditions to the burst conditions.

Casing/Tubing Design Manual 9-41

October 2005

0 Steam Injection Casing Design

10.1 Introduction ....................................................................................................................10-1

10.2 Casing Thermal Load in Steam Injection Wells..............................................................10-1

10.2.1 Casing Thermal Compressive Load ..........................................................................10-1

10.2.2 Casing Thermal Hot-Yield .........................................................................................10-3

10.2.3 Special Casing Thermal Load Design .......................................................................10-5

10.2.4 Casing Thermal Compression Design.......................................................................10-5

10.2.5 Casing Thermal Tension Design ...............................................................................10-8

10.2.6 Casing Design Practices to Reduce Hot-Yield ........................................................10-10

10.2.6.1 High-Strength Casing.....................................................................................10-10

10.2.6.2 Thermal Wellhead..........................................................................................10-12

10.2.6.3 Casing Pre-Tension Completion....................................................................10-13

10.3 Other Issues.................................................................................................................10-15

10.3.1 Casing Connection..................................................................................................10-15

10.3.2 Connection Lubricant...............................................................................................10-15

10.4 References...................................................................................................................10-15

10.1 Introduction

Steam injection is a successful operation that increases heavy oil production, but

produces severe thermal-loading to the production casing because of extreme

temperature elevation during steam injection operations. This is the cause of high

casing failure rates. The production casing failures in steam injection wells can

be casing ID restriction or buckling/collapse at steam injection period and casing

parting or leaking because of tensile load at the cooling period or cyclic fatigue.

This chapter will present discussions on production casing design in steam

injection wells, including casing thermal load calculation. You may also obtain

further information from the Chevron Best Practice Web site on steam injection

well design.

10.2 Casing Thermal Load in Steam

Injection Wells

10.2.1 Casing Thermal Compressive Load

Casing thermal stress in a steam injection well is produced as the casing is

heated during the steam injection period. As we know, the casing will expand and

become longer when it is heated. When casing is restricted from expanding and

becoming longer while heated, compressive thermal stress develops. For a

temperature increase of (∆T), the casing thermal expansion (∆L) and thermal

stress (∆σ) /thermal load (∆F) are defined as:

∆

(10-1)

∆L = εL (10-2

Casing/Tubing Design Manual 10-1

October 2005