casing design 4

8/17/2019 Casing Design 4

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CHAPTER-4

CASING DESIGN

Types of Casing

Drilling environments often require several casing strings in order to reach

the total desired depth. Some of the strings are as follows (Figure 3-1).

-drive or structural

-conductor

-surface

-intermediate (also known as protection pipe)

-liners

-production (also known as an oil string)

-tubing

Drive Pipe or Conductor Casing:

The first string run or placed in the well is usually the drive pipe or

conductor casing. The normal depth range is from 100-300 ft. In soft-rock

areas the pipe is hammered into the ground with large diesel hammer. Hard-rock

areas require that a large diameter shallow hole be drilled before running and

cementing the well. A primary purpose of this string of pipe is to provide a fluid


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conduit from the bit to the surface. An additional function of this string of pipe

is to minimize hole-caving problems.

Figure 3-1 Typical casing string relationship


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Structural Casing:

Drilling conditions will require that an additional string of casing be run

between the drive pipe and surface casing. Typical depth range from 600-1000

ft. Purpose of this pipe includes solving additional lost circulation or hole caving

problems and minimizing kick problems from shallow gas zones.

Surface Casing:

Many purposes exist for running surface casing, including:

-cover fresh water sands

-maintain hole integrity by preventing caving

-minimize lost circulation into shallow- permeable zones

-cover weak zones

-provide a means for attaching the blowout preventers

-support the weight of all casing strings (except liners) run below the surface pipe.

Intermediate Casing:

The primary applications of intermediate casing involve abnormally high

formation pressures. Since higher mud weights are required to control these

pressures, the shallower weak formations must be protected to prevent lost

circulation or stuck pipe. It is used to isolate salt zones or zones those cause

hole problems, such as heaving and sloughing shales.


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Liners:

Drilling liners are used for the same purpose of intermediate casing.

Instead of running the pipe to the surface, an abbreviated string is used from

the bottom of the hole to a shallower depth inside the intermediate pipe. Usually

the overlap between the two strings is 300-500 ft. Drilling liners are used

frequently as a cost-effective method to attain pressure or fracture gradient

control without the expense of running a string to the surface. When a liner is

used, the upper exposed casing, usually intermediate pipe, must be evaluated

with respect to burst and collapse pressures for drilling the open hole below the

liner.

Production Casing:

The production casing is often called the oil string. The pipe may be set at

a depth slightly above, or below the pay zone. The pipe has the following

purposes:

-isolate the producing zone from the other formations.

-provide a work shaft of a known diameter to the pay zone.

-protect the producing tubing equipment.

Casing Physical Properties

The physical properties of oil-field tubular goods include grade, pressure,

resistance, drift diameter and weight.


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Grade:

The pipe grade is the designation that defines the pipe’s yield strength

and certain special characteristics. The grade usually consists of a letter and a 2

or 3 digit number such as N-80. As the letter proceeds, the pipe increases in

yield strength. N-80 has greater yield strength than H-40. The numerical code

indicates the minimum yield strength of 80,000 psi. The average yield strength

is usually 10,000 psi greater than the minimum yield, 90,000 psi for N-80 pipe.

The minimum value is used in burst and collapse resistance calculations, whereas

the average is used for biaxial evaluation. C pipe is a controlled yield pipe used

primarily in environments.

Weight:

The pipe weight is usually defined in pounds per foot. The calculated

weights, as defined by the API, are determined by the following formula.

WL = (Wpc L ) + ew

WL = calculated weight of a pipe of length L, lb

Wpc = plain-end weight, lb/ft

L = length of pipe, ft

ew = weight gain or loss due to end finishing, lb

The cross-sectional area of the pipe can be approximated from the pipe weight;

Ap = 0.29 Wpc

Ap = cross sectional area, square-inch


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Range:

Pipe range is a value for approximating the length of a section of pipe.

Normal range sizes are 1,2 or 3.

Diameter:

The drilling engineer must consider three types of diameter data when

planning the tubular program. These are outer, inner and drift diameter.

Burst:

The burst rating of the casing is the amount of internal pressure that the

pipe can withstand prior to failure. The internal yield pressure for pipe is

calculated from the following equation.

