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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
16.3 Formation Pressure
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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
12.8 Formation Pressure
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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
The maximum length of Section-5 is:
(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
The maximum length of Section-6 is:
(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.