Casing/Tubing design manual october 2005 Chevron
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The load definitions for production casing are intended to represent the following:
• Collapse: Production tubing packer fluid leak late in the life of the
reservoir
• Burst: The maximum tubing leak pressure associated with (a) shut in
early in the life of the reservoir, (b) a stimulation, or (c) a well kill
operation, plus packer fluid, is modeled
• Tension: Running-in-hole tension is calculated using the buoyant
weight of the string plus 10,000-lb overpull
• Stability: Nominal production. In lieu of actually performing a multi-
phase flow analysis of reservoir fluid production, the flowing conditions
are taken conservatively to be identical to shut-in conditions
Figure 6-2. Production Casing Basic Load
Casing/Tubing Design Manual 6-11
October 2005
6.6.3 Intermediate Casing
All tubular strings between the production casing string and the surface casing
string are intermediate casing for the purpose of design load definition.
Table 6-3. Intermediate Casing Basic Load
Load
Condition
Internal
Fluids/
Pressures
External
Fluids/
Pressures
Axial load Temperature
Profile
Initial Surface: 0
Fluids: Mud
density at
casing point
Surface: 0
Fluids: Mud
density at
casing point to
cement top,
cement to
casing point
Initial axial load Undisturbed
geothermal
gradient
Collapse Surface: 0
Fluids: Next
mud drop (at
least 2000 ft)
Surface: 0
Fluids: Mud
density at
casing point
Initial axial load
plus load
change
Undisturbed
geothermal
gradient
Burst Surface:
Formation
pressure at
next TVD, less
2/3 gas column
on top of 1/3
drilling mud
column
Fluids:
Gas/Mud
Surface: 0
Fluids: Pore
pressure
Initial axial load
plus load
change
Drilling
temperature
gradient
Tension Surface: 0
Fluids: Mud
density at
casing point
Surface: 0
Fluids: Mud
density at
casing point
Casing
buoyant weight
plus 10,000 lb
overpull
Undisturbed
geothermal
gradient
Stability Surface: 0
Fluids:
Fracture
gradient - 0.5
ppg
Surface: 0
Fluids: Mud
density at
casing point
Initial axial load
plus load
change
Drilling
temperature
gradient
The load definitions for intermediate casing are intended to represent the
following:
• Collapse: Lost circulation. The next drilling mud drop to balance with the
openhole weak formation pressure (recommend the water gradient at
casing depth).
• Burst: Uncontrolled, large gas kick. One-half gas column instead of
two-thirds gas column has also been used occasionally in deep wells.
• Tension: Running-in-hole tension is calculated using the buoyant weight
of the string plus 10,000 lb.
• Stability: Drill ahead to the next casing point.
6-12 Casing/Tubing Design Manual
October 2005
Figure 6-3. Intermediate Casing Basic Load
6.7 Surface Casing
Surface casing is the outermost tubular string that is required to contain a
differential pressure. Surface casing may or may not support the wellhead, as
this function may be relegated to an outer conductor string that has no pressure
containment design responsibilities.
Table 6-4. Surface Casing Load Cases for Standard Wells
Load
Condition
Internal
Fluids/
Pressures
External
Fluids/
Pressures
Axial load Temperature
Profile
Initial Surface: 0
Fluids: Water
Surface: 0
Fluids:
Cement
Initial axial load N/A
Collapse Surface: 0
Fluids:
Evacuated
Surface: 0
Fluids: Mud
density at
casing point
Initial axial load
plus load
change
N/A
Burst Surface:
Fracture
gradient
pressure at
casing shoe,
less methane
gradient to
surface
Fluids:
Methane
Surface: 0
Fluids: Pore
pressure
Initial axial load
plus load
change
N/A
Tension Surface: 0
Fluids: Mud
Surface: 0
Fluids: Mud
Casing
buoyant weight
N/A
Casing/Tubing Design Manual 6-13
October 2005
Load
Condition
Internal
Fluids/
Pressures
External
Fluids/
Pressures
Axial load Temperature
Profile
density at
casing point
density at
casing point
plus 10,000 lb
overpull
The load definitions for surface casing are intended to represent the following:
• Collapse: Lost circulation. It is assumed that the hole for the next
(intermediate) string is sufficiently deep enough that a condition of lost
circulation will completely evacuate the surface casing.