PB = 0.875 [(2Yp t) / OD]

PB = burst pressure rounded to the nearest 10 psi

Yp = specified minimum yield strength, psi

t = nominal wall thickness, inch

OD = nominal outside diameter, inch

Example 3-1:

Calculate the internal yield (burst) pressure for 26.40 lb/ft, N-80, 7.625

inch pipe. Assume it has a wall thickness (t) of 0.328 inch. Use the API minimum


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wall thickness factor of 0.875. Recalculate the results and use 95 % wall

thickness.

Solution:

a) The internal yield stress (burst) is calculated as:

PB = 0.875 [(2Yp t) / OD]

PB = 0.875 [2(80000 psi) 0.328 inch) / 7.625 inch]

P = 6020 psi

b) Recalculate the results with a 95 % wall thickness.

PB = 0.95 [2(80000 psi) 0.328 inch) / 7.625 inch]

P = 6540 psi

Example 3-2:

A drilling engineer must design a production casing string for sour gas

service. The maximum anticipated surface pressure for the 5.5 inch OD pipe is

20800 psi. The engineer’s company dictates that pipe used in sour service will

not have a yield strength greater than 90,000 psi. After the engineer reviewed

the available, commonly used weights and grades of casing, he realized that the

string must be specially rolled to meet his requirements. Determine the wall

thickness requirements for the pipe. Use the yield strength of 90,000 psi and

assume that the API tolerance of 87.5 % wall thickness. Round up the wall

thickness to the nearest 1/8 inch.


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Solution:

PB = 0.875 [(2Yp t) / OD]

20800 = 0.875 [2 (90000) t) / 5.5]

t = 0.726 inch and nearest 1/8 is : t = 0.750 inch

Collapse:

Unlike internal yield resistance of the pipe, collapse resistance equations

vary depending on the D/t ratio. The collapse resistance is separated into four

categories.

a) yield strength collapse pressure

b) plastic collapse

c) transition collapse

d) elastic collapse

The D/t range must be evaluated and the proper equation must be

selected. Formula factors must be used in collapse calculations. The yield

strength collapse pressure is not a true collapse pressure, rather the external

pressure (P yp) that generates minimum yield stress (Yp) on the inside wall of a

tube.

Pyp = 2 Yp [ ((D/t) – 1) / (D/t)2]


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The formula for yield strength collapse pressure is applicable for D/t

values up to the value of D/t corresponding to the intersection with plastic

collapse formula. The intersection is calculated as follows:

(D/t)yp = SQRT [ (A-2)2 + 8 (B-(C / Yp))] + (A - 2)) / [ 2 (B + C/Yp)]

The applicable D/t ratios for yield strength collapse are given in Table-11-6.

The minimum collapse pressure for the plastic range of collapse (Pp) is

calculated as:

Pp = Yp [ (A / (D/t)) – B ] – C

The formula for minimum plastic collapse pressure is applicable for D/t

values ranging from (D/t)pt to the intersection for (D/t)t, transition collapse

pressure. Values for (D/t)pt are calculated by means of:

(D/t)pt = [Yp (A-F)] / [C + Yp (B-G)]

Example 3-3:

An engineer must calculate the collapse rating for the following section of

pipe. Using the API tables and equations, calculate the collapse pressure to the

nearest 10 psi.

Pipe diameter: 9.625 inch

Wall thickness: 0.472 inch

Grade: N-80

Weight: 47 lb/ft

Solution:


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1-Determine the D/t ratio:

D/t = 9.625 inch / 0.472 inch

D = 20.392 inch

From Table:

A = 3.071 : B = 0.0667:

C = 1955

Pp = Yp [ (A / (D/t)) – B ] – C

Pp = 80000 [ (3.071 / (20.392)) – 0.0667 ] – 1955

Pp = 4756 psi

Pp = 4750 – 4760 psi

The minimum collapse pressure for the plastic to elastic transition zone (Pt)

is calculated:

(Pt) = Yp [F /(D/t) – G]

Values for (D/t)te are calculated from the following equation:

(D/t)te = (2 + (B/A)) / (3 (B/A))

The minimum collapse pressure for the elastic range of collapse is calculated as:

Pe = 46.95 x 106 / (D/t) [(D/t)-1]2

Example 3-4:

The collapse rating for 47.0 lb/ft, C-95 grade, 9.625 inch pipe must be

calculated. The wall thickness is unknown. Use the API formulas and tables.


