Casing/Tubing design manual october 2005 Chevron

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9.4.1.10 Effective Force

(

)

FF pApA

ez iioo

=− −

(9-28)

9.4.1.11 Effective Weight

(

)

ww A A

esiioo

=+ −

γγ

.(9-29)

In reviewing the calculations, note the following points. As indicated by

equation19-8, there is a possibility of a discontinuity in axial force at a cross over

between two sections because of differences in cross-sectional geometry. The

magnitude of the discontinuity will be that of the latter two pressure terms in the

equation.

Interestingly, this same discontinuity will not appear in the effective force.

Rearranging equation (9-27):

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

()() ()( )

FpApA F wL

pA pA

−−

⎛

⎝

⎜

⎞

⎠

⎟

−−

⎛

⎝

⎜

⎞

⎠

⎟

(9-30)

The left-hand side of the above equation is the effective force just above the

section change. The right-hand side of the above equation is the effective force

just below the section change. The equality implies that these two effective

forces have the same value.

Casing/Tubing Design Manual 9-13

October 2005

9.4.2 Conditions during Stimulation

Repeating the previous calculations, the conditions during the stimulation (see

Table 9-7) can also be calculated. The equations used are identical to those

outlined above.

Table 9-7. Conditions during Stimulation

Segment Attribute Symbol Metric English

1 Axial force at bottom

96.98 kN 21,821 lb

Effective force at bottom

-58.94 kN -13,249 lb

Internal pressure at

bottom

42.71 MPa 6,195 psi

External pressure at

bottom

6.092 MPa 883.1 psi

Effective weight

13.62 kg/m 9.15 lb/ft

Average temperature

ave

10.70°C 51.2°F

2 Axial force at bottom

-100.0 kN -22,489 lb

Effective force at bottom

-201.9 kN -45,394 lb

Internal pressure at

bottom

63.30 MPa 9,182 psi

External pressure at

bottom

21.32 MPa 3,091 psi

Effective weight

9.56 kg/m 6.43 lb/ft

Average temperature

ave

13.15°C 55.6°F

3 Axial force at bottom

-128.9 kN -28,989 lb

Effective force at bottom

-230.4 kN -51,825 lb

Internal pressure at

bottom

67.42 MPa 9,779 psi

External pressure at

bottom

24.37 MPa 3,532 psi

Effective weight

9.56 kg/m 6.43 lb/ft

Average temperature

ave

15.25°C 59.4°F

9-14 Casing/Tubing Design Manual

October 2005

Changes in the temperature and pressure environment will attempt to induce

length changes. Since the packer here is assumed to permit motion, these length

changes will be realized. The length changes are summarized in Table 9-8,

where calculations proceed according to the following formulas.

Table 9-8. Length Changes because of Stimulation

Segment Length Change Symbol Meters Inches

1 Temperature

-0.129 -5.10

Axial force

-0.079 -3.12

Ballooning

-0.171 -6.72

Buckling

-0.014 -0.50

2 Temperature

-0.717 -28.32

Axial force

-0.633 -24.93

Ballooning

-0.449 -17.67

Buckling

-0.633 -24.89

3 Temperature

-0.212 -8.33

Axial force

-0.127 -4.99

Ballooning

-0.097 -3.82

Buckling

-0.198 -7.82

Total for all

Segments

Temperature

-1.058 -41.75

Axial force

-0.839 -33.04

Ballooning

-0.717 -28.21

Buckling

-0.845 -33.21

9.4.2.1 Temperature Change

The length change because of temperature change is,

(

)

δαδ

LLT

te ave

(9-31)

where for steel,

(

)

−−

12410 6910

././xmmCxininF

, and

ave

is the difference

in average temperatures between the initial conditions and the stimulation.

Casing/Tubing Design Manual 9-15

October 2005

9.4.2.2 Axial Force Change

The length change because of axial force changes at the shoulders must

consider the fact that, assuming the lower end of the tubing string to be free, the

effects of any axial force will be felt by all sections above the point of application

of the force. For each affected section, the change in length is given by,

= (9-32)

so that for Section I:

() ()

δδ

⎛

⎝

⎜

⎞

⎠

⎟

∑

(9-33)

where, for a generic change in areas between sections,

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

δδ δ

FpAA pAA

=−

⎛

⎝

⎜

⎞

⎠

⎟

−−

⎛

⎝

⎜

⎞

⎠

⎟

++11

(9-34)

For Section 1 in this example, there will be length changes because of the axial

force at the bottom of Section 3 (i.e., the bottom of the string) and at the cross

over between Sections 1 and 2. (Although the pressure changes at the cross

over between Sections 2 and 3, there is no shoulder to absorb the change.) The

force change at the bottom of Section 3 is -128.9 - (-28.49) = -100.4 kN (-28,989

- (-6,400) = -22,589 lb). The force change at the cross over between Sections 1

and 2 is in metric units,

()

()()

0001 42 71 6092 4536 3020 0 5551=− −−=... .N

and in English units,

()

()()

6195 8831 7 031 4 68 0 12488=− −−=.. . .