• Burst: Uncontrolled, large gas kick limited only by the pressure rating of
the shoe as determined by a leak-off test
• Tension: Running-in-hole tension is calculated using the buoyant weight
of the string plus 10,000-lb overpull
Figure 6-4. Surface Casing Basic Load
6-14 Casing/Tubing Design Manual
October 2005
6.7.1 Notes
In reading the load definition tables of the preceding section, the following
observations are pertinent:
• The term “mud density at casing point” refers to the last fluid weight used
in drilling the hole in which the target tubular string is being installed.
• In determining external loading (collapse) or backup (burst) fluids,
isolation of pore pressure by the cement sheath is ignored.
• The methane gradient is at 2.26 kPa/m (0.10 psi/ft) for basic design.
• Water means fresh water. Although formation brine may be a more
reasonable fluid, the selection of fresh water bypasses many local biases
on the exact “brine” to be used in design calculations. This is a minor
point instigated in the name of standardization.
• The temperature profile may consist of as little as one point. Typically,
the temperature profile will consist of two points, a surface temperature
and a bottomhole temperature. For the undisturbed or initial geothermal
gradient, at least, these two values should be known. For later
conditions, such as production or drilling, at least, the surface
temperature should be known. The bottomhole temperature, if not
known, can be maintained at the initial, undisturbed value.
6.8 References
1. Adams, N. J., and Charrier, T.: Drilling Engineering, a Complete Well
Planning Approach, PennWell Books, Tulsa, Oklahoma (1985).
2. Burgoyne, A. T. Jr., Millheim, K. K., Chenevert, M. E., and Young, F. S. Jr.:
Applied Drilling Engineering, SPE, Richardson, Texas (1986).
3. Rader, D. W., and Burgoyne, A. T.: “Factors Affecting Bubble Rise Velocity of
Gas Kicks,” Journal of Petroleum Technology, (1975) 571-584.
Casing/Tubing Design Manual 6-15
October 2005
7
7 Tube Buckling
7.1 Introduction ......................................................................................................................7-1
7.2 Effective Tension..............................................................................................................7-2
7.2.1 Example Problem........................................................................................................7-2
7.3 Buckling in a Vertical Wellbore.........................................................................................7-3
7.4 The Neutral Point .............................................................................................................7-4
7.4.1 Example Problem........................................................................................................7-4
7.5 Buckling in an Inclined Wellbore ......................................................................................7-5
7.6 Buckling in a Curved Wellbore .........................................................................................7-6
7.7 Effect of Inclination Increase (Build).................................................................................7-8
7.8 Effect of Inclination Decrease (Drop)................................................................................7-9
7.9 Effect of Azimuth Change (Turn)......................................................................................7-9
7.10 Length Change in a Vertical Wellbore..............................................................................7-9
7.10.1 Example Problem......................................................................................................7-10
7.11 Length Change in Inclined and Curved Wellbores .........................................................7-11
7.12 Permanent Corkscrewing...............................................................................................7-11
7.13 References.....................................................................................................................7-13
7.1 Introduction
The primary concern of tubular design is usually the failure of the tube body or
the threaded connection because of environmental loads. Analyses of the
structural integrity of these two components will normally suffice to produce a
tubular string capable of withstanding all anticipated loads throughout the well
life. There remains, however, one additional phenomenon worthy of
consideration – column buckling in unsupported intervals.
In many cases, column buckling of a tubular will produce no harmful side effects.
However, instances do exist where buckling can become more than an
inconvenience. For example, in uncemented intervals opposite long washouts,
conditions can arise where the lateral deflection accompanying column buckling
can be sufficient to cause a casing string to fail. Even more frequently, buckling
of casing or tubing can result in an inability to pass tools through the buckled
interval.
Perhaps the most subtle effect of buckling for casing can occur in the
intermediate strings in deep wells. This buckling, accompanied by long periods of
subsequent drilling, can do irreparable damage to the casing body from wear.
Tubing buckling is usually a more serious concern than casing buckling. The
relatively larger radial clearances associated with tubing installations can result in
significant axial movement and/or interaction forces particularly at the lower end
of the string.