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Solution:

1.Compute the cross-sectional area of the pipe.

Ap = 0.29 Wp

Ap = 0.29 (47 lb/ft)

Ap = 13.63 inch2

2.Determine the wall thickness of the pipe from the cross sectional area.

Ap = /4 (OD2 – ID2)

13.63 = /4 (9.6252 – ID2)

ID = 8.676 inch

t = (OD –ID) / 2

t = (9.625 – 8.676) / 2

t = 0.4745 inch

3. D/t ratio is:

D/t = 9.625 / 0.4745 = 20.284

4. The formula for C-95 pipe with a D/t ratio of 20.284 are:

A = 3.124 B = 0.0743 C = 2404

Pp = Yp [ (A / (D/t)) – B ] – C

Pp = 95000 [ (3.124 / (20.284)) – 0.0743 ] – 2404

Pp = 5168 psi


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Axial Stress:

An axial stress is calculated by modifying the yield stress to an axial stress

equivalent grade:

YPA = [SQRT (1 - 0.75 (SA / Yp)2) – 0.5 (SA / Yp) ] Yp

SA = axial stress, psi

Yp = minimum yield strength, psi

YPA = yield strength of axial stress equivalent grade, psi

Example 3-5:

The engineer must calculate the collapse pressure for the following pipe

characteristics.

Size: 7 inch OD; Weight : 26 lb/ft; Grade: P-110; SA = 11000 psi; t =

0.362 inch

Solution:

1. Axial stress equivalent grade is:

YPA = [SQRT (1 - 0.75 (SA / Yp)2) – 0.5 (SA / Yp) ] Yp

YPA = [SQRT (1 - 0.75 (11,000 / 110,000)2) – 0.5 (11,000 / 110,000) ) 110,000

YPA = 104,082 psi

2. D/t = ?

D/t = 7 / 0.362 = 19.34

3. A = 3.181 B = 0.0819 C = 2852


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Pp = Yp [ (A / (D/t)) – B ] – C

Pp = 104082 [ (3.181 / (19.34)) – 0.0819 ] – 2852

Pp = 5742 psi

Pipe Body Yield Strength:

The pipe body strength is the axial load required to yield the pipe. It is

the product of the cross-sectional area and the specified minimum yield

strength for the particular grade of pipe.

Py = 0.7854 (OD2 – ID2) Yp

Example 3-6:

A section of 10.75 inch, 55 lb/ft N-80 casing is to be run into a well. It

has a wall thickness of 0.495 inch. Determine the pipe body yield strength.

Solution:

1.The ID is computed from:

ID = OD – 2t

ID = 10.75 – 2 (0.495)

ID = 9.76 inch

2.The yield strength is calculated as:

P y = 0.7854 (OD2 – ID2) Yp

P y = 0.7854 (10.752 – 9.762) 80,000

Py = 1,275,000 psi


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Setting Depth Selection for Intermediate and Deeper Strings:

Setting depth selection should be made for the deepest strings to be run

in the well and then successfully designed from the bottom string to the

surface.

-The first criteria for selecting deeper casing depths are to let mud weights

control formation pressures without fracturing shallow formations. This

procedure is implemented bottom-to-top. After these depths have been

established, differential pressure sticking considerations are made to determine

if the casing string will become stuck when running it into the well. These

considerations are made from top-to-bottom.

-The initial design step is to establish the projected formation pressures and

fracture gradients. In fig. 3-2a, a 15.6 ppg formation pressure exists at the

hole bottom. To reach this depth, well-bore pressures greater than 15.6 ppg will

be necessary and must be taken into account.