The length change for Section 1 is in metric units,

()

609 6 1 10

206843 6207 4536

1004 5551 0079=

⋅

⋅−

⎛

⎝

⎜

⎞

⎠

⎟

−+ =−

.. .

and in English units

()

in ft

212

30 10 9 621 7 031

22589 12488 312=

⋅

⋅−

⎛

⎝

⎜

⎞

⎠

⎟

−+ =−

9-16 Casing/Tubing Design Manual

October 2005

9.4.2.3 Ballooning Change

(

)

(

)

δδ

pr pr

ave

=−

−

(9-35)

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

section.

For Section 3 in this example, the average initial internal pressure is (21.32 +

24.37) / 2 = 22.84 MPa [(3,091 + 3,532) / 2 = 3,312 psi)] and the average final

internal pressure is (63.30 + 67.42) / 2 = 65.36 MPa [(9,182 + 9,779) / 2 = 9,480

psi)]. The average internal pressure change is 65.36-22.84 = 45.52 MPa (9,480-

3,312 = 6,168 psi).

9.4.2.4 Buckling Change

Check to verify that buckling has occurred. This example is true for all sections,

that is, the effective force at the bottom of the section is negative. If not,

= 0 .

If the effective force is negative, the length change due to buckling is:

EIw

=−

(9-36)

One final correction may be necessary (in this example, for the bottom two

sections). 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:

δδ

′

=−

⎛

⎝

⎜

⎞

⎠

⎟

bu bu

(9-37)

9.4.2.5 Summary

The total length change or movement of the lower end of the tubing during the

hydraulic fracturing treatment is a shortening of 3.46 m (136.2 in.). Assuming the

tubing is “bottomed out” when it is landed; this will be the minimum length of

seals necessary to avoid unseating the tubing during the treatment.

9.5 Production Casing Design

A string of 177.8 mm (7 in.) production casing will be designed to 2,895.6 m

(9,500 ft) in a vertical wellbore using the design assumptions for a standard well.

The casing is to be run in 2,037-kg/m

(17-ppg) fluid and cemented with a 2,157-

kg/m

(18-ppg) slurry to 1,829 m (6,000 ft). The density of the completion fluid in

the tubing/casing annulus is 814.8 kg/m

(6.8 ppg). The previous casing string is

244.5 mm (9.625 in.) set at 1,676 m (5,500 ft).

Casing/Tubing Design Manual 9-17

October 2005

The pore pressure gradient is shown in Table 9-9.

Table 9-9. Pore Pressures for Production Casing Design Example

Depth (m)

Pore Pressure

Gradient

(kPa/m)

Depth (ft)

Pore Pressure Gradient (ppg)

426.7 10.58 1,400 9.00

1,524 15.86 5,000 13.50

1,828.8 15.98 6,000 13.60

2,133.6 16.22 7,000 13.80

2,194.6 19.62 7,200 16.70

2,438.4 17.27 8,000 14.70

The fracture gradient is shown in Table 9-10.

Table 9-10. Fracture Gradients for Production Casing Design Example

Depth (m)

Fracture

Gradient (kPa/m)

Depth (ft)

Fracture Gradient (ppg)

30.5 10.52 100 8.95

457.2 19.74 1,500 16.80

1,676.4 22.56 5,500 19.20

2,286 22.56 7,500 19.20

2,438.4 22.56 8,000 19.20

2,895.6 22.44 9,500 19.10

3,048 22.33 10,000 19.00

The pore pressure gradients and the fracture gradients are plotted in Figure 9-1.

9-18 Casing/Tubing Design Manual

October 2005

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

51015202

EMW (ppg)

TVD (ft)

Pore Pressure

Frac Gradient

Mud Weight

Figure 9-1. Pore Pressure and Fracture Gradients for Example Production Casing

Design

Casing/Tubing Design Manual 9-19

October 2005

The undisturbed surface temperature is 21.1°C (70°F), with a gradient of 2.04

°C/100 m (1.12°F/100 ft). The available inventory from which a design string may

be extracted is shown in Table 9-11Table 9-11.

Table 9-11. Tubular Inventory for Production Casing Design Example

Weight

kg/m

(lb/ft)

Grade ID

(in.)