This chapter is divided into two sections that roughly correspond to the procedure
followed when analyzing column buckling. The first portion of the chapter is
Casing/Tubing Design Manual 7-1
October 2005
devoted to a description of the relationships necessary to determine the buckling
load. There will also be a discussion of the “neutral point” concept.
The second section of this chapter deals with the post-buckled behavior of the
tubular string. In this section, an attempt to estimate the degree of buckling and
the possible associated complications are discussed.
7.2 Effective Tension
In a fluid environment, the bending and straightening of a tube is governed by the
effective tension. Given the following input variables:
• Axial force,
F
z
• Internal pressure,
p
i
• External pressure,
p
o
• Tube outside diameter,
D
• Tube wall thickness,
t
The effective tension,
, is related to the true tension by, F
e
(
)
ooiize
ApApFF
−
−
= (7-1)
where
is the inside area of the tube cross section and is the outside area
of the tube cross section:
A
i
A
o
(
ADt
i
=−
)
π
4
2
2
(7-2)
AD
o
=
π
4
2
(7-3)
7.2.1 Example Problem
At a depth of 3,000 m (9,842.5 ft.) in a wellbore the internal pressure is 35 MPa
(5,076 psi), the external pressure is 7.5 MPa (1,088 psi), and the axial force is
0.03 MN (6,744 lb). The tube is 73.03 mm, 9.67 kg/m (2.875 in., 6.5 lb/ft) with a
wall thickness of 5.515 mm (0.217 in.). Compute the effective tension.
The procedure is summarized in the following table.
Table 7-1. Example Procedure
Action Variable Metric English
Input variables
F
z
p
i
p
o
D
t
0.03 MN
35 Mpa
2.5 Mpa
73.03 mm
5.515 mm
6,744 lb
5,076 psi
3,62.6 psi
2.875 in.
0.217 in.
Compute areas
A
i
A
o
3,019.1 mm
2
4,188.8 mm
2
4.680 in
2
6.492 in
2
7-2 Casing/Tubing Design Manual
October 2005
Action Variable Metric English
Compute
effective tension
F
e
-0.0652 MN -14,658 lb
7.3 Buckling in a Vertical Wellbore
The effective force directly relates to the tendency of a tubular to undergo column
buckling, as summarized in the following table.
Table 7-2. Column Buckling
Condition Significance
F
e
< -F
c
Tube is unstable, tending to buckle
F
e
> -F
c
Tube is stable, not tending to buckle
F
e
= -F
c
Neutral stability, intermediate to other two conditions
The critical force
1
, , is given by classic calculations and, for the case of a
weightless tube in a vertical wellbore, is given in the Euler buckling formula [c.f.
Ziegler, 1968]:
F
c
Fk
EI
L
c
=
π
2
2
(7-4)
In the formula,
E
is Young's modulus,
I
is the moment of inertia of the tube
cross section,
L
is length and
k
varies with the conditions at either end of the
tube. The largest value of
corresponds to both ends of the tube being fixed so
that neither lateral displacement nor rotation is permitted,
k
k
=
4
.
When the weight of the tube is considered, the critical force becomes the axial
force acting on the bottom of the tube because of its own weight. The critical
force can be estimated from Lubinski [1987]:
()
FEIw
c
= 194
2
1
3
.
(7-5)
Consider the previous example problem involving 3,000 m (9,842.5 ft) of 73.03
mm (2.875 in.) tubing. For this string, assume both ends to be fixed, ignore the
weight of the string yields F
c
= 0.62 N (0.14 lb). The magnitude of the critical
force depends on the tube length; the longer the tube, the less the critical force.
Taking the string weight into account [(equation (7-5) yields F
c
= 2,080 N (470 lb)]
and note, in this latter case, the critical force is independent of tube length.
It is common to assume
F
c
=
0 for tubing, because the critical force is usually
small (see the example above). Under such an approximation, the test for
stability of tubing can simply reduce to determining whether
is negative,
positive, or zero. However, the critical force for casing should not be assumed to
F
e
1
Throughout this manual, tension is positive. Conversely, the critical force, ,
although compressive is usually presented as a positive value. This inconsistency leads to
the minus sign before
in the table summarizing the buckling condition.