-The pressures that must be considered include a trip margin of mud weight to

control swab pressures, an equivalent mud weight increase due to a surge

pressures associated with running the casing, and a safety factor. These

pressures usually range from 0.2 –0.3 ppg, respectively, and may vary due to

mud viscosity and hole geometry. Therefore, the actual pressures at the bottom


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of the well include the mud weight required to control the 15.6 ppg pore

pressure and the 0.6 - 0.9 ppg mud weight increases from the swab, surge and

safety factor considerations.

-As a result, formation exhibiting fracture gradients less than 16.5 ppg or less

(15.6 ppg + 0.9 ppg) must be protected with casing. The depth at which this

fracture gradient is encountered is the tentative intermediate pipe setting

depth.

Figure 3-2 (a) Projected formation pressures and fracture gradients,

(b) Selection of the tentative intermediate setting depth


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-The next step is to determine if pipe sticking will occur when running the

casing. Pipe sticking generally can occur at the point where the maximum

differential pressures are encountered. In most cases, this depth is the deepest

normal pressure zone, i.e . at the transition into abnormal pressures.

-Field studies have been used to establish general values for the amount of

differential pressure that can be tolerated before sticking occur.

Normal pressure zones: 2000-2300 psi

Abnormal pressure zones: 3000-3300 psi

The following equations can be used to determine the new intermediate depth if

sticking is a concern.

P = (MW – 9) x 0.052 x D

( P / 0.052 D) + 9 = MW

MW = mud weight, ppg

D = depth to deepest normal zone, ft

P = differential pressure, psi

An arbitrary limit of 2000-2300 psi is normally used for P. The mud weight

from above equation can be used to locate the depth where the P value will

exists.

MW – TM = P

TM = trip margin, ppg

P = formation pressure, psi


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The depth at which the formation pressure, P, occurs is defined as the

new intermediate pipe depth. The deepest liner setting depth is established

from the intermediate setting depths fracture gradient. Using reverse

procedure subtract the swab, surge and safety factors from the fracture

gradient to determine the maximum allowable formation pressure in the deeper

sections of the hole. The depth at which this pressure is encountered becomes

the deepest liner depth.

Example 3-7

Use Fig. 3-3 to select liner and intermediate setting depths. Assume a

differential pressure limit of 2200 psi. Use the following design factors.

Swab: 0.3 ppg

Surge: 0.3 ppg

Safety: 0.2 ppg

Solution:

1.From Fig. 3-3, the maximum equivalent mud weight that will be seen at the

bottom of the well can be calculated.

Amount, ppg Purpose

17.2 Formation pressure

0.3 Trip margin

0.3 Surge factor

0.2 Safety factor

18.0 Formation Pressure


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2.Construct a vertical line to intersect the fracture gradient curve (Fig. 3-3a).

The depth of intersection, 13000 ft, is the tentative intermediate casing setting

depth. All shallower formations must be protected with casing because their

respective fracture gradients are less than the maximum projected

requirements (18 ppg) at the bottom of the well.

3.Evaluate the tentative depth for differential sticking by assuming that 14.3

ppg mud will be required to drill the formation at 13,000 ft.

(9000) (0.052) (14.3-9) = 2480 psi

Since 2480 psi > 2200 psi, intermediate pipe can not safely run to 13,000 ft.

The depth of 13,000 ft is redefined as the shallowest liner depth.

Figure 3-3 Projected formation pressures and fracture gradients


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4. The intermediate pipe depth is:

P = (MW – 9) x 0.052 x D

2200 = (MW – 9) x 0.052 x 9000

MW = 13.7 ppg

MW – TM = P

13.7 – 0.3 = P

P = 13.4 ppg

From Fig. 3-3b, a 13.4 ppg formation pressure occurs at 10,900 ft.

5.The deepest possible setting depth for the liner is determined by evaluating

the fracture gradient at 10,900 ft.

What is the maximum formation pressure below 10,900 ft and that can

be safely controlled with a fracture gradient of 17.1 ppg.

Amount, ppg Purpose

17.1 Formation gradient

-0.3 Swab margin

-0.3 Surge factor-0.2 Safety factor



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Figure 3-3 (a) Tentative intermediate setting depth (b) Intermediate

depth

From Fig. 3-3c, a 16.3 ppg formation pressure occurs at 16300 ft. The

depth is defined as the deepest allowable depth for setting the liner.