Burst

MPa

(psi)

Collapse

MPa

(psi)

Axial

Yield

(klb)

Cost

Factor

34.23

(23)

K-55 161.7

(6.366)

30.06

(4,360)

22.55

(3,270)

1,628

(366)

1.00

38.69

(26)

K-55 159.4

(6.276)

34.34

(4,980)

29.85

(4,330)

1,846

(415)

1.13

38.69

(26)

N-80 159.4

(6.276)

49.92

(7,240)

37.30

(5,410)

2,687

(604)

1.42

43.16

(29)

N-80 157.1

(6.184)

56.26

(8,160)

48.47

(7,030)

3,007

(676)

1.59

43.16

(29)

P-110 157.1

(6.184)

77.36

(11,220)

58.81

(8,530)

4,132

(929)

1.85

47.62

(32)

N-80 154.8

(6.094)

62.47

(9,060)

59.29

(8,600)

3,314

(745)

1.75

47.62

(32)

P-110 154.8

(6.094)

85.91

(12,460)

74.33

(10,780)

4,559

(1,025)

2.04

9.5.1 Preliminary Design

As emphasized in Chapter 6 -Tube Load, setting the cement fixes both

extremities of the casing string

. Following waiting on cement (WOC),

subsequent changes in the temperature and pressure environment will induce

axial loads that are important both in their own right and as they affect collapse

and burst resistance. Unfortunately, calculation of these loads requires

knowledge of the geometry of each tube section which, at the onset of a design,

is not known. It is, therefore, necessary to perform a preliminary design to obtain

a trial design string, and then to check that design for environmental load

changes.

In the preliminary design the following working assumptions apply:

• Temperature change is ignored

• The pressure load environment is that specified with the load case definition

for the intended application (production tubing, production casing,

intermediate casing, and surface casing)

• A conservative, but not necessarily worst case, assumption is made for the

axial load

The lower end of the casing string is fixed by adjacent cement. The upper end of the

casing string is assumed fixed in the wellhead. The possibility of wellhead movement

will not be considered in this example.

9-20 Casing/Tubing Design Manual

October 2005

After this preliminary design is complete, the entire string geometry is defined

and a check for the effects of environmental load changes can be made. Should

any portion of the preliminary design fail the environmental load change check,

that portion of the design string can be amended and the check repeated. Note

that a repeat check is necessary, as amending the preliminary design may alter

the string geometry which, of course, alters the environmental load changes.

9.5.1.1 Collapse Design

In the preliminary design, a string is first designed that will withstand collapse

load conditions. The results of this design step are then checked for burst and

axial load resistance with amendments made, if necessary. You could

legitimately begin with the burst design and then check for collapse and axial

load.

The object of the collapse design is to arrive at the least expensive set of weight

and grade combinations that will just meet the design loads. The design starts at

the bottom because of the detrimental effect of tension on collapse. That is, to

include the effect of axial load at any depth, the weight of casing hanging below

that point must be known. As a reasonably conservative assumption, the axial

load at any depth in the preliminary design is calculated as the air weight of

casing suspended below the point of interest.

Figure 9-2 illustrates the collapse design procedure graphically. Plotting design

collapse differential pressure versus depth involves two steps:

1. Given the appropriate load case, compute the appropriate internal and

external pressure profiles. For production casing, the interior of the tube is

assumed evacuated (

0 ), while the exterior of the tube is subjected to

the drilling fluid in which the casing was run, in this case 2,037 kg/m

(17

ppg).

2. Apply the design factor for this load case to the difference of the external and

internal pressure profiles to arrive at a design collapse differential pressure.

In this particular design the collapse design factor above the cement top is

the Chevron default of 1.0, so the collapse differential pressure and the

design collapse differential pressure are identical. Below the cement top, the

collapse design factor could be 0.85 for good cement assumption, so the

design collapse differential pressure is actually less than the collapse

differential pressure as defined by the load case.

Casing/Tubing Design Manual 9-21

October 2005

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 2000 4000 6000 8000 10000

Differential Pressure (psi)

TVD (ft)

Differential Load

Load w/DF

Resistance

First Pass

29,N

26,N

26,K

23,K

32,N

Figure 9-2. Collapse Design for Production Casing Example

Starting at the bottom the least expensive weight/grade combination that will

resist a bottom hole collapse differential of 57.85 MPa (8,390 psi) is 47.62-kg/m

(32-ppf) N-80. The question then centers around how little of this weight/grade

must be used before a less expensive weight/grade combination is used. This

question is the most complicated aspect of collapse design, primarily because:

• The effect of tension on collapse

• The complex nature of the API adjustment of collapse resistance for axial

load.

To illustrate this point, consider the following thoughts:

• The next least expensive weight/grade combination is 43.16-kg/m (29-ppf) N-

80.

• The collapse resistance of this candidate is 48.47 MPa (7,030 psi) which,

when compared to the design collapse differential pressure corresponds to a

depth of 2,773 m (9,100 ft).

• If, however, such a candidate were run to this depth, its collapse resistance

would actually be 48.13 MPa (6,980 psi). This reduction is because of the

weight of 47.62- kg/m (32-ppf) N-80 casing suspended below the 43.16-kg/m

(29-ppf) N-80.

9-22 Casing/Tubing Design Manual

October 2005