F
c
F
c
Casing/Tubing Design Manual 7-3
October 2005
be zero, because the critical force of casing can be high, especially for large
diameters (see equation 7-5).
Further, the post-buckled configuration of a tube in a vertical wellbore will
assume a helical shape. The buckling load will increase from critical buckling to
helical buckling. The prediction of helical buckling is equally important because
the helical configuration is more damaging. A relationship between the helical
buckling force (F
c
) and helical buckling pitch (L) length for a tube in a vertical
wellbore was studied by Lubinski [1987] for a weightless tube:
F
EI
L
c
= 8
2
2
π
(7-6)
A helical buckling force formula for a tube in a vertical wellbore with the weight of
the tube being considered was proposed by Wu and Juvkam-Wold [1995]:
(
)
3
1
2
05.4 EIwF
h
=
(7-7)
7.4 The Neutral Point
Because of its importance as the boundary between portions of a tube tending to
buckle and portions that are not, the point of neutral stability is given the special
name of "neutral point." Recalling the equation for effective force, the gradient in
effective force is found from differentiation to be,
()
dF
d
z
wAAw
e
siioo
=− + − =−
γγ
e
, (7-8)
where
is the weight density of steel, w
s
γ
i
is the weight density of the internal
fluid,
γ
o
is the weight density of the external fluid, is called the effective
weight, and depth,
, is assumed to be positive downward. If, between the point
of interest and the neutral point the tubular density and fluid densities are
constant, then using the following input variables:
w
e
z
• Effective tension at the point of interest,
F
e
• Effective weight above point of interest,
w
e
the distance of the neutral point above the point of interest is given by:
δ
z
F
w
n
e
e
=− .(7-9)
7.4.1 Example Problem
Continuing with the previous example, assume that the tubular is surrounded by
internal and external fluids of densities 1,500 kg/m3 (12.52 ppg) and 1,000 kg/m3
(8.34 ppg), respectively. Compute the distance of the neutral point above the
depth of 3,000 m (9,842.5 ft).
It is important to note that at 3,000 m (9,842.5 ft), the effective force is negative,
and, therefore, the tubing is buckled at that depth. Had the effective force been
7-4 Casing/Tubing Design Manual
October 2005
positive, it would not be necessary to perform this calculation as the tubing would
be straight everywhere above the depth of interest.
However, given the effective force of -0.0652 MN (-14,658 lb), the distance to the
neutral point is shown in Table 7-3.
Table 7-3 The Neutral Point
Action Variable Metric English
Input variables
F
e
w
s
γ
i
γ
o
-0.0652 MN
9.67 kg/m
15 kg/m
3
10 kg/m
3
-14,658 lb
6.5 lb/ft
12.52 ppg
8.34 ppg
Compute effective
weight
w
e
10.01 kg/m 10.01 kg/m
Compute distance to
neutral point
δ
z
n
-664.2 m -2,178 ft
Where the minus sign for
δ
z
n
signifies that the neutral point is above the point
where
is given.
F
e
7.5 Buckling in an Inclined Wellbore
With increasing inclination, the tendency of the tube to gravitate to the low side of
the wellbore under its weight must also be overcome on tube buckling. Tube
buckling in an inclined wellbore also occurs in two stages. At first, the tube
buckles into a sinusoid that conforms to the lower portion of the confining hole.
The critical force,
, necessary to initiate sinusoidal buckling was derived by
Dawson and Paslay [1984]. Given the following input variables:
F
c
• Radial clearance,
r
c
• Young's modulus,
E
• Tube cross-sectional moment of inertia,
I
• Tube effective weight,
w
e
• Inclination of tube from vertical,
α
the critical buckling force is:
c
e
c
r
EIw
F
α
sin4
=
(7-10)
Notice that this formula will not apply to a vertical wellbore, because for a vertical
wellbore
α
= 0 and it results in F
c
=
0. This is simply because the derivation of
the above equation is based on an infinite length of tube, ignoring the axial
component of the tube weight in the inclined wellbore.
Casing/Tubing Design Manual 7-5
October 2005