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Figure 3-3 (c) Selection of the deepest liner depth (d) Final

configuration


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Surface Casing Depth Selection:

Surface setting depths are selected to cıontain kick pressures. A precise

determination of ivk-imposed pressures can be difficult.

EMWkick = (total depth / depth of interest) ( M) + OMW

EMWkick = equivalent mud weight at the depth of interest, ppg

total depth = deepest interval, ft

M = incremental kick mud weight increase, ppg

OMW = original mud weight, ppg

Example 3-8:

Using Fig-3.4a, select a suitable surface casing depth, if necesssary,

setting depths for deeper strings.

Swab: 0.3 ppg

Surge: 0.3 ppg

Safety: 0.2 ppg

Max. allowable differential pressure: 2200 psiSolution:

1.Evaluate the maximum pressure anticipated at the bottom of the well.

Amount, ppg Purpose

12.0 Formation pressure

0.3 Trip (swab) margin

0.3 Surge factor

0.2 Safety factor



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Figure 3-4 (a) Intermediate casing evaluation,

(b) Equivalent mud weight-fracture gradient relationship


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A vertical line from 12.8 ppg intersects the fracture gradient in normal region,

which indicates intermediate casing will not be required unless differential

sticking is a problem.

2. Assume that 12.3 ppg will be used at the bottom of the well and determine if

differential sticking may occur.

(12.3 – 9.0 ppg) (0.052) (9000 ft) = 1544 psi

Since 1544 psi is less than the arbitrary limit of 2200 psi intermediate casing

will not be used for pipe sticking considerations. Therefore, only surface casing

is required.

3. Construct the fracture gradient curve to determine the depth at which the

fracture exceeds the kick loading mud weight. Perform a first trial calculations

at 1000 ft.

EMWkick = (total depth / depth of interest) (M) + OMW

EMWkick = (12000/ 1000) (0.5) + 12.3

The fracture gradient at 1000 ft is 12.0 ppg. Since the kick loading is greater

than the rock strength, a deeper trial depth must be chosen.


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4. Results from several iterations are given below and plotted on Fig. 3-4b.

Depth, ft EMW, ppg

1000 18.3

2000 15.33000 14.3

3500 14.0

4000 13.8

4500 13.6

5000 13.5

6000 13.3

7000 13.2

5. A setting depth of 3600 ft is selected.

Example 3.9

Use Fig. 2-3a, to determine the proper setting depth for intermediate

pipe.Assume 0.3 ppg factor for swab and surge and a 0.2 ppg safety factor. Use

a arbitrary maximum limit of 2200 psi differential pressure for normal pressure

zones.

Solution:

1.Evaluate the maximum pressures at the total depth of the well.

Amount, ppg Purpose Type of

Pressure15.6 Form. Pressure Actual mud weight

0.3 Trip Margin Actual mud weight

0.3 Surge Pressure Equivalent Mud Weight

0.2 Safety Factor Equivalent Mud Weight

16.4 - -


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2. Determine the formations that can not withstand 16.4 ppg pressures, i.e.

those formations must be protected with casing. Construct a vertical line from

16.4 ppg to an intersection of the fracture gradient line (Fig. 2-2b). The depth

of intersection is the tentative intermediate casing depth, or 8600 ft in this

example.

3. Check the tentative depth to determine if differential pipe sticking will be a

problem when running the casing to 8600 ft. The mud required to reach 8600 ft

is,

10.4 ppg + 0.3 ppg = 10.7 ppg

Differential sticking potential is evaluated at the deepest normal pressure (9.0

ppg) zone, 8000 ft.

(10.7 – 9.0 ppg) (0.052) (8000 ft) = 707 psi

707 psi < 2200 psi

Since the pipe can be run to 8600 ft without differential sticking, the depth

becomes the actual intermediate setting depth rather than the tentative depth.

4. Check the interval from 8600-12000 ft to determine if the differential

pressure exceeds the 3000-3300 psi range. In this case, pressure is 2700 psi

at 8600 ft.


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Design of a Complete Casing String

A combination string (i.e., a casing siring consisting of more than one

section used in order to obtain a string which will satisfy the desired design

factors with the least investment. Thus the starting point for a design is a

statement of the weights and grades of easing available, together with the

design factors to be employed. In connection with the latter, it should be noted

that the physical properties almost universally considered are joint strength,

collapse pressure, and internal yield. Many authorities recommend, in addition,

the consideration of longitudinal yielding, although in most instances the design

factor for longitudinal yielding will automatically be satisfied if the design

factor for Joint strength is satisfied.

Once the available casing and the design factors to be used have been

determined, all grades and weights of casing which will not meet the

requirements for internal yield are eliminated. It will be called that the worst

possible conditions are used in determining loading data. In line with this, the

internal pressure (for design purposes) is assumed to be full reservoir pressure,

Pws, and the external pressure is assumed to be zero. Thus the minimum

allowable internal yield strength for the casing to be used in the string is,

Pi = Pws Ni

For casing which will meet the requirements for internal yield, the controlling

factor in the lower portions of the string is collapse pressure, and the controlling


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factor in the upper portions of thie string is joint strength (or, possibly,

longitudinal yielding). For purposes of investigating the setting depth limitations

imposed by collapse resistance, it is assumed that the external pressure is that

due to the external fluid column, and that the internal pressure is zero.

Accordingly, the lowest section of the casing string will be composed of casing of

the least expensive weight and grade which will satisfy the equation;

Pc = 0.052 N

c L

s

where, Ls is the setting depth for the casing and is the density (in ppg) of the

external fluid column. The factor 0.052 ( 0.433 / 8.33) is the pressure

gradient of tlic fluid column. In determining setting depths for sections other

than the lowest, the effect on collapse pressure of longitudinal tension must be

considered. This normally involves the use of either trial-and-error or graphical

solutions.

At some point up the hole, collapse resistance ceases to be the

controlling factor in casing string design. From this point to the top of the

string, the primary considerations are joint strength and longitudinal yielding.

In this region the casing must be designed to satisfy the equations:

F j = W N j

Ym A j = W Na

where, W is the weight of casing suspended below the casing under

consideration.


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Example 3-10

Design a 7 inch 8000 ft. combination casing string for a well where the

mud weight is 12 ppg and the expected formation pressure gradient is 0.5 psi/ft,

using a worst possible loading assumptions. All weights of API casing in grades J-

55 and N-80 are available. The design factors to be satisfied are 1.125 for

collapse, 2.00 for joint strength, 1.25 for yield strength and 1.00 for internal

yield. The properties of casings are given below.

Solution:

The available casings are listed below. In case the reservoir pressure is

not known, it is estimated by the use of a reasonable gradient:

Pws = 8000 ft x 0.5 psi/ft = 4000 psi

The minimum internal yield for any section of the string must be:

Pi = Pws x Ni

Pi = 4000 x 1.00 = 4000 psi


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Grade Weight Pi Pc K F j s F j s Ym A j

J-55 20 3740 2500 74700

0

- 25400

0

55000 4.198

J-55 23 4360 3290 86500

0

34400

0

30000

0

55000 5.105

J-55 26 4980 4060 981000 39500

0

34500

0

55000 5.998

N-80 23 6340 4300 113200

0

40000

0

- 80000 5.105

N-80 26 7240 5320 128300

0

46000

0

- 80000 5.998

N-80 29 8160 6370 143600

0

52000

0

- 80000 6.899

N-80 32 9060 7400 158400

0

57800

0

- 80000 7.766

N-80 35 9960 8420 172900

0

63500

0

- 80000 8.622

N-80 38 10800 9080 186300

0

68800

0

- 80000 9.408

This requirement excludes the use of 20 lb, J-55 casing (that has an internal

yield pressure of 3740 psi) at any point in the string. Since all other weights and

grades have internal yield pressure greater than 4000 psi, they are retained for


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further considerations. The lowest section of the string will consist of the least

expensive casing available with the collapse pressure is at least,

Pc = 0.052 Nc Ls

Pc = 0.052 (1.125) (12) (8000) = 5620 psi

Therefore the lowest section (which will hereafter be designated as Section-1)

will consist of 29 lb,- N-80 casing with long threads and coupling. The length

of section-1 is limited (physically) only by the axial load which can be sustained

at the top of joint of the section. Considering joint strength,

Wmax = F j / N j

Wmax = 520,000 / 2.00 = 260,000 lb

and considering yield strength,

Wmax = Ym A j / Na

Wmax = 80,000 (6.899) / 1.25 = 442,000 lb

The maximum length of the section-1 is,

260,000 / 29 lb/ft = 8970 ft

which is greater than the setting depth. The next lowest section (hereafter

called Section-2) will consist of next lighter casing, namely, 26 lb, N-80 casing

with long threads and coupling. Neglecting the effect of axial tension, (due to


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the weight of Section-1 suspended below it) the setting depth of Section-2 is,

Ls = Pc / (0.052 Nc )

Ls = 5320 / (0.052) (1.125) (12) = 7580 ft

This is the first assumed setting depth of Section-2. Under this assumption, the

weight of Section-1 is:

(8000 – 7580) ft x 29 lb/ft = 12,180 lb

For this axial load, the collapse pressure of Section-2 is:

Pcc = Pc / K [(SQRT K2 – 3W2) – W]

Pcc = 5320 / 1,283,000 [(SQRT 1.646 x 1012 – 0.445 x 109) – 12,180]

Pcc = 5270 psi

and the setting depth of Section-2 is:

Ls = Pc / (0.052 Nc )

Ls = 5270 / (0.052) (1.125) (12) = 7510 ft

This is the second assumed setting depth of Section-2. Under this assumption,

the weight of section-1 is:

(8000 – 7510) ft x 29 lb/ft = 14,210 lb

and hence,


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Pcc = 5320 / 1,283,000 [(SQRT 1.646 x 1012 – 0.606 x 109) – 14,210]

Pcc = 5260 psi

for Section-2. The third assumed depth for section-2 is

Ls = 5260 / (0.052) (1.125) (12) = 7490 ft

The weight of Section-1 and the collapse pressure of Section-2 are, under this

assumption is 14,790 lb and 5260 psi respectively. The resulting setting depth

agrees with the third assumed setting depth of 7490 ft, which is thus taken to

be correct setting depth for Section-2. Also, for Section-2 the maximum joint

load is:

F j / N j = 460,000 / 2.00 = 230,000 lb

and the maximum yield load is,

Wmax = Ym A j / Na

Wmax = 80,000 (9.998) / 1.25 = 384,000 lb

Since the weight of casing suspended below section-2 is 14,790 lb, the

maximum length of Section-2 is:

(230,000 – 14,790) lb / 26 lb/ft = 8280 ft

which is greater than the setting depth. Section-3 will consist of 23 lb N-80

casing with long threads and couplings, which has an uncorrected collapse

pressure of 4300 psi. Again neglecting the effect of axial tension due to the


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weights of Sections 1 & 2, the first assumed setting depth for Section-3 is:

Ls = Pc / (0.052 Nc )

Ls = 4300 / (0.052) (1.125) (12) = 6130 ft

On the basis, the weight of Section-2,

(7490 – 6130) ft x 26 lb/ft = 35,400 lb

and the total axial load below Section-3 is:

14,790 + 35,400 = 50,200 lb

The corrected collapse pressure for Section-3 is:

Pcc = Pc / K [(SQRT K2 – 3W2) – W]

Pcc = 4300 / 1,132,000 [(SQRT 1.281 x 1012 – 0.008 x 1012) – 50,200]

Pcc = 4090 psi

From which the second assumed setting depth for Section-3 is:

Ls = Pc / (0.052 Nc )

Ls = 4090 / (0.052) (1.125) (12) = 5830 ft

By continuing trial and error procedure, the setting depth for Section-3 is

calculated to be 5780 ft. For this setting depth, the total weights of section 1

and 2 are 59200 lb and the collapse pressure of Section-3 is 4060 psi.


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The maximum allowable joint load for Section-3 is:

F j / N j = 400,000 / 2.00 = 200,000 lb

and the maximum yield load is:

(80,000 x 5.105) / 1.25 = 327,000 lb

the maximum length of Section-3 is:

(200,000 – 59,200) lb / 23 lb/ft = 6120 ft

which is again greater than the setting depth. Thus collapse pressure continues

to be the controlling factor, and will determine the setting depth of Section-4.

The least expensive of the remaining grades and weights is 26 lb, J-55 casing

with short thread and couplings, and this will constitute Section-4. The setting

depth of Section-4 is found by trial and error to be 5310 ft, and the total

weight of Sections 1,2 and 3 is 71,400 lb, and the collapse pressure of

Section-4 is 3730 psi. The maximum allowable joint and yield loads for Section-

4 are, respectively:

345,000 / 2.00 = 172,500 lb

(55,000 x 5.998) / 1.25 = 264,000 lb

The maximum length of Section-4 is:

(172,500 – 71,400) lb / 26 lb/ft = 3890 ft


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Since 3890 ft is less than the allowable setting depth of Section-4, the

setting depth for Section-5 is governed not by collapse pressure but by joint

strength. Section-5 composed of 26 lb, J-55 casing with long threads and

couplings, has a setting depth given by:

Ls = 5310 – 3890 ft = 1420 ft

For Section-5 maximum allowable joint and yield loads are, respectively.

395,000 / 2.00 = 197,500 lb

and,

(55,000 x 5.998) / 1.25 = 264,000 lb

The weight of all casing below Section-5 is:

71,400 + (26 x 3890) = 172,500 lb


(197,500 – 172,500) lb / 26 lb/ft = 960 ft

The maximum setting depth of Section-6 is:

1420 – 960 = 460 ft

It is obvious that Section-6 must consist of casing with a joint strength greater

than that of Sction-5 (i.e. greater than 395,000 lb). No weight of J-55 casing

will satisfy this requirement, and we therefore must use 23 lb, N-80 casing with

long threads and couplings. For section-6, allowable joint and yield loads are,

respectively.


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400,000 / 2.00 = 200,000 lb

(80,000 x 5.105) / 1.25 = 327,000 lb

The weight of all casings below Section-6 is,

172,400 + (26 x 960) = 197,500 lb


(200,000 – 197,500) lb / 23 lb/ft = 110 ft

and the setting depth of Section-7 is:

460 – 110 = 350 ft

Section-7 must consist of casing with a joint strength greater than 400,000 lb.

The obvious choice is 26 lb, N-80 casing with long threads and couplings. For

this casing the maximum joint and yield loads are 230,000 lb and 384,000 lb

respectively. The maximum length for Section-7 is therefore:

(230,000 – 200,000) lb / 26 lb/ft = 1150ft

Since this is greater than the allowable setting depth of Section-7, this section

can continue to the top of the hole. So:


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Section Interval. ft Length, ft Grade Weight Coupling

1 7490-

8000

510 N-80 29 Long

2 5780-

7490

1710 N-80 26 Long

3 5310-

5780

470 N-80 23 Long

4 1420-5310 3890 J-55 26 Short

5 460-1420 960 J-55 26 Long

6 350-460 110 N-80 23 Long

7 0-350 350 N-80 26 Long

Example 3-11:

Considering Ex. 3-10 determine the setting of Section-2 of the

combination string using the collapse design chart for 7 inch casing?

Solution:

Section-1 consist of 29 lb, N-80 casing. Section-3 consist of 26 lb, N-80 casing.

Neglecting the effect of axial loading, Ls for Section-2 is 91,000 lb (Figure 3-

5). Therefore:

Ls = 91,000 / 12 = 7580 ft


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This is the first assumed setting depth. On this assumption, the axial load on

Section-2 is:

29 lb/ft x (8000– 7580) ft = 12,180 lb

From Fig. 3-5, Ls = 90000, and the second assuming setting depth is:

90000 / 12 = 7500 ft.

On this assumption the axial load is,

29 lb/ft x (8000 – 7500) ft = 14,500 lb

and within the limits to which the chart can be read, Ls , is again 90,000. Thus

the maximum setting depth for Section-2 is taken to be 7500 ft.

casing design 4

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